TSTP Solution File: COL039-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : COL039-1 : 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 00:42:27 EDT 2022
% Result : Unsatisfiable 0.15s 0.43s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of clauses : 8 ( 8 unt; 0 nHn; 8 RR)
% Number of literals : 8 ( 0 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 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('COL039-1.p',unknown),
[] ).
cnf(2,axiom,
equal(apply(m,u),apply(u,u)),
file('COL039-1.p',unknown),
[] ).
cnf(3,axiom,
equal(apply(apply(o,u),v),apply(v,apply(u,v))),
file('COL039-1.p',unknown),
[] ).
cnf(4,axiom,
~ equal(apply(f(u),apply(u,f(u))),apply(u,f(u))),
file('COL039-1.p',unknown),
[] ).
cnf(5,plain,
~ equal(apply(apply(o,u),f(u)),apply(u,f(u))),
inference(rew,[status(thm),theory(equality)],[3,4]),
[iquote('0:Rew:3.0,4.0')] ).
cnf(60,plain,
equal(apply(u,apply(v,apply(apply(b,u),v))),apply(m,apply(apply(b,u),v))),
inference(spr,[status(thm),theory(equality)],[1,2]),
[iquote('0:SpR:1.0,2.0')] ).
cnf(537,plain,
~ equal(apply(apply(m,apply(apply(b,o),u)),f(apply(u,apply(apply(b,o),u)))),apply(apply(u,apply(apply(b,o),u)),f(apply(u,apply(apply(b,o),u))))),
inference(spl,[status(thm),theory(equality)],[60,5]),
[iquote('0:SpL:60.0,5.0')] ).
cnf(574,plain,
$false,
inference(obv,[status(thm),theory(equality)],[537]),
[iquote('0:Obv:537.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : COL039-1 : TPTP v8.1.0. Released v1.0.0.
% 0.09/0.11 % Command : run_spass %d %s
% 0.11/0.30 % Computer : n032.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 600
% 0.11/0.30 % DateTime : Tue May 31 11:51:58 EDT 2022
% 0.11/0.30 % CPUTime :
% 0.15/0.43
% 0.15/0.43 SPASS V 3.9
% 0.15/0.43 SPASS beiseite: Proof found.
% 0.15/0.43 % SZS status Theorem
% 0.15/0.43 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.43 SPASS derived 330 clauses, backtracked 0 clauses, performed 0 splits and kept 97 clauses.
% 0.15/0.43 SPASS allocated 64045 KBytes.
% 0.15/0.43 SPASS spent 0:00:00.11 on the problem.
% 0.15/0.43 0:00:00.03 for the input.
% 0.15/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.15/0.43 0:00:00.01 for inferences.
% 0.15/0.43 0:00:00.00 for the backtracking.
% 0.15/0.43 0:00:00.06 for the reduction.
% 0.15/0.43
% 0.15/0.43
% 0.15/0.43 Here is a proof with depth 2, length 8 :
% 0.15/0.43 % SZS output start Refutation
% See solution above
% 0.15/0.43 Formulae used in the proof : b_definition m_definition o_definition prove_fixed_point
% 0.15/0.43
%------------------------------------------------------------------------------