%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : CAT004-2 : 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 : n031.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 17.68s 6.31s
% Output : CNFRefutation 17.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 14
% Syntax : Number of formulae : 71 ( 40 unt; 0 typ; 0 def)
% Number of atoms : 128 ( 125 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 120 ( 63 ~; 57 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 51 ( 51 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ compose > #nlpp > domain > codomain > h > g > b > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(h,type,
h: $i ).
tff(a,type,
a: $i ).
tff(domain,type,
domain: $i > $i ).
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_107,axiom,
h != g,
file(unknown,unknown) ).
tff(f_102,axiom,
codomain(a) = domain(b),
file(unknown,unknown) ).
tff(f_63,axiom,
! [X,Y] :
( ( codomain(X) != domain(Y) )
| ( codomain(compose(X,Y)) = codomain(Y) ) ),
file(unknown,unknown) ).
tff(f_104,axiom,
codomain(compose(a,b)) = domain(g),
file(unknown,unknown) ).
tff(f_103,axiom,
codomain(compose(a,b)) = domain(h),
file(unknown,unknown) ).
tff(f_58,axiom,
! [X,Y] :
( ( codomain(X) != domain(Y) )
| ( domain(compose(X,Y)) = domain(X) ) ),
file(unknown,unknown) ).
tff(f_71,axiom,
! [X,Y,Z] :
( ( codomain(X) != domain(Y) )
| ( codomain(Y) != domain(Z) )
| ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) ) ),
file(unknown,unknown) ).
tff(f_105,axiom,
compose(compose(a,b),h) = compose(compose(a,b),g),
file(unknown,unknown) ).
tff(f_51,axiom,
! [X] : ( compose(domain(X),X) = X ),
file(unknown,unknown) ).
tff(f_49,axiom,
! [X] : ( domain(codomain(X)) = codomain(X) ),
file(unknown,unknown) ).
tff(f_47,axiom,
! [X] : ( codomain(domain(X)) = domain(X) ),
file(unknown,unknown) ).
tff(f_53,axiom,
! [X] : ( compose(X,codomain(X)) = X ),
file(unknown,unknown) ).
tff(f_87,axiom,
! [X,Y,Z] :
( ( codomain(a) != domain(X) )
| ( compose(a,X) != Y )
| ( codomain(a) != domain(Z) )
| ( compose(a,Z) != Y )
| ( X = Z ) ),
file(unknown,unknown) ).
tff(f_101,axiom,
! [X,Y,Z] :
( ( codomain(b) != domain(X) )
| ( compose(b,X) != Y )
| ( codomain(b) != domain(Z) )
| ( compose(b,Z) != Y )
| ( X = Z ) ),
file(unknown,unknown) ).
tff(c_28,plain,
h != g,
inference(cnfTransformation,[status(thm)],[f_107]) ).
tff(c_20,plain,
domain(b) = codomain(a),
inference(cnfTransformation,[status(thm)],[f_102]) ).
tff(c_243,plain,
! [X_25,Y_26] :
( ( codomain(compose(X_25,Y_26)) = codomain(Y_26) )
| ( domain(Y_26) != codomain(X_25) ) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_24,plain,
codomain(compose(a,b)) = domain(g),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_252,plain,
( ( domain(g) = codomain(b) )
| ( domain(b) != codomain(a) ) ),
inference(superposition,[status(thm),theory(equality)],[c_243,c_24]) ).
tff(c_283,plain,
domain(g) = codomain(b),
inference(demodulation,[status(thm),theory(equality)],[c_20,c_252]) ).
tff(c_22,plain,
codomain(compose(a,b)) = domain(h),
inference(cnfTransformation,[status(thm)],[f_103]) ).
tff(c_29,plain,
domain(h) = domain(g),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_22]) ).
tff(c_303,plain,
domain(h) = codomain(b),
inference(demodulation,[status(thm),theory(equality)],[c_283,c_29]) ).
tff(c_10,plain,
! [X_5,Y_6] :
( ( domain(compose(X_5,Y_6)) = domain(X_5) )
| ( domain(Y_6) != codomain(X_5) ) ),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_12,plain,
! [X_7,Y_8] :
( ( codomain(compose(X_7,Y_8)) = codomain(Y_8) )
| ( domain(Y_8) != codomain(X_7) ) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_578,plain,
! [X_34,Y_35,Z_36] :
( ( compose(compose(X_34,Y_35),Z_36) = compose(X_34,compose(Y_35,Z_36)) )
| ( domain(Z_36) != codomain(Y_35) )
| ( domain(Y_35) != codomain(X_34) ) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_26,plain,
compose(compose(a,b),h) = compose(compose(a,b),g),
inference(cnfTransformation,[status(thm)],[f_105]) ).
tff(c_593,plain,
( ( compose(compose(a,b),g) = compose(a,compose(b,h)) )
| ( domain(h) != codomain(b) )
| ( domain(b) != codomain(a) ) ),
inference(superposition,[status(thm),theory(equality)],[c_578,c_26]) ).
tff(c_648,plain,
compose(compose(a,b),g) = compose(a,compose(b,h)),
inference(demodulation,[status(thm),theory(equality)],[c_20,c_303,c_593]) ).
tff(c_14,plain,
! [X_9,Y_10,Z_11] :
( ( compose(compose(X_9,Y_10),Z_11) = compose(X_9,compose(Y_10,Z_11)) )
| ( domain(Z_11) != codomain(Y_10) )
| ( domain(Y_10) != codomain(X_9) ) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_682,plain,
( ( compose(a,compose(b,h)) = compose(a,compose(b,g)) )
| ( domain(g) != codomain(b) )
| ( domain(b) != codomain(a) ) ),
inference(superposition,[status(thm),theory(equality)],[c_648,c_14]) ).
tff(c_697,plain,
compose(a,compose(b,h)) = compose(a,compose(b,g)),
inference(demodulation,[status(thm),theory(equality)],[c_20,c_283,c_682]) ).
tff(c_301,plain,
codomain(compose(a,b)) = codomain(b),
inference(demodulation,[status(thm),theory(equality)],[c_283,c_24]) ).
tff(c_688,plain,
( ( codomain(compose(a,compose(b,h))) = codomain(g) )
| ( codomain(compose(a,b)) != domain(g) ) ),
inference(superposition,[status(thm),theory(equality)],[c_648,c_12]) ).
tff(c_701,plain,
codomain(compose(a,compose(b,h))) = codomain(g),
inference(demodulation,[status(thm),theory(equality)],[c_301,c_283,c_688]) ).
tff(c_840,plain,
codomain(compose(a,compose(b,g))) = codomain(g),
inference(demodulation,[status(thm),theory(equality)],[c_697,c_701]) ).
tff(c_960,plain,
( ( codomain(compose(b,g)) = codomain(g) )
| ( domain(compose(b,g)) != codomain(a) ) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_840]) ).
tff(c_1126,plain,
domain(compose(b,g)) != codomain(a),
inference(splitLeft,[status(thm)],[c_960]) ).
tff(c_1129,plain,
( ( domain(b) != codomain(a) )
| ( domain(g) != codomain(b) ) ),
inference(superposition,[status(thm),theory(equality)],[c_10,c_1126]) ).
tff(c_1132,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_283,c_20,c_1129]) ).
tff(c_1134,plain,
domain(compose(b,g)) = codomain(a),
inference(splitRight,[status(thm)],[c_960]) ).
tff(c_451,plain,
! [X_28,Y_29] :
( ( domain(compose(X_28,Y_29)) = domain(X_28) )
| ( domain(Y_29) != codomain(X_28) ) ),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_484,plain,
( ( domain(compose(compose(a,b),g)) = domain(compose(a,b)) )
| ( codomain(compose(a,b)) != domain(h) ) ),
inference(superposition,[status(thm),theory(equality)],[c_26,c_451]) ).
tff(c_508,plain,
domain(compose(compose(a,b),g)) = domain(compose(a,b)),
inference(demodulation,[status(thm),theory(equality)],[c_301,c_303,c_484]) ).
tff(c_734,plain,
domain(compose(a,compose(b,h))) = domain(compose(a,b)),
inference(demodulation,[status(thm),theory(equality)],[c_648,c_508]) ).
tff(c_757,plain,
( ( domain(compose(a,b)) = domain(a) )
| ( domain(compose(b,h)) != codomain(a) ) ),
inference(superposition,[status(thm),theory(equality)],[c_10,c_734]) ).
tff(c_861,plain,
domain(compose(b,h)) != codomain(a),
inference(splitLeft,[status(thm)],[c_757]) ).
tff(c_864,plain,
( ( domain(b) != codomain(a) )
| ( domain(h) != codomain(b) ) ),
inference(superposition,[status(thm),theory(equality)],[c_10,c_861]) ).
tff(c_867,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_303,c_20,c_864]) ).
tff(c_869,plain,
domain(compose(b,h)) = codomain(a),
inference(splitRight,[status(thm)],[c_757]) ).
tff(c_6,plain,
! [X_3] : ( compose(domain(X_3),X_3) = X_3 ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_923,plain,
compose(codomain(a),compose(b,h)) = compose(b,h),
inference(superposition,[status(thm),theory(equality)],[c_869,c_6]) ).
tff(c_4,plain,
! [X_2] : ( domain(codomain(X_2)) = codomain(X_2) ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_74,plain,
! [X_21] : ( codomain(domain(X_21)) = domain(X_21) ),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_89,plain,
! [X_2] : ( domain(codomain(X_2)) = codomain(codomain(X_2)) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_74]) ).
tff(c_99,plain,
! [X_2] : ( codomain(codomain(X_2)) = codomain(X_2) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_89]) ).
tff(c_8,plain,
! [X_4] : ( compose(X_4,codomain(X_4)) = X_4 ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_639,plain,
! [X_4,Z_36] :
( ( compose(X_4,compose(codomain(X_4),Z_36)) = compose(X_4,Z_36) )
| ( domain(Z_36) != codomain(codomain(X_4)) )
| ( domain(codomain(X_4)) != codomain(X_4) ) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_578]) ).
tff(c_1678,plain,
! [X_43,Z_44] :
( ( compose(X_43,compose(codomain(X_43),Z_44)) = compose(X_43,Z_44) )
| ( domain(Z_44) != codomain(X_43) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_99,c_639]) ).
tff(c_16,plain,
! [Z_14,X_12] :
( ( Z_14 = X_12 )
| ( domain(Z_14) != codomain(a) )
| ( compose(a,Z_14) != compose(a,X_12) )
| ( domain(X_12) != codomain(a) ) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_36627,plain,
! [Z_235,Z_236] :
( ( compose(codomain(a),Z_235) = Z_236 )
| ( domain(Z_236) != codomain(a) )
| ( compose(a,Z_236) != compose(a,Z_235) )
| ( domain(compose(codomain(a),Z_235)) != codomain(a) )
| ( domain(Z_235) != codomain(a) ) ),
inference(superposition,[status(thm),theory(equality)],[c_1678,c_16]) ).
tff(c_36643,plain,
! [Z_236] :
( ( compose(codomain(a),compose(b,h)) = Z_236 )
| ( domain(Z_236) != codomain(a) )
| ( compose(a,compose(b,g)) != compose(a,Z_236) )
| ( domain(compose(codomain(a),compose(b,h))) != codomain(a) )
| ( domain(compose(b,h)) != codomain(a) ) ),
inference(superposition,[status(thm),theory(equality)],[c_697,c_36627]) ).
tff(c_36653,plain,
! [Z_236] :
( ( compose(b,h) = Z_236 )
| ( domain(Z_236) != codomain(a) )
| ( compose(a,compose(b,g)) != compose(a,Z_236) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_869,c_869,c_923,c_923,c_36643]) ).
tff(c_36660,plain,
( ( compose(b,h) = compose(b,g) )
| ( domain(compose(b,g)) != codomain(a) ) ),
inference(reflexivity,[status(thm),theory(equality)],[c_36653]) ).
tff(c_36662,plain,
compose(b,h) = compose(b,g),
inference(demodulation,[status(thm),theory(equality)],[c_1134,c_36660]) ).
tff(c_18,plain,
! [Z_17,X_15] :
( ( Z_17 = X_15 )
| ( domain(Z_17) != codomain(b) )
| ( compose(b,Z_17) != compose(b,X_15) )
| ( domain(X_15) != codomain(b) ) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_36800,plain,
! [X_15] :
( ( h = X_15 )
| ( domain(h) != codomain(b) )
| ( compose(b,g) != compose(b,X_15) )
| ( domain(X_15) != codomain(b) ) ),
inference(superposition,[status(thm),theory(equality)],[c_36662,c_18]) ).
tff(c_36888,plain,
! [X_15] :
( ( h = X_15 )
| ( compose(b,g) != compose(b,X_15) )
| ( domain(X_15) != codomain(b) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_303,c_36800]) ).
tff(c_36898,plain,
( ( h = g )
| ( domain(g) != codomain(b) ) ),
inference(reflexivity,[status(thm),theory(equality)],[c_36888]) ).
tff(c_36900,plain,
h = g,
inference(demodulation,[status(thm),theory(equality)],[c_283,c_36898]) ).
tff(c_36902,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_36900]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : CAT004-2 : TPTP v9.0.0. Released v1.0.0.
% 0.13/0.13 % 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 : n031.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 15:37:52 EDT 2025
% 0.13/0.34 % CPUTime :
% 17.68/6.31 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.68/6.32
% 17.68/6.32 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------