TSTP Solution File: COL036-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : COL036-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 0.18s 0.48s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of clauses : 10 ( 10 unt; 0 nHn; 10 RR)
% Number of literals : 10 ( 0 equ; 2 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('COL036-1.p',unknown),
[] ).
cnf(2,axiom,
equal(apply(apply(apply(b,u),v),w),apply(u,apply(v,w))),
file('COL036-1.p',unknown),
[] ).
cnf(3,axiom,
equal(apply(apply(t,u),v),apply(v,u)),
file('COL036-1.p',unknown),
[] ).
cnf(4,axiom,
~ equal(apply(f(u),apply(u,f(u))),apply(u,f(u))),
file('COL036-1.p',unknown),
[] ).
cnf(8,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)],[2,4]),
[iquote('0:SpL:2.0,4.0')] ).
cnf(12,plain,
equal(apply(apply(apply(s,t),u),v),apply(apply(u,v),v)),
inference(spr,[status(thm),theory(equality)],[1,3]),
[iquote('0:SpR:1.0,3.0')] ).
cnf(37,plain,
equal(apply(apply(apply(s,t),apply(b,u)),v),apply(u,apply(v,v))),
inference(spr,[status(thm),theory(equality)],[12,2]),
[iquote('0:SpR:12.0,2.0')] ).
cnf(150,plain,
equal(apply(u,apply(apply(v,apply(b,u)),apply(v,apply(b,u)))),apply(apply(apply(s,apply(s,t)),v),apply(b,u))),
inference(spr,[status(thm),theory(equality)],[37,1]),
[iquote('0:SpR:37.0,1.0')] ).
cnf(223,plain,
equal(apply(u,apply(apply(apply(s,v),v),apply(b,u))),apply(apply(apply(s,apply(s,t)),v),apply(b,u))),
inference(rew,[status(thm),theory(equality)],[1,150]),
[iquote('0:Rew:1.0,150.0')] ).
cnf(224,plain,
$false,
inference(unc,[status(thm)],[223,8]),
[iquote('0:UnC:223.0,8.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COL036-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue May 31 04:56:23 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.18/0.48
% 0.18/0.48 SPASS V 3.9
% 0.18/0.48 SPASS beiseite: Proof found.
% 0.18/0.48 % SZS status Theorem
% 0.18/0.48 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.48 SPASS derived 159 clauses, backtracked 0 clauses, performed 0 splits and kept 109 clauses.
% 0.18/0.48 SPASS allocated 63598 KBytes.
% 0.18/0.48 SPASS spent 0:00:00.13 on the problem.
% 0.18/0.48 0:00:00.04 for the input.
% 0.18/0.48 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.48 0:00:00.01 for inferences.
% 0.18/0.48 0:00:00.00 for the backtracking.
% 0.18/0.48 0:00:00.06 for the reduction.
% 0.18/0.48
% 0.18/0.48
% 0.18/0.48 Here is a proof with depth 3, length 10 :
% 0.18/0.48 % SZS output start Refutation
% See solution above
% 0.18/0.48 Formulae used in the proof : s_definition b_definition t_definition prove_fixed_point
% 0.18/0.48
%------------------------------------------------------------------------------