TSTP Solution File: COL075-2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : COL075-2 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 00:42:35 EDT 2022
% Result : Unsatisfiable 0.20s 0.43s
% Output : Refutation 0.20s
% 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; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(apply(apply(k,u),v),u),
file('COL075-2.p',unknown),
[] ).
cnf(2,axiom,
equal(apply(apply(u,apply(k,v)),apply(w,v)),apply(apply(apply(abstraction,u),w),v)),
file('COL075-2.p',unknown),
[] ).
cnf(3,axiom,
~ equal(apply(apply(u,b(u)),c(u)),apply(b(u),b(u))),
file('COL075-2.p',unknown),
[] ).
cnf(11,plain,
equal(apply(apply(apply(abstraction,u),apply(k,v)),w),apply(apply(u,apply(k,w)),v)),
inference(spr,[status(thm),theory(equality)],[1,2]),
[iquote('0:SpR:1.0,2.0')] ).
cnf(75,plain,
equal(apply(apply(apply(apply(abstraction,abstraction),k),u),v),apply(apply(apply(k,u),apply(k,v)),u)),
inference(spr,[status(thm),theory(equality)],[2,11]),
[iquote('0:SpR:2.0,11.0')] ).
cnf(82,plain,
equal(apply(apply(apply(apply(abstraction,abstraction),k),u),v),apply(u,u)),
inference(rew,[status(thm),theory(equality)],[1,75]),
[iquote('0:Rew:1.0,75.0')] ).
cnf(83,plain,
$false,
inference(unc,[status(thm)],[82,3]),
[iquote('0:UnC:82.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : COL075-2 : TPTP v8.1.0. Released v1.2.0.
% 0.11/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n028.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Tue May 31 12:27:21 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.20/0.43
% 0.20/0.43 SPASS V 3.9
% 0.20/0.43 SPASS beiseite: Proof found.
% 0.20/0.43 % SZS status Theorem
% 0.20/0.43 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.43 SPASS derived 58 clauses, backtracked 0 clauses, performed 0 splits and kept 46 clauses.
% 0.20/0.43 SPASS allocated 63335 KBytes.
% 0.20/0.43 SPASS spent 0:00:00.07 on the problem.
% 0.20/0.43 0:00:00.03 for the input.
% 0.20/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.43 0:00:00.00 for inferences.
% 0.20/0.43 0:00:00.00 for the backtracking.
% 0.20/0.43 0:00:00.01 for the reduction.
% 0.20/0.43
% 0.20/0.43
% 0.20/0.43 Here is a proof with depth 2, length 7 :
% 0.20/0.43 % SZS output start Refutation
% See solution above
% 0.20/0.43 Formulae used in the proof : k_definition abstraction prove_diagonal_combinator
% 0.20/0.43
%------------------------------------------------------------------------------