%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : COL061-2 : TPTP v8.1.0. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 00:42:31 EDT 2022
% Result : Unsatisfiable 0.20s 0.45s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 3
% Syntax : Number of clauses : 5 ( 5 unt; 0 nHn; 5 RR)
% Number of literals : 5 ( 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 : 9 ( 9 usr; 8 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('COL061-2.p',unknown),
[] ).
cnf(2,axiom,
equal(apply(apply(t,u),v),apply(v,u)),
file('COL061-2.p',unknown),
[] ).
cnf(3,axiom,
~ equal(apply(apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x__dfg),y__dfg),z__dfg),apply(x__dfg,apply(z__dfg,y__dfg))),
file('COL061-2.p',unknown),
[] ).
cnf(4,plain,
~ equal(apply(x__dfg,apply(z__dfg,y__dfg)),apply(x__dfg,apply(z__dfg,y__dfg))),
inference(rew,[status(thm),theory(equality)],[2,3,1]),
[iquote('0:Rew:2.0,3.0,1.0,3.0,1.0,3.0,2.0,3.0,1.0,3.0,1.0,3.0')] ).
cnf(5,plain,
$false,
inference(obv,[status(thm),theory(equality)],[4]),
[iquote('0:Obv:4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.16 % Problem : COL061-2 : TPTP v8.1.0. Bugfixed v1.2.0.
% 0.03/0.17 % Command : run_spass %d %s
% 0.13/0.38 % Computer : n021.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8042.1875MB
% 0.13/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 600
% 0.13/0.38 % DateTime : Tue May 31 16:03:30 EDT 2022
% 0.13/0.38 % CPUTime :
% 0.20/0.45
% 0.20/0.45 SPASS V 3.9
% 0.20/0.45 SPASS beiseite: Proof found.
% 0.20/0.45 % SZS status Theorem
% 0.20/0.45 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.45 SPASS derived 0 clauses, backtracked 0 clauses, performed 0 splits and kept 3 clauses.
% 0.20/0.45 SPASS allocated 63088 KBytes.
% 0.20/0.45 SPASS spent 0:00:00.06 on the problem.
% 0.20/0.45 0:00:00.03 for the input.
% 0.20/0.45 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.45 0:00:00.00 for inferences.
% 0.20/0.45 0:00:00.00 for the backtracking.
% 0.20/0.45 0:00:00.00 for the reduction.
% 0.20/0.45
% 0.20/0.45
% 0.20/0.45 Here is a proof with depth 0, length 5 :
% 0.20/0.45 % SZS output start Refutation
% See solution above
% 0.20/0.45 Formulae used in the proof : b_definition t_definition prove_q1_combinator
% 0.20/0.45
%------------------------------------------------------------------------------