%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : CAT003-1 : 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/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 : n017.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 96.50s 81.84s
% Output : CNFRefutation 96.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 19
% Syntax : Number of formulae : 74 ( 28 unt; 0 typ; 0 def)
% Number of atoms : 161 ( 14 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 176 ( 89 ~; 87 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 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 : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 127 ( 127 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ product > defined > identity_map > compose > #nlpp > domain > codomain > h > g > d > c > b > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(h,type,
h: $i ).
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(g,type,
g: $i ).
tff(codomain,type,
codomain: $i > $i ).
tff(d,type,
d: $i ).
tff(compose,type,
compose: ( $i * $i ) > $i ).
tff(c,type,
c: $i ).
tff(f_185,axiom,
h != g,
file(unknown,unknown) ).
tff(f_182,axiom,
product(h,a,d),
file(unknown,unknown) ).
tff(f_138,axiom,
! [X] : defined(X,domain(X)),
file(unknown,unknown) ).
tff(f_134,axiom,
! [X] : identity_map(domain(X)),
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_161,axiom,
! [X,Y] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) ),
file(unknown,unknown) ).
tff(f_173,axiom,
product(a,b,c),
file(unknown,unknown) ).
tff(f_59,axiom,
! [X,Y,Z] :
( ~ product(X,Y,Z)
| defined(X,Y) ),
file(unknown,unknown) ).
tff(f_131,axiom,
! [X,Y,Z] :
( ~ defined(X,Y)
| ~ defined(Y,Z)
| ~ identity_map(Y)
| defined(X,Z) ),
file(unknown,unknown) ).
tff(f_136,axiom,
! [X] : identity_map(codomain(X)),
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_153,axiom,
! [X,Y] :
( ~ defined(X,Y)
| ~ identity_map(X)
| product(X,Y,Y) ),
file(unknown,unknown) ).
tff(f_183,axiom,
product(g,a,d),
file(unknown,unknown) ).
tff(f_53,axiom,
! [X,Y] :
( ~ defined(X,Y)
| product(X,Y,compose(X,Y)) ),
file(unknown,unknown) ).
tff(f_120,axiom,
! [Xyz,Z,Yz,X,Y,Xy] :
( ~ product(Y,Z,Yz)
| ~ product(X,Yz,Xyz)
| ~ product(X,Y,Xy)
| product(Xy,Z,Xyz) ),
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_90,axiom,
! [Xyz,Z,Yz,X,Y,Xy] :
( ~ product(X,Y,Xy)
| ~ product(Xy,Z,Xyz)
| ~ product(Y,Z,Yz)
| product(X,Yz,Xyz) ),
file(unknown,unknown) ).
tff(f_181,axiom,
! [X,W,Y] :
( ~ product(X,c,W)
| ~ product(Y,c,W)
| ( X = Y ) ),
file(unknown,unknown) ).
tff(c_46,plain,
h != g,
inference(cnfTransformation,[status(thm)],[f_185]) ).
tff(c_42,plain,
product(h,a,d),
inference(cnfTransformation,[status(thm)],[f_182]) ).
tff(c_24,plain,
! [X_41] : defined(X_41,domain(X_41)),
inference(cnfTransformation,[status(thm)],[f_138]) ).
tff(c_20,plain,
! [X_39] : identity_map(domain(X_39)),
inference(cnfTransformation,[status(thm)],[f_134]) ).
tff(c_232,plain,
! [Y_85,Z_86,Xy_87,X_88] :
( defined(Y_85,Z_86)
| ~ defined(Xy_87,Z_86)
| ~ product(X_88,Y_85,Xy_87) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_949,plain,
! [Y_143,X_144,X_145] :
( defined(Y_143,domain(X_144))
| ~ product(X_145,Y_143,X_144) ),
inference(resolution,[status(thm)],[c_24,c_232]) ).
tff(c_974,plain,
defined(a,domain(d)),
inference(resolution,[status(thm)],[c_42,c_949]) ).
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_38,plain,
product(a,b,c),
inference(cnfTransformation,[status(thm)],[f_173]) ).
tff(c_53,plain,
! [X_62,Y_63,Z_64] :
( defined(X_62,Y_63)
| ~ product(X_62,Y_63,Z_64) ),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_74,plain,
defined(a,b),
inference(resolution,[status(thm)],[c_38,c_53]) ).
tff(c_800,plain,
! [Y_135,X_136] :
( defined(Y_135,b)
| ~ product(X_136,Y_135,a) ),
inference(resolution,[status(thm)],[c_74,c_232]) ).
tff(c_1528,plain,
! [Y_170] :
( defined(Y_170,b)
| ~ identity_map(Y_170)
| ~ defined(a,Y_170) ),
inference(resolution,[status(thm)],[c_34,c_800]) ).
tff(c_1533,plain,
( defined(domain(d),b)
| ~ identity_map(domain(d)) ),
inference(resolution,[status(thm)],[c_974,c_1528]) ).
tff(c_1546,plain,
defined(domain(d),b),
inference(demodulation,[status(thm),theory(equality)],[c_20,c_1533]) ).
tff(c_18,plain,
! [X_36,Z_38,Y_37] :
( defined(X_36,Z_38)
| ~ identity_map(Y_37)
| ~ defined(Y_37,Z_38)
| ~ defined(X_36,Y_37) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_1559,plain,
! [X_36] :
( defined(X_36,b)
| ~ identity_map(domain(d))
| ~ defined(X_36,domain(d)) ),
inference(resolution,[status(thm)],[c_1546,c_18]) ).
tff(c_1571,plain,
! [X_171] :
( defined(X_171,b)
| ~ defined(X_171,domain(d)) ),
inference(demodulation,[status(thm),theory(equality)],[c_20,c_1559]) ).
tff(c_1596,plain,
defined(d,b),
inference(resolution,[status(thm)],[c_24,c_1571]) ).
tff(c_22,plain,
! [X_40] : identity_map(codomain(X_40)),
inference(cnfTransformation,[status(thm)],[f_136]) ).
tff(c_26,plain,
! [X_42] : defined(codomain(X_42),X_42),
inference(cnfTransformation,[status(thm)],[f_140]) ).
tff(c_188,plain,
! [X_80,Y_81,Yz_82,Z_83] :
( defined(X_80,Y_81)
| ~ defined(X_80,Yz_82)
| ~ product(Y_81,Z_83,Yz_82) ),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_1307,plain,
! [X_159,Y_160,Z_161] :
( defined(codomain(X_159),Y_160)
| ~ product(Y_160,Z_161,X_159) ),
inference(resolution,[status(thm)],[c_26,c_188]) ).
tff(c_1341,plain,
defined(codomain(c),a),
inference(resolution,[status(thm)],[c_38,c_1307]) ).
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_44,plain,
product(g,a,d),
inference(cnfTransformation,[status(thm)],[f_183]) ).
tff(c_75,plain,
defined(g,a),
inference(resolution,[status(thm)],[c_44,c_53]) ).
tff(c_840,plain,
! [Y_137,Z_138] :
( defined(g,Y_137)
| ~ product(Y_137,Z_138,a) ),
inference(resolution,[status(thm)],[c_75,c_188]) ).
tff(c_1788,plain,
! [X_181] :
( defined(g,X_181)
| ~ identity_map(X_181)
| ~ defined(X_181,a) ),
inference(resolution,[status(thm)],[c_32,c_840]) ).
tff(c_1790,plain,
( defined(g,codomain(c))
| ~ identity_map(codomain(c)) ),
inference(resolution,[status(thm)],[c_1341,c_1788]) ).
tff(c_1804,plain,
defined(g,codomain(c)),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_1790]) ).
tff(c_294,plain,
! [X_90,Z_91,Y_92] :
( defined(X_90,Z_91)
| ~ identity_map(Y_92)
| ~ defined(Y_92,Z_91)
| ~ defined(X_90,Y_92) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_304,plain,
! [X_90,X_42] :
( defined(X_90,X_42)
| ~ identity_map(codomain(X_42))
| ~ defined(X_90,codomain(X_42)) ),
inference(resolution,[status(thm)],[c_26,c_294]) ).
tff(c_311,plain,
! [X_90,X_42] :
( defined(X_90,X_42)
| ~ defined(X_90,codomain(X_42)) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_304]) ).
tff(c_1839,plain,
defined(g,c),
inference(resolution,[status(thm)],[c_1804,c_311]) ).
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_735,plain,
! [Xy_128,Yz_129,Xyz_131,X_130,Y_132,Z_127] :
( product(Xy_128,Z_127,Xyz_131)
| ~ product(X_130,Y_132,Xy_128)
| ~ product(X_130,Yz_129,Xyz_131)
| ~ product(Y_132,Z_127,Yz_129) ),
inference(cnfTransformation,[status(thm)],[f_120]) ).
tff(c_3634,plain,
! [Z_268,Xyz_269,Yz_270] :
( product(d,Z_268,Xyz_269)
| ~ product(g,Yz_270,Xyz_269)
| ~ product(a,Z_268,Yz_270) ),
inference(resolution,[status(thm)],[c_44,c_735]) ).
tff(c_28246,plain,
! [Z_707,Y_708] :
( product(d,Z_707,compose(g,Y_708))
| ~ product(a,Z_707,Y_708)
| ~ defined(g,Y_708) ),
inference(resolution,[status(thm)],[c_2,c_3634]) ).
tff(c_125,plain,
! [Z_75,W_76,X_77,Y_78] :
( ( Z_75 = W_76 )
| ~ product(X_77,Y_78,W_76)
| ~ product(X_77,Y_78,Z_75) ),
inference(cnfTransformation,[status(thm)],[f_170]) ).
tff(c_143,plain,
! [X_1,Y_2,Z_75] :
( ( compose(X_1,Y_2) = Z_75 )
| ~ product(X_1,Y_2,Z_75)
| ~ defined(X_1,Y_2) ),
inference(resolution,[status(thm)],[c_2,c_125]) ).
tff(c_408601,plain,
! [Y_2732,Z_2733] :
( ( compose(g,Y_2732) = compose(d,Z_2733) )
| ~ defined(d,Z_2733)
| ~ product(a,Z_2733,Y_2732)
| ~ defined(g,Y_2732) ),
inference(resolution,[status(thm)],[c_28246,c_143]) ).
tff(c_408851,plain,
( ( compose(g,c) = compose(d,b) )
| ~ defined(d,b)
| ~ defined(g,c) ),
inference(resolution,[status(thm)],[c_38,c_408601]) ).
tff(c_408983,plain,
compose(g,c) = compose(d,b),
inference(demodulation,[status(thm),theory(equality)],[c_1839,c_1596,c_408851]) ).
tff(c_409257,plain,
( product(g,c,compose(d,b))
| ~ defined(g,c) ),
inference(superposition,[status(thm),theory(equality)],[c_408983,c_2]) ).
tff(c_409442,plain,
product(g,c,compose(d,b)),
inference(demodulation,[status(thm),theory(equality)],[c_1839,c_409257]) ).
tff(c_562,plain,
! [X_119,Yz_118,Xy_116,Xyz_120,Z_117,Y_121] :
( product(X_119,Yz_118,Xyz_120)
| ~ product(Y_121,Z_117,Yz_118)
| ~ product(Xy_116,Z_117,Xyz_120)
| ~ product(X_119,Y_121,Xy_116) ),
inference(cnfTransformation,[status(thm)],[f_90]) ).
tff(c_4037,plain,
! [X_285,Xyz_286,Xy_287] :
( product(X_285,c,Xyz_286)
| ~ product(Xy_287,b,Xyz_286)
| ~ product(X_285,a,Xy_287) ),
inference(resolution,[status(thm)],[c_38,c_562]) ).
tff(c_17612,plain,
! [X_577,X_578] :
( product(X_577,c,compose(X_578,b))
| ~ product(X_577,a,X_578)
| ~ defined(X_578,b) ),
inference(resolution,[status(thm)],[c_2,c_4037]) ).
tff(c_40,plain,
! [Y_55,X_53,W_54] :
( ( Y_55 = X_53 )
| ~ product(Y_55,c,W_54)
| ~ product(X_53,c,W_54) ),
inference(cnfTransformation,[status(thm)],[f_181]) ).
tff(c_17734,plain,
! [X_577,X_53,X_578] :
( ( X_577 = X_53 )
| ~ product(X_53,c,compose(X_578,b))
| ~ product(X_577,a,X_578)
| ~ defined(X_578,b) ),
inference(resolution,[status(thm)],[c_17612,c_40]) ).
tff(c_409455,plain,
! [X_577] :
( ( g = X_577 )
| ~ product(X_577,a,d)
| ~ defined(d,b) ),
inference(resolution,[status(thm)],[c_409442,c_17734]) ).
tff(c_409717,plain,
! [X_2734] :
( ( g = X_2734 )
| ~ product(X_2734,a,d) ),
inference(demodulation,[status(thm),theory(equality)],[c_1596,c_409455]) ).
tff(c_409772,plain,
h = g,
inference(resolution,[status(thm)],[c_42,c_409717]) ).
tff(c_409794,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_46,c_409772]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : CAT003-1 : TPTP v9.0.0. Released v1.0.0.
% 0.06/0.12 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/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
% 0.13/0.31 % Computer : n017.cluster.edu
% 0.13/0.31 % Model : x86_64 x86_64
% 0.13/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.31 % Memory : 8042.1875MB
% 0.13/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.31 % CPULimit : 300
% 0.13/0.31 % WCLimit : 300
% 0.13/0.31 % DateTime : Mon Apr 7 15:37:10 EDT 2025
% 0.13/0.32 % CPUTime :
% 96.50/81.84 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 96.50/81.85
% 96.50/81.85 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------