TSTP Solution File: GRP070-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP070-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 11:45:08 EDT 2022
% Result : Unsatisfiable 0.43s 0.60s
% Output : Refutation 0.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 3
% Syntax : Number of clauses : 31 ( 26 unt; 0 nHn; 31 RR)
% Number of literals : 39 ( 0 equ; 14 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 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(divide(divide(u,u),divide(v,divide(divide(w,divide(x,v)),inverse(x)))),w),
file('GRP070-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,inverse(v)),multiply(u,v)),
file('GRP070-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ 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('GRP070-1.p',unknown),
[] ).
cnf(4,plain,
equal(divide(divide(u,u),divide(v,multiply(divide(w,divide(x,v)),x))),w),
inference(rew,[status(thm),theory(equality)],[2,1]),
[iquote('0:Rew:2.0,1.0')] ).
cnf(7,plain,
equal(divide(divide(u,u),divide(multiply(divide(v,divide(w,x)),w),multiply(v,x))),divide(y,y)),
inference(spr,[status(thm),theory(equality)],[4]),
[iquote('0:SpR:4.0,4.0')] ).
cnf(9,plain,
equal(divide(divide(u,u),divide(inverse(v),multiply(divide(w,multiply(x,v)),x))),w),
inference(spr,[status(thm),theory(equality)],[2,4]),
[iquote('0:SpR:2.0,4.0')] ).
cnf(34,plain,
equal(divide(u,u),divide(v,v)),
inference(spr,[status(thm),theory(equality)],[7]),
[iquote('0:SpR:7.0,7.0')] ).
cnf(62,plain,
equal(divide(u,u),multiply(inverse(v),v)),
inference(spr,[status(thm),theory(equality)],[34,2]),
[iquote('0:SpR:34.0,2.0')] ).
cnf(70,plain,
equal(divide(divide(u,u),divide(v,multiply(divide(w,w),x))),divide(x,v)),
inference(spr,[status(thm),theory(equality)],[34,4]),
[iquote('0:SpR:34.0,4.0')] ).
cnf(100,plain,
equal(multiply(inverse(u),u),multiply(inverse(v),v)),
inference(spr,[status(thm),theory(equality)],[62,2]),
[iquote('0:SpR:62.0,2.0')] ).
cnf(122,plain,
( ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)))
| ~ equal(multiply(divide(u,u),a2),a2) ),
inference(spl,[status(thm),theory(equality)],[62,3]),
[iquote('0:SpL:62.0,3.2')] ).
cnf(234,plain,
equal(divide(u,multiply(divide(v,v),u)),divide(w,w)),
inference(spr,[status(thm),theory(equality)],[70,34]),
[iquote('0:SpR:70.0,34.0')] ).
cnf(252,plain,
equal(divide(divide(u,u),divide(multiply(divide(v,w),w),multiply(divide(x,x),multiply(divide(y,y),v)))),divide(z,z)),
inference(spr,[status(thm),theory(equality)],[70,7]),
[iquote('0:SpR:70.0,7.0')] ).
cnf(275,plain,
equal(divide(multiply(divide(u,u),v),multiply(divide(v,w),w)),divide(x,x)),
inference(rew,[status(thm),theory(equality)],[70,252]),
[iquote('0:Rew:70.0,252.0')] ).
cnf(284,plain,
equal(divide(divide(u,u),divide(inverse(v),multiply(divide(w,w),divide(x,x)))),v),
inference(spr,[status(thm),theory(equality)],[234,9]),
[iquote('0:SpR:234.0,9.0')] ).
cnf(327,plain,
equal(multiply(divide(u,u),v),v),
inference(rew,[status(thm),theory(equality)],[2,284,70]),
[iquote('0:Rew:2.0,284.0,70.0,284.0')] ).
cnf(329,plain,
equal(divide(divide(u,u),divide(v,w)),divide(w,v)),
inference(rew,[status(thm),theory(equality)],[327,70]),
[iquote('0:Rew:327.0,70.0')] ).
cnf(341,plain,
equal(divide(u,multiply(divide(u,v),v)),divide(w,w)),
inference(rew,[status(thm),theory(equality)],[327,275]),
[iquote('0:Rew:327.0,275.0')] ).
cnf(342,plain,
( ~ 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)],[327,122]),
[iquote('0:Rew:327.0,122.2')] ).
cnf(363,plain,
equal(divide(multiply(divide(u,multiply(v,w)),v),inverse(w)),u),
inference(rew,[status(thm),theory(equality)],[329,9]),
[iquote('0:Rew:329.0,9.0')] ).
cnf(364,plain,
equal(divide(multiply(divide(u,divide(v,w)),v),w),u),
inference(rew,[status(thm),theory(equality)],[329,4]),
[iquote('0:Rew:329.0,4.0')] ).
cnf(449,plain,
equal(multiply(multiply(divide(u,multiply(v,w)),v),w),u),
inference(rew,[status(thm),theory(equality)],[2,363]),
[iquote('0:Rew:2.0,363.0')] ).
cnf(504,plain,
( ~ 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)],[342]),
[iquote('0:Obv:342.2')] ).
cnf(617,plain,
equal(multiply(multiply(divide(u,u),divide(v,w)),w),v),
inference(spr,[status(thm),theory(equality)],[341,449]),
[iquote('0:SpR:341.0,449.0')] ).
cnf(619,plain,
equal(multiply(divide(u,divide(v,multiply(w,x))),v),multiply(multiply(u,w),x)),
inference(spr,[status(thm),theory(equality)],[364,449]),
[iquote('0:SpR:364.0,449.0')] ).
cnf(623,plain,
equal(multiply(divide(u,v),v),u),
inference(rew,[status(thm),theory(equality)],[327,617]),
[iquote('0:Rew:327.0,617.0')] ).
cnf(645,plain,
equal(multiply(divide(u,divide(v,w)),v),multiply(u,w)),
inference(spr,[status(thm),theory(equality)],[364,623]),
[iquote('0:SpR:364.0,623.0')] ).
cnf(652,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[645,619]),
[iquote('0:Rew:645.0,619.0')] ).
cnf(710,plain,
( ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(a3,multiply(b3,c3)),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[652,504]),
[iquote('0:Rew:652.0,504.1')] ).
cnf(756,plain,
~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1)),
inference(obv,[status(thm),theory(equality)],[710]),
[iquote('0:Obv:710.1')] ).
cnf(757,plain,
$false,
inference(unc,[status(thm)],[756,100]),
[iquote('0:UnC:756.0,100.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP070-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n025.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 13 19:47:54 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.43/0.60
% 0.43/0.60 SPASS V 3.9
% 0.43/0.60 SPASS beiseite: Proof found.
% 0.43/0.60 % SZS status Theorem
% 0.43/0.60 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.43/0.60 SPASS derived 595 clauses, backtracked 0 clauses, performed 0 splits and kept 267 clauses.
% 0.43/0.60 SPASS allocated 64292 KBytes.
% 0.43/0.60 SPASS spent 0:00:00.24 on the problem.
% 0.43/0.60 0:00:00.03 for the input.
% 0.43/0.60 0:00:00.00 for the FLOTTER CNF translation.
% 0.43/0.60 0:00:00.01 for inferences.
% 0.43/0.60 0:00:00.00 for the backtracking.
% 0.43/0.60 0:00:00.19 for the reduction.
% 0.43/0.60
% 0.43/0.60
% 0.43/0.60 Here is a proof with depth 6, length 31 :
% 0.43/0.60 % SZS output start Refutation
% See solution above
% 0.43/0.60 Formulae used in the proof : single_axiom multiply prove_these_axioms
% 0.43/0.60
%------------------------------------------------------------------------------