%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : HEN006-4 : TPTP v9.0.0. 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 : n009.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 06:45:53 PM UTC 2025
% Result : Unsatisfiable 4.49s 2.12s
% Output : CNFRefutation 4.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 26 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 41 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 32 ( 17 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 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 : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 36 ( 36 !; 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_95,axiom,
~ less_equal(divide(a,d),b),
file(unknown,unknown) ).
tff(f_62,axiom,
! [X] : less_equal(zero,X),
file(unknown,unknown) ).
tff(f_93,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(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_53,axiom,
! [X,Y] :
( ( divide(X,Y) != zero )
| less_equal(X,Y) ),
file(unknown,unknown) ).
tff(f_56,axiom,
! [X,Y] : less_equal(divide(X,Y),X),
file(unknown,unknown) ).
tff(f_92,axiom,
! [X,Y,Z] :
( ~ less_equal(X,Y)
| ~ less_equal(Y,Z)
| less_equal(X,Z) ),
file(unknown,unknown) ).
tff(c_28,plain,
~ less_equal(divide(a,d),b),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_10,plain,
! [X_10] : less_equal(zero,X_10),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_26,plain,
less_equal(divide(a,b),d),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_96,plain,
! [X_27,Y_28] :
( ( divide(X_27,Y_28) = zero )
| ~ less_equal(X_27,Y_28) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_115,plain,
divide(divide(a,b),d) = zero,
inference(resolution,[status(thm)],[c_26,c_96]) ).
tff(c_336,plain,
! [X_46,Z_47,Y_48] : less_equal(divide(divide(X_46,Z_47),divide(Y_48,Z_47)),divide(divide(X_46,Y_48),Z_47)),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_355,plain,
less_equal(divide(divide(a,d),divide(b,d)),zero),
inference(superposition,[status(thm),theory(equality)],[c_115,c_336]) ).
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_2186,plain,
( ( divide(divide(a,d),divide(b,d)) = zero )
| ~ less_equal(zero,divide(divide(a,d),divide(b,d))) ),
inference(resolution,[status(thm)],[c_355,c_12]) ).
tff(c_2201,plain,
divide(divide(a,d),divide(b,d)) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_10,c_2186]) ).
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_6,plain,
! [X_5,Y_6] : less_equal(divide(X_5,Y_6),X_5),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_258,plain,
! [X_38,Z_39,Y_40] :
( less_equal(X_38,Z_39)
| ~ less_equal(Y_40,Z_39)
| ~ less_equal(X_38,Y_40) ),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_487,plain,
! [X_51,X_52,Y_53] :
( less_equal(X_51,X_52)
| ~ less_equal(X_51,divide(X_52,Y_53)) ),
inference(resolution,[status(thm)],[c_6,c_258]) ).
tff(c_527,plain,
! [X_3,X_52,Y_53] :
( less_equal(X_3,X_52)
| ( divide(X_3,divide(X_52,Y_53)) != zero ) ),
inference(resolution,[status(thm)],[c_4,c_487]) ).
tff(c_2303,plain,
less_equal(divide(a,d),b),
inference(superposition,[status(thm),theory(equality)],[c_2201,c_527]) ).
tff(c_2355,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_2303]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : HEN006-4 : TPTP v9.0.0. Released v1.0.0.
% 0.12/0.13 % 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
% 0.12/0.33 % Computer : n009.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 : Mon Apr 7 22:50:56 EDT 2025
% 0.12/0.34 % CPUTime :
% 4.49/2.12 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.49/2.12
% 4.49/2.12 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------