TSTP Solution File: GRP075-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP075-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% 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 11:45:11 EDT 2022
% Result : Unsatisfiable 0.21s 0.52s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 5
% Syntax : Number of clauses : 54 ( 48 unt; 0 nHn; 54 RR)
% Number of literals : 64 ( 0 equ; 17 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(double_divide(double_divide(double_divide(u,double_divide(v,identity)),double_divide(double_divide(w,double_divide(x,double_divide(x,identity))),double_divide(u,identity))),v),w),
file('GRP075-1.p',unknown),
[] ).
cnf(2,axiom,
equal(double_divide(double_divide(u,v),identity),multiply(v,u)),
file('GRP075-1.p',unknown),
[] ).
cnf(3,axiom,
equal(double_divide(u,identity),inverse(u)),
file('GRP075-1.p',unknown),
[] ).
cnf(4,axiom,
equal(double_divide(u,inverse(u)),identity),
file('GRP075-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ equal(multiply(identity,a2),a2)
| ~ equal(multiply(inverse(a1),a1),identity)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
file('GRP075-1.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(double_divide(u,inverse(v)),double_divide(inverse(w),inverse(u))),v),w),
inference(rew,[status(thm),theory(equality)],[3,1,4]),
[iquote('0:Rew:3.0,1.0,3.0,1.0,4.0,1.0,3.0,1.0,3.0,1.0')] ).
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(14,plain,
( ~ equal(multiply(identity,a2),a2)
| ~ equal(inverse(identity),identity)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[12,5]),
[iquote('0:Rew:12.0,5.1')] ).
cnf(15,plain,
( ~ equal(inverse(inverse(a2)),a2)
| ~ equal(inverse(identity),identity)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[13,14]),
[iquote('0:Rew:13.0,14.0')] ).
cnf(18,plain,
equal(double_divide(double_divide(u,double_divide(inverse(v),inverse(double_divide(double_divide(w,inverse(inverse(x))),double_divide(inverse(u),inverse(w)))))),x),v),
inference(spr,[status(thm),theory(equality)],[7]),
[iquote('0:SpR:7.0,7.0')] ).
cnf(20,plain,
equal(multiply(u,double_divide(double_divide(v,inverse(u)),double_divide(inverse(w),inverse(v)))),inverse(w)),
inference(spr,[status(thm),theory(equality)],[7,6]),
[iquote('0:SpR:7.0,6.0')] ).
cnf(24,plain,
equal(double_divide(double_divide(double_divide(inverse(u),inverse(v)),identity),v),u),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(27,plain,
equal(double_divide(multiply(inverse(u),inverse(v)),u),v),
inference(rew,[status(thm),theory(equality)],[6,24,3]),
[iquote('0:Rew:6.0,24.0,3.0,24.0')] ).
cnf(29,plain,
equal(double_divide(double_divide(u,double_divide(inverse(v),multiply(double_divide(inverse(u),inverse(w)),double_divide(w,inverse(inverse(x)))))),x),v),
inference(rew,[status(thm),theory(equality)],[6,18]),
[iquote('0:Rew:6.0,18.0')] ).
cnf(50,plain,
equal(double_divide(multiply(inverse(u),multiply(v,w)),u),double_divide(w,v)),
inference(spr,[status(thm),theory(equality)],[6,27]),
[iquote('0:SpR:6.0,27.0')] ).
cnf(52,plain,
equal(double_divide(inverse(identity),inverse(u)),u),
inference(spr,[status(thm),theory(equality)],[12,27]),
[iquote('0:SpR:12.0,27.0')] ).
cnf(54,plain,
equal(inverse(identity),identity),
inference(spr,[status(thm),theory(equality)],[52,4]),
[iquote('0:SpR:52.0,4.0')] ).
cnf(55,plain,
equal(double_divide(double_divide(u,double_divide(inverse(v),inverse(inverse(identity)))),u),v),
inference(spr,[status(thm),theory(equality)],[52,7]),
[iquote('0:SpR:52.0,7.0')] ).
cnf(56,plain,
equal(multiply(inverse(u),inverse(identity)),inverse(u)),
inference(spr,[status(thm),theory(equality)],[52,6]),
[iquote('0:SpR:52.0,6.0')] ).
cnf(61,plain,
equal(multiply(inverse(u),u),identity),
inference(rew,[status(thm),theory(equality)],[54,12]),
[iquote('0:Rew:54.0,12.0')] ).
cnf(63,plain,
( ~ equal(inverse(inverse(a2)),a2)
| ~ equal(identity,identity)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[54,15]),
[iquote('0:Rew:54.0,15.1')] ).
cnf(68,plain,
equal(multiply(inverse(u),identity),inverse(u)),
inference(rew,[status(thm),theory(equality)],[54,56]),
[iquote('0:Rew:54.0,56.0')] ).
cnf(72,plain,
equal(double_divide(double_divide(u,double_divide(inverse(v),identity)),u),v),
inference(rew,[status(thm),theory(equality)],[54,55]),
[iquote('0:Rew:54.0,55.0,54.0,55.0')] ).
cnf(73,plain,
equal(double_divide(double_divide(u,inverse(inverse(v))),u),v),
inference(rew,[status(thm),theory(equality)],[3,72]),
[iquote('0:Rew:3.0,72.0')] ).
cnf(74,plain,
( ~ equal(inverse(inverse(a2)),a2)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(obv,[status(thm),theory(equality)],[63]),
[iquote('0:Obv:63.1')] ).
cnf(80,plain,
equal(double_divide(multiply(inverse(u),identity),u),identity),
inference(spr,[status(thm),theory(equality)],[54,27]),
[iquote('0:SpR:54.0,27.0')] ).
cnf(84,plain,
equal(double_divide(inverse(u),u),identity),
inference(rew,[status(thm),theory(equality)],[68,80]),
[iquote('0:Rew:68.0,80.0')] ).
cnf(110,plain,
equal(double_divide(double_divide(double_divide(u,inverse(v)),identity),v),inverse(u)),
inference(spr,[status(thm),theory(equality)],[84,7]),
[iquote('0:SpR:84.0,7.0')] ).
cnf(119,plain,
equal(double_divide(multiply(inverse(u),v),u),inverse(v)),
inference(rew,[status(thm),theory(equality)],[6,110,3]),
[iquote('0:Rew:6.0,110.0,3.0,110.0')] ).
cnf(120,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[119,27]),
[iquote('0:Rew:119.0,27.0')] ).
cnf(121,plain,
equal(inverse(multiply(u,v)),double_divide(v,u)),
inference(rew,[status(thm),theory(equality)],[119,50]),
[iquote('0:Rew:119.0,50.0')] ).
cnf(122,plain,
( ~ equal(a2,a2)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[120,74]),
[iquote('0:Rew:120.0,74.0')] ).
cnf(124,plain,
equal(double_divide(double_divide(u,v),u),v),
inference(rew,[status(thm),theory(equality)],[120,73]),
[iquote('0:Rew:120.0,73.0')] ).
cnf(127,plain,
equal(double_divide(double_divide(u,double_divide(inverse(v),multiply(double_divide(inverse(u),inverse(w)),double_divide(w,x)))),x),v),
inference(rew,[status(thm),theory(equality)],[120,29]),
[iquote('0:Rew:120.0,29.0')] ).
cnf(131,plain,
~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))),
inference(obv,[status(thm),theory(equality)],[122]),
[iquote('0:Obv:122.0')] ).
cnf(189,plain,
equal(multiply(u,double_divide(u,v)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[124,6]),
[iquote('0:SpR:124.0,6.0')] ).
cnf(191,plain,
equal(double_divide(u,double_divide(v,u)),v),
inference(spr,[status(thm),theory(equality)],[124]),
[iquote('0:SpR:124.0,124.0')] ).
cnf(247,plain,
equal(multiply(u,double_divide(double_divide(v,inverse(u)),identity)),inverse(inverse(v))),
inference(spr,[status(thm),theory(equality)],[84,20]),
[iquote('0:SpR:84.0,20.0')] ).
cnf(257,plain,
equal(multiply(u,multiply(inverse(u),v)),v),
inference(rew,[status(thm),theory(equality)],[6,247,3,120]),
[iquote('0:Rew:6.0,247.0,3.0,247.0,120.0,247.0')] ).
cnf(311,plain,
equal(double_divide(inverse(u),v),multiply(u,inverse(v))),
inference(spr,[status(thm),theory(equality)],[189,257]),
[iquote('0:SpR:189.0,257.0')] ).
cnf(319,plain,
equal(double_divide(double_divide(u,multiply(v,inverse(multiply(double_divide(inverse(u),inverse(w)),double_divide(w,x))))),x),v),
inference(rew,[status(thm),theory(equality)],[311,127]),
[iquote('0:Rew:311.0,127.0')] ).
cnf(345,plain,
equal(double_divide(double_divide(u,multiply(v,double_divide(double_divide(w,x),double_divide(inverse(u),inverse(w))))),x),v),
inference(rew,[status(thm),theory(equality)],[121,319]),
[iquote('0:Rew:121.0,319.0')] ).
cnf(346,plain,
equal(double_divide(double_divide(u,multiply(v,double_divide(double_divide(w,x),multiply(u,inverse(inverse(w)))))),x),v),
inference(rew,[status(thm),theory(equality)],[311,345]),
[iquote('0:Rew:311.0,345.0')] ).
cnf(347,plain,
equal(double_divide(double_divide(u,multiply(v,double_divide(double_divide(w,x),multiply(u,w)))),x),v),
inference(rew,[status(thm),theory(equality)],[120,346]),
[iquote('0:Rew:120.0,346.0')] ).
cnf(632,plain,
equal(double_divide(double_divide(inverse(u),multiply(v,double_divide(double_divide(u,w),identity))),w),v),
inference(spr,[status(thm),theory(equality)],[61,347]),
[iquote('0:SpR:61.0,347.0')] ).
cnf(672,plain,
equal(double_divide(double_divide(inverse(u),multiply(v,multiply(w,u))),w),v),
inference(rew,[status(thm),theory(equality)],[6,632,3]),
[iquote('0:Rew:6.0,632.0,3.0,632.0')] ).
cnf(673,plain,
equal(double_divide(multiply(u,inverse(multiply(v,multiply(w,u)))),w),v),
inference(rew,[status(thm),theory(equality)],[311,672]),
[iquote('0:Rew:311.0,672.0')] ).
cnf(674,plain,
equal(double_divide(multiply(u,double_divide(multiply(v,u),w)),v),w),
inference(rew,[status(thm),theory(equality)],[121,673]),
[iquote('0:Rew:121.0,673.0')] ).
cnf(889,plain,
equal(double_divide(multiply(u,v),w),double_divide(v,multiply(w,u))),
inference(spr,[status(thm),theory(equality)],[191,674]),
[iquote('0:SpR:191.0,674.0')] ).
cnf(1517,plain,
equal(inverse(double_divide(u,multiply(v,w))),multiply(v,multiply(w,u))),
inference(spr,[status(thm),theory(equality)],[889,6]),
[iquote('0:SpR:889.0,6.0')] ).
cnf(1553,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[6,1517]),
[iquote('0:Rew:6.0,1517.0')] ).
cnf(1554,plain,
$false,
inference(unc,[status(thm)],[1553,131]),
[iquote('0:UnC:1553.0,131.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.13 % Problem : GRP075-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% 0.13/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n020.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jun 14 00:15:20 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.21/0.52
% 0.21/0.52 SPASS V 3.9
% 0.21/0.52 SPASS beiseite: Proof found.
% 0.21/0.52 % SZS status Theorem
% 0.21/0.52 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.52 SPASS derived 828 clauses, backtracked 0 clauses, performed 0 splits and kept 163 clauses.
% 0.21/0.52 SPASS allocated 64608 KBytes.
% 0.21/0.52 SPASS spent 0:00:00.15 on the problem.
% 0.21/0.52 0:00:00.04 for the input.
% 0.21/0.52 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.52 0:00:00.01 for inferences.
% 0.21/0.52 0:00:00.00 for the backtracking.
% 0.21/0.52 0:00:00.09 for the reduction.
% 0.21/0.52
% 0.21/0.52
% 0.21/0.52 Here is a proof with depth 6, length 54 :
% 0.21/0.52 % SZS output start Refutation
% See solution above
% 0.21/0.52 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms
% 0.21/0.52
%------------------------------------------------------------------------------