%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU441+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 : n009.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 12:49:05 PM UTC 2026
% Result : Theorem 5.42s 1.67s
% Output : Refutation 6.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 23
% Syntax : Number of formulae : 131 ( 39 unt; 11 def)
% Number of atoms : 274 ( 55 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 254 ( 111 ~; 108 |; 12 &)
% ( 8 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 7 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 10 con; 0-5 aty)
% Number of variables : 162 ( 0 sgn 157 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1,X2,X3] :
( m2_relset_1(X3,X0,X1)
=> ! [X4] :
( m2_relset_1(X4,X1,X2)
=> ( k2_funct_5(k9_relset_2(X0,X1,X2,X3,X4)) = k10_relset_1(X1,X2,X4,k2_funct_5(X3))
& r1_tarski(k2_funct_5(k9_relset_2(X0,X1,X2,X3,X4)),k2_funct_5(X4)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_relset_2) ).
fof(f2,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( m2_relset_1(X3,X0,X1)
=> ! [X4] :
( m2_relset_1(X4,X1,X2)
=> ( k2_funct_5(k9_relset_2(X0,X1,X2,X3,X4)) = k10_relset_1(X1,X2,X4,k2_funct_5(X3))
& r1_tarski(k2_funct_5(k9_relset_2(X0,X1,X2,X3,X4)),k2_funct_5(X4)) ) ) ),
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,X2,X3] :
( m1_relset_1(X2,X0,X1)
=> m1_subset_1(k10_relset_1(X0,X1,X2,X3),k1_zfmisc_1(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_relset_1) ).
fof(f19,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(f22,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(f45,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(f48,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(f49,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(f51,axiom,
! [X0,X1,X2] :
( v1_relat_1(X2)
=> ( r1_tarski(X0,X1)
=> r1_tarski(k9_relat_1(X2,X0),k9_relat_1(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t156_relat_1) ).
fof(f52,axiom,
! [X0,X1] :
( v1_relat_1(X1)
=> ! [X2] :
( v1_relat_1(X2)
=> k9_relat_1(k5_relat_1(X1,X2),X0) = k9_relat_1(X2,k9_relat_1(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t159_relat_1) ).
fof(f56,axiom,
! [X0,X1] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
<=> r1_tarski(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f58,axiom,
! [X0,X1,X2] :
( m2_relset_1(X2,X1,X0)
=> ( k1_funct_5(X2) = k10_relset_1(X0,X1,k6_relset_1(X1,X0,X2),X0)
& k2_funct_5(X2) = k10_relset_1(X1,X0,X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_relset_2) ).
fof(f66,plain,
? [X0,X1,X2,X3] :
( ? [X4] :
( ( k2_funct_5(k9_relset_2(X0,X1,X2,X3,X4)) != k10_relset_1(X1,X2,X4,k2_funct_5(X3))
| ~ r1_tarski(k2_funct_5(k9_relset_2(X0,X1,X2,X3,X4)),k2_funct_5(X4)) )
& m2_relset_1(X4,X1,X2) )
& m2_relset_1(X3,X0,X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f69,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(f70,plain,
! [X0,X1,X2,X3] :
( m1_subset_1(k10_relset_1(X0,X1,X2,X3),k1_zfmisc_1(X1))
| ~ m1_relset_1(X2,X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f76,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,[],[f19]) ).
fof(f77,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,[],[f76]) ).
fof(f78,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,[],[f22]) ).
fof(f95,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,[],[f45]) ).
fof(f98,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,[],[f48]) ).
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(flattening,[],[f98]) ).
fof(f100,plain,
! [X0,X1,X2] :
( r1_tarski(k9_relat_1(X2,X0),k9_relat_1(X2,X1))
| ~ r1_tarski(X0,X1)
| ~ v1_relat_1(X2) ),
inference(ennf_transformation,[],[f51]) ).
fof(f101,plain,
! [X0,X1,X2] :
( r1_tarski(k9_relat_1(X2,X0),k9_relat_1(X2,X1))
| ~ r1_tarski(X0,X1)
| ~ v1_relat_1(X2) ),
inference(flattening,[],[f100]) ).
fof(f102,plain,
! [X0,X1] :
( ! [X2] :
( k9_relat_1(k5_relat_1(X1,X2),X0) = k9_relat_1(X2,k9_relat_1(X1,X0))
| ~ v1_relat_1(X2) )
| ~ v1_relat_1(X1) ),
inference(ennf_transformation,[],[f52]) ).
fof(f109,plain,
! [X0,X1,X2] :
( ( k1_funct_5(X2) = k10_relset_1(X0,X1,k6_relset_1(X1,X0,X2),X0)
& k2_funct_5(X2) = k10_relset_1(X1,X0,X2,X1) )
| ~ m2_relset_1(X2,X1,X0) ),
inference(ennf_transformation,[],[f58]) ).
fof(f114,plain,
( ( k2_funct_5(k9_relset_2(sK0,sK1,sK2,sK3,sK4)) != k10_relset_1(sK1,sK2,sK4,k2_funct_5(sK3))
| ~ r1_tarski(k2_funct_5(k9_relset_2(sK0,sK1,sK2,sK3,sK4)),k2_funct_5(sK4)) )
& m2_relset_1(sK4,sK1,sK2)
& m2_relset_1(sK3,sK0,sK1) ),
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(f123,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,[],[f49]) ).
fof(f124,plain,
! [X0,X1] :
( ( m1_subset_1(X0,k1_zfmisc_1(X1))
| ~ r1_tarski(X0,X1) )
& ( r1_tarski(X0,X1)
| ~ m1_subset_1(X0,k1_zfmisc_1(X1)) ) ),
inference(nnf_transformation,[],[f56]) ).
fof(f125,plain,
m2_relset_1(sK3,sK0,sK1),
inference(cnf_transformation,[],[f114]) ).
fof(f126,plain,
m2_relset_1(sK4,sK1,sK2),
inference(cnf_transformation,[],[f114]) ).
fof(f127,plain,
( k2_funct_5(k9_relset_2(sK0,sK1,sK2,sK3,sK4)) != k10_relset_1(sK1,sK2,sK4,k2_funct_5(sK3))
| ~ r1_tarski(k2_funct_5(k9_relset_2(sK0,sK1,sK2,sK3,sK4)),k2_funct_5(sK4)) ),
inference(cnf_transformation,[],[f114]) ).
fof(f130,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| v1_relat_1(X2) ),
inference(cnf_transformation,[],[f69]) ).
fof(f131,plain,
! [X2,X3,X0,X1] :
( m1_subset_1(k10_relset_1(X0,X1,X2,X3),k1_zfmisc_1(X1))
| ~ m1_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f136,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,[],[f77]) ).
fof(f137,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,[],[f78]) ).
fof(f171,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,[],[f95]) ).
fof(f174,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,[],[f99]) ).
fof(f175,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X2,X0,X1)
| m1_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f123]) ).
fof(f178,plain,
! [X2,X0,X1] :
( r1_tarski(k9_relat_1(X2,X0),k9_relat_1(X2,X1))
| ~ r1_tarski(X0,X1)
| ~ v1_relat_1(X2) ),
inference(cnf_transformation,[],[f101]) ).
fof(f179,plain,
! [X2,X0,X1] :
( ~ v1_relat_1(X2)
| k9_relat_1(k5_relat_1(X1,X2),X0) = k9_relat_1(X2,k9_relat_1(X1,X0))
| ~ v1_relat_1(X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f184,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,k1_zfmisc_1(X1))
| r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f124]) ).
fof(f187,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X2,X1,X0)
| k2_funct_5(X2) = k10_relset_1(X1,X0,X2,X1) ),
inference(cnf_transformation,[],[f109]) ).
fof(f193,definition,
sF13 = k9_relset_2(sK0,sK1,sK2,sK3,sK4),
introduced(definition,[new_symbols(definition,[sF13])],[function_definition]) ).
fof(f194,plain,
k9_relset_2(sK0,sK1,sK2,sK3,sK4) = sF13,
inference(reorient_equations,[],[f193]) ).
fof(f195,definition,
sF14 = k2_funct_5(sF13),
introduced(definition,[new_symbols(definition,[sF14])],[function_definition]) ).
fof(f196,plain,
k2_funct_5(sF13) = sF14,
inference(reorient_equations,[],[f195]) ).
fof(f197,definition,
sF15 = k2_funct_5(sK3),
introduced(definition,[new_symbols(definition,[sF15])],[function_definition]) ).
fof(f198,plain,
k2_funct_5(sK3) = sF15,
inference(reorient_equations,[],[f197]) ).
fof(f199,definition,
sF16 = k10_relset_1(sK1,sK2,sK4,sF15),
introduced(definition,[new_symbols(definition,[sF16])],[function_definition]) ).
fof(f200,plain,
k10_relset_1(sK1,sK2,sK4,sF15) = sF16,
inference(reorient_equations,[],[f199]) ).
fof(f201,definition,
sF17 = k2_funct_5(sK4),
introduced(definition,[new_symbols(definition,[sF17])],[function_definition]) ).
fof(f202,plain,
k2_funct_5(sK4) = sF17,
inference(reorient_equations,[],[f201]) ).
fof(f203,plain,
( sF14 != sF16
| ~ r1_tarski(sF14,sF17) ),
inference(definition_folding,[],[f127,f202,f196,f194,f200,f198,f196,f194]) ).
fof(f205,definition,
( spl18_1
<=> r1_tarski(sF14,sF17) ),
introduced(definition,[new_symbols(definition,[spl18_1])],[avatar_definition]) ).
fof(f207,plain,
( ~ r1_tarski(sF14,sF17)
| spl18_1 ),
inference(avatar_component_clause,[],[f205]) ).
fof(f209,definition,
( spl18_2
<=> sF14 = sF16 ),
introduced(definition,[new_symbols(definition,[spl18_2])],[avatar_definition]) ).
fof(f212,plain,
( ~ spl18_1
| ~ spl18_2 ),
inference(avatar_split_clause,[],[f203,f209,f205]) ).
fof(f213,plain,
k2_funct_5(sK4) = k10_relset_1(sK1,sK2,sK4,sK1),
inference(resolution,[],[f187,f126]) ).
fof(f214,plain,
k2_funct_5(sK3) = k10_relset_1(sK0,sK1,sK3,sK0),
inference(resolution,[],[f187,f125]) ).
fof(f215,plain,
sF15 = k10_relset_1(sK0,sK1,sK3,sK0),
inference(forward_demodulation,[],[f214,f198]) ).
fof(f216,plain,
sF17 = k10_relset_1(sK1,sK2,sK4,sK1),
inference(forward_demodulation,[],[f213,f202]) ).
fof(f217,plain,
m1_relset_1(sK4,sK1,sK2),
inference(resolution,[],[f175,f126]) ).
fof(f218,plain,
m1_relset_1(sK3,sK0,sK1),
inference(resolution,[],[f175,f125]) ).
fof(f219,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X0,X1,X2)
| v1_relat_1(X0) ),
inference(resolution,[],[f137,f130]) ).
fof(f220,plain,
v1_relat_1(sK4),
inference(resolution,[],[f219,f126]) ).
fof(f221,plain,
v1_relat_1(sK3),
inference(resolution,[],[f219,f125]) ).
fof(f222,plain,
! [X2,X3,X0,X1,X4] :
( ~ m1_subset_1(X0,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))
| k9_relset_2(X1,X2,X3,X0,X4) = k5_relat_1(X0,X4)
| ~ m2_relset_1(X4,X2,X3) ),
inference(resolution,[],[f174,f137]) ).
fof(f230,plain,
( m2_relset_1(sF13,sK0,sK2)
| ~ m1_subset_1(sK3,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))
| ~ m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK1,sK2))) ),
inference(superposition,[],[f136,f194]) ).
fof(f232,definition,
( spl18_3
<=> m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK1,sK2))) ),
introduced(definition,[new_symbols(definition,[spl18_3])],[avatar_definition]) ).
fof(f234,plain,
( ~ m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK1,sK2)))
| spl18_3 ),
inference(avatar_component_clause,[],[f232]) ).
fof(f236,definition,
( spl18_4
<=> m1_subset_1(sK3,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1))) ),
introduced(definition,[new_symbols(definition,[spl18_4])],[avatar_definition]) ).
fof(f237,plain,
( m1_subset_1(sK3,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))
| ~ spl18_4 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f238,plain,
( ~ m1_subset_1(sK3,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))
| spl18_4 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f240,definition,
( spl18_5
<=> m2_relset_1(sF13,sK0,sK2) ),
introduced(definition,[new_symbols(definition,[spl18_5])],[avatar_definition]) ).
fof(f242,plain,
( m2_relset_1(sF13,sK0,sK2)
| ~ spl18_5 ),
inference(avatar_component_clause,[],[f240]) ).
fof(f243,plain,
( ~ spl18_3
| ~ spl18_4
| spl18_5 ),
inference(avatar_split_clause,[],[f230,f240,f236,f232]) ).
fof(f247,plain,
! [X0] : k10_relset_1(sK1,sK2,sK4,X0) = k9_relat_1(sK4,X0),
inference(resolution,[],[f171,f217]) ).
fof(f248,plain,
! [X0] : k10_relset_1(sK0,sK1,sK3,X0) = k9_relat_1(sK3,X0),
inference(resolution,[],[f171,f218]) ).
fof(f251,plain,
sF16 = k9_relat_1(sK4,sF15),
inference(superposition,[],[f200,f247]) ).
fof(f252,plain,
sF17 = k9_relat_1(sK4,sK1),
inference(superposition,[],[f216,f247]) ).
fof(f257,plain,
! [X0] :
( r1_tarski(k9_relat_1(sK4,X0),sF17)
| ~ r1_tarski(X0,sK1)
| ~ v1_relat_1(sK4) ),
inference(superposition,[],[f178,f252]) ).
fof(f260,plain,
! [X0] :
( r1_tarski(k9_relat_1(sK4,X0),sF17)
| ~ r1_tarski(X0,sK1) ),
inference(forward_subsumption_resolution,[],[f257,f220]) ).
fof(f262,plain,
sF15 = k9_relat_1(sK3,sK0),
inference(superposition,[],[f215,f248]) ).
fof(f270,definition,
( spl18_6
<=> r1_tarski(sF15,sK1) ),
introduced(definition,[new_symbols(definition,[spl18_6])],[avatar_definition]) ).
fof(f271,plain,
( r1_tarski(sF15,sK1)
| ~ spl18_6 ),
inference(avatar_component_clause,[],[f270]) ).
fof(f272,plain,
( ~ r1_tarski(sF15,sK1)
| spl18_6 ),
inference(avatar_component_clause,[],[f270]) ).
fof(f279,plain,
( ~ m2_relset_1(sK4,sK1,sK2)
| spl18_3 ),
inference(resolution,[],[f234,f137]) ).
fof(f280,plain,
( $false
| spl18_3 ),
inference(forward_subsumption_resolution,[],[f279,f126]) ).
fof(f281,plain,
spl18_3,
inference(avatar_contradiction_clause,[],[f280]) ).
fof(f284,plain,
( ~ m2_relset_1(sK3,sK0,sK1)
| spl18_4 ),
inference(resolution,[],[f238,f137]) ).
fof(f285,plain,
( $false
| spl18_4 ),
inference(forward_subsumption_resolution,[],[f284,f125]) ).
fof(f286,plain,
spl18_4,
inference(avatar_contradiction_clause,[],[f285]) ).
fof(f289,plain,
( m1_relset_1(sF13,sK0,sK2)
| ~ spl18_5 ),
inference(resolution,[],[f242,f175]) ).
fof(f290,plain,
( k2_funct_5(sF13) = k10_relset_1(sK0,sK2,sF13,sK0)
| ~ spl18_5 ),
inference(resolution,[],[f242,f187]) ).
fof(f291,plain,
( sF14 = k10_relset_1(sK0,sK2,sF13,sK0)
| ~ spl18_5 ),
inference(forward_demodulation,[],[f290,f196]) ).
fof(f296,plain,
! [X0,X1] :
( ~ v1_relat_1(X0)
| k9_relat_1(k5_relat_1(X0,sK4),X1) = k9_relat_1(sK4,k9_relat_1(X0,X1)) ),
inference(resolution,[],[f179,f220]) ).
fof(f303,plain,
! [X0] : k9_relat_1(k5_relat_1(sK3,sK4),X0) = k9_relat_1(sK4,k9_relat_1(sK3,X0)),
inference(resolution,[],[f296,f221]) ).
fof(f378,plain,
( ! [X0] : k9_relat_1(sF13,X0) = k10_relset_1(sK0,sK2,sF13,X0)
| ~ spl18_5 ),
inference(resolution,[],[f289,f171]) ).
fof(f381,plain,
( sF14 = k9_relat_1(sF13,sK0)
| ~ spl18_5 ),
inference(superposition,[],[f291,f378]) ).
fof(f391,plain,
( m1_subset_1(sF15,k1_zfmisc_1(sK1))
| ~ m1_relset_1(sK3,sK0,sK1) ),
inference(superposition,[],[f131,f215]) ).
fof(f398,plain,
m1_subset_1(sF15,k1_zfmisc_1(sK1)),
inference(forward_subsumption_resolution,[],[f391,f218]) ).
fof(f441,plain,
( ! [X0,X1] :
( ~ m2_relset_1(X1,sK1,X0)
| k9_relset_2(sK0,sK1,X0,sK3,X1) = k5_relat_1(sK3,X1) )
| ~ spl18_4 ),
inference(resolution,[],[f222,f237]) ).
fof(f455,plain,
( k9_relset_2(sK0,sK1,sK2,sK3,sK4) = k5_relat_1(sK3,sK4)
| ~ spl18_4 ),
inference(resolution,[],[f441,f126]) ).
fof(f456,plain,
( sF13 = k5_relat_1(sK3,sK4)
| ~ spl18_4 ),
inference(forward_demodulation,[],[f455,f194]) ).
fof(f458,plain,
( ! [X0] : k9_relat_1(sF13,X0) = k9_relat_1(sK4,k9_relat_1(sK3,X0))
| ~ spl18_4 ),
inference(superposition,[],[f303,f456]) ).
fof(f464,plain,
( k9_relat_1(sK4,sF15) = k9_relat_1(sF13,sK0)
| ~ spl18_4 ),
inference(superposition,[],[f458,f262]) ).
fof(f468,plain,
( ! [X0] :
( ~ r1_tarski(k9_relat_1(sK3,X0),sK1)
| r1_tarski(k9_relat_1(sF13,X0),sF17) )
| ~ spl18_4 ),
inference(superposition,[],[f260,f458]) ).
fof(f473,plain,
( sF14 = k9_relat_1(sK4,sF15)
| ~ spl18_4
| ~ spl18_5 ),
inference(forward_demodulation,[],[f464,f381]) ).
fof(f474,plain,
( sF14 = sF16
| ~ spl18_4
| ~ spl18_5 ),
inference(forward_demodulation,[],[f473,f251]) ).
fof(f475,plain,
( spl18_2
| ~ spl18_4
| ~ spl18_5 ),
inference(avatar_split_clause,[],[f474,f240,f236,f209]) ).
fof(f516,plain,
( ~ r1_tarski(sF15,sK1)
| r1_tarski(k9_relat_1(sF13,sK0),sF17)
| ~ spl18_4 ),
inference(superposition,[],[f468,f262]) ).
fof(f529,plain,
r1_tarski(sF15,sK1),
inference(resolution,[],[f184,f398]) ).
fof(f536,plain,
( $false
| spl18_6 ),
inference(forward_subsumption_resolution,[],[f529,f272]) ).
fof(f537,plain,
spl18_6,
inference(avatar_contradiction_clause,[],[f536]) ).
fof(f540,plain,
( r1_tarski(k9_relat_1(sF13,sK0),sF17)
| ~ spl18_4
| ~ spl18_6 ),
inference(forward_subsumption_resolution,[],[f516,f271]) ).
fof(f544,plain,
( r1_tarski(sF14,sF17)
| ~ spl18_4
| ~ spl18_5
| ~ spl18_6 ),
inference(forward_demodulation,[],[f540,f381]) ).
fof(f547,plain,
( $false
| spl18_1
| ~ spl18_4
| ~ spl18_5
| ~ spl18_6 ),
inference(forward_subsumption_resolution,[],[f544,f207]) ).
fof(f548,plain,
( spl18_1
| ~ spl18_4
| ~ spl18_5
| ~ spl18_6 ),
inference(avatar_contradiction_clause,[],[f547]) ).
cnf(s1,plain,
( ~ spl18_1
| ~ spl18_2 ),
inference(sat_conversion,[],[f212]) ).
cnf(s2,plain,
( ~ spl18_3
| ~ spl18_4
| spl18_5 ),
inference(sat_conversion,[],[f243]) ).
cnf(s4,plain,
spl18_3,
inference(sat_conversion,[],[f281]) ).
cnf(s5,plain,
spl18_4,
inference(sat_conversion,[],[f286]) ).
cnf(s18,plain,
( spl18_2
| ~ spl18_4
| ~ spl18_5 ),
inference(sat_conversion,[],[f475]) ).
cnf(s20,plain,
spl18_6,
inference(sat_conversion,[],[f537]) ).
cnf(s23,plain,
( spl18_1
| ~ spl18_4
| ~ spl18_5
| ~ spl18_6 ),
inference(sat_conversion,[],[f548]) ).
cnf(s25,plain,
spl18_5,
inference(rat,[],[s2,s5,s4]) ).
cnf(s27,plain,
spl18_1,
inference(rat,[],[s23,s20,s5,s25]) ).
cnf(s28,plain,
spl18_2,
inference(rat,[],[s18,s5,s25]) ).
cnf(s30,plain,
$false,
inference(rat,[],[s1,s28,s27]) ).
fof(f549,plain,
$false,
inference(avatar_sat_refutation,[],[s30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU441+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 05:30:20 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 5.42/1.67 % (2711076)Detected formulas, will run a generic FOF schedule.
% 5.42/1.67 % (2711081)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=2927271416:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.42/1.67 % (2711086)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2765095790:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.42/1.67 % (2711085)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1597694728:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.42/1.67 % (2711084)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=837088981:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.42/1.67 % (2711083)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=4199582556:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.42/1.67 % (2711082)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=2957613898:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.42/1.67 % (2711084)Refutation not found, incomplete strategy
% 5.42/1.67 % (2711084)------------------------------
% 5.42/1.67 % (2711084)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.42/1.67 % (2711084)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.42/1.67 % (2711084)CaDiCaL version: 2.1.3
% 5.42/1.67 % (2711084)Termination reason: Refutation not found, incomplete strategy
% 5.42/1.67 % (2711084)Time elapsed: 0.002 s
% 5.42/1.67 % (2711084)Peak memory usage: 88 MB
% 5.42/1.67 % (2711084)Instructions burned: 1 (million)
% 5.42/1.67 % (2711085)Refutation not found, incomplete strategy
% 5.42/1.67 % (2711085)------------------------------
% 5.42/1.67 % (2711085)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.42/1.67 % (2711085)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.42/1.67 % (2711085)CaDiCaL version: 2.1.3
% 5.42/1.67 % (2711085)Termination reason: Refutation not found, incomplete strategy
% 5.42/1.67 % (2711085)Time elapsed: 0.006 s
% 5.42/1.67 % (2711085)Peak memory usage: 88 MB
% 5.42/1.67 % (2711085)Instructions burned: 7 (million)
% 5.42/1.67 % (2711087)dis-21_1_sil=8000:lcm=predicate:random_seed=647939535: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)
% 5.42/1.67 % (2711086)Instruction limit reached!
% 5.42/1.67 % (2711086)------------------------------
% 5.42/1.67 % (2711086)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.42/1.67 % (2711086)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.42/1.67 % (2711086)CaDiCaL version: 2.1.3
% 5.42/1.67 % (2711086)Termination reason: Instruction limit
% 5.42/1.67 % (2711086)Termination phase: Saturation
% 5.42/1.67 % (2711086)Time elapsed: 0.098 s
% 5.42/1.67 % (2711086)Peak memory usage: 90 MB
% 5.42/1.67 % (2711086)Instructions burned: 140 (million)
% 5.42/1.67 % (2711087)Instruction limit reached!
% 5.42/1.67 % (2711087)------------------------------
% 5.42/1.67 % (2711087)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.42/1.67 % (2711087)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.42/1.67 % (2711087)CaDiCaL version: 2.1.3
% 5.42/1.67 % (2711087)Termination reason: Instruction limit
% 5.42/1.67 % (2711087)Termination phase: Saturation
% 5.42/1.67 % (2711087)Time elapsed: 0.079 s
% 5.42/1.67 % (2711087)Peak memory usage: 90 MB
% 5.42/1.67 % (2711087)Instructions burned: 130 (million)
% 5.42/1.67 % (2711095)lrs+10_1_sil=8000:sp=occurrence:random_seed=3955663392:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 5.42/1.67 % (2711096)lrs+10_1_sil=32000:urr=on:br=off:random_seed=121643567:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.42/1.67 % (2711085)------------------------------
% 5.42/1.67 % (2711085)------------------------------
% 5.42/1.67 % (2711084)------------------------------
% 5.42/1.67 % (2711084)------------------------------
% 5.42/1.67 % (2711096)Instruction limit reached!
% 5.42/1.67 % (2711096)------------------------------
% 5.42/1.67 % (2711096)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.42/1.67 % (2711096)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.42/1.67 % (2711096)CaDiCaL version: 2.1.3
% 5.42/1.67 % (2711096)Termination reason: Instruction limit
% 5.42/1.67 % (2711096)Termination phase: Saturation
% 5.42/1.67 % (2711096)Time elapsed: 0.092 s
% 5.42/1.67 % (2711096)Peak memory usage: 91 MB
% 5.42/1.67 % (2711096)Instructions burned: 157 (million)
% 5.42/1.67 % (2711099)lrs+1011_1_sil=32000:sp=occurrence:random_seed=516937419:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 5.42/1.67 % (2711100)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=961990999:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 5.42/1.67 % (2711081)First to succeed.
% 5.42/1.67 % (2711095)Instruction limit reached!
% 5.42/1.67 % (2711095)------------------------------
% 5.42/1.67 % (2711095)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.42/1.67 % (2711095)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.42/1.67 % (2711095)CaDiCaL version: 2.1.3
% 5.42/1.67 % (2711095)Termination reason: Instruction limit
% 5.42/1.67 % (2711095)Termination phase: Saturation
% 5.42/1.67 % (2711095)Time elapsed: 0.161 s
% 5.42/1.67 % (2711095)Peak memory usage: 92 MB
% 5.42/1.67 % (2711095)Instructions burned: 285 (million)
% 5.42/1.67 % (2711081)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2711076"
% 5.42/1.67 % (2711101)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1729836598:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 5.42/1.67 % (2711101)Refutation not found, incomplete strategy
% 5.42/1.67 % (2711101)------------------------------
% 5.42/1.67 % (2711101)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.42/1.67 % (2711101)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.42/1.67 % (2711101)CaDiCaL version: 2.1.3
% 5.42/1.67 % (2711101)Termination reason: Refutation not found, incomplete strategy
% 5.42/1.67 % (2711101)Time elapsed: 0.002 s
% 5.42/1.67 % (2711101)Peak memory usage: 89 MB
% 5.42/1.67 % (2711101)Instructions burned: 5 (million)
% 5.42/1.67 % (2711100)Instruction limit reached!
% 5.42/1.67 % (2711100)------------------------------
% 5.42/1.67 % (2711100)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.42/1.67 % (2711100)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.42/1.67 % (2711100)CaDiCaL version: 2.1.3
% 5.42/1.67 % (2711100)Termination reason: Instruction limit
% 5.42/1.67 % (2711100)Termination phase: Saturation
% 5.42/1.67 % (2711100)Time elapsed: 0.138 s
% 5.42/1.67 % (2711100)Peak memory usage: 93 MB
% 5.42/1.67 % (2711100)Instructions burned: 248 (million)
% 5.42/1.67 % (2711104)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3400791187:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 5.42/1.67 % (2711101)------------------------------
% 5.42/1.67 % (2711101)------------------------------
% 5.42/1.67 % (2711099)Instruction limit reached!
% 5.42/1.67 % (2711099)------------------------------
% 5.42/1.67 % (2711099)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.42/1.67 % (2711099)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.42/1.67 % (2711099)CaDiCaL version: 2.1.3
% 5.42/1.67 % (2711099)Termination reason: Instruction limit
% 5.42/1.67 % (2711099)Termination phase: Saturation
% 5.42/1.67 % (2711099)Time elapsed: 0.218 s
% 5.42/1.67 % (2711099)Peak memory usage: 92 MB
% 5.42/1.67 % (2711099)Instructions burned: 326 (million)
% 5.42/1.67 % (2711106)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=549184965:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 5.42/1.67 % (2711108)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=341264120:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 5.42/1.67 % (2711081)Refutation found. Thanks to Tanya!
% 5.42/1.67 % SZS status Theorem for theBenchmark
% 5.42/1.67 % SZS output start Proof for theBenchmark
% See solution above
% 6.34/1.86 % (2711081)------------------------------
% 6.34/1.86 % (2711081)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.34/1.86 % (2711081)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/1.86 % (2711081)CaDiCaL version: 2.1.3
% 6.34/1.86 % (2711081)Termination reason: Refutation
% 6.34/1.86 % (2711081)Time elapsed: 0.446 s
% 6.34/1.86 % (2711081)Peak memory usage: 130 MB
% 6.34/1.86 % (2711081)Instructions burned: 1006 (million)
% 6.34/1.86 % (2711081)------------------------------
% 6.34/1.86 % (2711081)------------------------------
% 6.34/1.86 % (2711076)Success in time 0.817 s
% 6.34/1.86 % Vampire exiting
%------------------------------------------------------------------------------