TSTP Solution File: GRP079-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP079-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 11:45:12 EDT 2022
% Result : Unsatisfiable 0.19s 0.49s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 5
% Syntax : Number of clauses : 55 ( 49 unt; 0 nHn; 55 RR)
% Number of literals : 65 ( 0 equ; 17 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(double_divide(double_divide(identity,u),double_divide(double_divide(double_divide(v,w),double_divide(identity,identity)),double_divide(u,w))),v),
file('GRP079-1.p',unknown),
[] ).
cnf(2,axiom,
equal(double_divide(double_divide(u,v),identity),multiply(v,u)),
file('GRP079-1.p',unknown),
[] ).
cnf(3,axiom,
equal(double_divide(u,identity),inverse(u)),
file('GRP079-1.p',unknown),
[] ).
cnf(4,axiom,
equal(double_divide(u,inverse(u)),identity),
file('GRP079-1.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('GRP079-1.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(identity,u),double_divide(double_divide(double_divide(v,w),inverse(identity)),double_divide(u,w))),v),
inference(rew,[status(thm),theory(equality)],[3,1]),
[iquote('0:Rew: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(23,plain,
equal(double_divide(double_divide(identity,u),double_divide(double_divide(double_divide(v,identity),inverse(identity)),inverse(u))),v),
inference(spr,[status(thm),theory(equality)],[3,7]),
[iquote('0:SpR:3.0,7.0')] ).
cnf(24,plain,
equal(double_divide(double_divide(identity,u),double_divide(double_divide(identity,inverse(identity)),double_divide(u,inverse(v)))),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(29,plain,
equal(double_divide(double_divide(identity,u),double_divide(double_divide(inverse(v),inverse(identity)),inverse(u))),v),
inference(rew,[status(thm),theory(equality)],[3,23]),
[iquote('0:Rew:3.0,23.0')] ).
cnf(30,plain,
equal(double_divide(double_divide(identity,u),double_divide(identity,double_divide(u,inverse(v)))),v),
inference(rew,[status(thm),theory(equality)],[4,24]),
[iquote('0:Rew:4.0,24.0')] ).
cnf(75,plain,
equal(double_divide(double_divide(identity,u),double_divide(identity,identity)),u),
inference(spr,[status(thm),theory(equality)],[4,30]),
[iquote('0:SpR:4.0,30.0')] ).
cnf(76,plain,
equal(double_divide(identity,double_divide(identity,double_divide(inverse(identity),inverse(u)))),u),
inference(spr,[status(thm),theory(equality)],[4,30]),
[iquote('0:SpR:4.0,30.0')] ).
cnf(78,plain,
equal(double_divide(double_divide(identity,u),inverse(identity)),u),
inference(rew,[status(thm),theory(equality)],[3,75]),
[iquote('0:Rew:3.0,75.0')] ).
cnf(84,plain,
equal(double_divide(double_divide(identity,double_divide(identity,u)),double_divide(double_divide(double_divide(v,inverse(identity)),inverse(identity)),u)),v),
inference(spr,[status(thm),theory(equality)],[78,7]),
[iquote('0:SpR:78.0,7.0')] ).
cnf(85,plain,
equal(double_divide(double_divide(identity,u),double_divide(double_divide(v,inverse(identity)),double_divide(u,inverse(identity)))),double_divide(identity,v)),
inference(spr,[status(thm),theory(equality)],[78,7]),
[iquote('0:SpR:78.0,7.0')] ).
cnf(89,plain,
equal(double_divide(identity,inverse(identity)),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[4,78]),
[iquote('0:SpR:4.0,78.0')] ).
cnf(91,plain,
equal(inverse(identity),identity),
inference(rew,[status(thm),theory(equality)],[4,89]),
[iquote('0:Rew:4.0,89.0')] ).
cnf(93,plain,
equal(double_divide(double_divide(identity,u),double_divide(double_divide(double_divide(v,w),identity),double_divide(u,w))),v),
inference(rew,[status(thm),theory(equality)],[91,7]),
[iquote('0:Rew:91.0,7.0')] ).
cnf(95,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)],[91,15]),
[iquote('0:Rew:91.0,15.1')] ).
cnf(98,plain,
equal(double_divide(double_divide(identity,u),double_divide(double_divide(inverse(v),identity),inverse(u))),v),
inference(rew,[status(thm),theory(equality)],[91,29]),
[iquote('0:Rew:91.0,29.0')] ).
cnf(106,plain,
equal(double_divide(identity,double_divide(identity,double_divide(identity,inverse(u)))),u),
inference(rew,[status(thm),theory(equality)],[91,76]),
[iquote('0:Rew:91.0,76.0')] ).
cnf(122,plain,
equal(double_divide(double_divide(identity,u),double_divide(inverse(inverse(v)),inverse(u))),v),
inference(rew,[status(thm),theory(equality)],[3,98]),
[iquote('0:Rew:3.0,98.0')] ).
cnf(125,plain,
equal(double_divide(double_divide(identity,u),double_divide(multiply(v,w),double_divide(u,v))),w),
inference(rew,[status(thm),theory(equality)],[6,93,3]),
[iquote('0:Rew:6.0,93.0,3.0,93.0')] ).
cnf(128,plain,
equal(double_divide(double_divide(identity,double_divide(identity,u)),double_divide(double_divide(double_divide(v,identity),identity),u)),v),
inference(rew,[status(thm),theory(equality)],[91,84]),
[iquote('0:Rew:91.0,84.0')] ).
cnf(129,plain,
equal(double_divide(double_divide(identity,double_divide(identity,u)),double_divide(inverse(inverse(v)),u)),v),
inference(rew,[status(thm),theory(equality)],[3,128]),
[iquote('0:Rew:3.0,128.0,3.0,128.0')] ).
cnf(130,plain,
equal(double_divide(double_divide(identity,u),double_divide(double_divide(v,identity),double_divide(u,identity))),double_divide(identity,v)),
inference(rew,[status(thm),theory(equality)],[91,85]),
[iquote('0:Rew:91.0,85.0')] ).
cnf(131,plain,
equal(double_divide(double_divide(identity,u),double_divide(inverse(v),inverse(u))),double_divide(identity,v)),
inference(rew,[status(thm),theory(equality)],[3,130]),
[iquote('0:Rew:3.0,130.0,3.0,130.0')] ).
cnf(132,plain,
equal(double_divide(identity,inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[131,122]),
[iquote('0:Rew:131.0,122.0')] ).
cnf(133,plain,
equal(double_divide(identity,double_divide(identity,u)),u),
inference(rew,[status(thm),theory(equality)],[132,106]),
[iquote('0:Rew:132.0,106.0')] ).
cnf(135,plain,
equal(double_divide(u,double_divide(inverse(inverse(v)),u)),v),
inference(rew,[status(thm),theory(equality)],[133,129]),
[iquote('0:Rew:133.0,129.0')] ).
cnf(139,plain,
( ~ equal(inverse(inverse(a2)),a2)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(obv,[status(thm),theory(equality)],[95]),
[iquote('0:Obv:95.1')] ).
cnf(185,plain,
equal(double_divide(double_divide(identity,identity),double_divide(multiply(inverse(u),v),u)),v),
inference(spr,[status(thm),theory(equality)],[132,125]),
[iquote('0:SpR:132.0,125.0')] ).
cnf(194,plain,
equal(double_divide(identity,double_divide(multiply(inverse(u),v),u)),v),
inference(rew,[status(thm),theory(equality)],[91,185,3]),
[iquote('0:Rew:91.0,185.0,3.0,185.0')] ).
cnf(205,plain,
equal(double_divide(identity,u),inverse(u)),
inference(spr,[status(thm),theory(equality)],[132,133]),
[iquote('0:SpR:132.0,133.0')] ).
cnf(208,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[205,132]),
[iquote('0:Rew:205.0,132.0')] ).
cnf(209,plain,
equal(double_divide(inverse(u),double_divide(multiply(v,w),double_divide(u,v))),w),
inference(rew,[status(thm),theory(equality)],[205,125]),
[iquote('0:Rew:205.0,125.0')] ).
cnf(216,plain,
equal(inverse(double_divide(multiply(inverse(u),v),u)),v),
inference(rew,[status(thm),theory(equality)],[205,194]),
[iquote('0:Rew:205.0,194.0')] ).
cnf(227,plain,
( ~ equal(a2,a2)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[208,139]),
[iquote('0:Rew:208.0,139.0')] ).
cnf(228,plain,
equal(double_divide(u,double_divide(v,u)),v),
inference(rew,[status(thm),theory(equality)],[208,135]),
[iquote('0:Rew:208.0,135.0')] ).
cnf(234,plain,
equal(multiply(u,multiply(inverse(u),v)),v),
inference(rew,[status(thm),theory(equality)],[6,216]),
[iquote('0:Rew:6.0,216.0')] ).
cnf(256,plain,
~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))),
inference(obv,[status(thm),theory(equality)],[227]),
[iquote('0:Obv:227.0')] ).
cnf(299,plain,
equal(double_divide(double_divide(u,v),u),v),
inference(spr,[status(thm),theory(equality)],[228]),
[iquote('0:SpR:228.0,228.0')] ).
cnf(317,plain,
equal(double_divide(inverse(u),double_divide(multiply(double_divide(v,u),w),v)),w),
inference(spr,[status(thm),theory(equality)],[228,209]),
[iquote('0:SpR:228.0,209.0')] ).
cnf(346,plain,
equal(multiply(u,double_divide(u,v)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[299,6]),
[iquote('0:SpR:299.0,6.0')] ).
cnf(395,plain,
equal(multiply(double_divide(u,v),multiply(multiply(v,u),w)),w),
inference(spr,[status(thm),theory(equality)],[6,234]),
[iquote('0:SpR:6.0,234.0')] ).
cnf(496,plain,
equal(double_divide(inverse(u),v),multiply(u,inverse(v))),
inference(spr,[status(thm),theory(equality)],[346,234]),
[iquote('0:SpR:346.0,234.0')] ).
cnf(509,plain,
equal(multiply(u,inverse(double_divide(multiply(double_divide(v,u),w),v))),w),
inference(rew,[status(thm),theory(equality)],[496,317]),
[iquote('0:Rew:496.0,317.0')] ).
cnf(514,plain,
equal(multiply(u,multiply(v,multiply(double_divide(v,u),w))),w),
inference(rew,[status(thm),theory(equality)],[6,509]),
[iquote('0:Rew:6.0,509.0')] ).
cnf(1303,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(spr,[status(thm),theory(equality)],[395,514]),
[iquote('0:SpR:395.0,514.0')] ).
cnf(1317,plain,
$false,
inference(unc,[status(thm)],[1303,256]),
[iquote('0:UnC:1303.0,256.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP079-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 12:18:24 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.49
% 0.19/0.49 SPASS V 3.9
% 0.19/0.49 SPASS beiseite: Proof found.
% 0.19/0.49 % SZS status Theorem
% 0.19/0.49 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.49 SPASS derived 730 clauses, backtracked 0 clauses, performed 0 splits and kept 133 clauses.
% 0.19/0.49 SPASS allocated 64304 KBytes.
% 0.19/0.49 SPASS spent 0:00:00.13 on the problem.
% 0.19/0.49 0:00:00.03 for the input.
% 0.19/0.49 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.49 0:00:00.01 for inferences.
% 0.19/0.49 0:00:00.00 for the backtracking.
% 0.19/0.49 0:00:00.07 for the reduction.
% 0.19/0.49
% 0.19/0.49
% 0.19/0.49 Here is a proof with depth 6, length 55 :
% 0.19/0.49 % SZS output start Refutation
% See solution above
% 0.19/0.49 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms
% 0.19/0.49
%------------------------------------------------------------------------------