TSTP Solution File: GRP567-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP567-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 11:48:04 EDT 2022
% Result : Unsatisfiable 0.19s 0.52s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 5
% Syntax : Number of clauses : 81 ( 81 unt; 0 nHn; 81 RR)
% Number of literals : 81 ( 0 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 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(u,w)),double_divide(identity,w))),double_divide(identity,identity)),v),
file('GRP567-1.p',unknown),
[] ).
cnf(2,axiom,
equal(double_divide(double_divide(u,v),identity),multiply(v,u)),
file('GRP567-1.p',unknown),
[] ).
cnf(3,axiom,
equal(double_divide(u,identity),inverse(u)),
file('GRP567-1.p',unknown),
[] ).
cnf(4,axiom,
equal(double_divide(u,inverse(u)),identity),
file('GRP567-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))),
file('GRP567-1.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(u,w)),double_divide(identity,w))),inverse(identity)),v),
inference(rew,[status(thm),theory(equality)],[3,1]),
[iquote('0:Rew:3.0,1.0')] ).
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(49,plain,
equal(double_divide(double_divide(u,double_divide(double_divide(v,double_divide(u,inverse(identity))),identity)),inverse(identity)),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(50,plain,
equal(double_divide(double_divide(u,double_divide(double_divide(v,double_divide(u,identity)),inverse(identity))),inverse(identity)),v),
inference(spr,[status(thm),theory(equality)],[3,7]),
[iquote('0:SpR:3.0,7.0')] ).
cnf(51,plain,
equal(double_divide(double_divide(u,double_divide(double_divide(v,identity),double_divide(identity,inverse(u)))),inverse(identity)),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(54,plain,
equal(double_divide(double_divide(u,multiply(double_divide(u,inverse(identity)),v)),inverse(identity)),v),
inference(rew,[status(thm),theory(equality)],[6,49,3]),
[iquote('0:Rew:6.0,49.0,3.0,49.0')] ).
cnf(55,plain,
equal(double_divide(double_divide(u,double_divide(double_divide(v,inverse(u)),inverse(identity))),inverse(identity)),v),
inference(rew,[status(thm),theory(equality)],[3,50]),
[iquote('0:Rew:3.0,50.0')] ).
cnf(56,plain,
equal(double_divide(double_divide(u,double_divide(inverse(v),double_divide(identity,inverse(u)))),inverse(identity)),v),
inference(rew,[status(thm),theory(equality)],[3,51]),
[iquote('0:Rew:3.0,51.0')] ).
cnf(68,plain,
equal(double_divide(double_divide(identity,multiply(identity,u)),inverse(identity)),u),
inference(spr,[status(thm),theory(equality)],[4,54]),
[iquote('0:SpR:4.0,54.0')] ).
cnf(70,plain,
equal(double_divide(double_divide(identity,inverse(inverse(u))),inverse(identity)),u),
inference(rew,[status(thm),theory(equality)],[13,68]),
[iquote('0:Rew:13.0,68.0')] ).
cnf(74,plain,
equal(double_divide(double_divide(double_divide(identity,inverse(inverse(u))),multiply(u,v)),inverse(identity)),v),
inference(spr,[status(thm),theory(equality)],[70,54]),
[iquote('0:SpR:70.0,54.0')] ).
cnf(75,plain,
equal(multiply(inverse(identity),double_divide(identity,inverse(inverse(u)))),inverse(u)),
inference(spr,[status(thm),theory(equality)],[70,6]),
[iquote('0:SpR:70.0,6.0')] ).
cnf(125,plain,
equal(double_divide(double_divide(double_divide(u,v),double_divide(double_divide(w,multiply(v,u)),inverse(identity))),inverse(identity)),w),
inference(spr,[status(thm),theory(equality)],[6,55]),
[iquote('0:SpR:6.0,55.0')] ).
cnf(126,plain,
equal(double_divide(double_divide(u,double_divide(identity,inverse(identity))),inverse(identity)),u),
inference(spr,[status(thm),theory(equality)],[4,55]),
[iquote('0:SpR:4.0,55.0')] ).
cnf(127,plain,
equal(double_divide(double_divide(identity,double_divide(u,inverse(identity))),inverse(identity)),double_divide(v,multiply(double_divide(v,inverse(identity)),u))),
inference(spr,[status(thm),theory(equality)],[54,55]),
[iquote('0:SpR:54.0,55.0')] ).
cnf(128,plain,
equal(double_divide(u,double_divide(double_divide(v,double_divide(u,w)),double_divide(identity,w))),double_divide(double_divide(identity,double_divide(v,inverse(identity))),inverse(identity))),
inference(spr,[status(thm),theory(equality)],[7,55]),
[iquote('0:SpR:7.0,55.0')] ).
cnf(129,plain,
equal(double_divide(double_divide(identity,double_divide(u,inverse(identity))),inverse(identity)),double_divide(identity,inverse(inverse(u)))),
inference(spr,[status(thm),theory(equality)],[70,55]),
[iquote('0:SpR:70.0,55.0')] ).
cnf(131,plain,
equal(double_divide(double_divide(inverse(u),u),inverse(identity)),identity),
inference(spr,[status(thm),theory(equality)],[70,55]),
[iquote('0:SpR:70.0,55.0')] ).
cnf(133,plain,
equal(double_divide(inverse(u),inverse(identity)),u),
inference(rew,[status(thm),theory(equality)],[3,126,4]),
[iquote('0:Rew:3.0,126.0,4.0,126.0')] ).
cnf(136,plain,
equal(double_divide(u,multiply(double_divide(u,inverse(identity)),v)),double_divide(identity,inverse(inverse(v)))),
inference(rew,[status(thm),theory(equality)],[129,127]),
[iquote('0:Rew:129.0,127.0')] ).
cnf(146,plain,
equal(double_divide(u,double_divide(double_divide(v,double_divide(u,w)),double_divide(identity,w))),double_divide(identity,inverse(inverse(v)))),
inference(rew,[status(thm),theory(equality)],[129,128]),
[iquote('0:Rew:129.0,128.0')] ).
cnf(156,plain,
equal(double_divide(multiply(u,v),inverse(identity)),double_divide(v,u)),
inference(spr,[status(thm),theory(equality)],[6,133]),
[iquote('0:SpR:6.0,133.0')] ).
cnf(173,plain,
equal(double_divide(inverse(inverse(identity)),inverse(identity)),identity),
inference(spr,[status(thm),theory(equality)],[3,131]),
[iquote('0:SpR:3.0,131.0')] ).
cnf(175,plain,
equal(inverse(identity),identity),
inference(rew,[status(thm),theory(equality)],[133,173]),
[iquote('0:Rew:133.0,173.0')] ).
cnf(179,plain,
equal(multiply(identity,double_divide(identity,inverse(inverse(u)))),inverse(u)),
inference(rew,[status(thm),theory(equality)],[175,75]),
[iquote('0:Rew:175.0,75.0')] ).
cnf(182,plain,
equal(double_divide(inverse(u),identity),u),
inference(rew,[status(thm),theory(equality)],[175,133]),
[iquote('0:Rew:175.0,133.0')] ).
cnf(185,plain,
equal(double_divide(double_divide(u,double_divide(inverse(v),double_divide(identity,inverse(u)))),identity),v),
inference(rew,[status(thm),theory(equality)],[175,56]),
[iquote('0:Rew:175.0,56.0')] ).
cnf(187,plain,
equal(double_divide(u,multiply(double_divide(u,identity),v)),double_divide(identity,inverse(inverse(v)))),
inference(rew,[status(thm),theory(equality)],[175,136]),
[iquote('0:Rew:175.0,136.0')] ).
cnf(188,plain,
equal(double_divide(double_divide(double_divide(identity,inverse(inverse(u))),multiply(u,v)),identity),v),
inference(rew,[status(thm),theory(equality)],[175,74]),
[iquote('0:Rew:175.0,74.0')] ).
cnf(192,plain,
equal(double_divide(double_divide(double_divide(u,v),double_divide(double_divide(w,multiply(v,u)),identity)),identity),w),
inference(rew,[status(thm),theory(equality)],[175,125]),
[iquote('0:Rew:175.0,125.0')] ).
cnf(194,plain,
equal(double_divide(multiply(u,v),identity),double_divide(v,u)),
inference(rew,[status(thm),theory(equality)],[175,156]),
[iquote('0:Rew:175.0,156.0')] ).
cnf(196,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[3,182]),
[iquote('0:Rew:3.0,182.0')] ).
cnf(197,plain,
equal(multiply(identity,u),u),
inference(rew,[status(thm),theory(equality)],[196,13]),
[iquote('0:Rew:196.0,13.0')] ).
cnf(198,plain,
equal(double_divide(u,double_divide(double_divide(v,double_divide(u,w)),double_divide(identity,w))),double_divide(identity,v)),
inference(rew,[status(thm),theory(equality)],[196,146]),
[iquote('0:Rew:196.0,146.0')] ).
cnf(202,plain,
equal(inverse(multiply(u,v)),double_divide(v,u)),
inference(rew,[status(thm),theory(equality)],[3,194]),
[iquote('0:Rew:3.0,194.0')] ).
cnf(204,plain,
equal(double_divide(identity,u),inverse(u)),
inference(rew,[status(thm),theory(equality)],[197,179,196]),
[iquote('0:Rew:197.0,179.0,196.0,179.0')] ).
cnf(213,plain,
equal(multiply(double_divide(inverse(u),double_divide(identity,inverse(v))),v),u),
inference(rew,[status(thm),theory(equality)],[6,185,3]),
[iquote('0:Rew:6.0,185.0,3.0,185.0')] ).
cnf(214,plain,
equal(multiply(double_divide(inverse(u),v),v),u),
inference(rew,[status(thm),theory(equality)],[196,213,204]),
[iquote('0:Rew:196.0,213.0,204.0,213.0')] ).
cnf(215,plain,
equal(double_divide(u,multiply(inverse(u),v)),double_divide(identity,inverse(inverse(v)))),
inference(rew,[status(thm),theory(equality)],[3,187]),
[iquote('0:Rew:3.0,187.0')] ).
cnf(216,plain,
equal(double_divide(u,multiply(inverse(u),v)),inverse(v)),
inference(rew,[status(thm),theory(equality)],[204,215,196]),
[iquote('0:Rew:204.0,215.0,196.0,215.0')] ).
cnf(217,plain,
equal(multiply(multiply(u,v),double_divide(identity,inverse(inverse(u)))),v),
inference(rew,[status(thm),theory(equality)],[6,188,3]),
[iquote('0:Rew:6.0,188.0,3.0,188.0')] ).
cnf(218,plain,
equal(multiply(multiply(u,v),inverse(u)),v),
inference(rew,[status(thm),theory(equality)],[204,217,196]),
[iquote('0:Rew:204.0,217.0,196.0,217.0')] ).
cnf(223,plain,
equal(multiply(multiply(multiply(u,v),w),double_divide(v,u)),w),
inference(rew,[status(thm),theory(equality)],[6,192,3]),
[iquote('0:Rew:6.0,192.0,3.0,192.0,6.0,192.0,3.0,192.0')] ).
cnf(224,plain,
equal(double_divide(u,double_divide(double_divide(v,double_divide(u,w)),inverse(w))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[204,198]),
[iquote('0:Rew:204.0,198.0,204.0,198.0')] ).
cnf(263,plain,
equal(multiply(double_divide(u,v),v),inverse(u)),
inference(spr,[status(thm),theory(equality)],[196,214]),
[iquote('0:SpR:196.0,214.0')] ).
cnf(303,plain,
equal(multiply(u,inverse(multiply(v,u))),inverse(v)),
inference(spr,[status(thm),theory(equality)],[218]),
[iquote('0:SpR:218.0,218.0')] ).
cnf(316,plain,
equal(multiply(u,double_divide(u,v)),inverse(v)),
inference(rew,[status(thm),theory(equality)],[202,303]),
[iquote('0:Rew:202.0,303.0')] ).
cnf(349,plain,
equal(multiply(inverse(u),inverse(double_divide(u,v))),v),
inference(spr,[status(thm),theory(equality)],[263,218]),
[iquote('0:SpR:263.0,218.0')] ).
cnf(361,plain,
equal(multiply(inverse(u),multiply(v,u)),v),
inference(rew,[status(thm),theory(equality)],[6,349]),
[iquote('0:Rew:6.0,349.0')] ).
cnf(454,plain,
equal(multiply(inverse(u),inverse(v)),double_divide(v,u)),
inference(spr,[status(thm),theory(equality)],[316,218]),
[iquote('0:SpR:316.0,218.0')] ).
cnf(458,plain,
equal(inverse(double_divide(inverse(u),v)),double_divide(u,inverse(v))),
inference(spr,[status(thm),theory(equality)],[316,216]),
[iquote('0:SpR:316.0,216.0')] ).
cnf(471,plain,
equal(double_divide(u,inverse(v)),multiply(v,inverse(u))),
inference(rew,[status(thm),theory(equality)],[6,458]),
[iquote('0:Rew:6.0,458.0')] ).
cnf(474,plain,
equal(double_divide(u,multiply(v,inverse(double_divide(w,double_divide(u,v))))),inverse(w)),
inference(rew,[status(thm),theory(equality)],[471,224]),
[iquote('0:Rew:471.0,224.0')] ).
cnf(478,plain,
equal(double_divide(u,multiply(v,multiply(double_divide(u,v),w))),inverse(w)),
inference(rew,[status(thm),theory(equality)],[6,474]),
[iquote('0:Rew:6.0,474.0')] ).
cnf(498,plain,
equal(multiply(u,multiply(v,inverse(u))),v),
inference(spr,[status(thm),theory(equality)],[196,361]),
[iquote('0:SpR:196.0,361.0')] ).
cnf(780,plain,
equal(multiply(double_divide(u,v),inverse(w)),double_divide(w,multiply(v,u))),
inference(spr,[status(thm),theory(equality)],[202,454]),
[iquote('0:SpR:202.0,454.0')] ).
cnf(847,plain,
equal(inverse(multiply(u,inverse(double_divide(v,w)))),double_divide(v,multiply(w,u))),
inference(spr,[status(thm),theory(equality)],[498,478]),
[iquote('0:SpR:498.0,478.0')] ).
cnf(851,plain,
equal(double_divide(u,double_divide(u,v)),inverse(inverse(v))),
inference(spr,[status(thm),theory(equality)],[498,478]),
[iquote('0:SpR:498.0,478.0')] ).
cnf(852,plain,
equal(double_divide(u,double_divide(u,v)),v),
inference(rew,[status(thm),theory(equality)],[196,851]),
[iquote('0:Rew:196.0,851.0')] ).
cnf(873,plain,
equal(double_divide(multiply(u,v),w),double_divide(v,multiply(u,w))),
inference(rew,[status(thm),theory(equality)],[202,847,6]),
[iquote('0:Rew:202.0,847.0,6.0,847.0')] ).
cnf(915,plain,
equal(inverse(double_divide(u,v)),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[852,316]),
[iquote('0:SpR:852.0,316.0')] ).
cnf(942,plain,
equal(multiply(u,v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[6,915]),
[iquote('0:Rew:6.0,915.0')] ).
cnf(945,plain,
equal(multiply(double_divide(u,v),multiply(multiply(v,u),w)),w),
inference(rew,[status(thm),theory(equality)],[942,223]),
[iquote('0:Rew:942.0,223.0')] ).
cnf(946,plain,
~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))),
inference(rew,[status(thm),theory(equality)],[942,5]),
[iquote('0:Rew:942.0,5.0')] ).
cnf(1263,plain,
equal(multiply(double_divide(u,v),inverse(w)),double_divide(multiply(v,u),w)),
inference(spr,[status(thm),theory(equality)],[316,945]),
[iquote('0:SpR:316.0,945.0')] ).
cnf(1311,plain,
equal(double_divide(u,multiply(v,w)),double_divide(w,multiply(v,u))),
inference(rew,[status(thm),theory(equality)],[780,1263,873]),
[iquote('0:Rew:780.0,1263.0,873.0,1263.0')] ).
cnf(1639,plain,
equal(inverse(double_divide(u,multiply(v,w))),multiply(w,multiply(v,u))),
inference(spr,[status(thm),theory(equality)],[873,6]),
[iquote('0:SpR:873.0,6.0')] ).
cnf(1684,plain,
equal(multiply(multiply(u,v),w),multiply(v,multiply(u,w))),
inference(rew,[status(thm),theory(equality)],[6,1639]),
[iquote('0:Rew:6.0,1639.0')] ).
cnf(1876,plain,
equal(inverse(double_divide(u,multiply(v,w))),multiply(multiply(v,u),w)),
inference(spr,[status(thm),theory(equality)],[1311,6]),
[iquote('0:SpR:1311.0,6.0')] ).
cnf(1938,plain,
equal(multiply(multiply(u,v),w),multiply(multiply(u,w),v)),
inference(rew,[status(thm),theory(equality)],[6,1876]),
[iquote('0:Rew:6.0,1876.0')] ).
cnf(1939,plain,
equal(multiply(u,multiply(v,w)),multiply(w,multiply(v,u))),
inference(rew,[status(thm),theory(equality)],[1684,1938]),
[iquote('0:Rew:1684.0,1938.0,1684.0,1938.0')] ).
cnf(1941,plain,
~ equal(multiply(b3,multiply(a3,c3)),multiply(a3,multiply(b3,c3))),
inference(rew,[status(thm),theory(equality)],[1939,946]),
[iquote('0:Rew:1939.0,946.0')] ).
cnf(2149,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(spr,[status(thm),theory(equality)],[942,1684]),
[iquote('0:SpR:942.0,1684.0')] ).
cnf(2163,plain,
equal(multiply(u,multiply(v,w)),multiply(v,multiply(u,w))),
inference(rew,[status(thm),theory(equality)],[1684,2149]),
[iquote('0:Rew:1684.0,2149.0')] ).
cnf(2164,plain,
$false,
inference(unc,[status(thm)],[2163,1941]),
[iquote('0:UnC:2163.0,1941.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP567-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n020.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 : Mon Jun 13 17:20:35 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.52
% 0.19/0.52 SPASS V 3.9
% 0.19/0.52 SPASS beiseite: Proof found.
% 0.19/0.52 % SZS status Theorem
% 0.19/0.52 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.52 SPASS derived 1137 clauses, backtracked 0 clauses, performed 0 splits and kept 166 clauses.
% 0.19/0.52 SPASS allocated 64735 KBytes.
% 0.19/0.52 SPASS spent 0:00:00.17 on the problem.
% 0.19/0.52 0:00:00.03 for the input.
% 0.19/0.52 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.52 0:00:00.01 for inferences.
% 0.19/0.52 0:00:00.00 for the backtracking.
% 0.19/0.52 0:00:00.10 for the reduction.
% 0.19/0.52
% 0.19/0.52
% 0.19/0.52 Here is a proof with depth 8, length 81 :
% 0.19/0.52 % SZS output start Refutation
% See solution above
% 0.19/0.53 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_3
% 0.19/0.53
%------------------------------------------------------------------------------