TSTP Solution File: CAT009-1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : CAT009-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n003.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 20:13:19 EDT 2024
% Result : Unsatisfiable 0.21s 0.48s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 27
% Syntax : Number of formulae : 99 ( 33 unt; 0 def)
% Number of atoms : 188 ( 7 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 161 ( 72 ~; 78 |; 0 &)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 12 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 97 ( 97 !; 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(f12,axiom,
! [X] : defined(X,domain(X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X] : defined(codomain(X),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(b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
domain(compose(b,a)) != domain(a),
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(f40,plain,
! [X0] : defined(X0,domain(X0)),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f41,plain,
! [X0] : defined(codomain(X0),X0),
inference(cnf_transformation,[status(esa)],[f13]) ).
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(b,a),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f49,plain,
domain(compose(b,a)) != domain(a),
inference(cnf_transformation,[status(esa)],[f20]) ).
fof(f50,plain,
product(b,a,compose(b,a)),
inference(resolution,[status(thm)],[f21,f48]) ).
fof(f157,plain,
! [X0] :
( ~ defined(compose(b,a),X0)
| defined(a,X0) ),
inference(resolution,[status(thm)],[f25,f50]) ).
fof(f158,plain,
! [X0,X1] :
( ~ defined(X0,X1)
| defined(domain(X0),X1) ),
inference(resolution,[status(thm)],[f25,f42]) ).
fof(f175,plain,
defined(domain(b),a),
inference(resolution,[status(thm)],[f158,f48]) ).
fof(f336,plain,
! [X0,X1] :
( ~ defined(X0,X1)
| defined(X0,codomain(X1)) ),
inference(resolution,[status(thm)],[f31,f43]) ).
fof(f337,plain,
! [X0] :
( ~ defined(X0,compose(b,a))
| defined(X0,b) ),
inference(resolution,[status(thm)],[f31,f50]) ).
fof(f348,plain,
! [X0,X1,X2] :
( ~ product(X0,X1,X2)
| ~ defined(X0,X1)
| defined(X2,domain(X1)) ),
inference(resolution,[status(thm)],[f33,f42]) ).
fof(f349,plain,
! [X0,X1,X2] :
( ~ product(X0,X1,X2)
| defined(X2,domain(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f348,f23]) ).
fof(f403,plain,
defined(compose(b,a),domain(a)),
inference(resolution,[status(thm)],[f349,f50]) ).
fof(f440,plain,
( spl0_28
<=> identity_map(domain(a)) ),
introduced(split_symbol_definition) ).
fof(f442,plain,
( ~ identity_map(domain(a))
| spl0_28 ),
inference(component_clause,[status(thm)],[f440]) ).
fof(f445,plain,
defined(domain(compose(b,a)),domain(a)),
inference(resolution,[status(thm)],[f403,f158]) ).
fof(f457,plain,
( $false
| spl0_28 ),
inference(forward_subsumption_resolution,[status(thm)],[f442,f38]) ).
fof(f458,plain,
spl0_28,
inference(contradiction_clause,[status(thm)],[f457]) ).
fof(f533,plain,
defined(b,codomain(a)),
inference(resolution,[status(thm)],[f336,f48]) ).
fof(f772,plain,
defined(a,domain(compose(b,a))),
inference(resolution,[status(thm)],[f157,f40]) ).
fof(f914,plain,
( spl0_57
<=> defined(b,codomain(a)) ),
introduced(split_symbol_definition) ).
fof(f916,plain,
( ~ defined(b,codomain(a))
| spl0_57 ),
inference(component_clause,[status(thm)],[f914]) ).
fof(f1014,plain,
( spl0_62
<=> identity_map(domain(compose(b,a))) ),
introduced(split_symbol_definition) ).
fof(f1016,plain,
( ~ identity_map(domain(compose(b,a)))
| spl0_62 ),
inference(component_clause,[status(thm)],[f1014]) ).
fof(f1031,plain,
( $false
| spl0_62 ),
inference(forward_subsumption_resolution,[status(thm)],[f1016,f38]) ).
fof(f1032,plain,
spl0_62,
inference(contradiction_clause,[status(thm)],[f1031]) ).
fof(f1343,plain,
defined(codomain(compose(b,a)),b),
inference(resolution,[status(thm)],[f337,f41]) ).
fof(f1517,plain,
( spl0_82
<=> identity_map(codomain(compose(b,a))) ),
introduced(split_symbol_definition) ).
fof(f1519,plain,
( ~ identity_map(codomain(compose(b,a)))
| spl0_82 ),
inference(component_clause,[status(thm)],[f1517]) ).
fof(f1544,plain,
( $false
| spl0_82 ),
inference(forward_subsumption_resolution,[status(thm)],[f1519,f39]) ).
fof(f1545,plain,
spl0_82,
inference(contradiction_clause,[status(thm)],[f1544]) ).
fof(f1613,plain,
( spl0_89
<=> product(domain(compose(b,a)),domain(a),domain(compose(b,a))) ),
introduced(split_symbol_definition) ).
fof(f1614,plain,
( product(domain(compose(b,a)),domain(a),domain(compose(b,a)))
| ~ spl0_89 ),
inference(component_clause,[status(thm)],[f1613]) ).
fof(f1616,plain,
( ~ identity_map(domain(a))
| product(domain(compose(b,a)),domain(a),domain(compose(b,a))) ),
inference(resolution,[status(thm)],[f445,f45]) ).
fof(f1617,plain,
( ~ spl0_28
| spl0_89 ),
inference(split_clause,[status(thm)],[f1616,f440,f1613]) ).
fof(f1618,plain,
( spl0_90
<=> product(domain(compose(b,a)),domain(a),domain(a)) ),
introduced(split_symbol_definition) ).
fof(f1619,plain,
( product(domain(compose(b,a)),domain(a),domain(a))
| ~ spl0_90 ),
inference(component_clause,[status(thm)],[f1618]) ).
fof(f1621,plain,
( ~ identity_map(domain(compose(b,a)))
| product(domain(compose(b,a)),domain(a),domain(a)) ),
inference(resolution,[status(thm)],[f445,f44]) ).
fof(f1622,plain,
( ~ spl0_62
| spl0_90 ),
inference(split_clause,[status(thm)],[f1621,f1014,f1618]) ).
fof(f1679,plain,
( spl0_96
<=> defined(domain(b),a) ),
introduced(split_symbol_definition) ).
fof(f1681,plain,
( ~ defined(domain(b),a)
| spl0_96 ),
inference(component_clause,[status(thm)],[f1679]) ).
fof(f1707,plain,
( $false
| spl0_96 ),
inference(forward_subsumption_resolution,[status(thm)],[f1681,f175]) ).
fof(f1708,plain,
spl0_96,
inference(contradiction_clause,[status(thm)],[f1707]) ).
fof(f1742,plain,
( $false
| spl0_57 ),
inference(forward_subsumption_resolution,[status(thm)],[f916,f533]) ).
fof(f1743,plain,
spl0_57,
inference(contradiction_clause,[status(thm)],[f1742]) ).
fof(f1914,plain,
( spl0_104
<=> defined(compose(b,a),domain(compose(b,a))) ),
introduced(split_symbol_definition) ).
fof(f1916,plain,
( ~ defined(compose(b,a),domain(compose(b,a)))
| spl0_104 ),
inference(component_clause,[status(thm)],[f1914]) ).
fof(f2043,plain,
( spl0_109
<=> defined(codomain(compose(b,a)),compose(b,a)) ),
introduced(split_symbol_definition) ).
fof(f2045,plain,
( ~ defined(codomain(compose(b,a)),compose(b,a))
| spl0_109 ),
inference(component_clause,[status(thm)],[f2043]) ).
fof(f2613,plain,
! [X0] :
( ~ product(domain(compose(b,a)),domain(a),X0)
| domain(a) = X0
| ~ spl0_90 ),
inference(resolution,[status(thm)],[f1619,f47]) ).
fof(f2666,plain,
( spl0_111
<=> defined(a,domain(compose(b,a))) ),
introduced(split_symbol_definition) ).
fof(f2668,plain,
( ~ defined(a,domain(compose(b,a)))
| spl0_111 ),
inference(component_clause,[status(thm)],[f2666]) ).
fof(f2695,plain,
( $false
| spl0_111 ),
inference(forward_subsumption_resolution,[status(thm)],[f2668,f772]) ).
fof(f2696,plain,
spl0_111,
inference(contradiction_clause,[status(thm)],[f2695]) ).
fof(f2707,plain,
( spl0_113
<=> defined(codomain(compose(b,a)),b) ),
introduced(split_symbol_definition) ).
fof(f2709,plain,
( ~ defined(codomain(compose(b,a)),b)
| spl0_113 ),
inference(component_clause,[status(thm)],[f2707]) ).
fof(f2735,plain,
( $false
| spl0_113 ),
inference(forward_subsumption_resolution,[status(thm)],[f2709,f1343]) ).
fof(f2736,plain,
spl0_113,
inference(contradiction_clause,[status(thm)],[f2735]) ).
fof(f2981,plain,
( $false
| spl0_104 ),
inference(forward_subsumption_resolution,[status(thm)],[f1916,f40]) ).
fof(f2982,plain,
spl0_104,
inference(contradiction_clause,[status(thm)],[f2981]) ).
fof(f3032,plain,
( $false
| spl0_109 ),
inference(forward_subsumption_resolution,[status(thm)],[f2045,f41]) ).
fof(f3033,plain,
spl0_109,
inference(contradiction_clause,[status(thm)],[f3032]) ).
fof(f3064,plain,
( domain(a) = domain(compose(b,a))
| ~ spl0_89
| ~ spl0_90 ),
inference(resolution,[status(thm)],[f1614,f2613]) ).
fof(f3065,plain,
( $false
| ~ spl0_89
| ~ spl0_90 ),
inference(forward_subsumption_resolution,[status(thm)],[f3064,f49]) ).
fof(f3066,plain,
( ~ spl0_89
| ~ spl0_90 ),
inference(contradiction_clause,[status(thm)],[f3065]) ).
fof(f3067,plain,
$false,
inference(sat_refutation,[status(thm)],[f458,f1032,f1545,f1617,f1622,f1708,f1743,f2696,f2736,f2982,f3033,f3066]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : CAT009-1 : TPTP v8.1.2. Released v1.0.0.
% 0.08/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n003.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 22:20:48 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Drodi V3.6.0
% 0.21/0.48 % Refutation found
% 0.21/0.48 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.21/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.50 % Elapsed time: 0.144227 seconds
% 0.21/0.50 % CPU time: 1.055462 seconds
% 0.21/0.50 % Total memory used: 34.659 MB
% 0.21/0.50 % Net memory used: 32.598 MB
%------------------------------------------------------------------------------