TSTP Solution File: GRP104-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP104-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 11:45:19 EDT 2022
% Result : Unsatisfiable 0.61s 0.79s
% Output : Refutation 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 3
% Syntax : Number of clauses : 59 ( 46 unt; 0 nHn; 59 RR)
% Number of literals : 82 ( 0 equ; 37 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 : 16 ( 16 usr; 13 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(double_divide(u,inverse(double_divide(inverse(double_divide(double_divide(u,v),inverse(w))),v))),w),
file('GRP104-1.p',unknown),
[] ).
cnf(2,axiom,
equal(inverse(double_divide(u,v)),multiply(v,u)),
file('GRP104-1.p',unknown),
[] ).
cnf(3,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('GRP104-1.p',unknown),
[] ).
cnf(4,plain,
equal(double_divide(u,multiply(v,multiply(inverse(w),double_divide(u,v)))),w),
inference(rew,[status(thm),theory(equality)],[2,1]),
[iquote('0:Rew:2.0,1.0,2.0,1.0')] ).
cnf(6,plain,
equal(multiply(multiply(u,multiply(inverse(v),double_divide(w,u))),w),inverse(v)),
inference(spr,[status(thm),theory(equality)],[4,2]),
[iquote('0:SpR:4.0,2.0')] ).
cnf(7,plain,
equal(double_divide(u,multiply(multiply(v,multiply(inverse(w),double_divide(u,v))),multiply(inverse(x),w))),x),
inference(spr,[status(thm),theory(equality)],[4]),
[iquote('0:SpR:4.0,4.0')] ).
cnf(9,plain,
equal(double_divide(u,multiply(v,multiply(multiply(w,x),double_divide(u,v)))),double_divide(x,w)),
inference(spr,[status(thm),theory(equality)],[2,4]),
[iquote('0:SpR:2.0,4.0')] ).
cnf(12,plain,
equal(multiply(multiply(u,multiply(multiply(v,w),double_divide(x,u))),x),multiply(v,w)),
inference(spr,[status(thm),theory(equality)],[2,6]),
[iquote('0:SpR:2.0,6.0')] ).
cnf(44,plain,
equal(double_divide(multiply(inverse(u),v),inverse(v)),u),
inference(spr,[status(thm),theory(equality)],[6,7]),
[iquote('0:SpR:6.0,7.0')] ).
cnf(45,plain,
equal(multiply(inverse(u),multiply(inverse(v),u)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[44,2]),
[iquote('0:SpR:44.0,2.0')] ).
cnf(56,plain,
equal(double_divide(inverse(u),inverse(multiply(inverse(u),v))),v),
inference(spr,[status(thm),theory(equality)],[45,44]),
[iquote('0:SpR:45.0,44.0')] ).
cnf(57,plain,
equal(multiply(inverse(multiply(inverse(u),v)),inverse(u)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[45]),
[iquote('0:SpR:45.0,45.0')] ).
cnf(94,plain,
equal(double_divide(inverse(u),inverse(inverse(v))),multiply(inverse(v),u)),
inference(spr,[status(thm),theory(equality)],[45,56]),
[iquote('0:SpR:45.0,56.0')] ).
cnf(119,plain,
equal(double_divide(inverse(u),inverse(multiply(v,w))),multiply(multiply(v,w),u)),
inference(spr,[status(thm),theory(equality)],[2,94]),
[iquote('0:SpR:2.0,94.0')] ).
cnf(121,plain,
equal(multiply(multiply(inverse(u),v),u),v),
inference(rew,[status(thm),theory(equality)],[119,56]),
[iquote('0:Rew:119.0,56.0')] ).
cnf(124,plain,
equal(multiply(inverse(u),double_divide(v,inverse(v))),inverse(u)),
inference(spr,[status(thm),theory(equality)],[121,6]),
[iquote('0:SpR:121.0,6.0')] ).
cnf(127,plain,
equal(double_divide(u,inverse(double_divide(v,w))),double_divide(v,multiply(w,u))),
inference(spr,[status(thm),theory(equality)],[121,9]),
[iquote('0:SpR:121.0,9.0')] ).
cnf(128,plain,
equal(multiply(inverse(double_divide(u,v)),w),multiply(multiply(v,w),u)),
inference(spr,[status(thm),theory(equality)],[121,12]),
[iquote('0:SpR:121.0,12.0')] ).
cnf(134,plain,
equal(double_divide(u,multiply(v,w)),double_divide(w,multiply(v,u))),
inference(rew,[status(thm),theory(equality)],[2,127]),
[iquote('0:Rew:2.0,127.0')] ).
cnf(136,plain,
equal(multiply(multiply(u,v),w),multiply(multiply(u,w),v)),
inference(rew,[status(thm),theory(equality)],[2,128]),
[iquote('0:Rew:2.0,128.0')] ).
cnf(161,plain,
equal(double_divide(u,multiply(inverse(u),inverse(v))),v),
inference(spr,[status(thm),theory(equality)],[124,4]),
[iquote('0:SpR:124.0,4.0')] ).
cnf(167,plain,
equal(double_divide(inverse(u),inverse(double_divide(v,inverse(v)))),u),
inference(spr,[status(thm),theory(equality)],[124,44]),
[iquote('0:SpR:124.0,44.0')] ).
cnf(169,plain,
equal(multiply(inverse(u),u),double_divide(v,inverse(v))),
inference(spr,[status(thm),theory(equality)],[124,121]),
[iquote('0:SpR:124.0,121.0')] ).
cnf(176,plain,
equal(double_divide(inverse(u),multiply(inverse(v),v)),u),
inference(rew,[status(thm),theory(equality)],[2,167]),
[iquote('0:Rew:2.0,167.0')] ).
cnf(207,plain,
equal(multiply(double_divide(u,inverse(u)),v),v),
inference(spr,[status(thm),theory(equality)],[169,121]),
[iquote('0:SpR:169.0,121.0')] ).
cnf(210,plain,
equal(double_divide(u,inverse(u)),double_divide(v,inverse(v))),
inference(spr,[status(thm),theory(equality)],[169]),
[iquote('0:SpR:169.0,169.0')] ).
cnf(217,plain,
equal(multiply(inverse(u),u),multiply(inverse(v),v)),
inference(spr,[status(thm),theory(equality)],[169,94]),
[iquote('0:SpR:169.0,94.0')] ).
cnf(225,plain,
( ~ 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(double_divide(u,inverse(u)),a2),a2) ),
inference(spl,[status(thm),theory(equality)],[169,3]),
[iquote('0:SpL:169.0,3.3')] ).
cnf(242,plain,
( ~ 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(a2,a2) ),
inference(rew,[status(thm),theory(equality)],[207,225]),
[iquote('0:Rew:207.0,225.3')] ).
cnf(243,plain,
( ~ 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))) ),
inference(obv,[status(thm),theory(equality)],[242]),
[iquote('0:Obv:242.3')] ).
cnf(251,plain,
equal(multiply(multiply(inverse(u),u),v),v),
inference(spr,[status(thm),theory(equality)],[94,207]),
[iquote('0:SpR:94.0,207.0')] ).
cnf(315,plain,
equal(double_divide(u,multiply(inverse(v),double_divide(u,multiply(inverse(w),w)))),v),
inference(spr,[status(thm),theory(equality)],[251,4]),
[iquote('0:SpR:251.0,4.0')] ).
cnf(327,plain,
equal(double_divide(inverse(u),multiply(multiply(inverse(v),v),multiply(inverse(w),u))),w),
inference(spr,[status(thm),theory(equality)],[176,4]),
[iquote('0:SpR:176.0,4.0')] ).
cnf(337,plain,
equal(double_divide(inverse(u),multiply(inverse(v),u)),v),
inference(rew,[status(thm),theory(equality)],[251,327]),
[iquote('0:Rew:251.0,327.0')] ).
cnf(338,plain,
equal(double_divide(u,multiply(inverse(v),inverse(u))),v),
inference(rew,[status(thm),theory(equality)],[134,337]),
[iquote('0:Rew:134.0,337.0')] ).
cnf(550,plain,
equal(inverse(inverse(u)),u),
inference(spr,[status(thm),theory(equality)],[338,176]),
[iquote('0:SpR:338.0,176.0')] ).
cnf(553,plain,
equal(double_divide(u,multiply(inverse(v),v)),inverse(u)),
inference(spr,[status(thm),theory(equality)],[217,338]),
[iquote('0:SpR:217.0,338.0')] ).
cnf(556,plain,
equal(multiply(inverse(u),v),double_divide(u,inverse(v))),
inference(spr,[status(thm),theory(equality)],[57,338]),
[iquote('0:SpR:57.0,338.0')] ).
cnf(574,plain,
equal(double_divide(u,multiply(inverse(v),inverse(u))),v),
inference(rew,[status(thm),theory(equality)],[553,315]),
[iquote('0:Rew:553.0,315.0')] ).
cnf(605,plain,
equal(double_divide(u,double_divide(u,inverse(inverse(v)))),v),
inference(rew,[status(thm),theory(equality)],[556,161]),
[iquote('0:Rew:556.0,161.0')] ).
cnf(619,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(inverse(a1),a1),double_divide(b1,inverse(b1)))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[556,243]),
[iquote('0:Rew:556.0,243.1')] ).
cnf(698,plain,
equal(double_divide(u,double_divide(v,u)),v),
inference(rew,[status(thm),theory(equality)],[550,574,556]),
[iquote('0:Rew:550.0,574.0,556.0,574.0')] ).
cnf(703,plain,
equal(double_divide(u,double_divide(u,v)),v),
inference(rew,[status(thm),theory(equality)],[550,605]),
[iquote('0:Rew:550.0,605.0')] ).
cnf(918,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(double_divide(b1,inverse(b1)),double_divide(a1,inverse(a1)))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[556,619]),
[iquote('0:Rew:556.0,619.1')] ).
cnf(967,plain,
equal(double_divide(u,v),double_divide(v,u)),
inference(spr,[status(thm),theory(equality)],[698,703]),
[iquote('0:SpR:698.0,703.0')] ).
cnf(1024,plain,
equal(inverse(double_divide(u,v)),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[967,2]),
[iquote('0:SpR:967.0,2.0')] ).
cnf(1034,plain,
equal(multiply(u,v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[2,1024]),
[iquote('0:Rew:2.0,1024.0')] ).
cnf(1035,plain,
( ~ equal(multiply(a4,b4),multiply(a4,b4))
| ~ equal(double_divide(b1,inverse(b1)),double_divide(a1,inverse(a1)))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[1034,918]),
[iquote('0:Rew:1034.0,918.0')] ).
cnf(1078,plain,
( ~ equal(double_divide(b1,inverse(b1)),double_divide(a1,inverse(a1)))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(obv,[status(thm),theory(equality)],[1035]),
[iquote('0:Obv:1035.0')] ).
cnf(1079,plain,
( ~ equal(double_divide(b1,inverse(b1)),double_divide(a1,inverse(a1)))
| ~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[1034,1078]),
[iquote('0:Rew:1034.0,1078.1')] ).
cnf(1886,plain,
equal(multiply(multiply(u,v),w),multiply(v,multiply(u,w))),
inference(spr,[status(thm),theory(equality)],[136,1034]),
[iquote('0:SpR:136.0,1034.0')] ).
cnf(1908,plain,
equal(multiply(multiply(u,v),w),multiply(multiply(v,w),u)),
inference(spr,[status(thm),theory(equality)],[1034,136]),
[iquote('0:SpR:1034.0,136.0')] ).
cnf(1949,plain,
equal(multiply(u,multiply(v,w)),multiply(w,multiply(u,v))),
inference(rew,[status(thm),theory(equality)],[1886,1908]),
[iquote('0:Rew:1886.0,1908.0,1886.0,1908.0')] ).
cnf(1950,plain,
( ~ equal(double_divide(b1,inverse(b1)),double_divide(a1,inverse(a1)))
| ~ equal(multiply(b3,multiply(c3,a3)),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[1949,1079]),
[iquote('0:Rew:1949.0,1079.1')] ).
cnf(2021,plain,
( ~ equal(double_divide(b1,inverse(b1)),double_divide(a1,inverse(a1)))
| ~ equal(multiply(b3,multiply(a3,c3)),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[1034,1950]),
[iquote('0:Rew:1034.0,1950.1')] ).
cnf(2022,plain,
( ~ equal(double_divide(b1,inverse(b1)),double_divide(a1,inverse(a1)))
| ~ equal(multiply(a3,multiply(c3,b3)),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[1949,2021]),
[iquote('0:Rew:1949.0,2021.1')] ).
cnf(2023,plain,
( ~ equal(double_divide(b1,inverse(b1)),double_divide(a1,inverse(a1)))
| ~ equal(multiply(a3,multiply(b3,c3)),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[1034,2022]),
[iquote('0:Rew:1034.0,2022.1')] ).
cnf(2024,plain,
~ equal(double_divide(b1,inverse(b1)),double_divide(a1,inverse(a1))),
inference(obv,[status(thm),theory(equality)],[2023]),
[iquote('0:Obv:2023.1')] ).
cnf(2025,plain,
$false,
inference(unc,[status(thm)],[2024,210]),
[iquote('0:UnC:2024.0,210.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP104-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jun 14 05:08:19 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.61/0.79
% 0.61/0.79 SPASS V 3.9
% 0.61/0.79 SPASS beiseite: Proof found.
% 0.61/0.79 % SZS status Theorem
% 0.61/0.79 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.61/0.79 SPASS derived 1101 clauses, backtracked 0 clauses, performed 0 splits and kept 479 clauses.
% 0.61/0.79 SPASS allocated 66264 KBytes.
% 0.61/0.79 SPASS spent 0:00:00.41 on the problem.
% 0.61/0.79 0:00:00.04 for the input.
% 0.61/0.79 0:00:00.00 for the FLOTTER CNF translation.
% 0.61/0.79 0:00:00.01 for inferences.
% 0.61/0.79 0:00:00.00 for the backtracking.
% 0.61/0.79 0:00:00.35 for the reduction.
% 0.61/0.79
% 0.61/0.79
% 0.61/0.79 Here is a proof with depth 12, length 59 :
% 0.61/0.79 % SZS output start Refutation
% See solution above
% 0.61/0.79 Formulae used in the proof : single_axiom multiply prove_these_axioms
% 0.61/0.79
%------------------------------------------------------------------------------