%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : FLD023-3 : 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 : n031.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 06:10:41 PM UTC 2025
% Result : Unsatisfiable 8.13s 3.24s
% Output : CNFRefutation 8.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 25 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 46 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 44 ( 23 ~; 21 |; 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 : 8 ( 8 usr; 4 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 > 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(f_253,axiom,
~ sum(b,additive_inverse(a),additive_identity),
file(unknown,unknown) ).
tff(f_249,axiom,
defined(a),
file(unknown,unknown) ).
tff(f_78,axiom,
! [X] :
( sum(additive_inverse(X),X,additive_identity)
| ~ defined(X) ),
file(unknown,unknown) ).
tff(f_159,axiom,
defined(additive_identity),
file(unknown,unknown) ).
tff(f_251,axiom,
sum(additive_identity,a,b),
file(unknown,unknown) ).
tff(f_83,axiom,
! [Y,X,Z] :
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
file(unknown,unknown) ).
tff(f_73,axiom,
! [X] :
( sum(additive_identity,X,X)
| ~ defined(X) ),
file(unknown,unknown) ).
tff(f_57,axiom,
! [W,U,Z,X,Y,V] :
( sum(X,V,W)
| ~ sum(X,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(U,Z,W) ),
file(unknown,unknown) ).
tff(c_60,plain,
~ sum(b,additive_inverse(a),additive_identity),
inference(cnfTransformation,[status(thm)],[f_253]) ).
tff(c_54,plain,
defined(a),
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_8,plain,
! [X_14] :
( ~ defined(X_14)
| sum(additive_inverse(X_14),X_14,additive_identity) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_28,plain,
defined(additive_identity),
inference(cnfTransformation,[status(thm)],[f_159]) ).
tff(c_58,plain,
sum(additive_identity,a,b),
inference(cnfTransformation,[status(thm)],[f_251]) ).
tff(c_74,plain,
! [X_84,Y_85,Z_86] :
( ~ sum(X_84,Y_85,Z_86)
| sum(Y_85,X_84,Z_86) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_83,plain,
sum(a,additive_identity,b),
inference(resolution,[status(thm)],[c_58,c_74]) ).
tff(c_6,plain,
! [X_13] :
( ~ defined(X_13)
| sum(additive_identity,X_13,X_13) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_277,plain,
! [X_126,Z_122,Y_123,U_125,V_124,W_127] :
( ~ sum(U_125,Z_122,W_127)
| ~ sum(Y_123,Z_122,V_124)
| ~ sum(X_126,Y_123,U_125)
| sum(X_126,V_124,W_127) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_3048,plain,
! [Y_241,X_242,V_243,X_244] :
( ~ sum(Y_241,X_242,V_243)
| ~ sum(X_244,Y_241,additive_identity)
| sum(X_244,V_243,X_242)
| ~ defined(X_242) ),
inference(resolution,[status(thm)],[c_6,c_277]) ).
tff(c_3096,plain,
! [X_244] :
( ~ sum(X_244,a,additive_identity)
| sum(X_244,b,additive_identity)
| ~ defined(additive_identity) ),
inference(resolution,[status(thm)],[c_83,c_3048]) ).
tff(c_3166,plain,
! [X_245] :
( ~ sum(X_245,a,additive_identity)
| sum(X_245,b,additive_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_3096]) ).
tff(c_10,plain,
! [X_16,Y_15,Z_17] :
( ~ sum(X_16,Y_15,Z_17)
| sum(Y_15,X_16,Z_17) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_3249,plain,
! [X_248] :
( sum(b,X_248,additive_identity)
| ~ sum(X_248,a,additive_identity) ),
inference(resolution,[status(thm)],[c_3166,c_10]) ).
tff(c_3255,plain,
( sum(b,additive_inverse(a),additive_identity)
| ~ defined(a) ),
inference(resolution,[status(thm)],[c_8,c_3249]) ).
tff(c_3261,plain,
sum(b,additive_inverse(a),additive_identity),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_3255]) ).
tff(c_3263,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_60,c_3261]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : FLD023-3 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.06/0.12 % 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
% 0.11/0.32 % Computer : n031.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Apr 7 18:43:07 EDT 2025
% 0.11/0.32 % CPUTime :
% 8.13/3.24 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.13/3.24
% 8.13/3.24 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------