TSTP Solution File: KLE052+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE052+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n015.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 02:28:17 EDT 2022
% Result : Theorem 0.19s 0.49s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of clauses : 11 ( 11 unt; 0 nHn; 11 RR)
% Number of literals : 11 ( 0 equ; 1 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(5,axiom,
equal(multiplication(one,u),u),
file('KLE052+1.p',unknown),
[] ).
cnf(8,axiom,
equal(addition(domain__dfg(u),one),one),
file('KLE052+1.p',unknown),
[] ).
cnf(9,axiom,
~ equal(multiplication(domain__dfg(skc1),skc1),skc1),
file('KLE052+1.p',unknown),
[] ).
cnf(10,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE052+1.p',unknown),
[] ).
cnf(17,axiom,
equal(addition(u,multiplication(domain__dfg(u),u)),multiplication(domain__dfg(u),u)),
file('KLE052+1.p',unknown),
[] ).
cnf(19,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE052+1.p',unknown),
[] ).
cnf(20,plain,
equal(addition(one,domain__dfg(u)),one),
inference(rew,[status(thm),theory(equality)],[10,8]),
[iquote('0:Rew:10.0,8.0')] ).
cnf(768,plain,
equal(addition(multiplication(one,u),multiplication(domain__dfg(v),u)),multiplication(one,u)),
inference(spr,[status(thm),theory(equality)],[20,19]),
[iquote('0:SpR:20.0,19.0')] ).
cnf(778,plain,
equal(addition(u,multiplication(domain__dfg(v),u)),u),
inference(rew,[status(thm),theory(equality)],[5,768]),
[iquote('0:Rew:5.0,768.0')] ).
cnf(779,plain,
equal(multiplication(domain__dfg(u),u),u),
inference(rew,[status(thm),theory(equality)],[778,17]),
[iquote('0:Rew:778.0,17.0')] ).
cnf(782,plain,
$false,
inference(unc,[status(thm)],[779,9]),
[iquote('0:UnC:779.0,9.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE052+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n015.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 : Thu Jun 16 13:54:26 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.49
% 0.19/0.49 SPASS V 3.9
% 0.19/0.49 SPASS beiseite: Proof found.
% 0.19/0.49 % SZS status Theorem
% 0.19/0.49 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.49 SPASS derived 534 clauses, backtracked 0 clauses, performed 0 splits and kept 137 clauses.
% 0.19/0.49 SPASS allocated 85778 KBytes.
% 0.19/0.49 SPASS spent 0:00:00.13 on the problem.
% 0.19/0.49 0:00:00.04 for the input.
% 0.19/0.49 0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.49 0:00:00.01 for inferences.
% 0.19/0.49 0:00:00.00 for the backtracking.
% 0.19/0.49 0:00:00.05 for the reduction.
% 0.19/0.49
% 0.19/0.49
% 0.19/0.49 Here is a proof with depth 1, length 11 :
% 0.19/0.49 % SZS output start Refutation
% See solution above
% 0.19/0.49 Formulae used in the proof : multiplicative_left_identity domain3 goals additive_commutativity domain1 left_distributivity
% 0.19/0.49
%------------------------------------------------------------------------------