TSTP Solution File: CAT003-2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : CAT003-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 00:07:28 EDT 2022
% Result : Unsatisfiable 0.20s 0.54s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of clauses : 30 ( 11 unt; 0 nHn; 30 RR)
% Number of literals : 74 ( 0 equ; 55 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ equal(codomain(compose(a,b)),domain__dfg(u))
| ~ equal(codomain(compose(a,b)),domain__dfg(v))
| ~ equal(compose(compose(a,b),u),w)
| ~ equal(compose(compose(a,b),v),w)
| equal(v,u) ),
file('CAT003-2.p',unknown),
[] ).
cnf(2,axiom,
equal(domain__dfg(b),codomain(a)),
file('CAT003-2.p',unknown),
[] ).
cnf(3,axiom,
equal(domain__dfg(h),codomain(b)),
file('CAT003-2.p',unknown),
[] ).
cnf(4,axiom,
equal(domain__dfg(g),codomain(b)),
file('CAT003-2.p',unknown),
[] ).
cnf(5,axiom,
equal(compose(b,g),compose(b,h)),
file('CAT003-2.p',unknown),
[] ).
cnf(6,axiom,
~ equal(g,h),
file('CAT003-2.p',unknown),
[] ).
cnf(7,axiom,
equal(codomain(domain__dfg(u)),domain__dfg(u)),
file('CAT003-2.p',unknown),
[] ).
cnf(8,axiom,
equal(domain__dfg(codomain(u)),codomain(u)),
file('CAT003-2.p',unknown),
[] ).
cnf(9,axiom,
equal(compose(domain__dfg(u),u),u),
file('CAT003-2.p',unknown),
[] ).
cnf(12,axiom,
( ~ equal(codomain(u),domain__dfg(v))
| equal(codomain(compose(u,v)),codomain(v)) ),
file('CAT003-2.p',unknown),
[] ).
cnf(13,axiom,
( ~ equal(codomain(u),domain__dfg(v))
| ~ equal(codomain(w),domain__dfg(u))
| equal(compose(compose(w,u),v),compose(w,compose(u,v))) ),
file('CAT003-2.p',unknown),
[] ).
cnf(15,plain,
( ~ equal(codomain(compose(a,b)),domain__dfg(h))
| ~ equal(compose(compose(a,b),h),u)
| ~ equal(codomain(compose(a,b)),domain__dfg(g))
| ~ equal(compose(compose(a,b),g),u) ),
inference(res,[status(thm),theory(equality)],[1,6]),
[iquote('0:Res:1.4,6.0')] ).
cnf(16,plain,
( ~ equal(codomain(compose(a,b)),codomain(b))
| ~ equal(compose(compose(a,b),h),u)
| ~ equal(codomain(compose(a,b)),codomain(b))
| ~ equal(compose(compose(a,b),g),u) ),
inference(rew,[status(thm),theory(equality)],[4,15,3]),
[iquote('0:Rew:4.0,15.2,3.0,15.0')] ).
cnf(17,plain,
( ~ equal(codomain(compose(a,b)),codomain(b))
| ~ equal(compose(compose(a,b),g),u)
| ~ equal(compose(compose(a,b),h),u) ),
inference(obv,[status(thm),theory(equality)],[16]),
[iquote('0:Obv:16.0')] ).
cnf(29,plain,
equal(codomain(codomain(u)),codomain(u)),
inference(spr,[status(thm),theory(equality)],[8,7]),
[iquote('0:SpR:8.0,7.0')] ).
cnf(44,plain,
equal(compose(codomain(a),b),b),
inference(spr,[status(thm),theory(equality)],[2,9]),
[iquote('0:SpR:2.0,9.0')] ).
cnf(143,plain,
( ~ equal(codomain(u),domain__dfg(v))
| ~ equal(codomain(w),domain__dfg(u))
| ~ equal(codomain(compose(w,u)),domain__dfg(v))
| equal(codomain(compose(w,compose(u,v))),codomain(v)) ),
inference(spr,[status(thm),theory(equality)],[13,12]),
[iquote('0:SpR:13.2,12.1')] ).
cnf(176,plain,
( ~ equal(codomain(u),domain__dfg(v))
| ~ equal(codomain(w),domain__dfg(u))
| ~ equal(codomain(u),domain__dfg(v))
| equal(codomain(compose(w,compose(u,v))),codomain(v)) ),
inference(rew,[status(thm),theory(equality)],[12,143]),
[iquote('0:Rew:12.1,143.2')] ).
cnf(177,plain,
( ~ equal(codomain(u),domain__dfg(v))
| ~ equal(codomain(v),domain__dfg(w))
| equal(codomain(compose(u,compose(v,w))),codomain(w)) ),
inference(obv,[status(thm),theory(equality)],[176]),
[iquote('0:Obv:176.0')] ).
cnf(726,plain,
( ~ equal(codomain(u),domain__dfg(codomain(a)))
| ~ equal(codomain(codomain(a)),domain__dfg(b))
| equal(codomain(compose(u,b)),codomain(b)) ),
inference(spr,[status(thm),theory(equality)],[44,177]),
[iquote('0:SpR:44.0,177.2')] ).
cnf(760,plain,
( ~ equal(codomain(u),codomain(a))
| ~ equal(codomain(a),codomain(a))
| equal(codomain(compose(u,b)),codomain(b)) ),
inference(rew,[status(thm),theory(equality)],[29,726,2,8]),
[iquote('0:Rew:29.0,726.1,2.0,726.1,8.0,726.0')] ).
cnf(761,plain,
( ~ equal(codomain(u),codomain(a))
| equal(codomain(compose(u,b)),codomain(b)) ),
inference(obv,[status(thm),theory(equality)],[760]),
[iquote('0:Obv:760.1')] ).
cnf(1105,plain,
( ~ equal(domain__dfg(g),codomain(b))
| ~ equal(domain__dfg(b),codomain(a))
| ~ equal(codomain(compose(a,b)),codomain(b))
| ~ equal(compose(a,compose(b,g)),u)
| ~ equal(compose(compose(a,b),h),u) ),
inference(spl,[status(thm),theory(equality)],[13,17]),
[iquote('0:SpL:13.2,17.1')] ).
cnf(1106,plain,
( ~ equal(codomain(b),codomain(b))
| ~ equal(codomain(a),codomain(a))
| ~ equal(codomain(b),codomain(b))
| ~ equal(compose(a,compose(b,h)),u)
| ~ equal(compose(compose(a,b),h),u) ),
inference(rew,[status(thm),theory(equality)],[5,1105,761,2,4]),
[iquote('0:Rew:5.0,1105.3,761.1,1105.2,2.0,1105.1,4.0,1105.0')] ).
cnf(1107,plain,
( ~ equal(compose(a,compose(b,h)),u)
| ~ equal(compose(compose(a,b),h),u) ),
inference(obv,[status(thm),theory(equality)],[1106]),
[iquote('0:Obv:1106.2')] ).
cnf(1239,plain,
( ~ equal(domain__dfg(h),codomain(b))
| ~ equal(domain__dfg(b),codomain(a))
| ~ equal(compose(a,compose(b,h)),u)
| ~ equal(compose(a,compose(b,h)),u) ),
inference(spl,[status(thm),theory(equality)],[13,1107]),
[iquote('0:SpL:13.2,1107.1')] ).
cnf(1240,plain,
( ~ equal(domain__dfg(h),codomain(b))
| ~ equal(domain__dfg(b),codomain(a))
| ~ equal(compose(a,compose(b,h)),u) ),
inference(obv,[status(thm),theory(equality)],[1239]),
[iquote('0:Obv:1239.2')] ).
cnf(1241,plain,
( ~ equal(domain__dfg(h),codomain(b))
| ~ equal(domain__dfg(b),codomain(a)) ),
inference(aed,[status(thm),theory(equality)],[6,1240]),
[iquote('0:AED:6.0,1240.2')] ).
cnf(1242,plain,
( ~ equal(codomain(b),codomain(b))
| ~ equal(codomain(a),codomain(a)) ),
inference(rew,[status(thm),theory(equality)],[2,1241,3]),
[iquote('0:Rew:2.0,1241.1,3.0,1241.0')] ).
cnf(1243,plain,
$false,
inference(obv,[status(thm),theory(equality)],[1242]),
[iquote('0:Obv:1242.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : CAT003-2 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n022.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
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun May 29 17:19:52 EDT 2022
% 0.13/0.35 % 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 778 clauses, backtracked 0 clauses, performed 0 splits and kept 207 clauses.
% 0.20/0.54 SPASS allocated 64306 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 3, length 30 :
% 0.20/0.54 % SZS output start Refutation
% See solution above
% 0.20/0.54 Formulae used in the proof : endomorphism codomain_of_a_equals_domain_of_b codomain_of_b_equals_domain_of_h codomain_of_b_equals_domain_of_g bh_equals_bg prove_g_equals_h codomain_of_domain_is_domain domain_of_codomain_is_codomain domain_composition codomain_domain2 star_property
% 0.20/0.54
%------------------------------------------------------------------------------