%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : CAT002-1 : 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 : n006.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 05:46:24 PM UTC 2025
% Result : Unsatisfiable 176.99s 160.74s
% Output : CNFRefutation 176.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 22
% Syntax : Number of formulae : 133 ( 47 unt; 0 typ; 0 def)
% Number of atoms : 281 ( 42 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 298 ( 150 ~; 148 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 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 : 200 ( 200 !; 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_194,axiom,
h != g,
file(unknown,unknown) ).
tff(f_190,axiom,
product(a,b,c),
file(unknown,unknown) ).
tff(f_191,axiom,
product(c,h,d),
file(unknown,unknown) ).
tff(f_60,axiom,
! [X,Y,Z] :
( ~ product(X,Y,Z)
| defined(X,Y) ),
file(unknown,unknown) ).
tff(f_68,axiom,
! [X,Y,Xy,Z] :
( ~ product(X,Y,Xy)
| ~ defined(Xy,Z)
| defined(Y,Z) ),
file(unknown,unknown) ).
tff(f_137,axiom,
! [X] : identity_map(codomain(X)),
file(unknown,unknown) ).
tff(f_192,axiom,
product(c,g,d),
file(unknown,unknown) ).
tff(f_145,axiom,
! [X] : product(codomain(X),X,X),
file(unknown,unknown) ).
tff(f_99,axiom,
! [Y,Z,Yz,X] :
( ~ product(Y,Z,Yz)
| ~ defined(X,Yz)
| defined(X,Y) ),
file(unknown,unknown) ).
tff(f_162,axiom,
! [X,Y] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) ),
file(unknown,unknown) ).
tff(f_143,axiom,
! [X] : product(X,domain(X),X),
file(unknown,unknown) ).
tff(f_189,axiom,
! [X,W,Y] :
( ~ product(b,X,W)
| ~ product(b,Y,W)
| ( X = Y ) ),
file(unknown,unknown) ).
tff(f_54,axiom,
! [X,Y] :
( ~ defined(X,Y)
| product(X,Y,compose(X,Y)) ),
file(unknown,unknown) ).
tff(f_91,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_141,axiom,
! [X] : defined(codomain(X),X),
file(unknown,unknown) ).
tff(f_154,axiom,
! [X,Y] :
( ~ defined(X,Y)
| ~ identity_map(X)
| product(X,Y,Y) ),
file(unknown,unknown) ).
tff(f_132,axiom,
! [X,Y,Z] :
( ~ defined(X,Y)
| ~ defined(Y,Z)
| ~ identity_map(Y)
| defined(X,Z) ),
file(unknown,unknown) ).
tff(f_121,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_171,axiom,
! [X,Y,Z,W] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) ),
file(unknown,unknown) ).
tff(f_135,axiom,
! [X] : identity_map(domain(X)),
file(unknown,unknown) ).
tff(f_139,axiom,
! [X] : defined(X,domain(X)),
file(unknown,unknown) ).
tff(f_181,axiom,
! [X,W,Y] :
( ~ product(a,X,W)
| ~ product(a,Y,W)
| ( X = Y ) ),
file(unknown,unknown) ).
tff(c_48,plain,
h != g,
inference(cnfTransformation,[status(thm)],[f_194]) ).
tff(c_42,plain,
product(a,b,c),
inference(cnfTransformation,[status(thm)],[f_190]) ).
tff(c_44,plain,
product(c,h,d),
inference(cnfTransformation,[status(thm)],[f_191]) ).
tff(c_55,plain,
! [X_65,Y_66,Z_67] :
( defined(X_65,Y_66)
| ~ product(X_65,Y_66,Z_67) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_75,plain,
defined(c,h),
inference(resolution,[status(thm)],[c_44,c_55]) ).
tff(c_315,plain,
! [Y_97,Z_98,Xy_99,X_100] :
( defined(Y_97,Z_98)
| ~ defined(Xy_99,Z_98)
| ~ product(X_100,Y_97,Xy_99) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_942,plain,
! [Y_147,X_148] :
( defined(Y_147,h)
| ~ product(X_148,Y_147,c) ),
inference(resolution,[status(thm)],[c_75,c_315]) ).
tff(c_968,plain,
defined(b,h),
inference(resolution,[status(thm)],[c_42,c_942]) ).
tff(c_22,plain,
! [X_40] : identity_map(codomain(X_40)),
inference(cnfTransformation,[status(thm)],[f_137]) ).
tff(c_46,plain,
product(c,g,d),
inference(cnfTransformation,[status(thm)],[f_192]) ).
tff(c_77,plain,
defined(c,g),
inference(resolution,[status(thm)],[c_46,c_55]) ).
tff(c_1001,plain,
! [Y_149,X_150] :
( defined(Y_149,g)
| ~ product(X_150,Y_149,c) ),
inference(resolution,[status(thm)],[c_77,c_315]) ).
tff(c_1027,plain,
defined(b,g),
inference(resolution,[status(thm)],[c_42,c_1001]) ).
tff(c_30,plain,
! [X_44] : product(codomain(X_44),X_44,X_44),
inference(cnfTransformation,[status(thm)],[f_145]) ).
tff(c_12,plain,
! [X_24,Y_21,Yz_23,Z_22] :
( defined(X_24,Y_21)
| ~ defined(X_24,Yz_23)
| ~ product(Y_21,Z_22,Yz_23) ),
inference(cnfTransformation,[status(thm)],[f_99]) ).
tff(c_1320,plain,
! [Y_163,Z_164] :
( defined(b,Y_163)
| ~ product(Y_163,Z_164,g) ),
inference(resolution,[status(thm)],[c_1027,c_12]) ).
tff(c_1342,plain,
defined(b,codomain(g)),
inference(resolution,[status(thm)],[c_30,c_1320]) ).
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_162]) ).
tff(c_28,plain,
! [X_43] : product(X_43,domain(X_43),X_43),
inference(cnfTransformation,[status(thm)],[f_143]) ).
tff(c_93,plain,
! [Y_74,X_75,W_76] :
( ( Y_74 = X_75 )
| ~ product(b,Y_74,W_76)
| ~ product(b,X_75,W_76) ),
inference(cnfTransformation,[status(thm)],[f_189]) ).
tff(c_110,plain,
! [X_77] :
( ( domain(b) = X_77 )
| ~ product(b,X_77,b) ),
inference(resolution,[status(thm)],[c_28,c_93]) ).
tff(c_2025,plain,
! [Y_190] :
( ( domain(b) = Y_190 )
| ~ identity_map(Y_190)
| ~ defined(b,Y_190) ),
inference(resolution,[status(thm)],[c_34,c_110]) ).
tff(c_2038,plain,
( ( domain(b) = codomain(g) )
| ~ identity_map(codomain(g)) ),
inference(resolution,[status(thm)],[c_1342,c_2025]) ).
tff(c_2060,plain,
domain(b) = codomain(g),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_2038]) ).
tff(c_1548,plain,
! [Y_175,Z_176] :
( defined(b,Y_175)
| ~ product(Y_175,Z_176,h) ),
inference(resolution,[status(thm)],[c_968,c_12]) ).
tff(c_1570,plain,
defined(b,codomain(h)),
inference(resolution,[status(thm)],[c_30,c_1548]) ).
tff(c_2035,plain,
( ( domain(b) = codomain(h) )
| ~ identity_map(codomain(h)) ),
inference(resolution,[status(thm)],[c_1570,c_2025]) ).
tff(c_2057,plain,
domain(b) = codomain(h),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_2035]) ).
tff(c_2272,plain,
codomain(h) = codomain(g),
inference(demodulation,[status(thm),theory(equality)],[c_2060,c_2057]) ).
tff(c_2252,plain,
product(b,codomain(h),b),
inference(superposition,[status(thm),theory(equality)],[c_2057,c_28]) ).
tff(c_2669,plain,
product(b,codomain(g),b),
inference(demodulation,[status(thm),theory(equality)],[c_2272,c_2252]) ).
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_54]) ).
tff(c_637,plain,
! [Xy_123,X_126,Xyz_127,Yz_125,Y_128,Z_124] :
( product(X_126,Yz_125,Xyz_127)
| ~ product(Y_128,Z_124,Yz_125)
| ~ product(Xy_123,Z_124,Xyz_127)
| ~ product(X_126,Y_128,Xy_123) ),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_6455,plain,
! [X_356,X_357,Xyz_358,Xy_359] :
( product(X_356,X_357,Xyz_358)
| ~ product(Xy_359,X_357,Xyz_358)
| ~ product(X_356,codomain(X_357),Xy_359) ),
inference(resolution,[status(thm)],[c_30,c_637]) ).
tff(c_34958,plain,
! [X_763,Y_764,X_765] :
( product(X_763,Y_764,compose(X_765,Y_764))
| ~ product(X_763,codomain(Y_764),X_765)
| ~ defined(X_765,Y_764) ),
inference(resolution,[status(thm)],[c_2,c_6455]) ).
tff(c_34996,plain,
( product(b,g,compose(b,g))
| ~ defined(b,g) ),
inference(resolution,[status(thm)],[c_2669,c_34958]) ).
tff(c_35039,plain,
product(b,g,compose(b,g)),
inference(demodulation,[status(thm),theory(equality)],[c_1027,c_34996]) ).
tff(c_26,plain,
! [X_42] : defined(codomain(X_42),X_42),
inference(cnfTransformation,[status(thm)],[f_141]) ).
tff(c_127,plain,
! [X_78,Y_79,Yz_80,Z_81] :
( defined(X_78,Y_79)
| ~ defined(X_78,Yz_80)
| ~ product(Y_79,Z_81,Yz_80) ),
inference(cnfTransformation,[status(thm)],[f_99]) ).
tff(c_142,plain,
! [X_42,Y_79,Z_81] :
( defined(codomain(X_42),Y_79)
| ~ product(Y_79,Z_81,X_42) ),
inference(resolution,[status(thm)],[c_26,c_127]) ).
tff(c_35153,plain,
defined(codomain(compose(b,g)),b),
inference(resolution,[status(thm)],[c_35039,c_142]) ).
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_154]) ).
tff(c_76,plain,
defined(a,b),
inference(resolution,[status(thm)],[c_42,c_55]) ).
tff(c_143,plain,
! [Y_82,Z_83] :
( defined(a,Y_82)
| ~ product(Y_82,Z_83,b) ),
inference(resolution,[status(thm)],[c_76,c_127]) ).
tff(c_162,plain,
! [X_45] :
( defined(a,X_45)
| ~ identity_map(X_45)
| ~ defined(X_45,b) ),
inference(resolution,[status(thm)],[c_32,c_143]) ).
tff(c_35293,plain,
( defined(a,codomain(compose(b,g)))
| ~ identity_map(codomain(compose(b,g))) ),
inference(resolution,[status(thm)],[c_35153,c_162]) ).
tff(c_35332,plain,
defined(a,codomain(compose(b,g))),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_35293]) ).
tff(c_368,plain,
! [X_102,Z_103,Y_104] :
( defined(X_102,Z_103)
| ~ identity_map(Y_104)
| ~ defined(Y_104,Z_103)
| ~ defined(X_102,Y_104) ),
inference(cnfTransformation,[status(thm)],[f_132]) ).
tff(c_384,plain,
! [X_102,X_42] :
( defined(X_102,X_42)
| ~ identity_map(codomain(X_42))
| ~ defined(X_102,codomain(X_42)) ),
inference(resolution,[status(thm)],[c_26,c_368]) ).
tff(c_394,plain,
! [X_102,X_42] :
( defined(X_102,X_42)
| ~ defined(X_102,codomain(X_42)) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_384]) ).
tff(c_35534,plain,
defined(a,compose(b,g)),
inference(resolution,[status(thm)],[c_35332,c_394]) ).
tff(c_709,plain,
! [Z_132,X_135,Y_137,Xy_133,Xyz_136,Yz_134] :
( product(Xy_133,Z_132,Xyz_136)
| ~ product(X_135,Y_137,Xy_133)
| ~ product(X_135,Yz_134,Xyz_136)
| ~ product(Y_137,Z_132,Yz_134) ),
inference(cnfTransformation,[status(thm)],[f_121]) ).
tff(c_4700,plain,
! [Z_295,Xyz_296,Yz_297] :
( product(c,Z_295,Xyz_296)
| ~ product(a,Yz_297,Xyz_296)
| ~ product(b,Z_295,Yz_297) ),
inference(resolution,[status(thm)],[c_42,c_709]) ).
tff(c_26232,plain,
! [Z_674,Y_675] :
( product(c,Z_674,compose(a,Y_675))
| ~ product(b,Z_674,Y_675)
| ~ defined(a,Y_675) ),
inference(resolution,[status(thm)],[c_2,c_4700]) ).
tff(c_218,plain,
! [Z_88,W_89,X_90,Y_91] :
( ( Z_88 = W_89 )
| ~ product(X_90,Y_91,W_89)
| ~ product(X_90,Y_91,Z_88) ),
inference(cnfTransformation,[status(thm)],[f_171]) ).
tff(c_242,plain,
! [Z_88] :
( ( d = Z_88 )
| ~ product(c,g,Z_88) ),
inference(resolution,[status(thm)],[c_46,c_218]) ).
tff(c_136174,plain,
! [Y_1314] :
( ( compose(a,Y_1314) = d )
| ~ product(b,g,Y_1314)
| ~ defined(a,Y_1314) ),
inference(resolution,[status(thm)],[c_26232,c_242]) ).
tff(c_136197,plain,
( ( compose(a,compose(b,g)) = d )
| ~ defined(a,compose(b,g)) ),
inference(resolution,[status(thm)],[c_35039,c_136174]) ).
tff(c_136218,plain,
compose(a,compose(b,g)) = d,
inference(demodulation,[status(thm),theory(equality)],[c_35534,c_136197]) ).
tff(c_136309,plain,
( product(a,compose(b,g),d)
| ~ defined(a,compose(b,g)) ),
inference(superposition,[status(thm),theory(equality)],[c_136218,c_2]) ).
tff(c_136365,plain,
product(a,compose(b,g),d),
inference(demodulation,[status(thm),theory(equality)],[c_35534,c_136309]) ).
tff(c_20,plain,
! [X_39] : identity_map(domain(X_39)),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_681,plain,
! [Z_130,X_131] :
( ( Z_130 = X_131 )
| ~ product(codomain(X_131),X_131,Z_130) ),
inference(resolution,[status(thm)],[c_30,c_218]) ).
tff(c_685,plain,
! [Y_48] :
( ( codomain(Y_48) = Y_48 )
| ~ identity_map(Y_48)
| ~ defined(codomain(Y_48),Y_48) ),
inference(resolution,[status(thm)],[c_34,c_681]) ).
tff(c_734,plain,
! [Y_138] :
( ( codomain(Y_138) = Y_138 )
| ~ identity_map(Y_138) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_685]) ).
tff(c_741,plain,
! [X_39] : ( codomain(domain(X_39)) = domain(X_39) ),
inference(resolution,[status(thm)],[c_20,c_734]) ).
tff(c_24,plain,
! [X_41] : defined(X_41,domain(X_41)),
inference(cnfTransformation,[status(thm)],[f_139]) ).
tff(c_1594,plain,
! [Y_177,X_178,X_179] :
( defined(Y_177,domain(X_178))
| ~ product(X_179,Y_177,X_178) ),
inference(resolution,[status(thm)],[c_24,c_315]) ).
tff(c_1620,plain,
! [Y_2,X_1] :
( defined(Y_2,domain(compose(X_1,Y_2)))
| ~ defined(X_1,Y_2) ),
inference(resolution,[status(thm)],[c_2,c_1594]) ).
tff(c_1627,plain,
defined(h,domain(d)),
inference(resolution,[status(thm)],[c_44,c_1594]) ).
tff(c_6,plain,
! [Y_7,Z_9,Xy_8,X_6] :
( defined(Y_7,Z_9)
| ~ defined(Xy_8,Z_9)
| ~ product(X_6,Y_7,Xy_8) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_3456,plain,
! [Y_230,X_231] :
( defined(Y_230,domain(d))
| ~ product(X_231,Y_230,h) ),
inference(resolution,[status(thm)],[c_1627,c_6]) ).
tff(c_3473,plain,
! [Y_48] :
( defined(Y_48,domain(d))
| ~ identity_map(Y_48)
| ~ defined(h,Y_48) ),
inference(resolution,[status(thm)],[c_34,c_3456]) ).
tff(c_1043,plain,
! [X_151,Y_152,Z_153] :
( defined(codomain(X_151),Y_152)
| ~ product(Y_152,Z_153,X_151) ),
inference(resolution,[status(thm)],[c_26,c_127]) ).
tff(c_1063,plain,
! [Y_46,X_45] :
( defined(codomain(Y_46),X_45)
| ~ identity_map(X_45)
| ~ defined(X_45,Y_46) ),
inference(resolution,[status(thm)],[c_32,c_1043]) ).
tff(c_1960,plain,
! [Z_187,Y_188,X_189] :
( ( Z_187 = Y_188 )
| ~ product(X_189,Y_188,Z_187)
| ~ identity_map(X_189)
| ~ defined(X_189,Y_188) ),
inference(resolution,[status(thm)],[c_32,c_218]) ).
tff(c_10746,plain,
! [Y_436,X_437] :
( ( Y_436 = X_437 )
| ~ identity_map(X_437)
| ~ identity_map(Y_436)
| ~ defined(X_437,Y_436) ),
inference(resolution,[status(thm)],[c_34,c_1960]) ).
tff(c_10752,plain,
! [Y_46,X_45] :
( ( codomain(Y_46) = X_45 )
| ~ identity_map(codomain(Y_46))
| ~ identity_map(X_45)
| ~ defined(X_45,Y_46) ),
inference(resolution,[status(thm)],[c_1063,c_10746]) ).
tff(c_11143,plain,
! [Y_443,X_444] :
( ( codomain(Y_443) = X_444 )
| ~ identity_map(X_444)
| ~ defined(X_444,Y_443) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_10752]) ).
tff(c_11149,plain,
! [Y_46,X_45] :
( ( codomain(Y_46) = codomain(X_45) )
| ~ identity_map(codomain(Y_46))
| ~ identity_map(X_45)
| ~ defined(X_45,Y_46) ),
inference(resolution,[status(thm)],[c_1063,c_11143]) ).
tff(c_25184,plain,
! [Y_661,X_662] :
( ( codomain(Y_661) = codomain(X_662) )
| ~ identity_map(X_662)
| ~ defined(X_662,Y_661) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_11149]) ).
tff(c_25238,plain,
! [Y_48] :
( ( codomain(domain(d)) = codomain(Y_48) )
| ~ identity_map(Y_48)
| ~ defined(h,Y_48) ),
inference(resolution,[status(thm)],[c_3473,c_25184]) ).
tff(c_48783,plain,
! [Y_870] :
( ( domain(d) = codomain(Y_870) )
| ~ identity_map(Y_870)
| ~ defined(h,Y_870) ),
inference(demodulation,[status(thm),theory(equality)],[c_741,c_25238]) ).
tff(c_48840,plain,
! [X_1] :
( ( codomain(domain(compose(X_1,h))) = domain(d) )
| ~ identity_map(domain(compose(X_1,h)))
| ~ defined(X_1,h) ),
inference(resolution,[status(thm)],[c_1620,c_48783]) ).
tff(c_53709,plain,
! [X_899] :
( ( domain(compose(X_899,h)) = domain(d) )
| ~ defined(X_899,h) ),
inference(demodulation,[status(thm),theory(equality)],[c_20,c_741,c_48840]) ).
tff(c_487724,plain,
! [X_3145] :
( product(compose(X_3145,h),domain(d),compose(X_3145,h))
| ~ defined(X_3145,h) ),
inference(superposition,[status(thm),theory(equality)],[c_53709,c_28]) ).
tff(c_7582,plain,
! [X_402,Y_403] :
( defined(codomain(compose(X_402,Y_403)),X_402)
| ~ defined(X_402,Y_403) ),
inference(resolution,[status(thm)],[c_2,c_1043]) ).
tff(c_7631,plain,
! [Y_403] :
( defined(a,codomain(compose(b,Y_403)))
| ~ identity_map(codomain(compose(b,Y_403)))
| ~ defined(b,Y_403) ),
inference(resolution,[status(thm)],[c_7582,c_162]) ).
tff(c_31747,plain,
! [Y_734] :
( defined(a,codomain(compose(b,Y_734)))
| ~ defined(b,Y_734) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_7631]) ).
tff(c_31872,plain,
! [Y_735] :
( defined(a,compose(b,Y_735))
| ~ defined(b,Y_735) ),
inference(resolution,[status(thm)],[c_31747,c_394]) ).
tff(c_31946,plain,
! [Y_21,Z_22,Y_735] :
( defined(a,Y_21)
| ~ product(Y_21,Z_22,compose(b,Y_735))
| ~ defined(b,Y_735) ),
inference(resolution,[status(thm)],[c_31872,c_12]) ).
tff(c_487744,plain,
( defined(a,compose(b,h))
| ~ defined(b,h) ),
inference(resolution,[status(thm)],[c_487724,c_31946]) ).
tff(c_488014,plain,
defined(a,compose(b,h)),
inference(demodulation,[status(thm),theory(equality)],[c_968,c_487744]) ).
tff(c_31859,plain,
! [Y_734] :
( defined(a,compose(b,Y_734))
| ~ defined(b,Y_734) ),
inference(resolution,[status(thm)],[c_31747,c_394]) ).
tff(c_6927,plain,
! [X_377,Xy_375,Y_378,X_376,Xyz_374] :
( product(X_377,compose(X_376,Y_378),Xyz_374)
| ~ product(Xy_375,Y_378,Xyz_374)
| ~ product(X_377,X_376,Xy_375)
| ~ defined(X_376,Y_378) ),
inference(resolution,[status(thm)],[c_2,c_637]) ).
tff(c_30369,plain,
! [X_720,X_721] :
( product(X_720,compose(X_721,h),d)
| ~ product(X_720,X_721,c)
| ~ defined(X_721,h) ),
inference(resolution,[status(thm)],[c_44,c_6927]) ).
tff(c_236,plain,
! [X_1,Y_2,Z_88] :
( ( compose(X_1,Y_2) = Z_88 )
| ~ product(X_1,Y_2,Z_88)
| ~ defined(X_1,Y_2) ),
inference(resolution,[status(thm)],[c_2,c_218]) ).
tff(c_655778,plain,
! [X_3982,X_3983] :
( ( compose(X_3982,compose(X_3983,h)) = d )
| ~ defined(X_3982,compose(X_3983,h))
| ~ product(X_3982,X_3983,c)
| ~ defined(X_3983,h) ),
inference(resolution,[status(thm)],[c_30369,c_236]) ).
tff(c_656043,plain,
( ( compose(a,compose(b,h)) = d )
| ~ product(a,b,c)
| ~ defined(b,h) ),
inference(resolution,[status(thm)],[c_31859,c_655778]) ).
tff(c_656224,plain,
compose(a,compose(b,h)) = d,
inference(demodulation,[status(thm),theory(equality)],[c_968,c_42,c_656043]) ).
tff(c_656579,plain,
( product(a,compose(b,h),d)
| ~ defined(a,compose(b,h)) ),
inference(superposition,[status(thm),theory(equality)],[c_656224,c_2]) ).
tff(c_656812,plain,
product(a,compose(b,h),d),
inference(demodulation,[status(thm),theory(equality)],[c_488014,c_656579]) ).
tff(c_38,plain,
! [Y_55,X_53,W_54] :
( ( Y_55 = X_53 )
| ~ product(a,Y_55,W_54)
| ~ product(a,X_53,W_54) ),
inference(cnfTransformation,[status(thm)],[f_181]) ).
tff(c_663184,plain,
! [X_4004] :
( ( compose(b,h) = X_4004 )
| ~ product(a,X_4004,d) ),
inference(resolution,[status(thm)],[c_656812,c_38]) ).
tff(c_663275,plain,
compose(b,h) = compose(b,g),
inference(resolution,[status(thm)],[c_136365,c_663184]) ).
tff(c_664118,plain,
( product(b,h,compose(b,g))
| ~ defined(b,h) ),
inference(superposition,[status(thm),theory(equality)],[c_663275,c_2]) ).
tff(c_664409,plain,
product(b,h,compose(b,g)),
inference(demodulation,[status(thm),theory(equality)],[c_968,c_664118]) ).
tff(c_40,plain,
! [Y_58,X_56,W_57] :
( ( Y_58 = X_56 )
| ~ product(b,Y_58,W_57)
| ~ product(b,X_56,W_57) ),
inference(cnfTransformation,[status(thm)],[f_189]) ).
tff(c_35157,plain,
! [X_56] :
( ( g = X_56 )
| ~ product(b,X_56,compose(b,g)) ),
inference(resolution,[status(thm)],[c_35039,c_40]) ).
tff(c_664597,plain,
h = g,
inference(resolution,[status(thm)],[c_664409,c_35157]) ).
tff(c_664813,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_48,c_664597]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : CAT002-1 : TPTP v9.0.0. Released v1.0.0.
% 0.11/0.13 % 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 : n006.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 15:36:53 EDT 2025
% 0.13/0.34 % CPUTime :
% 176.99/160.74 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 176.99/160.75
% 176.99/160.75 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------