%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : CAT009-4 : 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 05:46:27 PM UTC 2025
% Result : Unsatisfiable 9.22s 3.74s
% Output : CNFRefutation 9.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 26 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 36 ( 15 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 24 ( 14 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 26 ( 26 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ equivalent > there_exists > compose > #nlpp > domain > codomain > b > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(equivalent,type,
equivalent: ( $i * $i ) > $o ).
tff(a,type,
a: $i ).
tff(domain,type,
domain: $i > $i ).
tff(there_exists,type,
there_exists: $i > $o ).
tff(b,type,
b: $i ).
tff(codomain,type,
codomain: $i > $i ).
tff(compose,type,
compose: ( $i * $i ) > $i ).
tff(f_109,axiom,
there_exists(compose(a,b)),
file(unknown,unknown) ).
tff(f_92,axiom,
! [X,Y] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) ),
file(unknown,unknown) ).
tff(f_87,axiom,
! [X,Y] :
( ~ there_exists(compose(X,Y))
| there_exists(domain(X)) ),
file(unknown,unknown) ).
tff(f_82,axiom,
! [X] :
( ~ there_exists(codomain(X))
| there_exists(X) ),
file(unknown,unknown) ).
tff(f_104,axiom,
! [X] : ( compose(X,domain(X)) = X ),
file(unknown,unknown) ).
tff(f_102,axiom,
! [X,Y,Z] : ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) ),
file(unknown,unknown) ).
tff(f_111,axiom,
domain(compose(a,b)) != domain(b),
file(unknown,unknown) ).
tff(c_24,plain,
there_exists(compose(a,b)),
inference(cnfTransformation,[status(thm)],[f_109]) ).
tff(c_89,plain,
! [X_34,Y_35] :
( ( domain(X_34) = codomain(Y_35) )
| ~ there_exists(compose(X_34,Y_35)) ),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_99,plain,
domain(a) = codomain(b),
inference(resolution,[status(thm)],[c_24,c_89]) ).
tff(c_59,plain,
! [X_29,Y_30] :
( there_exists(domain(X_29))
| ~ there_exists(compose(X_29,Y_30)) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_69,plain,
there_exists(domain(a)),
inference(resolution,[status(thm)],[c_24,c_59]) ).
tff(c_100,plain,
there_exists(codomain(b)),
inference(demodulation,[status(thm),theory(equality)],[c_99,c_69]) ).
tff(c_10,plain,
! [X_8] :
( there_exists(X_8)
| ~ there_exists(codomain(X_8)) ),
inference(cnfTransformation,[status(thm)],[f_82]) ).
tff(c_120,plain,
there_exists(b),
inference(resolution,[status(thm)],[c_100,c_10]) ).
tff(c_20,plain,
! [X_18] : ( compose(X_18,domain(X_18)) = X_18 ),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_95,plain,
! [X_18] :
( ( codomain(domain(X_18)) = domain(X_18) )
| ~ there_exists(X_18) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_89]) ).
tff(c_121,plain,
! [X_36,Y_37,Z_38] : ( compose(compose(X_36,Y_37),Z_38) = compose(X_36,compose(Y_37,Z_38)) ),
inference(cnfTransformation,[status(thm)],[f_102]) ).
tff(c_14,plain,
! [X_11,Y_12] :
( ( domain(X_11) = codomain(Y_12) )
| ~ there_exists(compose(X_11,Y_12)) ),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_3370,plain,
! [X_92,Y_93,Z_94] :
( ( domain(compose(X_92,Y_93)) = codomain(Z_94) )
| ~ there_exists(compose(X_92,compose(Y_93,Z_94))) ),
inference(superposition,[status(thm),theory(equality)],[c_121,c_14]) ).
tff(c_8526,plain,
! [X_136,X_137] :
( ( domain(compose(X_136,X_137)) = codomain(domain(X_137)) )
| ~ there_exists(compose(X_136,X_137)) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_3370]) ).
tff(c_8666,plain,
domain(compose(a,b)) = codomain(domain(b)),
inference(resolution,[status(thm)],[c_24,c_8526]) ).
tff(c_26,plain,
domain(compose(a,b)) != domain(b),
inference(cnfTransformation,[status(thm)],[f_111]) ).
tff(c_8667,plain,
codomain(domain(b)) != domain(b),
inference(demodulation,[status(thm),theory(equality)],[c_8666,c_26]) ).
tff(c_8843,plain,
~ there_exists(b),
inference(superposition,[status(thm),theory(equality)],[c_95,c_8667]) ).
tff(c_8847,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_120,c_8843]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : CAT009-4 : TPTP v9.0.0. Released v1.0.0.
% 0.00/0.09 % 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
% 0.08/0.29 % Computer : n003.cluster.edu
% 0.08/0.29 % Model : x86_64 x86_64
% 0.08/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.29 % Memory : 8042.1875MB
% 0.08/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.29 % CPULimit : 300
% 0.08/0.29 % WCLimit : 300
% 0.08/0.29 % DateTime : Mon Apr 7 15:38:18 EDT 2025
% 0.08/0.29 % CPUTime :
% 9.22/3.74 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.22/3.75
% 9.22/3.75 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------