TSTP Solution File: GRP412-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP412-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 11:47:15 EDT 2022
% Result : Unsatisfiable 12.22s 12.45s
% Output : Refutation 12.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 2
% Syntax : Number of clauses : 22 ( 22 unt; 0 nHn; 22 RR)
% Number of literals : 22 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 18 ( 3 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(multiply(u,inverse(multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(multiply(u,inverse(v))),w))),v))),w),
file('GRP412-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1)),
file('GRP412-1.p',unknown),
[] ).
cnf(3,plain,
equal(multiply(u,inverse(multiply(multiply(multiply(inverse(v),v),inverse(w)),v))),inverse(multiply(multiply(multiply(inverse(x),x),inverse(multiply(inverse(multiply(inverse(multiply(u,inverse(v))),inverse(x))),w))),x))),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(4,plain,
equal(multiply(u,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(multiply(u,inverse(v))),w))),v)),multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(multiply(u,inverse(v))),w))),v)),inverse(multiply(inverse(w),x))),multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(multiply(u,inverse(v))),w))),v)))),x),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(24,plain,
equal(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(multiply(multiply(multiply(inverse(v),v),inverse(w)),v)))),w),
inference(spr,[status(thm),theory(equality)],[3,1]),
[iquote('0:SpR:3.0,1.0')] ).
cnf(29,plain,
equal(inverse(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(multiply(inverse(multiply(v,inverse(w))),inverse(u))),multiply(multiply(multiply(inverse(x),x),inverse(multiply(inverse(multiply(multiply(inverse(w),w),inverse(x))),y))),x)))),u)),multiply(v,inverse(multiply(y,w)))),
inference(spr,[status(thm),theory(equality)],[1,3]),
[iquote('0:SpR:1.0,3.0')] ).
cnf(57,plain,
equal(inverse(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(multiply(inverse(multiply(v,inverse(multiply(multiply(multiply(inverse(w),w),inverse(multiply(inverse(multiply(v,inverse(w))),x))),w)))),inverse(u))),multiply(inverse(x),y)))),u)),y),
inference(spr,[status(thm),theory(equality)],[4,3]),
[iquote('0:SpR:4.0,3.0')] ).
cnf(99,plain,
equal(inverse(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(multiply(inverse(v),inverse(u))),multiply(inverse(v),w)))),u)),w),
inference(rew,[status(thm),theory(equality)],[1,57]),
[iquote('0:Rew:1.0,57.0')] ).
cnf(107,plain,
equal(inverse(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(multiply(v,inverse(u))),multiply(v,w)))),u)),w),
inference(spr,[status(thm),theory(equality)],[99]),
[iquote('0:SpR:99.0,99.0')] ).
cnf(151,plain,
equal(multiply(inverse(multiply(u,inverse(v))),multiply(u,w)),multiply(inverse(multiply(x,inverse(v))),multiply(x,w))),
inference(spr,[status(thm),theory(equality)],[107,24]),
[iquote('0:SpR:107.0,24.0')] ).
cnf(211,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,w)),multiply(inverse(multiply(x,v)),multiply(x,w))),
inference(spr,[status(thm),theory(equality)],[107,151]),
[iquote('0:SpR:107.0,151.0')] ).
cnf(297,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,w)),multiply(x,multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(multiply(y,inverse(v))),multiply(y,x)))),w))),
inference(spr,[status(thm),theory(equality)],[107,211]),
[iquote('0:SpR:107.0,211.0')] ).
cnf(2740,plain,
equal(inverse(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(multiply(v,w)),multiply(v,w)))),u)),multiply(x,inverse(multiply(multiply(multiply(inverse(y),y),inverse(multiply(inverse(multiply(x,inverse(y))),inverse(u)))),y)))),
inference(spr,[status(thm),theory(equality)],[297,29]),
[iquote('0:SpR:297.0,29.0')] ).
cnf(2923,plain,
equal(inverse(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(multiply(v,w)),multiply(v,w)))),u)),inverse(u)),
inference(rew,[status(thm),theory(equality)],[1,2740]),
[iquote('0:Rew:1.0,2740.0')] ).
cnf(2986,plain,
equal(inverse(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(v),v))),u)),inverse(u)),
inference(spr,[status(thm),theory(equality)],[24,2923]),
[iquote('0:SpR:24.0,2923.0')] ).
cnf(3117,plain,
equal(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(v))),multiply(inverse(w),w)),
inference(spr,[status(thm),theory(equality)],[2986,24]),
[iquote('0:SpR:2986.0,24.0')] ).
cnf(3145,plain,
equal(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(multiply(multiply(multiply(inverse(v),v),inverse(w)),v)))),multiply(multiply(multiply(inverse(w),w),inverse(multiply(inverse(x),x))),w)),
inference(spr,[status(thm),theory(equality)],[2986,24]),
[iquote('0:SpR:2986.0,24.0')] ).
cnf(3203,plain,
equal(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(v),v))),u),u),
inference(rew,[status(thm),theory(equality)],[24,3145]),
[iquote('0:Rew:24.0,3145.0')] ).
cnf(3506,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,v)),multiply(inverse(v),v)),
inference(spr,[status(thm),theory(equality)],[3203,297]),
[iquote('0:SpR:3203.0,297.0')] ).
cnf(3702,plain,
equal(multiply(inverse(inverse(u)),inverse(u)),multiply(inverse(v),v)),
inference(rew,[status(thm),theory(equality)],[3506,3117]),
[iquote('0:Rew:3506.0,3117.0')] ).
cnf(3849,plain,
equal(multiply(inverse(u),u),multiply(inverse(v),v)),
inference(spr,[status(thm),theory(equality)],[3702]),
[iquote('0:SpR:3702.0,3702.0')] ).
cnf(4029,plain,
$false,
inference(unc,[status(thm)],[3849,2]),
[iquote('0:UnC:3849.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP412-1 : TPTP v8.1.0. Released v2.6.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n023.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 : Tue Jun 14 06:44:20 EDT 2022
% 0.12/0.33 % CPUTime :
% 12.22/12.45
% 12.22/12.45 SPASS V 3.9
% 12.22/12.45 SPASS beiseite: Proof found.
% 12.22/12.45 % SZS status Theorem
% 12.22/12.45 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.22/12.45 SPASS derived 4694 clauses, backtracked 0 clauses, performed 0 splits and kept 1698 clauses.
% 12.22/12.45 SPASS allocated 95642 KBytes.
% 12.22/12.45 SPASS spent 0:0:11.91 on the problem.
% 12.22/12.45 0:00:00.04 for the input.
% 12.22/12.45 0:00:00.00 for the FLOTTER CNF translation.
% 12.22/12.45 0:00:00.08 for inferences.
% 12.22/12.45 0:00:00.00 for the backtracking.
% 12.22/12.45 0:0:11.77 for the reduction.
% 12.22/12.45
% 12.22/12.45
% 12.22/12.45 Here is a proof with depth 10, length 22 :
% 12.22/12.45 % SZS output start Refutation
% See solution above
% 12.22/12.45 Formulae used in the proof : single_axiom prove_these_axioms_1
% 12.22/12.45
%------------------------------------------------------------------------------