%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : COL015-1 : 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/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 : n022.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 3.11s 1.90s
% Output : CNFRefutation 3.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 9 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 9 ( 8 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 13 ( 13 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ apply > #nlpp > q > m > combinator
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(m,type,
m: $i ).
tff(apply,type,
apply: ( $i * $i ) > $i ).
tff(combinator,type,
combinator: $i ).
tff(q,type,
q: $i ).
tff(f_29,axiom,
! [X,Y,Z] : ( apply(apply(apply(q,X),Y),Z) = apply(Y,apply(X,Z)) ),
file(unknown,unknown) ).
tff(f_27,axiom,
! [X] : ( apply(m,X) = apply(X,X) ),
file(unknown,unknown) ).
tff(f_32,axiom,
! [Y] : ( Y != apply(combinator,Y) ),
file(unknown,unknown) ).
tff(c_25,plain,
! [X_8,Y_9,Z_10] : ( apply(apply(apply(q,X_8),Y_9),Z_10) = apply(Y_9,apply(X_8,Z_10)) ),
inference(cnfTransformation,[status(thm)],[f_29]) ).
tff(c_2,plain,
! [X_1] : ( apply(m,X_1) = apply(X_1,X_1) ),
inference(cnfTransformation,[status(thm)],[f_27]) ).
tff(c_125,plain,
! [Y_15,X_16] : ( apply(Y_15,apply(X_16,apply(apply(q,X_16),Y_15))) = apply(m,apply(apply(q,X_16),Y_15)) ),
inference(superposition,[status(thm),theory(equality)],[c_25,c_2]) ).
tff(c_6,plain,
! [Y_5] : ( apply(combinator,Y_5) != Y_5 ),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_179,plain,
! [X_16] : ( apply(m,apply(apply(q,X_16),combinator)) != apply(X_16,apply(apply(q,X_16),combinator)) ),
inference(superposition,[status(thm),theory(equality)],[c_125,c_6]) ).
tff(c_281,plain,
$false,
inference(reflexivity,[status(thm),theory(equality)],[c_179]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : COL015-1 : TPTP v9.0.0. Released v1.0.0.
% 0.11/0.14 % 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
% 0.13/0.35 % Computer : n022.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Apr 7 15:54:36 EDT 2025
% 0.13/0.35 % CPUTime :
% 3.11/1.90 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.11/1.90
% 3.11/1.90 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------