TSTP Solution File: HEN008-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HEN008-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 13:03:08 EDT 2022
% Result : Unsatisfiable 0.20s 0.48s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of clauses : 25 ( 12 unt; 0 nHn; 25 RR)
% Number of literals : 49 ( 0 equ; 26 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 2 ( 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(a,b),
file('HEN008-1.p',unknown),
[] ).
cnf(2,axiom,
quotient(a,c,aQc),
file('HEN008-1.p',unknown),
[] ).
cnf(3,axiom,
quotient(b,c,bQc),
file('HEN008-1.p',unknown),
[] ).
cnf(4,axiom,
~ less_equal(aQc,bQc),
file('HEN008-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ less_equal(u,v)
| quotient(u,v,zero) ),
file('HEN008-1.p',unknown),
[] ).
cnf(6,axiom,
( ~ quotient(u,v,zero)
| less_equal(u,v) ),
file('HEN008-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ quotient(u,v,w)
| less_equal(w,u) ),
file('HEN008-1.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('HEN008-1.p',unknown),
[] ).
cnf(9,axiom,
less_equal(zero,u),
file('HEN008-1.p',unknown),
[] ).
cnf(10,axiom,
( ~ less_equal(u,v)
| ~ less_equal(v,u)
| equal(v,u) ),
file('HEN008-1.p',unknown),
[] ).
cnf(12,axiom,
quotient(u,v,divide(u,v)),
file('HEN008-1.p',unknown),
[] ).
cnf(14,plain,
~ quotient(aQc,bQc,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(34,plain,
equal(divide(zero,u),zero),
inference(res,[status(thm),theory(equality)],[21,25]),
[iquote('0:Res:21.0,25.0')] ).
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(130,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(281,plain,
( ~ quotient(u,c,v)
| ~ quotient(a,u,w)
| less_equal(divide(aQc,v),divide(w,c)) ),
inference(res,[status(thm),theory(equality)],[2,130]),
[iquote('0:Res:2.0,130.0')] ).
cnf(355,plain,
( ~ quotient(a,b,u)
| less_equal(divide(aQc,bQc),divide(u,c)) ),
inference(res,[status(thm),theory(equality)],[3,281]),
[iquote('0:Res:3.0,281.0')] ).
cnf(486,plain,
( ~ quotient(a,b,zero)
| less_equal(divide(aQc,bQc),zero) ),
inference(spr,[status(thm),theory(equality)],[34,355]),
[iquote('0:SpR:34.0,355.1')] ).
cnf(494,plain,
( ~ quotient(a,b,zero)
| equal(divide(aQc,bQc),zero) ),
inference(res,[status(thm),theory(equality)],[486,25]),
[iquote('0:Res:486.1,25.0')] ).
cnf(496,plain,
( ~ less_equal(a,b)
| equal(divide(aQc,bQc),zero) ),
inference(res,[status(thm),theory(equality)],[5,494]),
[iquote('0:Res:5.1,494.0')] ).
cnf(497,plain,
equal(divide(aQc,bQc),zero),
inference(mrr,[status(thm)],[496,1]),
[iquote('0:MRR:496.0,1.0')] ).
cnf(515,plain,
quotient(aQc,bQc,zero),
inference(spr,[status(thm),theory(equality)],[497,12]),
[iquote('0:SpR:497.0,12.0')] ).
cnf(521,plain,
$false,
inference(mrr,[status(thm)],[515,14]),
[iquote('0:MRR:515.0,14.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : HEN008-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Fri Jul 1 15:09:04 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.48
% 0.20/0.48 SPASS V 3.9
% 0.20/0.48 SPASS beiseite: Proof found.
% 0.20/0.48 % SZS status Theorem
% 0.20/0.48 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.48 SPASS derived 454 clauses, backtracked 0 clauses, performed 0 splits and kept 206 clauses.
% 0.20/0.48 SPASS allocated 63560 KBytes.
% 0.20/0.48 SPASS spent 0:00:00.13 on the problem.
% 0.20/0.48 0:00:00.03 for the input.
% 0.20/0.48 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.48 0:00:00.01 for inferences.
% 0.20/0.48 0:00:00.00 for the backtracking.
% 0.20/0.48 0:00:00.06 for the reduction.
% 0.20/0.48
% 0.20/0.48
% 0.20/0.48 Here is a proof with depth 8, length 25 :
% 0.20/0.48 % SZS output start Refutation
% See solution above
% 0.20/0.48 Formulae used in the proof : aLEb aQc bQc prove_aQcLEbQc quotient_less_equal less_equal_quotient divisor_existence quotient_property zero_is_smallest less_equal_and_equal closure
% 0.20/0.48
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