%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : COL031-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 00:42:26 EDT 2022
% Result : Unsatisfiable 0.19s 0.41s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of clauses : 6 ( 6 unt; 0 nHn; 6 RR)
% Number of literals : 6 ( 0 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(apply(apply(l,u),v),apply(u,apply(v,v))),
file('COL031-1.p',unknown),
[] ).
cnf(2,axiom,
equal(apply(apply(o,u),v),apply(v,apply(u,v))),
file('COL031-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(apply(f(u),apply(u,f(u))),apply(u,f(u))),
file('COL031-1.p',unknown),
[] ).
cnf(4,plain,
~ equal(apply(apply(o,u),f(u)),apply(u,f(u))),
inference(rew,[status(thm),theory(equality)],[2,3]),
[iquote('0:Rew:2.0,3.0')] ).
cnf(22,plain,
~ equal(apply(apply(apply(l,o),u),f(apply(u,u))),apply(apply(u,u),f(apply(u,u)))),
inference(spl,[status(thm),theory(equality)],[1,4]),
[iquote('0:SpL:1.0,4.0')] ).
cnf(23,plain,
$false,
inference(obv,[status(thm),theory(equality)],[22]),
[iquote('0:Obv:22.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : COL031-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n026.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 11:29:11 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.41
% 0.19/0.41 SPASS V 3.9
% 0.19/0.41 SPASS beiseite: Proof found.
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.41 SPASS derived 18 clauses, backtracked 0 clauses, performed 0 splits and kept 15 clauses.
% 0.19/0.41 SPASS allocated 63123 KBytes.
% 0.19/0.41 SPASS spent 0:00:00.06 on the problem.
% 0.19/0.41 0:00:00.04 for the input.
% 0.19/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.41 0:00:00.00 for inferences.
% 0.19/0.41 0:00:00.00 for the backtracking.
% 0.19/0.41 0:00:00.00 for the reduction.
% 0.19/0.41
% 0.19/0.41
% 0.19/0.41 Here is a proof with depth 1, length 6 :
% 0.19/0.41 % SZS output start Refutation
% See solution above
% 0.19/0.41 Formulae used in the proof : l_definition o_definition prove_fixed_point
% 0.19/0.41
%------------------------------------------------------------------------------