TSTP Solution File: GRP586-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP586-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 11:48:09 EDT 2022
% Result : Unsatisfiable 0.19s 0.47s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of clauses : 18 ( 18 unt; 0 nHn; 18 RR)
% Number of literals : 18 ( 0 equ; 3 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(u,inverse(double_divide(inverse(double_divide(double_divide(u,v),inverse(w))),v))),w),
file('GRP586-1.p',unknown),
[] ).
cnf(2,axiom,
equal(inverse(double_divide(u,v)),multiply(v,u)),
file('GRP586-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(multiply(multiply(inverse(b2),b2),a2),a2),
file('GRP586-1.p',unknown),
[] ).
cnf(4,plain,
equal(double_divide(u,multiply(v,multiply(inverse(w),double_divide(u,v)))),w),
inference(rew,[status(thm),theory(equality)],[2,1]),
[iquote('0:Rew:2.0,1.0,2.0,1.0')] ).
cnf(6,plain,
equal(multiply(multiply(u,multiply(inverse(v),double_divide(w,u))),w),inverse(v)),
inference(spr,[status(thm),theory(equality)],[4,2]),
[iquote('0:SpR:4.0,2.0')] ).
cnf(7,plain,
equal(double_divide(u,multiply(multiply(v,multiply(inverse(w),double_divide(u,v))),multiply(inverse(x),w))),x),
inference(spr,[status(thm),theory(equality)],[4]),
[iquote('0:SpR:4.0,4.0')] ).
cnf(44,plain,
equal(double_divide(multiply(inverse(u),v),inverse(v)),u),
inference(spr,[status(thm),theory(equality)],[6,7]),
[iquote('0:SpR:6.0,7.0')] ).
cnf(45,plain,
equal(multiply(inverse(u),multiply(inverse(v),u)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[44,2]),
[iquote('0:SpR:44.0,2.0')] ).
cnf(56,plain,
equal(double_divide(inverse(u),inverse(multiply(inverse(u),v))),v),
inference(spr,[status(thm),theory(equality)],[45,44]),
[iquote('0:SpR:45.0,44.0')] ).
cnf(94,plain,
equal(double_divide(inverse(u),inverse(inverse(v))),multiply(inverse(v),u)),
inference(spr,[status(thm),theory(equality)],[45,56]),
[iquote('0:SpR:45.0,56.0')] ).
cnf(119,plain,
equal(double_divide(inverse(u),inverse(multiply(v,w))),multiply(multiply(v,w),u)),
inference(spr,[status(thm),theory(equality)],[2,94]),
[iquote('0:SpR:2.0,94.0')] ).
cnf(121,plain,
equal(multiply(multiply(inverse(u),v),u),v),
inference(rew,[status(thm),theory(equality)],[119,56]),
[iquote('0:Rew:119.0,56.0')] ).
cnf(125,plain,
equal(multiply(inverse(u),double_divide(v,inverse(v))),inverse(u)),
inference(spr,[status(thm),theory(equality)],[121,6]),
[iquote('0:SpR:121.0,6.0')] ).
cnf(167,plain,
equal(multiply(inverse(u),u),double_divide(v,inverse(v))),
inference(spr,[status(thm),theory(equality)],[125,121]),
[iquote('0:SpR:125.0,121.0')] ).
cnf(205,plain,
equal(multiply(double_divide(u,inverse(u)),v),v),
inference(spr,[status(thm),theory(equality)],[167,121]),
[iquote('0:SpR:167.0,121.0')] ).
cnf(225,plain,
~ equal(multiply(double_divide(u,inverse(u)),a2),a2),
inference(spl,[status(thm),theory(equality)],[167,3]),
[iquote('0:SpL:167.0,3.0')] ).
cnf(226,plain,
~ equal(a2,a2),
inference(rew,[status(thm),theory(equality)],[205,225]),
[iquote('0:Rew:205.0,225.0')] ).
cnf(227,plain,
$false,
inference(obv,[status(thm),theory(equality)],[226]),
[iquote('0:Obv:226.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP586-1 : TPTP v8.1.0. Released v2.6.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n028.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 23:38:08 EDT 2022
% 0.12/0.34 % 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/sandbox2/benchmark/theBenchmark.p
% 0.19/0.47 SPASS derived 186 clauses, backtracked 0 clauses, performed 0 splits and kept 120 clauses.
% 0.19/0.47 SPASS allocated 63623 KBytes.
% 0.19/0.47 SPASS spent 0:00:00.11 on the problem.
% 0.19/0.47 0:00:00.04 for the input.
% 0.19/0.47 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.47 0:00:00.00 for inferences.
% 0.19/0.47 0:00:00.00 for the backtracking.
% 0.19/0.47 0:00:00.04 for the reduction.
% 0.19/0.47
% 0.19/0.47
% 0.19/0.47 Here is a proof with depth 7, length 18 :
% 0.19/0.47 % SZS output start Refutation
% See solution above
% 0.19/0.47 Formulae used in the proof : single_axiom multiply prove_these_axioms_2
% 0.19/0.47
%------------------------------------------------------------------------------