TSTP Solution File: KLE064+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE064+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 02:28:20 EDT 2022
% Result : Theorem 8.01s 8.18s
% Output : Refutation 8.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of clauses : 19 ( 19 unt; 0 nHn; 19 RR)
% Number of literals : 19 ( 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 : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(5,axiom,
equal(multiplication(one,u),u),
file('KLE064+1.p',unknown),
[] ).
cnf(8,axiom,
equal(addition(domain__dfg(u),one),one),
file('KLE064+1.p',unknown),
[] ).
cnf(9,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE064+1.p',unknown),
[] ).
cnf(10,axiom,
equal(addition(domain__dfg(skc2),domain__dfg(skc3)),domain__dfg(skc3)),
file('KLE064+1.p',unknown),
[] ).
cnf(14,axiom,
equal(addition(domain__dfg(u),domain__dfg(v)),domain__dfg(addition(u,v))),
file('KLE064+1.p',unknown),
[] ).
cnf(17,axiom,
equal(addition(u,multiplication(domain__dfg(u),u)),multiplication(domain__dfg(u),u)),
file('KLE064+1.p',unknown),
[] ).
cnf(18,axiom,
~ equal(addition(skc2,multiplication(domain__dfg(skc3),skc2)),multiplication(domain__dfg(skc3),skc2)),
file('KLE064+1.p',unknown),
[] ).
cnf(20,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE064+1.p',unknown),
[] ).
cnf(21,plain,
equal(addition(one,domain__dfg(u)),one),
inference(rew,[status(thm),theory(equality)],[9,8]),
[iquote('0:Rew:9.0,8.0')] ).
cnf(22,plain,
equal(domain__dfg(addition(skc2,skc3)),domain__dfg(skc3)),
inference(rew,[status(thm),theory(equality)],[14,10]),
[iquote('0:Rew:14.0,10.0')] ).
cnf(719,plain,
equal(addition(multiplication(one,u),multiplication(domain__dfg(v),u)),multiplication(one,u)),
inference(spr,[status(thm),theory(equality)],[21,20]),
[iquote('0:SpR:21.0,20.0')] ).
cnf(720,plain,
equal(multiplication(domain__dfg(addition(u,v)),w),addition(multiplication(domain__dfg(u),w),multiplication(domain__dfg(v),w))),
inference(spr,[status(thm),theory(equality)],[14,20]),
[iquote('0:SpR:14.0,20.0')] ).
cnf(729,plain,
equal(addition(u,multiplication(domain__dfg(v),u)),u),
inference(rew,[status(thm),theory(equality)],[5,719]),
[iquote('0:Rew:5.0,719.0')] ).
cnf(730,plain,
~ equal(multiplication(domain__dfg(skc3),skc2),skc2),
inference(rew,[status(thm),theory(equality)],[729,18]),
[iquote('0:Rew:729.0,18.0')] ).
cnf(731,plain,
equal(multiplication(domain__dfg(u),u),u),
inference(rew,[status(thm),theory(equality)],[729,17]),
[iquote('0:Rew:729.0,17.0')] ).
cnf(6106,plain,
equal(addition(multiplication(domain__dfg(skc2),u),multiplication(domain__dfg(skc3),u)),multiplication(domain__dfg(skc3),u)),
inference(spr,[status(thm),theory(equality)],[22,720]),
[iquote('0:SpR:22.0,720.0')] ).
cnf(38205,plain,
equal(addition(skc2,multiplication(domain__dfg(skc3),skc2)),multiplication(domain__dfg(skc3),skc2)),
inference(spr,[status(thm),theory(equality)],[731,6106]),
[iquote('0:SpR:731.0,6106.0')] ).
cnf(38272,plain,
equal(multiplication(domain__dfg(skc3),skc2),skc2),
inference(rew,[status(thm),theory(equality)],[729,38205]),
[iquote('0:Rew:729.0,38205.0')] ).
cnf(38273,plain,
$false,
inference(mrr,[status(thm)],[38272,730]),
[iquote('0:MRR:38272.0,730.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE064+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n008.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 09:46:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 8.01/8.18
% 8.01/8.18 SPASS V 3.9
% 8.01/8.18 SPASS beiseite: Proof found.
% 8.01/8.18 % SZS status Theorem
% 8.01/8.18 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.01/8.18 SPASS derived 28613 clauses, backtracked 0 clauses, performed 0 splits and kept 4474 clauses.
% 8.01/8.18 SPASS allocated 110004 KBytes.
% 8.01/8.18 SPASS spent 0:00:07.63 on the problem.
% 8.01/8.18 0:00:00.04 for the input.
% 8.01/8.18 0:00:00.03 for the FLOTTER CNF translation.
% 8.01/8.18 0:00:00.16 for inferences.
% 8.01/8.18 0:00:00.00 for the backtracking.
% 8.01/8.18 0:00:07.35 for the reduction.
% 8.01/8.18
% 8.01/8.18
% 8.01/8.18 Here is a proof with depth 3, length 19 :
% 8.01/8.18 % SZS output start Refutation
% See solution above
% 8.01/8.18 Formulae used in the proof : multiplicative_left_identity domain3 additive_commutativity goals domain5 domain1 left_distributivity
% 8.01/8.18
%------------------------------------------------------------------------------