TSTP Solution File: LDA007-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LDA007-2 : TPTP v8.1.0. Bugfixed v2.6.0.
% 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 : Sun Jul 17 16:45:55 EDT 2022
% Result : Unsatisfiable 0.14s 0.46s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of clauses : 14 ( 14 unt; 0 nHn; 14 RR)
% Number of literals : 14 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 11 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(f(f(u,v),f(u,w)),f(u,f(v,w))),
file('LDA007-2.p',unknown),
[] ).
cnf(10,axiom,
equal(f(t,t),tt),
file('LDA007-2.p',unknown),
[] ).
cnf(12,axiom,
equal(f(t,s),ts),
file('LDA007-2.p',unknown),
[] ).
cnf(13,axiom,
equal(f(tt,ts),tt_ts),
file('LDA007-2.p',unknown),
[] ).
cnf(16,axiom,
equal(f(t,k),tk),
file('LDA007-2.p',unknown),
[] ).
cnf(18,axiom,
equal(f(ts,k),tsk),
file('LDA007-2.p',unknown),
[] ).
cnf(20,axiom,
~ equal(f(tt_ts,tk),f(t,tsk)),
file('LDA007-2.p',unknown),
[] ).
cnf(167,plain,
equal(f(f(t,u),tk),f(t,f(u,k))),
inference(spr,[status(thm),theory(equality)],[16,1]),
[iquote('0:SpR:16.0,1.0')] ).
cnf(170,plain,
equal(f(f(t,u),ts),f(t,f(u,s))),
inference(spr,[status(thm),theory(equality)],[12,1]),
[iquote('0:SpR:12.0,1.0')] ).
cnf(942,plain,
equal(f(t,f(t,s)),f(tt,ts)),
inference(spr,[status(thm),theory(equality)],[10,170]),
[iquote('0:SpR:10.0,170.0')] ).
cnf(945,plain,
equal(f(t,ts),tt_ts),
inference(rew,[status(thm),theory(equality)],[12,942,13]),
[iquote('0:Rew:12.0,942.0,13.0,942.0')] ).
cnf(958,plain,
equal(f(t,f(ts,k)),f(tt_ts,tk)),
inference(spr,[status(thm),theory(equality)],[945,167]),
[iquote('0:SpR:945.0,167.0')] ).
cnf(962,plain,
equal(f(tt_ts,tk),f(t,tsk)),
inference(rew,[status(thm),theory(equality)],[18,958]),
[iquote('0:Rew:18.0,958.0')] ).
cnf(963,plain,
$false,
inference(mrr,[status(thm)],[962,20]),
[iquote('0:MRR:962.0,20.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : LDA007-2 : TPTP v8.1.0. Bugfixed v2.6.0.
% 0.05/0.09 % Command : run_spass %d %s
% 0.08/0.29 % Computer : n024.cluster.edu
% 0.08/0.29 % Model : x86_64 x86_64
% 0.08/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.29 % Memory : 8042.1875MB
% 0.08/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.29 % CPULimit : 300
% 0.08/0.29 % WCLimit : 600
% 0.08/0.29 % DateTime : Mon May 30 04:28:06 EDT 2022
% 0.08/0.29 % CPUTime :
% 0.14/0.46
% 0.14/0.46 SPASS V 3.9
% 0.14/0.46 SPASS beiseite: Proof found.
% 0.14/0.46 % SZS status Theorem
% 0.14/0.46 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.46 SPASS derived 776 clauses, backtracked 0 clauses, performed 6 splits and kept 510 clauses.
% 0.14/0.46 SPASS allocated 64057 KBytes.
% 0.14/0.46 SPASS spent 0:00:00.16 on the problem.
% 0.14/0.46 0:00:00.03 for the input.
% 0.14/0.46 0:00:00.00 for the FLOTTER CNF translation.
% 0.14/0.46 0:00:00.01 for inferences.
% 0.14/0.46 0:00:00.00 for the backtracking.
% 0.14/0.46 0:00:00.09 for the reduction.
% 0.14/0.46
% 0.14/0.46
% 0.14/0.46 Here is a proof with depth 3, length 14 :
% 0.14/0.46 % SZS output start Refutation
% See solution above
% 0.14/0.46 Formulae used in the proof : a1 clause_1 clause_3 clause_4 clause_7 clause_9 prove_equation
% 0.14/0.46
%------------------------------------------------------------------------------