TSTP Solution File: KLE027+3 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE027+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 02:28:08 EDT 2022
% Result : Theorem 0.22s 0.56s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 21
% Syntax : Number of clauses : 71 ( 40 unt; 2 nHn; 71 RR)
% Number of literals : 114 ( 0 equ; 52 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
test__dfg(skc6),
file('KLE027+3.p',unknown),
[] ).
cnf(3,axiom,
equal(addition(u,zero),u),
file('KLE027+3.p',unknown),
[] ).
cnf(4,axiom,
equal(addition(u,u),u),
file('KLE027+3.p',unknown),
[] ).
cnf(6,axiom,
equal(multiplication(one,u),u),
file('KLE027+3.p',unknown),
[] ).
cnf(7,axiom,
equal(multiplication(u,zero),zero),
file('KLE027+3.p',unknown),
[] ).
cnf(8,axiom,
equal(multiplication(zero,u),zero),
file('KLE027+3.p',unknown),
[] ).
cnf(9,axiom,
( ~ complement(u,v)
| test__dfg(v) ),
file('KLE027+3.p',unknown),
[] ).
cnf(10,axiom,
( test__dfg(u)
| equal(c(u),zero) ),
file('KLE027+3.p',unknown),
[] ).
cnf(11,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE027+3.p',unknown),
[] ).
cnf(12,axiom,
( ~ test__dfg(u)
| complement(skf1(u),u) ),
file('KLE027+3.p',unknown),
[] ).
cnf(15,axiom,
( ~ complement(u,v)
| equal(multiplication(v,u),zero) ),
file('KLE027+3.p',unknown),
[] ).
cnf(16,axiom,
( ~ complement(u,v)
| equal(multiplication(u,v),zero) ),
file('KLE027+3.p',unknown),
[] ).
cnf(17,axiom,
( ~ complement(u,v)
| equal(addition(v,u),one) ),
file('KLE027+3.p',unknown),
[] ).
cnf(18,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE027+3.p',unknown),
[] ).
cnf(19,axiom,
equal(multiplication(multiplication(u,v),w),multiplication(u,multiplication(v,w))),
file('KLE027+3.p',unknown),
[] ).
cnf(20,axiom,
( ~ test__dfg(u)
| ~ equal(c(u),v)
| complement(u,v) ),
file('KLE027+3.p',unknown),
[] ).
cnf(21,axiom,
( ~ test__dfg(u)
| ~ complement(u,v)
| equal(c(u),v) ),
file('KLE027+3.p',unknown),
[] ).
cnf(22,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE027+3.p',unknown),
[] ).
cnf(25,axiom,
( ~ test__dfg(u)
| ~ test__dfg(v)
| equal(c(multiplication(v,u)),addition(c(v),c(u))) ),
file('KLE027+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('KLE027+3.p',unknown),
[] ).
cnf(27,axiom,
~ equal(addition(multiplication(skc6,addition(multiplication(skc6,skc7),multiplication(c(skc6),skc8))),multiplication(c(skc6),skc9)),addition(multiplication(skc6,skc7),multiplication(c(skc6),skc9))),
file('KLE027+3.p',unknown),
[] ).
cnf(28,plain,
~ equal(addition(multiplication(skc6,multiplication(skc6,skc7)),addition(multiplication(skc6,multiplication(c(skc6),skc8)),multiplication(c(skc6),skc9))),addition(multiplication(skc6,skc7),multiplication(c(skc6),skc9))),
inference(rew,[status(thm),theory(equality)],[18,27,22]),
[iquote('0:Rew:18.0,27.0,22.0,27.0')] ).
cnf(31,plain,
( ~ equal(c(skc6),u)
| complement(skc6,u) ),
inference(res,[status(thm),theory(equality)],[2,20]),
[iquote('0:Res:2.0,20.0')] ).
cnf(32,plain,
( ~ complement(skc6,u)
| equal(c(skc6),u) ),
inference(res,[status(thm),theory(equality)],[2,21]),
[iquote('0:Res:2.0,21.0')] ).
cnf(33,plain,
complement(skf1(skc6),skc6),
inference(res,[status(thm),theory(equality)],[2,12]),
[iquote('0:Res:2.0,12.0')] ).
cnf(35,plain,
( ~ test__dfg(u)
| equal(c(multiplication(u,skc6)),addition(c(u),c(skc6))) ),
inference(res,[status(thm),theory(equality)],[2,25]),
[iquote('0:Res:2.0,25.1')] ).
cnf(55,plain,
equal(c(multiplication(skc6,skc6)),addition(c(skc6),c(skc6))),
inference(res,[status(thm),theory(equality)],[2,35]),
[iquote('0:Res:2.0,35.0')] ).
cnf(67,plain,
equal(c(multiplication(skc6,skc6)),c(skc6)),
inference(rew,[status(thm),theory(equality)],[4,55]),
[iquote('0:Rew:4.0,55.0')] ).
cnf(87,plain,
( test__dfg(multiplication(skc6,skc6))
| equal(c(skc6),zero) ),
inference(spr,[status(thm),theory(equality)],[67,10]),
[iquote('0:SpR:67.0,10.1')] ).
cnf(90,plain,
equal(addition(zero,u),u),
inference(spr,[status(thm),theory(equality)],[11,3]),
[iquote('0:SpR:11.0,3.0')] ).
cnf(111,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(114,plain,
( ~ complement(u,zero)
| equal(one,u) ),
inference(spr,[status(thm),theory(equality)],[17,90]),
[iquote('0:SpR:17.1,90.0')] ).
cnf(233,plain,
( ~ test__dfg(skf1(skc6))
| equal(c(skf1(skc6)),skc6) ),
inference(res,[status(thm),theory(equality)],[33,21]),
[iquote('0:Res:33.0,21.1')] ).
cnf(246,plain,
( ~ test__dfg(u)
| complement(u,c(u)) ),
inference(eqr,[status(thm),theory(equality)],[20]),
[iquote('0:EqR:20.1')] ).
cnf(274,plain,
( ~ complement(u,v)
| equal(multiplication(zero,w),multiplication(v,multiplication(u,w))) ),
inference(spr,[status(thm),theory(equality)],[15,19]),
[iquote('0:SpR:15.1,19.0')] ).
cnf(284,plain,
( ~ complement(u,v)
| equal(multiplication(v,multiplication(u,w)),zero) ),
inference(rew,[status(thm),theory(equality)],[8,274]),
[iquote('0:Rew:8.0,274.1')] ).
cnf(325,plain,
( ~ test__dfg(multiplication(skc6,skc6))
| complement(multiplication(skc6,skc6),c(skc6)) ),
inference(spr,[status(thm),theory(equality)],[67,246]),
[iquote('0:SpR:67.0,246.1')] ).
cnf(330,plain,
( ~ test__dfg(u)
| test__dfg(c(u)) ),
inference(res,[status(thm),theory(equality)],[246,9]),
[iquote('0:Res:246.1,9.0')] ).
cnf(338,plain,
equal(c(skc6),zero),
inference(spt,[spt(split,[position(s1)])],[87]),
[iquote('1:Spt:87.1')] ).
cnf(348,plain,
~ equal(addition(multiplication(skc6,multiplication(skc6,skc7)),addition(multiplication(skc6,multiplication(zero,skc8)),multiplication(zero,skc9))),addition(multiplication(skc6,skc7),multiplication(zero,skc9))),
inference(rew,[status(thm),theory(equality)],[338,28]),
[iquote('1:Rew:338.0,28.0')] ).
cnf(359,plain,
~ equal(multiplication(skc6,multiplication(skc6,skc7)),multiplication(skc6,skc7)),
inference(rew,[status(thm),theory(equality)],[90,348,11,7,8]),
[iquote('1:Rew:90.0,348.0,11.0,348.0,90.0,348.0,7.0,348.0,8.0,348.0,90.0,348.0,11.0,348.0,8.0,348.0')] ).
cnf(361,plain,
( ~ test__dfg(skc6)
| complement(skc6,zero) ),
inference(spr,[status(thm),theory(equality)],[338,246]),
[iquote('1:SpR:338.0,246.1')] ).
cnf(365,plain,
complement(skc6,zero),
inference(ssi,[status(thm)],[361,2]),
[iquote('1:SSi:361.0,2.0')] ).
cnf(377,plain,
equal(skc6,one),
inference(res,[status(thm),theory(equality)],[365,114]),
[iquote('1:Res:365.0,114.0')] ).
cnf(382,plain,
~ equal(multiplication(one,multiplication(one,skc7)),multiplication(one,skc7)),
inference(rew,[status(thm),theory(equality)],[377,359]),
[iquote('1:Rew:377.0,359.0')] ).
cnf(407,plain,
~ equal(skc7,skc7),
inference(rew,[status(thm),theory(equality)],[6,382]),
[iquote('1:Rew:6.0,382.0,6.0,382.0')] ).
cnf(408,plain,
$false,
inference(obv,[status(thm),theory(equality)],[407]),
[iquote('1:Obv:407.0')] ).
cnf(415,plain,
~ equal(c(skc6),zero),
inference(spt,[spt(split,[position(sa)])],[408,338]),
[iquote('1:Spt:408.0,87.1,338.0')] ).
cnf(416,plain,
test__dfg(multiplication(skc6,skc6)),
inference(spt,[spt(split,[position(s2)])],[87]),
[iquote('1:Spt:408.0,87.0')] ).
cnf(420,plain,
complement(multiplication(skc6,skc6),c(skc6)),
inference(mrr,[status(thm)],[325,416]),
[iquote('1:MRR:325.0,416.0')] ).
cnf(616,plain,
complement(skc6,c(skc6)),
inference(eqr,[status(thm),theory(equality)],[31]),
[iquote('0:EqR:31.0')] ).
cnf(915,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)],[111,26]),
[iquote('0:SpL:111.1,26.0')] ).
cnf(920,plain,
( ~ complement(u,v)
| ~ equal(multiplication(v,u),zero)
| ~ equal(multiplication(u,v),zero)
| complement(v,u) ),
inference(obv,[status(thm),theory(equality)],[915]),
[iquote('0:Obv:915.1')] ).
cnf(921,plain,
( ~ complement(u,v)
| ~ equal(zero,zero)
| ~ equal(zero,zero)
| complement(v,u) ),
inference(rew,[status(thm),theory(equality)],[16,920,15]),
[iquote('0:Rew:16.1,920.2,15.1,920.1')] ).
cnf(922,plain,
( ~ complement(u,v)
| complement(v,u) ),
inference(obv,[status(thm),theory(equality)],[921]),
[iquote('0:Obv:921.2')] ).
cnf(925,plain,
complement(skc6,skf1(skc6)),
inference(res,[status(thm),theory(equality)],[33,922]),
[iquote('0:Res:33.0,922.0')] ).
cnf(932,plain,
complement(c(skc6),multiplication(skc6,skc6)),
inference(res,[status(thm),theory(equality)],[420,922]),
[iquote('1:Res:420.0,922.0')] ).
cnf(933,plain,
complement(c(skc6),skc6),
inference(res,[status(thm),theory(equality)],[616,922]),
[iquote('0:Res:616.0,922.0')] ).
cnf(936,plain,
test__dfg(skf1(skc6)),
inference(res,[status(thm),theory(equality)],[925,9]),
[iquote('0:Res:925.0,9.0')] ).
cnf(937,plain,
equal(skf1(skc6),c(skc6)),
inference(res,[status(thm),theory(equality)],[925,32]),
[iquote('0:Res:925.0,32.0')] ).
cnf(938,plain,
equal(c(skf1(skc6)),skc6),
inference(mrr,[status(thm)],[233,936]),
[iquote('0:MRR:233.0,936.0')] ).
cnf(944,plain,
equal(c(c(skc6)),skc6),
inference(rew,[status(thm),theory(equality)],[937,938]),
[iquote('0:Rew:937.0,938.0')] ).
cnf(1042,plain,
( ~ test__dfg(c(skc6))
| equal(multiplication(skc6,skc6),c(c(skc6))) ),
inference(res,[status(thm),theory(equality)],[932,21]),
[iquote('1:Res:932.0,21.1')] ).
cnf(1046,plain,
( ~ test__dfg(c(skc6))
| equal(multiplication(skc6,skc6),skc6) ),
inference(rew,[status(thm),theory(equality)],[944,1042]),
[iquote('1:Rew:944.0,1042.1')] ).
cnf(1047,plain,
equal(multiplication(skc6,skc6),skc6),
inference(ssi,[status(thm)],[1046,330,2]),
[iquote('1:SSi:1046.0,330.0,2.1')] ).
cnf(1085,plain,
equal(multiplication(skc6,multiplication(skc6,u)),multiplication(skc6,u)),
inference(spr,[status(thm),theory(equality)],[1047,19]),
[iquote('1:SpR:1047.0,19.0')] ).
cnf(1087,plain,
~ equal(addition(multiplication(skc6,skc7),addition(multiplication(skc6,multiplication(c(skc6),skc8)),multiplication(c(skc6),skc9))),addition(multiplication(skc6,skc7),multiplication(c(skc6),skc9))),
inference(rew,[status(thm),theory(equality)],[1085,28]),
[iquote('1:Rew:1085.0,28.0')] ).
cnf(1541,plain,
( ~ complement(c(skc6),skc6)
| ~ equal(addition(multiplication(skc6,skc7),addition(zero,multiplication(c(skc6),skc9))),addition(multiplication(skc6,skc7),multiplication(c(skc6),skc9))) ),
inference(spl,[status(thm),theory(equality)],[284,1087]),
[iquote('1:SpL:284.1,1087.0')] ).
cnf(1548,plain,
( ~ complement(c(skc6),skc6)
| ~ equal(addition(multiplication(skc6,skc7),multiplication(c(skc6),skc9)),addition(multiplication(skc6,skc7),multiplication(c(skc6),skc9))) ),
inference(rew,[status(thm),theory(equality)],[90,1541]),
[iquote('1:Rew:90.0,1541.1')] ).
cnf(1549,plain,
~ complement(c(skc6),skc6),
inference(obv,[status(thm),theory(equality)],[1548]),
[iquote('1:Obv:1548.1')] ).
cnf(1550,plain,
$false,
inference(mrr,[status(thm)],[1549,933]),
[iquote('1:MRR:1549.0,933.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : KLE027+3 : TPTP v8.1.0. Released v4.0.0.
% 0.09/0.14 % Command : run_spass %d %s
% 0.14/0.36 % Computer : n028.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 09:37:26 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.22/0.56
% 0.22/0.56 SPASS V 3.9
% 0.22/0.56 SPASS beiseite: Proof found.
% 0.22/0.56 % SZS status Theorem
% 0.22/0.56 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.56 SPASS derived 1195 clauses, backtracked 25 clauses, performed 2 splits and kept 466 clauses.
% 0.22/0.56 SPASS allocated 98774 KBytes.
% 0.22/0.56 SPASS spent 0:00:00.18 on the problem.
% 0.22/0.56 0:00:00.03 for the input.
% 0.22/0.56 0:00:00.03 for the FLOTTER CNF translation.
% 0.22/0.56 0:00:00.01 for inferences.
% 0.22/0.56 0:00:00.00 for the backtracking.
% 0.22/0.56 0:00:00.08 for the reduction.
% 0.22/0.56
% 0.22/0.56
% 0.22/0.56 Here is a proof with depth 6, length 71 :
% 0.22/0.56 % SZS output start Refutation
% See solution above
% 0.22/0.56 Formulae used in the proof : goals additive_identity additive_idempotence multiplicative_left_identity right_annihilation left_annihilation test_1 test_4 additive_commutativity test_2 additive_associativity multiplicative_associativity test_3 right_distributivity test_deMorgan2
% 0.22/0.56
%------------------------------------------------------------------------------