TSTP Solution File: KLE079+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE079+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n012.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 02:28:24 EDT 2022
% Result : Theorem 5.32s 5.50s
% Output : Refutation 5.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 19
% Syntax : Number of clauses : 85 ( 79 unt; 0 nHn; 85 RR)
% Number of literals : 92 ( 0 equ; 8 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(domain__dfg(zero),zero),
file('KLE079+1.p',unknown),
[] ).
cnf(2,axiom,
equal(addition(u,zero),u),
file('KLE079+1.p',unknown),
[] ).
cnf(3,axiom,
equal(addition(u,u),u),
file('KLE079+1.p',unknown),
[] ).
cnf(4,axiom,
equal(multiplication(u,one),u),
file('KLE079+1.p',unknown),
[] ).
cnf(5,axiom,
equal(multiplication(one,u),u),
file('KLE079+1.p',unknown),
[] ).
cnf(7,axiom,
equal(multiplication(zero,u),zero),
file('KLE079+1.p',unknown),
[] ).
cnf(8,axiom,
equal(addition(domain__dfg(u),one),one),
file('KLE079+1.p',unknown),
[] ).
cnf(9,axiom,
equal(addition(domain__dfg(u),antidomain(u)),one),
file('KLE079+1.p',unknown),
[] ).
cnf(10,axiom,
equal(multiplication(domain__dfg(u),antidomain(u)),zero),
file('KLE079+1.p',unknown),
[] ).
cnf(11,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE079+1.p',unknown),
[] ).
cnf(12,axiom,
~ equal(multiplication(antidomain(skc1),domain__dfg(skc1)),zero),
file('KLE079+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ leq(u,v)
| equal(addition(u,v),v) ),
file('KLE079+1.p',unknown),
[] ).
cnf(14,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE079+1.p',unknown),
[] ).
cnf(15,axiom,
equal(domain__dfg(multiplication(u,domain__dfg(v))),domain__dfg(multiplication(u,v))),
file('KLE079+1.p',unknown),
[] ).
cnf(16,axiom,
equal(addition(domain__dfg(u),domain__dfg(v)),domain__dfg(addition(u,v))),
file('KLE079+1.p',unknown),
[] ).
cnf(17,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE079+1.p',unknown),
[] ).
cnf(19,axiom,
equal(addition(u,multiplication(domain__dfg(u),u)),multiplication(domain__dfg(u),u)),
file('KLE079+1.p',unknown),
[] ).
cnf(20,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE079+1.p',unknown),
[] ).
cnf(21,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE079+1.p',unknown),
[] ).
cnf(22,plain,
equal(addition(one,domain__dfg(u)),one),
inference(rew,[status(thm),theory(equality)],[11,8]),
[iquote('0:Rew:11.0,8.0')] ).
cnf(42,plain,
equal(addition(zero,u),u),
inference(spr,[status(thm),theory(equality)],[11,2]),
[iquote('0:SpR:11.0,2.0')] ).
cnf(63,plain,
( ~ leq(u,v)
| equal(addition(v,u),v) ),
inference(spr,[status(thm),theory(equality)],[13,11]),
[iquote('0:SpR:13.1,11.0')] ).
cnf(99,plain,
equal(multiplication(domain__dfg(multiplication(u,v)),antidomain(multiplication(u,domain__dfg(v)))),zero),
inference(spr,[status(thm),theory(equality)],[15,10]),
[iquote('0:SpR:15.0,10.0')] ).
cnf(107,plain,
equal(domain__dfg(multiplication(one,u)),domain__dfg(domain__dfg(u))),
inference(spr,[status(thm),theory(equality)],[5,15]),
[iquote('0:SpR:5.0,15.0')] ).
cnf(110,plain,
equal(domain__dfg(domain__dfg(u)),domain__dfg(u)),
inference(rew,[status(thm),theory(equality)],[5,107]),
[iquote('0:Rew:5.0,107.0')] ).
cnf(116,plain,
equal(multiplication(domain__dfg(u),antidomain(domain__dfg(u))),zero),
inference(spr,[status(thm),theory(equality)],[110,10]),
[iquote('0:SpR:110.0,10.0')] ).
cnf(158,plain,
equal(addition(multiplication(u,domain__dfg(v)),multiplication(domain__dfg(multiplication(u,v)),multiplication(u,domain__dfg(v)))),multiplication(domain__dfg(multiplication(u,v)),multiplication(u,domain__dfg(v)))),
inference(spr,[status(thm),theory(equality)],[15,19]),
[iquote('0:SpR:15.0,19.0')] ).
cnf(161,plain,
equal(addition(one,domain__dfg(one)),domain__dfg(one)),
inference(spr,[status(thm),theory(equality)],[4,19]),
[iquote('0:SpR:4.0,19.0')] ).
cnf(163,plain,
equal(domain__dfg(one),one),
inference(rew,[status(thm),theory(equality)],[22,161]),
[iquote('0:Rew:22.0,161.0')] ).
cnf(169,plain,
equal(addition(one,domain__dfg(u)),domain__dfg(addition(one,u))),
inference(spr,[status(thm),theory(equality)],[163,16]),
[iquote('0:SpR:163.0,16.0')] ).
cnf(182,plain,
equal(domain__dfg(addition(one,u)),one),
inference(rew,[status(thm),theory(equality)],[22,169]),
[iquote('0:Rew:22.0,169.0')] ).
cnf(199,plain,
equal(addition(domain__dfg(u),one),domain__dfg(addition(u,addition(one,v)))),
inference(spr,[status(thm),theory(equality)],[182,16]),
[iquote('0:SpR:182.0,16.0')] ).
cnf(200,plain,
equal(domain__dfg(multiplication(u,addition(one,v))),domain__dfg(multiplication(u,one))),
inference(spr,[status(thm),theory(equality)],[182,15]),
[iquote('0:SpR:182.0,15.0')] ).
cnf(216,plain,
equal(domain__dfg(addition(u,addition(one,v))),one),
inference(rew,[status(thm),theory(equality)],[22,199,11]),
[iquote('0:Rew:22.0,199.0,11.0,199.0')] ).
cnf(217,plain,
equal(domain__dfg(multiplication(u,addition(one,v))),domain__dfg(u)),
inference(rew,[status(thm),theory(equality)],[4,200]),
[iquote('0:Rew:4.0,200.0')] ).
cnf(218,plain,
equal(domain__dfg(addition(multiplication(u,one),multiplication(u,v))),domain__dfg(u)),
inference(rew,[status(thm),theory(equality)],[20,217]),
[iquote('0:Rew:20.0,217.0')] ).
cnf(219,plain,
equal(domain__dfg(addition(u,multiplication(u,v))),domain__dfg(u)),
inference(rew,[status(thm),theory(equality)],[4,218]),
[iquote('0:Rew:4.0,218.0')] ).
cnf(317,plain,
equal(addition(u,addition(u,v)),addition(u,v)),
inference(spr,[status(thm),theory(equality)],[3,17]),
[iquote('0:SpR:3.0,17.0')] ).
cnf(319,plain,
equal(addition(addition(u,v),w),addition(v,addition(u,w))),
inference(spr,[status(thm),theory(equality)],[11,17]),
[iquote('0:SpR:11.0,17.0')] ).
cnf(330,plain,
equal(addition(u,addition(v,w)),addition(v,addition(u,w))),
inference(rew,[status(thm),theory(equality)],[17,319]),
[iquote('0:Rew:17.0,319.0')] ).
cnf(464,plain,
equal(addition(multiplication(one,u),multiplication(domain__dfg(v),u)),multiplication(one,u)),
inference(spr,[status(thm),theory(equality)],[22,21]),
[iquote('0:SpR:22.0,21.0')] ).
cnf(465,plain,
equal(addition(multiplication(domain__dfg(u),v),multiplication(antidomain(u),v)),multiplication(one,v)),
inference(spr,[status(thm),theory(equality)],[9,21]),
[iquote('0:SpR:9.0,21.0')] ).
cnf(467,plain,
equal(multiplication(domain__dfg(addition(u,v)),w),addition(multiplication(domain__dfg(u),w),multiplication(domain__dfg(v),w))),
inference(spr,[status(thm),theory(equality)],[16,21]),
[iquote('0:SpR:16.0,21.0')] ).
cnf(475,plain,
equal(addition(u,multiplication(domain__dfg(v),u)),u),
inference(rew,[status(thm),theory(equality)],[5,464]),
[iquote('0:Rew:5.0,464.0')] ).
cnf(476,plain,
equal(multiplication(domain__dfg(u),u),u),
inference(rew,[status(thm),theory(equality)],[475,19]),
[iquote('0:Rew:475.0,19.0')] ).
cnf(478,plain,
equal(multiplication(domain__dfg(multiplication(u,v)),multiplication(u,domain__dfg(v))),multiplication(u,domain__dfg(v))),
inference(rew,[status(thm),theory(equality)],[475,158]),
[iquote('0:Rew:475.0,158.0')] ).
cnf(483,plain,
equal(addition(multiplication(domain__dfg(u),v),multiplication(antidomain(u),v)),v),
inference(rew,[status(thm),theory(equality)],[5,465]),
[iquote('0:Rew:5.0,465.0')] ).
cnf(576,plain,
equal(addition(multiplication(u,domain__dfg(v)),multiplication(u,antidomain(v))),multiplication(u,one)),
inference(spr,[status(thm),theory(equality)],[9,20]),
[iquote('0:SpR:9.0,20.0')] ).
cnf(588,plain,
equal(addition(multiplication(u,domain__dfg(v)),multiplication(u,antidomain(v))),u),
inference(rew,[status(thm),theory(equality)],[4,576]),
[iquote('0:Rew:4.0,576.0')] ).
cnf(833,plain,
equal(domain__dfg(addition(addition(u,multiplication(u,v)),w)),addition(domain__dfg(u),domain__dfg(w))),
inference(spr,[status(thm),theory(equality)],[219,16]),
[iquote('0:SpR:219.0,16.0')] ).
cnf(878,plain,
equal(domain__dfg(addition(u,addition(multiplication(u,v),w))),domain__dfg(addition(u,w))),
inference(rew,[status(thm),theory(equality)],[17,833,16]),
[iquote('0:Rew:17.0,833.0,16.0,833.0')] ).
cnf(889,plain,
( ~ leq(u,v)
| ~ leq(v,u)
| equal(v,u) ),
inference(spr,[status(thm),theory(equality)],[63,13]),
[iquote('0:SpR:63.1,13.1')] ).
cnf(983,plain,
( ~ equal(addition(u,v),addition(u,v))
| leq(u,addition(u,v)) ),
inference(spl,[status(thm),theory(equality)],[317,14]),
[iquote('0:SpL:317.0,14.0')] ).
cnf(990,plain,
leq(u,addition(u,v)),
inference(obv,[status(thm),theory(equality)],[983]),
[iquote('0:Obv:983.0')] ).
cnf(998,plain,
leq(u,addition(v,u)),
inference(spr,[status(thm),theory(equality)],[11,990]),
[iquote('0:SpR:11.0,990.0')] ).
cnf(1908,plain,
equal(addition(zero,multiplication(antidomain(u),antidomain(domain__dfg(u)))),antidomain(domain__dfg(u))),
inference(spr,[status(thm),theory(equality)],[116,483]),
[iquote('0:SpR:116.0,483.0')] ).
cnf(1927,plain,
equal(multiplication(antidomain(u),antidomain(domain__dfg(u))),antidomain(domain__dfg(u))),
inference(rew,[status(thm),theory(equality)],[42,1908]),
[iquote('0:Rew:42.0,1908.0')] ).
cnf(2090,plain,
leq(multiplication(u,antidomain(v)),u),
inference(spr,[status(thm),theory(equality)],[588,998]),
[iquote('0:SpR:588.0,998.0')] ).
cnf(2169,plain,
leq(antidomain(u),domain__dfg(antidomain(u))),
inference(spr,[status(thm),theory(equality)],[476,2090]),
[iquote('0:SpR:476.0,2090.0')] ).
cnf(2991,plain,
equal(multiplication(domain__dfg(multiplication(u,addition(v,addition(one,w)))),antidomain(multiplication(u,one))),zero),
inference(spr,[status(thm),theory(equality)],[216,99]),
[iquote('0:SpR:216.0,99.0')] ).
cnf(3044,plain,
equal(multiplication(domain__dfg(addition(u,addition(multiplication(u,v),multiplication(u,w)))),antidomain(u)),zero),
inference(rew,[status(thm),theory(equality)],[330,2991,4,20]),
[iquote('0:Rew:330.0,2991.0,4.0,2991.0,20.0,2991.0,20.0,2991.0,4.0,2991.0')] ).
cnf(3045,plain,
equal(addition(multiplication(domain__dfg(u),antidomain(u)),multiplication(domain__dfg(multiplication(u,v)),antidomain(u))),zero),
inference(rew,[status(thm),theory(equality)],[467,3044,878]),
[iquote('0:Rew:467.0,3044.0,878.0,3044.0')] ).
cnf(3046,plain,
equal(multiplication(domain__dfg(multiplication(u,v)),antidomain(u)),zero),
inference(rew,[status(thm),theory(equality)],[42,3045,10]),
[iquote('0:Rew:42.0,3045.0,10.0,3045.0')] ).
cnf(6720,plain,
equal(multiplication(domain__dfg(zero),multiplication(domain__dfg(u),domain__dfg(antidomain(u)))),multiplication(domain__dfg(u),domain__dfg(antidomain(u)))),
inference(spr,[status(thm),theory(equality)],[10,478]),
[iquote('0:SpR:10.0,478.0')] ).
cnf(6758,plain,
equal(multiplication(domain__dfg(u),domain__dfg(antidomain(u))),zero),
inference(rew,[status(thm),theory(equality)],[7,6720,1]),
[iquote('0:Rew:7.0,6720.0,1.0,6720.0')] ).
cnf(7290,plain,
equal(addition(zero,multiplication(domain__dfg(u),antidomain(antidomain(u)))),domain__dfg(u)),
inference(spr,[status(thm),theory(equality)],[6758,588]),
[iquote('0:SpR:6758.0,588.0')] ).
cnf(7353,plain,
equal(multiplication(domain__dfg(u),antidomain(antidomain(u))),domain__dfg(u)),
inference(rew,[status(thm),theory(equality)],[42,7290]),
[iquote('0:Rew:42.0,7290.0')] ).
cnf(7541,plain,
equal(addition(multiplication(domain__dfg(domain__dfg(u)),v),multiplication(domain__dfg(antidomain(u)),v)),multiplication(domain__dfg(one),v)),
inference(spr,[status(thm),theory(equality)],[9,467]),
[iquote('0:SpR:9.0,467.0')] ).
cnf(7584,plain,
equal(addition(multiplication(domain__dfg(u),v),multiplication(domain__dfg(antidomain(u)),v)),v),
inference(rew,[status(thm),theory(equality)],[110,7541,5,163]),
[iquote('0:Rew:110.0,7541.0,5.0,7541.0,163.0,7541.0')] ).
cnf(17863,plain,
( ~ leq(domain__dfg(antidomain(u)),antidomain(u))
| equal(domain__dfg(antidomain(u)),antidomain(u)) ),
inference(res,[status(thm),theory(equality)],[2169,889]),
[iquote('0:Res:2169.0,889.0')] ).
cnf(27713,plain,
equal(multiplication(domain__dfg(antidomain(domain__dfg(u))),antidomain(antidomain(u))),zero),
inference(spr,[status(thm),theory(equality)],[1927,3046]),
[iquote('0:SpR:1927.0,3046.0')] ).
cnf(27726,plain,
leq(antidomain(domain__dfg(u)),antidomain(u)),
inference(spr,[status(thm),theory(equality)],[1927,2090]),
[iquote('0:SpR:1927.0,2090.0')] ).
cnf(30466,plain,
equal(addition(multiplication(domain__dfg(u),antidomain(antidomain(u))),zero),antidomain(antidomain(u))),
inference(spr,[status(thm),theory(equality)],[10,7584]),
[iquote('0:SpR:10.0,7584.0')] ).
cnf(30468,plain,
equal(addition(multiplication(domain__dfg(u),antidomain(antidomain(antidomain(u)))),domain__dfg(antidomain(u))),antidomain(antidomain(antidomain(u)))),
inference(spr,[status(thm),theory(equality)],[7353,7584]),
[iquote('0:SpR:7353.0,7584.0')] ).
cnf(30571,plain,
equal(antidomain(antidomain(u)),domain__dfg(u)),
inference(rew,[status(thm),theory(equality)],[42,30466,11,7353]),
[iquote('0:Rew:42.0,30466.0,11.0,30466.0,7353.0,30466.0')] ).
cnf(30587,plain,
equal(multiplication(domain__dfg(antidomain(domain__dfg(u))),domain__dfg(u)),zero),
inference(rew,[status(thm),theory(equality)],[30571,27713]),
[iquote('0:Rew:30571.0,27713.0')] ).
cnf(30865,plain,
equal(addition(domain__dfg(antidomain(u)),multiplication(domain__dfg(u),antidomain(antidomain(antidomain(u))))),antidomain(antidomain(antidomain(u)))),
inference(rew,[status(thm),theory(equality)],[11,30468]),
[iquote('0:Rew:11.0,30468.0')] ).
cnf(30866,plain,
equal(addition(domain__dfg(antidomain(u)),multiplication(domain__dfg(u),antidomain(domain__dfg(u)))),antidomain(domain__dfg(u))),
inference(rew,[status(thm),theory(equality)],[30571,30865]),
[iquote('0:Rew:30571.0,30865.0')] ).
cnf(30867,plain,
equal(antidomain(domain__dfg(u)),domain__dfg(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[42,30866,11,116]),
[iquote('0:Rew:42.0,30866.0,11.0,30866.0,116.0,30866.0')] ).
cnf(30888,plain,
leq(domain__dfg(antidomain(u)),antidomain(u)),
inference(rew,[status(thm),theory(equality)],[30867,27726]),
[iquote('0:Rew:30867.0,27726.0')] ).
cnf(31135,plain,
equal(multiplication(domain__dfg(domain__dfg(antidomain(u))),domain__dfg(u)),zero),
inference(rew,[status(thm),theory(equality)],[30867,30587]),
[iquote('0:Rew:30867.0,30587.0')] ).
cnf(31199,plain,
equal(domain__dfg(antidomain(u)),antidomain(u)),
inference(mrr,[status(thm)],[17863,30888]),
[iquote('0:MRR:17863.0,30888.0')] ).
cnf(31325,plain,
equal(multiplication(domain__dfg(antidomain(u)),domain__dfg(u)),zero),
inference(rew,[status(thm),theory(equality)],[110,31135]),
[iquote('0:Rew:110.0,31135.0')] ).
cnf(31326,plain,
equal(multiplication(antidomain(u),domain__dfg(u)),zero),
inference(rew,[status(thm),theory(equality)],[31199,31325]),
[iquote('0:Rew:31199.0,31325.0')] ).
cnf(31327,plain,
$false,
inference(unc,[status(thm)],[31326,12]),
[iquote('0:UnC:31326.0,12.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE079+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n012.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 09:07:54 EDT 2022
% 0.13/0.34 % CPUTime :
% 5.32/5.50
% 5.32/5.50 SPASS V 3.9
% 5.32/5.50 SPASS beiseite: Proof found.
% 5.32/5.50 % SZS status Theorem
% 5.32/5.50 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.32/5.50 SPASS derived 21967 clauses, backtracked 0 clauses, performed 0 splits and kept 3483 clauses.
% 5.32/5.50 SPASS allocated 106424 KBytes.
% 5.32/5.50 SPASS spent 0:00:05.13 on the problem.
% 5.32/5.50 0:00:00.04 for the input.
% 5.32/5.50 0:00:00.03 for the FLOTTER CNF translation.
% 5.32/5.50 0:00:00.11 for inferences.
% 5.32/5.50 0:00:00.00 for the backtracking.
% 5.32/5.50 0:00:04.91 for the reduction.
% 5.32/5.50
% 5.32/5.50
% 5.32/5.50 Here is a proof with depth 6, length 85 :
% 5.32/5.50 % SZS output start Refutation
% See solution above
% 5.47/5.63 Formulae used in the proof : domain4 additive_identity additive_idempotence multiplicative_right_identity multiplicative_left_identity left_annihilation domain3 goals additive_commutativity order domain2 domain5 additive_associativity domain1 right_distributivity left_distributivity
% 5.47/5.63
%------------------------------------------------------------------------------