TSTP Solution File: SEU045+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU045+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n008.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 12:35:45 EDT 2023
% Result : Theorem 0.14s 0.35s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 46 ( 8 unt; 0 def)
% Number of atoms : 191 ( 31 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 233 ( 88 ~; 87 |; 38 &)
% ( 11 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 80 (; 70 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f19,axiom,
! [A,B] :
( relation(B)
=> relation(relation_rng_restriction(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,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(f33,conjecture,
! [A,B,C] :
( ( relation(C)
& function(C) )
=> ( in(B,relation_dom(relation_rng_restriction(A,C)))
=> apply(relation_rng_restriction(A,C),B) = apply(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
~ ! [A,B,C] :
( ( relation(C)
& function(C) )
=> ( in(B,relation_dom(relation_rng_restriction(A,C)))
=> apply(relation_rng_restriction(A,C),B) = apply(C,B) ) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f35,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(f79,plain,
! [A,B] :
( ~ relation(B)
| relation(relation_rng_restriction(A,B)) ),
inference(pre_NNF_transformation,[status(esa)],[f19]) ).
fof(f80,plain,
! [B] :
( ~ relation(B)
| ! [A] : relation(relation_rng_restriction(A,B)) ),
inference(miniscoping,[status(esa)],[f79]) ).
fof(f81,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_rng_restriction(X1,X0)) ),
inference(cnf_transformation,[status(esa)],[f80]) ).
fof(f82,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)],[f20]) ).
fof(f83,plain,
! [B] :
( ~ relation(B)
| ~ function(B)
| ( ! [A] : relation(relation_rng_restriction(A,B))
& ! [A] : function(relation_rng_restriction(A,B)) ) ),
inference(miniscoping,[status(esa)],[f82]) ).
fof(f85,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ function(X0)
| function(relation_rng_restriction(X1,X0)) ),
inference(cnf_transformation,[status(esa)],[f83]) ).
fof(f122,plain,
? [A,B,C] :
( relation(C)
& function(C)
& in(B,relation_dom(relation_rng_restriction(A,C)))
& apply(relation_rng_restriction(A,C),B) != apply(C,B) ),
inference(pre_NNF_transformation,[status(esa)],[f34]) ).
fof(f123,plain,
? [C] :
( relation(C)
& function(C)
& ? [A,B] :
( in(B,relation_dom(relation_rng_restriction(A,C)))
& apply(relation_rng_restriction(A,C),B) != apply(C,B) ) ),
inference(miniscoping,[status(esa)],[f122]) ).
fof(f124,plain,
( relation(sk0_11)
& function(sk0_11)
& in(sk0_13,relation_dom(relation_rng_restriction(sk0_12,sk0_11)))
& apply(relation_rng_restriction(sk0_12,sk0_11),sk0_13) != apply(sk0_11,sk0_13) ),
inference(skolemization,[status(esa)],[f123]) ).
fof(f125,plain,
relation(sk0_11),
inference(cnf_transformation,[status(esa)],[f124]) ).
fof(f126,plain,
function(sk0_11),
inference(cnf_transformation,[status(esa)],[f124]) ).
fof(f127,plain,
in(sk0_13,relation_dom(relation_rng_restriction(sk0_12,sk0_11))),
inference(cnf_transformation,[status(esa)],[f124]) ).
fof(f128,plain,
apply(relation_rng_restriction(sk0_12,sk0_11),sk0_13) != apply(sk0_11,sk0_13),
inference(cnf_transformation,[status(esa)],[f124]) ).
fof(f129,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)],[f35]) ).
fof(f130,plain,
! [A,C,D] :
( pd0_0(D,C,A)
<=> ( in(D,relation_dom(C))
& in(apply(C,D),A) ) ),
introduced(predicate_definition,[f129]) ).
fof(f131,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)],[f129,f130]) ).
fof(f132,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)],[f131]) ).
fof(f133,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)],[f132]) ).
fof(f134,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_14(A,C,B),relation_dom(B))
| ~ pd0_0(sk0_14(A,C,B),C,A) )
& ( in(sk0_14(A,C,B),relation_dom(B))
| pd0_0(sk0_14(A,C,B),C,A) ) )
| ( in(sk0_15(A,C,B),relation_dom(B))
& apply(B,sk0_15(A,C,B)) != apply(C,sk0_15(A,C,B)) ) ) ) ) ),
inference(skolemization,[status(esa)],[f133]) ).
fof(f137,plain,
! [X0,X1,X2,X3] :
( ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1)
| X0 != relation_rng_restriction(X2,X1)
| ~ in(X3,relation_dom(X0))
| apply(X0,X3) = apply(X1,X3) ),
inference(cnf_transformation,[status(esa)],[f134]) ).
fof(f149,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)))
| apply(relation_rng_restriction(X0,X1),X2) = apply(X1,X2) ),
inference(destructive_equality_resolution,[status(esa)],[f137]) ).
fof(f151,plain,
! [X0,X1,X2] :
( ~ function(relation_rng_restriction(X0,X1))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_dom(relation_rng_restriction(X0,X1)))
| apply(relation_rng_restriction(X0,X1),X2) = apply(X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f149,f81]) ).
fof(f152,plain,
( spl0_0
<=> function(relation_rng_restriction(sk0_12,sk0_11)) ),
introduced(split_symbol_definition) ).
fof(f154,plain,
( ~ function(relation_rng_restriction(sk0_12,sk0_11))
| spl0_0 ),
inference(component_clause,[status(thm)],[f152]) ).
fof(f155,plain,
( spl0_1
<=> relation(sk0_11) ),
introduced(split_symbol_definition) ).
fof(f157,plain,
( ~ relation(sk0_11)
| spl0_1 ),
inference(component_clause,[status(thm)],[f155]) ).
fof(f158,plain,
( spl0_2
<=> function(sk0_11) ),
introduced(split_symbol_definition) ).
fof(f160,plain,
( ~ function(sk0_11)
| spl0_2 ),
inference(component_clause,[status(thm)],[f158]) ).
fof(f161,plain,
( spl0_3
<=> apply(relation_rng_restriction(sk0_12,sk0_11),sk0_13) = apply(sk0_11,sk0_13) ),
introduced(split_symbol_definition) ).
fof(f162,plain,
( apply(relation_rng_restriction(sk0_12,sk0_11),sk0_13) = apply(sk0_11,sk0_13)
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f161]) ).
fof(f164,plain,
( ~ function(relation_rng_restriction(sk0_12,sk0_11))
| ~ relation(sk0_11)
| ~ function(sk0_11)
| apply(relation_rng_restriction(sk0_12,sk0_11),sk0_13) = apply(sk0_11,sk0_13) ),
inference(resolution,[status(thm)],[f151,f127]) ).
fof(f165,plain,
( ~ spl0_0
| ~ spl0_1
| ~ spl0_2
| spl0_3 ),
inference(split_clause,[status(thm)],[f164,f152,f155,f158,f161]) ).
fof(f166,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f160,f126]) ).
fof(f167,plain,
spl0_2,
inference(contradiction_clause,[status(thm)],[f166]) ).
fof(f168,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f157,f125]) ).
fof(f169,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f168]) ).
fof(f187,plain,
( ~ relation(sk0_11)
| ~ function(sk0_11)
| spl0_0 ),
inference(resolution,[status(thm)],[f154,f85]) ).
fof(f188,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_0 ),
inference(split_clause,[status(thm)],[f187,f155,f158,f152]) ).
fof(f190,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f162,f128]) ).
fof(f191,plain,
~ spl0_3,
inference(contradiction_clause,[status(thm)],[f190]) ).
fof(f192,plain,
$false,
inference(sat_refutation,[status(thm)],[f165,f167,f169,f188,f191]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU045+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.34 % Computer : n008.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue May 30 09:16:23 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.14/0.35 % Drodi V3.5.1
% 0.14/0.35 % Refutation found
% 0.14/0.35 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.57 % Elapsed time: 0.013207 seconds
% 0.20/0.57 % CPU time: 0.031556 seconds
% 0.20/0.57 % Memory used: 11.886 MB
%------------------------------------------------------------------------------