TSTP Solution File: CAT008-1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : CAT008-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n020.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 Apr 30 20:13:18 EDT 2024
% Result : Unsatisfiable 0.19s 0.44s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 26
% Syntax : Number of formulae : 95 ( 28 unt; 0 def)
% Number of atoms : 185 ( 7 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 161 ( 71 ~; 78 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 13 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 91 ( 91 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( ~ defined(X,Y)
| product(X,Y,compose(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y,Z] :
( ~ product(X,Y,Z)
| defined(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Xy,Z] :
( ~ product(X,Y,Xy)
| ~ defined(Xy,Z)
| defined(Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [Y,Z,Yz,X] :
( ~ product(Y,Z,Yz)
| ~ defined(X,Yz)
| defined(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [Y,Z,Yz,X,Xy] :
( ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy)
| ~ defined(X,Yz)
| defined(Xy,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X] : identity_map(domain(X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X] : identity_map(codomain(X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X] : product(X,domain(X),X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X] : product(codomain(X),X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X,Y] :
( ~ defined(X,Y)
| ~ identity_map(X)
| product(X,Y,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X,Y] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X,Y,Z,W] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| Z = W ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,hypothesis,
defined(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
domain(a) != codomain(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,plain,
! [X0,X1] :
( ~ defined(X0,X1)
| product(X0,X1,compose(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f22,plain,
! [X,Y] :
( ! [Z] : ~ product(X,Y,Z)
| defined(X,Y) ),
inference(miniscoping,[status(esa)],[f2]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ~ product(X0,X1,X2)
| defined(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f24,plain,
! [Y,Z] :
( ! [Xy] :
( ! [X] : ~ product(X,Y,Xy)
| ~ defined(Xy,Z) )
| defined(Y,Z) ),
inference(miniscoping,[status(esa)],[f3]) ).
fof(f25,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ defined(X2,X3)
| defined(X1,X3) ),
inference(cnf_transformation,[status(esa)],[f24]) ).
fof(f30,plain,
! [Y,X] :
( ! [Yz] :
( ! [Z] : ~ product(Y,Z,Yz)
| ~ defined(X,Yz) )
| defined(X,Y) ),
inference(miniscoping,[status(esa)],[f6]) ).
fof(f31,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ defined(X3,X2)
| defined(X3,X0) ),
inference(cnf_transformation,[status(esa)],[f30]) ).
fof(f32,plain,
! [Z,Xy] :
( ! [Yz,X] :
( ! [Y] :
( ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) )
| ~ defined(X,Yz) )
| defined(Xy,Z) ),
inference(miniscoping,[status(esa)],[f7]) ).
fof(f33,plain,
! [X0,X1,X2,X3,X4] :
( ~ product(X0,X1,X2)
| ~ product(X3,X0,X4)
| ~ defined(X3,X2)
| defined(X4,X1) ),
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f38,plain,
! [X0] : identity_map(domain(X0)),
inference(cnf_transformation,[status(esa)],[f10]) ).
fof(f39,plain,
! [X0] : identity_map(codomain(X0)),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f42,plain,
! [X0] : product(X0,domain(X0),X0),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f43,plain,
! [X0] : product(codomain(X0),X0,X0),
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f44,plain,
! [X0,X1] :
( ~ defined(X0,X1)
| ~ identity_map(X0)
| product(X0,X1,X1) ),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f45,plain,
! [X0,X1] :
( ~ defined(X0,X1)
| ~ identity_map(X1)
| product(X0,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f46,plain,
! [Z,W] :
( ! [X,Y] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W) )
| Z = W ),
inference(miniscoping,[status(esa)],[f18]) ).
fof(f47,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X0,X1,X3)
| X2 = X3 ),
inference(cnf_transformation,[status(esa)],[f46]) ).
fof(f48,plain,
defined(a,b),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f49,plain,
domain(a) != codomain(b),
inference(cnf_transformation,[status(esa)],[f20]) ).
fof(f52,plain,
product(a,b,compose(a,b)),
inference(resolution,[status(thm)],[f21,f48]) ).
fof(f158,plain,
! [X0,X1] :
( ~ defined(X0,X1)
| defined(domain(X0),X1) ),
inference(resolution,[status(thm)],[f25,f42]) ).
fof(f171,plain,
defined(domain(a),b),
inference(resolution,[status(thm)],[f158,f48]) ).
fof(f184,plain,
( spl0_5
<=> identity_map(domain(a)) ),
introduced(split_symbol_definition) ).
fof(f186,plain,
( ~ identity_map(domain(a))
| spl0_5 ),
inference(component_clause,[status(thm)],[f184]) ).
fof(f193,plain,
( $false
| spl0_5 ),
inference(forward_subsumption_resolution,[status(thm)],[f186,f38]) ).
fof(f194,plain,
spl0_5,
inference(contradiction_clause,[status(thm)],[f193]) ).
fof(f320,plain,
! [X0,X1] :
( ~ defined(X0,X1)
| defined(X0,codomain(X1)) ),
inference(resolution,[status(thm)],[f31,f43]) ).
fof(f321,plain,
defined(domain(a),codomain(b)),
inference(resolution,[status(thm)],[f320,f171]) ).
fof(f323,plain,
defined(a,codomain(b)),
inference(resolution,[status(thm)],[f320,f48]) ).
fof(f335,plain,
( spl0_18
<=> identity_map(codomain(b)) ),
introduced(split_symbol_definition) ).
fof(f337,plain,
( ~ identity_map(codomain(b))
| spl0_18 ),
inference(component_clause,[status(thm)],[f335]) ).
fof(f349,plain,
( $false
| spl0_18 ),
inference(forward_subsumption_resolution,[status(thm)],[f337,f39]) ).
fof(f350,plain,
spl0_18,
inference(contradiction_clause,[status(thm)],[f349]) ).
fof(f361,plain,
! [X0,X1,X2] :
( ~ product(X0,X1,X2)
| ~ defined(X0,X1)
| defined(X2,domain(X1)) ),
inference(resolution,[status(thm)],[f33,f42]) ).
fof(f362,plain,
! [X0,X1,X2] :
( ~ product(X0,X1,X2)
| defined(X2,domain(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f361,f23]) ).
fof(f439,plain,
( spl0_28
<=> product(domain(a),codomain(b),domain(a)) ),
introduced(split_symbol_definition) ).
fof(f440,plain,
( product(domain(a),codomain(b),domain(a))
| ~ spl0_28 ),
inference(component_clause,[status(thm)],[f439]) ).
fof(f442,plain,
( ~ identity_map(codomain(b))
| product(domain(a),codomain(b),domain(a)) ),
inference(resolution,[status(thm)],[f321,f45]) ).
fof(f443,plain,
( ~ spl0_18
| spl0_28 ),
inference(split_clause,[status(thm)],[f442,f335,f439]) ).
fof(f444,plain,
( spl0_29
<=> product(domain(a),codomain(b),codomain(b)) ),
introduced(split_symbol_definition) ).
fof(f445,plain,
( product(domain(a),codomain(b),codomain(b))
| ~ spl0_29 ),
inference(component_clause,[status(thm)],[f444]) ).
fof(f447,plain,
( ~ identity_map(domain(a))
| product(domain(a),codomain(b),codomain(b)) ),
inference(resolution,[status(thm)],[f321,f44]) ).
fof(f448,plain,
( ~ spl0_5
| spl0_29 ),
inference(split_clause,[status(thm)],[f447,f184,f444]) ).
fof(f491,plain,
( spl0_31
<=> identity_map(codomain(codomain(b))) ),
introduced(split_symbol_definition) ).
fof(f493,plain,
( ~ identity_map(codomain(codomain(b)))
| spl0_31 ),
inference(component_clause,[status(thm)],[f491]) ).
fof(f509,plain,
( $false
| spl0_31 ),
inference(forward_subsumption_resolution,[status(thm)],[f493,f39]) ).
fof(f510,plain,
spl0_31,
inference(contradiction_clause,[status(thm)],[f509]) ).
fof(f569,plain,
defined(compose(a,b),domain(b)),
inference(resolution,[status(thm)],[f362,f52]) ).
fof(f785,plain,
( spl0_44
<=> identity_map(codomain(codomain(codomain(b)))) ),
introduced(split_symbol_definition) ).
fof(f787,plain,
( ~ identity_map(codomain(codomain(codomain(b))))
| spl0_44 ),
inference(component_clause,[status(thm)],[f785]) ).
fof(f803,plain,
( $false
| spl0_44 ),
inference(forward_subsumption_resolution,[status(thm)],[f787,f39]) ).
fof(f804,plain,
spl0_44,
inference(contradiction_clause,[status(thm)],[f803]) ).
fof(f913,plain,
( spl0_59
<=> defined(a,codomain(b)) ),
introduced(split_symbol_definition) ).
fof(f915,plain,
( ~ defined(a,codomain(b))
| spl0_59 ),
inference(component_clause,[status(thm)],[f913]) ).
fof(f970,plain,
( spl0_62
<=> identity_map(domain(b)) ),
introduced(split_symbol_definition) ).
fof(f972,plain,
( ~ identity_map(domain(b))
| spl0_62 ),
inference(component_clause,[status(thm)],[f970]) ).
fof(f988,plain,
( $false
| spl0_62 ),
inference(forward_subsumption_resolution,[status(thm)],[f972,f38]) ).
fof(f989,plain,
spl0_62,
inference(contradiction_clause,[status(thm)],[f988]) ).
fof(f1086,plain,
( spl0_75
<=> defined(compose(a,b),domain(b)) ),
introduced(split_symbol_definition) ).
fof(f1088,plain,
( ~ defined(compose(a,b),domain(b))
| spl0_75 ),
inference(component_clause,[status(thm)],[f1086]) ).
fof(f1091,plain,
( $false
| spl0_75 ),
inference(forward_subsumption_resolution,[status(thm)],[f1088,f569]) ).
fof(f1092,plain,
spl0_75,
inference(contradiction_clause,[status(thm)],[f1091]) ).
fof(f1106,plain,
( spl0_78
<=> identity_map(domain(compose(a,b))) ),
introduced(split_symbol_definition) ).
fof(f1108,plain,
( ~ identity_map(domain(compose(a,b)))
| spl0_78 ),
inference(component_clause,[status(thm)],[f1106]) ).
fof(f1124,plain,
( $false
| spl0_78 ),
inference(forward_subsumption_resolution,[status(thm)],[f1108,f38]) ).
fof(f1125,plain,
spl0_78,
inference(contradiction_clause,[status(thm)],[f1124]) ).
fof(f1398,plain,
( spl0_81
<=> identity_map(codomain(compose(a,b))) ),
introduced(split_symbol_definition) ).
fof(f1400,plain,
( ~ identity_map(codomain(compose(a,b)))
| spl0_81 ),
inference(component_clause,[status(thm)],[f1398]) ).
fof(f1425,plain,
( $false
| spl0_81 ),
inference(forward_subsumption_resolution,[status(thm)],[f1400,f39]) ).
fof(f1426,plain,
spl0_81,
inference(contradiction_clause,[status(thm)],[f1425]) ).
fof(f1478,plain,
( spl0_91
<=> defined(domain(a),b) ),
introduced(split_symbol_definition) ).
fof(f1480,plain,
( ~ defined(domain(a),b)
| spl0_91 ),
inference(component_clause,[status(thm)],[f1478]) ).
fof(f1504,plain,
! [X0] :
( ~ product(domain(a),codomain(b),X0)
| codomain(b) = X0
| ~ spl0_29 ),
inference(resolution,[status(thm)],[f445,f47]) ).
fof(f1506,plain,
( $false
| spl0_91 ),
inference(forward_subsumption_resolution,[status(thm)],[f1480,f171]) ).
fof(f1507,plain,
spl0_91,
inference(contradiction_clause,[status(thm)],[f1506]) ).
fof(f1548,plain,
( $false
| spl0_59 ),
inference(forward_subsumption_resolution,[status(thm)],[f915,f323]) ).
fof(f1549,plain,
spl0_59,
inference(contradiction_clause,[status(thm)],[f1548]) ).
fof(f2208,plain,
( codomain(b) = domain(a)
| ~ spl0_29
| ~ spl0_28 ),
inference(resolution,[status(thm)],[f1504,f440]) ).
fof(f2209,plain,
( $false
| ~ spl0_29
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[status(thm)],[f2208,f49]) ).
fof(f2210,plain,
( ~ spl0_29
| ~ spl0_28 ),
inference(contradiction_clause,[status(thm)],[f2209]) ).
fof(f2211,plain,
$false,
inference(sat_refutation,[status(thm)],[f194,f350,f443,f448,f510,f804,f989,f1092,f1125,f1426,f1507,f1549,f2210]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : CAT008-1 : TPTP v8.1.2. Released v1.0.0.
% 0.03/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n020.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 29 22:12:17 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Drodi V3.6.0
% 0.19/0.44 % Refutation found
% 0.19/0.44 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.19/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.45 % Elapsed time: 0.102285 seconds
% 0.19/0.45 % CPU time: 0.717949 seconds
% 0.19/0.45 % Total memory used: 28.749 MB
% 0.19/0.45 % Net memory used: 27.451 MB
%------------------------------------------------------------------------------