TSTP Solution File: HEN005-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HEN005-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 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 13:03:02 EDT 2022
% Result : Unsatisfiable 0.18s 0.47s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of clauses : 32 ( 11 unt; 0 nHn; 32 RR)
% Number of literals : 67 ( 0 equ; 38 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 : 13 ( 13 usr; 12 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
less_equal(x__dfg,y__dfg),
file('HEN005-1.p',unknown),
[] ).
cnf(2,axiom,
less_equal(y__dfg,z__dfg),
file('HEN005-1.p',unknown),
[] ).
cnf(3,axiom,
~ less_equal(x__dfg,z__dfg),
file('HEN005-1.p',unknown),
[] ).
cnf(4,axiom,
( ~ less_equal(u,v)
| quotient(u,v,zero) ),
file('HEN005-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ quotient(u,v,zero)
| less_equal(u,v) ),
file('HEN005-1.p',unknown),
[] ).
cnf(6,axiom,
( ~ quotient(u,v,w)
| less_equal(w,u) ),
file('HEN005-1.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('HEN005-1.p',unknown),
[] ).
cnf(8,axiom,
less_equal(zero,u),
file('HEN005-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ less_equal(u,v)
| ~ less_equal(v,u)
| equal(v,u) ),
file('HEN005-1.p',unknown),
[] ).
cnf(11,axiom,
quotient(u,v,divide(u,v)),
file('HEN005-1.p',unknown),
[] ).
cnf(12,axiom,
( ~ quotient(u,v,w)
| ~ quotient(u,v,x)
| equal(x,w) ),
file('HEN005-1.p',unknown),
[] ).
cnf(13,plain,
~ quotient(x__dfg,z__dfg,zero),
inference(res,[status(thm),theory(equality)],[5,3]),
[iquote('0:Res:5.1,3.0')] ).
cnf(18,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(25,plain,
( ~ quotient(u,v,w)
| equal(w,divide(u,v)) ),
inference(res,[status(thm),theory(equality)],[11,12]),
[iquote('0:Res:11.0,12.0')] ).
cnf(28,plain,
equal(divide(zero,u),zero),
inference(res,[status(thm),theory(equality)],[18,22]),
[iquote('0:Res:18.0,22.0')] ).
cnf(29,plain,
quotient(zero,u,zero),
inference(spr,[status(thm),theory(equality)],[28,11]),
[iquote('0:SpR:28.0,11.0')] ).
cnf(35,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)],[29,7]),
[iquote('0:Res:29.0,7.0')] ).
cnf(44,plain,
( ~ less_equal(u,v)
| equal(divide(u,v),zero) ),
inference(res,[status(thm),theory(equality)],[4,25]),
[iquote('0:Res:4.1,25.0')] ).
cnf(58,plain,
( ~ quotient(u,v,w)
| ~ quotient(x,v,y)
| ~ quotient(u,x,zero)
| less_equal(divide(w,y),zero) ),
inference(res,[status(thm),theory(equality)],[11,35]),
[iquote('0:Res:11.0,35.0')] ).
cnf(61,plain,
( ~ quotient(u,v,w)
| ~ quotient(x,u,zero)
| less_equal(divide(divide(x,v),w),zero) ),
inference(res,[status(thm),theory(equality)],[11,58]),
[iquote('0:Res:11.0,58.0')] ).
cnf(64,plain,
( ~ quotient(u,v,zero)
| less_equal(divide(divide(u,w),divide(v,w)),zero) ),
inference(res,[status(thm),theory(equality)],[11,61]),
[iquote('0:Res:11.0,61.0')] ).
cnf(159,plain,
( ~ quotient(u,v,zero)
| equal(divide(divide(u,w),divide(v,w)),zero) ),
inference(res,[status(thm),theory(equality)],[64,22]),
[iquote('0:Res:64.1,22.0')] ).
cnf(162,plain,
( ~ quotient(u,v,zero)
| quotient(divide(u,w),divide(v,w),zero) ),
inference(spr,[status(thm),theory(equality)],[159,11]),
[iquote('0:SpR:159.1,11.0')] ).
cnf(192,plain,
( ~ quotient(u,v,zero)
| less_equal(divide(u,w),divide(v,w)) ),
inference(res,[status(thm),theory(equality)],[162,5]),
[iquote('0:Res:162.1,5.0')] ).
cnf(208,plain,
( ~ less_equal(u,v)
| ~ quotient(w,u,zero)
| less_equal(divide(w,v),zero) ),
inference(spr,[status(thm),theory(equality)],[44,192]),
[iquote('0:SpR:44.1,192.1')] ).
cnf(467,plain,
( ~ less_equal(u,v)
| ~ less_equal(v,w)
| less_equal(divide(u,w),zero) ),
inference(res,[status(thm),theory(equality)],[4,208]),
[iquote('0:Res:4.1,208.1')] ).
cnf(471,plain,
( ~ less_equal(y__dfg,u)
| less_equal(divide(x__dfg,u),zero) ),
inference(res,[status(thm),theory(equality)],[1,467]),
[iquote('0:Res:1.0,467.0')] ).
cnf(497,plain,
( ~ less_equal(y__dfg,u)
| equal(divide(x__dfg,u),zero) ),
inference(res,[status(thm),theory(equality)],[471,22]),
[iquote('0:Res:471.1,22.0')] ).
cnf(548,plain,
( ~ less_equal(y__dfg,u)
| quotient(x__dfg,u,zero) ),
inference(spr,[status(thm),theory(equality)],[497,11]),
[iquote('0:SpR:497.1,11.0')] ).
cnf(562,plain,
~ less_equal(y__dfg,z__dfg),
inference(res,[status(thm),theory(equality)],[548,13]),
[iquote('0:Res:548.1,13.0')] ).
cnf(585,plain,
$false,
inference(mrr,[status(thm)],[562,2]),
[iquote('0:MRR:562.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : HEN005-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jul 1 13:12:15 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.47
% 0.18/0.47 SPASS V 3.9
% 0.18/0.47 SPASS beiseite: Proof found.
% 0.18/0.47 % SZS status Theorem
% 0.18/0.47 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.47 SPASS derived 519 clauses, backtracked 0 clauses, performed 0 splits and kept 170 clauses.
% 0.18/0.47 SPASS allocated 63578 KBytes.
% 0.18/0.47 SPASS spent 0:00:00.12 on the problem.
% 0.18/0.47 0:00:00.03 for the input.
% 0.18/0.47 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.47 0:00:00.01 for inferences.
% 0.18/0.47 0:00:00.00 for the backtracking.
% 0.18/0.47 0:00:00.06 for the reduction.
% 0.18/0.47
% 0.18/0.47
% 0.18/0.47 Here is a proof with depth 16, length 32 :
% 0.18/0.47 % SZS output start Refutation
% See solution above
% 0.18/0.47 Formulae used in the proof : xLEy yLEz prove_transitivity_of_less_equal quotient_less_equal less_equal_quotient divisor_existence quotient_property zero_is_smallest less_equal_and_equal closure well_defined
% 0.18/0.47
%------------------------------------------------------------------------------