%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU220+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 12:52:27 PM UTC 2026
% Result : Theorem 1.56s 0.73s
% Output : Refutation 1.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 15
% Syntax : Number of formulae : 102 ( 30 unt; 10 def)
% Number of atoms : 400 ( 128 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 507 ( 209 ~; 203 |; 72 &)
% ( 8 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 4 prp; 0-4 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-2 aty)
% Number of variables : 91 ( 0 sgn 81 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( relation(function_inverse(X0))
& function(function_inverse(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funct_1) ).
fof(f31,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X0,relation_dom(X1))
=> apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_1) ).
fof(f35,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( X1 = function_inverse(X0)
<=> ( relation_dom(X1) = relation_rng(X0)
& ! [X2,X3] :
( ( ( in(X2,relation_rng(X0))
& X3 = apply(X1,X2) )
=> ( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) ) )
& ( ( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
=> ( in(X2,relation_rng(X0))
& X3 = apply(X1,X2) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_funct_1) ).
fof(f36,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> ( relation_rng(X0) = relation_dom(function_inverse(X0))
& relation_dom(X0) = relation_rng(function_inverse(X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_funct_1) ).
fof(f37,conjecture,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( ( one_to_one(X1)
& in(X0,relation_rng(X1)) )
=> ( X0 = apply(X1,apply(function_inverse(X1),X0))
& X0 = apply(relation_composition(function_inverse(X1),X1),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_funct_1) ).
fof(f38,negated_conjecture,
~ ! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( ( one_to_one(X1)
& in(X0,relation_rng(X1)) )
=> ( X0 = apply(X1,apply(function_inverse(X1),X0))
& X0 = apply(relation_composition(function_inverse(X1),X1),X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f52,plain,
! [X0] :
( ( relation(function_inverse(X0))
& function(function_inverse(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f53,plain,
! [X0] :
( ( relation(function_inverse(X0))
& function(function_inverse(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f52]) ).
fof(f70,plain,
! [X0,X1] :
( ! [X2] :
( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f31]) ).
fof(f71,plain,
! [X0,X1] :
( ! [X2] :
( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f70]) ).
fof(f77,plain,
! [X0] :
( ! [X1] :
( ( X1 = function_inverse(X0)
<=> ( relation_dom(X1) = relation_rng(X0)
& ! [X2,X3] :
( ( ( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
| ~ in(X2,relation_rng(X0))
| apply(X1,X2) != X3 )
& ( ( in(X2,relation_rng(X0))
& X3 = apply(X1,X2) )
| ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 ) ) ) )
| ~ relation(X1)
| ~ function(X1) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f78,plain,
! [X0] :
( ! [X1] :
( ( X1 = function_inverse(X0)
<=> ( relation_dom(X1) = relation_rng(X0)
& ! [X2,X3] :
( ( ( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
| ~ in(X2,relation_rng(X0))
| apply(X1,X2) != X3 )
& ( ( in(X2,relation_rng(X0))
& X3 = apply(X1,X2) )
| ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 ) ) ) )
| ~ relation(X1)
| ~ function(X1) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f77]) ).
fof(f79,plain,
! [X0] :
( ( relation_rng(X0) = relation_dom(function_inverse(X0))
& relation_dom(X0) = relation_rng(function_inverse(X0)) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f80,plain,
! [X0] :
( ( relation_rng(X0) = relation_dom(function_inverse(X0))
& relation_dom(X0) = relation_rng(function_inverse(X0)) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f79]) ).
fof(f81,plain,
? [X0,X1] :
( ( apply(X1,apply(function_inverse(X1),X0)) != X0
| apply(relation_composition(function_inverse(X1),X1),X0) != X0 )
& one_to_one(X1)
& in(X0,relation_rng(X1))
& relation(X1)
& function(X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f82,plain,
? [X0,X1] :
( ( apply(X1,apply(function_inverse(X1),X0)) != X0
| apply(relation_composition(function_inverse(X1),X1),X0) != X0 )
& one_to_one(X1)
& in(X0,relation_rng(X1))
& relation(X1)
& function(X1) ),
inference(flattening,[],[f81]) ).
fof(f87,definition,
! [X0,X2,X3,X1] :
( sP0(X0,X2,X3,X1)
<=> ( ( in(X2,relation_rng(X0))
& X3 = apply(X1,X2) )
| ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f88,plain,
! [X0] :
( ! [X1] :
( ( X1 = function_inverse(X0)
<=> ( relation_dom(X1) = relation_rng(X0)
& ! [X2,X3] :
( ( ( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
| ~ in(X2,relation_rng(X0))
| apply(X1,X2) != X3 )
& sP0(X0,X2,X3,X1) ) ) )
| ~ relation(X1)
| ~ function(X1) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(definition_folding,[],[f78,f87]) ).
fof(f103,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = function_inverse(X0)
| relation_rng(X0) != relation_dom(X1)
| ? [X2,X3] :
( ( ( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 )
& in(X2,relation_rng(X0))
& apply(X1,X2) = X3 )
| ~ sP0(X0,X2,X3,X1) ) )
& ( ( relation_dom(X1) = relation_rng(X0)
& ! [X2,X3] :
( ( ( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
| ~ in(X2,relation_rng(X0))
| apply(X1,X2) != X3 )
& sP0(X0,X2,X3,X1) ) )
| function_inverse(X0) != X1 ) )
| ~ relation(X1)
| ~ function(X1) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f88]) ).
fof(f104,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = function_inverse(X0)
| relation_rng(X0) != relation_dom(X1)
| ? [X2,X3] :
( ( ( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 )
& in(X2,relation_rng(X0))
& apply(X1,X2) = X3 )
| ~ sP0(X0,X2,X3,X1) ) )
& ( ( relation_dom(X1) = relation_rng(X0)
& ! [X2,X3] :
( ( ( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
| ~ in(X2,relation_rng(X0))
| apply(X1,X2) != X3 )
& sP0(X0,X2,X3,X1) ) )
| function_inverse(X0) != X1 ) )
| ~ relation(X1)
| ~ function(X1) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f103]) ).
fof(f105,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = function_inverse(X0)
| relation_rng(X0) != relation_dom(X1)
| ? [X2,X3] :
( ( ( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 )
& in(X2,relation_rng(X0))
& apply(X1,X2) = X3 )
| ~ sP0(X0,X2,X3,X1) ) )
& ( ( relation_dom(X1) = relation_rng(X0)
& ! [X4,X5] :
( ( ( in(X5,relation_dom(X0))
& apply(X0,X5) = X4 )
| ~ in(X4,relation_rng(X0))
| apply(X1,X4) != X5 )
& sP0(X0,X4,X5,X1) ) )
| function_inverse(X0) != X1 ) )
| ~ relation(X1)
| ~ function(X1) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(rectify,[],[f104]) ).
fof(f106,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = function_inverse(X0)
| relation_rng(X0) != relation_dom(X1)
| ( ( ~ in(sK13(X0,X1),relation_dom(X0))
| sK12(X0,X1) != apply(X0,sK13(X0,X1)) )
& in(sK12(X0,X1),relation_rng(X0))
& sK13(X0,X1) = apply(X1,sK12(X0,X1)) )
| ~ sP0(X0,sK12(X0,X1),sK13(X0,X1),X1) )
& ( ( relation_dom(X1) = relation_rng(X0)
& ! [X4,X5] :
( ( ( in(X5,relation_dom(X0))
& apply(X0,X5) = X4 )
| ~ in(X4,relation_rng(X0))
| apply(X1,X4) != X5 )
& sP0(X0,X4,X5,X1) ) )
| function_inverse(X0) != X1 ) )
| ~ relation(X1)
| ~ function(X1) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13]),skolemize(X2,sK12(X0,X1)),skolemize(X3,sK13(X0,X1))],[f105]) ).
fof(f107,plain,
( ( sK14 != apply(sK15,apply(function_inverse(sK15),sK14))
| sK14 != apply(relation_composition(function_inverse(sK15),sK15),sK14) )
& one_to_one(sK15)
& in(sK14,relation_rng(sK15))
& relation(sK15)
& function(sK15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15]),skolemize(X0,sK14),skolemize(X1,sK15)],[f82]) ).
fof(f114,plain,
! [X0] :
( ~ relation(X0)
| function(function_inverse(X0))
| ~ function(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f115,plain,
! [X0] :
( relation(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f157,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_dom(X1))
| apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f167,plain,
! [X0,X1,X4,X5] :
( apply(X0,X5) = X4
| ~ in(X4,relation_rng(X0))
| apply(X1,X4) != X5
| function_inverse(X0) != X1
| ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f174,plain,
! [X0] :
( ~ one_to_one(X0)
| relation_rng(X0) = relation_dom(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f175,plain,
function(sK15),
inference(cnf_transformation,[],[f107]) ).
fof(f176,plain,
relation(sK15),
inference(cnf_transformation,[],[f107]) ).
fof(f177,plain,
in(sK14,relation_rng(sK15)),
inference(cnf_transformation,[],[f107]) ).
fof(f178,plain,
one_to_one(sK15),
inference(cnf_transformation,[],[f107]) ).
fof(f179,plain,
( sK14 != apply(sK15,apply(function_inverse(sK15),sK14))
| sK14 != apply(relation_composition(function_inverse(sK15),sK15),sK14) ),
inference(cnf_transformation,[],[f107]) ).
fof(f190,plain,
! [X0,X1,X4] :
( apply(X0,apply(X1,X4)) = X4
| ~ in(X4,relation_rng(X0))
| function_inverse(X0) != X1
| ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f167]) ).
fof(f191,plain,
! [X0,X4] :
( ~ in(X4,relation_rng(X0))
| apply(X0,apply(function_inverse(X0),X4)) = X4
| ~ relation(function_inverse(X0))
| ~ function(function_inverse(X0))
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f190]) ).
fof(f193,definition,
sF16 = function_inverse(sK15),
introduced(definition,[new_symbols(definition,[sF16])],[function_definition]) ).
fof(f194,plain,
function_inverse(sK15) = sF16,
inference(reorient_equations,[],[f193]) ).
fof(f195,definition,
sF17 = apply(sF16,sK14),
introduced(definition,[new_symbols(definition,[sF17])],[function_definition]) ).
fof(f196,plain,
apply(sF16,sK14) = sF17,
inference(reorient_equations,[],[f195]) ).
fof(f197,definition,
sF18 = apply(sK15,sF17),
introduced(definition,[new_symbols(definition,[sF18])],[function_definition]) ).
fof(f198,plain,
apply(sK15,sF17) = sF18,
inference(reorient_equations,[],[f197]) ).
fof(f199,definition,
sF19 = relation_composition(sF16,sK15),
introduced(definition,[new_symbols(definition,[sF19])],[function_definition]) ).
fof(f200,plain,
relation_composition(sF16,sK15) = sF19,
inference(reorient_equations,[],[f199]) ).
fof(f201,definition,
sF20 = apply(sF19,sK14),
introduced(definition,[new_symbols(definition,[sF20])],[function_definition]) ).
fof(f202,plain,
apply(sF19,sK14) = sF20,
inference(reorient_equations,[],[f201]) ).
fof(f203,plain,
( sK14 != sF18
| sK14 != sF20 ),
inference(definition_folding,[],[f179,f202,f200,f194,f198,f196,f194]) ).
fof(f204,definition,
sF21 = relation_rng(sK15),
introduced(definition,[new_symbols(definition,[sF21])],[function_definition]) ).
fof(f205,plain,
relation_rng(sK15) = sF21,
inference(reorient_equations,[],[f204]) ).
fof(f206,plain,
in(sK14,sF21),
inference(definition_folding,[],[f177,f205]) ).
fof(f208,definition,
( spl22_1
<=> sK14 = sF20 ),
introduced(definition,[new_symbols(definition,[spl22_1])],[avatar_definition]) ).
fof(f210,plain,
( sK14 != sF20
| spl22_1 ),
inference(avatar_component_clause,[],[f208]) ).
fof(f212,definition,
( spl22_2
<=> sK14 = sF18 ),
introduced(definition,[new_symbols(definition,[spl22_2])],[avatar_definition]) ).
fof(f214,plain,
( sK14 != sF18
| spl22_2 ),
inference(avatar_component_clause,[],[f212]) ).
fof(f215,plain,
( ~ spl22_1
| ~ spl22_2 ),
inference(avatar_split_clause,[],[f203,f212,f208]) ).
fof(f275,plain,
( function(function_inverse(sK15))
| ~ function(sK15) ),
inference(resolution,[],[f114,f176]) ).
fof(f276,plain,
function(function_inverse(sK15)),
inference(forward_subsumption_resolution,[],[f275,f175]) ).
fof(f304,plain,
function(sF16),
inference(forward_demodulation,[],[f276,f194]) ).
fof(f310,plain,
( relation(sF16)
| ~ relation(sK15)
| ~ function(sK15) ),
inference(superposition,[],[f115,f194]) ).
fof(f311,plain,
( relation(sF16)
| ~ function(sK15) ),
inference(forward_subsumption_resolution,[],[f310,f176]) ).
fof(f313,plain,
relation(sF16),
inference(forward_subsumption_resolution,[],[f311,f175]) ).
fof(f594,plain,
( relation_rng(sK15) = relation_dom(function_inverse(sK15))
| ~ relation(sK15)
| ~ function(sK15) ),
inference(resolution,[],[f174,f178]) ).
fof(f597,plain,
( relation_rng(sK15) = relation_dom(function_inverse(sK15))
| ~ function(sK15) ),
inference(forward_subsumption_resolution,[],[f594,f176]) ).
fof(f599,plain,
relation_rng(sK15) = relation_dom(function_inverse(sK15)),
inference(forward_subsumption_resolution,[],[f597,f175]) ).
fof(f600,plain,
relation_rng(sK15) = relation_dom(sF16),
inference(forward_demodulation,[],[f599,f194]) ).
fof(f602,plain,
sF21 = relation_dom(sF16),
inference(superposition,[],[f205,f600]) ).
fof(f627,definition,
( spl22_24
<=> in(sK14,relation_dom(sF16)) ),
introduced(definition,[new_symbols(definition,[spl22_24])],[avatar_definition]) ).
fof(f628,plain,
( in(sK14,relation_dom(sF16))
| ~ spl22_24 ),
inference(avatar_component_clause,[],[f627]) ).
fof(f629,plain,
( ~ in(sK14,relation_dom(sF16))
| spl22_24 ),
inference(avatar_component_clause,[],[f627]) ).
fof(f664,plain,
in(sK14,relation_dom(sF16)),
inference(superposition,[],[f206,f602]) ).
fof(f665,plain,
( $false
| spl22_24 ),
inference(forward_subsumption_resolution,[],[f664,f629]) ).
fof(f666,plain,
spl22_24,
inference(avatar_contradiction_clause,[],[f665]) ).
fof(f668,plain,
( ! [X0] :
( apply(X0,apply(sF16,sK14)) = apply(relation_composition(sF16,X0),sK14)
| ~ relation(X0)
| ~ function(X0)
| ~ relation(sF16)
| ~ function(sF16) )
| ~ spl22_24 ),
inference(resolution,[],[f628,f157]) ).
fof(f672,plain,
( ! [X0] :
( apply(X0,apply(sF16,sK14)) = apply(relation_composition(sF16,X0),sK14)
| ~ relation(X0)
| ~ function(X0)
| ~ function(sF16) )
| ~ spl22_24 ),
inference(forward_subsumption_resolution,[],[f668,f313]) ).
fof(f673,plain,
( ! [X0] :
( apply(X0,apply(sF16,sK14)) = apply(relation_composition(sF16,X0),sK14)
| ~ relation(X0)
| ~ function(X0) )
| ~ spl22_24 ),
inference(forward_subsumption_resolution,[],[f672,f304]) ).
fof(f674,plain,
( ! [X0] :
( ~ relation(X0)
| apply(X0,sF17) = apply(relation_composition(sF16,X0),sK14)
| ~ function(X0) )
| ~ spl22_24 ),
inference(forward_demodulation,[],[f673,f196]) ).
fof(f695,plain,
! [X0] :
( ~ in(X0,relation_dom(sF16))
| apply(sK15,apply(function_inverse(sK15),X0)) = X0
| ~ relation(function_inverse(sK15))
| ~ function(function_inverse(sK15))
| ~ one_to_one(sK15)
| ~ relation(sK15)
| ~ function(sK15) ),
inference(superposition,[],[f191,f600]) ).
fof(f700,plain,
! [X0] :
( ~ in(X0,relation_dom(sF16))
| apply(sK15,apply(function_inverse(sK15),X0)) = X0
| ~ function(function_inverse(sK15))
| ~ one_to_one(sK15)
| ~ relation(sK15)
| ~ function(sK15) ),
inference(forward_subsumption_resolution,[],[f695,f115]) ).
fof(f703,plain,
! [X0] :
( ~ in(X0,relation_dom(sF16))
| apply(sK15,apply(function_inverse(sK15),X0)) = X0
| ~ one_to_one(sK15)
| ~ relation(sK15)
| ~ function(sK15) ),
inference(forward_subsumption_resolution,[],[f700,f114]) ).
fof(f706,plain,
! [X0] :
( ~ in(X0,relation_dom(sF16))
| apply(sK15,apply(function_inverse(sK15),X0)) = X0
| ~ relation(sK15)
| ~ function(sK15) ),
inference(forward_subsumption_resolution,[],[f703,f178]) ).
fof(f709,plain,
! [X0] :
( ~ in(X0,relation_dom(sF16))
| apply(sK15,apply(function_inverse(sK15),X0)) = X0
| ~ function(sK15) ),
inference(forward_subsumption_resolution,[],[f706,f176]) ).
fof(f715,plain,
! [X0] :
( ~ in(X0,relation_dom(sF16))
| apply(sK15,apply(function_inverse(sK15),X0)) = X0 ),
inference(forward_subsumption_resolution,[],[f709,f175]) ).
fof(f717,plain,
! [X0] :
( ~ in(X0,relation_dom(sF16))
| apply(sK15,apply(sF16,X0)) = X0 ),
inference(forward_demodulation,[],[f715,f194]) ).
fof(f2797,plain,
( sK14 = apply(sK15,apply(sF16,sK14))
| ~ spl22_24 ),
inference(resolution,[],[f717,f628]) ).
fof(f2800,plain,
( sK14 = apply(sK15,sF17)
| ~ spl22_24 ),
inference(forward_demodulation,[],[f2797,f196]) ).
fof(f2861,plain,
( apply(sK15,sF17) = apply(relation_composition(sF16,sK15),sK14)
| ~ function(sK15)
| ~ spl22_24 ),
inference(resolution,[],[f674,f176]) ).
fof(f2866,plain,
( apply(sK15,sF17) = apply(relation_composition(sF16,sK15),sK14)
| ~ spl22_24 ),
inference(forward_subsumption_resolution,[],[f2861,f175]) ).
fof(f2879,plain,
( apply(sK15,sF17) = apply(sF19,sK14)
| ~ spl22_24 ),
inference(forward_demodulation,[],[f2866,f200]) ).
fof(f2885,plain,
( apply(sK15,sF17) = sF20
| ~ spl22_24 ),
inference(forward_demodulation,[],[f2879,f202]) ).
fof(f2890,plain,
( sF18 = sF20
| ~ spl22_24 ),
inference(forward_demodulation,[],[f2885,f198]) ).
fof(f2892,plain,
( sK14 != sF18
| spl22_1
| ~ spl22_24 ),
inference(superposition,[],[f210,f2890]) ).
fof(f2893,plain,
( ~ spl22_2
| spl22_1
| ~ spl22_24 ),
inference(avatar_split_clause,[],[f2892,f627,f208,f212]) ).
fof(f3596,plain,
( sK14 = sF18
| ~ spl22_24 ),
inference(superposition,[],[f2800,f198]) ).
fof(f3605,plain,
( $false
| spl22_2
| ~ spl22_24 ),
inference(forward_subsumption_resolution,[],[f3596,f214]) ).
fof(f3606,plain,
( spl22_2
| ~ spl22_24 ),
inference(avatar_contradiction_clause,[],[f3605]) ).
cnf(s1,plain,
( ~ spl22_1
| ~ spl22_2 ),
inference(sat_conversion,[],[f215]) ).
cnf(s15,plain,
spl22_24,
inference(sat_conversion,[],[f666]) ).
cnf(s33,plain,
( spl22_1
| ~ spl22_2
| ~ spl22_24 ),
inference(sat_conversion,[],[f2893]) ).
cnf(s35,plain,
( spl22_2
| ~ spl22_24 ),
inference(sat_conversion,[],[f3606]) ).
cnf(s43,plain,
spl22_2,
inference(rat,[],[s35,s15]) ).
cnf(s45,plain,
spl22_1,
inference(rat,[],[s33,s15,s43]) ).
cnf(s48,plain,
$false,
inference(rat,[],[s1,s43,s45]) ).
fof(f3608,plain,
$false,
inference(avatar_sat_refutation,[],[s48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU220+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.40 % Computer : n009.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Mon Sep 28 04:08:30 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.43 Running first-order model finding
% 0.12/0.43 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.56/0.73 % (2650162)Will run a generic schedule for satisfiability detection.
% 1.56/0.73 % (2650172)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=29940103:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.56/0.73 % (2650168)% WARNING: option uhcvi not known.
% 1.56/0.73 % (2650167)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1505985778_2999 on theBenchmark for (2999ds/0Mi)
% 1.56/0.73 % (2650168)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3448627167:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.56/0.73 % (2650169)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=11600327:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.56/0.73 % (2650170)dis+10_1_sil=32000:sp=arity:random_seed=1864996163:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.56/0.73 % (2650171)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=865883229:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.56/0.73 % (2650173)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=25083705:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.56/0.73 % TRYING [1]
% 1.56/0.73 % TRYING [2]
% 1.56/0.73 % TRYING [3]
% 1.56/0.73 % TRYING [4]
% 1.56/0.73 % TRYING [5]
% 1.56/0.73 % (2650172)Instruction limit reached!
% 1.56/0.73 % (2650172)------------------------------
% 1.56/0.73 % (2650172)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.56/0.73 % (2650172)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.56/0.73 % (2650172)CaDiCaL version: 2.1.3
% 1.56/0.73 % (2650172)Termination reason: Instruction limit
% 1.56/0.73 % (2650172)Termination phase: Saturation
% 1.56/0.73 % (2650172)Time elapsed: 0.043 s
% 1.56/0.73 % (2650172)Peak memory usage: 13 MB
% 1.56/0.73 % (2650172)Instructions burned: 132 (million)
% 1.56/0.73 % (2650181)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2725669718:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.56/0.73 % TRYING [1]
% 1.56/0.73 % TRYING [2]
% 1.56/0.73 % TRYING [3]
% 1.56/0.73 % TRYING [4]
% 1.56/0.73 % (2650170)Instruction limit reached!
% 1.56/0.73 % (2650170)------------------------------
% 1.56/0.73 % (2650170)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.56/0.73 % (2650170)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.56/0.73 % (2650170)CaDiCaL version: 2.1.3
% 1.56/0.73 % (2650170)Termination reason: Instruction limit
% 1.56/0.73 % (2650170)Termination phase: Saturation
% 1.56/0.73 % (2650170)Time elapsed: 0.057 s
% 1.56/0.73 % (2650170)Peak memory usage: 12 MB
% 1.56/0.73 % (2650170)Instructions burned: 104 (million)
% 1.56/0.73 % TRYING [6]
% 1.56/0.73 % TRYING [5]
% 1.56/0.73 % (2650171)Instruction limit reached!
% 1.56/0.73 % (2650171)------------------------------
% 1.56/0.73 % (2650171)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.56/0.73 % (2650171)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.56/0.73 % (2650171)CaDiCaL version: 2.1.3
% 1.56/0.73 % (2650171)Termination reason: Instruction limit
% 1.56/0.73 % (2650171)Termination phase: Saturation
% 1.56/0.73 % (2650171)Time elapsed: 0.069 s
% 1.56/0.73 % (2650171)Peak memory usage: 13 MB
% 1.56/0.73 % (2650171)Instructions burned: 117 (million)
% 1.56/0.73 % (2650183)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3320481544:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.56/0.73 % TRYING [6]
% 1.56/0.73 % (2650173)Instruction limit reached!
% 1.56/0.73 % (2650173)------------------------------
% 1.56/0.73 % (2650173)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.56/0.73 % (2650173)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.56/0.73 % (2650173)CaDiCaL version: 2.1.3
% 1.56/0.73 % (2650173)Termination reason: Instruction limit
% 1.56/0.73 % (2650173)Termination phase: Saturation
% 1.56/0.73 % (2650173)Time elapsed: 0.088 s
% 1.56/0.73 % (2650173)Peak memory usage: 13 MB
% 1.56/0.73 % (2650173)Instructions burned: 161 (million)
% 1.56/0.73 % (2650184)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=1123054720:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.56/0.73 % (2650187)ott-21_1_sil=16000:fs=off:random_seed=3127873223:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.56/0.73 % TRYING [7]
% 1.56/0.73 % TRYING [7]
% 1.56/0.73 % (2650183)Instruction limit reached!
% 1.56/0.73 % (2650183)------------------------------
% 1.56/0.73 % (2650183)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.56/0.73 % (2650183)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.56/0.73 % (2650183)CaDiCaL version: 2.1.3
% 1.56/0.73 % (2650183)Termination reason: Instruction limit
% 1.56/0.73 % (2650183)Termination phase: Saturation
% 1.56/0.73 % (2650183)Time elapsed: 0.084 s
% 1.56/0.73 % (2650183)Peak memory usage: 14 MB
% 1.56/0.73 % (2650183)Instructions burned: 133 (million)
% 1.56/0.73 % (2650189)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3498176066:i=477:bd=all_2997 on theBenchmark for (2997ds/477Mi)
% 1.56/0.73 % (2650187)Instruction limit reached!
% 1.56/0.73 % (2650187)------------------------------
% 1.56/0.73 % (2650187)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.56/0.73 % (2650187)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.56/0.73 % (2650187)CaDiCaL version: 2.1.3
% 1.56/0.73 % (2650187)Termination reason: Instruction limit
% 1.56/0.73 % (2650187)Termination phase: Saturation
% 1.56/0.73 % (2650187)Time elapsed: 0.078 s
% 1.56/0.73 % (2650187)Peak memory usage: 12 MB
% 1.56/0.73 % (2650187)Instructions burned: 180 (million)
% 1.56/0.73 % (2650181)Instruction limit reached!
% 1.56/0.73 % (2650181)------------------------------
% 1.56/0.73 % (2650181)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.56/0.73 % (2650181)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.56/0.73 % (2650181)CaDiCaL version: 2.1.3
% 1.56/0.73 % (2650181)Termination reason: Instruction limit
% 1.56/0.73 % (2650181)Termination phase: Finite model building SAT solving
% 1.56/0.73 % (2650181)Time elapsed: 0.145 s
% 1.56/0.73 % (2650181)Peak memory usage: 29 MB
% 1.56/0.73 % (2650181)Instructions burned: 717 (million)
% 1.56/0.73 % (2650191)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2449058773:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 1.56/0.73 % TRYING [1]
% 1.56/0.73 % TRYING [2]
% 1.56/0.73 % (2650192)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3323247169:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 1.56/0.73 % TRYING [3]
% 1.56/0.73 % TRYING [4]
% 1.56/0.73 % (2650192) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2650162-2650192"...
% 1.56/0.73 % (2650192)...printing done.
% 1.56/0.73 % (2650192)Refutation found. Thanks to Tanya!
% 1.56/0.73 % SZS status Theorem for theBenchmark
% 1.56/0.73 % SZS output start Proof for theBenchmark
% See solution above
% 1.56/0.73 % (2650192)------------------------------
% 1.56/0.73 % (2650192)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.56/0.73 % (2650192)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.56/0.73 % (2650192)CaDiCaL version: 2.1.3
% 1.56/0.73 % (2650192)Termination reason: Refutation
% 1.56/0.73 % (2650192)Time elapsed: 0.030 s
% 1.56/0.73 % (2650192)Peak memory usage: 13 MB
% 1.56/0.73 % (2650192)Instructions burned: 87 (million)
% 1.56/0.73 % (2650162)Success in time 0.287 s
% 1.56/0.73 % Vampire exiting
%------------------------------------------------------------------------------