TSTP Solution File: KLE069+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE069+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 02:28:21 EDT 2022
% Result : Theorem 0.18s 0.53s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of clauses : 25 ( 25 unt; 0 nHn; 25 RR)
% Number of literals : 25 ( 0 equ; 5 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(4,axiom,
equal(multiplication(u,one),u),
file('KLE069+1.p',unknown),
[] ).
cnf(5,axiom,
equal(multiplication(one,u),u),
file('KLE069+1.p',unknown),
[] ).
cnf(8,axiom,
equal(addition(domain__dfg(u),one),one),
file('KLE069+1.p',unknown),
[] ).
cnf(9,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE069+1.p',unknown),
[] ).
cnf(12,axiom,
equal(domain__dfg(multiplication(u,domain__dfg(v))),domain__dfg(multiplication(u,v))),
file('KLE069+1.p',unknown),
[] ).
cnf(13,axiom,
equal(addition(domain__dfg(u),domain__dfg(v)),domain__dfg(addition(u,v))),
file('KLE069+1.p',unknown),
[] ).
cnf(16,axiom,
equal(addition(u,multiplication(domain__dfg(u),u)),multiplication(domain__dfg(u),u)),
file('KLE069+1.p',unknown),
[] ).
cnf(17,axiom,
~ equal(multiplication(domain__dfg(skc3),addition(domain__dfg(skc3),domain__dfg(skc2))),domain__dfg(skc3)),
file('KLE069+1.p',unknown),
[] ).
cnf(18,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE069+1.p',unknown),
[] ).
cnf(19,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE069+1.p',unknown),
[] ).
cnf(20,plain,
equal(addition(one,domain__dfg(u)),one),
inference(rew,[status(thm),theory(equality)],[9,8]),
[iquote('0:Rew:9.0,8.0')] ).
cnf(21,plain,
~ equal(multiplication(domain__dfg(skc3),domain__dfg(addition(skc2,skc3))),domain__dfg(skc3)),
inference(rew,[status(thm),theory(equality)],[9,17,13]),
[iquote('0:Rew:9.0,17.0,13.0,17.0')] ).
cnf(91,plain,
equal(domain__dfg(multiplication(one,u)),domain__dfg(domain__dfg(u))),
inference(spr,[status(thm),theory(equality)],[5,12]),
[iquote('0:SpR:5.0,12.0')] ).
cnf(94,plain,
equal(domain__dfg(domain__dfg(u)),domain__dfg(u)),
inference(rew,[status(thm),theory(equality)],[5,91]),
[iquote('0:Rew:5.0,91.0')] ).
cnf(313,plain,
equal(addition(domain__dfg(u),multiplication(domain__dfg(u),domain__dfg(u))),multiplication(domain__dfg(u),domain__dfg(u))),
inference(spr,[status(thm),theory(equality)],[94,16]),
[iquote('0:SpR:94.0,16.0')] ).
cnf(724,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(734,plain,
equal(addition(u,multiplication(domain__dfg(v),u)),u),
inference(rew,[status(thm),theory(equality)],[5,724]),
[iquote('0:Rew:5.0,724.0')] ).
cnf(737,plain,
equal(multiplication(domain__dfg(u),domain__dfg(u)),domain__dfg(u)),
inference(rew,[status(thm),theory(equality)],[734,313]),
[iquote('0:Rew:734.0,313.0')] ).
cnf(912,plain,
equal(addition(multiplication(u,one),multiplication(u,domain__dfg(v))),multiplication(u,one)),
inference(spr,[status(thm),theory(equality)],[20,18]),
[iquote('0:SpR:20.0,18.0')] ).
cnf(913,plain,
equal(multiplication(u,domain__dfg(addition(v,w))),addition(multiplication(u,domain__dfg(v)),multiplication(u,domain__dfg(w)))),
inference(spr,[status(thm),theory(equality)],[13,18]),
[iquote('0:SpR:13.0,18.0')] ).
cnf(922,plain,
equal(addition(u,multiplication(u,domain__dfg(v))),u),
inference(rew,[status(thm),theory(equality)],[4,912]),
[iquote('0:Rew:4.0,912.0')] ).
cnf(926,plain,
~ equal(addition(multiplication(domain__dfg(skc3),domain__dfg(skc2)),multiplication(domain__dfg(skc3),domain__dfg(skc3))),domain__dfg(skc3)),
inference(rew,[status(thm),theory(equality)],[913,21]),
[iquote('0:Rew:913.0,21.0')] ).
cnf(927,plain,
~ equal(addition(domain__dfg(skc3),multiplication(domain__dfg(skc3),domain__dfg(skc2))),domain__dfg(skc3)),
inference(rew,[status(thm),theory(equality)],[9,926,737]),
[iquote('0:Rew:9.0,926.0,737.0,926.0')] ).
cnf(928,plain,
~ equal(domain__dfg(skc3),domain__dfg(skc3)),
inference(rew,[status(thm),theory(equality)],[922,927]),
[iquote('0:Rew:922.0,927.0')] ).
cnf(929,plain,
$false,
inference(obv,[status(thm),theory(equality)],[928]),
[iquote('0:Obv:928.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KLE069+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.32 % Computer : n020.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 16 10:48:04 EDT 2022
% 0.18/0.33 % CPUTime :
% 0.18/0.53
% 0.18/0.53 SPASS V 3.9
% 0.18/0.53 SPASS beiseite: Proof found.
% 0.18/0.53 % SZS status Theorem
% 0.18/0.53 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.53 SPASS derived 612 clauses, backtracked 0 clauses, performed 0 splits and kept 152 clauses.
% 0.18/0.53 SPASS allocated 85902 KBytes.
% 0.18/0.53 SPASS spent 0:00:00.18 on the problem.
% 0.18/0.53 0:00:00.04 for the input.
% 0.18/0.53 0:00:00.04 for the FLOTTER CNF translation.
% 0.18/0.53 0:00:00.01 for inferences.
% 0.18/0.53 0:00:00.00 for the backtracking.
% 0.18/0.53 0:00:00.07 for the reduction.
% 0.18/0.53
% 0.18/0.53
% 0.18/0.53 Here is a proof with depth 2, length 25 :
% 0.18/0.53 % SZS output start Refutation
% See solution above
% 0.18/0.53 Formulae used in the proof : multiplicative_right_identity multiplicative_left_identity domain3 additive_commutativity domain2 domain5 domain1 goals right_distributivity left_distributivity
% 0.18/0.53
%------------------------------------------------------------------------------