TSTP Solution File: HEN009-5 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HEN009-5 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 13:03:11 EDT 2022
% Result : Unsatisfiable 9.52s 9.76s
% Output : Refutation 9.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of clauses : 21 ( 8 unt; 0 nHn; 21 RR)
% Number of literals : 40 ( 0 equ; 20 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ equal(divide(divide(u,v),w),zero)
| equal(divide(divide(u,w),v),zero) ),
file('HEN009-5.p',unknown),
[] ).
cnf(3,axiom,
( ~ equal(divide(u,v),zero)
| equal(divide(divide(w,v),divide(w,u)),zero) ),
file('HEN009-5.p',unknown),
[] ).
cnf(4,axiom,
~ equal(divide(identity,divide(identity,divide(identity,a))),divide(identity,a)),
file('HEN009-5.p',unknown),
[] ).
cnf(5,axiom,
equal(divide(divide(u,v),u),zero),
file('HEN009-5.p',unknown),
[] ).
cnf(7,axiom,
equal(divide(zero,u),zero),
file('HEN009-5.p',unknown),
[] ).
cnf(8,axiom,
( ~ equal(divide(u,v),zero)
| ~ equal(divide(v,u),zero)
| equal(v,u) ),
file('HEN009-5.p',unknown),
[] ).
cnf(20,plain,
( ~ equal(zero,zero)
| ~ equal(divide(u,zero),zero)
| equal(u,zero) ),
inference(spl,[status(thm),theory(equality)],[7,8]),
[iquote('0:SpL:7.0,8.0')] ).
cnf(23,plain,
( ~ equal(divide(u,zero),zero)
| equal(u,zero) ),
inference(obv,[status(thm),theory(equality)],[20]),
[iquote('0:Obv:20.0')] ).
cnf(47,plain,
( ~ equal(divide(u,v),zero)
| ~ equal(zero,zero)
| ~ equal(divide(divide(w,u),divide(w,v)),zero)
| equal(divide(w,u),divide(w,v)) ),
inference(spl,[status(thm),theory(equality)],[3,8]),
[iquote('0:SpL:3.1,8.0')] ).
cnf(50,plain,
( ~ equal(divide(u,v),zero)
| ~ equal(divide(divide(w,u),divide(w,v)),zero)
| equal(divide(w,u),divide(w,v)) ),
inference(obv,[status(thm),theory(equality)],[47]),
[iquote('0:Obv:47.1')] ).
cnf(55,plain,
( ~ equal(zero,zero)
| equal(divide(divide(u,u),v),zero) ),
inference(spl,[status(thm),theory(equality)],[5,2]),
[iquote('0:SpL:5.0,2.0')] ).
cnf(58,plain,
equal(divide(divide(u,u),v),zero),
inference(obv,[status(thm),theory(equality)],[55]),
[iquote('0:Obv:55.0')] ).
cnf(81,plain,
( ~ equal(zero,zero)
| equal(divide(u,u),zero) ),
inference(spl,[status(thm),theory(equality)],[58,23]),
[iquote('0:SpL:58.0,23.0')] ).
cnf(84,plain,
equal(divide(u,u),zero),
inference(obv,[status(thm),theory(equality)],[81]),
[iquote('0:Obv:81.0')] ).
cnf(110,plain,
( ~ equal(zero,zero)
| equal(divide(divide(u,divide(u,v)),v),zero) ),
inference(spl,[status(thm),theory(equality)],[84,2]),
[iquote('0:SpL:84.0,2.0')] ).
cnf(112,plain,
equal(divide(divide(u,divide(u,v)),v),zero),
inference(obv,[status(thm),theory(equality)],[110]),
[iquote('0:Obv:110.0')] ).
cnf(28763,plain,
( ~ equal(divide(divide(u,divide(u,v)),v),zero)
| ~ equal(zero,zero)
| equal(divide(u,divide(u,divide(u,v))),divide(u,v)) ),
inference(spl,[status(thm),theory(equality)],[112,50]),
[iquote('0:SpL:112.0,50.1')] ).
cnf(28819,plain,
( ~ equal(divide(divide(u,divide(u,v)),v),zero)
| equal(divide(u,divide(u,divide(u,v))),divide(u,v)) ),
inference(obv,[status(thm),theory(equality)],[28763]),
[iquote('0:Obv:28763.1')] ).
cnf(28820,plain,
( ~ equal(zero,zero)
| equal(divide(u,divide(u,divide(u,v))),divide(u,v)) ),
inference(rew,[status(thm),theory(equality)],[112,28819]),
[iquote('0:Rew:112.0,28819.0')] ).
cnf(28821,plain,
equal(divide(u,divide(u,divide(u,v))),divide(u,v)),
inference(obv,[status(thm),theory(equality)],[28820]),
[iquote('0:Obv:28820.0')] ).
cnf(28822,plain,
$false,
inference(unc,[status(thm)],[28821,4]),
[iquote('0:UnC:28821.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : HEN009-5 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.09/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n009.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 : Fri Jul 1 13:11:52 EDT 2022
% 0.13/0.33 % CPUTime :
% 9.52/9.76
% 9.52/9.76 SPASS V 3.9
% 9.52/9.76 SPASS beiseite: Proof found.
% 9.52/9.76 % SZS status Theorem
% 9.52/9.76 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.52/9.76 SPASS derived 17779 clauses, backtracked 0 clauses, performed 0 splits and kept 1611 clauses.
% 9.52/9.76 SPASS allocated 86311 KBytes.
% 9.52/9.76 SPASS spent 0:00:08.63 on the problem.
% 9.52/9.76 0:00:00.04 for the input.
% 9.52/9.76 0:00:00.00 for the FLOTTER CNF translation.
% 9.52/9.76 0:00:00.12 for inferences.
% 9.52/9.76 0:00:00.00 for the backtracking.
% 9.52/9.76 0:00:08.45 for the reduction.
% 9.52/9.76
% 9.52/9.76
% 9.52/9.76 Here is a proof with depth 4, length 21 :
% 9.52/9.76 % SZS output start Refutation
% See solution above
% 9.52/9.76 Formulae used in the proof : property_of_divide1 property_of_divide2 prove_this quotient_smaller_than_numerator zero_is_smallest divide_and_equal
% 9.52/9.76
%------------------------------------------------------------------------------