%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP589-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 11:48:10 EDT 2022
% Result : Unsatisfiable 0.20s 0.45s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of clauses : 14 ( 14 unt; 0 nHn; 14 RR)
% Number of literals : 14 ( 0 equ; 1 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(inverse(double_divide(double_divide(u,v),inverse(double_divide(u,inverse(w))))),v),w),
file('GRP589-1.p',unknown),
[] ).
cnf(2,axiom,
equal(inverse(double_divide(u,v)),multiply(v,u)),
file('GRP589-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1)),
file('GRP589-1.p',unknown),
[] ).
cnf(4,plain,
equal(double_divide(multiply(multiply(inverse(u),v),double_divide(v,w)),w),u),
inference(rew,[status(thm),theory(equality)],[2,1]),
[iquote('0:Rew:2.0,1.0,2.0,1.0')] ).
cnf(6,plain,
equal(multiply(u,multiply(multiply(inverse(v),w),double_divide(w,u))),inverse(v)),
inference(spr,[status(thm),theory(equality)],[4,2]),
[iquote('0:SpR:4.0,2.0')] ).
cnf(7,plain,
equal(double_divide(multiply(multiply(inverse(u),multiply(multiply(inverse(v),w),double_divide(w,x))),v),x),u),
inference(spr,[status(thm),theory(equality)],[4]),
[iquote('0:SpR:4.0,4.0')] ).
cnf(50,plain,
equal(double_divide(multiply(inverse(u),u),inverse(v)),v),
inference(spr,[status(thm),theory(equality)],[6,7]),
[iquote('0:SpR:6.0,7.0')] ).
cnf(51,plain,
equal(multiply(inverse(u),multiply(inverse(v),v)),inverse(u)),
inference(spr,[status(thm),theory(equality)],[50,2]),
[iquote('0:SpR:50.0,2.0')] ).
cnf(52,plain,
equal(double_divide(multiply(multiply(inverse(u),multiply(inverse(v),v)),w),inverse(w)),u),
inference(spr,[status(thm),theory(equality)],[50,4]),
[iquote('0:SpR:50.0,4.0')] ).
cnf(60,plain,
equal(double_divide(multiply(inverse(u),v),inverse(v)),u),
inference(rew,[status(thm),theory(equality)],[51,52]),
[iquote('0:Rew:51.0,52.0')] ).
cnf(98,plain,
equal(double_divide(inverse(u),inverse(multiply(inverse(v),v))),u),
inference(spr,[status(thm),theory(equality)],[51,60]),
[iquote('0:SpR:51.0,60.0')] ).
cnf(101,plain,
equal(double_divide(inverse(multiply(inverse(u),u)),inverse(v)),v),
inference(spr,[status(thm),theory(equality)],[51,50]),
[iquote('0:SpR:51.0,50.0')] ).
cnf(192,plain,
equal(multiply(inverse(u),u),multiply(inverse(v),v)),
inference(spr,[status(thm),theory(equality)],[101,98]),
[iquote('0:SpR:101.0,98.0')] ).
cnf(197,plain,
$false,
inference(unc,[status(thm)],[192,3]),
[iquote('0:UnC:192.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP589-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n027.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 13 13:51:32 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.20/0.45
% 0.20/0.45 SPASS V 3.9
% 0.20/0.45 SPASS beiseite: Proof found.
% 0.20/0.45 % SZS status Theorem
% 0.20/0.45 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.45 SPASS derived 176 clauses, backtracked 0 clauses, performed 0 splits and kept 116 clauses.
% 0.20/0.45 SPASS allocated 63660 KBytes.
% 0.20/0.45 SPASS spent 0:00:00.10 on the problem.
% 0.20/0.45 0:00:00.03 for the input.
% 0.20/0.45 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.45 0:00:00.00 for inferences.
% 0.20/0.45 0:00:00.00 for the backtracking.
% 0.20/0.45 0:00:00.04 for the reduction.
% 0.20/0.45
% 0.20/0.45
% 0.20/0.45 Here is a proof with depth 5, length 14 :
% 0.20/0.45 % SZS output start Refutation
% See solution above
% 0.20/0.45 Formulae used in the proof : single_axiom multiply prove_these_axioms_1
% 0.20/0.45
%------------------------------------------------------------------------------