TSTP Solution File: KLE048+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE048+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n013.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 02:28:15 EDT 2022
% Result : Theorem 7.41s 7.62s
% Output : Refutation 7.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of clauses : 43 ( 24 unt; 0 nHn; 43 RR)
% Number of literals : 64 ( 0 equ; 22 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
test__dfg(skc1),
file('KLE048+1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(star(skc1),one),
file('KLE048+1.p',unknown),
[] ).
cnf(4,axiom,
equal(addition(u,u),u),
file('KLE048+1.p',unknown),
[] ).
cnf(5,axiom,
equal(multiplication(u,one),u),
file('KLE048+1.p',unknown),
[] ).
cnf(6,axiom,
equal(multiplication(one,u),u),
file('KLE048+1.p',unknown),
[] ).
cnf(11,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE048+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ leq(u,v)
| equal(addition(u,v),v) ),
file('KLE048+1.p',unknown),
[] ).
cnf(14,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE048+1.p',unknown),
[] ).
cnf(16,axiom,
leq(addition(one,multiplication(star(u),u)),star(u)),
file('KLE048+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ complement(u,v)
| equal(addition(v,u),one) ),
file('KLE048+1.p',unknown),
[] ).
cnf(20,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE048+1.p',unknown),
[] ).
cnf(22,axiom,
( ~ test__dfg(u)
| ~ equal(c(u),v)
| complement(u,v) ),
file('KLE048+1.p',unknown),
[] ).
cnf(25,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE048+1.p',unknown),
[] ).
cnf(26,axiom,
( ~ leq(addition(multiplication(u,v),w),v)
| leq(multiplication(star(u),w),v) ),
file('KLE048+1.p',unknown),
[] ).
cnf(29,plain,
( ~ equal(c(skc1),u)
| complement(skc1,u) ),
inference(res,[status(thm),theory(equality)],[1,22]),
[iquote('0:Res:1.0,22.0')] ).
cnf(62,plain,
complement(skc1,c(skc1)),
inference(eqr,[status(thm),theory(equality)],[29]),
[iquote('0:EqR:29.0')] ).
cnf(73,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(104,plain,
( ~ leq(u,v)
| equal(addition(v,u),v) ),
inference(spr,[status(thm),theory(equality)],[13,11]),
[iquote('0:SpR:13.1,11.0')] ).
cnf(124,plain,
( ~ equal(u,u)
| leq(u,u) ),
inference(spl,[status(thm),theory(equality)],[4,14]),
[iquote('0:SpL:4.0,14.0')] ).
cnf(131,plain,
leq(u,u),
inference(obv,[status(thm),theory(equality)],[124]),
[iquote('0:Obv:124.0')] ).
cnf(179,plain,
( ~ leq(u,v)
| ~ leq(v,u)
| equal(v,u) ),
inference(spr,[status(thm),theory(equality)],[104,13]),
[iquote('0:SpR:104.1,13.1')] ).
cnf(185,plain,
( ~ leq(multiplication(star(u),u),one)
| leq(one,star(u)) ),
inference(spr,[status(thm),theory(equality)],[104,16]),
[iquote('0:SpR:104.1,16.0')] ).
cnf(200,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(237,plain,
( ~ complement(u,v)
| equal(addition(u,one),one) ),
inference(spr,[status(thm),theory(equality)],[73,200]),
[iquote('0:SpR:73.1,200.0')] ).
cnf(245,plain,
( ~ equal(addition(u,v),addition(u,v))
| leq(u,addition(u,v)) ),
inference(spl,[status(thm),theory(equality)],[200,14]),
[iquote('0:SpL:200.0,14.0')] ).
cnf(249,plain,
leq(u,addition(u,v)),
inference(obv,[status(thm),theory(equality)],[245]),
[iquote('0:Obv:245.0')] ).
cnf(256,plain,
leq(u,addition(v,u)),
inference(spr,[status(thm),theory(equality)],[11,249]),
[iquote('0:SpR:11.0,249.0')] ).
cnf(359,plain,
( ~ leq(addition(u,multiplication(v,w)),w)
| leq(multiplication(star(v),u),w) ),
inference(spl,[status(thm),theory(equality)],[11,26]),
[iquote('0:SpL:11.0,26.0')] ).
cnf(456,plain,
equal(addition(skc1,one),one),
inference(res,[status(thm),theory(equality)],[62,237]),
[iquote('0:Res:62.0,237.0')] ).
cnf(457,plain,
equal(addition(one,skc1),one),
inference(rew,[status(thm),theory(equality)],[11,456]),
[iquote('0:Rew:11.0,456.0')] ).
cnf(462,plain,
equal(addition(one,addition(skc1,u)),addition(one,u)),
inference(spr,[status(thm),theory(equality)],[457,20]),
[iquote('0:SpR:457.0,20.0')] ).
cnf(465,plain,
equal(addition(multiplication(one,u),multiplication(skc1,u)),multiplication(one,u)),
inference(spr,[status(thm),theory(equality)],[457,25]),
[iquote('0:SpR:457.0,25.0')] ).
cnf(476,plain,
equal(addition(u,multiplication(skc1,u)),u),
inference(rew,[status(thm),theory(equality)],[6,465]),
[iquote('0:Rew:6.0,465.0')] ).
cnf(3754,plain,
( ~ leq(u,skc1)
| equal(addition(one,skc1),addition(one,u)) ),
inference(spr,[status(thm),theory(equality)],[104,462]),
[iquote('0:SpR:104.1,462.0')] ).
cnf(3782,plain,
( ~ leq(u,skc1)
| equal(addition(one,u),one) ),
inference(rew,[status(thm),theory(equality)],[457,3754]),
[iquote('0:Rew:457.0,3754.1')] ).
cnf(4142,plain,
( ~ leq(u,u)
| leq(multiplication(star(skc1),u),u) ),
inference(spl,[status(thm),theory(equality)],[476,359]),
[iquote('0:SpL:476.0,359.0')] ).
cnf(4165,plain,
leq(multiplication(star(skc1),u),u),
inference(mrr,[status(thm)],[4142,131]),
[iquote('0:MRR:4142.0,131.0')] ).
cnf(4188,plain,
leq(star(skc1),one),
inference(spr,[status(thm),theory(equality)],[5,4165]),
[iquote('0:SpR:5.0,4165.0')] ).
cnf(6822,plain,
( ~ leq(u,skc1)
| leq(u,one) ),
inference(spr,[status(thm),theory(equality)],[3782,256]),
[iquote('0:SpR:3782.1,256.0')] ).
cnf(6987,plain,
leq(multiplication(star(skc1),skc1),one),
inference(res,[status(thm),theory(equality)],[4165,6822]),
[iquote('0:Res:4165.0,6822.0')] ).
cnf(18774,plain,
leq(one,star(skc1)),
inference(res,[status(thm),theory(equality)],[6987,185]),
[iquote('0:Res:6987.0,185.0')] ).
cnf(27128,plain,
( ~ leq(star(skc1),one)
| equal(star(skc1),one) ),
inference(res,[status(thm),theory(equality)],[18774,179]),
[iquote('0:Res:18774.0,179.0')] ).
cnf(27800,plain,
$false,
inference(mrr,[status(thm)],[27128,4188,2]),
[iquote('0:MRR:27128.0,27128.1,4188.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : KLE048+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.14 % Command : run_spass %d %s
% 0.14/0.36 % Computer : n013.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Thu Jun 16 12:16:44 EDT 2022
% 0.14/0.36 % CPUTime :
% 7.41/7.62
% 7.41/7.62 SPASS V 3.9
% 7.41/7.62 SPASS beiseite: Proof found.
% 7.41/7.62 % SZS status Theorem
% 7.41/7.62 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.41/7.62 SPASS derived 20969 clauses, backtracked 0 clauses, performed 0 splits and kept 4805 clauses.
% 7.41/7.62 SPASS allocated 115931 KBytes.
% 7.41/7.62 SPASS spent 0:00:07.08 on the problem.
% 7.41/7.62 0:00:00.03 for the input.
% 7.41/7.62 0:00:00.03 for the FLOTTER CNF translation.
% 7.41/7.62 0:00:00.15 for inferences.
% 7.41/7.62 0:00:00.00 for the backtracking.
% 7.41/7.62 0:00:06.78 for the reduction.
% 7.41/7.62
% 7.41/7.62
% 7.41/7.62 Here is a proof with depth 9, length 43 :
% 7.41/7.62 % SZS output start Refutation
% See solution above
% 7.41/7.62 Formulae used in the proof : goals additive_idempotence multiplicative_right_identity multiplicative_left_identity additive_commutativity order star_unfold_left test_2 additive_associativity test_3 left_distributivity star_induction_left
% 7.41/7.62
%------------------------------------------------------------------------------