TSTP Solution File: GRP086-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP086-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 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 11:45:14 EDT 2022
% Result : Unsatisfiable 0.19s 0.49s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 2
% Syntax : Number of clauses : 31 ( 28 unt; 0 nHn; 31 RR)
% Number of literals : 40 ( 0 equ; 13 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 13 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(multiply(u,multiply(multiply(v,w),inverse(multiply(u,w)))),v),
file('GRP086-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)))
| ~ equal(multiply(multiply(inverse(b2),b2),a2),a2) ),
file('GRP086-1.p',unknown),
[] ).
cnf(3,plain,
equal(multiply(u,multiply(multiply(v,multiply(multiply(w,x),inverse(multiply(u,x)))),inverse(w))),v),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(13,plain,
equal(multiply(u,multiply(v,inverse(v))),u),
inference(spr,[status(thm),theory(equality)],[1,3]),
[iquote('0:SpR:1.0,3.0')] ).
cnf(20,plain,
equal(multiply(u,multiply(v,inverse(u))),v),
inference(spr,[status(thm),theory(equality)],[13,3]),
[iquote('0:SpR:13.0,3.0')] ).
cnf(32,plain,
equal(multiply(u,multiply(multiply(v,w),inverse(v))),multiply(u,w)),
inference(spr,[status(thm),theory(equality)],[20,3]),
[iquote('0:SpR:20.0,3.0')] ).
cnf(43,plain,
equal(multiply(u,multiply(multiply(v,w),inverse(multiply(x,w)))),multiply(u,multiply(v,inverse(x)))),
inference(spr,[status(thm),theory(equality)],[1,32]),
[iquote('0:SpR:1.0,32.0')] ).
cnf(86,plain,
equal(multiply(multiply(u,v),multiply(w,inverse(u))),multiply(w,v)),
inference(spr,[status(thm),theory(equality)],[43,20]),
[iquote('0:SpR:43.0,20.0')] ).
cnf(104,plain,
equal(multiply(multiply(u,v),w),multiply(multiply(u,w),v)),
inference(spr,[status(thm),theory(equality)],[86,32]),
[iquote('0:SpR:86.0,32.0')] ).
cnf(143,plain,
equal(multiply(u,multiply(multiply(v,inverse(v)),w)),multiply(u,w)),
inference(spr,[status(thm),theory(equality)],[104,32]),
[iquote('0:SpR:104.0,32.0')] ).
cnf(153,plain,
equal(multiply(u,multiply(multiply(v,inverse(u)),w)),multiply(v,w)),
inference(spr,[status(thm),theory(equality)],[104,20]),
[iquote('0:SpR:104.0,20.0')] ).
cnf(155,plain,
equal(multiply(multiply(u,v),multiply(multiply(w,inverse(u)),x)),multiply(multiply(w,x),v)),
inference(spr,[status(thm),theory(equality)],[104,86]),
[iquote('0:SpR:104.0,86.0')] ).
cnf(213,plain,
equal(multiply(multiply(u,v),inverse(u)),multiply(multiply(w,inverse(w)),v)),
inference(spr,[status(thm),theory(equality)],[143,86]),
[iquote('0:SpR:143.0,86.0')] ).
cnf(217,plain,
equal(multiply(u,inverse(multiply(v,inverse(w)))),multiply(u,multiply(w,inverse(v)))),
inference(spr,[status(thm),theory(equality)],[143,43]),
[iquote('0:SpR:143.0,43.0')] ).
cnf(219,plain,
equal(multiply(u,inverse(u)),multiply(v,inverse(v))),
inference(spr,[status(thm),theory(equality)],[143,20]),
[iquote('0:SpR:143.0,20.0')] ).
cnf(321,plain,
equal(multiply(u,multiply(v,inverse(multiply(u,inverse(w))))),multiply(w,v)),
inference(spr,[status(thm),theory(equality)],[20,153]),
[iquote('0:SpR:20.0,153.0')] ).
cnf(331,plain,
equal(multiply(u,multiply(v,multiply(w,inverse(u)))),multiply(w,v)),
inference(rew,[status(thm),theory(equality)],[217,321]),
[iquote('0:Rew:217.0,321.0')] ).
cnf(410,plain,
equal(multiply(multiply(u,v),multiply(w,multiply(x,inverse(u)))),multiply(multiply(x,w),v)),
inference(spr,[status(thm),theory(equality)],[331,104]),
[iquote('0:SpR:331.0,104.0')] ).
cnf(423,plain,
equal(multiply(u,multiply(v,w)),multiply(v,multiply(u,w))),
inference(spr,[status(thm),theory(equality)],[86,331]),
[iquote('0:SpR:86.0,331.0')] ).
cnf(426,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(w,v))),
inference(spr,[status(thm),theory(equality)],[32,331]),
[iquote('0:SpR:32.0,331.0')] ).
cnf(428,plain,
equal(multiply(u,v),multiply(v,u)),
inference(spr,[status(thm),theory(equality)],[20,331]),
[iquote('0:SpR:20.0,331.0')] ).
cnf(433,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3)))
| ~ equal(multiply(multiply(inverse(b2),b2),a2),a2) ),
inference(rew,[status(thm),theory(equality)],[428,2]),
[iquote('0:Rew:428.0,2.2')] ).
cnf(435,plain,
equal(multiply(inverse(u),multiply(u,v)),multiply(multiply(w,inverse(w)),v)),
inference(rew,[status(thm),theory(equality)],[428,213]),
[iquote('0:Rew:428.0,213.0')] ).
cnf(446,plain,
equal(multiply(multiply(u,v),multiply(w,multiply(x,inverse(u)))),multiply(multiply(w,x),v)),
inference(rew,[status(thm),theory(equality)],[426,155]),
[iquote('0:Rew:426.0,155.0')] ).
cnf(477,plain,
equal(multiply(u,multiply(inverse(u),v)),multiply(w,multiply(v,inverse(w)))),
inference(rew,[status(thm),theory(equality)],[423,435,426]),
[iquote('0:Rew:423.0,435.0,426.0,435.0')] ).
cnf(478,plain,
equal(multiply(u,multiply(inverse(u),v)),v),
inference(rew,[status(thm),theory(equality)],[20,477]),
[iquote('0:Rew:20.0,477.0')] ).
cnf(482,plain,
equal(multiply(u,multiply(v,multiply(w,multiply(x,inverse(u))))),multiply(x,multiply(w,v))),
inference(rew,[status(thm),theory(equality)],[426,410]),
[iquote('0:Rew:426.0,410.0,426.0,410.0,426.0,410.0')] ).
cnf(489,plain,
equal(multiply(u,multiply(v,w)),multiply(w,multiply(v,u))),
inference(rew,[status(thm),theory(equality)],[482,446,426]),
[iquote('0:Rew:482.0,446.0,426.0,446.0,426.0,446.0,426.0,446.0')] ).
cnf(512,plain,
( ~ equal(multiply(a4,b4),multiply(a4,b4))
| ~ equal(multiply(b1,inverse(b1)),multiply(a1,inverse(a1)))
| ~ equal(multiply(a3,multiply(b3,c3)),multiply(a3,multiply(b3,c3)))
| ~ equal(a2,a2) ),
inference(rew,[status(thm),theory(equality)],[478,433,489,428,423]),
[iquote('0:Rew:478.0,433.3,489.0,433.3,428.0,433.3,423.0,433.2,489.0,433.2,428.0,433.1,428.0,433.1,428.0,433.0')] ).
cnf(513,plain,
~ equal(multiply(b1,inverse(b1)),multiply(a1,inverse(a1))),
inference(obv,[status(thm),theory(equality)],[512]),
[iquote('0:Obv:512.3')] ).
cnf(514,plain,
$false,
inference(unc,[status(thm)],[513,219]),
[iquote('0:UnC:513.0,219.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP086-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n009.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 06:21:23 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.49
% 0.19/0.49 SPASS V 3.9
% 0.19/0.49 SPASS beiseite: Proof found.
% 0.19/0.49 % SZS status Theorem
% 0.19/0.49 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.49 SPASS derived 327 clauses, backtracked 0 clauses, performed 0 splits and kept 92 clauses.
% 0.19/0.49 SPASS allocated 63805 KBytes.
% 0.19/0.49 SPASS spent 0:00:00.14 on the problem.
% 0.19/0.49 0:00:00.04 for the input.
% 0.19/0.49 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.49 0:00:00.01 for inferences.
% 0.19/0.49 0:00:00.00 for the backtracking.
% 0.19/0.49 0:00:00.07 for the reduction.
% 0.19/0.49
% 0.19/0.49
% 0.19/0.49 Here is a proof with depth 10, length 31 :
% 0.19/0.49 % SZS output start Refutation
% See solution above
% 0.19/0.49 Formulae used in the proof : single_axiom prove_these_axioms
% 0.19/0.49
%------------------------------------------------------------------------------