%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : HEN012-3 : 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 : n003.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 06:45:58 PM UTC 2025
% Result : Unsatisfiable 3.12s 1.93s
% Output : CNFRefutation 3.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 27 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 41 ( 19 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 31 ( 17 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 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 : 39 ( 39 !; 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_62,axiom,
! [X] : less_equal(zero,X),
file(unknown,unknown) ).
tff(f_48,axiom,
! [X,Y] :
( ~ less_equal(X,Y)
| ( divide(X,Y) = zero ) ),
file(unknown,unknown) ).
tff(f_56,axiom,
! [X,Y] : less_equal(divide(X,Y),X),
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_79,axiom,
~ less_equal(a,a),
file(unknown,unknown) ).
tff(c_10,plain,
! [X_10] : less_equal(zero,X_10),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_25,plain,
! [X_20,Y_21] :
( ( divide(X_20,Y_21) = zero )
| ~ less_equal(X_20,Y_21) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_40,plain,
! [X_10] : ( divide(zero,X_10) = zero ),
inference(resolution,[status(thm)],[c_10,c_25]) ).
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_39,plain,
! [X_5,Y_6] : ( divide(divide(X_5,Y_6),X_5) = zero ),
inference(resolution,[status(thm)],[c_6,c_25]) ).
tff(c_170,plain,
! [X_32,Z_33,Y_34] : less_equal(divide(divide(X_32,Z_33),divide(Y_34,Z_33)),divide(divide(X_32,Y_34),Z_33)),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_312,plain,
! [X_41,Y_42] : less_equal(divide(divide(X_41,X_41),divide(Y_42,X_41)),zero),
inference(superposition,[status(thm),theory(equality)],[c_39,c_170]) ).
tff(c_352,plain,
! [X_43] : less_equal(divide(divide(X_43,X_43),zero),zero),
inference(superposition,[status(thm),theory(equality)],[c_39,c_312]) ).
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_72,plain,
! [Y_24,X_25] :
( ( Y_24 = X_25 )
| ~ less_equal(Y_24,X_25)
| ~ less_equal(X_25,Y_24) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_81,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_72]) ).
tff(c_355,plain,
! [X_43] :
( ( divide(divide(X_43,X_43),zero) = zero )
| ( divide(zero,divide(divide(X_43,X_43),zero)) != zero ) ),
inference(resolution,[status(thm)],[c_352,c_81]) ).
tff(c_386,plain,
! [X_44] : ( divide(divide(X_44,X_44),zero) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_40,c_355]) ).
tff(c_85,plain,
! [X_26] :
( ( zero = X_26 )
| ~ less_equal(X_26,zero) ),
inference(resolution,[status(thm)],[c_10,c_72]) ).
tff(c_98,plain,
! [X_3] :
( ( zero = X_3 )
| ( divide(X_3,zero) != zero ) ),
inference(resolution,[status(thm)],[c_4,c_85]) ).
tff(c_439,plain,
! [X_44] : ( divide(X_44,X_44) = zero ),
inference(superposition,[status(thm),theory(equality)],[c_386,c_98]) ).
tff(c_20,plain,
! [X_18,Y_19] :
( less_equal(X_18,Y_19)
| ( divide(X_18,Y_19) != zero ) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_16,plain,
~ less_equal(a,a),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_24,plain,
divide(a,a) != zero,
inference(resolution,[status(thm)],[c_20,c_16]) ).
tff(c_452,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_439,c_24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : HEN012-3 : TPTP v9.0.0. Released v1.0.0.
% 0.03/0.13 % 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 : n003.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 22:52:48 EDT 2025
% 0.13/0.34 % CPUTime :
% 3.12/1.93 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.12/1.93
% 3.12/1.93 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------