%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET676+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:26:08 AM UTC 2025
% Result : Theorem 0.22s 0.40s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : SET676+3 : TPTP v9.0.0. Released v2.2.0.
% 0.04/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n015.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Jun 20 05:36:40 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.22/0.40 % SZS status Theorem
% 0.22/0.40 % SZS output start Proof
% 0.22/0.40 tff(ilf_type_type, type, (
% 0.22/0.40 ilf_type: ( $i * $i ) > $o)).
% 0.22/0.40 tff(set_type_type, type, (
% 0.22/0.40 set_type: $i)).
% 0.22/0.40 tff(cross_product_type, type, (
% 0.22/0.40 cross_product: ( $i * $i ) > $i)).
% 0.22/0.40 tff(tptp_fun_B_11_type, type, (
% 0.22/0.40 tptp_fun_B_11: $i)).
% 0.22/0.40 tff(relation_type_type, type, (
% 0.22/0.40 relation_type: ( $i * $i ) > $i)).
% 0.22/0.40 tff(identity_relation_of_type_type, type, (
% 0.22/0.40 identity_relation_of_type: $i > $i)).
% 0.22/0.40 tff(1,plain,
% 0.22/0.40 ((~![B: $i] : ((~ilf_type(B, set_type)) | ilf_type(cross_product(B, B), identity_relation_of_type(B)))) <=> (~![B: $i] : ((~ilf_type(B, set_type)) | ilf_type(cross_product(B, B), identity_relation_of_type(B))))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(2,plain,
% 0.22/0.40 ((~![B: $i] : (ilf_type(B, set_type) => ilf_type(cross_product(B, B), identity_relation_of_type(B)))) <=> (~![B: $i] : ((~ilf_type(B, set_type)) | ilf_type(cross_product(B, B), identity_relation_of_type(B))))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(3,axiom,(~![B: $i] : (ilf_type(B, set_type) => ilf_type(cross_product(B, B), identity_relation_of_type(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_relset_1_41')).
% 0.22/0.40 tff(4,plain,
% 0.22/0.40 (~![B: $i] : ((~ilf_type(B, set_type)) | ilf_type(cross_product(B, B), identity_relation_of_type(B)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.22/0.40 tff(5,plain,
% 0.22/0.40 (~![B: $i] : ((~ilf_type(B, set_type)) | ilf_type(cross_product(B, B), identity_relation_of_type(B)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.22/0.40 tff(6,plain,
% 0.22/0.40 (~![B: $i] : ((~ilf_type(B, set_type)) | ilf_type(cross_product(B, B), identity_relation_of_type(B)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.22/0.40 tff(7,plain,
% 0.22/0.40 (~![B: $i] : ((~ilf_type(B, set_type)) | ilf_type(cross_product(B, B), identity_relation_of_type(B)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.22/0.40 tff(8,plain,(
% 0.22/0.40 ~((~ilf_type(B!11, set_type)) | ilf_type(cross_product(B!11, B!11), identity_relation_of_type(B!11)))),
% 0.22/0.40 inference(skolemize,[status(sab)],[7])).
% 0.22/0.40 tff(9,plain,
% 0.22/0.40 (ilf_type(B!11, set_type)),
% 0.22/0.40 inference(or_elim,[status(thm)],[8])).
% 0.22/0.40 tff(10,plain,
% 0.22/0.40 (^[B: $i] : refl(((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), relation_type(B, C)))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), relation_type(B, C)))))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(11,plain,
% 0.22/0.40 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), relation_type(B, C)))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), relation_type(B, C))))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[10])).
% 0.22/0.40 tff(12,plain,
% 0.22/0.40 (^[B: $i] : rewrite(((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), relation_type(B, C)))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), relation_type(B, C)))))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(13,plain,
% 0.22/0.40 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), relation_type(B, C)))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), relation_type(B, C))))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[12])).
% 0.22/0.40 tff(14,plain,
% 0.22/0.40 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), relation_type(B, C)))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), relation_type(B, C))))),
% 0.22/0.40 inference(transitivity,[status(thm)],[13, 11])).
% 0.22/0.40 tff(15,plain,
% 0.22/0.40 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), relation_type(B, C)))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), relation_type(B, C))))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(16,plain,
% 0.22/0.41 (^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((ilf_type(C, set_type) => ilf_type(cross_product(B, C), relation_type(B, C))) <=> ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), relation_type(B, C))))), (![C: $i] : (ilf_type(C, set_type) => ilf_type(cross_product(B, C), relation_type(B, C))) <=> ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), relation_type(B, C))))), ((ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => ilf_type(cross_product(B, C), relation_type(B, C)))) <=> (ilf_type(B, set_type) => ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), relation_type(B, C)))))), rewrite((ilf_type(B, set_type) => ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), relation_type(B, C)))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), relation_type(B, C))))), ((ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => ilf_type(cross_product(B, C), relation_type(B, C)))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), relation_type(B, C))))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(17,plain,
% 0.22/0.41 (![B: $i] : (ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => ilf_type(cross_product(B, C), relation_type(B, C)))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), relation_type(B, C))))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[16])).
% 0.22/0.41 tff(18,axiom,(![B: $i] : (ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => ilf_type(cross_product(B, C), relation_type(B, C))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p1')).
% 0.22/0.41 tff(19,plain,
% 0.22/0.41 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), relation_type(B, C))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.22/0.41 tff(20,plain,
% 0.22/0.41 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), relation_type(B, C))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.22/0.41 tff(21,plain,(
% 0.22/0.41 ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), relation_type(B, C))))),
% 0.22/0.41 inference(skolemize,[status(sab)],[20])).
% 0.22/0.41 tff(22,plain,
% 0.22/0.41 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), relation_type(B, C))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.22/0.41 tff(23,plain,
% 0.22/0.41 (((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), relation_type(B, C))))) | ((~ilf_type(B!11, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B!11, C), relation_type(B!11, C))))) <=> ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), relation_type(B, C))))) | (~ilf_type(B!11, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B!11, C), relation_type(B!11, C))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(24,plain,
% 0.22/0.41 ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), relation_type(B, C))))) | ((~ilf_type(B!11, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B!11, C), relation_type(B!11, C))))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(25,plain,
% 0.22/0.41 ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), relation_type(B, C))))) | (~ilf_type(B!11, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B!11, C), relation_type(B!11, C)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.22/0.41 tff(26,plain,
% 0.22/0.41 (![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B!11, C), relation_type(B!11, C)))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[25, 22, 9])).
% 0.22/0.41 tff(27,plain,
% 0.22/0.41 (((~![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B!11, C), relation_type(B!11, C)))) | ((~ilf_type(B!11, set_type)) | ilf_type(cross_product(B!11, B!11), relation_type(B!11, B!11)))) <=> ((~![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B!11, C), relation_type(B!11, C)))) | (~ilf_type(B!11, set_type)) | ilf_type(cross_product(B!11, B!11), relation_type(B!11, B!11)))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(28,plain,
% 0.22/0.41 ((~![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B!11, C), relation_type(B!11, C)))) | ((~ilf_type(B!11, set_type)) | ilf_type(cross_product(B!11, B!11), relation_type(B!11, B!11)))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(29,plain,
% 0.22/0.41 ((~![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B!11, C), relation_type(B!11, C)))) | (~ilf_type(B!11, set_type)) | ilf_type(cross_product(B!11, B!11), relation_type(B!11, B!11))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.22/0.41 tff(30,plain,
% 0.22/0.41 (ilf_type(cross_product(B!11, B!11), relation_type(B!11, B!11))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[29, 9, 26])).
% 0.22/0.41 tff(31,plain,
% 0.22/0.41 (~ilf_type(cross_product(B!11, B!11), identity_relation_of_type(B!11))),
% 0.22/0.41 inference(or_elim,[status(thm)],[8])).
% 0.22/0.41 tff(32,plain,
% 0.22/0.41 ((~(ilf_type(cross_product(B!11, B!11), identity_relation_of_type(B!11)) <=> ilf_type(cross_product(B!11, B!11), relation_type(B!11, B!11)))) | ilf_type(cross_product(B!11, B!11), identity_relation_of_type(B!11)) | (~ilf_type(cross_product(B!11, B!11), relation_type(B!11, B!11)))),
% 0.22/0.41 inference(tautology,[status(thm)],[])).
% 0.22/0.41 tff(33,plain,
% 0.22/0.41 (~(ilf_type(cross_product(B!11, B!11), identity_relation_of_type(B!11)) <=> ilf_type(cross_product(B!11, B!11), relation_type(B!11, B!11)))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[32, 31, 30])).
% 0.22/0.41 tff(34,plain,
% 0.22/0.41 (^[B: $i] : refl(((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, identity_relation_of_type(B)) <=> ilf_type(C, relation_type(B, B))))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, identity_relation_of_type(B)) <=> ilf_type(C, relation_type(B, B))))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(35,plain,
% 0.22/0.41 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, identity_relation_of_type(B)) <=> ilf_type(C, relation_type(B, B))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, identity_relation_of_type(B)) <=> ilf_type(C, relation_type(B, B)))))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[34])).
% 0.22/0.41 tff(36,plain,
% 0.22/0.41 (^[B: $i] : rewrite(((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, identity_relation_of_type(B)) <=> ilf_type(C, relation_type(B, B))))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, identity_relation_of_type(B)) <=> ilf_type(C, relation_type(B, B))))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(37,plain,
% 0.22/0.41 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, identity_relation_of_type(B)) <=> ilf_type(C, relation_type(B, B))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, identity_relation_of_type(B)) <=> ilf_type(C, relation_type(B, B)))))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[36])).
% 0.22/0.41 tff(38,plain,
% 0.22/0.41 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, identity_relation_of_type(B)) <=> ilf_type(C, relation_type(B, B))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, identity_relation_of_type(B)) <=> ilf_type(C, relation_type(B, B)))))),
% 0.22/0.41 inference(transitivity,[status(thm)],[37, 35])).
% 0.22/0.41 tff(39,plain,
% 0.22/0.41 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, identity_relation_of_type(B)) <=> ilf_type(C, relation_type(B, B))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, identity_relation_of_type(B)) <=> ilf_type(C, relation_type(B, B)))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(40,plain,
% 0.22/0.41 (^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((ilf_type(C, set_type) => (ilf_type(C, identity_relation_of_type(B)) <=> ilf_type(C, relation_type(B, B)))) <=> ((~ilf_type(C, set_type)) | (ilf_type(C, identity_relation_of_type(B)) <=> ilf_type(C, relation_type(B, B)))))), (![C: $i] : (ilf_type(C, set_type) => (ilf_type(C, identity_relation_of_type(B)) <=> ilf_type(C, relation_type(B, B)))) <=> ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, identity_relation_of_type(B)) <=> ilf_type(C, relation_type(B, B)))))), ((ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => (ilf_type(C, identity_relation_of_type(B)) <=> ilf_type(C, relation_type(B, B))))) <=> (ilf_type(B, set_type) => ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, identity_relation_of_type(B)) <=> ilf_type(C, relation_type(B, B))))))), rewrite((ilf_type(B, set_type) => ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, identity_relation_of_type(B)) <=> ilf_type(C, relation_type(B, B))))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, identity_relation_of_type(B)) <=> ilf_type(C, relation_type(B, B)))))), ((ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => (ilf_type(C, identity_relation_of_type(B)) <=> ilf_type(C, relation_type(B, B))))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, identity_relation_of_type(B)) <=> ilf_type(C, relation_type(B, B)))))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(41,plain,
% 0.22/0.41 (![B: $i] : (ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => (ilf_type(C, identity_relation_of_type(B)) <=> ilf_type(C, relation_type(B, B))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, identity_relation_of_type(B)) <=> ilf_type(C, relation_type(B, B)))))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[40])).
% 0.22/0.41 tff(42,axiom,(![B: $i] : (ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => (ilf_type(C, identity_relation_of_type(B)) <=> ilf_type(C, relation_type(B, B)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p4')).
% 0.22/0.41 tff(43,plain,
% 0.22/0.41 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, identity_relation_of_type(B)) <=> ilf_type(C, relation_type(B, B)))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.22/0.41 tff(44,plain,
% 0.22/0.41 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, identity_relation_of_type(B)) <=> ilf_type(C, relation_type(B, B)))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.22/0.41 tff(45,plain,(
% 0.22/0.41 ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, identity_relation_of_type(B)) <=> ilf_type(C, relation_type(B, B)))))),
% 0.22/0.41 inference(skolemize,[status(sab)],[44])).
% 0.22/0.41 tff(46,plain,
% 0.22/0.41 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, identity_relation_of_type(B)) <=> ilf_type(C, relation_type(B, B)))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.22/0.41 tff(47,plain,
% 0.22/0.41 (((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, identity_relation_of_type(B)) <=> ilf_type(C, relation_type(B, B)))))) | ((~ilf_type(B!11, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, identity_relation_of_type(B!11)) <=> ilf_type(C, relation_type(B!11, B!11)))))) <=> ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, identity_relation_of_type(B)) <=> ilf_type(C, relation_type(B, B)))))) | (~ilf_type(B!11, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, identity_relation_of_type(B!11)) <=> ilf_type(C, relation_type(B!11, B!11)))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(48,plain,
% 0.22/0.41 ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, identity_relation_of_type(B)) <=> ilf_type(C, relation_type(B, B)))))) | ((~ilf_type(B!11, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, identity_relation_of_type(B!11)) <=> ilf_type(C, relation_type(B!11, B!11)))))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(49,plain,
% 0.22/0.41 ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, identity_relation_of_type(B)) <=> ilf_type(C, relation_type(B, B)))))) | (~ilf_type(B!11, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, identity_relation_of_type(B!11)) <=> ilf_type(C, relation_type(B!11, B!11))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.22/0.41 tff(50,plain,
% 0.22/0.41 (![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, identity_relation_of_type(B!11)) <=> ilf_type(C, relation_type(B!11, B!11))))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[49, 46, 9])).
% 0.22/0.41 tff(51,plain,
% 0.22/0.41 (((~![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, identity_relation_of_type(B!11)) <=> ilf_type(C, relation_type(B!11, B!11))))) | ((~ilf_type(cross_product(B!11, B!11), set_type)) | (ilf_type(cross_product(B!11, B!11), identity_relation_of_type(B!11)) <=> ilf_type(cross_product(B!11, B!11), relation_type(B!11, B!11))))) <=> ((~![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, identity_relation_of_type(B!11)) <=> ilf_type(C, relation_type(B!11, B!11))))) | (~ilf_type(cross_product(B!11, B!11), set_type)) | (ilf_type(cross_product(B!11, B!11), identity_relation_of_type(B!11)) <=> ilf_type(cross_product(B!11, B!11), relation_type(B!11, B!11))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(52,plain,
% 0.22/0.41 ((~![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, identity_relation_of_type(B!11)) <=> ilf_type(C, relation_type(B!11, B!11))))) | ((~ilf_type(cross_product(B!11, B!11), set_type)) | (ilf_type(cross_product(B!11, B!11), identity_relation_of_type(B!11)) <=> ilf_type(cross_product(B!11, B!11), relation_type(B!11, B!11))))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(53,plain,
% 0.22/0.41 ((~![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, identity_relation_of_type(B!11)) <=> ilf_type(C, relation_type(B!11, B!11))))) | (~ilf_type(cross_product(B!11, B!11), set_type)) | (ilf_type(cross_product(B!11, B!11), identity_relation_of_type(B!11)) <=> ilf_type(cross_product(B!11, B!11), relation_type(B!11, B!11)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.22/0.41 tff(54,plain,
% 0.22/0.41 (~ilf_type(cross_product(B!11, B!11), set_type)),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[53, 50, 33])).
% 0.22/0.41 tff(55,plain,
% 0.22/0.41 (^[B: $i] : refl(((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(56,plain,
% 0.22/0.41 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[55])).
% 0.22/0.41 tff(57,plain,
% 0.22/0.41 (^[B: $i] : rewrite(((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(58,plain,
% 0.22/0.41 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[57])).
% 0.22/0.41 tff(59,plain,
% 0.22/0.41 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))),
% 0.22/0.41 inference(transitivity,[status(thm)],[58, 56])).
% 0.22/0.41 tff(60,plain,
% 0.22/0.41 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(61,plain,
% 0.22/0.42 (^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((ilf_type(C, set_type) => ilf_type(cross_product(B, C), set_type)) <=> ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))), (![C: $i] : (ilf_type(C, set_type) => ilf_type(cross_product(B, C), set_type)) <=> ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))), ((ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => ilf_type(cross_product(B, C), set_type))) <=> (ilf_type(B, set_type) => ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type))))), rewrite((ilf_type(B, set_type) => ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))), ((ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => ilf_type(cross_product(B, C), set_type))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(62,plain,
% 0.22/0.42 (![B: $i] : (ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => ilf_type(cross_product(B, C), set_type))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[61])).
% 0.22/0.42 tff(63,axiom,(![B: $i] : (ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => ilf_type(cross_product(B, C), set_type)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p3')).
% 0.22/0.42 tff(64,plain,
% 0.22/0.42 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.22/0.42 tff(65,plain,
% 0.22/0.42 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.22/0.42 tff(66,plain,(
% 0.22/0.42 ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))),
% 0.22/0.42 inference(skolemize,[status(sab)],[65])).
% 0.22/0.42 tff(67,plain,
% 0.22/0.42 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.22/0.42 tff(68,plain,
% 0.22/0.42 (((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))) | ((~ilf_type(B!11, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B!11, C), set_type)))) <=> ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))) | (~ilf_type(B!11, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B!11, C), set_type)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(69,plain,
% 0.22/0.42 ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))) | ((~ilf_type(B!11, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B!11, C), set_type)))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(70,plain,
% 0.22/0.42 ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))) | (~ilf_type(B!11, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B!11, C), set_type))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.22/0.42 tff(71,plain,
% 0.22/0.42 (![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B!11, C), set_type))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[70, 67, 9])).
% 0.22/0.42 tff(72,plain,
% 0.22/0.42 (((~![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B!11, C), set_type))) | ((~ilf_type(B!11, set_type)) | ilf_type(cross_product(B!11, B!11), set_type))) <=> ((~![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B!11, C), set_type))) | (~ilf_type(B!11, set_type)) | ilf_type(cross_product(B!11, B!11), set_type))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(73,plain,
% 0.22/0.42 ((~![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B!11, C), set_type))) | ((~ilf_type(B!11, set_type)) | ilf_type(cross_product(B!11, B!11), set_type))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(74,plain,
% 0.22/0.42 ((~![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B!11, C), set_type))) | (~ilf_type(B!11, set_type)) | ilf_type(cross_product(B!11, B!11), set_type)),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.22/0.42 tff(75,plain,
% 0.22/0.42 ($false),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[74, 9, 71, 54])).
% 0.22/0.42 % SZS output end Proof
% 0.22/0.42 % E exiting
%------------------------------------------------------------------------------