%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE009+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 02:27:59 EDT 2022
% Result : Theorem 3.22s 3.44s
% Output : Refutation 3.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 15
% Syntax : Number of clauses : 48 ( 21 unt; 0 nHn; 48 RR)
% Number of literals : 87 ( 0 equ; 48 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 6 ( 2 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(skc3),
file('KLE009+3.p',unknown),
[] ).
cnf(2,axiom,
test__dfg(skc2),
file('KLE009+3.p',unknown),
[] ).
cnf(4,axiom,
equal(addition(u,u),u),
file('KLE009+3.p',unknown),
[] ).
cnf(5,axiom,
equal(multiplication(u,one),u),
file('KLE009+3.p',unknown),
[] ).
cnf(11,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE009+3.p',unknown),
[] ).
cnf(13,axiom,
( ~ leq(u,v)
| equal(addition(u,v),v) ),
file('KLE009+3.p',unknown),
[] ).
cnf(14,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE009+3.p',unknown),
[] ).
cnf(15,axiom,
( ~ complement(u,v)
| equal(multiplication(v,u),zero) ),
file('KLE009+3.p',unknown),
[] ).
cnf(16,axiom,
( ~ complement(u,v)
| equal(multiplication(u,v),zero) ),
file('KLE009+3.p',unknown),
[] ).
cnf(17,axiom,
( ~ complement(u,v)
| equal(addition(v,u),one) ),
file('KLE009+3.p',unknown),
[] ).
cnf(18,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE009+3.p',unknown),
[] ).
cnf(20,axiom,
( ~ test__dfg(u)
| ~ equal(c(u),v)
| complement(u,v) ),
file('KLE009+3.p',unknown),
[] ).
cnf(22,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE009+3.p',unknown),
[] ).
cnf(24,axiom,
( ~ equal(addition(u,v),one)
| ~ equal(multiplication(v,u),zero)
| ~ equal(multiplication(u,v),zero)
| complement(v,u) ),
file('KLE009+3.p',unknown),
[] ).
cnf(25,axiom,
( ~ leq(one,addition(addition(addition(multiplication(skc3,skc2),multiplication(skc3,c(skc2))),multiplication(c(skc3),skc2)),multiplication(c(skc3),c(skc2))))
| ~ leq(addition(addition(addition(multiplication(skc3,skc2),multiplication(skc3,c(skc2))),multiplication(c(skc3),skc2)),multiplication(c(skc3),c(skc2))),one) ),
file('KLE009+3.p',unknown),
[] ).
cnf(26,plain,
( ~ leq(one,addition(multiplication(skc3,skc2),addition(multiplication(skc3,c(skc2)),addition(multiplication(c(skc3),skc2),multiplication(c(skc3),c(skc2))))))
| ~ leq(addition(multiplication(skc3,skc2),addition(multiplication(skc3,c(skc2)),addition(multiplication(c(skc3),skc2),multiplication(c(skc3),c(skc2))))),one) ),
inference(rew,[status(thm),theory(equality)],[18,25]),
[iquote('0:Rew:18.0,25.1,18.0,25.1,18.0,25.0,18.0,25.0')] ).
cnf(27,plain,
( ~ equal(c(skc2),u)
| complement(skc2,u) ),
inference(res,[status(thm),theory(equality)],[2,20]),
[iquote('0:Res:2.0,20.0')] ).
cnf(30,plain,
( ~ equal(c(skc3),u)
| complement(skc3,u) ),
inference(res,[status(thm),theory(equality)],[1,20]),
[iquote('0:Res:1.0,20.0')] ).
cnf(58,plain,
( ~ complement(u,v)
| equal(addition(u,v),one) ),
inference(spr,[status(thm),theory(equality)],[17,11]),
[iquote('0:SpR:17.1,11.0')] ).
cnf(80,plain,
complement(skc3,c(skc3)),
inference(eqr,[status(thm),theory(equality)],[30]),
[iquote('0:EqR:30.0')] ).
cnf(93,plain,
complement(skc2,c(skc2)),
inference(eqr,[status(thm),theory(equality)],[27]),
[iquote('0:EqR:27.0')] ).
cnf(99,plain,
( ~ equal(u,u)
| leq(u,u) ),
inference(spl,[status(thm),theory(equality)],[4,14]),
[iquote('0:SpL:4.0,14.0')] ).
cnf(105,plain,
leq(u,u),
inference(obv,[status(thm),theory(equality)],[99]),
[iquote('0:Obv:99.0')] ).
cnf(185,plain,
equal(addition(u,addition(v,w)),addition(w,addition(u,v))),
inference(spr,[status(thm),theory(equality)],[18,11]),
[iquote('0:SpR:18.0,11.0')] ).
cnf(194,plain,
equal(addition(u,addition(u,v)),addition(u,v)),
inference(spr,[status(thm),theory(equality)],[4,18]),
[iquote('0:SpR:4.0,18.0')] ).
cnf(220,plain,
( ~ complement(u,v)
| equal(addition(u,one),one) ),
inference(spr,[status(thm),theory(equality)],[58,194]),
[iquote('0:SpR:58.1,194.0')] ).
cnf(306,plain,
( ~ complement(u,v)
| equal(multiplication(w,one),addition(multiplication(w,v),multiplication(w,u))) ),
inference(spr,[status(thm),theory(equality)],[17,22]),
[iquote('0:SpR:17.1,22.0')] ).
cnf(318,plain,
( ~ complement(u,v)
| equal(addition(multiplication(w,v),multiplication(w,u)),w) ),
inference(rew,[status(thm),theory(equality)],[5,306]),
[iquote('0:Rew:5.0,306.1')] ).
cnf(332,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)],[58,24]),
[iquote('0:SpL:58.1,24.0')] ).
cnf(346,plain,
( ~ complement(u,v)
| ~ equal(multiplication(v,u),zero)
| ~ equal(multiplication(u,v),zero)
| complement(v,u) ),
inference(obv,[status(thm),theory(equality)],[332]),
[iquote('0:Obv:332.1')] ).
cnf(347,plain,
( ~ complement(u,v)
| ~ equal(zero,zero)
| ~ equal(zero,zero)
| complement(v,u) ),
inference(rew,[status(thm),theory(equality)],[16,346,15]),
[iquote('0:Rew:16.1,346.2,15.1,346.1')] ).
cnf(348,plain,
( ~ complement(u,v)
| complement(v,u) ),
inference(obv,[status(thm),theory(equality)],[347]),
[iquote('0:Obv:347.2')] ).
cnf(571,plain,
complement(c(skc3),skc3),
inference(res,[status(thm),theory(equality)],[80,348]),
[iquote('0:Res:80.0,348.0')] ).
cnf(572,plain,
complement(c(skc2),skc2),
inference(res,[status(thm),theory(equality)],[93,348]),
[iquote('0:Res:93.0,348.0')] ).
cnf(2347,plain,
( ~ complement(c(skc2),skc2)
| ~ leq(one,addition(multiplication(skc3,skc2),addition(multiplication(skc3,c(skc2)),addition(multiplication(c(skc3),skc2),multiplication(c(skc3),c(skc2))))))
| ~ leq(addition(multiplication(skc3,skc2),addition(multiplication(skc3,c(skc2)),c(skc3))),one) ),
inference(spl,[status(thm),theory(equality)],[318,26]),
[iquote('0:SpL:318.1,26.1')] ).
cnf(2382,plain,
( ~ complement(c(skc2),skc2)
| ~ leq(one,addition(skc3,c(skc3)))
| ~ leq(addition(skc3,c(skc3)),one) ),
inference(rew,[status(thm),theory(equality)],[11,2347,318,185]),
[iquote('0:Rew:11.0,2347.2,318.1,2347.2,185.0,2347.2,11.0,2347.1,318.1,2347.1,185.0,2347.1,318.1,2347.1')] ).
cnf(2383,plain,
( ~ leq(one,addition(skc3,c(skc3)))
| ~ leq(addition(skc3,c(skc3)),one) ),
inference(mrr,[status(thm)],[2382,572]),
[iquote('0:MRR:2382.0,572.0')] ).
cnf(2388,plain,
equal(addition(skc3,one),one),
inference(res,[status(thm),theory(equality)],[80,220]),
[iquote('0:Res:80.0,220.0')] ).
cnf(2397,plain,
equal(addition(c(skc3),one),one),
inference(res,[status(thm),theory(equality)],[571,220]),
[iquote('0:Res:571.0,220.0')] ).
cnf(2404,plain,
equal(addition(one,skc3),one),
inference(rew,[status(thm),theory(equality)],[11,2388]),
[iquote('0:Rew:11.0,2388.0')] ).
cnf(2406,plain,
equal(addition(one,c(skc3)),one),
inference(rew,[status(thm),theory(equality)],[11,2397]),
[iquote('0:Rew:11.0,2397.0')] ).
cnf(2423,plain,
equal(addition(one,addition(skc3,u)),addition(one,u)),
inference(spr,[status(thm),theory(equality)],[2404,18]),
[iquote('0:SpR:2404.0,18.0')] ).
cnf(16001,plain,
( ~ leq(one,addition(skc3,u))
| equal(addition(skc3,u),addition(one,u)) ),
inference(spr,[status(thm),theory(equality)],[2423,13]),
[iquote('0:SpR:2423.0,13.1')] ).
cnf(16191,plain,
( ~ leq(one,addition(skc3,c(skc3)))
| ~ leq(addition(one,c(skc3)),one) ),
inference(rew,[status(thm),theory(equality)],[16001,2383]),
[iquote('0:Rew:16001.1,2383.1')] ).
cnf(16205,plain,
( ~ leq(one,addition(skc3,c(skc3)))
| ~ leq(one,one) ),
inference(rew,[status(thm),theory(equality)],[2406,16191]),
[iquote('0:Rew:2406.0,16191.1')] ).
cnf(16206,plain,
~ leq(one,addition(skc3,c(skc3))),
inference(mrr,[status(thm)],[16205,105]),
[iquote('0:MRR:16205.1,105.0')] ).
cnf(16388,plain,
( ~ complement(skc3,c(skc3))
| ~ leq(one,one) ),
inference(spl,[status(thm),theory(equality)],[58,16206]),
[iquote('0:SpL:58.1,16206.0')] ).
cnf(16395,plain,
$false,
inference(mrr,[status(thm)],[16388,80,105]),
[iquote('0:MRR:16388.0,16388.1,80.0,105.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KLE009+3 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n026.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 08:49:23 EDT 2022
% 0.13/0.34 % CPUTime :
% 3.22/3.44
% 3.22/3.44 SPASS V 3.9
% 3.22/3.44 SPASS beiseite: Proof found.
% 3.22/3.44 % SZS status Theorem
% 3.22/3.44 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.22/3.44 SPASS derived 11665 clauses, backtracked 0 clauses, performed 0 splits and kept 2978 clauses.
% 3.22/3.44 SPASS allocated 108405 KBytes.
% 3.22/3.44 SPASS spent 0:00:03.04 on the problem.
% 3.22/3.44 0:00:00.03 for the input.
% 3.22/3.44 0:00:00.03 for the FLOTTER CNF translation.
% 3.22/3.44 0:00:00.08 for inferences.
% 3.22/3.44 0:00:00.00 for the backtracking.
% 3.22/3.44 0:00:02.86 for the reduction.
% 3.22/3.44
% 3.22/3.44
% 3.22/3.44 Here is a proof with depth 5, length 48 :
% 3.22/3.44 % SZS output start Refutation
% See solution above
% 3.22/3.44 Formulae used in the proof : goals additive_idempotence multiplicative_right_identity additive_commutativity order test_2 additive_associativity test_3 right_distributivity
% 3.22/3.44
%------------------------------------------------------------------------------