TSTP Solution File: KLE021+3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE021+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 02:28:04 EDT 2022
% Result : Theorem 0.60s 0.78s
% Output : Refutation 0.60s
% 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+3.p',unknown),
[] ).
cnf(5,axiom,
equal(multiplication(one,u),u),
file('KLE021+3.p',unknown),
[] ).
cnf(10,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE021+3.p',unknown),
[] ).
cnf(14,axiom,
( ~ complement(u,v)
| equal(multiplication(v,u),zero) ),
file('KLE021+3.p',unknown),
[] ).
cnf(15,axiom,
( ~ complement(u,v)
| equal(multiplication(u,v),zero) ),
file('KLE021+3.p',unknown),
[] ).
cnf(16,axiom,
( ~ complement(u,v)
| equal(addition(v,u),one) ),
file('KLE021+3.p',unknown),
[] ).
cnf(17,axiom,
~ equal(addition(multiplication(skc2,skc3),multiplication(c(skc2),skc3)),skc3),
file('KLE021+3.p',unknown),
[] ).
cnf(20,axiom,
( ~ test__dfg(u)
| ~ equal(c(u),v)
| complement(u,v) ),
file('KLE021+3.p',unknown),
[] ).
cnf(23,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE021+3.p',unknown),
[] ).
cnf(26,axiom,
( ~ equal(addition(u,v),one)
| ~ equal(multiplication(v,u),zero)
| ~ equal(multiplication(u,v),zero)
| complement(v,u) ),
file('KLE021+3.p',unknown),
[] ).
cnf(29,plain,
( ~ equal(c(skc2),u)
| complement(skc2,u) ),
inference(res,[status(thm),theory(equality)],[1,20]),
[iquote('0:Res:1.0,20.0')] ).
cnf(73,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(199,plain,
complement(skc2,c(skc2)),
inference(eqr,[status(thm),theory(equality)],[29]),
[iquote('0:EqR:29.0')] ).
cnf(292,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(302,plain,
( ~ complement(u,v)
| equal(addition(multiplication(v,w),multiplication(u,w)),w) ),
inference(rew,[status(thm),theory(equality)],[5,292]),
[iquote('0:Rew:5.0,292.1')] ).
cnf(516,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)],[73,26]),
[iquote('0:SpL:73.1,26.0')] ).
cnf(530,plain,
( ~ complement(u,v)
| ~ equal(multiplication(v,u),zero)
| ~ equal(multiplication(u,v),zero)
| complement(v,u) ),
inference(obv,[status(thm),theory(equality)],[516]),
[iquote('0:Obv:516.1')] ).
cnf(531,plain,
( ~ complement(u,v)
| ~ equal(zero,zero)
| ~ equal(zero,zero)
| complement(v,u) ),
inference(rew,[status(thm),theory(equality)],[15,530,14]),
[iquote('0:Rew:15.1,530.2,14.1,530.1')] ).
cnf(532,plain,
( ~ complement(u,v)
| complement(v,u) ),
inference(obv,[status(thm),theory(equality)],[531]),
[iquote('0:Obv:531.2')] ).
cnf(772,plain,
complement(c(skc2),skc2),
inference(res,[status(thm),theory(equality)],[199,532]),
[iquote('0:Res:199.0,532.0')] ).
cnf(3617,plain,
( ~ complement(c(skc2),skc2)
| ~ equal(skc3,skc3) ),
inference(spl,[status(thm),theory(equality)],[302,17]),
[iquote('0:SpL:302.1,17.0')] ).
cnf(3619,plain,
~ complement(c(skc2),skc2),
inference(obv,[status(thm),theory(equality)],[3617]),
[iquote('0:Obv:3617.1')] ).
cnf(3620,plain,
$false,
inference(mrr,[status(thm)],[3619,772]),
[iquote('0:MRR:3619.0,772.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE021+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n021.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
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 16 10:12:59 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.60/0.78
% 0.60/0.78 SPASS V 3.9
% 0.60/0.78 SPASS beiseite: Proof found.
% 0.60/0.78 % SZS status Theorem
% 0.60/0.78 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.60/0.78 SPASS derived 2851 clauses, backtracked 16 clauses, performed 1 splits and kept 989 clauses.
% 0.60/0.78 SPASS allocated 100267 KBytes.
% 0.60/0.78 SPASS spent 0:00:00.42 on the problem.
% 0.60/0.78 0:00:00.04 for the input.
% 0.60/0.78 0:00:00.03 for the FLOTTER CNF translation.
% 0.60/0.78 0:00:00.02 for inferences.
% 0.60/0.78 0:00:00.01 for the backtracking.
% 0.60/0.78 0:00:00.31 for the reduction.
% 0.60/0.78
% 0.60/0.78
% 0.60/0.78 Here is a proof with depth 3, length 23 :
% 0.60/0.78 % SZS output start Refutation
% See solution above
% 0.60/0.78 Formulae used in the proof : goals multiplicative_left_identity additive_commutativity test_2 test_3 left_distributivity
% 0.60/0.78
%------------------------------------------------------------------------------