%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU450+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 12:49:11 PM UTC 2026
% Result : Theorem 6.45s 1.95s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 29
% Syntax : Number of formulae : 184 ( 42 unt; 20 def)
% Number of atoms : 516 ( 42 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 621 ( 289 ~; 285 |; 16 &)
% ( 15 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 12 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 14 con; 0-4 aty)
% Number of variables : 150 ( 1 sgn 145 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(X0))
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(X1))
=> ! [X4] :
( m2_relset_1(X4,X0,X1)
=> ( k8_relset_2(X0,X1,X2,X4) = k8_relset_2(X0,X1,k8_relset_2(X1,X0,k8_relset_2(X0,X1,X2,X4),k6_relset_1(X0,X1,X4)),X4)
& k8_relset_2(X1,X0,X3,k6_relset_1(X0,X1,X4)) = k8_relset_2(X1,X0,k8_relset_2(X0,X1,k8_relset_2(X1,X0,X3,k6_relset_1(X0,X1,X4)),X4),k6_relset_1(X0,X1,X4)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_relset_2) ).
fof(f2,negated_conjecture,
~ ! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(X0))
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(X1))
=> ! [X4] :
( m2_relset_1(X4,X0,X1)
=> ( k8_relset_2(X0,X1,X2,X4) = k8_relset_2(X0,X1,k8_relset_2(X1,X0,k8_relset_2(X0,X1,X2,X4),k6_relset_1(X0,X1,X4)),X4)
& k8_relset_2(X1,X0,X3,k6_relset_1(X0,X1,X4)) = k8_relset_2(X1,X0,k8_relset_2(X0,X1,k8_relset_2(X1,X0,X3,k6_relset_1(X0,X1,X4)),X4),k6_relset_1(X0,X1,X4)) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f6,axiom,
! [X0,X1] :
( X0 = X1
<=> ( r1_tarski(X0,X1)
& r1_tarski(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f15,axiom,
! [X0,X1,X2] :
( m1_relset_1(X2,X0,X1)
=> m2_relset_1(k6_relset_1(X0,X1,X2),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relset_1) ).
fof(f18,axiom,
! [X0,X1,X2,X3] :
( ( m1_subset_1(X2,k1_zfmisc_1(X0))
& m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) )
=> m1_subset_1(k8_relset_2(X0,X1,X2,X3),k1_zfmisc_1(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_relset_2) ).
fof(f24,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/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f47,axiom,
! [X0,X1,X2] :
( m2_relset_1(X2,X0,X1)
<=> m1_relset_1(X2,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f48,axiom,
! [X0,X1] : r1_tarski(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f51,axiom,
! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(X0))
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(X0))
=> ! [X4] :
( m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
=> ( r1_tarski(X2,X3)
=> r1_tarski(k8_relset_2(X0,X1,X3,X4),k8_relset_2(X0,X1,X2,X4)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_relset_2) ).
fof(f55,axiom,
! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(X0))
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(X1))
=> ! [X4] :
( m2_relset_1(X4,X0,X1)
=> ( r1_tarski(X2,k8_relset_2(X1,X0,X3,k6_relset_1(X0,X1,X4)))
<=> r1_tarski(X3,k8_relset_2(X0,X1,X2,X4)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_relset_2) ).
fof(f59,plain,
! [X0] : r1_tarski(X0,X0),
inference(rectify,[],[f48]) ).
fof(f66,plain,
? [X0,X1,X2] :
( ? [X3] :
( ? [X4] :
( ( k8_relset_2(X0,X1,X2,X4) != k8_relset_2(X0,X1,k8_relset_2(X1,X0,k8_relset_2(X0,X1,X2,X4),k6_relset_1(X0,X1,X4)),X4)
| k8_relset_2(X1,X0,X3,k6_relset_1(X0,X1,X4)) != k8_relset_2(X1,X0,k8_relset_2(X0,X1,k8_relset_2(X1,X0,X3,k6_relset_1(X0,X1,X4)),X4),k6_relset_1(X0,X1,X4)) )
& m2_relset_1(X4,X0,X1) )
& m1_subset_1(X3,k1_zfmisc_1(X1)) )
& m1_subset_1(X2,k1_zfmisc_1(X0)) ),
inference(ennf_transformation,[],[f2]) ).
fof(f74,plain,
! [X0,X1,X2] :
( m2_relset_1(k6_relset_1(X0,X1,X2),X1,X0)
| ~ m1_relset_1(X2,X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f76,plain,
! [X0,X1,X2,X3] :
( m1_subset_1(k8_relset_2(X0,X1,X2,X3),k1_zfmisc_1(X1))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) ),
inference(ennf_transformation,[],[f18]) ).
fof(f77,plain,
! [X0,X1,X2,X3] :
( m1_subset_1(k8_relset_2(X0,X1,X2,X3),k1_zfmisc_1(X1))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) ),
inference(flattening,[],[f76]) ).
fof(f80,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,[],[f24]) ).
fof(f95,plain,
! [X0,X1,X2] :
( ! [X3] :
( ! [X4] :
( r1_tarski(k8_relset_2(X0,X1,X3,X4),k8_relset_2(X0,X1,X2,X4))
| ~ r1_tarski(X2,X3)
| ~ m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) )
| ~ m1_subset_1(X3,k1_zfmisc_1(X0)) )
| ~ m1_subset_1(X2,k1_zfmisc_1(X0)) ),
inference(ennf_transformation,[],[f51]) ).
fof(f96,plain,
! [X0,X1,X2] :
( ! [X3] :
( ! [X4] :
( r1_tarski(k8_relset_2(X0,X1,X3,X4),k8_relset_2(X0,X1,X2,X4))
| ~ r1_tarski(X2,X3)
| ~ m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) )
| ~ m1_subset_1(X3,k1_zfmisc_1(X0)) )
| ~ m1_subset_1(X2,k1_zfmisc_1(X0)) ),
inference(flattening,[],[f95]) ).
fof(f100,plain,
! [X0,X1,X2] :
( ! [X3] :
( ! [X4] :
( ( r1_tarski(X2,k8_relset_2(X1,X0,X3,k6_relset_1(X0,X1,X4)))
<=> r1_tarski(X3,k8_relset_2(X0,X1,X2,X4)) )
| ~ m2_relset_1(X4,X0,X1) )
| ~ m1_subset_1(X3,k1_zfmisc_1(X1)) )
| ~ m1_subset_1(X2,k1_zfmisc_1(X0)) ),
inference(ennf_transformation,[],[f55]) ).
fof(f104,plain,
( ( k8_relset_2(sK0,sK1,sK2,sK4) != k8_relset_2(sK0,sK1,k8_relset_2(sK1,sK0,k8_relset_2(sK0,sK1,sK2,sK4),k6_relset_1(sK0,sK1,sK4)),sK4)
| k8_relset_2(sK1,sK0,sK3,k6_relset_1(sK0,sK1,sK4)) != k8_relset_2(sK1,sK0,k8_relset_2(sK0,sK1,k8_relset_2(sK1,sK0,sK3,k6_relset_1(sK0,sK1,sK4)),sK4),k6_relset_1(sK0,sK1,sK4)) )
& m2_relset_1(sK4,sK0,sK1)
& m1_subset_1(sK3,k1_zfmisc_1(sK1))
& m1_subset_1(sK2,k1_zfmisc_1(sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f66]) ).
fof(f105,plain,
! [X0,X1] :
( ( X0 = X1
| ~ r1_tarski(X0,X1)
| ~ r1_tarski(X1,X0) )
& ( ( r1_tarski(X0,X1)
& r1_tarski(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f106,plain,
! [X0,X1] :
( ( X0 = X1
| ~ r1_tarski(X0,X1)
| ~ r1_tarski(X1,X0) )
& ( ( r1_tarski(X0,X1)
& r1_tarski(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f105]) ).
fof(f117,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,[],[f47]) ).
fof(f119,plain,
! [X0,X1,X2] :
( ! [X3] :
( ! [X4] :
( ( ( r1_tarski(X2,k8_relset_2(X1,X0,X3,k6_relset_1(X0,X1,X4)))
| ~ r1_tarski(X3,k8_relset_2(X0,X1,X2,X4)) )
& ( r1_tarski(X3,k8_relset_2(X0,X1,X2,X4))
| ~ r1_tarski(X2,k8_relset_2(X1,X0,X3,k6_relset_1(X0,X1,X4))) ) )
| ~ m2_relset_1(X4,X0,X1) )
| ~ m1_subset_1(X3,k1_zfmisc_1(X1)) )
| ~ m1_subset_1(X2,k1_zfmisc_1(X0)) ),
inference(nnf_transformation,[],[f100]) ).
fof(f120,plain,
m1_subset_1(sK2,k1_zfmisc_1(sK0)),
inference(cnf_transformation,[],[f104]) ).
fof(f121,plain,
m1_subset_1(sK3,k1_zfmisc_1(sK1)),
inference(cnf_transformation,[],[f104]) ).
fof(f122,plain,
m2_relset_1(sK4,sK0,sK1),
inference(cnf_transformation,[],[f104]) ).
fof(f123,plain,
( k8_relset_2(sK0,sK1,sK2,sK4) != k8_relset_2(sK0,sK1,k8_relset_2(sK1,sK0,k8_relset_2(sK0,sK1,sK2,sK4),k6_relset_1(sK0,sK1,sK4)),sK4)
| k8_relset_2(sK1,sK0,sK3,k6_relset_1(sK0,sK1,sK4)) != k8_relset_2(sK1,sK0,k8_relset_2(sK0,sK1,k8_relset_2(sK1,sK0,sK3,k6_relset_1(sK0,sK1,sK4)),sK4),k6_relset_1(sK0,sK1,sK4)) ),
inference(cnf_transformation,[],[f104]) ).
fof(f129,plain,
! [X0,X1] :
( ~ r1_tarski(X1,X0)
| ~ r1_tarski(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f106]) ).
fof(f135,plain,
! [X2,X0,X1] :
( m2_relset_1(k6_relset_1(X0,X1,X2),X1,X0)
| ~ m1_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f137,plain,
! [X2,X3,X0,X1] :
( m1_subset_1(k8_relset_2(X0,X1,X2,X3),k1_zfmisc_1(X1))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) ),
inference(cnf_transformation,[],[f77]) ).
fof(f140,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,[],[f80]) ).
fof(f171,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X2,X0,X1)
| m1_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f117]) ).
fof(f173,plain,
! [X0] : r1_tarski(X0,X0),
inference(cnf_transformation,[],[f59]) ).
fof(f176,plain,
! [X2,X3,X0,X1,X4] :
( r1_tarski(k8_relset_2(X0,X1,X3,X4),k8_relset_2(X0,X1,X2,X4))
| ~ r1_tarski(X2,X3)
| ~ m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m1_subset_1(X3,k1_zfmisc_1(X0))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0)) ),
inference(cnf_transformation,[],[f96]) ).
fof(f181,plain,
! [X2,X3,X0,X1,X4] :
( ~ r1_tarski(X2,k8_relset_2(X1,X0,X3,k6_relset_1(X0,X1,X4)))
| r1_tarski(X3,k8_relset_2(X0,X1,X2,X4))
| ~ m2_relset_1(X4,X0,X1)
| ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0)) ),
inference(cnf_transformation,[],[f119]) ).
fof(f182,plain,
! [X2,X3,X0,X1,X4] :
( r1_tarski(X2,k8_relset_2(X1,X0,X3,k6_relset_1(X0,X1,X4)))
| ~ r1_tarski(X3,k8_relset_2(X0,X1,X2,X4))
| ~ m2_relset_1(X4,X0,X1)
| ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0)) ),
inference(cnf_transformation,[],[f119]) ).
fof(f188,definition,
sF15 = k8_relset_2(sK0,sK1,sK2,sK4),
introduced(definition,[new_symbols(definition,[sF15])],[function_definition]) ).
fof(f189,plain,
k8_relset_2(sK0,sK1,sK2,sK4) = sF15,
inference(reorient_equations,[],[f188]) ).
fof(f190,definition,
sF16 = k6_relset_1(sK0,sK1,sK4),
introduced(definition,[new_symbols(definition,[sF16])],[function_definition]) ).
fof(f191,plain,
k6_relset_1(sK0,sK1,sK4) = sF16,
inference(reorient_equations,[],[f190]) ).
fof(f192,definition,
sF17 = k8_relset_2(sK1,sK0,sF15,sF16),
introduced(definition,[new_symbols(definition,[sF17])],[function_definition]) ).
fof(f193,plain,
k8_relset_2(sK1,sK0,sF15,sF16) = sF17,
inference(reorient_equations,[],[f192]) ).
fof(f194,definition,
sF18 = k8_relset_2(sK0,sK1,sF17,sK4),
introduced(definition,[new_symbols(definition,[sF18])],[function_definition]) ).
fof(f195,plain,
k8_relset_2(sK0,sK1,sF17,sK4) = sF18,
inference(reorient_equations,[],[f194]) ).
fof(f196,definition,
sF19 = k8_relset_2(sK1,sK0,sK3,sF16),
introduced(definition,[new_symbols(definition,[sF19])],[function_definition]) ).
fof(f197,plain,
k8_relset_2(sK1,sK0,sK3,sF16) = sF19,
inference(reorient_equations,[],[f196]) ).
fof(f198,definition,
sF20 = k8_relset_2(sK0,sK1,sF19,sK4),
introduced(definition,[new_symbols(definition,[sF20])],[function_definition]) ).
fof(f199,plain,
k8_relset_2(sK0,sK1,sF19,sK4) = sF20,
inference(reorient_equations,[],[f198]) ).
fof(f200,definition,
sF21 = k8_relset_2(sK1,sK0,sF20,sF16),
introduced(definition,[new_symbols(definition,[sF21])],[function_definition]) ).
fof(f201,plain,
k8_relset_2(sK1,sK0,sF20,sF16) = sF21,
inference(reorient_equations,[],[f200]) ).
fof(f202,plain,
( sF15 != sF18
| sF19 != sF21 ),
inference(definition_folding,[],[f123,f201,f191,f199,f197,f191,f197,f191,f195,f193,f191,f189,f189]) ).
fof(f203,definition,
sF22 = k1_zfmisc_1(sK1),
introduced(definition,[new_symbols(definition,[sF22])],[function_definition]) ).
fof(f204,plain,
k1_zfmisc_1(sK1) = sF22,
inference(reorient_equations,[],[f203]) ).
fof(f205,plain,
m1_subset_1(sK3,sF22),
inference(definition_folding,[],[f121,f204]) ).
fof(f206,definition,
sF23 = k1_zfmisc_1(sK0),
introduced(definition,[new_symbols(definition,[sF23])],[function_definition]) ).
fof(f207,plain,
k1_zfmisc_1(sK0) = sF23,
inference(reorient_equations,[],[f206]) ).
fof(f208,plain,
m1_subset_1(sK2,sF23),
inference(definition_folding,[],[f120,f207]) ).
fof(f210,definition,
( spl24_1
<=> sF19 = sF21 ),
introduced(definition,[new_symbols(definition,[spl24_1])],[avatar_definition]) ).
fof(f212,plain,
( sF19 != sF21
| spl24_1 ),
inference(avatar_component_clause,[],[f210]) ).
fof(f214,definition,
( spl24_2
<=> sF15 = sF18 ),
introduced(definition,[new_symbols(definition,[spl24_2])],[avatar_definition]) ).
fof(f217,plain,
( ~ spl24_1
| ~ spl24_2 ),
inference(avatar_split_clause,[],[f202,f214,f210]) ).
fof(f218,plain,
( m1_subset_1(sF15,k1_zfmisc_1(sK1))
| ~ m1_subset_1(sK2,k1_zfmisc_1(sK0))
| ~ m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1))) ),
inference(superposition,[],[f137,f189]) ).
fof(f220,plain,
( m1_subset_1(sF20,k1_zfmisc_1(sK1))
| ~ m1_subset_1(sF19,k1_zfmisc_1(sK0))
| ~ m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1))) ),
inference(superposition,[],[f137,f199]) ).
fof(f221,plain,
( m1_subset_1(sF19,k1_zfmisc_1(sK0))
| ~ m1_subset_1(sK3,k1_zfmisc_1(sK1))
| ~ m1_subset_1(sF16,k1_zfmisc_1(k2_zfmisc_1(sK1,sK0))) ),
inference(superposition,[],[f137,f197]) ).
fof(f223,plain,
( m1_subset_1(sF17,k1_zfmisc_1(sK0))
| ~ m1_subset_1(sF15,k1_zfmisc_1(sK1))
| ~ m1_subset_1(sF16,k1_zfmisc_1(k2_zfmisc_1(sK1,sK0))) ),
inference(superposition,[],[f137,f193]) ).
fof(f226,plain,
( m1_subset_1(sF17,sF23)
| ~ m1_subset_1(sF15,k1_zfmisc_1(sK1))
| ~ m1_subset_1(sF16,k1_zfmisc_1(k2_zfmisc_1(sK1,sK0))) ),
inference(forward_demodulation,[],[f223,f207]) ).
fof(f228,plain,
( m1_subset_1(sF19,sF23)
| ~ m1_subset_1(sK3,k1_zfmisc_1(sK1))
| ~ m1_subset_1(sF16,k1_zfmisc_1(k2_zfmisc_1(sK1,sK0))) ),
inference(forward_demodulation,[],[f221,f207]) ).
fof(f229,plain,
( m1_subset_1(sF20,sF22)
| ~ m1_subset_1(sF19,k1_zfmisc_1(sK0))
| ~ m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1))) ),
inference(forward_demodulation,[],[f220,f204]) ).
fof(f231,plain,
( m1_subset_1(sF15,sF22)
| ~ m1_subset_1(sK2,k1_zfmisc_1(sK0))
| ~ m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1))) ),
inference(forward_demodulation,[],[f218,f204]) ).
fof(f232,plain,
( ~ m1_subset_1(sF15,sF22)
| m1_subset_1(sF17,sF23)
| ~ m1_subset_1(sF16,k1_zfmisc_1(k2_zfmisc_1(sK1,sK0))) ),
inference(forward_demodulation,[],[f226,f204]) ).
fof(f234,plain,
( ~ m1_subset_1(sK3,sF22)
| m1_subset_1(sF19,sF23)
| ~ m1_subset_1(sF16,k1_zfmisc_1(k2_zfmisc_1(sK1,sK0))) ),
inference(forward_demodulation,[],[f228,f204]) ).
fof(f235,plain,
( ~ m1_subset_1(sF19,sF23)
| m1_subset_1(sF20,sF22)
| ~ m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1))) ),
inference(forward_demodulation,[],[f229,f207]) ).
fof(f237,plain,
( ~ m1_subset_1(sK2,sF23)
| m1_subset_1(sF15,sF22)
| ~ m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1))) ),
inference(forward_demodulation,[],[f231,f207]) ).
fof(f239,definition,
( spl24_3
<=> m1_subset_1(sF16,k1_zfmisc_1(k2_zfmisc_1(sK1,sK0))) ),
introduced(definition,[new_symbols(definition,[spl24_3])],[avatar_definition]) ).
fof(f240,plain,
( m1_subset_1(sF16,k1_zfmisc_1(k2_zfmisc_1(sK1,sK0)))
| ~ spl24_3 ),
inference(avatar_component_clause,[],[f239]) ).
fof(f241,plain,
( ~ m1_subset_1(sF16,k1_zfmisc_1(k2_zfmisc_1(sK1,sK0)))
| spl24_3 ),
inference(avatar_component_clause,[],[f239]) ).
fof(f243,definition,
( spl24_4
<=> m1_subset_1(sF17,sF23) ),
introduced(definition,[new_symbols(definition,[spl24_4])],[avatar_definition]) ).
fof(f245,plain,
( m1_subset_1(sF17,sF23)
| ~ spl24_4 ),
inference(avatar_component_clause,[],[f243]) ).
fof(f247,definition,
( spl24_5
<=> m1_subset_1(sF15,sF22) ),
introduced(definition,[new_symbols(definition,[spl24_5])],[avatar_definition]) ).
fof(f248,plain,
( m1_subset_1(sF15,sF22)
| ~ spl24_5 ),
inference(avatar_component_clause,[],[f247]) ).
fof(f250,plain,
( ~ spl24_3
| spl24_4
| ~ spl24_5 ),
inference(avatar_split_clause,[],[f232,f247,f243,f239]) ).
fof(f256,definition,
( spl24_7
<=> m1_subset_1(sF20,sF22) ),
introduced(definition,[new_symbols(definition,[spl24_7])],[avatar_definition]) ).
fof(f257,plain,
( m1_subset_1(sF20,sF22)
| ~ spl24_7 ),
inference(avatar_component_clause,[],[f256]) ).
fof(f260,plain,
( m1_subset_1(sF19,sF23)
| ~ m1_subset_1(sF16,k1_zfmisc_1(k2_zfmisc_1(sK1,sK0))) ),
inference(forward_subsumption_resolution,[],[f234,f205]) ).
fof(f262,definition,
( spl24_8
<=> m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1))) ),
introduced(definition,[new_symbols(definition,[spl24_8])],[avatar_definition]) ).
fof(f263,plain,
( m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))
| ~ spl24_8 ),
inference(avatar_component_clause,[],[f262]) ).
fof(f264,plain,
( ~ m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))
| spl24_8 ),
inference(avatar_component_clause,[],[f262]) ).
fof(f266,definition,
( spl24_9
<=> m1_subset_1(sF19,sF23) ),
introduced(definition,[new_symbols(definition,[spl24_9])],[avatar_definition]) ).
fof(f267,plain,
( m1_subset_1(sF19,sF23)
| ~ spl24_9 ),
inference(avatar_component_clause,[],[f266]) ).
fof(f269,plain,
( ~ spl24_8
| spl24_7
| ~ spl24_9 ),
inference(avatar_split_clause,[],[f235,f266,f256,f262]) ).
fof(f275,plain,
( m1_subset_1(sF15,sF22)
| ~ m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1))) ),
inference(forward_subsumption_resolution,[],[f237,f208]) ).
fof(f276,plain,
( ~ spl24_3
| spl24_9 ),
inference(avatar_split_clause,[],[f260,f266,f239]) ).
fof(f277,plain,
( ~ spl24_8
| spl24_5 ),
inference(avatar_split_clause,[],[f275,f247,f262]) ).
fof(f279,plain,
! [X0,X1] :
( r1_tarski(X0,k8_relset_2(sK1,sK0,X1,sF16))
| ~ r1_tarski(X1,k8_relset_2(sK0,sK1,X0,sK4))
| ~ m2_relset_1(sK4,sK0,sK1)
| ~ m1_subset_1(X1,k1_zfmisc_1(sK1))
| ~ m1_subset_1(X0,k1_zfmisc_1(sK0)) ),
inference(superposition,[],[f182,f191]) ).
fof(f280,plain,
! [X0,X1] :
( r1_tarski(X0,k8_relset_2(sK1,sK0,X1,sF16))
| ~ r1_tarski(X1,k8_relset_2(sK0,sK1,X0,sK4))
| ~ m1_subset_1(X1,k1_zfmisc_1(sK1))
| ~ m1_subset_1(X0,k1_zfmisc_1(sK0)) ),
inference(forward_subsumption_resolution,[],[f279,f122]) ).
fof(f281,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,sF22)
| r1_tarski(X0,k8_relset_2(sK1,sK0,X1,sF16))
| ~ r1_tarski(X1,k8_relset_2(sK0,sK1,X0,sK4))
| ~ m1_subset_1(X0,k1_zfmisc_1(sK0)) ),
inference(forward_demodulation,[],[f280,f204]) ).
fof(f282,plain,
! [X0,X1] :
( ~ r1_tarski(X1,k8_relset_2(sK0,sK1,X0,sK4))
| ~ m1_subset_1(X1,sF22)
| r1_tarski(X0,k8_relset_2(sK1,sK0,X1,sF16))
| ~ m1_subset_1(X0,sF23) ),
inference(forward_demodulation,[],[f281,f207]) ).
fof(f283,plain,
! [X0] :
( ~ r1_tarski(X0,sF15)
| ~ m1_subset_1(X0,sF22)
| r1_tarski(sK2,k8_relset_2(sK1,sK0,X0,sF16))
| ~ m1_subset_1(sK2,sF23) ),
inference(superposition,[],[f282,f189]) ).
fof(f285,plain,
! [X0] :
( ~ r1_tarski(X0,sF20)
| ~ m1_subset_1(X0,sF22)
| r1_tarski(sF19,k8_relset_2(sK1,sK0,X0,sF16))
| ~ m1_subset_1(sF19,sF23) ),
inference(superposition,[],[f282,f199]) ).
fof(f287,definition,
( spl24_11
<=> ! [X0] :
( ~ r1_tarski(X0,sF20)
| r1_tarski(sF19,k8_relset_2(sK1,sK0,X0,sF16))
| ~ m1_subset_1(X0,sF22) ) ),
introduced(definition,[new_symbols(definition,[spl24_11])],[avatar_definition]) ).
fof(f288,plain,
( ! [X0] :
( r1_tarski(sF19,k8_relset_2(sK1,sK0,X0,sF16))
| ~ r1_tarski(X0,sF20)
| ~ m1_subset_1(X0,sF22) )
| ~ spl24_11 ),
inference(avatar_component_clause,[],[f287]) ).
fof(f289,plain,
( ~ spl24_9
| spl24_11 ),
inference(avatar_split_clause,[],[f285,f287,f266]) ).
fof(f294,plain,
! [X0] :
( r1_tarski(sK2,k8_relset_2(sK1,sK0,X0,sF16))
| ~ m1_subset_1(X0,sF22)
| ~ r1_tarski(X0,sF15) ),
inference(forward_subsumption_resolution,[],[f283,f208]) ).
fof(f297,plain,
( r1_tarski(sK2,sF17)
| ~ m1_subset_1(sF15,sF22)
| ~ r1_tarski(sF15,sF15) ),
inference(superposition,[],[f294,f193]) ).
fof(f298,plain,
( r1_tarski(sK2,sF17)
| ~ m1_subset_1(sF15,sF22) ),
inference(forward_subsumption_resolution,[],[f297,f173]) ).
fof(f310,definition,
( spl24_15
<=> r1_tarski(sK2,sF17) ),
introduced(definition,[new_symbols(definition,[spl24_15])],[avatar_definition]) ).
fof(f312,plain,
( r1_tarski(sK2,sF17)
| ~ spl24_15 ),
inference(avatar_component_clause,[],[f310]) ).
fof(f313,plain,
( ~ spl24_5
| spl24_15 ),
inference(avatar_split_clause,[],[f298,f310,f247]) ).
fof(f327,plain,
( ~ m2_relset_1(sK4,sK0,sK1)
| spl24_8 ),
inference(resolution,[],[f140,f264]) ).
fof(f328,plain,
( ~ m2_relset_1(sF16,sK1,sK0)
| spl24_3 ),
inference(resolution,[],[f140,f241]) ).
fof(f332,plain,
( $false
| spl24_8 ),
inference(forward_subsumption_resolution,[],[f327,f122]) ).
fof(f333,plain,
spl24_8,
inference(avatar_contradiction_clause,[],[f332]) ).
fof(f344,plain,
! [X0] :
( r1_tarski(sF21,k8_relset_2(sK1,sK0,X0,sF16))
| ~ r1_tarski(X0,sF20)
| ~ m1_subset_1(sF16,k1_zfmisc_1(k2_zfmisc_1(sK1,sK0)))
| ~ m1_subset_1(sF20,k1_zfmisc_1(sK1))
| ~ m1_subset_1(X0,k1_zfmisc_1(sK1)) ),
inference(superposition,[],[f176,f201]) ).
fof(f346,plain,
! [X0] :
( r1_tarski(k8_relset_2(sK0,sK1,X0,sK4),sF15)
| ~ r1_tarski(sK2,X0)
| ~ m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))
| ~ m1_subset_1(X0,k1_zfmisc_1(sK0))
| ~ m1_subset_1(sK2,k1_zfmisc_1(sK0)) ),
inference(superposition,[],[f176,f189]) ).
fof(f354,plain,
( ! [X0] :
( r1_tarski(k8_relset_2(sK0,sK1,X0,sK4),sF15)
| ~ r1_tarski(sK2,X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(sK0))
| ~ m1_subset_1(sK2,k1_zfmisc_1(sK0)) )
| ~ spl24_8 ),
inference(forward_subsumption_resolution,[],[f346,f263]) ).
fof(f361,plain,
( ! [X0] :
( ~ m1_subset_1(X0,sF23)
| r1_tarski(k8_relset_2(sK0,sK1,X0,sK4),sF15)
| ~ r1_tarski(sK2,X0)
| ~ m1_subset_1(sK2,k1_zfmisc_1(sK0)) )
| ~ spl24_8 ),
inference(forward_demodulation,[],[f354,f207]) ).
fof(f368,plain,
( ! [X0] :
( ~ m1_subset_1(sK2,sF23)
| ~ m1_subset_1(X0,sF23)
| r1_tarski(k8_relset_2(sK0,sK1,X0,sK4),sF15)
| ~ r1_tarski(sK2,X0) )
| ~ spl24_8 ),
inference(forward_demodulation,[],[f361,f207]) ).
fof(f371,plain,
( ! [X0] :
( r1_tarski(k8_relset_2(sK0,sK1,X0,sK4),sF15)
| ~ m1_subset_1(X0,sF23)
| ~ r1_tarski(sK2,X0) )
| ~ spl24_8 ),
inference(forward_subsumption_resolution,[],[f368,f208]) ).
fof(f384,plain,
! [X0,X1] :
( ~ r1_tarski(X0,k8_relset_2(sK1,sK0,X1,sF16))
| r1_tarski(X1,k8_relset_2(sK0,sK1,X0,sK4))
| ~ m2_relset_1(sK4,sK0,sK1)
| ~ m1_subset_1(X1,k1_zfmisc_1(sK1))
| ~ m1_subset_1(X0,k1_zfmisc_1(sK0)) ),
inference(superposition,[],[f181,f191]) ).
fof(f387,plain,
! [X0,X1] :
( ~ r1_tarski(X0,k8_relset_2(sK1,sK0,X1,sF16))
| r1_tarski(X1,k8_relset_2(sK0,sK1,X0,sK4))
| ~ m1_subset_1(X1,k1_zfmisc_1(sK1))
| ~ m1_subset_1(X0,k1_zfmisc_1(sK0)) ),
inference(forward_subsumption_resolution,[],[f384,f122]) ).
fof(f389,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,sF22)
| ~ r1_tarski(X0,k8_relset_2(sK1,sK0,X1,sF16))
| r1_tarski(X1,k8_relset_2(sK0,sK1,X0,sK4))
| ~ m1_subset_1(X0,k1_zfmisc_1(sK0)) ),
inference(forward_demodulation,[],[f387,f204]) ).
fof(f390,plain,
! [X0,X1] :
( ~ r1_tarski(X0,k8_relset_2(sK1,sK0,X1,sF16))
| ~ m1_subset_1(X1,sF22)
| ~ m1_subset_1(X0,sF23)
| r1_tarski(X1,k8_relset_2(sK0,sK1,X0,sK4)) ),
inference(forward_demodulation,[],[f389,f207]) ).
fof(f393,plain,
! [X0] :
( ~ r1_tarski(X0,sF19)
| ~ m1_subset_1(sK3,sF22)
| ~ m1_subset_1(X0,sF23)
| r1_tarski(sK3,k8_relset_2(sK0,sK1,X0,sK4)) ),
inference(superposition,[],[f390,f197]) ).
fof(f395,plain,
! [X0] :
( ~ r1_tarski(X0,sF17)
| ~ m1_subset_1(sF15,sF22)
| ~ m1_subset_1(X0,sF23)
| r1_tarski(sF15,k8_relset_2(sK0,sK1,X0,sK4)) ),
inference(superposition,[],[f390,f193]) ).
fof(f397,plain,
( ! [X0] :
( r1_tarski(sF15,k8_relset_2(sK0,sK1,X0,sK4))
| ~ m1_subset_1(X0,sF23)
| ~ r1_tarski(X0,sF17) )
| ~ spl24_5 ),
inference(forward_subsumption_resolution,[],[f395,f248]) ).
fof(f402,plain,
! [X0] :
( r1_tarski(sK3,k8_relset_2(sK0,sK1,X0,sK4))
| ~ m1_subset_1(X0,sF23)
| ~ r1_tarski(X0,sF19) ),
inference(forward_subsumption_resolution,[],[f393,f205]) ).
fof(f409,plain,
( r1_tarski(sK3,sF20)
| ~ m1_subset_1(sF19,sF23)
| ~ r1_tarski(sF19,sF19) ),
inference(superposition,[],[f402,f199]) ).
fof(f434,plain,
( r1_tarski(sF15,sF18)
| ~ m1_subset_1(sF17,sF23)
| ~ r1_tarski(sF17,sF17)
| ~ spl24_5 ),
inference(superposition,[],[f397,f195]) ).
fof(f441,plain,
( r1_tarski(sF18,sF15)
| ~ m1_subset_1(sF17,sF23)
| ~ r1_tarski(sK2,sF17)
| ~ spl24_8 ),
inference(superposition,[],[f371,f195]) ).
fof(f443,plain,
m1_relset_1(sK4,sK0,sK1),
inference(resolution,[],[f171,f122]) ).
fof(f488,plain,
( m2_relset_1(sF16,sK1,sK0)
| ~ m1_relset_1(sK4,sK0,sK1) ),
inference(superposition,[],[f135,f191]) ).
fof(f499,plain,
( ~ m1_relset_1(sK4,sK0,sK1)
| spl24_3 ),
inference(forward_subsumption_resolution,[],[f488,f328]) ).
fof(f500,plain,
( $false
| spl24_3 ),
inference(forward_subsumption_resolution,[],[f499,f443]) ).
fof(f501,plain,
spl24_3,
inference(avatar_contradiction_clause,[],[f500]) ).
fof(f505,plain,
( r1_tarski(sK3,sF20)
| ~ r1_tarski(sF19,sF19)
| ~ spl24_9 ),
inference(forward_subsumption_resolution,[],[f409,f267]) ).
fof(f510,plain,
( r1_tarski(sF15,sF18)
| ~ r1_tarski(sF17,sF17)
| ~ spl24_4
| ~ spl24_5 ),
inference(forward_subsumption_resolution,[],[f434,f245]) ).
fof(f511,plain,
( r1_tarski(sF18,sF15)
| ~ r1_tarski(sK2,sF17)
| ~ spl24_4
| ~ spl24_8 ),
inference(forward_subsumption_resolution,[],[f441,f245]) ).
fof(f516,plain,
( ! [X0] :
( r1_tarski(sF21,k8_relset_2(sK1,sK0,X0,sF16))
| ~ r1_tarski(X0,sF20)
| ~ m1_subset_1(sF20,k1_zfmisc_1(sK1))
| ~ m1_subset_1(X0,k1_zfmisc_1(sK1)) )
| ~ spl24_3 ),
inference(forward_subsumption_resolution,[],[f344,f240]) ).
fof(f530,plain,
( r1_tarski(sK3,sF20)
| ~ spl24_9 ),
inference(forward_subsumption_resolution,[],[f505,f173]) ).
fof(f546,plain,
( r1_tarski(sF15,sF18)
| ~ spl24_4
| ~ spl24_5 ),
inference(forward_subsumption_resolution,[],[f510,f173]) ).
fof(f547,plain,
( r1_tarski(sF18,sF15)
| ~ spl24_4
| ~ spl24_8
| ~ spl24_15 ),
inference(forward_subsumption_resolution,[],[f511,f312]) ).
fof(f552,plain,
( ! [X0] :
( ~ m1_subset_1(sF20,sF22)
| r1_tarski(sF21,k8_relset_2(sK1,sK0,X0,sF16))
| ~ r1_tarski(X0,sF20)
| ~ m1_subset_1(X0,k1_zfmisc_1(sK1)) )
| ~ spl24_3 ),
inference(forward_demodulation,[],[f516,f204]) ).
fof(f559,plain,
( ! [X0] :
( r1_tarski(sF21,k8_relset_2(sK1,sK0,X0,sF16))
| ~ r1_tarski(X0,sF20)
| ~ m1_subset_1(X0,k1_zfmisc_1(sK1)) )
| ~ spl24_3
| ~ spl24_7 ),
inference(forward_subsumption_resolution,[],[f552,f257]) ).
fof(f567,plain,
( ! [X0] :
( r1_tarski(sF21,k8_relset_2(sK1,sK0,X0,sF16))
| ~ m1_subset_1(X0,sF22)
| ~ r1_tarski(X0,sF20) )
| ~ spl24_3
| ~ spl24_7 ),
inference(forward_demodulation,[],[f559,f204]) ).
fof(f592,definition,
( spl24_34
<=> r1_tarski(sF19,sF21) ),
introduced(definition,[new_symbols(definition,[spl24_34])],[avatar_definition]) ).
fof(f594,plain,
( r1_tarski(sF19,sF21)
| ~ spl24_34 ),
inference(avatar_component_clause,[],[f592]) ).
fof(f597,plain,
( ~ r1_tarski(sF15,sF18)
| sF15 = sF18
| ~ spl24_4
| ~ spl24_8
| ~ spl24_15 ),
inference(resolution,[],[f547,f129]) ).
fof(f598,plain,
( sF15 = sF18
| ~ spl24_4
| ~ spl24_5
| ~ spl24_8
| ~ spl24_15 ),
inference(forward_subsumption_resolution,[],[f597,f546]) ).
fof(f599,plain,
( spl24_2
| ~ spl24_4
| ~ spl24_5
| ~ spl24_8
| ~ spl24_15 ),
inference(avatar_split_clause,[],[f598,f310,f262,f247,f243,f214]) ).
fof(f618,plain,
( r1_tarski(sF19,sF21)
| ~ r1_tarski(sF20,sF20)
| ~ m1_subset_1(sF20,sF22)
| ~ spl24_11 ),
inference(superposition,[],[f288,f201]) ).
fof(f622,plain,
( r1_tarski(sF19,sF21)
| ~ m1_subset_1(sF20,sF22)
| ~ spl24_11 ),
inference(forward_subsumption_resolution,[],[f618,f173]) ).
fof(f625,plain,
( r1_tarski(sF19,sF21)
| ~ spl24_7
| ~ spl24_11 ),
inference(forward_subsumption_resolution,[],[f622,f257]) ).
fof(f628,plain,
( spl24_34
| ~ spl24_7
| ~ spl24_11 ),
inference(avatar_split_clause,[],[f625,f287,f256,f592]) ).
fof(f664,plain,
( ~ r1_tarski(sF21,sF19)
| sF19 = sF21
| ~ spl24_34 ),
inference(resolution,[],[f594,f129]) ).
fof(f665,plain,
( ~ r1_tarski(sF21,sF19)
| spl24_1
| ~ spl24_34 ),
inference(forward_subsumption_resolution,[],[f664,f212]) ).
fof(f763,plain,
( r1_tarski(sF21,sF19)
| ~ m1_subset_1(sK3,sF22)
| ~ r1_tarski(sK3,sF20)
| ~ spl24_3
| ~ spl24_7 ),
inference(superposition,[],[f567,f197]) ).
fof(f767,plain,
( ~ m1_subset_1(sK3,sF22)
| ~ r1_tarski(sK3,sF20)
| spl24_1
| ~ spl24_3
| ~ spl24_7
| ~ spl24_34 ),
inference(forward_subsumption_resolution,[],[f763,f665]) ).
fof(f769,plain,
( ~ r1_tarski(sK3,sF20)
| spl24_1
| ~ spl24_3
| ~ spl24_7
| ~ spl24_34 ),
inference(forward_subsumption_resolution,[],[f767,f205]) ).
fof(f771,plain,
( $false
| spl24_1
| ~ spl24_3
| ~ spl24_7
| ~ spl24_9
| ~ spl24_34 ),
inference(forward_subsumption_resolution,[],[f769,f530]) ).
fof(f772,plain,
( spl24_1
| ~ spl24_3
| ~ spl24_7
| ~ spl24_9
| ~ spl24_34 ),
inference(avatar_contradiction_clause,[],[f771]) ).
cnf(s1,plain,
( ~ spl24_1
| ~ spl24_2 ),
inference(sat_conversion,[],[f217]) ).
cnf(s2,plain,
( ~ spl24_3
| spl24_4
| ~ spl24_5 ),
inference(sat_conversion,[],[f250]) ).
cnf(s4,plain,
( spl24_7
| ~ spl24_8
| ~ spl24_9 ),
inference(sat_conversion,[],[f269]) ).
cnf(s6,plain,
( ~ spl24_3
| spl24_9 ),
inference(sat_conversion,[],[f276]) ).
cnf(s7,plain,
( spl24_5
| ~ spl24_8 ),
inference(sat_conversion,[],[f277]) ).
cnf(s8,plain,
( ~ spl24_9
| spl24_11 ),
inference(sat_conversion,[],[f289]) ).
cnf(s11,plain,
( ~ spl24_5
| spl24_15 ),
inference(sat_conversion,[],[f313]) ).
cnf(s13,plain,
spl24_8,
inference(sat_conversion,[],[f333]) ).
cnf(s21,plain,
spl24_3,
inference(sat_conversion,[],[f501]) ).
cnf(s26,plain,
( spl24_2
| ~ spl24_4
| ~ spl24_5
| ~ spl24_8
| ~ spl24_15 ),
inference(sat_conversion,[],[f599]) ).
cnf(s28,plain,
( ~ spl24_7
| ~ spl24_11
| spl24_34 ),
inference(sat_conversion,[],[f628]) ).
cnf(s36,plain,
( spl24_1
| ~ spl24_3
| ~ spl24_7
| ~ spl24_9
| ~ spl24_34 ),
inference(sat_conversion,[],[f772]) ).
cnf(s38,plain,
spl24_5,
inference(rat,[],[s7,s13]) ).
cnf(s39,plain,
spl24_15,
inference(rat,[],[s11,s38]) ).
cnf(s40,plain,
spl24_9,
inference(rat,[],[s6,s21]) ).
cnf(s41,plain,
spl24_11,
inference(rat,[],[s8,s40]) ).
cnf(s43,plain,
spl24_7,
inference(rat,[],[s4,s40,s13]) ).
cnf(s44,plain,
spl24_34,
inference(rat,[],[s28,s41,s43]) ).
cnf(s45,plain,
spl24_1,
inference(rat,[],[s36,s44,s40,s21,s43]) ).
cnf(s48,plain,
spl24_4,
inference(rat,[],[s2,s38,s21]) ).
cnf(s49,plain,
spl24_2,
inference(rat,[],[s26,s39,s13,s38,s48]) ).
cnf(s52,plain,
$false,
inference(rat,[],[s1,s49,s45]) ).
fof(f773,plain,
$false,
inference(avatar_sat_refutation,[],[s52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU450+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n008.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
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 05:37:25 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.45/1.95 % (1947181)Detected formulas, will run a generic FOF schedule.
% 6.45/1.95 % (1947190)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3795851215:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.45/1.95 % (1947188)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=4040860640:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.45/1.95 % (1947191)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1416021983:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.45/1.95 % (1947187)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=68956147:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.45/1.95 % (1947186)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=1024271517:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.45/1.95 % (1947192)dis-21_1_sil=8000:lcm=predicate:random_seed=807831648: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)
% 6.45/1.95 % (1947189)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1951642305:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.45/1.95 % (1947189)Refutation not found, incomplete strategy
% 6.45/1.95 % (1947189)------------------------------
% 6.45/1.95 % (1947189)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.45/1.95 % (1947189)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.45/1.95 % (1947189)CaDiCaL version: 2.1.3
% 6.45/1.95 % (1947189)Termination reason: Refutation not found, incomplete strategy
% 6.45/1.95 % (1947189)Time elapsed: 0.002 s
% 6.45/1.95 % (1947189)Peak memory usage: 88 MB
% 6.45/1.95 % (1947189)Instructions burned: 2 (million)
% 6.45/1.95 % (1947190)Instruction limit reached!
% 6.45/1.95 % (1947190)------------------------------
% 6.45/1.95 % (1947190)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.45/1.95 % (1947190)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.45/1.95 % (1947190)CaDiCaL version: 2.1.3
% 6.45/1.95 % (1947190)Termination reason: Instruction limit
% 6.45/1.95 % (1947190)Termination phase: Saturation
% 6.45/1.95 % (1947190)Time elapsed: 0.040 s
% 6.45/1.95 % (1947190)Peak memory usage: 88 MB
% 6.45/1.95 % (1947190)Instructions burned: 126 (million)
% 6.45/1.95 % (1947192)Instruction limit reached!
% 6.45/1.95 % (1947192)------------------------------
% 6.45/1.95 % (1947192)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.45/1.95 % (1947192)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.45/1.95 % (1947192)CaDiCaL version: 2.1.3
% 6.45/1.95 % (1947192)Termination reason: Instruction limit
% 6.45/1.95 % (1947192)Termination phase: Saturation
% 6.45/1.95 % (1947192)Time elapsed: 0.077 s
% 6.45/1.95 % (1947192)Peak memory usage: 91 MB
% 6.45/1.95 % (1947192)Instructions burned: 130 (million)
% 6.45/1.95 % (1947191)Instruction limit reached!
% 6.45/1.95 % (1947191)------------------------------
% 6.45/1.95 % (1947191)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.45/1.95 % (1947191)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.45/1.95 % (1947191)CaDiCaL version: 2.1.3
% 6.45/1.95 % (1947191)Termination reason: Instruction limit
% 6.45/1.95 % (1947191)Termination phase: Saturation
% 6.45/1.95 % (1947191)Time elapsed: 0.100 s
% 6.45/1.95 % (1947191)Peak memory usage: 89 MB
% 6.45/1.95 % (1947191)Instructions burned: 139 (million)
% 6.45/1.95 % (1947200)lrs+10_1_sil=8000:sp=occurrence:random_seed=3648939261:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 6.45/1.95 % (1947200)Instruction limit reached!
% 6.45/1.95 % (1947200)------------------------------
% 6.45/1.95 % (1947200)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.45/1.95 % (1947200)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.45/1.95 % (1947200)CaDiCaL version: 2.1.3
% 6.45/1.95 % (1947200)Termination reason: Instruction limit
% 6.45/1.95 % (1947200)Termination phase: Saturation
% 6.45/1.95 % (1947200)Time elapsed: 0.101 s
% 6.45/1.95 % (1947200)Peak memory usage: 93 MB
% 6.45/1.95 % (1947200)Instructions burned: 288 (million)
% 6.45/1.95 % (1947201)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3271576972:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.45/1.95 % (1947203)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2569254040:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.45/1.95 % (1947189)------------------------------
% 6.45/1.95 % (1947189)------------------------------
% 6.45/1.95 % (1947204)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=1521439457:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 6.45/1.95 % (1947201)Instruction limit reached!
% 6.45/1.95 % (1947201)------------------------------
% 6.45/1.95 % (1947201)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.45/1.95 % (1947201)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.45/1.95 % (1947201)CaDiCaL version: 2.1.3
% 6.45/1.95 % (1947201)Termination reason: Instruction limit
% 6.45/1.95 % (1947201)Termination phase: Saturation
% 6.45/1.95 % (1947201)Time elapsed: 0.087 s
% 6.45/1.95 % (1947201)Peak memory usage: 90 MB
% 6.45/1.95 % (1947201)Instructions burned: 157 (million)
% 6.45/1.95 % (1947204)Instruction limit reached!
% 6.45/1.95 % (1947204)------------------------------
% 6.45/1.95 % (1947204)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.45/1.95 % (1947204)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.45/1.95 % (1947204)CaDiCaL version: 2.1.3
% 6.45/1.95 % (1947204)Termination reason: Instruction limit
% 6.45/1.95 % (1947204)Termination phase: Saturation
% 6.45/1.95 % (1947204)Time elapsed: 0.073 s
% 6.45/1.95 % (1947204)Peak memory usage: 91 MB
% 6.45/1.95 % (1947204)Instructions burned: 249 (million)
% 6.45/1.95 % (1947207)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2071821764:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 6.45/1.95 % (1947207)Refutation not found, incomplete strategy
% 6.45/1.95 % (1947207)------------------------------
% 6.45/1.95 % (1947207)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.45/1.95 % (1947207)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.45/1.95 % (1947207)CaDiCaL version: 2.1.3
% 6.45/1.95 % (1947207)Termination reason: Refutation not found, incomplete strategy
% 6.45/1.95 % (1947207)Time elapsed: 0.004 s
% 6.45/1.95 % (1947207)Peak memory usage: 88 MB
% 6.45/1.95 % (1947207)Instructions burned: 4 (million)
% 6.45/1.95 % (1947209)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1522569681:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 6.45/1.95 % (1947210)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=915362167:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 6.45/1.95 % (1947203)Instruction limit reached!
% 6.45/1.95 % (1947203)------------------------------
% 6.45/1.95 % (1947203)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.45/1.95 % (1947203)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.45/1.95 % (1947203)CaDiCaL version: 2.1.3
% 6.45/1.95 % (1947203)Termination reason: Instruction limit
% 6.45/1.95 % (1947203)Termination phase: Saturation
% 6.45/1.95 % (1947203)Time elapsed: 0.223 s
% 6.45/1.95 % (1947203)Peak memory usage: 91 MB
% 6.45/1.95 % (1947203)Instructions burned: 325 (million)
% 6.45/1.95 % (1947210)Instruction limit reached!
% 6.45/1.95 % (1947210)------------------------------
% 6.45/1.95 % (1947210)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.45/1.95 % (1947210)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.45/1.95 % (1947210)CaDiCaL version: 2.1.3
% 6.45/1.95 % (1947210)Termination reason: Instruction limit
% 6.45/1.95 % (1947210)Termination phase: Saturation
% 6.45/1.95 % (1947210)Time elapsed: 0.040 s
% 6.45/1.95 % (1947210)Peak memory usage: 89 MB
% 6.45/1.95 % (1947210)Instructions burned: 115 (million)
% 6.45/1.95 % (1947215)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=866502099:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 6.45/1.95 % (1947214)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3358888402:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 6.45/1.95 % (1947215)Instruction limit reached!
% 6.45/1.95 % (1947215)------------------------------
% 6.45/1.95 % (1947215)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.45/1.95 % (1947215)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.45/1.95 % (1947215)CaDiCaL version: 2.1.3
% 6.45/1.95 % (1947215)Termination reason: Instruction limit
% 6.45/1.95 % (1947215)Termination phase: Saturation
% 6.45/1.95 % (1947215)Time elapsed: 0.037 s
% 6.45/1.95 % (1947215)Peak memory usage: 89 MB
% 6.45/1.95 % (1947215)Instructions burned: 115 (million)
% 6.45/1.95 % (1947207)------------------------------
% 6.45/1.95 % (1947207)------------------------------
% 6.45/1.95 % (1947214)Instruction limit reached!
% 6.45/1.95 % (1947214)------------------------------
% 6.45/1.95 % (1947214)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.45/1.95 % (1947214)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.45/1.95 % (1947214)CaDiCaL version: 2.1.3
% 6.45/1.95 % (1947214)Termination reason: Instruction limit
% 6.45/1.95 % (1947214)Termination phase: Saturation
% 6.45/1.95 % (1947214)Time elapsed: 0.069 s
% 6.45/1.95 % (1947214)Peak memory usage: 89 MB
% 6.45/1.95 % (1947214)Instructions burned: 128 (million)
% 6.45/1.95 % (1947186)First to succeed.
% 6.45/1.95 % (1947186)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1947181"
% 6.45/1.95 % (1947218)lrs+10_1_sil=8000:sp=occurrence:random_seed=2163401336:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 6.45/1.95 % (1947187)Also succeeded, but the first one will report.
% 6.45/1.95 % (1947219)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3812443865:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 6.45/1.95 % (1947220)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=154479951:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 6.45/1.95 % (1947219)Refutation not found, incomplete strategy
% 6.45/1.95 % (1947219)------------------------------
% 6.45/1.95 % (1947219)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.45/1.95 % (1947219)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.45/1.95 % (1947219)CaDiCaL version: 2.1.3
% 6.45/1.95 % (1947219)Termination reason: Refutation not found, incomplete strategy
% 6.45/1.95 % (1947219)Time elapsed: 0.004 s
% 6.45/1.95 % (1947219)Peak memory usage: 88 MB
% 6.45/1.95 % (1947219)Instructions burned: 4 (million)
% 6.45/1.95 % (1947186)Refutation found. Thanks to Tanya!
% 6.45/1.95 % SZS status Theorem for theBenchmark
% 6.45/1.95 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/2.14 % (1947186)------------------------------
% 0.17/2.14 % (1947186)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/2.14 % (1947186)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/2.14 % (1947186)CaDiCaL version: 2.1.3
% 0.17/2.14 % (1947186)Termination reason: Refutation
% 0.17/2.14 % (1947186)Time elapsed: 0.688 s
% 0.17/2.14 % (1947186)Peak memory usage: 130 MB
% 0.17/2.14 % (1947186)Instructions burned: 1016 (million)
% 0.17/2.14 % (1947186)------------------------------
% 0.17/2.14 % (1947186)------------------------------
% 0.17/2.14 % (1947181)Success in time 1.094 s
% 0.17/2.14 % Vampire exiting
%------------------------------------------------------------------------------