%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE024+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n012.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 3.53s 3.71s
% Output : Refutation 3.53s
% 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+1.p',unknown),
[] ).
cnf(3,axiom,
equal(addition(u,zero),u),
file('KLE024+1.p',unknown),
[] ).
cnf(8,axiom,
equal(multiplication(zero,u),zero),
file('KLE024+1.p',unknown),
[] ).
cnf(11,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE024+1.p',unknown),
[] ).
cnf(13,axiom,
~ equal(multiplication(multiplication(skc4,skc5),c(skc3)),zero),
file('KLE024+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ complement(u,v)
| equal(multiplication(u,v),zero) ),
file('KLE024+1.p',unknown),
[] ).
cnf(20,axiom,
equal(multiplication(multiplication(u,v),w),multiplication(u,multiplication(v,w))),
file('KLE024+1.p',unknown),
[] ).
cnf(21,axiom,
( ~ test__dfg(u)
| ~ equal(c(u),v)
| complement(u,v) ),
file('KLE024+1.p',unknown),
[] ).
cnf(23,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE024+1.p',unknown),
[] ).
cnf(25,axiom,
equal(addition(multiplication(skc5,c(skc3)),multiplication(c(skc4),skc5)),multiplication(c(skc4),skc5)),
file('KLE024+1.p',unknown),
[] ).
cnf(27,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(31,plain,
( ~ equal(c(skc4),u)
| complement(skc4,u) ),
inference(res,[status(thm),theory(equality)],[1,21]),
[iquote('0:Res:1.0,21.0')] ).
cnf(54,plain,
equal(addition(zero,u),u),
inference(spr,[status(thm),theory(equality)],[11,3]),
[iquote('0:SpR:11.0,3.0')] ).
cnf(68,plain,
complement(skc4,c(skc4)),
inference(eqr,[status(thm),theory(equality)],[31]),
[iquote('0:EqR:31.0')] ).
cnf(182,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(189,plain,
( ~ complement(u,v)
| equal(multiplication(u,multiplication(v,w)),zero) ),
inference(rew,[status(thm),theory(equality)],[8,182]),
[iquote('0:Rew:8.0,182.1')] ).
cnf(367,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(4169,plain,
( ~ complement(u,c(skc4))
| equal(addition(multiplication(u,multiplication(skc5,c(skc3))),zero),zero) ),
inference(spr,[status(thm),theory(equality)],[189,367]),
[iquote('0:SpR:189.1,367.0')] ).
cnf(4200,plain,
( ~ complement(u,c(skc4))
| equal(multiplication(u,multiplication(skc5,c(skc3))),zero) ),
inference(rew,[status(thm),theory(equality)],[54,4169,11]),
[iquote('0:Rew:54.0,4169.1,11.0,4169.1')] ).
cnf(20156,plain,
( ~ complement(skc4,c(skc4))
| ~ equal(zero,zero) ),
inference(spl,[status(thm),theory(equality)],[4200,27]),
[iquote('0:SpL:4200.1,27.0')] ).
cnf(20159,plain,
~ complement(skc4,c(skc4)),
inference(obv,[status(thm),theory(equality)],[20156]),
[iquote('0:Obv:20156.1')] ).
cnf(20160,plain,
$false,
inference(mrr,[status(thm)],[20159,68]),
[iquote('0:MRR:20159.0,68.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : KLE024+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n012.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 08:07:09 EDT 2022
% 0.12/0.34 % CPUTime :
% 3.53/3.71
% 3.53/3.71 SPASS V 3.9
% 3.53/3.71 SPASS beiseite: Proof found.
% 3.53/3.71 % SZS status Theorem
% 3.53/3.71 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.53/3.71 SPASS derived 15891 clauses, backtracked 0 clauses, performed 0 splits and kept 3524 clauses.
% 3.53/3.71 SPASS allocated 109920 KBytes.
% 3.53/3.71 SPASS spent 0:00:03.29 on the problem.
% 3.53/3.71 0:00:00.03 for the input.
% 3.53/3.71 0:00:00.03 for the FLOTTER CNF translation.
% 3.53/3.71 0:00:00.10 for inferences.
% 3.53/3.71 0:00:00.00 for the backtracking.
% 3.53/3.71 0:00:03.07 for the reduction.
% 3.53/3.71
% 3.53/3.71
% 3.53/3.71 Here is a proof with depth 3, length 22 :
% 3.53/3.71 % SZS output start Refutation
% See solution above
% 3.53/3.71 Formulae used in the proof : goals additive_identity left_annihilation additive_commutativity test_2 multiplicative_associativity test_3 right_distributivity
% 3.53/3.71
%------------------------------------------------------------------------------