%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HEN007-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 13:03:06 EDT 2022
% Result : Unsatisfiable 1.21s 1.40s
% Output : Refutation 1.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 11
% Syntax : Number of clauses : 44 ( 19 unt; 0 nHn; 44 RR)
% Number of literals : 95 ( 0 equ; 52 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 14 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
less_equal(x__dfg,y__dfg),
file('HEN007-1.p',unknown),
[] ).
cnf(2,axiom,
quotient(z__dfg,y__dfg,zQy),
file('HEN007-1.p',unknown),
[] ).
cnf(3,axiom,
quotient(z__dfg,x__dfg,zQx),
file('HEN007-1.p',unknown),
[] ).
cnf(4,axiom,
~ less_equal(zQy,zQx),
file('HEN007-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ less_equal(u,v)
| quotient(u,v,zero) ),
file('HEN007-1.p',unknown),
[] ).
cnf(6,axiom,
( ~ quotient(u,v,zero)
| less_equal(u,v) ),
file('HEN007-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ quotient(u,v,w)
| less_equal(w,u) ),
file('HEN007-1.p',unknown),
[] ).
cnf(8,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('HEN007-1.p',unknown),
[] ).
cnf(9,axiom,
less_equal(zero,u),
file('HEN007-1.p',unknown),
[] ).
cnf(10,axiom,
( ~ less_equal(u,v)
| ~ less_equal(v,u)
| equal(v,u) ),
file('HEN007-1.p',unknown),
[] ).
cnf(12,axiom,
quotient(u,v,divide(u,v)),
file('HEN007-1.p',unknown),
[] ).
cnf(19,plain,
less_equal(zQx,z__dfg),
inference(res,[status(thm),theory(equality)],[3,7]),
[iquote('0:Res:3.0,7.0')] ).
cnf(21,plain,
less_equal(divide(u,v),u),
inference(res,[status(thm),theory(equality)],[12,7]),
[iquote('0:Res:12.0,7.0')] ).
cnf(24,plain,
( ~ less_equal(u,zero)
| equal(u,zero) ),
inference(res,[status(thm),theory(equality)],[9,10]),
[iquote('0:Res:9.0,10.0')] ).
cnf(45,plain,
( ~ quotient(u,v,w)
| ~ quotient(x,y,u)
| ~ quotient(z,y,v)
| ~ quotient(x,z,x1)
| less_equal(w,divide(x1,y)) ),
inference(res,[status(thm),theory(equality)],[12,8]),
[iquote('0:Res:12.0,8.0')] ).
cnf(46,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)],[5,8]),
[iquote('0:Res:5.1,8.0')] ).
cnf(140,plain,
( ~ quotient(u,v,w)
| ~ quotient(x,v,y)
| ~ quotient(u,x,z)
| less_equal(divide(w,y),divide(z,v)) ),
inference(res,[status(thm),theory(equality)],[12,45]),
[iquote('0:Res:12.0,45.0')] ).
cnf(167,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)],[12,46]),
[iquote('0:Res:12.0,46.1')] ).
cnf(264,plain,
( ~ quotient(u,y__dfg,v)
| ~ quotient(z__dfg,u,w)
| less_equal(divide(zQy,v),divide(w,y__dfg)) ),
inference(res,[status(thm),theory(equality)],[2,140]),
[iquote('0:Res:2.0,140.0')] ).
cnf(293,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)],[12,167]),
[iquote('0:Res:12.0,167.1')] ).
cnf(330,plain,
( ~ less_equal(u,y__dfg)
| ~ quotient(z__dfg,u,v)
| less_equal(divide(zQy,zero),divide(v,y__dfg)) ),
inference(res,[status(thm),theory(equality)],[5,264]),
[iquote('0:Res:5.1,264.0')] ).
cnf(538,plain,
( ~ less_equal(u,y__dfg)
| ~ quotient(v,z__dfg,u)
| less_equal(divide(divide(v,y__dfg),zQy),zero) ),
inference(res,[status(thm),theory(equality)],[2,293]),
[iquote('0:Res:2.0,293.1')] ).
cnf(543,plain,
( ~ less_equal(u,v)
| ~ less_equal(w,v)
| ~ quotient(x,u,w)
| less_equal(divide(divide(x,v),zero),zero) ),
inference(res,[status(thm),theory(equality)],[5,293]),
[iquote('0:Res:5.1,293.1')] ).
cnf(940,plain,
( ~ less_equal(x__dfg,y__dfg)
| less_equal(divide(zQy,zero),divide(zQx,y__dfg)) ),
inference(res,[status(thm),theory(equality)],[3,330]),
[iquote('0:Res:3.0,330.1')] ).
cnf(944,plain,
less_equal(divide(zQy,zero),divide(zQx,y__dfg)),
inference(mrr,[status(thm)],[940,1]),
[iquote('0:MRR:940.0,1.0')] ).
cnf(1108,plain,
( ~ less_equal(u,z__dfg)
| ~ less_equal(zero,y__dfg)
| less_equal(divide(divide(u,y__dfg),zQy),zero) ),
inference(res,[status(thm),theory(equality)],[5,538]),
[iquote('0:Res:5.1,538.1')] ).
cnf(1110,plain,
( ~ less_equal(u,z__dfg)
| less_equal(divide(divide(u,y__dfg),zQy),zero) ),
inference(mrr,[status(thm)],[1108,9]),
[iquote('0:MRR:1108.1,9.0')] ).
cnf(1529,plain,
( ~ less_equal(u,z__dfg)
| equal(divide(divide(u,y__dfg),zQy),zero) ),
inference(res,[status(thm),theory(equality)],[1110,24]),
[iquote('0:Res:1110.1,24.0')] ).
cnf(1758,plain,
( ~ less_equal(u,z__dfg)
| quotient(divide(u,y__dfg),zQy,zero) ),
inference(spr,[status(thm),theory(equality)],[1529,12]),
[iquote('0:SpR:1529.1,12.0')] ).
cnf(1791,plain,
( ~ less_equal(u,z__dfg)
| less_equal(divide(u,y__dfg),zQy) ),
inference(res,[status(thm),theory(equality)],[1758,6]),
[iquote('0:Res:1758.1,6.0')] ).
cnf(1957,plain,
( ~ less_equal(u,v)
| ~ less_equal(divide(w,u),v)
| less_equal(divide(divide(w,v),zero),zero) ),
inference(res,[status(thm),theory(equality)],[12,543]),
[iquote('0:Res:12.0,543.2')] ).
cnf(5401,plain,
( ~ less_equal(zero,divide(zQx,y__dfg))
| less_equal(divide(divide(zQy,divide(zQx,y__dfg)),zero),zero) ),
inference(res,[status(thm),theory(equality)],[944,1957]),
[iquote('0:Res:944.0,1957.1')] ).
cnf(5418,plain,
less_equal(divide(divide(zQy,divide(zQx,y__dfg)),zero),zero),
inference(mrr,[status(thm)],[5401,9]),
[iquote('0:MRR:5401.0,9.0')] ).
cnf(5964,plain,
equal(divide(divide(zQy,divide(zQx,y__dfg)),zero),zero),
inference(res,[status(thm),theory(equality)],[5418,24]),
[iquote('0:Res:5418.0,24.0')] ).
cnf(6004,plain,
quotient(divide(zQy,divide(zQx,y__dfg)),zero,zero),
inference(spr,[status(thm),theory(equality)],[5964,12]),
[iquote('0:SpR:5964.0,12.0')] ).
cnf(6052,plain,
less_equal(divide(zQy,divide(zQx,y__dfg)),zero),
inference(res,[status(thm),theory(equality)],[6004,6]),
[iquote('0:Res:6004.0,6.0')] ).
cnf(6097,plain,
equal(divide(zQy,divide(zQx,y__dfg)),zero),
inference(res,[status(thm),theory(equality)],[6052,24]),
[iquote('0:Res:6052.0,24.0')] ).
cnf(6116,plain,
quotient(zQy,divide(zQx,y__dfg),zero),
inference(spr,[status(thm),theory(equality)],[6097,12]),
[iquote('0:SpR:6097.0,12.0')] ).
cnf(6181,plain,
less_equal(zQy,divide(zQx,y__dfg)),
inference(res,[status(thm),theory(equality)],[6116,6]),
[iquote('0:Res:6116.0,6.0')] ).
cnf(6215,plain,
( ~ less_equal(divide(zQx,y__dfg),zQy)
| equal(divide(zQx,y__dfg),zQy) ),
inference(res,[status(thm),theory(equality)],[6181,10]),
[iquote('0:Res:6181.0,10.0')] ).
cnf(7986,plain,
( ~ less_equal(zQx,z__dfg)
| equal(divide(zQx,y__dfg),zQy) ),
inference(res,[status(thm),theory(equality)],[1791,6215]),
[iquote('0:Res:1791.1,6215.0')] ).
cnf(7987,plain,
equal(divide(zQx,y__dfg),zQy),
inference(mrr,[status(thm)],[7986,19]),
[iquote('0:MRR:7986.0,19.0')] ).
cnf(8242,plain,
less_equal(zQy,zQx),
inference(spr,[status(thm),theory(equality)],[7987,21]),
[iquote('0:SpR:7987.0,21.0')] ).
cnf(8308,plain,
$false,
inference(mrr,[status(thm)],[8242,4]),
[iquote('0:MRR:8242.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : HEN007-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Fri Jul 1 13:45:22 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.21/1.40
% 1.21/1.40 SPASS V 3.9
% 1.21/1.40 SPASS beiseite: Proof found.
% 1.21/1.40 % SZS status Theorem
% 1.21/1.40 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.21/1.40 SPASS derived 6703 clauses, backtracked 0 clauses, performed 0 splits and kept 1713 clauses.
% 1.21/1.40 SPASS allocated 68681 KBytes.
% 1.21/1.40 SPASS spent 0:00:01.02 on the problem.
% 1.21/1.40 0:00:00.04 for the input.
% 1.21/1.40 0:00:00.00 for the FLOTTER CNF translation.
% 1.21/1.40 0:00:00.07 for inferences.
% 1.21/1.40 0:00:00.00 for the backtracking.
% 1.21/1.40 0:00:00.88 for the reduction.
% 1.21/1.40
% 1.21/1.40
% 1.21/1.40 Here is a proof with depth 15, length 44 :
% 1.21/1.40 % SZS output start Refutation
% See solution above
% 1.21/1.40 Formulae used in the proof : xLEy zQy zQx prove_zQyLEzQx quotient_less_equal less_equal_quotient divisor_existence quotient_property zero_is_smallest less_equal_and_equal closure
% 1.21/1.40
%------------------------------------------------------------------------------