%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU443+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:49:06 PM UTC 2026
% Result : Theorem 11.87s 2.66s
% Output : Refutation 13.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 30
% Syntax : Number of formulae : 220 ( 32 unt; 12 def)
% Number of atoms : 825 ( 74 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 1062 ( 457 ~; 484 |; 73 &)
% ( 27 <=>; 20 =>; 0 <=; 1 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 9 prp; 0-3 aty)
% Number of functors : 33 ( 33 usr; 8 con; 0-5 aty)
% Number of variables : 452 ( 0 sgn 409 !; 43 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(X1))
=> ! [X3] :
( m2_relset_1(X3,X0,X1)
=> ( r1_tarski(X2,k2_funct_5(X3))
<=> r1_tarski(X2,k10_relset_1(X1,X1,k9_relset_2(X1,X0,X1,k6_relset_1(X0,X1,X3),X3),X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_relset_2) ).
fof(f2,negated_conjecture,
~ ! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(X1))
=> ! [X3] :
( m2_relset_1(X3,X0,X1)
=> ( r1_tarski(X2,k2_funct_5(X3))
<=> r1_tarski(X2,k10_relset_1(X1,X1,k9_relset_2(X1,X0,X1,k6_relset_1(X0,X1,X3),X3),X2)) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f5,axiom,
! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
=> v1_relat_1(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f6,axiom,
! [X0,X1] : k2_tarski(X0,X1) = k2_tarski(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f7,axiom,
! [X0] :
( v1_relat_1(X0)
=> ! [X1,X2] :
( X2 = k9_relat_1(X0,X1)
<=> ! [X3] :
( r2_hidden(X3,X2)
<=> ? [X4] :
( r2_hidden(k4_tarski(X4,X3),X0)
& r2_hidden(X4,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_relat_1) ).
fof(f9,axiom,
! [X0,X1] :
( X1 = k2_funct_5(X0)
<=> ! [X2] :
( r2_hidden(X2,X1)
<=> ? [X3] : r2_hidden(k4_tarski(X3,X2),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_funct_5) ).
fof(f10,axiom,
! [X0,X1] :
( r1_tarski(X0,X1)
<=> ! [X2] :
( r2_hidden(X2,X0)
=> r2_hidden(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f11,axiom,
! [X0,X1] : k4_tarski(X0,X1) = k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f12,axiom,
! [X0] :
( v1_relat_1(X0)
=> ! [X1] :
( v1_relat_1(X1)
=> ( X1 = k4_relat_1(X0)
<=> ! [X2,X3] :
( r2_hidden(k4_tarski(X2,X3),X1)
<=> r2_hidden(k4_tarski(X3,X2),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_relat_1) ).
fof(f13,axiom,
! [X0] :
( v1_relat_1(X0)
=> ! [X1] :
( v1_relat_1(X1)
=> ! [X2] :
( v1_relat_1(X2)
=> ( X2 = k5_relat_1(X0,X1)
<=> ! [X3,X4] :
( r2_hidden(k4_tarski(X3,X4),X2)
<=> ? [X5] :
( r2_hidden(k4_tarski(X3,X5),X0)
& r2_hidden(k4_tarski(X5,X4),X1) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_relat_1) ).
fof(f22,axiom,
! [X0] :
( v1_relat_1(X0)
=> v1_relat_1(k4_relat_1(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relat_1) ).
fof(f24,axiom,
! [X0,X1] :
( ( v1_relat_1(X0)
& v1_relat_1(X1) )
=> v1_relat_1(k5_relat_1(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f25,axiom,
! [X0,X1,X2] :
( m1_relset_1(X2,X0,X1)
=> m2_relset_1(k6_relset_1(X0,X1,X2),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relset_1) ).
fof(f27,axiom,
! [X0,X1,X2,X3,X4] :
( ( m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
& m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) )
=> m2_relset_1(k9_relset_2(X0,X1,X2,X3,X4),X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_relset_2) ).
fof(f30,axiom,
! [X0,X1,X2] :
( m2_relset_1(X2,X0,X1)
=> m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f51,axiom,
! [X0,X1,X2,X3] :
( m1_relset_1(X2,X0,X1)
=> k10_relset_1(X0,X1,X2,X3) = k9_relat_1(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k10_relset_1) ).
fof(f52,axiom,
! [X0,X1,X2] :
( m1_relset_1(X2,X0,X1)
=> k6_relset_1(X0,X1,X2) = k4_relat_1(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_relset_1) ).
fof(f53,axiom,
! [X0,X1,X2,X3,X4] :
( ( m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
& m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) )
=> k9_relset_2(X0,X1,X2,X3,X4) = k5_relat_1(X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k9_relset_2) ).
fof(f54,axiom,
! [X0,X1,X2] :
( m2_relset_1(X2,X0,X1)
<=> m1_relset_1(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f71,plain,
? [X0,X1,X2] :
( ? [X3] :
( ( r1_tarski(X2,k2_funct_5(X3))
<~> r1_tarski(X2,k10_relset_1(X1,X1,k9_relset_2(X1,X0,X1,k6_relset_1(X0,X1,X3),X3),X2)) )
& m2_relset_1(X3,X0,X1) )
& m1_subset_1(X2,k1_zfmisc_1(X1)) ),
inference(ennf_transformation,[],[f2]) ).
fof(f74,plain,
! [X0,X1,X2] :
( v1_relat_1(X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) ),
inference(ennf_transformation,[],[f5]) ).
fof(f75,plain,
! [X0] :
( ! [X1,X2] :
( X2 = k9_relat_1(X0,X1)
<=> ! [X3] :
( r2_hidden(X3,X2)
<=> ? [X4] :
( r2_hidden(k4_tarski(X4,X3),X0)
& r2_hidden(X4,X1) ) ) )
| ~ v1_relat_1(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f76,plain,
! [X0,X1] :
( r1_tarski(X0,X1)
<=> ! [X2] :
( r2_hidden(X2,X1)
| ~ r2_hidden(X2,X0) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f77,plain,
! [X0] :
( ! [X1] :
( ( X1 = k4_relat_1(X0)
<=> ! [X2,X3] :
( r2_hidden(k4_tarski(X2,X3),X1)
<=> r2_hidden(k4_tarski(X3,X2),X0) ) )
| ~ v1_relat_1(X1) )
| ~ v1_relat_1(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f78,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X2 = k5_relat_1(X0,X1)
<=> ! [X3,X4] :
( r2_hidden(k4_tarski(X3,X4),X2)
<=> ? [X5] :
( r2_hidden(k4_tarski(X3,X5),X0)
& r2_hidden(k4_tarski(X5,X4),X1) ) ) )
| ~ v1_relat_1(X2) )
| ~ v1_relat_1(X1) )
| ~ v1_relat_1(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f80,plain,
! [X0] :
( v1_relat_1(k4_relat_1(X0))
| ~ v1_relat_1(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f81,plain,
! [X0,X1] :
( v1_relat_1(k5_relat_1(X0,X1))
| ~ v1_relat_1(X0)
| ~ v1_relat_1(X1) ),
inference(ennf_transformation,[],[f24]) ).
fof(f82,plain,
! [X0,X1] :
( v1_relat_1(k5_relat_1(X0,X1))
| ~ v1_relat_1(X0)
| ~ v1_relat_1(X1) ),
inference(flattening,[],[f81]) ).
fof(f83,plain,
! [X0,X1,X2] :
( m2_relset_1(k6_relset_1(X0,X1,X2),X1,X0)
| ~ m1_relset_1(X2,X0,X1) ),
inference(ennf_transformation,[],[f25]) ).
fof(f84,plain,
! [X0,X1,X2,X3,X4] :
( m2_relset_1(k9_relset_2(X0,X1,X2,X3,X4),X0,X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) ),
inference(ennf_transformation,[],[f27]) ).
fof(f85,plain,
! [X0,X1,X2,X3,X4] :
( m2_relset_1(k9_relset_2(X0,X1,X2,X3,X4),X0,X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) ),
inference(flattening,[],[f84]) ).
fof(f86,plain,
! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m2_relset_1(X2,X0,X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f97,plain,
! [X0,X1,X2,X3] :
( k10_relset_1(X0,X1,X2,X3) = k9_relat_1(X2,X3)
| ~ m1_relset_1(X2,X0,X1) ),
inference(ennf_transformation,[],[f51]) ).
fof(f98,plain,
! [X0,X1,X2] :
( k6_relset_1(X0,X1,X2) = k4_relat_1(X2)
| ~ m1_relset_1(X2,X0,X1) ),
inference(ennf_transformation,[],[f52]) ).
fof(f99,plain,
! [X0,X1,X2,X3,X4] :
( k9_relset_2(X0,X1,X2,X3,X4) = k5_relat_1(X3,X4)
| ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) ),
inference(ennf_transformation,[],[f53]) ).
fof(f100,plain,
! [X0,X1,X2,X3,X4] :
( k9_relset_2(X0,X1,X2,X3,X4) = k5_relat_1(X3,X4)
| ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) ),
inference(flattening,[],[f99]) ).
fof(f115,plain,
? [X0,X1,X2] :
( ? [X3] :
( ( ~ r1_tarski(X2,k10_relset_1(X1,X1,k9_relset_2(X1,X0,X1,k6_relset_1(X0,X1,X3),X3),X2))
| ~ r1_tarski(X2,k2_funct_5(X3)) )
& ( r1_tarski(X2,k10_relset_1(X1,X1,k9_relset_2(X1,X0,X1,k6_relset_1(X0,X1,X3),X3),X2))
| r1_tarski(X2,k2_funct_5(X3)) )
& m2_relset_1(X3,X0,X1) )
& m1_subset_1(X2,k1_zfmisc_1(X1)) ),
inference(nnf_transformation,[],[f71]) ).
fof(f116,plain,
? [X0,X1,X2] :
( ? [X3] :
( ( ~ r1_tarski(X2,k10_relset_1(X1,X1,k9_relset_2(X1,X0,X1,k6_relset_1(X0,X1,X3),X3),X2))
| ~ r1_tarski(X2,k2_funct_5(X3)) )
& ( r1_tarski(X2,k10_relset_1(X1,X1,k9_relset_2(X1,X0,X1,k6_relset_1(X0,X1,X3),X3),X2))
| r1_tarski(X2,k2_funct_5(X3)) )
& m2_relset_1(X3,X0,X1) )
& m1_subset_1(X2,k1_zfmisc_1(X1)) ),
inference(flattening,[],[f115]) ).
fof(f117,plain,
( ( ~ r1_tarski(sK2,k10_relset_1(sK1,sK1,k9_relset_2(sK1,sK0,sK1,k6_relset_1(sK0,sK1,sK3),sK3),sK2))
| ~ r1_tarski(sK2,k2_funct_5(sK3)) )
& ( r1_tarski(sK2,k10_relset_1(sK1,sK1,k9_relset_2(sK1,sK0,sK1,k6_relset_1(sK0,sK1,sK3),sK3),sK2))
| r1_tarski(sK2,k2_funct_5(sK3)) )
& m2_relset_1(sK3,sK0,sK1)
& m1_subset_1(sK2,k1_zfmisc_1(sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f116]) ).
fof(f118,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = k9_relat_1(X0,X1)
| ? [X3] :
( ( ! [X4] :
( ~ r2_hidden(k4_tarski(X4,X3),X0)
| ~ r2_hidden(X4,X1) )
| ~ r2_hidden(X3,X2) )
& ( ? [X4] :
( r2_hidden(k4_tarski(X4,X3),X0)
& r2_hidden(X4,X1) )
| r2_hidden(X3,X2) ) ) )
& ( ! [X3] :
( ( r2_hidden(X3,X2)
| ! [X4] :
( ~ r2_hidden(k4_tarski(X4,X3),X0)
| ~ r2_hidden(X4,X1) ) )
& ( ? [X4] :
( r2_hidden(k4_tarski(X4,X3),X0)
& r2_hidden(X4,X1) )
| ~ r2_hidden(X3,X2) ) )
| k9_relat_1(X0,X1) != X2 ) )
| ~ v1_relat_1(X0) ),
inference(nnf_transformation,[],[f75]) ).
fof(f119,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = k9_relat_1(X0,X1)
| ? [X3] :
( ( ! [X4] :
( ~ r2_hidden(k4_tarski(X4,X3),X0)
| ~ r2_hidden(X4,X1) )
| ~ r2_hidden(X3,X2) )
& ( ? [X5] :
( r2_hidden(k4_tarski(X5,X3),X0)
& r2_hidden(X5,X1) )
| r2_hidden(X3,X2) ) ) )
& ( ! [X6] :
( ( r2_hidden(X6,X2)
| ! [X7] :
( ~ r2_hidden(k4_tarski(X7,X6),X0)
| ~ r2_hidden(X7,X1) ) )
& ( ? [X8] :
( r2_hidden(k4_tarski(X8,X6),X0)
& r2_hidden(X8,X1) )
| ~ r2_hidden(X6,X2) ) )
| k9_relat_1(X0,X1) != X2 ) )
| ~ v1_relat_1(X0) ),
inference(rectify,[],[f118]) ).
fof(f120,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = k9_relat_1(X0,X1)
| ( ( ! [X4] :
( ~ r2_hidden(k4_tarski(X4,sK4(X0,X1,X2)),X0)
| ~ r2_hidden(X4,X1) )
| ~ r2_hidden(sK4(X0,X1,X2),X2) )
& ( ( r2_hidden(k4_tarski(sK5(X0,X1,X2),sK4(X0,X1,X2)),X0)
& r2_hidden(sK5(X0,X1,X2),X1) )
| r2_hidden(sK4(X0,X1,X2),X2) ) ) )
& ( ! [X6] :
( ( r2_hidden(X6,X2)
| ! [X7] :
( ~ r2_hidden(k4_tarski(X7,X6),X0)
| ~ r2_hidden(X7,X1) ) )
& ( ( r2_hidden(k4_tarski(sK6(X0,X1,X6),X6),X0)
& r2_hidden(sK6(X0,X1,X6),X1) )
| ~ r2_hidden(X6,X2) ) )
| k9_relat_1(X0,X1) != X2 ) )
| ~ v1_relat_1(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X3,sK4(X0,X1,X2)),skolemize(X5,sK5(X0,X1,X2)),skolemize(X8,sK6(X0,X1,X6))],[f119]) ).
fof(f124,plain,
! [X0,X1] :
( ( X1 = k2_funct_5(X0)
| ? [X2] :
( ( ! [X3] : ~ r2_hidden(k4_tarski(X3,X2),X0)
| ~ r2_hidden(X2,X1) )
& ( ? [X3] : r2_hidden(k4_tarski(X3,X2),X0)
| r2_hidden(X2,X1) ) ) )
& ( ! [X2] :
( ( r2_hidden(X2,X1)
| ! [X3] : ~ r2_hidden(k4_tarski(X3,X2),X0) )
& ( ? [X3] : r2_hidden(k4_tarski(X3,X2),X0)
| ~ r2_hidden(X2,X1) ) )
| k2_funct_5(X0) != X1 ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f125,plain,
! [X0,X1] :
( ( X1 = k2_funct_5(X0)
| ? [X2] :
( ( ! [X3] : ~ r2_hidden(k4_tarski(X3,X2),X0)
| ~ r2_hidden(X2,X1) )
& ( ? [X4] : r2_hidden(k4_tarski(X4,X2),X0)
| r2_hidden(X2,X1) ) ) )
& ( ! [X5] :
( ( r2_hidden(X5,X1)
| ! [X6] : ~ r2_hidden(k4_tarski(X6,X5),X0) )
& ( ? [X7] : r2_hidden(k4_tarski(X7,X5),X0)
| ~ r2_hidden(X5,X1) ) )
| k2_funct_5(X0) != X1 ) ),
inference(rectify,[],[f124]) ).
fof(f126,plain,
! [X0,X1] :
( ( X1 = k2_funct_5(X0)
| ( ( ! [X3] : ~ r2_hidden(k4_tarski(X3,sK8(X0,X1)),X0)
| ~ r2_hidden(sK8(X0,X1),X1) )
& ( r2_hidden(k4_tarski(sK9(X0,X1),sK8(X0,X1)),X0)
| r2_hidden(sK8(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( r2_hidden(X5,X1)
| ! [X6] : ~ r2_hidden(k4_tarski(X6,X5),X0) )
& ( r2_hidden(k4_tarski(sK10(X0,X5),X5),X0)
| ~ r2_hidden(X5,X1) ) )
| k2_funct_5(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10]),skolemize(X2,sK8(X0,X1)),skolemize(X4,sK9(X0,X1)),skolemize(X7,sK10(X0,X5))],[f125]) ).
fof(f127,plain,
! [X0,X1] :
( ( r1_tarski(X0,X1)
| ? [X2] :
( ~ r2_hidden(X2,X1)
& r2_hidden(X2,X0) ) )
& ( ! [X2] :
( r2_hidden(X2,X1)
| ~ r2_hidden(X2,X0) )
| ~ r1_tarski(X0,X1) ) ),
inference(nnf_transformation,[],[f76]) ).
fof(f128,plain,
! [X0,X1] :
( ( r1_tarski(X0,X1)
| ? [X2] :
( ~ r2_hidden(X2,X1)
& r2_hidden(X2,X0) ) )
& ( ! [X3] :
( r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0) )
| ~ r1_tarski(X0,X1) ) ),
inference(rectify,[],[f127]) ).
fof(f129,plain,
! [X0,X1] :
( ( r1_tarski(X0,X1)
| ( ~ r2_hidden(sK11(X0,X1),X1)
& r2_hidden(sK11(X0,X1),X0) ) )
& ( ! [X3] :
( r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0) )
| ~ r1_tarski(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X2,sK11(X0,X1))],[f128]) ).
fof(f130,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = k4_relat_1(X0)
| ? [X2,X3] :
( ( ~ r2_hidden(k4_tarski(X3,X2),X0)
| ~ r2_hidden(k4_tarski(X2,X3),X1) )
& ( r2_hidden(k4_tarski(X3,X2),X0)
| r2_hidden(k4_tarski(X2,X3),X1) ) ) )
& ( ! [X2,X3] :
( ( r2_hidden(k4_tarski(X2,X3),X1)
| ~ r2_hidden(k4_tarski(X3,X2),X0) )
& ( r2_hidden(k4_tarski(X3,X2),X0)
| ~ r2_hidden(k4_tarski(X2,X3),X1) ) )
| k4_relat_1(X0) != X1 ) )
| ~ v1_relat_1(X1) )
| ~ v1_relat_1(X0) ),
inference(nnf_transformation,[],[f77]) ).
fof(f131,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = k4_relat_1(X0)
| ? [X2,X3] :
( ( ~ r2_hidden(k4_tarski(X3,X2),X0)
| ~ r2_hidden(k4_tarski(X2,X3),X1) )
& ( r2_hidden(k4_tarski(X3,X2),X0)
| r2_hidden(k4_tarski(X2,X3),X1) ) ) )
& ( ! [X4,X5] :
( ( r2_hidden(k4_tarski(X4,X5),X1)
| ~ r2_hidden(k4_tarski(X5,X4),X0) )
& ( r2_hidden(k4_tarski(X5,X4),X0)
| ~ r2_hidden(k4_tarski(X4,X5),X1) ) )
| k4_relat_1(X0) != X1 ) )
| ~ v1_relat_1(X1) )
| ~ v1_relat_1(X0) ),
inference(rectify,[],[f130]) ).
fof(f132,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = k4_relat_1(X0)
| ( ( ~ r2_hidden(k4_tarski(sK13(X0,X1),sK12(X0,X1)),X0)
| ~ r2_hidden(k4_tarski(sK12(X0,X1),sK13(X0,X1)),X1) )
& ( r2_hidden(k4_tarski(sK13(X0,X1),sK12(X0,X1)),X0)
| r2_hidden(k4_tarski(sK12(X0,X1),sK13(X0,X1)),X1) ) ) )
& ( ! [X4,X5] :
( ( r2_hidden(k4_tarski(X4,X5),X1)
| ~ r2_hidden(k4_tarski(X5,X4),X0) )
& ( r2_hidden(k4_tarski(X5,X4),X0)
| ~ r2_hidden(k4_tarski(X4,X5),X1) ) )
| k4_relat_1(X0) != X1 ) )
| ~ v1_relat_1(X1) )
| ~ v1_relat_1(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13]),skolemize(X2,sK12(X0,X1)),skolemize(X3,sK13(X0,X1))],[f131]) ).
fof(f133,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = k5_relat_1(X0,X1)
| ? [X3,X4] :
( ( ! [X5] :
( ~ r2_hidden(k4_tarski(X3,X5),X0)
| ~ r2_hidden(k4_tarski(X5,X4),X1) )
| ~ r2_hidden(k4_tarski(X3,X4),X2) )
& ( ? [X5] :
( r2_hidden(k4_tarski(X3,X5),X0)
& r2_hidden(k4_tarski(X5,X4),X1) )
| r2_hidden(k4_tarski(X3,X4),X2) ) ) )
& ( ! [X3,X4] :
( ( r2_hidden(k4_tarski(X3,X4),X2)
| ! [X5] :
( ~ r2_hidden(k4_tarski(X3,X5),X0)
| ~ r2_hidden(k4_tarski(X5,X4),X1) ) )
& ( ? [X5] :
( r2_hidden(k4_tarski(X3,X5),X0)
& r2_hidden(k4_tarski(X5,X4),X1) )
| ~ r2_hidden(k4_tarski(X3,X4),X2) ) )
| k5_relat_1(X0,X1) != X2 ) )
| ~ v1_relat_1(X2) )
| ~ v1_relat_1(X1) )
| ~ v1_relat_1(X0) ),
inference(nnf_transformation,[],[f78]) ).
fof(f134,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = k5_relat_1(X0,X1)
| ? [X3,X4] :
( ( ! [X5] :
( ~ r2_hidden(k4_tarski(X3,X5),X0)
| ~ r2_hidden(k4_tarski(X5,X4),X1) )
| ~ r2_hidden(k4_tarski(X3,X4),X2) )
& ( ? [X6] :
( r2_hidden(k4_tarski(X3,X6),X0)
& r2_hidden(k4_tarski(X6,X4),X1) )
| r2_hidden(k4_tarski(X3,X4),X2) ) ) )
& ( ! [X7,X8] :
( ( r2_hidden(k4_tarski(X7,X8),X2)
| ! [X9] :
( ~ r2_hidden(k4_tarski(X7,X9),X0)
| ~ r2_hidden(k4_tarski(X9,X8),X1) ) )
& ( ? [X10] :
( r2_hidden(k4_tarski(X7,X10),X0)
& r2_hidden(k4_tarski(X10,X8),X1) )
| ~ r2_hidden(k4_tarski(X7,X8),X2) ) )
| k5_relat_1(X0,X1) != X2 ) )
| ~ v1_relat_1(X2) )
| ~ v1_relat_1(X1) )
| ~ v1_relat_1(X0) ),
inference(rectify,[],[f133]) ).
fof(f135,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = k5_relat_1(X0,X1)
| ( ( ! [X5] :
( ~ r2_hidden(k4_tarski(sK14(X0,X1,X2),X5),X0)
| ~ r2_hidden(k4_tarski(X5,sK15(X0,X1,X2)),X1) )
| ~ r2_hidden(k4_tarski(sK14(X0,X1,X2),sK15(X0,X1,X2)),X2) )
& ( ( r2_hidden(k4_tarski(sK14(X0,X1,X2),sK16(X0,X1,X2)),X0)
& r2_hidden(k4_tarski(sK16(X0,X1,X2),sK15(X0,X1,X2)),X1) )
| r2_hidden(k4_tarski(sK14(X0,X1,X2),sK15(X0,X1,X2)),X2) ) ) )
& ( ! [X7,X8] :
( ( r2_hidden(k4_tarski(X7,X8),X2)
| ! [X9] :
( ~ r2_hidden(k4_tarski(X7,X9),X0)
| ~ r2_hidden(k4_tarski(X9,X8),X1) ) )
& ( ( r2_hidden(k4_tarski(X7,sK17(X0,X1,X7,X8)),X0)
& r2_hidden(k4_tarski(sK17(X0,X1,X7,X8),X8),X1) )
| ~ r2_hidden(k4_tarski(X7,X8),X2) ) )
| k5_relat_1(X0,X1) != X2 ) )
| ~ v1_relat_1(X2) )
| ~ v1_relat_1(X1) )
| ~ v1_relat_1(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15,sK16,sK17]),skolemize(X3,sK14(X0,X1,X2)),skolemize(X4,sK15(X0,X1,X2)),skolemize(X6,sK16(X0,X1,X2)),skolemize(X10,sK17(X0,X1,X7,X8))],[f134]) ).
fof(f144,plain,
! [X0,X1,X2] :
( ( m2_relset_1(X2,X0,X1)
| ~ m1_relset_1(X2,X0,X1) )
& ( m1_relset_1(X2,X0,X1)
| ~ m2_relset_1(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f54]) ).
fof(f148,plain,
m2_relset_1(sK3,sK0,sK1),
inference(cnf_transformation,[],[f117]) ).
fof(f149,plain,
( r1_tarski(sK2,k10_relset_1(sK1,sK1,k9_relset_2(sK1,sK0,sK1,k6_relset_1(sK0,sK1,sK3),sK3),sK2))
| r1_tarski(sK2,k2_funct_5(sK3)) ),
inference(cnf_transformation,[],[f117]) ).
fof(f150,plain,
( ~ r1_tarski(sK2,k10_relset_1(sK1,sK1,k9_relset_2(sK1,sK0,sK1,k6_relset_1(sK0,sK1,sK3),sK3),sK2))
| ~ r1_tarski(sK2,k2_funct_5(sK3)) ),
inference(cnf_transformation,[],[f117]) ).
fof(f153,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| v1_relat_1(X2) ),
inference(cnf_transformation,[],[f74]) ).
fof(f154,plain,
! [X0,X1] : k2_tarski(X0,X1) = k2_tarski(X1,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f156,plain,
! [X2,X0,X1,X6] :
( r2_hidden(k4_tarski(sK6(X0,X1,X6),X6),X0)
| ~ r2_hidden(X6,X2)
| k9_relat_1(X0,X1) != X2
| ~ v1_relat_1(X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f157,plain,
! [X2,X0,X1,X6,X7] :
( r2_hidden(X6,X2)
| ~ r2_hidden(k4_tarski(X7,X6),X0)
| ~ r2_hidden(X7,X1)
| k9_relat_1(X0,X1) != X2
| ~ v1_relat_1(X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f165,plain,
! [X0,X1,X5] :
( r2_hidden(k4_tarski(sK10(X0,X5),X5),X0)
| ~ r2_hidden(X5,X1)
| k2_funct_5(X0) != X1 ),
inference(cnf_transformation,[],[f126]) ).
fof(f166,plain,
! [X0,X1,X6,X5] :
( r2_hidden(X5,X1)
| ~ r2_hidden(k4_tarski(X6,X5),X0)
| k2_funct_5(X0) != X1 ),
inference(cnf_transformation,[],[f126]) ).
fof(f169,plain,
! [X3,X0,X1] :
( ~ r2_hidden(X3,X0)
| r2_hidden(X3,X1)
| ~ r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f129]) ).
fof(f170,plain,
! [X0,X1] :
( r2_hidden(sK11(X0,X1),X0)
| r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f129]) ).
fof(f171,plain,
! [X0,X1] :
( ~ r2_hidden(sK11(X0,X1),X1)
| r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f129]) ).
fof(f172,plain,
! [X0,X1] : k4_tarski(X0,X1) = k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),
inference(cnf_transformation,[],[f11]) ).
fof(f174,plain,
! [X0,X1,X4,X5] :
( r2_hidden(k4_tarski(X4,X5),X1)
| ~ r2_hidden(k4_tarski(X5,X4),X0)
| k4_relat_1(X0) != X1
| ~ v1_relat_1(X1)
| ~ v1_relat_1(X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f177,plain,
! [X2,X0,X1,X8,X7] :
( r2_hidden(k4_tarski(sK17(X0,X1,X7,X8),X8),X1)
| ~ r2_hidden(k4_tarski(X7,X8),X2)
| k5_relat_1(X0,X1) != X2
| ~ v1_relat_1(X2)
| ~ v1_relat_1(X1)
| ~ v1_relat_1(X0) ),
inference(cnf_transformation,[],[f135]) ).
fof(f179,plain,
! [X2,X0,X1,X8,X9,X7] :
( r2_hidden(k4_tarski(X7,X8),X2)
| ~ r2_hidden(k4_tarski(X7,X9),X0)
| ~ r2_hidden(k4_tarski(X9,X8),X1)
| k5_relat_1(X0,X1) != X2
| ~ v1_relat_1(X2)
| ~ v1_relat_1(X1)
| ~ v1_relat_1(X0) ),
inference(cnf_transformation,[],[f135]) ).
fof(f184,plain,
! [X0] :
( v1_relat_1(k4_relat_1(X0))
| ~ v1_relat_1(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f185,plain,
! [X0,X1] :
( v1_relat_1(k5_relat_1(X0,X1))
| ~ v1_relat_1(X0)
| ~ v1_relat_1(X1) ),
inference(cnf_transformation,[],[f82]) ).
fof(f186,plain,
! [X2,X0,X1] :
( m2_relset_1(k6_relset_1(X0,X1,X2),X1,X0)
| ~ m1_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f83]) ).
fof(f187,plain,
! [X2,X3,X0,X1,X4] :
( m2_relset_1(k9_relset_2(X0,X1,X2,X3,X4),X0,X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) ),
inference(cnf_transformation,[],[f85]) ).
fof(f188,plain,
! [X2,X0,X1] :
( m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m2_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f86]) ).
fof(f218,plain,
! [X2,X3,X0,X1] :
( ~ m1_relset_1(X2,X0,X1)
| k10_relset_1(X0,X1,X2,X3) = k9_relat_1(X2,X3) ),
inference(cnf_transformation,[],[f97]) ).
fof(f219,plain,
! [X2,X0,X1] :
( ~ m1_relset_1(X2,X0,X1)
| k6_relset_1(X0,X1,X2) = k4_relat_1(X2) ),
inference(cnf_transformation,[],[f98]) ).
fof(f220,plain,
! [X2,X3,X0,X1,X4] :
( ~ m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))
| ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| k9_relset_2(X0,X1,X2,X3,X4) = k5_relat_1(X3,X4) ),
inference(cnf_transformation,[],[f100]) ).
fof(f221,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X2,X0,X1)
| m1_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f144]) ).
fof(f241,plain,
! [X2,X0,X1,X6,X7] :
( r2_hidden(X6,X2)
| ~ r2_hidden(k2_tarski(k2_tarski(X7,X6),k1_tarski(X7)),X0)
| ~ r2_hidden(X7,X1)
| k9_relat_1(X0,X1) != X2
| ~ v1_relat_1(X0) ),
inference(definition_unfolding,[],[f157,f172]) ).
fof(f242,plain,
! [X2,X0,X1,X6] :
( r2_hidden(k2_tarski(k2_tarski(sK6(X0,X1,X6),X6),k1_tarski(sK6(X0,X1,X6))),X0)
| ~ r2_hidden(X6,X2)
| k9_relat_1(X0,X1) != X2
| ~ v1_relat_1(X0) ),
inference(definition_unfolding,[],[f156,f172]) ).
fof(f245,plain,
! [X0,X1,X6,X5] :
( r2_hidden(X5,X1)
| ~ r2_hidden(k2_tarski(k2_tarski(X6,X5),k1_tarski(X6)),X0)
| k2_funct_5(X0) != X1 ),
inference(definition_unfolding,[],[f166,f172]) ).
fof(f246,plain,
! [X0,X1,X5] :
( r2_hidden(k2_tarski(k2_tarski(sK10(X0,X5),X5),k1_tarski(sK10(X0,X5))),X0)
| ~ r2_hidden(X5,X1)
| k2_funct_5(X0) != X1 ),
inference(definition_unfolding,[],[f165,f172]) ).
fof(f249,plain,
! [X0,X1,X4,X5] :
( r2_hidden(k2_tarski(k2_tarski(X4,X5),k1_tarski(X4)),X1)
| ~ r2_hidden(k2_tarski(k2_tarski(X5,X4),k1_tarski(X5)),X0)
| k4_relat_1(X0) != X1
| ~ v1_relat_1(X1)
| ~ v1_relat_1(X0) ),
inference(definition_unfolding,[],[f174,f172,f172]) ).
fof(f254,plain,
! [X2,X0,X1,X8,X9,X7] :
( r2_hidden(k2_tarski(k2_tarski(X7,X8),k1_tarski(X7)),X2)
| ~ r2_hidden(k2_tarski(k2_tarski(X7,X9),k1_tarski(X7)),X0)
| ~ r2_hidden(k2_tarski(k2_tarski(X9,X8),k1_tarski(X9)),X1)
| k5_relat_1(X0,X1) != X2
| ~ v1_relat_1(X2)
| ~ v1_relat_1(X1)
| ~ v1_relat_1(X0) ),
inference(definition_unfolding,[],[f179,f172,f172,f172]) ).
fof(f256,plain,
! [X2,X0,X1,X8,X7] :
( r2_hidden(k2_tarski(k2_tarski(sK17(X0,X1,X7,X8),X8),k1_tarski(sK17(X0,X1,X7,X8))),X1)
| ~ r2_hidden(k2_tarski(k2_tarski(X7,X8),k1_tarski(X7)),X2)
| k5_relat_1(X0,X1) != X2
| ~ v1_relat_1(X2)
| ~ v1_relat_1(X1)
| ~ v1_relat_1(X0) ),
inference(definition_unfolding,[],[f177,f172,f172]) ).
fof(f259,plain,
! [X0,X1,X6,X7] :
( ~ r2_hidden(k2_tarski(k2_tarski(X7,X6),k1_tarski(X7)),X0)
| r2_hidden(X6,k9_relat_1(X0,X1))
| ~ r2_hidden(X7,X1)
| ~ v1_relat_1(X0) ),
inference(equality_resolution,[],[f241]) ).
fof(f260,plain,
! [X0,X1,X6] :
( r2_hidden(k2_tarski(k2_tarski(sK6(X0,X1,X6),X6),k1_tarski(sK6(X0,X1,X6))),X0)
| ~ r2_hidden(X6,k9_relat_1(X0,X1))
| ~ v1_relat_1(X0) ),
inference(equality_resolution,[],[f242]) ).
fof(f265,plain,
! [X0,X6,X5] :
( ~ r2_hidden(k2_tarski(k2_tarski(X6,X5),k1_tarski(X6)),X0)
| r2_hidden(X5,k2_funct_5(X0)) ),
inference(equality_resolution,[],[f245]) ).
fof(f266,plain,
! [X0,X5] :
( r2_hidden(k2_tarski(k2_tarski(sK10(X0,X5),X5),k1_tarski(sK10(X0,X5))),X0)
| ~ r2_hidden(X5,k2_funct_5(X0)) ),
inference(equality_resolution,[],[f246]) ).
fof(f267,plain,
! [X0,X4,X5] :
( r2_hidden(k2_tarski(k2_tarski(X4,X5),k1_tarski(X4)),k4_relat_1(X0))
| ~ r2_hidden(k2_tarski(k2_tarski(X5,X4),k1_tarski(X5)),X0)
| ~ v1_relat_1(k4_relat_1(X0))
| ~ v1_relat_1(X0) ),
inference(equality_resolution,[],[f249]) ).
fof(f269,plain,
! [X0,X1,X8,X9,X7] :
( r2_hidden(k2_tarski(k2_tarski(X7,X8),k1_tarski(X7)),k5_relat_1(X0,X1))
| ~ r2_hidden(k2_tarski(k2_tarski(X7,X9),k1_tarski(X7)),X0)
| ~ r2_hidden(k2_tarski(k2_tarski(X9,X8),k1_tarski(X9)),X1)
| ~ v1_relat_1(k5_relat_1(X0,X1))
| ~ v1_relat_1(X1)
| ~ v1_relat_1(X0) ),
inference(equality_resolution,[],[f254]) ).
fof(f271,plain,
! [X0,X1,X8,X7] :
( r2_hidden(k2_tarski(k2_tarski(sK17(X0,X1,X7,X8),X8),k1_tarski(sK17(X0,X1,X7,X8))),X1)
| ~ r2_hidden(k2_tarski(k2_tarski(X7,X8),k1_tarski(X7)),k5_relat_1(X0,X1))
| ~ v1_relat_1(k5_relat_1(X0,X1))
| ~ v1_relat_1(X1)
| ~ v1_relat_1(X0) ),
inference(equality_resolution,[],[f256]) ).
fof(f272,definition,
sF26 = k6_relset_1(sK0,sK1,sK3),
introduced(definition,[new_symbols(definition,[sF26])],[function_definition]) ).
fof(f273,plain,
k6_relset_1(sK0,sK1,sK3) = sF26,
inference(reorient_equations,[],[f272]) ).
fof(f274,definition,
sF27 = k9_relset_2(sK1,sK0,sK1,sF26,sK3),
introduced(definition,[new_symbols(definition,[sF27])],[function_definition]) ).
fof(f275,plain,
k9_relset_2(sK1,sK0,sK1,sF26,sK3) = sF27,
inference(reorient_equations,[],[f274]) ).
fof(f276,definition,
sF28 = k10_relset_1(sK1,sK1,sF27,sK2),
introduced(definition,[new_symbols(definition,[sF28])],[function_definition]) ).
fof(f277,plain,
k10_relset_1(sK1,sK1,sF27,sK2) = sF28,
inference(reorient_equations,[],[f276]) ).
fof(f278,definition,
sF29 = k2_funct_5(sK3),
introduced(definition,[new_symbols(definition,[sF29])],[function_definition]) ).
fof(f279,plain,
k2_funct_5(sK3) = sF29,
inference(reorient_equations,[],[f278]) ).
fof(f280,plain,
( ~ r1_tarski(sK2,sF28)
| ~ r1_tarski(sK2,sF29) ),
inference(definition_folding,[],[f150,f279,f277,f275,f273]) ).
fof(f281,plain,
( r1_tarski(sK2,sF28)
| r1_tarski(sK2,sF29) ),
inference(definition_folding,[],[f149,f279,f277,f275,f273]) ).
fof(f285,plain,
! [X0,X1,X8,X7] :
( r2_hidden(k2_tarski(k2_tarski(sK17(X0,X1,X7,X8),X8),k1_tarski(sK17(X0,X1,X7,X8))),X1)
| ~ r2_hidden(k2_tarski(k2_tarski(X7,X8),k1_tarski(X7)),k5_relat_1(X0,X1))
| ~ v1_relat_1(X1)
| ~ v1_relat_1(X0) ),
inference(forward_subsumption_resolution,[],[f271,f185]) ).
fof(f287,plain,
! [X0,X1,X8,X9,X7] :
( ~ r2_hidden(k2_tarski(k2_tarski(X9,X8),k1_tarski(X9)),X1)
| ~ r2_hidden(k2_tarski(k2_tarski(X7,X9),k1_tarski(X7)),X0)
| r2_hidden(k2_tarski(k2_tarski(X7,X8),k1_tarski(X7)),k5_relat_1(X0,X1))
| ~ v1_relat_1(X1)
| ~ v1_relat_1(X0) ),
inference(forward_subsumption_resolution,[],[f269,f185]) ).
fof(f289,plain,
! [X0,X4,X5] :
( ~ r2_hidden(k2_tarski(k2_tarski(X5,X4),k1_tarski(X5)),X0)
| r2_hidden(k2_tarski(k2_tarski(X4,X5),k1_tarski(X4)),k4_relat_1(X0))
| ~ v1_relat_1(X0) ),
inference(forward_subsumption_resolution,[],[f267,f184]) ).
fof(f291,definition,
( spl31_1
<=> r1_tarski(sK2,sF29) ),
introduced(definition,[new_symbols(definition,[spl31_1])],[avatar_definition]) ).
fof(f292,plain,
( ~ r1_tarski(sK2,sF29)
| spl31_1 ),
inference(avatar_component_clause,[],[f291]) ).
fof(f293,plain,
( r1_tarski(sK2,sF29)
| ~ spl31_1 ),
inference(avatar_component_clause,[],[f291]) ).
fof(f295,definition,
( spl31_2
<=> r1_tarski(sK2,sF28) ),
introduced(definition,[new_symbols(definition,[spl31_2])],[avatar_definition]) ).
fof(f296,plain,
( ~ r1_tarski(sK2,sF28)
| spl31_2 ),
inference(avatar_component_clause,[],[f295]) ).
fof(f297,plain,
( r1_tarski(sK2,sF28)
| ~ spl31_2 ),
inference(avatar_component_clause,[],[f295]) ).
fof(f298,plain,
( spl31_1
| spl31_2 ),
inference(avatar_split_clause,[],[f281,f295,f291]) ).
fof(f299,plain,
( ~ spl31_1
| ~ spl31_2 ),
inference(avatar_split_clause,[],[f280,f295,f291]) ).
fof(f302,plain,
! [X2,X0,X1] :
( r2_hidden(sK11(X0,X1),X2)
| ~ r1_tarski(X0,X2)
| r1_tarski(X0,X1) ),
inference(resolution,[],[f169,f170]) ).
fof(f307,plain,
! [X0,X1] :
( r2_hidden(k2_tarski(k1_tarski(sK10(X0,X1)),k2_tarski(sK10(X0,X1),X1)),X0)
| ~ r2_hidden(X1,k2_funct_5(X0)) ),
inference(superposition,[],[f266,f154]) ).
fof(f326,plain,
m1_relset_1(sK3,sK0,sK1),
inference(resolution,[],[f221,f148]) ).
fof(f333,definition,
( spl31_3
<=> v1_relat_1(sK3) ),
introduced(definition,[new_symbols(definition,[spl31_3])],[avatar_definition]) ).
fof(f334,plain,
( v1_relat_1(sK3)
| ~ spl31_3 ),
inference(avatar_component_clause,[],[f333]) ).
fof(f335,plain,
( ~ v1_relat_1(sK3)
| spl31_3 ),
inference(avatar_component_clause,[],[f333]) ).
fof(f344,plain,
k6_relset_1(sK0,sK1,sK3) = k4_relat_1(sK3),
inference(resolution,[],[f219,f326]) ).
fof(f345,plain,
sF26 = k4_relat_1(sK3),
inference(forward_demodulation,[],[f344,f273]) ).
fof(f367,definition,
( spl31_6
<=> m1_relset_1(sF27,sK1,sK1) ),
introduced(definition,[new_symbols(definition,[spl31_6])],[avatar_definition]) ).
fof(f368,plain,
( m1_relset_1(sF27,sK1,sK1)
| ~ spl31_6 ),
inference(avatar_component_clause,[],[f367]) ).
fof(f369,plain,
( ~ m1_relset_1(sF27,sK1,sK1)
| spl31_6 ),
inference(avatar_component_clause,[],[f367]) ).
fof(f401,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X0,X1,X2)
| v1_relat_1(X0) ),
inference(resolution,[],[f188,f153]) ).
fof(f403,plain,
v1_relat_1(sK3),
inference(resolution,[],[f401,f148]) ).
fof(f404,plain,
( $false
| spl31_3 ),
inference(forward_subsumption_resolution,[],[f403,f335]) ).
fof(f405,plain,
spl31_3,
inference(avatar_contradiction_clause,[],[f404]) ).
fof(f411,plain,
( m2_relset_1(sF27,sK1,sK1)
| ~ m1_subset_1(sF26,k1_zfmisc_1(k2_zfmisc_1(sK1,sK0)))
| ~ m1_subset_1(sK3,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1))) ),
inference(superposition,[],[f187,f275]) ).
fof(f413,definition,
( spl31_8
<=> m1_subset_1(sK3,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1))) ),
introduced(definition,[new_symbols(definition,[spl31_8])],[avatar_definition]) ).
fof(f414,plain,
( m1_subset_1(sK3,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))
| ~ spl31_8 ),
inference(avatar_component_clause,[],[f413]) ).
fof(f415,plain,
( ~ m1_subset_1(sK3,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))
| spl31_8 ),
inference(avatar_component_clause,[],[f413]) ).
fof(f417,definition,
( spl31_9
<=> m1_subset_1(sF26,k1_zfmisc_1(k2_zfmisc_1(sK1,sK0))) ),
introduced(definition,[new_symbols(definition,[spl31_9])],[avatar_definition]) ).
fof(f418,plain,
( m1_subset_1(sF26,k1_zfmisc_1(k2_zfmisc_1(sK1,sK0)))
| ~ spl31_9 ),
inference(avatar_component_clause,[],[f417]) ).
fof(f419,plain,
( ~ m1_subset_1(sF26,k1_zfmisc_1(k2_zfmisc_1(sK1,sK0)))
| spl31_9 ),
inference(avatar_component_clause,[],[f417]) ).
fof(f421,definition,
( spl31_10
<=> m2_relset_1(sF27,sK1,sK1) ),
introduced(definition,[new_symbols(definition,[spl31_10])],[avatar_definition]) ).
fof(f423,plain,
( m2_relset_1(sF27,sK1,sK1)
| ~ spl31_10 ),
inference(avatar_component_clause,[],[f421]) ).
fof(f424,plain,
( ~ spl31_8
| ~ spl31_9
| spl31_10 ),
inference(avatar_split_clause,[],[f411,f421,f417,f413]) ).
fof(f425,plain,
( ~ m2_relset_1(sK3,sK0,sK1)
| spl31_8 ),
inference(resolution,[],[f415,f188]) ).
fof(f426,plain,
( $false
| spl31_8 ),
inference(forward_subsumption_resolution,[],[f425,f148]) ).
fof(f427,plain,
spl31_8,
inference(avatar_contradiction_clause,[],[f426]) ).
fof(f428,plain,
( ! [X0,X1] :
( ~ m1_subset_1(X0,k1_zfmisc_1(k2_zfmisc_1(X1,sK0)))
| k9_relset_2(X1,sK0,sK1,X0,sK3) = k5_relat_1(X0,sK3) )
| ~ spl31_8 ),
inference(resolution,[],[f414,f220]) ).
fof(f431,plain,
( ~ m2_relset_1(sF26,sK1,sK0)
| spl31_9 ),
inference(resolution,[],[f419,f188]) ).
fof(f457,plain,
! [X2,X3,X0,X1] :
( ~ r2_hidden(k2_tarski(k2_tarski(X0,sK10(X1,X2)),k1_tarski(X0)),X3)
| r2_hidden(k2_tarski(k2_tarski(X0,X2),k1_tarski(X0)),k5_relat_1(X3,X1))
| ~ v1_relat_1(X1)
| ~ v1_relat_1(X3)
| ~ r2_hidden(X2,k2_funct_5(X1)) ),
inference(resolution,[],[f287,f266]) ).
fof(f468,plain,
( m2_relset_1(sF26,sK1,sK0)
| ~ m1_relset_1(sK3,sK0,sK1) ),
inference(superposition,[],[f186,f273]) ).
fof(f479,plain,
( ~ m1_relset_1(sK3,sK0,sK1)
| spl31_9 ),
inference(forward_subsumption_resolution,[],[f468,f431]) ).
fof(f480,plain,
( $false
| spl31_9 ),
inference(forward_subsumption_resolution,[],[f479,f326]) ).
fof(f481,plain,
spl31_9,
inference(avatar_contradiction_clause,[],[f480]) ).
fof(f482,plain,
m2_relset_1(sF26,sK1,sK0),
inference(forward_subsumption_resolution,[],[f468,f326]) ).
fof(f483,plain,
v1_relat_1(sF26),
inference(resolution,[],[f482,f401]) ).
fof(f492,plain,
( v1_relat_1(sF27)
| ~ spl31_10 ),
inference(resolution,[],[f423,f401]) ).
fof(f493,plain,
( m1_relset_1(sF27,sK1,sK1)
| ~ spl31_10 ),
inference(resolution,[],[f423,f221]) ).
fof(f495,plain,
( $false
| spl31_6
| ~ spl31_10 ),
inference(forward_subsumption_resolution,[],[f493,f369]) ).
fof(f496,plain,
( spl31_6
| ~ spl31_10 ),
inference(avatar_contradiction_clause,[],[f495]) ).
fof(f500,plain,
( ! [X0] : k10_relset_1(sK1,sK1,sF27,X0) = k9_relat_1(sF27,X0)
| ~ spl31_6 ),
inference(resolution,[],[f368,f218]) ).
fof(f503,plain,
( sF28 = k9_relat_1(sF27,sK2)
| ~ spl31_6 ),
inference(superposition,[],[f277,f500]) ).
fof(f598,plain,
! [X0,X1] :
( r2_hidden(k2_tarski(k2_tarski(X0,sK10(X1,X0)),k1_tarski(X0)),k4_relat_1(X1))
| ~ v1_relat_1(X1)
| ~ r2_hidden(X0,k2_funct_5(X1)) ),
inference(resolution,[],[f289,f266]) ).
fof(f612,plain,
! [X0] :
( r2_hidden(k2_tarski(k2_tarski(X0,sK10(sK3,X0)),k1_tarski(X0)),sF26)
| ~ v1_relat_1(sK3)
| ~ r2_hidden(X0,k2_funct_5(sK3)) ),
inference(superposition,[],[f598,f345]) ).
fof(f614,plain,
( ! [X0] :
( r2_hidden(k2_tarski(k2_tarski(X0,sK10(sK3,X0)),k1_tarski(X0)),sF26)
| ~ r2_hidden(X0,k2_funct_5(sK3)) )
| ~ spl31_3 ),
inference(forward_subsumption_resolution,[],[f612,f334]) ).
fof(f617,plain,
( ! [X0] :
( r2_hidden(k2_tarski(k2_tarski(X0,sK10(sK3,X0)),k1_tarski(X0)),sF26)
| ~ r2_hidden(X0,sF29) )
| ~ spl31_3 ),
inference(forward_demodulation,[],[f614,f279]) ).
fof(f679,plain,
( ! [X0] :
( r2_hidden(k2_tarski(k2_tarski(X0,X0),k1_tarski(X0)),k5_relat_1(sF26,sK3))
| ~ v1_relat_1(sK3)
| ~ v1_relat_1(sF26)
| ~ r2_hidden(X0,k2_funct_5(sK3))
| ~ r2_hidden(X0,sF29) )
| ~ spl31_3 ),
inference(resolution,[],[f457,f617]) ).
fof(f685,plain,
( ! [X0] :
( r2_hidden(k2_tarski(k2_tarski(X0,X0),k1_tarski(X0)),k5_relat_1(sF26,sK3))
| ~ v1_relat_1(sF26)
| ~ r2_hidden(X0,k2_funct_5(sK3))
| ~ r2_hidden(X0,sF29) )
| ~ spl31_3 ),
inference(forward_subsumption_resolution,[],[f679,f334]) ).
fof(f689,plain,
( ! [X0] :
( r2_hidden(k2_tarski(k2_tarski(X0,X0),k1_tarski(X0)),k5_relat_1(sF26,sK3))
| ~ r2_hidden(X0,k2_funct_5(sK3))
| ~ r2_hidden(X0,sF29) )
| ~ spl31_3 ),
inference(forward_subsumption_resolution,[],[f685,f483]) ).
fof(f690,plain,
( ! [X0] :
( ~ r2_hidden(X0,sF29)
| r2_hidden(k2_tarski(k2_tarski(X0,X0),k1_tarski(X0)),k5_relat_1(sF26,sK3))
| ~ r2_hidden(X0,sF29) )
| ~ spl31_3 ),
inference(forward_demodulation,[],[f689,f279]) ).
fof(f691,plain,
( ! [X0] :
( r2_hidden(k2_tarski(k2_tarski(X0,X0),k1_tarski(X0)),k5_relat_1(sF26,sK3))
| ~ r2_hidden(X0,sF29) )
| ~ spl31_3 ),
inference(duplicate_literal_removal,[],[f690]) ).
fof(f707,plain,
( ! [X0] :
( r2_hidden(k2_tarski(k1_tarski(X0),k2_tarski(X0,X0)),k5_relat_1(sF26,sK3))
| ~ r2_hidden(X0,sF29) )
| ~ spl31_3 ),
inference(superposition,[],[f691,f154]) ).
fof(f818,plain,
! [X2,X3,X0,X1] :
( ~ r2_hidden(k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),k5_relat_1(X2,X3))
| ~ v1_relat_1(X3)
| ~ v1_relat_1(X2)
| r2_hidden(X1,k2_funct_5(X3)) ),
inference(resolution,[],[f285,f265]) ).
fof(f844,plain,
! [X2,X3,X0,X1] :
( ~ r2_hidden(k2_tarski(k1_tarski(X0),k2_tarski(X0,X1)),k5_relat_1(X2,X3))
| ~ v1_relat_1(X3)
| ~ v1_relat_1(X2)
| r2_hidden(X1,k2_funct_5(X3)) ),
inference(superposition,[],[f818,f154]) ).
fof(f875,plain,
! [X2,X0,X1] :
( ~ r2_hidden(X0,k9_relat_1(X1,X2))
| ~ v1_relat_1(X1)
| r2_hidden(X0,k2_funct_5(X1)) ),
inference(resolution,[],[f260,f265]) ).
fof(f907,plain,
( ! [X0] :
( ~ r2_hidden(X0,sF28)
| ~ v1_relat_1(sF27)
| r2_hidden(X0,k2_funct_5(sF27)) )
| ~ spl31_6 ),
inference(superposition,[],[f875,f503]) ).
fof(f909,plain,
( ! [X0] :
( r2_hidden(X0,k2_funct_5(sF27))
| ~ r2_hidden(X0,sF28) )
| ~ spl31_6
| ~ spl31_10 ),
inference(forward_subsumption_resolution,[],[f907,f492]) ).
fof(f1047,plain,
! [X2,X3,X0,X1] :
( ~ r2_hidden(k2_tarski(k1_tarski(X0),k2_tarski(X0,X1)),X2)
| r2_hidden(X1,k9_relat_1(X2,X3))
| ~ r2_hidden(X0,X3)
| ~ v1_relat_1(X2) ),
inference(superposition,[],[f259,f154]) ).
fof(f1551,definition,
( spl31_80
<=> ! [X0] :
( r2_hidden(X0,sF29)
| ~ r2_hidden(X0,sF28) ) ),
introduced(definition,[new_symbols(definition,[spl31_80])],[avatar_definition]) ).
fof(f1552,plain,
( ! [X0] :
( ~ r2_hidden(X0,sF28)
| r2_hidden(X0,sF29) )
| ~ spl31_80 ),
inference(avatar_component_clause,[],[f1551]) ).
fof(f2378,plain,
( k9_relset_2(sK1,sK0,sK1,sF26,sK3) = k5_relat_1(sF26,sK3)
| ~ spl31_8
| ~ spl31_9 ),
inference(resolution,[],[f428,f418]) ).
fof(f2379,plain,
( sF27 = k5_relat_1(sF26,sK3)
| ~ spl31_8
| ~ spl31_9 ),
inference(forward_demodulation,[],[f2378,f275]) ).
fof(f2381,plain,
( ! [X0] :
( r2_hidden(k2_tarski(k1_tarski(X0),k2_tarski(X0,X0)),sF27)
| ~ r2_hidden(X0,sF29) )
| ~ spl31_3
| ~ spl31_8
| ~ spl31_9 ),
inference(superposition,[],[f707,f2379]) ).
fof(f2390,plain,
( ! [X0,X1] :
( ~ r2_hidden(k2_tarski(k1_tarski(X0),k2_tarski(X0,X1)),sF27)
| ~ v1_relat_1(sK3)
| ~ v1_relat_1(sF26)
| r2_hidden(X1,k2_funct_5(sK3)) )
| ~ spl31_8
| ~ spl31_9 ),
inference(superposition,[],[f844,f2379]) ).
fof(f2397,plain,
( ! [X0,X1] :
( ~ r2_hidden(k2_tarski(k1_tarski(X0),k2_tarski(X0,X1)),sF27)
| ~ v1_relat_1(sF26)
| r2_hidden(X1,k2_funct_5(sK3)) )
| ~ spl31_3
| ~ spl31_8
| ~ spl31_9 ),
inference(forward_subsumption_resolution,[],[f2390,f334]) ).
fof(f2410,plain,
( ! [X0,X1] :
( ~ r2_hidden(k2_tarski(k1_tarski(X0),k2_tarski(X0,X1)),sF27)
| r2_hidden(X1,k2_funct_5(sK3)) )
| ~ spl31_3
| ~ spl31_8
| ~ spl31_9 ),
inference(forward_subsumption_resolution,[],[f2397,f483]) ).
fof(f2419,plain,
( ! [X0,X1] :
( ~ r2_hidden(k2_tarski(k1_tarski(X0),k2_tarski(X0,X1)),sF27)
| r2_hidden(X1,sF29) )
| ~ spl31_3
| ~ spl31_8
| ~ spl31_9 ),
inference(forward_demodulation,[],[f2410,f279]) ).
fof(f2454,plain,
( ! [X0] :
( ~ r2_hidden(X0,k2_funct_5(sF27))
| r2_hidden(X0,sF29) )
| ~ spl31_3
| ~ spl31_8
| ~ spl31_9 ),
inference(resolution,[],[f2419,f307]) ).
fof(f2496,plain,
( ! [X0,X1] :
( ~ r2_hidden(X0,sF29)
| r2_hidden(X0,k9_relat_1(sF27,X1))
| ~ r2_hidden(X0,X1)
| ~ v1_relat_1(sF27) )
| ~ spl31_3
| ~ spl31_8
| ~ spl31_9 ),
inference(resolution,[],[f2381,f1047]) ).
fof(f2500,plain,
( ! [X0,X1] :
( r2_hidden(X0,k9_relat_1(sF27,X1))
| ~ r2_hidden(X0,sF29)
| ~ r2_hidden(X0,X1) )
| ~ spl31_3
| ~ spl31_8
| ~ spl31_9
| ~ spl31_10 ),
inference(forward_subsumption_resolution,[],[f2496,f492]) ).
fof(f2525,plain,
( ! [X0] :
( r2_hidden(X0,sF29)
| ~ r2_hidden(X0,sF28) )
| ~ spl31_3
| ~ spl31_6
| ~ spl31_8
| ~ spl31_9
| ~ spl31_10 ),
inference(resolution,[],[f2454,f909]) ).
fof(f2565,plain,
( spl31_80
| ~ spl31_3
| ~ spl31_6
| ~ spl31_8
| ~ spl31_9
| ~ spl31_10 ),
inference(avatar_split_clause,[],[f2525,f421,f417,f413,f367,f333,f1551]) ).
fof(f2590,plain,
( ! [X0,X1] :
( r2_hidden(sK11(X0,X1),sF29)
| ~ r1_tarski(X0,sF28)
| r1_tarski(X0,X1) )
| ~ spl31_80 ),
inference(resolution,[],[f1552,f302]) ).
fof(f3013,plain,
( ! [X0] :
( ~ r2_hidden(X0,sF29)
| r2_hidden(X0,sF28)
| ~ r2_hidden(X0,sK2) )
| ~ spl31_3
| ~ spl31_6
| ~ spl31_8
| ~ spl31_9
| ~ spl31_10 ),
inference(superposition,[],[f2500,f503]) ).
fof(f3032,plain,
( ! [X0,X1] :
( ~ r2_hidden(sK11(X0,X1),sK2)
| r2_hidden(sK11(X0,X1),sF28)
| ~ r1_tarski(X0,sF29)
| r1_tarski(X0,X1) )
| ~ spl31_3
| ~ spl31_6
| ~ spl31_8
| ~ spl31_9
| ~ spl31_10 ),
inference(resolution,[],[f3013,f302]) ).
fof(f3167,plain,
( ! [X0] :
( r2_hidden(sK11(sK2,X0),sF28)
| ~ r1_tarski(sK2,sF29)
| r1_tarski(sK2,X0)
| r1_tarski(sK2,X0) )
| ~ spl31_3
| ~ spl31_6
| ~ spl31_8
| ~ spl31_9
| ~ spl31_10 ),
inference(resolution,[],[f3032,f170]) ).
fof(f3172,plain,
( ! [X0] :
( r2_hidden(sK11(sK2,X0),sF28)
| ~ r1_tarski(sK2,sF29)
| r1_tarski(sK2,X0) )
| ~ spl31_3
| ~ spl31_6
| ~ spl31_8
| ~ spl31_9
| ~ spl31_10 ),
inference(duplicate_literal_removal,[],[f3167]) ).
fof(f5484,plain,
( ! [X0] :
( ~ r1_tarski(X0,sF28)
| r1_tarski(X0,sF29)
| r1_tarski(X0,sF29) )
| ~ spl31_80 ),
inference(resolution,[],[f2590,f171]) ).
fof(f5488,plain,
( ! [X0] :
( ~ r1_tarski(X0,sF28)
| r1_tarski(X0,sF29) )
| ~ spl31_80 ),
inference(duplicate_literal_removal,[],[f5484]) ).
fof(f5491,plain,
( r1_tarski(sK2,sF29)
| ~ spl31_2
| ~ spl31_80 ),
inference(resolution,[],[f5488,f297]) ).
fof(f5492,plain,
( $false
| spl31_1
| ~ spl31_2
| ~ spl31_80 ),
inference(forward_subsumption_resolution,[],[f5491,f292]) ).
fof(f5493,plain,
( spl31_1
| ~ spl31_2
| ~ spl31_80 ),
inference(avatar_contradiction_clause,[],[f5492]) ).
fof(f5495,plain,
( ! [X0] :
( r2_hidden(sK11(sK2,X0),sF28)
| r1_tarski(sK2,X0) )
| ~ spl31_1
| ~ spl31_3
| ~ spl31_6
| ~ spl31_8
| ~ spl31_9
| ~ spl31_10 ),
inference(forward_subsumption_resolution,[],[f3172,f293]) ).
fof(f5497,plain,
( r1_tarski(sK2,sF28)
| r1_tarski(sK2,sF28)
| ~ spl31_1
| ~ spl31_3
| ~ spl31_6
| ~ spl31_8
| ~ spl31_9
| ~ spl31_10 ),
inference(resolution,[],[f5495,f171]) ).
fof(f5501,plain,
( r1_tarski(sK2,sF28)
| ~ spl31_1
| ~ spl31_3
| ~ spl31_6
| ~ spl31_8
| ~ spl31_9
| ~ spl31_10 ),
inference(duplicate_literal_removal,[],[f5497]) ).
fof(f5503,plain,
( $false
| ~ spl31_1
| spl31_2
| ~ spl31_3
| ~ spl31_6
| ~ spl31_8
| ~ spl31_9
| ~ spl31_10 ),
inference(forward_subsumption_resolution,[],[f5501,f296]) ).
fof(f5504,plain,
( ~ spl31_1
| spl31_2
| ~ spl31_3
| ~ spl31_6
| ~ spl31_8
| ~ spl31_9
| ~ spl31_10 ),
inference(avatar_contradiction_clause,[],[f5503]) ).
cnf(s1,plain,
( spl31_1
| spl31_2 ),
inference(sat_conversion,[],[f298]) ).
cnf(s2,plain,
( ~ spl31_1
| ~ spl31_2 ),
inference(sat_conversion,[],[f299]) ).
cnf(s6,plain,
spl31_3,
inference(sat_conversion,[],[f405]) ).
cnf(s7,plain,
( ~ spl31_8
| ~ spl31_9
| spl31_10 ),
inference(sat_conversion,[],[f424]) ).
cnf(s8,plain,
spl31_8,
inference(sat_conversion,[],[f427]) ).
cnf(s10,plain,
spl31_9,
inference(sat_conversion,[],[f481]) ).
cnf(s11,plain,
( spl31_6
| ~ spl31_10 ),
inference(sat_conversion,[],[f496]) ).
cnf(s83,plain,
( ~ spl31_3
| ~ spl31_6
| ~ spl31_8
| ~ spl31_9
| ~ spl31_10
| spl31_80 ),
inference(sat_conversion,[],[f2565]) ).
cnf(s214,plain,
( spl31_1
| ~ spl31_2
| ~ spl31_80 ),
inference(sat_conversion,[],[f5493]) ).
cnf(s215,plain,
( ~ spl31_1
| spl31_2
| ~ spl31_3
| ~ spl31_6
| ~ spl31_8
| ~ spl31_9
| ~ spl31_10 ),
inference(sat_conversion,[],[f5504]) ).
cnf(s216,plain,
spl31_10,
inference(rat,[],[s7,s10,s8]) ).
cnf(s217,plain,
spl31_6,
inference(rat,[],[s11,s216]) ).
cnf(s219,plain,
spl31_80,
inference(rat,[],[s83,s217,s216,s10,s8,s6]) ).
cnf(s226,plain,
spl31_1,
inference(rat,[],[s1,s214,s219]) ).
cnf(s227,plain,
spl31_2,
inference(rat,[],[s215,s216,s10,s8,s217,s6,s226]) ).
cnf(s228,plain,
$false,
inference(rat,[],[s2,s227,s226]) ).
fof(f5505,plain,
$false,
inference(avatar_sat_refutation,[],[s228]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU443+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n020.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 05:32:35 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.87/2.61 % (4083822)Detected formulas, will run a generic FOF schedule.
% 11.87/2.61 % (4083832)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1691858745:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 11.87/2.61 % (4083830)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=4263067171:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 11.87/2.61 % (4083829)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2545627289:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 11.87/2.61 % (4083828)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2221132129:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 11.87/2.61 % (4083832)Instruction limit reached!
% 11.87/2.61 % (4083832)------------------------------
% 11.87/2.61 % (4083832)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.87/2.61 % (4083832)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.87/2.61 % (4083832)CaDiCaL version: 2.1.3
% 11.87/2.61 % (4083832)Termination reason: Instruction limit
% 11.87/2.61 % (4083832)Termination phase: Saturation
% 11.87/2.61 % (4083832)Time elapsed: 0.042 s
% 11.87/2.61 % (4083832)Peak memory usage: 89 MB
% 11.87/2.61 % (4083832)Instructions burned: 122 (million)
% 11.87/2.61 % (4083833)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=140258967:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 11.87/2.61 % (4083831)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1644532315:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 11.87/2.61 % (4083834)dis-21_1_sil=8000:lcm=predicate:random_seed=3855620747:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 11.87/2.61 % (4083831)Refutation not found, incomplete strategy
% 11.87/2.61 % (4083831)------------------------------
% 11.87/2.61 % (4083831)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.87/2.61 % (4083831)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.87/2.61 % (4083831)CaDiCaL version: 2.1.3
% 11.87/2.61 % (4083831)Termination reason: Refutation not found, incomplete strategy
% 11.87/2.61 % (4083831)Time elapsed: 0.004 s
% 11.87/2.61 % (4083831)Peak memory usage: 89 MB
% 11.87/2.61 % (4083831)Instructions burned: 3 (million)
% 11.87/2.61 % (4083834)Instruction limit reached!
% 11.87/2.61 % (4083834)------------------------------
% 11.87/2.61 % (4083834)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.87/2.61 % (4083834)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.87/2.61 % (4083834)CaDiCaL version: 2.1.3
% 11.87/2.61 % (4083834)Termination reason: Instruction limit
% 11.87/2.61 % (4083834)Termination phase: Saturation
% 11.87/2.61 % (4083834)Time elapsed: 0.081 s
% 11.87/2.61 % (4083834)Peak memory usage: 90 MB
% 11.87/2.61 % (4083834)Instructions burned: 130 (million)
% 11.87/2.61 % (4083833)Instruction limit reached!
% 11.87/2.61 % (4083833)------------------------------
% 11.87/2.61 % (4083833)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.87/2.61 % (4083833)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.87/2.61 % (4083833)CaDiCaL version: 2.1.3
% 11.87/2.61 % (4083833)Termination reason: Instruction limit
% 11.87/2.61 % (4083833)Termination phase: Saturation
% 11.87/2.61 % (4083833)Time elapsed: 0.105 s
% 11.87/2.61 % (4083833)Peak memory usage: 90 MB
% 11.87/2.61 % (4083833)Instructions burned: 139 (million)
% 11.87/2.61 % (4083839)lrs+10_1_sil=8000:sp=occurrence:random_seed=4224979729:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 11.87/2.61 % (4083839)Instruction limit reached!
% 11.87/2.61 % (4083839)------------------------------
% 11.87/2.61 % (4083839)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.87/2.61 % (4083839)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.87/2.61 % (4083839)CaDiCaL version: 2.1.3
% 11.87/2.61 % (4083839)Termination reason: Instruction limit
% 11.87/2.61 % (4083839)Termination phase: Saturation
% 11.87/2.61 % (4083839)Time elapsed: 0.099 s
% 11.87/2.61 % (4083839)Peak memory usage: 92 MB
% 11.87/2.61 % (4083839)Instructions burned: 285 (million)
% 11.87/2.66 % (4083843)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2233621539:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 11.87/2.66 % (4083831)------------------------------
% 11.87/2.66 % (4083831)------------------------------
% 11.87/2.66 % (4083844)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2996928610:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 11.87/2.66 % (4083846)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=3502010146:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 11.87/2.66 % (4083843)Instruction limit reached!
% 11.87/2.66 % (4083843)------------------------------
% 11.87/2.66 % (4083843)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.87/2.66 % (4083843)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.87/2.66 % (4083843)CaDiCaL version: 2.1.3
% 11.87/2.66 % (4083843)Termination reason: Instruction limit
% 11.87/2.66 % (4083843)Termination phase: Saturation
% 11.87/2.66 % (4083843)Time elapsed: 0.101 s
% 11.87/2.66 % (4083843)Peak memory usage: 91 MB
% 11.87/2.66 % (4083843)Instructions burned: 157 (million)
% 11.87/2.66 % (4083848)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3395820656:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 11.87/2.66 % (4083846)Instruction limit reached!
% 11.87/2.66 % (4083846)------------------------------
% 11.87/2.66 % (4083846)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.87/2.66 % (4083846)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.87/2.66 % (4083846)CaDiCaL version: 2.1.3
% 11.87/2.66 % (4083846)Termination reason: Instruction limit
% 11.87/2.66 % (4083846)Termination phase: Saturation
% 11.87/2.66 % (4083846)Time elapsed: 0.076 s
% 11.87/2.66 % (4083846)Peak memory usage: 92 MB
% 11.87/2.66 % (4083846)Instructions burned: 249 (million)
% 11.87/2.66 % (4083851)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3704338325:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 11.87/2.66 % (4083844)Instruction limit reached!
% 11.87/2.66 % (4083844)------------------------------
% 11.87/2.66 % (4083844)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.87/2.66 % (4083844)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.87/2.66 % (4083844)CaDiCaL version: 2.1.3
% 11.87/2.66 % (4083844)Termination reason: Instruction limit
% 11.87/2.66 % (4083844)Termination phase: Saturation
% 11.87/2.66 % (4083844)Time elapsed: 0.235 s
% 11.87/2.66 % (4083844)Peak memory usage: 92 MB
% 11.87/2.66 % (4083844)Instructions burned: 325 (million)
% 11.87/2.66 % (4083853)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1401019546:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 11.87/2.66 % (4083848)Instruction limit reached!
% 11.87/2.66 % (4083848)------------------------------
% 11.87/2.66 % (4083848)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.87/2.66 % (4083848)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.87/2.66 % (4083848)CaDiCaL version: 2.1.3
% 11.87/2.66 % (4083848)Termination reason: Instruction limit
% 11.87/2.66 % (4083848)Termination phase: Saturation
% 11.87/2.66 % (4083848)Time elapsed: 0.155 s
% 11.87/2.66 % (4083848)Peak memory usage: 89 MB
% 11.87/2.66 % (4083848)Instructions burned: 295 (million)
% 11.87/2.66 % (4083853)Instruction limit reached!
% 11.87/2.66 % (4083853)------------------------------
% 11.87/2.66 % (4083853)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.87/2.66 % (4083853)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.87/2.66 % (4083853)CaDiCaL version: 2.1.3
% 11.87/2.66 % (4083853)Termination reason: Instruction limit
% 11.87/2.66 % (4083853)Termination phase: Saturation
% 11.87/2.66 % (4083853)Time elapsed: 0.044 s
% 11.87/2.66 % (4083853)Peak memory usage: 90 MB
% 11.87/2.66 % (4083853)Instructions burned: 113 (million)
% 11.87/2.66 % (4083855)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=140760977:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 11.87/2.66 % (4083858)lrs+10_1_sil=8000:sp=occurrence:random_seed=886423725:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 11.87/2.66 % (4083855)Instruction limit reached!
% 11.87/2.66 % (4083855)------------------------------
% 11.87/2.66 % (4083855)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.87/2.66 % (4083855)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.87/2.66 % (4083855)CaDiCaL version: 2.1.3
% 11.87/2.66 % (4083855)Termination reason: Instruction limit
% 11.87/2.66 % (4083855)Termination phase: Saturation
% 11.87/2.66 % (4083855)Time elapsed: 0.065 s
% 11.87/2.66 % (4083855)Peak memory usage: 89 MB
% 11.87/2.66 % (4083855)Instructions burned: 130 (million)
% 11.87/2.66 % (4083857)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2105817545:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 11.87/2.66 % (4083857)Instruction limit reached!
% 11.87/2.66 % (4083857)------------------------------
% 11.87/2.66 % (4083857)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.87/2.66 % (4083857)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.87/2.66 % (4083857)CaDiCaL version: 2.1.3
% 11.87/2.66 % (4083857)Termination reason: Instruction limit
% 11.87/2.66 % (4083857)Termination phase: Saturation
% 11.87/2.66 % (4083857)Time elapsed: 0.075 s
% 11.87/2.66 % (4083857)Peak memory usage: 89 MB
% 11.87/2.66 % (4083857)Instructions burned: 115 (million)
% 11.87/2.66 % (4083861)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3404438762:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 11.87/2.66 % (4083861)Refutation not found, incomplete strategy
% 11.87/2.66 % (4083861)------------------------------
% 11.87/2.66 % (4083861)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.87/2.66 % (4083861)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.87/2.66 % (4083861)CaDiCaL version: 2.1.3
% 11.87/2.66 % (4083861)Termination reason: Refutation not found, incomplete strategy
% 11.87/2.66 % (4083861)Time elapsed: 0.008 s
% 11.87/2.66 % (4083861)Peak memory usage: 89 MB
% 11.87/2.66 % (4083861)Instructions burned: 11 (million)
% 11.87/2.66 % (4083863)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2972161873:i=5202:ss=axioms:sgt=16_2990 on theBenchmark for (2990ds/5202Mi)
% 11.87/2.66 % (4083858)Instruction limit reached!
% 11.87/2.66 % (4083858)------------------------------
% 11.87/2.66 % (4083858)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.87/2.66 % (4083858)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.87/2.66 % (4083858)CaDiCaL version: 2.1.3
% 11.87/2.66 % (4083858)Termination reason: Instruction limit
% 11.87/2.66 % (4083858)Termination phase: Saturation
% 11.87/2.66 % (4083858)Time elapsed: 0.296 s
% 11.87/2.66 % (4083858)Peak memory usage: 99 MB
% 11.87/2.66 % (4083858)Instructions burned: 909 (million)
% 11.87/2.66 % (4083866)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=1487063130:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2988 on theBenchmark for (2988ds/134Mi)
% 11.87/2.66 % (4083861)------------------------------
% 11.87/2.66 % (4083861)------------------------------
% 11.87/2.66 % (4083866)Instruction limit reached!
% 11.87/2.66 % (4083866)------------------------------
% 11.87/2.66 % (4083866)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.87/2.66 % (4083866)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.87/2.66 % (4083866)CaDiCaL version: 2.1.3
% 11.87/2.66 % (4083866)Termination reason: Instruction limit
% 11.87/2.66 % (4083866)Termination phase: Saturation
% 11.87/2.66 % (4083866)Time elapsed: 0.041 s
% 11.87/2.66 % (4083866)Peak memory usage: 91 MB
% 11.87/2.66 % (4083866)Instructions burned: 135 (million)
% 11.87/2.66 % (4083869)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=37674976:st=3:i=13193:sd=3:ss=axioms_2986 on theBenchmark for (2986ds/13193Mi)
% 11.87/2.66 % (4083868)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=3111696452:st=8:i=592:sd=3:ep=RST:ss=axioms_2987 on theBenchmark for (2987ds/592Mi)
% 11.87/2.66 % (4083828)First to succeed.
% 11.87/2.66 % (4083828)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4083822"
% 11.87/2.66 % (4083851)Also succeeded, but the first one will report.
% 11.87/2.66 % (4083868)Instruction limit reached!
% 11.87/2.66 % (4083868)------------------------------
% 11.87/2.66 % (4083868)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.87/2.66 % (4083868)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.87/2.66 % (4083868)CaDiCaL version: 2.1.3
% 11.87/2.66 % (4083868)Termination reason: Instruction limit
% 11.87/2.66 % (4083868)Termination phase: Saturation
% 11.87/2.66 % (4083868)Time elapsed: 0.311 s
% 11.87/2.66 % (4083868)Peak memory usage: 93 MB
% 11.87/2.66 % (4083868)Instructions burned: 594 (million)
% 11.87/2.66 % (4083828)Refutation found. Thanks to Tanya!
% 11.87/2.66 % SZS status Theorem for theBenchmark
% 11.87/2.66 % SZS output start Proof for theBenchmark
% See solution above
% 13.30/2.86 % (4083828)------------------------------
% 13.30/2.86 % (4083828)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.30/2.86 % (4083828)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.30/2.86 % (4083828)CaDiCaL version: 2.1.3
% 13.30/2.86 % (4083828)Termination reason: Refutation
% 13.30/2.86 % (4083828)Time elapsed: 1.369 s
% 13.30/2.86 % (4083828)Peak memory usage: 139 MB
% 13.30/2.86 % (4083828)Instructions burned: 2070 (million)
% 13.30/2.86 % (4083828)------------------------------
% 13.30/2.86 % (4083828)------------------------------
% 13.30/2.86 % (4083822)Success in time 1.8 s
% 13.30/2.86 % Vampire exiting
%------------------------------------------------------------------------------