%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET643+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:26:05 AM UTC 2025
% Result : Theorem 0.19s 0.49s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET643+3 : TPTP v9.0.0. Released v2.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.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 05:32:20 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.49 % SZS status Theorem
% 0.19/0.49 % SZS output start Proof
% 0.19/0.49 tff(subset_type, type, (
% 0.19/0.49 subset: ( $i * $i ) > $o)).
% 0.19/0.49 tff(cross_product_type, type, (
% 0.19/0.49 cross_product: ( $i * $i ) > $i)).
% 0.19/0.49 tff(tptp_fun_B_10_type, type, (
% 0.19/0.49 tptp_fun_B_10: $i)).
% 0.19/0.49 tff(tptp_fun_C_11_type, type, (
% 0.19/0.49 tptp_fun_C_11: $i)).
% 0.19/0.49 tff(ilf_type_type, type, (
% 0.19/0.49 ilf_type: ( $i * $i ) > $o)).
% 0.19/0.49 tff(relation_type_type, type, (
% 0.19/0.49 relation_type: ( $i * $i ) > $i)).
% 0.19/0.49 tff(set_type_type, type, (
% 0.19/0.49 set_type: $i)).
% 0.19/0.49 tff(1,plain,
% 0.19/0.49 ((~![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)))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(2,plain,
% 0.19/0.49 ((~![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)))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(3,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','prove_relset_1_5')).
% 0.19/0.49 tff(4,plain,
% 0.19/0.49 (~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), relation_type(B, C))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.19/0.49 tff(5,plain,
% 0.19/0.49 (~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), relation_type(B, C))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.19/0.49 tff(6,plain,
% 0.19/0.49 (~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), relation_type(B, C))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.19/0.49 tff(7,plain,
% 0.19/0.49 (~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), relation_type(B, C))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.19/0.49 tff(8,plain,
% 0.19/0.49 (ilf_type(B!10, set_type)),
% 0.19/0.49 inference(and_elim,[status(thm)],[7])).
% 0.19/0.49 tff(9,plain,
% 0.19/0.49 (^[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))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(10,plain,
% 0.19/0.49 (![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)))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[9])).
% 0.19/0.49 tff(11,plain,
% 0.19/0.49 (^[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))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(12,plain,
% 0.19/0.49 (![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)))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[11])).
% 0.19/0.49 tff(13,plain,
% 0.19/0.49 (![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)))),
% 0.19/0.49 inference(transitivity,[status(thm)],[12, 10])).
% 0.19/0.49 tff(14,plain,
% 0.19/0.49 (![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)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(15,plain,
% 0.19/0.49 (^[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)))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(16,plain,
% 0.19/0.49 (![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)))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[15])).
% 0.19/0.49 tff(17,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')).
% 0.19/0.49 tff(18,plain,
% 0.19/0.49 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.19/0.49 tff(19,plain,
% 0.19/0.49 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.19/0.49 tff(20,plain,(
% 0.19/0.49 ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))),
% 0.19/0.49 inference(skolemize,[status(sab)],[19])).
% 0.19/0.49 tff(21,plain,
% 0.19/0.49 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.19/0.49 tff(22,plain,
% 0.19/0.49 (((~![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!10, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B!10, 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!10, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B!10, C), set_type)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(23,plain,
% 0.19/0.49 ((~![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!10, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B!10, C), set_type)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(24,plain,
% 0.19/0.49 ((~![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!10, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B!10, C), set_type))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.19/0.49 tff(25,plain,
% 0.19/0.49 (![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B!10, C), set_type))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[24, 21, 8])).
% 0.19/0.49 tff(26,plain,
% 0.19/0.49 (~((~ilf_type(C!11, set_type)) | ilf_type(cross_product(B!10, C!11), relation_type(B!10, C!11)))),
% 0.19/0.49 inference(and_elim,[status(thm)],[7])).
% 0.19/0.49 tff(27,plain,
% 0.19/0.49 (ilf_type(C!11, set_type)),
% 0.19/0.49 inference(or_elim,[status(thm)],[26])).
% 0.19/0.49 tff(28,plain,
% 0.19/0.49 (((~![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B!10, C), set_type))) | ((~ilf_type(C!11, set_type)) | ilf_type(cross_product(B!10, C!11), set_type))) <=> ((~![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B!10, C), set_type))) | (~ilf_type(C!11, set_type)) | ilf_type(cross_product(B!10, C!11), set_type))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(29,plain,
% 0.19/0.49 ((~![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B!10, C), set_type))) | ((~ilf_type(C!11, set_type)) | ilf_type(cross_product(B!10, C!11), set_type))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(30,plain,
% 0.19/0.49 ((~![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B!10, C), set_type))) | (~ilf_type(C!11, set_type)) | ilf_type(cross_product(B!10, C!11), set_type)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.19/0.49 tff(31,plain,
% 0.19/0.49 (ilf_type(cross_product(B!10, C!11), set_type)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[30, 27, 25])).
% 0.19/0.49 tff(32,plain,
% 0.19/0.49 (^[B: $i] : refl(((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~subset(B, cross_product(C, D))) | (~ilf_type(D, set_type))))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~subset(B, cross_product(C, D))) | (~ilf_type(D, set_type))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(33,plain,
% 0.19/0.49 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~subset(B, cross_product(C, D))) | (~ilf_type(D, set_type))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~subset(B, cross_product(C, D))) | (~ilf_type(D, set_type)))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[32])).
% 0.19/0.49 tff(34,plain,
% 0.19/0.49 (^[B: $i] : rewrite(((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~subset(B, cross_product(C, D))) | (~ilf_type(D, set_type))))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~subset(B, cross_product(C, D))) | (~ilf_type(D, set_type))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(35,plain,
% 0.19/0.49 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~subset(B, cross_product(C, D))) | (~ilf_type(D, set_type))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~subset(B, cross_product(C, D))) | (~ilf_type(D, set_type)))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[34])).
% 0.19/0.49 tff(36,plain,
% 0.19/0.49 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~subset(B, cross_product(C, D))) | (~ilf_type(D, set_type))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~subset(B, cross_product(C, D))) | (~ilf_type(D, set_type)))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[35, 33])).
% 0.19/0.49 tff(37,plain,
% 0.19/0.49 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~subset(B, cross_product(C, D))) | (~ilf_type(D, set_type))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~subset(B, cross_product(C, D))) | (~ilf_type(D, set_type)))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(38,plain,
% 0.19/0.49 (^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : trans(monotonicity(rewrite((subset(B, cross_product(C, D)) => ilf_type(B, relation_type(C, D))) <=> ((~subset(B, cross_product(C, D))) | ilf_type(B, relation_type(C, D)))), ((ilf_type(D, set_type) => (subset(B, cross_product(C, D)) => ilf_type(B, relation_type(C, D)))) <=> (ilf_type(D, set_type) => ((~subset(B, cross_product(C, D))) | ilf_type(B, relation_type(C, D)))))), rewrite((ilf_type(D, set_type) => ((~subset(B, cross_product(C, D))) | ilf_type(B, relation_type(C, D)))) <=> (ilf_type(B, relation_type(C, D)) | (~subset(B, cross_product(C, D))) | (~ilf_type(D, set_type)))), ((ilf_type(D, set_type) => (subset(B, cross_product(C, D)) => ilf_type(B, relation_type(C, D)))) <=> (ilf_type(B, relation_type(C, D)) | (~subset(B, cross_product(C, D))) | (~ilf_type(D, set_type)))))), (![D: $i] : (ilf_type(D, set_type) => (subset(B, cross_product(C, D)) => ilf_type(B, relation_type(C, D)))) <=> ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~subset(B, cross_product(C, D))) | (~ilf_type(D, set_type))))), ((ilf_type(C, set_type) => ![D: $i] : (ilf_type(D, set_type) => (subset(B, cross_product(C, D)) => ilf_type(B, relation_type(C, D))))) <=> (ilf_type(C, set_type) => ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~subset(B, cross_product(C, D))) | (~ilf_type(D, set_type)))))), rewrite((ilf_type(C, set_type) => ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~subset(B, cross_product(C, D))) | (~ilf_type(D, set_type)))) <=> ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~subset(B, cross_product(C, D))) | (~ilf_type(D, set_type))))), ((ilf_type(C, set_type) => ![D: $i] : (ilf_type(D, set_type) => (subset(B, cross_product(C, D)) => ilf_type(B, relation_type(C, D))))) <=> ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~subset(B, cross_product(C, D))) | (~ilf_type(D, set_type))))))), (![C: $i] : (ilf_type(C, set_type) => ![D: $i] : (ilf_type(D, set_type) => (subset(B, cross_product(C, D)) => ilf_type(B, relation_type(C, D))))) <=> ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~subset(B, cross_product(C, D))) | (~ilf_type(D, set_type)))))), ((ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => ![D: $i] : (ilf_type(D, set_type) => (subset(B, cross_product(C, D)) => ilf_type(B, relation_type(C, D)))))) <=> (ilf_type(B, set_type) => ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~subset(B, cross_product(C, D))) | (~ilf_type(D, set_type))))))), rewrite((ilf_type(B, set_type) => ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~subset(B, cross_product(C, D))) | (~ilf_type(D, set_type))))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~subset(B, cross_product(C, D))) | (~ilf_type(D, set_type)))))), ((ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => ![D: $i] : (ilf_type(D, set_type) => (subset(B, cross_product(C, D)) => ilf_type(B, relation_type(C, D)))))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~subset(B, cross_product(C, D))) | (~ilf_type(D, set_type)))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(39,plain,
% 0.19/0.49 (![B: $i] : (ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => ![D: $i] : (ilf_type(D, set_type) => (subset(B, cross_product(C, D)) => ilf_type(B, relation_type(C, D)))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~subset(B, cross_product(C, D))) | (~ilf_type(D, set_type)))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[38])).
% 0.19/0.49 tff(40,axiom,(![B: $i] : (ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => ![D: $i] : (ilf_type(D, set_type) => (subset(B, cross_product(C, D)) => ilf_type(B, relation_type(C, D))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p1')).
% 0.19/0.49 tff(41,plain,
% 0.19/0.49 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~subset(B, cross_product(C, D))) | (~ilf_type(D, set_type)))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.19/0.49 tff(42,plain,
% 0.19/0.49 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~subset(B, cross_product(C, D))) | (~ilf_type(D, set_type)))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.19/0.49 tff(43,plain,(
% 0.19/0.49 ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~subset(B, cross_product(C, D))) | (~ilf_type(D, set_type)))))),
% 0.19/0.49 inference(skolemize,[status(sab)],[42])).
% 0.19/0.49 tff(44,plain,
% 0.19/0.49 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~subset(B, cross_product(C, D))) | (~ilf_type(D, set_type)))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.19/0.49 tff(45,plain,
% 0.19/0.49 (((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~subset(B, cross_product(C, D))) | (~ilf_type(D, set_type)))))) | ((~ilf_type(cross_product(B!10, C!11), set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : ((~ilf_type(D, set_type)) | ilf_type(cross_product(B!10, C!11), relation_type(C, D)) | (~subset(cross_product(B!10, C!11), cross_product(C, D))))))) <=> ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~subset(B, cross_product(C, D))) | (~ilf_type(D, set_type)))))) | (~ilf_type(cross_product(B!10, C!11), set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : ((~ilf_type(D, set_type)) | ilf_type(cross_product(B!10, C!11), relation_type(C, D)) | (~subset(cross_product(B!10, C!11), cross_product(C, D))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(46,plain,
% 0.19/0.49 (((~ilf_type(cross_product(B!10, C!11), set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(cross_product(B!10, C!11), relation_type(C, D)) | (~subset(cross_product(B!10, C!11), cross_product(C, D))) | (~ilf_type(D, set_type))))) <=> ((~ilf_type(cross_product(B!10, C!11), set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : ((~ilf_type(D, set_type)) | ilf_type(cross_product(B!10, C!11), relation_type(C, D)) | (~subset(cross_product(B!10, C!11), cross_product(C, D))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(47,plain,
% 0.19/0.49 (((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~subset(B, cross_product(C, D))) | (~ilf_type(D, set_type)))))) | ((~ilf_type(cross_product(B!10, C!11), set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(cross_product(B!10, C!11), relation_type(C, D)) | (~subset(cross_product(B!10, C!11), cross_product(C, D))) | (~ilf_type(D, set_type)))))) <=> ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~subset(B, cross_product(C, D))) | (~ilf_type(D, set_type)))))) | ((~ilf_type(cross_product(B!10, C!11), set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : ((~ilf_type(D, set_type)) | ilf_type(cross_product(B!10, C!11), relation_type(C, D)) | (~subset(cross_product(B!10, C!11), cross_product(C, D)))))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[46])).
% 0.19/0.49 tff(48,plain,
% 0.19/0.49 (((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~subset(B, cross_product(C, D))) | (~ilf_type(D, set_type)))))) | ((~ilf_type(cross_product(B!10, C!11), set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(cross_product(B!10, C!11), relation_type(C, D)) | (~subset(cross_product(B!10, C!11), cross_product(C, D))) | (~ilf_type(D, set_type)))))) <=> ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~subset(B, cross_product(C, D))) | (~ilf_type(D, set_type)))))) | (~ilf_type(cross_product(B!10, C!11), set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : ((~ilf_type(D, set_type)) | ilf_type(cross_product(B!10, C!11), relation_type(C, D)) | (~subset(cross_product(B!10, C!11), cross_product(C, D))))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[47, 45])).
% 0.19/0.49 tff(49,plain,
% 0.19/0.49 ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~subset(B, cross_product(C, D))) | (~ilf_type(D, set_type)))))) | ((~ilf_type(cross_product(B!10, C!11), set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(cross_product(B!10, C!11), relation_type(C, D)) | (~subset(cross_product(B!10, C!11), cross_product(C, D))) | (~ilf_type(D, set_type)))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(50,plain,
% 0.19/0.50 ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~subset(B, cross_product(C, D))) | (~ilf_type(D, set_type)))))) | (~ilf_type(cross_product(B!10, C!11), set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : ((~ilf_type(D, set_type)) | ilf_type(cross_product(B!10, C!11), relation_type(C, D)) | (~subset(cross_product(B!10, C!11), cross_product(C, D)))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.50 tff(51,plain,
% 0.19/0.50 (![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : ((~ilf_type(D, set_type)) | ilf_type(cross_product(B!10, C!11), relation_type(C, D)) | (~subset(cross_product(B!10, C!11), cross_product(C, D)))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[50, 44, 31])).
% 0.19/0.50 tff(52,plain,
% 0.19/0.50 (((~![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : ((~ilf_type(D, set_type)) | ilf_type(cross_product(B!10, C!11), relation_type(C, D)) | (~subset(cross_product(B!10, C!11), cross_product(C, D)))))) | ((~ilf_type(B!10, set_type)) | ![D: $i] : ((~ilf_type(D, set_type)) | ilf_type(cross_product(B!10, C!11), relation_type(B!10, D)) | (~subset(cross_product(B!10, C!11), cross_product(B!10, D)))))) <=> ((~![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : ((~ilf_type(D, set_type)) | ilf_type(cross_product(B!10, C!11), relation_type(C, D)) | (~subset(cross_product(B!10, C!11), cross_product(C, D)))))) | (~ilf_type(B!10, set_type)) | ![D: $i] : ((~ilf_type(D, set_type)) | ilf_type(cross_product(B!10, C!11), relation_type(B!10, D)) | (~subset(cross_product(B!10, C!11), cross_product(B!10, D)))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(53,plain,
% 0.19/0.50 ((~![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : ((~ilf_type(D, set_type)) | ilf_type(cross_product(B!10, C!11), relation_type(C, D)) | (~subset(cross_product(B!10, C!11), cross_product(C, D)))))) | ((~ilf_type(B!10, set_type)) | ![D: $i] : ((~ilf_type(D, set_type)) | ilf_type(cross_product(B!10, C!11), relation_type(B!10, D)) | (~subset(cross_product(B!10, C!11), cross_product(B!10, D)))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(54,plain,
% 0.19/0.50 ((~![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : ((~ilf_type(D, set_type)) | ilf_type(cross_product(B!10, C!11), relation_type(C, D)) | (~subset(cross_product(B!10, C!11), cross_product(C, D)))))) | (~ilf_type(B!10, set_type)) | ![D: $i] : ((~ilf_type(D, set_type)) | ilf_type(cross_product(B!10, C!11), relation_type(B!10, D)) | (~subset(cross_product(B!10, C!11), cross_product(B!10, D))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.19/0.50 tff(55,plain,
% 0.19/0.50 (![D: $i] : ((~ilf_type(D, set_type)) | ilf_type(cross_product(B!10, C!11), relation_type(B!10, D)) | (~subset(cross_product(B!10, C!11), cross_product(B!10, D))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[54, 8, 51])).
% 0.19/0.50 tff(56,plain,
% 0.19/0.50 (^[B: $i] : refl(((~ilf_type(B, set_type)) | subset(B, B)) <=> ((~ilf_type(B, set_type)) | subset(B, B)))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(57,plain,
% 0.19/0.50 (![B: $i] : ((~ilf_type(B, set_type)) | subset(B, B)) <=> ![B: $i] : ((~ilf_type(B, set_type)) | subset(B, B))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[56])).
% 0.19/0.50 tff(58,plain,
% 0.19/0.50 (![B: $i] : ((~ilf_type(B, set_type)) | subset(B, B)) <=> ![B: $i] : ((~ilf_type(B, set_type)) | subset(B, B))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(59,plain,
% 0.19/0.50 (^[B: $i] : rewrite((ilf_type(B, set_type) => subset(B, B)) <=> ((~ilf_type(B, set_type)) | subset(B, B)))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(60,plain,
% 0.19/0.50 (![B: $i] : (ilf_type(B, set_type) => subset(B, B)) <=> ![B: $i] : ((~ilf_type(B, set_type)) | subset(B, B))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[59])).
% 0.19/0.50 tff(61,axiom,(![B: $i] : (ilf_type(B, set_type) => subset(B, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p10')).
% 0.19/0.50 tff(62,plain,
% 0.19/0.50 (![B: $i] : ((~ilf_type(B, set_type)) | subset(B, B))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.19/0.50 tff(63,plain,
% 0.19/0.50 (![B: $i] : ((~ilf_type(B, set_type)) | subset(B, B))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.19/0.50 tff(64,plain,(
% 0.19/0.50 ![B: $i] : ((~ilf_type(B, set_type)) | subset(B, B))),
% 0.19/0.50 inference(skolemize,[status(sab)],[63])).
% 0.19/0.50 tff(65,plain,
% 0.19/0.50 (![B: $i] : ((~ilf_type(B, set_type)) | subset(B, B))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[64, 57])).
% 0.19/0.50 tff(66,plain,
% 0.19/0.50 (((~![B: $i] : ((~ilf_type(B, set_type)) | subset(B, B))) | ((~ilf_type(cross_product(B!10, C!11), set_type)) | subset(cross_product(B!10, C!11), cross_product(B!10, C!11)))) <=> ((~![B: $i] : ((~ilf_type(B, set_type)) | subset(B, B))) | (~ilf_type(cross_product(B!10, C!11), set_type)) | subset(cross_product(B!10, C!11), cross_product(B!10, C!11)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(67,plain,
% 0.19/0.50 ((~![B: $i] : ((~ilf_type(B, set_type)) | subset(B, B))) | ((~ilf_type(cross_product(B!10, C!11), set_type)) | subset(cross_product(B!10, C!11), cross_product(B!10, C!11)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(68,plain,
% 0.19/0.50 ((~![B: $i] : ((~ilf_type(B, set_type)) | subset(B, B))) | (~ilf_type(cross_product(B!10, C!11), set_type)) | subset(cross_product(B!10, C!11), cross_product(B!10, C!11))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.19/0.50 tff(69,plain,
% 0.19/0.50 (subset(cross_product(B!10, C!11), cross_product(B!10, C!11))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[68, 65, 31])).
% 0.19/0.50 tff(70,plain,
% 0.19/0.50 (~ilf_type(cross_product(B!10, C!11), relation_type(B!10, C!11))),
% 0.19/0.50 inference(or_elim,[status(thm)],[26])).
% 0.19/0.50 tff(71,plain,
% 0.19/0.50 (((~![D: $i] : ((~ilf_type(D, set_type)) | ilf_type(cross_product(B!10, C!11), relation_type(B!10, D)) | (~subset(cross_product(B!10, C!11), cross_product(B!10, D))))) | ((~ilf_type(C!11, set_type)) | ilf_type(cross_product(B!10, C!11), relation_type(B!10, C!11)) | (~subset(cross_product(B!10, C!11), cross_product(B!10, C!11))))) <=> ((~![D: $i] : ((~ilf_type(D, set_type)) | ilf_type(cross_product(B!10, C!11), relation_type(B!10, D)) | (~subset(cross_product(B!10, C!11), cross_product(B!10, D))))) | (~ilf_type(C!11, set_type)) | ilf_type(cross_product(B!10, C!11), relation_type(B!10, C!11)) | (~subset(cross_product(B!10, C!11), cross_product(B!10, C!11))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(72,plain,
% 0.19/0.50 ((~![D: $i] : ((~ilf_type(D, set_type)) | ilf_type(cross_product(B!10, C!11), relation_type(B!10, D)) | (~subset(cross_product(B!10, C!11), cross_product(B!10, D))))) | ((~ilf_type(C!11, set_type)) | ilf_type(cross_product(B!10, C!11), relation_type(B!10, C!11)) | (~subset(cross_product(B!10, C!11), cross_product(B!10, C!11))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(73,plain,
% 0.19/0.50 ((~![D: $i] : ((~ilf_type(D, set_type)) | ilf_type(cross_product(B!10, C!11), relation_type(B!10, D)) | (~subset(cross_product(B!10, C!11), cross_product(B!10, D))))) | (~ilf_type(C!11, set_type)) | ilf_type(cross_product(B!10, C!11), relation_type(B!10, C!11)) | (~subset(cross_product(B!10, C!11), cross_product(B!10, C!11)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.19/0.50 tff(74,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[73, 27, 70, 69, 55])).
% 0.19/0.50 % SZS output end Proof
% 0.19/0.50 % E exiting
%------------------------------------------------------------------------------