TSTP Solution File: SEU181+1 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU181+1 : TPTP v8.1.2. Released v3.3.0.
% 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 12:36:09 EDT 2023
% Result : Theorem 2.30s 0.66s
% Output : CNFRefutation 2.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 15
% Syntax : Number of formulae : 102 ( 6 unt; 0 def)
% Number of atoms : 366 ( 53 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 443 ( 179 ~; 191 |; 42 &)
% ( 22 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 8 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 1 con; 0-3 aty)
% Number of variables : 214 (; 191 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B] :
( A = B
<=> ( subset(A,B)
& subset(B,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( B = relation_inverse(A)
<=> ! [C,D] :
( in(ordered_pair(C,D),B)
<=> in(ordered_pair(D,C),A) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A] :
( relation(A)
=> relation(relation_inverse(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [A] :
( relation(A)
=> relation_inverse(relation_inverse(A)) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,conjecture,
! [A] :
( relation(A)
=> ( relation_rng(A) = relation_dom(relation_inverse(A))
& relation_dom(A) = relation_rng(relation_inverse(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
~ ! [A] :
( relation(A)
=> ( relation_rng(A) = relation_dom(relation_inverse(A))
& relation_dom(A) = relation_rng(relation_inverse(A)) ) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f44,plain,
! [A,B] :
( ( A != B
| ( subset(A,B)
& subset(B,A) ) )
& ( A = B
| ~ subset(A,B)
| ~ subset(B,A) ) ),
inference(NNF_transformation,[status(esa)],[f3]) ).
fof(f45,plain,
( ! [A,B] :
( A != B
| ( subset(A,B)
& subset(B,A) ) )
& ! [A,B] :
( A = B
| ~ subset(A,B)
| ~ subset(B,A) ) ),
inference(miniscoping,[status(esa)],[f44]) ).
fof(f48,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f45]) ).
fof(f49,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( ~ in(C,A)
| in(C,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f50,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)],[f49]) ).
fof(f51,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)],[f50]) ).
fof(f52,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)],[f51]) ).
fof(f54,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sk0_0(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f52]) ).
fof(f55,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sk0_0(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f52]) ).
fof(f56,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f57,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( ( B != relation_dom(A)
| ! [C] :
( ( ~ in(C,B)
| ? [D] : in(ordered_pair(C,D),A) )
& ( in(C,B)
| ! [D] : ~ in(ordered_pair(C,D),A) ) ) )
& ( B = relation_dom(A)
| ? [C] :
( ( ~ in(C,B)
| ! [D] : ~ in(ordered_pair(C,D),A) )
& ( in(C,B)
| ? [D] : in(ordered_pair(C,D),A) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f56]) ).
fof(f58,plain,
! [A] :
( ~ relation(A)
| ( ! [B] :
( B != relation_dom(A)
| ( ! [C] :
( ~ in(C,B)
| ? [D] : in(ordered_pair(C,D),A) )
& ! [C] :
( in(C,B)
| ! [D] : ~ in(ordered_pair(C,D),A) ) ) )
& ! [B] :
( B = relation_dom(A)
| ? [C] :
( ( ~ in(C,B)
| ! [D] : ~ in(ordered_pair(C,D),A) )
& ( in(C,B)
| ? [D] : in(ordered_pair(C,D),A) ) ) ) ) ),
inference(miniscoping,[status(esa)],[f57]) ).
fof(f59,plain,
! [A] :
( ~ relation(A)
| ( ! [B] :
( B != relation_dom(A)
| ( ! [C] :
( ~ in(C,B)
| in(ordered_pair(C,sk0_1(C,B,A)),A) )
& ! [C] :
( in(C,B)
| ! [D] : ~ in(ordered_pair(C,D),A) ) ) )
& ! [B] :
( B = relation_dom(A)
| ( ( ~ in(sk0_2(B,A),B)
| ! [D] : ~ in(ordered_pair(sk0_2(B,A),D),A) )
& ( in(sk0_2(B,A),B)
| in(ordered_pair(sk0_2(B,A),sk0_3(B,A)),A) ) ) ) ) ),
inference(skolemization,[status(esa)],[f58]) ).
fof(f60,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| X1 != relation_dom(X0)
| ~ in(X2,X1)
| in(ordered_pair(X2,sk0_1(X2,X1,X0)),X0) ),
inference(cnf_transformation,[status(esa)],[f59]) ).
fof(f61,plain,
! [X0,X1,X2,X3] :
( ~ relation(X0)
| X1 != relation_dom(X0)
| in(X2,X1)
| ~ in(ordered_pair(X2,X3),X0) ),
inference(cnf_transformation,[status(esa)],[f59]) ).
fof(f64,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f6]) ).
fof(f65,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( ( B != relation_rng(A)
| ! [C] :
( ( ~ in(C,B)
| ? [D] : in(ordered_pair(D,C),A) )
& ( in(C,B)
| ! [D] : ~ in(ordered_pair(D,C),A) ) ) )
& ( B = relation_rng(A)
| ? [C] :
( ( ~ in(C,B)
| ! [D] : ~ in(ordered_pair(D,C),A) )
& ( in(C,B)
| ? [D] : in(ordered_pair(D,C),A) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f64]) ).
fof(f66,plain,
! [A] :
( ~ relation(A)
| ( ! [B] :
( B != relation_rng(A)
| ( ! [C] :
( ~ in(C,B)
| ? [D] : in(ordered_pair(D,C),A) )
& ! [C] :
( in(C,B)
| ! [D] : ~ in(ordered_pair(D,C),A) ) ) )
& ! [B] :
( B = relation_rng(A)
| ? [C] :
( ( ~ in(C,B)
| ! [D] : ~ in(ordered_pair(D,C),A) )
& ( in(C,B)
| ? [D] : in(ordered_pair(D,C),A) ) ) ) ) ),
inference(miniscoping,[status(esa)],[f65]) ).
fof(f67,plain,
! [A] :
( ~ relation(A)
| ( ! [B] :
( B != relation_rng(A)
| ( ! [C] :
( ~ in(C,B)
| in(ordered_pair(sk0_4(C,B,A),C),A) )
& ! [C] :
( in(C,B)
| ! [D] : ~ in(ordered_pair(D,C),A) ) ) )
& ! [B] :
( B = relation_rng(A)
| ( ( ~ in(sk0_5(B,A),B)
| ! [D] : ~ in(ordered_pair(D,sk0_5(B,A)),A) )
& ( in(sk0_5(B,A),B)
| in(ordered_pair(sk0_6(B,A),sk0_5(B,A)),A) ) ) ) ) ),
inference(skolemization,[status(esa)],[f66]) ).
fof(f68,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| X1 != relation_rng(X0)
| ~ in(X2,X1)
| in(ordered_pair(sk0_4(X2,X1,X0),X2),X0) ),
inference(cnf_transformation,[status(esa)],[f67]) ).
fof(f69,plain,
! [X0,X1,X2,X3] :
( ~ relation(X0)
| X1 != relation_rng(X0)
| in(X2,X1)
| ~ in(ordered_pair(X3,X2),X0) ),
inference(cnf_transformation,[status(esa)],[f67]) ).
fof(f73,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( ~ relation(B)
| ( B = relation_inverse(A)
<=> ! [C,D] :
( in(ordered_pair(C,D),B)
<=> in(ordered_pair(D,C),A) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f8]) ).
fof(f74,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( ~ relation(B)
| ( ( B != relation_inverse(A)
| ! [C,D] :
( ( ~ in(ordered_pair(C,D),B)
| in(ordered_pair(D,C),A) )
& ( in(ordered_pair(C,D),B)
| ~ in(ordered_pair(D,C),A) ) ) )
& ( B = relation_inverse(A)
| ? [C,D] :
( ( ~ in(ordered_pair(C,D),B)
| ~ in(ordered_pair(D,C),A) )
& ( in(ordered_pair(C,D),B)
| in(ordered_pair(D,C),A) ) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f73]) ).
fof(f75,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( ~ relation(B)
| ( ( B != relation_inverse(A)
| ( ! [C,D] :
( ~ in(ordered_pair(C,D),B)
| in(ordered_pair(D,C),A) )
& ! [C,D] :
( in(ordered_pair(C,D),B)
| ~ in(ordered_pair(D,C),A) ) ) )
& ( B = relation_inverse(A)
| ? [C,D] :
( ( ~ in(ordered_pair(C,D),B)
| ~ in(ordered_pair(D,C),A) )
& ( in(ordered_pair(C,D),B)
| in(ordered_pair(D,C),A) ) ) ) ) ) ),
inference(miniscoping,[status(esa)],[f74]) ).
fof(f76,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( ~ relation(B)
| ( ( B != relation_inverse(A)
| ( ! [C,D] :
( ~ in(ordered_pair(C,D),B)
| in(ordered_pair(D,C),A) )
& ! [C,D] :
( in(ordered_pair(C,D),B)
| ~ in(ordered_pair(D,C),A) ) ) )
& ( B = relation_inverse(A)
| ( ( ~ in(ordered_pair(sk0_7(B,A),sk0_8(B,A)),B)
| ~ in(ordered_pair(sk0_8(B,A),sk0_7(B,A)),A) )
& ( in(ordered_pair(sk0_7(B,A),sk0_8(B,A)),B)
| in(ordered_pair(sk0_8(B,A),sk0_7(B,A)),A) ) ) ) ) ) ),
inference(skolemization,[status(esa)],[f75]) ).
fof(f78,plain,
! [X0,X1,X2,X3] :
( ~ relation(X0)
| ~ relation(X1)
| X1 != relation_inverse(X0)
| in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X3,X2),X0) ),
inference(cnf_transformation,[status(esa)],[f76]) ).
fof(f81,plain,
! [A] :
( ~ relation(A)
| relation(relation_inverse(A)) ),
inference(pre_NNF_transformation,[status(esa)],[f15]) ).
fof(f82,plain,
! [X0] :
( ~ relation(X0)
| relation(relation_inverse(X0)) ),
inference(cnf_transformation,[status(esa)],[f81]) ).
fof(f90,plain,
! [A] :
( ~ relation(A)
| relation_inverse(relation_inverse(A)) = A ),
inference(pre_NNF_transformation,[status(esa)],[f24]) ).
fof(f91,plain,
! [X0] :
( ~ relation(X0)
| relation_inverse(relation_inverse(X0)) = X0 ),
inference(cnf_transformation,[status(esa)],[f90]) ).
fof(f112,plain,
? [A] :
( relation(A)
& ( relation_rng(A) != relation_dom(relation_inverse(A))
| relation_dom(A) != relation_rng(relation_inverse(A)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f34]) ).
fof(f113,plain,
( relation(sk0_15)
& ( relation_rng(sk0_15) != relation_dom(relation_inverse(sk0_15))
| relation_dom(sk0_15) != relation_rng(relation_inverse(sk0_15)) ) ),
inference(skolemization,[status(esa)],[f112]) ).
fof(f114,plain,
relation(sk0_15),
inference(cnf_transformation,[status(esa)],[f113]) ).
fof(f115,plain,
( relation_rng(sk0_15) != relation_dom(relation_inverse(sk0_15))
| relation_dom(sk0_15) != relation_rng(relation_inverse(sk0_15)) ),
inference(cnf_transformation,[status(esa)],[f113]) ).
fof(f134,plain,
( spl0_0
<=> relation_rng(sk0_15) = relation_dom(relation_inverse(sk0_15)) ),
introduced(split_symbol_definition) ).
fof(f137,plain,
( spl0_1
<=> relation_dom(sk0_15) = relation_rng(relation_inverse(sk0_15)) ),
introduced(split_symbol_definition) ).
fof(f140,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f115,f134,f137]) ).
fof(f143,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| in(ordered_pair(X1,sk0_1(X1,relation_dom(X0),X0)),X0) ),
inference(destructive_equality_resolution,[status(esa)],[f60]) ).
fof(f144,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| in(X1,relation_dom(X0))
| ~ in(ordered_pair(X1,X2),X0) ),
inference(destructive_equality_resolution,[status(esa)],[f61]) ).
fof(f145,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ in(X1,relation_rng(X0))
| in(ordered_pair(sk0_4(X1,relation_rng(X0),X0),X1),X0) ),
inference(destructive_equality_resolution,[status(esa)],[f68]) ).
fof(f146,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| in(X1,relation_rng(X0))
| ~ in(ordered_pair(X2,X1),X0) ),
inference(destructive_equality_resolution,[status(esa)],[f69]) ).
fof(f149,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| ~ relation(relation_inverse(X0))
| in(ordered_pair(X1,X2),relation_inverse(X0))
| ~ in(ordered_pair(X2,X1),X0) ),
inference(destructive_equality_resolution,[status(esa)],[f78]) ).
fof(f150,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| in(ordered_pair(X1,X2),relation_inverse(X0))
| ~ in(ordered_pair(X2,X1),X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f149,f82]) ).
fof(f153,plain,
relation_inverse(relation_inverse(sk0_15)) = sk0_15,
inference(resolution,[status(thm)],[f91,f114]) ).
fof(f154,plain,
( spl0_2
<=> relation(relation_inverse(sk0_15)) ),
introduced(split_symbol_definition) ).
fof(f155,plain,
( relation(relation_inverse(sk0_15))
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f154]) ).
fof(f156,plain,
( ~ relation(relation_inverse(sk0_15))
| spl0_2 ),
inference(component_clause,[status(thm)],[f154]) ).
fof(f162,plain,
! [X0,X1,X2] :
( in(X0,relation_dom(relation_inverse(X1)))
| ~ in(ordered_pair(X0,X2),relation_inverse(X1))
| ~ relation(X1) ),
inference(resolution,[status(thm)],[f144,f82]) ).
fof(f164,plain,
! [X0,X1,X2] :
( in(X0,relation_rng(relation_inverse(X1)))
| ~ in(ordered_pair(X2,X0),relation_inverse(X1))
| ~ relation(X1) ),
inference(resolution,[status(thm)],[f146,f82]) ).
fof(f171,plain,
! [X0,X1,X2] :
( in(X0,relation_dom(relation_inverse(X1)))
| ~ relation(X1)
| ~ relation(X1)
| ~ in(ordered_pair(X2,X0),X1) ),
inference(resolution,[status(thm)],[f162,f150]) ).
fof(f172,plain,
! [X0,X1,X2] :
( in(X0,relation_dom(relation_inverse(X1)))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X0),X1) ),
inference(duplicate_literals_removal,[status(esa)],[f171]) ).
fof(f179,plain,
! [X0,X1] :
( in(X0,relation_dom(relation_inverse(sk0_15)))
| ~ in(ordered_pair(X1,X0),sk0_15) ),
inference(resolution,[status(thm)],[f172,f114]) ).
fof(f180,plain,
! [X0,X1,X2] :
( in(X0,relation_rng(relation_inverse(X1)))
| ~ relation(X1)
| ~ relation(X1)
| ~ in(ordered_pair(X0,X2),X1) ),
inference(resolution,[status(thm)],[f164,f150]) ).
fof(f181,plain,
! [X0,X1,X2] :
( in(X0,relation_rng(relation_inverse(X1)))
| ~ relation(X1)
| ~ in(ordered_pair(X0,X2),X1) ),
inference(duplicate_literals_removal,[status(esa)],[f180]) ).
fof(f188,plain,
! [X0,X1] :
( in(X0,relation_rng(relation_inverse(sk0_15)))
| ~ in(ordered_pair(X0,X1),sk0_15) ),
inference(resolution,[status(thm)],[f181,f114]) ).
fof(f250,plain,
( ~ relation(sk0_15)
| spl0_2 ),
inference(resolution,[status(thm)],[f156,f82]) ).
fof(f251,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f250,f114]) ).
fof(f252,plain,
spl0_2,
inference(contradiction_clause,[status(thm)],[f251]) ).
fof(f262,plain,
! [X0,X1] :
( in(X0,relation_rng(relation_inverse(relation_inverse(sk0_15))))
| ~ in(ordered_pair(X0,X1),relation_inverse(sk0_15))
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f155,f181]) ).
fof(f263,plain,
! [X0,X1] :
( in(X0,relation_rng(sk0_15))
| ~ in(ordered_pair(X0,X1),relation_inverse(sk0_15))
| ~ spl0_2 ),
inference(forward_demodulation,[status(thm)],[f153,f262]) ).
fof(f264,plain,
! [X0,X1] :
( in(X0,relation_dom(relation_inverse(relation_inverse(sk0_15))))
| ~ in(ordered_pair(X1,X0),relation_inverse(sk0_15))
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f155,f172]) ).
fof(f265,plain,
! [X0,X1] :
( in(X0,relation_dom(sk0_15))
| ~ in(ordered_pair(X1,X0),relation_inverse(sk0_15))
| ~ spl0_2 ),
inference(forward_demodulation,[status(thm)],[f153,f264]) ).
fof(f857,plain,
! [X0] :
( ~ in(X0,relation_dom(relation_inverse(sk0_15)))
| in(ordered_pair(X0,sk0_1(X0,relation_dom(relation_inverse(sk0_15)),relation_inverse(sk0_15))),relation_inverse(sk0_15))
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f143,f155]) ).
fof(f859,plain,
! [X0] :
( ~ in(X0,relation_dom(sk0_15))
| in(ordered_pair(X0,sk0_1(X0,relation_dom(sk0_15),sk0_15)),sk0_15) ),
inference(resolution,[status(thm)],[f143,f114]) ).
fof(f867,plain,
! [X0] :
( ~ in(X0,relation_dom(relation_inverse(sk0_15)))
| in(X0,relation_rng(sk0_15))
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f857,f263]) ).
fof(f957,plain,
! [X0] :
( in(sk0_0(X0,relation_dom(relation_inverse(sk0_15))),relation_rng(sk0_15))
| subset(relation_dom(relation_inverse(sk0_15)),X0)
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f867,f54]) ).
fof(f958,plain,
( spl0_67
<=> subset(relation_dom(relation_inverse(sk0_15)),relation_rng(sk0_15)) ),
introduced(split_symbol_definition) ).
fof(f959,plain,
( subset(relation_dom(relation_inverse(sk0_15)),relation_rng(sk0_15))
| ~ spl0_67 ),
inference(component_clause,[status(thm)],[f958]) ).
fof(f961,plain,
( subset(relation_dom(relation_inverse(sk0_15)),relation_rng(sk0_15))
| subset(relation_dom(relation_inverse(sk0_15)),relation_rng(sk0_15))
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f957,f55]) ).
fof(f962,plain,
( spl0_67
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f961,f958,f154]) ).
fof(f964,plain,
( spl0_68
<=> subset(relation_rng(sk0_15),relation_dom(relation_inverse(sk0_15))) ),
introduced(split_symbol_definition) ).
fof(f967,plain,
( relation_rng(sk0_15) = relation_dom(relation_inverse(sk0_15))
| ~ subset(relation_rng(sk0_15),relation_dom(relation_inverse(sk0_15)))
| ~ spl0_67 ),
inference(resolution,[status(thm)],[f959,f48]) ).
fof(f968,plain,
( spl0_0
| ~ spl0_68
| ~ spl0_67 ),
inference(split_clause,[status(thm)],[f967,f134,f964,f958]) ).
fof(f1046,plain,
! [X0] :
( ~ in(X0,relation_dom(sk0_15))
| in(X0,relation_rng(relation_inverse(sk0_15))) ),
inference(resolution,[status(thm)],[f859,f188]) ).
fof(f1050,plain,
! [X0] :
( ~ in(sk0_0(relation_rng(relation_inverse(sk0_15)),X0),relation_dom(sk0_15))
| subset(X0,relation_rng(relation_inverse(sk0_15))) ),
inference(resolution,[status(thm)],[f1046,f55]) ).
fof(f1060,plain,
( spl0_74
<=> subset(relation_dom(sk0_15),relation_rng(relation_inverse(sk0_15))) ),
introduced(split_symbol_definition) ).
fof(f1061,plain,
( subset(relation_dom(sk0_15),relation_rng(relation_inverse(sk0_15)))
| ~ spl0_74 ),
inference(component_clause,[status(thm)],[f1060]) ).
fof(f1063,plain,
( subset(relation_dom(sk0_15),relation_rng(relation_inverse(sk0_15)))
| subset(relation_dom(sk0_15),relation_rng(relation_inverse(sk0_15))) ),
inference(resolution,[status(thm)],[f1050,f54]) ).
fof(f1064,plain,
spl0_74,
inference(split_clause,[status(thm)],[f1063,f1060]) ).
fof(f1066,plain,
( spl0_75
<=> subset(relation_rng(relation_inverse(sk0_15)),relation_dom(sk0_15)) ),
introduced(split_symbol_definition) ).
fof(f1069,plain,
( relation_rng(relation_inverse(sk0_15)) = relation_dom(sk0_15)
| ~ subset(relation_rng(relation_inverse(sk0_15)),relation_dom(sk0_15))
| ~ spl0_74 ),
inference(resolution,[status(thm)],[f1061,f48]) ).
fof(f1070,plain,
( spl0_1
| ~ spl0_75
| ~ spl0_74 ),
inference(split_clause,[status(thm)],[f1069,f137,f1066,f1060]) ).
fof(f1629,plain,
! [X0] :
( ~ in(X0,relation_rng(relation_inverse(sk0_15)))
| in(ordered_pair(sk0_4(X0,relation_rng(relation_inverse(sk0_15)),relation_inverse(sk0_15)),X0),relation_inverse(sk0_15))
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f145,f155]) ).
fof(f1631,plain,
! [X0] :
( ~ in(X0,relation_rng(sk0_15))
| in(ordered_pair(sk0_4(X0,relation_rng(sk0_15),sk0_15),X0),sk0_15) ),
inference(resolution,[status(thm)],[f145,f114]) ).
fof(f1739,plain,
! [X0] :
( ~ in(X0,relation_rng(relation_inverse(sk0_15)))
| in(X0,relation_dom(sk0_15))
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f1629,f265]) ).
fof(f1832,plain,
! [X0] :
( in(sk0_0(X0,relation_rng(relation_inverse(sk0_15))),relation_dom(sk0_15))
| subset(relation_rng(relation_inverse(sk0_15)),X0)
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f1739,f54]) ).
fof(f1838,plain,
( subset(relation_rng(relation_inverse(sk0_15)),relation_dom(sk0_15))
| subset(relation_rng(relation_inverse(sk0_15)),relation_dom(sk0_15))
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f1832,f55]) ).
fof(f1839,plain,
( spl0_75
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f1838,f1066,f154]) ).
fof(f2084,plain,
! [X0] :
( ~ in(X0,relation_rng(sk0_15))
| in(X0,relation_dom(relation_inverse(sk0_15))) ),
inference(resolution,[status(thm)],[f1631,f179]) ).
fof(f2087,plain,
! [X0] :
( ~ in(sk0_0(relation_dom(relation_inverse(sk0_15)),X0),relation_rng(sk0_15))
| subset(X0,relation_dom(relation_inverse(sk0_15))) ),
inference(resolution,[status(thm)],[f2084,f55]) ).
fof(f2757,plain,
( subset(relation_rng(sk0_15),relation_dom(relation_inverse(sk0_15)))
| subset(relation_rng(sk0_15),relation_dom(relation_inverse(sk0_15))) ),
inference(resolution,[status(thm)],[f2087,f54]) ).
fof(f2758,plain,
spl0_68,
inference(split_clause,[status(thm)],[f2757,f964]) ).
fof(f2759,plain,
$false,
inference(sat_refutation,[status(thm)],[f140,f252,f962,f968,f1064,f1070,f1839,f2758]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SEU181+1 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue May 30 09:10:23 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.12/0.33 % Drodi V3.5.1
% 2.30/0.66 % Refutation found
% 2.30/0.66 % SZS status Theorem for theBenchmark: Theorem is valid
% 2.30/0.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.30/0.68 % Elapsed time: 0.346652 seconds
% 2.30/0.68 % CPU time: 2.644271 seconds
% 2.30/0.68 % Memory used: 99.213 MB
%------------------------------------------------------------------------------