%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : HEN008-3 : 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 : n026.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 06:45:55 PM UTC 2025
% Result : Unsatisfiable 3.26s 1.90s
% Output : CNFRefutation 3.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of formulae : 21 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 31 ( 12 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 23 ( 13 ~; 10 |; 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 : 26 ( 26 !; 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_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_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(f_53,axiom,
! [X,Y] :
( ( divide(X,Y) != zero )
| less_equal(X,Y) ),
file(unknown,unknown) ).
tff(f_80,axiom,
~ less_equal(divide(a,c),divide(b,c)),
file(unknown,unknown) ).
tff(c_10,plain,
! [X_10] : less_equal(zero,X_10),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_22,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_37,plain,
! [X_10] : ( divide(zero,X_10) = zero ),
inference(resolution,[status(thm)],[c_10,c_22]) ).
tff(c_16,plain,
less_equal(a,b),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_38,plain,
divide(a,b) = zero,
inference(resolution,[status(thm)],[c_16,c_22]) ).
tff(c_158,plain,
! [X_29,Z_30,Y_31] : less_equal(divide(divide(X_29,Z_30),divide(Y_31,Z_30)),divide(divide(X_29,Y_31),Z_30)),
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_910,plain,
! [X_52,Z_53,Y_54] :
( ( divide(divide(X_52,Z_53),divide(Y_54,Z_53)) = divide(divide(X_52,Y_54),Z_53) )
| ~ less_equal(divide(divide(X_52,Y_54),Z_53),divide(divide(X_52,Z_53),divide(Y_54,Z_53))) ),
inference(resolution,[status(thm)],[c_158,c_12]) ).
tff(c_982,plain,
! [Z_53] :
( ( divide(divide(a,Z_53),divide(b,Z_53)) = divide(divide(a,b),Z_53) )
| ~ less_equal(divide(zero,Z_53),divide(divide(a,Z_53),divide(b,Z_53))) ),
inference(superposition,[status(thm),theory(equality)],[c_38,c_910]) ).
tff(c_1042,plain,
! [Z_53] : ( divide(divide(a,Z_53),divide(b,Z_53)) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_37,c_37,c_38,c_982]) ).
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_18,plain,
~ less_equal(divide(a,c),divide(b,c)),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_85,plain,
divide(divide(a,c),divide(b,c)) != zero,
inference(resolution,[status(thm)],[c_4,c_18]) ).
tff(c_1060,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1042,c_85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : HEN008-3 : 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
% 0.14/0.34 % Computer : n026.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Apr 7 22:51:38 EDT 2025
% 0.14/0.34 % CPUTime :
% 3.26/1.90 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.26/1.91
% 3.26/1.91 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------