%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : CAT002-3 : 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 : 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 05:46:24 PM UTC 2025
% Result : Unsatisfiable 15.70s 5.33s
% Output : CNFRefutation 15.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 16 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 24 ( 23 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 18 ( 10 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 18 ( 18 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ equivalent > there_exists > f1 > compose > #nlpp > domain > codomain > h > g > b > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(equivalent,type,
equivalent: ( $i * $i ) > $o ).
tff(h,type,
h: $i ).
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(g,type,
g: $i ).
tff(codomain,type,
codomain: $i > $i ).
tff(compose,type,
compose: ( $i * $i ) > $i ).
tff(f1,type,
f1: ( $i * $i ) > $i ).
tff(f_178,axiom,
g != h,
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_176,axiom,
compose(compose(a,b),h) = compose(compose(a,b),g),
file(unknown,unknown) ).
tff(f_166,axiom,
! [X,Y,Z] :
( ( compose(a,X) != Y )
| ( compose(a,Z) != Y )
| ( X = Z ) ),
file(unknown,unknown) ).
tff(f_174,axiom,
! [X,Y,Z] :
( ( compose(b,X) != Y )
| ( compose(b,Z) != Y )
| ( X = Z ) ),
file(unknown,unknown) ).
tff(c_46,plain,
h != g,
inference(cnfTransformation,[status(thm)],[f_178]) ).
tff(c_18,plain,
! [X_15,Y_16,Z_17] : ( compose(compose(X_15,Y_16),Z_17) = compose(X_15,compose(Y_16,Z_17)) ),
inference(cnfTransformation,[status(thm)],[f_102]) ).
tff(c_44,plain,
compose(compose(a,b),h) = compose(compose(a,b),g),
inference(cnfTransformation,[status(thm)],[f_176]) ).
tff(c_47,plain,
compose(a,compose(b,h)) = compose(a,compose(b,g)),
inference(demodulation,[status(thm),theory(equality)],[c_18,c_18,c_44]) ).
tff(c_38,plain,
! [Z_34,X_32] :
( ( Z_34 = X_32 )
| ( compose(a,Z_34) != compose(a,X_32) ) ),
inference(cnfTransformation,[status(thm)],[f_166]) ).
tff(c_349,plain,
! [X_32] :
( ( compose(b,h) = X_32 )
| ( compose(a,compose(b,g)) != compose(a,X_32) ) ),
inference(superposition,[status(thm),theory(equality)],[c_47,c_38]) ).
tff(c_73212,plain,
compose(b,h) = compose(b,g),
inference(reflexivity,[status(thm),theory(equality)],[c_349]) ).
tff(c_40,plain,
! [Z_37,X_35] :
( ( Z_37 = X_35 )
| ( compose(b,Z_37) != compose(b,X_35) ) ),
inference(cnfTransformation,[status(thm)],[f_174]) ).
tff(c_73669,plain,
! [X_35] :
( ( h = X_35 )
| ( compose(b,g) != compose(b,X_35) ) ),
inference(superposition,[status(thm),theory(equality)],[c_73212,c_40]) ).
tff(c_74225,plain,
h = g,
inference(reflexivity,[status(thm),theory(equality)],[c_73669]) ).
tff(c_74227,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_46,c_74225]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : CAT002-3 : TPTP v9.0.0. Released v1.0.0.
% 0.07/0.13 % 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
% 0.12/0.34 % 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 15:37:06 EDT 2025
% 0.12/0.34 % CPUTime :
% 15.70/5.33 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.70/5.33
% 15.70/5.33 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------