TSTP Solution File: SET643+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET643+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 : Tue Sep 20 05:07:29 EDT 2022
% Result : Theorem 0.20s 0.50s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET643+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 07:19:20 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.50 % SZS status Theorem
% 0.20/0.50 % SZS output start Proof
% 0.20/0.50 tff(subset_type, type, (
% 0.20/0.50 subset: ( $i * $i ) > $o)).
% 0.20/0.50 tff(cross_product_type, type, (
% 0.20/0.50 cross_product: ( $i * $i ) > $i)).
% 0.20/0.50 tff(tptp_fun_B_10_type, type, (
% 0.20/0.50 tptp_fun_B_10: $i)).
% 0.20/0.50 tff(tptp_fun_C_11_type, type, (
% 0.20/0.50 tptp_fun_C_11: $i)).
% 0.20/0.50 tff(ilf_type_type, type, (
% 0.20/0.50 ilf_type: ( $i * $i ) > $o)).
% 0.20/0.50 tff(relation_type_type, type, (
% 0.20/0.50 relation_type: ( $i * $i ) > $i)).
% 0.20/0.50 tff(set_type_type, type, (
% 0.20/0.50 set_type: $i)).
% 0.20/0.50 tff(1,plain,
% 0.20/0.50 (((~(~ilf_type(B!10, set_type))) & (~((~ilf_type(C!11, set_type)) | ilf_type(cross_product(B!10, C!11), relation_type(B!10, C!11))))) <=> (ilf_type(B!10, set_type) & (~((~ilf_type(C!11, set_type)) | ilf_type(cross_product(B!10, C!11), relation_type(B!10, C!11)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(2,plain,
% 0.20/0.50 ((~![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)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(3,plain,
% 0.20/0.50 ((~![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)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(4,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/sandbox2/benchmark/theBenchmark.p','prove_relset_1_5')).
% 0.20/0.50 tff(5,plain,
% 0.20/0.50 (~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), relation_type(B, C))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.50 tff(6,plain,
% 0.20/0.50 (~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), relation_type(B, C))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.20/0.50 tff(7,plain,
% 0.20/0.50 (~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), relation_type(B, C))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.50 tff(8,plain,
% 0.20/0.50 (~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), relation_type(B, C))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.20/0.50 tff(9,plain,
% 0.20/0.50 (~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), relation_type(B, C))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[8, 2])).
% 0.20/0.50 tff(10,plain,
% 0.20/0.50 (~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), relation_type(B, C))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.20/0.50 tff(11,plain,
% 0.20/0.50 (~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), relation_type(B, C))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.20/0.50 tff(12,plain,
% 0.20/0.50 (ilf_type(B!10, set_type) & (~((~ilf_type(C!11, set_type)) | ilf_type(cross_product(B!10, C!11), relation_type(B!10, C!11))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[11, 1])).
% 0.20/0.50 tff(13,plain,
% 0.20/0.50 (ilf_type(B!10, set_type)),
% 0.20/0.50 inference(and_elim,[status(thm)],[12])).
% 0.20/0.50 tff(14,plain,
% 0.20/0.50 (^[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))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(15,plain,
% 0.20/0.50 (![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)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[14])).
% 0.20/0.50 tff(16,plain,
% 0.20/0.50 (^[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))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(17,plain,
% 0.20/0.50 (![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)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[16])).
% 0.20/0.50 tff(18,plain,
% 0.20/0.50 (![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)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[17, 15])).
% 0.20/0.50 tff(19,plain,
% 0.20/0.50 (![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)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(20,plain,
% 0.20/0.50 (^[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)))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(21,plain,
% 0.20/0.50 (![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)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[20])).
% 0.20/0.50 tff(22,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/sandbox2/benchmark/theBenchmark.p','p3')).
% 0.20/0.50 tff(23,plain,
% 0.20/0.50 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.20/0.50 tff(24,plain,
% 0.20/0.50 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.20/0.50 tff(25,plain,(
% 0.20/0.50 ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[24])).
% 0.20/0.50 tff(26,plain,
% 0.20/0.50 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.20/0.50 tff(27,plain,
% 0.20/0.50 (((~![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)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(28,plain,
% 0.20/0.50 ((~![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)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(29,plain,
% 0.20/0.50 ((~![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))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.20/0.50 tff(30,plain,
% 0.20/0.50 (![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B!10, C), set_type))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[29, 26, 13])).
% 0.20/0.50 tff(31,plain,
% 0.20/0.50 (~((~ilf_type(C!11, set_type)) | ilf_type(cross_product(B!10, C!11), relation_type(B!10, C!11)))),
% 0.20/0.50 inference(and_elim,[status(thm)],[12])).
% 0.20/0.50 tff(32,plain,
% 0.20/0.50 (ilf_type(C!11, set_type)),
% 0.20/0.50 inference(or_elim,[status(thm)],[31])).
% 0.20/0.50 tff(33,plain,
% 0.20/0.50 (((~![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))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(34,plain,
% 0.20/0.50 ((~![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))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(35,plain,
% 0.20/0.50 ((~![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)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.20/0.50 tff(36,plain,
% 0.20/0.50 (ilf_type(cross_product(B!10, C!11), set_type)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[35, 32, 30])).
% 0.20/0.50 tff(37,plain,
% 0.20/0.50 (^[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))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(38,plain,
% 0.20/0.50 (![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))))) <=> ![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)))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[37])).
% 0.20/0.50 tff(39,plain,
% 0.20/0.50 (^[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))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(40,plain,
% 0.20/0.50 (![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))))) <=> ![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)))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[39])).
% 0.20/0.50 tff(41,plain,
% 0.20/0.50 (![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))))) <=> ![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)))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[40, 38])).
% 0.20/0.50 tff(42,plain,
% 0.20/0.50 (![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))))) <=> ![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)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(43,plain,
% 0.20/0.50 (^[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)))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(44,plain,
% 0.20/0.50 (![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)))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[43])).
% 0.20/0.50 tff(45,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/sandbox2/benchmark/theBenchmark.p','p1')).
% 0.20/0.50 tff(46,plain,
% 0.20/0.50 (![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)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.20/0.50 tff(47,plain,
% 0.20/0.50 (![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)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.20/0.50 tff(48,plain,(
% 0.20/0.50 ![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)))))),
% 0.20/0.50 inference(skolemize,[status(sab)],[47])).
% 0.20/0.50 tff(49,plain,
% 0.20/0.50 (![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)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[48, 41])).
% 0.20/0.50 tff(50,plain,
% 0.20/0.50 (((~![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))))))) <=> ((~![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))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(51,plain,
% 0.20/0.50 (((~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))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(52,plain,
% 0.20/0.50 (((~![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(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)))))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[51])).
% 0.20/0.51 tff(53,plain,
% 0.20/0.51 (((~![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))))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[52, 50])).
% 0.20/0.51 tff(54,plain,
% 0.20/0.51 ((~![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)))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(55,plain,
% 0.20/0.51 ((~![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)))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.20/0.51 tff(56,plain,
% 0.20/0.51 (![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)))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[55, 49, 36])).
% 0.20/0.51 tff(57,plain,
% 0.20/0.51 (((~![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)))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(58,plain,
% 0.20/0.51 ((~![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)))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(59,plain,
% 0.20/0.51 ((~![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))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.20/0.51 tff(60,plain,
% 0.20/0.51 (![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))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[59, 13, 56])).
% 0.20/0.51 tff(61,plain,
% 0.20/0.51 (^[B: $i] : refl(((~ilf_type(B, set_type)) | subset(B, B)) <=> ((~ilf_type(B, set_type)) | subset(B, B)))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(62,plain,
% 0.20/0.51 (![B: $i] : ((~ilf_type(B, set_type)) | subset(B, B)) <=> ![B: $i] : ((~ilf_type(B, set_type)) | subset(B, B))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[61])).
% 0.20/0.51 tff(63,plain,
% 0.20/0.51 (![B: $i] : ((~ilf_type(B, set_type)) | subset(B, B)) <=> ![B: $i] : ((~ilf_type(B, set_type)) | subset(B, B))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(64,plain,
% 0.20/0.51 (^[B: $i] : rewrite((ilf_type(B, set_type) => subset(B, B)) <=> ((~ilf_type(B, set_type)) | subset(B, B)))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(65,plain,
% 0.20/0.51 (![B: $i] : (ilf_type(B, set_type) => subset(B, B)) <=> ![B: $i] : ((~ilf_type(B, set_type)) | subset(B, B))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[64])).
% 0.20/0.51 tff(66,axiom,(![B: $i] : (ilf_type(B, set_type) => subset(B, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p10')).
% 0.20/0.51 tff(67,plain,
% 0.20/0.51 (![B: $i] : ((~ilf_type(B, set_type)) | subset(B, B))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.20/0.51 tff(68,plain,
% 0.20/0.51 (![B: $i] : ((~ilf_type(B, set_type)) | subset(B, B))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.20/0.51 tff(69,plain,(
% 0.20/0.51 ![B: $i] : ((~ilf_type(B, set_type)) | subset(B, B))),
% 0.20/0.51 inference(skolemize,[status(sab)],[68])).
% 0.20/0.51 tff(70,plain,
% 0.20/0.51 (![B: $i] : ((~ilf_type(B, set_type)) | subset(B, B))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.20/0.51 tff(71,plain,
% 0.20/0.51 (((~![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)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(72,plain,
% 0.20/0.51 ((~![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)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(73,plain,
% 0.20/0.51 ((~![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))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.20/0.51 tff(74,plain,
% 0.20/0.51 (subset(cross_product(B!10, C!11), cross_product(B!10, C!11))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[73, 70, 36])).
% 0.20/0.51 tff(75,plain,
% 0.20/0.51 (~ilf_type(cross_product(B!10, C!11), relation_type(B!10, C!11))),
% 0.20/0.51 inference(or_elim,[status(thm)],[31])).
% 0.20/0.51 tff(76,plain,
% 0.20/0.51 (((~![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))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(77,plain,
% 0.20/0.51 ((~![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))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(78,plain,
% 0.20/0.51 ((~![D: $i] : ((~ilf_type(D, set_type)) | ilf_type(cross_product(B!10, C!11), relation_type(B!10, D)) | (~subset(cross_product(B!10, C!11), cross_product(B!10, D))))) | (~ilf_type(C!11, set_type)) | ilf_type(cross_product(B!10, C!11), relation_type(B!10, C!11)) | (~subset(cross_product(B!10, C!11), cross_product(B!10, C!11)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.20/0.51 tff(79,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[78, 32, 75, 74, 60])).
% 0.20/0.51 % SZS output end Proof
%------------------------------------------------------------------------------