%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : COL075-2 : TPTP v9.0.0. Released v1.2.0.
% 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 : 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 05:47:59 PM UTC 2025
% Result : Unsatisfiable 3.09s 1.86s
% Output : CNFRefutation 3.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 11 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 11 ( 10 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 : 5 ( 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; 2 con; 0-2 aty)
% Number of variables : 22 ( 22 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ apply > #nlpp > c > b > k > abstraction
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(apply,type,
apply: ( $i * $i ) > $i ).
tff(b,type,
b: $i > $i ).
tff(c,type,
c: $i > $i ).
tff(k,type,
k: $i ).
tff(abstraction,type,
abstraction: $i ).
tff(f_30,axiom,
! [X,Y] : ( apply(apply(k,X),Y) = X ),
file(unknown,unknown) ).
tff(f_36,axiom,
! [X,Y,Z] : ( apply(apply(apply(abstraction,X),Y),Z) = apply(apply(X,apply(k,Z)),apply(Y,Z)) ),
file(unknown,unknown) ).
tff(f_40,axiom,
! [Y] : ( apply(apply(Y,b(Y)),c(Y)) != apply(b(Y),b(Y)) ),
file(unknown,unknown) ).
tff(c_2,plain,
! [X_1,Y_2] : ( apply(apply(k,X_1),Y_2) = X_1 ),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_4,plain,
! [X_3,Z_5,Y_4] : ( apply(apply(X_3,apply(k,Z_5)),apply(Y_4,Z_5)) = apply(apply(apply(abstraction,X_3),Y_4),Z_5) ),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_26,plain,
! [X_11,Z_12,Y_13] : ( apply(apply(X_11,apply(k,Z_12)),apply(Y_13,Z_12)) = apply(apply(apply(abstraction,X_11),Y_13),Z_12) ),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_281,plain,
! [X_29,X_30,Y_31] : ( apply(apply(apply(abstraction,X_29),apply(k,X_30)),Y_31) = apply(apply(X_29,apply(k,Y_31)),X_30) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_26]) ).
tff(c_354,plain,
! [Z_5,Y_31] : ( apply(apply(apply(k,Z_5),apply(k,Y_31)),Z_5) = apply(apply(apply(apply(abstraction,abstraction),k),Z_5),Y_31) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_281]) ).
tff(c_370,plain,
! [Z_32,Y_33] : ( apply(apply(apply(apply(abstraction,abstraction),k),Z_32),Y_33) = apply(Z_32,Z_32) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_354]) ).
tff(c_6,plain,
! [Y_6] : ( apply(apply(Y_6,b(Y_6)),c(Y_6)) != apply(b(Y_6),b(Y_6)) ),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_512,plain,
$false,
inference(superposition,[status(thm),theory(equality)],[c_370,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : COL075-2 : TPTP v9.0.0. Released v1.2.0.
% 0.11/0.13 % 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 : 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 16:01:25 EDT 2025
% 0.13/0.34 % CPUTime :
% 3.09/1.86 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.09/1.87
% 3.09/1.87 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------