%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : CAT005-4 : 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 : n012.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 05:46:26 PM UTC 2025
% Result : Unsatisfiable 2.92s 1.76s
% Output : CNFRefutation 3.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 37 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 54 ( 21 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 37 ( 20 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 1 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 : 22 ( 22 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ equivalent > there_exists > compose > #nlpp > domain > codomain > d > 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(d,type,
d: $i ).
tff(compose,type,
compose: ( $i * $i ) > $i ).
tff(f_121,axiom,
domain(a) != d,
file(unknown,unknown) ).
tff(f_109,axiom,
there_exists(compose(a,d)),
file(unknown,unknown) ).
tff(f_86,axiom,
! [X,Y] :
( ~ there_exists(compose(X,Y))
| there_exists(domain(X)) ),
file(unknown,unknown) ).
tff(f_76,axiom,
! [X] :
( ~ there_exists(domain(X))
| there_exists(X) ),
file(unknown,unknown) ).
tff(f_103,axiom,
! [X] : ( compose(X,domain(X)) = X ),
file(unknown,unknown) ).
tff(f_119,axiom,
! [Y] :
( ~ there_exists(compose(d,Y))
| ( compose(d,Y) = Y ) ),
file(unknown,unknown) ).
tff(f_91,axiom,
! [X,Y] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) ),
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_114,axiom,
! [X] :
( ~ there_exists(compose(X,d))
| ( compose(X,d) = X ) ),
file(unknown,unknown) ).
tff(c_30,plain,
domain(a) != d,
inference(cnfTransformation,[status(thm)],[f_121]) ).
tff(c_24,plain,
there_exists(compose(a,d)),
inference(cnfTransformation,[status(thm)],[f_109]) ).
tff(c_63,plain,
! [X_31,Y_32] :
( there_exists(domain(X_31))
| ~ there_exists(compose(X_31,Y_32)) ),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_73,plain,
there_exists(domain(a)),
inference(resolution,[status(thm)],[c_24,c_63]) ).
tff(c_8,plain,
! [X_7] :
( there_exists(X_7)
| ~ there_exists(domain(X_7)) ),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_77,plain,
there_exists(a),
inference(resolution,[status(thm)],[c_73,c_8]) ).
tff(c_20,plain,
! [X_18] : ( compose(X_18,domain(X_18)) = X_18 ),
inference(cnfTransformation,[status(thm)],[f_103]) ).
tff(c_93,plain,
! [Y_36] :
( ( compose(d,Y_36) = Y_36 )
| ~ there_exists(compose(d,Y_36)) ),
inference(cnfTransformation,[status(thm)],[f_119]) ).
tff(c_97,plain,
( ( compose(d,domain(d)) = domain(d) )
| ~ there_exists(d) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_93]) ).
tff(c_98,plain,
( ( domain(d) = d )
| ~ there_exists(d) ),
inference(demodulation,[status(thm),theory(equality)],[c_20,c_97]) ).
tff(c_99,plain,
~ there_exists(d),
inference(splitLeft,[status(thm)],[c_98]) ).
tff(c_110,plain,
! [X_38,Y_39] :
( ( domain(X_38) = codomain(Y_39) )
| ~ there_exists(compose(X_38,Y_39)) ),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_120,plain,
domain(a) = codomain(d),
inference(resolution,[status(thm)],[c_24,c_110]) ).
tff(c_142,plain,
there_exists(codomain(d)),
inference(demodulation,[status(thm),theory(equality)],[c_120,c_73]) ).
tff(c_10,plain,
! [X_8] :
( there_exists(X_8)
| ~ there_exists(codomain(X_8)) ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_162,plain,
there_exists(d),
inference(resolution,[status(thm)],[c_142,c_10]) ).
tff(c_166,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_99,c_162]) ).
tff(c_168,plain,
there_exists(d),
inference(splitRight,[status(thm)],[c_98]) ).
tff(c_22,plain,
! [X_19] : ( compose(codomain(X_19),X_19) = X_19 ),
inference(cnfTransformation,[status(thm)],[f_105]) ).
tff(c_186,plain,
! [X_40] :
( ( compose(X_40,d) = X_40 )
| ~ there_exists(compose(X_40,d)) ),
inference(cnfTransformation,[status(thm)],[f_114]) ).
tff(c_190,plain,
( ( compose(codomain(d),d) = codomain(d) )
| ~ there_exists(d) ),
inference(superposition,[status(thm),theory(equality)],[c_22,c_186]) ).
tff(c_195,plain,
codomain(d) = d,
inference(demodulation,[status(thm),theory(equality)],[c_168,c_22,c_190]) ).
tff(c_196,plain,
compose(a,d) = a,
inference(resolution,[status(thm)],[c_24,c_186]) ).
tff(c_254,plain,
! [X_41,Y_42] :
( ( domain(X_41) = codomain(Y_42) )
| ~ there_exists(compose(X_41,Y_42)) ),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_260,plain,
( ( domain(a) = codomain(d) )
| ~ there_exists(a) ),
inference(superposition,[status(thm),theory(equality)],[c_196,c_254]) ).
tff(c_270,plain,
domain(a) = d,
inference(demodulation,[status(thm),theory(equality)],[c_77,c_195,c_260]) ).
tff(c_272,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_30,c_270]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : CAT005-4 : TPTP v9.0.0. Released v1.0.0.
% 0.10/0.13 % 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
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Apr 7 15:37:45 EDT 2025
% 0.13/0.34 % CPUTime :
% 2.92/1.76 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.92/1.77
% 2.92/1.77 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------