TSTP Solution File: GRP574-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP574-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n014.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 0.44s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of clauses : 38 ( 38 unt; 0 nHn; 38 RR)
% Number of literals : 38 ( 0 equ; 2 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 : 9 ( 9 usr; 6 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('GRP574-1.p',unknown),
[] ).
cnf(2,axiom,
equal(double_divide(double_divide(u,v),identity),multiply(v,u)),
file('GRP574-1.p',unknown),
[] ).
cnf(3,axiom,
equal(double_divide(u,identity),inverse(u)),
file('GRP574-1.p',unknown),
[] ).
cnf(4,axiom,
equal(double_divide(u,inverse(u)),identity),
file('GRP574-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(multiply(identity,a2),a2),
file('GRP574-1.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(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(inverse(inverse(a2)),a2),
inference(rew,[status(thm),theory(equality)],[13,5]),
[iquote('0:Rew:13.0,5.0')] ).
cnf(50,plain,
equal(double_divide(double_divide(u,double_divide(double_divide(v,double_divide(double_divide(w,x),u)),multiply(x,w))),inverse(identity)),v),
inference(spr,[status(thm),theory(equality)],[6,7]),
[iquote('0:SpR:6.0,7.0')] ).
cnf(51,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(52,plain,
equal(double_divide(double_divide(identity,double_divide(double_divide(u,inverse(v)),inverse(v))),inverse(identity)),u),
inference(spr,[status(thm),theory(equality)],[3,7]),
[iquote('0:SpR:3.0,7.0')] ).
cnf(54,plain,
equal(double_divide(double_divide(inverse(u),double_divide(inverse(v),inverse(u))),inverse(identity)),v),
inference(rew,[status(thm),theory(equality)],[3,51]),
[iquote('0:Rew:3.0,51.0')] ).
cnf(66,plain,
equal(double_divide(double_divide(inverse(inverse(u)),identity),inverse(identity)),u),
inference(spr,[status(thm),theory(equality)],[4,54]),
[iquote('0:SpR:4.0,54.0')] ).
cnf(68,plain,
equal(double_divide(inverse(inverse(inverse(u))),inverse(identity)),u),
inference(rew,[status(thm),theory(equality)],[3,66]),
[iquote('0:Rew:3.0,66.0')] ).
cnf(76,plain,
equal(double_divide(double_divide(inverse(identity),u),inverse(identity)),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[68,54]),
[iquote('0:SpR:68.0,54.0')] ).
cnf(97,plain,
equal(inverse(inverse(double_divide(inverse(u),inverse(identity)))),u),
inference(spr,[status(thm),theory(equality)],[76,54]),
[iquote('0:SpR:76.0,54.0')] ).
cnf(101,plain,
equal(inverse(inverse(inverse(inverse(identity)))),double_divide(identity,inverse(identity))),
inference(spr,[status(thm),theory(equality)],[4,76]),
[iquote('0:SpR:4.0,76.0')] ).
cnf(103,plain,
equal(inverse(multiply(inverse(identity),inverse(u))),u),
inference(rew,[status(thm),theory(equality)],[6,97]),
[iquote('0:Rew:6.0,97.0')] ).
cnf(104,plain,
equal(inverse(inverse(inverse(inverse(identity)))),identity),
inference(rew,[status(thm),theory(equality)],[4,101]),
[iquote('0:Rew:4.0,101.0')] ).
cnf(121,plain,
equal(double_divide(double_divide(identity,double_divide(inverse(inverse(u)),inverse(identity))),inverse(identity)),double_divide(inverse(identity),u)),
inference(spr,[status(thm),theory(equality)],[76,52]),
[iquote('0:SpR:76.0,52.0')] ).
cnf(122,plain,
equal(double_divide(double_divide(identity,double_divide(u,inverse(identity))),inverse(identity)),inverse(inverse(inverse(u)))),
inference(spr,[status(thm),theory(equality)],[68,52]),
[iquote('0:SpR:68.0,52.0')] ).
cnf(125,plain,
equal(inverse(inverse(inverse(inverse(inverse(u))))),double_divide(inverse(identity),u)),
inference(rew,[status(thm),theory(equality)],[122,121]),
[iquote('0:Rew:122.0,121.0')] ).
cnf(143,plain,
equal(double_divide(identity,inverse(identity)),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[104,68]),
[iquote('0:SpR:104.0,68.0')] ).
cnf(146,plain,
equal(inverse(identity),identity),
inference(rew,[status(thm),theory(equality)],[4,143]),
[iquote('0:Rew:4.0,143.0')] ).
cnf(147,plain,
equal(multiply(inverse(u),u),identity),
inference(rew,[status(thm),theory(equality)],[146,12]),
[iquote('0:Rew:146.0,12.0')] ).
cnf(154,plain,
equal(double_divide(double_divide(u,double_divide(double_divide(v,double_divide(double_divide(w,x),u)),multiply(x,w))),identity),v),
inference(rew,[status(thm),theory(equality)],[146,50]),
[iquote('0:Rew:146.0,50.0')] ).
cnf(158,plain,
equal(inverse(multiply(identity,inverse(u))),u),
inference(rew,[status(thm),theory(equality)],[146,103]),
[iquote('0:Rew:146.0,103.0')] ).
cnf(160,plain,
equal(inverse(inverse(inverse(inverse(inverse(u))))),double_divide(identity,u)),
inference(rew,[status(thm),theory(equality)],[146,125]),
[iquote('0:Rew:146.0,125.0')] ).
cnf(170,plain,
equal(inverse(inverse(inverse(inverse(u)))),u),
inference(rew,[status(thm),theory(equality)],[13,158]),
[iquote('0:Rew:13.0,158.0')] ).
cnf(191,plain,
equal(double_divide(identity,u),inverse(u)),
inference(rew,[status(thm),theory(equality)],[170,160]),
[iquote('0:Rew:170.0,160.0')] ).
cnf(213,plain,
equal(multiply(double_divide(double_divide(u,double_divide(double_divide(v,w),x)),multiply(w,v)),x),u),
inference(rew,[status(thm),theory(equality)],[6,154,3]),
[iquote('0:Rew:6.0,154.0,3.0,154.0')] ).
cnf(234,plain,
equal(multiply(double_divide(double_divide(u,double_divide(double_divide(v,inverse(v)),w)),identity),w),u),
inference(spr,[status(thm),theory(equality)],[147,213]),
[iquote('0:SpR:147.0,213.0')] ).
cnf(244,plain,
equal(multiply(multiply(inverse(u),v),u),v),
inference(rew,[status(thm),theory(equality)],[6,234,3,191,4]),
[iquote('0:Rew:6.0,234.0,3.0,234.0,191.0,234.0,4.0,234.0')] ).
cnf(412,plain,
equal(multiply(identity,u),u),
inference(spr,[status(thm),theory(equality)],[147,244]),
[iquote('0:SpR:147.0,244.0')] ).
cnf(417,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[13,412]),
[iquote('0:Rew:13.0,412.0')] ).
cnf(418,plain,
$false,
inference(unc,[status(thm)],[417,14]),
[iquote('0:UnC:417.0,14.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP574-1 : TPTP v8.1.0. Released v2.6.0.
% 0.13/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n014.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 : Tue Jun 14 05:17:21 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.44
% 0.19/0.44 SPASS V 3.9
% 0.19/0.44 SPASS beiseite: Proof found.
% 0.19/0.44 % SZS status Theorem
% 0.19/0.44 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 SPASS derived 248 clauses, backtracked 0 clauses, performed 0 splits and kept 89 clauses.
% 0.19/0.44 SPASS allocated 63644 KBytes.
% 0.19/0.44 SPASS spent 0:00:00.08 on the problem.
% 0.19/0.44 0:00:00.03 for the input.
% 0.19/0.44 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.44 0:00:00.00 for inferences.
% 0.19/0.44 0:00:00.00 for the backtracking.
% 0.19/0.44 0:00:00.03 for the reduction.
% 0.19/0.44
% 0.19/0.44
% 0.19/0.44 Here is a proof with depth 5, length 38 :
% 0.19/0.44 % SZS output start Refutation
% See solution above
% 0.19/0.44 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_2
% 0.19/0.44
%------------------------------------------------------------------------------