TSTP Solution File: SEU046+1 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SEU046+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n004.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 20:40:56 EDT 2024
% Result : Theorem 0.16s 0.44s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of formulae : 64 ( 6 unt; 0 def)
% Number of atoms : 257 ( 19 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 312 ( 119 ~; 124 |; 47 &)
% ( 13 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 5 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 135 ( 124 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B] :
( relation(B)
=> relation(relation_rng_restriction(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B] :
( ( relation(B)
& function(B) )
=> ( relation(relation_rng_restriction(A,B))
& function(relation_rng_restriction(A,B)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [A,B] :
( relation(B)
=> subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [A,B] :
( ( relation(B)
& function(B) )
=> ! [C] :
( ( relation(C)
& function(C) )
=> ( B = relation_rng_restriction(A,C)
<=> ( ! [D] :
( in(D,relation_dom(B))
<=> ( in(D,relation_dom(C))
& in(apply(C,D),A) ) )
& ! [D] :
( in(D,relation_dom(B))
=> apply(B,D) = apply(C,D) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,conjecture,
! [A,B] :
( ( relation(B)
& function(B) )
=> ( subset(relation_dom(relation_rng_restriction(A,B)),relation_dom(B))
& subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
~ ! [A,B] :
( ( relation(B)
& function(B) )
=> ( subset(relation_dom(relation_rng_restriction(A,B)),relation_dom(B))
& subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B)) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f50,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( ~ in(C,A)
| in(C,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f51,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)],[f50]) ).
fof(f52,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)],[f51]) ).
fof(f53,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [C] :
( ~ in(C,A)
| in(C,B) ) )
& ! [A,B] :
( subset(A,B)
| ( in(sk0_0(B,A),A)
& ~ in(sk0_0(B,A),B) ) ) ),
inference(skolemization,[status(esa)],[f52]) ).
fof(f55,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sk0_0(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f53]) ).
fof(f56,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sk0_0(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f53]) ).
fof(f57,plain,
! [A,B] :
( ~ relation(B)
| relation(relation_rng_restriction(A,B)) ),
inference(pre_NNF_transformation,[status(esa)],[f6]) ).
fof(f58,plain,
! [B] :
( ~ relation(B)
| ! [A] : relation(relation_rng_restriction(A,B)) ),
inference(miniscoping,[status(esa)],[f57]) ).
fof(f59,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_rng_restriction(X1,X0)) ),
inference(cnf_transformation,[status(esa)],[f58]) ).
fof(f69,plain,
! [A,B] :
( ~ relation(B)
| ~ function(B)
| ( relation(relation_rng_restriction(A,B))
& function(relation_rng_restriction(A,B)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f12]) ).
fof(f70,plain,
! [B] :
( ~ relation(B)
| ~ function(B)
| ( ! [A] : relation(relation_rng_restriction(A,B))
& ! [A] : function(relation_rng_restriction(A,B)) ) ),
inference(miniscoping,[status(esa)],[f69]) ).
fof(f72,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ function(X0)
| function(relation_rng_restriction(X1,X0)) ),
inference(cnf_transformation,[status(esa)],[f70]) ).
fof(f116,plain,
! [A,B] :
( ~ relation(B)
| subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B)) ),
inference(pre_NNF_transformation,[status(esa)],[f28]) ).
fof(f117,plain,
! [B] :
( ~ relation(B)
| ! [A] : subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B)) ),
inference(miniscoping,[status(esa)],[f116]) ).
fof(f118,plain,
! [X0,X1] :
( ~ relation(X0)
| subset(relation_rng(relation_rng_restriction(X1,X0)),relation_rng(X0)) ),
inference(cnf_transformation,[status(esa)],[f117]) ).
fof(f138,plain,
! [A,B] :
( ~ relation(B)
| ~ function(B)
| ! [C] :
( ~ relation(C)
| ~ function(C)
| ( B = relation_rng_restriction(A,C)
<=> ( ! [D] :
( in(D,relation_dom(B))
<=> ( in(D,relation_dom(C))
& in(apply(C,D),A) ) )
& ! [D] :
( ~ in(D,relation_dom(B))
| apply(B,D) = apply(C,D) ) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f36]) ).
fof(f139,plain,
! [A,C,D] :
( pd0_0(D,C,A)
<=> ( in(D,relation_dom(C))
& in(apply(C,D),A) ) ),
introduced(predicate_definition,[f138]) ).
fof(f140,plain,
! [A,B] :
( ~ relation(B)
| ~ function(B)
| ! [C] :
( ~ relation(C)
| ~ function(C)
| ( B = relation_rng_restriction(A,C)
<=> ( ! [D] :
( in(D,relation_dom(B))
<=> pd0_0(D,C,A) )
& ! [D] :
( ~ in(D,relation_dom(B))
| apply(B,D) = apply(C,D) ) ) ) ) ),
inference(formula_renaming,[status(thm)],[f138,f139]) ).
fof(f141,plain,
! [A,B] :
( ~ relation(B)
| ~ function(B)
| ! [C] :
( ~ relation(C)
| ~ function(C)
| ( ( B != relation_rng_restriction(A,C)
| ( ! [D] :
( ( ~ in(D,relation_dom(B))
| pd0_0(D,C,A) )
& ( in(D,relation_dom(B))
| ~ pd0_0(D,C,A) ) )
& ! [D] :
( ~ in(D,relation_dom(B))
| apply(B,D) = apply(C,D) ) ) )
& ( B = relation_rng_restriction(A,C)
| ? [D] :
( ( ~ in(D,relation_dom(B))
| ~ pd0_0(D,C,A) )
& ( in(D,relation_dom(B))
| pd0_0(D,C,A) ) )
| ? [D] :
( in(D,relation_dom(B))
& apply(B,D) != apply(C,D) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f140]) ).
fof(f142,plain,
! [B] :
( ~ relation(B)
| ~ function(B)
| ! [C] :
( ~ relation(C)
| ~ function(C)
| ( ! [A] :
( B != relation_rng_restriction(A,C)
| ( ! [D] :
( ~ in(D,relation_dom(B))
| pd0_0(D,C,A) )
& ! [D] :
( in(D,relation_dom(B))
| ~ pd0_0(D,C,A) )
& ! [D] :
( ~ in(D,relation_dom(B))
| apply(B,D) = apply(C,D) ) ) )
& ! [A] :
( B = relation_rng_restriction(A,C)
| ? [D] :
( ( ~ in(D,relation_dom(B))
| ~ pd0_0(D,C,A) )
& ( in(D,relation_dom(B))
| pd0_0(D,C,A) ) )
| ? [D] :
( in(D,relation_dom(B))
& apply(B,D) != apply(C,D) ) ) ) ) ),
inference(miniscoping,[status(esa)],[f141]) ).
fof(f143,plain,
! [B] :
( ~ relation(B)
| ~ function(B)
| ! [C] :
( ~ relation(C)
| ~ function(C)
| ( ! [A] :
( B != relation_rng_restriction(A,C)
| ( ! [D] :
( ~ in(D,relation_dom(B))
| pd0_0(D,C,A) )
& ! [D] :
( in(D,relation_dom(B))
| ~ pd0_0(D,C,A) )
& ! [D] :
( ~ in(D,relation_dom(B))
| apply(B,D) = apply(C,D) ) ) )
& ! [A] :
( B = relation_rng_restriction(A,C)
| ( ( ~ in(sk0_12(A,C,B),relation_dom(B))
| ~ pd0_0(sk0_12(A,C,B),C,A) )
& ( in(sk0_12(A,C,B),relation_dom(B))
| pd0_0(sk0_12(A,C,B),C,A) ) )
| ( in(sk0_13(A,C,B),relation_dom(B))
& apply(B,sk0_13(A,C,B)) != apply(C,sk0_13(A,C,B)) ) ) ) ) ),
inference(skolemization,[status(esa)],[f142]) ).
fof(f144,plain,
! [X0,X1,X2,X3] :
( ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1)
| X0 != relation_rng_restriction(X2,X1)
| ~ in(X3,relation_dom(X0))
| pd0_0(X3,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f143]) ).
fof(f151,plain,
? [A,B] :
( relation(B)
& function(B)
& ( ~ subset(relation_dom(relation_rng_restriction(A,B)),relation_dom(B))
| ~ subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f38]) ).
fof(f152,plain,
? [B] :
( relation(B)
& function(B)
& ( ? [A] : ~ subset(relation_dom(relation_rng_restriction(A,B)),relation_dom(B))
| ? [A] : ~ subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B)) ) ),
inference(miniscoping,[status(esa)],[f151]) ).
fof(f153,plain,
( relation(sk0_14)
& function(sk0_14)
& ( ~ subset(relation_dom(relation_rng_restriction(sk0_15,sk0_14)),relation_dom(sk0_14))
| ~ subset(relation_rng(relation_rng_restriction(sk0_16,sk0_14)),relation_rng(sk0_14)) ) ),
inference(skolemization,[status(esa)],[f152]) ).
fof(f154,plain,
relation(sk0_14),
inference(cnf_transformation,[status(esa)],[f153]) ).
fof(f155,plain,
function(sk0_14),
inference(cnf_transformation,[status(esa)],[f153]) ).
fof(f156,plain,
( ~ subset(relation_dom(relation_rng_restriction(sk0_15,sk0_14)),relation_dom(sk0_14))
| ~ subset(relation_rng(relation_rng_restriction(sk0_16,sk0_14)),relation_rng(sk0_14)) ),
inference(cnf_transformation,[status(esa)],[f153]) ).
fof(f160,plain,
! [A,C,D] :
( ( ~ pd0_0(D,C,A)
| ( in(D,relation_dom(C))
& in(apply(C,D),A) ) )
& ( pd0_0(D,C,A)
| ~ in(D,relation_dom(C))
| ~ in(apply(C,D),A) ) ),
inference(NNF_transformation,[status(esa)],[f139]) ).
fof(f161,plain,
( ! [A,C,D] :
( ~ pd0_0(D,C,A)
| ( in(D,relation_dom(C))
& in(apply(C,D),A) ) )
& ! [A,C,D] :
( pd0_0(D,C,A)
| ~ in(D,relation_dom(C))
| ~ in(apply(C,D),A) ) ),
inference(miniscoping,[status(esa)],[f160]) ).
fof(f162,plain,
! [X0,X1,X2] :
( ~ pd0_0(X0,X1,X2)
| in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[status(esa)],[f161]) ).
fof(f165,plain,
( spl0_0
<=> subset(relation_dom(relation_rng_restriction(sk0_15,sk0_14)),relation_dom(sk0_14)) ),
introduced(split_symbol_definition) ).
fof(f167,plain,
( ~ subset(relation_dom(relation_rng_restriction(sk0_15,sk0_14)),relation_dom(sk0_14))
| spl0_0 ),
inference(component_clause,[status(thm)],[f165]) ).
fof(f168,plain,
( spl0_1
<=> subset(relation_rng(relation_rng_restriction(sk0_16,sk0_14)),relation_rng(sk0_14)) ),
introduced(split_symbol_definition) ).
fof(f170,plain,
( ~ subset(relation_rng(relation_rng_restriction(sk0_16,sk0_14)),relation_rng(sk0_14))
| spl0_1 ),
inference(component_clause,[status(thm)],[f168]) ).
fof(f171,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f156,f165,f168]) ).
fof(f172,plain,
! [X0,X1,X2] :
( ~ relation(relation_rng_restriction(X0,X1))
| ~ function(relation_rng_restriction(X0,X1))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_dom(relation_rng_restriction(X0,X1)))
| pd0_0(X2,X1,X0) ),
inference(destructive_equality_resolution,[status(esa)],[f144]) ).
fof(f226,plain,
! [X0,X1,X2] :
( ~ function(relation_rng_restriction(X0,X1))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_dom(relation_rng_restriction(X0,X1)))
| pd0_0(X2,X1,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f172,f59]) ).
fof(f237,plain,
! [X0,X1,X2] :
( subset(relation_dom(relation_rng_restriction(X0,X1)),X2)
| ~ function(relation_rng_restriction(X0,X1))
| ~ relation(X1)
| ~ function(X1)
| pd0_0(sk0_0(X2,relation_dom(relation_rng_restriction(X0,X1))),X1,X0) ),
inference(resolution,[status(thm)],[f55,f226]) ).
fof(f238,plain,
! [X0,X1,X2] :
( subset(relation_dom(relation_rng_restriction(X0,X1)),X2)
| ~ relation(X1)
| ~ function(X1)
| pd0_0(sk0_0(X2,relation_dom(relation_rng_restriction(X0,X1))),X1,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f237,f72]) ).
fof(f246,plain,
! [X0,X1,X2] :
( subset(relation_dom(relation_rng_restriction(X0,X1)),X2)
| ~ relation(X1)
| ~ function(X1)
| in(sk0_0(X2,relation_dom(relation_rng_restriction(X0,X1))),relation_dom(X1)) ),
inference(resolution,[status(thm)],[f238,f162]) ).
fof(f259,plain,
( spl0_10
<=> relation(sk0_14) ),
introduced(split_symbol_definition) ).
fof(f261,plain,
( ~ relation(sk0_14)
| spl0_10 ),
inference(component_clause,[status(thm)],[f259]) ).
fof(f262,plain,
( spl0_11
<=> function(sk0_14) ),
introduced(split_symbol_definition) ).
fof(f264,plain,
( ~ function(sk0_14)
| spl0_11 ),
inference(component_clause,[status(thm)],[f262]) ).
fof(f379,plain,
( ~ relation(sk0_14)
| spl0_1 ),
inference(resolution,[status(thm)],[f170,f118]) ).
fof(f380,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f379,f154]) ).
fof(f381,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f380]) ).
fof(f492,plain,
! [X0,X1] :
( subset(relation_dom(relation_rng_restriction(X0,X1)),relation_dom(X1))
| subset(relation_dom(relation_rng_restriction(X0,X1)),relation_dom(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(resolution,[status(thm)],[f56,f246]) ).
fof(f493,plain,
! [X0,X1] :
( subset(relation_dom(relation_rng_restriction(X0,X1)),relation_dom(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(duplicate_literals_removal,[status(esa)],[f492]) ).
fof(f676,plain,
( ~ relation(sk0_14)
| ~ function(sk0_14)
| spl0_0 ),
inference(resolution,[status(thm)],[f493,f167]) ).
fof(f677,plain,
( ~ spl0_10
| ~ spl0_11
| spl0_0 ),
inference(split_clause,[status(thm)],[f676,f259,f262,f165]) ).
fof(f679,plain,
( $false
| spl0_10 ),
inference(forward_subsumption_resolution,[status(thm)],[f261,f154]) ).
fof(f680,plain,
spl0_10,
inference(contradiction_clause,[status(thm)],[f679]) ).
fof(f681,plain,
( $false
| spl0_11 ),
inference(forward_subsumption_resolution,[status(thm)],[f264,f155]) ).
fof(f682,plain,
spl0_11,
inference(contradiction_clause,[status(thm)],[f681]) ).
fof(f683,plain,
$false,
inference(sat_refutation,[status(thm)],[f171,f381,f677,f680,f682]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : SEU046+1 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.31 % Computer : n004.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Mon Apr 29 19:39:18 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.16/0.32 % Drodi V3.6.0
% 0.16/0.44 % Refutation found
% 0.16/0.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.45 % Elapsed time: 0.135784 seconds
% 0.16/0.45 % CPU time: 0.953837 seconds
% 0.16/0.45 % Total memory used: 65.812 MB
% 0.16/0.45 % Net memory used: 65.408 MB
%------------------------------------------------------------------------------