TSTP Solution File: GRP554-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP554-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 11:48:01 EDT 2022
% Result : Unsatisfiable 0.18s 0.44s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of clauses : 32 ( 32 unt; 0 nHn; 32 RR)
% Number of literals : 32 ( 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,inverse(divide(v,divide(u,w)))),w),v),
file('GRP554-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,inverse(v)),multiply(u,v)),
file('GRP554-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(multiply(multiply(inverse(b2),b2),a2),a2),
file('GRP554-1.p',unknown),
[] ).
cnf(4,plain,
equal(divide(multiply(u,divide(v,divide(u,w))),w),v),
inference(rew,[status(thm),theory(equality)],[2,1]),
[iquote('0:Rew:2.0,1.0')] ).
cnf(6,plain,
equal(multiply(multiply(u,divide(v,divide(u,inverse(w)))),w),v),
inference(spr,[status(thm),theory(equality)],[4,2]),
[iquote('0:SpR:4.0,2.0')] ).
cnf(7,plain,
equal(divide(multiply(multiply(u,divide(v,divide(u,w))),divide(x,v)),w),x),
inference(spr,[status(thm),theory(equality)],[4]),
[iquote('0:SpR:4.0,4.0')] ).
cnf(8,plain,
equal(multiply(u,divide(v,divide(u,divide(w,x)))),divide(multiply(w,v),x)),
inference(spr,[status(thm),theory(equality)],[4]),
[iquote('0:SpR:4.0,4.0')] ).
cnf(11,plain,
equal(multiply(multiply(u,divide(v,multiply(u,w))),w),v),
inference(rew,[status(thm),theory(equality)],[2,6]),
[iquote('0:Rew:2.0,6.0')] ).
cnf(13,plain,
equal(multiply(multiply(multiply(u,divide(v,multiply(u,w))),divide(x,v)),w),x),
inference(spr,[status(thm),theory(equality)],[11]),
[iquote('0:SpR:11.0,11.0')] ).
cnf(35,plain,
equal(divide(divide(multiply(u,v),w),divide(u,w)),v),
inference(spr,[status(thm),theory(equality)],[8,4]),
[iquote('0:SpR:8.0,4.0')] ).
cnf(64,plain,
equal(divide(divide(multiply(u,v),inverse(w)),multiply(u,w)),v),
inference(spr,[status(thm),theory(equality)],[2,35]),
[iquote('0:SpR:2.0,35.0')] ).
cnf(72,plain,
equal(divide(multiply(multiply(u,v),w),multiply(u,w)),v),
inference(rew,[status(thm),theory(equality)],[2,64]),
[iquote('0:Rew:2.0,64.0')] ).
cnf(81,plain,
equal(divide(u,divide(v,multiply(v,divide(w,u)))),w),
inference(spr,[status(thm),theory(equality)],[72,7]),
[iquote('0:SpR:72.0,7.0')] ).
cnf(96,plain,
equal(divide(divide(multiply(u,v),divide(w,multiply(w,divide(x,u)))),x),v),
inference(spr,[status(thm),theory(equality)],[81,35]),
[iquote('0:SpR:81.0,35.0')] ).
cnf(97,plain,
equal(divide(multiply(u,v),multiply(u,divide(w,x))),multiply(x,divide(v,w))),
inference(spr,[status(thm),theory(equality)],[81,8]),
[iquote('0:SpR:81.0,8.0')] ).
cnf(99,plain,
equal(divide(multiply(u,v),multiply(u,divide(v,w))),w),
inference(spr,[status(thm),theory(equality)],[81,4]),
[iquote('0:SpR:81.0,4.0')] ).
cnf(103,plain,
equal(multiply(u,divide(v,divide(u,w))),divide(multiply(x,v),divide(y,multiply(y,divide(w,x))))),
inference(spr,[status(thm),theory(equality)],[81,8]),
[iquote('0:SpR:81.0,8.0')] ).
cnf(108,plain,
equal(divide(multiply(u,v),divide(w,multiply(w,x))),multiply(multiply(u,x),v)),
inference(spr,[status(thm),theory(equality)],[72,81]),
[iquote('0:SpR:72.0,81.0')] ).
cnf(112,plain,
equal(multiply(u,divide(v,v)),u),
inference(rew,[status(thm),theory(equality)],[97,99]),
[iquote('0:Rew:97.0,99.0')] ).
cnf(113,plain,
equal(divide(multiply(multiply(u,divide(v,u)),w),v),w),
inference(rew,[status(thm),theory(equality)],[108,96]),
[iquote('0:Rew:108.0,96.0')] ).
cnf(119,plain,
equal(multiply(u,divide(v,divide(u,w))),multiply(multiply(x,divide(w,x)),v)),
inference(rew,[status(thm),theory(equality)],[108,103]),
[iquote('0:Rew:108.0,103.0')] ).
cnf(139,plain,
equal(multiply(u,divide(v,u)),v),
inference(spr,[status(thm),theory(equality)],[11,13]),
[iquote('0:SpR:11.0,13.0')] ).
cnf(140,plain,
equal(divide(multiply(u,v),u),v),
inference(rew,[status(thm),theory(equality)],[139,113]),
[iquote('0:Rew:139.0,113.0')] ).
cnf(142,plain,
equal(multiply(u,divide(v,divide(u,w))),multiply(w,v)),
inference(rew,[status(thm),theory(equality)],[139,119]),
[iquote('0:Rew:139.0,119.0')] ).
cnf(143,plain,
equal(multiply(divide(u,v),w),divide(multiply(u,w),v)),
inference(rew,[status(thm),theory(equality)],[142,8]),
[iquote('0:Rew:142.0,8.0')] ).
cnf(198,plain,
equal(divide(divide(u,v),divide(u,v)),divide(w,w)),
inference(spr,[status(thm),theory(equality)],[112,35]),
[iquote('0:SpR:112.0,35.0')] ).
cnf(206,plain,
equal(divide(divide(u,v),divide(w,v)),divide(u,w)),
inference(spr,[status(thm),theory(equality)],[139,35]),
[iquote('0:SpR:139.0,35.0')] ).
cnf(220,plain,
equal(divide(u,u),divide(v,v)),
inference(rew,[status(thm),theory(equality)],[206,198]),
[iquote('0:Rew:206.0,198.0')] ).
cnf(231,plain,
equal(divide(u,u),multiply(inverse(v),v)),
inference(spr,[status(thm),theory(equality)],[220,2]),
[iquote('0:SpR:220.0,2.0')] ).
cnf(292,plain,
~ equal(multiply(divide(u,u),a2),a2),
inference(spl,[status(thm),theory(equality)],[231,3]),
[iquote('0:SpL:231.0,3.0')] ).
cnf(295,plain,
~ equal(a2,a2),
inference(rew,[status(thm),theory(equality)],[140,292,143]),
[iquote('0:Rew:140.0,292.0,143.0,292.0')] ).
cnf(296,plain,
$false,
inference(obv,[status(thm),theory(equality)],[295]),
[iquote('0:Obv:295.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : GRP554-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.11/0.33 % Computer : n009.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Mon Jun 13 09:16:38 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.18/0.44
% 0.18/0.44 SPASS V 3.9
% 0.18/0.44 SPASS beiseite: Proof found.
% 0.18/0.44 % SZS status Theorem
% 0.18/0.44 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 SPASS derived 233 clauses, backtracked 0 clauses, performed 0 splits and kept 110 clauses.
% 0.18/0.44 SPASS allocated 63549 KBytes.
% 0.18/0.44 SPASS spent 0:00:00.09 on the problem.
% 0.18/0.44 0:00:00.03 for the input.
% 0.18/0.44 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.44 0:00:00.00 for inferences.
% 0.18/0.44 0:00:00.00 for the backtracking.
% 0.18/0.44 0:00:00.03 for the reduction.
% 0.18/0.44
% 0.18/0.44
% 0.18/0.44 Here is a proof with depth 8, length 32 :
% 0.18/0.44 % SZS output start Refutation
% See solution above
% 0.18/0.44 Formulae used in the proof : single_axiom multiply prove_these_axioms_2
% 0.18/0.44
%------------------------------------------------------------------------------