TSTP Solution File: GRP575-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP575-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 : Sat Jul 16 11:48:06 EDT 2022
% Result : Unsatisfiable 0.19s 0.47s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 5
% Syntax : Number of clauses : 75 ( 75 unt; 0 nHn; 75 RR)
% Number of literals : 75 ( 0 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 1 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(double_divide(double_divide(u,double_divide(double_divide(v,double_divide(w,u)),double_divide(w,identity))),double_divide(identity,identity)),v),
file('GRP575-1.p',unknown),
[] ).
cnf(2,axiom,
equal(double_divide(double_divide(u,v),identity),multiply(v,u)),
file('GRP575-1.p',unknown),
[] ).
cnf(3,axiom,
equal(double_divide(u,identity),inverse(u)),
file('GRP575-1.p',unknown),
[] ).
cnf(4,axiom,
equal(double_divide(u,inverse(u)),identity),
file('GRP575-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))),
file('GRP575-1.p',unknown),
[] ).
cnf(6,plain,
equal(inverse(double_divide(u,v)),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[3,2]),
[iquote('0:Rew:3.0,2.0')] ).
cnf(7,plain,
equal(double_divide(double_divide(u,double_divide(double_divide(v,double_divide(w,u)),inverse(w))),inverse(identity)),v),
inference(rew,[status(thm),theory(equality)],[3,1]),
[iquote('0:Rew:3.0,1.0,3.0,1.0')] ).
cnf(10,plain,
equal(double_divide(double_divide(u,v),multiply(v,u)),identity),
inference(spr,[status(thm),theory(equality)],[6,4]),
[iquote('0:SpR:6.0,4.0')] ).
cnf(12,plain,
equal(multiply(inverse(u),u),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[4,6]),
[iquote('0:SpR:4.0,6.0')] ).
cnf(13,plain,
equal(multiply(identity,u),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[3,6]),
[iquote('0:SpR:3.0,6.0')] ).
cnf(50,plain,
equal(double_divide(double_divide(inverse(u),double_divide(double_divide(v,identity),inverse(u))),inverse(identity)),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(53,plain,
equal(double_divide(double_divide(inverse(u),double_divide(inverse(v),inverse(u))),inverse(identity)),v),
inference(rew,[status(thm),theory(equality)],[3,50]),
[iquote('0:Rew:3.0,50.0')] ).
cnf(65,plain,
equal(double_divide(double_divide(inverse(inverse(u)),identity),inverse(identity)),u),
inference(spr,[status(thm),theory(equality)],[4,53]),
[iquote('0:SpR:4.0,53.0')] ).
cnf(67,plain,
equal(double_divide(inverse(inverse(inverse(u))),inverse(identity)),u),
inference(rew,[status(thm),theory(equality)],[3,65]),
[iquote('0:Rew:3.0,65.0')] ).
cnf(74,plain,
equal(double_divide(double_divide(inverse(identity),double_divide(double_divide(u,v),inverse(inverse(inverse(inverse(v)))))),inverse(identity)),u),
inference(spr,[status(thm),theory(equality)],[67,7]),
[iquote('0:SpR:67.0,7.0')] ).
cnf(75,plain,
equal(double_divide(double_divide(inverse(identity),u),inverse(identity)),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[67,53]),
[iquote('0:SpR:67.0,53.0')] ).
cnf(77,plain,
equal(double_divide(inverse(inverse(multiply(u,v))),inverse(identity)),double_divide(v,u)),
inference(spr,[status(thm),theory(equality)],[6,67]),
[iquote('0:SpR:6.0,67.0')] ).
cnf(83,plain,
equal(inverse(inverse(double_divide(double_divide(u,v),inverse(inverse(inverse(inverse(v))))))),u),
inference(rew,[status(thm),theory(equality)],[75,74]),
[iquote('0:Rew:75.0,74.0')] ).
cnf(84,plain,
equal(inverse(multiply(inverse(inverse(inverse(inverse(u)))),double_divide(v,u))),v),
inference(rew,[status(thm),theory(equality)],[6,83]),
[iquote('0:Rew:6.0,83.0')] ).
cnf(96,plain,
equal(inverse(inverse(double_divide(inverse(u),inverse(identity)))),u),
inference(spr,[status(thm),theory(equality)],[75,53]),
[iquote('0:SpR:75.0,53.0')] ).
cnf(100,plain,
equal(inverse(inverse(inverse(inverse(identity)))),double_divide(identity,inverse(identity))),
inference(spr,[status(thm),theory(equality)],[4,75]),
[iquote('0:SpR:4.0,75.0')] ).
cnf(102,plain,
equal(inverse(multiply(inverse(identity),inverse(u))),u),
inference(rew,[status(thm),theory(equality)],[6,96]),
[iquote('0:Rew:6.0,96.0')] ).
cnf(103,plain,
equal(inverse(inverse(inverse(inverse(identity)))),identity),
inference(rew,[status(thm),theory(equality)],[4,100]),
[iquote('0:Rew:4.0,100.0')] ).
cnf(116,plain,
equal(double_divide(identity,inverse(identity)),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[103,67]),
[iquote('0:SpR:103.0,67.0')] ).
cnf(119,plain,
equal(double_divide(double_divide(u,double_divide(double_divide(v,double_divide(inverse(inverse(inverse(identity))),u)),identity)),inverse(identity)),v),
inference(spr,[status(thm),theory(equality)],[103,7]),
[iquote('0:SpR:103.0,7.0')] ).
cnf(121,plain,
equal(inverse(identity),identity),
inference(rew,[status(thm),theory(equality)],[4,116]),
[iquote('0:Rew:4.0,116.0')] ).
cnf(122,plain,
equal(multiply(inverse(u),u),identity),
inference(rew,[status(thm),theory(equality)],[121,12]),
[iquote('0:Rew:121.0,12.0')] ).
cnf(124,plain,
equal(double_divide(double_divide(u,double_divide(double_divide(v,double_divide(w,u)),inverse(w))),identity),v),
inference(rew,[status(thm),theory(equality)],[121,7]),
[iquote('0:Rew:121.0,7.0')] ).
cnf(128,plain,
equal(double_divide(double_divide(identity,u),identity),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[121,75]),
[iquote('0:Rew:121.0,75.0')] ).
cnf(136,plain,
equal(double_divide(inverse(inverse(multiply(u,v))),identity),double_divide(v,u)),
inference(rew,[status(thm),theory(equality)],[121,77]),
[iquote('0:Rew:121.0,77.0')] ).
cnf(138,plain,
equal(inverse(multiply(identity,inverse(u))),u),
inference(rew,[status(thm),theory(equality)],[121,102]),
[iquote('0:Rew:121.0,102.0')] ).
cnf(145,plain,
equal(inverse(inverse(inverse(inverse(u)))),u),
inference(rew,[status(thm),theory(equality)],[13,138]),
[iquote('0:Rew:13.0,138.0')] ).
cnf(146,plain,
equal(inverse(multiply(u,double_divide(v,u))),v),
inference(rew,[status(thm),theory(equality)],[145,84]),
[iquote('0:Rew:145.0,84.0')] ).
cnf(161,plain,
equal(multiply(u,identity),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[6,128,3]),
[iquote('0:Rew:6.0,128.0,3.0,128.0')] ).
cnf(173,plain,
equal(inverse(inverse(inverse(multiply(u,v)))),double_divide(v,u)),
inference(rew,[status(thm),theory(equality)],[3,136]),
[iquote('0:Rew:3.0,136.0')] ).
cnf(184,plain,
equal(multiply(double_divide(double_divide(u,double_divide(v,w)),inverse(v)),w),u),
inference(rew,[status(thm),theory(equality)],[6,124,3]),
[iquote('0:Rew:6.0,124.0,3.0,124.0')] ).
cnf(192,plain,
equal(double_divide(double_divide(u,multiply(double_divide(inverse(inverse(inverse(identity))),u),v)),inverse(identity)),v),
inference(rew,[status(thm),theory(equality)],[6,119,3]),
[iquote('0:Rew:6.0,119.0,3.0,119.0')] ).
cnf(193,plain,
equal(double_divide(double_divide(u,multiply(double_divide(identity,u),v)),identity),v),
inference(rew,[status(thm),theory(equality)],[121,192]),
[iquote('0:Rew:121.0,192.0,121.0,192.0,121.0,192.0')] ).
cnf(194,plain,
equal(multiply(multiply(double_divide(identity,u),v),u),v),
inference(rew,[status(thm),theory(equality)],[6,193,3]),
[iquote('0:Rew:6.0,193.0,3.0,193.0')] ).
cnf(217,plain,
equal(double_divide(inverse(inverse(inverse(u))),u),identity),
inference(spr,[status(thm),theory(equality)],[145,4]),
[iquote('0:SpR:145.0,4.0')] ).
cnf(219,plain,
equal(multiply(u,inverse(inverse(inverse(u)))),identity),
inference(spr,[status(thm),theory(equality)],[145,122]),
[iquote('0:SpR:145.0,122.0')] ).
cnf(227,plain,
equal(double_divide(double_divide(identity,u),inverse(inverse(u))),identity),
inference(spr,[status(thm),theory(equality)],[161,10]),
[iquote('0:SpR:161.0,10.0')] ).
cnf(274,plain,
equal(multiply(double_divide(identity,inverse(u)),v),inverse(inverse(inverse(double_divide(u,v))))),
inference(spr,[status(thm),theory(equality)],[217,184]),
[iquote('0:SpR:217.0,184.0')] ).
cnf(286,plain,
equal(multiply(double_divide(identity,inverse(u)),v),inverse(inverse(multiply(v,u)))),
inference(rew,[status(thm),theory(equality)],[6,274]),
[iquote('0:Rew:6.0,274.0')] ).
cnf(334,plain,
equal(multiply(u,double_divide(v,u)),inverse(inverse(inverse(v)))),
inference(spr,[status(thm),theory(equality)],[146,145]),
[iquote('0:SpR:146.0,145.0')] ).
cnf(386,plain,
equal(double_divide(double_divide(identity,inverse(inverse(u))),u),identity),
inference(spr,[status(thm),theory(equality)],[145,227]),
[iquote('0:SpR:145.0,227.0')] ).
cnf(401,plain,
equal(multiply(u,double_divide(identity,inverse(inverse(u)))),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[386,6]),
[iquote('0:SpR:386.0,6.0')] ).
cnf(415,plain,
equal(multiply(u,double_divide(identity,inverse(inverse(u)))),identity),
inference(rew,[status(thm),theory(equality)],[121,401]),
[iquote('0:Rew:121.0,401.0')] ).
cnf(503,plain,
equal(inverse(inverse(inverse(double_divide(identity,u)))),multiply(identity,u)),
inference(spr,[status(thm),theory(equality)],[219,194]),
[iquote('0:SpR:219.0,194.0')] ).
cnf(504,plain,
equal(double_divide(identity,inverse(inverse(double_divide(identity,u)))),multiply(identity,u)),
inference(spr,[status(thm),theory(equality)],[415,194]),
[iquote('0:SpR:415.0,194.0')] ).
cnf(510,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[145,503,161,6,13]),
[iquote('0:Rew:145.0,503.0,161.0,503.0,6.0,503.0,13.0,503.0')] ).
cnf(515,plain,
equal(multiply(identity,u),u),
inference(rew,[status(thm),theory(equality)],[510,13]),
[iquote('0:Rew:510.0,13.0')] ).
cnf(516,plain,
equal(multiply(u,identity),u),
inference(rew,[status(thm),theory(equality)],[510,161]),
[iquote('0:Rew:510.0,161.0')] ).
cnf(522,plain,
equal(multiply(u,double_divide(v,u)),inverse(v)),
inference(rew,[status(thm),theory(equality)],[510,334]),
[iquote('0:Rew:510.0,334.0')] ).
cnf(525,plain,
equal(multiply(double_divide(identity,inverse(u)),v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[510,286]),
[iquote('0:Rew:510.0,286.0')] ).
cnf(527,plain,
equal(inverse(multiply(u,v)),double_divide(v,u)),
inference(rew,[status(thm),theory(equality)],[510,173]),
[iquote('0:Rew:510.0,173.0')] ).
cnf(538,plain,
equal(double_divide(identity,inverse(multiply(u,identity))),multiply(identity,u)),
inference(rew,[status(thm),theory(equality)],[6,504]),
[iquote('0:Rew:6.0,504.0')] ).
cnf(539,plain,
equal(double_divide(identity,inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[516,538,515]),
[iquote('0:Rew:516.0,538.0,515.0,538.0')] ).
cnf(540,plain,
equal(multiply(u,v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[539,525]),
[iquote('0:Rew:539.0,525.0')] ).
cnf(542,plain,
equal(multiply(u,double_divide(double_divide(v,double_divide(w,u)),inverse(w))),v),
inference(rew,[status(thm),theory(equality)],[540,184]),
[iquote('0:Rew:540.0,184.0')] ).
cnf(543,plain,
~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))),
inference(rew,[status(thm),theory(equality)],[540,5]),
[iquote('0:Rew:540.0,5.0')] ).
cnf(544,plain,
equal(multiply(u,multiply(double_divide(identity,u),v)),v),
inference(rew,[status(thm),theory(equality)],[540,194]),
[iquote('0:Rew:540.0,194.0')] ).
cnf(594,plain,
equal(double_divide(identity,u),inverse(u)),
inference(spr,[status(thm),theory(equality)],[510,539]),
[iquote('0:SpR:510.0,539.0')] ).
cnf(604,plain,
equal(multiply(u,multiply(inverse(u),v)),v),
inference(rew,[status(thm),theory(equality)],[594,544]),
[iquote('0:Rew:594.0,544.0')] ).
cnf(680,plain,
equal(inverse(multiply(u,v)),double_divide(u,v)),
inference(spr,[status(thm),theory(equality)],[540,527]),
[iquote('0:SpR:540.0,527.0')] ).
cnf(689,plain,
equal(double_divide(u,v),double_divide(v,u)),
inference(rew,[status(thm),theory(equality)],[527,680]),
[iquote('0:Rew:527.0,680.0')] ).
cnf(691,plain,
equal(multiply(u,double_divide(inverse(v),double_divide(w,double_divide(v,u)))),w),
inference(rew,[status(thm),theory(equality)],[689,542]),
[iquote('0:Rew:689.0,542.0')] ).
cnf(756,plain,
equal(multiply(u,double_divide(u,v)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[689,522]),
[iquote('0:SpR:689.0,522.0')] ).
cnf(828,plain,
equal(multiply(u,multiply(v,inverse(u))),v),
inference(spr,[status(thm),theory(equality)],[540,604]),
[iquote('0:SpR:540.0,604.0')] ).
cnf(920,plain,
equal(double_divide(inverse(u),v),multiply(u,inverse(v))),
inference(spr,[status(thm),theory(equality)],[756,604]),
[iquote('0:SpR:756.0,604.0')] ).
cnf(934,plain,
equal(multiply(u,multiply(v,inverse(double_divide(w,double_divide(v,u))))),w),
inference(rew,[status(thm),theory(equality)],[920,691]),
[iquote('0:Rew:920.0,691.0')] ).
cnf(947,plain,
equal(multiply(u,multiply(v,multiply(double_divide(v,u),w))),w),
inference(rew,[status(thm),theory(equality)],[6,934]),
[iquote('0:Rew:6.0,934.0')] ).
cnf(1082,plain,
equal(multiply(u,inverse(double_divide(v,w))),multiply(w,multiply(v,u))),
inference(spr,[status(thm),theory(equality)],[828,947]),
[iquote('0:SpR:828.0,947.0')] ).
cnf(1116,plain,
equal(multiply(u,multiply(v,w)),multiply(v,multiply(w,u))),
inference(rew,[status(thm),theory(equality)],[6,1082]),
[iquote('0:Rew:6.0,1082.0')] ).
cnf(1117,plain,
$false,
inference(unc,[status(thm)],[1116,543]),
[iquote('0:UnC:1116.0,543.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP575-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n023.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
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 05:32:21 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.47
% 0.19/0.47 SPASS V 3.9
% 0.19/0.47 SPASS beiseite: Proof found.
% 0.19/0.47 % SZS status Theorem
% 0.19/0.47 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.47 SPASS derived 690 clauses, backtracked 0 clauses, performed 0 splits and kept 183 clauses.
% 0.19/0.47 SPASS allocated 64220 KBytes.
% 0.19/0.47 SPASS spent 0:00:00.13 on the problem.
% 0.19/0.47 0:00:00.04 for the input.
% 0.19/0.47 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.47 0:00:00.01 for inferences.
% 0.19/0.47 0:00:00.00 for the backtracking.
% 0.19/0.47 0:00:00.06 for the reduction.
% 0.19/0.47
% 0.19/0.47
% 0.19/0.47 Here is a proof with depth 9, length 75 :
% 0.19/0.47 % SZS output start Refutation
% See solution above
% 0.19/0.48 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_3
% 0.19/0.48
%------------------------------------------------------------------------------