TSTP Solution File: HEN010-6 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HEN010-6 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n003.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 13:03:13 EDT 2022
% Result : Unsatisfiable 0.19s 0.43s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of clauses : 24 ( 16 unt; 0 nHn; 24 RR)
% Number of literals : 33 ( 0 equ; 12 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 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(3,axiom,
equal(divide(u,u),zero),
file('HEN010-6.p',unknown),
[] ).
cnf(5,axiom,
( ~ less_equal(divide(u,v),w)
| less_equal(divide(u,w),v) ),
file('HEN010-6.p',unknown),
[] ).
cnf(8,axiom,
equal(divide(identity,divide(identity,divide(identity,u))),divide(identity,u)),
file('HEN010-6.p',unknown),
[] ).
cnf(9,axiom,
~ equal(divide(divide(identity,a),divide(identity,divide(identity,a))),divide(identity,a)),
file('HEN010-6.p',unknown),
[] ).
cnf(11,axiom,
( ~ equal(divide(u,v),zero)
| less_equal(u,v) ),
file('HEN010-6.p',unknown),
[] ).
cnf(12,axiom,
less_equal(divide(u,v),u),
file('HEN010-6.p',unknown),
[] ).
cnf(13,axiom,
less_equal(divide(divide(u,v),divide(w,v)),divide(divide(u,w),v)),
file('HEN010-6.p',unknown),
[] ).
cnf(14,axiom,
less_equal(zero,u),
file('HEN010-6.p',unknown),
[] ).
cnf(15,axiom,
( ~ less_equal(u,v)
| ~ less_equal(v,u)
| equal(v,u) ),
file('HEN010-6.p',unknown),
[] ).
cnf(18,plain,
( ~ less_equal(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a))))
| ~ less_equal(divide(divide(identity,a),divide(identity,divide(identity,a))),divide(identity,a)) ),
inference(res,[status(thm),theory(equality)],[15,9]),
[iquote('0:Res:15.2,9.0')] ).
cnf(19,plain,
~ less_equal(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))),
inference(mrr,[status(thm)],[18,12]),
[iquote('0:MRR:18.1,12.0')] ).
cnf(40,plain,
( ~ equal(zero,zero)
| less_equal(u,u) ),
inference(spl,[status(thm),theory(equality)],[3,11]),
[iquote('0:SpL:3.0,11.0')] ).
cnf(44,plain,
less_equal(u,u),
inference(obv,[status(thm),theory(equality)],[40]),
[iquote('0:Obv:40.0')] ).
cnf(56,plain,
( ~ less_equal(u,zero)
| equal(u,zero) ),
inference(res,[status(thm),theory(equality)],[14,15]),
[iquote('0:Res:14.0,15.0')] ).
cnf(164,plain,
less_equal(divide(u,divide(u,v)),v),
inference(res,[status(thm),theory(equality)],[44,5]),
[iquote('0:Res:44.0,5.0')] ).
cnf(189,plain,
equal(divide(u,divide(u,zero)),zero),
inference(res,[status(thm),theory(equality)],[164,56]),
[iquote('0:Res:164.0,56.0')] ).
cnf(211,plain,
( ~ equal(zero,zero)
| less_equal(u,divide(u,zero)) ),
inference(spl,[status(thm),theory(equality)],[189,11]),
[iquote('0:SpL:189.0,11.0')] ).
cnf(213,plain,
less_equal(u,divide(u,zero)),
inference(obv,[status(thm),theory(equality)],[211]),
[iquote('0:Obv:211.0')] ).
cnf(220,plain,
( ~ less_equal(divide(u,zero),u)
| equal(divide(u,zero),u) ),
inference(res,[status(thm),theory(equality)],[213,15]),
[iquote('0:Res:213.0,15.0')] ).
cnf(222,plain,
equal(divide(u,zero),u),
inference(mrr,[status(thm)],[220,12]),
[iquote('0:MRR:220.0,12.0')] ).
cnf(242,plain,
less_equal(divide(divide(u,v),zero),divide(divide(u,v),v)),
inference(spr,[status(thm),theory(equality)],[3,13]),
[iquote('0:SpR:3.0,13.0')] ).
cnf(259,plain,
less_equal(divide(u,v),divide(divide(u,v),v)),
inference(rew,[status(thm),theory(equality)],[222,242]),
[iquote('0:Rew:222.0,242.0')] ).
cnf(464,plain,
less_equal(divide(identity,u),divide(divide(identity,u),divide(identity,divide(identity,u)))),
inference(spr,[status(thm),theory(equality)],[8,259]),
[iquote('0:SpR:8.0,259.0')] ).
cnf(480,plain,
$false,
inference(unc,[status(thm)],[464,19]),
[iquote('0:UnC:464.0,19.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : HEN010-6 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n003.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 14:23:22 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.19/0.43
% 0.19/0.43 SPASS V 3.9
% 0.19/0.43 SPASS beiseite: Proof found.
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.43 SPASS derived 381 clauses, backtracked 0 clauses, performed 0 splits and kept 113 clauses.
% 0.19/0.43 SPASS allocated 63398 KBytes.
% 0.19/0.43 SPASS spent 0:00:00.08 on the problem.
% 0.19/0.43 0:00:00.04 for the input.
% 0.19/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.43 0:00:00.00 for inferences.
% 0.19/0.43 0:00:00.00 for the backtracking.
% 0.19/0.43 0:00:00.02 for the reduction.
% 0.19/0.43
% 0.19/0.43
% 0.19/0.43 Here is a proof with depth 5, length 24 :
% 0.19/0.43 % SZS output start Refutation
% See solution above
% 0.19/0.43 Formulae used in the proof : x_divide_x_is_zero property_of_divide1 one_inversion_equals_three prove_property_of_inversion quotient_less_equal2 quotient_smaller_than_numerator quotient_property zero_is_smallest less_equal_and_equal
% 0.19/0.43
%------------------------------------------------------------------------------