%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP510-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n012.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 11:47:49 EDT 2022
% Result : Unsatisfiable 0.20s 0.47s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 2
% Syntax : Number of clauses : 41 ( 41 unt; 0 nHn; 41 RR)
% Number of literals : 41 ( 0 equ; 4 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 : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(multiply(multiply(multiply(u,v),w),inverse(multiply(u,w))),v),
file('GRP510-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(multiply(multiply(inverse(b2),b2),a2),a2),
file('GRP510-1.p',unknown),
[] ).
cnf(3,plain,
equal(multiply(u,inverse(multiply(multiply(v,u),inverse(multiply(v,w))))),w),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(5,plain,
equal(multiply(multiply(multiply(multiply(multiply(u,v),w),x),inverse(multiply(u,w))),inverse(v)),x),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(6,plain,
equal(multiply(multiply(u,v),inverse(multiply(multiply(multiply(w,u),x),v))),inverse(multiply(w,x))),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(7,plain,
equal(multiply(u,inverse(multiply(v,inverse(multiply(multiply(w,multiply(v,x)),inverse(multiply(w,u))))))),x),
inference(spr,[status(thm),theory(equality)],[3,1]),
[iquote('0:SpR:3.0,1.0')] ).
cnf(9,plain,
equal(multiply(multiply(u,v),inverse(multiply(w,v))),inverse(multiply(multiply(x,w),inverse(multiply(x,u))))),
inference(spr,[status(thm),theory(equality)],[3,1]),
[iquote('0:SpR:3.0,1.0')] ).
cnf(11,plain,
equal(multiply(u,inverse(multiply(multiply(v,u),inverse(w)))),inverse(multiply(multiply(x,v),inverse(multiply(x,w))))),
inference(spr,[status(thm),theory(equality)],[3]),
[iquote('0:SpR:3.0,3.0')] ).
cnf(17,plain,
equal(multiply(multiply(u,inverse(multiply(multiply(multiply(v,w),x),inverse(multiply(v,x))))),inverse(u)),inverse(w)),
inference(spr,[status(thm),theory(equality)],[5]),
[iquote('0:SpR:5.0,5.0')] ).
cnf(33,plain,
equal(multiply(multiply(u,inverse(v)),inverse(u)),inverse(v)),
inference(rew,[status(thm),theory(equality)],[1,17]),
[iquote('0:Rew:1.0,17.0')] ).
cnf(58,plain,
equal(multiply(multiply(u,v),inverse(multiply(w,v))),inverse(multiply(x,inverse(multiply(multiply(y,multiply(x,u)),inverse(multiply(y,w))))))),
inference(spr,[status(thm),theory(equality)],[3,6]),
[iquote('0:SpR:3.0,6.0')] ).
cnf(75,plain,
equal(multiply(multiply(inverse(u),inverse(multiply(v,inverse(u)))),inverse(w)),inverse(multiply(v,w))),
inference(spr,[status(thm),theory(equality)],[33,5]),
[iquote('0:SpR:33.0,5.0')] ).
cnf(77,plain,
equal(multiply(multiply(inverse(u),v),inverse(multiply(inverse(u),v))),inverse(multiply(w,inverse(w)))),
inference(spr,[status(thm),theory(equality)],[33,6]),
[iquote('0:SpR:33.0,6.0')] ).
cnf(83,plain,
equal(multiply(inverse(u),inverse(multiply(v,inverse(u)))),inverse(v)),
inference(spr,[status(thm),theory(equality)],[33]),
[iquote('0:SpR:33.0,33.0')] ).
cnf(87,plain,
equal(multiply(u,inverse(multiply(multiply(v,u),w))),inverse(multiply(v,w))),
inference(spr,[status(thm),theory(equality)],[1,33]),
[iquote('0:SpR:1.0,33.0')] ).
cnf(90,plain,
equal(inverse(multiply(multiply(u,v),inverse(multiply(u,w)))),multiply(w,inverse(v))),
inference(spr,[status(thm),theory(equality)],[3,33]),
[iquote('0:SpR:3.0,33.0')] ).
cnf(94,plain,
equal(inverse(multiply(multiply(u,v),inverse(multiply(u,w)))),inverse(multiply(v,inverse(w)))),
inference(rew,[status(thm),theory(equality)],[87,11]),
[iquote('0:Rew:87.0,11.0')] ).
cnf(96,plain,
equal(multiply(multiply(u,v),inverse(multiply(w,v))),inverse(multiply(x,multiply(w,inverse(multiply(x,u)))))),
inference(rew,[status(thm),theory(equality)],[90,58]),
[iquote('0:Rew:90.0,58.0')] ).
cnf(102,plain,
equal(multiply(multiply(u,v),inverse(multiply(w,v))),multiply(u,inverse(w))),
inference(rew,[status(thm),theory(equality)],[90,9]),
[iquote('0:Rew:90.0,9.0')] ).
cnf(105,plain,
equal(multiply(u,inverse(multiply(v,multiply(u,inverse(multiply(v,w)))))),w),
inference(rew,[status(thm),theory(equality)],[90,7]),
[iquote('0:Rew:90.0,7.0')] ).
cnf(107,plain,
equal(multiply(multiply(u,v),inverse(u)),v),
inference(rew,[status(thm),theory(equality)],[102,1]),
[iquote('0:Rew:102.0,1.0')] ).
cnf(113,plain,
equal(inverse(multiply(u,inverse(v))),multiply(v,inverse(u))),
inference(rew,[status(thm),theory(equality)],[90,94]),
[iquote('0:Rew:90.0,94.0')] ).
cnf(116,plain,
equal(multiply(inverse(u),multiply(u,inverse(v))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[113,83]),
[iquote('0:Rew:113.0,83.0')] ).
cnf(124,plain,
equal(multiply(multiply(u,v),inverse(multiply(u,w))),multiply(v,inverse(w))),
inference(rew,[status(thm),theory(equality)],[113,90]),
[iquote('0:Rew:113.0,90.0')] ).
cnf(129,plain,
equal(multiply(inverse(u),inverse(v)),inverse(multiply(u,v))),
inference(rew,[status(thm),theory(equality)],[116,75,113]),
[iquote('0:Rew:116.0,75.0,113.0,75.0')] ).
cnf(132,plain,
equal(multiply(u,inverse(u)),multiply(v,inverse(v))),
inference(rew,[status(thm),theory(equality)],[124,77,113]),
[iquote('0:Rew:124.0,77.0,113.0,77.0')] ).
cnf(142,plain,
equal(inverse(multiply(u,multiply(v,inverse(multiply(u,w))))),multiply(w,inverse(v))),
inference(rew,[status(thm),theory(equality)],[102,96]),
[iquote('0:Rew:102.0,96.0')] ).
cnf(143,plain,
equal(multiply(u,multiply(v,inverse(u))),v),
inference(rew,[status(thm),theory(equality)],[142,105]),
[iquote('0:Rew:142.0,105.0')] ).
cnf(169,plain,
equal(multiply(u,inverse(multiply(v,u))),inverse(v)),
inference(spr,[status(thm),theory(equality)],[107]),
[iquote('0:SpR:107.0,107.0')] ).
cnf(177,plain,
equal(multiply(u,multiply(v,inverse(v))),u),
inference(spr,[status(thm),theory(equality)],[132,143]),
[iquote('0:SpR:132.0,143.0')] ).
cnf(187,plain,
equal(multiply(inverse(multiply(u,v)),inverse(inverse(u))),inverse(v)),
inference(spr,[status(thm),theory(equality)],[169]),
[iquote('0:SpR:169.0,169.0')] ).
cnf(192,plain,
equal(multiply(u,inverse(multiply(u,v))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[113,187,129]),
[iquote('0:Rew:113.0,187.0,129.0,187.0')] ).
cnf(205,plain,
equal(multiply(multiply(u,v),inverse(v)),u),
inference(spr,[status(thm),theory(equality)],[192,143]),
[iquote('0:SpR:192.0,143.0')] ).
cnf(207,plain,
equal(multiply(multiply(u,v),inverse(v)),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[107,192]),
[iquote('0:SpR:107.0,192.0')] ).
cnf(211,plain,
equal(multiply(u,inverse(inverse(v))),inverse(inverse(multiply(v,u)))),
inference(spr,[status(thm),theory(equality)],[169,192]),
[iquote('0:SpR:169.0,192.0')] ).
cnf(214,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[205,207]),
[iquote('0:Rew:205.0,207.0')] ).
cnf(225,plain,
equal(multiply(u,v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[214,211]),
[iquote('0:Rew:214.0,211.0,214.0,211.0')] ).
cnf(227,plain,
~ equal(multiply(a2,multiply(inverse(b2),b2)),a2),
inference(rew,[status(thm),theory(equality)],[225,2]),
[iquote('0:Rew:225.0,2.0')] ).
cnf(239,plain,
~ equal(multiply(a2,multiply(b2,inverse(b2))),a2),
inference(rew,[status(thm),theory(equality)],[225,227]),
[iquote('0:Rew:225.0,227.0')] ).
cnf(240,plain,
~ equal(a2,a2),
inference(rew,[status(thm),theory(equality)],[177,239]),
[iquote('0:Rew:177.0,239.0')] ).
cnf(241,plain,
$false,
inference(obv,[status(thm),theory(equality)],[240]),
[iquote('0:Obv:240.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP510-1 : TPTP v8.1.0. Released v2.6.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n012.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jun 13 10:26:25 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.20/0.47
% 0.20/0.47 SPASS V 3.9
% 0.20/0.47 SPASS beiseite: Proof found.
% 0.20/0.47 % SZS status Theorem
% 0.20/0.47 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.47 SPASS derived 183 clauses, backtracked 0 clauses, performed 0 splits and kept 117 clauses.
% 0.20/0.47 SPASS allocated 63668 KBytes.
% 0.20/0.47 SPASS spent 0:00:00.11 on the problem.
% 0.20/0.47 0:00:00.04 for the input.
% 0.20/0.47 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.47 0:00:00.00 for inferences.
% 0.20/0.47 0:00:00.00 for the backtracking.
% 0.20/0.47 0:00:00.05 for the reduction.
% 0.20/0.47
% 0.20/0.47
% 0.20/0.47 Here is a proof with depth 4, length 41 :
% 0.20/0.47 % SZS output start Refutation
% See solution above
% 0.20/0.47 Formulae used in the proof : single_axiom prove_these_axioms_2
% 0.20/0.47
%------------------------------------------------------------------------------