TSTP Solution File: CAT004-2 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : CAT004-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n022.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 20:13:17 EDT 2024
% Result : Unsatisfiable 0.14s 0.33s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 22
% Syntax : Number of formulae : 90 ( 16 unt; 0 def)
% Number of atoms : 221 ( 128 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 247 ( 116 ~; 119 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 13 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 44 ( 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X,Y] :
( codomain(X) != domain(Y)
| domain(compose(X,Y)) = domain(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y] :
( codomain(X) != domain(Y)
| codomain(compose(X,Y)) = codomain(Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y,Z] :
( codomain(X) != domain(Y)
| codomain(Y) != domain(Z)
| compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,hypothesis,
! [X,Y,Z] :
( codomain(a) != domain(X)
| compose(a,X) != Y
| codomain(a) != domain(Z)
| compose(a,Z) != Y
| X = Z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,hypothesis,
! [X,Y,Z] :
( codomain(b) != domain(X)
| compose(b,X) != Y
| codomain(b) != domain(Z)
| compose(b,Z) != Y
| X = Z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,hypothesis,
codomain(a) = domain(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,hypothesis,
codomain(compose(a,b)) = domain(h),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,hypothesis,
codomain(compose(a,b)) = domain(g),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,hypothesis,
compose(compose(a,b),h) = compose(compose(a,b),g),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
h != g,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,plain,
! [X0,X1] :
( codomain(X0) != domain(X1)
| domain(compose(X0,X1)) = domain(X0) ),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f20,plain,
! [X0,X1] :
( codomain(X0) != domain(X1)
| codomain(compose(X0,X1)) = codomain(X1) ),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f21,plain,
! [X0,X1,X2] :
( codomain(X0) != domain(X1)
| codomain(X1) != domain(X2)
| compose(X0,compose(X1,X2)) = compose(compose(X0,X1),X2) ),
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f22,plain,
! [X,Z] :
( ! [Y] :
( codomain(a) != domain(X)
| compose(a,X) != Y
| codomain(a) != domain(Z)
| compose(a,Z) != Y )
| X = Z ),
inference(miniscoping,[status(esa)],[f8]) ).
fof(f23,plain,
! [X0,X1,X2] :
( codomain(a) != domain(X0)
| compose(a,X0) != X1
| codomain(a) != domain(X2)
| compose(a,X2) != X1
| X0 = X2 ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f24,plain,
! [X,Z] :
( ! [Y] :
( codomain(b) != domain(X)
| compose(b,X) != Y
| codomain(b) != domain(Z)
| compose(b,Z) != Y )
| X = Z ),
inference(miniscoping,[status(esa)],[f9]) ).
fof(f25,plain,
! [X0,X1,X2] :
( codomain(b) != domain(X0)
| compose(b,X0) != X1
| codomain(b) != domain(X2)
| compose(b,X2) != X1
| X0 = X2 ),
inference(cnf_transformation,[status(esa)],[f24]) ).
fof(f26,plain,
codomain(a) = domain(b),
inference(cnf_transformation,[status(esa)],[f10]) ).
fof(f27,plain,
codomain(compose(a,b)) = domain(h),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f28,plain,
codomain(compose(a,b)) = domain(g),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f29,plain,
compose(compose(a,b),h) = compose(compose(a,b),g),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f30,plain,
h != g,
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f31,plain,
! [X0,X1] :
( codomain(a) != domain(X0)
| codomain(a) != domain(X1)
| compose(a,X1) != compose(a,X0)
| X0 = X1 ),
inference(destructive_equality_resolution,[status(esa)],[f23]) ).
fof(f32,plain,
! [X0,X1] :
( codomain(b) != domain(X0)
| codomain(b) != domain(X1)
| compose(b,X1) != compose(b,X0)
| X0 = X1 ),
inference(destructive_equality_resolution,[status(esa)],[f25]) ).
fof(f33,plain,
domain(h) = domain(g),
inference(forward_demodulation,[status(thm)],[f27,f28]) ).
fof(f34,plain,
! [X0,X1] :
( codomain(a) != domain(X0)
| domain(b) != domain(X1)
| compose(a,X1) != compose(a,X0)
| X0 = X1 ),
inference(backward_demodulation,[status(thm)],[f26,f31]) ).
fof(f35,plain,
! [X0,X1] :
( domain(b) != domain(X0)
| domain(b) != domain(X1)
| compose(a,X1) != compose(a,X0)
| X0 = X1 ),
inference(forward_demodulation,[status(thm)],[f26,f34]) ).
fof(f156,plain,
( spl0_8
<=> codomain(a) = domain(b) ),
introduced(split_symbol_definition) ).
fof(f158,plain,
( codomain(a) != domain(b)
| spl0_8 ),
inference(component_clause,[status(thm)],[f156]) ).
fof(f159,plain,
( spl0_9
<=> domain(h) = codomain(b) ),
introduced(split_symbol_definition) ).
fof(f160,plain,
( domain(h) = codomain(b)
| ~ spl0_9 ),
inference(component_clause,[status(thm)],[f159]) ).
fof(f162,plain,
( codomain(a) != domain(b)
| domain(h) = codomain(b) ),
inference(paramodulation,[status(thm)],[f27,f20]) ).
fof(f163,plain,
( ~ spl0_8
| spl0_9 ),
inference(split_clause,[status(thm)],[f162,f156,f159]) ).
fof(f186,plain,
( domain(b) != domain(b)
| spl0_8 ),
inference(forward_demodulation,[status(thm)],[f26,f158]) ).
fof(f187,plain,
( $false
| spl0_8 ),
inference(trivial_equality_resolution,[status(esa)],[f186]) ).
fof(f188,plain,
spl0_8,
inference(contradiction_clause,[status(thm)],[f187]) ).
fof(f191,plain,
! [X0,X1] :
( codomain(b) != domain(X0)
| domain(h) != domain(X1)
| compose(b,X1) != compose(b,X0)
| X0 = X1
| ~ spl0_9 ),
inference(backward_demodulation,[status(thm)],[f160,f32]) ).
fof(f192,plain,
! [X0,X1] :
( domain(h) != domain(X0)
| domain(h) != domain(X1)
| compose(b,X1) != compose(b,X0)
| X0 = X1
| ~ spl0_9 ),
inference(forward_demodulation,[status(thm)],[f160,f191]) ).
fof(f201,plain,
( spl0_16
<=> codomain(b) = domain(g) ),
introduced(split_symbol_definition) ).
fof(f203,plain,
( codomain(b) != domain(g)
| spl0_16 ),
inference(component_clause,[status(thm)],[f201]) ).
fof(f204,plain,
( spl0_17
<=> compose(a,compose(b,g)) = compose(compose(a,b),h) ),
introduced(split_symbol_definition) ).
fof(f205,plain,
( compose(a,compose(b,g)) = compose(compose(a,b),h)
| ~ spl0_17 ),
inference(component_clause,[status(thm)],[f204]) ).
fof(f207,plain,
( codomain(a) != domain(b)
| codomain(b) != domain(g)
| compose(a,compose(b,g)) = compose(compose(a,b),h) ),
inference(paramodulation,[status(thm)],[f29,f21]) ).
fof(f208,plain,
( ~ spl0_8
| ~ spl0_16
| spl0_17 ),
inference(split_clause,[status(thm)],[f207,f156,f201,f204]) ).
fof(f253,plain,
( domain(h) != domain(g)
| ~ spl0_9
| spl0_16 ),
inference(forward_demodulation,[status(thm)],[f160,f203]) ).
fof(f254,plain,
( domain(h) != domain(h)
| ~ spl0_9
| spl0_16 ),
inference(forward_demodulation,[status(thm)],[f33,f253]) ).
fof(f255,plain,
( $false
| ~ spl0_9
| spl0_16 ),
inference(trivial_equality_resolution,[status(esa)],[f254]) ).
fof(f256,plain,
( ~ spl0_9
| spl0_16 ),
inference(contradiction_clause,[status(thm)],[f255]) ).
fof(f388,plain,
( spl0_28
<=> domain(h) = domain(g) ),
introduced(split_symbol_definition) ).
fof(f390,plain,
( domain(h) != domain(g)
| spl0_28 ),
inference(component_clause,[status(thm)],[f388]) ).
fof(f412,plain,
( domain(h) != domain(h)
| spl0_28 ),
inference(forward_demodulation,[status(thm)],[f33,f390]) ).
fof(f413,plain,
( $false
| spl0_28 ),
inference(trivial_equality_resolution,[status(esa)],[f412]) ).
fof(f414,plain,
spl0_28,
inference(contradiction_clause,[status(thm)],[f413]) ).
fof(f567,plain,
( spl0_46
<=> compose(a,compose(b,h)) = compose(a,compose(b,g)) ),
introduced(split_symbol_definition) ).
fof(f568,plain,
( compose(a,compose(b,h)) = compose(a,compose(b,g))
| ~ spl0_46 ),
inference(component_clause,[status(thm)],[f567]) ).
fof(f570,plain,
( codomain(a) != domain(b)
| codomain(b) != domain(h)
| compose(a,compose(b,h)) = compose(a,compose(b,g))
| ~ spl0_17 ),
inference(paramodulation,[status(thm)],[f205,f21]) ).
fof(f571,plain,
( ~ spl0_8
| ~ spl0_9
| spl0_46
| ~ spl0_17 ),
inference(split_clause,[status(thm)],[f570,f156,f159,f567,f204]) ).
fof(f704,plain,
( spl0_63
<=> domain(b) = domain(compose(b,h)) ),
introduced(split_symbol_definition) ).
fof(f706,plain,
( domain(b) != domain(compose(b,h))
| spl0_63 ),
inference(component_clause,[status(thm)],[f704]) ).
fof(f715,plain,
( spl0_66
<=> codomain(a) = domain(compose(b,h)) ),
introduced(split_symbol_definition) ).
fof(f716,plain,
( codomain(a) = domain(compose(b,h))
| ~ spl0_66 ),
inference(component_clause,[status(thm)],[f715]) ).
fof(f717,plain,
( codomain(a) != domain(compose(b,h))
| spl0_66 ),
inference(component_clause,[status(thm)],[f715]) ).
fof(f749,plain,
( domain(b) != domain(compose(b,h))
| spl0_66 ),
inference(forward_demodulation,[status(thm)],[f26,f717]) ).
fof(f865,plain,
( codomain(b) != domain(h)
| spl0_66 ),
inference(resolution,[status(thm)],[f749,f19]) ).
fof(f866,plain,
( domain(h) != domain(h)
| ~ spl0_9
| spl0_66 ),
inference(forward_demodulation,[status(thm)],[f160,f865]) ).
fof(f867,plain,
( $false
| ~ spl0_9
| spl0_66 ),
inference(trivial_equality_resolution,[status(esa)],[f866]) ).
fof(f868,plain,
( ~ spl0_9
| spl0_66 ),
inference(contradiction_clause,[status(thm)],[f867]) ).
fof(f869,plain,
( domain(b) = domain(compose(b,h))
| ~ spl0_66 ),
inference(forward_demodulation,[status(thm)],[f26,f716]) ).
fof(f909,plain,
( domain(b) != domain(b)
| ~ spl0_66
| spl0_63 ),
inference(forward_demodulation,[status(thm)],[f869,f706]) ).
fof(f910,plain,
( $false
| ~ spl0_66
| spl0_63 ),
inference(trivial_equality_resolution,[status(esa)],[f909]) ).
fof(f911,plain,
( ~ spl0_66
| spl0_63 ),
inference(contradiction_clause,[status(thm)],[f910]) ).
fof(f970,plain,
( spl0_85
<=> domain(h) = domain(h) ),
introduced(split_symbol_definition) ).
fof(f972,plain,
( domain(h) != domain(h)
| spl0_85 ),
inference(component_clause,[status(thm)],[f970]) ).
fof(f986,plain,
( $false
| spl0_85 ),
inference(trivial_equality_resolution,[status(esa)],[f972]) ).
fof(f987,plain,
spl0_85,
inference(contradiction_clause,[status(thm)],[f986]) ).
fof(f1140,plain,
( spl0_114
<=> domain(b) = domain(compose(b,g)) ),
introduced(split_symbol_definition) ).
fof(f1142,plain,
( domain(b) != domain(compose(b,g))
| spl0_114 ),
inference(component_clause,[status(thm)],[f1140]) ).
fof(f1143,plain,
( spl0_115
<=> compose(b,g) = compose(b,h) ),
introduced(split_symbol_definition) ).
fof(f1144,plain,
( compose(b,g) = compose(b,h)
| ~ spl0_115 ),
inference(component_clause,[status(thm)],[f1143]) ).
fof(f1146,plain,
( domain(b) != domain(compose(b,g))
| domain(b) != domain(compose(b,h))
| compose(b,g) = compose(b,h)
| ~ spl0_46 ),
inference(resolution,[status(thm)],[f568,f35]) ).
fof(f1147,plain,
( ~ spl0_114
| ~ spl0_63
| spl0_115
| ~ spl0_46 ),
inference(split_clause,[status(thm)],[f1146,f1140,f704,f1143,f567]) ).
fof(f1193,plain,
( codomain(b) != domain(g)
| spl0_114 ),
inference(resolution,[status(thm)],[f1142,f19]) ).
fof(f1194,plain,
( ~ spl0_16
| spl0_114 ),
inference(split_clause,[status(thm)],[f1193,f201,f1140]) ).
fof(f1220,plain,
( spl0_125
<=> h = g ),
introduced(split_symbol_definition) ).
fof(f1221,plain,
( h = g
| ~ spl0_125 ),
inference(component_clause,[status(thm)],[f1220]) ).
fof(f1223,plain,
( domain(h) != domain(h)
| domain(h) != domain(g)
| h = g
| ~ spl0_115
| ~ spl0_9 ),
inference(resolution,[status(thm)],[f1144,f192]) ).
fof(f1224,plain,
( ~ spl0_85
| ~ spl0_28
| spl0_125
| ~ spl0_115
| ~ spl0_9 ),
inference(split_clause,[status(thm)],[f1223,f970,f388,f1220,f1143,f159]) ).
fof(f1264,plain,
( $false
| ~ spl0_125 ),
inference(forward_subsumption_resolution,[status(thm)],[f1221,f30]) ).
fof(f1265,plain,
~ spl0_125,
inference(contradiction_clause,[status(thm)],[f1264]) ).
fof(f1266,plain,
$false,
inference(sat_refutation,[status(thm)],[f163,f188,f208,f256,f414,f571,f868,f911,f987,f1147,f1194,f1224,f1265]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : CAT004-2 : TPTP v8.1.2. Released v1.0.0.
% 0.02/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30 % Computer : n022.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Mon Apr 29 22:09:28 EDT 2024
% 0.09/0.30 % CPUTime :
% 0.09/0.31 % Drodi V3.6.0
% 0.14/0.33 % Refutation found
% 0.14/0.33 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.34 % Elapsed time: 0.027500 seconds
% 0.14/0.34 % CPU time: 0.128954 seconds
% 0.14/0.34 % Total memory used: 21.619 MB
% 0.14/0.34 % Net memory used: 21.508 MB
%------------------------------------------------------------------------------