TSTP Solution File: KLE082+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE082+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 02:28:25 EDT 2022
% Result : Theorem 5.65s 5.89s
% Output : Refutation 5.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 19
% Syntax : Number of clauses : 67 ( 61 unt; 0 nHn; 67 RR)
% Number of literals : 74 ( 0 equ; 9 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 : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(domain__dfg(zero),zero),
file('KLE082+1.p',unknown),
[] ).
cnf(2,axiom,
equal(addition(u,zero),u),
file('KLE082+1.p',unknown),
[] ).
cnf(3,axiom,
equal(addition(u,u),u),
file('KLE082+1.p',unknown),
[] ).
cnf(4,axiom,
equal(multiplication(u,one),u),
file('KLE082+1.p',unknown),
[] ).
cnf(5,axiom,
equal(multiplication(one,u),u),
file('KLE082+1.p',unknown),
[] ).
cnf(7,axiom,
equal(multiplication(zero,u),zero),
file('KLE082+1.p',unknown),
[] ).
cnf(8,axiom,
equal(addition(domain__dfg(u),one),one),
file('KLE082+1.p',unknown),
[] ).
cnf(9,axiom,
equal(addition(domain__dfg(u),antidomain(u)),one),
file('KLE082+1.p',unknown),
[] ).
cnf(10,axiom,
equal(multiplication(domain__dfg(u),antidomain(u)),zero),
file('KLE082+1.p',unknown),
[] ).
cnf(11,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE082+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ leq(u,v)
| equal(addition(u,v),v) ),
file('KLE082+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE082+1.p',unknown),
[] ).
cnf(14,axiom,
equal(domain__dfg(multiplication(u,domain__dfg(v))),domain__dfg(multiplication(u,v))),
file('KLE082+1.p',unknown),
[] ).
cnf(15,axiom,
equal(addition(domain__dfg(u),domain__dfg(v)),domain__dfg(addition(u,v))),
file('KLE082+1.p',unknown),
[] ).
cnf(16,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE082+1.p',unknown),
[] ).
cnf(18,axiom,
equal(addition(u,multiplication(domain__dfg(u),u)),multiplication(domain__dfg(u),u)),
file('KLE082+1.p',unknown),
[] ).
cnf(19,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE082+1.p',unknown),
[] ).
cnf(20,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE082+1.p',unknown),
[] ).
cnf(21,axiom,
~ equal(addition(antidomain(multiplication(skc2,skc3)),antidomain(multiplication(skc2,domain__dfg(skc3)))),antidomain(multiplication(skc2,domain__dfg(skc3)))),
file('KLE082+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(23,plain,
~ leq(antidomain(multiplication(skc2,skc3)),antidomain(multiplication(skc2,domain__dfg(skc3)))),
inference(res,[status(thm),theory(equality)],[12,21]),
[iquote('0:Res:12.1,21.0')] ).
cnf(43,plain,
equal(addition(zero,u),u),
inference(spr,[status(thm),theory(equality)],[11,2]),
[iquote('0:SpR:11.0,2.0')] ).
cnf(64,plain,
( ~ leq(u,v)
| equal(addition(v,u),v) ),
inference(spr,[status(thm),theory(equality)],[12,11]),
[iquote('0:SpR:12.1,11.0')] ).
cnf(112,plain,
equal(domain__dfg(multiplication(one,u)),domain__dfg(domain__dfg(u))),
inference(spr,[status(thm),theory(equality)],[5,14]),
[iquote('0:SpR:5.0,14.0')] ).
cnf(115,plain,
equal(domain__dfg(domain__dfg(u)),domain__dfg(u)),
inference(rew,[status(thm),theory(equality)],[5,112]),
[iquote('0:Rew:5.0,112.0')] ).
cnf(122,plain,
equal(multiplication(domain__dfg(u),antidomain(domain__dfg(u))),zero),
inference(spr,[status(thm),theory(equality)],[115,10]),
[iquote('0:SpR:115.0,10.0')] ).
cnf(160,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)],[14,18]),
[iquote('0:SpR:14.0,18.0')] ).
cnf(163,plain,
equal(addition(one,domain__dfg(one)),domain__dfg(one)),
inference(spr,[status(thm),theory(equality)],[4,18]),
[iquote('0:SpR:4.0,18.0')] ).
cnf(165,plain,
equal(domain__dfg(one),one),
inference(rew,[status(thm),theory(equality)],[22,163]),
[iquote('0:Rew:22.0,163.0')] ).
cnf(347,plain,
equal(addition(u,addition(u,v)),addition(u,v)),
inference(spr,[status(thm),theory(equality)],[3,16]),
[iquote('0:SpR:3.0,16.0')] ).
cnf(492,plain,
equal(addition(multiplication(one,u),multiplication(domain__dfg(v),u)),multiplication(one,u)),
inference(spr,[status(thm),theory(equality)],[22,20]),
[iquote('0:SpR:22.0,20.0')] ).
cnf(493,plain,
equal(addition(multiplication(domain__dfg(u),v),multiplication(antidomain(u),v)),multiplication(one,v)),
inference(spr,[status(thm),theory(equality)],[9,20]),
[iquote('0:SpR:9.0,20.0')] ).
cnf(495,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)],[15,20]),
[iquote('0:SpR:15.0,20.0')] ).
cnf(503,plain,
equal(addition(u,multiplication(domain__dfg(v),u)),u),
inference(rew,[status(thm),theory(equality)],[5,492]),
[iquote('0:Rew:5.0,492.0')] ).
cnf(504,plain,
equal(multiplication(domain__dfg(u),u),u),
inference(rew,[status(thm),theory(equality)],[503,18]),
[iquote('0:Rew:503.0,18.0')] ).
cnf(506,plain,
equal(multiplication(domain__dfg(multiplication(u,v)),multiplication(u,domain__dfg(v))),multiplication(u,domain__dfg(v))),
inference(rew,[status(thm),theory(equality)],[503,160]),
[iquote('0:Rew:503.0,160.0')] ).
cnf(511,plain,
equal(addition(multiplication(domain__dfg(u),v),multiplication(antidomain(u),v)),v),
inference(rew,[status(thm),theory(equality)],[5,493]),
[iquote('0:Rew:5.0,493.0')] ).
cnf(631,plain,
equal(addition(multiplication(u,domain__dfg(v)),multiplication(u,antidomain(v))),multiplication(u,one)),
inference(spr,[status(thm),theory(equality)],[9,19]),
[iquote('0:SpR:9.0,19.0')] ).
cnf(643,plain,
equal(addition(multiplication(u,domain__dfg(v)),multiplication(u,antidomain(v))),u),
inference(rew,[status(thm),theory(equality)],[4,631]),
[iquote('0:Rew:4.0,631.0')] ).
cnf(893,plain,
( ~ leq(u,v)
| ~ leq(v,u)
| equal(v,u) ),
inference(spr,[status(thm),theory(equality)],[64,12]),
[iquote('0:SpR:64.1,12.1')] ).
cnf(988,plain,
( ~ equal(addition(u,v),addition(u,v))
| leq(u,addition(u,v)) ),
inference(spl,[status(thm),theory(equality)],[347,13]),
[iquote('0:SpL:347.0,13.0')] ).
cnf(995,plain,
leq(u,addition(u,v)),
inference(obv,[status(thm),theory(equality)],[988]),
[iquote('0:Obv:988.0')] ).
cnf(1003,plain,
leq(u,addition(v,u)),
inference(spr,[status(thm),theory(equality)],[11,995]),
[iquote('0:SpR:11.0,995.0')] ).
cnf(2051,plain,
equal(addition(zero,multiplication(antidomain(u),antidomain(domain__dfg(u)))),antidomain(domain__dfg(u))),
inference(spr,[status(thm),theory(equality)],[122,511]),
[iquote('0:SpR:122.0,511.0')] ).
cnf(2070,plain,
equal(multiplication(antidomain(u),antidomain(domain__dfg(u))),antidomain(domain__dfg(u))),
inference(rew,[status(thm),theory(equality)],[43,2051]),
[iquote('0:Rew:43.0,2051.0')] ).
cnf(2217,plain,
leq(multiplication(u,antidomain(v)),u),
inference(spr,[status(thm),theory(equality)],[643,1003]),
[iquote('0:SpR:643.0,1003.0')] ).
cnf(2296,plain,
leq(antidomain(u),domain__dfg(antidomain(u))),
inference(spr,[status(thm),theory(equality)],[504,2217]),
[iquote('0:SpR:504.0,2217.0')] ).
cnf(6754,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)],[10,506]),
[iquote('0:SpR:10.0,506.0')] ).
cnf(6792,plain,
equal(multiplication(domain__dfg(u),domain__dfg(antidomain(u))),zero),
inference(rew,[status(thm),theory(equality)],[7,6754,1]),
[iquote('0:Rew:7.0,6754.0,1.0,6754.0')] ).
cnf(7405,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)],[9,495]),
[iquote('0:SpR:9.0,495.0')] ).
cnf(7448,plain,
equal(addition(multiplication(domain__dfg(u),v),multiplication(domain__dfg(antidomain(u)),v)),v),
inference(rew,[status(thm),theory(equality)],[115,7405,5,165]),
[iquote('0:Rew:115.0,7405.0,5.0,7405.0,165.0,7405.0')] ).
cnf(7534,plain,
equal(addition(zero,multiplication(domain__dfg(u),antidomain(antidomain(u)))),domain__dfg(u)),
inference(spr,[status(thm),theory(equality)],[6792,643]),
[iquote('0:SpR:6792.0,643.0')] ).
cnf(7598,plain,
equal(multiplication(domain__dfg(u),antidomain(antidomain(u))),domain__dfg(u)),
inference(rew,[status(thm),theory(equality)],[43,7534]),
[iquote('0:Rew:43.0,7534.0')] ).
cnf(16697,plain,
( ~ leq(domain__dfg(antidomain(u)),antidomain(u))
| equal(domain__dfg(antidomain(u)),antidomain(u)) ),
inference(res,[status(thm),theory(equality)],[2296,893]),
[iquote('0:Res:2296.0,893.0')] ).
cnf(28528,plain,
leq(antidomain(domain__dfg(u)),antidomain(u)),
inference(spr,[status(thm),theory(equality)],[2070,2217]),
[iquote('0:SpR:2070.0,2217.0')] ).
cnf(29065,plain,
leq(antidomain(domain__dfg(multiplication(u,v))),antidomain(multiplication(u,domain__dfg(v)))),
inference(spr,[status(thm),theory(equality)],[14,28528]),
[iquote('0:SpR:14.0,28528.0')] ).
cnf(29524,plain,
equal(addition(multiplication(domain__dfg(u),antidomain(antidomain(u))),zero),antidomain(antidomain(u))),
inference(spr,[status(thm),theory(equality)],[10,7448]),
[iquote('0:SpR:10.0,7448.0')] ).
cnf(29526,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)],[7598,7448]),
[iquote('0:SpR:7598.0,7448.0')] ).
cnf(29626,plain,
equal(antidomain(antidomain(u)),domain__dfg(u)),
inference(rew,[status(thm),theory(equality)],[43,29524,11,7598]),
[iquote('0:Rew:43.0,29524.0,11.0,29524.0,7598.0,29524.0')] ).
cnf(29890,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)],[11,29526]),
[iquote('0:Rew:11.0,29526.0')] ).
cnf(29891,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)],[29626,29890]),
[iquote('0:Rew:29626.0,29890.0')] ).
cnf(29892,plain,
equal(antidomain(domain__dfg(u)),domain__dfg(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[43,29891,11,122]),
[iquote('0:Rew:43.0,29891.0,11.0,29891.0,122.0,29891.0')] ).
cnf(29911,plain,
leq(domain__dfg(antidomain(u)),antidomain(u)),
inference(rew,[status(thm),theory(equality)],[29892,28528]),
[iquote('0:Rew:29892.0,28528.0')] ).
cnf(29942,plain,
leq(domain__dfg(antidomain(multiplication(u,v))),antidomain(multiplication(u,domain__dfg(v)))),
inference(rew,[status(thm),theory(equality)],[29892,29065]),
[iquote('0:Rew:29892.0,29065.0')] ).
cnf(30125,plain,
equal(domain__dfg(antidomain(u)),antidomain(u)),
inference(mrr,[status(thm)],[16697,29911]),
[iquote('0:MRR:16697.0,29911.0')] ).
cnf(30290,plain,
leq(antidomain(multiplication(u,v)),antidomain(multiplication(u,domain__dfg(v)))),
inference(rew,[status(thm),theory(equality)],[30125,29942]),
[iquote('0:Rew:30125.0,29942.0')] ).
cnf(30291,plain,
$false,
inference(unc,[status(thm)],[30290,23]),
[iquote('0:UnC:30290.0,23.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : KLE082+1 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n008.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
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Thu Jun 16 15:30:07 EDT 2022
% 0.14/0.36 % CPUTime :
% 5.65/5.89
% 5.65/5.89 SPASS V 3.9
% 5.65/5.89 SPASS beiseite: Proof found.
% 5.65/5.89 % SZS status Theorem
% 5.65/5.89 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.65/5.89 SPASS derived 21261 clauses, backtracked 0 clauses, performed 0 splits and kept 3304 clauses.
% 5.65/5.89 SPASS allocated 105615 KBytes.
% 5.65/5.89 SPASS spent 0:00:05.35 on the problem.
% 5.65/5.89 0:00:00.03 for the input.
% 5.65/5.89 0:00:00.03 for the FLOTTER CNF translation.
% 5.65/5.89 0:00:00.13 for inferences.
% 5.65/5.89 0:00:00.00 for the backtracking.
% 5.65/5.89 0:00:05.12 for the reduction.
% 5.65/5.89
% 5.65/5.89
% 5.65/5.89 Here is a proof with depth 6, length 67 :
% 5.65/5.89 % SZS output start Refutation
% See solution above
% 5.65/5.89 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
% 5.65/5.89
%------------------------------------------------------------------------------