TSTP Solution File: HEN012-3 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HEN012-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n013.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 13:03:16 EDT 2022
% Result : Unsatisfiable 0.19s 0.43s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of clauses : 18 ( 10 unt; 0 nHn; 18 RR)
% Number of literals : 28 ( 0 equ; 12 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(1,axiom,
~ less_equal(a,a),
file('HEN012-3.p',unknown),
[] ).
cnf(2,axiom,
( ~ less_equal(u,v)
| equal(divide(u,v),zero) ),
file('HEN012-3.p',unknown),
[] ).
cnf(3,axiom,
( ~ equal(divide(u,v),zero)
| less_equal(u,v) ),
file('HEN012-3.p',unknown),
[] ).
cnf(4,axiom,
less_equal(divide(u,v),u),
file('HEN012-3.p',unknown),
[] ).
cnf(5,axiom,
less_equal(divide(divide(u,v),divide(w,v)),divide(divide(u,w),v)),
file('HEN012-3.p',unknown),
[] ).
cnf(6,axiom,
less_equal(zero,u),
file('HEN012-3.p',unknown),
[] ).
cnf(7,axiom,
( ~ less_equal(u,v)
| ~ less_equal(v,u)
| equal(v,u) ),
file('HEN012-3.p',unknown),
[] ).
cnf(9,plain,
~ equal(divide(a,a),zero),
inference(res,[status(thm),theory(equality)],[3,1]),
[iquote('0:Res:3.1,1.0')] ).
cnf(15,plain,
( ~ less_equal(u,zero)
| equal(u,zero) ),
inference(res,[status(thm),theory(equality)],[6,7]),
[iquote('0:Res:6.0,7.0')] ).
cnf(19,plain,
equal(divide(zero,u),zero),
inference(res,[status(thm),theory(equality)],[4,15]),
[iquote('0:Res:4.0,15.0')] ).
cnf(32,plain,
less_equal(divide(divide(u,v),zero),divide(divide(u,zero),v)),
inference(spr,[status(thm),theory(equality)],[19,5]),
[iquote('0:SpR:19.0,5.0')] ).
cnf(40,plain,
( ~ less_equal(divide(u,zero),v)
| less_equal(divide(divide(u,v),zero),zero) ),
inference(spr,[status(thm),theory(equality)],[2,32]),
[iquote('0:SpR:2.1,32.0')] ).
cnf(202,plain,
( ~ less_equal(divide(u,zero),v)
| equal(divide(divide(u,v),zero),zero) ),
inference(res,[status(thm),theory(equality)],[40,15]),
[iquote('0:Res:40.1,15.0')] ).
cnf(239,plain,
( ~ less_equal(divide(u,zero),v)
| ~ equal(zero,zero)
| less_equal(divide(u,v),zero) ),
inference(spl,[status(thm),theory(equality)],[202,3]),
[iquote('0:SpL:202.1,3.0')] ).
cnf(242,plain,
( ~ less_equal(divide(u,zero),v)
| less_equal(divide(u,v),zero) ),
inference(obv,[status(thm),theory(equality)],[239]),
[iquote('0:Obv:239.1')] ).
cnf(252,plain,
less_equal(divide(u,u),zero),
inference(res,[status(thm),theory(equality)],[4,242]),
[iquote('0:Res:4.0,242.0')] ).
cnf(323,plain,
equal(divide(u,u),zero),
inference(res,[status(thm),theory(equality)],[252,15]),
[iquote('0:Res:252.0,15.0')] ).
cnf(326,plain,
$false,
inference(unc,[status(thm)],[323,9]),
[iquote('0:UnC:323.0,9.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : HEN012-3 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Fri Jul 1 12:56:44 EDT 2022
% 0.13/0.35 % 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 240 clauses, backtracked 0 clauses, performed 0 splits and kept 68 clauses.
% 0.19/0.43 SPASS allocated 63303 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 0:00:00.01 for the reduction.
% 0.19/0.43
% 0.19/0.43
% 0.19/0.43 Here is a proof with depth 8, length 18 :
% 0.19/0.43 % SZS output start Refutation
% See solution above
% 0.19/0.43 Formulae used in the proof : prove_a_LE_a quotient_less_equal1 quotient_less_equal2 quotient_smaller_than_numerator quotient_property zero_is_smallest less_equal_and_equal
% 0.19/0.43
%------------------------------------------------------------------------------