TSTP Solution File: GRP467-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP467-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 0.18s 0.55s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of clauses : 26 ( 26 unt; 0 nHn; 26 RR)
% Number of literals : 26 ( 0 equ; 4 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 : 11 ( 11 usr; 8 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('GRP467-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,inverse(v)),multiply(u,v)),
file('GRP467-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(multiply(multiply(inverse(b2),b2),a2),a2),
file('GRP467-1.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(55,plain,
equal(divide(divide(u,u),divide(multiply(v,w),multiply(divide(x,x),multiply(divide(v,divide(y,w)),y)))),divide(z,z)),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(62,plain,
equal(divide(u,u),multiply(inverse(v),v)),
inference(spr,[status(thm),theory(equality)],[34,2]),
[iquote('0:SpR:34.0,2.0')] ).
cnf(67,plain,
equal(divide(divide(u,u),divide(v,multiply(divide(w,divide(x,x)),v))),w),
inference(spr,[status(thm),theory(equality)],[34,4]),
[iquote('0:SpR:34.0,4.0')] ).
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(94,plain,
equal(divide(multiply(divide(u,divide(v,w)),v),multiply(u,w)),divide(x,x)),
inference(rew,[status(thm),theory(equality)],[70,55]),
[iquote('0:Rew:70.0,55.0')] ).
cnf(106,plain,
equal(divide(divide(u,u),divide(v,multiply(divide(w,multiply(inverse(x),x)),v))),w),
inference(spr,[status(thm),theory(equality)],[62,4]),
[iquote('0:SpR:62.0,4.0')] ).
cnf(122,plain,
~ equal(multiply(divide(u,u),a2),a2),
inference(spl,[status(thm),theory(equality)],[62,3]),
[iquote('0:SpL:62.0,3.0')] ).
cnf(241,plain,
equal(divide(divide(u,u),divide(inverse(v),multiply(divide(w,w),x))),multiply(divide(x,divide(y,v)),y)),
inference(spr,[status(thm),theory(equality)],[94,9]),
[iquote('0:SpR:94.0,9.0')] ).
cnf(301,plain,
equal(multiply(divide(u,divide(v,w)),v),divide(u,inverse(w))),
inference(rew,[status(thm),theory(equality)],[70,241]),
[iquote('0:Rew:70.0,241.0')] ).
cnf(302,plain,
equal(multiply(divide(u,divide(v,w)),v),multiply(u,w)),
inference(rew,[status(thm),theory(equality)],[2,301]),
[iquote('0:Rew:2.0,301.0')] ).
cnf(305,plain,
equal(divide(divide(u,u),divide(v,multiply(w,v))),w),
inference(rew,[status(thm),theory(equality)],[302,4]),
[iquote('0:Rew:302.0,4.0')] ).
cnf(361,plain,
equal(divide(u,divide(v,v)),u),
inference(rew,[status(thm),theory(equality)],[305,67]),
[iquote('0:Rew:305.0,67.0')] ).
cnf(362,plain,
equal(divide(u,multiply(inverse(v),v)),u),
inference(rew,[status(thm),theory(equality)],[305,106]),
[iquote('0:Rew:305.0,106.0')] ).
cnf(498,plain,
~ equal(multiply(divide(a2,u),u),a2),
inference(spl,[status(thm),theory(equality)],[302,122]),
[iquote('0:SpL:302.0,122.0')] ).
cnf(534,plain,
~ equal(multiply(a2,divide(u,u)),a2),
inference(spl,[status(thm),theory(equality)],[361,498]),
[iquote('0:SpL:361.0,498.0')] ).
cnf(544,plain,
equal(divide(divide(u,u),v),inverse(v)),
inference(spr,[status(thm),theory(equality)],[362,305]),
[iquote('0:SpR:362.0,305.0')] ).
cnf(692,plain,
equal(divide(u,inverse(divide(v,v))),u),
inference(spr,[status(thm),theory(equality)],[544,361]),
[iquote('0:SpR:544.0,361.0')] ).
cnf(707,plain,
equal(multiply(u,divide(v,v)),u),
inference(rew,[status(thm),theory(equality)],[2,692]),
[iquote('0:Rew:2.0,692.0')] ).
cnf(708,plain,
$false,
inference(unc,[status(thm)],[707,534]),
[iquote('0:UnC:707.0,534.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP467-1 : TPTP v8.1.0. Released v2.6.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n029.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 : Tue Jun 14 02:14:10 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.18/0.55
% 0.18/0.55 SPASS V 3.9
% 0.18/0.55 SPASS beiseite: Proof found.
% 0.18/0.55 % SZS status Theorem
% 0.18/0.55 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.55 SPASS derived 532 clauses, backtracked 0 clauses, performed 0 splits and kept 215 clauses.
% 0.18/0.55 SPASS allocated 64376 KBytes.
% 0.18/0.55 SPASS spent 0:00:00.20 on the problem.
% 0.18/0.55 0:00:00.03 for the input.
% 0.18/0.55 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.55 0:00:00.01 for inferences.
% 0.18/0.55 0:00:00.00 for the backtracking.
% 0.18/0.55 0:00:00.14 for the reduction.
% 0.18/0.55
% 0.18/0.55
% 0.18/0.55 Here is a proof with depth 6, length 26 :
% 0.18/0.55 % SZS output start Refutation
% See solution above
% 0.18/0.55 Formulae used in the proof : single_axiom multiply prove_these_axioms_2
% 0.18/0.55
%------------------------------------------------------------------------------