%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : BOO009-4 : TPTP v9.0.0. Released v1.1.0.
% 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 : n003.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 05:45:02 PM UTC 2025
% Result : Unsatisfiable 4.04s 2.58s
% Output : CNFRefutation 4.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 23 ( 22 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 : 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 36 ( 36 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ multiply > add > #nlpp > inverse > multiplicative_identity > b > additive_identity > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(a,type,
a: $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(b,type,
b: $i ).
tff(add,type,
add: ( $i * $i ) > $i ).
tff(f_52,axiom,
! [X] : ( add(X,additive_identity) = X ),
file(unknown,unknown) ).
tff(f_58,axiom,
! [X] : ( multiply(X,inverse(X)) = additive_identity ),
file(unknown,unknown) ).
tff(f_44,axiom,
! [X,Y] : ( add(X,Y) = add(Y,X) ),
file(unknown,unknown) ).
tff(f_50,axiom,
! [X,Y,Z] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
file(unknown,unknown) ).
tff(f_46,axiom,
! [X,Y] : ( multiply(X,Y) = multiply(Y,X) ),
file(unknown,unknown) ).
tff(f_48,axiom,
! [X,Y,Z] : ( add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)) ),
file(unknown,unknown) ).
tff(f_62,axiom,
multiply(a,add(a,b)) != a,
file(unknown,unknown) ).
tff(c_10,plain,
! [X_11] : ( add(X_11,additive_identity) = X_11 ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_16,plain,
! [X_14] : ( multiply(X_14,inverse(X_14)) = additive_identity ),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_156,plain,
! [Y_22,X_23] : ( add(Y_22,X_23) = add(X_23,Y_22) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_194,plain,
! [X_11] : ( add(additive_identity,X_11) = X_11 ),
inference(superposition,[status(thm),theory(equality)],[c_10,c_156]) ).
tff(c_263,plain,
! [X_25,Y_26,Z_27] : ( add(multiply(X_25,Y_26),multiply(X_25,Z_27)) = multiply(X_25,add(Y_26,Z_27)) ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_302,plain,
! [X_14,Z_27] : ( multiply(X_14,add(inverse(X_14),Z_27)) = add(additive_identity,multiply(X_14,Z_27)) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_263]) ).
tff(c_389,plain,
! [X_31,Z_32] : ( multiply(X_31,add(inverse(X_31),Z_32)) = multiply(X_31,Z_32) ),
inference(demodulation,[status(thm),theory(equality)],[c_194,c_302]) ).
tff(c_431,plain,
! [X_31] : ( multiply(X_31,inverse(X_31)) = multiply(X_31,additive_identity) ),
inference(superposition,[status(thm),theory(equality)],[c_10,c_389]) ).
tff(c_441,plain,
! [X_33] : ( multiply(X_33,additive_identity) = additive_identity ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_431]) ).
tff(c_4,plain,
! [Y_4,X_3] : ( multiply(Y_4,X_3) = multiply(X_3,Y_4) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_456,plain,
! [X_33] : ( multiply(additive_identity,X_33) = additive_identity ),
inference(superposition,[status(thm),theory(equality)],[c_441,c_4]) ).
tff(c_321,plain,
! [X_28,Y_29,Z_30] : ( multiply(add(X_28,Y_29),add(X_28,Z_30)) = add(X_28,multiply(Y_29,Z_30)) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_378,plain,
! [X_11,Z_30] : ( multiply(X_11,add(X_11,Z_30)) = add(X_11,multiply(additive_identity,Z_30)) ),
inference(superposition,[status(thm),theory(equality)],[c_10,c_321]) ).
tff(c_1285,plain,
! [X_11,Z_30] : ( multiply(X_11,add(X_11,Z_30)) = X_11 ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_456,c_378]) ).
tff(c_18,plain,
multiply(a,add(a,b)) != a,
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_1288,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1285,c_18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12 % Problem : BOO009-4 : TPTP v9.0.0. Released v1.1.0.
% 0.12/0.13 % 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 : n003.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 : Mon Apr 7 15:21:33 EDT 2025
% 0.13/0.35 % CPUTime :
% 4.04/2.58 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.04/2.58
% 4.04/2.58 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------