%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : COL066-3 : TPTP v9.0.0. Bugfixed v1.2.0.
% 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 : n029.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 05:47:58 PM UTC 2025
% Result : Unsatisfiable 7.69s 3.34s
% Output : CNFRefutation 7.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 17 ( 16 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 10 ( 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; 6 con; 0-2 aty)
% Number of variables : 26 ( 26 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ apply > #nlpp > z > y > x > w > q > b
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(x,type,
x: $i ).
tff(apply,type,
apply: ( $i * $i ) > $i ).
tff(w,type,
w: $i ).
tff(b,type,
b: $i ).
tff(y,type,
y: $i ).
tff(q,type,
q: $i ).
tff(z,type,
z: $i ).
tff(f_32,axiom,
! [X,Y] : ( apply(apply(w,X),Y) = apply(apply(X,Y),Y) ),
file(unknown,unknown) ).
tff(f_30,axiom,
! [X,Y,Z] : ( apply(apply(apply(q,X),Y),Z) = apply(Y,apply(X,Z)) ),
file(unknown,unknown) ).
tff(f_28,axiom,
! [X,Y,Z] : ( apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ),
file(unknown,unknown) ).
tff(f_35,axiom,
apply(apply(apply(apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x),y),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
file(unknown,unknown) ).
tff(c_6,plain,
! [X_7,Y_8] : ( apply(apply(w,X_7),Y_8) = apply(apply(X_7,Y_8),Y_8) ),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_93,plain,
! [X_12,Y_13,Z_14] : ( apply(apply(apply(q,X_12),Y_13),Z_14) = apply(Y_13,apply(X_12,Z_14)) ),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_122,plain,
! [Y_8,Z_14] : ( apply(apply(apply(w,q),Y_8),Z_14) = apply(Y_8,apply(Y_8,Z_14)) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_93]) ).
tff(c_4,plain,
! [X_4,Y_5,Z_6] : ( apply(apply(apply(q,X_4),Y_5),Z_6) = apply(Y_5,apply(X_4,Z_6)) ),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_107,plain,
! [X_12,Y_13,Z_14] : ( apply(apply(w,apply(apply(q,X_12),Y_13)),Z_14) = apply(apply(Y_13,apply(X_12,Z_14)),Z_14) ),
inference(superposition,[status(thm),theory(equality)],[c_93,c_6]) ).
tff(c_126,plain,
! [X_12,Y_8] : ( apply(apply(w,apply(q,X_12)),Y_8) = apply(Y_8,apply(X_12,Y_8)) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_93]) ).
tff(c_2,plain,
! [X_1,Y_2,Z_3] : ( apply(apply(apply(b,X_1),Y_2),Z_3) = apply(X_1,apply(Y_2,Z_3)) ),
inference(cnfTransformation,[status(thm)],[f_28]) ).
tff(c_8,plain,
apply(apply(apply(apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x),y),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_9,plain,
apply(apply(apply(w,apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x)),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_8]) ).
tff(c_10,plain,
apply(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_9]) ).
tff(c_1077,plain,
apply(apply(apply(w,apply(apply(q,x),apply(apply(q,q),apply(q,x)))),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(demodulation,[status(thm),theory(equality)],[c_126,c_10]) ).
tff(c_3282,plain,
apply(apply(apply(apply(apply(q,q),apply(q,x)),apply(x,y)),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(demodulation,[status(thm),theory(equality)],[c_107,c_1077]) ).
tff(c_3285,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_122,c_6,c_4,c_4,c_3282]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COL066-3 : TPTP v9.0.0. Bugfixed v1.2.0.
% 0.07/0.13 % 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
% 0.13/0.34 % Computer : n029.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 16:00:34 EDT 2025
% 0.13/0.34 % CPUTime :
% 7.69/3.34 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.69/3.35
% 7.69/3.35 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------