TSTP Solution File: HEN010-5 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HEN010-5 : TPTP v8.1.0. Bugfixed v1.2.1.
% 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 13:03:13 EDT 2022
% Result : Unsatisfiable 11.89s 12.08s
% Output : Refutation 11.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 8
% Syntax : Number of clauses : 74 ( 41 unt; 0 nHn; 74 RR)
% Number of literals : 113 ( 0 equ; 40 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 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(divide(u,v),w),zero)
| equal(divide(divide(u,w),v),zero) ),
file('HEN010-5.p',unknown),
[] ).
cnf(3,axiom,
( ~ equal(divide(u,v),zero)
| equal(divide(divide(u,w),divide(v,w)),zero) ),
file('HEN010-5.p',unknown),
[] ).
cnf(4,axiom,
~ equal(divide(divide(identity,a),divide(identity,divide(identity,a))),divide(identity,a)),
file('HEN010-5.p',unknown),
[] ).
cnf(5,axiom,
equal(divide(divide(u,v),u),zero),
file('HEN010-5.p',unknown),
[] ).
cnf(6,axiom,
equal(divide(divide(divide(u,v),divide(w,v)),divide(divide(u,w),v)),zero),
file('HEN010-5.p',unknown),
[] ).
cnf(7,axiom,
equal(divide(zero,u),zero),
file('HEN010-5.p',unknown),
[] ).
cnf(8,axiom,
( ~ equal(divide(u,v),zero)
| ~ equal(divide(v,u),zero)
| equal(v,u) ),
file('HEN010-5.p',unknown),
[] ).
cnf(9,axiom,
equal(divide(u,identity),zero),
file('HEN010-5.p',unknown),
[] ).
cnf(20,plain,
( ~ equal(zero,zero)
| ~ equal(divide(u,zero),zero)
| equal(u,zero) ),
inference(spl,[status(thm),theory(equality)],[7,8]),
[iquote('0:SpL:7.0,8.0')] ).
cnf(21,plain,
( ~ equal(zero,zero)
| ~ equal(divide(u,divide(u,v)),zero)
| equal(divide(u,v),u) ),
inference(spl,[status(thm),theory(equality)],[5,8]),
[iquote('0:SpL:5.0,8.0')] ).
cnf(23,plain,
( ~ equal(divide(u,zero),zero)
| equal(u,zero) ),
inference(obv,[status(thm),theory(equality)],[20]),
[iquote('0:Obv:20.0')] ).
cnf(25,plain,
( ~ equal(divide(u,divide(u,v)),zero)
| equal(divide(u,v),u) ),
inference(obv,[status(thm),theory(equality)],[21]),
[iquote('0:Obv:21.0')] ).
cnf(43,plain,
( ~ equal(divide(u,divide(v,w)),zero)
| equal(divide(divide(u,v),zero),zero) ),
inference(spr,[status(thm),theory(equality)],[5,3]),
[iquote('0:SpR:5.0,3.1')] ).
cnf(60,plain,
( ~ equal(zero,zero)
| equal(divide(divide(u,u),v),zero) ),
inference(spl,[status(thm),theory(equality)],[5,2]),
[iquote('0:SpL:5.0,2.0')] ).
cnf(63,plain,
equal(divide(divide(u,u),v),zero),
inference(obv,[status(thm),theory(equality)],[60]),
[iquote('0:Obv:60.0')] ).
cnf(86,plain,
( ~ equal(zero,zero)
| equal(divide(u,u),zero) ),
inference(spl,[status(thm),theory(equality)],[63,23]),
[iquote('0:SpL:63.0,23.0')] ).
cnf(89,plain,
equal(divide(u,u),zero),
inference(obv,[status(thm),theory(equality)],[86]),
[iquote('0:Obv:86.0')] ).
cnf(115,plain,
( ~ equal(zero,zero)
| equal(divide(divide(u,divide(u,v)),v),zero) ),
inference(spl,[status(thm),theory(equality)],[89,2]),
[iquote('0:SpL:89.0,2.0')] ).
cnf(117,plain,
equal(divide(divide(u,divide(u,v)),v),zero),
inference(obv,[status(thm),theory(equality)],[115]),
[iquote('0:Obv:115.0')] ).
cnf(173,plain,
( ~ equal(divide(zero,u),zero)
| equal(divide(divide(divide(v,divide(v,w)),u),w),zero) ),
inference(spl,[status(thm),theory(equality)],[117,2]),
[iquote('0:SpL:117.0,2.0')] ).
cnf(174,plain,
( ~ equal(zero,zero)
| equal(divide(u,divide(u,zero)),zero) ),
inference(spl,[status(thm),theory(equality)],[117,23]),
[iquote('0:SpL:117.0,23.0')] ).
cnf(178,plain,
equal(divide(u,divide(u,zero)),zero),
inference(obv,[status(thm),theory(equality)],[174]),
[iquote('0:Obv:174.0')] ).
cnf(180,plain,
( ~ equal(zero,zero)
| equal(divide(divide(divide(u,divide(u,v)),w),v),zero) ),
inference(rew,[status(thm),theory(equality)],[7,173]),
[iquote('0:Rew:7.0,173.0')] ).
cnf(181,plain,
equal(divide(divide(divide(u,divide(u,v)),w),v),zero),
inference(obv,[status(thm),theory(equality)],[180]),
[iquote('0:Obv:180.0')] ).
cnf(189,plain,
equal(divide(divide(divide(divide(divide(u,v),divide(w,v)),x),divide(divide(divide(u,w),v),x)),divide(zero,x)),zero),
inference(spr,[status(thm),theory(equality)],[6]),
[iquote('0:SpR:6.0,6.0')] ).
cnf(196,plain,
equal(divide(divide(divide(divide(u,v),w),divide(u,w)),divide(zero,w)),zero),
inference(spr,[status(thm),theory(equality)],[5,6]),
[iquote('0:SpR:5.0,6.0')] ).
cnf(197,plain,
equal(divide(divide(divide(u,v),divide(identity,v)),divide(zero,v)),zero),
inference(spr,[status(thm),theory(equality)],[9,6]),
[iquote('0:SpR:9.0,6.0')] ).
cnf(207,plain,
equal(divide(divide(divide(u,v),divide(divide(u,v),v)),zero),zero),
inference(spr,[status(thm),theory(equality)],[117,6]),
[iquote('0:SpR:117.0,6.0')] ).
cnf(209,plain,
equal(divide(divide(divide(u,v),zero),divide(divide(u,divide(v,w)),v)),zero),
inference(spr,[status(thm),theory(equality)],[5,6]),
[iquote('0:SpR:5.0,6.0')] ).
cnf(226,plain,
( ~ equal(zero,zero)
| ~ equal(divide(divide(divide(u,v),w),divide(divide(u,w),divide(v,w))),zero)
| equal(divide(divide(u,w),divide(v,w)),divide(divide(u,v),w)) ),
inference(spl,[status(thm),theory(equality)],[6,8]),
[iquote('0:SpL:6.0,8.0')] ).
cnf(228,plain,
( ~ equal(divide(zero,u),zero)
| equal(divide(divide(divide(divide(v,w),divide(x,w)),u),divide(divide(v,x),w)),zero) ),
inference(spl,[status(thm),theory(equality)],[6,2]),
[iquote('0:SpL:6.0,2.0')] ).
cnf(233,plain,
equal(divide(divide(divide(u,v),divide(identity,v)),zero),zero),
inference(rew,[status(thm),theory(equality)],[7,197]),
[iquote('0:Rew:7.0,197.0')] ).
cnf(240,plain,
equal(divide(divide(divide(divide(u,v),w),divide(u,w)),zero),zero),
inference(rew,[status(thm),theory(equality)],[7,196]),
[iquote('0:Rew:7.0,196.0')] ).
cnf(247,plain,
( ~ equal(zero,zero)
| equal(divide(divide(divide(divide(u,v),divide(w,v)),x),divide(divide(u,w),v)),zero) ),
inference(rew,[status(thm),theory(equality)],[7,228]),
[iquote('0:Rew:7.0,228.0')] ).
cnf(248,plain,
equal(divide(divide(divide(divide(u,v),divide(w,v)),x),divide(divide(u,w),v)),zero),
inference(obv,[status(thm),theory(equality)],[247]),
[iquote('0:Obv:247.0')] ).
cnf(250,plain,
equal(divide(divide(divide(divide(divide(u,v),divide(w,v)),x),divide(divide(divide(u,w),v),x)),zero),zero),
inference(rew,[status(thm),theory(equality)],[7,189]),
[iquote('0:Rew:7.0,189.0')] ).
cnf(254,plain,
( ~ equal(divide(divide(divide(u,v),w),divide(divide(u,w),divide(v,w))),zero)
| equal(divide(divide(u,w),divide(v,w)),divide(divide(u,v),w)) ),
inference(obv,[status(thm),theory(equality)],[226]),
[iquote('0:Obv:226.0')] ).
cnf(278,plain,
( ~ equal(zero,zero)
| equal(divide(u,zero),u) ),
inference(spl,[status(thm),theory(equality)],[178,25]),
[iquote('0:SpL:178.0,25.0')] ).
cnf(282,plain,
equal(divide(u,zero),u),
inference(obv,[status(thm),theory(equality)],[278]),
[iquote('0:Obv:278.0')] ).
cnf(288,plain,
equal(divide(divide(divide(divide(u,v),divide(w,v)),x),divide(divide(divide(u,w),v),x)),zero),
inference(rew,[status(thm),theory(equality)],[282,250]),
[iquote('0:Rew:282.0,250.0')] ).
cnf(292,plain,
equal(divide(divide(u,v),divide(divide(u,v),v)),zero),
inference(rew,[status(thm),theory(equality)],[282,207]),
[iquote('0:Rew:282.0,207.0')] ).
cnf(293,plain,
equal(divide(divide(u,v),divide(identity,v)),zero),
inference(rew,[status(thm),theory(equality)],[282,233]),
[iquote('0:Rew:282.0,233.0')] ).
cnf(294,plain,
equal(divide(divide(divide(u,v),w),divide(u,w)),zero),
inference(rew,[status(thm),theory(equality)],[282,240]),
[iquote('0:Rew:282.0,240.0')] ).
cnf(300,plain,
( ~ equal(divide(u,divide(v,w)),zero)
| equal(divide(u,v),zero) ),
inference(rew,[status(thm),theory(equality)],[282,43]),
[iquote('0:Rew:282.0,43.1')] ).
cnf(304,plain,
equal(divide(divide(u,v),divide(divide(u,divide(v,w)),v)),zero),
inference(rew,[status(thm),theory(equality)],[282,209]),
[iquote('0:Rew:282.0,209.0')] ).
cnf(385,plain,
( ~ equal(zero,zero)
| equal(divide(divide(u,divide(identity,v)),v),zero) ),
inference(spl,[status(thm),theory(equality)],[293,2]),
[iquote('0:SpL:293.0,2.0')] ).
cnf(391,plain,
equal(divide(divide(u,divide(identity,v)),v),zero),
inference(obv,[status(thm),theory(equality)],[385]),
[iquote('0:Obv:385.0')] ).
cnf(1447,plain,
( ~ equal(zero,zero)
| ~ equal(divide(divide(divide(u,divide(v,w)),v),divide(u,v)),zero)
| equal(divide(divide(u,divide(v,w)),v),divide(u,v)) ),
inference(spl,[status(thm),theory(equality)],[304,8]),
[iquote('0:SpL:304.0,8.0')] ).
cnf(1450,plain,
( ~ equal(zero,zero)
| equal(divide(divide(u,v),divide(u,divide(v,w))),zero) ),
inference(spl,[status(thm),theory(equality)],[304,300]),
[iquote('0:SpL:304.0,300.0')] ).
cnf(1491,plain,
equal(divide(divide(u,v),divide(u,divide(v,w))),zero),
inference(obv,[status(thm),theory(equality)],[1450]),
[iquote('0:Obv:1450.0')] ).
cnf(1517,plain,
( ~ equal(divide(divide(divide(u,divide(v,w)),v),divide(u,v)),zero)
| equal(divide(divide(u,divide(v,w)),v),divide(u,v)) ),
inference(obv,[status(thm),theory(equality)],[1447]),
[iquote('0:Obv:1447.0')] ).
cnf(1518,plain,
( ~ equal(zero,zero)
| equal(divide(divide(u,divide(v,w)),v),divide(u,v)) ),
inference(rew,[status(thm),theory(equality)],[294,1517]),
[iquote('0:Rew:294.0,1517.0')] ).
cnf(1519,plain,
equal(divide(divide(u,divide(v,w)),v),divide(u,v)),
inference(obv,[status(thm),theory(equality)],[1518]),
[iquote('0:Obv:1518.0')] ).
cnf(1745,plain,
( ~ equal(zero,zero)
| equal(divide(divide(u,v),v),divide(u,v)) ),
inference(spl,[status(thm),theory(equality)],[292,25]),
[iquote('0:SpL:292.0,25.0')] ).
cnf(1769,plain,
equal(divide(divide(u,v),v),divide(u,v)),
inference(obv,[status(thm),theory(equality)],[1745]),
[iquote('0:Obv:1745.0')] ).
cnf(2313,plain,
equal(divide(divide(divide(divide(u,v),zero),w),divide(u,divide(v,x))),zero),
inference(spr,[status(thm),theory(equality)],[1491,181]),
[iquote('0:SpR:1491.0,181.0')] ).
cnf(2463,plain,
equal(divide(divide(divide(u,v),w),divide(u,divide(v,x))),zero),
inference(rew,[status(thm),theory(equality)],[282,2313]),
[iquote('0:Rew:282.0,2313.0')] ).
cnf(4365,plain,
equal(divide(divide(divide(u,v),w),divide(divide(u,w),v)),zero),
inference(spr,[status(thm),theory(equality)],[1519,248]),
[iquote('0:SpR:1519.0,248.0')] ).
cnf(8811,plain,
equal(divide(divide(divide(u,v),w),divide(divide(divide(u,w),v),w)),zero),
inference(spr,[status(thm),theory(equality)],[1519,288]),
[iquote('0:SpR:1519.0,288.0')] ).
cnf(26871,plain,
( ~ equal(divide(divide(divide(divide(u,v),w),v),divide(divide(u,v),divide(w,v))),zero)
| equal(divide(divide(divide(u,v),v),divide(w,v)),divide(divide(divide(u,v),w),v)) ),
inference(spl,[status(thm),theory(equality)],[1769,254]),
[iquote('0:SpL:1769.0,254.0')] ).
cnf(27163,plain,
( ~ equal(divide(divide(divide(divide(u,v),w),v),divide(divide(u,v),divide(w,v))),zero)
| equal(divide(divide(divide(u,v),w),v),divide(divide(u,v),divide(w,v))) ),
inference(rew,[status(thm),theory(equality)],[1769,26871]),
[iquote('0:Rew:1769.0,26871.1')] ).
cnf(27164,plain,
( ~ equal(zero,zero)
| equal(divide(divide(divide(u,v),w),v),divide(divide(u,v),divide(w,v))) ),
inference(rew,[status(thm),theory(equality)],[2463,27163]),
[iquote('0:Rew:2463.0,27163.0')] ).
cnf(27165,plain,
equal(divide(divide(divide(u,v),w),v),divide(divide(u,v),divide(w,v))),
inference(obv,[status(thm),theory(equality)],[27164]),
[iquote('0:Obv:27164.0')] ).
cnf(27170,plain,
equal(divide(divide(divide(u,v),w),divide(divide(u,w),divide(v,w))),zero),
inference(rew,[status(thm),theory(equality)],[27165,8811]),
[iquote('0:Rew:27165.0,8811.0')] ).
cnf(27176,plain,
( ~ equal(zero,zero)
| equal(divide(divide(u,v),divide(w,v)),divide(divide(u,w),v)) ),
inference(rew,[status(thm),theory(equality)],[27170,254]),
[iquote('0:Rew:27170.0,254.0')] ).
cnf(27177,plain,
equal(divide(divide(u,v),divide(w,v)),divide(divide(u,w),v)),
inference(obv,[status(thm),theory(equality)],[27176]),
[iquote('0:Obv:27176.0')] ).
cnf(30260,plain,
equal(divide(divide(u,divide(v,divide(identity,w))),w),divide(divide(u,w),zero)),
inference(spr,[status(thm),theory(equality)],[391,27177]),
[iquote('0:SpR:391.0,27177.0')] ).
cnf(30440,plain,
equal(divide(divide(u,divide(v,divide(identity,w))),w),divide(u,w)),
inference(rew,[status(thm),theory(equality)],[282,30260]),
[iquote('0:Rew:282.0,30260.0')] ).
cnf(33239,plain,
( ~ equal(zero,zero)
| ~ equal(divide(divide(divide(u,v),w),divide(divide(u,w),v)),zero)
| equal(divide(divide(u,v),w),divide(divide(u,w),v)) ),
inference(spl,[status(thm),theory(equality)],[4365,8]),
[iquote('0:SpL:4365.0,8.0')] ).
cnf(33484,plain,
( ~ equal(divide(divide(divide(u,v),w),divide(divide(u,w),v)),zero)
| equal(divide(divide(u,v),w),divide(divide(u,w),v)) ),
inference(obv,[status(thm),theory(equality)],[33239]),
[iquote('0:Obv:33239.0')] ).
cnf(33485,plain,
( ~ equal(zero,zero)
| equal(divide(divide(u,v),w),divide(divide(u,w),v)) ),
inference(rew,[status(thm),theory(equality)],[4365,33484]),
[iquote('0:Rew:4365.0,33484.0')] ).
cnf(33486,plain,
equal(divide(divide(u,v),w),divide(divide(u,w),v)),
inference(obv,[status(thm),theory(equality)],[33485]),
[iquote('0:Obv:33485.0')] ).
cnf(33622,plain,
equal(divide(divide(u,v),divide(w,divide(identity,v))),divide(u,v)),
inference(rew,[status(thm),theory(equality)],[33486,30440]),
[iquote('0:Rew:33486.0,30440.0')] ).
cnf(33645,plain,
$false,
inference(unc,[status(thm)],[33622,4]),
[iquote('0:UnC:33622.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : HEN010-5 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % 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 14:13:08 EDT 2022
% 0.13/0.34 % CPUTime :
% 11.89/12.08
% 11.89/12.08 SPASS V 3.9
% 11.89/12.08 SPASS beiseite: Proof found.
% 11.89/12.08 % SZS status Theorem
% 11.89/12.08 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.89/12.08 SPASS derived 20365 clauses, backtracked 0 clauses, performed 0 splits and kept 1702 clauses.
% 11.89/12.08 SPASS allocated 89395 KBytes.
% 11.89/12.08 SPASS spent 0:0:10.74 on the problem.
% 11.89/12.08 0:00:00.04 for the input.
% 11.89/12.08 0:00:00.00 for the FLOTTER CNF translation.
% 11.89/12.08 0:00:00.13 for inferences.
% 11.89/12.08 0:00:00.00 for the backtracking.
% 11.89/12.08 0:0:10.54 for the reduction.
% 11.89/12.08
% 11.89/12.08
% 11.89/12.08 Here is a proof with depth 6, length 74 :
% 11.89/12.08 % SZS output start Refutation
% See solution above
% 11.89/12.08 Formulae used in the proof : property_of_divide1 property_of_divide3 prove_this quotient_smaller_than_numerator quotient_property zero_is_smallest divide_and_equal identity_is_largest
% 11.89/12.08
%------------------------------------------------------------------------------