TSTP Solution File: KLE024+2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE024+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 02:28:06 EDT 2022
% Result : Theorem 7.08s 7.25s
% Output : Refutation 7.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of clauses : 22 ( 14 unt; 0 nHn; 22 RR)
% Number of literals : 31 ( 0 equ; 13 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
test__dfg(skc4),
file('KLE024+2.p',unknown),
[] ).
cnf(3,axiom,
equal(addition(u,zero),u),
file('KLE024+2.p',unknown),
[] ).
cnf(8,axiom,
equal(multiplication(zero,u),zero),
file('KLE024+2.p',unknown),
[] ).
cnf(11,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE024+2.p',unknown),
[] ).
cnf(13,axiom,
~ equal(multiplication(multiplication(skc4,skc5),c(skc3)),zero),
file('KLE024+2.p',unknown),
[] ).
cnf(17,axiom,
( ~ complement(u,v)
| equal(multiplication(u,v),zero) ),
file('KLE024+2.p',unknown),
[] ).
cnf(20,axiom,
equal(multiplication(multiplication(u,v),w),multiplication(u,multiplication(v,w))),
file('KLE024+2.p',unknown),
[] ).
cnf(21,axiom,
( ~ test__dfg(u)
| ~ equal(c(u),v)
| complement(u,v) ),
file('KLE024+2.p',unknown),
[] ).
cnf(23,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE024+2.p',unknown),
[] ).
cnf(25,axiom,
equal(addition(multiplication(skc5,c(skc3)),multiplication(c(skc4),skc5)),multiplication(c(skc4),skc5)),
file('KLE024+2.p',unknown),
[] ).
cnf(29,plain,
~ equal(multiplication(skc4,multiplication(skc5,c(skc3))),zero),
inference(rew,[status(thm),theory(equality)],[20,13]),
[iquote('0:Rew:20.0,13.0')] ).
cnf(39,plain,
( ~ equal(c(skc4),u)
| complement(skc4,u) ),
inference(res,[status(thm),theory(equality)],[1,21]),
[iquote('0:Res:1.0,21.0')] ).
cnf(96,plain,
equal(addition(zero,u),u),
inference(spr,[status(thm),theory(equality)],[11,3]),
[iquote('0:SpR:11.0,3.0')] ).
cnf(203,plain,
complement(skc4,c(skc4)),
inference(eqr,[status(thm),theory(equality)],[39]),
[iquote('0:EqR:39.0')] ).
cnf(346,plain,
( ~ complement(u,v)
| equal(multiplication(zero,w),multiplication(u,multiplication(v,w))) ),
inference(spr,[status(thm),theory(equality)],[17,20]),
[iquote('0:SpR:17.1,20.0')] ).
cnf(355,plain,
( ~ complement(u,v)
| equal(multiplication(u,multiplication(v,w)),zero) ),
inference(rew,[status(thm),theory(equality)],[8,346]),
[iquote('0:Rew:8.0,346.1')] ).
cnf(501,plain,
equal(addition(multiplication(u,multiplication(skc5,c(skc3))),multiplication(u,multiplication(c(skc4),skc5))),multiplication(u,multiplication(c(skc4),skc5))),
inference(spr,[status(thm),theory(equality)],[25,23]),
[iquote('0:SpR:25.0,23.0')] ).
cnf(7580,plain,
( ~ complement(u,c(skc4))
| equal(addition(multiplication(u,multiplication(skc5,c(skc3))),zero),zero) ),
inference(spr,[status(thm),theory(equality)],[355,501]),
[iquote('0:SpR:355.1,501.0')] ).
cnf(7614,plain,
( ~ complement(u,c(skc4))
| equal(multiplication(u,multiplication(skc5,c(skc3))),zero) ),
inference(rew,[status(thm),theory(equality)],[96,7580,11]),
[iquote('0:Rew:96.0,7580.1,11.0,7580.1')] ).
cnf(31467,plain,
( ~ complement(skc4,c(skc4))
| ~ equal(zero,zero) ),
inference(spl,[status(thm),theory(equality)],[7614,29]),
[iquote('0:SpL:7614.1,29.0')] ).
cnf(31470,plain,
~ complement(skc4,c(skc4)),
inference(obv,[status(thm),theory(equality)],[31467]),
[iquote('0:Obv:31467.1')] ).
cnf(31471,plain,
$false,
inference(mrr,[status(thm)],[31470,203]),
[iquote('0:MRR:31470.0,203.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE024+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n019.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jun 16 13:42:09 EDT 2022
% 0.13/0.33 % CPUTime :
% 7.08/7.25
% 7.08/7.25 SPASS V 3.9
% 7.08/7.25 SPASS beiseite: Proof found.
% 7.08/7.25 % SZS status Theorem
% 7.08/7.25 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.08/7.25 SPASS derived 23960 clauses, backtracked 38 clauses, performed 2 splits and kept 5149 clauses.
% 7.08/7.25 SPASS allocated 118240 KBytes.
% 7.08/7.25 SPASS spent 0:00:06.69 on the problem.
% 7.08/7.25 0:00:00.03 for the input.
% 7.08/7.25 0:00:00.03 for the FLOTTER CNF translation.
% 7.08/7.25 0:00:00.16 for inferences.
% 7.08/7.25 0:00:00.25 for the backtracking.
% 7.08/7.25 0:00:06.14 for the reduction.
% 7.08/7.25
% 7.08/7.25
% 7.08/7.25 Here is a proof with depth 3, length 22 :
% 7.08/7.25 % SZS output start Refutation
% See solution above
% 7.08/7.25 Formulae used in the proof : goals additive_identity left_annihilation additive_commutativity test_2 multiplicative_associativity test_3 right_distributivity
% 7.08/7.25
%------------------------------------------------------------------------------