TSTP Solution File: KLE099+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE099+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n014.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 02:28:30 EDT 2022
% Result : Theorem 16.03s 16.25s
% Output : Refutation 16.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 18
% Syntax : Number of clauses : 72 ( 65 unt; 0 nHn; 72 RR)
% Number of literals : 79 ( 0 equ; 12 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(addition(u,zero),u),
file('KLE099+1.p',unknown),
[] ).
cnf(2,axiom,
equal(addition(u,u),u),
file('KLE099+1.p',unknown),
[] ).
cnf(3,axiom,
equal(multiplication(u,one),u),
file('KLE099+1.p',unknown),
[] ).
cnf(4,axiom,
equal(multiplication(one,u),u),
file('KLE099+1.p',unknown),
[] ).
cnf(7,axiom,
equal(multiplication(antidomain(u),u),zero),
file('KLE099+1.p',unknown),
[] ).
cnf(8,axiom,
equal(domain__dfg(u),antidomain(antidomain(u))),
file('KLE099+1.p',unknown),
[] ).
cnf(12,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE099+1.p',unknown),
[] ).
cnf(13,axiom,
equal(addition(antidomain(antidomain(u)),antidomain(u)),one),
file('KLE099+1.p',unknown),
[] ).
cnf(15,axiom,
( ~ leq(u,v)
| equal(addition(u,v),v) ),
file('KLE099+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE099+1.p',unknown),
[] ).
cnf(17,axiom,
equal(multiplication(domain__dfg(u),antidomain(v)),domain_difference(u,v)),
file('KLE099+1.p',unknown),
[] ).
cnf(18,axiom,
equal(domain__dfg(multiplication(u,domain__dfg(v))),forward_diamond(u,v)),
file('KLE099+1.p',unknown),
[] ).
cnf(22,axiom,
equal(addition(forward_diamond(skc3,domain__dfg(skc4)),domain__dfg(skc5)),domain__dfg(skc5)),
file('KLE099+1.p',unknown),
[] ).
cnf(23,axiom,
~ equal(multiplication(antidomain(skc5),multiplication(skc3,domain__dfg(skc4))),zero),
file('KLE099+1.p',unknown),
[] ).
cnf(24,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE099+1.p',unknown),
[] ).
cnf(26,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE099+1.p',unknown),
[] ).
cnf(27,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE099+1.p',unknown),
[] ).
cnf(28,axiom,
equal(addition(antidomain(multiplication(u,v)),antidomain(multiplication(u,antidomain(antidomain(v))))),antidomain(multiplication(u,antidomain(antidomain(v))))),
file('KLE099+1.p',unknown),
[] ).
cnf(32,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(37,plain,
equal(antidomain(antidomain(multiplication(u,antidomain(antidomain(v))))),forward_diamond(u,v)),
inference(rew,[status(thm),theory(equality)],[8,18]),
[iquote('0:Rew:8.0,18.0,8.0,18.0')] ).
cnf(38,plain,
equal(multiplication(antidomain(antidomain(u)),antidomain(v)),domain_difference(u,v)),
inference(rew,[status(thm),theory(equality)],[8,17]),
[iquote('0:Rew:8.0,17.0')] ).
cnf(39,plain,
~ equal(multiplication(antidomain(skc5),multiplication(skc3,antidomain(antidomain(skc4)))),zero),
inference(rew,[status(thm),theory(equality)],[8,23]),
[iquote('0:Rew:8.0,23.0')] ).
cnf(40,plain,
equal(addition(antidomain(antidomain(skc5)),forward_diamond(skc3,antidomain(antidomain(skc4)))),antidomain(antidomain(skc5))),
inference(rew,[status(thm),theory(equality)],[12,22,8]),
[iquote('0:Rew:12.0,22.0,8.0,22.0,8.0,22.0')] ).
cnf(54,plain,
equal(antidomain(one),zero),
inference(spr,[status(thm),theory(equality)],[7,3]),
[iquote('0:SpR:7.0,3.0')] ).
cnf(65,plain,
equal(addition(zero,u),u),
inference(spr,[status(thm),theory(equality)],[12,1]),
[iquote('0:SpR:12.0,1.0')] ).
cnf(88,plain,
equal(addition(zero,antidomain(zero)),one),
inference(spr,[status(thm),theory(equality)],[54,32]),
[iquote('0:SpR:54.0,32.0')] ).
cnf(90,plain,
equal(antidomain(zero),one),
inference(rew,[status(thm),theory(equality)],[65,88]),
[iquote('0:Rew:65.0,88.0')] ).
cnf(193,plain,
equal(multiplication(forward_diamond(u,v),antidomain(w)),domain_difference(multiplication(u,antidomain(antidomain(v))),w)),
inference(spr,[status(thm),theory(equality)],[37,38]),
[iquote('0:SpR:37.0,38.0')] ).
cnf(312,plain,
equal(addition(u,addition(u,v)),addition(u,v)),
inference(spr,[status(thm),theory(equality)],[2,24]),
[iquote('0:SpR:2.0,24.0')] ).
cnf(342,plain,
equal(addition(antidomain(u),one),one),
inference(spr,[status(thm),theory(equality)],[32,312]),
[iquote('0:SpR:32.0,312.0')] ).
cnf(344,plain,
( ~ equal(addition(u,v),addition(u,v))
| leq(u,addition(u,v)) ),
inference(spl,[status(thm),theory(equality)],[312,16]),
[iquote('0:SpL:312.0,16.0')] ).
cnf(347,plain,
equal(addition(one,antidomain(u)),one),
inference(rew,[status(thm),theory(equality)],[12,342]),
[iquote('0:Rew:12.0,342.0')] ).
cnf(350,plain,
leq(u,addition(u,v)),
inference(obv,[status(thm),theory(equality)],[344]),
[iquote('0:Obv:344.0')] ).
cnf(356,plain,
leq(u,addition(v,u)),
inference(spr,[status(thm),theory(equality)],[12,350]),
[iquote('0:SpR:12.0,350.0')] ).
cnf(490,plain,
( ~ leq(u,v)
| equal(addition(multiplication(u,w),multiplication(v,w)),multiplication(v,w)) ),
inference(spr,[status(thm),theory(equality)],[15,27]),
[iquote('0:SpR:15.1,27.0')] ).
cnf(498,plain,
equal(addition(multiplication(antidomain(u),v),multiplication(antidomain(antidomain(u)),v)),multiplication(one,v)),
inference(spr,[status(thm),theory(equality)],[32,27]),
[iquote('0:SpR:32.0,27.0')] ).
cnf(499,plain,
equal(addition(multiplication(antidomain(antidomain(skc5)),u),multiplication(forward_diamond(skc3,antidomain(antidomain(skc4))),u)),multiplication(antidomain(antidomain(skc5)),u)),
inference(spr,[status(thm),theory(equality)],[40,27]),
[iquote('0:SpR:40.0,27.0')] ).
cnf(514,plain,
equal(addition(multiplication(antidomain(u),v),multiplication(antidomain(antidomain(u)),v)),v),
inference(rew,[status(thm),theory(equality)],[4,498]),
[iquote('0:Rew:4.0,498.0')] ).
cnf(589,plain,
equal(addition(multiplication(u,antidomain(v)),multiplication(u,antidomain(antidomain(v)))),multiplication(u,one)),
inference(spr,[status(thm),theory(equality)],[32,26]),
[iquote('0:SpR:32.0,26.0')] ).
cnf(592,plain,
equal(addition(multiplication(u,one),multiplication(u,antidomain(v))),multiplication(u,one)),
inference(spr,[status(thm),theory(equality)],[347,26]),
[iquote('0:SpR:347.0,26.0')] ).
cnf(600,plain,
equal(addition(u,multiplication(u,antidomain(v))),u),
inference(rew,[status(thm),theory(equality)],[3,592]),
[iquote('0:Rew:3.0,592.0')] ).
cnf(606,plain,
equal(addition(multiplication(u,antidomain(v)),multiplication(u,antidomain(antidomain(v)))),u),
inference(rew,[status(thm),theory(equality)],[3,589]),
[iquote('0:Rew:3.0,589.0')] ).
cnf(912,plain,
equal(addition(antidomain(zero),antidomain(multiplication(antidomain(u),antidomain(antidomain(u))))),antidomain(multiplication(antidomain(u),antidomain(antidomain(u))))),
inference(spr,[status(thm),theory(equality)],[7,28]),
[iquote('0:SpR:7.0,28.0')] ).
cnf(935,plain,
equal(antidomain(multiplication(antidomain(u),antidomain(antidomain(u)))),one),
inference(rew,[status(thm),theory(equality)],[347,912,90]),
[iquote('0:Rew:347.0,912.0,90.0,912.0')] ).
cnf(1221,plain,
leq(multiplication(u,antidomain(v)),u),
inference(spr,[status(thm),theory(equality)],[600,356]),
[iquote('0:SpR:600.0,356.0')] ).
cnf(1257,plain,
leq(domain_difference(u,v),antidomain(antidomain(u))),
inference(spr,[status(thm),theory(equality)],[38,1221]),
[iquote('0:SpR:38.0,1221.0')] ).
cnf(1275,plain,
equal(multiplication(one,multiplication(antidomain(u),antidomain(antidomain(u)))),zero),
inference(spr,[status(thm),theory(equality)],[935,7]),
[iquote('0:SpR:935.0,7.0')] ).
cnf(1323,plain,
equal(multiplication(antidomain(u),antidomain(antidomain(u))),zero),
inference(rew,[status(thm),theory(equality)],[4,1275]),
[iquote('0:Rew:4.0,1275.0')] ).
cnf(4113,plain,
equal(addition(multiplication(antidomain(u),antidomain(antidomain(antidomain(u)))),zero),antidomain(antidomain(antidomain(u)))),
inference(spr,[status(thm),theory(equality)],[1323,514]),
[iquote('0:SpR:1323.0,514.0')] ).
cnf(4125,plain,
equal(addition(domain_difference(u,v),multiplication(antidomain(antidomain(antidomain(u))),antidomain(v))),antidomain(v)),
inference(spr,[status(thm),theory(equality)],[38,514]),
[iquote('0:SpR:38.0,514.0')] ).
cnf(4155,plain,
equal(multiplication(antidomain(u),antidomain(antidomain(antidomain(u)))),antidomain(antidomain(antidomain(u)))),
inference(rew,[status(thm),theory(equality)],[65,4113,12]),
[iquote('0:Rew:65.0,4113.0,12.0,4113.0')] ).
cnf(4156,plain,
equal(addition(domain_difference(u,v),domain_difference(antidomain(u),v)),antidomain(v)),
inference(rew,[status(thm),theory(equality)],[38,4125]),
[iquote('0:Rew:38.0,4125.0')] ).
cnf(4662,plain,
equal(addition(zero,multiplication(antidomain(u),antidomain(antidomain(antidomain(u))))),antidomain(u)),
inference(spr,[status(thm),theory(equality)],[1323,606]),
[iquote('0:SpR:1323.0,606.0')] ).
cnf(4683,plain,
equal(multiplication(antidomain(u),antidomain(antidomain(antidomain(u)))),antidomain(u)),
inference(rew,[status(thm),theory(equality)],[65,4662]),
[iquote('0:Rew:65.0,4662.0')] ).
cnf(4684,plain,
equal(antidomain(antidomain(antidomain(u))),antidomain(u)),
inference(rew,[status(thm),theory(equality)],[4155,4683]),
[iquote('0:Rew:4155.0,4683.0')] ).
cnf(4828,plain,
leq(domain_difference(antidomain(u),v),antidomain(u)),
inference(spr,[status(thm),theory(equality)],[4684,1257]),
[iquote('0:SpR:4684.0,1257.0')] ).
cnf(4839,plain,
equal(antidomain(antidomain(multiplication(u,antidomain(v)))),forward_diamond(u,antidomain(v))),
inference(spr,[status(thm),theory(equality)],[4684,37]),
[iquote('0:SpR:4684.0,37.0')] ).
cnf(4872,plain,
equal(antidomain(multiplication(u,antidomain(antidomain(v)))),antidomain(forward_diamond(u,v))),
inference(spr,[status(thm),theory(equality)],[37,4684]),
[iquote('0:SpR:37.0,4684.0')] ).
cnf(4919,plain,
equal(forward_diamond(u,antidomain(antidomain(v))),forward_diamond(u,v)),
inference(rew,[status(thm),theory(equality)],[4839,37]),
[iquote('0:Rew:4839.0,37.0')] ).
cnf(4930,plain,
equal(addition(multiplication(antidomain(antidomain(skc5)),u),multiplication(forward_diamond(skc3,skc4),u)),multiplication(antidomain(antidomain(skc5)),u)),
inference(rew,[status(thm),theory(equality)],[4919,499]),
[iquote('0:Rew:4919.0,499.0')] ).
cnf(11374,plain,
( ~ leq(u,antidomain(v))
| equal(addition(multiplication(u,v),zero),zero) ),
inference(spr,[status(thm),theory(equality)],[7,490]),
[iquote('0:SpR:7.0,490.1')] ).
cnf(11433,plain,
( ~ leq(u,antidomain(v))
| equal(multiplication(u,v),zero) ),
inference(rew,[status(thm),theory(equality)],[65,11374,12]),
[iquote('0:Rew:65.0,11374.1,12.0,11374.1')] ).
cnf(12481,plain,
equal(addition(zero,multiplication(forward_diamond(skc3,skc4),antidomain(skc5))),zero),
inference(spr,[status(thm),theory(equality)],[7,4930]),
[iquote('0:SpR:7.0,4930.0')] ).
cnf(12499,plain,
equal(domain_difference(multiplication(skc3,antidomain(antidomain(skc4))),skc5),zero),
inference(rew,[status(thm),theory(equality)],[65,12481,193]),
[iquote('0:Rew:65.0,12481.0,193.0,12481.0')] ).
cnf(36314,plain,
( ~ leq(antidomain(skc5),antidomain(multiplication(skc3,antidomain(antidomain(skc4)))))
| ~ equal(zero,zero) ),
inference(spl,[status(thm),theory(equality)],[11433,39]),
[iquote('0:SpL:11433.1,39.0')] ).
cnf(36341,plain,
~ leq(antidomain(skc5),antidomain(multiplication(skc3,antidomain(antidomain(skc4))))),
inference(obv,[status(thm),theory(equality)],[36314]),
[iquote('0:Obv:36314.1')] ).
cnf(36342,plain,
~ leq(antidomain(skc5),antidomain(forward_diamond(skc3,skc4))),
inference(rew,[status(thm),theory(equality)],[4872,36341]),
[iquote('0:Rew:4872.0,36341.0')] ).
cnf(52950,plain,
equal(addition(zero,domain_difference(antidomain(multiplication(skc3,antidomain(antidomain(skc4)))),skc5)),antidomain(skc5)),
inference(spr,[status(thm),theory(equality)],[12499,4156]),
[iquote('0:SpR:12499.0,4156.0')] ).
cnf(53040,plain,
equal(domain_difference(antidomain(multiplication(skc3,antidomain(antidomain(skc4)))),skc5),antidomain(skc5)),
inference(rew,[status(thm),theory(equality)],[65,52950]),
[iquote('0:Rew:65.0,52950.0')] ).
cnf(53041,plain,
equal(domain_difference(antidomain(forward_diamond(skc3,skc4)),skc5),antidomain(skc5)),
inference(rew,[status(thm),theory(equality)],[4872,53040]),
[iquote('0:Rew:4872.0,53040.0')] ).
cnf(53130,plain,
leq(antidomain(skc5),antidomain(forward_diamond(skc3,skc4))),
inference(spr,[status(thm),theory(equality)],[53041,4828]),
[iquote('0:SpR:53041.0,4828.0')] ).
cnf(53160,plain,
$false,
inference(mrr,[status(thm)],[53130,36342]),
[iquote('0:MRR:53130.0,36342.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE099+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 16 15:23:35 EDT 2022
% 0.12/0.33 % CPUTime :
% 16.03/16.25
% 16.03/16.25 SPASS V 3.9
% 16.03/16.25 SPASS beiseite: Proof found.
% 16.03/16.25 % SZS status Theorem
% 16.03/16.25 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.03/16.25 SPASS derived 34985 clauses, backtracked 0 clauses, performed 0 splits and kept 5302 clauses.
% 16.03/16.25 SPASS allocated 128764 KBytes.
% 16.03/16.25 SPASS spent 0:0:15.85 on the problem.
% 16.03/16.25 0:00:00.04 for the input.
% 16.03/16.25 0:00:00.03 for the FLOTTER CNF translation.
% 16.03/16.25 0:00:00.23 for inferences.
% 16.03/16.25 0:00:00.00 for the backtracking.
% 16.03/16.25 0:0:15.46 for the reduction.
% 16.03/16.25
% 16.03/16.25
% 16.03/16.25 Here is a proof with depth 7, length 72 :
% 16.03/16.25 % SZS output start Refutation
% See solution above
% 16.48/16.67 Formulae used in the proof : additive_identity additive_idempotence multiplicative_right_identity multiplicative_left_identity domain1 domain4 additive_commutativity domain3 order domain_difference forward_diamond goals additive_associativity right_distributivity left_distributivity domain2
% 16.48/16.67
%------------------------------------------------------------------------------