TSTP Solution File: HEN010-3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HEN010-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 13:03:12 EDT 2022
% Result : Unsatisfiable 0.77s 0.94s
% Output : Refutation 0.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 8
% Syntax : Number of clauses : 76 ( 36 unt; 0 nHn; 76 RR)
% Number of literals : 120 ( 0 equ; 45 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 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,
~ equal(divide(divide(identity,a),divide(identity,divide(identity,a))),divide(identity,a)),
file('HEN010-3.p',unknown),
[] ).
cnf(2,axiom,
( ~ less_equal(u,v)
| equal(divide(u,v),zero) ),
file('HEN010-3.p',unknown),
[] ).
cnf(3,axiom,
( ~ equal(divide(u,v),zero)
| less_equal(u,v) ),
file('HEN010-3.p',unknown),
[] ).
cnf(4,axiom,
less_equal(divide(u,v),u),
file('HEN010-3.p',unknown),
[] ).
cnf(5,axiom,
less_equal(divide(divide(u,v),divide(w,v)),divide(divide(u,w),v)),
file('HEN010-3.p',unknown),
[] ).
cnf(6,axiom,
less_equal(zero,u),
file('HEN010-3.p',unknown),
[] ).
cnf(7,axiom,
( ~ less_equal(u,v)
| ~ less_equal(v,u)
| equal(v,u) ),
file('HEN010-3.p',unknown),
[] ).
cnf(8,axiom,
less_equal(u,identity),
file('HEN010-3.p',unknown),
[] ).
cnf(15,plain,
( ~ less_equal(u,zero)
| equal(u,zero) ),
inference(res,[status(thm),theory(equality)],[6,7]),
[iquote('0:Res:6.0,7.0')] ).
cnf(16,plain,
( ~ less_equal(u,divide(u,v))
| equal(divide(u,v),u) ),
inference(res,[status(thm),theory(equality)],[4,7]),
[iquote('0:Res:4.0,7.0')] ).
cnf(19,plain,
equal(divide(zero,u),zero),
inference(res,[status(thm),theory(equality)],[4,15]),
[iquote('0:Res:4.0,15.0')] ).
cnf(26,plain,
( ~ less_equal(u,v)
| less_equal(divide(divide(u,w),divide(v,w)),divide(zero,w)) ),
inference(spr,[status(thm),theory(equality)],[2,5]),
[iquote('0:SpR:2.1,5.0')] ).
cnf(29,plain,
( ~ less_equal(u,v)
| less_equal(divide(divide(w,v),zero),divide(divide(w,u),v)) ),
inference(spr,[status(thm),theory(equality)],[2,5]),
[iquote('0:SpR:2.1,5.0')] ).
cnf(30,plain,
less_equal(divide(divide(u,v),zero),divide(divide(u,zero),v)),
inference(spr,[status(thm),theory(equality)],[19,5]),
[iquote('0:SpR:19.0,5.0')] ).
cnf(34,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)],[5,7]),
[iquote('0:Res:5.0,7.0')] ).
cnf(36,plain,
( ~ less_equal(u,v)
| less_equal(divide(divide(u,w),divide(v,w)),zero) ),
inference(rew,[status(thm),theory(equality)],[19,26]),
[iquote('0:Rew:19.0,26.1')] ).
cnf(40,plain,
( ~ less_equal(divide(u,zero),v)
| less_equal(divide(divide(u,v),zero),zero) ),
inference(spr,[status(thm),theory(equality)],[2,30]),
[iquote('0:SpR:2.1,30.0')] ).
cnf(184,plain,
( ~ less_equal(u,v)
| equal(divide(divide(u,w),divide(v,w)),zero) ),
inference(res,[status(thm),theory(equality)],[36,15]),
[iquote('0:Res:36.1,15.0')] ).
cnf(204,plain,
( ~ less_equal(divide(u,zero),v)
| equal(divide(divide(u,v),zero),zero) ),
inference(res,[status(thm),theory(equality)],[40,15]),
[iquote('0:Res:40.1,15.0')] ).
cnf(241,plain,
( ~ less_equal(divide(u,zero),v)
| ~ equal(zero,zero)
| less_equal(divide(u,v),zero) ),
inference(spl,[status(thm),theory(equality)],[204,3]),
[iquote('0:SpL:204.1,3.0')] ).
cnf(244,plain,
( ~ less_equal(divide(u,zero),v)
| less_equal(divide(u,v),zero) ),
inference(obv,[status(thm),theory(equality)],[241]),
[iquote('0:Obv:241.1')] ).
cnf(268,plain,
less_equal(divide(u,u),zero),
inference(res,[status(thm),theory(equality)],[4,244]),
[iquote('0:Res:4.0,244.0')] ).
cnf(269,plain,
less_equal(divide(u,identity),zero),
inference(res,[status(thm),theory(equality)],[8,244]),
[iquote('0:Res:8.0,244.0')] ).
cnf(278,plain,
equal(divide(u,identity),zero),
inference(res,[status(thm),theory(equality)],[269,15]),
[iquote('0:Res:269.0,15.0')] ).
cnf(325,plain,
equal(divide(u,u),zero),
inference(res,[status(thm),theory(equality)],[268,15]),
[iquote('0:Res:268.0,15.0')] ).
cnf(344,plain,
( ~ equal(zero,zero)
| less_equal(u,u) ),
inference(spl,[status(thm),theory(equality)],[325,3]),
[iquote('0:SpL:325.0,3.0')] ).
cnf(348,plain,
less_equal(u,u),
inference(obv,[status(thm),theory(equality)],[344]),
[iquote('0:Obv:344.0')] ).
cnf(357,plain,
less_equal(divide(u,divide(u,zero)),zero),
inference(res,[status(thm),theory(equality)],[348,244]),
[iquote('0:Res:348.0,244.0')] ).
cnf(368,plain,
equal(divide(u,divide(u,zero)),zero),
inference(res,[status(thm),theory(equality)],[357,15]),
[iquote('0:Res:357.0,15.0')] ).
cnf(430,plain,
( ~ equal(zero,zero)
| less_equal(u,divide(u,zero)) ),
inference(spl,[status(thm),theory(equality)],[368,3]),
[iquote('0:SpL:368.0,3.0')] ).
cnf(432,plain,
less_equal(u,divide(u,zero)),
inference(obv,[status(thm),theory(equality)],[430]),
[iquote('0:Obv:430.0')] ).
cnf(447,plain,
equal(divide(u,zero),u),
inference(res,[status(thm),theory(equality)],[432,16]),
[iquote('0:Res:432.0,16.0')] ).
cnf(449,plain,
( ~ less_equal(u,v)
| less_equal(divide(w,v),divide(divide(w,u),v)) ),
inference(rew,[status(thm),theory(equality)],[447,29]),
[iquote('0:Rew:447.0,29.1')] ).
cnf(550,plain,
( ~ less_equal(u,u)
| equal(divide(divide(v,u),u),divide(v,u)) ),
inference(res,[status(thm),theory(equality)],[449,16]),
[iquote('0:Res:449.1,16.0')] ).
cnf(556,plain,
equal(divide(divide(u,v),v),divide(u,v)),
inference(mrr,[status(thm)],[550,348]),
[iquote('0:MRR:550.0,348.0')] ).
cnf(590,plain,
( ~ less_equal(divide(zero,u),divide(divide(v,u),divide(identity,u)))
| equal(divide(divide(v,u),divide(identity,u)),divide(divide(v,identity),u)) ),
inference(spl,[status(thm),theory(equality)],[278,34]),
[iquote('0:SpL:278.0,34.0')] ).
cnf(605,plain,
( ~ less_equal(zero,divide(divide(u,v),divide(identity,v)))
| equal(divide(divide(u,v),divide(identity,v)),zero) ),
inference(rew,[status(thm),theory(equality)],[19,590,278]),
[iquote('0:Rew:19.0,590.1,278.0,590.1,19.0,590.0')] ).
cnf(606,plain,
equal(divide(divide(u,v),divide(identity,v)),zero),
inference(mrr,[status(thm)],[605,6]),
[iquote('0:MRR:605.0,6.0')] ).
cnf(684,plain,
( ~ less_equal(zero,divide(divide(u,divide(identity,v)),divide(v,divide(identity,v))))
| equal(divide(divide(u,divide(identity,v)),divide(v,divide(identity,v))),divide(divide(u,v),divide(identity,v))) ),
inference(spl,[status(thm),theory(equality)],[606,34]),
[iquote('0:SpL:606.0,34.0')] ).
cnf(698,plain,
( ~ less_equal(zero,divide(divide(u,divide(identity,v)),divide(v,divide(identity,v))))
| equal(divide(divide(u,divide(identity,v)),divide(v,divide(identity,v))),zero) ),
inference(rew,[status(thm),theory(equality)],[606,684]),
[iquote('0:Rew:606.0,684.1')] ).
cnf(699,plain,
equal(divide(divide(u,divide(identity,v)),divide(v,divide(identity,v))),zero),
inference(mrr,[status(thm)],[698,6]),
[iquote('0:MRR:698.0,6.0')] ).
cnf(749,plain,
( ~ less_equal(divide(divide(divide(u,v),w),v),divide(divide(u,v),divide(w,v)))
| equal(divide(divide(divide(u,v),v),divide(w,v)),divide(divide(divide(u,v),w),v)) ),
inference(spl,[status(thm),theory(equality)],[556,34]),
[iquote('0:SpL:556.0,34.0')] ).
cnf(754,plain,
( ~ less_equal(divide(divide(divide(u,v),w),v),divide(divide(u,v),divide(w,v)))
| equal(divide(divide(divide(u,v),w),v),divide(divide(u,v),divide(w,v))) ),
inference(rew,[status(thm),theory(equality)],[556,749]),
[iquote('0:Rew:556.0,749.1')] ).
cnf(863,plain,
( ~ less_equal(u,v)
| ~ less_equal(w,u)
| equal(divide(divide(w,v),zero),zero) ),
inference(spr,[status(thm),theory(equality)],[2,184]),
[iquote('0:SpR:2.1,184.1')] ).
cnf(894,plain,
( ~ less_equal(u,v)
| ~ less_equal(w,u)
| equal(divide(w,v),zero) ),
inference(rew,[status(thm),theory(equality)],[447,863]),
[iquote('0:Rew:447.0,863.2')] ).
cnf(1450,plain,
( ~ equal(zero,zero)
| less_equal(divide(u,divide(identity,v)),divide(v,divide(identity,v))) ),
inference(spl,[status(thm),theory(equality)],[699,3]),
[iquote('0:SpL:699.0,3.0')] ).
cnf(1468,plain,
less_equal(divide(u,divide(identity,v)),divide(v,divide(identity,v))),
inference(obv,[status(thm),theory(equality)],[1450]),
[iquote('0:Obv:1450.0')] ).
cnf(1486,plain,
( ~ less_equal(u,divide(v,w))
| equal(divide(u,v),zero) ),
inference(res,[status(thm),theory(equality)],[4,894]),
[iquote('0:Res:4.0,894.0')] ).
cnf(2023,plain,
equal(divide(divide(divide(u,v),w),u),zero),
inference(res,[status(thm),theory(equality)],[4,1486]),
[iquote('0:Res:4.0,1486.0')] ).
cnf(2025,plain,
equal(divide(divide(u,v),u),zero),
inference(res,[status(thm),theory(equality)],[348,1486]),
[iquote('0:Res:348.0,1486.0')] ).
cnf(2030,plain,
equal(divide(divide(u,divide(identity,v)),v),zero),
inference(res,[status(thm),theory(equality)],[1468,1486]),
[iquote('0:Res:1468.0,1486.0')] ).
cnf(2083,plain,
( ~ less_equal(divide(zero,u),divide(divide(divide(v,w),u),divide(v,u)))
| equal(divide(divide(divide(v,w),u),divide(v,u)),divide(divide(divide(v,w),v),u)) ),
inference(spl,[status(thm),theory(equality)],[2025,34]),
[iquote('0:SpL:2025.0,34.0')] ).
cnf(2089,plain,
( ~ less_equal(divide(divide(u,divide(v,w)),v),divide(divide(u,v),zero))
| equal(divide(divide(u,v),divide(divide(v,w),v)),divide(divide(u,divide(v,w)),v)) ),
inference(spl,[status(thm),theory(equality)],[2025,34]),
[iquote('0:SpL:2025.0,34.0')] ).
cnf(2104,plain,
( ~ less_equal(divide(divide(u,divide(v,w)),v),divide(u,v))
| equal(divide(divide(u,divide(v,w)),v),divide(u,v)) ),
inference(rew,[status(thm),theory(equality)],[447,2089,2025]),
[iquote('0:Rew:447.0,2089.1,2025.0,2089.1,447.0,2089.0')] ).
cnf(2106,plain,
( ~ less_equal(zero,divide(divide(divide(u,v),w),divide(u,w)))
| equal(divide(divide(divide(u,v),w),divide(u,w)),zero) ),
inference(rew,[status(thm),theory(equality)],[19,2083,2025]),
[iquote('0:Rew:19.0,2083.1,2025.0,2083.1,19.0,2083.0')] ).
cnf(2107,plain,
equal(divide(divide(divide(u,v),w),divide(u,w)),zero),
inference(mrr,[status(thm)],[2106,6]),
[iquote('0:MRR:2106.0,6.0')] ).
cnf(2168,plain,
( ~ less_equal(divide(divide(u,divide(v,divide(identity,w))),w),divide(divide(u,w),zero))
| equal(divide(divide(u,w),divide(divide(v,divide(identity,w)),w)),divide(divide(u,divide(v,divide(identity,w))),w)) ),
inference(spl,[status(thm),theory(equality)],[2030,34]),
[iquote('0:SpL:2030.0,34.0')] ).
cnf(2187,plain,
( ~ less_equal(divide(divide(u,divide(v,divide(identity,w))),w),divide(u,w))
| equal(divide(divide(u,divide(v,divide(identity,w))),w),divide(u,w)) ),
inference(rew,[status(thm),theory(equality)],[447,2168,2030]),
[iquote('0:Rew:447.0,2168.1,2030.0,2168.1,447.0,2168.0')] ).
cnf(2432,plain,
( ~ equal(zero,zero)
| less_equal(divide(divide(u,v),w),u) ),
inference(spl,[status(thm),theory(equality)],[2023,3]),
[iquote('0:SpL:2023.0,3.0')] ).
cnf(2456,plain,
less_equal(divide(divide(u,v),w),u),
inference(obv,[status(thm),theory(equality)],[2432]),
[iquote('0:Obv:2432.0')] ).
cnf(3704,plain,
( ~ equal(zero,zero)
| less_equal(divide(divide(u,v),w),divide(u,w)) ),
inference(spl,[status(thm),theory(equality)],[2107,3]),
[iquote('0:SpL:2107.0,3.0')] ).
cnf(3747,plain,
less_equal(divide(divide(u,v),w),divide(u,w)),
inference(obv,[status(thm),theory(equality)],[3704]),
[iquote('0:Obv:3704.0')] ).
cnf(3753,plain,
equal(divide(divide(u,divide(v,w)),v),divide(u,v)),
inference(mrr,[status(thm)],[2104,3747]),
[iquote('0:MRR:2104.0,3747.0')] ).
cnf(3754,plain,
equal(divide(divide(u,divide(v,divide(identity,w))),w),divide(u,w)),
inference(mrr,[status(thm)],[2187,3747]),
[iquote('0:MRR:2187.0,3747.0')] ).
cnf(5257,plain,
less_equal(divide(u,v),divide(u,divide(v,w))),
inference(spr,[status(thm),theory(equality)],[3753,4]),
[iquote('0:SpR:3753.0,4.0')] ).
cnf(5265,plain,
less_equal(divide(divide(u,v),w),divide(u,divide(v,x))),
inference(spr,[status(thm),theory(equality)],[3753,2456]),
[iquote('0:SpR:3753.0,2456.0')] ).
cnf(5410,plain,
equal(divide(divide(divide(u,v),w),v),divide(divide(u,v),divide(w,v))),
inference(mrr,[status(thm)],[754,5265]),
[iquote('0:MRR:754.0,5265.0')] ).
cnf(6087,plain,
( ~ less_equal(divide(divide(u,v),w),divide(divide(u,v),divide(w,v)))
| equal(divide(divide(divide(u,v),w),v),divide(divide(u,v),w)) ),
inference(spl,[status(thm),theory(equality)],[5410,16]),
[iquote('0:SpL:5410.0,16.0')] ).
cnf(6176,plain,
( ~ less_equal(divide(divide(u,v),w),divide(divide(u,v),divide(w,v)))
| equal(divide(divide(u,v),divide(w,v)),divide(divide(u,v),w)) ),
inference(rew,[status(thm),theory(equality)],[5410,6087]),
[iquote('0:Rew:5410.0,6087.1')] ).
cnf(6177,plain,
equal(divide(divide(u,v),divide(w,v)),divide(divide(u,v),w)),
inference(mrr,[status(thm)],[6176,5257]),
[iquote('0:MRR:6176.0,5257.0')] ).
cnf(6182,plain,
( ~ less_equal(divide(divide(u,v),w),divide(divide(u,w),v))
| equal(divide(divide(u,w),divide(v,w)),divide(divide(u,v),w)) ),
inference(rew,[status(thm),theory(equality)],[6177,34]),
[iquote('0:Rew:6177.0,34.0')] ).
cnf(6185,plain,
less_equal(divide(divide(u,v),w),divide(divide(u,w),v)),
inference(rew,[status(thm),theory(equality)],[6177,5]),
[iquote('0:Rew:6177.0,5.0')] ).
cnf(6315,plain,
( ~ less_equal(divide(divide(u,v),w),divide(divide(u,w),v))
| equal(divide(divide(u,w),v),divide(divide(u,v),w)) ),
inference(rew,[status(thm),theory(equality)],[6177,6182]),
[iquote('0:Rew:6177.0,6182.1')] ).
cnf(6316,plain,
equal(divide(divide(u,v),w),divide(divide(u,w),v)),
inference(mrr,[status(thm)],[6315,6185]),
[iquote('0:MRR:6315.0,6185.0')] ).
cnf(6338,plain,
equal(divide(divide(u,v),divide(w,divide(identity,v))),divide(u,v)),
inference(rew,[status(thm),theory(equality)],[6316,3754]),
[iquote('0:Rew:6316.0,3754.0')] ).
cnf(6352,plain,
$false,
inference(unc,[status(thm)],[6338,1]),
[iquote('0:UnC:6338.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : HEN010-3 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jul 1 12:48:24 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.77/0.94
% 0.77/0.94 SPASS V 3.9
% 0.77/0.94 SPASS beiseite: Proof found.
% 0.77/0.94 % SZS status Theorem
% 0.77/0.94 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.77/0.94 SPASS derived 4488 clauses, backtracked 0 clauses, performed 0 splits and kept 720 clauses.
% 0.77/0.94 SPASS allocated 67192 KBytes.
% 0.77/0.94 SPASS spent 0:00:00.59 on the problem.
% 0.77/0.94 0:00:00.03 for the input.
% 0.77/0.94 0:00:00.00 for the FLOTTER CNF translation.
% 0.77/0.94 0:00:00.04 for inferences.
% 0.77/0.94 0:00:00.00 for the backtracking.
% 0.77/0.94 0:00:00.50 for the reduction.
% 0.77/0.94
% 0.77/0.94
% 0.77/0.94 Here is a proof with depth 13, length 76 :
% 0.77/0.94 % SZS output start Refutation
% See solution above
% 0.77/0.96 Formulae used in the proof : prove_property_of_inversion quotient_less_equal1 quotient_less_equal2 quotient_smaller_than_numerator quotient_property zero_is_smallest less_equal_and_equal identity_is_largest
% 0.77/0.96
%------------------------------------------------------------------------------