%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HEN005-6 : 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 13:03:03 EDT 2022
% Result : Unsatisfiable 0.47s 0.70s
% Output : Refutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 10
% Syntax : Number of clauses : 36 ( 18 unt; 0 nHn; 36 RR)
% Number of literals : 58 ( 0 equ; 26 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('HEN005-6.p',unknown),
[] ).
cnf(3,axiom,
less_equal(a,b),
file('HEN005-6.p',unknown),
[] ).
cnf(4,axiom,
less_equal(b,c),
file('HEN005-6.p',unknown),
[] ).
cnf(5,axiom,
~ less_equal(a,c),
file('HEN005-6.p',unknown),
[] ).
cnf(6,axiom,
( ~ less_equal(u,v)
| equal(divide(u,v),zero) ),
file('HEN005-6.p',unknown),
[] ).
cnf(7,axiom,
( ~ equal(divide(u,v),zero)
| less_equal(u,v) ),
file('HEN005-6.p',unknown),
[] ).
cnf(8,axiom,
less_equal(divide(u,v),u),
file('HEN005-6.p',unknown),
[] ).
cnf(9,axiom,
less_equal(divide(divide(u,v),divide(w,v)),divide(divide(u,w),v)),
file('HEN005-6.p',unknown),
[] ).
cnf(10,axiom,
less_equal(zero,u),
file('HEN005-6.p',unknown),
[] ).
cnf(11,axiom,
( ~ less_equal(u,v)
| ~ less_equal(v,u)
| equal(v,u) ),
file('HEN005-6.p',unknown),
[] ).
cnf(13,plain,
~ equal(divide(a,c),zero),
inference(res,[status(thm),theory(equality)],[7,5]),
[iquote('0:Res:7.1,5.0')] ).
cnf(32,plain,
( ~ less_equal(u,zero)
| equal(u,zero) ),
inference(res,[status(thm),theory(equality)],[10,11]),
[iquote('0:Res:10.0,11.0')] ).
cnf(33,plain,
( ~ less_equal(u,divide(u,v))
| equal(divide(u,v),u) ),
inference(res,[status(thm),theory(equality)],[8,11]),
[iquote('0:Res:8.0,11.0')] ).
cnf(37,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(40,plain,
less_equal(divide(divide(u,v),zero),divide(divide(u,zero),v)),
inference(spr,[status(thm),theory(equality)],[2,9]),
[iquote('0:SpR:2.0,9.0')] ).
cnf(53,plain,
( ~ less_equal(u,v)
| less_equal(divide(divide(u,w),divide(v,w)),zero) ),
inference(rew,[status(thm),theory(equality)],[2,37]),
[iquote('0:Rew:2.0,37.1')] ).
cnf(91,plain,
( ~ less_equal(divide(u,zero),v)
| less_equal(divide(divide(u,v),zero),zero) ),
inference(spr,[status(thm),theory(equality)],[6,40]),
[iquote('0:SpR:6.1,40.0')] ).
cnf(235,plain,
( ~ less_equal(u,v)
| equal(divide(divide(u,w),divide(v,w)),zero) ),
inference(res,[status(thm),theory(equality)],[53,32]),
[iquote('0:Res:53.1,32.0')] ).
cnf(732,plain,
( ~ less_equal(divide(u,zero),v)
| equal(divide(divide(u,v),zero),zero) ),
inference(res,[status(thm),theory(equality)],[91,32]),
[iquote('0:Res:91.1,32.0')] ).
cnf(919,plain,
( ~ less_equal(u,v)
| ~ less_equal(w,u)
| equal(divide(divide(w,v),zero),zero) ),
inference(spr,[status(thm),theory(equality)],[6,235]),
[iquote('0:SpR:6.1,235.1')] ).
cnf(2036,plain,
( ~ less_equal(divide(u,zero),v)
| ~ equal(zero,zero)
| less_equal(divide(u,v),zero) ),
inference(spl,[status(thm),theory(equality)],[732,7]),
[iquote('0:SpL:732.1,7.0')] ).
cnf(2061,plain,
( ~ less_equal(divide(u,zero),v)
| less_equal(divide(u,v),zero) ),
inference(obv,[status(thm),theory(equality)],[2036]),
[iquote('0:Obv:2036.1')] ).
cnf(2102,plain,
less_equal(divide(u,u),zero),
inference(res,[status(thm),theory(equality)],[8,2061]),
[iquote('0:Res:8.0,2061.0')] ).
cnf(2128,plain,
equal(divide(u,u),zero),
inference(res,[status(thm),theory(equality)],[2102,32]),
[iquote('0:Res:2102.0,32.0')] ).
cnf(2184,plain,
( ~ equal(zero,zero)
| less_equal(u,u) ),
inference(spl,[status(thm),theory(equality)],[2128,7]),
[iquote('0:SpL:2128.0,7.0')] ).
cnf(2208,plain,
less_equal(u,u),
inference(obv,[status(thm),theory(equality)],[2184]),
[iquote('0:Obv:2184.0')] ).
cnf(2251,plain,
less_equal(divide(u,divide(u,zero)),zero),
inference(res,[status(thm),theory(equality)],[2208,2061]),
[iquote('0:Res:2208.0,2061.0')] ).
cnf(2390,plain,
equal(divide(u,divide(u,zero)),zero),
inference(res,[status(thm),theory(equality)],[2251,32]),
[iquote('0:Res:2251.0,32.0')] ).
cnf(2454,plain,
( ~ equal(zero,zero)
| less_equal(u,divide(u,zero)) ),
inference(spl,[status(thm),theory(equality)],[2390,7]),
[iquote('0:SpL:2390.0,7.0')] ).
cnf(2473,plain,
less_equal(u,divide(u,zero)),
inference(obv,[status(thm),theory(equality)],[2454]),
[iquote('0:Obv:2454.0')] ).
cnf(2518,plain,
equal(divide(u,zero),u),
inference(res,[status(thm),theory(equality)],[2473,33]),
[iquote('0:Res:2473.0,33.0')] ).
cnf(2632,plain,
( ~ less_equal(u,v)
| ~ less_equal(w,u)
| equal(divide(w,v),zero) ),
inference(rew,[status(thm),theory(equality)],[2518,919]),
[iquote('0:Rew:2518.0,919.2')] ).
cnf(3658,plain,
( ~ less_equal(u,b)
| equal(divide(u,c),zero) ),
inference(res,[status(thm),theory(equality)],[4,2632]),
[iquote('0:Res:4.0,2632.0')] ).
cnf(3716,plain,
( ~ less_equal(a,b)
| ~ equal(zero,zero) ),
inference(spl,[status(thm),theory(equality)],[3658,13]),
[iquote('0:SpL:3658.1,13.0')] ).
cnf(3720,plain,
~ less_equal(a,b),
inference(obv,[status(thm),theory(equality)],[3716]),
[iquote('0:Obv:3716.1')] ).
cnf(3721,plain,
$false,
inference(mrr,[status(thm)],[3720,3]),
[iquote('0:MRR:3720.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : HEN005-6 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n020.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 14:22:15 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.47/0.70
% 0.47/0.70 SPASS V 3.9
% 0.47/0.70 SPASS beiseite: Proof found.
% 0.47/0.70 % SZS status Theorem
% 0.47/0.70 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.47/0.70 SPASS derived 2524 clauses, backtracked 0 clauses, performed 0 splits and kept 480 clauses.
% 0.47/0.70 SPASS allocated 65596 KBytes.
% 0.47/0.70 SPASS spent 0:00:00.33 on the problem.
% 0.47/0.70 0:00:00.03 for the input.
% 0.47/0.70 0:00:00.00 for the FLOTTER CNF translation.
% 0.47/0.70 0:00:00.03 for inferences.
% 0.47/0.70 0:00:00.00 for the backtracking.
% 0.47/0.70 0:00:00.24 for the reduction.
% 0.47/0.70
% 0.47/0.70
% 0.47/0.70 Here is a proof with depth 11, length 36 :
% 0.47/0.70 % SZS output start Refutation
% See solution above
% 0.47/0.70 Formulae used in the proof : zero_divide_anything_is_zero a_LE_b b_LE_c prove_a_LE_c quotient_less_equal1 quotient_less_equal2 quotient_smaller_than_numerator quotient_property zero_is_smallest less_equal_and_equal
% 0.47/0.70
%------------------------------------------------------------------------------