TSTP Solution File: SEU215+1 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SEU215+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n019.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 20:41:31 EDT 2024
% Result : Theorem 0.19s 0.52s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 20
% Syntax : Number of formulae : 90 ( 14 unt; 0 def)
% Number of atoms : 322 ( 36 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 381 ( 149 ~; 152 |; 45 &)
% ( 17 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 12 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 96 ( 90 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [A] :
( ( relation(A)
& function(A) )
=> ! [B,C] :
( ( in(B,relation_dom(A))
=> ( C = apply(A,B)
<=> in(ordered_pair(B,C),A) ) )
& ( ~ in(B,relation_dom(A))
=> ( C = apply(A,B)
<=> C = empty_set ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A,B] :
( ( relation(A)
& relation(B) )
=> relation(relation_composition(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [A,B] :
( ( relation(A)
& function(A)
& relation(B)
& function(B) )
=> ( relation(relation_composition(A,B))
& function(relation_composition(A,B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [A,B] :
( ( relation(B)
& function(B) )
=> ! [C] :
( ( relation(C)
& function(C) )
=> ( in(A,relation_dom(relation_composition(C,B)))
<=> ( in(A,relation_dom(C))
& in(apply(C,A),relation_dom(B)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [A,B] :
( ( relation(B)
& function(B) )
=> ! [C] :
( ( relation(C)
& function(C) )
=> ( in(A,relation_dom(relation_composition(C,B)))
=> apply(relation_composition(C,B),A) = apply(B,apply(C,A)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,conjecture,
! [A,B] :
( ( relation(B)
& function(B) )
=> ! [C] :
( ( relation(C)
& function(C) )
=> ( in(A,relation_dom(B))
=> apply(relation_composition(B,C),A) = apply(C,apply(B,A)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
~ ! [A,B] :
( ( relation(B)
& function(B) )
=> ! [C] :
( ( relation(C)
& function(C) )
=> ( in(A,relation_dom(B))
=> apply(relation_composition(B,C),A) = apply(C,apply(B,A)) ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f38,axiom,
! [A,B] :
( element(A,B)
=> ( empty(B)
| in(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,axiom,
! [A,B] :
~ ( in(A,B)
& empty(B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,plain,
! [A] :
( ~ relation(A)
| ~ function(A)
| ! [B,C] :
( ( ~ in(B,relation_dom(A))
| ( C = apply(A,B)
<=> in(ordered_pair(B,C),A) ) )
& ( in(B,relation_dom(A))
| ( C = apply(A,B)
<=> C = empty_set ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f50,plain,
! [A] :
( ~ relation(A)
| ~ function(A)
| ! [B,C] :
( ( ~ in(B,relation_dom(A))
| ( ( C != apply(A,B)
| in(ordered_pair(B,C),A) )
& ( C = apply(A,B)
| ~ in(ordered_pair(B,C),A) ) ) )
& ( in(B,relation_dom(A))
| ( ( C != apply(A,B)
| C = empty_set )
& ( C = apply(A,B)
| C != empty_set ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f49]) ).
fof(f51,plain,
! [A] :
( ~ relation(A)
| ~ function(A)
| ( ! [B] :
( ~ in(B,relation_dom(A))
| ( ! [C] :
( C != apply(A,B)
| in(ordered_pair(B,C),A) )
& ! [C] :
( C = apply(A,B)
| ~ in(ordered_pair(B,C),A) ) ) )
& ! [B] :
( in(B,relation_dom(A))
| ( ! [C] :
( C != apply(A,B)
| C = empty_set )
& ! [C] :
( C = apply(A,B)
| C != empty_set ) ) ) ) ),
inference(miniscoping,[status(esa)],[f50]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| ~ function(X0)
| in(X1,relation_dom(X0))
| X2 != apply(X0,X1)
| X2 = empty_set ),
inference(cnf_transformation,[status(esa)],[f51]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| ~ function(X0)
| in(X1,relation_dom(X0))
| X2 = apply(X0,X1)
| X2 != empty_set ),
inference(cnf_transformation,[status(esa)],[f51]) ).
fof(f57,plain,
! [A,B] :
( ~ relation(A)
| ~ relation(B)
| relation(relation_composition(A,B)) ),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f58,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| relation(relation_composition(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f57]) ).
fof(f67,plain,
! [A,B] :
( ~ relation(A)
| ~ function(A)
| ~ relation(B)
| ~ function(B)
| ( relation(relation_composition(A,B))
& function(relation_composition(A,B)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f18]) ).
fof(f69,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1)
| function(relation_composition(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f67]) ).
fof(f100,plain,
! [A,B] :
( ~ in(A,B)
| element(A,B) ),
inference(pre_NNF_transformation,[status(esa)],[f33]) ).
fof(f101,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f100]) ).
fof(f102,plain,
! [A,B] :
( ~ relation(B)
| ~ function(B)
| ! [C] :
( ~ relation(C)
| ~ function(C)
| ( in(A,relation_dom(relation_composition(C,B)))
<=> ( in(A,relation_dom(C))
& in(apply(C,A),relation_dom(B)) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f34]) ).
fof(f103,plain,
! [A,B] :
( ~ relation(B)
| ~ function(B)
| ! [C] :
( ~ relation(C)
| ~ function(C)
| ( ( ~ in(A,relation_dom(relation_composition(C,B)))
| ( in(A,relation_dom(C))
& in(apply(C,A),relation_dom(B)) ) )
& ( in(A,relation_dom(relation_composition(C,B)))
| ~ in(A,relation_dom(C))
| ~ in(apply(C,A),relation_dom(B)) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f102]) ).
fof(f104,plain,
! [B] :
( ~ relation(B)
| ~ function(B)
| ! [C] :
( ~ relation(C)
| ~ function(C)
| ( ! [A] :
( ~ in(A,relation_dom(relation_composition(C,B)))
| ( in(A,relation_dom(C))
& in(apply(C,A),relation_dom(B)) ) )
& ! [A] :
( in(A,relation_dom(relation_composition(C,B)))
| ~ in(A,relation_dom(C))
| ~ in(apply(C,A),relation_dom(B)) ) ) ) ),
inference(miniscoping,[status(esa)],[f103]) ).
fof(f107,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1)
| in(X2,relation_dom(relation_composition(X1,X0)))
| ~ in(X2,relation_dom(X1))
| ~ in(apply(X1,X2),relation_dom(X0)) ),
inference(cnf_transformation,[status(esa)],[f104]) ).
fof(f108,plain,
! [A,B] :
( ~ relation(B)
| ~ function(B)
| ! [C] :
( ~ relation(C)
| ~ function(C)
| ~ in(A,relation_dom(relation_composition(C,B)))
| apply(relation_composition(C,B),A) = apply(B,apply(C,A)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f35]) ).
fof(f109,plain,
! [B] :
( ~ relation(B)
| ~ function(B)
| ! [C] :
( ~ relation(C)
| ~ function(C)
| ! [A] :
( ~ in(A,relation_dom(relation_composition(C,B)))
| apply(relation_composition(C,B),A) = apply(B,apply(C,A)) ) ) ),
inference(miniscoping,[status(esa)],[f108]) ).
fof(f110,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_dom(relation_composition(X1,X0)))
| apply(relation_composition(X1,X0),X2) = apply(X0,apply(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f109]) ).
fof(f111,plain,
? [A,B] :
( relation(B)
& function(B)
& ? [C] :
( relation(C)
& function(C)
& in(A,relation_dom(B))
& apply(relation_composition(B,C),A) != apply(C,apply(B,A)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f37]) ).
fof(f112,plain,
? [B] :
( relation(B)
& function(B)
& ? [C] :
( relation(C)
& function(C)
& ? [A] :
( in(A,relation_dom(B))
& apply(relation_composition(B,C),A) != apply(C,apply(B,A)) ) ) ),
inference(miniscoping,[status(esa)],[f111]) ).
fof(f113,plain,
( relation(sk0_7)
& function(sk0_7)
& relation(sk0_8)
& function(sk0_8)
& in(sk0_9,relation_dom(sk0_7))
& apply(relation_composition(sk0_7,sk0_8),sk0_9) != apply(sk0_8,apply(sk0_7,sk0_9)) ),
inference(skolemization,[status(esa)],[f112]) ).
fof(f114,plain,
relation(sk0_7),
inference(cnf_transformation,[status(esa)],[f113]) ).
fof(f115,plain,
function(sk0_7),
inference(cnf_transformation,[status(esa)],[f113]) ).
fof(f116,plain,
relation(sk0_8),
inference(cnf_transformation,[status(esa)],[f113]) ).
fof(f117,plain,
function(sk0_8),
inference(cnf_transformation,[status(esa)],[f113]) ).
fof(f118,plain,
in(sk0_9,relation_dom(sk0_7)),
inference(cnf_transformation,[status(esa)],[f113]) ).
fof(f119,plain,
apply(relation_composition(sk0_7,sk0_8),sk0_9) != apply(sk0_8,apply(sk0_7,sk0_9)),
inference(cnf_transformation,[status(esa)],[f113]) ).
fof(f120,plain,
! [A,B] :
( ~ element(A,B)
| empty(B)
| in(A,B) ),
inference(pre_NNF_transformation,[status(esa)],[f38]) ).
fof(f121,plain,
! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f120]) ).
fof(f124,plain,
! [A,B] :
( ~ in(A,B)
| ~ empty(B) ),
inference(pre_NNF_transformation,[status(esa)],[f40]) ).
fof(f125,plain,
! [B] :
( ! [A] : ~ in(A,B)
| ~ empty(B) ),
inference(miniscoping,[status(esa)],[f124]) ).
fof(f126,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[status(esa)],[f125]) ).
fof(f130,plain,
~ empty(relation_dom(sk0_7)),
inference(resolution,[status(thm)],[f126,f118]) ).
fof(f136,plain,
( spl0_0
<=> relation(sk0_8) ),
introduced(split_symbol_definition) ).
fof(f138,plain,
( ~ relation(sk0_8)
| spl0_0 ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f139,plain,
( spl0_1
<=> function(sk0_8) ),
introduced(split_symbol_definition) ).
fof(f141,plain,
( ~ function(sk0_8)
| spl0_1 ),
inference(component_clause,[status(thm)],[f139]) ).
fof(f142,plain,
( spl0_2
<=> relation(sk0_7) ),
introduced(split_symbol_definition) ).
fof(f144,plain,
( ~ relation(sk0_7)
| spl0_2 ),
inference(component_clause,[status(thm)],[f142]) ).
fof(f145,plain,
( spl0_3
<=> function(sk0_7) ),
introduced(split_symbol_definition) ).
fof(f147,plain,
( ~ function(sk0_7)
| spl0_3 ),
inference(component_clause,[status(thm)],[f145]) ).
fof(f148,plain,
( spl0_4
<=> in(sk0_9,relation_dom(relation_composition(sk0_7,sk0_8))) ),
introduced(split_symbol_definition) ).
fof(f151,plain,
( ~ relation(sk0_8)
| ~ function(sk0_8)
| ~ relation(sk0_7)
| ~ function(sk0_7)
| ~ in(sk0_9,relation_dom(relation_composition(sk0_7,sk0_8))) ),
inference(resolution,[status(thm)],[f110,f119]) ).
fof(f152,plain,
( ~ spl0_0
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(split_clause,[status(thm)],[f151,f136,f139,f142,f145,f148]) ).
fof(f165,plain,
element(sk0_9,relation_dom(sk0_7)),
inference(resolution,[status(thm)],[f101,f118]) ).
fof(f348,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ function(X0)
| in(X1,relation_dom(X0))
| apply(X0,X1) = empty_set ),
inference(equality_resolution,[status(esa)],[f54]) ).
fof(f369,plain,
( spl0_16
<=> relation(relation_composition(sk0_7,sk0_8)) ),
introduced(split_symbol_definition) ).
fof(f371,plain,
( ~ relation(relation_composition(sk0_7,sk0_8))
| spl0_16 ),
inference(component_clause,[status(thm)],[f369]) ).
fof(f372,plain,
( spl0_17
<=> function(relation_composition(sk0_7,sk0_8)) ),
introduced(split_symbol_definition) ).
fof(f374,plain,
( ~ function(relation_composition(sk0_7,sk0_8))
| spl0_17 ),
inference(component_clause,[status(thm)],[f372]) ).
fof(f384,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f147,f115]) ).
fof(f385,plain,
spl0_3,
inference(contradiction_clause,[status(thm)],[f384]) ).
fof(f386,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f144,f114]) ).
fof(f387,plain,
spl0_2,
inference(contradiction_clause,[status(thm)],[f386]) ).
fof(f388,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f141,f117]) ).
fof(f389,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f388]) ).
fof(f390,plain,
( $false
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f138,f116]) ).
fof(f391,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f390]) ).
fof(f402,plain,
( ~ relation(sk0_7)
| ~ function(sk0_7)
| ~ relation(sk0_8)
| ~ function(sk0_8)
| spl0_17 ),
inference(resolution,[status(thm)],[f374,f69]) ).
fof(f403,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_0
| ~ spl0_1
| spl0_17 ),
inference(split_clause,[status(thm)],[f402,f142,f145,f136,f139,f372]) ).
fof(f408,plain,
( ~ relation(sk0_7)
| ~ relation(sk0_8)
| spl0_16 ),
inference(resolution,[status(thm)],[f371,f58]) ).
fof(f409,plain,
( ~ spl0_2
| ~ spl0_0
| spl0_16 ),
inference(split_clause,[status(thm)],[f408,f142,f136,f369]) ).
fof(f410,plain,
( spl0_20
<=> in(apply(sk0_7,sk0_9),relation_dom(sk0_8)) ),
introduced(split_symbol_definition) ).
fof(f411,plain,
( in(apply(sk0_7,sk0_9),relation_dom(sk0_8))
| ~ spl0_20 ),
inference(component_clause,[status(thm)],[f410]) ).
fof(f418,plain,
( spl0_22
<=> apply(sk0_8,apply(sk0_7,sk0_9)) = empty_set ),
introduced(split_symbol_definition) ).
fof(f420,plain,
( apply(sk0_8,apply(sk0_7,sk0_9)) != empty_set
| spl0_22 ),
inference(component_clause,[status(thm)],[f418]) ).
fof(f421,plain,
( ~ relation(relation_composition(sk0_7,sk0_8))
| ~ function(relation_composition(sk0_7,sk0_8))
| in(sk0_9,relation_dom(relation_composition(sk0_7,sk0_8)))
| apply(sk0_8,apply(sk0_7,sk0_9)) != empty_set ),
inference(resolution,[status(thm)],[f55,f119]) ).
fof(f422,plain,
( ~ spl0_16
| ~ spl0_17
| spl0_4
| ~ spl0_22 ),
inference(split_clause,[status(thm)],[f421,f369,f372,f148,f418]) ).
fof(f423,plain,
( ~ relation(sk0_8)
| ~ function(sk0_8)
| in(apply(sk0_7,sk0_9),relation_dom(sk0_8))
| spl0_22 ),
inference(resolution,[status(thm)],[f420,f348]) ).
fof(f424,plain,
( ~ spl0_0
| ~ spl0_1
| spl0_20
| spl0_22 ),
inference(split_clause,[status(thm)],[f423,f136,f139,f410,f418]) ).
fof(f607,plain,
( spl0_33
<=> empty(relation_dom(sk0_7)) ),
introduced(split_symbol_definition) ).
fof(f608,plain,
( empty(relation_dom(sk0_7))
| ~ spl0_33 ),
inference(component_clause,[status(thm)],[f607]) ).
fof(f610,plain,
( spl0_34
<=> in(sk0_9,relation_dom(sk0_7)) ),
introduced(split_symbol_definition) ).
fof(f613,plain,
( empty(relation_dom(sk0_7))
| in(sk0_9,relation_dom(sk0_7)) ),
inference(resolution,[status(thm)],[f121,f165]) ).
fof(f614,plain,
( spl0_33
| spl0_34 ),
inference(split_clause,[status(thm)],[f613,f607,f610]) ).
fof(f615,plain,
( $false
| ~ spl0_33 ),
inference(forward_subsumption_resolution,[status(thm)],[f608,f130]) ).
fof(f616,plain,
~ spl0_33,
inference(contradiction_clause,[status(thm)],[f615]) ).
fof(f617,plain,
( ~ relation(sk0_8)
| ~ function(sk0_8)
| ~ relation(sk0_7)
| ~ function(sk0_7)
| in(sk0_9,relation_dom(relation_composition(sk0_7,sk0_8)))
| ~ in(sk0_9,relation_dom(sk0_7))
| ~ spl0_20 ),
inference(resolution,[status(thm)],[f107,f411]) ).
fof(f618,plain,
( ~ spl0_0
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_34
| ~ spl0_20 ),
inference(split_clause,[status(thm)],[f617,f136,f139,f142,f145,f148,f610,f410]) ).
fof(f619,plain,
$false,
inference(sat_refutation,[status(thm)],[f152,f385,f387,f389,f391,f403,f409,f422,f424,f614,f616,f618]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU215+1 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n019.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 19:50:29 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % Drodi V3.6.0
% 0.19/0.52 % Refutation found
% 0.19/0.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.53 % Elapsed time: 0.181820 seconds
% 0.19/0.53 % CPU time: 1.339401 seconds
% 0.19/0.53 % Total memory used: 78.254 MB
% 0.19/0.53 % Net memory used: 77.567 MB
%------------------------------------------------------------------------------