TSTP Solution File: SEU251+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU251+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n026.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 : Wed May 31 12:36:28 EDT 2023
% Result : Theorem 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 66 ( 7 unt; 0 def)
% Number of atoms : 216 ( 31 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 252 ( 102 ~; 98 |; 32 &)
% ( 14 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 7 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 118 (; 108 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( C = fiber(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D != B
& in(ordered_pair(D,B),A) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A,B] :
( relation(A)
=> relation(relation_restriction(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_restriction(C,B))
<=> ( in(A,C)
& in(A,cartesian_product2(B,B)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,conjecture,
! [A,B,C] :
( relation(C)
=> subset(fiber(relation_restriction(C,A),B),fiber(C,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
~ ! [A,B,C] :
( relation(C)
=> subset(fiber(relation_restriction(C,A),B),fiber(C,B)) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f52,plain,
! [A] :
( ~ relation(A)
| ! [B,C] :
( C = fiber(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D != B
& in(ordered_pair(D,B),A) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f6]) ).
fof(f53,plain,
! [A] :
( ~ relation(A)
| ! [B,C] :
( ( C != fiber(A,B)
| ! [D] :
( ( ~ in(D,C)
| ( D != B
& in(ordered_pair(D,B),A) ) )
& ( in(D,C)
| D = B
| ~ in(ordered_pair(D,B),A) ) ) )
& ( C = fiber(A,B)
| ? [D] :
( ( ~ in(D,C)
| D = B
| ~ in(ordered_pair(D,B),A) )
& ( in(D,C)
| ( D != B
& in(ordered_pair(D,B),A) ) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f52]) ).
fof(f54,plain,
! [A] :
( ~ relation(A)
| ( ! [B,C] :
( C != fiber(A,B)
| ( ! [D] :
( ~ in(D,C)
| ( D != B
& in(ordered_pair(D,B),A) ) )
& ! [D] :
( in(D,C)
| D = B
| ~ in(ordered_pair(D,B),A) ) ) )
& ! [B,C] :
( C = fiber(A,B)
| ? [D] :
( ( ~ in(D,C)
| D = B
| ~ in(ordered_pair(D,B),A) )
& ( in(D,C)
| ( D != B
& in(ordered_pair(D,B),A) ) ) ) ) ) ),
inference(miniscoping,[status(esa)],[f53]) ).
fof(f55,plain,
! [A] :
( ~ relation(A)
| ( ! [B,C] :
( C != fiber(A,B)
| ( ! [D] :
( ~ in(D,C)
| ( D != B
& in(ordered_pair(D,B),A) ) )
& ! [D] :
( in(D,C)
| D = B
| ~ in(ordered_pair(D,B),A) ) ) )
& ! [B,C] :
( C = fiber(A,B)
| ( ( ~ in(sk0_0(C,B,A),C)
| sk0_0(C,B,A) = B
| ~ in(ordered_pair(sk0_0(C,B,A),B),A) )
& ( in(sk0_0(C,B,A),C)
| ( sk0_0(C,B,A) != B
& in(ordered_pair(sk0_0(C,B,A),B),A) ) ) ) ) ) ),
inference(skolemization,[status(esa)],[f54]) ).
fof(f56,plain,
! [X0,X1,X2,X3] :
( ~ relation(X0)
| X1 != fiber(X0,X2)
| ~ in(X3,X1)
| X3 != X2 ),
inference(cnf_transformation,[status(esa)],[f55]) ).
fof(f57,plain,
! [X0,X1,X2,X3] :
( ~ relation(X0)
| X1 != fiber(X0,X2)
| ~ in(X3,X1)
| in(ordered_pair(X3,X2),X0) ),
inference(cnf_transformation,[status(esa)],[f55]) ).
fof(f58,plain,
! [X0,X1,X2,X3] :
( ~ relation(X0)
| X1 != fiber(X0,X2)
| in(X3,X1)
| X3 = X2
| ~ in(ordered_pair(X3,X2),X0) ),
inference(cnf_transformation,[status(esa)],[f55]) ).
fof(f62,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( ~ in(C,A)
| in(C,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f7]) ).
fof(f63,plain,
! [A,B] :
( ( ~ subset(A,B)
| ! [C] :
( ~ in(C,A)
| in(C,B) ) )
& ( subset(A,B)
| ? [C] :
( in(C,A)
& ~ in(C,B) ) ) ),
inference(NNF_transformation,[status(esa)],[f62]) ).
fof(f64,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [C] :
( ~ in(C,A)
| in(C,B) ) )
& ! [A,B] :
( subset(A,B)
| ? [C] :
( in(C,A)
& ~ in(C,B) ) ) ),
inference(miniscoping,[status(esa)],[f63]) ).
fof(f65,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [C] :
( ~ in(C,A)
| in(C,B) ) )
& ! [A,B] :
( subset(A,B)
| ( in(sk0_1(B,A),A)
& ~ in(sk0_1(B,A),B) ) ) ),
inference(skolemization,[status(esa)],[f64]) ).
fof(f67,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sk0_1(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f65]) ).
fof(f68,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sk0_1(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f65]) ).
fof(f72,plain,
! [A,B] :
( ~ relation(A)
| relation(relation_restriction(A,B)) ),
inference(pre_NNF_transformation,[status(esa)],[f15]) ).
fof(f73,plain,
! [A] :
( ~ relation(A)
| ! [B] : relation(relation_restriction(A,B)) ),
inference(miniscoping,[status(esa)],[f72]) ).
fof(f74,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_restriction(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f73]) ).
fof(f98,plain,
! [A,B,C] :
( ~ relation(C)
| ( in(A,relation_restriction(C,B))
<=> ( in(A,C)
& in(A,cartesian_product2(B,B)) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f30]) ).
fof(f99,plain,
! [A,B,C] :
( ~ relation(C)
| ( ( ~ in(A,relation_restriction(C,B))
| ( in(A,C)
& in(A,cartesian_product2(B,B)) ) )
& ( in(A,relation_restriction(C,B))
| ~ in(A,C)
| ~ in(A,cartesian_product2(B,B)) ) ) ),
inference(NNF_transformation,[status(esa)],[f98]) ).
fof(f100,plain,
! [C] :
( ~ relation(C)
| ( ! [A,B] :
( ~ in(A,relation_restriction(C,B))
| ( in(A,C)
& in(A,cartesian_product2(B,B)) ) )
& ! [A,B] :
( in(A,relation_restriction(C,B))
| ~ in(A,C)
| ~ in(A,cartesian_product2(B,B)) ) ) ),
inference(miniscoping,[status(esa)],[f99]) ).
fof(f101,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| ~ in(X1,relation_restriction(X0,X2))
| in(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f100]) ).
fof(f106,plain,
? [A,B,C] :
( relation(C)
& ~ subset(fiber(relation_restriction(C,A),B),fiber(C,B)) ),
inference(pre_NNF_transformation,[status(esa)],[f33]) ).
fof(f107,plain,
? [C] :
( relation(C)
& ? [A,B] : ~ subset(fiber(relation_restriction(C,A),B),fiber(C,B)) ),
inference(miniscoping,[status(esa)],[f106]) ).
fof(f108,plain,
( relation(sk0_8)
& ~ subset(fiber(relation_restriction(sk0_8,sk0_9),sk0_10),fiber(sk0_8,sk0_10)) ),
inference(skolemization,[status(esa)],[f107]) ).
fof(f109,plain,
relation(sk0_8),
inference(cnf_transformation,[status(esa)],[f108]) ).
fof(f110,plain,
~ subset(fiber(relation_restriction(sk0_8,sk0_9),sk0_10),fiber(sk0_8,sk0_10)),
inference(cnf_transformation,[status(esa)],[f108]) ).
fof(f132,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ in(X1,fiber(X0,X1)) ),
inference(destructive_equality_resolution,[status(esa)],[f56]) ).
fof(f133,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| ~ in(X1,fiber(X0,X2))
| in(ordered_pair(X1,X2),X0) ),
inference(destructive_equality_resolution,[status(esa)],[f57]) ).
fof(f134,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| in(X1,fiber(X0,X2))
| X1 = X2
| ~ in(ordered_pair(X1,X2),X0) ),
inference(destructive_equality_resolution,[status(esa)],[f58]) ).
fof(f135,plain,
in(sk0_1(fiber(sk0_8,sk0_10),fiber(relation_restriction(sk0_8,sk0_9),sk0_10)),fiber(relation_restriction(sk0_8,sk0_9),sk0_10)),
inference(resolution,[status(thm)],[f67,f110]) ).
fof(f158,plain,
! [X0,X1,X2,X3] :
( ~ relation(relation_restriction(X0,X1))
| ~ in(X2,fiber(relation_restriction(X0,X1),X3))
| ~ relation(X0)
| in(ordered_pair(X2,X3),X0) ),
inference(resolution,[status(thm)],[f133,f101]) ).
fof(f159,plain,
! [X0,X1,X2,X3] :
( ~ in(X0,fiber(relation_restriction(X1,X2),X3))
| ~ relation(X1)
| in(ordered_pair(X0,X3),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f158,f74]) ).
fof(f165,plain,
( spl0_3
<=> relation(sk0_8) ),
introduced(split_symbol_definition) ).
fof(f167,plain,
( ~ relation(sk0_8)
| spl0_3 ),
inference(component_clause,[status(thm)],[f165]) ).
fof(f168,plain,
( spl0_4
<=> in(ordered_pair(sk0_1(fiber(sk0_8,sk0_10),fiber(relation_restriction(sk0_8,sk0_9),sk0_10)),sk0_10),sk0_8) ),
introduced(split_symbol_definition) ).
fof(f169,plain,
( in(ordered_pair(sk0_1(fiber(sk0_8,sk0_10),fiber(relation_restriction(sk0_8,sk0_9),sk0_10)),sk0_10),sk0_8)
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f168]) ).
fof(f171,plain,
( ~ relation(sk0_8)
| in(ordered_pair(sk0_1(fiber(sk0_8,sk0_10),fiber(relation_restriction(sk0_8,sk0_9),sk0_10)),sk0_10),sk0_8) ),
inference(resolution,[status(thm)],[f159,f135]) ).
fof(f172,plain,
( ~ spl0_3
| spl0_4 ),
inference(split_clause,[status(thm)],[f171,f165,f168]) ).
fof(f183,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f167,f109]) ).
fof(f184,plain,
spl0_3,
inference(contradiction_clause,[status(thm)],[f183]) ).
fof(f190,plain,
( spl0_7
<=> relation(relation_restriction(sk0_8,sk0_9)) ),
introduced(split_symbol_definition) ).
fof(f192,plain,
( ~ relation(relation_restriction(sk0_8,sk0_9))
| spl0_7 ),
inference(component_clause,[status(thm)],[f190]) ).
fof(f216,plain,
( ~ relation(sk0_8)
| spl0_7 ),
inference(resolution,[status(thm)],[f192,f74]) ).
fof(f217,plain,
( ~ spl0_3
| spl0_7 ),
inference(split_clause,[status(thm)],[f216,f165,f190]) ).
fof(f218,plain,
( spl0_11
<=> in(sk0_1(fiber(sk0_8,sk0_10),fiber(relation_restriction(sk0_8,sk0_9),sk0_10)),fiber(sk0_8,sk0_10)) ),
introduced(split_symbol_definition) ).
fof(f219,plain,
( in(sk0_1(fiber(sk0_8,sk0_10),fiber(relation_restriction(sk0_8,sk0_9),sk0_10)),fiber(sk0_8,sk0_10))
| ~ spl0_11 ),
inference(component_clause,[status(thm)],[f218]) ).
fof(f221,plain,
( spl0_12
<=> sk0_1(fiber(sk0_8,sk0_10),fiber(relation_restriction(sk0_8,sk0_9),sk0_10)) = sk0_10 ),
introduced(split_symbol_definition) ).
fof(f222,plain,
( sk0_1(fiber(sk0_8,sk0_10),fiber(relation_restriction(sk0_8,sk0_9),sk0_10)) = sk0_10
| ~ spl0_12 ),
inference(component_clause,[status(thm)],[f221]) ).
fof(f224,plain,
( ~ relation(sk0_8)
| in(sk0_1(fiber(sk0_8,sk0_10),fiber(relation_restriction(sk0_8,sk0_9),sk0_10)),fiber(sk0_8,sk0_10))
| sk0_1(fiber(sk0_8,sk0_10),fiber(relation_restriction(sk0_8,sk0_9),sk0_10)) = sk0_10
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f169,f134]) ).
fof(f225,plain,
( ~ spl0_3
| spl0_11
| spl0_12
| ~ spl0_4 ),
inference(split_clause,[status(thm)],[f224,f165,f218,f221,f168]) ).
fof(f228,plain,
( subset(fiber(relation_restriction(sk0_8,sk0_9),sk0_10),fiber(sk0_8,sk0_10))
| ~ spl0_11 ),
inference(resolution,[status(thm)],[f219,f68]) ).
fof(f229,plain,
( $false
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[status(thm)],[f228,f110]) ).
fof(f230,plain,
~ spl0_11,
inference(contradiction_clause,[status(thm)],[f229]) ).
fof(f260,plain,
( in(sk0_10,fiber(relation_restriction(sk0_8,sk0_9),sk0_10))
| ~ spl0_12 ),
inference(backward_demodulation,[status(thm)],[f222,f135]) ).
fof(f261,plain,
( spl0_17
<=> subset(fiber(relation_restriction(sk0_8,sk0_9),sk0_10),fiber(sk0_8,sk0_10)) ),
introduced(split_symbol_definition) ).
fof(f262,plain,
( subset(fiber(relation_restriction(sk0_8,sk0_9),sk0_10),fiber(sk0_8,sk0_10))
| ~ spl0_17 ),
inference(component_clause,[status(thm)],[f261]) ).
fof(f276,plain,
( $false
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[status(thm)],[f262,f110]) ).
fof(f277,plain,
~ spl0_17,
inference(contradiction_clause,[status(thm)],[f276]) ).
fof(f288,plain,
( ~ relation(relation_restriction(sk0_8,sk0_9))
| ~ spl0_12 ),
inference(resolution,[status(thm)],[f260,f132]) ).
fof(f289,plain,
( ~ spl0_7
| ~ spl0_12 ),
inference(split_clause,[status(thm)],[f288,f190,f221]) ).
fof(f292,plain,
$false,
inference(sat_refutation,[status(thm)],[f172,f184,f217,f225,f230,f277,f289]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : SEU251+1 : TPTP v8.1.2. Released v3.3.0.
% 0.05/0.09 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30 % Computer : n026.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 : Tue May 30 09:32:58 EDT 2023
% 0.09/0.30 % CPUTime :
% 0.09/0.30 % Drodi V3.5.1
% 0.14/0.39 % Refutation found
% 0.14/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.41 % Elapsed time: 0.107349 seconds
% 0.14/0.41 % CPU time: 0.320174 seconds
% 0.14/0.41 % Memory used: 53.346 MB
%------------------------------------------------------------------------------