TSTP Solution File: CAT004-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : CAT004-1 : TPTP v8.1.2. 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 : n023.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 : Tue Aug 22 10:34:35 EDT 2023
% Result : Unsatisfiable 31.53s 20.28s
% Output : CNFRefutation 31.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 33
% Syntax : Number of formulae : 142 ( 51 unt; 12 typ; 0 def)
% Number of atoms : 257 ( 41 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 256 ( 129 ~; 127 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 6 >; 4 *; 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 : 179 (; 179 !; 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_193,axiom,
h != g,
file(unknown,unknown) ).
tff(f_189,axiom,
product(a,b,c),
file(unknown,unknown) ).
tff(f_190,axiom,
product(h,c,d),
file(unknown,unknown) ).
tff(f_59,axiom,
! [X,Y,Z] :
( ~ product(X,Y,Z)
| defined(X,Y) ),
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_134,axiom,
! [X] : identity_map(domain(X)),
file(unknown,unknown) ).
tff(f_142,axiom,
! [X] : product(X,domain(X),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_144,axiom,
! [X] : product(codomain(X),X,X),
file(unknown,unknown) ).
tff(f_153,axiom,
! [X,Y] :
( ~ defined(X,Y)
| ~ identity_map(X)
| product(X,Y,Y) ),
file(unknown,unknown) ).
tff(f_180,axiom,
! [X,W,Y] :
( ~ product(X,a,W)
| ~ product(Y,a,W)
| ( X = Y ) ),
file(unknown,unknown) ).
tff(f_53,axiom,
! [X,Y] :
( ~ defined(X,Y)
| product(X,Y,compose(X,Y)) ),
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_138,axiom,
! [X] : defined(X,domain(X)),
file(unknown,unknown) ).
tff(f_140,axiom,
! [X] : defined(codomain(X),X),
file(unknown,unknown) ).
tff(f_161,axiom,
! [X,Y] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) ),
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_136,axiom,
! [X] : identity_map(codomain(X)),
file(unknown,unknown) ).
tff(f_188,axiom,
! [X,W,Y] :
( ~ product(X,b,W)
| ~ product(Y,b,W)
| ( 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_191,axiom,
product(g,c,d),
file(unknown,unknown) ).
tff(c_48,plain,
h != g,
inference(cnfTransformation,[status(thm)],[f_193]) ).
tff(c_42,plain,
product(a,b,c),
inference(cnfTransformation,[status(thm)],[f_189]) ).
tff(c_44,plain,
product(h,c,d),
inference(cnfTransformation,[status(thm)],[f_190]) ).
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_59]) ).
tff(c_75,plain,
defined(h,c),
inference(resolution,[status(thm)],[c_44,c_55]) ).
tff(c_285,plain,
! [X_92,Y_93,Yz_94,Z_95] :
( defined(X_92,Y_93)
| ~ defined(X_92,Yz_94)
| ~ product(Y_93,Z_95,Yz_94) ),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_962,plain,
! [Y_148,Z_149] :
( defined(h,Y_148)
| ~ product(Y_148,Z_149,c) ),
inference(resolution,[status(thm)],[c_75,c_285]) ).
tff(c_988,plain,
defined(h,a),
inference(resolution,[status(thm)],[c_42,c_962]) ).
tff(c_20,plain,
! [X_39] : identity_map(domain(X_39)),
inference(cnfTransformation,[status(thm)],[f_134]) ).
tff(c_28,plain,
! [X_43] : product(X_43,domain(X_43),X_43),
inference(cnfTransformation,[status(thm)],[f_142]) ).
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_67]) ).
tff(c_1602,plain,
! [Y_176,X_177] :
( defined(Y_176,a)
| ~ product(X_177,Y_176,h) ),
inference(resolution,[status(thm)],[c_988,c_6]) ).
tff(c_1622,plain,
defined(domain(h),a),
inference(resolution,[status(thm)],[c_28,c_1602]) ).
tff(c_30,plain,
! [X_44] : product(codomain(X_44),X_44,X_44),
inference(cnfTransformation,[status(thm)],[f_144]) ).
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_187,plain,
! [Y_83,X_84,W_85] :
( ( Y_83 = X_84 )
| ~ product(Y_83,a,W_85)
| ~ product(X_84,a,W_85) ),
inference(cnfTransformation,[status(thm)],[f_180]) ).
tff(c_1800,plain,
! [X_186,X_185] :
( ( X_186 = X_185 )
| ~ product(X_185,a,a)
| ~ identity_map(X_186)
| ~ defined(X_186,a) ),
inference(resolution,[status(thm)],[c_32,c_187]) ).
tff(c_2040,plain,
! [X_193] :
( ( codomain(a) = X_193 )
| ~ identity_map(X_193)
| ~ defined(X_193,a) ),
inference(resolution,[status(thm)],[c_30,c_1800]) ).
tff(c_2043,plain,
( ( domain(h) = codomain(a) )
| ~ identity_map(domain(h)) ),
inference(resolution,[status(thm)],[c_1622,c_2040]) ).
tff(c_2062,plain,
domain(h) = codomain(a),
inference(demodulation,[status(thm),theory(equality)],[c_20,c_2043]) ).
tff(c_2276,plain,
product(h,codomain(a),h),
inference(superposition,[status(thm),theory(equality)],[c_2062,c_28]) ).
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_627,plain,
! [Xy_124,Xyz_128,Yz_126,Z_125,X_127,Y_129] :
( product(X_127,Yz_126,Xyz_128)
| ~ product(Y_129,Z_125,Yz_126)
| ~ product(Xy_124,Z_125,Xyz_128)
| ~ product(X_127,Y_129,Xy_124) ),
inference(cnfTransformation,[status(thm)],[f_90]) ).
tff(c_5829,plain,
! [X_340,X_341,Xyz_342,Xy_343] :
( product(X_340,X_341,Xyz_342)
| ~ product(Xy_343,X_341,Xyz_342)
| ~ product(X_340,codomain(X_341),Xy_343) ),
inference(resolution,[status(thm)],[c_30,c_627]) ).
tff(c_40613,plain,
! [X_819,Y_820,X_821] :
( product(X_819,Y_820,compose(X_821,Y_820))
| ~ product(X_819,codomain(Y_820),X_821)
| ~ defined(X_821,Y_820) ),
inference(resolution,[status(thm)],[c_2,c_5829]) ).
tff(c_40650,plain,
( product(h,a,compose(h,a))
| ~ defined(h,a) ),
inference(resolution,[status(thm)],[c_2276,c_40613]) ).
tff(c_40689,plain,
product(h,a,compose(h,a)),
inference(demodulation,[status(thm),theory(equality)],[c_988,c_40650]) ).
tff(c_24,plain,
! [X_41] : defined(X_41,domain(X_41)),
inference(cnfTransformation,[status(thm)],[f_138]) ).
tff(c_240,plain,
! [Y_87,Z_88,Xy_89,X_90] :
( defined(Y_87,Z_88)
| ~ defined(Xy_89,Z_88)
| ~ product(X_90,Y_87,Xy_89) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_254,plain,
! [Y_87,X_41,X_90] :
( defined(Y_87,domain(X_41))
| ~ product(X_90,Y_87,X_41) ),
inference(resolution,[status(thm)],[c_24,c_240]) ).
tff(c_40906,plain,
defined(a,domain(compose(h,a))),
inference(resolution,[status(thm)],[c_40689,c_254]) ).
tff(c_26,plain,
! [X_42] : defined(codomain(X_42),X_42),
inference(cnfTransformation,[status(thm)],[f_140]) ).
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_124,plain,
! [Z_78,W_79,X_80,Y_81] :
( ( Z_78 = W_79 )
| ~ product(X_80,Y_81,W_79)
| ~ product(X_80,Y_81,Z_78) ),
inference(cnfTransformation,[status(thm)],[f_170]) ).
tff(c_599,plain,
! [Z_122,X_123] :
( ( Z_122 = X_123 )
| ~ product(codomain(X_123),X_123,Z_122) ),
inference(resolution,[status(thm)],[c_30,c_124]) ).
tff(c_603,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_599]) ).
tff(c_652,plain,
! [Y_130] :
( ( codomain(Y_130) = Y_130 )
| ~ identity_map(Y_130) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_603]) ).
tff(c_659,plain,
! [X_39] : ( codomain(domain(X_39)) = domain(X_39) ),
inference(resolution,[status(thm)],[c_20,c_652]) ).
tff(c_22,plain,
! [X_40] : identity_map(codomain(X_40)),
inference(cnfTransformation,[status(thm)],[f_136]) ).
tff(c_346,plain,
! [Z_100,X_101] :
( ( Z_100 = X_101 )
| ~ product(X_101,domain(X_101),Z_100) ),
inference(resolution,[status(thm)],[c_28,c_124]) ).
tff(c_358,plain,
! [X_45] :
( ( domain(X_45) = X_45 )
| ~ identity_map(X_45)
| ~ defined(X_45,domain(X_45)) ),
inference(resolution,[status(thm)],[c_32,c_346]) ).
tff(c_388,plain,
! [X_103] :
( ( domain(X_103) = X_103 )
| ~ identity_map(X_103) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_358]) ).
tff(c_396,plain,
! [X_40] : ( domain(codomain(X_40)) = codomain(X_40) ),
inference(resolution,[status(thm)],[c_22,c_388]) ).
tff(c_76,plain,
defined(a,b),
inference(resolution,[status(thm)],[c_42,c_55]) ).
tff(c_922,plain,
! [Y_146,X_147] :
( defined(Y_146,b)
| ~ product(X_147,Y_146,a) ),
inference(resolution,[status(thm)],[c_76,c_240]) ).
tff(c_942,plain,
defined(domain(a),b),
inference(resolution,[status(thm)],[c_28,c_922]) ).
tff(c_93,plain,
! [Y_74,X_75,W_76] :
( ( Y_74 = X_75 )
| ~ product(Y_74,b,W_76)
| ~ product(X_75,b,W_76) ),
inference(cnfTransformation,[status(thm)],[f_188]) ).
tff(c_329,plain,
! [X_99] :
( ( codomain(b) = X_99 )
| ~ product(X_99,b,b) ),
inference(resolution,[status(thm)],[c_30,c_93]) ).
tff(c_1839,plain,
! [X_188] :
( ( codomain(b) = X_188 )
| ~ identity_map(X_188)
| ~ defined(X_188,b) ),
inference(resolution,[status(thm)],[c_32,c_329]) ).
tff(c_1842,plain,
( ( domain(a) = codomain(b) )
| ~ identity_map(domain(a)) ),
inference(resolution,[status(thm)],[c_942,c_1839]) ).
tff(c_1852,plain,
domain(a) = codomain(b),
inference(demodulation,[status(thm),theory(equality)],[c_20,c_1842]) ).
tff(c_1262,plain,
! [Y_161,X_162,X_163] :
( defined(Y_161,domain(X_162))
| ~ product(X_163,Y_161,X_162) ),
inference(resolution,[status(thm)],[c_24,c_240]) ).
tff(c_11416,plain,
! [Y_454,X_455] :
( defined(Y_454,domain(X_455))
| ~ identity_map(Y_454)
| ~ defined(X_455,Y_454) ),
inference(resolution,[status(thm)],[c_34,c_1262]) ).
tff(c_1455,plain,
! [Y_169,X_170,X_171] :
( defined(Y_169,X_170)
| ~ product(X_171,Y_169,codomain(X_170)) ),
inference(resolution,[status(thm)],[c_26,c_240]) ).
tff(c_1483,plain,
! [Y_48,X_170] :
( defined(Y_48,X_170)
| ~ identity_map(Y_48)
| ~ defined(codomain(X_170),Y_48) ),
inference(resolution,[status(thm)],[c_34,c_1455]) ).
tff(c_11453,plain,
! [X_455,X_170] :
( defined(domain(X_455),X_170)
| ~ identity_map(domain(X_455))
| ~ identity_map(codomain(X_170))
| ~ defined(X_455,codomain(X_170)) ),
inference(resolution,[status(thm)],[c_11416,c_1483]) ).
tff(c_11775,plain,
! [X_458,X_459] :
( defined(domain(X_458),X_459)
| ~ defined(X_458,codomain(X_459)) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_20,c_11453]) ).
tff(c_13319,plain,
! [X_482] :
( defined(codomain(b),X_482)
| ~ defined(a,codomain(X_482)) ),
inference(superposition,[status(thm),theory(equality)],[c_1852,c_11775]) ).
tff(c_1064,plain,
! [X_152,Y_153,Z_154] :
( defined(codomain(X_152),Y_153)
| ~ product(Y_153,Z_154,X_152) ),
inference(resolution,[status(thm)],[c_26,c_285]) ).
tff(c_1084,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_1064]) ).
tff(c_872,plain,
! [X_143,Y_144,Z_145] :
( defined(X_143,Y_144)
| ~ product(Y_144,Z_145,domain(X_143)) ),
inference(resolution,[status(thm)],[c_24,c_285]) ).
tff(c_10945,plain,
! [X_443,X_444] :
( defined(X_443,X_444)
| ~ identity_map(X_444)
| ~ defined(X_444,domain(X_443)) ),
inference(resolution,[status(thm)],[c_32,c_872]) ).
tff(c_10957,plain,
! [X_443,Y_46] :
( defined(X_443,codomain(Y_46))
| ~ identity_map(codomain(Y_46))
| ~ identity_map(domain(X_443))
| ~ defined(domain(X_443),Y_46) ),
inference(resolution,[status(thm)],[c_1084,c_10945]) ).
tff(c_11030,plain,
! [X_443,Y_46] :
( defined(X_443,codomain(Y_46))
| ~ defined(domain(X_443),Y_46) ),
inference(demodulation,[status(thm),theory(equality)],[c_20,c_22,c_10957]) ).
tff(c_11440,plain,
! [X_443,X_455] :
( defined(X_443,codomain(domain(X_455)))
| ~ identity_map(domain(X_443))
| ~ defined(X_455,domain(X_443)) ),
inference(resolution,[status(thm)],[c_11416,c_11030]) ).
tff(c_11544,plain,
! [X_443,X_455] :
( defined(X_443,domain(X_455))
| ~ defined(X_455,domain(X_443)) ),
inference(demodulation,[status(thm),theory(equality)],[c_20,c_659,c_11440]) ).
tff(c_13347,plain,
! [X_443] :
( defined(X_443,domain(codomain(b)))
| ~ defined(a,codomain(domain(X_443))) ),
inference(resolution,[status(thm)],[c_13319,c_11544]) ).
tff(c_13434,plain,
! [X_443] :
( defined(X_443,codomain(b))
| ~ defined(a,domain(X_443)) ),
inference(demodulation,[status(thm),theory(equality)],[c_659,c_396,c_13347]) ).
tff(c_41328,plain,
defined(compose(h,a),codomain(b)),
inference(resolution,[status(thm)],[c_40906,c_13434]) ).
tff(c_311,plain,
! [X_96,Z_97,Y_98] :
( defined(X_96,Z_97)
| ~ identity_map(Y_98)
| ~ defined(Y_98,Z_97)
| ~ defined(X_96,Y_98) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_321,plain,
! [X_96,X_42] :
( defined(X_96,X_42)
| ~ identity_map(codomain(X_42))
| ~ defined(X_96,codomain(X_42)) ),
inference(resolution,[status(thm)],[c_26,c_311]) ).
tff(c_328,plain,
! [X_96,X_42] :
( defined(X_96,X_42)
| ~ defined(X_96,codomain(X_42)) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_321]) ).
tff(c_42828,plain,
defined(compose(h,a),b),
inference(resolution,[status(thm)],[c_41328,c_328]) ).
tff(c_5271,plain,
! [X_318,Xyz_319,Xy_320] :
( product(X_318,c,Xyz_319)
| ~ product(Xy_320,b,Xyz_319)
| ~ product(X_318,a,Xy_320) ),
inference(resolution,[status(thm)],[c_42,c_627]) ).
tff(c_23380,plain,
! [X_626,X_627] :
( product(X_626,c,compose(X_627,b))
| ~ product(X_626,a,X_627)
| ~ defined(X_627,b) ),
inference(resolution,[status(thm)],[c_2,c_5271]) ).
tff(c_146,plain,
! [Z_78] :
( ( d = Z_78 )
| ~ product(h,c,Z_78) ),
inference(resolution,[status(thm)],[c_44,c_124]) ).
tff(c_141283,plain,
! [X_1343] :
( ( compose(X_1343,b) = d )
| ~ product(h,a,X_1343)
| ~ defined(X_1343,b) ),
inference(resolution,[status(thm)],[c_23380,c_146]) ).
tff(c_141314,plain,
( ( compose(compose(h,a),b) = d )
| ~ defined(compose(h,a),b) ),
inference(resolution,[status(thm)],[c_40689,c_141283]) ).
tff(c_141344,plain,
compose(compose(h,a),b) = d,
inference(demodulation,[status(thm),theory(equality)],[c_42828,c_141314]) ).
tff(c_141432,plain,
( product(compose(h,a),b,d)
| ~ defined(compose(h,a),b) ),
inference(superposition,[status(thm),theory(equality)],[c_141344,c_2]) ).
tff(c_141486,plain,
product(compose(h,a),b,d),
inference(demodulation,[status(thm),theory(equality)],[c_42828,c_141432]) ).
tff(c_46,plain,
product(g,c,d),
inference(cnfTransformation,[status(thm)],[f_191]) ).
tff(c_77,plain,
defined(g,c),
inference(resolution,[status(thm)],[c_46,c_55]) ).
tff(c_830,plain,
! [Y_141,Z_142] :
( defined(g,Y_141)
| ~ product(Y_141,Z_142,c) ),
inference(resolution,[status(thm)],[c_77,c_285]) ).
tff(c_856,plain,
defined(g,a),
inference(resolution,[status(thm)],[c_42,c_830]) ).
tff(c_1543,plain,
! [Y_173,X_174] :
( defined(Y_173,a)
| ~ product(X_174,Y_173,g) ),
inference(resolution,[status(thm)],[c_856,c_6]) ).
tff(c_1563,plain,
defined(domain(g),a),
inference(resolution,[status(thm)],[c_28,c_1543]) ).
tff(c_2046,plain,
( ( domain(g) = codomain(a) )
| ~ identity_map(domain(g)) ),
inference(resolution,[status(thm)],[c_1563,c_2040]) ).
tff(c_2065,plain,
domain(g) = codomain(a),
inference(demodulation,[status(thm),theory(equality)],[c_20,c_2046]) ).
tff(c_2208,plain,
product(g,codomain(a),g),
inference(superposition,[status(thm),theory(equality)],[c_2065,c_28]) ).
tff(c_40648,plain,
( product(g,a,compose(g,a))
| ~ defined(g,a) ),
inference(resolution,[status(thm)],[c_2208,c_40613]) ).
tff(c_40686,plain,
product(g,a,compose(g,a)),
inference(demodulation,[status(thm),theory(equality)],[c_856,c_40648]) ).
tff(c_40802,plain,
defined(a,domain(compose(g,a))),
inference(resolution,[status(thm)],[c_40686,c_254]) ).
tff(c_40935,plain,
defined(compose(g,a),domain(a)),
inference(resolution,[status(thm)],[c_40802,c_11544]) ).
tff(c_40984,plain,
defined(compose(g,a),codomain(b)),
inference(demodulation,[status(thm),theory(equality)],[c_1852,c_40935]) ).
tff(c_42199,plain,
defined(compose(g,a),b),
inference(resolution,[status(thm)],[c_40984,c_328]) ).
tff(c_148,plain,
! [Z_78] :
( ( d = Z_78 )
| ~ product(g,c,Z_78) ),
inference(resolution,[status(thm)],[c_46,c_124]) ).
tff(c_132410,plain,
! [X_1296] :
( ( compose(X_1296,b) = d )
| ~ product(g,a,X_1296)
| ~ defined(X_1296,b) ),
inference(resolution,[status(thm)],[c_23380,c_148]) ).
tff(c_132441,plain,
( ( compose(compose(g,a),b) = d )
| ~ defined(compose(g,a),b) ),
inference(resolution,[status(thm)],[c_40686,c_132410]) ).
tff(c_132471,plain,
compose(compose(g,a),b) = d,
inference(demodulation,[status(thm),theory(equality)],[c_42199,c_132441]) ).
tff(c_109,plain,
! [X_75,X_1] :
( ( X_75 = X_1 )
| ~ product(X_75,b,compose(X_1,b))
| ~ defined(X_1,b) ),
inference(resolution,[status(thm)],[c_2,c_93]) ).
tff(c_132556,plain,
! [X_75] :
( ( compose(g,a) = X_75 )
| ~ product(X_75,b,d)
| ~ defined(compose(g,a),b) ),
inference(superposition,[status(thm),theory(equality)],[c_132471,c_109]) ).
tff(c_132611,plain,
! [X_75] :
( ( compose(g,a) = X_75 )
| ~ product(X_75,b,d) ),
inference(demodulation,[status(thm),theory(equality)],[c_42199,c_132556]) ).
tff(c_141588,plain,
compose(h,a) = compose(g,a),
inference(resolution,[status(thm)],[c_141486,c_132611]) ).
tff(c_141756,plain,
product(h,a,compose(g,a)),
inference(demodulation,[status(thm),theory(equality)],[c_141588,c_40689]) ).
tff(c_38,plain,
! [Y_55,X_53,W_54] :
( ( Y_55 = X_53 )
| ~ product(Y_55,a,W_54)
| ~ product(X_53,a,W_54) ),
inference(cnfTransformation,[status(thm)],[f_180]) ).
tff(c_40806,plain,
! [X_53] :
( ( g = X_53 )
| ~ product(X_53,a,compose(g,a)) ),
inference(resolution,[status(thm)],[c_40686,c_38]) ).
tff(c_141985,plain,
h = g,
inference(resolution,[status(thm)],[c_141756,c_40806]) ).
tff(c_142090,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_48,c_141985]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.07 % Problem : CAT004-1 : TPTP v8.1.2. Released v1.0.0.
% 0.04/0.08 % 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
% 0.07/0.27 % Computer : n023.cluster.edu
% 0.07/0.27 % Model : x86_64 x86_64
% 0.07/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27 % Memory : 8042.1875MB
% 0.07/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27 % CPULimit : 300
% 0.07/0.27 % WCLimit : 300
% 0.07/0.27 % DateTime : Thu Aug 3 18:03:22 EDT 2023
% 0.07/0.27 % CPUTime :
% 31.53/20.28 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 31.58/20.30
% 31.58/20.30 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 31.86/20.35
% 31.86/20.35 Inference rules
% 31.86/20.35 ----------------------
% 31.86/20.35 #Ref : 0
% 31.86/20.35 #Sup : 29925
% 31.86/20.35 #Fact : 0
% 31.86/20.35 #Define : 0
% 31.86/20.35 #Split : 31
% 31.86/20.35 #Chain : 0
% 31.86/20.35 #Close : 0
% 31.86/20.35
% 31.86/20.35 Ordering : KBO
% 31.86/20.35
% 31.86/20.35 Simplification rules
% 31.86/20.35 ----------------------
% 31.86/20.35 #Subsume : 14486
% 31.86/20.35 #Demod : 26069
% 31.86/20.35 #Tautology : 4990
% 31.86/20.35 #SimpNegUnit : 1767
% 31.86/20.35 #BackRed : 113
% 31.86/20.35
% 31.86/20.35 #Partial instantiations: 0
% 31.86/20.35 #Strategies tried : 1
% 31.86/20.35
% 31.86/20.35 Timing (in seconds)
% 31.86/20.35 ----------------------
% 31.86/20.35 Preprocessing : 0.58
% 31.86/20.35 Parsing : 0.29
% 31.86/20.35 CNF conversion : 0.03
% 31.86/20.35 Main loop : 18.74
% 31.86/20.35 Inferencing : 2.59
% 31.86/20.35 Reduction : 6.87
% 31.86/20.35 Demodulation : 4.85
% 31.86/20.35 BG Simplification : 0.13
% 31.86/20.35 Subsumption : 8.20
% 31.86/20.35 Abstraction : 0.22
% 31.86/20.35 MUC search : 0.00
% 31.86/20.35 Cooper : 0.00
% 31.86/20.35 Total : 19.40
% 31.86/20.35 Index Insertion : 0.00
% 31.86/20.35 Index Deletion : 0.00
% 31.86/20.35 Index Matching : 0.00
% 31.86/20.35 BG Taut test : 0.00
%------------------------------------------------------------------------------