%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HEN003-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 0.18s 0.39s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% 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(1,axiom,
~ equal(divide(a,a),zero),
file('HEN003-3.p',unknown),
[] ).
cnf(2,axiom,
( ~ less_equal(u,v)
| equal(divide(u,v),zero) ),
file('HEN003-3.p',unknown),
[] ).
cnf(3,axiom,
( ~ equal(divide(u,v),zero)
| less_equal(u,v) ),
file('HEN003-3.p',unknown),
[] ).
cnf(4,axiom,
less_equal(divide(u,v),u),
file('HEN003-3.p',unknown),
[] ).
cnf(5,axiom,
less_equal(divide(divide(u,v),divide(w,v)),divide(divide(u,w),v)),
file('HEN003-3.p',unknown),
[] ).
cnf(6,axiom,
less_equal(zero,u),
file('HEN003-3.p',unknown),
[] ).
cnf(7,axiom,
( ~ less_equal(u,v)
| ~ less_equal(v,u)
| equal(v,u) ),
file('HEN003-3.p',unknown),
[] ).
cnf(10,plain,
( ~ less_equal(divide(a,a),zero)
| ~ less_equal(zero,divide(a,a)) ),
inference(res,[status(thm),theory(equality)],[7,1]),
[iquote('0:Res:7.2,1.0')] ).
cnf(12,plain,
~ less_equal(divide(a,a),zero),
inference(mrr,[status(thm)],[10,6]),
[iquote('0:MRR:10.1,6.0')] ).
cnf(19,plain,
( ~ less_equal(u,zero)
| equal(u,zero) ),
inference(res,[status(thm),theory(equality)],[6,7]),
[iquote('0:Res:6.0,7.0')] ).
cnf(29,plain,
equal(divide(zero,u),zero),
inference(res,[status(thm),theory(equality)],[4,19]),
[iquote('0:Res:4.0,19.0')] ).
cnf(36,plain,
less_equal(divide(divide(u,v),zero),divide(divide(u,zero),v)),
inference(spr,[status(thm),theory(equality)],[29,5]),
[iquote('0:SpR:29.0,5.0')] ).
cnf(44,plain,
( ~ less_equal(divide(u,zero),v)
| less_equal(divide(divide(u,v),zero),zero) ),
inference(spr,[status(thm),theory(equality)],[2,36]),
[iquote('0:SpR:2.1,36.0')] ).
cnf(205,plain,
( ~ less_equal(divide(u,zero),v)
| equal(divide(divide(u,v),zero),zero) ),
inference(res,[status(thm),theory(equality)],[44,19]),
[iquote('0:Res:44.1,19.0')] ).
cnf(242,plain,
( ~ less_equal(divide(u,zero),v)
| ~ equal(zero,zero)
| less_equal(divide(u,v),zero) ),
inference(spl,[status(thm),theory(equality)],[205,3]),
[iquote('0:SpL:205.1,3.0')] ).
cnf(245,plain,
( ~ less_equal(divide(u,zero),v)
| less_equal(divide(u,v),zero) ),
inference(obv,[status(thm),theory(equality)],[242]),
[iquote('0:Obv:242.1')] ).
cnf(279,plain,
less_equal(divide(u,u),zero),
inference(res,[status(thm),theory(equality)],[4,245]),
[iquote('0:Res:4.0,245.0')] ).
cnf(283,plain,
$false,
inference(unc,[status(thm)],[279,12]),
[iquote('0:UnC:279.0,12.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : HEN003-3 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n017.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 13:42:24 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.39
% 0.18/0.39 SPASS V 3.9
% 0.18/0.39 SPASS beiseite: Proof found.
% 0.18/0.39 % SZS status Theorem
% 0.18/0.39 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.39 SPASS derived 211 clauses, backtracked 0 clauses, performed 0 splits and kept 63 clauses.
% 0.18/0.39 SPASS allocated 63278 KBytes.
% 0.18/0.39 SPASS spent 0:00:00.04 on the problem.
% 0.18/0.39 0:00:00.02 for the input.
% 0.18/0.39 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.39 0:00:00.00 for inferences.
% 0.18/0.39 0:00:00.00 for the backtracking.
% 0.18/0.39 0:00:00.00 for the reduction.
% 0.18/0.39
% 0.18/0.39
% 0.18/0.39 Here is a proof with depth 7, length 18 :
% 0.18/0.39 % SZS output start Refutation
% See solution above
% 0.18/0.39 Formulae used in the proof : 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
% 0.18/0.39
%------------------------------------------------------------------------------