%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : HEN005-3 : 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 : n029.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 3.53s 2.05s
% Output : CNFRefutation 3.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 30 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 45 ( 20 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 33 ( 18 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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 : 32 ( 32 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ less_equal > divide > #nlpp > zero > identity > c > 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(identity,type,
identity: $i ).
tff(zero,type,
zero: $i ).
tff(c,type,
c: $i ).
tff(f_53,axiom,
! [X,Y] :
( ( divide(X,Y) != zero )
| less_equal(X,Y) ),
file(unknown,unknown) ).
tff(f_81,axiom,
~ less_equal(a,c),
file(unknown,unknown) ).
tff(f_79,axiom,
less_equal(b,c),
file(unknown,unknown) ).
tff(f_48,axiom,
! [X,Y] :
( ~ less_equal(X,Y)
| ( divide(X,Y) = zero ) ),
file(unknown,unknown) ).
tff(f_62,axiom,
! [X] : less_equal(zero,X),
file(unknown,unknown) ).
tff(f_78,axiom,
less_equal(a,b),
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(c_64,plain,
! [X_21,Y_22] :
( less_equal(X_21,Y_22)
| ( divide(X_21,Y_22) != zero ) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_20,plain,
~ less_equal(a,c),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_72,plain,
divide(a,c) != zero,
inference(resolution,[status(thm)],[c_64,c_20]) ).
tff(c_18,plain,
less_equal(b,c),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_24,plain,
! [X_18,Y_19] :
( ( divide(X_18,Y_19) = zero )
| ~ less_equal(X_18,Y_19) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_44,plain,
divide(b,c) = zero,
inference(resolution,[status(thm)],[c_18,c_24]) ).
tff(c_10,plain,
! [X_10] : less_equal(zero,X_10),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_41,plain,
! [X_10] : ( divide(zero,X_10) = zero ),
inference(resolution,[status(thm)],[c_10,c_24]) ).
tff(c_16,plain,
less_equal(a,b),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_42,plain,
divide(a,b) = zero,
inference(resolution,[status(thm)],[c_16,c_24]) ).
tff(c_162,plain,
! [X_28,Z_29,Y_30] : less_equal(divide(divide(X_28,Z_29),divide(Y_30,Z_29)),divide(divide(X_28,Y_30),Z_29)),
inference(cnfTransformation,[status(thm)],[f_59]) ).
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_854,plain,
! [X_49,Z_50,Y_51] :
( ( divide(divide(X_49,Z_50),divide(Y_51,Z_50)) = divide(divide(X_49,Y_51),Z_50) )
| ~ less_equal(divide(divide(X_49,Y_51),Z_50),divide(divide(X_49,Z_50),divide(Y_51,Z_50))) ),
inference(resolution,[status(thm)],[c_162,c_12]) ).
tff(c_930,plain,
! [Z_50] :
( ( divide(divide(a,Z_50),divide(b,Z_50)) = divide(divide(a,b),Z_50) )
| ~ less_equal(divide(zero,Z_50),divide(divide(a,Z_50),divide(b,Z_50))) ),
inference(superposition,[status(thm),theory(equality)],[c_42,c_854]) ).
tff(c_1155,plain,
! [Z_54] : ( divide(divide(a,Z_54),divide(b,Z_54)) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_41,c_41,c_42,c_930]) ).
tff(c_1238,plain,
divide(divide(a,c),zero) = zero,
inference(superposition,[status(thm),theory(equality)],[c_44,c_1155]) ).
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_143,plain,
! [Y_26,X_27] :
( ( Y_26 = X_27 )
| ~ less_equal(Y_26,X_27)
| ~ less_equal(X_27,Y_26) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_239,plain,
! [X_31] :
( ( zero = X_31 )
| ~ less_equal(X_31,zero) ),
inference(resolution,[status(thm)],[c_10,c_143]) ).
tff(c_252,plain,
! [X_3] :
( ( zero = X_3 )
| ( divide(X_3,zero) != zero ) ),
inference(resolution,[status(thm)],[c_4,c_239]) ).
tff(c_1294,plain,
divide(a,c) = zero,
inference(superposition,[status(thm),theory(equality)],[c_1238,c_252]) ).
tff(c_1330,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_72,c_1294]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : HEN005-3 : TPTP v9.0.0. Released v1.0.0.
% 0.11/0.13 % 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
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Apr 7 22:50:34 EDT 2025
% 0.12/0.34 % CPUTime :
% 3.53/2.05 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.53/2.05
% 3.53/2.05 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------