%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HEN008-6 : 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 13:03:09 EDT 2022
% Result : Unsatisfiable 0.36s 0.55s
% Output : Refutation 0.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of clauses : 16 ( 7 unt; 0 nHn; 16 RR)
% Number of literals : 27 ( 0 equ; 13 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 : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
equal(divide(zero,u),zero),
file('HEN008-6.p',unknown),
[] ).
cnf(4,axiom,
less_equal(a,b),
file('HEN008-6.p',unknown),
[] ).
cnf(5,axiom,
~ less_equal(divide(a,c),divide(b,c)),
file('HEN008-6.p',unknown),
[] ).
cnf(6,axiom,
( ~ less_equal(u,v)
| equal(divide(u,v),zero) ),
file('HEN008-6.p',unknown),
[] ).
cnf(7,axiom,
( ~ equal(divide(u,v),zero)
| less_equal(u,v) ),
file('HEN008-6.p',unknown),
[] ).
cnf(9,axiom,
less_equal(divide(divide(u,v),divide(w,v)),divide(divide(u,w),v)),
file('HEN008-6.p',unknown),
[] ).
cnf(10,axiom,
less_equal(zero,u),
file('HEN008-6.p',unknown),
[] ).
cnf(11,axiom,
( ~ less_equal(u,v)
| ~ less_equal(v,u)
| equal(v,u) ),
file('HEN008-6.p',unknown),
[] ).
cnf(40,plain,
( ~ less_equal(u,zero)
| equal(u,zero) ),
inference(res,[status(thm),theory(equality)],[10,11]),
[iquote('0:Res:10.0,11.0')] ).
cnf(47,plain,
( ~ less_equal(u,v)
| less_equal(divide(divide(u,w),divide(v,w)),divide(zero,w)) ),
inference(spr,[status(thm),theory(equality)],[6,9]),
[iquote('0:SpR:6.1,9.0')] ).
cnf(69,plain,
( ~ less_equal(u,v)
| less_equal(divide(divide(u,w),divide(v,w)),zero) ),
inference(rew,[status(thm),theory(equality)],[2,47]),
[iquote('0:Rew:2.0,47.1')] ).
cnf(405,plain,
( ~ less_equal(u,v)
| equal(divide(divide(u,w),divide(v,w)),zero) ),
inference(res,[status(thm),theory(equality)],[69,40]),
[iquote('0:Res:69.1,40.0')] ).
cnf(987,plain,
( ~ less_equal(u,v)
| ~ equal(zero,zero)
| less_equal(divide(u,w),divide(v,w)) ),
inference(spl,[status(thm),theory(equality)],[405,7]),
[iquote('0:SpL:405.1,7.0')] ).
cnf(1008,plain,
( ~ less_equal(u,v)
| less_equal(divide(u,w),divide(v,w)) ),
inference(obv,[status(thm),theory(equality)],[987]),
[iquote('0:Obv:987.1')] ).
cnf(1780,plain,
~ less_equal(a,b),
inference(res,[status(thm),theory(equality)],[1008,5]),
[iquote('0:Res:1008.1,5.0')] ).
cnf(1782,plain,
$false,
inference(mrr,[status(thm)],[1780,4]),
[iquote('0:MRR:1780.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : HEN008-6 : 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 15:00:09 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.36/0.55
% 0.36/0.55 SPASS V 3.9
% 0.36/0.55 SPASS beiseite: Proof found.
% 0.36/0.55 % SZS status Theorem
% 0.36/0.55 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.36/0.55 SPASS derived 1230 clauses, backtracked 0 clauses, performed 0 splits and kept 249 clauses.
% 0.36/0.55 SPASS allocated 64336 KBytes.
% 0.36/0.55 SPASS spent 0:00:00.18 on the problem.
% 0.36/0.55 0:00:00.04 for the input.
% 0.36/0.55 0:00:00.00 for the FLOTTER CNF translation.
% 0.36/0.55 0:00:00.02 for inferences.
% 0.36/0.55 0:00:00.00 for the backtracking.
% 0.36/0.55 0:00:00.11 for the reduction.
% 0.36/0.55
% 0.36/0.55
% 0.36/0.55 Here is a proof with depth 4, length 16 :
% 0.36/0.55 % SZS output start Refutation
% See solution above
% 0.36/0.55 Formulae used in the proof : zero_divide_anything_is_zero a_LE_b prove_a_divide_c_LE_b_divide_c quotient_less_equal1 quotient_less_equal2 quotient_property zero_is_smallest less_equal_and_equal
% 0.36/0.55
%------------------------------------------------------------------------------