TSTP Solution File: KLE090+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE090+1 : 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 02:28:28 EDT 2022
% Result : Theorem 0.69s 0.88s
% Output : Refutation 0.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of clauses : 46 ( 41 unt; 0 nHn; 46 RR)
% Number of literals : 51 ( 0 equ; 9 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 : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(addition(skc2,skc3),skc3),
file('KLE090+1.p',unknown),
[] ).
cnf(2,axiom,
equal(addition(u,zero),u),
file('KLE090+1.p',unknown),
[] ).
cnf(3,axiom,
equal(addition(u,u),u),
file('KLE090+1.p',unknown),
[] ).
cnf(4,axiom,
equal(multiplication(u,one),u),
file('KLE090+1.p',unknown),
[] ).
cnf(5,axiom,
equal(multiplication(one,u),u),
file('KLE090+1.p',unknown),
[] ).
cnf(8,axiom,
equal(multiplication(antidomain(u),u),zero),
file('KLE090+1.p',unknown),
[] ).
cnf(12,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE090+1.p',unknown),
[] ).
cnf(13,axiom,
equal(addition(antidomain(antidomain(u)),antidomain(u)),one),
file('KLE090+1.p',unknown),
[] ).
cnf(15,axiom,
~ equal(addition(antidomain(skc3),antidomain(skc2)),antidomain(skc2)),
file('KLE090+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ leq(u,v)
| equal(addition(u,v),v) ),
file('KLE090+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE090+1.p',unknown),
[] ).
cnf(18,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE090+1.p',unknown),
[] ).
cnf(20,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE090+1.p',unknown),
[] ).
cnf(21,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE090+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('KLE090+1.p',unknown),
[] ).
cnf(25,plain,
equal(addition(antidomain(u),antidomain(antidomain(u))),one),
inference(rew,[status(thm),theory(equality)],[12,13]),
[iquote('0:Rew:12.0,13.0')] ).
cnf(26,plain,
~ equal(addition(antidomain(skc2),antidomain(skc3)),antidomain(skc2)),
inference(rew,[status(thm),theory(equality)],[12,15]),
[iquote('0:Rew:12.0,15.0')] ).
cnf(42,plain,
equal(antidomain(one),zero),
inference(spr,[status(thm),theory(equality)],[8,4]),
[iquote('0:SpR:8.0,4.0')] ).
cnf(52,plain,
equal(addition(zero,u),u),
inference(spr,[status(thm),theory(equality)],[12,2]),
[iquote('0:SpR:12.0,2.0')] ).
cnf(75,plain,
equal(addition(zero,antidomain(zero)),one),
inference(spr,[status(thm),theory(equality)],[42,25]),
[iquote('0:SpR:42.0,25.0')] ).
cnf(77,plain,
equal(antidomain(zero),one),
inference(rew,[status(thm),theory(equality)],[52,75]),
[iquote('0:Rew:52.0,75.0')] ).
cnf(86,plain,
( ~ leq(u,v)
| equal(addition(v,u),v) ),
inference(spr,[status(thm),theory(equality)],[16,12]),
[iquote('0:SpR:16.1,12.0')] ).
cnf(137,plain,
equal(addition(u,addition(u,v)),addition(u,v)),
inference(spr,[status(thm),theory(equality)],[3,18]),
[iquote('0:SpR:3.0,18.0')] ).
cnf(246,plain,
equal(addition(multiplication(u,skc2),multiplication(u,skc3)),multiplication(u,skc3)),
inference(spr,[status(thm),theory(equality)],[1,20]),
[iquote('0:SpR:1.0,20.0')] ).
cnf(255,plain,
equal(addition(multiplication(u,antidomain(v)),multiplication(u,antidomain(antidomain(v)))),multiplication(u,one)),
inference(spr,[status(thm),theory(equality)],[25,20]),
[iquote('0:SpR:25.0,20.0')] ).
cnf(266,plain,
equal(addition(multiplication(u,antidomain(v)),multiplication(u,antidomain(antidomain(v)))),u),
inference(rew,[status(thm),theory(equality)],[4,255]),
[iquote('0:Rew:4.0,255.0')] ).
cnf(578,plain,
( ~ leq(antidomain(skc3),antidomain(skc2))
| ~ equal(antidomain(skc2),antidomain(skc2)) ),
inference(spl,[status(thm),theory(equality)],[86,26]),
[iquote('0:SpL:86.1,26.0')] ).
cnf(580,plain,
~ leq(antidomain(skc3),antidomain(skc2)),
inference(obv,[status(thm),theory(equality)],[578]),
[iquote('0:Obv:578.1')] ).
cnf(680,plain,
equal(addition(antidomain(u),one),one),
inference(spr,[status(thm),theory(equality)],[25,137]),
[iquote('0:SpR:25.0,137.0')] ).
cnf(683,plain,
( ~ equal(addition(u,v),addition(u,v))
| leq(u,addition(u,v)) ),
inference(spl,[status(thm),theory(equality)],[137,17]),
[iquote('0:SpL:137.0,17.0')] ).
cnf(691,plain,
equal(addition(one,antidomain(u)),one),
inference(rew,[status(thm),theory(equality)],[12,680]),
[iquote('0:Rew:12.0,680.0')] ).
cnf(698,plain,
leq(u,addition(u,v)),
inference(obv,[status(thm),theory(equality)],[683]),
[iquote('0:Obv:683.0')] ).
cnf(709,plain,
leq(u,addition(v,u)),
inference(spr,[status(thm),theory(equality)],[12,698]),
[iquote('0:SpR:12.0,698.0')] ).
cnf(794,plain,
equal(addition(multiplication(one,u),multiplication(antidomain(v),u)),multiplication(one,u)),
inference(spr,[status(thm),theory(equality)],[691,21]),
[iquote('0:SpR:691.0,21.0')] ).
cnf(808,plain,
equal(addition(u,multiplication(antidomain(v),u)),u),
inference(rew,[status(thm),theory(equality)],[5,794]),
[iquote('0:Rew:5.0,794.0')] ).
cnf(1342,plain,
equal(addition(multiplication(antidomain(skc3),skc2),zero),zero),
inference(spr,[status(thm),theory(equality)],[8,246]),
[iquote('0:SpR:8.0,246.0')] ).
cnf(1356,plain,
equal(multiplication(antidomain(skc3),skc2),zero),
inference(rew,[status(thm),theory(equality)],[52,1342,12]),
[iquote('0:Rew:52.0,1342.0,12.0,1342.0')] ).
cnf(1369,plain,
equal(addition(antidomain(zero),antidomain(multiplication(antidomain(skc3),antidomain(antidomain(skc2))))),antidomain(multiplication(antidomain(skc3),antidomain(antidomain(skc2))))),
inference(spr,[status(thm),theory(equality)],[1356,22]),
[iquote('0:SpR:1356.0,22.0')] ).
cnf(1376,plain,
equal(antidomain(multiplication(antidomain(skc3),antidomain(antidomain(skc2)))),one),
inference(rew,[status(thm),theory(equality)],[691,1369,77]),
[iquote('0:Rew:691.0,1369.0,77.0,1369.0')] ).
cnf(2010,plain,
leq(multiplication(antidomain(u),v),v),
inference(spr,[status(thm),theory(equality)],[808,709]),
[iquote('0:SpR:808.0,709.0')] ).
cnf(3104,plain,
equal(multiplication(one,multiplication(antidomain(skc3),antidomain(antidomain(skc2)))),zero),
inference(spr,[status(thm),theory(equality)],[1376,8]),
[iquote('0:SpR:1376.0,8.0')] ).
cnf(3162,plain,
equal(multiplication(antidomain(skc3),antidomain(antidomain(skc2))),zero),
inference(rew,[status(thm),theory(equality)],[5,3104]),
[iquote('0:Rew:5.0,3104.0')] ).
cnf(4266,plain,
equal(addition(multiplication(antidomain(skc3),antidomain(skc2)),zero),antidomain(skc3)),
inference(spr,[status(thm),theory(equality)],[3162,266]),
[iquote('0:SpR:3162.0,266.0')] ).
cnf(4299,plain,
equal(multiplication(antidomain(skc3),antidomain(skc2)),antidomain(skc3)),
inference(rew,[status(thm),theory(equality)],[52,4266,12]),
[iquote('0:Rew:52.0,4266.0,12.0,4266.0')] ).
cnf(5574,plain,
leq(antidomain(skc3),antidomain(skc2)),
inference(spr,[status(thm),theory(equality)],[4299,2010]),
[iquote('0:SpR:4299.0,2010.0')] ).
cnf(5580,plain,
$false,
inference(mrr,[status(thm)],[5574,580]),
[iquote('0:MRR:5574.0,580.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KLE090+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jun 16 14:49:56 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.69/0.88
% 0.69/0.88 SPASS V 3.9
% 0.69/0.88 SPASS beiseite: Proof found.
% 0.69/0.88 % SZS status Theorem
% 0.69/0.88 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.69/0.88 SPASS derived 4084 clauses, backtracked 0 clauses, performed 0 splits and kept 972 clauses.
% 0.69/0.88 SPASS allocated 89431 KBytes.
% 0.69/0.88 SPASS spent 0:00:00.52 on the problem.
% 0.69/0.88 0:00:00.03 for the input.
% 0.69/0.88 0:00:00.03 for the FLOTTER CNF translation.
% 0.69/0.88 0:00:00.03 for inferences.
% 0.69/0.88 0:00:00.00 for the backtracking.
% 0.69/0.88 0:00:00.40 for the reduction.
% 0.69/0.88
% 0.69/0.88
% 0.69/0.88 Here is a proof with depth 6, length 46 :
% 0.69/0.88 % SZS output start Refutation
% See solution above
% 0.69/0.88 Formulae used in the proof : goals additive_identity additive_idempotence multiplicative_right_identity multiplicative_left_identity domain1 additive_commutativity domain3 order additive_associativity right_distributivity left_distributivity domain2
% 0.69/0.88
%------------------------------------------------------------------------------