%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : RNG023-6 : 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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n011.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 08:31:17 PM UTC 2025
% Result : Unsatisfiable 3.83s 1.99s
% Output : CNFRefutation 3.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 11 ( 10 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 16 ( 16 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ associator > multiply > commutator > add > #nlpp > additive_inverse > y > x > additive_identity
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(x,type,
x: $i ).
tff(additive_identity,type,
additive_identity: $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(associator,type,
associator: ( $i * $i * $i ) > $i ).
tff(commutator,type,
commutator: ( $i * $i ) > $i ).
tff(additive_inverse,type,
additive_inverse: $i > $i ).
tff(y,type,
y: $i ).
tff(add,type,
add: ( $i * $i ) > $i ).
tff(f_59,axiom,
! [X] : ( add(X,additive_inverse(X)) = additive_identity ),
file(unknown,unknown) ).
tff(f_79,axiom,
! [X,Y] : ( multiply(multiply(X,X),Y) = multiply(X,multiply(X,Y)) ),
file(unknown,unknown) ).
tff(f_82,axiom,
! [X,Y,Z] : ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) ),
file(unknown,unknown) ).
tff(f_89,axiom,
associator(x,x,y) != additive_identity,
file(unknown,unknown) ).
tff(c_12,plain,
! [X_6] : ( add(X_6,additive_inverse(X_6)) = additive_identity ),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_26,plain,
! [X_21,Y_22] : ( multiply(multiply(X_21,X_21),Y_22) = multiply(X_21,multiply(X_21,Y_22)) ),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_1297,plain,
! [X_69,Y_70,Z_71] : ( add(multiply(multiply(X_69,Y_70),Z_71),additive_inverse(multiply(X_69,multiply(Y_70,Z_71)))) = associator(X_69,Y_70,Z_71) ),
inference(cnfTransformation,[status(thm)],[f_82]) ).
tff(c_1332,plain,
! [X_21,Y_22] : ( add(multiply(X_21,multiply(X_21,Y_22)),additive_inverse(multiply(X_21,multiply(X_21,Y_22)))) = associator(X_21,X_21,Y_22) ),
inference(superposition,[status(thm),theory(equality)],[c_26,c_1297]) ).
tff(c_1377,plain,
! [X_21,Y_22] : ( associator(X_21,X_21,Y_22) = additive_identity ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_1332]) ).
tff(c_32,plain,
associator(x,x,y) != additive_identity,
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_1388,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1377,c_32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG023-6 : TPTP v9.0.0. Released v1.0.0.
% 0.07/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.34 % Computer : n011.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 : Tue Apr 8 18:21:03 EDT 2025
% 0.13/0.34 % CPUTime :
% 3.83/1.99 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.83/2.00
% 3.83/2.00 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------