TSTP Solution File: GRP527-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP527-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 11:47:53 EDT 2022
% Result : Unsatisfiable 0.21s 0.45s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of clauses : 27 ( 27 unt; 0 nHn; 27 RR)
% Number of literals : 27 ( 0 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 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,divide(divide(u,v),divide(w,v))),w),
file('GRP527-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,divide(divide(v,v),w)),multiply(u,w)),
file('GRP527-1.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(divide(u,u),v),inverse(v)),
file('GRP527-1.p',unknown),
[] ).
cnf(4,axiom,
~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))),
file('GRP527-1.p',unknown),
[] ).
cnf(5,plain,
equal(divide(u,inverse(v)),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[3,2]),
[iquote('0:Rew:3.0,2.0')] ).
cnf(27,plain,
equal(divide(divide(u,divide(v,w)),w),divide(u,v)),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(36,plain,
equal(divide(u,inverse(divide(v,u))),v),
inference(spr,[status(thm),theory(equality)],[3,1]),
[iquote('0:SpR:3.0,1.0')] ).
cnf(37,plain,
equal(multiply(u,divide(v,u)),v),
inference(rew,[status(thm),theory(equality)],[5,36]),
[iquote('0:Rew:5.0,36.0')] ).
cnf(50,plain,
equal(multiply(inverse(u),multiply(v,u)),v),
inference(spr,[status(thm),theory(equality)],[5,37]),
[iquote('0:SpR:5.0,37.0')] ).
cnf(52,plain,
equal(multiply(u,inverse(u)),divide(v,v)),
inference(spr,[status(thm),theory(equality)],[3,37]),
[iquote('0:SpR:3.0,37.0')] ).
cnf(66,plain,
equal(divide(u,divide(divide(u,v),multiply(w,inverse(w)))),v),
inference(spr,[status(thm),theory(equality)],[52,1]),
[iquote('0:SpR:52.0,1.0')] ).
cnf(69,plain,
equal(divide(u,multiply(v,inverse(v))),u),
inference(spr,[status(thm),theory(equality)],[52,1]),
[iquote('0:SpR:52.0,1.0')] ).
cnf(71,plain,
equal(divide(u,divide(u,v)),v),
inference(rew,[status(thm),theory(equality)],[69,66]),
[iquote('0:Rew:69.0,66.0')] ).
cnf(140,plain,
equal(multiply(divide(u,v),v),u),
inference(spr,[status(thm),theory(equality)],[71,37]),
[iquote('0:SpR:71.0,37.0')] ).
cnf(142,plain,
equal(divide(u,multiply(u,v)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[5,71]),
[iquote('0:SpR:5.0,71.0')] ).
cnf(211,plain,
equal(multiply(inverse(u),v),divide(v,u)),
inference(spr,[status(thm),theory(equality)],[140,50]),
[iquote('0:SpR:140.0,50.0')] ).
cnf(222,plain,
equal(divide(multiply(u,v),v),u),
inference(rew,[status(thm),theory(equality)],[211,50]),
[iquote('0:Rew:211.0,50.0')] ).
cnf(245,plain,
equal(multiply(u,v),multiply(v,u)),
inference(spr,[status(thm),theory(equality)],[222,37]),
[iquote('0:SpR:222.0,37.0')] ).
cnf(251,plain,
~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))),
inference(rew,[status(thm),theory(equality)],[245,4]),
[iquote('0:Rew:245.0,4.0')] ).
cnf(331,plain,
equal(inverse(divide(u,v)),divide(v,u)),
inference(spr,[status(thm),theory(equality)],[37,142]),
[iquote('0:SpR:37.0,142.0')] ).
cnf(367,plain,
equal(divide(u,divide(v,w)),multiply(w,divide(u,v))),
inference(spr,[status(thm),theory(equality)],[27,37]),
[iquote('0:SpR:27.0,37.0')] ).
cnf(444,plain,
equal(divide(inverse(u),v),inverse(multiply(v,u))),
inference(spr,[status(thm),theory(equality)],[5,331]),
[iquote('0:SpR:5.0,331.0')] ).
cnf(540,plain,
equal(divide(u,inverse(multiply(v,w))),multiply(v,divide(u,inverse(w)))),
inference(spr,[status(thm),theory(equality)],[444,367]),
[iquote('0:SpR:444.0,367.0')] ).
cnf(559,plain,
equal(multiply(u,multiply(v,w)),multiply(v,multiply(u,w))),
inference(rew,[status(thm),theory(equality)],[5,540]),
[iquote('0:Rew:5.0,540.0,5.0,540.0')] ).
cnf(560,plain,
~ equal(multiply(a3,multiply(c3,b3)),multiply(a3,multiply(b3,c3))),
inference(rew,[status(thm),theory(equality)],[559,251]),
[iquote('0:Rew:559.0,251.0')] ).
cnf(561,plain,
~ equal(multiply(a3,multiply(b3,c3)),multiply(a3,multiply(b3,c3))),
inference(rew,[status(thm),theory(equality)],[245,560]),
[iquote('0:Rew:245.0,560.0')] ).
cnf(562,plain,
$false,
inference(obv,[status(thm),theory(equality)],[561]),
[iquote('0:Obv:561.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP527-1 : TPTP v8.1.0. Released v2.6.0.
% 0.08/0.13 % Command : run_spass %d %s
% 0.15/0.35 % Computer : n024.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Tue Jun 14 11:40:03 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.21/0.45
% 0.21/0.45 SPASS V 3.9
% 0.21/0.45 SPASS beiseite: Proof found.
% 0.21/0.45 % SZS status Theorem
% 0.21/0.45 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.45 SPASS derived 398 clauses, backtracked 0 clauses, performed 0 splits and kept 94 clauses.
% 0.21/0.45 SPASS allocated 63475 KBytes.
% 0.21/0.45 SPASS spent 0:00:00.08 on the problem.
% 0.21/0.45 0:00:00.03 for the input.
% 0.21/0.45 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.45 0:00:00.00 for inferences.
% 0.21/0.45 0:00:00.00 for the backtracking.
% 0.21/0.45 0:00:00.02 for the reduction.
% 0.21/0.45
% 0.21/0.45
% 0.21/0.45 Here is a proof with depth 7, length 27 :
% 0.21/0.45 % SZS output start Refutation
% See solution above
% 0.21/0.45 Formulae used in the proof : single_axiom multiply inverse prove_these_axioms_3
% 0.21/0.45
%------------------------------------------------------------------------------