TSTP Solution File: CAT009-4 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : CAT009-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 0.20s 0.54s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of clauses : 41 ( 18 unt; 0 nHn; 41 RR)
% Number of literals : 65 ( 0 equ; 28 neg)
% Maximal clause size : 3 ( 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('CAT009-4.p',unknown),
[] ).
cnf(2,axiom,
~ equal(domain__dfg(compose(a,b)),domain__dfg(b)),
file('CAT009-4.p',unknown),
[] ).
cnf(7,axiom,
( ~ there_exists(codomain(u))
| there_exists(u) ),
file('CAT009-4.p',unknown),
[] ).
cnf(8,axiom,
( ~ there_exists(compose(u,v))
| there_exists(domain__dfg(u)) ),
file('CAT009-4.p',unknown),
[] ).
cnf(9,axiom,
( ~ there_exists(compose(u,v))
| equal(domain__dfg(u),codomain(v)) ),
file('CAT009-4.p',unknown),
[] ).
cnf(11,axiom,
equal(compose(compose(u,v),w),compose(u,compose(v,w))),
file('CAT009-4.p',unknown),
[] ).
cnf(12,axiom,
equal(compose(u,domain__dfg(u)),u),
file('CAT009-4.p',unknown),
[] ).
cnf(13,axiom,
equal(compose(codomain(u),u),u),
file('CAT009-4.p',unknown),
[] ).
cnf(26,plain,
equal(codomain(b),domain__dfg(a)),
inference(res,[status(thm),theory(equality)],[1,9]),
[iquote('0:Res:1.0,9.0')] ).
cnf(28,plain,
equal(compose(domain__dfg(a),b),b),
inference(spr,[status(thm),theory(equality)],[26,13]),
[iquote('0:SpR:26.0,13.0')] ).
cnf(58,plain,
equal(compose(u,compose(v,domain__dfg(compose(u,v)))),compose(u,v)),
inference(spr,[status(thm),theory(equality)],[11,12]),
[iquote('0:SpR:11.0,12.0')] ).
cnf(61,plain,
equal(compose(domain__dfg(a),compose(b,u)),compose(b,u)),
inference(spr,[status(thm),theory(equality)],[28,11]),
[iquote('0:SpR:28.0,11.0')] ).
cnf(62,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(63,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(65,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(66,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(155,plain,
equal(compose(codomain(codomain(u)),u),u),
inference(spr,[status(thm),theory(equality)],[13,62]),
[iquote('0:SpR:13.0,62.0')] ).
cnf(187,plain,
( ~ there_exists(compose(u,v))
| equal(codomain(compose(domain__dfg(u),v)),domain__dfg(u)) ),
inference(spl,[status(thm),theory(equality)],[63,9]),
[iquote('0:SpL:63.0,9.0')] ).
cnf(203,plain,
( ~ there_exists(u)
| equal(domain__dfg(codomain(codomain(u))),codomain(u)) ),
inference(spl,[status(thm),theory(equality)],[155,9]),
[iquote('0:SpL:155.0,9.0')] ).
cnf(256,plain,
( ~ there_exists(compose(u,v))
| there_exists(domain__dfg(compose(u,codomain(v)))) ),
inference(spl,[status(thm),theory(equality)],[13,66]),
[iquote('0:SpL:13.0,66.0')] ).
cnf(403,plain,
( ~ there_exists(u)
| equal(compose(codomain(codomain(u)),codomain(u)),codomain(codomain(u))) ),
inference(spr,[status(thm),theory(equality)],[203,12]),
[iquote('0:SpR:203.1,12.0')] ).
cnf(423,plain,
( ~ there_exists(u)
| equal(codomain(codomain(u)),codomain(u)) ),
inference(rew,[status(thm),theory(equality)],[13,403]),
[iquote('0:Rew:13.0,403.1')] ).
cnf(580,plain,
( ~ there_exists(compose(u,v))
| equal(domain__dfg(compose(u,codomain(v))),codomain(v)) ),
inference(spl,[status(thm),theory(equality)],[13,65]),
[iquote('0:SpL:13.0,65.0')] ).
cnf(584,plain,
( ~ there_exists(compose(u,v))
| equal(domain__dfg(compose(u,v)),codomain(domain__dfg(v))) ),
inference(spl,[status(thm),theory(equality)],[12,65]),
[iquote('0:SpL:12.0,65.0')] ).
cnf(606,plain,
( ~ there_exists(compose(u,v))
| there_exists(codomain(v)) ),
inference(rew,[status(thm),theory(equality)],[580,256]),
[iquote('0:Rew:580.1,256.1')] ).
cnf(641,plain,
( ~ there_exists(compose(u,compose(v,w)))
| there_exists(codomain(w)) ),
inference(spl,[status(thm),theory(equality)],[11,606]),
[iquote('0:SpL:11.0,606.0')] ).
cnf(733,plain,
( ~ there_exists(compose(u,v))
| there_exists(codomain(domain__dfg(v))) ),
inference(spl,[status(thm),theory(equality)],[12,641]),
[iquote('0:SpL:12.0,641.0')] ).
cnf(817,plain,
there_exists(codomain(domain__dfg(b))),
inference(res,[status(thm),theory(equality)],[1,733]),
[iquote('0:Res:1.0,733.0')] ).
cnf(1603,plain,
( ~ there_exists(compose(u,v))
| ~ there_exists(domain__dfg(u))
| there_exists(compose(domain__dfg(u),v)) ),
inference(spl,[status(thm),theory(equality)],[187,7]),
[iquote('0:SpL:187.1,7.0')] ).
cnf(1609,plain,
( ~ there_exists(compose(u,v))
| there_exists(compose(domain__dfg(u),v)) ),
inference(mrr,[status(thm)],[1603,8]),
[iquote('0:MRR:1603.1,8.1')] ).
cnf(1644,plain,
( ~ there_exists(compose(a,compose(b,u)))
| there_exists(compose(b,u)) ),
inference(spr,[status(thm),theory(equality)],[61,1609]),
[iquote('0:SpR:61.0,1609.1')] ).
cnf(1849,plain,
( ~ there_exists(compose(a,b))
| there_exists(compose(b,domain__dfg(compose(a,b)))) ),
inference(spl,[status(thm),theory(equality)],[58,1644]),
[iquote('0:SpL:58.0,1644.0')] ).
cnf(1855,plain,
( ~ there_exists(compose(a,b))
| there_exists(compose(b,codomain(domain__dfg(b)))) ),
inference(rew,[status(thm),theory(equality)],[584,1849]),
[iquote('0:Rew:584.1,1849.1')] ).
cnf(1856,plain,
there_exists(compose(b,codomain(domain__dfg(b)))),
inference(mrr,[status(thm)],[1855,1]),
[iquote('0:MRR:1855.0,1.0')] ).
cnf(1952,plain,
equal(codomain(codomain(domain__dfg(b))),domain__dfg(b)),
inference(res,[status(thm),theory(equality)],[1856,9]),
[iquote('0:Res:1856.0,9.0')] ).
cnf(1987,plain,
( ~ there_exists(codomain(domain__dfg(b)))
| equal(codomain(domain__dfg(b)),domain__dfg(b)) ),
inference(spr,[status(thm),theory(equality)],[1952,423]),
[iquote('0:SpR:1952.0,423.1')] ).
cnf(2007,plain,
equal(codomain(domain__dfg(b)),domain__dfg(b)),
inference(mrr,[status(thm)],[1987,817]),
[iquote('0:MRR:1987.0,817.0')] ).
cnf(2069,plain,
( ~ there_exists(compose(a,b))
| ~ equal(codomain(domain__dfg(b)),domain__dfg(b)) ),
inference(spl,[status(thm),theory(equality)],[584,2]),
[iquote('0:SpL:584.1,2.0')] ).
cnf(2073,plain,
( ~ there_exists(compose(a,b))
| ~ equal(domain__dfg(b),domain__dfg(b)) ),
inference(rew,[status(thm),theory(equality)],[2007,2069]),
[iquote('0:Rew:2007.0,2069.1')] ).
cnf(2074,plain,
~ there_exists(compose(a,b)),
inference(obv,[status(thm),theory(equality)],[2073]),
[iquote('0:Obv:2073.1')] ).
cnf(2075,plain,
$false,
inference(mrr,[status(thm)],[2074,1]),
[iquote('0:MRR:2074.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : CAT009-4 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n018.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 19:32:41 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.54
% 0.20/0.54 SPASS V 3.9
% 0.20/0.54 SPASS beiseite: Proof found.
% 0.20/0.54 % SZS status Theorem
% 0.20/0.54 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.54 SPASS derived 1544 clauses, backtracked 0 clauses, performed 0 splits and kept 328 clauses.
% 0.20/0.54 SPASS allocated 77103 KBytes.
% 0.20/0.54 SPASS spent 0:00:00.18 on the problem.
% 0.20/0.54 0:00:00.04 for the input.
% 0.20/0.54 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.54 0:00:00.02 for inferences.
% 0.20/0.54 0:00:00.00 for the backtracking.
% 0.20/0.54 0:00:00.10 for the reduction.
% 0.20/0.54
% 0.20/0.54
% 0.20/0.54 Here is a proof with depth 7, length 41 :
% 0.20/0.54 % SZS output start Refutation
% See solution above
% 0.20/0.54 Formulae used in the proof : ab_exists prove_domain_of_ab_equals_domain_of_b codomain_has_elements composition_implies_domain domain_codomain_composition1 associativity_of_compose compose_domain compose_codomain
% 0.20/0.54
%------------------------------------------------------------------------------