TSTP Solution File: KLE072+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE072+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n032.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 02:28:22 EDT 2022
% Result : Theorem 0.14s 0.36s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of clauses : 13 ( 13 unt; 0 nHn; 13 RR)
% Number of literals : 13 ( 0 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(9,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE072+1.p',unknown),
[] ).
cnf(12,axiom,
equal(domain__dfg(multiplication(u,domain__dfg(v))),domain__dfg(multiplication(u,v))),
file('KLE072+1.p',unknown),
[] ).
cnf(13,axiom,
equal(addition(domain__dfg(u),domain__dfg(v)),domain__dfg(addition(u,v))),
file('KLE072+1.p',unknown),
[] ).
cnf(18,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE072+1.p',unknown),
[] ).
cnf(19,axiom,
~ equal(domain__dfg(multiplication(addition(skc5,skc4),domain__dfg(skc3))),addition(domain__dfg(multiplication(skc5,domain__dfg(skc3))),domain__dfg(multiplication(skc4,domain__dfg(skc3))))),
file('KLE072+1.p',unknown),
[] ).
cnf(21,plain,
~ equal(domain__dfg(addition(multiplication(skc4,domain__dfg(skc3)),multiplication(skc5,domain__dfg(skc3)))),domain__dfg(addition(multiplication(skc4,skc3),multiplication(skc5,skc3)))),
inference(rew,[status(thm),theory(equality)],[18,19,9,13,12]),
[iquote('0:Rew:18.0,19.0,9.0,19.0,9.0,19.0,13.0,19.0,12.0,19.0,12.0,19.0')] ).
cnf(85,plain,
equal(domain__dfg(addition(multiplication(u,domain__dfg(v)),w)),addition(domain__dfg(multiplication(u,v)),domain__dfg(w))),
inference(spr,[status(thm),theory(equality)],[12,13]),
[iquote('0:SpR:12.0,13.0')] ).
cnf(86,plain,
equal(addition(domain__dfg(u),domain__dfg(multiplication(v,w))),domain__dfg(addition(u,multiplication(v,domain__dfg(w))))),
inference(spr,[status(thm),theory(equality)],[12,13]),
[iquote('0:SpR:12.0,13.0')] ).
cnf(96,plain,
equal(domain__dfg(addition(multiplication(u,domain__dfg(v)),w)),domain__dfg(addition(multiplication(u,v),w))),
inference(rew,[status(thm),theory(equality)],[13,85]),
[iquote('0:Rew:13.0,85.0')] ).
cnf(97,plain,
~ equal(domain__dfg(addition(multiplication(skc4,skc3),multiplication(skc5,domain__dfg(skc3)))),domain__dfg(addition(multiplication(skc4,skc3),multiplication(skc5,skc3)))),
inference(rew,[status(thm),theory(equality)],[96,21]),
[iquote('0:Rew:96.0,21.0')] ).
cnf(98,plain,
equal(domain__dfg(addition(u,multiplication(v,domain__dfg(w)))),domain__dfg(addition(u,multiplication(v,w)))),
inference(rew,[status(thm),theory(equality)],[13,86]),
[iquote('0:Rew:13.0,86.0')] ).
cnf(100,plain,
~ equal(domain__dfg(addition(multiplication(skc4,skc3),multiplication(skc5,skc3))),domain__dfg(addition(multiplication(skc4,skc3),multiplication(skc5,skc3)))),
inference(rew,[status(thm),theory(equality)],[98,97]),
[iquote('0:Rew:98.0,97.0')] ).
cnf(101,plain,
$false,
inference(obv,[status(thm),theory(equality)],[100]),
[iquote('0:Obv:100.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.10 % Problem : KLE072+1 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.10 % Command : run_spass %d %s
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.14/0.29 % WCLimit : 600
% 0.14/0.29 % DateTime : Thu Jun 16 09:02:59 EDT 2022
% 0.14/0.29 % CPUTime :
% 0.14/0.36
% 0.14/0.36 SPASS V 3.9
% 0.14/0.36 SPASS beiseite: Proof found.
% 0.14/0.36 % SZS status Theorem
% 0.14/0.36 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.36 SPASS derived 65 clauses, backtracked 0 clauses, performed 0 splits and kept 38 clauses.
% 0.14/0.36 SPASS allocated 85161 KBytes.
% 0.14/0.36 SPASS spent 0:00:00.06 on the problem.
% 0.14/0.36 0:00:00.02 for the input.
% 0.14/0.36 0:00:00.02 for the FLOTTER CNF translation.
% 0.14/0.36 0:00:00.00 for inferences.
% 0.14/0.36 0:00:00.00 for the backtracking.
% 0.14/0.36 0:00:00.00 for the reduction.
% 0.14/0.36
% 0.14/0.36
% 0.14/0.36 Here is a proof with depth 1, length 13 :
% 0.14/0.36 % SZS output start Refutation
% See solution above
% 0.14/0.36 Formulae used in the proof : additive_commutativity domain2 domain5 left_distributivity goals
% 0.14/0.36
%------------------------------------------------------------------------------