%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LDA007-3 : TPTP v8.1.0. Released v1.0.0.
% 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 : Sun Jul 17 16:45:55 EDT 2022
% Result : Unsatisfiable 0.19s 0.42s
% Output : Refutation 0.19s
% 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('LDA007-3.p',unknown),
[] ).
cnf(2,axiom,
equal(f(t,t),tt),
file('LDA007-3.p',unknown),
[] ).
cnf(3,axiom,
equal(f(t,s),ts),
file('LDA007-3.p',unknown),
[] ).
cnf(4,axiom,
equal(f(tt,ts),tt_ts),
file('LDA007-3.p',unknown),
[] ).
cnf(5,axiom,
equal(f(t,k),tk),
file('LDA007-3.p',unknown),
[] ).
cnf(6,axiom,
equal(f(ts,k),tsk),
file('LDA007-3.p',unknown),
[] ).
cnf(7,axiom,
~ equal(f(tt_ts,tk),f(t,tsk)),
file('LDA007-3.p',unknown),
[] ).
cnf(17,plain,
equal(f(f(t,u),tk),f(t,f(u,k))),
inference(spr,[status(thm),theory(equality)],[5,1]),
[iquote('0:SpR:5.0,1.0')] ).
cnf(19,plain,
equal(f(f(t,u),ts),f(t,f(u,s))),
inference(spr,[status(thm),theory(equality)],[3,1]),
[iquote('0:SpR:3.0,1.0')] ).
cnf(81,plain,
equal(f(t,f(t,s)),f(tt,ts)),
inference(spr,[status(thm),theory(equality)],[2,19]),
[iquote('0:SpR:2.0,19.0')] ).
cnf(85,plain,
equal(f(t,ts),tt_ts),
inference(rew,[status(thm),theory(equality)],[3,81,4]),
[iquote('0:Rew:3.0,81.0,4.0,81.0')] ).
cnf(90,plain,
equal(f(t,f(ts,k)),f(tt_ts,tk)),
inference(spr,[status(thm),theory(equality)],[85,17]),
[iquote('0:SpR:85.0,17.0')] ).
cnf(95,plain,
equal(f(tt_ts,tk),f(t,tsk)),
inference(rew,[status(thm),theory(equality)],[6,90]),
[iquote('0:Rew:6.0,90.0')] ).
cnf(96,plain,
$false,
inference(mrr,[status(thm)],[95,7]),
[iquote('0:MRR:95.0,7.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LDA007-3 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n028.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon May 30 03:41:04 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.42
% 0.19/0.42 SPASS V 3.9
% 0.19/0.42 SPASS beiseite: Proof found.
% 0.19/0.42 % SZS status Theorem
% 0.19/0.42 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.42 SPASS derived 69 clauses, backtracked 0 clauses, performed 0 splits and kept 51 clauses.
% 0.19/0.42 SPASS allocated 63224 KBytes.
% 0.19/0.42 SPASS spent 0:00:00.07 on the problem.
% 0.19/0.42 0:00:00.04 for the input.
% 0.19/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.42 0:00:00.00 for inferences.
% 0.19/0.42 0:00:00.00 for the backtracking.
% 0.19/0.42 0:00:00.01 for the reduction.
% 0.19/0.42
% 0.19/0.42
% 0.19/0.42 Here is a proof with depth 3, length 14 :
% 0.19/0.42 % SZS output start Refutation
% See solution above
% 0.19/0.42 Formulae used in the proof : a1 clause_1 clause_2 clause_3 clause_4 clause_5 prove_equation
% 0.19/0.42
%------------------------------------------------------------------------------