TSTP Solution File: KLE035+2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE035+2 : 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 02:28:11 EDT 2022
% Result : Theorem 0.20s 0.46s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 20 ( 18 unt; 0 nHn; 20 RR)
% Number of literals : 22 ( 0 equ; 8 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
equal(addition(u,zero),u),
file('KLE035+2.p',unknown),
[] ).
cnf(11,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE035+2.p',unknown),
[] ).
cnf(13,axiom,
leq(multiplication(multiplication(skc5,skc7),c(skc4)),zero),
file('KLE035+2.p',unknown),
[] ).
cnf(14,axiom,
leq(multiplication(multiplication(skc5,skc6),c(skc4)),zero),
file('KLE035+2.p',unknown),
[] ).
cnf(15,axiom,
( ~ leq(u,v)
| equal(addition(u,v),v) ),
file('KLE035+2.p',unknown),
[] ).
cnf(20,axiom,
~ leq(multiplication(multiplication(skc5,addition(skc7,skc6)),c(skc4)),zero),
file('KLE035+2.p',unknown),
[] ).
cnf(22,axiom,
equal(multiplication(multiplication(u,v),w),multiplication(u,multiplication(v,w))),
file('KLE035+2.p',unknown),
[] ).
cnf(25,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE035+2.p',unknown),
[] ).
cnf(26,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE035+2.p',unknown),
[] ).
cnf(30,plain,
leq(multiplication(skc5,multiplication(skc7,c(skc4))),zero),
inference(rew,[status(thm),theory(equality)],[22,13]),
[iquote('0:Rew:22.0,13.0')] ).
cnf(31,plain,
leq(multiplication(skc5,multiplication(skc6,c(skc4))),zero),
inference(rew,[status(thm),theory(equality)],[22,14]),
[iquote('0:Rew:22.0,14.0')] ).
cnf(32,plain,
~ leq(multiplication(skc5,multiplication(addition(skc6,skc7),c(skc4))),zero),
inference(rew,[status(thm),theory(equality)],[22,20,11]),
[iquote('0:Rew:22.0,20.0,11.0,20.0')] ).
cnf(33,plain,
~ leq(multiplication(skc5,addition(multiplication(skc6,c(skc4)),multiplication(skc7,c(skc4)))),zero),
inference(rew,[status(thm),theory(equality)],[26,32]),
[iquote('0:Rew:26.0,32.0')] ).
cnf(34,plain,
~ leq(addition(multiplication(skc5,multiplication(skc6,c(skc4))),multiplication(skc5,multiplication(skc7,c(skc4)))),zero),
inference(rew,[status(thm),theory(equality)],[25,33]),
[iquote('0:Rew:25.0,33.0')] ).
cnf(99,plain,
equal(addition(zero,u),u),
inference(spr,[status(thm),theory(equality)],[11,3]),
[iquote('0:SpR:11.0,3.0')] ).
cnf(190,plain,
( ~ leq(u,zero)
| equal(zero,u) ),
inference(spr,[status(thm),theory(equality)],[15,3]),
[iquote('0:SpR:15.1,3.0')] ).
cnf(328,plain,
equal(multiplication(skc5,multiplication(skc6,c(skc4))),zero),
inference(res,[status(thm),theory(equality)],[31,190]),
[iquote('0:Res:31.0,190.0')] ).
cnf(330,plain,
~ leq(addition(zero,multiplication(skc5,multiplication(skc7,c(skc4)))),zero),
inference(rew,[status(thm),theory(equality)],[328,34]),
[iquote('0:Rew:328.0,34.0')] ).
cnf(333,plain,
~ leq(multiplication(skc5,multiplication(skc7,c(skc4))),zero),
inference(rew,[status(thm),theory(equality)],[99,330]),
[iquote('0:Rew:99.0,330.0')] ).
cnf(334,plain,
$false,
inference(mrr,[status(thm)],[333,30]),
[iquote('0:MRR:333.0,30.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : KLE035+2 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jun 16 10:40:22 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.20/0.46
% 0.20/0.46 SPASS V 3.9
% 0.20/0.46 SPASS beiseite: Proof found.
% 0.20/0.46 % SZS status Theorem
% 0.20/0.46 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.46 SPASS derived 247 clauses, backtracked 28 clauses, performed 1 splits and kept 164 clauses.
% 0.20/0.46 SPASS allocated 97807 KBytes.
% 0.20/0.46 SPASS spent 0:00:00.11 on the problem.
% 0.20/0.46 0:00:00.04 for the input.
% 0.20/0.46 0:00:00.03 for the FLOTTER CNF translation.
% 0.20/0.46 0:00:00.00 for inferences.
% 0.20/0.46 0:00:00.00 for the backtracking.
% 0.20/0.46 0:00:00.01 for the reduction.
% 0.20/0.46
% 0.20/0.46
% 0.20/0.46 Here is a proof with depth 2, length 20 :
% 0.20/0.46 % SZS output start Refutation
% See solution above
% 0.20/0.46 Formulae used in the proof : additive_identity additive_commutativity goals order multiplicative_associativity right_distributivity left_distributivity
% 0.20/0.46
%------------------------------------------------------------------------------