%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : CAT014-4 : 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/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 : n027.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 05:46:30 PM UTC 2025
% Result : Unsatisfiable 3.47s 1.84s
% Output : CNFRefutation 3.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 30 ( 16 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 17 ( 10 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 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 : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 23 ( 23 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ equivalent > there_exists > compose > #nlpp > domain > codomain > 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(codomain,type,
codomain: $i > $i ).
tff(compose,type,
compose: ( $i * $i ) > $i ).
tff(f_108,axiom,
there_exists(codomain(a)),
file(unknown,unknown) ).
tff(f_81,axiom,
! [X] :
( ~ there_exists(codomain(X))
| there_exists(X) ),
file(unknown,unknown) ).
tff(f_105,axiom,
! [X] : ( compose(codomain(X),X) = X ),
file(unknown,unknown) ).
tff(f_101,axiom,
! [X,Y,Z] : ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) ),
file(unknown,unknown) ).
tff(f_91,axiom,
! [X,Y] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) ),
file(unknown,unknown) ).
tff(f_103,axiom,
! [X] : ( compose(X,domain(X)) = X ),
file(unknown,unknown) ).
tff(f_110,axiom,
codomain(codomain(a)) != codomain(a),
file(unknown,unknown) ).
tff(c_24,plain,
there_exists(codomain(a)),
inference(cnfTransformation,[status(thm)],[f_108]) ).
tff(c_42,plain,
! [X_24] :
( there_exists(X_24)
| ~ there_exists(codomain(X_24)) ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_46,plain,
there_exists(a),
inference(resolution,[status(thm)],[c_24,c_42]) ).
tff(c_22,plain,
! [X_19] : ( compose(codomain(X_19),X_19) = X_19 ),
inference(cnfTransformation,[status(thm)],[f_105]) ).
tff(c_92,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_101]) ).
tff(c_471,plain,
! [X_50,Z_51] : ( compose(codomain(X_50),compose(X_50,Z_51)) = compose(X_50,Z_51) ),
inference(superposition,[status(thm),theory(equality)],[c_22,c_92]) ).
tff(c_519,plain,
! [X_19] : ( compose(codomain(codomain(X_19)),X_19) = compose(codomain(X_19),X_19) ),
inference(superposition,[status(thm),theory(equality)],[c_22,c_471]) ).
tff(c_536,plain,
! [X_52] : ( compose(codomain(codomain(X_52)),X_52) = X_52 ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_519]) ).
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_91]) ).
tff(c_649,plain,
! [X_58] :
( ( domain(codomain(codomain(X_58))) = codomain(X_58) )
| ~ there_exists(X_58) ),
inference(superposition,[status(thm),theory(equality)],[c_536,c_14]) ).
tff(c_20,plain,
! [X_18] : ( compose(X_18,domain(X_18)) = X_18 ),
inference(cnfTransformation,[status(thm)],[f_103]) ).
tff(c_691,plain,
! [X_58] :
( ( compose(codomain(codomain(X_58)),codomain(X_58)) = codomain(codomain(X_58)) )
| ~ there_exists(X_58) ),
inference(superposition,[status(thm),theory(equality)],[c_649,c_20]) ).
tff(c_708,plain,
! [X_59] :
( ( codomain(codomain(X_59)) = codomain(X_59) )
| ~ there_exists(X_59) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_691]) ).
tff(c_26,plain,
codomain(codomain(a)) != codomain(a),
inference(cnfTransformation,[status(thm)],[f_110]) ).
tff(c_768,plain,
~ there_exists(a),
inference(superposition,[status(thm),theory(equality)],[c_708,c_26]) ).
tff(c_791,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_46,c_768]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : CAT014-4 : TPTP v9.0.0. Released v1.0.0.
% 0.03/0.13 % 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 : n027.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 15:38:50 EDT 2025
% 0.12/0.34 % CPUTime :
% 3.47/1.84 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.47/1.85
% 3.47/1.85 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------