TSTP Solution File: GRP456-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP456-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 11:47:33 EDT 2022
% Result : Unsatisfiable 0.19s 0.47s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of clauses : 35 ( 35 unt; 0 nHn; 35 RR)
% Number of literals : 35 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 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(divide(divide(identity,divide(u,divide(v,divide(divide(divide(u,u),u),w)))),w),v),
file('GRP456-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,divide(identity,v)),multiply(u,v)),
file('GRP456-1.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(identity,u),inverse(u)),
file('GRP456-1.p',unknown),
[] ).
cnf(4,axiom,
equal(divide(u,u),identity),
file('GRP456-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))),
file('GRP456-1.p',unknown),
[] ).
cnf(6,plain,
equal(divide(u,inverse(v)),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[3,2]),
[iquote('0:Rew:3.0,2.0')] ).
cnf(7,plain,
equal(divide(inverse(divide(u,divide(v,divide(inverse(u),w)))),w),v),
inference(rew,[status(thm),theory(equality)],[3,1,4]),
[iquote('0:Rew:3.0,1.0,3.0,1.0,4.0,1.0')] ).
cnf(9,plain,
equal(inverse(identity),identity),
inference(spr,[status(thm),theory(equality)],[3,4]),
[iquote('0:SpR:3.0,4.0')] ).
cnf(13,plain,
equal(multiply(identity,u),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[6,3]),
[iquote('0:SpR:6.0,3.0')] ).
cnf(15,plain,
equal(divide(u,identity),multiply(u,identity)),
inference(spr,[status(thm),theory(equality)],[9,6]),
[iquote('0:SpR:9.0,6.0')] ).
cnf(31,plain,
equal(divide(inverse(divide(identity,divide(u,divide(identity,v)))),v),u),
inference(spr,[status(thm),theory(equality)],[9,7]),
[iquote('0:SpR:9.0,7.0')] ).
cnf(32,plain,
equal(divide(inverse(divide(u,divide(v,identity))),inverse(u)),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(38,plain,
equal(multiply(inverse(divide(u,multiply(v,identity))),u),v),
inference(rew,[status(thm),theory(equality)],[6,32,15]),
[iquote('0:Rew:6.0,32.0,15.0,32.0')] ).
cnf(40,plain,
equal(divide(inverse(inverse(multiply(u,v))),v),u),
inference(rew,[status(thm),theory(equality)],[3,31,6]),
[iquote('0:Rew:3.0,31.0,6.0,31.0,3.0,31.0')] ).
cnf(51,plain,
equal(multiply(inverse(identity),multiply(u,identity)),u),
inference(spr,[status(thm),theory(equality)],[4,38]),
[iquote('0:SpR:4.0,38.0')] ).
cnf(52,plain,
equal(multiply(inverse(inverse(multiply(u,identity))),identity),u),
inference(spr,[status(thm),theory(equality)],[3,38]),
[iquote('0:SpR:3.0,38.0')] ).
cnf(54,plain,
equal(inverse(inverse(multiply(u,identity))),u),
inference(rew,[status(thm),theory(equality)],[13,51,9]),
[iquote('0:Rew:13.0,51.0,9.0,51.0')] ).
cnf(56,plain,
equal(multiply(u,identity),u),
inference(rew,[status(thm),theory(equality)],[54,52]),
[iquote('0:Rew:54.0,52.0')] ).
cnf(57,plain,
equal(multiply(inverse(divide(u,v)),u),v),
inference(rew,[status(thm),theory(equality)],[56,38]),
[iquote('0:Rew:56.0,38.0')] ).
cnf(60,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[56,54]),
[iquote('0:Rew:56.0,54.0')] ).
cnf(63,plain,
equal(divide(multiply(u,v),v),u),
inference(rew,[status(thm),theory(equality)],[60,40]),
[iquote('0:Rew:60.0,40.0')] ).
cnf(78,plain,
equal(divide(inverse(divide(inverse(u),divide(v,divide(u,w)))),w),v),
inference(spr,[status(thm),theory(equality)],[60,7]),
[iquote('0:SpR:60.0,7.0')] ).
cnf(80,plain,
equal(multiply(u,inverse(v)),divide(u,v)),
inference(spr,[status(thm),theory(equality)],[60,6]),
[iquote('0:SpR:60.0,6.0')] ).
cnf(98,plain,
equal(multiply(multiply(u,inverse(v)),v),u),
inference(spr,[status(thm),theory(equality)],[63,6]),
[iquote('0:SpR:63.0,6.0')] ).
cnf(105,plain,
equal(inverse(divide(u,v)),divide(v,u)),
inference(spr,[status(thm),theory(equality)],[57,63]),
[iquote('0:SpR:57.0,63.0')] ).
cnf(107,plain,
equal(multiply(divide(u,v),v),u),
inference(rew,[status(thm),theory(equality)],[80,98]),
[iquote('0:Rew:80.0,98.0')] ).
cnf(111,plain,
equal(divide(divide(divide(u,divide(v,w)),inverse(v)),w),u),
inference(rew,[status(thm),theory(equality)],[105,78]),
[iquote('0:Rew:105.0,78.0')] ).
cnf(115,plain,
equal(divide(multiply(divide(u,divide(v,w)),v),w),u),
inference(rew,[status(thm),theory(equality)],[6,111]),
[iquote('0:Rew:6.0,111.0')] ).
cnf(191,plain,
equal(divide(u,divide(v,w)),multiply(u,divide(w,v))),
inference(spr,[status(thm),theory(equality)],[105,6]),
[iquote('0:SpR:105.0,6.0')] ).
cnf(205,plain,
equal(divide(multiply(multiply(u,divide(v,w)),w),v),u),
inference(rew,[status(thm),theory(equality)],[191,115]),
[iquote('0:Rew:191.0,115.0')] ).
cnf(686,plain,
equal(divide(multiply(u,v),w),divide(u,divide(w,v))),
inference(spr,[status(thm),theory(equality)],[107,205]),
[iquote('0:SpR:107.0,205.0')] ).
cnf(703,plain,
equal(divide(multiply(u,v),w),multiply(u,divide(v,w))),
inference(rew,[status(thm),theory(equality)],[191,686]),
[iquote('0:Rew:191.0,686.0')] ).
cnf(943,plain,
equal(multiply(u,divide(v,inverse(w))),multiply(multiply(u,v),w)),
inference(spr,[status(thm),theory(equality)],[703,6]),
[iquote('0:SpR:703.0,6.0')] ).
cnf(973,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[6,943]),
[iquote('0:Rew:6.0,943.0')] ).
cnf(974,plain,
$false,
inference(unc,[status(thm)],[973,5]),
[iquote('0:UnC:973.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP456-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n021.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
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 23:39:42 EDT 2022
% 0.12/0.33 % 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 546 clauses, backtracked 0 clauses, performed 0 splits and kept 120 clauses.
% 0.19/0.47 SPASS allocated 64103 KBytes.
% 0.19/0.47 SPASS spent 0:00:00.12 on the problem.
% 0.19/0.47 0:00:00.03 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 5, length 35 :
% 0.19/0.47 % SZS output start Refutation
% See solution above
% 0.19/0.47 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_3
% 0.19/0.47
%------------------------------------------------------------------------------