%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : CAT008-1 : 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 05:46:27 PM UTC 2025
% Result : Unsatisfiable 4.85s 2.22s
% Output : CNFRefutation 4.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 41 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 78 ( 14 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 76 ( 39 ~; 37 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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 : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 60 ( 60 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ product > defined > identity_map > compose > #nlpp > domain > codomain > b > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(a,type,
a: $i ).
tff(product,type,
product: ( $i * $i * $i ) > $o ).
tff(domain,type,
domain: $i > $i ).
tff(defined,type,
defined: ( $i * $i ) > $o ).
tff(b,type,
b: $i ).
tff(identity_map,type,
identity_map: $i > $o ).
tff(codomain,type,
codomain: $i > $i ).
tff(compose,type,
compose: ( $i * $i ) > $i ).
tff(f_175,axiom,
domain(a) != codomain(b),
file(unknown,unknown) ).
tff(f_134,axiom,
! [X] : identity_map(domain(X)),
file(unknown,unknown) ).
tff(f_136,axiom,
! [X] : identity_map(codomain(X)),
file(unknown,unknown) ).
tff(f_142,axiom,
! [X] : product(X,domain(X),X),
file(unknown,unknown) ).
tff(f_173,axiom,
defined(a,b),
file(unknown,unknown) ).
tff(f_67,axiom,
! [X,Y,Xy,Z] :
( ~ product(X,Y,Xy)
| ~ defined(Xy,Z)
| defined(Y,Z) ),
file(unknown,unknown) ).
tff(f_153,axiom,
! [X,Y] :
( ~ defined(X,Y)
| ~ identity_map(X)
| product(X,Y,Y) ),
file(unknown,unknown) ).
tff(f_53,axiom,
! [X,Y] :
( ~ defined(X,Y)
| product(X,Y,compose(X,Y)) ),
file(unknown,unknown) ).
tff(f_170,axiom,
! [X,Y,Z,W] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) ),
file(unknown,unknown) ).
tff(f_140,axiom,
! [X] : defined(codomain(X),X),
file(unknown,unknown) ).
tff(f_98,axiom,
! [Y,Z,Yz,X] :
( ~ product(Y,Z,Yz)
| ~ defined(X,Yz)
| defined(X,Y) ),
file(unknown,unknown) ).
tff(f_161,axiom,
! [X,Y] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) ),
file(unknown,unknown) ).
tff(c_40,plain,
domain(a) != codomain(b),
inference(cnfTransformation,[status(thm)],[f_175]) ).
tff(c_20,plain,
! [X_39] : identity_map(domain(X_39)),
inference(cnfTransformation,[status(thm)],[f_134]) ).
tff(c_22,plain,
! [X_40] : identity_map(codomain(X_40)),
inference(cnfTransformation,[status(thm)],[f_136]) ).
tff(c_28,plain,
! [X_43] : product(X_43,domain(X_43),X_43),
inference(cnfTransformation,[status(thm)],[f_142]) ).
tff(c_38,plain,
defined(a,b),
inference(cnfTransformation,[status(thm)],[f_173]) ).
tff(c_73,plain,
! [Y_68,Z_69,Xy_70,X_71] :
( defined(Y_68,Z_69)
| ~ defined(Xy_70,Z_69)
| ~ product(X_71,Y_68,Xy_70) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_83,plain,
! [Y_72,X_73] :
( defined(Y_72,b)
| ~ product(X_73,Y_72,a) ),
inference(resolution,[status(thm)],[c_38,c_73]) ).
tff(c_105,plain,
defined(domain(a),b),
inference(resolution,[status(thm)],[c_28,c_83]) ).
tff(c_32,plain,
! [X_45,Y_46] :
( product(X_45,Y_46,Y_46)
| ~ identity_map(X_45)
| ~ defined(X_45,Y_46) ),
inference(cnfTransformation,[status(thm)],[f_153]) ).
tff(c_2,plain,
! [X_1,Y_2] :
( product(X_1,Y_2,compose(X_1,Y_2))
| ~ defined(X_1,Y_2) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_109,plain,
! [Z_74,W_75,X_76,Y_77] :
( ( Z_74 = W_75 )
| ~ product(X_76,Y_77,W_75)
| ~ product(X_76,Y_77,Z_74) ),
inference(cnfTransformation,[status(thm)],[f_170]) ).
tff(c_1759,plain,
! [X_182,Y_183,Z_184] :
( ( compose(X_182,Y_183) = Z_184 )
| ~ product(X_182,Y_183,Z_184)
| ~ defined(X_182,Y_183) ),
inference(resolution,[status(thm)],[c_2,c_109]) ).
tff(c_1874,plain,
! [X_187,Y_188] :
( ( compose(X_187,Y_188) = Y_188 )
| ~ identity_map(X_187)
| ~ defined(X_187,Y_188) ),
inference(resolution,[status(thm)],[c_32,c_1759]) ).
tff(c_1916,plain,
( ( compose(domain(a),b) = b )
| ~ identity_map(domain(a)) ),
inference(resolution,[status(thm)],[c_105,c_1874]) ).
tff(c_1957,plain,
compose(domain(a),b) = b,
inference(demodulation,[status(thm),theory(equality)],[c_20,c_1916]) ).
tff(c_26,plain,
! [X_42] : defined(codomain(X_42),X_42),
inference(cnfTransformation,[status(thm)],[f_140]) ).
tff(c_176,plain,
! [X_82,Y_83,Yz_84,Z_85] :
( defined(X_82,Y_83)
| ~ defined(X_82,Yz_84)
| ~ product(Y_83,Z_85,Yz_84) ),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_819,plain,
! [X_136,Y_137,Z_138] :
( defined(codomain(X_136),Y_137)
| ~ product(Y_137,Z_138,X_136) ),
inference(resolution,[status(thm)],[c_26,c_176]) ).
tff(c_841,plain,
! [X_1,Y_2] :
( defined(codomain(compose(X_1,Y_2)),X_1)
| ~ defined(X_1,Y_2) ),
inference(resolution,[status(thm)],[c_2,c_819]) ).
tff(c_1967,plain,
( defined(codomain(b),domain(a))
| ~ defined(domain(a),b) ),
inference(superposition,[status(thm),theory(equality)],[c_1957,c_841]) ).
tff(c_1977,plain,
defined(codomain(b),domain(a)),
inference(demodulation,[status(thm),theory(equality)],[c_105,c_1967]) ).
tff(c_1787,plain,
! [X_45,Y_46] :
( ( compose(X_45,Y_46) = Y_46 )
| ~ identity_map(X_45)
| ~ defined(X_45,Y_46) ),
inference(resolution,[status(thm)],[c_32,c_1759]) ).
tff(c_1985,plain,
( ( compose(codomain(b),domain(a)) = domain(a) )
| ~ identity_map(codomain(b)) ),
inference(resolution,[status(thm)],[c_1977,c_1787]) ).
tff(c_2014,plain,
compose(codomain(b),domain(a)) = domain(a),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_1985]) ).
tff(c_34,plain,
! [X_47,Y_48] :
( product(X_47,Y_48,X_47)
| ~ identity_map(Y_48)
| ~ defined(X_47,Y_48) ),
inference(cnfTransformation,[status(thm)],[f_161]) ).
tff(c_2246,plain,
! [X_194,Y_195] :
( ( compose(X_194,Y_195) = X_194 )
| ~ identity_map(Y_195)
| ~ defined(X_194,Y_195) ),
inference(resolution,[status(thm)],[c_34,c_1759]) ).
tff(c_2249,plain,
( ( compose(codomain(b),domain(a)) = codomain(b) )
| ~ identity_map(domain(a)) ),
inference(resolution,[status(thm)],[c_1977,c_2246]) ).
tff(c_2303,plain,
domain(a) = codomain(b),
inference(demodulation,[status(thm),theory(equality)],[c_20,c_2014,c_2249]) ).
tff(c_2305,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_40,c_2303]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : CAT008-1 : TPTP v9.0.0. Released v1.0.0.
% 0.06/0.12 % 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
% 0.12/0.33 % Computer : n012.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 15:38:00 EDT 2025
% 0.12/0.33 % CPUTime :
% 4.85/2.22 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.85/2.22
% 4.85/2.22 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------