TSTP Solution File: GRP117-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP117-1 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 0.42s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of clauses : 17 ( 17 unt; 0 nHn; 17 RR)
% Number of literals : 17 ( 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('GRP117-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(multiply(a,identity),a),
file('GRP117-1.p',unknown),
[] ).
cnf(4,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(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)],[4]),
[iquote('0:SpR:4.0,4.0')] ).
cnf(19,plain,
equal(multiply(multiply(u,v),multiply(identity,w)),multiply(u,multiply(v,w))),
inference(spr,[status(thm),theory(equality)],[1,4]),
[iquote('0:SpR:1.0,4.0')] ).
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(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(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(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,
$false,
inference(unc,[status(thm)],[94,2]),
[iquote('0:UnC:94.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP117-1 : TPTP v8.1.0. Released v1.2.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 20:38:51 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.42
% 0.19/0.42 SPASS V 3.9
% 0.19/0.42 SPASS beiseite: Proof found.
% 0.19/0.42 % SZS status Theorem
% 0.19/0.42 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.42 SPASS derived 71 clauses, backtracked 0 clauses, performed 0 splits and kept 41 clauses.
% 0.19/0.42 SPASS allocated 63367 KBytes.
% 0.19/0.42 SPASS spent 0:00:00.07 on the problem.
% 0.19/0.42 0:00:00.03 for the input.
% 0.19/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.42 0:00:00.00 for inferences.
% 0.19/0.42 0:00:00.00 for the backtracking.
% 0.19/0.42 0:00:00.01 for the reduction.
% 0.19/0.42
% 0.19/0.42
% 0.19/0.42 Here is a proof with depth 4, length 17 :
% 0.19/0.42 % SZS output start Refutation
% See solution above
% 0.19/0.42 Formulae used in the proof : single_axiom prove_order3
% 0.19/0.42
%------------------------------------------------------------------------------