TSTP Solution File: HEN006-6 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HEN006-6 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n004.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 13:03:05 EDT 2022
% Result : Unsatisfiable 0.76s 0.95s
% Output : Refutation 0.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 10
% Syntax : Number of clauses : 45 ( 26 unt; 0 nHn; 45 RR)
% Number of literals : 67 ( 0 equ; 23 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 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(2,axiom,
equal(divide(zero,u),zero),
file('HEN006-6.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(u,u),zero),
file('HEN006-6.p',unknown),
[] ).
cnf(4,axiom,
less_equal(divide(a,b),d),
file('HEN006-6.p',unknown),
[] ).
cnf(5,axiom,
~ less_equal(divide(a,d),b),
file('HEN006-6.p',unknown),
[] ).
cnf(6,axiom,
( ~ less_equal(u,v)
| equal(divide(u,v),zero) ),
file('HEN006-6.p',unknown),
[] ).
cnf(7,axiom,
( ~ equal(divide(u,v),zero)
| less_equal(u,v) ),
file('HEN006-6.p',unknown),
[] ).
cnf(8,axiom,
less_equal(divide(u,v),u),
file('HEN006-6.p',unknown),
[] ).
cnf(9,axiom,
less_equal(divide(divide(u,v),divide(w,v)),divide(divide(u,w),v)),
file('HEN006-6.p',unknown),
[] ).
cnf(10,axiom,
less_equal(zero,u),
file('HEN006-6.p',unknown),
[] ).
cnf(11,axiom,
( ~ less_equal(u,v)
| ~ less_equal(v,u)
| equal(v,u) ),
file('HEN006-6.p',unknown),
[] ).
cnf(33,plain,
( ~ equal(zero,zero)
| less_equal(u,u) ),
inference(spl,[status(thm),theory(equality)],[3,7]),
[iquote('0:SpL:3.0,7.0')] ).
cnf(37,plain,
less_equal(u,u),
inference(obv,[status(thm),theory(equality)],[33]),
[iquote('0:Obv:33.0')] ).
cnf(38,plain,
( ~ less_equal(u,zero)
| equal(u,zero) ),
inference(res,[status(thm),theory(equality)],[10,11]),
[iquote('0:Res:10.0,11.0')] ).
cnf(42,plain,
( ~ less_equal(u,divide(u,v))
| equal(divide(u,v),u) ),
inference(res,[status(thm),theory(equality)],[8,11]),
[iquote('0:Res:8.0,11.0')] ).
cnf(49,plain,
( ~ less_equal(u,v)
| less_equal(divide(divide(u,w),divide(v,w)),divide(zero,w)) ),
inference(spr,[status(thm),theory(equality)],[6,9]),
[iquote('0:SpR:6.1,9.0')] ).
cnf(51,plain,
less_equal(divide(divide(u,divide(u,v)),divide(v,divide(u,v))),zero),
inference(spr,[status(thm),theory(equality)],[3,9]),
[iquote('0:SpR:3.0,9.0')] ).
cnf(53,plain,
less_equal(divide(divide(u,v),zero),divide(divide(u,zero),v)),
inference(spr,[status(thm),theory(equality)],[2,9]),
[iquote('0:SpR:2.0,9.0')] ).
cnf(63,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)],[9,11]),
[iquote('0:Res:9.0,11.0')] ).
cnf(71,plain,
( ~ less_equal(u,v)
| less_equal(divide(divide(u,w),divide(v,w)),zero) ),
inference(rew,[status(thm),theory(equality)],[2,49]),
[iquote('0:Rew:2.0,49.1')] ).
cnf(173,plain,
less_equal(divide(divide(u,divide(u,zero)),zero),zero),
inference(spr,[status(thm),theory(equality)],[3,53]),
[iquote('0:SpR:3.0,53.0')] ).
cnf(377,plain,
equal(divide(divide(u,divide(u,zero)),zero),zero),
inference(res,[status(thm),theory(equality)],[173,38]),
[iquote('0:Res:173.0,38.0')] ).
cnf(406,plain,
( ~ equal(zero,zero)
| less_equal(divide(u,divide(u,zero)),zero) ),
inference(spl,[status(thm),theory(equality)],[377,7]),
[iquote('0:SpL:377.0,7.0')] ).
cnf(413,plain,
less_equal(divide(u,divide(u,zero)),zero),
inference(obv,[status(thm),theory(equality)],[406]),
[iquote('0:Obv:406.0')] ).
cnf(429,plain,
equal(divide(u,divide(u,zero)),zero),
inference(res,[status(thm),theory(equality)],[413,38]),
[iquote('0:Res:413.0,38.0')] ).
cnf(463,plain,
equal(divide(divide(u,divide(u,v)),divide(v,divide(u,v))),zero),
inference(res,[status(thm),theory(equality)],[51,38]),
[iquote('0:Res:51.0,38.0')] ).
cnf(497,plain,
( ~ equal(zero,zero)
| less_equal(u,divide(u,zero)) ),
inference(spl,[status(thm),theory(equality)],[429,7]),
[iquote('0:SpL:429.0,7.0')] ).
cnf(502,plain,
less_equal(u,divide(u,zero)),
inference(obv,[status(thm),theory(equality)],[497]),
[iquote('0:Obv:497.0')] ).
cnf(515,plain,
equal(divide(u,zero),u),
inference(res,[status(thm),theory(equality)],[502,42]),
[iquote('0:Res:502.0,42.0')] ).
cnf(588,plain,
( ~ less_equal(u,v)
| equal(divide(divide(u,w),divide(v,w)),zero) ),
inference(res,[status(thm),theory(equality)],[71,38]),
[iquote('0:Res:71.1,38.0')] ).
cnf(1073,plain,
( ~ equal(zero,zero)
| less_equal(divide(u,divide(u,v)),divide(v,divide(u,v))) ),
inference(spl,[status(thm),theory(equality)],[463,7]),
[iquote('0:SpL:463.0,7.0')] ).
cnf(1100,plain,
less_equal(divide(u,divide(u,v)),divide(v,divide(u,v))),
inference(obv,[status(thm),theory(equality)],[1073]),
[iquote('0:Obv:1073.0')] ).
cnf(1165,plain,
( ~ less_equal(u,v)
| ~ less_equal(w,u)
| equal(divide(divide(w,v),zero),zero) ),
inference(spr,[status(thm),theory(equality)],[6,588]),
[iquote('0:SpR:6.1,588.1')] ).
cnf(1197,plain,
( ~ less_equal(u,v)
| ~ less_equal(w,u)
| equal(divide(w,v),zero) ),
inference(rew,[status(thm),theory(equality)],[515,1165]),
[iquote('0:Rew:515.0,1165.2')] ).
cnf(3226,plain,
( ~ less_equal(u,divide(a,b))
| equal(divide(u,d),zero) ),
inference(res,[status(thm),theory(equality)],[4,1197]),
[iquote('0:Res:4.0,1197.0')] ).
cnf(3227,plain,
( ~ less_equal(u,divide(v,w))
| equal(divide(u,v),zero) ),
inference(res,[status(thm),theory(equality)],[8,1197]),
[iquote('0:Res:8.0,1197.0')] ).
cnf(3319,plain,
equal(divide(divide(a,b),d),zero),
inference(res,[status(thm),theory(equality)],[37,3226]),
[iquote('0:Res:37.0,3226.0')] ).
cnf(3380,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)],[3319,63]),
[iquote('0:SpL:3319.0,63.0')] ).
cnf(3398,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)],[3319,3380]),
[iquote('0:Rew:3319.0,3380.1')] ).
cnf(3399,plain,
equal(divide(divide(a,d),divide(b,d)),zero),
inference(mrr,[status(thm)],[3398,10]),
[iquote('0:MRR:3398.0,10.0')] ).
cnf(3423,plain,
less_equal(divide(divide(a,d),zero),divide(divide(b,d),zero)),
inference(spr,[status(thm),theory(equality)],[3399,1100]),
[iquote('0:SpR:3399.0,1100.0')] ).
cnf(3478,plain,
less_equal(divide(a,d),divide(b,d)),
inference(rew,[status(thm),theory(equality)],[515,3423]),
[iquote('0:Rew:515.0,3423.0,515.0,3423.0')] ).
cnf(5891,plain,
equal(divide(divide(a,d),b),zero),
inference(res,[status(thm),theory(equality)],[3478,3227]),
[iquote('0:Res:3478.0,3227.0')] ).
cnf(6022,plain,
less_equal(divide(divide(a,d),zero),divide(b,zero)),
inference(spr,[status(thm),theory(equality)],[5891,1100]),
[iquote('0:SpR:5891.0,1100.0')] ).
cnf(6077,plain,
less_equal(divide(a,d),b),
inference(rew,[status(thm),theory(equality)],[515,6022]),
[iquote('0:Rew:515.0,6022.0,515.0,6022.0')] ).
cnf(6078,plain,
$false,
inference(mrr,[status(thm)],[6077,5]),
[iquote('0:MRR:6077.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : HEN006-6 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n004.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Fri Jul 1 14:48:38 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.76/0.95
% 0.76/0.95 SPASS V 3.9
% 0.76/0.95 SPASS beiseite: Proof found.
% 0.76/0.95 % SZS status Theorem
% 0.76/0.95 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.76/0.95 SPASS derived 4302 clauses, backtracked 0 clauses, performed 0 splits and kept 677 clauses.
% 0.76/0.95 SPASS allocated 67218 KBytes.
% 0.76/0.95 SPASS spent 0:00:00.56 on the problem.
% 0.76/0.95 0:00:00.03 for the input.
% 0.76/0.95 0:00:00.00 for the FLOTTER CNF translation.
% 0.76/0.95 0:00:00.04 for inferences.
% 0.76/0.95 0:00:00.00 for the backtracking.
% 0.76/0.95 0:00:00.47 for the reduction.
% 0.76/0.95
% 0.76/0.95
% 0.76/0.95 Here is a proof with depth 9, length 45 :
% 0.76/0.95 % SZS output start Refutation
% See solution above
% 0.76/0.95 Formulae used in the proof : zero_divide_anything_is_zero x_divide_x_is_zero 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
% 0.76/0.95
%------------------------------------------------------------------------------