%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : CAT018-4 : 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 : n010.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 05:46:31 PM UTC 2025
% Result : Unsatisfiable 7.52s 2.94s
% Output : CNFRefutation 7.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 38 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 54 ( 24 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 36 ( 20 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 31 ( 31 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ equivalent > there_exists > compose > #nlpp > domain > codomain > c > b > 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(b,type,
b: $i ).
tff(codomain,type,
codomain: $i > $i ).
tff(compose,type,
compose: ( $i * $i ) > $i ).
tff(c,type,
c: $i ).
tff(f_108,axiom,
there_exists(compose(a,b)),
file(unknown,unknown) ).
tff(f_91,axiom,
! [X,Y] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) ),
file(unknown,unknown) ).
tff(f_86,axiom,
! [X,Y] :
( ~ there_exists(compose(X,Y))
| there_exists(domain(X)) ),
file(unknown,unknown) ).
tff(f_99,axiom,
! [X,Y] :
( ~ there_exists(domain(X))
| ( domain(X) != codomain(Y) )
| there_exists(compose(X,Y)) ),
file(unknown,unknown) ).
tff(f_111,axiom,
~ there_exists(compose(a,compose(b,c))),
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_105,axiom,
! [X] : ( compose(codomain(X),X) = X ),
file(unknown,unknown) ).
tff(f_109,axiom,
there_exists(compose(b,c)),
file(unknown,unknown) ).
tff(f_101,axiom,
! [X,Y,Z] : ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) ),
file(unknown,unknown) ).
tff(c_24,plain,
there_exists(compose(a,b)),
inference(cnfTransformation,[status(thm)],[f_108]) ).
tff(c_84,plain,
! [X_31,Y_32] :
( ( domain(X_31) = codomain(Y_32) )
| ~ there_exists(compose(X_31,Y_32)) ),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_97,plain,
domain(a) = codomain(b),
inference(resolution,[status(thm)],[c_24,c_84]) ).
tff(c_61,plain,
! [X_29,Y_30] :
( there_exists(domain(X_29))
| ~ there_exists(compose(X_29,Y_30)) ),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_74,plain,
there_exists(domain(a)),
inference(resolution,[status(thm)],[c_24,c_61]) ).
tff(c_99,plain,
there_exists(codomain(b)),
inference(demodulation,[status(thm),theory(equality)],[c_97,c_74]) ).
tff(c_218,plain,
! [X_37,Y_38] :
( there_exists(compose(X_37,Y_38))
| ( domain(X_37) != codomain(Y_38) )
| ~ there_exists(domain(X_37)) ),
inference(cnfTransformation,[status(thm)],[f_99]) ).
tff(c_28,plain,
~ there_exists(compose(a,compose(b,c))),
inference(cnfTransformation,[status(thm)],[f_111]) ).
tff(c_227,plain,
( ( codomain(compose(b,c)) != domain(a) )
| ~ there_exists(domain(a)) ),
inference(resolution,[status(thm)],[c_218,c_28]) ).
tff(c_247,plain,
codomain(compose(b,c)) != codomain(b),
inference(demodulation,[status(thm),theory(equality)],[c_99,c_97,c_97,c_227]) ).
tff(c_8,plain,
! [X_7] :
( there_exists(X_7)
| ~ there_exists(domain(X_7)) ),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_79,plain,
there_exists(a),
inference(resolution,[status(thm)],[c_74,c_8]) ).
tff(c_20,plain,
! [X_18] : ( compose(X_18,domain(X_18)) = X_18 ),
inference(cnfTransformation,[status(thm)],[f_103]) ).
tff(c_106,plain,
compose(a,codomain(b)) = a,
inference(superposition,[status(thm),theory(equality)],[c_97,c_20]) ).
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_207,plain,
( ( codomain(codomain(b)) = domain(a) )
| ~ there_exists(a) ),
inference(superposition,[status(thm),theory(equality)],[c_106,c_14]) ).
tff(c_214,plain,
codomain(codomain(b)) = codomain(b),
inference(demodulation,[status(thm),theory(equality)],[c_79,c_97,c_207]) ).
tff(c_22,plain,
! [X_19] : ( compose(codomain(X_19),X_19) = X_19 ),
inference(cnfTransformation,[status(thm)],[f_105]) ).
tff(c_347,plain,
! [X_42] :
( ( domain(codomain(X_42)) = codomain(X_42) )
| ~ there_exists(X_42) ),
inference(superposition,[status(thm),theory(equality)],[c_22,c_84]) ).
tff(c_380,plain,
( ( domain(codomain(b)) = codomain(codomain(b)) )
| ~ there_exists(codomain(b)) ),
inference(superposition,[status(thm),theory(equality)],[c_214,c_347]) ).
tff(c_391,plain,
domain(codomain(b)) = codomain(b),
inference(demodulation,[status(thm),theory(equality)],[c_99,c_214,c_380]) ).
tff(c_26,plain,
there_exists(compose(b,c)),
inference(cnfTransformation,[status(thm)],[f_109]) ).
tff(c_128,plain,
! [X_33,Y_34,Z_35] : ( compose(compose(X_33,Y_34),Z_35) = compose(X_33,compose(Y_34,Z_35)) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_746,plain,
! [X_48,Z_49] : ( compose(codomain(X_48),compose(X_48,Z_49)) = compose(X_48,Z_49) ),
inference(superposition,[status(thm),theory(equality)],[c_22,c_128]) ).
tff(c_10326,plain,
! [X_141,Z_142] :
( ( domain(codomain(X_141)) = codomain(compose(X_141,Z_142)) )
| ~ there_exists(compose(X_141,Z_142)) ),
inference(superposition,[status(thm),theory(equality)],[c_746,c_14]) ).
tff(c_10443,plain,
domain(codomain(b)) = codomain(compose(b,c)),
inference(resolution,[status(thm)],[c_26,c_10326]) ).
tff(c_10488,plain,
codomain(compose(b,c)) = codomain(b),
inference(demodulation,[status(thm),theory(equality)],[c_391,c_10443]) ).
tff(c_10490,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_247,c_10488]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : CAT018-4 : TPTP v9.0.0. Released v1.0.0.
% 0.03/0.13 % 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
% 0.12/0.34 % Computer : n010.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 15:40:02 EDT 2025
% 0.12/0.34 % CPUTime :
% 7.52/2.94 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.52/2.95
% 7.52/2.95 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------