%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP468-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 11:47:36 EDT 2022
% Result : Unsatisfiable 0.47s 0.66s
% Output : Refutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of clauses : 24 ( 24 unt; 0 nHn; 24 RR)
% Number of literals : 24 ( 0 equ; 1 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 : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(divide(divide(u,u),divide(v,divide(divide(w,divide(x,v)),inverse(x)))),w),
file('GRP468-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,inverse(v)),multiply(u,v)),
file('GRP468-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))),
file('GRP468-1.p',unknown),
[] ).
cnf(4,plain,
equal(divide(divide(u,u),divide(v,multiply(divide(w,divide(x,v)),x))),w),
inference(rew,[status(thm),theory(equality)],[2,1]),
[iquote('0:Rew:2.0,1.0')] ).
cnf(7,plain,
equal(divide(divide(u,u),divide(multiply(divide(v,divide(w,x)),w),multiply(v,x))),divide(y,y)),
inference(spr,[status(thm),theory(equality)],[4]),
[iquote('0:SpR:4.0,4.0')] ).
cnf(9,plain,
equal(divide(divide(u,u),divide(inverse(v),multiply(divide(w,multiply(x,v)),x))),w),
inference(spr,[status(thm),theory(equality)],[2,4]),
[iquote('0:SpR:2.0,4.0')] ).
cnf(34,plain,
equal(divide(u,u),divide(v,v)),
inference(spr,[status(thm),theory(equality)],[7]),
[iquote('0:SpR:7.0,7.0')] ).
cnf(70,plain,
equal(divide(divide(u,u),divide(v,multiply(divide(w,w),x))),divide(x,v)),
inference(spr,[status(thm),theory(equality)],[34,4]),
[iquote('0:SpR:34.0,4.0')] ).
cnf(231,plain,
equal(divide(u,multiply(divide(v,v),u)),divide(w,w)),
inference(spr,[status(thm),theory(equality)],[70,34]),
[iquote('0:SpR:70.0,34.0')] ).
cnf(249,plain,
equal(divide(divide(u,u),divide(multiply(divide(v,w),w),multiply(divide(x,x),multiply(divide(y,y),v)))),divide(z,z)),
inference(spr,[status(thm),theory(equality)],[70,7]),
[iquote('0:SpR:70.0,7.0')] ).
cnf(272,plain,
equal(divide(multiply(divide(u,u),v),multiply(divide(v,w),w)),divide(x,x)),
inference(rew,[status(thm),theory(equality)],[70,249]),
[iquote('0:Rew:70.0,249.0')] ).
cnf(281,plain,
equal(divide(divide(u,u),divide(inverse(v),multiply(divide(w,w),divide(x,x)))),v),
inference(spr,[status(thm),theory(equality)],[231,9]),
[iquote('0:SpR:231.0,9.0')] ).
cnf(324,plain,
equal(multiply(divide(u,u),v),v),
inference(rew,[status(thm),theory(equality)],[2,281,70]),
[iquote('0:Rew:2.0,281.0,70.0,281.0')] ).
cnf(326,plain,
equal(divide(divide(u,u),divide(v,w)),divide(w,v)),
inference(rew,[status(thm),theory(equality)],[324,70]),
[iquote('0:Rew:324.0,70.0')] ).
cnf(337,plain,
equal(divide(u,multiply(divide(u,v),v)),divide(w,w)),
inference(rew,[status(thm),theory(equality)],[324,272]),
[iquote('0:Rew:324.0,272.0')] ).
cnf(359,plain,
equal(divide(multiply(divide(u,multiply(v,w)),v),inverse(w)),u),
inference(rew,[status(thm),theory(equality)],[326,9]),
[iquote('0:Rew:326.0,9.0')] ).
cnf(360,plain,
equal(divide(multiply(divide(u,divide(v,w)),v),w),u),
inference(rew,[status(thm),theory(equality)],[326,4]),
[iquote('0:Rew:326.0,4.0')] ).
cnf(445,plain,
equal(multiply(multiply(divide(u,multiply(v,w)),v),w),u),
inference(rew,[status(thm),theory(equality)],[2,359]),
[iquote('0:Rew:2.0,359.0')] ).
cnf(612,plain,
equal(multiply(multiply(divide(u,u),divide(v,w)),w),v),
inference(spr,[status(thm),theory(equality)],[337,445]),
[iquote('0:SpR:337.0,445.0')] ).
cnf(614,plain,
equal(multiply(divide(u,divide(v,multiply(w,x))),v),multiply(multiply(u,w),x)),
inference(spr,[status(thm),theory(equality)],[360,445]),
[iquote('0:SpR:360.0,445.0')] ).
cnf(618,plain,
equal(multiply(divide(u,v),v),u),
inference(rew,[status(thm),theory(equality)],[324,612]),
[iquote('0:Rew:324.0,612.0')] ).
cnf(640,plain,
equal(multiply(divide(u,divide(v,w)),v),multiply(u,w)),
inference(spr,[status(thm),theory(equality)],[360,618]),
[iquote('0:SpR:360.0,618.0')] ).
cnf(655,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[640,614]),
[iquote('0:Rew:640.0,614.0')] ).
cnf(699,plain,
$false,
inference(unc,[status(thm)],[655,3]),
[iquote('0:UnC:655.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : GRP468-1 : TPTP v8.1.0. Released v2.6.0.
% 0.13/0.15 % Command : run_spass %d %s
% 0.14/0.37 % Computer : n018.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 600
% 0.14/0.37 % DateTime : Mon Jun 13 18:51:43 EDT 2022
% 0.14/0.37 % CPUTime :
% 0.47/0.66
% 0.47/0.66 SPASS V 3.9
% 0.47/0.66 SPASS beiseite: Proof found.
% 0.47/0.66 % SZS status Theorem
% 0.47/0.66 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.47/0.66 SPASS derived 583 clauses, backtracked 0 clauses, performed 0 splits and kept 265 clauses.
% 0.47/0.66 SPASS allocated 64292 KBytes.
% 0.47/0.66 SPASS spent 0:00:00.27 on the problem.
% 0.47/0.66 0:00:00.03 for the input.
% 0.47/0.66 0:00:00.00 for the FLOTTER CNF translation.
% 0.47/0.66 0:00:00.01 for inferences.
% 0.47/0.66 0:00:00.00 for the backtracking.
% 0.47/0.66 0:00:00.21 for the reduction.
% 0.47/0.66
% 0.47/0.66
% 0.47/0.66 Here is a proof with depth 6, length 24 :
% 0.47/0.66 % SZS output start Refutation
% See solution above
% 0.47/0.66 Formulae used in the proof : single_axiom multiply prove_these_axioms_3
% 0.47/0.66
%------------------------------------------------------------------------------