%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : COL004-3 : 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 : n017.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 05:47:45 PM UTC 2025
% Result : Unsatisfiable 2.69s 1.79s
% Output : CNFRefutation 2.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 12 ( 11 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 9 ( 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 16 ( 16 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ apply > #nlpp > y > x > s > k
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(x,type,
x: $i ).
tff(apply,type,
apply: ( $i * $i ) > $i ).
tff(s,type,
s: $i ).
tff(k,type,
k: $i ).
tff(y,type,
y: $i ).
tff(f_28,axiom,
! [X,Y] : ( apply(apply(k,X),Y) = X ),
file(unknown,unknown) ).
tff(f_26,axiom,
! [X,Y,Z] : ( apply(apply(apply(s,X),Y),Z) = apply(apply(X,Z),apply(Y,Z)) ),
file(unknown,unknown) ).
tff(f_31,axiom,
apply(apply(apply(apply(s,apply(k,apply(s,apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),x),y) != apply(y,apply(apply(x,x),y)),
file(unknown,unknown) ).
tff(c_4,plain,
! [X_4,Y_5] : ( apply(apply(k,X_4),Y_5) = X_4 ),
inference(cnfTransformation,[status(thm)],[f_28]) ).
tff(c_18,plain,
! [X_8,Y_9,Z_10] : ( apply(apply(apply(s,X_8),Y_9),Z_10) = apply(apply(X_8,Z_10),apply(Y_9,Z_10)) ),
inference(cnfTransformation,[status(thm)],[f_26]) ).
tff(c_69,plain,
! [X_4,Y_9,Y_5] : ( apply(apply(apply(s,apply(k,X_4)),Y_9),Y_5) = apply(X_4,apply(Y_9,Y_5)) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_18]) ).
tff(c_2,plain,
! [X_1,Y_2,Z_3] : ( apply(apply(apply(s,X_1),Y_2),Z_3) = apply(apply(X_1,Z_3),apply(Y_2,Z_3)) ),
inference(cnfTransformation,[status(thm)],[f_26]) ).
tff(c_6,plain,
apply(apply(apply(apply(s,apply(k,apply(s,apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),x),y) != apply(y,apply(apply(x,x),y)),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_7,plain,
apply(apply(apply(apply(k,apply(s,apply(apply(s,k),k))),x),apply(apply(apply(s,apply(k,x)),apply(k,x)),apply(k,x))),y) != apply(y,apply(apply(x,x),y)),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2,c_2,c_2,c_2,c_6]) ).
tff(c_8,plain,
apply(y,apply(apply(apply(apply(s,apply(k,x)),apply(k,x)),apply(k,x)),y)) != apply(y,apply(apply(x,x),y)),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_2,c_2,c_4,c_7]) ).
tff(c_151,plain,
apply(y,apply(apply(x,apply(apply(k,x),apply(k,x))),y)) != apply(y,apply(apply(x,x),y)),
inference(demodulation,[status(thm),theory(equality)],[c_69,c_8]) ).
tff(c_154,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_151]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : COL004-3 : TPTP v9.0.0. Released v1.0.0.
% 0.13/0.13 % 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 : n017.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 15:51:55 EDT 2025
% 0.13/0.34 % CPUTime :
% 2.69/1.79 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.69/1.79
% 2.69/1.79 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------