TSTP Solution File: HEN011-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : HEN011-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %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 : 300s
% DateTime : Wed Jul 27 12:58:00 EDT 2022
% Result : Unsatisfiable 2.74s 2.95s
% Output : Refutation 2.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 16
% Syntax : Number of clauses : 139 ( 130 unt; 0 nHn; 79 RR)
% Number of literals : 159 ( 27 equ; 22 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 10 con; 0-2 aty)
% Number of variables : 94 ( 45 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ less_e_qual(A,B)
| quotient(A,B,zero) ),
file('HEN011-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ quotient(A,B,zero)
| less_e_qual(A,B) ),
file('HEN011-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ quotient(A,B,C)
| less_e_qual(C,A) ),
file('HEN011-1.p',unknown),
[] ).
cnf(4,axiom,
( ~ quotient(A,B,C)
| ~ quotient(B,D,E)
| ~ quotient(A,D,F)
| ~ quotient(F,E,G)
| ~ quotient(C,D,H)
| less_e_qual(G,H) ),
file('HEN011-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ less_e_qual(A,B)
| ~ less_e_qual(B,A)
| A = B ),
file('HEN011-1.p',unknown),
[] ).
cnf(6,axiom,
( ~ quotient(A,B,C)
| ~ quotient(A,B,D)
| C = D ),
file('HEN011-1.p',unknown),
[] ).
cnf(7,axiom,
idQa_Q__idQ_idQb != idQb_Q__idQ_idQa,
file('HEN011-1.p',unknown),
[] ).
cnf(8,plain,
idQb_Q__idQ_idQa != idQa_Q__idQ_idQb,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[7])]),
[iquote('copy,7,flip.1')] ).
cnf(10,axiom,
less_e_qual(zero,A),
file('HEN011-1.p',unknown),
[] ).
cnf(11,axiom,
less_e_qual(A,identity),
file('HEN011-1.p',unknown),
[] ).
cnf(12,axiom,
quotient(A,B,divide(A,B)),
file('HEN011-1.p',unknown),
[] ).
cnf(13,axiom,
quotient(identity,a,idQa),
file('HEN011-1.p',unknown),
[] ).
cnf(14,axiom,
quotient(identity,b,idQb),
file('HEN011-1.p',unknown),
[] ).
cnf(15,axiom,
quotient(identity,idQb,idQ_idQb),
file('HEN011-1.p',unknown),
[] ).
cnf(16,axiom,
quotient(idQa,idQ_idQb,idQa_Q__idQ_idQb),
file('HEN011-1.p',unknown),
[] ).
cnf(17,axiom,
quotient(identity,idQa,idQ_idQa),
file('HEN011-1.p',unknown),
[] ).
cnf(18,axiom,
quotient(idQb,idQ_idQa,idQb_Q__idQ_idQa),
file('HEN011-1.p',unknown),
[] ).
cnf(19,plain,
quotient(zero,A,zero),
inference(hyper,[status(thm)],[10,1]),
[iquote('hyper,10,1')] ).
cnf(21,plain,
( less_e_qual(A,B)
| ~ less_e_qual(zero,A)
| ~ less_e_qual(A,zero) ),
inference(para_into,[status(thm),theory(equality)],[10,5]),
[iquote('para_into,10.1.1,5.3.1')] ).
cnf(22,plain,
quotient(A,identity,zero),
inference(hyper,[status(thm)],[11,1]),
[iquote('hyper,11,1')] ).
cnf(54,plain,
less_e_qual(divide(A,B),A),
inference(hyper,[status(thm)],[12,3]),
[iquote('hyper,12,3')] ).
cnf(56,plain,
( quotient(A,B,C)
| ~ less_e_qual(divide(A,B),C)
| ~ less_e_qual(C,divide(A,B)) ),
inference(para_into,[status(thm),theory(equality)],[12,5]),
[iquote('para_into,12.1.3,5.3.1')] ).
cnf(60,plain,
less_e_qual(divide(idQ_idQb,divide(b,idQb)),divide(idQb,idQb)),
inference(hyper,[status(thm)],[15,4,14,12,12,12]),
[iquote('hyper,15,4,14,12,12,12')] ).
cnf(65,plain,
less_e_qual(divide(idQb,divide(idQb,b)),divide(idQ_idQb,b)),
inference(hyper,[status(thm)],[15,4,12,14,12,12]),
[iquote('hyper,15,4,12,14,12,12')] ).
cnf(79,plain,
less_e_qual(divide(idQa_Q__idQ_idQb,divide(A,idQ_idQb)),divide(divide(idQa,A),idQ_idQb)),
inference(hyper,[status(thm)],[16,4,12,12,12,12]),
[iquote('hyper,16,4,12,12,12,12')] ).
cnf(99,plain,
less_e_qual(divide(idQ_idQa,divide(a,idQa)),divide(idQa,idQa)),
inference(hyper,[status(thm)],[17,4,13,12,12,12]),
[iquote('hyper,17,4,13,12,12,12')] ).
cnf(103,plain,
less_e_qual(divide(divide(identity,idQ_idQb),idQa_Q__idQ_idQb),divide(idQ_idQa,idQ_idQb)),
inference(hyper,[status(thm)],[17,4,16,12,12,12]),
[iquote('hyper,17,4,16,12,12,12')] ).
cnf(106,plain,
less_e_qual(divide(idQa,divide(idQa,a)),divide(idQ_idQa,a)),
inference(hyper,[status(thm)],[17,4,12,13,12,12]),
[iquote('hyper,17,4,12,13,12,12')] ).
cnf(119,plain,
less_e_qual(divide(idQb_Q__idQ_idQa,divide(A,idQ_idQa)),divide(divide(idQb,A),idQ_idQa)),
inference(hyper,[status(thm)],[18,4,12,12,12,12]),
[iquote('hyper,18,4,12,12,12,12')] ).
cnf(120,plain,
less_e_qual(divide(divide(identity,idQ_idQa),idQb_Q__idQ_idQa),divide(idQ_idQb,idQ_idQa)),
inference(hyper,[status(thm)],[18,4,15,12,12,12]),
[iquote('hyper,18,4,15,12,12,12')] ).
cnf(151,plain,
less_e_qual(divide(divide(A,idQa),idQ_idQa),zero),
inference(hyper,[status(thm)],[22,4,17,12,12,19]),
[iquote('hyper,22,4,17,12,12,19')] ).
cnf(153,plain,
less_e_qual(divide(divide(A,idQb),idQ_idQb),zero),
inference(hyper,[status(thm)],[22,4,15,12,12,19]),
[iquote('hyper,22,4,15,12,12,19')] ).
cnf(154,plain,
less_e_qual(divide(idQb,idQb),zero),
inference(hyper,[status(thm)],[22,4,14,14,12,19]),
[iquote('hyper,22,4,14,14,12,19')] ).
cnf(155,plain,
less_e_qual(divide(divide(A,b),idQb),zero),
inference(hyper,[status(thm)],[22,4,14,12,12,19]),
[iquote('hyper,22,4,14,12,12,19')] ).
cnf(156,plain,
less_e_qual(divide(idQa,idQa),zero),
inference(hyper,[status(thm)],[22,4,13,13,12,19]),
[iquote('hyper,22,4,13,13,12,19')] ).
cnf(157,plain,
less_e_qual(divide(divide(A,a),idQa),zero),
inference(hyper,[status(thm)],[22,4,13,12,12,19]),
[iquote('hyper,22,4,13,12,12,19')] ).
cnf(160,plain,
less_e_qual(divide(divide(A,B),divide(identity,B)),zero),
inference(hyper,[status(thm)],[22,4,12,12,12,19]),
[iquote('hyper,22,4,12,12,12,19')] ).
cnf(201,plain,
quotient(divide(A,B),A,zero),
inference(hyper,[status(thm)],[54,1]),
[iquote('hyper,54,1')] ).
cnf(207,plain,
( less_e_qual(A,B)
| ~ less_e_qual(zero,A)
| ~ less_e_qual(A,C)
| ~ less_e_qual(zero,C)
| ~ less_e_qual(C,zero) ),
inference(para_into,[status(thm),theory(equality)],[21,5]),
[iquote('para_into,21.3.2,5.3.1')] ).
cnf(244,plain,
divide(idQb,idQb) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[154,5,10])]),
[iquote('hyper,154,5,10,flip.1')] ).
cnf(246,plain,
less_e_qual(divide(idQ_idQb,divide(b,idQb)),zero),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[60]),244]),
[iquote('back_demod,60,demod,244')] ).
cnf(250,plain,
divide(idQa,idQa) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[156,5,10])]),
[iquote('hyper,156,5,10,flip.1')] ).
cnf(251,plain,
less_e_qual(divide(idQ_idQa,divide(a,idQa)),zero),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[99]),250]),
[iquote('back_demod,99,demod,250')] ).
cnf(386,plain,
divide(divide(A,B),A) = zero,
inference(hyper,[status(thm)],[201,6,12]),
[iquote('hyper,201,6,12')] ).
cnf(388,plain,
less_e_qual(divide(divide(A,A),zero),zero),
inference(hyper,[status(thm)],[201,4,12,201,12,12]),
[iquote('hyper,201,4,12,201,12,12')] ).
cnf(408,plain,
divide(divide(A,idQa),idQ_idQa) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[151,5,10])]),
[iquote('hyper,151,5,10,flip.1')] ).
cnf(411,plain,
divide(divide(A,idQb),idQ_idQb) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[153,5,10])]),
[iquote('hyper,153,5,10,flip.1')] ).
cnf(414,plain,
divide(divide(A,b),idQb) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[155,5,10])]),
[iquote('hyper,155,5,10,flip.1')] ).
cnf(423,plain,
divide(divide(A,a),idQa) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[157,5,10])]),
[iquote('hyper,157,5,10,flip.1')] ).
cnf(466,plain,
divide(idQ_idQb,divide(b,idQb)) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[246,5,10])]),
[iquote('hyper,246,5,10,flip.1')] ).
cnf(482,plain,
divide(idQ_idQa,divide(a,idQa)) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[251,5,10])]),
[iquote('hyper,251,5,10,flip.1')] ).
cnf(504,plain,
divide(divide(A,A),zero) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[388,5,10])]),
[iquote('hyper,388,5,10,flip.1')] ).
cnf(512,plain,
quotient(divide(A,idQa),idQ_idQa,zero),
inference(para_from,[status(thm),theory(equality)],[408,12]),
[iquote('para_from,408.1.1,12.1.3')] ).
cnf(520,plain,
less_e_qual(divide(divide(A,idQ_idQa),divide(idQa,idQ_idQa)),zero),
inference(hyper,[status(thm)],[512,4,12,12,12,12]),
[iquote('hyper,512,4,12,12,12,12')] ).
cnf(525,plain,
less_e_qual(divide(A,idQa),idQ_idQa),
inference(hyper,[status(thm)],[512,2]),
[iquote('hyper,512,2')] ).
cnf(546,plain,
quotient(divide(A,idQb),idQ_idQb,zero),
inference(para_from,[status(thm),theory(equality)],[411,12]),
[iquote('para_from,411.1.1,12.1.3')] ).
cnf(548,plain,
less_e_qual(divide(divide(A,idQ_idQb),divide(idQb,idQ_idQb)),zero),
inference(hyper,[status(thm)],[546,4,12,12,12,12]),
[iquote('hyper,546,4,12,12,12,12')] ).
cnf(553,plain,
less_e_qual(divide(A,idQb),idQ_idQb),
inference(hyper,[status(thm)],[546,2]),
[iquote('hyper,546,2')] ).
cnf(576,plain,
quotient(divide(A,b),idQb,zero),
inference(para_from,[status(thm),theory(equality)],[414,12]),
[iquote('para_from,414.1.1,12.1.3')] ).
cnf(583,plain,
less_e_qual(divide(A,b),idQb),
inference(hyper,[status(thm)],[576,2]),
[iquote('hyper,576,2')] ).
cnf(608,plain,
quotient(divide(A,a),idQa,zero),
inference(para_from,[status(thm),theory(equality)],[423,12]),
[iquote('para_from,423.1.1,12.1.3')] ).
cnf(615,plain,
less_e_qual(divide(A,a),idQa),
inference(hyper,[status(thm)],[608,2]),
[iquote('hyper,608,2')] ).
cnf(736,plain,
quotient(idQ_idQb,divide(b,idQb),zero),
inference(para_from,[status(thm),theory(equality)],[466,12]),
[iquote('para_from,466.1.1,12.1.3')] ).
cnf(744,plain,
less_e_qual(idQ_idQb,divide(b,idQb)),
inference(hyper,[status(thm)],[736,2]),
[iquote('hyper,736,2')] ).
cnf(755,plain,
divide(b,idQb) = idQ_idQb,
inference(hyper,[status(thm)],[744,5,553]),
[iquote('hyper,744,5,553')] ).
cnf(777,plain,
divide(idQ_idQb,b) = zero,
inference(para_from,[status(thm),theory(equality)],[755,386]),
[iquote('para_from,755.1.1,386.1.1.1')] ).
cnf(778,plain,
quotient(idQ_idQb,b,zero),
inference(para_from,[status(thm),theory(equality)],[755,201]),
[iquote('para_from,755.1.1,201.1.1')] ).
cnf(781,plain,
less_e_qual(divide(idQb,divide(idQb,b)),zero),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[65]),777]),
[iquote('back_demod,65,demod,777')] ).
cnf(840,plain,
quotient(idQ_idQa,divide(a,idQa),zero),
inference(para_from,[status(thm),theory(equality)],[482,12]),
[iquote('para_from,482.1.1,12.1.3')] ).
cnf(848,plain,
less_e_qual(idQ_idQa,divide(a,idQa)),
inference(hyper,[status(thm)],[840,2]),
[iquote('hyper,840,2')] ).
cnf(859,plain,
divide(a,idQa) = idQ_idQa,
inference(hyper,[status(thm)],[848,5,525]),
[iquote('hyper,848,5,525')] ).
cnf(883,plain,
divide(idQ_idQa,a) = zero,
inference(para_from,[status(thm),theory(equality)],[859,386]),
[iquote('para_from,859.1.1,386.1.1.1')] ).
cnf(884,plain,
quotient(idQ_idQa,a,zero),
inference(para_from,[status(thm),theory(equality)],[859,201]),
[iquote('para_from,859.1.1,201.1.1')] ).
cnf(887,plain,
less_e_qual(divide(idQa,divide(idQa,a)),zero),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[106]),883]),
[iquote('back_demod,106,demod,883')] ).
cnf(940,plain,
quotient(divide(A,A),zero,zero),
inference(para_from,[status(thm),theory(equality)],[504,12]),
[iquote('para_from,504.1.1,12.1.3')] ).
cnf(945,plain,
less_e_qual(divide(A,A),zero),
inference(hyper,[status(thm)],[940,2]),
[iquote('hyper,940,2')] ).
cnf(953,plain,
divide(A,A) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[945,5,10])]),
[iquote('hyper,945,5,10,flip.1')] ).
cnf(1000,plain,
quotient(A,A,zero),
inference(para_from,[status(thm),theory(equality)],[953,12]),
[iquote('para_from,953.1.1,12.1.3')] ).
cnf(1001,plain,
less_e_qual(divide(divide(A,divide(A,zero)),zero),zero),
inference(hyper,[status(thm)],[1000,4,12,19,12,12]),
[iquote('hyper,1000,4,12,19,12,12')] ).
cnf(1031,plain,
divide(idQb,divide(idQb,b)) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[781,5,10])]),
[iquote('hyper,781,5,10,flip.1')] ).
cnf(1034,plain,
divide(idQa,divide(idQa,a)) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[887,5,10])]),
[iquote('hyper,887,5,10,flip.1')] ).
cnf(1126,plain,
quotient(idQb,divide(idQb,b),zero),
inference(para_from,[status(thm),theory(equality)],[1031,12]),
[iquote('para_from,1031.1.1,12.1.3')] ).
cnf(1138,plain,
less_e_qual(idQb,divide(idQb,b)),
inference(hyper,[status(thm)],[1126,2]),
[iquote('hyper,1126,2')] ).
cnf(1148,plain,
quotient(idQb,b,idQb),
inference(hyper,[status(thm)],[1138,56,583]),
[iquote('hyper,1138,56,583')] ).
cnf(1157,plain,
less_e_qual(divide(idQb,zero),divide(divide(idQb,idQ_idQb),b)),
inference(hyper,[status(thm)],[1148,4,12,778,12,12]),
[iquote('hyper,1148,4,12,778,12,12')] ).
cnf(1200,plain,
quotient(idQa,divide(idQa,a),zero),
inference(para_from,[status(thm),theory(equality)],[1034,12]),
[iquote('para_from,1034.1.1,12.1.3')] ).
cnf(1207,plain,
less_e_qual(idQa,divide(idQa,a)),
inference(hyper,[status(thm)],[1200,2]),
[iquote('hyper,1200,2')] ).
cnf(1217,plain,
quotient(idQa,a,idQa),
inference(hyper,[status(thm)],[1207,56,615]),
[iquote('hyper,1207,56,615')] ).
cnf(1226,plain,
less_e_qual(divide(idQa,zero),divide(divide(idQa,idQ_idQa),a)),
inference(hyper,[status(thm)],[1217,4,12,884,12,12]),
[iquote('hyper,1217,4,12,884,12,12')] ).
cnf(1627,plain,
quotient(divide(divide(identity,idQ_idQb),idQa_Q__idQ_idQb),divide(idQ_idQa,idQ_idQb),zero),
inference(hyper,[status(thm)],[103,1]),
[iquote('hyper,103,1')] ).
cnf(1699,plain,
quotient(divide(divide(identity,idQ_idQa),idQb_Q__idQ_idQa),divide(idQ_idQb,idQ_idQa),zero),
inference(hyper,[status(thm)],[120,1]),
[iquote('hyper,120,1')] ).
cnf(1863,plain,
quotient(divide(A,B),divide(identity,B),zero),
inference(hyper,[status(thm)],[160,56,10]),
[iquote('hyper,160,56,10')] ).
cnf(1888,plain,
less_e_qual(divide(A,B),divide(identity,B)),
inference(hyper,[status(thm)],[1863,2]),
[iquote('hyper,1863,2')] ).
cnf(2276,plain,
quotient(divide(A,idQ_idQa),divide(idQa,idQ_idQa),zero),
inference(hyper,[status(thm)],[520,56,10]),
[iquote('hyper,520,56,10')] ).
cnf(2283,plain,
less_e_qual(divide(divide(divide(A,idQ_idQa),idQa),zero),zero),
inference(hyper,[status(thm)],[2276,4,201,12,12,19]),
[iquote('hyper,2276,4,201,12,12,19')] ).
cnf(2286,plain,
less_e_qual(divide(A,idQ_idQa),divide(idQa,idQ_idQa)),
inference(hyper,[status(thm)],[2276,2]),
[iquote('hyper,2276,2')] ).
cnf(2319,plain,
divide(identity,idQ_idQa) = divide(idQa,idQ_idQa),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[2286,5,1888])]),
[iquote('hyper,2286,5,1888,flip.1')] ).
cnf(2332,plain,
quotient(divide(divide(idQa,idQ_idQa),idQb_Q__idQ_idQa),divide(idQ_idQb,idQ_idQa),zero),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1699]),2319]),
[iquote('back_demod,1699,demod,2319')] ).
cnf(2453,plain,
quotient(divide(A,idQ_idQb),divide(idQb,idQ_idQb),zero),
inference(hyper,[status(thm)],[548,56,10]),
[iquote('hyper,548,56,10')] ).
cnf(2460,plain,
less_e_qual(divide(divide(divide(A,idQ_idQb),idQb),zero),zero),
inference(hyper,[status(thm)],[2453,4,201,12,12,19]),
[iquote('hyper,2453,4,201,12,12,19')] ).
cnf(2463,plain,
less_e_qual(divide(A,idQ_idQb),divide(idQb,idQ_idQb)),
inference(hyper,[status(thm)],[2453,2]),
[iquote('hyper,2453,2')] ).
cnf(2479,plain,
divide(identity,idQ_idQb) = divide(idQb,idQ_idQb),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[2463,5,1888])]),
[iquote('hyper,2463,5,1888,flip.1')] ).
cnf(2492,plain,
quotient(divide(divide(idQb,idQ_idQb),idQa_Q__idQ_idQb),divide(idQ_idQa,idQ_idQb),zero),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1627]),2479]),
[iquote('back_demod,1627,demod,2479')] ).
cnf(3187,plain,
quotient(divide(A,divide(A,zero)),zero,zero),
inference(hyper,[status(thm)],[1001,56,10]),
[iquote('hyper,1001,56,10')] ).
cnf(3200,plain,
less_e_qual(divide(A,divide(A,zero)),zero),
inference(hyper,[status(thm)],[3187,2]),
[iquote('hyper,3187,2')] ).
cnf(3214,plain,
quotient(A,divide(A,zero),zero),
inference(hyper,[status(thm)],[3200,56,10]),
[iquote('hyper,3200,56,10')] ).
cnf(3288,plain,
less_e_qual(A,divide(A,zero)),
inference(hyper,[status(thm)],[3214,2]),
[iquote('hyper,3214,2')] ).
cnf(3312,plain,
quotient(A,zero,A),
inference(hyper,[status(thm)],[3288,56,54]),
[iquote('hyper,3288,56,54')] ).
cnf(3325,plain,
divide(A,zero) = A,
inference(hyper,[status(thm)],[3288,5,54]),
[iquote('hyper,3288,5,54')] ).
cnf(3433,plain,
less_e_qual(divide(divide(A,idQ_idQb),idQb),zero),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2460]),3325]),
[iquote('back_demod,2460,demod,3325')] ).
cnf(3443,plain,
less_e_qual(divide(divide(A,idQ_idQa),idQa),zero),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2283]),3325]),
[iquote('back_demod,2283,demod,3325')] ).
cnf(3575,plain,
less_e_qual(idQa,divide(divide(idQa,idQ_idQa),a)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1226]),3325]),
[iquote('back_demod,1226,demod,3325')] ).
cnf(3577,plain,
less_e_qual(idQb,divide(divide(idQb,idQ_idQb),b)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1157]),3325]),
[iquote('back_demod,1157,demod,3325')] ).
cnf(4064,plain,
quotient(divide(A,idQ_idQb),idQb,zero),
inference(hyper,[status(thm)],[3433,56,10]),
[iquote('hyper,3433,56,10')] ).
cnf(4075,plain,
less_e_qual(divide(A,idQ_idQb),idQb),
inference(hyper,[status(thm)],[4064,2]),
[iquote('hyper,4064,2')] ).
cnf(4230,plain,
quotient(divide(A,idQ_idQa),idQa,zero),
inference(hyper,[status(thm)],[3443,56,10]),
[iquote('hyper,3443,56,10')] ).
cnf(4239,plain,
less_e_qual(divide(A,idQ_idQa),idQa),
inference(hyper,[status(thm)],[4230,2]),
[iquote('hyper,4230,2')] ).
cnf(4300,plain,
quotient(divide(idQa,idQ_idQa),a,idQa),
inference(hyper,[status(thm)],[3575,56,615]),
[iquote('hyper,3575,56,615')] ).
cnf(4305,plain,
less_e_qual(idQa,divide(idQa,idQ_idQa)),
inference(hyper,[status(thm)],[4300,3]),
[iquote('hyper,4300,3')] ).
cnf(4313,plain,
divide(idQa,idQ_idQa) = idQa,
inference(hyper,[status(thm)],[4305,5,4239]),
[iquote('hyper,4305,5,4239')] ).
cnf(4324,plain,
quotient(divide(idQa,idQb_Q__idQ_idQa),divide(idQ_idQb,idQ_idQa),zero),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2332]),4313]),
[iquote('back_demod,2332,demod,4313')] ).
cnf(4340,plain,
quotient(divide(idQb,idQ_idQb),b,idQb),
inference(hyper,[status(thm)],[3577,56,583]),
[iquote('hyper,3577,56,583')] ).
cnf(4345,plain,
less_e_qual(idQb,divide(idQb,idQ_idQb)),
inference(hyper,[status(thm)],[4340,3]),
[iquote('hyper,4340,3')] ).
cnf(4353,plain,
divide(idQb,idQ_idQb) = idQb,
inference(hyper,[status(thm)],[4345,5,4075]),
[iquote('hyper,4345,5,4075')] ).
cnf(4366,plain,
quotient(divide(idQb,idQa_Q__idQ_idQb),divide(idQ_idQa,idQ_idQb),zero),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2492]),4353]),
[iquote('back_demod,2492,demod,4353')] ).
cnf(4587,plain,
less_e_qual(divide(divide(idQa,idQb_Q__idQ_idQa),idQ_idQb),zero),
inference(hyper,[status(thm)],[4324,4,201,12,3312,19]),
[iquote('hyper,4324,4,201,12,3312,19')] ).
cnf(4619,plain,
less_e_qual(divide(idQa_Q__idQ_idQb,divide(idQb_Q__idQ_idQa,idQ_idQb)),A),
inference(hyper,[status(thm)],[4587,207,10,79,10]),
[iquote('hyper,4587,207,10,79,10')] ).
cnf(4665,plain,
quotient(idQa_Q__idQ_idQb,divide(idQb_Q__idQ_idQa,idQ_idQb),zero),
inference(hyper,[status(thm)],[4619,56,10]),
[iquote('hyper,4619,56,10')] ).
cnf(4670,plain,
less_e_qual(divide(idQa_Q__idQ_idQb,idQb_Q__idQ_idQa),zero),
inference(hyper,[status(thm)],[4665,4,201,12,3312,19]),
[iquote('hyper,4665,4,201,12,3312,19')] ).
cnf(4680,plain,
quotient(idQa_Q__idQ_idQb,idQb_Q__idQ_idQa,zero),
inference(hyper,[status(thm)],[4670,56,10]),
[iquote('hyper,4670,56,10')] ).
cnf(4689,plain,
less_e_qual(idQa_Q__idQ_idQb,idQb_Q__idQ_idQa),
inference(hyper,[status(thm)],[4680,2]),
[iquote('hyper,4680,2')] ).
cnf(4773,plain,
less_e_qual(divide(divide(idQb,idQa_Q__idQ_idQb),idQ_idQa),zero),
inference(hyper,[status(thm)],[4366,4,201,12,3312,19]),
[iquote('hyper,4366,4,201,12,3312,19')] ).
cnf(4804,plain,
less_e_qual(divide(idQb_Q__idQ_idQa,divide(idQa_Q__idQ_idQb,idQ_idQa)),A),
inference(hyper,[status(thm)],[4773,207,10,119,10]),
[iquote('hyper,4773,207,10,119,10')] ).
cnf(4850,plain,
quotient(idQb_Q__idQ_idQa,divide(idQa_Q__idQ_idQb,idQ_idQa),zero),
inference(hyper,[status(thm)],[4804,56,10]),
[iquote('hyper,4804,56,10')] ).
cnf(4858,plain,
less_e_qual(divide(idQb_Q__idQ_idQa,idQa_Q__idQ_idQb),zero),
inference(hyper,[status(thm)],[4850,4,201,12,3312,19]),
[iquote('hyper,4850,4,201,12,3312,19')] ).
cnf(4869,plain,
quotient(idQb_Q__idQ_idQa,idQa_Q__idQ_idQb,zero),
inference(hyper,[status(thm)],[4858,56,10]),
[iquote('hyper,4858,56,10')] ).
cnf(4879,plain,
less_e_qual(idQb_Q__idQ_idQa,idQa_Q__idQ_idQb),
inference(hyper,[status(thm)],[4869,2]),
[iquote('hyper,4869,2')] ).
cnf(4882,plain,
idQb_Q__idQ_idQa = idQa_Q__idQ_idQb,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[4879,5,4689])]),
[iquote('hyper,4879,5,4689,flip.1')] ).
cnf(4884,plain,
$false,
inference(binary,[status(thm)],[4882,8]),
[iquote('binary,4882.1,8.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : HEN011-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.11/0.33 % Computer : n027.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Wed Jul 27 09:13:36 EDT 2022
% 0.11/0.33 % CPUTime :
% 2.74/2.95 ----- Otter 3.3f, August 2004 -----
% 2.74/2.95 The process was started by sandbox on n027.cluster.edu,
% 2.74/2.95 Wed Jul 27 09:13:36 2022
% 2.74/2.95 The command was "./otter". The process ID is 18340.
% 2.74/2.95
% 2.74/2.95 set(prolog_style_variables).
% 2.74/2.95 set(auto).
% 2.74/2.95 dependent: set(auto1).
% 2.74/2.95 dependent: set(process_input).
% 2.74/2.95 dependent: clear(print_kept).
% 2.74/2.95 dependent: clear(print_new_demod).
% 2.74/2.95 dependent: clear(print_back_demod).
% 2.74/2.95 dependent: clear(print_back_sub).
% 2.74/2.95 dependent: set(control_memory).
% 2.74/2.95 dependent: assign(max_mem, 12000).
% 2.74/2.95 dependent: assign(pick_given_ratio, 4).
% 2.74/2.95 dependent: assign(stats_level, 1).
% 2.74/2.95 dependent: assign(max_seconds, 10800).
% 2.74/2.95 clear(print_given).
% 2.74/2.95
% 2.74/2.95 list(usable).
% 2.74/2.95 0 [] A=A.
% 2.74/2.95 0 [] -less_e_qual(X,Y)|quotient(X,Y,zero).
% 2.74/2.95 0 [] -quotient(X,Y,zero)|less_e_qual(X,Y).
% 2.74/2.95 0 [] -quotient(X,Y,Z)|less_e_qual(Z,X).
% 2.74/2.95 0 [] -quotient(X,Y,V1)| -quotient(Y,Z,V2)| -quotient(X,Z,V3)| -quotient(V3,V2,V4)| -quotient(V1,Z,V5)|less_e_qual(V4,V5).
% 2.74/2.95 0 [] less_e_qual(zero,X).
% 2.74/2.95 0 [] -less_e_qual(X,Y)| -less_e_qual(Y,X)|X=Y.
% 2.74/2.95 0 [] less_e_qual(X,identity).
% 2.74/2.95 0 [] quotient(X,Y,divide(X,Y)).
% 2.74/2.95 0 [] -quotient(X,Y,Z)| -quotient(X,Y,W)|Z=W.
% 2.74/2.95 0 [] quotient(identity,a,idQa).
% 2.74/2.95 0 [] quotient(identity,b,idQb).
% 2.74/2.95 0 [] quotient(identity,idQb,idQ_idQb).
% 2.74/2.95 0 [] quotient(idQa,idQ_idQb,idQa_Q__idQ_idQb).
% 2.74/2.95 0 [] quotient(identity,idQa,idQ_idQa).
% 2.74/2.95 0 [] quotient(idQb,idQ_idQa,idQb_Q__idQ_idQa).
% 2.74/2.95 0 [] idQa_Q__idQ_idQb!=idQb_Q__idQ_idQa.
% 2.74/2.95 end_of_list.
% 2.74/2.95
% 2.74/2.95 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=6.
% 2.74/2.95
% 2.74/2.95 This is a Horn set with equality. The strategy will be
% 2.74/2.95 Knuth-Bendix and hyper_res, with positive clauses in
% 2.74/2.95 sos and nonpositive clauses in usable.
% 2.74/2.95
% 2.74/2.95 dependent: set(knuth_bendix).
% 2.74/2.95 dependent: set(anl_eq).
% 2.74/2.95 dependent: set(para_from).
% 2.74/2.95 dependent: set(para_into).
% 2.74/2.95 dependent: clear(para_from_right).
% 2.74/2.95 dependent: clear(para_into_right).
% 2.74/2.95 dependent: set(para_from_vars).
% 2.74/2.95 dependent: set(eq_units_both_ways).
% 2.74/2.95 dependent: set(dynamic_demod_all).
% 2.74/2.95 dependent: set(dynamic_demod).
% 2.74/2.95 dependent: set(order_eq).
% 2.74/2.95 dependent: set(back_demod).
% 2.74/2.95 dependent: set(lrpo).
% 2.74/2.95 dependent: set(hyper_res).
% 2.74/2.95 dependent: clear(order_hyper).
% 2.74/2.95
% 2.74/2.95 ------------> process usable:
% 2.74/2.95 ** KEPT (pick-wt=7): 1 [] -less_e_qual(A,B)|quotient(A,B,zero).
% 2.74/2.95 ** KEPT (pick-wt=7): 2 [] -quotient(A,B,zero)|less_e_qual(A,B).
% 2.74/2.95 ** KEPT (pick-wt=7): 3 [] -quotient(A,B,C)|less_e_qual(C,A).
% 2.74/2.95 ** KEPT (pick-wt=23): 4 [] -quotient(A,B,C)| -quotient(B,D,E)| -quotient(A,D,F)| -quotient(F,E,G)| -quotient(C,D,H)|less_e_qual(G,H).
% 2.74/2.95 ** KEPT (pick-wt=9): 5 [] -less_e_qual(A,B)| -less_e_qual(B,A)|A=B.
% 2.74/2.95 ** KEPT (pick-wt=11): 6 [] -quotient(A,B,C)| -quotient(A,B,D)|C=D.
% 2.74/2.95 ** KEPT (pick-wt=3): 8 [copy,7,flip.1] idQb_Q__idQ_idQa!=idQa_Q__idQ_idQb.
% 2.74/2.95
% 2.74/2.95 ------------> process sos:
% 2.74/2.95 ** KEPT (pick-wt=3): 9 [] A=A.
% 2.74/2.95 ** KEPT (pick-wt=3): 10 [] less_e_qual(zero,A).
% 2.74/2.95 ** KEPT (pick-wt=3): 11 [] less_e_qual(A,identity).
% 2.74/2.95 ** KEPT (pick-wt=6): 12 [] quotient(A,B,divide(A,B)).
% 2.74/2.95 ** KEPT (pick-wt=4): 13 [] quotient(identity,a,idQa).
% 2.74/2.95 ** KEPT (pick-wt=4): 14 [] quotient(identity,b,idQb).
% 2.74/2.95 ** KEPT (pick-wt=4): 15 [] quotient(identity,idQb,idQ_idQb).
% 2.74/2.95 ** KEPT (pick-wt=4): 16 [] quotient(idQa,idQ_idQb,idQa_Q__idQ_idQb).
% 2.74/2.95 ** KEPT (pick-wt=4): 17 [] quotient(identity,idQa,idQ_idQa).
% 2.74/2.95 ** KEPT (pick-wt=4): 18 [] quotient(idQb,idQ_idQa,idQb_Q__idQ_idQa).
% 2.74/2.95 Following clause subsumed by 9 during input processing: 0 [copy,9,flip.1] A=A.
% 2.74/2.95
% 2.74/2.95 ======= end of input processing =======
% 2.74/2.95
% 2.74/2.95 =========== start of search ===========
% 2.74/2.95
% 2.74/2.95
% 2.74/2.95 Resetting weight limit to 9.
% 2.74/2.95
% 2.74/2.95
% 2.74/2.95 Resetting weight limit to 9.
% 2.74/2.95
% 2.74/2.95 sos_size=2381
% 2.74/2.95
% 2.74/2.95 -------- PROOF --------
% 2.74/2.95
% 2.74/2.95 ----> UNIT CONFLICT at 1.03 sec ----> 4884 [binary,4882.1,8.1] $F.
% 2.74/2.95
% 2.74/2.95 Length of proof is 122. Level of proof is 27.
% 2.74/2.95
% 2.74/2.95 ---------------- PROOF ----------------
% 2.74/2.95 % SZS status Unsatisfiable
% 2.74/2.95 % SZS output start Refutation
% See solution above
% 2.74/2.95 ------------ end of proof -------------
% 2.74/2.95
% 2.74/2.95
% 2.74/2.95 Search stopped by max_proofs option.
% 2.74/2.95
% 2.74/2.95
% 2.74/2.95 Search stopped by max_proofs option.
% 2.74/2.95
% 2.74/2.95 ============ end of search ============
% 2.74/2.95
% 2.74/2.95 -------------- statistics -------------
% 2.74/2.95 clauses given 597
% 2.74/2.95 clauses generated 102455
% 2.74/2.95 clauses kept 4732
% 2.74/2.95 clauses forward subsumed 93661
% 2.74/2.95 clauses back subsumed 240
% 2.74/2.95 Kbytes malloced 4882
% 2.74/2.95
% 2.74/2.95 ----------- times (seconds) -----------
% 2.74/2.95 user CPU time 1.03 (0 hr, 0 min, 1 sec)
% 2.74/2.95 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.74/2.95 wall-clock time 3 (0 hr, 0 min, 3 sec)
% 2.74/2.95
% 2.74/2.95 That finishes the proof of the theorem.
% 2.74/2.95
% 2.74/2.95 Process 18340 finished Wed Jul 27 09:13:39 2022
% 2.74/2.95 Otter interrupted
% 2.74/2.95 PROOF FOUND
%------------------------------------------------------------------------------