TSTP Solution File: HEN005-3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HEN005-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 13:03:02 EDT 2022
% Result : Unsatisfiable 0.19s 0.51s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 9
% Syntax : Number of clauses : 36 ( 18 unt; 0 nHn; 36 RR)
% Number of literals : 58 ( 0 equ; 26 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('HEN005-3.p',unknown),
[] ).
cnf(2,axiom,
less_equal(b,c),
file('HEN005-3.p',unknown),
[] ).
cnf(3,axiom,
~ less_equal(a,c),
file('HEN005-3.p',unknown),
[] ).
cnf(4,axiom,
( ~ less_equal(u,v)
| equal(divide(u,v),zero) ),
file('HEN005-3.p',unknown),
[] ).
cnf(5,axiom,
( ~ equal(divide(u,v),zero)
| less_equal(u,v) ),
file('HEN005-3.p',unknown),
[] ).
cnf(6,axiom,
less_equal(divide(u,v),u),
file('HEN005-3.p',unknown),
[] ).
cnf(7,axiom,
less_equal(divide(divide(u,v),divide(w,v)),divide(divide(u,w),v)),
file('HEN005-3.p',unknown),
[] ).
cnf(8,axiom,
less_equal(zero,u),
file('HEN005-3.p',unknown),
[] ).
cnf(9,axiom,
( ~ less_equal(u,v)
| ~ less_equal(v,u)
| equal(v,u) ),
file('HEN005-3.p',unknown),
[] ).
cnf(11,plain,
~ equal(divide(a,c),zero),
inference(res,[status(thm),theory(equality)],[5,3]),
[iquote('0:Res:5.1,3.0')] ).
cnf(19,plain,
( ~ less_equal(u,zero)
| equal(u,zero) ),
inference(res,[status(thm),theory(equality)],[8,9]),
[iquote('0:Res:8.0,9.0')] ).
cnf(20,plain,
( ~ less_equal(u,divide(u,v))
| equal(divide(u,v),u) ),
inference(res,[status(thm),theory(equality)],[6,9]),
[iquote('0:Res:6.0,9.0')] ).
cnf(23,plain,
equal(divide(zero,u),zero),
inference(res,[status(thm),theory(equality)],[6,19]),
[iquote('0:Res:6.0,19.0')] ).
cnf(29,plain,
( ~ less_equal(u,v)
| less_equal(divide(divide(u,w),divide(v,w)),divide(zero,w)) ),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.1,7.0')] ).
cnf(33,plain,
less_equal(divide(divide(u,v),zero),divide(divide(u,zero),v)),
inference(spr,[status(thm),theory(equality)],[23,7]),
[iquote('0:SpR:23.0,7.0')] ).
cnf(39,plain,
( ~ less_equal(u,v)
| less_equal(divide(divide(u,w),divide(v,w)),zero) ),
inference(rew,[status(thm),theory(equality)],[23,29]),
[iquote('0:Rew:23.0,29.1')] ).
cnf(44,plain,
( ~ less_equal(divide(u,zero),v)
| less_equal(divide(divide(u,v),zero),zero) ),
inference(spr,[status(thm),theory(equality)],[4,33]),
[iquote('0:SpR:4.1,33.0')] ).
cnf(137,plain,
( ~ less_equal(u,v)
| equal(divide(divide(u,w),divide(v,w)),zero) ),
inference(res,[status(thm),theory(equality)],[39,19]),
[iquote('0:Res:39.1,19.0')] ).
cnf(193,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(244,plain,
( ~ less_equal(divide(u,zero),v)
| ~ equal(zero,zero)
| less_equal(divide(u,v),zero) ),
inference(spl,[status(thm),theory(equality)],[193,5]),
[iquote('0:SpL:193.1,5.0')] ).
cnf(247,plain,
( ~ less_equal(divide(u,zero),v)
| less_equal(divide(u,v),zero) ),
inference(obv,[status(thm),theory(equality)],[244]),
[iquote('0:Obv:244.1')] ).
cnf(257,plain,
less_equal(divide(u,u),zero),
inference(res,[status(thm),theory(equality)],[6,247]),
[iquote('0:Res:6.0,247.0')] ).
cnf(328,plain,
equal(divide(u,u),zero),
inference(res,[status(thm),theory(equality)],[257,19]),
[iquote('0:Res:257.0,19.0')] ).
cnf(350,plain,
( ~ equal(zero,zero)
| less_equal(u,u) ),
inference(spl,[status(thm),theory(equality)],[328,5]),
[iquote('0:SpL:328.0,5.0')] ).
cnf(354,plain,
less_equal(u,u),
inference(obv,[status(thm),theory(equality)],[350]),
[iquote('0:Obv:350.0')] ).
cnf(365,plain,
less_equal(divide(u,divide(u,zero)),zero),
inference(res,[status(thm),theory(equality)],[354,247]),
[iquote('0:Res:354.0,247.0')] ).
cnf(438,plain,
equal(divide(u,divide(u,zero)),zero),
inference(res,[status(thm),theory(equality)],[365,19]),
[iquote('0:Res:365.0,19.0')] ).
cnf(464,plain,
( ~ equal(zero,zero)
| less_equal(u,divide(u,zero)) ),
inference(spl,[status(thm),theory(equality)],[438,5]),
[iquote('0:SpL:438.0,5.0')] ).
cnf(471,plain,
less_equal(u,divide(u,zero)),
inference(obv,[status(thm),theory(equality)],[464]),
[iquote('0:Obv:464.0')] ).
cnf(494,plain,
equal(divide(u,zero),u),
inference(res,[status(thm),theory(equality)],[471,20]),
[iquote('0:Res:471.0,20.0')] ).
cnf(651,plain,
( ~ less_equal(u,v)
| ~ less_equal(w,u)
| equal(divide(divide(w,v),zero),zero) ),
inference(spr,[status(thm),theory(equality)],[4,137]),
[iquote('0:SpR:4.1,137.1')] ).
cnf(676,plain,
( ~ less_equal(u,v)
| ~ less_equal(w,u)
| equal(divide(w,v),zero) ),
inference(rew,[status(thm),theory(equality)],[494,651]),
[iquote('0:Rew:494.0,651.2')] ).
cnf(1234,plain,
( ~ less_equal(u,b)
| equal(divide(u,c),zero) ),
inference(res,[status(thm),theory(equality)],[2,676]),
[iquote('0:Res:2.0,676.0')] ).
cnf(1275,plain,
( ~ less_equal(a,b)
| ~ equal(zero,zero) ),
inference(spl,[status(thm),theory(equality)],[1234,11]),
[iquote('0:SpL:1234.1,11.0')] ).
cnf(1279,plain,
~ less_equal(a,b),
inference(obv,[status(thm),theory(equality)],[1275]),
[iquote('0:Obv:1275.1')] ).
cnf(1280,plain,
$false,
inference(mrr,[status(thm)],[1279,1]),
[iquote('0:MRR:1279.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : HEN005-3 : TPTP v8.1.0. Released v1.0.0.
% 0.13/0.13 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n027.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % 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 14:05:07 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.51
% 0.19/0.51 SPASS V 3.9
% 0.19/0.51 SPASS beiseite: Proof found.
% 0.19/0.51 % SZS status Theorem
% 0.19/0.51 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.51 SPASS derived 906 clauses, backtracked 0 clauses, performed 0 splits and kept 234 clauses.
% 0.19/0.51 SPASS allocated 64026 KBytes.
% 0.19/0.51 SPASS spent 0:00:00.16 on the problem.
% 0.19/0.51 0:00:00.04 for the input.
% 0.19/0.51 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.51 0:00:00.01 for inferences.
% 0.19/0.51 0:00:00.00 for the backtracking.
% 0.19/0.51 0:00:00.08 for the reduction.
% 0.19/0.51
% 0.19/0.51
% 0.19/0.51 Here is a proof with depth 13, length 36 :
% 0.19/0.51 % SZS output start Refutation
% See solution above
% 0.19/0.51 Formulae used in the proof : a_LE_b b_LE_c prove_a_LE_c quotient_less_equal1 quotient_less_equal2 quotient_smaller_than_numerator quotient_property zero_is_smallest less_equal_and_equal
% 0.19/0.51
%------------------------------------------------------------------------------