%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU245+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:27:22 AM UTC 2025
% Result : Theorem 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU245+1 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n001.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Jun 20 06:32:35 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.20/0.38 % SZS status Theorem
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(in_type, type, (
% 0.20/0.38 in: ( $i * $i ) > $o)).
% 0.20/0.38 tff(set_intersection2_type, type, (
% 0.20/0.38 set_intersection2: ( $i * $i ) > $i)).
% 0.20/0.38 tff(cartesian_product2_type, type, (
% 0.20/0.38 cartesian_product2: ( $i * $i ) > $i)).
% 0.20/0.38 tff(tptp_fun_B_7_type, type, (
% 0.20/0.38 tptp_fun_B_7: $i)).
% 0.20/0.38 tff(tptp_fun_C_6_type, type, (
% 0.20/0.38 tptp_fun_C_6: $i)).
% 0.20/0.38 tff(tptp_fun_A_8_type, type, (
% 0.20/0.38 tptp_fun_A_8: $i)).
% 0.20/0.38 tff(relation_restriction_type, type, (
% 0.20/0.38 relation_restriction: ( $i * $i ) > $i)).
% 0.20/0.38 tff(relation_type, type, (
% 0.20/0.38 relation: $i > $o)).
% 0.20/0.38 tff(tptp_fun_D_9_type, type, (
% 0.20/0.38 tptp_fun_D_9: ( $i * $i * $i ) > $i)).
% 0.20/0.38 tff(1,plain,
% 0.20/0.38 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))) <=> (~![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B))))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(2,plain,
% 0.20/0.38 ((~![A: $i, B: $i, C: $i] : (relation(C) => (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))) <=> (~![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B))))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(3,axiom,(~![A: $i, B: $i, C: $i] : (relation(C) => (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t16_wellord1')).
% 0.20/0.38 tff(4,plain,
% 0.20/0.38 (~![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.20/0.38 tff(5,plain,
% 0.20/0.38 (~![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.20/0.38 tff(6,plain,
% 0.20/0.38 (~![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.20/0.38 tff(7,plain,
% 0.20/0.38 (~![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.20/0.38 tff(8,plain,(
% 0.20/0.38 ~((~relation(C!6)) | (in(A!8, relation_restriction(C!6, B!7)) <=> (in(A!8, C!6) & in(A!8, cartesian_product2(B!7, B!7)))))),
% 0.20/0.38 inference(skolemize,[status(sab)],[7])).
% 0.20/0.38 tff(9,plain,
% 0.20/0.38 (relation(C!6)),
% 0.20/0.38 inference(or_elim,[status(thm)],[8])).
% 0.20/0.38 tff(10,plain,
% 0.20/0.38 (^[A: $i] : refl(((~relation(A)) | ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B)))) <=> ((~relation(A)) | ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(11,plain,
% 0.20/0.38 (![A: $i] : ((~relation(A)) | ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[10])).
% 0.20/0.38 tff(12,plain,
% 0.20/0.38 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B)))) <=> ((~relation(A)) | ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(13,plain,
% 0.20/0.38 (![A: $i] : ((~relation(A)) | ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.38 tff(14,plain,
% 0.20/0.38 (![A: $i] : ((~relation(A)) | ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B))))),
% 0.20/0.38 inference(transitivity,[status(thm)],[13, 11])).
% 0.20/0.38 tff(15,plain,
% 0.20/0.38 (![A: $i] : ((~relation(A)) | ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(16,plain,
% 0.20/0.38 (^[A: $i] : rewrite((relation(A) => ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B)))) <=> ((~relation(A)) | ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(17,plain,
% 0.20/0.38 (![A: $i] : (relation(A) => ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[16])).
% 0.20/0.38 tff(18,axiom,(![A: $i] : (relation(A) => ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d6_wellord1')).
% 0.20/0.38 tff(19,plain,
% 0.20/0.38 (![A: $i] : ((~relation(A)) | ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.20/0.38 tff(20,plain,
% 0.20/0.38 (![A: $i] : ((~relation(A)) | ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.20/0.38 tff(21,plain,(
% 0.20/0.38 ![A: $i] : ((~relation(A)) | ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B))))),
% 0.20/0.38 inference(skolemize,[status(sab)],[20])).
% 0.20/0.38 tff(22,plain,
% 0.20/0.38 (![A: $i] : ((~relation(A)) | ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.20/0.38 tff(23,plain,
% 0.20/0.38 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B))))) | ((~relation(C!6)) | ![B: $i] : (relation_restriction(C!6, B) = set_intersection2(C!6, cartesian_product2(B, B))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B))))) | (~relation(C!6)) | ![B: $i] : (relation_restriction(C!6, B) = set_intersection2(C!6, cartesian_product2(B, B))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(24,plain,
% 0.20/0.38 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B))))) | ((~relation(C!6)) | ![B: $i] : (relation_restriction(C!6, B) = set_intersection2(C!6, cartesian_product2(B, B))))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(25,plain,
% 0.20/0.38 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (relation_restriction(A, B) = set_intersection2(A, cartesian_product2(B, B))))) | (~relation(C!6)) | ![B: $i] : (relation_restriction(C!6, B) = set_intersection2(C!6, cartesian_product2(B, B)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.38 tff(26,plain,
% 0.20/0.38 (![B: $i] : (relation_restriction(C!6, B) = set_intersection2(C!6, cartesian_product2(B, B)))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[25, 22, 9])).
% 0.20/0.38 tff(27,plain,
% 0.20/0.38 ((~![B: $i] : (relation_restriction(C!6, B) = set_intersection2(C!6, cartesian_product2(B, B)))) | (relation_restriction(C!6, B!7) = set_intersection2(C!6, cartesian_product2(B!7, B!7)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(28,plain,
% 0.20/0.38 (relation_restriction(C!6, B!7) = set_intersection2(C!6, cartesian_product2(B!7, B!7))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.20/0.38 tff(29,plain,
% 0.20/0.38 (set_intersection2(C!6, cartesian_product2(B!7, B!7)) = relation_restriction(C!6, B!7)),
% 0.20/0.38 inference(symmetry,[status(thm)],[28])).
% 0.20/0.38 tff(30,plain,
% 0.20/0.38 (in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7))) <=> in(A!8, relation_restriction(C!6, B!7))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[29])).
% 0.20/0.38 tff(31,plain,
% 0.20/0.38 (in(A!8, relation_restriction(C!6, B!7)) <=> in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7)))),
% 0.20/0.38 inference(symmetry,[status(thm)],[30])).
% 0.20/0.39 tff(32,plain,
% 0.20/0.39 ((~in(A!8, relation_restriction(C!6, B!7))) <=> (~in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[31])).
% 0.20/0.39 tff(33,assumption,((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))), introduced(assumption)).
% 0.20/0.39 tff(34,plain,
% 0.20/0.39 ((~(~(((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))) <=> in(A!8, relation_restriction(C!6, B!7))))) <=> (((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))) <=> in(A!8, relation_restriction(C!6, B!7)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(35,plain,
% 0.20/0.39 ((~(((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))) <=> in(A!8, relation_restriction(C!6, B!7)))) <=> (~(((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))) <=> in(A!8, relation_restriction(C!6, B!7))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(36,plain,
% 0.20/0.39 ((in(A!8, relation_restriction(C!6, B!7)) <=> (~((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))))) <=> (~(((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))) <=> in(A!8, relation_restriction(C!6, B!7))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(37,plain,
% 0.20/0.39 ((in(A!8, C!6) & in(A!8, cartesian_product2(B!7, B!7))) <=> (~((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(38,plain,
% 0.20/0.39 ((in(A!8, relation_restriction(C!6, B!7)) <=> (in(A!8, C!6) & in(A!8, cartesian_product2(B!7, B!7)))) <=> (in(A!8, relation_restriction(C!6, B!7)) <=> (~((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7))))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[37])).
% 0.20/0.39 tff(39,plain,
% 0.20/0.39 ((in(A!8, relation_restriction(C!6, B!7)) <=> (in(A!8, C!6) & in(A!8, cartesian_product2(B!7, B!7)))) <=> (~(((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))) <=> in(A!8, relation_restriction(C!6, B!7))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[38, 36])).
% 0.20/0.39 tff(40,plain,
% 0.20/0.39 ((in(A!8, relation_restriction(C!6, B!7)) <=> (in(A!8, C!6) & in(A!8, cartesian_product2(B!7, B!7)))) <=> (~(((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))) <=> in(A!8, relation_restriction(C!6, B!7))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[39, 35])).
% 0.20/0.39 tff(41,plain,
% 0.20/0.39 ((~(in(A!8, relation_restriction(C!6, B!7)) <=> (in(A!8, C!6) & in(A!8, cartesian_product2(B!7, B!7))))) <=> (~(~(((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))) <=> in(A!8, relation_restriction(C!6, B!7)))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[40])).
% 0.20/0.39 tff(42,plain,
% 0.20/0.39 ((~(in(A!8, relation_restriction(C!6, B!7)) <=> (in(A!8, C!6) & in(A!8, cartesian_product2(B!7, B!7))))) <=> (((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))) <=> in(A!8, relation_restriction(C!6, B!7)))),
% 0.20/0.39 inference(transitivity,[status(thm)],[41, 34])).
% 0.20/0.39 tff(43,plain,
% 0.20/0.39 (~(in(A!8, relation_restriction(C!6, B!7)) <=> (in(A!8, C!6) & in(A!8, cartesian_product2(B!7, B!7))))),
% 0.20/0.39 inference(or_elim,[status(thm)],[8])).
% 0.20/0.39 tff(44,plain,
% 0.20/0.39 (((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))) <=> in(A!8, relation_restriction(C!6, B!7))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.20/0.39 tff(45,plain,
% 0.20/0.39 ((~((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7))))) | in(A!8, relation_restriction(C!6, B!7)) | (~(((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))) <=> in(A!8, relation_restriction(C!6, B!7))))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(46,plain,
% 0.20/0.39 ((~((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7))))) | in(A!8, relation_restriction(C!6, B!7))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.20/0.39 tff(47,plain,
% 0.20/0.39 (in(A!8, relation_restriction(C!6, B!7))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[46, 33])).
% 0.20/0.39 tff(48,plain,
% 0.20/0.39 (in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[47, 31])).
% 0.20/0.39 tff(49,assumption,((~((~(set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(cartesian_product2(B!7, B!7), C!6))) | (~(((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))) <=> in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7))))))) | (~((set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(cartesian_product2(B!7, B!7), C!6)) | (((~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7))) | (~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), C!6, cartesian_product2(B!7, B!7)), C!6))) <=> in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), C!6, cartesian_product2(B!7, B!7)), set_intersection2(C!6, cartesian_product2(B!7, B!7))))))), introduced(assumption)).
% 0.20/0.39 tff(50,plain,
% 0.20/0.39 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))) <=> in(tptp_fun_D_9(C, B, A), C)))))) <=> (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))) <=> in(tptp_fun_D_9(C, B, A), C)))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(51,plain,
% 0.20/0.39 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))) <=> in(tptp_fun_D_9(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))) <=> in(tptp_fun_D_9(C, B, A), C))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[50])).
% 0.20/0.39 tff(52,plain,
% 0.20/0.39 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))) <=> in(tptp_fun_D_9(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))) <=> in(tptp_fun_D_9(C, B, A), C))))))),
% 0.20/0.39 inference(pull_quant,[status(thm)],[])).
% 0.20/0.39 tff(53,plain,
% 0.20/0.39 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C)))) <=> ![D: $i] : ((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))), ((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) <=> (~![D: $i] : ((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))))), pull_quant((~![D: $i] : ((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) <=> ?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C)))))), ((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) <=> ?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))))), (((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))) <=> in(tptp_fun_D_9(C, B, A), C))))) <=> (?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))) <=> in(tptp_fun_D_9(C, B, A), C))))))), pull_quant((?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))) <=> in(tptp_fun_D_9(C, B, A), C))))) <=> ?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))) <=> in(tptp_fun_D_9(C, B, A), C)))))), (((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))) <=> in(tptp_fun_D_9(C, B, A), C))))) <=> ?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))) <=> in(tptp_fun_D_9(C, B, A), C))))))), ((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))) <=> in(tptp_fun_D_9(C, B, A), C)))))) <=> (~?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))) <=> in(tptp_fun_D_9(C, B, A), C)))))))), pull_quant((~?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))) <=> in(tptp_fun_D_9(C, B, A), C)))))) <=> ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))) <=> in(tptp_fun_D_9(C, B, A), C))))))), ((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))) <=> in(tptp_fun_D_9(C, B, A), C)))))) <=> ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))) <=> in(tptp_fun_D_9(C, B, A), C))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(54,plain,
% 0.20/0.39 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))) <=> in(tptp_fun_D_9(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))) <=> in(tptp_fun_D_9(C, B, A), C))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[53])).
% 0.20/0.39 tff(55,plain,
% 0.20/0.39 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))) <=> in(tptp_fun_D_9(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))) <=> in(tptp_fun_D_9(C, B, A), C))))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[54, 52])).
% 0.20/0.39 tff(56,plain,
% 0.20/0.39 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))) <=> in(tptp_fun_D_9(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))) <=> in(tptp_fun_D_9(C, B, A), C))))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[55, 51])).
% 0.20/0.39 tff(57,plain,
% 0.20/0.39 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))) <=> in(tptp_fun_D_9(C, B, A), C)))))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))) <=> in(tptp_fun_D_9(C, B, A), C)))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(58,plain,
% 0.20/0.39 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))) <=> in(tptp_fun_D_9(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))) <=> in(tptp_fun_D_9(C, B, A), C))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[57])).
% 0.20/0.39 tff(59,plain,
% 0.20/0.39 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))) <=> in(tptp_fun_D_9(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))) <=> in(tptp_fun_D_9(C, B, A), C))))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[58, 56])).
% 0.20/0.39 tff(60,plain,
% 0.20/0.39 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) <=> ((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))), rewrite(((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_9(C, B, A), C) <=> (in(tptp_fun_D_9(C, B, A), A) & in(tptp_fun_D_9(C, B, A), B))))) <=> ((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))) <=> in(tptp_fun_D_9(C, B, A), C)))), ((((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_9(C, B, A), C) <=> (in(tptp_fun_D_9(C, B, A), A) & in(tptp_fun_D_9(C, B, A), B)))))) <=> (((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C)))) & ((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))) <=> in(tptp_fun_D_9(C, B, A), C)))))), rewrite((((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C)))) & ((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))) <=> in(tptp_fun_D_9(C, B, A), C)))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))) <=> in(tptp_fun_D_9(C, B, A), C))))))), ((((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_9(C, B, A), C) <=> (in(tptp_fun_D_9(C, B, A), A) & in(tptp_fun_D_9(C, B, A), B)))))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))) <=> in(tptp_fun_D_9(C, B, A), C))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(61,plain,
% 0.20/0.39 (![A: $i, B: $i, C: $i] : (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_9(C, B, A), C) <=> (in(tptp_fun_D_9(C, B, A), A) & in(tptp_fun_D_9(C, B, A), B)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))) <=> in(tptp_fun_D_9(C, B, A), C))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[60])).
% 0.20/0.40 tff(62,plain,
% 0.20/0.40 (![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) <=> ![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(63,axiom,(![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d3_xboole_0')).
% 0.20/0.40 tff(64,plain,
% 0.20/0.40 (![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.20/0.40 tff(65,plain,(
% 0.20/0.40 ![A: $i, B: $i, C: $i] : (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_9(C, B, A), C) <=> (in(tptp_fun_D_9(C, B, A), A) & in(tptp_fun_D_9(C, B, A), B))))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[64])).
% 0.20/0.40 tff(66,plain,
% 0.20/0.40 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))) <=> in(tptp_fun_D_9(C, B, A), C))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.20/0.40 tff(67,plain,
% 0.20/0.40 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))) <=> in(tptp_fun_D_9(C, B, A), C))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.20/0.40 tff(68,plain,
% 0.20/0.40 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))) <=> in(tptp_fun_D_9(C, B, A), C))))))) | (~((~((~(set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(cartesian_product2(B!7, B!7), C!6))) | (~(((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))) <=> in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7))))))) | (~((set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(cartesian_product2(B!7, B!7), C!6)) | (((~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7))) | (~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), C!6, cartesian_product2(B!7, B!7)), C!6))) <=> in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), C!6, cartesian_product2(B!7, B!7)), set_intersection2(C!6, cartesian_product2(B!7, B!7))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))) <=> in(tptp_fun_D_9(C, B, A), C))))))) | (~((~((~(set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(cartesian_product2(B!7, B!7), C!6))) | (~(((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))) <=> in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7))))))) | (~((set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(cartesian_product2(B!7, B!7), C!6)) | (((~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7))) | (~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), C!6, cartesian_product2(B!7, B!7)), C!6))) <=> in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), C!6, cartesian_product2(B!7, B!7)), set_intersection2(C!6, cartesian_product2(B!7, B!7)))))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(69,plain,
% 0.20/0.40 ((~((~((~(set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(cartesian_product2(B!7, B!7), C!6))) | (~(((~in(A!8, cartesian_product2(B!7, B!7))) | (~in(A!8, C!6))) <=> in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7))))))) | (~((set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(cartesian_product2(B!7, B!7), C!6)) | (((~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7))) | (~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), C!6, cartesian_product2(B!7, B!7)), C!6))) <=> in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), C!6, cartesian_product2(B!7, B!7)), set_intersection2(C!6, cartesian_product2(B!7, B!7)))))))) <=> (~((~((~(set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(cartesian_product2(B!7, B!7), C!6))) | (~(((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))) <=> in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7))))))) | (~((set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(cartesian_product2(B!7, B!7), C!6)) | (((~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7))) | (~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), C!6, cartesian_product2(B!7, B!7)), C!6))) <=> in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), C!6, cartesian_product2(B!7, B!7)), set_intersection2(C!6, cartesian_product2(B!7, B!7))))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(70,plain,
% 0.20/0.40 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))) <=> in(tptp_fun_D_9(C, B, A), C))))))) | (~((~((~(set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(cartesian_product2(B!7, B!7), C!6))) | (~(((~in(A!8, cartesian_product2(B!7, B!7))) | (~in(A!8, C!6))) <=> in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7))))))) | (~((set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(cartesian_product2(B!7, B!7), C!6)) | (((~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7))) | (~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), C!6, cartesian_product2(B!7, B!7)), C!6))) <=> in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), C!6, cartesian_product2(B!7, B!7)), set_intersection2(C!6, cartesian_product2(B!7, B!7))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))) <=> in(tptp_fun_D_9(C, B, A), C))))))) | (~((~((~(set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(cartesian_product2(B!7, B!7), C!6))) | (~(((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))) <=> in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7))))))) | (~((set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(cartesian_product2(B!7, B!7), C!6)) | (((~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7))) | (~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), C!6, cartesian_product2(B!7, B!7)), C!6))) <=> in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), C!6, cartesian_product2(B!7, B!7)), set_intersection2(C!6, cartesian_product2(B!7, B!7)))))))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[69])).
% 0.20/0.40 tff(71,plain,
% 0.20/0.40 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))) <=> in(tptp_fun_D_9(C, B, A), C))))))) | (~((~((~(set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(cartesian_product2(B!7, B!7), C!6))) | (~(((~in(A!8, cartesian_product2(B!7, B!7))) | (~in(A!8, C!6))) <=> in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7))))))) | (~((set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(cartesian_product2(B!7, B!7), C!6)) | (((~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7))) | (~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), C!6, cartesian_product2(B!7, B!7)), C!6))) <=> in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), C!6, cartesian_product2(B!7, B!7)), set_intersection2(C!6, cartesian_product2(B!7, B!7))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))) <=> in(tptp_fun_D_9(C, B, A), C))))))) | (~((~((~(set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(cartesian_product2(B!7, B!7), C!6))) | (~(((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))) <=> in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7))))))) | (~((set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(cartesian_product2(B!7, B!7), C!6)) | (((~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7))) | (~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), C!6, cartesian_product2(B!7, B!7)), C!6))) <=> in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), C!6, cartesian_product2(B!7, B!7)), set_intersection2(C!6, cartesian_product2(B!7, B!7)))))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[70, 68])).
% 0.20/0.40 tff(72,plain,
% 0.20/0.40 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))) <=> in(tptp_fun_D_9(C, B, A), C))))))) | (~((~((~(set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(cartesian_product2(B!7, B!7), C!6))) | (~(((~in(A!8, cartesian_product2(B!7, B!7))) | (~in(A!8, C!6))) <=> in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7))))))) | (~((set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(cartesian_product2(B!7, B!7), C!6)) | (((~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7))) | (~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), C!6, cartesian_product2(B!7, B!7)), C!6))) <=> in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), C!6, cartesian_product2(B!7, B!7)), set_intersection2(C!6, cartesian_product2(B!7, B!7))))))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(73,plain,
% 0.20/0.40 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_9(C, B, A), A)) | (~in(tptp_fun_D_9(C, B, A), B))) <=> in(tptp_fun_D_9(C, B, A), C))))))) | (~((~((~(set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(cartesian_product2(B!7, B!7), C!6))) | (~(((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))) <=> in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7))))))) | (~((set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(cartesian_product2(B!7, B!7), C!6)) | (((~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7))) | (~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), C!6, cartesian_product2(B!7, B!7)), C!6))) <=> in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), C!6, cartesian_product2(B!7, B!7)), set_intersection2(C!6, cartesian_product2(B!7, B!7))))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.20/0.41 tff(74,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[73, 67, 49])).
% 0.20/0.41 tff(75,plain,(~((~((~(set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(cartesian_product2(B!7, B!7), C!6))) | (~(((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))) <=> in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7))))))) | (~((set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(cartesian_product2(B!7, B!7), C!6)) | (((~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7))) | (~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), C!6, cartesian_product2(B!7, B!7)), C!6))) <=> in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), C!6, cartesian_product2(B!7, B!7)), set_intersection2(C!6, cartesian_product2(B!7, B!7)))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(76,plain,
% 0.20/0.41 (((~((~(set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(cartesian_product2(B!7, B!7), C!6))) | (~(((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))) <=> in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7))))))) | (~((set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(cartesian_product2(B!7, B!7), C!6)) | (((~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), C!6, cartesian_product2(B!7, B!7)), cartesian_product2(B!7, B!7))) | (~in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), C!6, cartesian_product2(B!7, B!7)), C!6))) <=> in(tptp_fun_D_9(set_intersection2(C!6, cartesian_product2(B!7, B!7)), C!6, cartesian_product2(B!7, B!7)), set_intersection2(C!6, cartesian_product2(B!7, B!7))))))) | ((~(set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(cartesian_product2(B!7, B!7), C!6))) | (~(((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))) <=> in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7))))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(77,plain,
% 0.20/0.41 ((~(set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(cartesian_product2(B!7, B!7), C!6))) | (~(((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))) <=> in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7)))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.20/0.41 tff(78,plain,
% 0.20/0.41 (^[A: $i, B: $i] : refl((set_intersection2(A, B) = set_intersection2(B, A)) <=> (set_intersection2(A, B) = set_intersection2(B, A)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(79,plain,
% 0.20/0.41 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[78])).
% 0.20/0.41 tff(80,plain,
% 0.20/0.41 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(81,axiom,(![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k3_xboole_0')).
% 0.20/0.41 tff(82,plain,
% 0.20/0.41 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.20/0.41 tff(83,plain,(
% 0.20/0.41 ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.20/0.41 inference(skolemize,[status(sab)],[82])).
% 0.20/0.41 tff(84,plain,
% 0.20/0.41 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.20/0.41 tff(85,plain,
% 0.20/0.41 ((~![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))) | (set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(cartesian_product2(B!7, B!7), C!6))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(86,plain,
% 0.20/0.41 (set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(cartesian_product2(B!7, B!7), C!6)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.20/0.41 tff(87,plain,
% 0.20/0.41 ((~((~(set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(cartesian_product2(B!7, B!7), C!6))) | (~(((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))) <=> in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7))))))) | (~(set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(cartesian_product2(B!7, B!7), C!6))) | (~(((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))) <=> in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7)))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(88,plain,
% 0.20/0.41 ((~((~(set_intersection2(C!6, cartesian_product2(B!7, B!7)) = set_intersection2(cartesian_product2(B!7, B!7), C!6))) | (~(((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))) <=> in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7))))))) | (~(((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))) <=> in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7)))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.20/0.41 tff(89,plain,
% 0.20/0.41 (~(((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))) <=> in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[88, 77])).
% 0.20/0.41 tff(90,plain,
% 0.20/0.41 ((((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))) <=> in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7)))) | (~((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7))))) | (~in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(91,plain,
% 0.20/0.41 (~in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[90, 33, 89])).
% 0.20/0.41 tff(92,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[91, 48])).
% 0.20/0.41 tff(93,plain,(~((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(94,plain,
% 0.20/0.41 (((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))) | (~in(A!8, relation_restriction(C!6, B!7))) | (~(((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))) <=> in(A!8, relation_restriction(C!6, B!7))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(95,plain,
% 0.20/0.41 (((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))) | (~in(A!8, relation_restriction(C!6, B!7)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[94, 44])).
% 0.20/0.41 tff(96,plain,
% 0.20/0.41 (~in(A!8, relation_restriction(C!6, B!7))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[95, 93])).
% 0.20/0.41 tff(97,plain,
% 0.20/0.41 (~in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[96, 32])).
% 0.20/0.41 tff(98,plain,
% 0.20/0.41 ((((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))) <=> in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7)))) | ((~in(A!8, C!6)) | (~in(A!8, cartesian_product2(B!7, B!7)))) | in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(99,plain,
% 0.20/0.41 (in(A!8, set_intersection2(C!6, cartesian_product2(B!7, B!7)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[98, 93, 89])).
% 0.20/0.41 tff(100,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[99, 97])).
% 0.20/0.41 % SZS output end Proof
% 0.20/0.41 % E exiting
%------------------------------------------------------------------------------