TSTP Solution File: GRP116-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP116-1 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n004.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 11:45:23 EDT 2022
% Result : Unsatisfiable 0.19s 0.45s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 2
% Syntax : Number of clauses : 33 ( 33 unt; 0 nHn; 33 RR)
% Number of literals : 33 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(multiply(u,multiply(multiply(u,multiply(multiply(u,v),w)),multiply(identity,multiply(w,w)))),v),
file('GRP116-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(multiply(identity,a),a),
file('GRP116-1.p',unknown),
[] ).
cnf(3,plain,
equal(multiply(u,multiply(multiply(u,multiply(multiply(u,v),multiply(identity,multiply(multiply(identity,w),multiply(identity,w))))),w)),v),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(5,plain,
equal(multiply(u,multiply(multiply(u,multiply(v,w)),multiply(identity,multiply(w,w)))),multiply(multiply(u,multiply(multiply(u,v),x)),multiply(identity,multiply(x,x)))),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(6,plain,
equal(multiply(u,multiply(v,multiply(identity,multiply(multiply(identity,multiply(w,w)),multiply(identity,multiply(w,w)))))),multiply(multiply(u,v),w)),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(14,plain,
equal(multiply(multiply(u,v),multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(identity,w),multiply(identity,w)))),multiply(identity,multiply(identity,multiply(multiply(identity,w),multiply(identity,w))))))),multiply(u,multiply(v,w))),
inference(spr,[status(thm),theory(equality)],[3]),
[iquote('0:SpR:3.0,3.0')] ).
cnf(16,plain,
equal(multiply(u,multiply(multiply(u,multiply(multiply(u,v),multiply(identity,multiply(w,w)))),multiply(multiply(identity,multiply(multiply(identity,w),x)),multiply(identity,multiply(x,x))))),v),
inference(spr,[status(thm),theory(equality)],[1,3]),
[iquote('0:SpR:1.0,3.0')] ).
cnf(19,plain,
equal(multiply(multiply(u,v),multiply(identity,w)),multiply(u,multiply(v,w))),
inference(spr,[status(thm),theory(equality)],[1,3]),
[iquote('0:SpR:1.0,3.0')] ).
cnf(21,plain,
equal(multiply(u,multiply(u,multiply(multiply(multiply(u,v),w),multiply(w,w)))),v),
inference(rew,[status(thm),theory(equality)],[19,1]),
[iquote('0:Rew:19.0,1.0')] ).
cnf(23,plain,
equal(multiply(u,multiply(multiply(u,multiply(v,w)),multiply(identity,multiply(w,w)))),multiply(u,multiply(multiply(multiply(u,v),x),multiply(x,x)))),
inference(rew,[status(thm),theory(equality)],[19,5]),
[iquote('0:Rew:19.0,5.0')] ).
cnf(24,plain,
equal(multiply(u,multiply(v,multiply(identity,multiply(identity,multiply(multiply(w,w),multiply(w,w)))))),multiply(multiply(u,v),w)),
inference(rew,[status(thm),theory(equality)],[19,6]),
[iquote('0:Rew:19.0,6.0')] ).
cnf(28,plain,
equal(multiply(u,multiply(u,multiply(multiply(v,w),multiply(w,w)))),multiply(u,multiply(multiply(multiply(u,v),x),multiply(x,x)))),
inference(rew,[status(thm),theory(equality)],[19,23]),
[iquote('0:Rew:19.0,23.0')] ).
cnf(29,plain,
equal(multiply(u,multiply(u,multiply(multiply(u,multiply(v,multiply(w,w))),multiply(multiply(multiply(identity,w),x),multiply(x,x))))),v),
inference(rew,[status(thm),theory(equality)],[19,16]),
[iquote('0:Rew:19.0,16.0,19.0,16.0,19.0,16.0')] ).
cnf(34,plain,
equal(multiply(multiply(u,v),multiply(multiply(identity,identity),w)),multiply(u,multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[24,14,19]),
[iquote('0:Rew:24.0,14.0,19.0,14.0,19.0,14.0,19.0,14.0,19.0,14.0')] ).
cnf(38,plain,
equal(multiply(multiply(u,multiply(v,w)),multiply(identity,x)),multiply(multiply(u,v),multiply(multiply(identity,w),x))),
inference(spr,[status(thm),theory(equality)],[19]),
[iquote('0:SpR:19.0,19.0')] ).
cnf(40,plain,
equal(multiply(multiply(u,v),multiply(multiply(identity,w),x)),multiply(u,multiply(multiply(v,w),x))),
inference(rew,[status(thm),theory(equality)],[19,38]),
[iquote('0:Rew:19.0,38.0')] ).
cnf(42,plain,
equal(multiply(u,multiply(multiply(v,identity),w)),multiply(u,multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[40,34]),
[iquote('0:Rew:40.0,34.0')] ).
cnf(52,plain,
equal(multiply(u,multiply(u,multiply(multiply(u,v),multiply(identity,identity)))),v),
inference(spr,[status(thm),theory(equality)],[19,21]),
[iquote('0:SpR:19.0,21.0')] ).
cnf(53,plain,
equal(multiply(u,multiply(u,multiply(u,multiply(v,identity)))),v),
inference(rew,[status(thm),theory(equality)],[19,52]),
[iquote('0:Rew:19.0,52.0')] ).
cnf(60,plain,
equal(multiply(u,multiply(u,multiply(multiply(v,w),multiply(w,w)))),multiply(u,multiply(u,multiply(v,identity)))),
inference(spr,[status(thm),theory(equality)],[53,21]),
[iquote('0:SpR:53.0,21.0')] ).
cnf(65,plain,
equal(multiply(u,multiply(multiply(multiply(u,v),w),multiply(w,w))),multiply(u,multiply(u,multiply(v,identity)))),
inference(rew,[status(thm),theory(equality)],[60,28]),
[iquote('0:Rew:60.0,28.0')] ).
cnf(87,plain,
equal(multiply(u,multiply(u,multiply(u,multiply(v,identity)))),multiply(v,identity)),
inference(spr,[status(thm),theory(equality)],[42,53]),
[iquote('0:SpR:42.0,53.0')] ).
cnf(94,plain,
equal(multiply(u,identity),u),
inference(rew,[status(thm),theory(equality)],[53,87]),
[iquote('0:Rew:53.0,87.0')] ).
cnf(95,plain,
equal(multiply(u,multiply(u,multiply(u,v))),v),
inference(rew,[status(thm),theory(equality)],[94,53]),
[iquote('0:Rew:94.0,53.0')] ).
cnf(103,plain,
equal(multiply(u,multiply(multiply(multiply(u,v),w),multiply(w,w))),multiply(u,multiply(u,v))),
inference(rew,[status(thm),theory(equality)],[94,65]),
[iquote('0:Rew:94.0,65.0')] ).
cnf(121,plain,
equal(multiply(u,multiply(v,multiply(multiply(multiply(identity,w),x),multiply(x,x)))),multiply(multiply(u,v),multiply(identity,multiply(identity,w)))),
inference(spr,[status(thm),theory(equality)],[103,19]),
[iquote('0:SpR:103.0,19.0')] ).
cnf(139,plain,
equal(multiply(u,multiply(v,multiply(multiply(multiply(identity,w),x),multiply(x,x)))),multiply(u,multiply(v,multiply(identity,w)))),
inference(rew,[status(thm),theory(equality)],[19,121]),
[iquote('0:Rew:19.0,121.0')] ).
cnf(140,plain,
equal(multiply(u,multiply(u,multiply(multiply(u,multiply(v,multiply(w,w))),multiply(identity,w)))),v),
inference(rew,[status(thm),theory(equality)],[139,29]),
[iquote('0:Rew:139.0,29.0')] ).
cnf(141,plain,
equal(multiply(u,multiply(u,multiply(u,multiply(multiply(v,multiply(w,w)),w)))),v),
inference(rew,[status(thm),theory(equality)],[19,140]),
[iquote('0:Rew:19.0,140.0')] ).
cnf(142,plain,
equal(multiply(multiply(u,multiply(v,v)),v),u),
inference(rew,[status(thm),theory(equality)],[95,141]),
[iquote('0:Rew:95.0,141.0')] ).
cnf(152,plain,
equal(multiply(u,multiply(u,u)),identity),
inference(spr,[status(thm),theory(equality)],[94,95]),
[iquote('0:SpR:94.0,95.0')] ).
cnf(179,plain,
equal(multiply(identity,u),u),
inference(spr,[status(thm),theory(equality)],[152,142]),
[iquote('0:SpR:152.0,142.0')] ).
cnf(181,plain,
$false,
inference(unc,[status(thm)],[179,2]),
[iquote('0:UnC:179.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP116-1 : TPTP v8.1.0. Released v1.2.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 18:23:39 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.19/0.45
% 0.19/0.45 SPASS V 3.9
% 0.19/0.45 SPASS beiseite: Proof found.
% 0.19/0.45 % SZS status Theorem
% 0.19/0.45 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 SPASS derived 133 clauses, backtracked 0 clauses, performed 0 splits and kept 63 clauses.
% 0.19/0.45 SPASS allocated 63451 KBytes.
% 0.19/0.45 SPASS spent 0:00:00.09 on the problem.
% 0.19/0.45 0:00:00.04 for the input.
% 0.19/0.45 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.45 0:00:00.00 for inferences.
% 0.19/0.45 0:00:00.00 for the backtracking.
% 0.19/0.45 0:00:00.02 for the reduction.
% 0.19/0.45
% 0.19/0.45
% 0.19/0.45 Here is a proof with depth 6, length 33 :
% 0.19/0.45 % SZS output start Refutation
% See solution above
% 0.19/0.45 Formulae used in the proof : single_axiom prove_order3
% 0.19/0.45
%------------------------------------------------------------------------------