%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : BOO012-2 : 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 : 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 05:45:03 PM UTC 2025
% Result : Unsatisfiable 4.33s 2.48s
% Output : CNFRefutation 4.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 35 ( 35 unt; 0 typ; 0 def)
% Number of atoms : 35 ( 34 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 50 ( 50 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ multiply > add > #nlpp > inverse > x > multiplicative_identity > additive_identity
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(x,type,
x: $i ).
tff(inverse,type,
inverse: $i > $i ).
tff(additive_identity,type,
additive_identity: $i ).
tff(multiplicative_identity,type,
multiplicative_identity: $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(add,type,
add: ( $i * $i ) > $i ).
tff(f_70,axiom,
! [X] : ( add(additive_identity,X) = X ),
file(unknown,unknown) ).
tff(f_60,axiom,
! [X] : ( multiply(X,inverse(X)) = additive_identity ),
file(unknown,unknown) ).
tff(f_66,axiom,
! [X] : ( multiply(multiplicative_identity,X) = X ),
file(unknown,unknown) ).
tff(f_58,axiom,
! [X] : ( add(inverse(X),X) = multiplicative_identity ),
file(unknown,unknown) ).
tff(f_48,axiom,
! [X,Y,Z] : ( add(multiply(X,Y),Z) = multiply(add(X,Z),add(Y,Z)) ),
file(unknown,unknown) ).
tff(f_64,axiom,
! [X] : ( multiply(X,multiplicative_identity) = X ),
file(unknown,unknown) ).
tff(f_56,axiom,
! [X] : ( add(X,inverse(X)) = multiplicative_identity ),
file(unknown,unknown) ).
tff(f_54,axiom,
! [X,Y,Z] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
file(unknown,unknown) ).
tff(f_52,axiom,
! [X,Y,Z] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ),
file(unknown,unknown) ).
tff(f_74,axiom,
inverse(inverse(x)) != x,
file(unknown,unknown) ).
tff(c_28,plain,
! [X_24] : ( add(additive_identity,X_24) = X_24 ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_18,plain,
! [X_19] : ( multiply(X_19,inverse(X_19)) = additive_identity ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_24,plain,
! [X_22] : ( multiply(multiplicative_identity,X_22) = X_22 ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_16,plain,
! [X_18] : ( add(inverse(X_18),X_18) = multiplicative_identity ),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_367,plain,
! [X_37,Z_38,Y_39] : ( multiply(add(X_37,Z_38),add(Y_39,Z_38)) = add(multiply(X_37,Y_39),Z_38) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_406,plain,
! [X_18,Y_39] : ( add(multiply(inverse(X_18),Y_39),X_18) = multiply(multiplicative_identity,add(Y_39,X_18)) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_367]) ).
tff(c_430,plain,
! [X_40,Y_41] : ( add(multiply(inverse(X_40),Y_41),X_40) = add(Y_41,X_40) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_406]) ).
tff(c_472,plain,
! [X_40] : ( add(inverse(inverse(X_40)),X_40) = add(additive_identity,X_40) ),
inference(superposition,[status(thm),theory(equality)],[c_18,c_430]) ).
tff(c_495,plain,
! [X_40] : ( add(inverse(inverse(X_40)),X_40) = X_40 ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_472]) ).
tff(c_22,plain,
! [X_21] : ( multiply(X_21,multiplicative_identity) = X_21 ),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_14,plain,
! [X_17] : ( add(X_17,inverse(X_17)) = multiplicative_identity ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_594,plain,
! [X_44,Y_45,Z_46] : ( add(multiply(X_44,Y_45),multiply(X_44,Z_46)) = multiply(X_44,add(Y_45,Z_46)) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_647,plain,
! [X_19,Z_46] : ( multiply(X_19,add(inverse(X_19),Z_46)) = add(additive_identity,multiply(X_19,Z_46)) ),
inference(superposition,[status(thm),theory(equality)],[c_18,c_594]) ).
tff(c_1376,plain,
! [X_61,Z_62] : ( multiply(X_61,add(inverse(X_61),Z_62)) = multiply(X_61,Z_62) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_647]) ).
tff(c_1458,plain,
! [X_61] : ( multiply(X_61,inverse(inverse(X_61))) = multiply(X_61,multiplicative_identity) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_1376]) ).
tff(c_1593,plain,
! [X_64] : ( multiply(X_64,inverse(inverse(X_64))) = X_64 ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_1458]) ).
tff(c_489,plain,
! [X_40] : ( add(inverse(X_40),X_40) = add(multiplicative_identity,X_40) ),
inference(superposition,[status(thm),theory(equality)],[c_22,c_430]) ).
tff(c_499,plain,
! [X_40] : ( add(multiplicative_identity,X_40) = multiplicative_identity ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_489]) ).
tff(c_1063,plain,
! [X_55,Z_56,Y_57] : ( add(multiply(X_55,Z_56),multiply(Y_57,Z_56)) = multiply(add(X_55,Y_57),Z_56) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_1182,plain,
! [Y_57,X_22] : ( multiply(add(multiplicative_identity,Y_57),X_22) = add(X_22,multiply(Y_57,X_22)) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_1063]) ).
tff(c_1206,plain,
! [X_22,Y_57] : ( add(X_22,multiply(Y_57,X_22)) = X_22 ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_499,c_1182]) ).
tff(c_1599,plain,
! [X_64] : ( add(inverse(inverse(X_64)),X_64) = inverse(inverse(X_64)) ),
inference(superposition,[status(thm),theory(equality)],[c_1593,c_1206]) ).
tff(c_1645,plain,
! [X_64] : ( inverse(inverse(X_64)) = X_64 ),
inference(demodulation,[status(thm),theory(equality)],[c_495,c_1599]) ).
tff(c_30,plain,
inverse(inverse(x)) != x,
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_1664,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1645,c_30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : BOO012-2 : TPTP v9.0.0. Released v1.0.0.
% 0.02/0.09 % 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
% 0.09/0.28 % Computer : n011.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Mon Apr 7 15:22:18 EDT 2025
% 0.09/0.29 % CPUTime :
% 4.33/2.48 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.33/2.49
% 4.33/2.49 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------