TSTP Solution File: COL009-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : COL009-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 00:42:23 EDT 2022
% Result : Unsatisfiable 0.20s 0.53s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of clauses : 7 ( 7 unt; 0 nHn; 7 RR)
% Number of literals : 7 ( 0 equ; 2 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; 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('COL009-1.p',unknown),
[] ).
cnf(2,axiom,
equal(apply(apply(l2,u),v),apply(v,apply(u,u))),
file('COL009-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(apply(combinator,u),u),
file('COL009-1.p',unknown),
[] ).
cnf(16,plain,
equal(apply(u,apply(v,apply(w,apply(apply(b,v),w)))),apply(apply(l2,apply(apply(b,v),w)),u)),
inference(spr,[status(thm),theory(equality)],[1,2]),
[iquote('0:SpR:1.0,2.0')] ).
cnf(17,plain,
equal(apply(apply(l2,u),apply(apply(b,v),w)),apply(v,apply(w,apply(u,u)))),
inference(spr,[status(thm),theory(equality)],[1,2]),
[iquote('0:SpR:1.0,2.0')] ).
cnf(539,plain,
~ equal(apply(apply(l2,u),apply(apply(b,combinator),v)),apply(v,apply(u,u))),
inference(spl,[status(thm),theory(equality)],[17,3]),
[iquote('0:SpL:17.0,3.0')] ).
cnf(551,plain,
$false,
inference(unc,[status(thm)],[539,16]),
[iquote('0:UnC:539.0,16.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COL009-1 : TPTP v8.1.0. Released v1.0.0.
% 0.13/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n017.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 14:37:26 EDT 2022
% 0.19/0.34 % CPUTime :
% 0.20/0.53
% 0.20/0.53 SPASS V 3.9
% 0.20/0.53 SPASS beiseite: Proof found.
% 0.20/0.53 % SZS status Theorem
% 0.20/0.53 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.53 SPASS derived 358 clauses, backtracked 0 clauses, performed 0 splits and kept 117 clauses.
% 0.20/0.53 SPASS allocated 64191 KBytes.
% 0.20/0.53 SPASS spent 0:00:00.18 on the problem.
% 0.20/0.53 0:00:00.04 for the input.
% 0.20/0.53 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.53 0:00:00.01 for inferences.
% 0.20/0.53 0:00:00.00 for the backtracking.
% 0.20/0.53 0:00:00.11 for the reduction.
% 0.20/0.53
% 0.20/0.53
% 0.20/0.53 Here is a proof with depth 2, length 7 :
% 0.20/0.53 % SZS output start Refutation
% See solution above
% 0.20/0.53 Formulae used in the proof : b_definition l2_definition prove_fixed_point
% 0.20/0.53
%------------------------------------------------------------------------------