TSTP Solution File: HEN004-4 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HEN004-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 13:03:01 EDT 2022
% Result : Unsatisfiable 0.21s 0.44s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of clauses : 20 ( 14 unt; 0 nHn; 20 RR)
% Number of literals : 27 ( 0 equ; 10 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 : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
equal(divide(zero,u),zero),
file('HEN004-4.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(u,u),zero),
file('HEN004-4.p',unknown),
[] ).
cnf(4,axiom,
~ equal(divide(a,zero),a),
file('HEN004-4.p',unknown),
[] ).
cnf(6,axiom,
( ~ equal(divide(u,v),zero)
| less_equal(u,v) ),
file('HEN004-4.p',unknown),
[] ).
cnf(7,axiom,
less_equal(divide(u,v),u),
file('HEN004-4.p',unknown),
[] ).
cnf(8,axiom,
less_equal(divide(divide(u,v),divide(w,v)),divide(divide(u,w),v)),
file('HEN004-4.p',unknown),
[] ).
cnf(9,axiom,
less_equal(zero,u),
file('HEN004-4.p',unknown),
[] ).
cnf(10,axiom,
( ~ less_equal(u,v)
| ~ less_equal(v,u)
| equal(v,u) ),
file('HEN004-4.p',unknown),
[] ).
cnf(12,plain,
( ~ less_equal(divide(a,zero),a)
| ~ less_equal(a,divide(a,zero)) ),
inference(res,[status(thm),theory(equality)],[10,4]),
[iquote('0:Res:10.2,4.0')] ).
cnf(14,plain,
~ less_equal(a,divide(a,zero)),
inference(mrr,[status(thm)],[12,7]),
[iquote('0:MRR:12.0,7.0')] ).
cnf(39,plain,
( ~ less_equal(u,zero)
| equal(u,zero) ),
inference(res,[status(thm),theory(equality)],[9,10]),
[iquote('0:Res:9.0,10.0')] ).
cnf(53,plain,
less_equal(divide(divide(u,v),zero),divide(divide(u,zero),v)),
inference(spr,[status(thm),theory(equality)],[2,8]),
[iquote('0:SpR:2.0,8.0')] ).
cnf(128,plain,
less_equal(divide(divide(u,divide(u,zero)),zero),zero),
inference(spr,[status(thm),theory(equality)],[3,53]),
[iquote('0:SpR:3.0,53.0')] ).
cnf(370,plain,
equal(divide(divide(u,divide(u,zero)),zero),zero),
inference(res,[status(thm),theory(equality)],[128,39]),
[iquote('0:Res:128.0,39.0')] ).
cnf(398,plain,
( ~ equal(zero,zero)
| less_equal(divide(u,divide(u,zero)),zero) ),
inference(spl,[status(thm),theory(equality)],[370,6]),
[iquote('0:SpL:370.0,6.0')] ).
cnf(405,plain,
less_equal(divide(u,divide(u,zero)),zero),
inference(obv,[status(thm),theory(equality)],[398]),
[iquote('0:Obv:398.0')] ).
cnf(420,plain,
equal(divide(u,divide(u,zero)),zero),
inference(res,[status(thm),theory(equality)],[405,39]),
[iquote('0:Res:405.0,39.0')] ).
cnf(450,plain,
( ~ equal(zero,zero)
| less_equal(u,divide(u,zero)) ),
inference(spl,[status(thm),theory(equality)],[420,6]),
[iquote('0:SpL:420.0,6.0')] ).
cnf(455,plain,
less_equal(u,divide(u,zero)),
inference(obv,[status(thm),theory(equality)],[450]),
[iquote('0:Obv:450.0')] ).
cnf(456,plain,
$false,
inference(unc,[status(thm)],[455,14]),
[iquote('0:UnC:455.0,14.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : HEN004-4 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n029.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 : Fri Jul 1 15:03:09 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.21/0.44
% 0.21/0.44 SPASS V 3.9
% 0.21/0.44 SPASS beiseite: Proof found.
% 0.21/0.44 % SZS status Theorem
% 0.21/0.44 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.44 SPASS derived 336 clauses, backtracked 0 clauses, performed 0 splits and kept 71 clauses.
% 0.21/0.44 SPASS allocated 63380 KBytes.
% 0.21/0.44 SPASS spent 0:00:00.07 on the problem.
% 0.21/0.44 0:00:00.03 for the input.
% 0.21/0.44 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.44 0:00:00.00 for inferences.
% 0.21/0.44 0:00:00.00 for the backtracking.
% 0.21/0.44 0:00:00.01 for the reduction.
% 0.21/0.44
% 0.21/0.44
% 0.21/0.44 Here is a proof with depth 6, length 20 :
% 0.21/0.44 % SZS output start Refutation
% See solution above
% 0.21/0.44 Formulae used in the proof : zero_divide_anything_is_zero x_divide_x_is_zero prove_x_divide_zero_is_x quotient_less_equal2 quotient_smaller_than_numerator quotient_property zero_is_smallest less_equal_and_equal
% 0.21/0.44
%------------------------------------------------------------------------------