TSTP Solution File: KLE062+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE062+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 02:28:19 EDT 2022
% Result : Theorem 112.33s 112.57s
% Output : Refutation 115.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 15
% Syntax : Number of clauses : 72 ( 66 unt; 0 nHn; 72 RR)
% Number of literals : 79 ( 0 equ; 10 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 : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
equal(addition(u,u),u),
file('KLE062+1.p',unknown),
[] ).
cnf(4,axiom,
equal(multiplication(u,one),u),
file('KLE062+1.p',unknown),
[] ).
cnf(5,axiom,
equal(multiplication(one,u),u),
file('KLE062+1.p',unknown),
[] ).
cnf(8,axiom,
equal(addition(domain__dfg(u),one),one),
file('KLE062+1.p',unknown),
[] ).
cnf(9,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE062+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ leq(u,v)
| equal(addition(u,v),v) ),
file('KLE062+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE062+1.p',unknown),
[] ).
cnf(12,axiom,
equal(domain__dfg(multiplication(u,domain__dfg(v))),domain__dfg(multiplication(u,v))),
file('KLE062+1.p',unknown),
[] ).
cnf(13,axiom,
equal(addition(domain__dfg(u),domain__dfg(v)),domain__dfg(addition(u,v))),
file('KLE062+1.p',unknown),
[] ).
cnf(14,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE062+1.p',unknown),
[] ).
cnf(15,axiom,
equal(multiplication(multiplication(u,v),w),multiplication(u,multiplication(v,w))),
file('KLE062+1.p',unknown),
[] ).
cnf(16,axiom,
equal(addition(u,multiplication(domain__dfg(u),u)),multiplication(domain__dfg(u),u)),
file('KLE062+1.p',unknown),
[] ).
cnf(17,axiom,
~ equal(multiplication(domain__dfg(skc3),domain__dfg(skc2)),multiplication(domain__dfg(skc2),domain__dfg(skc3))),
file('KLE062+1.p',unknown),
[] ).
cnf(18,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE062+1.p',unknown),
[] ).
cnf(19,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE062+1.p',unknown),
[] ).
cnf(20,plain,
equal(addition(one,domain__dfg(u)),one),
inference(rew,[status(thm),theory(equality)],[9,8]),
[iquote('0:Rew:9.0,8.0')] ).
cnf(45,plain,
( ~ leq(u,v)
| equal(addition(v,u),v) ),
inference(spr,[status(thm),theory(equality)],[10,9]),
[iquote('0:SpR:10.1,9.0')] ).
cnf(90,plain,
equal(domain__dfg(multiplication(one,u)),domain__dfg(domain__dfg(u))),
inference(spr,[status(thm),theory(equality)],[5,12]),
[iquote('0:SpR:5.0,12.0')] ).
cnf(93,plain,
equal(domain__dfg(domain__dfg(u)),domain__dfg(u)),
inference(rew,[status(thm),theory(equality)],[5,90]),
[iquote('0:Rew:5.0,90.0')] ).
cnf(99,plain,
equal(addition(domain__dfg(u),domain__dfg(v)),domain__dfg(addition(domain__dfg(u),v))),
inference(spr,[status(thm),theory(equality)],[93,13]),
[iquote('0:SpR:93.0,13.0')] ).
cnf(108,plain,
equal(domain__dfg(addition(domain__dfg(u),v)),domain__dfg(addition(u,v))),
inference(rew,[status(thm),theory(equality)],[13,99]),
[iquote('0:Rew:13.0,99.0')] ).
cnf(172,plain,
( ~ leq(u,v)
| ~ leq(v,u)
| equal(v,u) ),
inference(spr,[status(thm),theory(equality)],[45,10]),
[iquote('0:SpR:45.1,10.1')] ).
cnf(190,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)],[12,16]),
[iquote('0:SpR:12.0,16.0')] ).
cnf(191,plain,
equal(addition(domain__dfg(u),multiplication(domain__dfg(u),domain__dfg(u))),multiplication(domain__dfg(u),domain__dfg(u))),
inference(spr,[status(thm),theory(equality)],[93,16]),
[iquote('0:SpR:93.0,16.0')] ).
cnf(193,plain,
equal(addition(one,domain__dfg(one)),domain__dfg(one)),
inference(spr,[status(thm),theory(equality)],[4,16]),
[iquote('0:SpR:4.0,16.0')] ).
cnf(195,plain,
equal(domain__dfg(one),one),
inference(rew,[status(thm),theory(equality)],[20,193]),
[iquote('0:Rew:20.0,193.0')] ).
cnf(201,plain,
equal(addition(one,domain__dfg(u)),domain__dfg(addition(one,u))),
inference(spr,[status(thm),theory(equality)],[195,13]),
[iquote('0:SpR:195.0,13.0')] ).
cnf(208,plain,
equal(domain__dfg(addition(one,u)),one),
inference(rew,[status(thm),theory(equality)],[20,201]),
[iquote('0:Rew:20.0,201.0')] ).
cnf(220,plain,
equal(domain__dfg(multiplication(u,addition(one,v))),domain__dfg(multiplication(u,one))),
inference(spr,[status(thm),theory(equality)],[208,12]),
[iquote('0:SpR:208.0,12.0')] ).
cnf(234,plain,
equal(domain__dfg(multiplication(u,addition(one,v))),domain__dfg(u)),
inference(rew,[status(thm),theory(equality)],[4,220]),
[iquote('0:Rew:4.0,220.0')] ).
cnf(235,plain,
equal(domain__dfg(addition(multiplication(u,one),multiplication(u,v))),domain__dfg(u)),
inference(rew,[status(thm),theory(equality)],[18,234]),
[iquote('0:Rew:18.0,234.0')] ).
cnf(236,plain,
equal(domain__dfg(addition(u,multiplication(u,v))),domain__dfg(u)),
inference(rew,[status(thm),theory(equality)],[4,235]),
[iquote('0:Rew:4.0,235.0')] ).
cnf(467,plain,
equal(addition(u,addition(u,v)),addition(u,v)),
inference(spr,[status(thm),theory(equality)],[3,14]),
[iquote('0:SpR:3.0,14.0')] ).
cnf(569,plain,
( ~ equal(addition(u,v),addition(u,v))
| leq(u,addition(u,v)) ),
inference(spl,[status(thm),theory(equality)],[467,11]),
[iquote('0:SpL:467.0,11.0')] ).
cnf(574,plain,
leq(u,addition(u,v)),
inference(obv,[status(thm),theory(equality)],[569]),
[iquote('0:Obv:569.0')] ).
cnf(586,plain,
leq(u,addition(v,u)),
inference(spr,[status(thm),theory(equality)],[9,574]),
[iquote('0:SpR:9.0,574.0')] ).
cnf(619,plain,
equal(addition(multiplication(one,u),multiplication(domain__dfg(v),u)),multiplication(one,u)),
inference(spr,[status(thm),theory(equality)],[20,19]),
[iquote('0:SpR:20.0,19.0')] ).
cnf(620,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)],[13,19]),
[iquote('0:SpR:13.0,19.0')] ).
cnf(629,plain,
equal(addition(u,multiplication(domain__dfg(v),u)),u),
inference(rew,[status(thm),theory(equality)],[5,619]),
[iquote('0:Rew:5.0,619.0')] ).
cnf(630,plain,
equal(multiplication(domain__dfg(u),u),u),
inference(rew,[status(thm),theory(equality)],[629,16]),
[iquote('0:Rew:629.0,16.0')] ).
cnf(631,plain,
equal(multiplication(domain__dfg(multiplication(u,v)),multiplication(u,domain__dfg(v))),multiplication(u,domain__dfg(v))),
inference(rew,[status(thm),theory(equality)],[629,190]),
[iquote('0:Rew:629.0,190.0')] ).
cnf(632,plain,
equal(multiplication(domain__dfg(u),domain__dfg(u)),domain__dfg(u)),
inference(rew,[status(thm),theory(equality)],[629,191]),
[iquote('0:Rew:629.0,191.0')] ).
cnf(822,plain,
equal(addition(multiplication(u,one),multiplication(u,domain__dfg(v))),multiplication(u,one)),
inference(spr,[status(thm),theory(equality)],[20,18]),
[iquote('0:SpR:20.0,18.0')] ).
cnf(823,plain,
equal(multiplication(u,domain__dfg(addition(v,w))),addition(multiplication(u,domain__dfg(v)),multiplication(u,domain__dfg(w)))),
inference(spr,[status(thm),theory(equality)],[13,18]),
[iquote('0:SpR:13.0,18.0')] ).
cnf(832,plain,
equal(addition(u,multiplication(u,domain__dfg(v))),u),
inference(rew,[status(thm),theory(equality)],[4,822]),
[iquote('0:Rew:4.0,822.0')] ).
cnf(942,plain,
equal(addition(multiplication(u,v),multiplication(u,multiplication(domain__dfg(w),v))),multiplication(u,v)),
inference(spr,[status(thm),theory(equality)],[629,18]),
[iquote('0:SpR:629.0,18.0')] ).
cnf(1092,plain,
leq(multiplication(u,domain__dfg(v)),u),
inference(spr,[status(thm),theory(equality)],[832,586]),
[iquote('0:SpR:832.0,586.0')] ).
cnf(1147,plain,
leq(multiplication(u,multiplication(v,domain__dfg(w))),multiplication(u,v)),
inference(spr,[status(thm),theory(equality)],[15,1092]),
[iquote('0:SpR:15.0,1092.0')] ).
cnf(5713,plain,
equal(addition(multiplication(domain__dfg(u),v),multiplication(domain__dfg(multiplication(domain__dfg(w),u)),v)),multiplication(domain__dfg(u),v)),
inference(spr,[status(thm),theory(equality)],[629,620]),
[iquote('0:SpR:629.0,620.0')] ).
cnf(6144,plain,
equal(addition(multiplication(u,domain__dfg(v)),multiplication(u,domain__dfg(multiplication(domain__dfg(w),v)))),multiplication(u,domain__dfg(v))),
inference(spr,[status(thm),theory(equality)],[629,823]),
[iquote('0:SpR:629.0,823.0')] ).
cnf(8489,plain,
equal(domain__dfg(addition(u,multiplication(domain__dfg(u),v))),domain__dfg(domain__dfg(u))),
inference(spr,[status(thm),theory(equality)],[108,236]),
[iquote('0:SpR:108.0,236.0')] ).
cnf(8586,plain,
equal(domain__dfg(addition(u,multiplication(domain__dfg(u),v))),domain__dfg(u)),
inference(rew,[status(thm),theory(equality)],[93,8489]),
[iquote('0:Rew:93.0,8489.0')] ).
cnf(18258,plain,
equal(addition(multiplication(domain__dfg(u),v),multiplication(domain__dfg(multiplication(domain__dfg(u),w)),v)),multiplication(domain__dfg(u),v)),
inference(spr,[status(thm),theory(equality)],[8586,620]),
[iquote('0:SpR:8586.0,620.0')] ).
cnf(22443,plain,
leq(multiplication(u,domain__dfg(v)),multiplication(domain__dfg(multiplication(u,v)),u)),
inference(spr,[status(thm),theory(equality)],[631,1147]),
[iquote('0:SpR:631.0,1147.0')] ).
cnf(56025,plain,
equal(addition(multiplication(domain__dfg(multiplication(domain__dfg(u),v)),domain__dfg(v)),multiplication(domain__dfg(u),domain__dfg(v))),multiplication(domain__dfg(multiplication(domain__dfg(u),v)),domain__dfg(v))),
inference(spr,[status(thm),theory(equality)],[631,942]),
[iquote('0:SpR:631.0,942.0')] ).
cnf(56199,plain,
equal(addition(multiplication(domain__dfg(u),domain__dfg(v)),multiplication(domain__dfg(multiplication(domain__dfg(u),v)),domain__dfg(v))),multiplication(domain__dfg(multiplication(domain__dfg(u),v)),domain__dfg(v))),
inference(rew,[status(thm),theory(equality)],[9,56025]),
[iquote('0:Rew:9.0,56025.0')] ).
cnf(56200,plain,
equal(multiplication(domain__dfg(multiplication(domain__dfg(u),v)),domain__dfg(v)),multiplication(domain__dfg(u),domain__dfg(v))),
inference(rew,[status(thm),theory(equality)],[18258,56199]),
[iquote('0:Rew:18258.0,56199.0')] ).
cnf(127673,plain,
equal(addition(multiplication(domain__dfg(u),multiplication(domain__dfg(v),u)),multiplication(domain__dfg(v),u)),multiplication(domain__dfg(u),multiplication(domain__dfg(v),u))),
inference(spr,[status(thm),theory(equality)],[630,5713]),
[iquote('0:SpR:630.0,5713.0')] ).
cnf(127936,plain,
equal(multiplication(domain__dfg(u),multiplication(domain__dfg(v),u)),multiplication(domain__dfg(v),u)),
inference(rew,[status(thm),theory(equality)],[629,127673,9]),
[iquote('0:Rew:629.0,127673.0,9.0,127673.0')] ).
cnf(129236,plain,
equal(addition(multiplication(domain__dfg(multiplication(domain__dfg(u),v)),domain__dfg(v)),domain__dfg(multiplication(domain__dfg(u),v))),multiplication(domain__dfg(multiplication(domain__dfg(u),v)),domain__dfg(v))),
inference(spr,[status(thm),theory(equality)],[632,6144]),
[iquote('0:SpR:632.0,6144.0')] ).
cnf(129591,plain,
equal(multiplication(domain__dfg(multiplication(domain__dfg(u),v)),domain__dfg(v)),domain__dfg(multiplication(domain__dfg(u),v))),
inference(rew,[status(thm),theory(equality)],[832,129236,9]),
[iquote('0:Rew:832.0,129236.0,9.0,129236.0')] ).
cnf(129592,plain,
equal(multiplication(domain__dfg(u),domain__dfg(v)),domain__dfg(multiplication(domain__dfg(u),v))),
inference(rew,[status(thm),theory(equality)],[56200,129591]),
[iquote('0:Rew:56200.0,129591.0')] ).
cnf(129626,plain,
~ equal(domain__dfg(multiplication(domain__dfg(skc3),skc2)),multiplication(domain__dfg(skc2),domain__dfg(skc3))),
inference(rew,[status(thm),theory(equality)],[129592,17]),
[iquote('0:Rew:129592.0,17.0')] ).
cnf(130613,plain,
~ equal(domain__dfg(multiplication(domain__dfg(skc3),skc2)),domain__dfg(multiplication(domain__dfg(skc2),skc3))),
inference(rew,[status(thm),theory(equality)],[129592,129626]),
[iquote('0:Rew:129592.0,129626.0')] ).
cnf(132413,plain,
equal(multiplication(domain__dfg(multiplication(domain__dfg(u),v)),w),multiplication(domain__dfg(u),multiplication(domain__dfg(v),w))),
inference(spr,[status(thm),theory(equality)],[129592,15]),
[iquote('0:SpR:129592.0,15.0')] ).
cnf(132451,plain,
leq(domain__dfg(multiplication(domain__dfg(u),v)),multiplication(domain__dfg(multiplication(domain__dfg(u),v)),domain__dfg(u))),
inference(spr,[status(thm),theory(equality)],[129592,22443]),
[iquote('0:SpR:129592.0,22443.0')] ).
cnf(132743,plain,
leq(domain__dfg(multiplication(domain__dfg(u),v)),domain__dfg(multiplication(domain__dfg(multiplication(domain__dfg(u),v)),u))),
inference(rew,[status(thm),theory(equality)],[129592,132451]),
[iquote('0:Rew:129592.0,132451.0')] ).
cnf(132813,plain,
leq(domain__dfg(multiplication(domain__dfg(u),v)),domain__dfg(multiplication(domain__dfg(u),multiplication(domain__dfg(v),u)))),
inference(rew,[status(thm),theory(equality)],[132413,132743]),
[iquote('0:Rew:132413.0,132743.0')] ).
cnf(132975,plain,
leq(domain__dfg(multiplication(domain__dfg(u),v)),domain__dfg(multiplication(domain__dfg(v),u))),
inference(rew,[status(thm),theory(equality)],[127936,132813]),
[iquote('0:Rew:127936.0,132813.0')] ).
cnf(133268,plain,
( ~ leq(domain__dfg(multiplication(domain__dfg(u),v)),domain__dfg(multiplication(domain__dfg(v),u)))
| equal(domain__dfg(multiplication(domain__dfg(u),v)),domain__dfg(multiplication(domain__dfg(v),u))) ),
inference(res,[status(thm),theory(equality)],[132975,172]),
[iquote('0:Res:132975.0,172.0')] ).
cnf(133449,plain,
equal(domain__dfg(multiplication(domain__dfg(u),v)),domain__dfg(multiplication(domain__dfg(v),u))),
inference(mrr,[status(thm)],[133268,132975]),
[iquote('0:MRR:133268.0,132975.0')] ).
cnf(133450,plain,
$false,
inference(unc,[status(thm)],[133449,130613]),
[iquote('0:UnC:133449.0,130613.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE062+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n025.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 13:33:11 EDT 2022
% 0.13/0.34 % CPUTime :
% 112.33/112.57
% 112.33/112.57 SPASS V 3.9
% 112.33/112.57 SPASS beiseite: Proof found.
% 112.33/112.57 % SZS status Theorem
% 112.33/112.57 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 112.33/112.57 SPASS derived 91795 clauses, backtracked 0 clauses, performed 0 splits and kept 15237 clauses.
% 112.33/112.57 SPASS allocated 168696 KBytes.
% 112.33/112.57 SPASS spent 0:1:52.09 on the problem.
% 112.33/112.57 0:00:00.04 for the input.
% 112.33/112.57 0:00:00.04 for the FLOTTER CNF translation.
% 112.33/112.57 0:00:00.59 for inferences.
% 112.33/112.57 0:00:00.00 for the backtracking.
% 112.33/112.57 0:1:51.30 for the reduction.
% 112.33/112.57
% 112.33/112.57
% 112.33/112.57 Here is a proof with depth 8, length 72 :
% 112.33/112.57 % SZS output start Refutation
% See solution above
% 115.37/115.57 Formulae used in the proof : additive_idempotence multiplicative_right_identity multiplicative_left_identity domain3 additive_commutativity order domain2 domain5 additive_associativity multiplicative_associativity domain1 goals right_distributivity left_distributivity
% 115.37/115.57
%------------------------------------------------------------------------------