%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : CAT002-4 : 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 : n026.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 05:46:25 PM UTC 2025
% Result : Unsatisfiable 5.68s 2.39s
% Output : CNFRefutation 5.68s
% 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 18 ( 18 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ equivalent > there_exists > 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(f_129,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_127,axiom,
compose(compose(a,b),h) = compose(compose(a,b),g),
file(unknown,unknown) ).
tff(f_117,axiom,
! [X,Y,Z] :
( ( compose(a,X) != Y )
| ( compose(a,Z) != Y )
| ( X = Z ) ),
file(unknown,unknown) ).
tff(f_125,axiom,
! [X,Y,Z] :
( ( compose(b,X) != Y )
| ( compose(b,Z) != Y )
| ( X = Z ) ),
file(unknown,unknown) ).
tff(c_34,plain,
h != g,
inference(cnfTransformation,[status(thm)],[f_129]) ).
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_32,plain,
compose(compose(a,b),h) = compose(compose(a,b),g),
inference(cnfTransformation,[status(thm)],[f_127]) ).
tff(c_35,plain,
compose(a,compose(b,h)) = compose(a,compose(b,g)),
inference(demodulation,[status(thm),theory(equality)],[c_18,c_18,c_32]) ).
tff(c_26,plain,
! [Z_22,X_20] :
( ( Z_22 = X_20 )
| ( compose(a,Z_22) != compose(a,X_20) ) ),
inference(cnfTransformation,[status(thm)],[f_117]) ).
tff(c_381,plain,
! [Z_22] :
( ( compose(b,h) = Z_22 )
| ( compose(a,compose(b,g)) != compose(a,Z_22) ) ),
inference(superposition,[status(thm),theory(equality)],[c_35,c_26]) ).
tff(c_3527,plain,
compose(b,h) = compose(b,g),
inference(reflexivity,[status(thm),theory(equality)],[c_381]) ).
tff(c_28,plain,
! [Z_25,X_23] :
( ( Z_25 = X_23 )
| ( compose(b,Z_25) != compose(b,X_23) ) ),
inference(cnfTransformation,[status(thm)],[f_125]) ).
tff(c_3604,plain,
! [X_23] :
( ( h = X_23 )
| ( compose(b,g) != compose(b,X_23) ) ),
inference(superposition,[status(thm),theory(equality)],[c_3527,c_28]) ).
tff(c_3625,plain,
h = g,
inference(reflexivity,[status(thm),theory(equality)],[c_3604]) ).
tff(c_3627,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_34,c_3625]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : CAT002-4 : TPTP v9.0.0. Released v1.0.0.
% 0.02/0.12 % 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
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Apr 7 15:37:23 EDT 2025
% 0.12/0.33 % CPUTime :
% 5.68/2.39 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.68/2.40
% 5.68/2.40 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------