TSTP Solution File: KLE089+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE089+1 : TPTP v8.1.0. Released v4.0.0.
% 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 02:28:27 EDT 2022
% Result : Theorem 0.58s 0.76s
% Output : Refutation 0.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% 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 : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(addition(u,zero),u),
file('KLE089+1.p',unknown),
[] ).
cnf(7,axiom,
equal(multiplication(antidomain(u),u),zero),
file('KLE089+1.p',unknown),
[] ).
cnf(11,axiom,
~ equal(multiplication(domain__dfg(skc2),skc3),zero),
file('KLE089+1.p',unknown),
[] ).
cnf(12,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE089+1.p',unknown),
[] ).
cnf(13,axiom,
equal(addition(domain__dfg(skc2),antidomain(skc3)),antidomain(skc3)),
file('KLE089+1.p',unknown),
[] ).
cnf(21,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE089+1.p',unknown),
[] ).
cnf(80,plain,
equal(addition(zero,u),u),
inference(spr,[status(thm),theory(equality)],[12,1]),
[iquote('0:SpR:12.0,1.0')] ).
cnf(338,plain,
equal(addition(multiplication(domain__dfg(skc2),u),multiplication(antidomain(skc3),u)),multiplication(antidomain(skc3),u)),
inference(spr,[status(thm),theory(equality)],[13,21]),
[iquote('0:SpR:13.0,21.0')] ).
cnf(4281,plain,
equal(addition(multiplication(domain__dfg(skc2),skc3),zero),zero),
inference(spr,[status(thm),theory(equality)],[7,338]),
[iquote('0:SpR:7.0,338.0')] ).
cnf(4310,plain,
equal(multiplication(domain__dfg(skc2),skc3),zero),
inference(rew,[status(thm),theory(equality)],[80,4281,12]),
[iquote('0:Rew:80.0,4281.0,12.0,4281.0')] ).
cnf(4311,plain,
$false,
inference(mrr,[status(thm)],[4310,11]),
[iquote('0:MRR:4310.0,11.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE089+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 16 10:10:11 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.58/0.76
% 0.58/0.76 SPASS V 3.9
% 0.58/0.76 SPASS beiseite: Proof found.
% 0.58/0.76 % SZS status Theorem
% 0.58/0.76 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.58/0.76 SPASS derived 3202 clauses, backtracked 0 clauses, performed 0 splits and kept 794 clauses.
% 0.58/0.76 SPASS allocated 88479 KBytes.
% 0.58/0.76 SPASS spent 0:00:00.39 on the problem.
% 0.58/0.76 0:00:00.04 for the input.
% 0.58/0.76 0:00:00.03 for the FLOTTER CNF translation.
% 0.58/0.76 0:00:00.02 for inferences.
% 0.58/0.76 0:00:00.00 for the backtracking.
% 0.58/0.76 0:00:00.27 for the reduction.
% 0.58/0.76
% 0.58/0.76
% 0.58/0.76 Here is a proof with depth 2, length 11 :
% 0.58/0.76 % SZS output start Refutation
% See solution above
% 0.58/0.76 Formulae used in the proof : additive_identity domain1 goals additive_commutativity left_distributivity
% 0.58/0.76
%------------------------------------------------------------------------------