%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET031-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 : Tue Jul 19 05:22:53 EDT 2022
% Result : Unsatisfiable 1.37s 1.56s
% Output : Refutation 1.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of clauses : 13 ( 3 unt; 2 nHn; 13 RR)
% Number of literals : 28 ( 0 equ; 14 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ relation(compose(a,b)),
file('SET031-4.p',unknown),
[] ).
cnf(15,axiom,
( ~ little_set(u)
| ~ little_set(v)
| ~ equal(w,ordered_pair(v,u))
| ordered_pair_predicate(w) ),
file('SET031-4.p',unknown),
[] ).
cnf(78,axiom,
( relation(u)
| member(f18(u),u) ),
file('SET031-4.p',unknown),
[] ).
cnf(79,axiom,
( ~ ordered_pair_predicate(f18(u))
| relation(u) ),
file('SET031-4.p',unknown),
[] ).
cnf(129,axiom,
( ~ member(u,compose(v,w))
| little_set(f29(u,v,w)) ),
file('SET031-4.p',unknown),
[] ).
cnf(130,axiom,
( ~ member(u,compose(v,w))
| little_set(f30(u,v,w)) ),
file('SET031-4.p',unknown),
[] ).
cnf(132,axiom,
( ~ member(u,compose(v,w))
| equal(ordered_pair(f29(u,v,w),f30(u,v,w)),u) ),
file('SET031-4.p',unknown),
[] ).
cnf(3697,plain,
( ~ little_set(u)
| ~ little_set(v)
| ordered_pair_predicate(ordered_pair(v,u)) ),
inference(eqr,[status(thm),theory(equality)],[15]),
[iquote('0:EqR:15.2')] ).
cnf(5761,plain,
( ~ little_set(f30(u,v,w))
| ~ little_set(f29(u,v,w))
| ~ member(u,compose(v,w))
| ordered_pair_predicate(u) ),
inference(spr,[status(thm),theory(equality)],[132,3697]),
[iquote('0:SpR:132.1,3697.2')] ).
cnf(5769,plain,
( ~ member(u,compose(v,w))
| ordered_pair_predicate(u) ),
inference(mrr,[status(thm)],[5761,130,129]),
[iquote('0:MRR:5761.0,5761.1,130.1,129.1')] ).
cnf(6394,plain,
( relation(compose(u,v))
| ordered_pair_predicate(f18(compose(u,v))) ),
inference(res,[status(thm),theory(equality)],[78,5769]),
[iquote('0:Res:78.1,5769.0')] ).
cnf(6427,plain,
relation(compose(u,v)),
inference(mrr,[status(thm)],[6394,79]),
[iquote('0:MRR:6394.1,79.0')] ).
cnf(6428,plain,
$false,
inference(unc,[status(thm)],[6427,1]),
[iquote('0:UnC:6427.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET031-4 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sat Jul 9 22:40:26 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.37/1.56
% 1.37/1.56 SPASS V 3.9
% 1.37/1.56 SPASS beiseite: Proof found.
% 1.37/1.56 % SZS status Theorem
% 1.37/1.56 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.37/1.56 SPASS derived 5009 clauses, backtracked 687 clauses, performed 8 splits and kept 3124 clauses.
% 1.37/1.56 SPASS allocated 81098 KBytes.
% 1.37/1.56 SPASS spent 0:00:01.17 on the problem.
% 1.37/1.56 0:00:00.04 for the input.
% 1.37/1.56 0:00:00.00 for the FLOTTER CNF translation.
% 1.37/1.56 0:00:00.06 for inferences.
% 1.37/1.56 0:00:00.05 for the backtracking.
% 1.37/1.56 0:00:00.96 for the reduction.
% 1.37/1.56
% 1.37/1.56
% 1.37/1.56 Here is a proof with depth 3, length 13 :
% 1.37/1.56 % SZS output start Refutation
% See solution above
% 1.37/1.56 Formulae used in the proof : prove_composition_is_a_relation ordered_pair_predicate4 relation2 relation3 compose1 compose2 compose4
% 1.37/1.56
%------------------------------------------------------------------------------