TSTP Solution File: CAT018-3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : CAT018-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n032.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 00:07:32 EDT 2022
% Result : Unsatisfiable 0.57s 0.75s
% Output : Refutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 15
% Syntax : Number of clauses : 61 ( 16 unt; 22 nHn; 61 RR)
% Number of literals : 124 ( 0 equ; 40 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 3 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('CAT018-3.p',unknown),
[] ).
cnf(2,axiom,
there_exists(compose(b,c)),
file('CAT018-3.p',unknown),
[] ).
cnf(3,axiom,
~ there_exists(compose(a,compose(b,c))),
file('CAT018-3.p',unknown),
[] ).
cnf(4,axiom,
( ~ equivalent(u,v)
| there_exists(u) ),
file('CAT018-3.p',unknown),
[] ).
cnf(6,axiom,
( ~ there_exists(u)
| ~ equal(u,v)
| equivalent(u,v) ),
file('CAT018-3.p',unknown),
[] ).
cnf(7,axiom,
( ~ there_exists(domain__dfg(u))
| there_exists(u) ),
file('CAT018-3.p',unknown),
[] ).
cnf(8,axiom,
( ~ there_exists(codomain(u))
| there_exists(u) ),
file('CAT018-3.p',unknown),
[] ).
cnf(9,axiom,
( ~ there_exists(compose(u,v))
| there_exists(domain__dfg(u)) ),
file('CAT018-3.p',unknown),
[] ).
cnf(10,axiom,
( ~ there_exists(compose(u,v))
| equal(domain__dfg(u),codomain(v)) ),
file('CAT018-3.p',unknown),
[] ).
cnf(11,axiom,
( ~ there_exists(domain__dfg(u))
| ~ equal(domain__dfg(u),codomain(v))
| there_exists(compose(u,v)) ),
file('CAT018-3.p',unknown),
[] ).
cnf(12,axiom,
equal(compose(compose(u,v),w),compose(u,compose(v,w))),
file('CAT018-3.p',unknown),
[] ).
cnf(13,axiom,
equal(compose(u,domain__dfg(u)),u),
file('CAT018-3.p',unknown),
[] ).
cnf(14,axiom,
equal(compose(codomain(u),u),u),
file('CAT018-3.p',unknown),
[] ).
cnf(18,axiom,
( there_exists(f1(u,v))
| equal(u,v) ),
file('CAT018-3.p',unknown),
[] ).
cnf(19,axiom,
( equal(u,v)
| equal(f1(u,v),v)
| equal(f1(u,v),u) ),
file('CAT018-3.p',unknown),
[] ).
cnf(21,plain,
( ~ there_exists(domain__dfg(a))
| ~ equal(codomain(compose(b,c)),domain__dfg(a)) ),
inference(res,[status(thm),theory(equality)],[11,3]),
[iquote('0:Res:11.2,3.0')] ).
cnf(23,plain,
~ equivalent(compose(a,compose(b,c)),u),
inference(res,[status(thm),theory(equality)],[4,3]),
[iquote('0:Res:4.1,3.0')] ).
cnf(35,plain,
there_exists(domain__dfg(a)),
inference(res,[status(thm),theory(equality)],[1,9]),
[iquote('0:Res:1.0,9.0')] ).
cnf(36,plain,
~ equal(codomain(compose(b,c)),domain__dfg(a)),
inference(mrr,[status(thm)],[21,35]),
[iquote('0:MRR:21.0,35.0')] ).
cnf(39,plain,
( ~ there_exists(u)
| equal(domain__dfg(codomain(u)),codomain(u)) ),
inference(spl,[status(thm),theory(equality)],[14,10]),
[iquote('0:SpL:14.0,10.0')] ).
cnf(40,plain,
( ~ there_exists(u)
| equal(codomain(domain__dfg(u)),domain__dfg(u)) ),
inference(spl,[status(thm),theory(equality)],[13,10]),
[iquote('0:SpL:13.0,10.0')] ).
cnf(42,plain,
equal(codomain(b),domain__dfg(a)),
inference(res,[status(thm),theory(equality)],[1,10]),
[iquote('0:Res:1.0,10.0')] ).
cnf(55,plain,
( ~ there_exists(compose(a,compose(b,c)))
| ~ equal(compose(a,compose(b,c)),u) ),
inference(res,[status(thm),theory(equality)],[6,23]),
[iquote('0:Res:6.2,23.0')] ).
cnf(56,plain,
~ there_exists(compose(a,compose(b,c))),
inference(aed,[status(thm),theory(equality)],[55]),
[iquote('0:AED:55.1')] ).
cnf(79,plain,
equal(compose(u,compose(v,domain__dfg(compose(u,v)))),compose(u,v)),
inference(spr,[status(thm),theory(equality)],[12,13]),
[iquote('0:SpR:12.0,13.0')] ).
cnf(83,plain,
equal(compose(codomain(u),compose(u,v)),compose(u,v)),
inference(spr,[status(thm),theory(equality)],[14,12]),
[iquote('0:SpR:14.0,12.0')] ).
cnf(103,plain,
( equal(u,v)
| equal(f1(u,v),u)
| there_exists(v)
| equal(u,v) ),
inference(spr,[status(thm),theory(equality)],[19,18]),
[iquote('0:SpR:19.1,18.0')] ).
cnf(109,plain,
( equal(f1(u,v),u)
| there_exists(v)
| equal(u,v) ),
inference(obv,[status(thm),theory(equality)],[103]),
[iquote('0:Obv:103.0')] ).
cnf(176,plain,
( ~ there_exists(u)
| ~ there_exists(codomain(u))
| equal(codomain(codomain(u)),codomain(u)) ),
inference(spr,[status(thm),theory(equality)],[39,40]),
[iquote('0:SpR:39.1,40.1')] ).
cnf(179,plain,
( ~ there_exists(codomain(u))
| equal(codomain(codomain(u)),codomain(u)) ),
inference(mrr,[status(thm)],[176,8]),
[iquote('0:MRR:176.0,8.1')] ).
cnf(212,plain,
( ~ there_exists(compose(u,v))
| equal(codomain(compose(u,v)),domain__dfg(codomain(u))) ),
inference(spl,[status(thm),theory(equality)],[83,10]),
[iquote('0:SpL:83.0,10.0')] ).
cnf(352,plain,
( there_exists(u)
| equal(v,u)
| there_exists(v)
| equal(v,u) ),
inference(spr,[status(thm),theory(equality)],[109,18]),
[iquote('0:SpR:109.0,18.0')] ).
cnf(357,plain,
( there_exists(u)
| there_exists(v)
| equal(v,u) ),
inference(obv,[status(thm),theory(equality)],[352]),
[iquote('0:Obv:352.1')] ).
cnf(359,plain,
( equal(u,compose(a,compose(b,c)))
| there_exists(u) ),
inference(sor,[status(thm)],[56,357]),
[iquote('0:SoR:56.0,357.0')] ).
cnf(545,plain,
( there_exists(u)
| equal(u,codomain(v))
| there_exists(v) ),
inference(res,[status(thm),theory(equality)],[357,8]),
[iquote('0:Res:357.0,8.0')] ).
cnf(650,plain,
( there_exists(u)
| equal(compose(a,compose(b,c)),codomain(u)) ),
inference(sor,[status(thm)],[56,545]),
[iquote('0:SoR:56.0,545.0')] ).
cnf(746,plain,
( ~ equivalent(codomain(u),v)
| there_exists(compose(a,compose(b,c)))
| there_exists(u) ),
inference(spl,[status(thm),theory(equality)],[545,23]),
[iquote('0:SpL:545.1,23.0')] ).
cnf(764,plain,
( equal(domain__dfg(u),codomain(v))
| there_exists(v)
| there_exists(u) ),
inference(res,[status(thm),theory(equality)],[545,7]),
[iquote('0:Res:545.0,7.0')] ).
cnf(791,plain,
( ~ equivalent(codomain(u),v)
| there_exists(u) ),
inference(mrr,[status(thm)],[746,56]),
[iquote('0:MRR:746.1,56.0')] ).
cnf(1036,plain,
( there_exists(domain__dfg(u))
| equal(compose(u,compose(a,compose(b,c))),u) ),
inference(spr,[status(thm),theory(equality)],[359,13]),
[iquote('0:SpR:359.0,13.0')] ).
cnf(1078,plain,
( equal(compose(u,v),compose(a,compose(b,c)))
| there_exists(domain__dfg(u)) ),
inference(res,[status(thm),theory(equality)],[359,9]),
[iquote('0:Res:359.1,9.0')] ).
cnf(1087,plain,
( there_exists(domain__dfg(u))
| equal(compose(a,compose(b,c)),u) ),
inference(rew,[status(thm),theory(equality)],[1078,1036]),
[iquote('0:Rew:1078.0,1036.1')] ).
cnf(1759,plain,
( ~ equivalent(domain__dfg(u),v)
| there_exists(w)
| there_exists(u)
| there_exists(w) ),
inference(spl,[status(thm),theory(equality)],[764,791]),
[iquote('0:SpL:764.0,791.0')] ).
cnf(1772,plain,
( ~ equivalent(domain__dfg(u),v)
| there_exists(u)
| there_exists(w) ),
inference(obv,[status(thm),theory(equality)],[1759]),
[iquote('0:Obv:1759.1')] ).
cnf(1773,plain,
( ~ equivalent(domain__dfg(u),v)
| there_exists(u) ),
inference(con,[status(thm)],[1772]),
[iquote('0:Con:1772.2')] ).
cnf(1814,plain,
( ~ there_exists(domain__dfg(u))
| ~ equal(domain__dfg(u),v)
| there_exists(u) ),
inference(res,[status(thm),theory(equality)],[6,1773]),
[iquote('0:Res:6.2,1773.0')] ).
cnf(1819,plain,
( ~ there_exists(domain__dfg(u))
| there_exists(u) ),
inference(aed,[status(thm),theory(equality)],[1814]),
[iquote('0:AED:1814.1')] ).
cnf(2223,plain,
( there_exists(u)
| equal(compose(compose(a,compose(b,c)),u),u) ),
inference(spr,[status(thm),theory(equality)],[650,14]),
[iquote('0:SpR:650.1,14.0')] ).
cnf(2276,plain,
( there_exists(u)
| equal(compose(a,compose(b,compose(c,u))),u) ),
inference(rew,[status(thm),theory(equality)],[12,2223]),
[iquote('0:Rew:12.0,2223.1,12.0,2223.1')] ).
cnf(2532,plain,
( there_exists(domain__dfg(u))
| equal(compose(a,compose(compose(b,c),domain__dfg(u))),u) ),
inference(spr,[status(thm),theory(equality)],[1087,79]),
[iquote('0:SpR:1087.1,79.0')] ).
cnf(2636,plain,
( there_exists(domain__dfg(u))
| equal(compose(a,compose(b,compose(c,domain__dfg(u)))),u) ),
inference(rew,[status(thm),theory(equality)],[12,2532]),
[iquote('0:Rew:12.0,2532.1')] ).
cnf(2637,plain,
( there_exists(domain__dfg(u))
| equal(domain__dfg(u),u) ),
inference(rew,[status(thm),theory(equality)],[2276,2636]),
[iquote('0:Rew:2276.1,2636.1')] ).
cnf(3036,plain,
( there_exists(u)
| equal(domain__dfg(u),u) ),
inference(sor,[status(thm)],[1819,2637]),
[iquote('0:SoR:1819.0,2637.0')] ).
cnf(3267,plain,
( ~ there_exists(codomain(u))
| ~ there_exists(codomain(u))
| equal(domain__dfg(codomain(u)),codomain(u)) ),
inference(spr,[status(thm),theory(equality)],[179,39]),
[iquote('0:SpR:179.1,39.1')] ).
cnf(3313,plain,
( ~ there_exists(codomain(u))
| equal(domain__dfg(codomain(u)),codomain(u)) ),
inference(obv,[status(thm),theory(equality)],[3267]),
[iquote('0:Obv:3267.0')] ).
cnf(3314,plain,
equal(domain__dfg(codomain(u)),codomain(u)),
inference(mrr,[status(thm)],[3313,3036]),
[iquote('0:MRR:3313.0,3036.0')] ).
cnf(3349,plain,
( ~ there_exists(compose(u,v))
| equal(codomain(compose(u,v)),codomain(u)) ),
inference(rew,[status(thm),theory(equality)],[3314,212]),
[iquote('0:Rew:3314.0,212.1')] ).
cnf(4557,plain,
( ~ there_exists(compose(b,c))
| ~ equal(codomain(b),domain__dfg(a)) ),
inference(spl,[status(thm),theory(equality)],[3349,36]),
[iquote('0:SpL:3349.1,36.0')] ).
cnf(4558,plain,
( ~ there_exists(compose(b,c))
| ~ equal(domain__dfg(a),domain__dfg(a)) ),
inference(rew,[status(thm),theory(equality)],[42,4557]),
[iquote('0:Rew:42.0,4557.1')] ).
cnf(4559,plain,
~ there_exists(compose(b,c)),
inference(obv,[status(thm),theory(equality)],[4558]),
[iquote('0:Obv:4558.1')] ).
cnf(4560,plain,
$false,
inference(mrr,[status(thm)],[4559,2]),
[iquote('0:MRR:4559.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : CAT018-3 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.11 % Command : run_spass %d %s
% 0.11/0.31 % Computer : n032.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 600
% 0.11/0.31 % DateTime : Sun May 29 21:12:41 EDT 2022
% 0.11/0.31 % CPUTime :
% 0.57/0.75
% 0.57/0.75 SPASS V 3.9
% 0.57/0.75 SPASS beiseite: Proof found.
% 0.57/0.75 % SZS status Theorem
% 0.57/0.75 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.57/0.75 SPASS derived 3476 clauses, backtracked 0 clauses, performed 0 splits and kept 686 clauses.
% 0.57/0.75 SPASS allocated 78145 KBytes.
% 0.57/0.75 SPASS spent 0:00:00.38 on the problem.
% 0.57/0.75 0:00:00.03 for the input.
% 0.57/0.75 0:00:00.00 for the FLOTTER CNF translation.
% 0.57/0.75 0:00:00.04 for inferences.
% 0.57/0.75 0:00:00.00 for the backtracking.
% 0.57/0.75 0:00:00.29 for the reduction.
% 0.57/0.75
% 0.57/0.75
% 0.57/0.75 Here is a proof with depth 7, length 61 :
% 0.57/0.75 % SZS output start Refutation
% See solution above
% 0.57/0.75 Formulae used in the proof : assume_ab_exists assume_bc_exists prove_a_bc_exists equivalence_implies_existence1 existence_and_equality_implies_equivalence1 domain_has_elements codomain_has_elements composition_implies_domain domain_codomain_composition1 domain_codomain_composition2 associativity_of_compose compose_domain compose_codomain indiscernibles1 indiscernibles2
% 0.57/0.75
%------------------------------------------------------------------------------