%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HEN003-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 0.10s 0.33s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of clauses : 23 ( 9 unt; 0 nHn; 23 RR)
% Number of literals : 52 ( 0 equ; 30 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
quotient(zero,u,zero),
file('HEN003-2.p',unknown),
[] ).
cnf(3,axiom,
~ quotient(x__dfg,x__dfg,zero),
file('HEN003-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ less_equal(u,v)
| quotient(u,v,zero) ),
file('HEN003-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ quotient(u,v,zero)
| less_equal(u,v) ),
file('HEN003-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ quotient(u,v,w)
| less_equal(w,u) ),
file('HEN003-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ quotient(u,v,w)
| ~ quotient(x,y,z)
| ~ quotient(x1,v,x)
| ~ quotient(x2,v,y)
| ~ quotient(x1,x2,u)
| less_equal(z,w) ),
file('HEN003-2.p',unknown),
[] ).
cnf(8,axiom,
less_equal(zero,u),
file('HEN003-2.p',unknown),
[] ).
cnf(9,axiom,
( ~ less_equal(u,v)
| ~ less_equal(v,u)
| equal(v,u) ),
file('HEN003-2.p',unknown),
[] ).
cnf(11,axiom,
quotient(u,v,divide(u,v)),
file('HEN003-2.p',unknown),
[] ).
cnf(21,plain,
less_equal(divide(u,v),u),
inference(res,[status(thm),theory(equality)],[11,6]),
[iquote('0:Res:11.0,6.0')] ).
cnf(22,plain,
( ~ less_equal(u,zero)
| equal(u,zero) ),
inference(res,[status(thm),theory(equality)],[8,9]),
[iquote('0:Res:8.0,9.0')] ).
cnf(49,plain,
( ~ less_equal(u,v)
| ~ quotient(w,x,y)
| ~ quotient(z,v,w)
| ~ quotient(x1,v,x)
| ~ quotient(z,x1,u)
| less_equal(y,zero) ),
inference(res,[status(thm),theory(equality)],[4,7]),
[iquote('0:Res:4.1,7.0')] ).
cnf(146,plain,
( ~ less_equal(u,v)
| ~ quotient(w,v,x)
| ~ quotient(y,v,z)
| ~ quotient(w,y,u)
| less_equal(divide(x,z),zero) ),
inference(res,[status(thm),theory(equality)],[11,49]),
[iquote('0:Res:11.0,49.1')] ).
cnf(233,plain,
( ~ less_equal(u,v)
| ~ quotient(w,v,x)
| ~ quotient(y,w,u)
| less_equal(divide(divide(y,v),x),zero) ),
inference(res,[status(thm),theory(equality)],[11,146]),
[iquote('0:Res:11.0,146.1')] ).
cnf(347,plain,
( ~ less_equal(u,v)
| ~ quotient(w,zero,u)
| less_equal(divide(divide(w,v),zero),zero) ),
inference(res,[status(thm),theory(equality)],[2,233]),
[iquote('0:Res:2.0,233.1')] ).
cnf(460,plain,
( ~ less_equal(divide(u,zero),v)
| less_equal(divide(divide(u,v),zero),zero) ),
inference(res,[status(thm),theory(equality)],[11,347]),
[iquote('0:Res:11.0,347.1')] ).
cnf(476,plain,
( ~ less_equal(divide(u,zero),v)
| equal(divide(divide(u,v),zero),zero) ),
inference(res,[status(thm),theory(equality)],[460,22]),
[iquote('0:Res:460.1,22.0')] ).
cnf(479,plain,
( ~ less_equal(divide(u,zero),v)
| quotient(divide(u,v),zero,zero) ),
inference(spr,[status(thm),theory(equality)],[476,11]),
[iquote('0:SpR:476.1,11.0')] ).
cnf(513,plain,
( ~ less_equal(divide(u,zero),v)
| less_equal(divide(u,v),zero) ),
inference(res,[status(thm),theory(equality)],[479,5]),
[iquote('0:Res:479.1,5.0')] ).
cnf(542,plain,
less_equal(divide(u,u),zero),
inference(res,[status(thm),theory(equality)],[21,513]),
[iquote('0:Res:21.0,513.0')] ).
cnf(592,plain,
equal(divide(u,u),zero),
inference(res,[status(thm),theory(equality)],[542,22]),
[iquote('0:Res:542.0,22.0')] ).
cnf(596,plain,
quotient(u,u,zero),
inference(spr,[status(thm),theory(equality)],[592,11]),
[iquote('0:SpR:592.0,11.0')] ).
cnf(620,plain,
$false,
inference(unc,[status(thm)],[596,3]),
[iquote('0:UnC:596.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.07 % Problem : HEN003-2 : TPTP v8.1.0. Released v1.0.0.
% 0.02/0.07 % Command : run_spass %d %s
% 0.06/0.25 % Computer : n011.cluster.edu
% 0.06/0.25 % Model : x86_64 x86_64
% 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25 % Memory : 8042.1875MB
% 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25 % CPULimit : 300
% 0.06/0.25 % WCLimit : 600
% 0.06/0.25 % DateTime : Fri Jul 1 13:20:18 EDT 2022
% 0.06/0.26 % CPUTime :
% 0.10/0.33
% 0.10/0.33 SPASS V 3.9
% 0.10/0.33 SPASS beiseite: Proof found.
% 0.10/0.33 % SZS status Theorem
% 0.10/0.33 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.33 SPASS derived 526 clauses, backtracked 0 clauses, performed 0 splits and kept 134 clauses.
% 0.10/0.33 SPASS allocated 63587 KBytes.
% 0.10/0.33 SPASS spent 0:00:00.06 on the problem.
% 0.10/0.33 0:00:00.02 for the input.
% 0.10/0.33 0:00:00.00 for the FLOTTER CNF translation.
% 0.10/0.33 0:00:00.00 for inferences.
% 0.10/0.33 0:00:00.00 for the backtracking.
% 0.10/0.33 0:00:00.02 for the reduction.
% 0.10/0.33
% 0.10/0.33
% 0.10/0.33 Here is a proof with depth 11, length 23 :
% 0.10/0.33 % SZS output start Refutation
% See solution above
% 0.10/0.33 Formulae used in the proof : zero_divide_anything_is_zero prove_x_divide_x_is_zero quotient_less_equal less_equal_quotient divisor_existence quotient_property zero_is_smallest less_equal_and_equal closure
% 0.10/0.33
%------------------------------------------------------------------------------