TSTP Solution File: HEN003-4 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HEN003-4 : 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 13:02:59 EDT 2022
% Result : Unsatisfiable 0.40s 0.60s
% Output : Refutation 0.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of clauses : 18 ( 9 unt; 0 nHn; 18 RR)
% Number of literals : 29 ( 0 equ; 14 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('HEN003-4.p',unknown),
[] ).
cnf(3,axiom,
~ equal(divide(a,a),zero),
file('HEN003-4.p',unknown),
[] ).
cnf(4,axiom,
( ~ less_equal(u,v)
| equal(divide(u,v),zero) ),
file('HEN003-4.p',unknown),
[] ).
cnf(5,axiom,
( ~ equal(divide(u,v),zero)
| less_equal(u,v) ),
file('HEN003-4.p',unknown),
[] ).
cnf(6,axiom,
less_equal(divide(u,v),u),
file('HEN003-4.p',unknown),
[] ).
cnf(7,axiom,
less_equal(divide(divide(u,v),divide(w,v)),divide(divide(u,w),v)),
file('HEN003-4.p',unknown),
[] ).
cnf(8,axiom,
less_equal(zero,u),
file('HEN003-4.p',unknown),
[] ).
cnf(9,axiom,
( ~ less_equal(u,v)
| ~ less_equal(v,u)
| equal(v,u) ),
file('HEN003-4.p',unknown),
[] ).
cnf(12,plain,
( ~ less_equal(divide(a,a),zero)
| ~ less_equal(zero,divide(a,a)) ),
inference(res,[status(thm),theory(equality)],[9,3]),
[iquote('0:Res:9.2,3.0')] ).
cnf(14,plain,
~ less_equal(divide(a,a),zero),
inference(mrr,[status(thm)],[12,8]),
[iquote('0:MRR:12.1,8.0')] ).
cnf(32,plain,
( ~ less_equal(u,zero)
| equal(u,zero) ),
inference(res,[status(thm),theory(equality)],[8,9]),
[iquote('0:Res:8.0,9.0')] ).
cnf(50,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(118,plain,
( ~ less_equal(divide(u,zero),v)
| less_equal(divide(divide(u,v),zero),zero) ),
inference(spr,[status(thm),theory(equality)],[4,50]),
[iquote('0:SpR:4.1,50.0')] ).
cnf(752,plain,
( ~ less_equal(divide(u,zero),v)
| equal(divide(divide(u,v),zero),zero) ),
inference(res,[status(thm),theory(equality)],[118,32]),
[iquote('0:Res:118.1,32.0')] ).
cnf(2108,plain,
( ~ less_equal(divide(u,zero),v)
| ~ equal(zero,zero)
| less_equal(divide(u,v),zero) ),
inference(spl,[status(thm),theory(equality)],[752,5]),
[iquote('0:SpL:752.1,5.0')] ).
cnf(2133,plain,
( ~ less_equal(divide(u,zero),v)
| less_equal(divide(u,v),zero) ),
inference(obv,[status(thm),theory(equality)],[2108]),
[iquote('0:Obv:2108.1')] ).
cnf(2175,plain,
less_equal(divide(u,u),zero),
inference(res,[status(thm),theory(equality)],[6,2133]),
[iquote('0:Res:6.0,2133.0')] ).
cnf(2181,plain,
$false,
inference(unc,[status(thm)],[2175,14]),
[iquote('0:UnC:2175.0,14.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : HEN003-4 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n013.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Fri Jul 1 12:59:14 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.40/0.60
% 0.40/0.60 SPASS V 3.9
% 0.40/0.60 SPASS beiseite: Proof found.
% 0.40/0.60 % SZS status Theorem
% 0.40/0.60 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.40/0.60 SPASS derived 1446 clauses, backtracked 0 clauses, performed 0 splits and kept 283 clauses.
% 0.40/0.60 SPASS allocated 64652 KBytes.
% 0.40/0.60 SPASS spent 0:00:00.24 on the problem.
% 0.40/0.60 0:00:00.04 for the input.
% 0.40/0.60 0:00:00.00 for the FLOTTER CNF translation.
% 0.40/0.60 0:00:00.02 for inferences.
% 0.40/0.60 0:00:00.00 for the backtracking.
% 0.40/0.60 0:00:00.16 for the reduction.
% 0.40/0.60
% 0.40/0.60
% 0.40/0.60 Here is a proof with depth 5, length 18 :
% 0.40/0.60 % SZS output start Refutation
% See solution above
% 0.40/0.60 Formulae used in the proof : zero_divide_anything_is_zero prove_x_divide_x_is_zero quotient_less_equal1 quotient_less_equal2 quotient_smaller_than_numerator quotient_property zero_is_smallest less_equal_and_equal
% 0.40/0.60
%------------------------------------------------------------------------------