TSTP Solution File: COL061-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : COL061-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 00:42:31 EDT 2022
% Result : Unsatisfiable 0.91s 1.13s
% Output : Refutation 0.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of clauses : 10 ( 10 unt; 0 nHn; 10 RR)
% Number of literals : 10 ( 0 equ; 7 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(apply(apply(apply(b,u),v),w),apply(u,apply(v,w))),
file('COL061-1.p',unknown),
[] ).
cnf(2,axiom,
equal(apply(apply(t,u),v),apply(v,u)),
file('COL061-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(apply(apply(apply(u,f(u)),g(u)),h(u)),apply(f(u),apply(h(u),g(u)))),
file('COL061-1.p',unknown),
[] ).
cnf(7,plain,
~ equal(apply(apply(apply(u,apply(v,f(apply(apply(b,u),v)))),g(apply(apply(b,u),v))),h(apply(apply(b,u),v))),apply(f(apply(apply(b,u),v)),apply(h(apply(apply(b,u),v)),g(apply(apply(b,u),v))))),
inference(spl,[status(thm),theory(equality)],[1,3]),
[iquote('0:SpL:1.0,3.0')] ).
cnf(19,plain,
~ equal(apply(apply(apply(apply(u,f(apply(apply(b,apply(t,v)),u))),v),g(apply(apply(b,apply(t,v)),u))),h(apply(apply(b,apply(t,v)),u))),apply(f(apply(apply(b,apply(t,v)),u)),apply(h(apply(apply(b,apply(t,v)),u)),g(apply(apply(b,apply(t,v)),u))))),
inference(spl,[status(thm),theory(equality)],[2,7]),
[iquote('0:SpL:2.0,7.0')] ).
cnf(57,plain,
~ equal(apply(apply(apply(apply(u,apply(v,f(apply(apply(b,apply(t,w)),apply(apply(b,u),v))))),w),g(apply(apply(b,apply(t,w)),apply(apply(b,u),v)))),h(apply(apply(b,apply(t,w)),apply(apply(b,u),v)))),apply(f(apply(apply(b,apply(t,w)),apply(apply(b,u),v))),apply(h(apply(apply(b,apply(t,w)),apply(apply(b,u),v))),g(apply(apply(b,apply(t,w)),apply(apply(b,u),v)))))),
inference(spl,[status(thm),theory(equality)],[1,19]),
[iquote('0:SpL:1.0,19.0')] ).
cnf(260,plain,
~ equal(apply(apply(apply(u,f(apply(apply(b,apply(t,v)),apply(apply(b,b),u)))),apply(v,g(apply(apply(b,apply(t,v)),apply(apply(b,b),u))))),h(apply(apply(b,apply(t,v)),apply(apply(b,b),u)))),apply(f(apply(apply(b,apply(t,v)),apply(apply(b,b),u))),apply(h(apply(apply(b,apply(t,v)),apply(apply(b,b),u))),g(apply(apply(b,apply(t,v)),apply(apply(b,b),u)))))),
inference(spl,[status(thm),theory(equality)],[1,57]),
[iquote('0:SpL:1.0,57.0')] ).
cnf(512,plain,
~ equal(apply(f(apply(apply(b,apply(t,u)),apply(apply(b,b),b))),apply(apply(u,g(apply(apply(b,apply(t,u)),apply(apply(b,b),b)))),h(apply(apply(b,apply(t,u)),apply(apply(b,b),b))))),apply(f(apply(apply(b,apply(t,u)),apply(apply(b,b),b))),apply(h(apply(apply(b,apply(t,u)),apply(apply(b,b),b))),g(apply(apply(b,apply(t,u)),apply(apply(b,b),b)))))),
inference(spl,[status(thm),theory(equality)],[1,260]),
[iquote('0:SpL:1.0,260.0')] ).
cnf(515,plain,
~ equal(apply(f(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),b))))),apply(f(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),b)))))),
inference(spl,[status(thm),theory(equality)],[2,512]),
[iquote('0:SpL:2.0,512.0')] ).
cnf(517,plain,
$false,
inference(obv,[status(thm),theory(equality)],[515]),
[iquote('0:Obv:515.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COL061-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue May 31 08:23:41 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.91/1.13
% 0.91/1.13 SPASS V 3.9
% 0.91/1.13 SPASS beiseite: Proof found.
% 0.91/1.13 % SZS status Theorem
% 0.91/1.13 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.91/1.13 SPASS derived 513 clauses, backtracked 0 clauses, performed 0 splits and kept 411 clauses.
% 0.91/1.13 SPASS allocated 69874 KBytes.
% 0.91/1.13 SPASS spent 0:00:00.76 on the problem.
% 0.91/1.13 0:00:00.03 for the input.
% 0.91/1.13 0:00:00.00 for the FLOTTER CNF translation.
% 0.91/1.13 0:00:00.15 for inferences.
% 0.91/1.13 0:00:00.00 for the backtracking.
% 0.91/1.13 0:00:00.53 for the reduction.
% 0.91/1.13
% 0.91/1.13
% 0.91/1.13 Here is a proof with depth 6, length 10 :
% 0.91/1.13 % SZS output start Refutation
% See solution above
% 0.91/1.13 Formulae used in the proof : b_definition t_definition prove_q1_combinator
% 0.91/1.13
%------------------------------------------------------------------------------