%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : HEN004-4 : 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 : n007.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 06:45:52 PM UTC 2025
% Result : Unsatisfiable 3.25s 1.94s
% Output : CNFRefutation 3.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 26 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 39 ( 24 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 15 ~; 13 |; 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 : 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 : 37 ( 37 !; 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_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_53,axiom,
! [X,Y] :
( ( divide(X,Y) != zero )
| less_equal(X,Y) ),
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_85,axiom,
divide(a,zero) != a,
file(unknown,unknown) ).
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_217,plain,
! [X_36,Z_37,Y_38] : less_equal(divide(divide(X_36,Z_37),divide(Y_38,Z_37)),divide(divide(X_36,Y_38),Z_37)),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_517,plain,
! [X_49,X_50] : less_equal(divide(divide(X_49,X_50),zero),divide(divide(X_49,zero),X_50)),
inference(superposition,[status(thm),theory(equality)],[c_18,c_217]) ).
tff(c_587,plain,
! [X_51] : less_equal(divide(divide(X_51,divide(X_51,zero)),zero),zero),
inference(superposition,[status(thm),theory(equality)],[c_20,c_517]) ).
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_103,plain,
! [Y_28,X_29] :
( ( Y_28 = X_29 )
| ~ less_equal(Y_28,X_29)
| ~ less_equal(X_29,Y_28) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_112,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_103]) ).
tff(c_590,plain,
! [X_51] :
( ( divide(divide(X_51,divide(X_51,zero)),zero) = zero )
| ( divide(zero,divide(divide(X_51,divide(X_51,zero)),zero)) != zero ) ),
inference(resolution,[status(thm)],[c_587,c_112]) ).
tff(c_619,plain,
! [X_51] : ( divide(divide(X_51,divide(X_51,zero)),zero) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_18,c_590]) ).
tff(c_632,plain,
! [X_52] : ( divide(divide(X_52,divide(X_52,zero)),zero) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_18,c_590]) ).
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_293,plain,
! [Y_39,X_40] :
( ( Y_39 = X_40 )
| ~ less_equal(Y_39,X_40)
| ( divide(X_40,Y_39) != zero ) ),
inference(resolution,[status(thm)],[c_4,c_103]) ).
tff(c_311,plain,
! [X_5,Y_6] :
( ( divide(X_5,Y_6) = X_5 )
| ( divide(X_5,divide(X_5,Y_6)) != zero ) ),
inference(resolution,[status(thm)],[c_6,c_293]) ).
tff(c_652,plain,
! [X_52] :
( ( divide(divide(X_52,divide(X_52,zero)),zero) = divide(X_52,divide(X_52,zero)) )
| ( divide(divide(X_52,divide(X_52,zero)),zero) != zero ) ),
inference(superposition,[status(thm),theory(equality)],[c_632,c_311]) ).
tff(c_727,plain,
! [X_53] : ( divide(X_53,divide(X_53,zero)) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_619,c_619,c_652]) ).
tff(c_804,plain,
! [X_53] : ( divide(X_53,zero) = X_53 ),
inference(superposition,[status(thm),theory(equality)],[c_727,c_311]) ).
tff(c_22,plain,
divide(a,zero) != a,
inference(cnfTransformation,[status(thm)],[f_85]) ).
tff(c_848,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_804,c_22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : HEN004-4 : TPTP v9.0.0. Released v1.0.0.
% 0.07/0.13 % 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
% 0.13/0.34 % Computer : n007.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 22:50:38 EDT 2025
% 0.13/0.34 % CPUTime :
% 3.25/1.94 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.25/1.95
% 3.25/1.95 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------