%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : CAT011-4 : 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/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 : 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 05:46:28 PM UTC 2025
% Result : Unsatisfiable 2.95s 1.76s
% Output : CNFRefutation 2.95s
% 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(domain(a)),
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_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_105,axiom,
! [X] : ( compose(codomain(X),X) = X ),
file(unknown,unknown) ).
tff(f_110,axiom,
domain(domain(a)) != domain(a),
file(unknown,unknown) ).
tff(c_24,plain,
there_exists(domain(a)),
inference(cnfTransformation,[status(thm)],[f_108]) ).
tff(c_49,plain,
! [X_27] :
( there_exists(X_27)
| ~ there_exists(domain(X_27)) ),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_53,plain,
there_exists(a),
inference(resolution,[status(thm)],[c_24,c_49]) ).
tff(c_20,plain,
! [X_18] : ( compose(X_18,domain(X_18)) = X_18 ),
inference(cnfTransformation,[status(thm)],[f_103]) ).
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_177,plain,
! [X_41,Z_42] : ( compose(X_41,compose(domain(X_41),Z_42)) = compose(X_41,Z_42) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_92]) ).
tff(c_215,plain,
! [X_41] : ( compose(X_41,domain(domain(X_41))) = compose(X_41,domain(X_41)) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_177]) ).
tff(c_245,plain,
! [X_45] : ( compose(X_45,domain(domain(X_45))) = X_45 ),
inference(demodulation,[status(thm),theory(equality)],[c_20,c_215]) ).
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_321,plain,
! [X_47] :
( ( codomain(domain(domain(X_47))) = domain(X_47) )
| ~ there_exists(X_47) ),
inference(superposition,[status(thm),theory(equality)],[c_245,c_14]) ).
tff(c_22,plain,
! [X_19] : ( compose(codomain(X_19),X_19) = X_19 ),
inference(cnfTransformation,[status(thm)],[f_105]) ).
tff(c_339,plain,
! [X_47] :
( ( compose(domain(X_47),domain(domain(X_47))) = domain(domain(X_47)) )
| ~ there_exists(X_47) ),
inference(superposition,[status(thm),theory(equality)],[c_321,c_22]) ).
tff(c_355,plain,
! [X_48] :
( ( domain(domain(X_48)) = domain(X_48) )
| ~ there_exists(X_48) ),
inference(demodulation,[status(thm),theory(equality)],[c_20,c_339]) ).
tff(c_26,plain,
domain(domain(a)) != domain(a),
inference(cnfTransformation,[status(thm)],[f_110]) ).
tff(c_400,plain,
~ there_exists(a),
inference(superposition,[status(thm),theory(equality)],[c_355,c_26]) ).
tff(c_420,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_53,c_400]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : CAT011-4 : TPTP v9.0.0. Released v1.0.0.
% 0.11/0.13 % 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
% 0.13/0.32 % Computer : n012.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Mon Apr 7 15:38:30 EDT 2025
% 0.17/0.33 % CPUTime :
% 2.95/1.76 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.95/1.77
% 2.95/1.77 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------