TSTP Solution File: HEN004-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HEN004-1 : 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 13:03:00 EDT 2022
% Result : Unsatisfiable 0.17s 0.51s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 8
% Syntax : Number of clauses : 32 ( 17 unt; 0 nHn; 32 RR)
% Number of literals : 62 ( 0 equ; 31 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(1,axiom,
~ quotient(x__dfg,zero,x__dfg),
file('HEN004-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ less_equal(u,v)
| quotient(u,v,zero) ),
file('HEN004-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ quotient(u,v,zero)
| less_equal(u,v) ),
file('HEN004-1.p',unknown),
[] ).
cnf(4,axiom,
( ~ quotient(u,v,w)
| less_equal(w,u) ),
file('HEN004-1.p',unknown),
[] ).
cnf(5,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('HEN004-1.p',unknown),
[] ).
cnf(6,axiom,
less_equal(zero,u),
file('HEN004-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ less_equal(u,v)
| ~ less_equal(v,u)
| equal(v,u) ),
file('HEN004-1.p',unknown),
[] ).
cnf(9,axiom,
quotient(u,v,divide(u,v)),
file('HEN004-1.p',unknown),
[] ).
cnf(12,plain,
less_equal(divide(u,v),u),
inference(res,[status(thm),theory(equality)],[9,4]),
[iquote('0:Res:9.0,4.0')] ).
cnf(14,plain,
( ~ less_equal(u,zero)
| equal(u,zero) ),
inference(res,[status(thm),theory(equality)],[6,7]),
[iquote('0:Res:6.0,7.0')] ).
cnf(15,plain,
( ~ less_equal(u,divide(u,v))
| equal(divide(u,v),u) ),
inference(res,[status(thm),theory(equality)],[12,7]),
[iquote('0:Res:12.0,7.0')] ).
cnf(20,plain,
equal(divide(zero,u),zero),
inference(res,[status(thm),theory(equality)],[12,14]),
[iquote('0:Res:12.0,14.0')] ).
cnf(21,plain,
quotient(zero,u,zero),
inference(spr,[status(thm),theory(equality)],[20,9]),
[iquote('0:SpR:20.0,9.0')] ).
cnf(29,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)],[2,5]),
[iquote('0:Res:2.1,5.0')] ).
cnf(104,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)],[9,29]),
[iquote('0:Res:9.0,29.1')] ).
cnf(208,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)],[9,104]),
[iquote('0:Res:9.0,104.1')] ).
cnf(293,plain,
( ~ less_equal(u,v)
| ~ quotient(w,zero,u)
| less_equal(divide(divide(w,v),zero),zero) ),
inference(res,[status(thm),theory(equality)],[21,208]),
[iquote('0:Res:21.0,208.1')] ).
cnf(469,plain,
( ~ less_equal(divide(u,zero),v)
| less_equal(divide(divide(u,v),zero),zero) ),
inference(res,[status(thm),theory(equality)],[9,293]),
[iquote('0:Res:9.0,293.1')] ).
cnf(520,plain,
( ~ less_equal(divide(u,zero),v)
| equal(divide(divide(u,v),zero),zero) ),
inference(res,[status(thm),theory(equality)],[469,14]),
[iquote('0:Res:469.1,14.0')] ).
cnf(564,plain,
( ~ less_equal(divide(u,zero),v)
| quotient(divide(u,v),zero,zero) ),
inference(spr,[status(thm),theory(equality)],[520,9]),
[iquote('0:SpR:520.1,9.0')] ).
cnf(607,plain,
( ~ less_equal(divide(u,zero),v)
| less_equal(divide(u,v),zero) ),
inference(res,[status(thm),theory(equality)],[564,3]),
[iquote('0:Res:564.1,3.0')] ).
cnf(640,plain,
less_equal(divide(u,u),zero),
inference(res,[status(thm),theory(equality)],[12,607]),
[iquote('0:Res:12.0,607.0')] ).
cnf(751,plain,
equal(divide(u,u),zero),
inference(res,[status(thm),theory(equality)],[640,14]),
[iquote('0:Res:640.0,14.0')] ).
cnf(756,plain,
quotient(u,u,zero),
inference(spr,[status(thm),theory(equality)],[751,9]),
[iquote('0:SpR:751.0,9.0')] ).
cnf(807,plain,
less_equal(u,u),
inference(res,[status(thm),theory(equality)],[756,3]),
[iquote('0:Res:756.0,3.0')] ).
cnf(846,plain,
less_equal(divide(u,divide(u,zero)),zero),
inference(res,[status(thm),theory(equality)],[807,607]),
[iquote('0:Res:807.0,607.0')] ).
cnf(866,plain,
equal(divide(u,divide(u,zero)),zero),
inference(res,[status(thm),theory(equality)],[846,14]),
[iquote('0:Res:846.0,14.0')] ).
cnf(871,plain,
quotient(u,divide(u,zero),zero),
inference(spr,[status(thm),theory(equality)],[866,9]),
[iquote('0:SpR:866.0,9.0')] ).
cnf(935,plain,
less_equal(u,divide(u,zero)),
inference(res,[status(thm),theory(equality)],[871,3]),
[iquote('0:Res:871.0,3.0')] ).
cnf(977,plain,
equal(divide(u,zero),u),
inference(res,[status(thm),theory(equality)],[935,15]),
[iquote('0:Res:935.0,15.0')] ).
cnf(1079,plain,
quotient(u,zero,u),
inference(spr,[status(thm),theory(equality)],[977,9]),
[iquote('0:SpR:977.0,9.0')] ).
cnf(1102,plain,
$false,
inference(unc,[status(thm)],[1079,1]),
[iquote('0:UnC:1079.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : HEN004-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.11/0.33 % Computer : n009.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Fri Jul 1 14:32:07 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.17/0.51
% 0.17/0.51 SPASS V 3.9
% 0.17/0.51 SPASS beiseite: Proof found.
% 0.17/0.51 % SZS status Theorem
% 0.17/0.51 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.51 SPASS derived 903 clauses, backtracked 0 clauses, performed 0 splits and kept 220 clauses.
% 0.17/0.51 SPASS allocated 63881 KBytes.
% 0.17/0.51 SPASS spent 0:00:00.17 on the problem.
% 0.17/0.51 0:00:00.04 for the input.
% 0.17/0.51 0:00:00.00 for the FLOTTER CNF translation.
% 0.17/0.51 0:00:00.01 for inferences.
% 0.17/0.51 0:00:00.00 for the backtracking.
% 0.17/0.51 0:00:00.09 for the reduction.
% 0.17/0.51
% 0.17/0.51
% 0.17/0.51 Here is a proof with depth 18, length 32 :
% 0.17/0.51 % SZS output start Refutation
% See solution above
% 0.17/0.51 Formulae used in the proof : prove_x_divde_zero_is_x quotient_less_equal less_equal_quotient divisor_existence quotient_property zero_is_smallest less_equal_and_equal closure
% 0.17/0.51
%------------------------------------------------------------------------------