TSTP Solution File: KLE026+2 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE026+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 0.39s 0.56s
% Output : Refutation 0.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 23
% Syntax : Number of clauses : 87 ( 46 unt; 2 nHn; 87 RR)
% Number of literals : 147 ( 0 equ; 63 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
test__dfg(skc4),
file('KLE026+2.p',unknown),
[] ).
cnf(3,axiom,
equal(addition(u,zero),u),
file('KLE026+2.p',unknown),
[] ).
cnf(4,axiom,
equal(addition(u,u),u),
file('KLE026+2.p',unknown),
[] ).
cnf(6,axiom,
equal(multiplication(one,u),u),
file('KLE026+2.p',unknown),
[] ).
cnf(7,axiom,
equal(multiplication(u,zero),zero),
file('KLE026+2.p',unknown),
[] ).
cnf(8,axiom,
equal(multiplication(zero,u),zero),
file('KLE026+2.p',unknown),
[] ).
cnf(9,axiom,
( ~ complement(u,v)
| test__dfg(v) ),
file('KLE026+2.p',unknown),
[] ).
cnf(10,axiom,
( test__dfg(u)
| equal(c(u),zero) ),
file('KLE026+2.p',unknown),
[] ).
cnf(11,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE026+2.p',unknown),
[] ).
cnf(12,axiom,
( ~ test__dfg(u)
| complement(skf1(u),u) ),
file('KLE026+2.p',unknown),
[] ).
cnf(13,axiom,
~ leq(multiplication(skc4,skc5),multiplication(skc5,skc3)),
file('KLE026+2.p',unknown),
[] ).
cnf(14,axiom,
equal(multiplication(multiplication(skc4,skc5),skc3),multiplication(skc4,skc5)),
file('KLE026+2.p',unknown),
[] ).
cnf(16,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE026+2.p',unknown),
[] ).
cnf(17,axiom,
( ~ complement(u,v)
| equal(multiplication(v,u),zero) ),
file('KLE026+2.p',unknown),
[] ).
cnf(18,axiom,
( ~ complement(u,v)
| equal(multiplication(u,v),zero) ),
file('KLE026+2.p',unknown),
[] ).
cnf(19,axiom,
( ~ complement(u,v)
| equal(addition(v,u),one) ),
file('KLE026+2.p',unknown),
[] ).
cnf(20,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE026+2.p',unknown),
[] ).
cnf(21,axiom,
equal(multiplication(multiplication(u,v),w),multiplication(u,multiplication(v,w))),
file('KLE026+2.p',unknown),
[] ).
cnf(22,axiom,
( ~ test__dfg(u)
| ~ equal(c(u),v)
| complement(u,v) ),
file('KLE026+2.p',unknown),
[] ).
cnf(23,axiom,
( ~ test__dfg(u)
| ~ complement(u,v)
| equal(c(u),v) ),
file('KLE026+2.p',unknown),
[] ).
cnf(25,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE026+2.p',unknown),
[] ).
cnf(27,axiom,
( ~ test__dfg(u)
| ~ test__dfg(v)
| equal(c(multiplication(v,u)),addition(c(v),c(u))) ),
file('KLE026+2.p',unknown),
[] ).
cnf(28,axiom,
( ~ equal(addition(u,v),one)
| ~ equal(multiplication(v,u),zero)
| ~ equal(multiplication(u,v),zero)
| complement(v,u) ),
file('KLE026+2.p',unknown),
[] ).
cnf(29,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(39,plain,
( ~ equal(c(skc4),u)
| complement(skc4,u) ),
inference(res,[status(thm),theory(equality)],[1,22]),
[iquote('0:Res:1.0,22.0')] ).
cnf(40,plain,
( ~ complement(skc4,u)
| equal(c(skc4),u) ),
inference(res,[status(thm),theory(equality)],[1,23]),
[iquote('0:Res:1.0,23.0')] ).
cnf(41,plain,
complement(skf1(skc4),skc4),
inference(res,[status(thm),theory(equality)],[1,12]),
[iquote('0:Res:1.0,12.0')] ).
cnf(43,plain,
( ~ test__dfg(u)
| equal(c(multiplication(u,skc4)),addition(c(u),c(skc4))) ),
inference(res,[status(thm),theory(equality)],[1,27]),
[iquote('0:Res:1.0,27.1')] ).
cnf(45,plain,
equal(c(multiplication(skc4,skc4)),addition(c(skc4),c(skc4))),
inference(res,[status(thm),theory(equality)],[1,43]),
[iquote('0:Res:1.0,43.0')] ).
cnf(61,plain,
equal(c(multiplication(skc4,skc4)),c(skc4)),
inference(rew,[status(thm),theory(equality)],[4,45]),
[iquote('0:Rew:4.0,45.0')] ).
cnf(87,plain,
( test__dfg(multiplication(skc4,skc4))
| equal(c(skc4),zero) ),
inference(spr,[status(thm),theory(equality)],[61,10]),
[iquote('0:SpR:61.0,10.1')] ).
cnf(92,plain,
equal(addition(zero,u),u),
inference(spr,[status(thm),theory(equality)],[11,3]),
[iquote('0:SpR:11.0,3.0')] ).
cnf(112,plain,
equal(c(skc4),zero),
inference(spt,[spt(split,[position(s1)])],[87]),
[iquote('1:Spt:87.1')] ).
cnf(115,plain,
( ~ equal(zero,u)
| complement(skc4,u) ),
inference(rew,[status(thm),theory(equality)],[112,39]),
[iquote('1:Rew:112.0,39.0')] ).
cnf(141,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(144,plain,
( ~ complement(u,zero)
| equal(one,u) ),
inference(spr,[status(thm),theory(equality)],[19,92]),
[iquote('0:SpR:19.1,92.0')] ).
cnf(168,plain,
( ~ test__dfg(zero)
| equal(skf1(zero),one) ),
inference(res,[status(thm),theory(equality)],[12,144]),
[iquote('0:Res:12.1,144.0')] ).
cnf(169,plain,
( ~ equal(zero,zero)
| equal(skc4,one) ),
inference(res,[status(thm),theory(equality)],[115,144]),
[iquote('1:Res:115.1,144.0')] ).
cnf(170,plain,
equal(skc4,one),
inference(obv,[status(thm),theory(equality)],[169]),
[iquote('1:Obv:169.0')] ).
cnf(173,plain,
~ leq(multiplication(one,skc5),multiplication(skc5,skc3)),
inference(rew,[status(thm),theory(equality)],[170,13]),
[iquote('1:Rew:170.0,13.0')] ).
cnf(174,plain,
equal(multiplication(one,multiplication(skc5,skc3)),multiplication(one,skc5)),
inference(rew,[status(thm),theory(equality)],[170,29]),
[iquote('1:Rew:170.0,29.0')] ).
cnf(199,plain,
~ leq(skc5,multiplication(skc5,skc3)),
inference(rew,[status(thm),theory(equality)],[6,173]),
[iquote('1:Rew:6.0,173.0')] ).
cnf(202,plain,
equal(multiplication(skc5,skc3),skc5),
inference(rew,[status(thm),theory(equality)],[6,174]),
[iquote('1:Rew:6.0,174.0,6.0,174.0')] ).
cnf(203,plain,
~ leq(skc5,skc5),
inference(rew,[status(thm),theory(equality)],[202,199]),
[iquote('1:Rew:202.0,199.0')] ).
cnf(245,plain,
( ~ equal(u,u)
| leq(u,u) ),
inference(spl,[status(thm),theory(equality)],[4,16]),
[iquote('0:SpL:4.0,16.0')] ).
cnf(251,plain,
leq(u,u),
inference(obv,[status(thm),theory(equality)],[245]),
[iquote('0:Obv:245.0')] ).
cnf(252,plain,
$false,
inference(unc,[status(thm)],[251,203]),
[iquote('1:UnC:251.0,203.0')] ).
cnf(256,plain,
~ equal(c(skc4),zero),
inference(spt,[spt(split,[position(sa)])],[252,112]),
[iquote('1:Spt:252.0,87.1,112.0')] ).
cnf(257,plain,
test__dfg(multiplication(skc4,skc4)),
inference(spt,[spt(split,[position(s2)])],[87]),
[iquote('1:Spt:252.0,87.0')] ).
cnf(288,plain,
( ~ test__dfg(skf1(skc4))
| equal(c(skf1(skc4)),skc4) ),
inference(res,[status(thm),theory(equality)],[41,23]),
[iquote('0:Res:41.0,23.1')] ).
cnf(318,plain,
( ~ test__dfg(u)
| complement(u,c(u)) ),
inference(eqr,[status(thm),theory(equality)],[22]),
[iquote('0:EqR:22.1')] ).
cnf(379,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(570,plain,
( ~ test__dfg(u)
| ~ test__dfg(zero)
| equal(addition(c(zero),c(u)),c(zero)) ),
inference(spr,[status(thm),theory(equality)],[8,27]),
[iquote('0:SpR:8.0,27.2')] ).
cnf(609,plain,
( ~ test__dfg(multiplication(skc4,skc4))
| complement(multiplication(skc4,skc4),c(skc4)) ),
inference(spr,[status(thm),theory(equality)],[61,318]),
[iquote('0:SpR:61.0,318.1')] ).
cnf(620,plain,
complement(multiplication(skc4,skc4),c(skc4)),
inference(ssi,[status(thm)],[609,257]),
[iquote('1:SSi:609.0,257.0')] ).
cnf(628,plain,
( ~ equal(u,one)
| ~ equal(multiplication(u,zero),zero)
| ~ equal(multiplication(zero,u),zero)
| complement(u,zero) ),
inference(spl,[status(thm),theory(equality)],[92,28]),
[iquote('0:SpL:92.0,28.0')] ).
cnf(631,plain,
( ~ equal(u,one)
| ~ equal(zero,zero)
| ~ equal(zero,zero)
| complement(u,zero) ),
inference(rew,[status(thm),theory(equality)],[8,628,7]),
[iquote('0:Rew:8.0,628.2,7.0,628.1')] ).
cnf(632,plain,
( ~ equal(u,one)
| complement(u,zero) ),
inference(obv,[status(thm),theory(equality)],[631]),
[iquote('0:Obv:631.2')] ).
cnf(638,plain,
test__dfg(c(skc4)),
inference(res,[status(thm),theory(equality)],[620,9]),
[iquote('1:Res:620.0,9.0')] ).
cnf(649,plain,
( ~ equal(u,one)
| test__dfg(zero) ),
inference(res,[status(thm),theory(equality)],[632,9]),
[iquote('0:Res:632.1,9.0')] ).
cnf(654,plain,
test__dfg(zero),
inference(aed,[status(thm),theory(equality)],[649]),
[iquote('0:AED:649.0')] ).
cnf(888,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)],[141,28]),
[iquote('0:SpL:141.1,28.0')] ).
cnf(891,plain,
( ~ complement(u,v)
| ~ equal(multiplication(v,u),zero)
| ~ equal(multiplication(u,v),zero)
| complement(v,u) ),
inference(obv,[status(thm),theory(equality)],[888]),
[iquote('0:Obv:888.1')] ).
cnf(892,plain,
( ~ complement(u,v)
| ~ equal(zero,zero)
| ~ equal(zero,zero)
| complement(v,u) ),
inference(rew,[status(thm),theory(equality)],[18,891,17]),
[iquote('0:Rew:18.1,891.2,17.1,891.1')] ).
cnf(893,plain,
( ~ complement(u,v)
| complement(v,u) ),
inference(obv,[status(thm),theory(equality)],[892]),
[iquote('0:Obv:892.2')] ).
cnf(894,plain,
( ~ test__dfg(u)
| complement(u,skf1(u)) ),
inference(res,[status(thm),theory(equality)],[12,893]),
[iquote('0:Res:12.1,893.0')] ).
cnf(895,plain,
complement(skc4,skf1(skc4)),
inference(res,[status(thm),theory(equality)],[41,893]),
[iquote('0:Res:41.0,893.0')] ).
cnf(906,plain,
test__dfg(skf1(skc4)),
inference(res,[status(thm),theory(equality)],[895,9]),
[iquote('0:Res:895.0,9.0')] ).
cnf(907,plain,
equal(skf1(skc4),c(skc4)),
inference(res,[status(thm),theory(equality)],[895,40]),
[iquote('0:Res:895.0,40.0')] ).
cnf(908,plain,
equal(c(skf1(skc4)),skc4),
inference(mrr,[status(thm)],[288,906]),
[iquote('0:MRR:288.0,906.0')] ).
cnf(912,plain,
equal(c(c(skc4)),skc4),
inference(rew,[status(thm),theory(equality)],[907,908]),
[iquote('0:Rew:907.0,908.0')] ).
cnf(1081,plain,
( ~ equal(addition(u,v),addition(u,v))
| leq(u,addition(u,v)) ),
inference(spl,[status(thm),theory(equality)],[379,16]),
[iquote('0:SpL:379.0,16.0')] ).
cnf(1087,plain,
leq(u,addition(u,v)),
inference(obv,[status(thm),theory(equality)],[1081]),
[iquote('0:Obv:1081.0')] ).
cnf(1097,plain,
leq(u,addition(v,u)),
inference(spr,[status(thm),theory(equality)],[11,1087]),
[iquote('0:SpR:11.0,1087.0')] ).
cnf(1237,plain,
( ~ test__dfg(u)
| ~ test__dfg(u)
| equal(skf1(u),c(u)) ),
inference(res,[status(thm),theory(equality)],[894,23]),
[iquote('0:Res:894.1,23.1')] ).
cnf(1245,plain,
( ~ test__dfg(u)
| equal(skf1(u),c(u)) ),
inference(obv,[status(thm),theory(equality)],[1237]),
[iquote('0:Obv:1237.0')] ).
cnf(1308,plain,
( ~ test__dfg(zero)
| equal(c(zero),one) ),
inference(rew,[status(thm),theory(equality)],[1245,168]),
[iquote('0:Rew:1245.1,168.1')] ).
cnf(1309,plain,
equal(c(zero),one),
inference(mrr,[status(thm)],[1308,654]),
[iquote('0:MRR:1308.0,654.0')] ).
cnf(1324,plain,
( ~ test__dfg(u)
| ~ test__dfg(zero)
| equal(addition(one,c(u)),one) ),
inference(rew,[status(thm),theory(equality)],[1309,570]),
[iquote('0:Rew:1309.0,570.2')] ).
cnf(1325,plain,
( ~ test__dfg(u)
| equal(addition(one,c(u)),one) ),
inference(mrr,[status(thm)],[1324,654]),
[iquote('0:MRR:1324.1,654.0')] ).
cnf(1573,plain,
( ~ test__dfg(c(skc4))
| equal(addition(one,skc4),one) ),
inference(spr,[status(thm),theory(equality)],[912,1325]),
[iquote('0:SpR:912.0,1325.1')] ).
cnf(1581,plain,
equal(addition(one,skc4),one),
inference(ssi,[status(thm)],[1573,638]),
[iquote('1:SSi:1573.0,638.0')] ).
cnf(1594,plain,
equal(addition(multiplication(one,u),multiplication(skc4,u)),multiplication(one,u)),
inference(spr,[status(thm),theory(equality)],[1581,25]),
[iquote('1:SpR:1581.0,25.0')] ).
cnf(1608,plain,
equal(addition(u,multiplication(skc4,u)),u),
inference(rew,[status(thm),theory(equality)],[6,1594]),
[iquote('1:Rew:6.0,1594.0')] ).
cnf(1927,plain,
leq(multiplication(skc4,u),u),
inference(spr,[status(thm),theory(equality)],[1608,1097]),
[iquote('1:SpR:1608.0,1097.0')] ).
cnf(1960,plain,
leq(multiplication(skc4,skc5),multiplication(skc5,skc3)),
inference(spr,[status(thm),theory(equality)],[29,1927]),
[iquote('1:SpR:29.0,1927.0')] ).
cnf(1963,plain,
$false,
inference(mrr,[status(thm)],[1960,13]),
[iquote('1:MRR:1960.0,13.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE026+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jun 16 14:27:52 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.39/0.56
% 0.39/0.56 SPASS V 3.9
% 0.39/0.56 SPASS beiseite: Proof found.
% 0.39/0.56 % SZS status Theorem
% 0.39/0.56 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.39/0.56 SPASS derived 1499 clauses, backtracked 82 clauses, performed 2 splits and kept 610 clauses.
% 0.39/0.56 SPASS allocated 98894 KBytes.
% 0.39/0.56 SPASS spent 0:00:00.20 on the problem.
% 0.39/0.56 0:00:00.03 for the input.
% 0.39/0.56 0:00:00.03 for the FLOTTER CNF translation.
% 0.39/0.56 0:00:00.01 for inferences.
% 0.39/0.56 0:00:00.00 for the backtracking.
% 0.39/0.56 0:00:00.10 for the reduction.
% 0.39/0.56
% 0.39/0.56
% 0.39/0.56 Here is a proof with depth 6, length 87 :
% 0.39/0.56 % SZS output start Refutation
% See solution above
% 0.39/0.56 Formulae used in the proof : goals additive_identity additive_idempotence multiplicative_left_identity right_annihilation left_annihilation test_1 test_4 additive_commutativity order test_2 additive_associativity multiplicative_associativity test_3 left_distributivity test_deMorgan2
% 0.39/0.56
%------------------------------------------------------------------------------