TSTP Solution File: KLE007+2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE007+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n003.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 02:27:57 EDT 2022
% Result : Theorem 3.44s 3.68s
% Output : Refutation 3.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 16
% Syntax : Number of clauses : 53 ( 24 unt; 0 nHn; 53 RR)
% Number of literals : 94 ( 0 equ; 52 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('KLE007+2.p',unknown),
[] ).
cnf(2,axiom,
test__dfg(skc2),
file('KLE007+2.p',unknown),
[] ).
cnf(4,axiom,
equal(addition(u,u),u),
file('KLE007+2.p',unknown),
[] ).
cnf(5,axiom,
equal(multiplication(u,one),u),
file('KLE007+2.p',unknown),
[] ).
cnf(11,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE007+2.p',unknown),
[] ).
cnf(13,axiom,
( ~ leq(u,v)
| equal(addition(u,v),v) ),
file('KLE007+2.p',unknown),
[] ).
cnf(14,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE007+2.p',unknown),
[] ).
cnf(15,axiom,
( ~ complement(u,v)
| equal(multiplication(v,u),zero) ),
file('KLE007+2.p',unknown),
[] ).
cnf(16,axiom,
( ~ complement(u,v)
| equal(multiplication(u,v),zero) ),
file('KLE007+2.p',unknown),
[] ).
cnf(17,axiom,
( ~ complement(u,v)
| equal(addition(v,u),one) ),
file('KLE007+2.p',unknown),
[] ).
cnf(18,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE007+2.p',unknown),
[] ).
cnf(20,axiom,
( ~ test__dfg(u)
| ~ equal(c(u),v)
| complement(u,v) ),
file('KLE007+2.p',unknown),
[] ).
cnf(22,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE007+2.p',unknown),
[] ).
cnf(23,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE007+2.p',unknown),
[] ).
cnf(24,axiom,
( ~ equal(addition(u,v),one)
| ~ equal(multiplication(v,u),zero)
| ~ equal(multiplication(u,v),zero)
| complement(v,u) ),
file('KLE007+2.p',unknown),
[] ).
cnf(25,axiom,
( ~ leq(one,addition(multiplication(addition(skc3,c(skc3)),skc2),multiplication(addition(skc3,c(skc3)),c(skc2))))
| ~ leq(addition(multiplication(addition(skc3,c(skc3)),skc2),multiplication(addition(skc3,c(skc3)),c(skc2))),one) ),
file('KLE007+2.p',unknown),
[] ).
cnf(26,plain,
( ~ leq(one,addition(multiplication(skc3,c(skc2)),addition(multiplication(skc3,skc2),addition(multiplication(c(skc3),skc2),multiplication(c(skc3),c(skc2))))))
| ~ leq(addition(multiplication(skc3,c(skc2)),addition(multiplication(skc3,skc2),addition(multiplication(c(skc3),skc2),multiplication(c(skc3),c(skc2))))),one) ),
inference(rew,[status(thm),theory(equality)],[18,25,11,23]),
[iquote('0:Rew:18.0,25.1,11.0,25.1,23.0,25.1,18.0,25.1,11.0,25.1,23.0,25.1,18.0,25.0,11.0,25.0,23.0,25.0,18.0,25.0,11.0,25.0,23.0,25.0')] ).
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(197,plain,
equal(addition(addition(u,v),w),addition(v,addition(u,w))),
inference(spr,[status(thm),theory(equality)],[11,18]),
[iquote('0:SpR:11.0,18.0')] ).
cnf(206,plain,
equal(addition(u,addition(v,w)),addition(v,addition(u,w))),
inference(rew,[status(thm),theory(equality)],[18,197]),
[iquote('0:Rew:18.0,197.0')] ).
cnf(207,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,c(skc2)),addition(multiplication(skc3,skc2),addition(multiplication(c(skc3),skc2),multiplication(c(skc3),c(skc2))))),one) ),
inference(rew,[status(thm),theory(equality)],[206,26]),
[iquote('0:Rew:206.0,26.0')] ).
cnf(210,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)],[206,207]),
[iquote('0:Rew:206.0,207.1')] ).
cnf(222,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(308,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(320,plain,
( ~ complement(u,v)
| equal(addition(multiplication(w,v),multiplication(w,u)),w) ),
inference(rew,[status(thm),theory(equality)],[5,308]),
[iquote('0:Rew:5.0,308.1')] ).
cnf(334,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(348,plain,
( ~ complement(u,v)
| ~ equal(multiplication(v,u),zero)
| ~ equal(multiplication(u,v),zero)
| complement(v,u) ),
inference(obv,[status(thm),theory(equality)],[334]),
[iquote('0:Obv:334.1')] ).
cnf(349,plain,
( ~ complement(u,v)
| ~ equal(zero,zero)
| ~ equal(zero,zero)
| complement(v,u) ),
inference(rew,[status(thm),theory(equality)],[16,348,15]),
[iquote('0:Rew:16.1,348.2,15.1,348.1')] ).
cnf(350,plain,
( ~ complement(u,v)
| complement(v,u) ),
inference(obv,[status(thm),theory(equality)],[349]),
[iquote('0:Obv:349.2')] ).
cnf(573,plain,
complement(c(skc3),skc3),
inference(res,[status(thm),theory(equality)],[80,350]),
[iquote('0:Res:80.0,350.0')] ).
cnf(574,plain,
complement(c(skc2),skc2),
inference(res,[status(thm),theory(equality)],[93,350]),
[iquote('0:Res:93.0,350.0')] ).
cnf(2349,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)],[320,210]),
[iquote('0:SpL:320.1,210.1')] ).
cnf(2384,plain,
( ~ complement(c(skc2),skc2)
| ~ leq(one,addition(skc3,c(skc3)))
| ~ leq(addition(skc3,c(skc3)),one) ),
inference(rew,[status(thm),theory(equality)],[11,2349,320,185]),
[iquote('0:Rew:11.0,2349.2,320.1,2349.2,185.0,2349.2,11.0,2349.1,320.1,2349.1,185.0,2349.1,320.1,2349.1')] ).
cnf(2385,plain,
( ~ leq(one,addition(skc3,c(skc3)))
| ~ leq(addition(skc3,c(skc3)),one) ),
inference(mrr,[status(thm)],[2384,574]),
[iquote('0:MRR:2384.0,574.0')] ).
cnf(2390,plain,
equal(addition(skc3,one),one),
inference(res,[status(thm),theory(equality)],[80,222]),
[iquote('0:Res:80.0,222.0')] ).
cnf(2399,plain,
equal(addition(c(skc3),one),one),
inference(res,[status(thm),theory(equality)],[573,222]),
[iquote('0:Res:573.0,222.0')] ).
cnf(2406,plain,
equal(addition(one,skc3),one),
inference(rew,[status(thm),theory(equality)],[11,2390]),
[iquote('0:Rew:11.0,2390.0')] ).
cnf(2408,plain,
equal(addition(one,c(skc3)),one),
inference(rew,[status(thm),theory(equality)],[11,2399]),
[iquote('0:Rew:11.0,2399.0')] ).
cnf(2425,plain,
equal(addition(one,addition(skc3,u)),addition(one,u)),
inference(spr,[status(thm),theory(equality)],[2406,18]),
[iquote('0:SpR:2406.0,18.0')] ).
cnf(16003,plain,
( ~ leq(one,addition(skc3,u))
| equal(addition(skc3,u),addition(one,u)) ),
inference(spr,[status(thm),theory(equality)],[2425,13]),
[iquote('0:SpR:2425.0,13.1')] ).
cnf(16193,plain,
( ~ leq(one,addition(skc3,c(skc3)))
| ~ leq(addition(one,c(skc3)),one) ),
inference(rew,[status(thm),theory(equality)],[16003,2385]),
[iquote('0:Rew:16003.1,2385.1')] ).
cnf(16207,plain,
( ~ leq(one,addition(skc3,c(skc3)))
| ~ leq(one,one) ),
inference(rew,[status(thm),theory(equality)],[2408,16193]),
[iquote('0:Rew:2408.0,16193.1')] ).
cnf(16208,plain,
~ leq(one,addition(skc3,c(skc3))),
inference(mrr,[status(thm)],[16207,105]),
[iquote('0:MRR:16207.1,105.0')] ).
cnf(16390,plain,
( ~ complement(skc3,c(skc3))
| ~ leq(one,one) ),
inference(spl,[status(thm),theory(equality)],[58,16208]),
[iquote('0:SpL:58.1,16208.0')] ).
cnf(16397,plain,
$false,
inference(mrr,[status(thm)],[16390,80,105]),
[iquote('0:MRR:16390.0,16390.1,80.0,105.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KLE007+2 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n003.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 13:31:11 EDT 2022
% 0.13/0.34 % CPUTime :
% 3.44/3.68
% 3.44/3.68 SPASS V 3.9
% 3.44/3.68 SPASS beiseite: Proof found.
% 3.44/3.68 % SZS status Theorem
% 3.44/3.68 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.44/3.68 SPASS derived 11666 clauses, backtracked 0 clauses, performed 0 splits and kept 2979 clauses.
% 3.44/3.68 SPASS allocated 108413 KBytes.
% 3.44/3.68 SPASS spent 0:00:03.27 on the problem.
% 3.44/3.68 0:00:00.04 for the input.
% 3.44/3.68 0:00:00.03 for the FLOTTER CNF translation.
% 3.44/3.68 0:00:00.09 for inferences.
% 3.44/3.68 0:00:00.00 for the backtracking.
% 3.44/3.68 0:00:03.07 for the reduction.
% 3.44/3.68
% 3.44/3.68
% 3.44/3.68 Here is a proof with depth 5, length 53 :
% 3.44/3.68 % SZS output start Refutation
% See solution above
% 3.44/3.68 Formulae used in the proof : goals additive_idempotence multiplicative_right_identity additive_commutativity order test_2 additive_associativity test_3 right_distributivity left_distributivity
% 3.44/3.68
%------------------------------------------------------------------------------