TSTP Solution File: HEN006-3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HEN006-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 13:03:04 EDT 2022
% Result : Unsatisfiable 0.62s 0.79s
% Output : Refutation 0.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 8
% Syntax : Number of clauses : 43 ( 20 unt; 0 nHn; 43 RR)
% Number of literals : 70 ( 0 equ; 28 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(divide(a,b),d),
file('HEN006-3.p',unknown),
[] ).
cnf(2,axiom,
~ less_equal(divide(a,d),b),
file('HEN006-3.p',unknown),
[] ).
cnf(3,axiom,
( ~ less_equal(u,v)
| equal(divide(u,v),zero) ),
file('HEN006-3.p',unknown),
[] ).
cnf(4,axiom,
( ~ equal(divide(u,v),zero)
| less_equal(u,v) ),
file('HEN006-3.p',unknown),
[] ).
cnf(5,axiom,
less_equal(divide(u,v),u),
file('HEN006-3.p',unknown),
[] ).
cnf(6,axiom,
less_equal(divide(divide(u,v),divide(w,v)),divide(divide(u,w),v)),
file('HEN006-3.p',unknown),
[] ).
cnf(7,axiom,
less_equal(zero,u),
file('HEN006-3.p',unknown),
[] ).
cnf(8,axiom,
( ~ less_equal(u,v)
| ~ less_equal(v,u)
| equal(v,u) ),
file('HEN006-3.p',unknown),
[] ).
cnf(17,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(21,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(26,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(28,plain,
equal(divide(zero,u),zero),
inference(res,[status(thm),theory(equality)],[5,17]),
[iquote('0:Res:5.0,17.0')] ).
cnf(30,plain,
( ~ less_equal(u,v)
| less_equal(divide(divide(u,w),divide(v,w)),zero) ),
inference(rew,[status(thm),theory(equality)],[28,21]),
[iquote('0:Rew:28.0,21.1')] ).
cnf(35,plain,
less_equal(divide(divide(u,v),zero),divide(divide(u,zero),v)),
inference(spr,[status(thm),theory(equality)],[28,6]),
[iquote('0:SpR:28.0,6.0')] ).
cnf(50,plain,
( ~ less_equal(divide(u,zero),v)
| less_equal(divide(divide(u,v),zero),zero) ),
inference(spr,[status(thm),theory(equality)],[3,35]),
[iquote('0:SpR:3.1,35.0')] ).
cnf(107,plain,
( ~ less_equal(u,v)
| equal(divide(divide(u,w),divide(v,w)),zero) ),
inference(res,[status(thm),theory(equality)],[30,17]),
[iquote('0:Res:30.1,17.0')] ).
cnf(204,plain,
( ~ less_equal(divide(u,zero),v)
| equal(divide(divide(u,v),zero),zero) ),
inference(res,[status(thm),theory(equality)],[50,17]),
[iquote('0:Res:50.1,17.0')] ).
cnf(263,plain,
( ~ less_equal(divide(u,zero),v)
| ~ equal(zero,zero)
| less_equal(divide(u,v),zero) ),
inference(spl,[status(thm),theory(equality)],[204,4]),
[iquote('0:SpL:204.1,4.0')] ).
cnf(266,plain,
( ~ less_equal(divide(u,zero),v)
| less_equal(divide(u,v),zero) ),
inference(obv,[status(thm),theory(equality)],[263]),
[iquote('0:Obv:263.1')] ).
cnf(279,plain,
less_equal(divide(u,u),zero),
inference(res,[status(thm),theory(equality)],[5,266]),
[iquote('0:Res:5.0,266.0')] ).
cnf(375,plain,
equal(divide(u,u),zero),
inference(res,[status(thm),theory(equality)],[279,17]),
[iquote('0:Res:279.0,17.0')] ).
cnf(397,plain,
( ~ equal(zero,zero)
| less_equal(u,u) ),
inference(spl,[status(thm),theory(equality)],[375,4]),
[iquote('0:SpL:375.0,4.0')] ).
cnf(406,plain,
less_equal(u,u),
inference(obv,[status(thm),theory(equality)],[397]),
[iquote('0:Obv:397.0')] ).
cnf(424,plain,
less_equal(divide(u,divide(u,zero)),zero),
inference(res,[status(thm),theory(equality)],[406,266]),
[iquote('0:Res:406.0,266.0')] ).
cnf(435,plain,
equal(divide(u,divide(u,zero)),zero),
inference(res,[status(thm),theory(equality)],[424,17]),
[iquote('0:Res:424.0,17.0')] ).
cnf(459,plain,
( ~ less_equal(u,v)
| ~ less_equal(w,u)
| equal(divide(divide(w,v),zero),zero) ),
inference(spr,[status(thm),theory(equality)],[3,107]),
[iquote('0:SpR:3.1,107.1')] ).
cnf(521,plain,
( ~ equal(zero,zero)
| less_equal(u,divide(u,zero)) ),
inference(spl,[status(thm),theory(equality)],[435,4]),
[iquote('0:SpL:435.0,4.0')] ).
cnf(528,plain,
less_equal(u,divide(u,zero)),
inference(obv,[status(thm),theory(equality)],[521]),
[iquote('0:Obv:521.0')] ).
cnf(552,plain,
equal(divide(u,zero),u),
inference(res,[status(thm),theory(equality)],[528,20]),
[iquote('0:Res:528.0,20.0')] ).
cnf(583,plain,
( ~ less_equal(u,v)
| ~ less_equal(w,u)
| equal(divide(w,v),zero) ),
inference(rew,[status(thm),theory(equality)],[552,459]),
[iquote('0:Rew:552.0,459.2')] ).
cnf(1091,plain,
( ~ less_equal(u,divide(a,b))
| equal(divide(u,d),zero) ),
inference(res,[status(thm),theory(equality)],[1,583]),
[iquote('0:Res:1.0,583.0')] ).
cnf(1092,plain,
( ~ less_equal(u,divide(v,w))
| equal(divide(u,v),zero) ),
inference(res,[status(thm),theory(equality)],[5,583]),
[iquote('0:Res:5.0,583.0')] ).
cnf(1554,plain,
equal(divide(divide(a,b),d),zero),
inference(res,[status(thm),theory(equality)],[406,1091]),
[iquote('0:Res:406.0,1091.0')] ).
cnf(1592,plain,
( ~ less_equal(zero,divide(divide(a,d),divide(b,d)))
| equal(divide(divide(a,d),divide(b,d)),divide(divide(a,b),d)) ),
inference(spl,[status(thm),theory(equality)],[1554,26]),
[iquote('0:SpL:1554.0,26.0')] ).
cnf(1606,plain,
( ~ less_equal(zero,divide(divide(a,d),divide(b,d)))
| equal(divide(divide(a,d),divide(b,d)),zero) ),
inference(rew,[status(thm),theory(equality)],[1554,1592]),
[iquote('0:Rew:1554.0,1592.1')] ).
cnf(1607,plain,
equal(divide(divide(a,d),divide(b,d)),zero),
inference(mrr,[status(thm)],[1606,7]),
[iquote('0:MRR:1606.0,7.0')] ).
cnf(1869,plain,
( ~ equal(zero,zero)
| less_equal(divide(a,d),divide(b,d)) ),
inference(spl,[status(thm),theory(equality)],[1607,4]),
[iquote('0:SpL:1607.0,4.0')] ).
cnf(1879,plain,
less_equal(divide(a,d),divide(b,d)),
inference(obv,[status(thm),theory(equality)],[1869]),
[iquote('0:Obv:1869.0')] ).
cnf(3549,plain,
equal(divide(divide(a,d),b),zero),
inference(res,[status(thm),theory(equality)],[1879,1092]),
[iquote('0:Res:1879.0,1092.0')] ).
cnf(3594,plain,
( ~ equal(zero,zero)
| less_equal(divide(a,d),b) ),
inference(spl,[status(thm),theory(equality)],[3549,4]),
[iquote('0:SpL:3549.0,4.0')] ).
cnf(3611,plain,
less_equal(divide(a,d),b),
inference(obv,[status(thm),theory(equality)],[3594]),
[iquote('0:Obv:3594.0')] ).
cnf(3612,plain,
$false,
inference(mrr,[status(thm)],[3611,2]),
[iquote('0:MRR:3611.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : HEN006-3 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n018.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 14:10:47 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.62/0.79
% 0.62/0.79 SPASS V 3.9
% 0.62/0.79 SPASS beiseite: Proof found.
% 0.62/0.79 % SZS status Theorem
% 0.62/0.79 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.62/0.79 SPASS derived 2576 clauses, backtracked 0 clauses, performed 0 splits and kept 586 clauses.
% 0.62/0.79 SPASS allocated 65879 KBytes.
% 0.62/0.79 SPASS spent 0:00:00.43 on the problem.
% 0.62/0.79 0:00:00.04 for the input.
% 0.62/0.79 0:00:00.00 for the FLOTTER CNF translation.
% 0.62/0.79 0:00:00.03 for inferences.
% 0.62/0.79 0:00:00.00 for the backtracking.
% 0.62/0.79 0:00:00.34 for the reduction.
% 0.62/0.79
% 0.62/0.79
% 0.62/0.79 Here is a proof with depth 14, length 43 :
% 0.62/0.79 % SZS output start Refutation
% See solution above
% 0.62/0.79 Formulae used in the proof : a_divide_b_LE_d prove_a_divide_d_LE_b quotient_less_equal1 quotient_less_equal2 quotient_smaller_than_numerator quotient_property zero_is_smallest less_equal_and_equal
% 0.62/0.79
%------------------------------------------------------------------------------