TSTP Solution File: SEU263+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU263+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.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 07:28:34 EDT 2022
% Result : Theorem 0.14s 0.40s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU263+1 : TPTP v8.1.0. Released v3.3.0.
% 0.00/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.30 % Computer : n022.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Sat Sep 3 11:16:09 EDT 2022
% 0.10/0.30 % CPUTime :
% 0.10/0.30 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.10/0.30 Usage: tptp [options] [-file:]file
% 0.10/0.30 -h, -? prints this message.
% 0.10/0.30 -smt2 print SMT-LIB2 benchmark.
% 0.10/0.30 -m, -model generate model.
% 0.10/0.30 -p, -proof generate proof.
% 0.10/0.30 -c, -core generate unsat core of named formulas.
% 0.10/0.30 -st, -statistics display statistics.
% 0.10/0.30 -t:timeout set timeout (in second).
% 0.10/0.30 -smt2status display status in smt2 format instead of SZS.
% 0.10/0.30 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.10/0.30 -<param>:<value> configuration parameter and value.
% 0.10/0.30 -o:<output-file> file to place output in.
% 0.14/0.40 % SZS status Theorem
% 0.14/0.40 % SZS output start Proof
% 0.14/0.40 tff(subset_type, type, (
% 0.14/0.40 subset: ( $i * $i ) > $o)).
% 0.14/0.40 tff(cartesian_product2_type, type, (
% 0.14/0.40 cartesian_product2: ( $i * $i ) > $i)).
% 0.14/0.40 tff(tptp_fun_B_5_type, type, (
% 0.14/0.40 tptp_fun_B_5: $i)).
% 0.14/0.40 tff(tptp_fun_C_4_type, type, (
% 0.14/0.40 tptp_fun_C_4: $i)).
% 0.14/0.40 tff(relation_rng_type, type, (
% 0.14/0.40 relation_rng: $i > $i)).
% 0.14/0.40 tff(tptp_fun_D_3_type, type, (
% 0.14/0.40 tptp_fun_D_3: $i)).
% 0.14/0.40 tff(relation_dom_type, type, (
% 0.14/0.40 relation_dom: $i > $i)).
% 0.14/0.40 tff(tptp_fun_A_6_type, type, (
% 0.14/0.40 tptp_fun_A_6: $i)).
% 0.14/0.40 tff(relation_of2_as_subset_type, type, (
% 0.14/0.40 relation_of2_as_subset: ( $i * $i * $i ) > $o)).
% 0.14/0.40 tff(relation_of2_type, type, (
% 0.14/0.40 relation_of2: ( $i * $i * $i ) > $o)).
% 0.14/0.40 tff(relation_type, type, (
% 0.14/0.40 relation: $i > $o)).
% 0.14/0.40 tff(element_type, type, (
% 0.14/0.40 element: ( $i * $i ) > $o)).
% 0.14/0.40 tff(powerset_type, type, (
% 0.14/0.40 powerset: $i > $i)).
% 0.14/0.40 tff(1,plain,
% 0.14/0.40 ((~(relation_of2_as_subset(D!3, C!4, B!5) | (~subset(relation_rng(D!3), B!5)) | (~relation_of2_as_subset(D!3, C!4, A!6)))) <=> (~(relation_of2_as_subset(D!3, C!4, B!5) | (~subset(relation_rng(D!3), B!5)) | (~relation_of2_as_subset(D!3, C!4, A!6))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(2,plain,
% 0.14/0.40 ((~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~subset(relation_rng(D), B)) | (~relation_of2_as_subset(D, C, A)))) <=> (~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~subset(relation_rng(D), B)) | (~relation_of2_as_subset(D, C, A))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(3,plain,
% 0.14/0.40 ((~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, A) => (subset(relation_rng(D), B) => relation_of2_as_subset(D, C, B)))) <=> (~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~subset(relation_rng(D), B)) | (~relation_of2_as_subset(D, C, A))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(4,axiom,(~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, A) => (subset(relation_rng(D), B) => relation_of2_as_subset(D, C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t14_relset_1')).
% 0.14/0.40 tff(5,plain,
% 0.14/0.40 (~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~subset(relation_rng(D), B)) | (~relation_of2_as_subset(D, C, A)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.14/0.40 tff(6,plain,
% 0.14/0.40 (~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~subset(relation_rng(D), B)) | (~relation_of2_as_subset(D, C, A)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.14/0.40 tff(7,plain,
% 0.14/0.40 (~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~subset(relation_rng(D), B)) | (~relation_of2_as_subset(D, C, A)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.14/0.40 tff(8,plain,
% 0.14/0.40 (~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~subset(relation_rng(D), B)) | (~relation_of2_as_subset(D, C, A)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.14/0.40 tff(9,plain,
% 0.14/0.40 (~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~subset(relation_rng(D), B)) | (~relation_of2_as_subset(D, C, A)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[8, 2])).
% 0.14/0.40 tff(10,plain,
% 0.14/0.40 (~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~subset(relation_rng(D), B)) | (~relation_of2_as_subset(D, C, A)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.14/0.40 tff(11,plain,
% 0.14/0.40 (~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~subset(relation_rng(D), B)) | (~relation_of2_as_subset(D, C, A)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.14/0.40 tff(12,plain,(
% 0.14/0.40 ~(relation_of2_as_subset(D!3, C!4, B!5) | (~subset(relation_rng(D!3), B!5)) | (~relation_of2_as_subset(D!3, C!4, A!6)))),
% 0.14/0.40 inference(skolemize,[status(sab)],[11])).
% 0.14/0.40 tff(13,plain,
% 0.14/0.40 (~(relation_of2_as_subset(D!3, C!4, B!5) | (~subset(relation_rng(D!3), B!5)) | (~relation_of2_as_subset(D!3, C!4, A!6)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[12, 1])).
% 0.14/0.40 tff(14,plain,
% 0.14/0.40 (relation_of2_as_subset(D!3, C!4, A!6)),
% 0.14/0.40 inference(or_elim,[status(thm)],[13])).
% 0.14/0.40 tff(15,plain,
% 0.14/0.40 (^[A: $i, B: $i, C: $i] : refl(((~relation_of2_as_subset(C, A, B)) | (~((~subset(relation_dom(C), A)) | (~subset(relation_rng(C), B))))) <=> ((~relation_of2_as_subset(C, A, B)) | (~((~subset(relation_dom(C), A)) | (~subset(relation_rng(C), B))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(16,plain,
% 0.14/0.40 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~subset(relation_dom(C), A)) | (~subset(relation_rng(C), B))))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~subset(relation_dom(C), A)) | (~subset(relation_rng(C), B)))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[15])).
% 0.14/0.40 tff(17,plain,
% 0.14/0.40 (^[A: $i, B: $i, C: $i] : rewrite(((~relation_of2_as_subset(C, A, B)) | (subset(relation_dom(C), A) & subset(relation_rng(C), B))) <=> ((~relation_of2_as_subset(C, A, B)) | (~((~subset(relation_dom(C), A)) | (~subset(relation_rng(C), B))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(18,plain,
% 0.14/0.40 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (subset(relation_dom(C), A) & subset(relation_rng(C), B))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~subset(relation_dom(C), A)) | (~subset(relation_rng(C), B)))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[17])).
% 0.14/0.40 tff(19,plain,
% 0.14/0.40 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (subset(relation_dom(C), A) & subset(relation_rng(C), B))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (subset(relation_dom(C), A) & subset(relation_rng(C), B)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(20,plain,
% 0.14/0.40 (^[A: $i, B: $i, C: $i] : rewrite((relation_of2_as_subset(C, A, B) => (subset(relation_dom(C), A) & subset(relation_rng(C), B))) <=> ((~relation_of2_as_subset(C, A, B)) | (subset(relation_dom(C), A) & subset(relation_rng(C), B))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(21,plain,
% 0.14/0.40 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) => (subset(relation_dom(C), A) & subset(relation_rng(C), B))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (subset(relation_dom(C), A) & subset(relation_rng(C), B)))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[20])).
% 0.14/0.40 tff(22,axiom,(![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) => (subset(relation_dom(C), A) & subset(relation_rng(C), B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t12_relset_1')).
% 0.14/0.40 tff(23,plain,
% 0.14/0.40 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (subset(relation_dom(C), A) & subset(relation_rng(C), B)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.14/0.40 tff(24,plain,
% 0.14/0.40 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (subset(relation_dom(C), A) & subset(relation_rng(C), B)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.14/0.40 tff(25,plain,(
% 0.14/0.40 ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (subset(relation_dom(C), A) & subset(relation_rng(C), B)))),
% 0.14/0.40 inference(skolemize,[status(sab)],[24])).
% 0.14/0.40 tff(26,plain,
% 0.14/0.40 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~subset(relation_dom(C), A)) | (~subset(relation_rng(C), B)))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.14/0.40 tff(27,plain,
% 0.14/0.40 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~subset(relation_dom(C), A)) | (~subset(relation_rng(C), B)))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[26, 16])).
% 0.14/0.40 tff(28,plain,
% 0.14/0.40 (((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~subset(relation_dom(C), A)) | (~subset(relation_rng(C), B)))))) | ((~relation_of2_as_subset(D!3, C!4, A!6)) | (~((~subset(relation_dom(D!3), C!4)) | (~subset(relation_rng(D!3), A!6)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~subset(relation_dom(C), A)) | (~subset(relation_rng(C), B)))))) | (~relation_of2_as_subset(D!3, C!4, A!6)) | (~((~subset(relation_dom(D!3), C!4)) | (~subset(relation_rng(D!3), A!6)))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(29,plain,
% 0.14/0.40 ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~subset(relation_dom(C), A)) | (~subset(relation_rng(C), B)))))) | ((~relation_of2_as_subset(D!3, C!4, A!6)) | (~((~subset(relation_dom(D!3), C!4)) | (~subset(relation_rng(D!3), A!6)))))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(30,plain,
% 0.14/0.41 ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~subset(relation_dom(C), A)) | (~subset(relation_rng(C), B)))))) | (~relation_of2_as_subset(D!3, C!4, A!6)) | (~((~subset(relation_dom(D!3), C!4)) | (~subset(relation_rng(D!3), A!6))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.14/0.41 tff(31,plain,
% 0.14/0.41 (~((~subset(relation_dom(D!3), C!4)) | (~subset(relation_rng(D!3), A!6)))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[30, 27, 14])).
% 0.14/0.41 tff(32,plain,
% 0.14/0.41 (((~subset(relation_dom(D!3), C!4)) | (~subset(relation_rng(D!3), A!6))) | subset(relation_dom(D!3), C!4)),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(33,plain,
% 0.14/0.41 (subset(relation_dom(D!3), C!4)),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.14/0.41 tff(34,plain,
% 0.14/0.41 (subset(relation_rng(D!3), B!5)),
% 0.14/0.41 inference(or_elim,[status(thm)],[13])).
% 0.14/0.41 tff(35,plain,
% 0.14/0.41 (^[A: $i, B: $i, C: $i, D: $i] : refl((subset(cartesian_product2(A, C), cartesian_product2(B, D)) | (~subset(A, B)) | (~subset(C, D))) <=> (subset(cartesian_product2(A, C), cartesian_product2(B, D)) | (~subset(A, B)) | (~subset(C, D))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(36,plain,
% 0.14/0.41 (![A: $i, B: $i, C: $i, D: $i] : (subset(cartesian_product2(A, C), cartesian_product2(B, D)) | (~subset(A, B)) | (~subset(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : (subset(cartesian_product2(A, C), cartesian_product2(B, D)) | (~subset(A, B)) | (~subset(C, D)))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[35])).
% 0.14/0.41 tff(37,plain,
% 0.14/0.41 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite((subset(A, B) & subset(C, D)) <=> (~((~subset(A, B)) | (~subset(C, D))))), ((~(subset(A, B) & subset(C, D))) <=> (~(~((~subset(A, B)) | (~subset(C, D))))))), rewrite((~(~((~subset(A, B)) | (~subset(C, D))))) <=> ((~subset(A, B)) | (~subset(C, D)))), ((~(subset(A, B) & subset(C, D))) <=> ((~subset(A, B)) | (~subset(C, D))))), (((~(subset(A, B) & subset(C, D))) | subset(cartesian_product2(A, C), cartesian_product2(B, D))) <=> (((~subset(A, B)) | (~subset(C, D))) | subset(cartesian_product2(A, C), cartesian_product2(B, D))))), rewrite((((~subset(A, B)) | (~subset(C, D))) | subset(cartesian_product2(A, C), cartesian_product2(B, D))) <=> (subset(cartesian_product2(A, C), cartesian_product2(B, D)) | (~subset(A, B)) | (~subset(C, D)))), (((~(subset(A, B) & subset(C, D))) | subset(cartesian_product2(A, C), cartesian_product2(B, D))) <=> (subset(cartesian_product2(A, C), cartesian_product2(B, D)) | (~subset(A, B)) | (~subset(C, D)))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(38,plain,
% 0.14/0.41 (![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, B) & subset(C, D))) | subset(cartesian_product2(A, C), cartesian_product2(B, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : (subset(cartesian_product2(A, C), cartesian_product2(B, D)) | (~subset(A, B)) | (~subset(C, D)))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[37])).
% 0.14/0.41 tff(39,plain,
% 0.14/0.41 (![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, B) & subset(C, D))) | subset(cartesian_product2(A, C), cartesian_product2(B, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, B) & subset(C, D))) | subset(cartesian_product2(A, C), cartesian_product2(B, D)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(40,plain,
% 0.14/0.41 (^[A: $i, B: $i, C: $i, D: $i] : rewrite(((subset(A, B) & subset(C, D)) => subset(cartesian_product2(A, C), cartesian_product2(B, D))) <=> ((~(subset(A, B) & subset(C, D))) | subset(cartesian_product2(A, C), cartesian_product2(B, D))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(41,plain,
% 0.14/0.41 (![A: $i, B: $i, C: $i, D: $i] : ((subset(A, B) & subset(C, D)) => subset(cartesian_product2(A, C), cartesian_product2(B, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, B) & subset(C, D))) | subset(cartesian_product2(A, C), cartesian_product2(B, D)))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[40])).
% 0.14/0.41 tff(42,axiom,(![A: $i, B: $i, C: $i, D: $i] : ((subset(A, B) & subset(C, D)) => subset(cartesian_product2(A, C), cartesian_product2(B, D)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t119_zfmisc_1')).
% 0.14/0.41 tff(43,plain,
% 0.14/0.41 (![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, B) & subset(C, D))) | subset(cartesian_product2(A, C), cartesian_product2(B, D)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.14/0.41 tff(44,plain,
% 0.14/0.41 (![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, B) & subset(C, D))) | subset(cartesian_product2(A, C), cartesian_product2(B, D)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.14/0.41 tff(45,plain,(
% 0.14/0.41 ![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, B) & subset(C, D))) | subset(cartesian_product2(A, C), cartesian_product2(B, D)))),
% 0.14/0.41 inference(skolemize,[status(sab)],[44])).
% 0.14/0.41 tff(46,plain,
% 0.14/0.41 (![A: $i, B: $i, C: $i, D: $i] : (subset(cartesian_product2(A, C), cartesian_product2(B, D)) | (~subset(A, B)) | (~subset(C, D)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.14/0.41 tff(47,plain,
% 0.14/0.41 (![A: $i, B: $i, C: $i, D: $i] : (subset(cartesian_product2(A, C), cartesian_product2(B, D)) | (~subset(A, B)) | (~subset(C, D)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[46, 36])).
% 0.14/0.41 tff(48,plain,
% 0.14/0.41 (((~![A: $i, B: $i, C: $i, D: $i] : (subset(cartesian_product2(A, C), cartesian_product2(B, D)) | (~subset(A, B)) | (~subset(C, D)))) | ((~subset(relation_rng(D!3), B!5)) | (~subset(relation_dom(D!3), C!4)) | subset(cartesian_product2(relation_dom(D!3), relation_rng(D!3)), cartesian_product2(C!4, B!5)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (subset(cartesian_product2(A, C), cartesian_product2(B, D)) | (~subset(A, B)) | (~subset(C, D)))) | (~subset(relation_rng(D!3), B!5)) | (~subset(relation_dom(D!3), C!4)) | subset(cartesian_product2(relation_dom(D!3), relation_rng(D!3)), cartesian_product2(C!4, B!5)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(49,plain,
% 0.14/0.41 ((subset(cartesian_product2(relation_dom(D!3), relation_rng(D!3)), cartesian_product2(C!4, B!5)) | (~subset(relation_dom(D!3), C!4)) | (~subset(relation_rng(D!3), B!5))) <=> ((~subset(relation_rng(D!3), B!5)) | (~subset(relation_dom(D!3), C!4)) | subset(cartesian_product2(relation_dom(D!3), relation_rng(D!3)), cartesian_product2(C!4, B!5)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(50,plain,
% 0.14/0.41 (((~![A: $i, B: $i, C: $i, D: $i] : (subset(cartesian_product2(A, C), cartesian_product2(B, D)) | (~subset(A, B)) | (~subset(C, D)))) | (subset(cartesian_product2(relation_dom(D!3), relation_rng(D!3)), cartesian_product2(C!4, B!5)) | (~subset(relation_dom(D!3), C!4)) | (~subset(relation_rng(D!3), B!5)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (subset(cartesian_product2(A, C), cartesian_product2(B, D)) | (~subset(A, B)) | (~subset(C, D)))) | ((~subset(relation_rng(D!3), B!5)) | (~subset(relation_dom(D!3), C!4)) | subset(cartesian_product2(relation_dom(D!3), relation_rng(D!3)), cartesian_product2(C!4, B!5))))),
% 0.14/0.41 inference(monotonicity,[status(thm)],[49])).
% 0.14/0.41 tff(51,plain,
% 0.14/0.41 (((~![A: $i, B: $i, C: $i, D: $i] : (subset(cartesian_product2(A, C), cartesian_product2(B, D)) | (~subset(A, B)) | (~subset(C, D)))) | (subset(cartesian_product2(relation_dom(D!3), relation_rng(D!3)), cartesian_product2(C!4, B!5)) | (~subset(relation_dom(D!3), C!4)) | (~subset(relation_rng(D!3), B!5)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (subset(cartesian_product2(A, C), cartesian_product2(B, D)) | (~subset(A, B)) | (~subset(C, D)))) | (~subset(relation_rng(D!3), B!5)) | (~subset(relation_dom(D!3), C!4)) | subset(cartesian_product2(relation_dom(D!3), relation_rng(D!3)), cartesian_product2(C!4, B!5)))),
% 0.14/0.41 inference(transitivity,[status(thm)],[50, 48])).
% 0.14/0.41 tff(52,plain,
% 0.14/0.41 ((~![A: $i, B: $i, C: $i, D: $i] : (subset(cartesian_product2(A, C), cartesian_product2(B, D)) | (~subset(A, B)) | (~subset(C, D)))) | (subset(cartesian_product2(relation_dom(D!3), relation_rng(D!3)), cartesian_product2(C!4, B!5)) | (~subset(relation_dom(D!3), C!4)) | (~subset(relation_rng(D!3), B!5)))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(53,plain,
% 0.14/0.41 ((~![A: $i, B: $i, C: $i, D: $i] : (subset(cartesian_product2(A, C), cartesian_product2(B, D)) | (~subset(A, B)) | (~subset(C, D)))) | (~subset(relation_rng(D!3), B!5)) | (~subset(relation_dom(D!3), C!4)) | subset(cartesian_product2(relation_dom(D!3), relation_rng(D!3)), cartesian_product2(C!4, B!5))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.14/0.41 tff(54,plain,
% 0.14/0.41 (subset(cartesian_product2(relation_dom(D!3), relation_rng(D!3)), cartesian_product2(C!4, B!5))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[53, 47, 34, 33])).
% 0.14/0.41 tff(55,plain,
% 0.14/0.41 (^[A: $i, B: $i, C: $i] : refl((relation_of2(C, A, B) <=> subset(C, cartesian_product2(A, B))) <=> (relation_of2(C, A, B) <=> subset(C, cartesian_product2(A, B))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(56,plain,
% 0.14/0.41 (![A: $i, B: $i, C: $i] : (relation_of2(C, A, B) <=> subset(C, cartesian_product2(A, B))) <=> ![A: $i, B: $i, C: $i] : (relation_of2(C, A, B) <=> subset(C, cartesian_product2(A, B)))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[55])).
% 0.14/0.41 tff(57,plain,
% 0.14/0.41 (![A: $i, B: $i, C: $i] : (relation_of2(C, A, B) <=> subset(C, cartesian_product2(A, B))) <=> ![A: $i, B: $i, C: $i] : (relation_of2(C, A, B) <=> subset(C, cartesian_product2(A, B)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(58,axiom,(![A: $i, B: $i, C: $i] : (relation_of2(C, A, B) <=> subset(C, cartesian_product2(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_relset_1')).
% 0.14/0.41 tff(59,plain,
% 0.14/0.41 (![A: $i, B: $i, C: $i] : (relation_of2(C, A, B) <=> subset(C, cartesian_product2(A, B)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.14/0.41 tff(60,plain,(
% 0.14/0.41 ![A: $i, B: $i, C: $i] : (relation_of2(C, A, B) <=> subset(C, cartesian_product2(A, B)))),
% 0.14/0.41 inference(skolemize,[status(sab)],[59])).
% 0.14/0.41 tff(61,plain,
% 0.14/0.41 (![A: $i, B: $i, C: $i] : (relation_of2(C, A, B) <=> subset(C, cartesian_product2(A, B)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.14/0.41 tff(62,plain,
% 0.14/0.41 ((~![A: $i, B: $i, C: $i] : (relation_of2(C, A, B) <=> subset(C, cartesian_product2(A, B)))) | (relation_of2(D!3, C!4, B!5) <=> subset(D!3, cartesian_product2(C!4, B!5)))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(63,plain,
% 0.14/0.41 (relation_of2(D!3, C!4, B!5) <=> subset(D!3, cartesian_product2(C!4, B!5))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.14/0.41 tff(64,plain,
% 0.14/0.41 (^[A: $i, B: $i, C: $i] : refl((relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B)) <=> (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B)))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(65,plain,
% 0.14/0.41 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[64])).
% 0.14/0.41 tff(66,plain,
% 0.14/0.41 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(67,axiom,(![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 0.14/0.41 tff(68,plain,
% 0.14/0.41 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.14/0.41 tff(69,plain,(
% 0.14/0.41 ![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 0.14/0.41 inference(skolemize,[status(sab)],[68])).
% 0.14/0.41 tff(70,plain,
% 0.14/0.41 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.14/0.41 tff(71,plain,
% 0.14/0.41 ((~![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))) | (relation_of2_as_subset(D!3, C!4, B!5) <=> relation_of2(D!3, C!4, B!5))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(72,plain,
% 0.14/0.41 (relation_of2_as_subset(D!3, C!4, B!5) <=> relation_of2(D!3, C!4, B!5)),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.14/0.41 tff(73,plain,
% 0.14/0.41 (~relation_of2_as_subset(D!3, C!4, B!5)),
% 0.14/0.41 inference(or_elim,[status(thm)],[13])).
% 0.14/0.41 tff(74,plain,
% 0.14/0.41 ((~(relation_of2_as_subset(D!3, C!4, B!5) <=> relation_of2(D!3, C!4, B!5))) | relation_of2_as_subset(D!3, C!4, B!5) | (~relation_of2(D!3, C!4, B!5))),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(75,plain,
% 0.14/0.41 ((~(relation_of2_as_subset(D!3, C!4, B!5) <=> relation_of2(D!3, C!4, B!5))) | (~relation_of2(D!3, C!4, B!5))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.14/0.41 tff(76,plain,
% 0.14/0.41 (~relation_of2(D!3, C!4, B!5)),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[75, 72])).
% 0.14/0.41 tff(77,plain,
% 0.14/0.41 ((~(relation_of2(D!3, C!4, B!5) <=> subset(D!3, cartesian_product2(C!4, B!5)))) | relation_of2(D!3, C!4, B!5) | (~subset(D!3, cartesian_product2(C!4, B!5)))),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(78,plain,
% 0.14/0.41 ((~(relation_of2(D!3, C!4, B!5) <=> subset(D!3, cartesian_product2(C!4, B!5)))) | (~subset(D!3, cartesian_product2(C!4, B!5)))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.14/0.41 tff(79,plain,
% 0.14/0.41 (~subset(D!3, cartesian_product2(C!4, B!5))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[78, 63])).
% 0.14/0.41 tff(80,plain,
% 0.14/0.41 (^[A: $i, B: $i, C: $i] : refl(((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B)))) <=> ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B)))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(81,plain,
% 0.14/0.41 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[80])).
% 0.14/0.41 tff(82,plain,
% 0.14/0.41 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(83,plain,
% 0.14/0.41 (^[A: $i, B: $i, C: $i] : rewrite((relation_of2_as_subset(C, A, B) => element(C, powerset(cartesian_product2(A, B)))) <=> ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B)))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(84,plain,
% 0.14/0.41 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) => element(C, powerset(cartesian_product2(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[83])).
% 0.14/0.41 tff(85,axiom,(![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) => element(C, powerset(cartesian_product2(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_m2_relset_1')).
% 0.14/0.41 tff(86,plain,
% 0.14/0.41 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.14/0.41 tff(87,plain,
% 0.14/0.41 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.14/0.41 tff(88,plain,(
% 0.14/0.41 ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 0.14/0.41 inference(skolemize,[status(sab)],[87])).
% 0.14/0.41 tff(89,plain,
% 0.14/0.41 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.14/0.41 tff(90,plain,
% 0.14/0.41 (((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))) | ((~relation_of2_as_subset(D!3, C!4, A!6)) | element(D!3, powerset(cartesian_product2(C!4, A!6))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))) | (~relation_of2_as_subset(D!3, C!4, A!6)) | element(D!3, powerset(cartesian_product2(C!4, A!6))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(91,plain,
% 0.14/0.41 ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))) | ((~relation_of2_as_subset(D!3, C!4, A!6)) | element(D!3, powerset(cartesian_product2(C!4, A!6))))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(92,plain,
% 0.14/0.41 ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))) | (~relation_of2_as_subset(D!3, C!4, A!6)) | element(D!3, powerset(cartesian_product2(C!4, A!6)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.14/0.41 tff(93,plain,
% 0.14/0.41 (element(D!3, powerset(cartesian_product2(C!4, A!6)))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[92, 89, 14])).
% 0.14/0.41 tff(94,plain,
% 0.14/0.41 (^[A: $i, B: $i, C: $i] : refl((relation(C) | (~element(C, powerset(cartesian_product2(A, B))))) <=> (relation(C) | (~element(C, powerset(cartesian_product2(A, B))))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(95,plain,
% 0.14/0.41 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B))))) <=> ![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[94])).
% 0.14/0.41 tff(96,plain,
% 0.14/0.41 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B))))) <=> ![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(97,plain,
% 0.14/0.42 (^[A: $i, B: $i, C: $i] : rewrite((element(C, powerset(cartesian_product2(A, B))) => relation(C)) <=> (relation(C) | (~element(C, powerset(cartesian_product2(A, B))))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(98,plain,
% 0.14/0.42 (![A: $i, B: $i, C: $i] : (element(C, powerset(cartesian_product2(A, B))) => relation(C)) <=> ![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[97])).
% 0.14/0.42 tff(99,axiom,(![A: $i, B: $i, C: $i] : (element(C, powerset(cartesian_product2(A, B))) => relation(C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cc1_relset_1')).
% 0.14/0.42 tff(100,plain,
% 0.14/0.42 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.14/0.42 tff(101,plain,
% 0.14/0.42 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[100, 96])).
% 0.14/0.42 tff(102,plain,(
% 0.14/0.42 ![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 0.14/0.42 inference(skolemize,[status(sab)],[101])).
% 0.14/0.42 tff(103,plain,
% 0.14/0.42 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[102, 95])).
% 0.14/0.42 tff(104,plain,
% 0.14/0.42 (((~![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))) | (relation(D!3) | (~element(D!3, powerset(cartesian_product2(C!4, A!6)))))) <=> ((~![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))) | relation(D!3) | (~element(D!3, powerset(cartesian_product2(C!4, A!6)))))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(105,plain,
% 0.14/0.42 ((~![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))) | (relation(D!3) | (~element(D!3, powerset(cartesian_product2(C!4, A!6)))))),
% 0.14/0.42 inference(quant_inst,[status(thm)],[])).
% 0.14/0.42 tff(106,plain,
% 0.14/0.42 ((~![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))) | relation(D!3) | (~element(D!3, powerset(cartesian_product2(C!4, A!6))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.14/0.42 tff(107,plain,
% 0.14/0.42 (relation(D!3)),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[106, 103, 93])).
% 0.14/0.42 tff(108,plain,
% 0.14/0.42 (^[A: $i] : refl(((~relation(A)) | subset(A, cartesian_product2(relation_dom(A), relation_rng(A)))) <=> ((~relation(A)) | subset(A, cartesian_product2(relation_dom(A), relation_rng(A)))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(109,plain,
% 0.14/0.42 (![A: $i] : ((~relation(A)) | subset(A, cartesian_product2(relation_dom(A), relation_rng(A)))) <=> ![A: $i] : ((~relation(A)) | subset(A, cartesian_product2(relation_dom(A), relation_rng(A))))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[108])).
% 0.14/0.42 tff(110,plain,
% 0.14/0.42 (![A: $i] : ((~relation(A)) | subset(A, cartesian_product2(relation_dom(A), relation_rng(A)))) <=> ![A: $i] : ((~relation(A)) | subset(A, cartesian_product2(relation_dom(A), relation_rng(A))))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(111,plain,
% 0.14/0.42 (^[A: $i] : rewrite((relation(A) => subset(A, cartesian_product2(relation_dom(A), relation_rng(A)))) <=> ((~relation(A)) | subset(A, cartesian_product2(relation_dom(A), relation_rng(A)))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(112,plain,
% 0.14/0.42 (![A: $i] : (relation(A) => subset(A, cartesian_product2(relation_dom(A), relation_rng(A)))) <=> ![A: $i] : ((~relation(A)) | subset(A, cartesian_product2(relation_dom(A), relation_rng(A))))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[111])).
% 0.14/0.42 tff(113,axiom,(![A: $i] : (relation(A) => subset(A, cartesian_product2(relation_dom(A), relation_rng(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t21_relat_1')).
% 0.14/0.42 tff(114,plain,
% 0.14/0.42 (![A: $i] : ((~relation(A)) | subset(A, cartesian_product2(relation_dom(A), relation_rng(A))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.14/0.42 tff(115,plain,
% 0.14/0.42 (![A: $i] : ((~relation(A)) | subset(A, cartesian_product2(relation_dom(A), relation_rng(A))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[114, 110])).
% 0.14/0.42 tff(116,plain,(
% 0.14/0.42 ![A: $i] : ((~relation(A)) | subset(A, cartesian_product2(relation_dom(A), relation_rng(A))))),
% 0.14/0.42 inference(skolemize,[status(sab)],[115])).
% 0.14/0.42 tff(117,plain,
% 0.14/0.42 (![A: $i] : ((~relation(A)) | subset(A, cartesian_product2(relation_dom(A), relation_rng(A))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[116, 109])).
% 0.14/0.42 tff(118,plain,
% 0.14/0.42 (((~![A: $i] : ((~relation(A)) | subset(A, cartesian_product2(relation_dom(A), relation_rng(A))))) | ((~relation(D!3)) | subset(D!3, cartesian_product2(relation_dom(D!3), relation_rng(D!3))))) <=> ((~![A: $i] : ((~relation(A)) | subset(A, cartesian_product2(relation_dom(A), relation_rng(A))))) | (~relation(D!3)) | subset(D!3, cartesian_product2(relation_dom(D!3), relation_rng(D!3))))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(119,plain,
% 0.14/0.42 ((~![A: $i] : ((~relation(A)) | subset(A, cartesian_product2(relation_dom(A), relation_rng(A))))) | ((~relation(D!3)) | subset(D!3, cartesian_product2(relation_dom(D!3), relation_rng(D!3))))),
% 0.14/0.42 inference(quant_inst,[status(thm)],[])).
% 0.14/0.42 tff(120,plain,
% 0.14/0.42 ((~![A: $i] : ((~relation(A)) | subset(A, cartesian_product2(relation_dom(A), relation_rng(A))))) | (~relation(D!3)) | subset(D!3, cartesian_product2(relation_dom(D!3), relation_rng(D!3)))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.14/0.42 tff(121,plain,
% 0.14/0.42 ((~relation(D!3)) | subset(D!3, cartesian_product2(relation_dom(D!3), relation_rng(D!3)))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[120, 117])).
% 0.14/0.42 tff(122,plain,
% 0.14/0.42 (subset(D!3, cartesian_product2(relation_dom(D!3), relation_rng(D!3)))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[121, 107])).
% 0.14/0.42 tff(123,plain,
% 0.14/0.42 (![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B))) <=> ![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(124,plain,
% 0.14/0.42 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((subset(A, B) & subset(B, C)) <=> (~((~subset(B, C)) | (~subset(A, B))))), ((~(subset(A, B) & subset(B, C))) <=> (~(~((~subset(B, C)) | (~subset(A, B))))))), rewrite((~(~((~subset(B, C)) | (~subset(A, B))))) <=> ((~subset(B, C)) | (~subset(A, B)))), ((~(subset(A, B) & subset(B, C))) <=> ((~subset(B, C)) | (~subset(A, B))))), (((~(subset(A, B) & subset(B, C))) | subset(A, C)) <=> (((~subset(B, C)) | (~subset(A, B))) | subset(A, C)))), rewrite((((~subset(B, C)) | (~subset(A, B))) | subset(A, C)) <=> (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))), (((~(subset(A, B) & subset(B, C))) | subset(A, C)) <=> (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(125,plain,
% 0.14/0.42 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C)) <=> ![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[124])).
% 0.14/0.42 tff(126,plain,
% 0.14/0.42 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(127,plain,
% 0.14/0.42 (^[A: $i, B: $i, C: $i] : rewrite(((subset(A, B) & subset(B, C)) => subset(A, C)) <=> ((~(subset(A, B) & subset(B, C))) | subset(A, C)))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(128,plain,
% 0.14/0.42 (![A: $i, B: $i, C: $i] : ((subset(A, B) & subset(B, C)) => subset(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[127])).
% 0.14/0.42 tff(129,axiom,(![A: $i, B: $i, C: $i] : ((subset(A, B) & subset(B, C)) => subset(A, C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t1_xboole_1')).
% 0.14/0.42 tff(130,plain,
% 0.14/0.42 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.14/0.42 tff(131,plain,
% 0.14/0.42 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[130, 126])).
% 0.14/0.42 tff(132,plain,(
% 0.14/0.42 ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.14/0.42 inference(skolemize,[status(sab)],[131])).
% 0.14/0.42 tff(133,plain,
% 0.14/0.42 (![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[132, 125])).
% 0.14/0.42 tff(134,plain,
% 0.14/0.42 (![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[133, 123])).
% 0.14/0.42 tff(135,plain,
% 0.14/0.42 (((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | (subset(D!3, cartesian_product2(C!4, B!5)) | (~subset(D!3, cartesian_product2(relation_dom(D!3), relation_rng(D!3)))) | (~subset(cartesian_product2(relation_dom(D!3), relation_rng(D!3)), cartesian_product2(C!4, B!5))))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | subset(D!3, cartesian_product2(C!4, B!5)) | (~subset(D!3, cartesian_product2(relation_dom(D!3), relation_rng(D!3)))) | (~subset(cartesian_product2(relation_dom(D!3), relation_rng(D!3)), cartesian_product2(C!4, B!5))))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(136,plain,
% 0.14/0.42 ((subset(D!3, cartesian_product2(C!4, B!5)) | (~subset(cartesian_product2(relation_dom(D!3), relation_rng(D!3)), cartesian_product2(C!4, B!5))) | (~subset(D!3, cartesian_product2(relation_dom(D!3), relation_rng(D!3))))) <=> (subset(D!3, cartesian_product2(C!4, B!5)) | (~subset(D!3, cartesian_product2(relation_dom(D!3), relation_rng(D!3)))) | (~subset(cartesian_product2(relation_dom(D!3), relation_rng(D!3)), cartesian_product2(C!4, B!5))))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(137,plain,
% 0.14/0.42 (((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | (subset(D!3, cartesian_product2(C!4, B!5)) | (~subset(cartesian_product2(relation_dom(D!3), relation_rng(D!3)), cartesian_product2(C!4, B!5))) | (~subset(D!3, cartesian_product2(relation_dom(D!3), relation_rng(D!3)))))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | (subset(D!3, cartesian_product2(C!4, B!5)) | (~subset(D!3, cartesian_product2(relation_dom(D!3), relation_rng(D!3)))) | (~subset(cartesian_product2(relation_dom(D!3), relation_rng(D!3)), cartesian_product2(C!4, B!5)))))),
% 0.14/0.42 inference(monotonicity,[status(thm)],[136])).
% 0.14/0.42 tff(138,plain,
% 0.14/0.42 (((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | (subset(D!3, cartesian_product2(C!4, B!5)) | (~subset(cartesian_product2(relation_dom(D!3), relation_rng(D!3)), cartesian_product2(C!4, B!5))) | (~subset(D!3, cartesian_product2(relation_dom(D!3), relation_rng(D!3)))))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | subset(D!3, cartesian_product2(C!4, B!5)) | (~subset(D!3, cartesian_product2(relation_dom(D!3), relation_rng(D!3)))) | (~subset(cartesian_product2(relation_dom(D!3), relation_rng(D!3)), cartesian_product2(C!4, B!5))))),
% 0.14/0.42 inference(transitivity,[status(thm)],[137, 135])).
% 0.14/0.42 tff(139,plain,
% 0.14/0.42 ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | (subset(D!3, cartesian_product2(C!4, B!5)) | (~subset(cartesian_product2(relation_dom(D!3), relation_rng(D!3)), cartesian_product2(C!4, B!5))) | (~subset(D!3, cartesian_product2(relation_dom(D!3), relation_rng(D!3)))))),
% 0.14/0.42 inference(quant_inst,[status(thm)],[])).
% 0.14/0.42 tff(140,plain,
% 0.14/0.42 ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | subset(D!3, cartesian_product2(C!4, B!5)) | (~subset(D!3, cartesian_product2(relation_dom(D!3), relation_rng(D!3)))) | (~subset(cartesian_product2(relation_dom(D!3), relation_rng(D!3)), cartesian_product2(C!4, B!5)))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.14/0.42 tff(141,plain,
% 0.14/0.42 ($false),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[140, 134, 122, 79, 54])).
% 0.14/0.42 % SZS output end Proof
%------------------------------------------------------------------------------