TSTP Solution File: COL057-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : COL057-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 00:42:30 EDT 2022
% Result : Unsatisfiable 0.51s 0.73s
% Output : Refutation 0.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of clauses : 10 ( 10 unt; 0 nHn; 10 RR)
% Number of literals : 10 ( 0 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 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(s,u),v),w),apply(apply(u,w),apply(v,w))),
file('COL057-1.p',unknown),
[] ).
cnf(2,axiom,
equal(apply(apply(apply(b,u),v),w),apply(u,apply(v,w))),
file('COL057-1.p',unknown),
[] ).
cnf(4,axiom,
equal(apply(i,u),u),
file('COL057-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(apply(f(u),apply(u,f(u))),apply(u,f(u))),
file('COL057-1.p',unknown),
[] ).
cnf(23,plain,
equal(apply(apply(apply(s,u),i),v),apply(apply(u,v),v)),
inference(spr,[status(thm),theory(equality)],[4,1]),
[iquote('0:SpR:4.0,1.0')] ).
cnf(26,plain,
equal(apply(apply(apply(s,i),u),v),apply(v,apply(u,v))),
inference(spr,[status(thm),theory(equality)],[4,1]),
[iquote('0:SpR:4.0,1.0')] ).
cnf(42,plain,
equal(apply(apply(apply(s,apply(b,u)),i),v),apply(u,apply(v,v))),
inference(spr,[status(thm),theory(equality)],[23,2]),
[iquote('0:SpR:23.0,2.0')] ).
cnf(107,plain,
~ equal(apply(apply(apply(s,i),u),f(u)),apply(u,f(u))),
inference(spl,[status(thm),theory(equality)],[26,5]),
[iquote('0:SpL:26.0,5.0')] ).
cnf(643,plain,
~ equal(apply(apply(apply(apply(s,apply(b,apply(s,i))),i),u),f(apply(u,u))),apply(apply(u,u),f(apply(u,u)))),
inference(spl,[status(thm),theory(equality)],[42,107]),
[iquote('0:SpL:42.0,107.0')] ).
cnf(700,plain,
$false,
inference(obv,[status(thm),theory(equality)],[643]),
[iquote('0:Obv:643.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COL057-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n025.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 09:44:28 EDT 2022
% 0.12/0.35 % CPUTime :
% 0.51/0.73
% 0.51/0.73 SPASS V 3.9
% 0.51/0.73 SPASS beiseite: Proof found.
% 0.51/0.73 % SZS status Theorem
% 0.51/0.73 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.51/0.73 SPASS derived 511 clauses, backtracked 0 clauses, performed 0 splits and kept 362 clauses.
% 0.51/0.73 SPASS allocated 64735 KBytes.
% 0.51/0.73 SPASS spent 0:00:00.37 on the problem.
% 0.51/0.73 0:00:00.04 for the input.
% 0.51/0.73 0:00:00.00 for the FLOTTER CNF translation.
% 0.51/0.73 0:00:00.01 for inferences.
% 0.51/0.73 0:00:00.00 for the backtracking.
% 0.51/0.73 0:00:00.30 for the reduction.
% 0.51/0.73
% 0.51/0.73
% 0.51/0.73 Here is a proof with depth 3, length 10 :
% 0.51/0.73 % SZS output start Refutation
% See solution above
% 0.51/0.73 Formulae used in the proof : s_definition b_definition i_definition prove_strong_fixed_point
% 0.51/0.73
%------------------------------------------------------------------------------