TSTP Solution File: HEN004-6 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HEN004-6 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 0.37s 0.60s
% Output : Refutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of clauses : 25 ( 14 unt; 0 nHn; 25 RR)
% Number of literals : 38 ( 0 equ; 16 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 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('HEN004-6.p',unknown),
[] ).
cnf(3,axiom,
~ equal(divide(a,zero),a),
file('HEN004-6.p',unknown),
[] ).
cnf(4,axiom,
( ~ less_equal(u,v)
| equal(divide(u,v),zero) ),
file('HEN004-6.p',unknown),
[] ).
cnf(5,axiom,
( ~ equal(divide(u,v),zero)
| less_equal(u,v) ),
file('HEN004-6.p',unknown),
[] ).
cnf(6,axiom,
less_equal(divide(u,v),u),
file('HEN004-6.p',unknown),
[] ).
cnf(7,axiom,
less_equal(divide(divide(u,v),divide(w,v)),divide(divide(u,w),v)),
file('HEN004-6.p',unknown),
[] ).
cnf(8,axiom,
less_equal(zero,u),
file('HEN004-6.p',unknown),
[] ).
cnf(9,axiom,
( ~ less_equal(u,v)
| ~ less_equal(v,u)
| equal(v,u) ),
file('HEN004-6.p',unknown),
[] ).
cnf(11,plain,
( ~ less_equal(divide(a,zero),a)
| ~ less_equal(a,divide(a,zero)) ),
inference(res,[status(thm),theory(equality)],[9,3]),
[iquote('0:Res:9.2,3.0')] ).
cnf(13,plain,
~ less_equal(a,divide(a,zero)),
inference(mrr,[status(thm)],[11,6]),
[iquote('0:MRR:11.0,6.0')] ).
cnf(31,plain,
( ~ less_equal(u,zero)
| equal(u,zero) ),
inference(res,[status(thm),theory(equality)],[8,9]),
[iquote('0:Res:8.0,9.0')] ).
cnf(49,plain,
less_equal(divide(divide(u,v),zero),divide(divide(u,zero),v)),
inference(spr,[status(thm),theory(equality)],[2,7]),
[iquote('0:SpR:2.0,7.0')] ).
cnf(116,plain,
( ~ less_equal(divide(u,zero),v)
| less_equal(divide(divide(u,v),zero),zero) ),
inference(spr,[status(thm),theory(equality)],[4,49]),
[iquote('0:SpR:4.1,49.0')] ).
cnf(696,plain,
( ~ less_equal(divide(u,zero),v)
| equal(divide(divide(u,v),zero),zero) ),
inference(res,[status(thm),theory(equality)],[116,31]),
[iquote('0:Res:116.1,31.0')] ).
cnf(2109,plain,
( ~ less_equal(divide(u,zero),v)
| ~ equal(zero,zero)
| less_equal(divide(u,v),zero) ),
inference(spl,[status(thm),theory(equality)],[696,5]),
[iquote('0:SpL:696.1,5.0')] ).
cnf(2134,plain,
( ~ less_equal(divide(u,zero),v)
| less_equal(divide(u,v),zero) ),
inference(obv,[status(thm),theory(equality)],[2109]),
[iquote('0:Obv:2109.1')] ).
cnf(2176,plain,
less_equal(divide(u,u),zero),
inference(res,[status(thm),theory(equality)],[6,2134]),
[iquote('0:Res:6.0,2134.0')] ).
cnf(2201,plain,
equal(divide(u,u),zero),
inference(res,[status(thm),theory(equality)],[2176,31]),
[iquote('0:Res:2176.0,31.0')] ).
cnf(2257,plain,
( ~ equal(zero,zero)
| less_equal(u,u) ),
inference(spl,[status(thm),theory(equality)],[2201,5]),
[iquote('0:SpL:2201.0,5.0')] ).
cnf(2281,plain,
less_equal(u,u),
inference(obv,[status(thm),theory(equality)],[2257]),
[iquote('0:Obv:2257.0')] ).
cnf(2324,plain,
less_equal(divide(u,divide(u,zero)),zero),
inference(res,[status(thm),theory(equality)],[2281,2134]),
[iquote('0:Res:2281.0,2134.0')] ).
cnf(2467,plain,
equal(divide(u,divide(u,zero)),zero),
inference(res,[status(thm),theory(equality)],[2324,31]),
[iquote('0:Res:2324.0,31.0')] ).
cnf(2533,plain,
( ~ equal(zero,zero)
| less_equal(u,divide(u,zero)) ),
inference(spl,[status(thm),theory(equality)],[2467,5]),
[iquote('0:SpL:2467.0,5.0')] ).
cnf(2553,plain,
less_equal(u,divide(u,zero)),
inference(obv,[status(thm),theory(equality)],[2533]),
[iquote('0:Obv:2533.0')] ).
cnf(2554,plain,
$false,
inference(unc,[status(thm)],[2553,13]),
[iquote('0:UnC:2553.0,13.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : HEN004-6 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jul 1 13:38:45 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.37/0.60
% 0.37/0.60 SPASS V 3.9
% 0.37/0.60 SPASS beiseite: Proof found.
% 0.37/0.60 % SZS status Theorem
% 0.37/0.60 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.37/0.60 SPASS derived 1728 clauses, backtracked 0 clauses, performed 0 splits and kept 331 clauses.
% 0.37/0.60 SPASS allocated 64886 KBytes.
% 0.37/0.60 SPASS spent 0:00:00.25 on the problem.
% 0.37/0.60 0:00:00.04 for the input.
% 0.37/0.60 0:00:00.00 for the FLOTTER CNF translation.
% 0.37/0.60 0:00:00.02 for inferences.
% 0.37/0.60 0:00:00.00 for the backtracking.
% 0.37/0.60 0:00:00.17 for the reduction.
% 0.37/0.60
% 0.37/0.60
% 0.37/0.60 Here is a proof with depth 10, length 25 :
% 0.37/0.60 % SZS output start Refutation
% See solution above
% 0.37/0.60 Formulae used in the proof : zero_divide_anything_is_zero prove_x_divide_zero_is_x quotient_less_equal1 quotient_less_equal2 quotient_smaller_than_numerator quotient_property zero_is_smallest less_equal_and_equal
% 0.37/0.60
%------------------------------------------------------------------------------