%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : TOP002-2 : 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 : n018.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 10:52:22 PM UTC 2025
% Result : Unsatisfiable 2.48s 1.59s
% Output : CNFRefutation 2.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 8 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 10 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 4 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 7 ( 7 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ element_of_set > element_of_collection > f11 > #nlpp > top_of_basis > f > empty_set
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(f11,type,
f11: ( $i * $i ) > $i ).
tff(element_of_collection,type,
element_of_collection: ( $i * $i ) > $o ).
tff(f,type,
f: $i ).
tff(element_of_set,type,
element_of_set: ( $i * $i ) > $o ).
tff(top_of_basis,type,
top_of_basis: $i > $i ).
tff(empty_set,type,
empty_set: $i ).
tff(f_31,axiom,
! [U,Vf] :
( element_of_collection(U,top_of_basis(Vf))
| element_of_set(f11(Vf,U),U) ),
file(unknown,unknown) ).
tff(f_34,axiom,
! [X] : ~ element_of_set(X,empty_set),
file(unknown,unknown) ).
tff(f_39,axiom,
~ element_of_collection(empty_set,top_of_basis(f)),
file(unknown,unknown) ).
tff(c_8,plain,
! [Vf_5,U_6] :
( element_of_set(f11(Vf_5,U_6),U_6)
| element_of_collection(U_6,top_of_basis(Vf_5)) ),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_4,plain,
! [X_3] : ~ element_of_set(X_3,empty_set),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_13,plain,
! [Vf_5] : element_of_collection(empty_set,top_of_basis(Vf_5)),
inference(resolution,[status(thm)],[c_8,c_4]) ).
tff(c_6,plain,
~ element_of_collection(empty_set,top_of_basis(f)),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_16,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_13,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : TOP002-2 : TPTP v9.0.0. Released v1.0.0.
% 0.12/0.14 % 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
% 0.14/0.35 % Computer : n018.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Apr 9 10:28:47 EDT 2025
% 0.14/0.35 % CPUTime :
% 2.48/1.59 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.48/1.59
% 2.48/1.59 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------