TSTP Solution File: KLE055+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE055+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 02:28:18 EDT 2022
% Result : Theorem 0.20s 0.47s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of clauses : 19 ( 19 unt; 0 nHn; 19 RR)
% Number of literals : 19 ( 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(2,axiom,
equal(addition(skc1,one),one),
file('KLE055+1.p',unknown),
[] ).
cnf(5,axiom,
equal(multiplication(u,one),u),
file('KLE055+1.p',unknown),
[] ).
cnf(6,axiom,
equal(multiplication(one,u),u),
file('KLE055+1.p',unknown),
[] ).
cnf(9,axiom,
equal(addition(domain__dfg(u),one),one),
file('KLE055+1.p',unknown),
[] ).
cnf(10,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE055+1.p',unknown),
[] ).
cnf(11,axiom,
~ equal(addition(skc1,domain__dfg(skc1)),domain__dfg(skc1)),
file('KLE055+1.p',unknown),
[] ).
cnf(18,axiom,
equal(addition(u,multiplication(domain__dfg(u),u)),multiplication(domain__dfg(u),u)),
file('KLE055+1.p',unknown),
[] ).
cnf(19,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE055+1.p',unknown),
[] ).
cnf(20,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE055+1.p',unknown),
[] ).
cnf(21,plain,
equal(addition(one,domain__dfg(u)),one),
inference(rew,[status(thm),theory(equality)],[10,9]),
[iquote('0:Rew:10.0,9.0')] ).
cnf(22,plain,
equal(addition(one,skc1),one),
inference(rew,[status(thm),theory(equality)],[10,2]),
[iquote('0:Rew:10.0,2.0')] ).
cnf(516,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(533,plain,
equal(addition(u,multiplication(domain__dfg(v),u)),u),
inference(rew,[status(thm),theory(equality)],[6,516]),
[iquote('0:Rew:6.0,516.0')] ).
cnf(534,plain,
equal(multiplication(domain__dfg(u),u),u),
inference(rew,[status(thm),theory(equality)],[533,18]),
[iquote('0:Rew:533.0,18.0')] ).
cnf(640,plain,
equal(addition(multiplication(u,one),multiplication(u,skc1)),multiplication(u,one)),
inference(spr,[status(thm),theory(equality)],[22,19]),
[iquote('0:SpR:22.0,19.0')] ).
cnf(656,plain,
equal(addition(u,multiplication(u,skc1)),u),
inference(rew,[status(thm),theory(equality)],[5,640]),
[iquote('0:Rew:5.0,640.0')] ).
cnf(686,plain,
equal(addition(domain__dfg(skc1),skc1),domain__dfg(skc1)),
inference(spr,[status(thm),theory(equality)],[534,656]),
[iquote('0:SpR:534.0,656.0')] ).
cnf(690,plain,
equal(addition(skc1,domain__dfg(skc1)),domain__dfg(skc1)),
inference(rew,[status(thm),theory(equality)],[10,686]),
[iquote('0:Rew:10.0,686.0')] ).
cnf(691,plain,
$false,
inference(mrr,[status(thm)],[690,11]),
[iquote('0:MRR:690.0,11.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : KLE055+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 16 11:41:07 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.20/0.47
% 0.20/0.47 SPASS V 3.9
% 0.20/0.47 SPASS beiseite: Proof found.
% 0.20/0.47 % SZS status Theorem
% 0.20/0.47 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.47 SPASS derived 478 clauses, backtracked 0 clauses, performed 0 splits and kept 134 clauses.
% 0.20/0.47 SPASS allocated 85700 KBytes.
% 0.20/0.47 SPASS spent 0:00:00.12 on the problem.
% 0.20/0.47 0:00:00.03 for the input.
% 0.20/0.47 0:00:00.03 for the FLOTTER CNF translation.
% 0.20/0.47 0:00:00.01 for inferences.
% 0.20/0.47 0:00:00.00 for the backtracking.
% 0.20/0.47 0:00:00.04 for the reduction.
% 0.20/0.47
% 0.20/0.47
% 0.20/0.47 Here is a proof with depth 2, length 19 :
% 0.20/0.47 % SZS output start Refutation
% See solution above
% 0.20/0.47 Formulae used in the proof : goals multiplicative_right_identity multiplicative_left_identity domain3 additive_commutativity domain1 right_distributivity left_distributivity
% 0.20/0.47
%------------------------------------------------------------------------------