%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HEN007-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n004.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 0.58s 0.75s
% Output : Refutation 0.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 8
% Syntax : Number of clauses : 46 ( 21 unt; 0 nHn; 46 RR)
% Number of literals : 75 ( 0 equ; 30 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
less_equal(a,b),
file('HEN007-3.p',unknown),
[] ).
cnf(2,axiom,
~ less_equal(divide(c,b),divide(c,a)),
file('HEN007-3.p',unknown),
[] ).
cnf(3,axiom,
( ~ less_equal(u,v)
| equal(divide(u,v),zero) ),
file('HEN007-3.p',unknown),
[] ).
cnf(4,axiom,
( ~ equal(divide(u,v),zero)
| less_equal(u,v) ),
file('HEN007-3.p',unknown),
[] ).
cnf(5,axiom,
less_equal(divide(u,v),u),
file('HEN007-3.p',unknown),
[] ).
cnf(6,axiom,
less_equal(divide(divide(u,v),divide(w,v)),divide(divide(u,w),v)),
file('HEN007-3.p',unknown),
[] ).
cnf(7,axiom,
less_equal(zero,u),
file('HEN007-3.p',unknown),
[] ).
cnf(8,axiom,
( ~ less_equal(u,v)
| ~ less_equal(v,u)
| equal(v,u) ),
file('HEN007-3.p',unknown),
[] ).
cnf(19,plain,
( ~ less_equal(u,zero)
| equal(u,zero) ),
inference(res,[status(thm),theory(equality)],[7,8]),
[iquote('0:Res:7.0,8.0')] ).
cnf(20,plain,
( ~ less_equal(u,divide(u,v))
| equal(divide(u,v),u) ),
inference(res,[status(thm),theory(equality)],[5,8]),
[iquote('0:Res:5.0,8.0')] ).
cnf(23,plain,
equal(divide(zero,u),zero),
inference(res,[status(thm),theory(equality)],[5,19]),
[iquote('0:Res:5.0,19.0')] ).
cnf(30,plain,
( ~ less_equal(u,v)
| less_equal(divide(divide(u,w),divide(v,w)),divide(zero,w)) ),
inference(spr,[status(thm),theory(equality)],[3,6]),
[iquote('0:SpR:3.1,6.0')] ).
cnf(34,plain,
less_equal(divide(divide(u,v),zero),divide(divide(u,zero),v)),
inference(spr,[status(thm),theory(equality)],[23,6]),
[iquote('0:SpR:23.0,6.0')] ).
cnf(38,plain,
( ~ less_equal(divide(divide(u,v),w),divide(divide(u,w),divide(v,w)))
| equal(divide(divide(u,w),divide(v,w)),divide(divide(u,v),w)) ),
inference(res,[status(thm),theory(equality)],[6,8]),
[iquote('0:Res:6.0,8.0')] ).
cnf(40,plain,
( ~ less_equal(u,v)
| less_equal(divide(divide(u,w),divide(v,w)),zero) ),
inference(rew,[status(thm),theory(equality)],[23,30]),
[iquote('0:Rew:23.0,30.1')] ).
cnf(44,plain,
( ~ less_equal(divide(u,zero),v)
| less_equal(divide(divide(u,v),zero),zero) ),
inference(spr,[status(thm),theory(equality)],[3,34]),
[iquote('0:SpR:3.1,34.0')] ).
cnf(139,plain,
( ~ less_equal(u,v)
| equal(divide(divide(u,w),divide(v,w)),zero) ),
inference(res,[status(thm),theory(equality)],[40,19]),
[iquote('0:Res:40.1,19.0')] ).
cnf(195,plain,
( ~ less_equal(divide(u,zero),v)
| equal(divide(divide(u,v),zero),zero) ),
inference(res,[status(thm),theory(equality)],[44,19]),
[iquote('0:Res:44.1,19.0')] ).
cnf(246,plain,
( ~ less_equal(divide(u,zero),v)
| ~ equal(zero,zero)
| less_equal(divide(u,v),zero) ),
inference(spl,[status(thm),theory(equality)],[195,4]),
[iquote('0:SpL:195.1,4.0')] ).
cnf(249,plain,
( ~ less_equal(divide(u,zero),v)
| less_equal(divide(u,v),zero) ),
inference(obv,[status(thm),theory(equality)],[246]),
[iquote('0:Obv:246.1')] ).
cnf(259,plain,
less_equal(divide(u,u),zero),
inference(res,[status(thm),theory(equality)],[5,249]),
[iquote('0:Res:5.0,249.0')] ).
cnf(330,plain,
equal(divide(u,u),zero),
inference(res,[status(thm),theory(equality)],[259,19]),
[iquote('0:Res:259.0,19.0')] ).
cnf(352,plain,
( ~ equal(zero,zero)
| less_equal(u,u) ),
inference(spl,[status(thm),theory(equality)],[330,4]),
[iquote('0:SpL:330.0,4.0')] ).
cnf(356,plain,
less_equal(u,u),
inference(obv,[status(thm),theory(equality)],[352]),
[iquote('0:Obv:352.0')] ).
cnf(367,plain,
less_equal(divide(u,divide(u,zero)),zero),
inference(res,[status(thm),theory(equality)],[356,249]),
[iquote('0:Res:356.0,249.0')] ).
cnf(372,plain,
( ~ less_equal(divide(divide(u,v),v),divide(divide(u,v),zero))
| equal(divide(divide(u,v),divide(v,v)),divide(divide(u,v),v)) ),
inference(spl,[status(thm),theory(equality)],[330,38]),
[iquote('0:SpL:330.0,38.0')] ).
cnf(404,plain,
( ~ less_equal(divide(divide(u,v),v),divide(divide(u,v),zero))
| equal(divide(divide(u,v),zero),divide(divide(u,v),v)) ),
inference(rew,[status(thm),theory(equality)],[330,372]),
[iquote('0:Rew:330.0,372.1')] ).
cnf(440,plain,
equal(divide(u,divide(u,zero)),zero),
inference(res,[status(thm),theory(equality)],[367,19]),
[iquote('0:Res:367.0,19.0')] ).
cnf(466,plain,
( ~ equal(zero,zero)
| less_equal(u,divide(u,zero)) ),
inference(spl,[status(thm),theory(equality)],[440,4]),
[iquote('0:SpL:440.0,4.0')] ).
cnf(473,plain,
less_equal(u,divide(u,zero)),
inference(obv,[status(thm),theory(equality)],[466]),
[iquote('0:Obv:466.0')] ).
cnf(496,plain,
equal(divide(u,zero),u),
inference(res,[status(thm),theory(equality)],[473,20]),
[iquote('0:Res:473.0,20.0')] ).
cnf(528,plain,
( ~ less_equal(divide(divide(u,v),v),divide(u,v))
| equal(divide(divide(u,v),zero),divide(divide(u,v),v)) ),
inference(rew,[status(thm),theory(equality)],[496,404]),
[iquote('0:Rew:496.0,404.0')] ).
cnf(561,plain,
( ~ less_equal(divide(divide(u,v),v),divide(u,v))
| equal(divide(divide(u,v),v),divide(u,v)) ),
inference(rew,[status(thm),theory(equality)],[496,528]),
[iquote('0:Rew:496.0,528.1')] ).
cnf(562,plain,
equal(divide(divide(u,v),v),divide(u,v)),
inference(mrr,[status(thm)],[561,5]),
[iquote('0:MRR:561.0,5.0')] ).
cnf(655,plain,
( ~ less_equal(u,v)
| ~ less_equal(w,u)
| equal(divide(divide(w,v),zero),zero) ),
inference(spr,[status(thm),theory(equality)],[3,139]),
[iquote('0:SpR:3.1,139.1')] ).
cnf(680,plain,
( ~ less_equal(u,v)
| ~ less_equal(w,u)
| equal(divide(w,v),zero) ),
inference(rew,[status(thm),theory(equality)],[496,655]),
[iquote('0:Rew:496.0,655.2')] ).
cnf(1242,plain,
( ~ less_equal(u,a)
| equal(divide(u,b),zero) ),
inference(res,[status(thm),theory(equality)],[1,680]),
[iquote('0:Res:1.0,680.0')] ).
cnf(1244,plain,
( ~ less_equal(u,divide(v,w))
| equal(divide(u,v),zero) ),
inference(res,[status(thm),theory(equality)],[5,680]),
[iquote('0:Res:5.0,680.0')] ).
cnf(1277,plain,
( ~ less_equal(divide(u,b),a)
| equal(divide(u,b),zero) ),
inference(spr,[status(thm),theory(equality)],[1242,562]),
[iquote('0:SpR:1242.1,562.0')] ).
cnf(1427,plain,
equal(divide(a,b),zero),
inference(res,[status(thm),theory(equality)],[5,1277]),
[iquote('0:Res:5.0,1277.0')] ).
cnf(1445,plain,
less_equal(divide(divide(u,b),zero),divide(divide(u,a),b)),
inference(spr,[status(thm),theory(equality)],[1427,6]),
[iquote('0:SpR:1427.0,6.0')] ).
cnf(1463,plain,
less_equal(divide(u,b),divide(divide(u,a),b)),
inference(rew,[status(thm),theory(equality)],[496,1445]),
[iquote('0:Rew:496.0,1445.0')] ).
cnf(3030,plain,
equal(divide(divide(u,b),divide(u,a)),zero),
inference(res,[status(thm),theory(equality)],[1463,1244]),
[iquote('0:Res:1463.0,1244.0')] ).
cnf(3393,plain,
( ~ equal(zero,zero)
| less_equal(divide(u,b),divide(u,a)) ),
inference(spl,[status(thm),theory(equality)],[3030,4]),
[iquote('0:SpL:3030.0,4.0')] ).
cnf(3413,plain,
less_equal(divide(u,b),divide(u,a)),
inference(obv,[status(thm),theory(equality)],[3393]),
[iquote('0:Obv:3393.0')] ).
cnf(3414,plain,
$false,
inference(unc,[status(thm)],[3413,2]),
[iquote('0:UnC:3413.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : HEN007-3 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n004.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Fri Jul 1 14:45:53 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.58/0.75
% 0.58/0.75 SPASS V 3.9
% 0.58/0.75 SPASS beiseite: Proof found.
% 0.58/0.75 % SZS status Theorem
% 0.58/0.75 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.58/0.75 SPASS derived 2433 clauses, backtracked 0 clauses, performed 0 splits and kept 505 clauses.
% 0.58/0.75 SPASS allocated 65620 KBytes.
% 0.58/0.75 SPASS spent 0:00:00.38 on the problem.
% 0.58/0.75 0:00:00.04 for the input.
% 0.58/0.75 0:00:00.00 for the FLOTTER CNF translation.
% 0.58/0.75 0:00:00.03 for inferences.
% 0.58/0.75 0:00:00.00 for the backtracking.
% 0.58/0.75 0:00:00.29 for the reduction.
% 0.58/0.75
% 0.58/0.75
% 0.58/0.75 Here is a proof with depth 14, length 46 :
% 0.58/0.75 % SZS output start Refutation
% See solution above
% 0.58/0.75 Formulae used in the proof : a_LE_b prove_c_divide_b_LE_c_divide_a quotient_less_equal1 quotient_less_equal2 quotient_smaller_than_numerator quotient_property zero_is_smallest less_equal_and_equal
% 0.58/0.75
%------------------------------------------------------------------------------