TSTP Solution File: HEN009-2 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : HEN009-2 : 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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Aug 22 10:42:18 EDT 2023
% Result : Unsatisfiable 6.72s 2.58s
% Output : CNFRefutation 6.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 18
% Syntax : Number of formulae : 40 ( 16 unt; 9 typ; 0 def)
% Number of atoms : 59 ( 5 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 59 ( 31 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 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 : 39 (; 39 !; 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_162,axiom,
idQa != idQ__idQ_idQa,
file(unknown,unknown) ).
tff(f_116,axiom,
! [X] : quotient(X,zero,X),
file(unknown,unknown) ).
tff(f_60,axiom,
! [X,Y,Z] :
( ~ quotient(X,Y,Z)
| less_equal(Z,X) ),
file(unknown,unknown) ).
tff(f_159,axiom,
quotient(identity,idQa,idQ_idQa),
file(unknown,unknown) ).
tff(f_160,axiom,
quotient(identity,idQ_idQa,idQ__idQ_idQa),
file(unknown,unknown) ).
tff(f_135,axiom,
! [W1,Z,X,Y,W2] :
( ~ quotient(X,Y,W1)
| ~ less_equal(W1,Z)
| ~ quotient(X,Z,W2)
| less_equal(W2,Y) ),
file(unknown,unknown) ).
tff(f_90,axiom,
! [X,Y] :
( ~ less_equal(X,Y)
| ~ less_equal(Y,X)
| ( X = Y ) ),
file(unknown,unknown) ).
tff(f_158,axiom,
quotient(identity,a,idQa),
file(unknown,unknown) ).
tff(f_146,axiom,
! [W1,Z,X,Y,W2] :
( ~ less_equal(X,Y)
| ~ quotient(Z,Y,W1)
| ~ quotient(Z,X,W2)
| less_equal(W1,W2) ),
file(unknown,unknown) ).
tff(c_42,plain,
idQa != idQ__idQ_idQa,
inference(cnfTransformation,[status(thm)],[f_162]) ).
tff(c_26,plain,
! [X_29] : quotient(X_29,zero,X_29),
inference(cnfTransformation,[status(thm)],[f_116]) ).
tff(c_51,plain,
! [Z_58,X_59,Y_60] :
( less_equal(Z_58,X_59)
| ~ quotient(X_59,Y_60,Z_58) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_90,plain,
! [X_29] : less_equal(X_29,X_29),
inference(resolution,[status(thm)],[c_26,c_51]) ).
tff(c_38,plain,
quotient(identity,idQa,idQ_idQa),
inference(cnfTransformation,[status(thm)],[f_159]) ).
tff(c_40,plain,
quotient(identity,idQ_idQa,idQ__idQ_idQa),
inference(cnfTransformation,[status(thm)],[f_160]) ).
tff(c_621,plain,
! [Y_108,W2_106,X_107,W1_105,Z_109] :
( less_equal(W2_106,Y_108)
| ~ quotient(X_107,Z_109,W2_106)
| ~ less_equal(W1_105,Z_109)
| ~ quotient(X_107,Y_108,W1_105) ),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_5479,plain,
! [Y_241,W1_242] :
( less_equal(idQ__idQ_idQa,Y_241)
| ~ less_equal(W1_242,idQ_idQa)
| ~ quotient(identity,Y_241,W1_242) ),
inference(resolution,[status(thm)],[c_40,c_621]) ).
tff(c_5498,plain,
( less_equal(idQ__idQ_idQa,idQa)
| ~ less_equal(idQ_idQa,idQ_idQa) ),
inference(resolution,[status(thm)],[c_38,c_5479]) ).
tff(c_5521,plain,
less_equal(idQ__idQ_idQa,idQa),
inference(demodulation,[status(thm),theory(equality)],[c_90,c_5498]) ).
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_90]) ).
tff(c_5532,plain,
( ( idQa = idQ__idQ_idQa )
| ~ less_equal(idQa,idQ__idQ_idQa) ),
inference(resolution,[status(thm)],[c_5521,c_12]) ).
tff(c_5537,plain,
~ less_equal(idQa,idQ__idQ_idQa),
inference(negUnitSimplification,[status(thm)],[c_42,c_5532]) ).
tff(c_36,plain,
quotient(identity,a,idQa),
inference(cnfTransformation,[status(thm)],[f_158]) ).
tff(c_1601,plain,
! [Y_151,W1_152] :
( less_equal(idQ_idQa,Y_151)
| ~ less_equal(W1_152,idQa)
| ~ quotient(identity,Y_151,W1_152) ),
inference(resolution,[status(thm)],[c_38,c_621]) ).
tff(c_1627,plain,
( less_equal(idQ_idQa,a)
| ~ less_equal(idQa,idQa) ),
inference(resolution,[status(thm)],[c_36,c_1601]) ).
tff(c_1645,plain,
less_equal(idQ_idQa,a),
inference(demodulation,[status(thm),theory(equality)],[c_90,c_1627]) ).
tff(c_410,plain,
! [Z_93,X_95,W2_94,Y_97,W1_96] :
( less_equal(W1_96,W2_94)
| ~ quotient(Z_93,X_95,W2_94)
| ~ quotient(Z_93,Y_97,W1_96)
| ~ less_equal(X_95,Y_97) ),
inference(cnfTransformation,[status(thm)],[f_146]) ).
tff(c_8036,plain,
! [W1_282,Y_283] :
( less_equal(W1_282,idQ__idQ_idQa)
| ~ quotient(identity,Y_283,W1_282)
| ~ less_equal(idQ_idQa,Y_283) ),
inference(resolution,[status(thm)],[c_40,c_410]) ).
tff(c_8062,plain,
( less_equal(idQa,idQ__idQ_idQa)
| ~ less_equal(idQ_idQa,a) ),
inference(resolution,[status(thm)],[c_36,c_8036]) ).
tff(c_8080,plain,
less_equal(idQa,idQ__idQ_idQa),
inference(demodulation,[status(thm),theory(equality)],[c_1645,c_8062]) ).
tff(c_8082,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_5537,c_8080]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : HEN009-2 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.12 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.12/0.33 % Computer : n004.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 : 300
% 0.12/0.33 % DateTime : Thu Aug 3 13:04:41 EDT 2023
% 0.12/0.33 % CPUTime :
% 6.72/2.58 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.72/2.58
% 6.72/2.58 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.72/2.61
% 6.72/2.61 Inference rules
% 6.72/2.61 ----------------------
% 6.72/2.61 #Ref : 0
% 6.72/2.61 #Sup : 1932
% 6.72/2.61 #Fact : 0
% 6.72/2.61 #Define : 0
% 6.72/2.61 #Split : 6
% 6.72/2.61 #Chain : 0
% 6.72/2.61 #Close : 0
% 6.72/2.61
% 6.72/2.61 Ordering : KBO
% 6.72/2.61
% 6.72/2.61 Simplification rules
% 6.72/2.61 ----------------------
% 6.72/2.61 #Subsume : 277
% 6.72/2.61 #Demod : 1619
% 6.72/2.61 #Tautology : 1393
% 6.72/2.61 #SimpNegUnit : 29
% 6.72/2.61 #BackRed : 0
% 6.72/2.61
% 6.72/2.61 #Partial instantiations: 0
% 6.72/2.61 #Strategies tried : 1
% 6.72/2.61
% 6.72/2.61 Timing (in seconds)
% 6.72/2.61 ----------------------
% 6.72/2.61 Preprocessing : 0.47
% 6.72/2.61 Parsing : 0.23
% 6.72/2.62 CNF conversion : 0.03
% 6.72/2.62 Main loop : 1.11
% 6.72/2.62 Inferencing : 0.40
% 6.72/2.62 Reduction : 0.39
% 6.72/2.62 Demodulation : 0.29
% 6.72/2.62 BG Simplification : 0.03
% 6.72/2.62 Subsumption : 0.22
% 6.72/2.62 Abstraction : 0.04
% 6.72/2.62 MUC search : 0.00
% 6.72/2.62 Cooper : 0.00
% 6.72/2.62 Total : 1.64
% 6.72/2.62 Index Insertion : 0.00
% 6.72/2.62 Index Deletion : 0.00
% 6.72/2.62 Index Matching : 0.00
% 6.72/2.62 BG Taut test : 0.00
%------------------------------------------------------------------------------