%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : COL023-1 : 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 : 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 05:47:48 PM UTC 2025
% Result : Unsatisfiable 4.84s 2.22s
% Output : CNFRefutation 5.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 10 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 10 ( 9 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 4 avg)
% Maximal term depth : 6 ( 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 22 ( 22 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ apply > #nlpp > n > combinator > b
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(apply,type,
apply: ( $i * $i ) > $i ).
tff(combinator,type,
combinator: $i ).
tff(b,type,
b: $i ).
tff(n,type,
n: $i ).
tff(f_28,axiom,
! [X,Y,Z] : ( apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ),
file(unknown,unknown) ).
tff(f_30,axiom,
! [X,Y,Z] : ( apply(apply(apply(n,X),Y),Z) = apply(apply(apply(X,Z),Y),Z) ),
file(unknown,unknown) ).
tff(f_33,axiom,
! [Y] : ( Y != apply(combinator,Y) ),
file(unknown,unknown) ).
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_17,plain,
! [X_12,Y_13,Z_14] : ( apply(apply(apply(n,X_12),Y_13),Z_14) = apply(apply(apply(X_12,Z_14),Y_13),Z_14) ),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_253,plain,
! [X_19,Z_20,Y_21] : ( apply(apply(apply(n,apply(b,X_19)),Z_20),Y_21) = apply(apply(X_19,apply(Y_21,Z_20)),Y_21) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_17]) ).
tff(c_1730,plain,
! [X_35,Z_36,Y_37] : ( apply(apply(apply(n,apply(b,apply(b,X_35))),Z_36),Y_37) = apply(X_35,apply(apply(Y_37,Z_36),Y_37)) ),
inference(superposition,[status(thm),theory(equality)],[c_253,c_2]) ).
tff(c_6,plain,
! [Y_7] : ( apply(combinator,Y_7) != Y_7 ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_2003,plain,
! [Z_36,Y_37] : ( apply(apply(apply(n,apply(b,apply(b,combinator))),Z_36),Y_37) != apply(apply(Y_37,Z_36),Y_37) ),
inference(superposition,[status(thm),theory(equality)],[c_1730,c_6]) ).
tff(c_2231,plain,
$false,
inference(reflexivity,[status(thm),theory(equality)],[c_2003]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COL023-1 : TPTP v9.0.0. Released v1.0.0.
% 0.12/0.12 % 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
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Apr 7 15:54:48 EDT 2025
% 0.12/0.33 % CPUTime :
% 4.84/2.22 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.84/2.22
% 4.84/2.22 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------