TSTP Solution File: HEN004-3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HEN004-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 0.43s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of clauses : 25 ( 14 unt; 0 nHn; 25 RR)
% Number of literals : 38 ( 0 equ; 16 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 : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(divide(a,zero),a),
file('HEN004-3.p',unknown),
[] ).
cnf(2,axiom,
( ~ less_equal(u,v)
| equal(divide(u,v),zero) ),
file('HEN004-3.p',unknown),
[] ).
cnf(3,axiom,
( ~ equal(divide(u,v),zero)
| less_equal(u,v) ),
file('HEN004-3.p',unknown),
[] ).
cnf(4,axiom,
less_equal(divide(u,v),u),
file('HEN004-3.p',unknown),
[] ).
cnf(5,axiom,
less_equal(divide(divide(u,v),divide(w,v)),divide(divide(u,w),v)),
file('HEN004-3.p',unknown),
[] ).
cnf(6,axiom,
less_equal(zero,u),
file('HEN004-3.p',unknown),
[] ).
cnf(7,axiom,
( ~ less_equal(u,v)
| ~ less_equal(v,u)
| equal(v,u) ),
file('HEN004-3.p',unknown),
[] ).
cnf(9,plain,
( ~ less_equal(divide(a,zero),a)
| ~ less_equal(a,divide(a,zero)) ),
inference(res,[status(thm),theory(equality)],[7,1]),
[iquote('0:Res:7.2,1.0')] ).
cnf(11,plain,
~ less_equal(a,divide(a,zero)),
inference(mrr,[status(thm)],[9,4]),
[iquote('0:MRR:9.0,4.0')] ).
cnf(18,plain,
( ~ less_equal(u,zero)
| equal(u,zero) ),
inference(res,[status(thm),theory(equality)],[6,7]),
[iquote('0:Res:6.0,7.0')] ).
cnf(28,plain,
equal(divide(zero,u),zero),
inference(res,[status(thm),theory(equality)],[4,18]),
[iquote('0:Res:4.0,18.0')] ).
cnf(35,plain,
less_equal(divide(divide(u,v),zero),divide(divide(u,zero),v)),
inference(spr,[status(thm),theory(equality)],[28,5]),
[iquote('0:SpR:28.0,5.0')] ).
cnf(43,plain,
( ~ less_equal(divide(u,zero),v)
| less_equal(divide(divide(u,v),zero),zero) ),
inference(spr,[status(thm),theory(equality)],[2,35]),
[iquote('0:SpR:2.1,35.0')] ).
cnf(206,plain,
( ~ less_equal(divide(u,zero),v)
| equal(divide(divide(u,v),zero),zero) ),
inference(res,[status(thm),theory(equality)],[43,18]),
[iquote('0:Res:43.1,18.0')] ).
cnf(243,plain,
( ~ less_equal(divide(u,zero),v)
| ~ equal(zero,zero)
| less_equal(divide(u,v),zero) ),
inference(spl,[status(thm),theory(equality)],[206,3]),
[iquote('0:SpL:206.1,3.0')] ).
cnf(246,plain,
( ~ less_equal(divide(u,zero),v)
| less_equal(divide(u,v),zero) ),
inference(obv,[status(thm),theory(equality)],[243]),
[iquote('0:Obv:243.1')] ).
cnf(256,plain,
less_equal(divide(u,u),zero),
inference(res,[status(thm),theory(equality)],[4,246]),
[iquote('0:Res:4.0,246.0')] ).
cnf(327,plain,
equal(divide(u,u),zero),
inference(res,[status(thm),theory(equality)],[256,18]),
[iquote('0:Res:256.0,18.0')] ).
cnf(349,plain,
( ~ equal(zero,zero)
| less_equal(u,u) ),
inference(spl,[status(thm),theory(equality)],[327,3]),
[iquote('0:SpL:327.0,3.0')] ).
cnf(353,plain,
less_equal(u,u),
inference(obv,[status(thm),theory(equality)],[349]),
[iquote('0:Obv:349.0')] ).
cnf(426,plain,
less_equal(divide(u,divide(u,zero)),zero),
inference(res,[status(thm),theory(equality)],[353,246]),
[iquote('0:Res:353.0,246.0')] ).
cnf(437,plain,
equal(divide(u,divide(u,zero)),zero),
inference(res,[status(thm),theory(equality)],[426,18]),
[iquote('0:Res:426.0,18.0')] ).
cnf(463,plain,
( ~ equal(zero,zero)
| less_equal(u,divide(u,zero)) ),
inference(spl,[status(thm),theory(equality)],[437,3]),
[iquote('0:SpL:437.0,3.0')] ).
cnf(470,plain,
less_equal(u,divide(u,zero)),
inference(obv,[status(thm),theory(equality)],[463]),
[iquote('0:Obv:463.0')] ).
cnf(471,plain,
$false,
inference(unc,[status(thm)],[470,11]),
[iquote('0:UnC:470.0,11.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : HEN004-3 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.12 % Command : run_spass %d %s
% 0.13/0.32 % Computer : n025.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 600
% 0.13/0.32 % DateTime : Fri Jul 1 13:26:09 EDT 2022
% 0.13/0.32 % CPUTime :
% 0.17/0.43
% 0.17/0.43 SPASS V 3.9
% 0.17/0.43 SPASS beiseite: Proof found.
% 0.17/0.43 % SZS status Theorem
% 0.17/0.43 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 SPASS derived 347 clauses, backtracked 0 clauses, performed 0 splits and kept 94 clauses.
% 0.17/0.43 SPASS allocated 63446 KBytes.
% 0.17/0.43 SPASS spent 0:00:00.09 on the problem.
% 0.17/0.43 0:00:00.04 for the input.
% 0.17/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.17/0.43 0:00:00.01 for inferences.
% 0.17/0.43 0:00:00.00 for the backtracking.
% 0.17/0.43 0:00:00.03 for the reduction.
% 0.17/0.43
% 0.17/0.43
% 0.17/0.43 Here is a proof with depth 12, length 25 :
% 0.17/0.43 % SZS output start Refutation
% See solution above
% 0.17/0.43 Formulae used in the proof : prove_x_divide_zero_is_x quotient_less_equal1 quotient_less_equal2 quotient_smaller_than_numerator quotient_property zero_is_smallest less_equal_and_equal
% 0.17/0.43
%------------------------------------------------------------------------------