%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : CAT005-3 : 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/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 : n008.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 3.31s 1.84s
% Output : CNFRefutation 3.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 22 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 31 ( 12 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 21 ( 12 ~; 9 |; 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 : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 14 ( 14 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ equivalent > there_exists > f1 > 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(f1,type,
f1: ( $i * $i ) > $i ).
tff(f_158,axiom,
there_exists(compose(a,d)),
file(unknown,unknown) ).
tff(f_91,axiom,
! [X,Y] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) ),
file(unknown,unknown) ).
tff(f_170,axiom,
domain(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_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_163,axiom,
! [X] :
( ~ there_exists(compose(X,d))
| ( compose(X,d) = X ) ),
file(unknown,unknown) ).
tff(c_36,plain,
there_exists(compose(a,d)),
inference(cnfTransformation,[status(thm)],[f_158]) ).
tff(c_127,plain,
! [X_54,Y_55] :
( ( domain(X_54) = codomain(Y_55) )
| ~ there_exists(compose(X_54,Y_55)) ),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_137,plain,
domain(a) = codomain(d),
inference(resolution,[status(thm)],[c_36,c_127]) ).
tff(c_42,plain,
domain(a) != d,
inference(cnfTransformation,[status(thm)],[f_170]) ).
tff(c_139,plain,
codomain(d) != d,
inference(demodulation,[status(thm),theory(equality)],[c_137,c_42]) ).
tff(c_81,plain,
! [X_47,Y_48] :
( there_exists(domain(X_47))
| ~ there_exists(compose(X_47,Y_48)) ),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_91,plain,
there_exists(domain(a)),
inference(resolution,[status(thm)],[c_36,c_81]) ).
tff(c_138,plain,
there_exists(codomain(d)),
inference(demodulation,[status(thm),theory(equality)],[c_137,c_91]) ).
tff(c_10,plain,
! [X_8] :
( there_exists(X_8)
| ~ there_exists(codomain(X_8)) ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_159,plain,
there_exists(d),
inference(resolution,[status(thm)],[c_138,c_10]) ).
tff(c_22,plain,
! [X_19] : ( compose(codomain(X_19),X_19) = X_19 ),
inference(cnfTransformation,[status(thm)],[f_105]) ).
tff(c_161,plain,
! [X_56] :
( ( compose(X_56,d) = X_56 )
| ~ there_exists(compose(X_56,d)) ),
inference(cnfTransformation,[status(thm)],[f_163]) ).
tff(c_165,plain,
( ( compose(codomain(d),d) = codomain(d) )
| ~ there_exists(d) ),
inference(superposition,[status(thm),theory(equality)],[c_22,c_161]) ).
tff(c_170,plain,
codomain(d) = d,
inference(demodulation,[status(thm),theory(equality)],[c_159,c_22,c_165]) ).
tff(c_172,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_139,c_170]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : CAT005-3 : TPTP v9.0.0. Released v1.0.0.
% 0.07/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/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 : n008.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 15:37:47 EDT 2025
% 0.13/0.35 % CPUTime :
% 3.31/1.84 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.31/1.84
% 3.31/1.84 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------