%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : COL030-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 0.47s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of clauses : 7 ( 7 unt; 0 nHn; 7 RR)
% Number of literals : 7 ( 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 : 7 ( 7 usr; 5 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('COL030-1.p',unknown),
[] ).
cnf(2,axiom,
equal(apply(apply(l,u),v),apply(u,apply(v,v))),
file('COL030-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(apply(f(u),apply(u,f(u))),apply(u,f(u))),
file('COL030-1.p',unknown),
[] ).
cnf(48,plain,
equal(apply(u,apply(apply(apply(s,v),v),w)),apply(apply(l,u),apply(v,w))),
inference(spr,[status(thm),theory(equality)],[1,2]),
[iquote('0:SpR:1.0,2.0')] ).
cnf(238,plain,
~ equal(apply(apply(l,f(apply(apply(s,u),u))),apply(u,f(apply(apply(s,u),u)))),apply(apply(apply(s,u),u),f(apply(apply(s,u),u)))),
inference(spl,[status(thm),theory(equality)],[48,3]),
[iquote('0:SpL:48.0,3.0')] ).
cnf(248,plain,
~ equal(apply(apply(apply(s,l),u),f(apply(apply(s,u),u))),apply(apply(apply(s,u),u),f(apply(apply(s,u),u)))),
inference(rew,[status(thm),theory(equality)],[1,238]),
[iquote('0:Rew:1.0,238.0')] ).
cnf(249,plain,
$false,
inference(obv,[status(thm),theory(equality)],[248]),
[iquote('0:Obv:248.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COL030-1 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n024.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 09:07:36 EDT 2022
% 0.19/0.34 % CPUTime :
% 0.19/0.47
% 0.19/0.47 SPASS V 3.9
% 0.19/0.47 SPASS beiseite: Proof found.
% 0.19/0.47 % SZS status Theorem
% 0.19/0.47 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.47 SPASS derived 174 clauses, backtracked 0 clauses, performed 0 splits and kept 84 clauses.
% 0.19/0.47 SPASS allocated 63742 KBytes.
% 0.19/0.47 SPASS spent 0:00:00.12 on the problem.
% 0.19/0.47 0:00:00.03 for the input.
% 0.19/0.47 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.47 0:00:00.01 for inferences.
% 0.19/0.47 0:00:00.00 for the backtracking.
% 0.19/0.47 0:00:00.06 for the reduction.
% 0.19/0.47
% 0.19/0.47
% 0.19/0.47 Here is a proof with depth 2, length 7 :
% 0.19/0.47 % SZS output start Refutation
% See solution above
% 0.19/0.47 Formulae used in the proof : s_definition l_definition prove_fixed_point
% 0.19/0.47
%------------------------------------------------------------------------------