TSTP Solution File: HEN009-1 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : HEN009-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n024.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 : Tue Aug 22 10:42:17 EDT 2023
% Result : Unsatisfiable 23.90s 12.30s
% Output : CNFRefutation 23.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 22
% Syntax : Number of formulae : 131 ( 70 unt; 9 typ; 0 def)
% Number of atoms : 213 ( 37 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 184 ( 93 ~; 91 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 3 >; 4 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 171 (; 171 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ quotient > less_equal > divide > #nlpp > zero > identity > idQa > idQ_idQa > idQ__idQ_idQa > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(less_equal,type,
less_equal: ( $i * $i ) > $o ).
tff(a,type,
a: $i ).
tff(divide,type,
divide: ( $i * $i ) > $i ).
tff(idQa,type,
idQa: $i ).
tff(quotient,type,
quotient: ( $i * $i * $i ) > $o ).
tff(idQ__idQ_idQa,type,
idQ__idQ_idQa: $i ).
tff(identity,type,
identity: $i ).
tff(idQ_idQa,type,
idQ_idQa: $i ).
tff(zero,type,
zero: $i ).
tff(f_111,axiom,
idQa != idQ__idQ_idQa,
file(unknown,unknown) ).
tff(f_92,axiom,
! [X] : less_equal(X,identity),
file(unknown,unknown) ).
tff(f_48,axiom,
! [X,Y] :
( ~ less_equal(X,Y)
| quotient(X,Y,zero) ),
file(unknown,unknown) ).
tff(f_95,axiom,
! [X,Y] : quotient(X,Y,divide(X,Y)),
file(unknown,unknown) ).
tff(f_104,axiom,
! [X,Y,Z,W] :
( ~ quotient(X,Y,Z)
| ~ quotient(X,Y,W)
| ( Z = W ) ),
file(unknown,unknown) ).
tff(f_59,axiom,
! [X,Y,Z] :
( ~ quotient(X,Y,Z)
| less_equal(Z,X) ),
file(unknown,unknown) ).
tff(f_80,axiom,
! [X] : less_equal(zero,X),
file(unknown,unknown) ).
tff(f_89,axiom,
! [X,Y] :
( ~ less_equal(X,Y)
| ~ less_equal(Y,X)
| ( X = Y ) ),
file(unknown,unknown) ).
tff(f_108,axiom,
quotient(identity,idQa,idQ_idQa),
file(unknown,unknown) ).
tff(f_77,axiom,
! [V3,V5,Z,V1,X,Y,V2,V4] :
( ~ quotient(X,Y,V1)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Z,V3)
| ~ quotient(V3,V2,V4)
| ~ quotient(V1,Z,V5)
| less_equal(V4,V5) ),
file(unknown,unknown) ).
tff(f_53,axiom,
! [X,Y] :
( ~ quotient(X,Y,zero)
| less_equal(X,Y) ),
file(unknown,unknown) ).
tff(f_109,axiom,
quotient(identity,idQ_idQa,idQ__idQ_idQa),
file(unknown,unknown) ).
tff(f_107,axiom,
quotient(identity,a,idQa),
file(unknown,unknown) ).
tff(c_26,plain,
idQa != idQ__idQ_idQa,
inference(cnfTransformation,[status(thm)],[f_111]) ).
tff(c_14,plain,
! [X_19] : less_equal(X_19,identity),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_2,plain,
! [X_1,Y_2] :
( quotient(X_1,Y_2,zero)
| ~ less_equal(X_1,Y_2) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_16,plain,
! [X_20,Y_21] : quotient(X_20,Y_21,divide(X_20,Y_21)),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_105,plain,
! [Z_44,W_45,X_46,Y_47] :
( ( Z_44 = W_45 )
| ~ quotient(X_46,Y_47,W_45)
| ~ quotient(X_46,Y_47,Z_44) ),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_261,plain,
! [X_62,Y_63,Z_64] :
( ( divide(X_62,Y_63) = Z_64 )
| ~ quotient(X_62,Y_63,Z_64) ),
inference(resolution,[status(thm)],[c_16,c_105]) ).
tff(c_291,plain,
! [X_65,Y_66] :
( ( divide(X_65,Y_66) = zero )
| ~ less_equal(X_65,Y_66) ),
inference(resolution,[status(thm)],[c_2,c_261]) ).
tff(c_305,plain,
! [X_67] : ( divide(X_67,identity) = zero ),
inference(resolution,[status(thm)],[c_14,c_291]) ).
tff(c_316,plain,
! [X_67] : quotient(X_67,identity,zero),
inference(superposition,[status(thm),theory(equality)],[c_305,c_16]) ).
tff(c_31,plain,
! [Z_32,X_33,Y_34] :
( less_equal(Z_32,X_33)
| ~ quotient(X_33,Y_34,Z_32) ),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_44,plain,
! [X_20,Y_21] : less_equal(divide(X_20,Y_21),X_20),
inference(resolution,[status(thm)],[c_16,c_31]) ).
tff(c_10,plain,
! [X_16] : less_equal(zero,X_16),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_62,plain,
! [Y_39,X_40] :
( ( Y_39 = X_40 )
| ~ less_equal(Y_39,X_40)
| ~ less_equal(X_40,Y_39) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_79,plain,
! [X_42] :
( ( zero = X_42 )
| ~ less_equal(X_42,zero) ),
inference(resolution,[status(thm)],[c_10,c_62]) ).
tff(c_88,plain,
! [Y_21] : ( divide(zero,Y_21) = zero ),
inference(resolution,[status(thm)],[c_44,c_79]) ).
tff(c_22,plain,
quotient(identity,idQa,idQ_idQa),
inference(cnfTransformation,[status(thm)],[f_108]) ).
tff(c_163,plain,
! [X_54,V5_57,Z_53,V2_50,V3_51,V4_52,V1_55,Y_56] :
( less_equal(V4_52,V5_57)
| ~ quotient(V1_55,Z_53,V5_57)
| ~ quotient(V3_51,V2_50,V4_52)
| ~ quotient(X_54,Z_53,V3_51)
| ~ quotient(Y_56,Z_53,V2_50)
| ~ quotient(X_54,Y_56,V1_55) ),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_778,plain,
! [Y_130,X_126,V4_125,Y_124,V3_128,V2_129,X_127] :
( less_equal(V4_125,divide(X_126,Y_124))
| ~ quotient(V3_128,V2_129,V4_125)
| ~ quotient(X_127,Y_124,V3_128)
| ~ quotient(Y_130,Y_124,V2_129)
| ~ quotient(X_127,Y_130,X_126) ),
inference(resolution,[status(thm)],[c_16,c_163]) ).
tff(c_3303,plain,
! [X_275,Y_272,Y_274,X_273,Y_271,X_276] :
( less_equal(divide(X_273,Y_271),divide(X_276,Y_272))
| ~ quotient(X_275,Y_272,X_273)
| ~ quotient(Y_274,Y_272,Y_271)
| ~ quotient(X_275,Y_274,X_276) ),
inference(resolution,[status(thm)],[c_16,c_778]) ).
tff(c_3368,plain,
! [Y_277,X_278,Y_279] :
( less_equal(divide(idQ_idQa,Y_277),divide(X_278,idQa))
| ~ quotient(Y_279,idQa,Y_277)
| ~ quotient(identity,Y_279,X_278) ),
inference(resolution,[status(thm)],[c_22,c_3303]) ).
tff(c_3502,plain,
! [X_287] :
( less_equal(divide(idQ_idQa,idQ_idQa),divide(X_287,idQa))
| ~ quotient(identity,identity,X_287) ),
inference(resolution,[status(thm)],[c_22,c_3368]) ).
tff(c_3531,plain,
( less_equal(divide(idQ_idQa,idQ_idQa),zero)
| ~ quotient(identity,identity,zero) ),
inference(superposition,[status(thm),theory(equality)],[c_88,c_3502]) ).
tff(c_3537,plain,
less_equal(divide(idQ_idQa,idQ_idQa),zero),
inference(demodulation,[status(thm),theory(equality)],[c_316,c_3531]) ).
tff(c_71,plain,
! [X_16] :
( ( zero = X_16 )
| ~ less_equal(X_16,zero) ),
inference(resolution,[status(thm)],[c_10,c_62]) ).
tff(c_3547,plain,
divide(idQ_idQa,idQ_idQa) = zero,
inference(resolution,[status(thm)],[c_3537,c_71]) ).
tff(c_3632,plain,
quotient(idQ_idQa,idQ_idQa,zero),
inference(superposition,[status(thm),theory(equality)],[c_3547,c_16]) ).
tff(c_4,plain,
! [X_3,Y_4] :
( less_equal(X_3,Y_4)
| ~ quotient(X_3,Y_4,zero) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_3714,plain,
less_equal(idQ_idQa,idQ_idQa),
inference(resolution,[status(thm)],[c_3632,c_4]) ).
tff(c_24,plain,
quotient(identity,idQ_idQa,idQ__idQ_idQa),
inference(cnfTransformation,[status(thm)],[f_109]) ).
tff(c_1094,plain,
! [V3_145,Y_148,X_144,Y_147,X_143,V2_146,V4_142] :
( less_equal(V4_142,zero)
| ~ quotient(V3_145,V2_146,V4_142)
| ~ quotient(X_144,Y_148,V3_145)
| ~ quotient(Y_147,Y_148,V2_146)
| ~ quotient(X_144,Y_147,X_143)
| ~ less_equal(X_143,Y_148) ),
inference(resolution,[status(thm)],[c_2,c_163]) ).
tff(c_3436,plain,
! [Y_282,X_286,X_285,X_283,Y_284,Y_281] :
( less_equal(divide(X_283,Y_282),zero)
| ~ quotient(X_285,Y_281,X_283)
| ~ quotient(Y_284,Y_281,Y_282)
| ~ quotient(X_285,Y_284,X_286)
| ~ less_equal(X_286,Y_281) ),
inference(resolution,[status(thm)],[c_16,c_1094]) ).
tff(c_4610,plain,
! [Y_317,Y_318,X_319] :
( less_equal(divide(idQ__idQ_idQa,Y_317),zero)
| ~ quotient(Y_318,idQ_idQa,Y_317)
| ~ quotient(identity,Y_318,X_319)
| ~ less_equal(X_319,idQ_idQa) ),
inference(resolution,[status(thm)],[c_24,c_3436]) ).
tff(c_6666,plain,
! [X_380,X_381] :
( less_equal(divide(idQ__idQ_idQa,divide(X_380,idQ_idQa)),zero)
| ~ quotient(identity,X_380,X_381)
| ~ less_equal(X_381,idQ_idQa) ),
inference(resolution,[status(thm)],[c_16,c_4610]) ).
tff(c_6677,plain,
( less_equal(divide(idQ__idQ_idQa,divide(idQa,idQ_idQa)),zero)
| ~ less_equal(idQ_idQa,idQ_idQa) ),
inference(resolution,[status(thm)],[c_22,c_6666]) ).
tff(c_6691,plain,
less_equal(divide(idQ__idQ_idQa,divide(idQa,idQ_idQa)),zero),
inference(demodulation,[status(thm),theory(equality)],[c_3714,c_6677]) ).
tff(c_6707,plain,
divide(idQ__idQ_idQa,divide(idQa,idQ_idQa)) = zero,
inference(resolution,[status(thm)],[c_6691,c_71]) ).
tff(c_6747,plain,
quotient(idQ__idQ_idQa,divide(idQa,idQ_idQa),zero),
inference(superposition,[status(thm),theory(equality)],[c_6707,c_16]) ).
tff(c_6824,plain,
less_equal(idQ__idQ_idQa,divide(idQa,idQ_idQa)),
inference(resolution,[status(thm)],[c_6747,c_4]) ).
tff(c_4822,plain,
! [X_328,X_327,Y_326,Y_330,Y_329] :
( less_equal(divide(divide(X_327,Y_326),Y_330),divide(X_328,Y_326))
| ~ quotient(Y_329,Y_326,Y_330)
| ~ quotient(X_327,Y_329,X_328) ),
inference(resolution,[status(thm)],[c_16,c_3303]) ).
tff(c_5878,plain,
! [X_358,X_359] :
( less_equal(divide(divide(X_358,idQ_idQa),idQ__idQ_idQa),divide(X_359,idQ_idQa))
| ~ quotient(X_358,identity,X_359) ),
inference(resolution,[status(thm)],[c_24,c_4822]) ).
tff(c_5937,plain,
! [X_358] :
( less_equal(divide(divide(X_358,idQ_idQa),idQ__idQ_idQa),zero)
| ~ quotient(X_358,identity,zero) ),
inference(superposition,[status(thm),theory(equality)],[c_88,c_5878]) ).
tff(c_5951,plain,
! [X_360] : less_equal(divide(divide(X_360,idQ_idQa),idQ__idQ_idQa),zero),
inference(demodulation,[status(thm),theory(equality)],[c_316,c_5937]) ).
tff(c_6004,plain,
! [X_361] : ( divide(divide(X_361,idQ_idQa),idQ__idQ_idQa) = zero ),
inference(resolution,[status(thm)],[c_5951,c_71]) ).
tff(c_6065,plain,
! [X_362] : quotient(divide(X_362,idQ_idQa),idQ__idQ_idQa,zero),
inference(superposition,[status(thm),theory(equality)],[c_6004,c_16]) ).
tff(c_6154,plain,
! [X_363] : less_equal(divide(X_363,idQ_idQa),idQ__idQ_idQa),
inference(resolution,[status(thm)],[c_6065,c_4]) ).
tff(c_12,plain,
! [Y_18,X_17] :
( ( Y_18 = X_17 )
| ~ less_equal(Y_18,X_17)
| ~ less_equal(X_17,Y_18) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_6178,plain,
! [X_363] :
( ( divide(X_363,idQ_idQa) = idQ__idQ_idQa )
| ~ less_equal(idQ__idQ_idQa,divide(X_363,idQ_idQa)) ),
inference(resolution,[status(thm)],[c_6154,c_12]) ).
tff(c_6833,plain,
divide(idQa,idQ_idQa) = idQ__idQ_idQa,
inference(resolution,[status(thm)],[c_6824,c_6178]) ).
tff(c_6947,plain,
less_equal(idQ__idQ_idQa,idQa),
inference(superposition,[status(thm),theory(equality)],[c_6833,c_44]) ).
tff(c_20,plain,
quotient(identity,a,idQa),
inference(cnfTransformation,[status(thm)],[f_107]) ).
tff(c_3749,plain,
! [Y_289,X_290,Y_291] :
( less_equal(divide(idQa,Y_289),divide(X_290,a))
| ~ quotient(Y_291,a,Y_289)
| ~ quotient(identity,Y_291,X_290) ),
inference(resolution,[status(thm)],[c_20,c_3303]) ).
tff(c_3794,plain,
! [X_293] :
( less_equal(divide(idQa,idQa),divide(X_293,a))
| ~ quotient(identity,identity,X_293) ),
inference(resolution,[status(thm)],[c_20,c_3749]) ).
tff(c_3814,plain,
( less_equal(divide(idQa,idQa),zero)
| ~ quotient(identity,identity,zero) ),
inference(superposition,[status(thm),theory(equality)],[c_88,c_3794]) ).
tff(c_3820,plain,
less_equal(divide(idQa,idQa),zero),
inference(demodulation,[status(thm),theory(equality)],[c_316,c_3814]) ).
tff(c_3830,plain,
divide(idQa,idQa) = zero,
inference(resolution,[status(thm)],[c_3820,c_71]) ).
tff(c_3979,plain,
quotient(idQa,idQa,zero),
inference(superposition,[status(thm),theory(equality)],[c_3830,c_16]) ).
tff(c_4065,plain,
less_equal(idQa,idQa),
inference(resolution,[status(thm)],[c_3979,c_4]) ).
tff(c_4422,plain,
! [Y_308,Y_309,X_310] :
( less_equal(divide(idQ_idQa,Y_308),zero)
| ~ quotient(Y_309,idQa,Y_308)
| ~ quotient(identity,Y_309,X_310)
| ~ less_equal(X_310,idQa) ),
inference(resolution,[status(thm)],[c_22,c_3436]) ).
tff(c_7379,plain,
! [X_388,X_389] :
( less_equal(divide(idQ_idQa,divide(X_388,idQa)),zero)
| ~ quotient(identity,X_388,X_389)
| ~ less_equal(X_389,idQa) ),
inference(resolution,[status(thm)],[c_16,c_4422]) ).
tff(c_7392,plain,
( less_equal(divide(idQ_idQa,divide(a,idQa)),zero)
| ~ less_equal(idQa,idQa) ),
inference(resolution,[status(thm)],[c_20,c_7379]) ).
tff(c_7406,plain,
less_equal(divide(idQ_idQa,divide(a,idQa)),zero),
inference(demodulation,[status(thm),theory(equality)],[c_4065,c_7392]) ).
tff(c_7419,plain,
divide(idQ_idQa,divide(a,idQa)) = zero,
inference(resolution,[status(thm)],[c_7406,c_71]) ).
tff(c_7461,plain,
quotient(idQ_idQa,divide(a,idQa),zero),
inference(superposition,[status(thm),theory(equality)],[c_7419,c_16]) ).
tff(c_7530,plain,
less_equal(idQ_idQa,divide(a,idQa)),
inference(resolution,[status(thm)],[c_7461,c_4]) ).
tff(c_4888,plain,
! [X_331,X_332] :
( less_equal(divide(divide(X_331,idQa),idQ_idQa),divide(X_332,idQa))
| ~ quotient(X_331,identity,X_332) ),
inference(resolution,[status(thm)],[c_22,c_4822]) ).
tff(c_4947,plain,
! [X_331] :
( less_equal(divide(divide(X_331,idQa),idQ_idQa),zero)
| ~ quotient(X_331,identity,zero) ),
inference(superposition,[status(thm),theory(equality)],[c_88,c_4888]) ).
tff(c_4961,plain,
! [X_333] : less_equal(divide(divide(X_333,idQa),idQ_idQa),zero),
inference(demodulation,[status(thm),theory(equality)],[c_316,c_4947]) ).
tff(c_5014,plain,
! [X_334] : ( divide(divide(X_334,idQa),idQ_idQa) = zero ),
inference(resolution,[status(thm)],[c_4961,c_71]) ).
tff(c_5170,plain,
! [X_335] : quotient(divide(X_335,idQa),idQ_idQa,zero),
inference(superposition,[status(thm),theory(equality)],[c_5014,c_16]) ).
tff(c_5269,plain,
! [X_336] : less_equal(divide(X_336,idQa),idQ_idQa),
inference(resolution,[status(thm)],[c_5170,c_4]) ).
tff(c_5293,plain,
! [X_336] :
( ( divide(X_336,idQa) = idQ_idQa )
| ~ less_equal(idQ_idQa,divide(X_336,idQa)) ),
inference(resolution,[status(thm)],[c_5269,c_12]) ).
tff(c_7539,plain,
divide(a,idQa) = idQ_idQa,
inference(resolution,[status(thm)],[c_7530,c_5293]) ).
tff(c_7642,plain,
less_equal(idQ_idQa,a),
inference(superposition,[status(thm),theory(equality)],[c_7539,c_44]) ).
tff(c_7751,plain,
! [X_390,X_391] :
( less_equal(divide(idQa,zero),divide(X_390,a))
| ~ quotient(identity,X_391,X_390)
| ~ less_equal(X_391,a) ),
inference(resolution,[status(thm)],[c_2,c_3749]) ).
tff(c_7766,plain,
( less_equal(divide(idQa,zero),divide(idQ__idQ_idQa,a))
| ~ less_equal(idQ_idQa,a) ),
inference(resolution,[status(thm)],[c_24,c_7751]) ).
tff(c_7776,plain,
less_equal(divide(idQa,zero),divide(idQ__idQ_idQa,a)),
inference(demodulation,[status(thm),theory(equality)],[c_7642,c_7766]) ).
tff(c_282,plain,
! [X_1,Y_2] :
( ( divide(X_1,Y_2) = zero )
| ~ less_equal(X_1,Y_2) ),
inference(resolution,[status(thm)],[c_2,c_261]) ).
tff(c_8440,plain,
divide(divide(idQa,zero),divide(idQ__idQ_idQa,a)) = zero,
inference(resolution,[status(thm)],[c_7776,c_282]) ).
tff(c_13461,plain,
! [X_466,Y_467,X_468,X_469] :
( less_equal(divide(divide(X_466,Y_467),zero),divide(X_468,Y_467))
| ~ quotient(X_466,X_469,X_468)
| ~ less_equal(X_469,Y_467) ),
inference(resolution,[status(thm)],[c_2,c_4822]) ).
tff(c_92673,plain,
! [X_1094,Y_1095,Y_1096] :
( less_equal(divide(divide(X_1094,Y_1095),zero),divide(divide(X_1094,Y_1096),Y_1095))
| ~ less_equal(Y_1096,Y_1095) ),
inference(resolution,[status(thm)],[c_16,c_13461]) ).
tff(c_93131,plain,
( less_equal(divide(divide(idQa,divide(idQ__idQ_idQa,a)),zero),zero)
| ~ less_equal(zero,divide(idQ__idQ_idQa,a)) ),
inference(superposition,[status(thm),theory(equality)],[c_8440,c_92673]) ).
tff(c_93389,plain,
less_equal(divide(divide(idQa,divide(idQ__idQ_idQa,a)),zero),zero),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_93131]) ).
tff(c_97843,plain,
divide(divide(idQa,divide(idQ__idQ_idQa,a)),zero) = zero,
inference(resolution,[status(thm)],[c_93389,c_71]) ).
tff(c_98141,plain,
quotient(divide(idQa,divide(idQ__idQ_idQa,a)),zero,zero),
inference(superposition,[status(thm),theory(equality)],[c_97843,c_16]) ).
tff(c_98345,plain,
less_equal(divide(idQa,divide(idQ__idQ_idQa,a)),zero),
inference(resolution,[status(thm)],[c_98141,c_4]) ).
tff(c_98379,plain,
divide(idQa,divide(idQ__idQ_idQa,a)) = zero,
inference(resolution,[status(thm)],[c_98345,c_71]) ).
tff(c_99262,plain,
quotient(idQa,divide(idQ__idQ_idQa,a),zero),
inference(superposition,[status(thm),theory(equality)],[c_98379,c_16]) ).
tff(c_99406,plain,
less_equal(idQa,divide(idQ__idQ_idQa,a)),
inference(resolution,[status(thm)],[c_99262,c_4]) ).
tff(c_301,plain,
! [X_20,Y_21] : ( divide(divide(X_20,Y_21),X_20) = zero ),
inference(resolution,[status(thm)],[c_44,c_291]) ).
tff(c_6944,plain,
divide(idQ__idQ_idQa,idQa) = zero,
inference(superposition,[status(thm),theory(equality)],[c_6833,c_301]) ).
tff(c_391,plain,
! [X_72,Y_73] : ( divide(divide(X_72,Y_73),X_72) = zero ),
inference(resolution,[status(thm)],[c_44,c_291]) ).
tff(c_405,plain,
! [X_72,Y_73] : quotient(divide(X_72,Y_73),X_72,zero),
inference(superposition,[status(thm),theory(equality)],[c_391,c_16]) ).
tff(c_5301,plain,
! [Y_339,X_341,X_338,Y_337,Y_340] :
( less_equal(divide(divide(X_338,Y_337),Y_339),zero)
| ~ quotient(Y_340,Y_337,Y_339)
| ~ quotient(X_338,Y_340,X_341)
| ~ less_equal(X_341,Y_337) ),
inference(resolution,[status(thm)],[c_16,c_3436]) ).
tff(c_12267,plain,
! [X_451,Y_452,X_453,X_454] :
( less_equal(divide(divide(X_451,Y_452),divide(X_453,Y_452)),zero)
| ~ quotient(X_451,X_453,X_454)
| ~ less_equal(X_454,Y_452) ),
inference(resolution,[status(thm)],[c_16,c_5301]) ).
tff(c_12317,plain,
! [X_72,Y_73,Y_452] :
( less_equal(divide(divide(divide(X_72,Y_73),Y_452),divide(X_72,Y_452)),zero)
| ~ less_equal(zero,Y_452) ),
inference(resolution,[status(thm)],[c_405,c_12267]) ).
tff(c_18939,plain,
! [X_526,Y_527,Y_528] : less_equal(divide(divide(divide(X_526,Y_527),Y_528),divide(X_526,Y_528)),zero),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_12317]) ).
tff(c_20168,plain,
! [Y_538] : less_equal(divide(divide(divide(idQ__idQ_idQa,Y_538),idQa),zero),zero),
inference(superposition,[status(thm),theory(equality)],[c_6944,c_18939]) ).
tff(c_20245,plain,
! [Y_540] : ( divide(divide(divide(idQ__idQ_idQa,Y_540),idQa),zero) = zero ),
inference(resolution,[status(thm)],[c_20168,c_71]) ).
tff(c_20435,plain,
! [Y_541] : quotient(divide(divide(idQ__idQ_idQa,Y_541),idQa),zero,zero),
inference(superposition,[status(thm),theory(equality)],[c_20245,c_16]) ).
tff(c_20548,plain,
! [Y_542] : less_equal(divide(divide(idQ__idQ_idQa,Y_542),idQa),zero),
inference(resolution,[status(thm)],[c_20435,c_4]) ).
tff(c_20601,plain,
! [Y_543] : ( divide(divide(idQ__idQ_idQa,Y_543),idQa) = zero ),
inference(resolution,[status(thm)],[c_20548,c_71]) ).
tff(c_20860,plain,
! [Y_545] : quotient(divide(idQ__idQ_idQa,Y_545),idQa,zero),
inference(superposition,[status(thm),theory(equality)],[c_20601,c_16]) ).
tff(c_20973,plain,
! [Y_546] : less_equal(divide(idQ__idQ_idQa,Y_546),idQa),
inference(resolution,[status(thm)],[c_20860,c_4]) ).
tff(c_20995,plain,
! [Y_546] :
( ( divide(idQ__idQ_idQa,Y_546) = idQa )
| ~ less_equal(idQa,divide(idQ__idQ_idQa,Y_546)) ),
inference(resolution,[status(thm)],[c_20973,c_12]) ).
tff(c_99429,plain,
divide(idQ__idQ_idQa,a) = idQa,
inference(resolution,[status(thm)],[c_99406,c_20995]) ).
tff(c_69,plain,
! [X_20,Y_21] :
( ( divide(X_20,Y_21) = X_20 )
| ~ less_equal(X_20,divide(X_20,Y_21)) ),
inference(resolution,[status(thm)],[c_44,c_62]) ).
tff(c_99841,plain,
( ( divide(idQ__idQ_idQa,a) = idQ__idQ_idQa )
| ~ less_equal(idQ__idQ_idQa,idQa) ),
inference(superposition,[status(thm),theory(equality)],[c_99429,c_69]) ).
tff(c_99921,plain,
idQa = idQ__idQ_idQa,
inference(demodulation,[status(thm),theory(equality)],[c_6947,c_99429,c_99841]) ).
tff(c_99923,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_26,c_99921]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : HEN009-1 : TPTP v8.1.2. Released v1.0.0.
% 0.08/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.35 % Computer : n024.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 3 13:08:45 EDT 2023
% 0.14/0.35 % CPUTime :
% 23.90/12.30 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 23.94/12.32
% 23.94/12.32 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 23.94/12.36
% 23.94/12.36 Inference rules
% 23.94/12.36 ----------------------
% 23.94/12.36 #Ref : 0
% 23.94/12.36 #Sup : 25062
% 23.94/12.36 #Fact : 0
% 23.94/12.36 #Define : 0
% 23.94/12.36 #Split : 70
% 23.94/12.36 #Chain : 0
% 23.94/12.36 #Close : 0
% 23.94/12.36
% 23.94/12.36 Ordering : KBO
% 23.94/12.36
% 23.94/12.36 Simplification rules
% 23.94/12.36 ----------------------
% 23.94/12.36 #Subsume : 9604
% 23.94/12.36 #Demod : 17179
% 23.94/12.36 #Tautology : 11464
% 23.94/12.36 #SimpNegUnit : 337
% 23.94/12.36 #BackRed : 89
% 23.94/12.36
% 23.94/12.36 #Partial instantiations: 0
% 23.94/12.36 #Strategies tried : 1
% 23.94/12.36
% 23.94/12.36 Timing (in seconds)
% 23.94/12.36 ----------------------
% 23.94/12.36 Preprocessing : 0.49
% 23.94/12.36 Parsing : 0.27
% 23.94/12.36 CNF conversion : 0.02
% 23.94/12.36 Main loop : 10.75
% 23.94/12.36 Inferencing : 1.77
% 23.94/12.36 Reduction : 4.94
% 23.94/12.36 Demodulation : 3.74
% 23.94/12.36 BG Simplification : 0.10
% 23.94/12.36 Subsumption : 3.51
% 23.94/12.36 Abstraction : 0.14
% 23.94/12.36 MUC search : 0.00
% 23.94/12.37 Cooper : 0.00
% 23.94/12.37 Total : 11.31
% 23.94/12.37 Index Insertion : 0.00
% 23.94/12.37 Index Deletion : 0.00
% 23.94/12.37 Index Matching : 0.00
% 23.94/12.37 BG Taut test : 0.00
%------------------------------------------------------------------------------