%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : COL049-1 : 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 00:42:29 EDT 2022
% Result : Unsatisfiable 0.92s 1.09s
% Output : Refutation 0.92s
% 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 : 10 ( 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('COL049-1.p',unknown),
[] ).
cnf(2,axiom,
equal(apply(apply(w__dfg,u),v),apply(apply(u,v),v)),
file('COL049-1.p',unknown),
[] ).
cnf(3,axiom,
equal(apply(m,u),apply(u,u)),
file('COL049-1.p',unknown),
[] ).
cnf(4,axiom,
~ equal(apply(f(u),apply(u,f(u))),apply(u,f(u))),
file('COL049-1.p',unknown),
[] ).
cnf(68,plain,
equal(apply(apply(w__dfg,apply(b,u)),v),apply(u,apply(v,v))),
inference(spr,[status(thm),theory(equality)],[1,2]),
[iquote('0:SpR:1.0,2.0')] ).
cnf(72,plain,
~ equal(apply(f(apply(apply(b,u),v)),apply(u,apply(v,f(apply(apply(b,u),v))))),apply(u,apply(v,f(apply(apply(b,u),v))))),
inference(spl,[status(thm),theory(equality)],[1,4]),
[iquote('0:SpL:1.0,4.0')] ).
cnf(93,plain,
equal(apply(apply(w__dfg,apply(b,u)),v),apply(u,apply(m,v))),
inference(spr,[status(thm),theory(equality)],[3,68]),
[iquote('0:SpR:3.0,68.0')] ).
cnf(172,plain,
equal(apply(u,apply(m,apply(w__dfg,apply(b,u)))),apply(m,apply(w__dfg,apply(b,u)))),
inference(spr,[status(thm),theory(equality)],[93,3]),
[iquote('0:SpR:93.0,3.0')] ).
cnf(2579,plain,
~ equal(apply(f(apply(apply(b,apply(apply(b,u),v)),w)),apply(u,apply(v,apply(w,f(apply(apply(b,apply(apply(b,u),v)),w)))))),apply(u,apply(v,apply(w,f(apply(apply(b,apply(apply(b,u),v)),w)))))),
inference(spl,[status(thm),theory(equality)],[1,72]),
[iquote('0:SpL:1.0,72.0')] ).
cnf(2618,plain,
$false,
inference(unc,[status(thm)],[2579,172]),
[iquote('0:UnC:2579.0,172.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COL049-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue May 31 13:16:26 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.92/1.09
% 0.92/1.09 SPASS V 3.9
% 0.92/1.09 SPASS beiseite: Proof found.
% 0.92/1.09 % SZS status Theorem
% 0.92/1.09 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.92/1.09 SPASS derived 1647 clauses, backtracked 0 clauses, performed 0 splits and kept 522 clauses.
% 0.92/1.09 SPASS allocated 66863 KBytes.
% 0.92/1.09 SPASS spent 0:00:00.72 on the problem.
% 0.92/1.09 0:00:00.03 for the input.
% 0.92/1.09 0:00:00.00 for the FLOTTER CNF translation.
% 0.92/1.09 0:00:00.04 for inferences.
% 0.92/1.09 0:00:00.00 for the backtracking.
% 0.92/1.09 0:00:00.62 for the reduction.
% 0.92/1.09
% 0.92/1.09
% 0.92/1.09 Here is a proof with depth 3, length 10 :
% 0.92/1.09 % SZS output start Refutation
% See solution above
% 0.92/1.09 Formulae used in the proof : b_definition w_definition m_definition prove_strong_fixed_point
% 0.92/1.09
%------------------------------------------------------------------------------