%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : CAT010-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 0.19s 0.52s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of clauses : 29 ( 16 unt; 0 nHn; 29 RR)
% Number of literals : 42 ( 0 equ; 16 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
there_exists(compose(a,b)),
file('CAT010-4.p',unknown),
[] ).
cnf(2,axiom,
~ equal(codomain(compose(a,b)),codomain(a)),
file('CAT010-4.p',unknown),
[] ).
cnf(6,axiom,
( ~ there_exists(domain__dfg(u))
| there_exists(u) ),
file('CAT010-4.p',unknown),
[] ).
cnf(8,axiom,
( ~ there_exists(compose(u,v))
| there_exists(domain__dfg(u)) ),
file('CAT010-4.p',unknown),
[] ).
cnf(9,axiom,
( ~ there_exists(compose(u,v))
| equal(domain__dfg(u),codomain(v)) ),
file('CAT010-4.p',unknown),
[] ).
cnf(11,axiom,
equal(compose(compose(u,v),w),compose(u,compose(v,w))),
file('CAT010-4.p',unknown),
[] ).
cnf(12,axiom,
equal(compose(u,domain__dfg(u)),u),
file('CAT010-4.p',unknown),
[] ).
cnf(13,axiom,
equal(compose(codomain(u),u),u),
file('CAT010-4.p',unknown),
[] ).
cnf(57,plain,
equal(compose(codomain(u),compose(u,v)),compose(u,v)),
inference(spr,[status(thm),theory(equality)],[13,11]),
[iquote('0:SpR:13.0,11.0')] ).
cnf(59,plain,
equal(compose(u,compose(domain__dfg(u),v)),compose(u,v)),
inference(spr,[status(thm),theory(equality)],[12,11]),
[iquote('0:SpR:12.0,11.0')] ).
cnf(61,plain,
( ~ there_exists(compose(u,compose(v,w)))
| there_exists(domain__dfg(compose(u,v))) ),
inference(spl,[status(thm),theory(equality)],[11,8]),
[iquote('0:SpL:11.0,8.0')] ).
cnf(166,plain,
( ~ there_exists(compose(u,v))
| equal(codomain(compose(u,v)),domain__dfg(codomain(u))) ),
inference(spl,[status(thm),theory(equality)],[57,9]),
[iquote('0:SpL:57.0,9.0')] ).
cnf(167,plain,
( ~ there_exists(compose(u,v))
| there_exists(domain__dfg(codomain(u))) ),
inference(spl,[status(thm),theory(equality)],[57,8]),
[iquote('0:SpL:57.0,8.0')] ).
cnf(205,plain,
there_exists(domain__dfg(codomain(a))),
inference(res,[status(thm),theory(equality)],[1,167]),
[iquote('0:Res:1.0,167.0')] ).
cnf(226,plain,
equal(compose(u,domain__dfg(domain__dfg(u))),compose(u,domain__dfg(u))),
inference(spr,[status(thm),theory(equality)],[12,59]),
[iquote('0:SpR:12.0,59.0')] ).
cnf(230,plain,
equal(compose(u,domain__dfg(domain__dfg(u))),u),
inference(rew,[status(thm),theory(equality)],[12,226]),
[iquote('0:Rew:12.0,226.0')] ).
cnf(250,plain,
( ~ there_exists(u)
| equal(codomain(domain__dfg(domain__dfg(u))),domain__dfg(u)) ),
inference(spl,[status(thm),theory(equality)],[230,9]),
[iquote('0:SpL:230.0,9.0')] ).
cnf(307,plain,
( ~ there_exists(compose(u,v))
| there_exists(domain__dfg(compose(codomain(compose(u,v)),u))) ),
inference(spl,[status(thm),theory(equality)],[13,61]),
[iquote('0:SpL:13.0,61.0')] ).
cnf(318,plain,
( ~ there_exists(compose(u,v))
| there_exists(domain__dfg(compose(domain__dfg(codomain(u)),u))) ),
inference(rew,[status(thm),theory(equality)],[166,307]),
[iquote('0:Rew:166.1,307.1')] ).
cnf(500,plain,
( ~ there_exists(u)
| equal(compose(domain__dfg(u),domain__dfg(domain__dfg(u))),domain__dfg(domain__dfg(u))) ),
inference(spr,[status(thm),theory(equality)],[250,13]),
[iquote('0:SpR:250.1,13.0')] ).
cnf(521,plain,
( ~ there_exists(u)
| equal(domain__dfg(domain__dfg(u)),domain__dfg(u)) ),
inference(rew,[status(thm),theory(equality)],[12,500]),
[iquote('0:Rew:12.0,500.1')] ).
cnf(1450,plain,
there_exists(domain__dfg(compose(domain__dfg(codomain(a)),a))),
inference(res,[status(thm),theory(equality)],[1,318]),
[iquote('0:Res:1.0,318.0')] ).
cnf(1472,plain,
there_exists(compose(domain__dfg(codomain(a)),a)),
inference(res,[status(thm),theory(equality)],[1450,6]),
[iquote('0:Res:1450.0,6.0')] ).
cnf(1482,plain,
equal(domain__dfg(domain__dfg(codomain(a))),codomain(a)),
inference(res,[status(thm),theory(equality)],[1472,9]),
[iquote('0:Res:1472.0,9.0')] ).
cnf(1545,plain,
( ~ there_exists(compose(a,b))
| ~ equal(domain__dfg(codomain(a)),codomain(a)) ),
inference(spl,[status(thm),theory(equality)],[166,2]),
[iquote('0:SpL:166.1,2.0')] ).
cnf(1551,plain,
~ equal(domain__dfg(codomain(a)),codomain(a)),
inference(mrr,[status(thm)],[1545,1]),
[iquote('0:MRR:1545.0,1.0')] ).
cnf(1612,plain,
( ~ there_exists(domain__dfg(codomain(a)))
| equal(domain__dfg(codomain(a)),codomain(a)) ),
inference(spr,[status(thm),theory(equality)],[1482,521]),
[iquote('0:SpR:1482.0,521.1')] ).
cnf(1637,plain,
equal(domain__dfg(codomain(a)),codomain(a)),
inference(mrr,[status(thm)],[1612,205]),
[iquote('0:MRR:1612.0,205.0')] ).
cnf(1638,plain,
$false,
inference(mrr,[status(thm)],[1637,1551]),
[iquote('0:MRR:1637.0,1551.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : CAT010-4 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n025.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % 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 17:57:11 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.52
% 0.19/0.52 SPASS V 3.9
% 0.19/0.52 SPASS beiseite: Proof found.
% 0.19/0.52 % SZS status Theorem
% 0.19/0.52 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.52 SPASS derived 1230 clauses, backtracked 0 clauses, performed 0 splits and kept 292 clauses.
% 0.19/0.52 SPASS allocated 76783 KBytes.
% 0.19/0.52 SPASS spent 0:00:00.16 on the problem.
% 0.19/0.52 0:00:00.04 for the input.
% 0.19/0.52 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.52 0:00:00.02 for inferences.
% 0.19/0.52 0:00:00.00 for the backtracking.
% 0.19/0.52 0:00:00.08 for the reduction.
% 0.19/0.52
% 0.19/0.52
% 0.19/0.52 Here is a proof with depth 6, length 29 :
% 0.19/0.52 % SZS output start Refutation
% See solution above
% 0.19/0.52 Formulae used in the proof : ab_exists prove_codomain_of_ab_equals_codomain_of_a domain_has_elements composition_implies_domain domain_codomain_composition1 associativity_of_compose compose_domain compose_codomain
% 0.19/0.52
%------------------------------------------------------------------------------