%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : CAT009-3 : 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 : n016.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 34.31s 19.24s
% Output : CNFRefutation 34.31s
% 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 : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 26 ( 26 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ equivalent > there_exists > f1 > 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(f1,type,
f1: ( $i * $i ) > $i ).
tff(f_158,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_160,axiom,
domain(compose(a,b)) != domain(b),
file(unknown,unknown) ).
tff(c_36,plain,
there_exists(compose(a,b)),
inference(cnfTransformation,[status(thm)],[f_158]) ).
tff(c_123,plain,
! [X_52,Y_53] :
( ( domain(X_52) = codomain(Y_53) )
| ~ there_exists(compose(X_52,Y_53)) ),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_133,plain,
domain(a) = codomain(b),
inference(resolution,[status(thm)],[c_36,c_123]) ).
tff(c_97,plain,
! [X_48,Y_49] :
( there_exists(domain(X_48))
| ~ there_exists(compose(X_48,Y_49)) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_107,plain,
there_exists(domain(a)),
inference(resolution,[status(thm)],[c_36,c_97]) ).
tff(c_134,plain,
there_exists(codomain(b)),
inference(demodulation,[status(thm),theory(equality)],[c_133,c_107]) ).
tff(c_10,plain,
! [X_8] :
( there_exists(X_8)
| ~ there_exists(codomain(X_8)) ),
inference(cnfTransformation,[status(thm)],[f_82]) ).
tff(c_154,plain,
there_exists(b),
inference(resolution,[status(thm)],[c_134,c_10]) ).
tff(c_20,plain,
! [X_18] : ( compose(X_18,domain(X_18)) = X_18 ),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_126,plain,
! [X_18] :
( ( codomain(domain(X_18)) = domain(X_18) )
| ~ there_exists(X_18) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_123]) ).
tff(c_175,plain,
! [X_54,Y_55,Z_56] : ( compose(compose(X_54,Y_55),Z_56) = compose(X_54,compose(Y_55,Z_56)) ),
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_66793,plain,
! [X_10650,Y_10651,Z_10652] :
( ( domain(compose(X_10650,Y_10651)) = codomain(Z_10652) )
| ~ there_exists(compose(X_10650,compose(Y_10651,Z_10652))) ),
inference(superposition,[status(thm),theory(equality)],[c_175,c_14]) ).
tff(c_228511,plain,
! [X_36731,X_36732] :
( ( domain(compose(X_36731,X_36732)) = codomain(domain(X_36732)) )
| ~ there_exists(compose(X_36731,X_36732)) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_66793]) ).
tff(c_229478,plain,
domain(compose(a,b)) = codomain(domain(b)),
inference(resolution,[status(thm)],[c_36,c_228511]) ).
tff(c_38,plain,
domain(compose(a,b)) != domain(b),
inference(cnfTransformation,[status(thm)],[f_160]) ).
tff(c_229479,plain,
codomain(domain(b)) != domain(b),
inference(demodulation,[status(thm),theory(equality)],[c_229478,c_38]) ).
tff(c_231908,plain,
~ there_exists(b),
inference(superposition,[status(thm),theory(equality)],[c_126,c_229479]) ).
tff(c_231935,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_154,c_231908]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12 % Problem : CAT009-3 : TPTP v9.0.0. Released v1.0.0.
% 0.09/0.12 % 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
% 0.10/0.33 % Computer : n016.cluster.edu
% 0.10/0.33 % Model : x86_64 x86_64
% 0.10/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.33 % Memory : 8042.1875MB
% 0.10/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.33 % CPULimit : 300
% 0.10/0.33 % WCLimit : 300
% 0.10/0.33 % DateTime : Mon Apr 7 15:38:23 EDT 2025
% 0.10/0.33 % CPUTime :
% 34.31/19.24 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 34.31/19.24
% 34.31/19.24 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------