%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : CAT006-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 00:07:29 EDT 2022
% Result : Unsatisfiable 0.12s 0.41s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of clauses : 17 ( 9 unt; 0 nHn; 17 RR)
% Number of literals : 25 ( 0 equ; 9 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
there_exists(compose(d,a)),
file('CAT006-4.p',unknown),
[] ).
cnf(3,axiom,
( ~ there_exists(compose(d,u))
| equal(compose(d,u),u) ),
file('CAT006-4.p',unknown),
[] ).
cnf(4,axiom,
~ equal(codomain(a),d),
file('CAT006-4.p',unknown),
[] ).
cnf(8,axiom,
( ~ there_exists(domain__dfg(u))
| there_exists(u) ),
file('CAT006-4.p',unknown),
[] ).
cnf(10,axiom,
( ~ there_exists(compose(u,v))
| there_exists(domain__dfg(u)) ),
file('CAT006-4.p',unknown),
[] ).
cnf(11,axiom,
( ~ there_exists(compose(u,v))
| equal(domain__dfg(u),codomain(v)) ),
file('CAT006-4.p',unknown),
[] ).
cnf(14,axiom,
equal(compose(u,domain__dfg(u)),u),
file('CAT006-4.p',unknown),
[] ).
cnf(22,plain,
there_exists(domain__dfg(d)),
inference(res,[status(thm),theory(equality)],[1,10]),
[iquote('0:Res:1.0,10.0')] ).
cnf(23,plain,
there_exists(d),
inference(res,[status(thm),theory(equality)],[22,8]),
[iquote('0:Res:22.0,8.0')] ).
cnf(25,plain,
( ~ there_exists(d)
| equal(compose(d,domain__dfg(d)),domain__dfg(d)) ),
inference(spl,[status(thm),theory(equality)],[14,3]),
[iquote('0:SpL:14.0,3.0')] ).
cnf(26,plain,
equal(compose(d,a),a),
inference(res,[status(thm),theory(equality)],[1,3]),
[iquote('0:Res:1.0,3.0')] ).
cnf(27,plain,
there_exists(a),
inference(rew,[status(thm),theory(equality)],[26,1]),
[iquote('0:Rew:26.0,1.0')] ).
cnf(28,plain,
( ~ there_exists(d)
| equal(domain__dfg(d),d) ),
inference(rew,[status(thm),theory(equality)],[14,25]),
[iquote('0:Rew:14.0,25.1')] ).
cnf(29,plain,
equal(domain__dfg(d),d),
inference(mrr,[status(thm)],[28,23]),
[iquote('0:MRR:28.0,23.0')] ).
cnf(55,plain,
( ~ there_exists(a)
| equal(domain__dfg(d),codomain(a)) ),
inference(spl,[status(thm),theory(equality)],[26,11]),
[iquote('0:SpL:26.0,11.0')] ).
cnf(57,plain,
( ~ there_exists(a)
| equal(codomain(a),d) ),
inference(rew,[status(thm),theory(equality)],[29,55]),
[iquote('0:Rew:29.0,55.1')] ).
cnf(58,plain,
$false,
inference(mrr,[status(thm)],[57,27,4]),
[iquote('0:MRR:57.0,57.1,27.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : CAT006-4 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n028.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun May 29 17:58:03 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.41
% 0.12/0.41 SPASS V 3.9
% 0.12/0.41 SPASS beiseite: Proof found.
% 0.12/0.41 % SZS status Theorem
% 0.12/0.41 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.41 SPASS derived 37 clauses, backtracked 0 clauses, performed 0 splits and kept 30 clauses.
% 0.12/0.41 SPASS allocated 75622 KBytes.
% 0.12/0.41 SPASS spent 0:00:00.06 on the problem.
% 0.12/0.41 0:00:00.03 for the input.
% 0.12/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.12/0.41 0:00:00.00 for inferences.
% 0.12/0.41 0:00:00.00 for the backtracking.
% 0.12/0.41 0:00:00.00 for the reduction.
% 0.12/0.41
% 0.12/0.41
% 0.12/0.41 Here is a proof with depth 2, length 17 :
% 0.12/0.41 % SZS output start Refutation
% See solution above
% 0.12/0.41 Formulae used in the proof : da_exists dx_equals_x prove_codomain_of_a_is_d domain_has_elements composition_implies_domain domain_codomain_composition1 compose_domain
% 0.12/0.41
%------------------------------------------------------------------------------