TSTP Solution File: GRP557-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP557-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n013.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 11:48:02 EDT 2022
% Result : Unsatisfiable 0.18s 0.46s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of clauses : 26 ( 26 unt; 0 nHn; 26 RR)
% Number of literals : 26 ( 0 equ; 5 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 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(divide(u,inverse(divide(divide(v,w),divide(u,w)))),v),
file('GRP557-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,inverse(v)),multiply(u,v)),
file('GRP557-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1)),
file('GRP557-1.p',unknown),
[] ).
cnf(4,plain,
equal(multiply(u,divide(divide(v,w),divide(u,w))),v),
inference(rew,[status(thm),theory(equality)],[2,1]),
[iquote('0:Rew:2.0,1.0')] ).
cnf(7,plain,
equal(multiply(u,divide(divide(v,inverse(w)),multiply(u,w))),v),
inference(spr,[status(thm),theory(equality)],[2,4]),
[iquote('0:SpR:2.0,4.0')] ).
cnf(9,plain,
equal(multiply(u,divide(multiply(v,w),multiply(u,w))),v),
inference(rew,[status(thm),theory(equality)],[2,7]),
[iquote('0:Rew:2.0,7.0')] ).
cnf(12,plain,
equal(multiply(u,divide(multiply(v,divide(multiply(w,x),multiply(u,x))),w)),v),
inference(spr,[status(thm),theory(equality)],[9]),
[iquote('0:SpR:9.0,9.0')] ).
cnf(25,plain,
equal(multiply(u,divide(v,v)),u),
inference(spr,[status(thm),theory(equality)],[9,12]),
[iquote('0:SpR:9.0,12.0')] ).
cnf(33,plain,
equal(multiply(u,divide(v,u)),v),
inference(spr,[status(thm),theory(equality)],[25,12]),
[iquote('0:SpR:25.0,12.0')] ).
cnf(48,plain,
equal(multiply(inverse(u),multiply(v,u)),v),
inference(spr,[status(thm),theory(equality)],[2,33]),
[iquote('0:SpR:2.0,33.0')] ).
cnf(70,plain,
equal(multiply(inverse(divide(u,u)),v),v),
inference(spr,[status(thm),theory(equality)],[25,48]),
[iquote('0:SpR:25.0,48.0')] ).
cnf(120,plain,
equal(divide(multiply(u,v),multiply(inverse(divide(w,w)),v)),u),
inference(spr,[status(thm),theory(equality)],[70,9]),
[iquote('0:SpR:70.0,9.0')] ).
cnf(141,plain,
equal(divide(multiply(u,v),v),u),
inference(rew,[status(thm),theory(equality)],[70,120]),
[iquote('0:Rew:70.0,120.0')] ).
cnf(151,plain,
equal(multiply(multiply(u,inverse(v)),v),u),
inference(spr,[status(thm),theory(equality)],[141,2]),
[iquote('0:SpR:141.0,2.0')] ).
cnf(154,plain,
equal(multiply(u,v),multiply(v,u)),
inference(spr,[status(thm),theory(equality)],[141,33]),
[iquote('0:SpR:141.0,33.0')] ).
cnf(159,plain,
equal(divide(u,divide(v,v)),u),
inference(spr,[status(thm),theory(equality)],[25,141]),
[iquote('0:SpR:25.0,141.0')] ).
cnf(160,plain,
equal(divide(u,divide(u,v)),v),
inference(spr,[status(thm),theory(equality)],[33,141]),
[iquote('0:SpR:33.0,141.0')] ).
cnf(167,plain,
~ equal(multiply(inverse(a1),a1),multiply(b1,inverse(b1))),
inference(rew,[status(thm),theory(equality)],[154,3]),
[iquote('0:Rew:154.0,3.0')] ).
cnf(179,plain,
equal(multiply(u,multiply(v,inverse(u))),v),
inference(rew,[status(thm),theory(equality)],[154,151]),
[iquote('0:Rew:154.0,151.0')] ).
cnf(184,plain,
~ equal(multiply(b1,inverse(b1)),multiply(a1,inverse(a1))),
inference(rew,[status(thm),theory(equality)],[154,167]),
[iquote('0:Rew:154.0,167.0')] ).
cnf(187,plain,
equal(divide(multiply(u,v),u),v),
inference(spr,[status(thm),theory(equality)],[154,141]),
[iquote('0:SpR:154.0,141.0')] ).
cnf(234,plain,
equal(divide(u,u),divide(v,v)),
inference(spr,[status(thm),theory(equality)],[159,160]),
[iquote('0:SpR:159.0,160.0')] ).
cnf(428,plain,
equal(multiply(u,inverse(v)),divide(u,v)),
inference(spr,[status(thm),theory(equality)],[179,187]),
[iquote('0:SpR:179.0,187.0')] ).
cnf(444,plain,
~ equal(multiply(a1,inverse(a1)),divide(b1,b1)),
inference(rew,[status(thm),theory(equality)],[428,184]),
[iquote('0:Rew:428.0,184.0')] ).
cnf(464,plain,
~ equal(divide(b1,b1),divide(a1,a1)),
inference(rew,[status(thm),theory(equality)],[428,444]),
[iquote('0:Rew:428.0,444.0')] ).
cnf(465,plain,
$false,
inference(unc,[status(thm)],[464,234]),
[iquote('0:UnC:464.0,234.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP557-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n013.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 : Tue Jun 14 00:28:14 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.46
% 0.18/0.46 SPASS V 3.9
% 0.18/0.46 SPASS beiseite: Proof found.
% 0.18/0.46 % SZS status Theorem
% 0.18/0.46 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.46 SPASS derived 363 clauses, backtracked 0 clauses, performed 0 splits and kept 135 clauses.
% 0.18/0.46 SPASS allocated 63686 KBytes.
% 0.18/0.46 SPASS spent 0:00:00.12 on the problem.
% 0.18/0.46 0:00:00.03 for the input.
% 0.18/0.46 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.46 0:00:00.00 for inferences.
% 0.18/0.46 0:00:00.00 for the backtracking.
% 0.18/0.46 0:00:00.06 for the reduction.
% 0.18/0.46
% 0.18/0.46
% 0.18/0.46 Here is a proof with depth 10, length 26 :
% 0.18/0.46 % SZS output start Refutation
% See solution above
% 0.18/0.46 Formulae used in the proof : single_axiom multiply prove_these_axioms_1
% 0.18/0.46
%------------------------------------------------------------------------------