TSTP Solution File: KLE011+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE011+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 02:28:00 EDT 2022
% Result : Theorem 0.54s 0.74s
% Output : Refutation 0.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of clauses : 48 ( 24 unt; 0 nHn; 48 RR)
% Number of literals : 82 ( 0 equ; 44 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
test__dfg(skc3),
file('KLE011+1.p',unknown),
[] ).
cnf(2,axiom,
test__dfg(skc2),
file('KLE011+1.p',unknown),
[] ).
cnf(4,axiom,
equal(addition(u,u),u),
file('KLE011+1.p',unknown),
[] ).
cnf(5,axiom,
equal(multiplication(u,one),u),
file('KLE011+1.p',unknown),
[] ).
cnf(6,axiom,
equal(multiplication(one,u),u),
file('KLE011+1.p',unknown),
[] ).
cnf(11,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE011+1.p',unknown),
[] ).
cnf(15,axiom,
( ~ complement(u,v)
| equal(multiplication(v,u),zero) ),
file('KLE011+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ complement(u,v)
| equal(multiplication(u,v),zero) ),
file('KLE011+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ complement(u,v)
| equal(addition(v,u),one) ),
file('KLE011+1.p',unknown),
[] ).
cnf(18,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE011+1.p',unknown),
[] ).
cnf(20,axiom,
( ~ test__dfg(u)
| ~ equal(c(u),v)
| complement(u,v) ),
file('KLE011+1.p',unknown),
[] ).
cnf(22,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE011+1.p',unknown),
[] ).
cnf(23,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE011+1.p',unknown),
[] ).
cnf(24,axiom,
( ~ equal(addition(u,v),one)
| ~ equal(multiplication(v,u),zero)
| ~ equal(multiplication(u,v),zero)
| complement(v,u) ),
file('KLE011+1.p',unknown),
[] ).
cnf(25,axiom,
~ equal(addition(addition(multiplication(addition(skc2,c(skc2)),skc3),multiplication(addition(skc3,c(skc3)),skc2)),multiplication(c(skc3),c(skc2))),one),
file('KLE011+1.p',unknown),
[] ).
cnf(26,plain,
~ equal(addition(multiplication(skc2,skc3),addition(multiplication(c(skc2),skc3),addition(multiplication(skc3,skc2),addition(multiplication(c(skc3),skc2),multiplication(c(skc3),c(skc2)))))),one),
inference(rew,[status(thm),theory(equality)],[18,25,23]),
[iquote('0:Rew:18.0,25.0,18.0,25.0,18.0,25.0,18.0,25.0,23.0,25.0,23.0,25.0')] ).
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(59,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(81,plain,
complement(skc3,c(skc3)),
inference(eqr,[status(thm),theory(equality)],[30]),
[iquote('0:EqR:30.0')] ).
cnf(94,plain,
complement(skc2,c(skc2)),
inference(eqr,[status(thm),theory(equality)],[27]),
[iquote('0:EqR:27.0')] ).
cnf(186,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(195,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(198,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(207,plain,
equal(addition(u,addition(v,w)),addition(v,addition(u,w))),
inference(rew,[status(thm),theory(equality)],[18,198]),
[iquote('0:Rew:18.0,198.0')] ).
cnf(209,plain,
~ equal(addition(multiplication(skc2,skc3),addition(multiplication(skc3,skc2),addition(multiplication(c(skc2),skc3),addition(multiplication(c(skc3),skc2),multiplication(c(skc3),c(skc2)))))),one),
inference(rew,[status(thm),theory(equality)],[207,26]),
[iquote('0:Rew:207.0,26.0')] ).
cnf(279,plain,
( ~ complement(u,v)
| equal(multiplication(one,w),addition(multiplication(v,w),multiplication(u,w))) ),
inference(spr,[status(thm),theory(equality)],[17,23]),
[iquote('0:SpR:17.1,23.0')] ).
cnf(291,plain,
( ~ complement(u,v)
| equal(addition(multiplication(v,w),multiplication(u,w)),w) ),
inference(rew,[status(thm),theory(equality)],[6,279]),
[iquote('0:Rew:6.0,279.1')] ).
cnf(309,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(321,plain,
( ~ complement(u,v)
| equal(addition(multiplication(w,v),multiplication(w,u)),w) ),
inference(rew,[status(thm),theory(equality)],[5,309]),
[iquote('0:Rew:5.0,309.1')] ).
cnf(335,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)],[59,24]),
[iquote('0:SpL:59.1,24.0')] ).
cnf(349,plain,
( ~ complement(u,v)
| ~ equal(multiplication(v,u),zero)
| ~ equal(multiplication(u,v),zero)
| complement(v,u) ),
inference(obv,[status(thm),theory(equality)],[335]),
[iquote('0:Obv:335.1')] ).
cnf(350,plain,
( ~ complement(u,v)
| ~ equal(zero,zero)
| ~ equal(zero,zero)
| complement(v,u) ),
inference(rew,[status(thm),theory(equality)],[16,349,15]),
[iquote('0:Rew:16.1,349.2,15.1,349.1')] ).
cnf(351,plain,
( ~ complement(u,v)
| complement(v,u) ),
inference(obv,[status(thm),theory(equality)],[350]),
[iquote('0:Obv:350.2')] ).
cnf(568,plain,
complement(c(skc2),skc2),
inference(res,[status(thm),theory(equality)],[94,351]),
[iquote('0:Res:94.0,351.0')] ).
cnf(790,plain,
equal(addition(u,addition(v,w)),addition(addition(u,w),v)),
inference(spr,[status(thm),theory(equality)],[207,11]),
[iquote('0:SpR:207.0,11.0')] ).
cnf(878,plain,
equal(addition(u,addition(v,w)),addition(u,addition(w,v))),
inference(rew,[status(thm),theory(equality)],[18,790]),
[iquote('0:Rew:18.0,790.0')] ).
cnf(2063,plain,
( ~ complement(u,v)
| equal(addition(multiplication(v,w),addition(x,multiplication(u,w))),addition(x,w)) ),
inference(spr,[status(thm),theory(equality)],[291,207]),
[iquote('0:SpR:291.1,207.0')] ).
cnf(2285,plain,
( ~ complement(u,v)
| equal(addition(multiplication(w,v),w),w) ),
inference(spr,[status(thm),theory(equality)],[321,195]),
[iquote('0:SpR:321.1,195.0')] ).
cnf(2334,plain,
( ~ complement(c(skc2),skc2)
| ~ equal(addition(multiplication(skc2,skc3),addition(multiplication(skc3,skc2),addition(multiplication(c(skc2),skc3),c(skc3)))),one) ),
inference(spl,[status(thm),theory(equality)],[321,209]),
[iquote('0:SpL:321.1,209.0')] ).
cnf(2335,plain,
( ~ complement(u,v)
| equal(addition(w,multiplication(w,v)),w) ),
inference(rew,[status(thm),theory(equality)],[11,2285]),
[iquote('0:Rew:11.0,2285.1')] ).
cnf(2368,plain,
( ~ complement(c(skc2),skc2)
| ~ equal(addition(c(skc3),addition(multiplication(skc2,skc3),addition(multiplication(skc3,skc2),multiplication(c(skc2),skc3)))),one) ),
inference(rew,[status(thm),theory(equality)],[207,2334,186]),
[iquote('0:Rew:207.0,2334.1,186.0,2334.1')] ).
cnf(2369,plain,
( ~ complement(c(skc2),skc2)
| ~ equal(addition(c(skc3),skc3),one) ),
inference(rew,[status(thm),theory(equality)],[2335,2368,878,2063]),
[iquote('0:Rew:2335.1,2368.1,878.0,2368.1,2063.1,2368.1')] ).
cnf(2370,plain,
( ~ complement(c(skc2),skc2)
| ~ equal(addition(skc3,c(skc3)),one) ),
inference(rew,[status(thm),theory(equality)],[11,2369]),
[iquote('0:Rew:11.0,2369.1')] ).
cnf(2371,plain,
~ equal(addition(skc3,c(skc3)),one),
inference(mrr,[status(thm)],[2370,568]),
[iquote('0:MRR:2370.0,568.0')] ).
cnf(2380,plain,
( ~ complement(skc3,c(skc3))
| ~ equal(one,one) ),
inference(spl,[status(thm),theory(equality)],[59,2371]),
[iquote('0:SpL:59.1,2371.0')] ).
cnf(2384,plain,
~ complement(skc3,c(skc3)),
inference(obv,[status(thm),theory(equality)],[2380]),
[iquote('0:Obv:2380.1')] ).
cnf(2385,plain,
$false,
inference(mrr,[status(thm)],[2384,81]),
[iquote('0:MRR:2384.0,81.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : KLE011+1 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n009.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Thu Jun 16 10:16:08 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.54/0.74
% 0.54/0.74 SPASS V 3.9
% 0.54/0.74 SPASS beiseite: Proof found.
% 0.54/0.74 % SZS status Theorem
% 0.54/0.74 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.54/0.74 SPASS derived 1841 clauses, backtracked 0 clauses, performed 0 splits and kept 704 clauses.
% 0.54/0.74 SPASS allocated 99396 KBytes.
% 0.54/0.74 SPASS spent 0:00:00.36 on the problem.
% 0.54/0.74 0:00:00.04 for the input.
% 0.54/0.74 0:00:00.03 for the FLOTTER CNF translation.
% 0.54/0.74 0:00:00.02 for inferences.
% 0.54/0.74 0:00:00.00 for the backtracking.
% 0.54/0.74 0:00:00.25 for the reduction.
% 0.54/0.74
% 0.54/0.74
% 0.54/0.74 Here is a proof with depth 3, length 48 :
% 0.54/0.74 % SZS output start Refutation
% See solution above
% 0.54/0.74 Formulae used in the proof : goals additive_idempotence multiplicative_right_identity multiplicative_left_identity additive_commutativity test_2 additive_associativity test_3 right_distributivity left_distributivity
% 0.54/0.74
%------------------------------------------------------------------------------