TSTP Solution File: HEN006-6 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : HEN006-6 : 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 : n005.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 10:42:15 EDT 2023
% Result : Unsatisfiable 5.99s 2.54s
% Output : CNFRefutation 6.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 17
% Syntax : Number of formulae : 63 ( 36 unt; 7 typ; 0 def)
% Number of atoms : 80 ( 39 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 52 ( 28 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 2 >; 2 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 72 (; 72 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ less_equal > divide > #nlpp > zero > identity > d > b > 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(b,type,
b: $i ).
tff(d,type,
d: $i ).
tff(identity,type,
identity: $i ).
tff(zero,type,
zero: $i ).
tff(f_53,axiom,
! [X,Y] :
( ( divide(X,Y) != zero )
| less_equal(X,Y) ),
file(unknown,unknown) ).
tff(f_86,axiom,
~ less_equal(divide(a,d),b),
file(unknown,unknown) ).
tff(f_81,axiom,
! [X] : ( divide(zero,X) = zero ),
file(unknown,unknown) ).
tff(f_83,axiom,
! [X] : ( divide(X,X) = zero ),
file(unknown,unknown) ).
tff(f_59,axiom,
! [X,Z,Y] : less_equal(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)),
file(unknown,unknown) ).
tff(f_71,axiom,
! [X,Y] :
( ~ less_equal(X,Y)
| ~ less_equal(Y,X)
| ( X = Y ) ),
file(unknown,unknown) ).
tff(f_56,axiom,
! [X,Y] : less_equal(divide(X,Y),X),
file(unknown,unknown) ).
tff(f_62,axiom,
! [X] : less_equal(zero,X),
file(unknown,unknown) ).
tff(f_84,axiom,
less_equal(divide(a,b),d),
file(unknown,unknown) ).
tff(f_48,axiom,
! [X,Y] :
( ~ less_equal(X,Y)
| ( divide(X,Y) = zero ) ),
file(unknown,unknown) ).
tff(c_104,plain,
! [X_26,Y_27] :
( less_equal(X_26,Y_27)
| ( divide(X_26,Y_27) != zero ) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_24,plain,
~ less_equal(divide(a,d),b),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_112,plain,
divide(divide(a,d),b) != zero,
inference(resolution,[status(thm)],[c_104,c_24]) ).
tff(c_18,plain,
! [X_15] : ( divide(zero,X_15) = zero ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_20,plain,
! [X_16] : ( divide(X_16,X_16) = zero ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_198,plain,
! [X_33,Z_34,Y_35] : less_equal(divide(divide(X_33,Z_34),divide(Y_35,Z_34)),divide(divide(X_33,Y_35),Z_34)),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_671,plain,
! [X_51,X_52] : less_equal(divide(divide(X_51,X_52),zero),divide(divide(X_51,zero),X_52)),
inference(superposition,[status(thm),theory(equality)],[c_18,c_198]) ).
tff(c_749,plain,
! [X_53] : less_equal(divide(divide(X_53,divide(X_53,zero)),zero),zero),
inference(superposition,[status(thm),theory(equality)],[c_20,c_671]) ).
tff(c_4,plain,
! [X_3,Y_4] :
( less_equal(X_3,Y_4)
| ( divide(X_3,Y_4) != zero ) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_164,plain,
! [Y_30,X_31] :
( ( Y_30 = X_31 )
| ~ less_equal(Y_30,X_31)
| ~ less_equal(X_31,Y_30) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_175,plain,
! [Y_4,X_3] :
( ( Y_4 = X_3 )
| ~ less_equal(Y_4,X_3)
| ( divide(X_3,Y_4) != zero ) ),
inference(resolution,[status(thm)],[c_4,c_164]) ).
tff(c_752,plain,
! [X_53] :
( ( divide(divide(X_53,divide(X_53,zero)),zero) = zero )
| ( divide(zero,divide(divide(X_53,divide(X_53,zero)),zero)) != zero ) ),
inference(resolution,[status(thm)],[c_749,c_175]) ).
tff(c_781,plain,
! [X_53] : ( divide(divide(X_53,divide(X_53,zero)),zero) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_18,c_752]) ).
tff(c_794,plain,
! [X_54] : ( divide(divide(X_54,divide(X_54,zero)),zero) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_18,c_752]) ).
tff(c_6,plain,
! [X_5,Y_6] : less_equal(divide(X_5,Y_6),X_5),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_509,plain,
! [X_45,Y_46] :
( ( divide(X_45,Y_46) = X_45 )
| ~ less_equal(X_45,divide(X_45,Y_46)) ),
inference(resolution,[status(thm)],[c_6,c_164]) ).
tff(c_539,plain,
! [X_3,Y_46] :
( ( divide(X_3,Y_46) = X_3 )
| ( divide(X_3,divide(X_3,Y_46)) != zero ) ),
inference(resolution,[status(thm)],[c_4,c_509]) ).
tff(c_811,plain,
! [X_54] :
( ( divide(divide(X_54,divide(X_54,zero)),zero) = divide(X_54,divide(X_54,zero)) )
| ( divide(divide(X_54,divide(X_54,zero)),zero) != zero ) ),
inference(superposition,[status(thm),theory(equality)],[c_794,c_539]) ).
tff(c_894,plain,
! [X_55] : ( divide(X_55,divide(X_55,zero)) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_781,c_781,c_811]) ).
tff(c_972,plain,
! [X_55] : ( divide(X_55,zero) = X_55 ),
inference(superposition,[status(thm),theory(equality)],[c_894,c_539]) ).
tff(c_237,plain,
! [X_33,X_16] : less_equal(divide(divide(X_33,X_16),zero),divide(divide(X_33,X_16),X_16)),
inference(superposition,[status(thm),theory(equality)],[c_20,c_198]) ).
tff(c_1118,plain,
! [X_58,X_59] : less_equal(divide(X_58,X_59),divide(divide(X_58,X_59),X_59)),
inference(demodulation,[status(thm),theory(equality)],[c_972,c_237]) ).
tff(c_176,plain,
! [X_5,Y_6] :
( ( divide(X_5,Y_6) = X_5 )
| ~ less_equal(X_5,divide(X_5,Y_6)) ),
inference(resolution,[status(thm)],[c_6,c_164]) ).
tff(c_1190,plain,
! [X_58,X_59] : ( divide(divide(X_58,X_59),X_59) = divide(X_58,X_59) ),
inference(resolution,[status(thm)],[c_1118,c_176]) ).
tff(c_10,plain,
! [X_10] : less_equal(zero,X_10),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_22,plain,
less_equal(divide(a,b),d),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_85,plain,
! [X_24,Y_25] :
( ( divide(X_24,Y_25) = zero )
| ~ less_equal(X_24,Y_25) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_99,plain,
divide(divide(a,b),d) = zero,
inference(resolution,[status(thm)],[c_22,c_85]) ).
tff(c_12,plain,
! [Y_12,X_11] :
( ( Y_12 = X_11 )
| ~ less_equal(Y_12,X_11)
| ~ less_equal(X_11,Y_12) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_2655,plain,
! [X_81,Z_82,Y_83] :
( ( divide(divide(X_81,Z_82),divide(Y_83,Z_82)) = divide(divide(X_81,Y_83),Z_82) )
| ~ less_equal(divide(divide(X_81,Y_83),Z_82),divide(divide(X_81,Z_82),divide(Y_83,Z_82))) ),
inference(resolution,[status(thm)],[c_198,c_12]) ).
tff(c_2784,plain,
! [Z_82] :
( ( divide(divide(divide(a,b),Z_82),divide(d,Z_82)) = divide(divide(divide(a,b),d),Z_82) )
| ~ less_equal(divide(zero,Z_82),divide(divide(divide(a,b),Z_82),divide(d,Z_82))) ),
inference(superposition,[status(thm),theory(equality)],[c_99,c_2655]) ).
tff(c_2934,plain,
! [Z_84] : ( divide(divide(divide(a,b),Z_84),divide(d,Z_84)) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_18,c_18,c_99,c_2784]) ).
tff(c_3031,plain,
divide(divide(a,b),divide(d,b)) = zero,
inference(superposition,[status(thm),theory(equality)],[c_1190,c_2934]) ).
tff(c_271,plain,
! [X_33,Z_34,Y_35] :
( ( divide(divide(X_33,Z_34),divide(Y_35,Z_34)) = divide(divide(X_33,Y_35),Z_34) )
| ~ less_equal(divide(divide(X_33,Y_35),Z_34),divide(divide(X_33,Z_34),divide(Y_35,Z_34))) ),
inference(resolution,[status(thm)],[c_198,c_12]) ).
tff(c_3126,plain,
( ( divide(divide(a,b),divide(d,b)) = divide(divide(a,d),b) )
| ~ less_equal(divide(divide(a,d),b),zero) ),
inference(superposition,[status(thm),theory(equality)],[c_3031,c_271]) ).
tff(c_3209,plain,
( ( divide(divide(a,d),b) = zero )
| ~ less_equal(divide(divide(a,d),b),zero) ),
inference(demodulation,[status(thm),theory(equality)],[c_3031,c_3126]) ).
tff(c_3210,plain,
~ less_equal(divide(divide(a,d),b),zero),
inference(negUnitSimplification,[status(thm)],[c_112,c_3209]) ).
tff(c_231,plain,
less_equal(divide(divide(a,d),divide(b,d)),zero),
inference(superposition,[status(thm),theory(equality)],[c_99,c_198]) ).
tff(c_178,plain,
! [X_10] :
( ( zero = X_10 )
| ~ less_equal(X_10,zero) ),
inference(resolution,[status(thm)],[c_10,c_164]) ).
tff(c_562,plain,
divide(divide(a,d),divide(b,d)) = zero,
inference(resolution,[status(thm)],[c_231,c_178]) ).
tff(c_98,plain,
! [X_5,Y_6] : ( divide(divide(X_5,Y_6),X_5) = zero ),
inference(resolution,[status(thm)],[c_6,c_85]) ).
tff(c_209,plain,
! [X_33,X_5,Y_6] : less_equal(divide(divide(X_33,X_5),zero),divide(divide(X_33,divide(X_5,Y_6)),X_5)),
inference(superposition,[status(thm),theory(equality)],[c_98,c_198]) ).
tff(c_7149,plain,
! [X_119,X_120,Y_121] : less_equal(divide(X_119,X_120),divide(divide(X_119,divide(X_120,Y_121)),X_120)),
inference(demodulation,[status(thm),theory(equality)],[c_972,c_209]) ).
tff(c_7353,plain,
less_equal(divide(divide(a,d),b),divide(zero,b)),
inference(superposition,[status(thm),theory(equality)],[c_562,c_7149]) ).
tff(c_7476,plain,
less_equal(divide(divide(a,d),b),zero),
inference(demodulation,[status(thm),theory(equality)],[c_18,c_7353]) ).
tff(c_7478,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3210,c_7476]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : HEN006-6 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14 % 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 : n005.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 13:08:27 EDT 2023
% 0.14/0.35 % CPUTime :
% 5.99/2.54 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.01/2.55
% 6.01/2.55 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.01/2.59
% 6.01/2.59 Inference rules
% 6.01/2.59 ----------------------
% 6.01/2.59 #Ref : 0
% 6.01/2.59 #Sup : 1775
% 6.01/2.59 #Fact : 0
% 6.01/2.59 #Define : 0
% 6.01/2.59 #Split : 1
% 6.01/2.59 #Chain : 0
% 6.01/2.59 #Close : 0
% 6.01/2.59
% 6.01/2.59 Ordering : KBO
% 6.01/2.59
% 6.01/2.59 Simplification rules
% 6.01/2.59 ----------------------
% 6.01/2.59 #Subsume : 60
% 6.01/2.59 #Demod : 2972
% 6.01/2.59 #Tautology : 1410
% 6.01/2.59 #SimpNegUnit : 2
% 6.01/2.59 #BackRed : 17
% 6.01/2.59
% 6.01/2.59 #Partial instantiations: 0
% 6.01/2.59 #Strategies tried : 1
% 6.01/2.59
% 6.01/2.59 Timing (in seconds)
% 6.01/2.59 ----------------------
% 6.01/2.59 Preprocessing : 0.44
% 6.01/2.59 Parsing : 0.25
% 6.01/2.59 CNF conversion : 0.02
% 6.01/2.59 Main loop : 0.98
% 6.01/2.59 Inferencing : 0.33
% 6.01/2.59 Reduction : 0.43
% 6.01/2.59 Demodulation : 0.35
% 6.01/2.59 BG Simplification : 0.03
% 6.01/2.59 Subsumption : 0.14
% 6.01/2.59 Abstraction : 0.04
% 6.01/2.59 MUC search : 0.00
% 6.01/2.59 Cooper : 0.00
% 6.01/2.59 Total : 1.47
% 6.01/2.59 Index Insertion : 0.00
% 6.01/2.59 Index Deletion : 0.00
% 6.01/2.59 Index Matching : 0.00
% 6.01/2.59 BG Taut test : 0.00
%------------------------------------------------------------------------------