%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HEN005-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 13:03:02 EDT 2022
% Result : Unsatisfiable 0.20s 0.50s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of clauses : 23 ( 10 unt; 0 nHn; 23 RR)
% Number of literals : 49 ( 0 equ; 29 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 12 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
quotient(zero,u,zero),
file('HEN005-2.p',unknown),
[] ).
cnf(4,axiom,
quotient(u,zero,u),
file('HEN005-2.p',unknown),
[] ).
cnf(5,axiom,
less_equal(x__dfg,y__dfg),
file('HEN005-2.p',unknown),
[] ).
cnf(6,axiom,
less_equal(y__dfg,z__dfg),
file('HEN005-2.p',unknown),
[] ).
cnf(7,axiom,
~ less_equal(x__dfg,z__dfg),
file('HEN005-2.p',unknown),
[] ).
cnf(8,axiom,
( ~ less_equal(u,v)
| quotient(u,v,zero) ),
file('HEN005-2.p',unknown),
[] ).
cnf(9,axiom,
( ~ quotient(u,v,zero)
| less_equal(u,v) ),
file('HEN005-2.p',unknown),
[] ).
cnf(11,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('HEN005-2.p',unknown),
[] ).
cnf(12,axiom,
less_equal(zero,u),
file('HEN005-2.p',unknown),
[] ).
cnf(13,axiom,
( ~ less_equal(u,v)
| ~ less_equal(v,u)
| equal(v,u) ),
file('HEN005-2.p',unknown),
[] ).
cnf(15,axiom,
quotient(u,v,divide(u,v)),
file('HEN005-2.p',unknown),
[] ).
cnf(17,plain,
~ quotient(x__dfg,z__dfg,zero),
inference(res,[status(thm),theory(equality)],[9,7]),
[iquote('0:Res:9.1,7.0')] ).
cnf(34,plain,
( ~ less_equal(u,zero)
| equal(u,zero) ),
inference(res,[status(thm),theory(equality)],[12,13]),
[iquote('0:Res:12.0,13.0')] ).
cnf(52,plain,
( ~ quotient(u,v,w)
| ~ quotient(x,y,u)
| ~ quotient(z,y,v)
| ~ quotient(x,z,zero)
| less_equal(w,zero) ),
inference(res,[status(thm),theory(equality)],[2,11]),
[iquote('0:Res:2.0,11.0')] ).
cnf(173,plain,
( ~ quotient(u,v,w)
| ~ quotient(x,v,zero)
| ~ quotient(u,x,zero)
| less_equal(w,zero) ),
inference(res,[status(thm),theory(equality)],[4,52]),
[iquote('0:Res:4.0,52.0')] ).
cnf(329,plain,
( ~ quotient(u,v,zero)
| ~ quotient(w,u,zero)
| less_equal(divide(w,v),zero) ),
inference(res,[status(thm),theory(equality)],[15,173]),
[iquote('0:Res:15.0,173.0')] ).
cnf(338,plain,
( ~ less_equal(u,v)
| ~ quotient(w,u,zero)
| less_equal(divide(w,v),zero) ),
inference(res,[status(thm),theory(equality)],[8,329]),
[iquote('0:Res:8.1,329.0')] ).
cnf(459,plain,
( ~ less_equal(u,v)
| ~ less_equal(v,w)
| less_equal(divide(u,w),zero) ),
inference(res,[status(thm),theory(equality)],[8,338]),
[iquote('0:Res:8.1,338.1')] ).
cnf(583,plain,
( ~ less_equal(y__dfg,u)
| less_equal(divide(x__dfg,u),zero) ),
inference(res,[status(thm),theory(equality)],[5,459]),
[iquote('0:Res:5.0,459.0')] ).
cnf(631,plain,
( ~ less_equal(y__dfg,u)
| equal(divide(x__dfg,u),zero) ),
inference(res,[status(thm),theory(equality)],[583,34]),
[iquote('0:Res:583.1,34.0')] ).
cnf(716,plain,
( ~ less_equal(y__dfg,u)
| quotient(x__dfg,u,zero) ),
inference(spr,[status(thm),theory(equality)],[631,15]),
[iquote('0:SpR:631.1,15.0')] ).
cnf(728,plain,
~ less_equal(y__dfg,z__dfg),
inference(res,[status(thm),theory(equality)],[716,17]),
[iquote('0:Res:716.1,17.0')] ).
cnf(769,plain,
$false,
inference(mrr,[status(thm)],[728,6]),
[iquote('0:MRR:728.0,6.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : HEN005-2 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n008.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 13:25:53 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.20/0.50
% 0.20/0.50 SPASS V 3.9
% 0.20/0.50 SPASS beiseite: Proof found.
% 0.20/0.50 % SZS status Theorem
% 0.20/0.50 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.50 SPASS derived 687 clauses, backtracked 0 clauses, performed 0 splits and kept 181 clauses.
% 0.20/0.50 SPASS allocated 63606 KBytes.
% 0.20/0.50 SPASS spent 0:00:00.14 on the problem.
% 0.20/0.50 0:00:00.04 for the input.
% 0.20/0.50 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.50 0:00:00.01 for inferences.
% 0.20/0.50 0:00:00.00 for the backtracking.
% 0.20/0.50 0:00:00.06 for the reduction.
% 0.20/0.50
% 0.20/0.50
% 0.20/0.50 Here is a proof with depth 9, length 23 :
% 0.20/0.50 % SZS output start Refutation
% See solution above
% 0.20/0.50 Formulae used in the proof : zero_divide_anything_is_zero x_divde_zero_is_x xLEy yLEz prove_transitivity_of_less_equal quotient_less_equal less_equal_quotient quotient_property zero_is_smallest less_equal_and_equal closure
% 0.20/0.50
%------------------------------------------------------------------------------