TSTP Solution File: KLE088+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE088+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n032.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 02:28:27 EDT 2022
% Result : Theorem 0.35s 0.55s
% Output : Refutation 0.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 16
% Syntax : Number of clauses : 48 ( 45 unt; 0 nHn; 48 RR)
% Number of literals : 51 ( 0 equ; 5 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(addition(u,zero),u),
file('KLE088+1.p',unknown),
[] ).
cnf(2,axiom,
equal(addition(u,u),u),
file('KLE088+1.p',unknown),
[] ).
cnf(3,axiom,
equal(multiplication(u,one),u),
file('KLE088+1.p',unknown),
[] ).
cnf(4,axiom,
equal(multiplication(one,u),u),
file('KLE088+1.p',unknown),
[] ).
cnf(7,axiom,
equal(multiplication(domain__dfg(skc2),skc3),zero),
file('KLE088+1.p',unknown),
[] ).
cnf(8,axiom,
equal(multiplication(antidomain(u),u),zero),
file('KLE088+1.p',unknown),
[] ).
cnf(9,axiom,
equal(antidomain(antidomain(u)),domain__dfg(u)),
file('KLE088+1.p',unknown),
[] ).
cnf(12,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE088+1.p',unknown),
[] ).
cnf(13,axiom,
equal(addition(antidomain(antidomain(u)),antidomain(u)),one),
file('KLE088+1.p',unknown),
[] ).
cnf(15,axiom,
~ equal(addition(domain__dfg(skc2),antidomain(skc3)),antidomain(skc3)),
file('KLE088+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ leq(u,v)
| equal(addition(u,v),v) ),
file('KLE088+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE088+1.p',unknown),
[] ).
cnf(18,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE088+1.p',unknown),
[] ).
cnf(20,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE088+1.p',unknown),
[] ).
cnf(21,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE088+1.p',unknown),
[] ).
cnf(22,axiom,
equal(addition(antidomain(multiplication(u,v)),antidomain(multiplication(u,antidomain(antidomain(v))))),antidomain(multiplication(u,antidomain(antidomain(v))))),
file('KLE088+1.p',unknown),
[] ).
cnf(25,plain,
equal(addition(domain__dfg(u),antidomain(u)),one),
inference(rew,[status(thm),theory(equality)],[9,13]),
[iquote('0:Rew:9.0,13.0')] ).
cnf(26,plain,
equal(addition(antidomain(multiplication(u,v)),antidomain(multiplication(u,domain__dfg(v)))),antidomain(multiplication(u,domain__dfg(v)))),
inference(rew,[status(thm),theory(equality)],[9,22]),
[iquote('0:Rew:9.0,22.0')] ).
cnf(27,plain,
~ leq(domain__dfg(skc2),antidomain(skc3)),
inference(res,[status(thm),theory(equality)],[16,15]),
[iquote('0:Res:16.1,15.0')] ).
cnf(42,plain,
equal(antidomain(one),zero),
inference(spr,[status(thm),theory(equality)],[8,3]),
[iquote('0:SpR:8.0,3.0')] ).
cnf(53,plain,
equal(antidomain(zero),domain__dfg(one)),
inference(spr,[status(thm),theory(equality)],[42,9]),
[iquote('0:SpR:42.0,9.0')] ).
cnf(61,plain,
equal(addition(domain__dfg(one),zero),one),
inference(spr,[status(thm),theory(equality)],[42,25]),
[iquote('0:SpR:42.0,25.0')] ).
cnf(64,plain,
equal(domain__dfg(one),one),
inference(rew,[status(thm),theory(equality)],[1,61]),
[iquote('0:Rew:1.0,61.0')] ).
cnf(65,plain,
equal(antidomain(zero),one),
inference(rew,[status(thm),theory(equality)],[64,53]),
[iquote('0:Rew:64.0,53.0')] ).
cnf(81,plain,
equal(addition(zero,u),u),
inference(spr,[status(thm),theory(equality)],[12,1]),
[iquote('0:SpR:12.0,1.0')] ).
cnf(233,plain,
equal(addition(u,addition(u,v)),addition(u,v)),
inference(spr,[status(thm),theory(equality)],[2,18]),
[iquote('0:SpR:2.0,18.0')] ).
cnf(236,plain,
equal(addition(domain__dfg(u),addition(antidomain(u),v)),addition(one,v)),
inference(spr,[status(thm),theory(equality)],[25,18]),
[iquote('0:SpR:25.0,18.0')] ).
cnf(378,plain,
equal(addition(domain__dfg(u),one),one),
inference(spr,[status(thm),theory(equality)],[25,233]),
[iquote('0:SpR:25.0,233.0')] ).
cnf(386,plain,
( ~ equal(addition(u,v),addition(u,v))
| leq(u,addition(u,v)) ),
inference(spl,[status(thm),theory(equality)],[233,17]),
[iquote('0:SpL:233.0,17.0')] ).
cnf(388,plain,
equal(addition(one,domain__dfg(u)),one),
inference(rew,[status(thm),theory(equality)],[12,378]),
[iquote('0:Rew:12.0,378.0')] ).
cnf(394,plain,
leq(u,addition(u,v)),
inference(obv,[status(thm),theory(equality)],[386]),
[iquote('0:Obv:386.0')] ).
cnf(401,plain,
leq(u,addition(v,u)),
inference(spr,[status(thm),theory(equality)],[12,394]),
[iquote('0:SpR:12.0,394.0')] ).
cnf(429,plain,
equal(addition(multiplication(u,domain__dfg(v)),multiplication(u,antidomain(v))),multiplication(u,one)),
inference(spr,[status(thm),theory(equality)],[25,20]),
[iquote('0:SpR:25.0,20.0')] ).
cnf(445,plain,
equal(addition(multiplication(u,domain__dfg(v)),multiplication(u,antidomain(v))),u),
inference(rew,[status(thm),theory(equality)],[3,429]),
[iquote('0:Rew:3.0,429.0')] ).
cnf(477,plain,
equal(addition(multiplication(one,u),multiplication(domain__dfg(v),u)),multiplication(one,u)),
inference(spr,[status(thm),theory(equality)],[388,21]),
[iquote('0:SpR:388.0,21.0')] ).
cnf(489,plain,
equal(addition(u,multiplication(domain__dfg(v),u)),u),
inference(rew,[status(thm),theory(equality)],[4,477]),
[iquote('0:Rew:4.0,477.0')] ).
cnf(517,plain,
equal(addition(antidomain(zero),antidomain(multiplication(domain__dfg(skc2),domain__dfg(skc3)))),antidomain(multiplication(domain__dfg(skc2),domain__dfg(skc3)))),
inference(spr,[status(thm),theory(equality)],[7,26]),
[iquote('0:SpR:7.0,26.0')] ).
cnf(539,plain,
equal(addition(one,antidomain(multiplication(domain__dfg(skc2),domain__dfg(skc3)))),antidomain(multiplication(domain__dfg(skc2),domain__dfg(skc3)))),
inference(rew,[status(thm),theory(equality)],[65,517]),
[iquote('0:Rew:65.0,517.0')] ).
cnf(1086,plain,
leq(multiplication(domain__dfg(u),v),v),
inference(spr,[status(thm),theory(equality)],[489,401]),
[iquote('0:SpR:489.0,401.0')] ).
cnf(1546,plain,
equal(addition(domain__dfg(u),antidomain(u)),addition(one,antidomain(u))),
inference(spr,[status(thm),theory(equality)],[2,236]),
[iquote('0:SpR:2.0,236.0')] ).
cnf(1566,plain,
equal(addition(one,antidomain(u)),one),
inference(rew,[status(thm),theory(equality)],[25,1546]),
[iquote('0:Rew:25.0,1546.0')] ).
cnf(1575,plain,
equal(antidomain(multiplication(domain__dfg(skc2),domain__dfg(skc3))),one),
inference(rew,[status(thm),theory(equality)],[1566,539]),
[iquote('0:Rew:1566.0,539.0')] ).
cnf(1648,plain,
equal(multiplication(one,multiplication(domain__dfg(skc2),domain__dfg(skc3))),zero),
inference(spr,[status(thm),theory(equality)],[1575,8]),
[iquote('0:SpR:1575.0,8.0')] ).
cnf(1681,plain,
equal(multiplication(domain__dfg(skc2),domain__dfg(skc3)),zero),
inference(rew,[status(thm),theory(equality)],[4,1648]),
[iquote('0:Rew:4.0,1648.0')] ).
cnf(2062,plain,
equal(addition(zero,multiplication(domain__dfg(skc2),antidomain(skc3))),domain__dfg(skc2)),
inference(spr,[status(thm),theory(equality)],[1681,445]),
[iquote('0:SpR:1681.0,445.0')] ).
cnf(2077,plain,
equal(multiplication(domain__dfg(skc2),antidomain(skc3)),domain__dfg(skc2)),
inference(rew,[status(thm),theory(equality)],[81,2062]),
[iquote('0:Rew:81.0,2062.0')] ).
cnf(2852,plain,
leq(domain__dfg(skc2),antidomain(skc3)),
inference(spr,[status(thm),theory(equality)],[2077,1086]),
[iquote('0:SpR:2077.0,1086.0')] ).
cnf(2855,plain,
$false,
inference(mrr,[status(thm)],[2852,27]),
[iquote('0:MRR:2852.0,27.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.10 % Problem : KLE088+1 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.10 % Command : run_spass %d %s
% 0.10/0.30 % Computer : n032.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 600
% 0.10/0.30 % DateTime : Thu Jun 16 08:30:44 EDT 2022
% 0.10/0.30 % CPUTime :
% 0.35/0.55
% 0.35/0.55 SPASS V 3.9
% 0.35/0.55 SPASS beiseite: Proof found.
% 0.35/0.55 % SZS status Theorem
% 0.35/0.55 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.35/0.55 SPASS derived 2125 clauses, backtracked 0 clauses, performed 0 splits and kept 501 clauses.
% 0.35/0.55 SPASS allocated 87360 KBytes.
% 0.35/0.55 SPASS spent 0:00:00.23 on the problem.
% 0.35/0.55 0:00:00.02 for the input.
% 0.35/0.55 0:00:00.02 for the FLOTTER CNF translation.
% 0.35/0.55 0:00:00.01 for inferences.
% 0.35/0.55 0:00:00.00 for the backtracking.
% 0.35/0.55 0:00:00.15 for the reduction.
% 0.35/0.55
% 0.35/0.55
% 0.35/0.55 Here is a proof with depth 5, length 48 :
% 0.35/0.55 % SZS output start Refutation
% See solution above
% 0.35/0.55 Formulae used in the proof : additive_identity additive_idempotence multiplicative_right_identity multiplicative_left_identity goals domain1 domain4 additive_commutativity domain3 order additive_associativity right_distributivity left_distributivity domain2
% 0.35/0.55
%------------------------------------------------------------------------------