TSTP Solution File: KLE085+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE085+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n010.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 02:28:26 EDT 2022
% Result : Theorem 0.21s 0.42s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of clauses : 12 ( 12 unt; 0 nHn; 12 RR)
% Number of literals : 12 ( 0 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 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(2,axiom,
equal(addition(u,u),u),
file('KLE085+1.p',unknown),
[] ).
cnf(8,axiom,
equal(antidomain(antidomain(u)),domain__dfg(u)),
file('KLE085+1.p',unknown),
[] ).
cnf(11,axiom,
~ equal(addition(domain__dfg(skc1),one),one),
file('KLE085+1.p',unknown),
[] ).
cnf(12,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE085+1.p',unknown),
[] ).
cnf(13,axiom,
equal(addition(antidomain(antidomain(u)),antidomain(u)),one),
file('KLE085+1.p',unknown),
[] ).
cnf(17,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE085+1.p',unknown),
[] ).
cnf(23,plain,
~ equal(addition(one,domain__dfg(skc1)),one),
inference(rew,[status(thm),theory(equality)],[12,11]),
[iquote('0:Rew:12.0,11.0')] ).
cnf(25,plain,
equal(addition(domain__dfg(u),antidomain(u)),one),
inference(rew,[status(thm),theory(equality)],[8,13]),
[iquote('0:Rew:8.0,13.0')] ).
cnf(277,plain,
equal(addition(u,addition(u,v)),addition(u,v)),
inference(spr,[status(thm),theory(equality)],[2,17]),
[iquote('0:SpR:2.0,17.0')] ).
cnf(333,plain,
equal(addition(domain__dfg(u),one),one),
inference(spr,[status(thm),theory(equality)],[25,277]),
[iquote('0:SpR:25.0,277.0')] ).
cnf(343,plain,
equal(addition(one,domain__dfg(u)),one),
inference(rew,[status(thm),theory(equality)],[12,333]),
[iquote('0:Rew:12.0,333.0')] ).
cnf(344,plain,
$false,
inference(unc,[status(thm)],[343,23]),
[iquote('0:UnC:343.0,23.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : KLE085+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n010.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Thu Jun 16 15:47:38 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.21/0.42
% 0.21/0.42 SPASS V 3.9
% 0.21/0.42 SPASS beiseite: Proof found.
% 0.21/0.42 % SZS status Theorem
% 0.21/0.42 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.42 SPASS derived 253 clauses, backtracked 0 clauses, performed 0 splits and kept 99 clauses.
% 0.21/0.42 SPASS allocated 85346 KBytes.
% 0.21/0.42 SPASS spent 0:00:00.07 on the problem.
% 0.21/0.42 0:00:00.02 for the input.
% 0.21/0.42 0:00:00.02 for the FLOTTER CNF translation.
% 0.21/0.42 0:00:00.00 for inferences.
% 0.21/0.42 0:00:00.00 for the backtracking.
% 0.21/0.42 0:00:00.01 for the reduction.
% 0.21/0.42
% 0.21/0.42
% 0.21/0.42 Here is a proof with depth 2, length 12 :
% 0.21/0.42 % SZS output start Refutation
% See solution above
% 0.21/0.42 Formulae used in the proof : additive_idempotence domain4 goals additive_commutativity domain3 additive_associativity
% 0.21/0.42
%------------------------------------------------------------------------------