%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : FLD030-3 : TPTP v9.0.0. Bugfixed v2.1.0.
% 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 : n006.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 06:10:43 PM UTC 2025
% Result : Unsatisfiable 22.63s 11.85s
% Output : CNFRefutation 22.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of formulae : 21 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 44 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 49 ( 26 ~; 23 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 32 ( 32 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sum > product > less_or_equal > defined > multiply > add > #nlpp > multiplicative_inverse > additive_inverse > multiplicative_identity > d > b > additive_identity > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(sum,type,
sum: ( $i * $i * $i ) > $o ).
tff(less_or_equal,type,
less_or_equal: ( $i * $i ) > $o ).
tff(a,type,
a: $i ).
tff(product,type,
product: ( $i * $i * $i ) > $o ).
tff(additive_identity,type,
additive_identity: $i ).
tff(multiplicative_identity,type,
multiplicative_identity: $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(additive_inverse,type,
additive_inverse: $i > $i ).
tff(b,type,
b: $i ).
tff(defined,type,
defined: $i > $o ).
tff(multiplicative_inverse,type,
multiplicative_inverse: $i > $i ).
tff(add,type,
add: ( $i * $i ) > $i ).
tff(d,type,
d: $i ).
tff(f_250,axiom,
defined(b),
file(unknown,unknown) ).
tff(f_249,axiom,
defined(a),
file(unknown,unknown) ).
tff(f_252,axiom,
product(multiplicative_identity,a,d),
file(unknown,unknown) ).
tff(f_122,axiom,
! [Y,X,Z] :
( product(Y,X,Z)
| ~ product(X,Y,Z) ),
file(unknown,unknown) ).
tff(f_110,axiom,
! [X] :
( product(multiplicative_identity,X,X)
| ~ defined(X) ),
file(unknown,unknown) ).
tff(f_196,axiom,
! [X,Y] :
( product(X,Y,multiply(X,Y))
| ~ defined(X)
| ~ defined(Y) ),
file(unknown,unknown) ).
tff(f_105,axiom,
! [W,U,Z,X,Y,V] :
( product(U,Z,W)
| ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(X,V,W) ),
file(unknown,unknown) ).
tff(f_254,axiom,
~ product(d,b,multiply(a,b)),
file(unknown,unknown) ).
tff(c_56,plain,
defined(b),
inference(cnfTransformation,[status(thm)],[f_250]) ).
tff(c_54,plain,
defined(a),
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_60,plain,
product(multiplicative_identity,a,d),
inference(cnfTransformation,[status(thm)],[f_252]) ).
tff(c_69,plain,
! [X_82,Y_83,Z_84] :
( ~ product(X_82,Y_83,Z_84)
| product(Y_83,X_82,Z_84) ),
inference(cnfTransformation,[status(thm)],[f_122]) ).
tff(c_75,plain,
product(a,multiplicative_identity,d),
inference(resolution,[status(thm)],[c_60,c_69]) ).
tff(c_16,plain,
! [X_30] :
( ~ defined(X_30)
| product(multiplicative_identity,X_30,X_30) ),
inference(cnfTransformation,[status(thm)],[f_110]) ).
tff(c_40,plain,
! [Y_58,X_57] :
( ~ defined(Y_58)
| ~ defined(X_57)
| product(X_57,Y_58,multiply(X_57,Y_58)) ),
inference(cnfTransformation,[status(thm)],[f_196]) ).
tff(c_583,plain,
! [U_164,Z_163,X_165,V_167,W_166,Y_162] :
( ~ product(X_165,V_167,W_166)
| ~ product(Y_162,Z_163,V_167)
| ~ product(X_165,Y_162,U_164)
| product(U_164,Z_163,W_166) ),
inference(cnfTransformation,[status(thm)],[f_105]) ).
tff(c_7909,plain,
! [Y_342,X_340,Y_343,Z_344,U_341] :
( ~ product(Y_342,Z_344,Y_343)
| ~ product(X_340,Y_342,U_341)
| product(U_341,Z_344,multiply(X_340,Y_343))
| ~ defined(Y_343)
| ~ defined(X_340) ),
inference(resolution,[status(thm)],[c_40,c_583]) ).
tff(c_45669,plain,
! [X_590,U_591,X_592] :
( ~ product(X_590,multiplicative_identity,U_591)
| product(U_591,X_592,multiply(X_590,X_592))
| ~ defined(X_590)
| ~ defined(X_592) ),
inference(resolution,[status(thm)],[c_16,c_7909]) ).
tff(c_62,plain,
~ product(d,b,multiply(a,b)),
inference(cnfTransformation,[status(thm)],[f_254]) ).
tff(c_45794,plain,
( ~ product(a,multiplicative_identity,d)
| ~ defined(a)
| ~ defined(b) ),
inference(resolution,[status(thm)],[c_45669,c_62]) ).
tff(c_45893,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_56,c_54,c_75,c_45794]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : FLD030-3 : TPTP v9.0.0. Bugfixed v2.1.0.
% 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
% 0.13/0.35 % Computer : n006.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Apr 7 18:44:08 EDT 2025
% 0.13/0.35 % CPUTime :
% 22.63/11.85 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.63/11.85
% 22.63/11.85 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------