TSTP Solution File: SEU292+1 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU292+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n021.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 12:36:35 EDT 2023
% Result : Theorem 3.23s 0.85s
% Output : CNFRefutation 3.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 18
% Syntax : Number of formulae : 87 ( 17 unt; 0 def)
% Number of atoms : 255 ( 58 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 257 ( 89 ~; 94 |; 40 &)
% ( 17 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 11 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 103 (; 93 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A,B,C] :
( element(C,powerset(cartesian_product2(A,B)))
=> relation(C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> ( ( ( B = empty_set
=> A = empty_set )
=> ( quasi_total(C,A,B)
<=> A = relation_dom_as_subset(A,B,C) ) )
& ( B = empty_set
=> ( A = empty_set
| ( quasi_total(C,A,B)
<=> C = empty_set ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> element(C,powerset(cartesian_product2(A,B))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,axiom,
! [A,B,C] :
( relation_of2(C,A,B)
=> relation_dom_as_subset(A,B,C) = relation_dom(C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
<=> relation_of2(C,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,conjecture,
! [A,B,C,D] :
( ( function(D)
& quasi_total(D,A,B)
& relation_of2_as_subset(D,A,B) )
=> ! [E] :
( ( relation(E)
& function(E) )
=> ( in(C,A)
=> ( B = empty_set
| apply(relation_composition(D,E),C) = apply(E,apply(D,C)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,negated_conjecture,
~ ! [A,B,C,D] :
( ( function(D)
& quasi_total(D,A,B)
& relation_of2_as_subset(D,A,B) )
=> ! [E] :
( ( relation(E)
& function(E) )
=> ( in(C,A)
=> ( B = empty_set
| apply(relation_composition(D,E),C) = apply(E,apply(D,C)) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f48]) ).
fof(f50,axiom,
! [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/sandbox2/benchmark/theBenchmark.p') ).
fof(f64,plain,
! [A,B,C] :
( ~ element(C,powerset(cartesian_product2(A,B)))
| relation(C) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f65,plain,
! [C] :
( ! [A,B] : ~ element(C,powerset(cartesian_product2(A,B)))
| relation(C) ),
inference(miniscoping,[status(esa)],[f64]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ~ element(X0,powerset(cartesian_product2(X1,X2)))
| relation(X0) ),
inference(cnf_transformation,[status(esa)],[f65]) ).
fof(f71,plain,
! [A,B,C] :
( ~ relation_of2_as_subset(C,A,B)
| ( ( ( B = empty_set
& A != empty_set )
| ( quasi_total(C,A,B)
<=> A = relation_dom_as_subset(A,B,C) ) )
& ( B != empty_set
| A = empty_set
| ( quasi_total(C,A,B)
<=> C = empty_set ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f6]) ).
fof(f72,plain,
! [A,B] :
( pd0_0(B,A)
=> ( B = empty_set
& A != empty_set ) ),
introduced(predicate_definition,[f71]) ).
fof(f73,plain,
! [A,B,C] :
( ~ relation_of2_as_subset(C,A,B)
| ( ( pd0_0(B,A)
| ( quasi_total(C,A,B)
<=> A = relation_dom_as_subset(A,B,C) ) )
& ( B != empty_set
| A = empty_set
| ( quasi_total(C,A,B)
<=> C = empty_set ) ) ) ),
inference(formula_renaming,[status(thm)],[f71,f72]) ).
fof(f74,plain,
! [A,B,C] :
( ~ relation_of2_as_subset(C,A,B)
| ( ( pd0_0(B,A)
| ( ( ~ quasi_total(C,A,B)
| A = relation_dom_as_subset(A,B,C) )
& ( quasi_total(C,A,B)
| A != relation_dom_as_subset(A,B,C) ) ) )
& ( B != empty_set
| A = empty_set
| ( ( ~ quasi_total(C,A,B)
| C = empty_set )
& ( quasi_total(C,A,B)
| C != empty_set ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f73]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ~ relation_of2_as_subset(X0,X1,X2)
| pd0_0(X2,X1)
| ~ quasi_total(X0,X1,X2)
| X1 = relation_dom_as_subset(X1,X2,X0) ),
inference(cnf_transformation,[status(esa)],[f74]) ).
fof(f83,plain,
! [A,B,C] :
( ~ relation_of2_as_subset(C,A,B)
| element(C,powerset(cartesian_product2(A,B))) ),
inference(pre_NNF_transformation,[status(esa)],[f16]) ).
fof(f84,plain,
! [X0,X1,X2] :
( ~ relation_of2_as_subset(X0,X1,X2)
| element(X0,powerset(cartesian_product2(X1,X2))) ),
inference(cnf_transformation,[status(esa)],[f83]) ).
fof(f163,plain,
! [A,B,C] :
( ~ relation_of2(C,A,B)
| relation_dom_as_subset(A,B,C) = relation_dom(C) ),
inference(pre_NNF_transformation,[status(esa)],[f44]) ).
fof(f164,plain,
! [X0,X1,X2] :
( ~ relation_of2(X0,X1,X2)
| relation_dom_as_subset(X1,X2,X0) = relation_dom(X0) ),
inference(cnf_transformation,[status(esa)],[f163]) ).
fof(f165,plain,
! [A,B,C] :
( ( ~ relation_of2_as_subset(C,A,B)
| relation_of2(C,A,B) )
& ( relation_of2_as_subset(C,A,B)
| ~ relation_of2(C,A,B) ) ),
inference(NNF_transformation,[status(esa)],[f45]) ).
fof(f166,plain,
( ! [A,B,C] :
( ~ relation_of2_as_subset(C,A,B)
| relation_of2(C,A,B) )
& ! [A,B,C] :
( relation_of2_as_subset(C,A,B)
| ~ relation_of2(C,A,B) ) ),
inference(miniscoping,[status(esa)],[f165]) ).
fof(f167,plain,
! [X0,X1,X2] :
( ~ relation_of2_as_subset(X0,X1,X2)
| relation_of2(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f166]) ).
fof(f173,plain,
? [A,B,C,D] :
( function(D)
& quasi_total(D,A,B)
& relation_of2_as_subset(D,A,B)
& ? [E] :
( relation(E)
& function(E)
& in(C,A)
& B != empty_set
& apply(relation_composition(D,E),C) != apply(E,apply(D,C)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f49]) ).
fof(f174,plain,
? [A,B,D] :
( function(D)
& quasi_total(D,A,B)
& relation_of2_as_subset(D,A,B)
& ? [E] :
( relation(E)
& function(E)
& ? [C] :
( in(C,A)
& B != empty_set
& apply(relation_composition(D,E),C) != apply(E,apply(D,C)) ) ) ),
inference(miniscoping,[status(esa)],[f173]) ).
fof(f175,plain,
( function(sk0_19)
& quasi_total(sk0_19,sk0_17,sk0_18)
& relation_of2_as_subset(sk0_19,sk0_17,sk0_18)
& relation(sk0_20)
& function(sk0_20)
& in(sk0_21,sk0_17)
& sk0_18 != empty_set
& apply(relation_composition(sk0_19,sk0_20),sk0_21) != apply(sk0_20,apply(sk0_19,sk0_21)) ),
inference(skolemization,[status(esa)],[f174]) ).
fof(f176,plain,
function(sk0_19),
inference(cnf_transformation,[status(esa)],[f175]) ).
fof(f177,plain,
quasi_total(sk0_19,sk0_17,sk0_18),
inference(cnf_transformation,[status(esa)],[f175]) ).
fof(f178,plain,
relation_of2_as_subset(sk0_19,sk0_17,sk0_18),
inference(cnf_transformation,[status(esa)],[f175]) ).
fof(f179,plain,
relation(sk0_20),
inference(cnf_transformation,[status(esa)],[f175]) ).
fof(f180,plain,
function(sk0_20),
inference(cnf_transformation,[status(esa)],[f175]) ).
fof(f181,plain,
in(sk0_21,sk0_17),
inference(cnf_transformation,[status(esa)],[f175]) ).
fof(f182,plain,
sk0_18 != empty_set,
inference(cnf_transformation,[status(esa)],[f175]) ).
fof(f183,plain,
apply(relation_composition(sk0_19,sk0_20),sk0_21) != apply(sk0_20,apply(sk0_19,sk0_21)),
inference(cnf_transformation,[status(esa)],[f175]) ).
fof(f184,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)],[f50]) ).
fof(f185,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)],[f184]) ).
fof(f186,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_dom(X0))
| apply(relation_composition(X0,X1),X2) = apply(X1,apply(X0,X2)) ),
inference(cnf_transformation,[status(esa)],[f185]) ).
fof(f207,plain,
! [A,B] :
( ~ pd0_0(B,A)
| ( B = empty_set
& A != empty_set ) ),
inference(pre_NNF_transformation,[status(esa)],[f72]) ).
fof(f208,plain,
! [X0,X1] :
( ~ pd0_0(X0,X1)
| X0 = empty_set ),
inference(cnf_transformation,[status(esa)],[f207]) ).
fof(f250,plain,
( spl0_0
<=> relation(sk0_20) ),
introduced(split_symbol_definition) ).
fof(f252,plain,
( ~ relation(sk0_20)
| spl0_0 ),
inference(component_clause,[status(thm)],[f250]) ).
fof(f263,plain,
( $false
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f252,f179]) ).
fof(f264,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f263]) ).
fof(f282,plain,
( spl0_6
<=> function(sk0_20) ),
introduced(split_symbol_definition) ).
fof(f284,plain,
( ~ function(sk0_20)
| spl0_6 ),
inference(component_clause,[status(thm)],[f282]) ).
fof(f720,plain,
element(sk0_19,powerset(cartesian_product2(sk0_17,sk0_18))),
inference(resolution,[status(thm)],[f84,f178]) ).
fof(f1084,plain,
( spl0_18
<=> relation(sk0_19) ),
introduced(split_symbol_definition) ).
fof(f1086,plain,
( ~ relation(sk0_19)
| spl0_18 ),
inference(component_clause,[status(thm)],[f1084]) ).
fof(f1087,plain,
( spl0_19
<=> function(sk0_19) ),
introduced(split_symbol_definition) ).
fof(f1089,plain,
( ~ function(sk0_19)
| spl0_19 ),
inference(component_clause,[status(thm)],[f1087]) ).
fof(f1093,plain,
( $false
| spl0_19 ),
inference(forward_subsumption_resolution,[status(thm)],[f1089,f176]) ).
fof(f1094,plain,
spl0_19,
inference(contradiction_clause,[status(thm)],[f1093]) ).
fof(f1095,plain,
! [X0,X1] :
( ~ element(sk0_19,powerset(cartesian_product2(X0,X1)))
| spl0_18 ),
inference(resolution,[status(thm)],[f1086,f66]) ).
fof(f1097,plain,
( $false
| spl0_18 ),
inference(backward_subsumption_resolution,[status(thm)],[f720,f1095]) ).
fof(f1098,plain,
spl0_18,
inference(contradiction_clause,[status(thm)],[f1097]) ).
fof(f1809,plain,
! [X0,X1,X2] :
( X0 = empty_set
| ~ relation_of2_as_subset(X1,X2,X0)
| ~ quasi_total(X1,X2,X0)
| X2 = relation_dom_as_subset(X2,X0,X1) ),
inference(resolution,[status(thm)],[f208,f75]) ).
fof(f3478,plain,
( $false
| spl0_6 ),
inference(forward_subsumption_resolution,[status(thm)],[f284,f180]) ).
fof(f3479,plain,
spl0_6,
inference(contradiction_clause,[status(thm)],[f3478]) ).
fof(f3608,plain,
( spl0_88
<=> in(sk0_21,relation_dom(sk0_19)) ),
introduced(split_symbol_definition) ).
fof(f3610,plain,
( ~ in(sk0_21,relation_dom(sk0_19))
| spl0_88 ),
inference(component_clause,[status(thm)],[f3608]) ).
fof(f3611,plain,
( ~ relation(sk0_19)
| ~ function(sk0_19)
| ~ relation(sk0_20)
| ~ function(sk0_20)
| ~ in(sk0_21,relation_dom(sk0_19)) ),
inference(resolution,[status(thm)],[f183,f186]) ).
fof(f3612,plain,
( ~ spl0_18
| ~ spl0_19
| ~ spl0_0
| ~ spl0_6
| ~ spl0_88 ),
inference(split_clause,[status(thm)],[f3611,f1084,f1087,f250,f282,f3608]) ).
fof(f5844,plain,
( spl0_148
<=> sk0_18 = empty_set ),
introduced(split_symbol_definition) ).
fof(f5845,plain,
( sk0_18 = empty_set
| ~ spl0_148 ),
inference(component_clause,[status(thm)],[f5844]) ).
fof(f5847,plain,
( spl0_149
<=> quasi_total(sk0_19,sk0_17,sk0_18) ),
introduced(split_symbol_definition) ).
fof(f5849,plain,
( ~ quasi_total(sk0_19,sk0_17,sk0_18)
| spl0_149 ),
inference(component_clause,[status(thm)],[f5847]) ).
fof(f5850,plain,
( spl0_150
<=> sk0_17 = relation_dom_as_subset(sk0_17,sk0_18,sk0_19) ),
introduced(split_symbol_definition) ).
fof(f5851,plain,
( sk0_17 = relation_dom_as_subset(sk0_17,sk0_18,sk0_19)
| ~ spl0_150 ),
inference(component_clause,[status(thm)],[f5850]) ).
fof(f5853,plain,
( sk0_18 = empty_set
| ~ quasi_total(sk0_19,sk0_17,sk0_18)
| sk0_17 = relation_dom_as_subset(sk0_17,sk0_18,sk0_19) ),
inference(resolution,[status(thm)],[f1809,f178]) ).
fof(f5854,plain,
( spl0_148
| ~ spl0_149
| spl0_150 ),
inference(split_clause,[status(thm)],[f5853,f5844,f5847,f5850]) ).
fof(f5857,plain,
( $false
| spl0_149 ),
inference(forward_subsumption_resolution,[status(thm)],[f5849,f177]) ).
fof(f5858,plain,
spl0_149,
inference(contradiction_clause,[status(thm)],[f5857]) ).
fof(f5859,plain,
( $false
| ~ spl0_148 ),
inference(forward_subsumption_resolution,[status(thm)],[f5845,f182]) ).
fof(f5860,plain,
~ spl0_148,
inference(contradiction_clause,[status(thm)],[f5859]) ).
fof(f5866,plain,
( spl0_151
<=> relation_of2(sk0_19,sk0_17,sk0_18) ),
introduced(split_symbol_definition) ).
fof(f5868,plain,
( ~ relation_of2(sk0_19,sk0_17,sk0_18)
| spl0_151 ),
inference(component_clause,[status(thm)],[f5866]) ).
fof(f5869,plain,
( spl0_152
<=> sk0_17 = relation_dom(sk0_19) ),
introduced(split_symbol_definition) ).
fof(f5870,plain,
( sk0_17 = relation_dom(sk0_19)
| ~ spl0_152 ),
inference(component_clause,[status(thm)],[f5869]) ).
fof(f5872,plain,
( ~ relation_of2(sk0_19,sk0_17,sk0_18)
| sk0_17 = relation_dom(sk0_19)
| ~ spl0_150 ),
inference(paramodulation,[status(thm)],[f5851,f164]) ).
fof(f5873,plain,
( ~ spl0_151
| spl0_152
| ~ spl0_150 ),
inference(split_clause,[status(thm)],[f5872,f5866,f5869,f5850]) ).
fof(f5874,plain,
( ~ relation_of2_as_subset(sk0_19,sk0_17,sk0_18)
| spl0_151 ),
inference(resolution,[status(thm)],[f5868,f167]) ).
fof(f5875,plain,
( $false
| spl0_151 ),
inference(forward_subsumption_resolution,[status(thm)],[f5874,f178]) ).
fof(f5876,plain,
spl0_151,
inference(contradiction_clause,[status(thm)],[f5875]) ).
fof(f5877,plain,
( ~ in(sk0_21,sk0_17)
| ~ spl0_152
| spl0_88 ),
inference(backward_demodulation,[status(thm)],[f5870,f3610]) ).
fof(f5878,plain,
( $false
| ~ spl0_152
| spl0_88 ),
inference(forward_subsumption_resolution,[status(thm)],[f5877,f181]) ).
fof(f5879,plain,
( ~ spl0_152
| spl0_88 ),
inference(contradiction_clause,[status(thm)],[f5878]) ).
fof(f5880,plain,
$false,
inference(sat_refutation,[status(thm)],[f264,f1094,f1098,f3479,f3612,f5854,f5858,f5860,f5873,f5876,f5879]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU292+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue May 30 09:14:22 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % Drodi V3.5.1
% 3.23/0.85 % Refutation found
% 3.23/0.85 % SZS status Theorem for theBenchmark: Theorem is valid
% 3.23/0.85 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.20/0.87 % Elapsed time: 0.514959 seconds
% 4.20/0.87 % CPU time: 3.945519 seconds
% 4.20/0.87 % Memory used: 96.988 MB
%------------------------------------------------------------------------------