TSTP Solution File: CAT009-3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : CAT009-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 0.67s 0.91s
% Output : Refutation 0.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 11
% Syntax : Number of clauses : 50 ( 13 unt; 17 nHn; 50 RR)
% Number of literals : 105 ( 0 equ; 28 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
there_exists(compose(a,b)),
file('CAT009-3.p',unknown),
[] ).
cnf(2,axiom,
~ equal(domain__dfg(compose(a,b)),domain__dfg(b)),
file('CAT009-3.p',unknown),
[] ).
cnf(6,axiom,
( ~ there_exists(domain__dfg(u))
| there_exists(u) ),
file('CAT009-3.p',unknown),
[] ).
cnf(7,axiom,
( ~ there_exists(codomain(u))
| there_exists(u) ),
file('CAT009-3.p',unknown),
[] ).
cnf(8,axiom,
( ~ there_exists(compose(u,v))
| there_exists(domain__dfg(u)) ),
file('CAT009-3.p',unknown),
[] ).
cnf(9,axiom,
( ~ there_exists(compose(u,v))
| equal(domain__dfg(u),codomain(v)) ),
file('CAT009-3.p',unknown),
[] ).
cnf(11,axiom,
equal(compose(compose(u,v),w),compose(u,compose(v,w))),
file('CAT009-3.p',unknown),
[] ).
cnf(12,axiom,
equal(compose(u,domain__dfg(u)),u),
file('CAT009-3.p',unknown),
[] ).
cnf(13,axiom,
equal(compose(codomain(u),u),u),
file('CAT009-3.p',unknown),
[] ).
cnf(17,axiom,
( there_exists(f1(u,v))
| equal(u,v) ),
file('CAT009-3.p',unknown),
[] ).
cnf(18,axiom,
( equal(u,v)
| equal(f1(u,v),v)
| equal(f1(u,v),u) ),
file('CAT009-3.p',unknown),
[] ).
cnf(40,plain,
( ~ there_exists(u)
| equal(domain__dfg(codomain(u)),codomain(u)) ),
inference(spl,[status(thm),theory(equality)],[13,9]),
[iquote('0:SpL:13.0,9.0')] ).
cnf(41,plain,
( ~ there_exists(u)
| equal(codomain(domain__dfg(u)),domain__dfg(u)) ),
inference(spl,[status(thm),theory(equality)],[12,9]),
[iquote('0:SpL:12.0,9.0')] ).
cnf(89,plain,
( ~ there_exists(compose(u,compose(v,w)))
| equal(domain__dfg(compose(u,v)),codomain(w)) ),
inference(spl,[status(thm),theory(equality)],[11,9]),
[iquote('0:SpL:11.0,9.0')] ).
cnf(90,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(102,plain,
( ~ there_exists(u)
| ~ there_exists(domain__dfg(u))
| equal(domain__dfg(domain__dfg(u)),domain__dfg(u)) ),
inference(spr,[status(thm),theory(equality)],[41,40]),
[iquote('0:SpR:41.1,40.1')] ).
cnf(108,plain,
( ~ there_exists(domain__dfg(u))
| equal(domain__dfg(domain__dfg(u)),domain__dfg(u)) ),
inference(mrr,[status(thm)],[102,6]),
[iquote('0:MRR:102.0,6.1')] ).
cnf(124,plain,
( equal(u,v)
| equal(f1(u,v),u)
| there_exists(v)
| equal(u,v) ),
inference(spr,[status(thm),theory(equality)],[18,17]),
[iquote('0:SpR:18.1,17.0')] ).
cnf(130,plain,
( equal(f1(u,v),u)
| there_exists(v)
| equal(u,v) ),
inference(obv,[status(thm),theory(equality)],[124]),
[iquote('0:Obv:124.0')] ).
cnf(136,plain,
( ~ there_exists(domain__dfg(u))
| ~ there_exists(domain__dfg(u))
| equal(codomain(domain__dfg(u)),domain__dfg(u)) ),
inference(spr,[status(thm),theory(equality)],[108,41]),
[iquote('0:SpR:108.1,41.1')] ).
cnf(143,plain,
( ~ there_exists(domain__dfg(u))
| equal(codomain(domain__dfg(u)),domain__dfg(u)) ),
inference(obv,[status(thm),theory(equality)],[136]),
[iquote('0:Obv:136.0')] ).
cnf(396,plain,
( there_exists(u)
| equal(v,u)
| there_exists(v)
| equal(v,u) ),
inference(spr,[status(thm),theory(equality)],[130,17]),
[iquote('0:SpR:130.0,17.0')] ).
cnf(401,plain,
( there_exists(u)
| there_exists(v)
| equal(v,u) ),
inference(obv,[status(thm),theory(equality)],[396]),
[iquote('0:Obv:396.1')] ).
cnf(424,plain,
( there_exists(u)
| there_exists(codomain(v))
| equal(compose(u,v),v) ),
inference(spr,[status(thm),theory(equality)],[401,13]),
[iquote('0:SpR:401.2,13.0')] ).
cnf(1355,plain,
( ~ there_exists(compose(u,v))
| there_exists(domain__dfg(compose(u,codomain(v)))) ),
inference(spl,[status(thm),theory(equality)],[13,90]),
[iquote('0:SpL:13.0,90.0')] ).
cnf(2611,plain,
( ~ there_exists(compose(u,v))
| equal(domain__dfg(compose(u,codomain(v))),codomain(v)) ),
inference(spl,[status(thm),theory(equality)],[13,89]),
[iquote('0:SpL:13.0,89.0')] ).
cnf(2616,plain,
( ~ there_exists(compose(u,v))
| equal(domain__dfg(compose(u,v)),codomain(domain__dfg(v))) ),
inference(spl,[status(thm),theory(equality)],[12,89]),
[iquote('0:SpL:12.0,89.0')] ).
cnf(2652,plain,
( ~ there_exists(compose(u,v))
| there_exists(codomain(v)) ),
inference(rew,[status(thm),theory(equality)],[2611,1355]),
[iquote('0:Rew:2611.1,1355.1')] ).
cnf(2696,plain,
( ~ there_exists(compose(u,compose(v,w)))
| there_exists(codomain(w)) ),
inference(spl,[status(thm),theory(equality)],[11,2652]),
[iquote('0:SpL:11.0,2652.0')] ).
cnf(2705,plain,
( there_exists(u)
| equal(u,compose(v,w))
| there_exists(codomain(w)) ),
inference(res,[status(thm),theory(equality)],[401,2652]),
[iquote('0:Res:401.0,2652.0')] ).
cnf(2731,plain,
( ~ there_exists(compose(u,v))
| there_exists(compose(w,x))
| there_exists(v)
| there_exists(codomain(x)) ),
inference(spl,[status(thm),theory(equality)],[401,2696]),
[iquote('0:SpL:401.2,2696.0')] ).
cnf(2757,plain,
( ~ there_exists(compose(u,v))
| there_exists(v)
| there_exists(codomain(w)) ),
inference(mrr,[status(thm)],[2731,2652]),
[iquote('0:MRR:2731.1,2652.0')] ).
cnf(2887,plain,
( ~ there_exists(compose(u,v))
| there_exists(v) ),
inference(spt,[spt(split,[position(s1)])],[2757]),
[iquote('1:Spt:2757.0,2757.1')] ).
cnf(2915,plain,
( there_exists(u)
| equal(u,compose(v,w))
| there_exists(w) ),
inference(res,[status(thm),theory(equality)],[401,2887]),
[iquote('1:Res:401.0,2887.0')] ).
cnf(3073,plain,
( there_exists(codomain(u))
| there_exists(v)
| equal(compose(compose(w,v),u),u) ),
inference(spr,[status(thm),theory(equality)],[2915,13]),
[iquote('1:SpR:2915.1,13.0')] ).
cnf(3229,plain,
( there_exists(codomain(u))
| there_exists(v)
| equal(compose(w,u),u) ),
inference(rew,[status(thm),theory(equality)],[424,3073,11]),
[iquote('1:Rew:424.2,3073.2,11.0,3073.2')] ).
cnf(3230,plain,
( there_exists(codomain(u))
| equal(compose(v,u),u) ),
inference(con,[status(thm)],[3229]),
[iquote('1:Con:3229.1')] ).
cnf(3238,plain,
( there_exists(u)
| equal(u,v)
| there_exists(codomain(v)) ),
inference(rew,[status(thm),theory(equality)],[3230,2705]),
[iquote('1:Rew:3230.1,2705.1')] ).
cnf(4026,plain,
( equal(codomain(u),u)
| there_exists(codomain(u)) ),
inference(fac,[status(thm)],[3238]),
[iquote('1:Fac:3238.0,3238.2')] ).
cnf(5191,plain,
( equal(codomain(u),u)
| there_exists(u) ),
inference(res,[status(thm),theory(equality)],[4026,7]),
[iquote('1:Res:4026.1,7.0')] ).
cnf(5193,plain,
equal(codomain(domain__dfg(u)),domain__dfg(u)),
inference(mrr,[status(thm)],[143,5191]),
[iquote('1:MRR:143.0,5191.1')] ).
cnf(5307,plain,
( ~ there_exists(compose(u,v))
| equal(domain__dfg(compose(u,v)),domain__dfg(v)) ),
inference(rew,[status(thm),theory(equality)],[5193,2616]),
[iquote('1:Rew:5193.0,2616.1')] ).
cnf(5450,plain,
( ~ there_exists(compose(a,b))
| ~ equal(domain__dfg(b),domain__dfg(b)) ),
inference(spl,[status(thm),theory(equality)],[5307,2]),
[iquote('1:SpL:5307.1,2.0')] ).
cnf(5453,plain,
~ there_exists(compose(a,b)),
inference(obv,[status(thm),theory(equality)],[5450]),
[iquote('1:Obv:5450.1')] ).
cnf(5454,plain,
$false,
inference(mrr,[status(thm)],[5453,1]),
[iquote('1:MRR:5453.0,1.0')] ).
cnf(5473,plain,
there_exists(codomain(u)),
inference(spt,[spt(split,[position(s2)])],[2757]),
[iquote('1:Spt:5454.0,2757.2')] ).
cnf(5474,plain,
there_exists(u),
inference(mrr,[status(thm)],[7,5473]),
[iquote('1:MRR:7.0,5473.0')] ).
cnf(5475,plain,
equal(domain__dfg(u),codomain(v)),
inference(mrr,[status(thm)],[9,5474]),
[iquote('1:MRR:9.0,5474.0')] ).
cnf(5515,plain,
~ equal(codomain(u),domain__dfg(b)),
inference(spl,[status(thm),theory(equality)],[5475,2]),
[iquote('1:SpL:5475.0,2.0')] ).
cnf(5522,plain,
$false,
inference(unc,[status(thm)],[5515,5475]),
[iquote('1:UnC:5515.0,5475.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : CAT009-3 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n020.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun May 29 20:22:39 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.67/0.91
% 0.67/0.91 SPASS V 3.9
% 0.67/0.91 SPASS beiseite: Proof found.
% 0.67/0.91 % SZS status Theorem
% 0.67/0.91 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.67/0.91 SPASS derived 4037 clauses, backtracked 215 clauses, performed 2 splits and kept 636 clauses.
% 0.67/0.91 SPASS allocated 78672 KBytes.
% 0.67/0.91 SPASS spent 0:00:00.46 on the problem.
% 0.67/0.91 0:00:00.04 for the input.
% 0.67/0.91 0:00:00.00 for the FLOTTER CNF translation.
% 0.67/0.91 0:00:00.05 for inferences.
% 0.67/0.91 0:00:00.01 for the backtracking.
% 0.67/0.91 0:00:00.34 for the reduction.
% 0.67/0.91
% 0.67/0.91
% 0.67/0.91 Here is a proof with depth 7, length 50 :
% 0.67/0.91 % SZS output start Refutation
% See solution above
% 0.67/0.91 Formulae used in the proof : ab_exists prove_domain_of_ab_equals_domain_of_b domain_has_elements codomain_has_elements composition_implies_domain domain_codomain_composition1 associativity_of_compose compose_domain compose_codomain indiscernibles1 indiscernibles2
% 0.67/0.91
%------------------------------------------------------------------------------