TSTP Solution File: CAT010-10 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : CAT010-10 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 : 600s
% DateTime : Fri Jul 15 00:07:30 EDT 2022
% Result : Unsatisfiable 0.92s 1.09s
% Output : Refutation 0.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of clauses : 21 ( 21 unt; 0 nHn; 21 RR)
% Number of literals : 21 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
equal(ifeq2(u,u,v,w),v),
file('CAT010-10.p',unknown),
[] ).
cnf(3,axiom,
equal(ifeq(u,u,v,w),v),
file('CAT010-10.p',unknown),
[] ).
cnf(7,axiom,
equal(ifeq(there_exists(domain__dfg(u)),true__dfg,there_exists(u),true__dfg),true__dfg),
file('CAT010-10.p',unknown),
[] ).
cnf(9,axiom,
equal(ifeq(there_exists(compose(u,v)),true__dfg,there_exists(domain__dfg(u)),true__dfg),true__dfg),
file('CAT010-10.p',unknown),
[] ).
cnf(10,axiom,
equal(ifeq2(there_exists(compose(u,v)),true__dfg,domain__dfg(u),codomain(v)),codomain(v)),
file('CAT010-10.p',unknown),
[] ).
cnf(12,axiom,
equal(compose(compose(u,v),w),compose(u,compose(v,w))),
file('CAT010-10.p',unknown),
[] ).
cnf(14,axiom,
equal(compose(codomain(u),u),u),
file('CAT010-10.p',unknown),
[] ).
cnf(15,axiom,
equal(there_exists(compose(a,b)),true__dfg),
file('CAT010-10.p',unknown),
[] ).
cnf(16,axiom,
~ equal(codomain(compose(a,b)),codomain(a)),
file('CAT010-10.p',unknown),
[] ).
cnf(69,plain,
equal(ifeq(there_exists(compose(u,compose(v,w))),true__dfg,there_exists(domain__dfg(compose(u,v))),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[12,9]),
[iquote('0:SpR:12.0,9.0')] ).
cnf(101,plain,
equal(ifeq2(there_exists(u),true__dfg,domain__dfg(codomain(u)),codomain(u)),codomain(u)),
inference(spr,[status(thm),theory(equality)],[14,10]),
[iquote('0:SpR:14.0,10.0')] ).
cnf(481,plain,
equal(ifeq2(true__dfg,true__dfg,domain__dfg(codomain(compose(a,b))),codomain(compose(a,b))),codomain(compose(a,b))),
inference(spr,[status(thm),theory(equality)],[15,101]),
[iquote('0:SpR:15.0,101.0')] ).
cnf(522,plain,
equal(domain__dfg(codomain(compose(a,b))),codomain(compose(a,b))),
inference(rew,[status(thm),theory(equality)],[2,481]),
[iquote('0:Rew:2.0,481.0')] ).
cnf(979,plain,
equal(ifeq(there_exists(compose(u,v)),true__dfg,there_exists(domain__dfg(compose(codomain(compose(u,v)),u))),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[14,69]),
[iquote('0:SpR:14.0,69.0')] ).
cnf(4852,plain,
equal(ifeq(true__dfg,true__dfg,there_exists(domain__dfg(compose(codomain(compose(a,b)),a))),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[15,979]),
[iquote('0:SpR:15.0,979.0')] ).
cnf(4887,plain,
equal(there_exists(domain__dfg(compose(codomain(compose(a,b)),a))),true__dfg),
inference(rew,[status(thm),theory(equality)],[3,4852]),
[iquote('0:Rew:3.0,4852.0')] ).
cnf(4907,plain,
equal(ifeq(true__dfg,true__dfg,there_exists(compose(codomain(compose(a,b)),a)),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[4887,7]),
[iquote('0:SpR:4887.0,7.0')] ).
cnf(4916,plain,
equal(there_exists(compose(codomain(compose(a,b)),a)),true__dfg),
inference(rew,[status(thm),theory(equality)],[3,4907]),
[iquote('0:Rew:3.0,4907.0')] ).
cnf(4939,plain,
equal(ifeq2(true__dfg,true__dfg,domain__dfg(codomain(compose(a,b))),codomain(a)),codomain(a)),
inference(spr,[status(thm),theory(equality)],[4916,10]),
[iquote('0:SpR:4916.0,10.0')] ).
cnf(4961,plain,
equal(codomain(compose(a,b)),codomain(a)),
inference(rew,[status(thm),theory(equality)],[2,4939,522]),
[iquote('0:Rew:2.0,4939.0,522.0,4939.0')] ).
cnf(4962,plain,
$false,
inference(mrr,[status(thm)],[4961,16]),
[iquote('0:MRR:4961.0,16.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : CAT010-10 : TPTP v8.1.0. Released v7.3.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n024.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 : 600
% 0.12/0.33 % DateTime : Sun May 29 22:21:36 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.92/1.09
% 0.92/1.09 SPASS V 3.9
% 0.92/1.09 SPASS beiseite: Proof found.
% 0.92/1.09 % SZS status Theorem
% 0.92/1.09 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.92/1.09 SPASS derived 3377 clauses, backtracked 0 clauses, performed 0 splits and kept 924 clauses.
% 0.92/1.09 SPASS allocated 68454 KBytes.
% 0.92/1.09 SPASS spent 0:00:00.71 on the problem.
% 0.92/1.09 0:00:00.03 for the input.
% 0.92/1.09 0:00:00.00 for the FLOTTER CNF translation.
% 0.92/1.09 0:00:00.04 for inferences.
% 0.92/1.09 0:00:00.00 for the backtracking.
% 0.92/1.09 0:00:00.62 for the reduction.
% 0.92/1.09
% 0.92/1.09
% 0.92/1.09 Here is a proof with depth 5, length 21 :
% 0.92/1.09 % SZS output start Refutation
% See solution above
% 0.92/1.09 Formulae used in the proof : ifeq_axiom_001 ifeq_axiom_002 domain_has_elements composition_implies_domain domain_codomain_composition1 associativity_of_compose compose_codomain ab_exists prove_codomain_of_ab_equals_codomain_of_a
% 0.92/1.09
%------------------------------------------------------------------------------