%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : HEN009-4 : TPTP v9.0.0. Bugfixed v1.2.1.
% 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 : n011.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 Apr 9 06:45:56 PM UTC 2025
% Result : Unsatisfiable 18.58s 8.45s
% Output : CNFRefutation 18.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 34 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 61 ( 13 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 57 ( 30 ~; 27 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 68 ( 68 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ less_equal > divide > #nlpp > zero > identity > 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(identity,type,
identity: $i ).
tff(zero,type,
zero: $i ).
tff(f_58,axiom,
! [X,Y] : less_equal(divide(X,Y),X),
file(unknown,unknown) ).
tff(f_94,axiom,
! [X,Y,Z] :
( ~ less_equal(X,Y)
| ~ less_equal(Y,Z)
| less_equal(X,Z) ),
file(unknown,unknown) ).
tff(f_104,axiom,
! [X,Y,Z] :
( ~ less_equal(X,Y)
| less_equal(divide(Z,Y),divide(Z,X)) ),
file(unknown,unknown) ).
tff(f_99,axiom,
! [X,Y,Z] :
( ~ less_equal(divide(X,Y),Z)
| less_equal(divide(X,Z),Y) ),
file(unknown,unknown) ).
tff(f_64,axiom,
! [X] : less_equal(zero,X),
file(unknown,unknown) ).
tff(f_73,axiom,
! [X,Y] :
( ~ less_equal(X,Y)
| ~ less_equal(Y,X)
| ( X = Y ) ),
file(unknown,unknown) ).
tff(f_55,axiom,
! [X,Y] :
( ( divide(X,Y) != zero )
| less_equal(X,Y) ),
file(unknown,unknown) ).
tff(f_111,axiom,
divide(identity,a) != divide(identity,divide(identity,divide(identity,a))),
file(unknown,unknown) ).
tff(c_6,plain,
! [X_5,Y_6] : less_equal(divide(X_5,Y_6),X_5),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_239,plain,
! [X_47,Z_48,Y_49] :
( less_equal(X_47,Z_48)
| ~ less_equal(Y_49,Z_48)
| ~ less_equal(X_47,Y_49) ),
inference(cnfTransformation,[status(thm)],[f_94]) ).
tff(c_310,plain,
! [X_55,X_56,Y_57] :
( less_equal(X_55,X_56)
| ~ less_equal(X_55,divide(X_56,Y_57)) ),
inference(resolution,[status(thm)],[c_6,c_239]) ).
tff(c_344,plain,
! [X_56,Y_57,Y_6] : less_equal(divide(divide(X_56,Y_57),Y_6),X_56),
inference(resolution,[status(thm)],[c_6,c_310]) ).
tff(c_28,plain,
! [Z_25,Y_24,X_23] :
( less_equal(divide(Z_25,Y_24),divide(Z_25,X_23))
| ~ less_equal(X_23,Y_24) ),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_521,plain,
! [X_68,Z_69,Y_70] :
( less_equal(divide(X_68,Z_69),Y_70)
| ~ less_equal(divide(X_68,Y_70),Z_69) ),
inference(cnfTransformation,[status(thm)],[f_99]) ).
tff(c_2636,plain,
! [Z_137,X_138,Y_139] :
( less_equal(divide(Z_137,divide(Z_137,X_138)),Y_139)
| ~ less_equal(X_138,Y_139) ),
inference(resolution,[status(thm)],[c_28,c_521]) ).
tff(c_10,plain,
! [X_10] : less_equal(zero,X_10),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_168,plain,
! [Y_42,X_43] :
( ( Y_42 = X_43 )
| ~ less_equal(Y_42,X_43)
| ~ less_equal(X_43,Y_42) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_185,plain,
! [X_10] :
( ( zero = X_10 )
| ~ less_equal(X_10,zero) ),
inference(resolution,[status(thm)],[c_10,c_168]) ).
tff(c_3255,plain,
! [Z_150,X_151] :
( ( divide(Z_150,divide(Z_150,X_151)) = zero )
| ~ less_equal(X_151,zero) ),
inference(resolution,[status(thm)],[c_2636,c_185]) ).
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_55]) ).
tff(c_343,plain,
! [X_3,X_56,Y_57] :
( less_equal(X_3,X_56)
| ( divide(X_3,divide(X_56,Y_57)) != zero ) ),
inference(resolution,[status(thm)],[c_4,c_310]) ).
tff(c_3430,plain,
! [Z_150,X_151] :
( less_equal(Z_150,Z_150)
| ~ less_equal(X_151,zero) ),
inference(superposition,[status(thm),theory(equality)],[c_3255,c_343]) ).
tff(c_3468,plain,
! [X_152] : ~ less_equal(X_152,zero),
inference(splitLeft,[status(thm)],[c_3430]) ).
tff(c_3518,plain,
$false,
inference(resolution,[status(thm)],[c_344,c_3468]) ).
tff(c_3521,plain,
! [Z_153] : less_equal(Z_153,Z_153),
inference(splitRight,[status(thm)],[c_3430]) ).
tff(c_26,plain,
! [X_20,Z_22,Y_21] :
( less_equal(divide(X_20,Z_22),Y_21)
| ~ less_equal(divide(X_20,Y_21),Z_22) ),
inference(cnfTransformation,[status(thm)],[f_99]) ).
tff(c_3585,plain,
! [X_20,Y_21] : less_equal(divide(X_20,divide(X_20,Y_21)),Y_21),
inference(resolution,[status(thm)],[c_3521,c_26]) ).
tff(c_424,plain,
! [Z_63,Y_64,X_65] :
( less_equal(divide(Z_63,Y_64),divide(Z_63,X_65))
| ~ less_equal(X_65,Y_64) ),
inference(cnfTransformation,[status(thm)],[f_104]) ).
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_73]) ).
tff(c_17510,plain,
! [Z_288,Y_289,X_290] :
( ( divide(Z_288,Y_289) = divide(Z_288,X_290) )
| ~ less_equal(divide(Z_288,X_290),divide(Z_288,Y_289))
| ~ less_equal(X_290,Y_289) ),
inference(resolution,[status(thm)],[c_424,c_12]) ).
tff(c_17635,plain,
! [X_20,Y_289] :
( ( divide(X_20,divide(X_20,divide(X_20,Y_289))) = divide(X_20,Y_289) )
| ~ less_equal(divide(X_20,divide(X_20,Y_289)),Y_289) ),
inference(resolution,[status(thm)],[c_3585,c_17510]) ).
tff(c_17798,plain,
! [X_20,Y_289] : ( divide(X_20,divide(X_20,divide(X_20,Y_289))) = divide(X_20,Y_289) ),
inference(demodulation,[status(thm),theory(equality)],[c_3585,c_17635]) ).
tff(c_32,plain,
divide(identity,divide(identity,divide(identity,a))) != divide(identity,a),
inference(cnfTransformation,[status(thm)],[f_111]) ).
tff(c_99302,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_17798,c_32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : HEN009-4 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.03/0.13 % 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
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Apr 7 22:52:03 EDT 2025
% 0.13/0.34 % CPUTime :
% 18.58/8.45 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.58/8.46
% 18.58/8.46 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------