%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : COL012-1 : 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 : n032.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 05:47:47 PM UTC 2025
% Result : Unsatisfiable 2.76s 1.99s
% Output : CNFRefutation 2.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 2
% Syntax : Number of formulae : 6 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 6 ( 5 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 3 avg)
% Maximal term depth : 4 ( 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 : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 7 ( 7 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ apply > #nlpp > u > combinator
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(apply,type,
apply: ( $i * $i ) > $i ).
tff(u,type,
u: $i ).
tff(combinator,type,
combinator: $i ).
tff(f_27,axiom,
! [X,Y] : ( apply(apply(u,X),Y) = apply(Y,apply(apply(X,X),Y)) ),
file(unknown,unknown) ).
tff(f_30,axiom,
! [Y] : ( Y != apply(combinator,Y) ),
file(unknown,unknown) ).
tff(c_6,plain,
! [Y_5,X_6] : ( apply(Y_5,apply(apply(X_6,X_6),Y_5)) = apply(apply(u,X_6),Y_5) ),
inference(cnfTransformation,[status(thm)],[f_27]) ).
tff(c_4,plain,
! [Y_3] : ( apply(combinator,Y_3) != Y_3 ),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_17,plain,
! [X_6] : ( apply(apply(u,X_6),combinator) != apply(apply(X_6,X_6),combinator) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_4]) ).
tff(c_30,plain,
$false,
inference(reflexivity,[status(thm),theory(equality)],[c_17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : COL012-1 : TPTP v9.0.0. Released v1.0.0.
% 0.00/0.08 % 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
% 0.06/0.26 % Computer : n032.cluster.edu
% 0.06/0.26 % Model : x86_64 x86_64
% 0.06/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.26 % Memory : 8042.1875MB
% 0.06/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.26 % CPULimit : 300
% 0.06/0.26 % WCLimit : 300
% 0.06/0.26 % DateTime : Mon Apr 7 15:53:31 EDT 2025
% 0.06/0.26 % CPUTime :
% 2.76/1.99 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.76/2.00
% 2.76/2.00 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------