%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : BOO001-1 : 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 : n007.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 05:44:59 PM UTC 2025
% Result : Unsatisfiable 3.66s 1.91s
% Output : CNFRefutation 3.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 18 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 18 ( 17 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 1 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 : 3 ( 3 usr; 1 con; 0-3 aty)
% Number of variables : 42 ( 42 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ multiply > #nlpp > inverse > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(a,type,
a: $i ).
tff(inverse,type,
inverse: $i > $i ).
tff(multiply,type,
multiply: ( $i * $i * $i ) > $i ).
tff(f_49,axiom,
! [Y,X] : ( multiply(Y,X,X) = X ),
file(unknown,unknown) ).
tff(f_47,axiom,
! [W,Z,X,Y,V] : ( multiply(multiply(V,W,X),Y,multiply(V,W,Z)) = multiply(V,W,multiply(X,Y,Z)) ),
file(unknown,unknown) ).
tff(f_55,axiom,
! [X,Y] : ( multiply(X,Y,inverse(Y)) = X ),
file(unknown,unknown) ).
tff(f_51,axiom,
! [X,Y] : ( multiply(X,X,Y) = X ),
file(unknown,unknown) ).
tff(f_59,axiom,
inverse(inverse(a)) != a,
file(unknown,unknown) ).
tff(c_4,plain,
! [Y_6,X_7] : ( multiply(Y_6,X_7,X_7) = X_7 ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_89,plain,
! [W_24,Y_26,V_25,X_23,Z_22] : ( multiply(multiply(V_25,W_24,X_23),Y_26,multiply(V_25,W_24,Z_22)) = multiply(V_25,W_24,multiply(X_23,Y_26,Z_22)) ),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_1107,plain,
! [Y_54,X_55,Y_56,Z_57] : ( multiply(Y_54,X_55,multiply(X_55,Y_56,Z_57)) = multiply(X_55,Y_56,multiply(Y_54,X_55,Z_57)) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_89]) ).
tff(c_10,plain,
! [X_12,Y_13] : ( multiply(X_12,Y_13,inverse(Y_13)) = X_12 ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_6,plain,
! [X_8,Y_9] : ( multiply(X_8,X_8,Y_9) = X_8 ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_220,plain,
! [V_29,W_30,X_31,Z_32] : ( multiply(V_29,W_30,multiply(X_31,multiply(V_29,W_30,X_31),Z_32)) = multiply(V_29,W_30,X_31) ),
inference(superposition,[status(thm),theory(equality)],[c_89,c_6]) ).
tff(c_278,plain,
! [X_12,Y_13,Z_32] : ( multiply(X_12,Y_13,multiply(inverse(Y_13),X_12,Z_32)) = multiply(X_12,Y_13,inverse(Y_13)) ),
inference(superposition,[status(thm),theory(equality)],[c_10,c_220]) ).
tff(c_312,plain,
! [X_12,Y_13,Z_32] : ( multiply(X_12,Y_13,multiply(inverse(Y_13),X_12,Z_32)) = X_12 ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_278]) ).
tff(c_1464,plain,
! [Y_58,X_59,Z_60] : ( multiply(inverse(Y_58),X_59,multiply(X_59,Y_58,Z_60)) = X_59 ),
inference(superposition,[status(thm),theory(equality)],[c_1107,c_312]) ).
tff(c_1611,plain,
! [X_61,Y_62] : ( multiply(inverse(X_61),Y_62,X_61) = Y_62 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_1464]) ).
tff(c_1675,plain,
! [Y_62] : ( inverse(inverse(Y_62)) = Y_62 ),
inference(superposition,[status(thm),theory(equality)],[c_1611,c_10]) ).
tff(c_12,plain,
inverse(inverse(a)) != a,
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_1729,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1675,c_12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : BOO001-1 : TPTP v9.0.0. Released v1.0.0.
% 0.07/0.12 % 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
% 0.13/0.33 % Computer : n007.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Apr 7 15:20:53 EDT 2025
% 0.13/0.34 % CPUTime :
% 3.66/1.91 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.66/1.91
% 3.66/1.91 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------