TSTP Solution File: KLE021+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE021+1 : 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 02:28:03 EDT 2022
% Result : Theorem 0.20s 0.62s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of clauses : 23 ( 9 unt; 0 nHn; 23 RR)
% Number of literals : 47 ( 0 equ; 27 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 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(skc2),
file('KLE021+1.p',unknown),
[] ).
cnf(5,axiom,
equal(multiplication(one,u),u),
file('KLE021+1.p',unknown),
[] ).
cnf(10,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE021+1.p',unknown),
[] ).
cnf(14,axiom,
( ~ complement(u,v)
| equal(multiplication(v,u),zero) ),
file('KLE021+1.p',unknown),
[] ).
cnf(15,axiom,
( ~ complement(u,v)
| equal(multiplication(u,v),zero) ),
file('KLE021+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ complement(u,v)
| equal(addition(v,u),one) ),
file('KLE021+1.p',unknown),
[] ).
cnf(17,axiom,
~ equal(addition(multiplication(skc2,skc3),multiplication(c(skc2),skc3)),skc3),
file('KLE021+1.p',unknown),
[] ).
cnf(20,axiom,
( ~ test__dfg(u)
| ~ equal(c(u),v)
| complement(u,v) ),
file('KLE021+1.p',unknown),
[] ).
cnf(23,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE021+1.p',unknown),
[] ).
cnf(24,axiom,
( ~ equal(addition(u,v),one)
| ~ equal(multiplication(v,u),zero)
| ~ equal(multiplication(u,v),zero)
| complement(v,u) ),
file('KLE021+1.p',unknown),
[] ).
cnf(25,plain,
( ~ equal(c(skc2),u)
| complement(skc2,u) ),
inference(res,[status(thm),theory(equality)],[1,20]),
[iquote('0:Res:1.0,20.0')] ).
cnf(57,plain,
( ~ complement(u,v)
| equal(addition(u,v),one) ),
inference(spr,[status(thm),theory(equality)],[16,10]),
[iquote('0:SpR:16.1,10.0')] ).
cnf(68,plain,
complement(skc2,c(skc2)),
inference(eqr,[status(thm),theory(equality)],[25]),
[iquote('0:EqR:25.0')] ).
cnf(272,plain,
( ~ complement(u,v)
| equal(multiplication(one,w),addition(multiplication(v,w),multiplication(u,w))) ),
inference(spr,[status(thm),theory(equality)],[16,23]),
[iquote('0:SpR:16.1,23.0')] ).
cnf(284,plain,
( ~ complement(u,v)
| equal(addition(multiplication(v,w),multiplication(u,w)),w) ),
inference(rew,[status(thm),theory(equality)],[5,272]),
[iquote('0:Rew:5.0,272.1')] ).
cnf(342,plain,
( ~ complement(u,v)
| ~ equal(one,one)
| ~ equal(multiplication(v,u),zero)
| ~ equal(multiplication(u,v),zero)
| complement(v,u) ),
inference(spl,[status(thm),theory(equality)],[57,24]),
[iquote('0:SpL:57.1,24.0')] ).
cnf(355,plain,
( ~ complement(u,v)
| ~ equal(multiplication(v,u),zero)
| ~ equal(multiplication(u,v),zero)
| complement(v,u) ),
inference(obv,[status(thm),theory(equality)],[342]),
[iquote('0:Obv:342.1')] ).
cnf(356,plain,
( ~ complement(u,v)
| ~ equal(zero,zero)
| ~ equal(zero,zero)
| complement(v,u) ),
inference(rew,[status(thm),theory(equality)],[15,355,14]),
[iquote('0:Rew:15.1,355.2,14.1,355.1')] ).
cnf(357,plain,
( ~ complement(u,v)
| complement(v,u) ),
inference(obv,[status(thm),theory(equality)],[356]),
[iquote('0:Obv:356.2')] ).
cnf(548,plain,
complement(c(skc2),skc2),
inference(res,[status(thm),theory(equality)],[68,357]),
[iquote('0:Res:68.0,357.0')] ).
cnf(1962,plain,
( ~ complement(c(skc2),skc2)
| ~ equal(skc3,skc3) ),
inference(spl,[status(thm),theory(equality)],[284,17]),
[iquote('0:SpL:284.1,17.0')] ).
cnf(1964,plain,
~ complement(c(skc2),skc2),
inference(obv,[status(thm),theory(equality)],[1962]),
[iquote('0:Obv:1962.1')] ).
cnf(1965,plain,
$false,
inference(mrr,[status(thm)],[1964,548]),
[iquote('0:MRR:1964.0,548.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE021+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 16 15:17:39 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.62
% 0.20/0.62 SPASS V 3.9
% 0.20/0.62 SPASS beiseite: Proof found.
% 0.20/0.62 % SZS status Theorem
% 0.20/0.62 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.62 SPASS derived 1538 clauses, backtracked 0 clauses, performed 0 splits and kept 572 clauses.
% 0.20/0.62 SPASS allocated 99010 KBytes.
% 0.20/0.62 SPASS spent 0:00:00.25 on the problem.
% 0.20/0.62 0:00:00.04 for the input.
% 0.20/0.62 0:00:00.03 for the FLOTTER CNF translation.
% 0.20/0.62 0:00:00.01 for inferences.
% 0.20/0.62 0:00:00.00 for the backtracking.
% 0.20/0.62 0:00:00.15 for the reduction.
% 0.20/0.62
% 0.20/0.62
% 0.20/0.62 Here is a proof with depth 3, length 23 :
% 0.20/0.62 % SZS output start Refutation
% See solution above
% 0.20/0.62 Formulae used in the proof : goals multiplicative_left_identity additive_commutativity test_2 test_3 left_distributivity
% 0.20/0.62
%------------------------------------------------------------------------------