TSTP Solution File: HEN011-5 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HEN011-5 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 13:03:15 EDT 2022
% Result : Unsatisfiable 15.94s 16.15s
% Output : Refutation 15.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of clauses : 30 ( 19 unt; 0 nHn; 30 RR)
% Number of literals : 43 ( 0 equ; 17 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 : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(divide(u,u),zero),
file('HEN011-5.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,zero),u),
file('HEN011-5.p',unknown),
[] ).
cnf(4,axiom,
( ~ equal(divide(divide(u,v),w),zero)
| equal(divide(divide(u,w),v),zero) ),
file('HEN011-5.p',unknown),
[] ).
cnf(6,axiom,
( ~ equal(divide(u,v),zero)
| equal(divide(divide(u,w),divide(v,w)),zero) ),
file('HEN011-5.p',unknown),
[] ).
cnf(7,axiom,
equal(divide(identity,divide(identity,divide(identity,u))),divide(identity,u)),
file('HEN011-5.p',unknown),
[] ).
cnf(9,axiom,
~ equal(divide(divide(identity,b),divide(identity,divide(identity,a))),divide(divide(identity,a),divide(identity,divide(identity,b)))),
file('HEN011-5.p',unknown),
[] ).
cnf(10,axiom,
equal(divide(divide(u,v),u),zero),
file('HEN011-5.p',unknown),
[] ).
cnf(11,axiom,
equal(divide(divide(divide(u,v),divide(w,v)),divide(divide(u,w),v)),zero),
file('HEN011-5.p',unknown),
[] ).
cnf(13,axiom,
( ~ equal(divide(u,v),zero)
| ~ equal(divide(v,u),zero)
| equal(v,u) ),
file('HEN011-5.p',unknown),
[] ).
cnf(98,plain,
( ~ equal(divide(u,divide(v,w)),zero)
| equal(divide(divide(u,v),zero),zero) ),
inference(spr,[status(thm),theory(equality)],[10,6]),
[iquote('0:SpR:10.0,6.1')] ).
cnf(121,plain,
( ~ equal(divide(u,divide(v,w)),zero)
| equal(divide(u,v),zero) ),
inference(rew,[status(thm),theory(equality)],[2,98]),
[iquote('0:Rew:2.0,98.1')] ).
cnf(320,plain,
( ~ equal(zero,zero)
| equal(divide(divide(u,divide(u,v)),v),zero) ),
inference(spl,[status(thm),theory(equality)],[1,4]),
[iquote('0:SpL:1.0,4.0')] ).
cnf(330,plain,
equal(divide(divide(u,divide(u,v)),v),zero),
inference(obv,[status(thm),theory(equality)],[320]),
[iquote('0:Obv:320.0')] ).
cnf(718,plain,
( ~ equal(zero,zero)
| equal(divide(divide(divide(u,v),divide(divide(u,w),v)),divide(w,v)),zero) ),
inference(spl,[status(thm),theory(equality)],[11,4]),
[iquote('0:SpL:11.0,4.0')] ).
cnf(764,plain,
equal(divide(divide(divide(u,v),divide(divide(u,w),v)),divide(w,v)),zero),
inference(obv,[status(thm),theory(equality)],[718]),
[iquote('0:Obv:718.0')] ).
cnf(2013,plain,
( ~ equal(zero,zero)
| equal(divide(divide(u,divide(u,divide(v,w))),v),zero) ),
inference(spl,[status(thm),theory(equality)],[330,121]),
[iquote('0:SpL:330.0,121.0')] ).
cnf(2036,plain,
equal(divide(divide(u,divide(u,divide(v,w))),v),zero),
inference(obv,[status(thm),theory(equality)],[2013]),
[iquote('0:Obv:2013.0')] ).
cnf(11420,plain,
equal(divide(divide(divide(divide(u,v),divide(divide(u,w),v)),zero),w),zero),
inference(spr,[status(thm),theory(equality)],[764,2036]),
[iquote('0:SpR:764.0,2036.0')] ).
cnf(11752,plain,
equal(divide(divide(divide(u,v),divide(divide(u,w),v)),w),zero),
inference(rew,[status(thm),theory(equality)],[2,11420]),
[iquote('0:Rew:2.0,11420.0')] ).
cnf(32603,plain,
equal(divide(divide(divide(divide(u,v),w),zero),divide(divide(u,w),v)),zero),
inference(spr,[status(thm),theory(equality)],[11752]),
[iquote('0:SpR:11752.0,11752.0')] ).
cnf(32977,plain,
equal(divide(divide(divide(u,v),w),divide(divide(u,w),v)),zero),
inference(rew,[status(thm),theory(equality)],[2,32603]),
[iquote('0:Rew:2.0,32603.0')] ).
cnf(39535,plain,
( ~ equal(zero,zero)
| ~ equal(divide(divide(divide(u,v),w),divide(divide(u,w),v)),zero)
| equal(divide(divide(u,v),w),divide(divide(u,w),v)) ),
inference(spl,[status(thm),theory(equality)],[32977,13]),
[iquote('0:SpL:32977.0,13.0')] ).
cnf(39938,plain,
( ~ equal(divide(divide(divide(u,v),w),divide(divide(u,w),v)),zero)
| equal(divide(divide(u,v),w),divide(divide(u,w),v)) ),
inference(obv,[status(thm),theory(equality)],[39535]),
[iquote('0:Obv:39535.0')] ).
cnf(39939,plain,
( ~ equal(zero,zero)
| equal(divide(divide(u,v),w),divide(divide(u,w),v)) ),
inference(rew,[status(thm),theory(equality)],[32977,39938]),
[iquote('0:Rew:32977.0,39938.0')] ).
cnf(39940,plain,
equal(divide(divide(u,v),w),divide(divide(u,w),v)),
inference(obv,[status(thm),theory(equality)],[39939]),
[iquote('0:Obv:39939.0')] ).
cnf(42030,plain,
equal(divide(divide(identity,u),divide(identity,divide(identity,v))),divide(divide(identity,v),u)),
inference(spr,[status(thm),theory(equality)],[7,39940]),
[iquote('0:SpR:7.0,39940.0')] ).
cnf(42322,plain,
~ equal(divide(divide(identity,a),divide(identity,divide(identity,b))),divide(divide(identity,a),b)),
inference(rew,[status(thm),theory(equality)],[42030,9]),
[iquote('0:Rew:42030.0,9.0')] ).
cnf(42352,plain,
~ equal(divide(divide(identity,b),a),divide(divide(identity,a),b)),
inference(rew,[status(thm),theory(equality)],[42030,42322]),
[iquote('0:Rew:42030.0,42322.0')] ).
cnf(42353,plain,
~ equal(divide(divide(identity,a),b),divide(divide(identity,a),b)),
inference(rew,[status(thm),theory(equality)],[39940,42352]),
[iquote('0:Rew:39940.0,42352.0')] ).
cnf(42354,plain,
$false,
inference(obv,[status(thm),theory(equality)],[42353]),
[iquote('0:Obv:42353.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : HEN011-5 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.06/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n024.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 : Fri Jul 1 13:43:30 EDT 2022
% 0.12/0.34 % CPUTime :
% 15.94/16.15
% 15.94/16.15 SPASS V 3.9
% 15.94/16.15 SPASS beiseite: Proof found.
% 15.94/16.15 % SZS status Theorem
% 15.94/16.15 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.94/16.15 SPASS derived 27235 clauses, backtracked 0 clauses, performed 0 splits and kept 2001 clauses.
% 15.94/16.15 SPASS allocated 92817 KBytes.
% 15.94/16.15 SPASS spent 0:0:14.22 on the problem.
% 15.94/16.15 0:00:00.04 for the input.
% 15.94/16.15 0:00:00.00 for the FLOTTER CNF translation.
% 15.94/16.15 0:00:00.17 for inferences.
% 15.94/16.15 0:00:00.00 for the backtracking.
% 15.94/16.15 0:0:13.98 for the reduction.
% 15.94/16.15
% 15.94/16.15
% 15.94/16.15 Here is a proof with depth 6, length 30 :
% 15.94/16.15 % SZS output start Refutation
% See solution above
% 15.94/16.15 Formulae used in the proof : x_divide_x_is_zero x_divide_zero_is_x property_of_divide1 property_of_divide3 one_inversion_equals_three prove_this quotient_smaller_than_numerator quotient_property divide_and_equal
% 15.94/16.15
%------------------------------------------------------------------------------