TSTP Solution File: COL035-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : COL035-1 : TPTP v8.1.0. Released v1.0.0.
% 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 00:42:27 EDT 2022
% Result : Unsatisfiable 1.27s 1.45s
% Output : Refutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of clauses : 9 ( 9 unt; 0 nHn; 9 RR)
% Number of literals : 9 ( 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 : 8 ( 8 usr; 6 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('COL035-1.p',unknown),
[] ).
cnf(2,axiom,
equal(apply(apply(w__dfg,u),v),apply(apply(u,v),v)),
file('COL035-1.p',unknown),
[] ).
cnf(3,axiom,
equal(apply(apply(apply(q,u),v),w),apply(v,apply(u,w))),
file('COL035-1.p',unknown),
[] ).
cnf(4,axiom,
~ equal(apply(f(u),apply(u,f(u))),apply(u,f(u))),
file('COL035-1.p',unknown),
[] ).
cnf(49,plain,
equal(apply(apply(w__dfg,apply(q,u)),v),apply(v,apply(u,v))),
inference(spr,[status(thm),theory(equality)],[3,2]),
[iquote('0:SpR:3.0,2.0')] ).
cnf(54,plain,
equal(apply(apply(l,apply(apply(q,u),v)),w),apply(v,apply(u,apply(w,w)))),
inference(spr,[status(thm),theory(equality)],[3,1]),
[iquote('0:SpR:3.0,1.0')] ).
cnf(112,plain,
~ equal(apply(apply(w__dfg,apply(q,u)),f(u)),apply(u,f(u))),
inference(spl,[status(thm),theory(equality)],[49,4]),
[iquote('0:SpL:49.0,4.0')] ).
cnf(2911,plain,
~ equal(apply(apply(apply(l,apply(apply(q,q),w__dfg)),u),f(apply(u,u))),apply(apply(u,u),f(apply(u,u)))),
inference(spl,[status(thm),theory(equality)],[54,112]),
[iquote('0:SpL:54.0,112.0')] ).
cnf(2971,plain,
$false,
inference(obv,[status(thm),theory(equality)],[2911]),
[iquote('0:Obv:2911.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : COL035-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n021.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 09:40:44 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.27/1.45
% 1.27/1.45 SPASS V 3.9
% 1.27/1.45 SPASS beiseite: Proof found.
% 1.27/1.45 % SZS status Theorem
% 1.27/1.45 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.27/1.45 SPASS derived 1698 clauses, backtracked 0 clauses, performed 0 splits and kept 686 clauses.
% 1.27/1.45 SPASS allocated 68714 KBytes.
% 1.27/1.45 SPASS spent 0:00:01.08 on the problem.
% 1.27/1.45 0:00:00.03 for the input.
% 1.27/1.45 0:00:00.00 for the FLOTTER CNF translation.
% 1.27/1.45 0:00:00.04 for inferences.
% 1.27/1.45 0:00:00.00 for the backtracking.
% 1.27/1.45 0:00:00.98 for the reduction.
% 1.27/1.45
% 1.27/1.45
% 1.27/1.45 Here is a proof with depth 3, length 9 :
% 1.27/1.45 % SZS output start Refutation
% See solution above
% 1.27/1.45 Formulae used in the proof : l_definition w_definition q_definition prove_fixed_point
% 1.27/1.45
%------------------------------------------------------------------------------