TSTP Solution File: HEN006-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HEN006-1 : 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 13:03:03 EDT 2022
% Result : Unsatisfiable 0.46s 0.65s
% Output : Refutation 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 12
% Syntax : Number of clauses : 37 ( 18 unt; 0 nHn; 37 RR)
% Number of literals : 75 ( 0 equ; 40 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,
quotient(x__dfg,y__dfg,xQy),
file('HEN006-1.p',unknown),
[] ).
cnf(2,axiom,
less_equal(xQy,z__dfg),
file('HEN006-1.p',unknown),
[] ).
cnf(3,axiom,
quotient(x__dfg,z__dfg,xQz),
file('HEN006-1.p',unknown),
[] ).
cnf(4,axiom,
~ less_equal(xQz,y__dfg),
file('HEN006-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ less_equal(u,v)
| quotient(u,v,zero) ),
file('HEN006-1.p',unknown),
[] ).
cnf(6,axiom,
( ~ quotient(u,v,zero)
| less_equal(u,v) ),
file('HEN006-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ quotient(u,v,w)
| less_equal(w,u) ),
file('HEN006-1.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('HEN006-1.p',unknown),
[] ).
cnf(9,axiom,
less_equal(zero,u),
file('HEN006-1.p',unknown),
[] ).
cnf(10,axiom,
( ~ less_equal(u,v)
| ~ less_equal(v,u)
| equal(v,u) ),
file('HEN006-1.p',unknown),
[] ).
cnf(12,axiom,
quotient(u,v,divide(u,v)),
file('HEN006-1.p',unknown),
[] ).
cnf(13,axiom,
( ~ quotient(u,v,w)
| ~ quotient(u,v,x)
| equal(x,w) ),
file('HEN006-1.p',unknown),
[] ).
cnf(14,plain,
~ quotient(xQz,y__dfg,zero),
inference(res,[status(thm),theory(equality)],[6,4]),
[iquote('0:Res:6.1,4.0')] ).
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(25,plain,
( ~ less_equal(u,zero)
| equal(u,zero) ),
inference(res,[status(thm),theory(equality)],[9,10]),
[iquote('0:Res:9.0,10.0')] ).
cnf(31,plain,
( ~ quotient(u,v,w)
| equal(w,divide(u,v)) ),
inference(res,[status(thm),theory(equality)],[12,13]),
[iquote('0:Res:12.0,13.0')] ).
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(60,plain,
( ~ less_equal(u,v)
| equal(divide(u,v),zero) ),
inference(res,[status(thm),theory(equality)],[5,31]),
[iquote('0:Res:5.1,31.0')] ).
cnf(166,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(299,plain,
( ~ less_equal(u,z__dfg)
| ~ quotient(v,z__dfg,w)
| ~ quotient(x__dfg,v,u)
| less_equal(divide(xQz,w),zero) ),
inference(res,[status(thm),theory(equality)],[3,166]),
[iquote('0:Res:3.0,166.1')] ).
cnf(302,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)],[12,166]),
[iquote('0:Res:12.0,166.1')] ).
cnf(433,plain,
( ~ less_equal(u,z__dfg)
| ~ quotient(x__dfg,v,u)
| less_equal(divide(xQz,divide(v,z__dfg)),zero) ),
inference(res,[status(thm),theory(equality)],[12,299]),
[iquote('0:Res:12.0,299.1')] ).
cnf(547,plain,
( ~ less_equal(u,v)
| ~ quotient(w,x,u)
| less_equal(divide(divide(w,v),divide(x,v)),zero) ),
inference(res,[status(thm),theory(equality)],[12,302]),
[iquote('0:Res:12.0,302.1')] ).
cnf(1051,plain,
( ~ less_equal(xQy,z__dfg)
| less_equal(divide(xQz,divide(y__dfg,z__dfg)),zero) ),
inference(res,[status(thm),theory(equality)],[1,433]),
[iquote('0:Res:1.0,433.1')] ).
cnf(1054,plain,
less_equal(divide(xQz,divide(y__dfg,z__dfg)),zero),
inference(mrr,[status(thm)],[1051,2]),
[iquote('0:MRR:1051.0,2.0')] ).
cnf(1084,plain,
equal(divide(xQz,divide(y__dfg,z__dfg)),zero),
inference(res,[status(thm),theory(equality)],[1054,25]),
[iquote('0:Res:1054.0,25.0')] ).
cnf(1088,plain,
quotient(xQz,divide(y__dfg,z__dfg),zero),
inference(spr,[status(thm),theory(equality)],[1084,12]),
[iquote('0:SpR:1084.0,12.0')] ).
cnf(1741,plain,
( ~ less_equal(zero,u)
| less_equal(divide(divide(xQz,u),divide(divide(y__dfg,z__dfg),u)),zero) ),
inference(res,[status(thm),theory(equality)],[1088,547]),
[iquote('0:Res:1088.0,547.1')] ).
cnf(1754,plain,
less_equal(divide(divide(xQz,u),divide(divide(y__dfg,z__dfg),u)),zero),
inference(mrr,[status(thm)],[1741,9]),
[iquote('0:MRR:1741.0,9.0')] ).
cnf(1784,plain,
equal(divide(divide(xQz,u),divide(divide(y__dfg,z__dfg),u)),zero),
inference(res,[status(thm),theory(equality)],[1754,25]),
[iquote('0:Res:1754.0,25.0')] ).
cnf(1788,plain,
quotient(divide(xQz,u),divide(divide(y__dfg,z__dfg),u),zero),
inference(spr,[status(thm),theory(equality)],[1784,12]),
[iquote('0:SpR:1784.0,12.0')] ).
cnf(1833,plain,
less_equal(divide(xQz,u),divide(divide(y__dfg,z__dfg),u)),
inference(res,[status(thm),theory(equality)],[1788,6]),
[iquote('0:Res:1788.0,6.0')] ).
cnf(1857,plain,
( ~ less_equal(divide(y__dfg,z__dfg),u)
| less_equal(divide(xQz,u),zero) ),
inference(spr,[status(thm),theory(equality)],[60,1833]),
[iquote('0:SpR:60.1,1833.0')] ).
cnf(1882,plain,
( ~ less_equal(divide(y__dfg,z__dfg),u)
| equal(divide(xQz,u),zero) ),
inference(res,[status(thm),theory(equality)],[1857,25]),
[iquote('0:Res:1857.1,25.0')] ).
cnf(1888,plain,
equal(divide(xQz,y__dfg),zero),
inference(res,[status(thm),theory(equality)],[21,1882]),
[iquote('0:Res:21.0,1882.0')] ).
cnf(1897,plain,
quotient(xQz,y__dfg,zero),
inference(spr,[status(thm),theory(equality)],[1888,12]),
[iquote('0:SpR:1888.0,12.0')] ).
cnf(1935,plain,
$false,
inference(mrr,[status(thm)],[1897,14]),
[iquote('0:MRR:1897.0,14.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : HEN006-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % 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 13:36:07 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.46/0.65
% 0.46/0.65 SPASS V 3.9
% 0.46/0.65 SPASS beiseite: Proof found.
% 0.46/0.65 % SZS status Theorem
% 0.46/0.65 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.46/0.65 SPASS derived 1603 clauses, backtracked 0 clauses, performed 0 splits and kept 613 clauses.
% 0.46/0.65 SPASS allocated 64682 KBytes.
% 0.46/0.65 SPASS spent 0:00:00.31 on the problem.
% 0.46/0.65 0:00:00.04 for the input.
% 0.46/0.65 0:00:00.00 for the FLOTTER CNF translation.
% 0.46/0.65 0:00:00.03 for inferences.
% 0.46/0.65 0:00:00.00 for the backtracking.
% 0.46/0.65 0:00:00.21 for the reduction.
% 0.46/0.65
% 0.46/0.65
% 0.46/0.65 Here is a proof with depth 15, length 37 :
% 0.46/0.65 % SZS output start Refutation
% See solution above
% 0.46/0.65 Formulae used in the proof : xQy xQyLEz xQz prove_xQzLEy quotient_less_equal less_equal_quotient divisor_existence quotient_property zero_is_smallest less_equal_and_equal closure well_defined
% 0.46/0.65
%------------------------------------------------------------------------------