TSTP Solution File: KLE026+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE026+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n015.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 02:28:07 EDT 2022
% Result : Theorem 0.61s 0.81s
% Output : Refutation 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of clauses : 28 ( 21 unt; 0 nHn; 28 RR)
% Number of literals : 36 ( 0 equ; 9 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 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('KLE026+1.p',unknown),
[] ).
cnf(4,axiom,
equal(addition(u,u),u),
file('KLE026+1.p',unknown),
[] ).
cnf(6,axiom,
equal(multiplication(one,u),u),
file('KLE026+1.p',unknown),
[] ).
cnf(11,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE026+1.p',unknown),
[] ).
cnf(13,axiom,
~ leq(multiplication(skc4,skc5),multiplication(skc5,skc3)),
file('KLE026+1.p',unknown),
[] ).
cnf(14,axiom,
equal(multiplication(multiplication(skc4,skc5),skc3),multiplication(skc4,skc5)),
file('KLE026+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE026+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ complement(u,v)
| equal(addition(v,u),one) ),
file('KLE026+1.p',unknown),
[] ).
cnf(20,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE026+1.p',unknown),
[] ).
cnf(21,axiom,
equal(multiplication(multiplication(u,v),w),multiplication(u,multiplication(v,w))),
file('KLE026+1.p',unknown),
[] ).
cnf(22,axiom,
( ~ test__dfg(u)
| ~ equal(c(u),v)
| complement(u,v) ),
file('KLE026+1.p',unknown),
[] ).
cnf(25,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE026+1.p',unknown),
[] ).
cnf(27,plain,
equal(multiplication(skc4,multiplication(skc5,skc3)),multiplication(skc4,skc5)),
inference(rew,[status(thm),theory(equality)],[21,14]),
[iquote('0:Rew:21.0,14.0')] ).
cnf(31,plain,
( ~ equal(c(skc4),u)
| complement(skc4,u) ),
inference(res,[status(thm),theory(equality)],[1,22]),
[iquote('0:Res:1.0,22.0')] ).
cnf(63,plain,
complement(skc4,c(skc4)),
inference(eqr,[status(thm),theory(equality)],[31]),
[iquote('0:EqR:31.0')] ).
cnf(77,plain,
( ~ complement(u,v)
| equal(addition(u,v),one) ),
inference(spr,[status(thm),theory(equality)],[19,11]),
[iquote('0:SpR:19.1,11.0')] ).
cnf(204,plain,
equal(addition(u,addition(u,v)),addition(u,v)),
inference(spr,[status(thm),theory(equality)],[4,20]),
[iquote('0:SpR:4.0,20.0')] ).
cnf(279,plain,
( ~ complement(u,v)
| equal(addition(u,one),one) ),
inference(spr,[status(thm),theory(equality)],[77,204]),
[iquote('0:SpR:77.1,204.0')] ).
cnf(287,plain,
( ~ equal(addition(u,v),addition(u,v))
| leq(u,addition(u,v)) ),
inference(spl,[status(thm),theory(equality)],[204,16]),
[iquote('0:SpL:204.0,16.0')] ).
cnf(291,plain,
leq(u,addition(u,v)),
inference(obv,[status(thm),theory(equality)],[287]),
[iquote('0:Obv:287.0')] ).
cnf(299,plain,
leq(u,addition(v,u)),
inference(spr,[status(thm),theory(equality)],[11,291]),
[iquote('0:SpR:11.0,291.0')] ).
cnf(2288,plain,
equal(addition(skc4,one),one),
inference(res,[status(thm),theory(equality)],[63,279]),
[iquote('0:Res:63.0,279.0')] ).
cnf(2301,plain,
equal(addition(one,skc4),one),
inference(rew,[status(thm),theory(equality)],[11,2288]),
[iquote('0:Rew:11.0,2288.0')] ).
cnf(2321,plain,
equal(addition(multiplication(one,u),multiplication(skc4,u)),multiplication(one,u)),
inference(spr,[status(thm),theory(equality)],[2301,25]),
[iquote('0:SpR:2301.0,25.0')] ).
cnf(2347,plain,
equal(addition(u,multiplication(skc4,u)),u),
inference(rew,[status(thm),theory(equality)],[6,2321]),
[iquote('0:Rew:6.0,2321.0')] ).
cnf(3493,plain,
leq(multiplication(skc4,u),u),
inference(spr,[status(thm),theory(equality)],[2347,299]),
[iquote('0:SpR:2347.0,299.0')] ).
cnf(3712,plain,
leq(multiplication(skc4,skc5),multiplication(skc5,skc3)),
inference(spr,[status(thm),theory(equality)],[27,3493]),
[iquote('0:SpR:27.0,3493.0')] ).
cnf(3717,plain,
$false,
inference(mrr,[status(thm)],[3712,13]),
[iquote('0:MRR:3712.0,13.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE026+1 : TPTP v8.1.0. Released v4.0.0.
% 0.13/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n015.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 15:07:11 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.61/0.81
% 0.61/0.81 SPASS V 3.9
% 0.61/0.81 SPASS beiseite: Proof found.
% 0.61/0.81 % SZS status Theorem
% 0.61/0.81 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.61/0.81 SPASS derived 2682 clauses, backtracked 0 clauses, performed 0 splits and kept 894 clauses.
% 0.61/0.81 SPASS allocated 100175 KBytes.
% 0.61/0.81 SPASS spent 0:00:00.46 on the problem.
% 0.61/0.81 0:00:00.04 for the input.
% 0.61/0.81 0:00:00.03 for the FLOTTER CNF translation.
% 0.61/0.81 0:00:00.02 for inferences.
% 0.61/0.81 0:00:00.00 for the backtracking.
% 0.61/0.81 0:00:00.35 for the reduction.
% 0.61/0.81
% 0.61/0.81
% 0.61/0.81 Here is a proof with depth 6, length 28 :
% 0.61/0.81 % SZS output start Refutation
% See solution above
% 0.61/0.81 Formulae used in the proof : goals additive_idempotence multiplicative_left_identity additive_commutativity order test_2 additive_associativity multiplicative_associativity test_3 left_distributivity
% 0.61/0.81
%------------------------------------------------------------------------------