%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : COL031-1 : 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 : n019.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 05:47:49 PM UTC 2025
% Result : Unsatisfiable 5.60s 2.44s
% Output : CNFRefutation 5.60s
% 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 : 4 ( 4 ~; 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 12 ( 12 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ apply > #nlpp > f > o > l
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(apply,type,
apply: ( $i * $i ) > $i ).
tff(l,type,
l: $i ).
tff(f,type,
f: $i > $i ).
tff(o,type,
o: $i ).
tff(f_28,axiom,
! [X,Y] : ( apply(apply(l,X),Y) = apply(X,apply(Y,Y)) ),
file(unknown,unknown) ).
tff(f_30,axiom,
! [X,Y] : ( apply(apply(o,X),Y) = apply(Y,apply(X,Y)) ),
file(unknown,unknown) ).
tff(f_33,axiom,
! [Y] : ( apply(Y,f(Y)) != apply(f(Y),apply(Y,f(Y))) ),
file(unknown,unknown) ).
tff(c_2,plain,
! [X_1,Y_2] : ( apply(apply(l,X_1),Y_2) = apply(X_1,apply(Y_2,Y_2)) ),
inference(cnfTransformation,[status(thm)],[f_28]) ).
tff(c_4,plain,
! [X_3,Y_4] : ( apply(apply(o,X_3),Y_4) = apply(Y_4,apply(X_3,Y_4)) ),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_6,plain,
! [Y_5] : ( apply(f(Y_5),apply(Y_5,f(Y_5))) != apply(Y_5,f(Y_5)) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_88,plain,
! [Y_10] : ( apply(apply(o,Y_10),f(Y_10)) != apply(Y_10,f(Y_10)) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_6]) ).
tff(c_92,plain,
! [Y_2] : ( apply(apply(apply(l,o),Y_2),f(apply(Y_2,Y_2))) != apply(apply(Y_2,Y_2),f(apply(Y_2,Y_2))) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_88]) ).
tff(c_2592,plain,
$false,
inference(reflexivity,[status(thm),theory(equality)],[c_92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : COL031-1 : TPTP v9.0.0. Released v1.0.0.
% 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
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Apr 7 15:54:47 EDT 2025
% 0.12/0.34 % CPUTime :
% 5.60/2.44 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.60/2.44
% 5.60/2.44 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------