TSTP Solution File: HEN010-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : HEN010-1 : 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 : n018.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 10:42:18 EDT 2023
% Result : Unsatisfiable 33.40s 20.13s
% Output : CNFRefutation 33.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 22
% Syntax : Number of formulae : 148 ( 73 unt; 9 typ; 0 def)
% Number of atoms : 247 ( 39 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 221 ( 113 ~; 108 |; 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 : 204 (; 204 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ quotient > less_equal > divide > #nlpp > zero > identity > idQa_Q__idQ_idQa > idQa > 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(idQa_Q__idQ_idQa,type,
idQa_Q__idQ_idQa: $i ).
tff(quotient,type,
quotient: ( $i * $i * $i ) > $o ).
tff(identity,type,
identity: $i ).
tff(idQ_idQa,type,
idQ_idQa: $i ).
tff(zero,type,
zero: $i ).
tff(f_111,axiom,
idQa != idQa_Q__idQ_idQa,
file(unknown,unknown) ).
tff(f_109,axiom,
quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa),
file(unknown,unknown) ).
tff(f_59,axiom,
! [X,Y,Z] :
( ~ quotient(X,Y,Z)
| less_equal(Z,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_80,axiom,
! [X] : less_equal(zero,X),
file(unknown,unknown) ).
tff(f_108,axiom,
quotient(identity,idQa,idQ_idQa),
file(unknown,unknown) ).
tff(f_95,axiom,
! [X,Y] : quotient(X,Y,divide(X,Y)),
file(unknown,unknown) ).
tff(f_107,axiom,
quotient(identity,a,idQa),
file(unknown,unknown) ).
tff(f_48,axiom,
! [X,Y] :
( ~ less_equal(X,Y)
| quotient(X,Y,zero) ),
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_92,axiom,
! [X] : less_equal(X,identity),
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_53,axiom,
! [X,Y] :
( ~ quotient(X,Y,zero)
| less_equal(X,Y) ),
file(unknown,unknown) ).
tff(c_26,plain,
idQa_Q__idQ_idQa != idQa,
inference(cnfTransformation,[status(thm)],[f_111]) ).
tff(c_24,plain,
quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa),
inference(cnfTransformation,[status(thm)],[f_109]) ).
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_49,plain,
less_equal(idQa_Q__idQ_idQa,idQa),
inference(resolution,[status(thm)],[c_24,c_31]) ).
tff(c_61,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_65,plain,
( ( idQa_Q__idQ_idQa = idQa )
| ~ less_equal(idQa,idQa_Q__idQ_idQa) ),
inference(resolution,[status(thm)],[c_49,c_61]) ).
tff(c_73,plain,
~ less_equal(idQa,idQa_Q__idQ_idQa),
inference(negUnitSimplification,[status(thm)],[c_26,c_65]) ).
tff(c_10,plain,
! [X_16] : less_equal(zero,X_16),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_22,plain,
quotient(identity,idQa,idQ_idQa),
inference(cnfTransformation,[status(thm)],[f_108]) ).
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_20,plain,
quotient(identity,a,idQa),
inference(cnfTransformation,[status(thm)],[f_107]) ).
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_139,plain,
! [V1_54,V3_50,Y_55,X_53,V4_51,V2_49,V5_56,Z_52] :
( less_equal(V4_51,V5_56)
| ~ quotient(V1_54,Z_52,V5_56)
| ~ quotient(V3_50,V2_49,V4_51)
| ~ quotient(X_53,Z_52,V3_50)
| ~ quotient(Y_55,Z_52,V2_49)
| ~ quotient(X_53,Y_55,V1_54) ),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_1448,plain,
! [Y_160,V3_157,X_158,V4_159,X_161,Y_162,V2_156] :
( less_equal(V4_159,zero)
| ~ quotient(V3_157,V2_156,V4_159)
| ~ quotient(X_161,Y_162,V3_157)
| ~ quotient(Y_160,Y_162,V2_156)
| ~ quotient(X_161,Y_160,X_158)
| ~ less_equal(X_158,Y_162) ),
inference(resolution,[status(thm)],[c_2,c_139]) ).
tff(c_4018,plain,
! [X_292,Y_294,Y_291,X_293,X_290,Y_295] :
( less_equal(divide(X_292,Y_291),zero)
| ~ quotient(X_293,Y_294,X_292)
| ~ quotient(Y_295,Y_294,Y_291)
| ~ quotient(X_293,Y_295,X_290)
| ~ less_equal(X_290,Y_294) ),
inference(resolution,[status(thm)],[c_16,c_1448]) ).
tff(c_5181,plain,
! [Y_318,Y_319,X_320] :
( less_equal(divide(idQa,Y_318),zero)
| ~ quotient(Y_319,a,Y_318)
| ~ quotient(identity,Y_319,X_320)
| ~ less_equal(X_320,a) ),
inference(resolution,[status(thm)],[c_20,c_4018]) ).
tff(c_17315,plain,
! [X_533,X_534] :
( less_equal(divide(idQa,divide(X_533,a)),zero)
| ~ quotient(identity,X_533,X_534)
| ~ less_equal(X_534,a) ),
inference(resolution,[status(thm)],[c_16,c_5181]) ).
tff(c_17339,plain,
( less_equal(divide(idQa,divide(idQa,a)),zero)
| ~ less_equal(idQ_idQa,a) ),
inference(resolution,[status(thm)],[c_22,c_17315]) ).
tff(c_17735,plain,
~ less_equal(idQ_idQa,a),
inference(splitLeft,[status(thm)],[c_17339]) ).
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_99,plain,
! [X_46] :
( ( zero = X_46 )
| ~ less_equal(X_46,zero) ),
inference(resolution,[status(thm)],[c_10,c_61]) ).
tff(c_108,plain,
! [Y_21] : ( divide(zero,Y_21) = zero ),
inference(resolution,[status(thm)],[c_44,c_99]) ).
tff(c_1350,plain,
! [V3_141,V2_140,X_144,X_139,Y_138,Y_143,V4_142] :
( less_equal(V4_142,divide(X_139,Y_138))
| ~ quotient(V3_141,V2_140,V4_142)
| ~ quotient(X_144,Y_138,V3_141)
| ~ quotient(Y_143,Y_138,V2_140)
| ~ quotient(X_144,Y_143,X_139) ),
inference(resolution,[status(thm)],[c_16,c_139]) ).
tff(c_3874,plain,
! [Y_282,X_281,Y_280,X_283,Y_285,X_284] :
( less_equal(divide(X_281,Y_280),divide(X_284,Y_282))
| ~ quotient(X_283,Y_282,X_281)
| ~ quotient(Y_285,Y_282,Y_280)
| ~ quotient(X_283,Y_285,X_284) ),
inference(resolution,[status(thm)],[c_16,c_1350]) ).
tff(c_4384,plain,
! [Y_299,X_300,Y_301] :
( less_equal(divide(idQa_Q__idQ_idQa,Y_299),divide(X_300,idQ_idQa))
| ~ quotient(Y_301,idQ_idQa,Y_299)
| ~ quotient(idQa,Y_301,X_300) ),
inference(resolution,[status(thm)],[c_24,c_3874]) ).
tff(c_4441,plain,
! [X_303] :
( less_equal(divide(idQa_Q__idQ_idQa,idQa_Q__idQ_idQa),divide(X_303,idQ_idQa))
| ~ quotient(idQa,idQa,X_303) ),
inference(resolution,[status(thm)],[c_24,c_4384]) ).
tff(c_4476,plain,
( less_equal(divide(idQa_Q__idQ_idQa,idQa_Q__idQ_idQa),zero)
| ~ quotient(idQa,idQa,zero) ),
inference(superposition,[status(thm),theory(equality)],[c_108,c_4441]) ).
tff(c_4481,plain,
~ quotient(idQa,idQa,zero),
inference(splitLeft,[status(thm)],[c_4476]) ).
tff(c_14,plain,
! [X_19] : less_equal(X_19,identity),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_83,plain,
! [Z_42,W_43,X_44,Y_45] :
( ( Z_42 = W_43 )
| ~ quotient(X_44,Y_45,W_43)
| ~ quotient(X_44,Y_45,Z_42) ),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_265,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_83]) ).
tff(c_295,plain,
! [X_65,Y_66] :
( ( divide(X_65,Y_66) = zero )
| ~ less_equal(X_65,Y_66) ),
inference(resolution,[status(thm)],[c_2,c_265]) ).
tff(c_353,plain,
! [X_70] : ( divide(X_70,identity) = zero ),
inference(resolution,[status(thm)],[c_14,c_295]) ).
tff(c_364,plain,
! [X_70] : quotient(X_70,identity,zero),
inference(superposition,[status(thm),theory(equality)],[c_353,c_16]) ).
tff(c_4487,plain,
! [Y_304,X_305,Y_306] :
( less_equal(divide(idQa,Y_304),divide(X_305,a))
| ~ quotient(Y_306,a,Y_304)
| ~ quotient(identity,Y_306,X_305) ),
inference(resolution,[status(thm)],[c_20,c_3874]) ).
tff(c_4553,plain,
! [X_308] :
( less_equal(divide(idQa,idQa),divide(X_308,a))
| ~ quotient(identity,identity,X_308) ),
inference(resolution,[status(thm)],[c_20,c_4487]) ).
tff(c_4573,plain,
( less_equal(divide(idQa,idQa),zero)
| ~ quotient(identity,identity,zero) ),
inference(superposition,[status(thm),theory(equality)],[c_108,c_4553]) ).
tff(c_4579,plain,
less_equal(divide(idQa,idQa),zero),
inference(demodulation,[status(thm),theory(equality)],[c_364,c_4573]) ).
tff(c_75,plain,
! [X_16] :
( ( zero = X_16 )
| ~ less_equal(X_16,zero) ),
inference(resolution,[status(thm)],[c_10,c_61]) ).
tff(c_4589,plain,
divide(idQa,idQa) = zero,
inference(resolution,[status(thm)],[c_4579,c_75]) ).
tff(c_4698,plain,
quotient(idQa,idQa,zero),
inference(superposition,[status(thm),theory(equality)],[c_4589,c_16]) ).
tff(c_4726,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_4481,c_4698]) ).
tff(c_4728,plain,
quotient(idQa,idQa,zero),
inference(splitRight,[status(thm)],[c_4476]) ).
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_4810,plain,
less_equal(idQa,idQa),
inference(resolution,[status(thm)],[c_4728,c_4]) ).
tff(c_5069,plain,
! [Y_313,Y_314,X_315] :
( less_equal(divide(idQ_idQa,Y_313),zero)
| ~ quotient(Y_314,idQa,Y_313)
| ~ quotient(identity,Y_314,X_315)
| ~ less_equal(X_315,idQa) ),
inference(resolution,[status(thm)],[c_22,c_4018]) ).
tff(c_17736,plain,
! [X_543,X_544] :
( less_equal(divide(idQ_idQa,divide(X_543,idQa)),zero)
| ~ quotient(identity,X_543,X_544)
| ~ less_equal(X_544,idQa) ),
inference(resolution,[status(thm)],[c_16,c_5069]) ).
tff(c_17751,plain,
( less_equal(divide(idQ_idQa,divide(a,idQa)),zero)
| ~ less_equal(idQa,idQa) ),
inference(resolution,[status(thm)],[c_20,c_17736]) ).
tff(c_17766,plain,
less_equal(divide(idQ_idQa,divide(a,idQa)),zero),
inference(demodulation,[status(thm),theory(equality)],[c_4810,c_17751]) ).
tff(c_17785,plain,
divide(idQ_idQa,divide(a,idQa)) = zero,
inference(resolution,[status(thm)],[c_17766,c_75]) ).
tff(c_17875,plain,
quotient(idQ_idQa,divide(a,idQa),zero),
inference(superposition,[status(thm),theory(equality)],[c_17785,c_16]) ).
tff(c_17969,plain,
less_equal(idQ_idQa,divide(a,idQa)),
inference(resolution,[status(thm)],[c_17875,c_4]) ).
tff(c_5387,plain,
! [X_331,Y_333,Y_330,X_332,Y_334] :
( less_equal(divide(divide(X_331,Y_330),Y_333),divide(X_332,Y_330))
| ~ quotient(Y_334,Y_330,Y_333)
| ~ quotient(X_331,Y_334,X_332) ),
inference(resolution,[status(thm)],[c_16,c_3874]) ).
tff(c_12921,plain,
! [X_462,X_463] :
( less_equal(divide(divide(X_462,idQa),idQ_idQa),divide(X_463,idQa))
| ~ quotient(X_462,identity,X_463) ),
inference(resolution,[status(thm)],[c_22,c_5387]) ).
tff(c_12992,plain,
! [X_462] :
( less_equal(divide(divide(X_462,idQa),idQ_idQa),zero)
| ~ quotient(X_462,identity,zero) ),
inference(superposition,[status(thm),theory(equality)],[c_108,c_12921]) ).
tff(c_13008,plain,
! [X_464] : less_equal(divide(divide(X_464,idQa),idQ_idQa),zero),
inference(demodulation,[status(thm),theory(equality)],[c_364,c_12992]) ).
tff(c_13067,plain,
! [X_465] : ( divide(divide(X_465,idQa),idQ_idQa) = zero ),
inference(resolution,[status(thm)],[c_13008,c_75]) ).
tff(c_13242,plain,
! [X_466] : quotient(divide(X_466,idQa),idQ_idQa,zero),
inference(superposition,[status(thm),theory(equality)],[c_13067,c_16]) ).
tff(c_13350,plain,
! [X_467] : less_equal(divide(X_467,idQa),idQ_idQa),
inference(resolution,[status(thm)],[c_13242,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_13378,plain,
! [X_467] :
( ( divide(X_467,idQa) = idQ_idQa )
| ~ less_equal(idQ_idQa,divide(X_467,idQa)) ),
inference(resolution,[status(thm)],[c_13350,c_12]) ).
tff(c_17978,plain,
divide(a,idQa) = idQ_idQa,
inference(resolution,[status(thm)],[c_17969,c_13378]) ).
tff(c_18162,plain,
less_equal(idQ_idQa,a),
inference(superposition,[status(thm),theory(equality)],[c_17978,c_44]) ).
tff(c_18206,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_17735,c_18162]) ).
tff(c_18208,plain,
less_equal(idQ_idQa,a),
inference(splitRight,[status(thm)],[c_17339]) ).
tff(c_18207,plain,
less_equal(divide(idQa,divide(idQa,a)),zero),
inference(splitRight,[status(thm)],[c_17339]) ).
tff(c_18536,plain,
divide(idQa,divide(idQa,a)) = zero,
inference(resolution,[status(thm)],[c_18207,c_75]) ).
tff(c_18621,plain,
quotient(idQa,divide(idQa,a),zero),
inference(superposition,[status(thm),theory(equality)],[c_18536,c_16]) ).
tff(c_18706,plain,
less_equal(idQa,divide(idQa,a)),
inference(resolution,[status(thm)],[c_18621,c_4]) ).
tff(c_70,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_61]) ).
tff(c_18719,plain,
divide(idQa,a) = idQa,
inference(resolution,[status(thm)],[c_18706,c_70]) ).
tff(c_23407,plain,
! [X_612,Y_613,X_614,X_615] :
( less_equal(divide(divide(X_612,Y_613),zero),divide(X_614,Y_613))
| ~ quotient(X_612,X_615,X_614)
| ~ less_equal(X_615,Y_613) ),
inference(resolution,[status(thm)],[c_2,c_5387]) ).
tff(c_59054,plain,
! [Y_921] :
( less_equal(divide(divide(idQa,Y_921),zero),divide(idQa_Q__idQ_idQa,Y_921))
| ~ less_equal(idQ_idQa,Y_921) ),
inference(resolution,[status(thm)],[c_24,c_23407]) ).
tff(c_59086,plain,
( less_equal(divide(idQa,zero),divide(idQa_Q__idQ_idQa,a))
| ~ less_equal(idQ_idQa,a) ),
inference(superposition,[status(thm),theory(equality)],[c_18719,c_59054]) ).
tff(c_59128,plain,
less_equal(divide(idQa,zero),divide(idQa_Q__idQ_idQa,a)),
inference(demodulation,[status(thm),theory(equality)],[c_18208,c_59086]) ).
tff(c_286,plain,
! [X_1,Y_2] :
( ( divide(X_1,Y_2) = zero )
| ~ less_equal(X_1,Y_2) ),
inference(resolution,[status(thm)],[c_2,c_265]) ).
tff(c_59145,plain,
divide(divide(idQa,zero),divide(idQa_Q__idQ_idQa,a)) = zero,
inference(resolution,[status(thm)],[c_59128,c_286]) ).
tff(c_114644,plain,
! [X_1238,Y_1239,Y_1240] :
( less_equal(divide(divide(X_1238,Y_1239),zero),divide(divide(X_1238,Y_1240),Y_1239))
| ~ less_equal(Y_1240,Y_1239) ),
inference(resolution,[status(thm)],[c_16,c_23407]) ).
tff(c_114920,plain,
( less_equal(divide(divide(idQa,divide(idQa_Q__idQ_idQa,a)),zero),zero)
| ~ less_equal(zero,divide(idQa_Q__idQ_idQa,a)) ),
inference(superposition,[status(thm),theory(equality)],[c_59145,c_114644]) ).
tff(c_115409,plain,
less_equal(divide(divide(idQa,divide(idQa_Q__idQ_idQa,a)),zero),zero),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_114920]) ).
tff(c_117544,plain,
divide(divide(idQa,divide(idQa_Q__idQ_idQa,a)),zero) = zero,
inference(resolution,[status(thm)],[c_115409,c_75]) ).
tff(c_117813,plain,
quotient(divide(idQa,divide(idQa_Q__idQ_idQa,a)),zero,zero),
inference(superposition,[status(thm),theory(equality)],[c_117544,c_16]) ).
tff(c_118018,plain,
less_equal(divide(idQa,divide(idQa_Q__idQ_idQa,a)),zero),
inference(resolution,[status(thm)],[c_117813,c_4]) ).
tff(c_118053,plain,
divide(idQa,divide(idQa_Q__idQ_idQa,a)) = zero,
inference(resolution,[status(thm)],[c_118018,c_75]) ).
tff(c_118352,plain,
quotient(idQa,divide(idQa_Q__idQ_idQa,a),zero),
inference(superposition,[status(thm),theory(equality)],[c_118053,c_16]) ).
tff(c_118549,plain,
less_equal(idQa,divide(idQa_Q__idQ_idQa,a)),
inference(resolution,[status(thm)],[c_118352,c_4]) ).
tff(c_5623,plain,
! [X_344,X_341,Y_342,Y_343,Y_340] :
( less_equal(divide(divide(X_341,Y_340),Y_343),zero)
| ~ quotient(Y_342,Y_340,Y_343)
| ~ quotient(X_341,Y_342,X_344)
| ~ less_equal(X_344,Y_340) ),
inference(resolution,[status(thm)],[c_16,c_4018]) ).
tff(c_22067,plain,
! [X_594,Y_595,X_596,X_597] :
( less_equal(divide(divide(X_594,Y_595),divide(X_596,Y_595)),zero)
| ~ quotient(X_594,X_596,X_597)
| ~ less_equal(X_597,Y_595) ),
inference(resolution,[status(thm)],[c_16,c_5623]) ).
tff(c_22133,plain,
! [X_1,Y_595,Y_2] :
( less_equal(divide(divide(X_1,Y_595),divide(Y_2,Y_595)),zero)
| ~ less_equal(zero,Y_595)
| ~ less_equal(X_1,Y_2) ),
inference(resolution,[status(thm)],[c_2,c_22067]) ).
tff(c_57859,plain,
! [X_910,Y_911,Y_912] :
( less_equal(divide(divide(X_910,Y_911),divide(Y_912,Y_911)),zero)
| ~ less_equal(X_910,Y_912) ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_22133]) ).
tff(c_82644,plain,
! [Y_1056] :
( less_equal(divide(idQa,divide(Y_1056,a)),zero)
| ~ less_equal(idQa,Y_1056) ),
inference(superposition,[status(thm),theory(equality)],[c_18719,c_57859]) ).
tff(c_82757,plain,
! [Y_1057] :
( ( divide(idQa,divide(Y_1057,a)) = zero )
| ~ less_equal(idQa,Y_1057) ),
inference(resolution,[status(thm)],[c_82644,c_75]) ).
tff(c_83354,plain,
! [Y_1059] :
( quotient(idQa,divide(Y_1059,a),zero)
| ~ less_equal(idQa,Y_1059) ),
inference(superposition,[status(thm),theory(equality)],[c_82757,c_16]) ).
tff(c_13340,plain,
! [X_466] : less_equal(divide(X_466,idQa),idQ_idQa),
inference(resolution,[status(thm)],[c_13242,c_4]) ).
tff(c_19489,plain,
! [X_551,X_552] :
( less_equal(divide(divide(X_551,idQ_idQa),idQa_Q__idQ_idQa),zero)
| ~ quotient(X_551,idQa,X_552)
| ~ less_equal(X_552,idQ_idQa) ),
inference(resolution,[status(thm)],[c_24,c_5623]) ).
tff(c_19516,plain,
! [X_20] :
( less_equal(divide(divide(X_20,idQ_idQa),idQa_Q__idQ_idQa),zero)
| ~ less_equal(divide(X_20,idQa),idQ_idQa) ),
inference(resolution,[status(thm)],[c_16,c_19489]) ).
tff(c_19656,plain,
! [X_554] : less_equal(divide(divide(X_554,idQ_idQa),idQa_Q__idQ_idQa),zero),
inference(demodulation,[status(thm),theory(equality)],[c_13340,c_19516]) ).
tff(c_19730,plain,
! [X_555] : ( divide(divide(X_555,idQ_idQa),idQa_Q__idQ_idQa) = zero ),
inference(resolution,[status(thm)],[c_19656,c_75]) ).
tff(c_19860,plain,
! [X_556] : quotient(divide(X_556,idQ_idQa),idQa_Q__idQ_idQa,zero),
inference(superposition,[status(thm),theory(equality)],[c_19730,c_16]) ).
tff(c_19953,plain,
! [X_556] : less_equal(divide(X_556,idQ_idQa),idQa_Q__idQ_idQa),
inference(resolution,[status(thm)],[c_19860,c_4]) ).
tff(c_13903,plain,
! [X_481,X_482] :
( less_equal(divide(idQa_Q__idQ_idQa,divide(X_481,idQ_idQa)),divide(X_482,idQ_idQa))
| ~ quotient(idQa,X_481,X_482) ),
inference(resolution,[status(thm)],[c_16,c_4384]) ).
tff(c_34893,plain,
! [X_724] :
( less_equal(divide(idQa_Q__idQ_idQa,divide(X_724,idQ_idQa)),zero)
| ~ quotient(idQa,X_724,zero) ),
inference(superposition,[status(thm),theory(equality)],[c_108,c_13903]) ).
tff(c_34905,plain,
! [X_724] :
( ( divide(idQa_Q__idQ_idQa,divide(X_724,idQ_idQa)) = zero )
| ~ less_equal(zero,divide(idQa_Q__idQ_idQa,divide(X_724,idQ_idQa)))
| ~ quotient(idQa,X_724,zero) ),
inference(resolution,[status(thm)],[c_34893,c_12]) ).
tff(c_35204,plain,
! [X_731] :
( ( divide(idQa_Q__idQ_idQa,divide(X_731,idQ_idQa)) = zero )
| ~ quotient(idQa,X_731,zero) ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_34905]) ).
tff(c_37277,plain,
! [X_744] :
( quotient(idQa_Q__idQ_idQa,divide(X_744,idQ_idQa),zero)
| ~ quotient(idQa,X_744,zero) ),
inference(superposition,[status(thm),theory(equality)],[c_35204,c_16]) ).
tff(c_37403,plain,
! [X_745] :
( less_equal(idQa_Q__idQ_idQa,divide(X_745,idQ_idQa))
| ~ quotient(idQa,X_745,zero) ),
inference(resolution,[status(thm)],[c_37277,c_4]) ).
tff(c_37415,plain,
! [X_745] :
( ( divide(X_745,idQ_idQa) = idQa_Q__idQ_idQa )
| ~ less_equal(divide(X_745,idQ_idQa),idQa_Q__idQ_idQa)
| ~ quotient(idQa,X_745,zero) ),
inference(resolution,[status(thm)],[c_37403,c_12]) ).
tff(c_37465,plain,
! [X_745] :
( ( divide(X_745,idQ_idQa) = idQa_Q__idQ_idQa )
| ~ quotient(idQa,X_745,zero) ),
inference(demodulation,[status(thm),theory(equality)],[c_19953,c_37415]) ).
tff(c_84993,plain,
! [Y_1076] :
( ( divide(divide(Y_1076,a),idQ_idQa) = idQa_Q__idQ_idQa )
| ~ less_equal(idQa,Y_1076) ),
inference(resolution,[status(thm)],[c_83354,c_37465]) ).
tff(c_308,plain,
! [X_20,Y_21] : ( divide(divide(X_20,Y_21),X_20) = zero ),
inference(resolution,[status(thm)],[c_44,c_295]) ).
tff(c_438,plain,
! [X_72,Y_73] : ( divide(divide(X_72,Y_73),X_72) = zero ),
inference(resolution,[status(thm)],[c_44,c_295]) ).
tff(c_452,plain,
! [X_72,Y_73] : quotient(divide(X_72,Y_73),X_72,zero),
inference(superposition,[status(thm),theory(equality)],[c_438,c_16]) ).
tff(c_22125,plain,
! [X_72,Y_73,Y_595] :
( less_equal(divide(divide(divide(X_72,Y_73),Y_595),divide(X_72,Y_595)),zero)
| ~ less_equal(zero,Y_595) ),
inference(resolution,[status(thm)],[c_452,c_22067]) ).
tff(c_32376,plain,
! [X_702,Y_703,Y_704] : less_equal(divide(divide(divide(X_702,Y_703),Y_704),divide(X_702,Y_704)),zero),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_22125]) ).
tff(c_35508,plain,
! [X_733,Y_734,Y_735] : ( divide(divide(divide(X_733,Y_734),Y_735),divide(X_733,Y_735)) = zero ),
inference(resolution,[status(thm)],[c_32376,c_75]) ).
tff(c_37547,plain,
! [X_749,Y_750,Y_751] : quotient(divide(divide(X_749,Y_750),Y_751),divide(X_749,Y_751),zero),
inference(superposition,[status(thm),theory(equality)],[c_35508,c_16]) ).
tff(c_38116,plain,
! [X_752,Y_753,Y_754] : less_equal(divide(divide(X_752,Y_753),Y_754),divide(X_752,Y_754)),
inference(resolution,[status(thm)],[c_37547,c_4]) ).
tff(c_39910,plain,
! [X_771,Y_772,Y_773] : less_equal(divide(divide(divide(X_771,Y_772),Y_773),X_771),zero),
inference(superposition,[status(thm),theory(equality)],[c_308,c_38116]) ).
tff(c_40302,plain,
! [X_774,Y_775,Y_776] : ( divide(divide(divide(X_774,Y_775),Y_776),X_774) = zero ),
inference(resolution,[status(thm)],[c_39910,c_75]) ).
tff(c_41676,plain,
! [X_779,Y_780,Y_781] : quotient(divide(divide(X_779,Y_780),Y_781),X_779,zero),
inference(superposition,[status(thm),theory(equality)],[c_40302,c_16]) ).
tff(c_42140,plain,
! [X_779,Y_780,Y_781] : less_equal(divide(divide(X_779,Y_780),Y_781),X_779),
inference(resolution,[status(thm)],[c_41676,c_4]) ).
tff(c_85655,plain,
! [Y_1077] :
( less_equal(idQa_Q__idQ_idQa,Y_1077)
| ~ less_equal(idQa,Y_1077) ),
inference(superposition,[status(thm),theory(equality)],[c_84993,c_42140]) ).
tff(c_85725,plain,
! [Y_21] :
( ( divide(idQa_Q__idQ_idQa,Y_21) = idQa_Q__idQ_idQa )
| ~ less_equal(idQa,divide(idQa_Q__idQ_idQa,Y_21)) ),
inference(resolution,[status(thm)],[c_85655,c_70]) ).
tff(c_119581,plain,
divide(idQa_Q__idQ_idQa,a) = idQa_Q__idQ_idQa,
inference(resolution,[status(thm)],[c_118549,c_85725]) ).
tff(c_119599,plain,
less_equal(idQa,idQa_Q__idQ_idQa),
inference(demodulation,[status(thm),theory(equality)],[c_119581,c_118549]) ).
tff(c_119608,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_73,c_119599]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : HEN010-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n018.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Thu Aug 3 13:19:05 EDT 2023
% 0.14/0.32 % CPUTime :
% 33.40/20.13 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 33.51/20.14
% 33.51/20.14 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 33.55/20.19
% 33.55/20.19 Inference rules
% 33.55/20.19 ----------------------
% 33.55/20.19 #Ref : 0
% 33.55/20.19 #Sup : 29720
% 33.55/20.19 #Fact : 0
% 33.55/20.19 #Define : 0
% 33.55/20.19 #Split : 82
% 33.55/20.19 #Chain : 0
% 33.55/20.19 #Close : 0
% 33.55/20.19
% 33.55/20.19 Ordering : KBO
% 33.55/20.19
% 33.55/20.19 Simplification rules
% 33.55/20.19 ----------------------
% 33.55/20.19 #Subsume : 11997
% 33.55/20.19 #Demod : 22015
% 33.55/20.19 #Tautology : 13141
% 33.55/20.19 #SimpNegUnit : 457
% 33.55/20.19 #BackRed : 124
% 33.55/20.19
% 33.55/20.19 #Partial instantiations: 0
% 33.55/20.19 #Strategies tried : 1
% 33.55/20.19
% 33.55/20.19 Timing (in seconds)
% 33.55/20.19 ----------------------
% 33.55/20.19 Preprocessing : 0.65
% 33.55/20.19 Parsing : 0.36
% 33.55/20.19 CNF conversion : 0.03
% 33.55/20.19 Main loop : 18.29
% 33.55/20.19 Inferencing : 2.88
% 33.55/20.19 Reduction : 8.28
% 33.55/20.19 Demodulation : 6.15
% 33.55/20.19 BG Simplification : 0.13
% 33.55/20.19 Subsumption : 6.27
% 33.55/20.19 Abstraction : 0.24
% 33.55/20.19 MUC search : 0.00
% 33.55/20.19 Cooper : 0.00
% 33.55/20.19 Total : 19.02
% 33.55/20.19 Index Insertion : 0.00
% 33.55/20.19 Index Deletion : 0.00
% 33.55/20.19 Index Matching : 0.00
% 33.55/20.19 BG Taut test : 0.00
%------------------------------------------------------------------------------