TSTP Solution File: KLE081+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE081+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 6.91s 7.09s
% Output : Refutation 7.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 20
% Syntax : Number of clauses : 107 ( 87 unt; 0 nHn; 107 RR)
% Number of literals : 128 ( 0 equ; 22 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 : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(domain__dfg(zero),zero),
file('KLE081+1.p',unknown),
[] ).
cnf(2,axiom,
equal(addition(u,zero),u),
file('KLE081+1.p',unknown),
[] ).
cnf(3,axiom,
equal(addition(u,u),u),
file('KLE081+1.p',unknown),
[] ).
cnf(4,axiom,
equal(multiplication(u,one),u),
file('KLE081+1.p',unknown),
[] ).
cnf(5,axiom,
equal(multiplication(one,u),u),
file('KLE081+1.p',unknown),
[] ).
cnf(7,axiom,
equal(multiplication(zero,u),zero),
file('KLE081+1.p',unknown),
[] ).
cnf(8,axiom,
equal(addition(domain__dfg(u),one),one),
file('KLE081+1.p',unknown),
[] ).
cnf(9,axiom,
~ equal(multiplication(antidomain(skc1),skc1),zero),
file('KLE081+1.p',unknown),
[] ).
cnf(10,axiom,
equal(addition(domain__dfg(u),antidomain(u)),one),
file('KLE081+1.p',unknown),
[] ).
cnf(11,axiom,
equal(multiplication(domain__dfg(u),antidomain(u)),zero),
file('KLE081+1.p',unknown),
[] ).
cnf(12,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE081+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ leq(u,v)
| equal(addition(u,v),v) ),
file('KLE081+1.p',unknown),
[] ).
cnf(14,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE081+1.p',unknown),
[] ).
cnf(15,axiom,
equal(domain__dfg(multiplication(u,domain__dfg(v))),domain__dfg(multiplication(u,v))),
file('KLE081+1.p',unknown),
[] ).
cnf(16,axiom,
equal(addition(domain__dfg(u),domain__dfg(v)),domain__dfg(addition(u,v))),
file('KLE081+1.p',unknown),
[] ).
cnf(17,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE081+1.p',unknown),
[] ).
cnf(18,axiom,
equal(multiplication(multiplication(u,v),w),multiplication(u,multiplication(v,w))),
file('KLE081+1.p',unknown),
[] ).
cnf(19,axiom,
equal(addition(u,multiplication(domain__dfg(u),u)),multiplication(domain__dfg(u),u)),
file('KLE081+1.p',unknown),
[] ).
cnf(20,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE081+1.p',unknown),
[] ).
cnf(21,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE081+1.p',unknown),
[] ).
cnf(22,plain,
equal(addition(one,domain__dfg(u)),one),
inference(rew,[status(thm),theory(equality)],[12,8]),
[iquote('0:Rew:12.0,8.0')] ).
cnf(42,plain,
equal(addition(zero,u),u),
inference(spr,[status(thm),theory(equality)],[12,2]),
[iquote('0:SpR:12.0,2.0')] ).
cnf(56,plain,
( ~ leq(u,zero)
| equal(zero,u) ),
inference(spr,[status(thm),theory(equality)],[13,2]),
[iquote('0:SpR:13.1,2.0')] ).
cnf(58,plain,
( ~ leq(u,v)
| equal(addition(v,u),v) ),
inference(spr,[status(thm),theory(equality)],[13,12]),
[iquote('0:SpR:13.1,12.0')] ).
cnf(71,plain,
( ~ equal(u,zero)
| leq(u,zero) ),
inference(spl,[status(thm),theory(equality)],[2,14]),
[iquote('0:SpL:2.0,14.0')] ).
cnf(99,plain,
equal(multiplication(domain__dfg(multiplication(u,v)),antidomain(multiplication(u,domain__dfg(v)))),zero),
inference(spr,[status(thm),theory(equality)],[15,11]),
[iquote('0:SpR:15.0,11.0')] ).
cnf(107,plain,
equal(domain__dfg(multiplication(one,u)),domain__dfg(domain__dfg(u))),
inference(spr,[status(thm),theory(equality)],[5,15]),
[iquote('0:SpR:5.0,15.0')] ).
cnf(110,plain,
equal(domain__dfg(domain__dfg(u)),domain__dfg(u)),
inference(rew,[status(thm),theory(equality)],[5,107]),
[iquote('0:Rew:5.0,107.0')] ).
cnf(116,plain,
equal(multiplication(domain__dfg(u),antidomain(domain__dfg(u))),zero),
inference(spr,[status(thm),theory(equality)],[110,11]),
[iquote('0:SpR:110.0,11.0')] ).
cnf(158,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)],[15,19]),
[iquote('0:SpR:15.0,19.0')] ).
cnf(161,plain,
equal(addition(one,domain__dfg(one)),domain__dfg(one)),
inference(spr,[status(thm),theory(equality)],[4,19]),
[iquote('0:SpR:4.0,19.0')] ).
cnf(163,plain,
equal(domain__dfg(one),one),
inference(rew,[status(thm),theory(equality)],[22,161]),
[iquote('0:Rew:22.0,161.0')] ).
cnf(169,plain,
equal(addition(one,domain__dfg(u)),domain__dfg(addition(one,u))),
inference(spr,[status(thm),theory(equality)],[163,16]),
[iquote('0:SpR:163.0,16.0')] ).
cnf(182,plain,
equal(domain__dfg(addition(one,u)),one),
inference(rew,[status(thm),theory(equality)],[22,169]),
[iquote('0:Rew:22.0,169.0')] ).
cnf(199,plain,
equal(addition(domain__dfg(u),one),domain__dfg(addition(u,addition(one,v)))),
inference(spr,[status(thm),theory(equality)],[182,16]),
[iquote('0:SpR:182.0,16.0')] ).
cnf(200,plain,
equal(domain__dfg(multiplication(u,addition(one,v))),domain__dfg(multiplication(u,one))),
inference(spr,[status(thm),theory(equality)],[182,15]),
[iquote('0:SpR:182.0,15.0')] ).
cnf(216,plain,
equal(domain__dfg(addition(u,addition(one,v))),one),
inference(rew,[status(thm),theory(equality)],[22,199,12]),
[iquote('0:Rew:22.0,199.0,12.0,199.0')] ).
cnf(217,plain,
equal(domain__dfg(multiplication(u,addition(one,v))),domain__dfg(u)),
inference(rew,[status(thm),theory(equality)],[4,200]),
[iquote('0:Rew:4.0,200.0')] ).
cnf(218,plain,
equal(domain__dfg(addition(multiplication(u,one),multiplication(u,v))),domain__dfg(u)),
inference(rew,[status(thm),theory(equality)],[20,217]),
[iquote('0:Rew:20.0,217.0')] ).
cnf(219,plain,
equal(domain__dfg(addition(u,multiplication(u,v))),domain__dfg(u)),
inference(rew,[status(thm),theory(equality)],[4,218]),
[iquote('0:Rew:4.0,218.0')] ).
cnf(317,plain,
equal(addition(u,addition(u,v)),addition(u,v)),
inference(spr,[status(thm),theory(equality)],[3,17]),
[iquote('0:SpR:3.0,17.0')] ).
cnf(318,plain,
( ~ leq(u,v)
| equal(addition(u,addition(v,w)),addition(v,w)) ),
inference(spr,[status(thm),theory(equality)],[13,17]),
[iquote('0:SpR:13.1,17.0')] ).
cnf(319,plain,
equal(addition(addition(u,v),w),addition(v,addition(u,w))),
inference(spr,[status(thm),theory(equality)],[12,17]),
[iquote('0:SpR:12.0,17.0')] ).
cnf(330,plain,
equal(addition(u,addition(v,w)),addition(v,addition(u,w))),
inference(rew,[status(thm),theory(equality)],[17,319]),
[iquote('0:Rew:17.0,319.0')] ).
cnf(473,plain,
equal(addition(multiplication(u,v),multiplication(multiplication(domain__dfg(u),u),v)),multiplication(multiplication(domain__dfg(u),u),v)),
inference(spr,[status(thm),theory(equality)],[19,21]),
[iquote('0:SpR:19.0,21.0')] ).
cnf(474,plain,
equal(addition(multiplication(one,u),multiplication(domain__dfg(v),u)),multiplication(one,u)),
inference(spr,[status(thm),theory(equality)],[22,21]),
[iquote('0:SpR:22.0,21.0')] ).
cnf(475,plain,
equal(addition(multiplication(domain__dfg(u),v),multiplication(antidomain(u),v)),multiplication(one,v)),
inference(spr,[status(thm),theory(equality)],[10,21]),
[iquote('0:SpR:10.0,21.0')] ).
cnf(477,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)],[16,21]),
[iquote('0:SpR:16.0,21.0')] ).
cnf(485,plain,
equal(addition(u,multiplication(domain__dfg(v),u)),u),
inference(rew,[status(thm),theory(equality)],[5,474]),
[iquote('0:Rew:5.0,474.0')] ).
cnf(486,plain,
equal(multiplication(domain__dfg(u),u),u),
inference(rew,[status(thm),theory(equality)],[485,19]),
[iquote('0:Rew:485.0,19.0')] ).
cnf(488,plain,
equal(multiplication(domain__dfg(multiplication(u,v)),multiplication(u,domain__dfg(v))),multiplication(u,domain__dfg(v))),
inference(rew,[status(thm),theory(equality)],[485,158]),
[iquote('0:Rew:485.0,158.0')] ).
cnf(493,plain,
equal(addition(multiplication(domain__dfg(u),v),multiplication(antidomain(u),v)),v),
inference(rew,[status(thm),theory(equality)],[5,475]),
[iquote('0:Rew:5.0,475.0')] ).
cnf(501,plain,
equal(addition(multiplication(u,v),multiplication(domain__dfg(u),multiplication(u,v))),multiplication(domain__dfg(u),multiplication(u,v))),
inference(rew,[status(thm),theory(equality)],[18,473]),
[iquote('0:Rew:18.0,473.0')] ).
cnf(502,plain,
equal(multiplication(domain__dfg(u),multiplication(u,v)),multiplication(u,v)),
inference(rew,[status(thm),theory(equality)],[485,501]),
[iquote('0:Rew:485.0,501.0')] ).
cnf(574,plain,
equal(addition(multiplication(u,domain__dfg(v)),multiplication(u,antidomain(v))),multiplication(u,one)),
inference(spr,[status(thm),theory(equality)],[10,20]),
[iquote('0:SpR:10.0,20.0')] ).
cnf(586,plain,
equal(addition(multiplication(u,domain__dfg(v)),multiplication(u,antidomain(v))),u),
inference(rew,[status(thm),theory(equality)],[4,574]),
[iquote('0:Rew:4.0,574.0')] ).
cnf(831,plain,
equal(domain__dfg(addition(addition(u,multiplication(u,v)),w)),addition(domain__dfg(u),domain__dfg(w))),
inference(spr,[status(thm),theory(equality)],[219,16]),
[iquote('0:SpR:219.0,16.0')] ).
cnf(876,plain,
equal(domain__dfg(addition(u,addition(multiplication(u,v),w))),domain__dfg(addition(u,w))),
inference(rew,[status(thm),theory(equality)],[17,831,16]),
[iquote('0:Rew:17.0,831.0,16.0,831.0')] ).
cnf(887,plain,
( ~ leq(u,v)
| ~ leq(v,u)
| equal(v,u) ),
inference(spr,[status(thm),theory(equality)],[58,13]),
[iquote('0:SpR:58.1,13.1')] ).
cnf(981,plain,
( ~ equal(addition(u,v),addition(u,v))
| leq(u,addition(u,v)) ),
inference(spl,[status(thm),theory(equality)],[317,14]),
[iquote('0:SpL:317.0,14.0')] ).
cnf(988,plain,
leq(u,addition(u,v)),
inference(obv,[status(thm),theory(equality)],[981]),
[iquote('0:Obv:981.0')] ).
cnf(996,plain,
leq(u,addition(v,u)),
inference(spr,[status(thm),theory(equality)],[12,988]),
[iquote('0:SpR:12.0,988.0')] ).
cnf(1003,plain,
leq(domain__dfg(u),domain__dfg(addition(u,v))),
inference(spr,[status(thm),theory(equality)],[16,988]),
[iquote('0:SpR:16.0,988.0')] ).
cnf(1120,plain,
( ~ leq(u,v)
| leq(domain__dfg(u),domain__dfg(v)) ),
inference(spr,[status(thm),theory(equality)],[13,1003]),
[iquote('0:SpR:13.1,1003.0')] ).
cnf(1940,plain,
equal(addition(zero,multiplication(antidomain(u),antidomain(domain__dfg(u)))),antidomain(domain__dfg(u))),
inference(spr,[status(thm),theory(equality)],[116,493]),
[iquote('0:SpR:116.0,493.0')] ).
cnf(1959,plain,
equal(multiplication(antidomain(u),antidomain(domain__dfg(u))),antidomain(domain__dfg(u))),
inference(rew,[status(thm),theory(equality)],[42,1940]),
[iquote('0:Rew:42.0,1940.0')] ).
cnf(2073,plain,
leq(multiplication(u,antidomain(v)),u),
inference(spr,[status(thm),theory(equality)],[586,996]),
[iquote('0:SpR:586.0,996.0')] ).
cnf(2157,plain,
leq(antidomain(u),domain__dfg(antidomain(u))),
inference(spr,[status(thm),theory(equality)],[486,2073]),
[iquote('0:SpR:486.0,2073.0')] ).
cnf(3012,plain,
equal(multiplication(domain__dfg(multiplication(u,addition(v,addition(one,w)))),antidomain(multiplication(u,one))),zero),
inference(spr,[status(thm),theory(equality)],[216,99]),
[iquote('0:SpR:216.0,99.0')] ).
cnf(3067,plain,
equal(multiplication(domain__dfg(addition(u,addition(multiplication(u,v),multiplication(u,w)))),antidomain(u)),zero),
inference(rew,[status(thm),theory(equality)],[330,3012,4,20]),
[iquote('0:Rew:330.0,3012.0,4.0,3012.0,20.0,3012.0,20.0,3012.0,4.0,3012.0')] ).
cnf(3068,plain,
equal(addition(multiplication(domain__dfg(u),antidomain(u)),multiplication(domain__dfg(multiplication(u,v)),antidomain(u))),zero),
inference(rew,[status(thm),theory(equality)],[477,3067,876]),
[iquote('0:Rew:477.0,3067.0,876.0,3067.0')] ).
cnf(3069,plain,
equal(multiplication(domain__dfg(multiplication(u,v)),antidomain(u)),zero),
inference(rew,[status(thm),theory(equality)],[42,3068,11]),
[iquote('0:Rew:42.0,3068.0,11.0,3068.0')] ).
cnf(4550,plain,
( ~ leq(u,zero)
| equal(addition(u,v),v) ),
inference(spr,[status(thm),theory(equality)],[42,318]),
[iquote('0:SpR:42.0,318.1')] ).
cnf(6661,plain,
( ~ leq(u,zero)
| leq(domain__dfg(u),zero) ),
inference(spr,[status(thm),theory(equality)],[1,1120]),
[iquote('0:SpR:1.0,1120.1')] ).
cnf(6742,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)],[11,488]),
[iquote('0:SpR:11.0,488.0')] ).
cnf(6777,plain,
equal(multiplication(domain__dfg(u),domain__dfg(antidomain(u))),zero),
inference(rew,[status(thm),theory(equality)],[7,6742,1]),
[iquote('0:Rew:7.0,6742.0,1.0,6742.0')] ).
cnf(6846,plain,
( ~ leq(u,zero)
| equal(domain__dfg(u),zero) ),
inference(res,[status(thm),theory(equality)],[6661,56]),
[iquote('0:Res:6661.1,56.0')] ).
cnf(6863,plain,
equal(addition(zero,multiplication(domain__dfg(u),antidomain(antidomain(u)))),domain__dfg(u)),
inference(spr,[status(thm),theory(equality)],[6777,586]),
[iquote('0:SpR:6777.0,586.0')] ).
cnf(6920,plain,
equal(multiplication(domain__dfg(u),antidomain(antidomain(u))),domain__dfg(u)),
inference(rew,[status(thm),theory(equality)],[42,6863]),
[iquote('0:Rew:42.0,6863.0')] ).
cnf(6987,plain,
( ~ leq(u,zero)
| equal(multiplication(zero,multiplication(u,v)),multiplication(u,v)) ),
inference(spr,[status(thm),theory(equality)],[6846,502]),
[iquote('0:SpR:6846.1,502.0')] ).
cnf(7109,plain,
( ~ leq(u,zero)
| equal(multiplication(u,v),zero) ),
inference(rew,[status(thm),theory(equality)],[7,6987]),
[iquote('0:Rew:7.0,6987.1')] ).
cnf(7685,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)],[10,477]),
[iquote('0:SpR:10.0,477.0')] ).
cnf(7728,plain,
equal(addition(multiplication(domain__dfg(u),v),multiplication(domain__dfg(antidomain(u)),v)),v),
inference(rew,[status(thm),theory(equality)],[110,7685,5,163]),
[iquote('0:Rew:110.0,7685.0,5.0,7685.0,163.0,7685.0')] ).
cnf(9286,plain,
( ~ leq(domain__dfg(u),zero)
| equal(zero,u) ),
inference(spr,[status(thm),theory(equality)],[7109,486]),
[iquote('0:SpR:7109.1,486.0')] ).
cnf(9421,plain,
( ~ leq(u,zero)
| leq(u,v) ),
inference(spr,[status(thm),theory(equality)],[4550,988]),
[iquote('0:SpR:4550.1,988.0')] ).
cnf(9619,plain,
( ~ equal(u,zero)
| leq(u,v) ),
inference(res,[status(thm),theory(equality)],[71,9421]),
[iquote('0:Res:71.1,9421.0')] ).
cnf(9666,plain,
( ~ equal(domain__dfg(u),zero)
| equal(zero,u) ),
inference(res,[status(thm),theory(equality)],[9619,9286]),
[iquote('0:Res:9619.1,9286.0')] ).
cnf(18516,plain,
( ~ leq(domain__dfg(antidomain(u)),antidomain(u))
| equal(domain__dfg(antidomain(u)),antidomain(u)) ),
inference(res,[status(thm),theory(equality)],[2157,887]),
[iquote('0:Res:2157.0,887.0')] ).
cnf(27487,plain,
equal(multiplication(domain__dfg(antidomain(domain__dfg(u))),antidomain(antidomain(u))),zero),
inference(spr,[status(thm),theory(equality)],[1959,3069]),
[iquote('0:SpR:1959.0,3069.0')] ).
cnf(27500,plain,
leq(antidomain(domain__dfg(u)),antidomain(u)),
inference(spr,[status(thm),theory(equality)],[1959,2073]),
[iquote('0:SpR:1959.0,2073.0')] ).
cnf(31073,plain,
equal(addition(multiplication(domain__dfg(u),antidomain(antidomain(u))),zero),antidomain(antidomain(u))),
inference(spr,[status(thm),theory(equality)],[11,7728]),
[iquote('0:SpR:11.0,7728.0')] ).
cnf(31075,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)],[6920,7728]),
[iquote('0:SpR:6920.0,7728.0')] ).
cnf(31177,plain,
equal(antidomain(antidomain(u)),domain__dfg(u)),
inference(rew,[status(thm),theory(equality)],[42,31073,12,6920]),
[iquote('0:Rew:42.0,31073.0,12.0,31073.0,6920.0,31073.0')] ).
cnf(31193,plain,
equal(multiplication(domain__dfg(antidomain(domain__dfg(u))),domain__dfg(u)),zero),
inference(rew,[status(thm),theory(equality)],[31177,27487]),
[iquote('0:Rew:31177.0,27487.0')] ).
cnf(31471,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)],[12,31075]),
[iquote('0:Rew:12.0,31075.0')] ).
cnf(31472,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)],[31177,31471]),
[iquote('0:Rew:31177.0,31471.0')] ).
cnf(31473,plain,
equal(antidomain(domain__dfg(u)),domain__dfg(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[42,31472,12,116]),
[iquote('0:Rew:42.0,31472.0,12.0,31472.0,116.0,31472.0')] ).
cnf(31494,plain,
leq(domain__dfg(antidomain(u)),antidomain(u)),
inference(rew,[status(thm),theory(equality)],[31473,27500]),
[iquote('0:Rew:31473.0,27500.0')] ).
cnf(31741,plain,
equal(multiplication(domain__dfg(domain__dfg(antidomain(u))),domain__dfg(u)),zero),
inference(rew,[status(thm),theory(equality)],[31473,31193]),
[iquote('0:Rew:31473.0,31193.0')] ).
cnf(31805,plain,
equal(domain__dfg(antidomain(u)),antidomain(u)),
inference(mrr,[status(thm)],[18516,31494]),
[iquote('0:MRR:18516.0,31494.0')] ).
cnf(31930,plain,
equal(multiplication(domain__dfg(antidomain(u)),domain__dfg(u)),zero),
inference(rew,[status(thm),theory(equality)],[110,31741]),
[iquote('0:Rew:110.0,31741.0')] ).
cnf(31931,plain,
equal(multiplication(antidomain(u),domain__dfg(u)),zero),
inference(rew,[status(thm),theory(equality)],[31805,31930]),
[iquote('0:Rew:31805.0,31930.0')] ).
cnf(33476,plain,
equal(domain__dfg(multiplication(antidomain(u),u)),domain__dfg(zero)),
inference(spr,[status(thm),theory(equality)],[31931,15]),
[iquote('0:SpR:31931.0,15.0')] ).
cnf(33574,plain,
equal(domain__dfg(multiplication(antidomain(u),u)),zero),
inference(rew,[status(thm),theory(equality)],[1,33476]),
[iquote('0:Rew:1.0,33476.0')] ).
cnf(34131,plain,
( ~ equal(zero,zero)
| equal(multiplication(antidomain(u),u),zero) ),
inference(spl,[status(thm),theory(equality)],[33574,9666]),
[iquote('0:SpL:33574.0,9666.0')] ).
cnf(34202,plain,
equal(multiplication(antidomain(u),u),zero),
inference(obv,[status(thm),theory(equality)],[34131]),
[iquote('0:Obv:34131.0')] ).
cnf(34203,plain,
$false,
inference(unc,[status(thm)],[34202,9]),
[iquote('0:UnC:34202.0,9.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.14 % Problem : KLE081+1 : TPTP v8.1.0. Released v4.0.0.
% 0.14/0.15 % Command : run_spass %d %s
% 0.15/0.37 % Computer : n021.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 600
% 0.15/0.37 % DateTime : Thu Jun 16 16:18:00 EDT 2022
% 0.15/0.37 % CPUTime :
% 6.91/7.09
% 6.91/7.09 SPASS V 3.9
% 6.91/7.09 SPASS beiseite: Proof found.
% 6.91/7.09 % SZS status Theorem
% 6.91/7.09 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.91/7.09 SPASS derived 23626 clauses, backtracked 0 clauses, performed 0 splits and kept 3672 clauses.
% 6.91/7.09 SPASS allocated 107878 KBytes.
% 6.91/7.09 SPASS spent 0:00:06.67 on the problem.
% 6.91/7.09 0:00:00.04 for the input.
% 6.91/7.09 0:00:00.03 for the FLOTTER CNF translation.
% 6.91/7.09 0:00:00.14 for inferences.
% 6.91/7.09 0:00:00.00 for the backtracking.
% 6.91/7.09 0:00:06.42 for the reduction.
% 6.91/7.09
% 6.91/7.09
% 6.91/7.09 Here is a proof with depth 10, length 107 :
% 6.91/7.09 % SZS output start Refutation
% See solution above
% 7.11/7.27 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 multiplicative_associativity domain1 right_distributivity left_distributivity
% 7.11/7.27
%------------------------------------------------------------------------------