TSTP Solution File: CAT018-4 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : CAT018-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 00:07:32 EDT 2022
% Result : Unsatisfiable 0.20s 0.53s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of clauses : 25 ( 15 unt; 0 nHn; 25 RR)
% Number of literals : 36 ( 0 equ; 17 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
there_exists(compose(a,b)),
file('CAT018-4.p',unknown),
[] ).
cnf(2,axiom,
there_exists(compose(b,c)),
file('CAT018-4.p',unknown),
[] ).
cnf(3,axiom,
~ there_exists(compose(a,compose(b,c))),
file('CAT018-4.p',unknown),
[] ).
cnf(7,axiom,
( ~ there_exists(domain__dfg(u))
| there_exists(u) ),
file('CAT018-4.p',unknown),
[] ).
cnf(9,axiom,
( ~ there_exists(compose(u,v))
| there_exists(domain__dfg(u)) ),
file('CAT018-4.p',unknown),
[] ).
cnf(10,axiom,
( ~ there_exists(compose(u,v))
| equal(domain__dfg(u),codomain(v)) ),
file('CAT018-4.p',unknown),
[] ).
cnf(11,axiom,
( ~ there_exists(domain__dfg(u))
| ~ equal(domain__dfg(u),codomain(v))
| there_exists(compose(u,v)) ),
file('CAT018-4.p',unknown),
[] ).
cnf(12,axiom,
equal(compose(compose(u,v),w),compose(u,compose(v,w))),
file('CAT018-4.p',unknown),
[] ).
cnf(14,axiom,
equal(compose(codomain(u),u),u),
file('CAT018-4.p',unknown),
[] ).
cnf(15,plain,
( ~ there_exists(domain__dfg(a))
| ~ equal(codomain(compose(b,c)),domain__dfg(a)) ),
inference(res,[status(thm),theory(equality)],[11,3]),
[iquote('0:Res:11.2,3.0')] ).
cnf(23,plain,
there_exists(domain__dfg(b)),
inference(res,[status(thm),theory(equality)],[2,9]),
[iquote('0:Res:2.0,9.0')] ).
cnf(24,plain,
there_exists(domain__dfg(a)),
inference(res,[status(thm),theory(equality)],[1,9]),
[iquote('0:Res:1.0,9.0')] ).
cnf(25,plain,
~ equal(codomain(compose(b,c)),domain__dfg(a)),
inference(mrr,[status(thm)],[15,24]),
[iquote('0:MRR:15.0,24.0')] ).
cnf(26,plain,
there_exists(b),
inference(res,[status(thm),theory(equality)],[23,7]),
[iquote('0:Res:23.0,7.0')] ).
cnf(31,plain,
equal(codomain(b),domain__dfg(a)),
inference(res,[status(thm),theory(equality)],[1,10]),
[iquote('0:Res:1.0,10.0')] ).
cnf(37,plain,
equal(compose(domain__dfg(a),b),b),
inference(spr,[status(thm),theory(equality)],[31,14]),
[iquote('0:SpR:31.0,14.0')] ).
cnf(50,plain,
( ~ there_exists(b)
| equal(domain__dfg(domain__dfg(a)),codomain(b)) ),
inference(spl,[status(thm),theory(equality)],[37,10]),
[iquote('0:SpL:37.0,10.0')] ).
cnf(53,plain,
( ~ there_exists(b)
| equal(domain__dfg(domain__dfg(a)),domain__dfg(a)) ),
inference(rew,[status(thm),theory(equality)],[31,50]),
[iquote('0:Rew:31.0,50.1')] ).
cnf(54,plain,
equal(domain__dfg(domain__dfg(a)),domain__dfg(a)),
inference(mrr,[status(thm)],[53,26]),
[iquote('0:MRR:53.0,26.0')] ).
cnf(69,plain,
equal(compose(codomain(u),compose(u,v)),compose(u,v)),
inference(spr,[status(thm),theory(equality)],[14,12]),
[iquote('0:SpR:14.0,12.0')] ).
cnf(183,plain,
( ~ there_exists(compose(u,v))
| equal(codomain(compose(u,v)),domain__dfg(codomain(u))) ),
inference(spl,[status(thm),theory(equality)],[69,10]),
[iquote('0:SpL:69.0,10.0')] ).
cnf(1650,plain,
( ~ there_exists(compose(b,c))
| ~ equal(domain__dfg(codomain(b)),domain__dfg(a)) ),
inference(spl,[status(thm),theory(equality)],[183,25]),
[iquote('0:SpL:183.1,25.0')] ).
cnf(1652,plain,
( ~ there_exists(compose(b,c))
| ~ equal(domain__dfg(a),domain__dfg(a)) ),
inference(rew,[status(thm),theory(equality)],[54,1650,31]),
[iquote('0:Rew:54.0,1650.1,31.0,1650.1')] ).
cnf(1653,plain,
~ there_exists(compose(b,c)),
inference(obv,[status(thm),theory(equality)],[1652]),
[iquote('0:Obv:1652.1')] ).
cnf(1654,plain,
$false,
inference(mrr,[status(thm)],[1653,2]),
[iquote('0:MRR:1653.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : CAT018-4 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n019.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun May 29 16:53:40 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.53
% 0.20/0.53 SPASS V 3.9
% 0.20/0.53 SPASS beiseite: Proof found.
% 0.20/0.53 % SZS status Theorem
% 0.20/0.53 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.53 SPASS derived 1252 clauses, backtracked 0 clauses, performed 0 splits and kept 278 clauses.
% 0.20/0.53 SPASS allocated 76833 KBytes.
% 0.20/0.53 SPASS spent 0:00:00.16 on the problem.
% 0.20/0.53 0:00:00.03 for the input.
% 0.20/0.53 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.53 0:00:00.02 for inferences.
% 0.20/0.53 0:00:00.00 for the backtracking.
% 0.20/0.53 0:00:00.08 for the reduction.
% 0.20/0.53
% 0.20/0.53
% 0.20/0.53 Here is a proof with depth 3, length 25 :
% 0.20/0.53 % SZS output start Refutation
% See solution above
% 0.20/0.53 Formulae used in the proof : assume_ab_exists assume_bc_exists prove_a_bc_exists domain_has_elements composition_implies_domain domain_codomain_composition1 domain_codomain_composition2 associativity_of_compose compose_codomain
% 0.20/0.53
%------------------------------------------------------------------------------