TSTP Solution File: GRP535-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP535-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 11:47:56 EDT 2022
% Result : Unsatisfiable 0.19s 0.47s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 5
% Syntax : Number of clauses : 43 ( 43 unt; 0 nHn; 43 RR)
% Number of literals : 43 ( 0 equ; 3 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 : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(divide(divide(u,divide(divide(u,v),w)),v),w),
file('GRP535-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,divide(divide(v,v),w)),multiply(u,w)),
file('GRP535-1.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(divide(u,u),v),inverse(v)),
file('GRP535-1.p',unknown),
[] ).
cnf(4,axiom,
equal(divide(u,u),identity),
file('GRP535-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))),
file('GRP535-1.p',unknown),
[] ).
cnf(6,plain,
equal(divide(identity,u),inverse(u)),
inference(rew,[status(thm),theory(equality)],[4,3]),
[iquote('0:Rew:4.0,3.0')] ).
cnf(7,plain,
equal(divide(u,inverse(v)),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[6,2,4]),
[iquote('0:Rew:6.0,2.0,4.0,2.0')] ).
cnf(9,plain,
equal(inverse(identity),identity),
inference(spr,[status(thm),theory(equality)],[6,4]),
[iquote('0:SpR:6.0,4.0')] ).
cnf(12,plain,
equal(multiply(inverse(u),u),identity),
inference(spr,[status(thm),theory(equality)],[7,4]),
[iquote('0:SpR:7.0,4.0')] ).
cnf(13,plain,
equal(multiply(identity,u),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[7,6]),
[iquote('0:SpR:7.0,6.0')] ).
cnf(15,plain,
equal(divide(u,identity),multiply(u,identity)),
inference(spr,[status(thm),theory(equality)],[9,7]),
[iquote('0:SpR:9.0,7.0')] ).
cnf(16,plain,
equal(multiply(divide(u,divide(divide(u,inverse(v)),w)),v),w),
inference(spr,[status(thm),theory(equality)],[1,7]),
[iquote('0:SpR:1.0,7.0')] ).
cnf(20,plain,
equal(divide(divide(u,divide(identity,v)),u),v),
inference(spr,[status(thm),theory(equality)],[4,1]),
[iquote('0:SpR:4.0,1.0')] ).
cnf(26,plain,
equal(divide(multiply(u,v),u),v),
inference(rew,[status(thm),theory(equality)],[7,20,6]),
[iquote('0:Rew:7.0,20.0,6.0,20.0')] ).
cnf(30,plain,
equal(multiply(divide(u,divide(multiply(u,v),w)),v),w),
inference(rew,[status(thm),theory(equality)],[7,16]),
[iquote('0:Rew:7.0,16.0')] ).
cnf(51,plain,
equal(multiply(multiply(identity,u),identity),u),
inference(spr,[status(thm),theory(equality)],[26,15]),
[iquote('0:SpR:26.0,15.0')] ).
cnf(52,plain,
equal(divide(identity,inverse(u)),u),
inference(spr,[status(thm),theory(equality)],[12,26]),
[iquote('0:SpR:12.0,26.0')] ).
cnf(54,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[13,52,7]),
[iquote('0:Rew:13.0,52.0,7.0,52.0')] ).
cnf(55,plain,
equal(multiply(identity,u),u),
inference(rew,[status(thm),theory(equality)],[54,13]),
[iquote('0:Rew:54.0,13.0')] ).
cnf(56,plain,
equal(multiply(u,identity),u),
inference(rew,[status(thm),theory(equality)],[55,51]),
[iquote('0:Rew:55.0,51.0')] ).
cnf(57,plain,
equal(divide(u,identity),u),
inference(rew,[status(thm),theory(equality)],[56,15]),
[iquote('0:Rew:56.0,15.0')] ).
cnf(62,plain,
equal(multiply(u,inverse(v)),divide(u,v)),
inference(spr,[status(thm),theory(equality)],[54,7]),
[iquote('0:SpR:54.0,7.0')] ).
cnf(75,plain,
equal(divide(divide(u,divide(u,v)),identity),v),
inference(spr,[status(thm),theory(equality)],[57,1]),
[iquote('0:SpR:57.0,1.0')] ).
cnf(79,plain,
equal(divide(u,divide(u,v)),v),
inference(rew,[status(thm),theory(equality)],[57,75]),
[iquote('0:Rew:57.0,75.0')] ).
cnf(106,plain,
equal(divide(multiply(u,v),v),u),
inference(spr,[status(thm),theory(equality)],[26,79]),
[iquote('0:SpR:26.0,79.0')] ).
cnf(108,plain,
equal(divide(u,multiply(u,v)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[7,79]),
[iquote('0:SpR:7.0,79.0')] ).
cnf(120,plain,
equal(multiply(multiply(u,inverse(v)),v),u),
inference(spr,[status(thm),theory(equality)],[106,7]),
[iquote('0:SpR:106.0,7.0')] ).
cnf(127,plain,
equal(multiply(divide(u,v),v),u),
inference(rew,[status(thm),theory(equality)],[62,120]),
[iquote('0:Rew:62.0,120.0')] ).
cnf(134,plain,
equal(multiply(u,v),multiply(v,u)),
inference(spr,[status(thm),theory(equality)],[26,127]),
[iquote('0:SpR:26.0,127.0')] ).
cnf(136,plain,
equal(multiply(u,divide(v,u)),v),
inference(spr,[status(thm),theory(equality)],[79,127]),
[iquote('0:SpR:79.0,127.0')] ).
cnf(140,plain,
~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))),
inference(rew,[status(thm),theory(equality)],[134,5]),
[iquote('0:Rew:134.0,5.0')] ).
cnf(144,plain,
equal(multiply(u,divide(v,divide(multiply(v,u),w))),w),
inference(rew,[status(thm),theory(equality)],[134,30]),
[iquote('0:Rew:134.0,30.0')] ).
cnf(175,plain,
equal(multiply(inverse(u),v),divide(v,u)),
inference(spr,[status(thm),theory(equality)],[62,134]),
[iquote('0:SpR:62.0,134.0')] ).
cnf(191,plain,
equal(inverse(divide(u,v)),divide(v,u)),
inference(spr,[status(thm),theory(equality)],[136,108]),
[iquote('0:SpR:136.0,108.0')] ).
cnf(332,plain,
equal(divide(u,divide(v,w)),multiply(divide(w,v),u)),
inference(spr,[status(thm),theory(equality)],[191,175]),
[iquote('0:SpR:191.0,175.0')] ).
cnf(358,plain,
equal(multiply(u,multiply(divide(v,multiply(w,u)),w)),v),
inference(rew,[status(thm),theory(equality)],[332,144]),
[iquote('0:Rew:332.0,144.0')] ).
cnf(367,plain,
equal(multiply(u,multiply(v,divide(w,multiply(v,u)))),w),
inference(rew,[status(thm),theory(equality)],[134,358]),
[iquote('0:Rew:134.0,358.0')] ).
cnf(421,plain,
equal(multiply(multiply(u,v),w),multiply(v,multiply(u,w))),
inference(spr,[status(thm),theory(equality)],[26,367]),
[iquote('0:SpR:26.0,367.0')] ).
cnf(425,plain,
equal(multiply(u,multiply(v,w)),multiply(w,multiply(v,u))),
inference(spr,[status(thm),theory(equality)],[106,367]),
[iquote('0:SpR:106.0,367.0')] ).
cnf(443,plain,
~ equal(multiply(b3,multiply(a3,c3)),multiply(a3,multiply(b3,c3))),
inference(rew,[status(thm),theory(equality)],[425,140]),
[iquote('0:Rew:425.0,140.0')] ).
cnf(787,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(spr,[status(thm),theory(equality)],[134,421]),
[iquote('0:SpR:134.0,421.0')] ).
cnf(798,plain,
equal(multiply(u,multiply(v,w)),multiply(v,multiply(u,w))),
inference(rew,[status(thm),theory(equality)],[421,787]),
[iquote('0:Rew:421.0,787.0')] ).
cnf(799,plain,
$false,
inference(unc,[status(thm)],[798,443]),
[iquote('0:UnC:798.0,443.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.12 % Problem : GRP535-1 : TPTP v8.1.0. Released v2.6.0.
% 0.05/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n025.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 : Tue Jun 14 00:42:39 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/sandbox/benchmark/theBenchmark.p
% 0.19/0.47 SPASS derived 472 clauses, backtracked 0 clauses, performed 0 splits and kept 113 clauses.
% 0.19/0.47 SPASS allocated 63734 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 0:00:00.01 for inferences.
% 0.19/0.47 0:00:00.00 for the backtracking.
% 0.19/0.47 0:00:00.05 for the reduction.
% 0.19/0.47
% 0.19/0.47
% 0.19/0.47 Here is a proof with depth 8, length 43 :
% 0.19/0.47 % SZS output start Refutation
% See solution above
% 0.19/0.47 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_3
% 0.19/0.47
%------------------------------------------------------------------------------