TSTP Solution File: HEN004-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HEN004-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n013.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 13:03:00 EDT 2022
% Result : Unsatisfiable 0.21s 0.48s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of clauses : 26 ( 12 unt; 0 nHn; 26 RR)
% Number of literals : 51 ( 0 equ; 26 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
quotient(zero,u,zero),
file('HEN004-2.p',unknown),
[] ).
cnf(3,axiom,
quotient(u,u,zero),
file('HEN004-2.p',unknown),
[] ).
cnf(4,axiom,
~ quotient(x__dfg,zero,x__dfg),
file('HEN004-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ quotient(u,v,zero)
| less_equal(u,v) ),
file('HEN004-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ quotient(u,v,w)
| less_equal(w,u) ),
file('HEN004-2.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('HEN004-2.p',unknown),
[] ).
cnf(9,axiom,
less_equal(zero,u),
file('HEN004-2.p',unknown),
[] ).
cnf(10,axiom,
( ~ less_equal(u,v)
| ~ less_equal(v,u)
| equal(v,u) ),
file('HEN004-2.p',unknown),
[] ).
cnf(12,axiom,
quotient(u,v,divide(u,v)),
file('HEN004-2.p',unknown),
[] ).
cnf(22,plain,
less_equal(divide(u,v),u),
inference(res,[status(thm),theory(equality)],[12,7]),
[iquote('0:Res:12.0,7.0')] ).
cnf(23,plain,
( ~ less_equal(u,zero)
| equal(u,zero) ),
inference(res,[status(thm),theory(equality)],[9,10]),
[iquote('0:Res:9.0,10.0')] ).
cnf(24,plain,
( ~ less_equal(u,divide(u,v))
| equal(divide(u,v),u) ),
inference(res,[status(thm),theory(equality)],[22,10]),
[iquote('0:Res:22.0,10.0')] ).
cnf(52,plain,
( ~ quotient(u,v,w)
| ~ quotient(x,y,u)
| ~ quotient(z,y,v)
| ~ quotient(x,z,y)
| less_equal(w,zero) ),
inference(res,[status(thm),theory(equality)],[3,8]),
[iquote('0:Res:3.0,8.0')] ).
cnf(144,plain,
( ~ quotient(u,v,w)
| ~ quotient(x,v,y)
| ~ quotient(u,x,v)
| less_equal(divide(w,y),zero) ),
inference(res,[status(thm),theory(equality)],[12,52]),
[iquote('0:Res:12.0,52.0')] ).
cnf(295,plain,
( ~ quotient(u,v,w)
| ~ quotient(x,u,v)
| less_equal(divide(divide(x,v),w),zero) ),
inference(res,[status(thm),theory(equality)],[12,144]),
[iquote('0:Res:12.0,144.0')] ).
cnf(546,plain,
( ~ quotient(u,zero,v)
| less_equal(divide(divide(u,v),zero),zero) ),
inference(res,[status(thm),theory(equality)],[2,295]),
[iquote('0:Res:2.0,295.0')] ).
cnf(570,plain,
( ~ quotient(u,zero,v)
| equal(divide(divide(u,v),zero),zero) ),
inference(res,[status(thm),theory(equality)],[546,23]),
[iquote('0:Res:546.1,23.0')] ).
cnf(572,plain,
( ~ quotient(u,zero,v)
| quotient(divide(u,v),zero,zero) ),
inference(spr,[status(thm),theory(equality)],[570,12]),
[iquote('0:SpR:570.1,12.0')] ).
cnf(609,plain,
( ~ quotient(u,zero,v)
| less_equal(divide(u,v),zero) ),
inference(res,[status(thm),theory(equality)],[572,6]),
[iquote('0:Res:572.1,6.0')] ).
cnf(643,plain,
( ~ quotient(u,zero,v)
| equal(divide(u,v),zero) ),
inference(res,[status(thm),theory(equality)],[609,23]),
[iquote('0:Res:609.1,23.0')] ).
cnf(673,plain,
equal(divide(u,divide(u,zero)),zero),
inference(res,[status(thm),theory(equality)],[12,643]),
[iquote('0:Res:12.0,643.0')] ).
cnf(674,plain,
quotient(u,divide(u,zero),zero),
inference(spr,[status(thm),theory(equality)],[673,12]),
[iquote('0:SpR:673.0,12.0')] ).
cnf(707,plain,
less_equal(u,divide(u,zero)),
inference(res,[status(thm),theory(equality)],[674,6]),
[iquote('0:Res:674.0,6.0')] ).
cnf(738,plain,
equal(divide(u,zero),u),
inference(res,[status(thm),theory(equality)],[707,24]),
[iquote('0:Res:707.0,24.0')] ).
cnf(794,plain,
quotient(u,zero,u),
inference(spr,[status(thm),theory(equality)],[738,12]),
[iquote('0:SpR:738.0,12.0')] ).
cnf(813,plain,
$false,
inference(unc,[status(thm)],[794,4]),
[iquote('0:UnC:794.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : HEN004-2 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n013.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Fri Jul 1 13:24:59 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.21/0.48
% 0.21/0.48 SPASS V 3.9
% 0.21/0.48 SPASS beiseite: Proof found.
% 0.21/0.48 % SZS status Theorem
% 0.21/0.48 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.48 SPASS derived 730 clauses, backtracked 0 clauses, performed 0 splits and kept 165 clauses.
% 0.21/0.48 SPASS allocated 63658 KBytes.
% 0.21/0.48 SPASS spent 0:00:00.13 on the problem.
% 0.21/0.48 0:00:00.03 for the input.
% 0.21/0.48 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.48 0:00:00.01 for inferences.
% 0.21/0.48 0:00:00.00 for the backtracking.
% 0.21/0.48 0:00:00.06 for the reduction.
% 0.21/0.48
% 0.21/0.48
% 0.21/0.48 Here is a proof with depth 13, length 26 :
% 0.21/0.48 % SZS output start Refutation
% See solution above
% 0.21/0.48 Formulae used in the proof : zero_divide_anything_is_zero x_divide_x_is_zero prove_x_divde_zero_is_x less_equal_quotient divisor_existence quotient_property zero_is_smallest less_equal_and_equal closure
% 0.21/0.48
%------------------------------------------------------------------------------