%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU027+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n019.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 12:51:48 PM UTC 2026
% Result : Theorem 0.15s 0.47s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 7
% Syntax : Number of formulae : 132 ( 14 unt; 4 def)
% Number of atoms : 621 ( 211 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 814 ( 325 ~; 410 |; 48 &)
% ( 17 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 91 ( 0 sgn 84 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).
fof(f31,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/sandbox2/benchmark/theBenchmark.p',t54_funct_1) ).
fof(f33,conjecture,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( ( one_to_one(X0)
& relation_dom(X0) = relation_rng(X1)
& relation_rng(X0) = relation_dom(X1)
& ! [X2,X3] :
( ( in(X2,relation_dom(X0))
& in(X3,relation_dom(X1)) )
=> ( apply(X0,X2) = X3
<=> apply(X1,X3) = X2 ) ) )
=> X1 = function_inverse(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_funct_1) ).
fof(f34,negated_conjecture,
~ ! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( ( one_to_one(X0)
& relation_dom(X0) = relation_rng(X1)
& relation_rng(X0) = relation_dom(X1)
& ! [X2,X3] :
( ( in(X2,relation_dom(X0))
& in(X3,relation_dom(X1)) )
=> ( apply(X0,X2) = X3
<=> apply(X1,X3) = X2 ) ) )
=> X1 = function_inverse(X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f48,plain,
! [X0] :
( ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f49,plain,
! [X0] :
( ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f48]) ).
fof(f65,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,[],[f31]) ).
fof(f66,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,[],[f65]) ).
fof(f68,plain,
? [X0] :
( ? [X1] :
( function_inverse(X0) != X1
& one_to_one(X0)
& relation_dom(X0) = relation_rng(X1)
& relation_rng(X0) = relation_dom(X1)
& ! [X2,X3] :
( ( apply(X0,X2) = X3
<=> apply(X1,X3) = X2 )
| ~ in(X2,relation_dom(X0))
| ~ in(X3,relation_dom(X1)) )
& relation(X1)
& function(X1) )
& relation(X0)
& function(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f69,plain,
? [X0] :
( ? [X1] :
( function_inverse(X0) != X1
& one_to_one(X0)
& relation_dom(X0) = relation_rng(X1)
& relation_rng(X0) = relation_dom(X1)
& ! [X2,X3] :
( ( apply(X0,X2) = X3
<=> apply(X1,X3) = X2 )
| ~ in(X2,relation_dom(X0))
| ~ in(X3,relation_dom(X1)) )
& relation(X1)
& function(X1) )
& relation(X0)
& function(X0) ),
inference(flattening,[],[f68]) ).
fof(f84,plain,
! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0))
| in(X2,X1)
| relation_rng(X0) != X1 ),
inference(cnf_transformation,[],[f49]) ).
fof(f126,plain,
! [X0,X1] :
( ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0)
| ~ function(X1)
| ~ relation(X1)
| sK15(X0,X1) != apply(X1,sK14(X0,X1))
| ~ in(sK14(X0,X1),relation_rng(X0))
| sK14(X0,X1) != apply(X0,sK15(X0,X1))
| ~ in(sK15(X0,X1),relation_dom(X0))
| relation_rng(X0) != relation_dom(X1)
| function_inverse(X0) = X1 ),
inference(cnf_transformation,[],[f66]) ).
fof(f129,plain,
! [X0,X1] :
( ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0)
| ~ function(X1)
| ~ relation(X1)
| in(sK15(X0,X1),relation_dom(X0))
| sK15(X0,X1) = apply(X1,sK14(X0,X1))
| relation_rng(X0) != relation_dom(X1)
| function_inverse(X0) = X1 ),
inference(cnf_transformation,[],[f66]) ).
fof(f130,plain,
! [X0,X1] :
( ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0)
| ~ function(X1)
| ~ relation(X1)
| in(sK15(X0,X1),relation_dom(X0))
| in(sK14(X0,X1),relation_rng(X0))
| relation_rng(X0) != relation_dom(X1)
| function_inverse(X0) = X1 ),
inference(cnf_transformation,[],[f66]) ).
fof(f131,plain,
! [X0,X1] :
( ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0)
| ~ function(X1)
| ~ relation(X1)
| sK14(X0,X1) = apply(X0,sK15(X0,X1))
| sK15(X0,X1) = apply(X1,sK14(X0,X1))
| relation_rng(X0) != relation_dom(X1)
| function_inverse(X0) = X1 ),
inference(cnf_transformation,[],[f66]) ).
fof(f132,plain,
! [X0,X1] :
( ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0)
| ~ function(X1)
| ~ relation(X1)
| sK14(X0,X1) = apply(X0,sK15(X0,X1))
| in(sK14(X0,X1),relation_rng(X0))
| relation_rng(X0) != relation_dom(X1)
| function_inverse(X0) = X1 ),
inference(cnf_transformation,[],[f66]) ).
fof(f135,plain,
! [X2,X3] :
( ~ in(X3,relation_dom(sK17))
| ~ in(X2,relation_dom(sK16))
| apply(sK17,X3) != X2
| apply(sK16,X2) = X3 ),
inference(cnf_transformation,[],[f69]) ).
fof(f136,plain,
! [X2,X3] :
( ~ in(X3,relation_dom(sK17))
| ~ in(X2,relation_dom(sK16))
| apply(sK17,X3) = X2
| apply(sK16,X2) != X3 ),
inference(cnf_transformation,[],[f69]) ).
fof(f137,plain,
function(sK17),
inference(cnf_transformation,[],[f69]) ).
fof(f138,plain,
relation(sK17),
inference(cnf_transformation,[],[f69]) ).
fof(f139,plain,
relation_dom(sK17) = relation_rng(sK16),
inference(cnf_transformation,[],[f69]) ).
fof(f140,plain,
relation_dom(sK16) = relation_rng(sK17),
inference(cnf_transformation,[],[f69]) ).
fof(f141,plain,
one_to_one(sK16),
inference(cnf_transformation,[],[f69]) ).
fof(f142,plain,
sK17 != function_inverse(sK16),
inference(cnf_transformation,[],[f69]) ).
fof(f143,plain,
function(sK16),
inference(cnf_transformation,[],[f69]) ).
fof(f144,plain,
relation(sK16),
inference(cnf_transformation,[],[f69]) ).
fof(f150,plain,
! [X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X3,relation_dom(X0))
| in(apply(X0,X3),X1)
| relation_rng(X0) != X1 ),
inference(equality_resolution,[],[f84]) ).
fof(f151,plain,
! [X3,X0] :
( in(apply(X0,X3),relation_rng(X0))
| ~ relation(X0)
| ~ in(X3,relation_dom(X0))
| ~ function(X0) ),
inference(equality_resolution,[],[f150]) ).
fof(f163,plain,
! [X2] :
( ~ in(apply(sK16,X2),relation_dom(sK17))
| ~ in(X2,relation_dom(sK16))
| apply(sK17,apply(sK16,X2)) = X2 ),
inference(equality_resolution,[],[f136]) ).
fof(f164,plain,
! [X3] :
( ~ in(apply(sK17,X3),relation_dom(sK16))
| ~ in(X3,relation_dom(sK17))
| apply(sK16,apply(sK17,X3)) = X3 ),
inference(equality_resolution,[],[f135]) ).
fof(f329,plain,
! [X0] :
( in(apply(sK16,X0),relation_dom(sK17))
| ~ relation(sK16)
| ~ in(X0,relation_dom(sK16))
| ~ function(sK16) ),
inference(superposition,[],[f151,f139]) ).
fof(f332,plain,
! [X0] :
( in(apply(sK16,X0),relation_dom(sK17))
| ~ in(X0,relation_dom(sK16))
| ~ function(sK16) ),
inference(forward_subsumption_resolution,[],[f329,f144]) ).
fof(f334,plain,
! [X0] :
( in(apply(sK16,X0),relation_dom(sK17))
| ~ in(X0,relation_dom(sK16)) ),
inference(forward_subsumption_resolution,[],[f332,f143]) ).
fof(f592,plain,
! [X0] :
( ~ relation(sK16)
| ~ function(sK16)
| ~ function(X0)
| ~ relation(X0)
| in(sK15(sK16,X0),relation_dom(sK16))
| in(sK14(sK16,X0),relation_rng(sK16))
| relation_dom(X0) != relation_rng(sK16)
| function_inverse(sK16) = X0 ),
inference(resolution,[],[f130,f141]) ).
fof(f598,plain,
! [X0] :
( ~ function(sK16)
| ~ function(X0)
| ~ relation(X0)
| in(sK15(sK16,X0),relation_dom(sK16))
| in(sK14(sK16,X0),relation_rng(sK16))
| relation_dom(X0) != relation_rng(sK16)
| function_inverse(sK16) = X0 ),
inference(forward_subsumption_resolution,[],[f592,f144]) ).
fof(f601,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| in(sK15(sK16,X0),relation_dom(sK16))
| in(sK14(sK16,X0),relation_rng(sK16))
| relation_dom(X0) != relation_rng(sK16)
| function_inverse(sK16) = X0 ),
inference(forward_subsumption_resolution,[],[f598,f143]) ).
fof(f603,plain,
! [X0] :
( in(sK14(sK16,X0),relation_dom(sK17))
| ~ function(X0)
| ~ relation(X0)
| in(sK15(sK16,X0),relation_dom(sK16))
| relation_dom(X0) != relation_rng(sK16)
| function_inverse(sK16) = X0 ),
inference(forward_demodulation,[],[f601,f139]) ).
fof(f605,plain,
! [X0] :
( in(sK15(sK16,X0),relation_dom(sK16))
| in(sK14(sK16,X0),relation_dom(sK17))
| ~ function(X0)
| ~ relation(X0)
| relation_dom(X0) != relation_dom(sK17)
| function_inverse(sK16) = X0 ),
inference(forward_demodulation,[],[f603,f139]) ).
fof(f620,plain,
! [X0] :
( ~ relation(sK16)
| ~ function(sK16)
| ~ function(X0)
| ~ relation(X0)
| in(sK15(sK16,X0),relation_dom(sK16))
| sK15(sK16,X0) = apply(X0,sK14(sK16,X0))
| relation_dom(X0) != relation_rng(sK16)
| function_inverse(sK16) = X0 ),
inference(resolution,[],[f129,f141]) ).
fof(f625,plain,
! [X0] :
( ~ function(sK16)
| ~ function(X0)
| ~ relation(X0)
| in(sK15(sK16,X0),relation_dom(sK16))
| sK15(sK16,X0) = apply(X0,sK14(sK16,X0))
| relation_dom(X0) != relation_rng(sK16)
| function_inverse(sK16) = X0 ),
inference(forward_subsumption_resolution,[],[f620,f144]) ).
fof(f627,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| in(sK15(sK16,X0),relation_dom(sK16))
| sK15(sK16,X0) = apply(X0,sK14(sK16,X0))
| relation_dom(X0) != relation_rng(sK16)
| function_inverse(sK16) = X0 ),
inference(forward_subsumption_resolution,[],[f625,f143]) ).
fof(f628,plain,
! [X0] :
( in(sK15(sK16,X0),relation_dom(sK16))
| ~ function(X0)
| ~ relation(X0)
| relation_dom(X0) != relation_dom(sK17)
| sK15(sK16,X0) = apply(X0,sK14(sK16,X0))
| function_inverse(sK16) = X0 ),
inference(forward_demodulation,[],[f627,f139]) ).
fof(f629,plain,
! [X0] :
( ~ relation(sK16)
| ~ function(sK16)
| ~ function(X0)
| ~ relation(X0)
| sK14(sK16,X0) = apply(sK16,sK15(sK16,X0))
| in(sK14(sK16,X0),relation_rng(sK16))
| relation_dom(X0) != relation_rng(sK16)
| function_inverse(sK16) = X0 ),
inference(resolution,[],[f132,f141]) ).
fof(f634,plain,
! [X0] :
( ~ function(sK16)
| ~ function(X0)
| ~ relation(X0)
| sK14(sK16,X0) = apply(sK16,sK15(sK16,X0))
| in(sK14(sK16,X0),relation_rng(sK16))
| relation_dom(X0) != relation_rng(sK16)
| function_inverse(sK16) = X0 ),
inference(forward_subsumption_resolution,[],[f629,f144]) ).
fof(f636,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| sK14(sK16,X0) = apply(sK16,sK15(sK16,X0))
| in(sK14(sK16,X0),relation_rng(sK16))
| relation_dom(X0) != relation_rng(sK16)
| function_inverse(sK16) = X0 ),
inference(forward_subsumption_resolution,[],[f634,f143]) ).
fof(f637,plain,
! [X0] :
( in(sK14(sK16,X0),relation_dom(sK17))
| ~ function(X0)
| ~ relation(X0)
| sK14(sK16,X0) = apply(sK16,sK15(sK16,X0))
| relation_dom(X0) != relation_rng(sK16)
| function_inverse(sK16) = X0 ),
inference(forward_demodulation,[],[f636,f139]) ).
fof(f638,plain,
! [X0] :
( in(sK14(sK16,X0),relation_dom(sK17))
| relation_dom(X0) != relation_dom(sK17)
| ~ function(X0)
| ~ relation(X0)
| sK14(sK16,X0) = apply(sK16,sK15(sK16,X0))
| function_inverse(sK16) = X0 ),
inference(forward_demodulation,[],[f637,f139]) ).
fof(f653,plain,
! [X0] :
( ~ relation(sK16)
| ~ function(sK16)
| ~ function(X0)
| ~ relation(X0)
| sK14(sK16,X0) = apply(sK16,sK15(sK16,X0))
| sK15(sK16,X0) = apply(X0,sK14(sK16,X0))
| relation_dom(X0) != relation_rng(sK16)
| function_inverse(sK16) = X0 ),
inference(resolution,[],[f131,f141]) ).
fof(f658,plain,
! [X0] :
( ~ function(sK16)
| ~ function(X0)
| ~ relation(X0)
| sK14(sK16,X0) = apply(sK16,sK15(sK16,X0))
| sK15(sK16,X0) = apply(X0,sK14(sK16,X0))
| relation_dom(X0) != relation_rng(sK16)
| function_inverse(sK16) = X0 ),
inference(forward_subsumption_resolution,[],[f653,f144]) ).
fof(f660,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| sK14(sK16,X0) = apply(sK16,sK15(sK16,X0))
| sK15(sK16,X0) = apply(X0,sK14(sK16,X0))
| relation_dom(X0) != relation_rng(sK16)
| function_inverse(sK16) = X0 ),
inference(forward_subsumption_resolution,[],[f658,f143]) ).
fof(f661,plain,
! [X0] :
( ~ function(X0)
| relation_dom(X0) != relation_dom(sK17)
| ~ relation(X0)
| sK14(sK16,X0) = apply(sK16,sK15(sK16,X0))
| sK15(sK16,X0) = apply(X0,sK14(sK16,X0))
| function_inverse(sK16) = X0 ),
inference(forward_demodulation,[],[f660,f139]) ).
fof(f675,plain,
! [X0] :
( ~ relation(sK16)
| ~ function(sK16)
| ~ function(X0)
| ~ relation(X0)
| sK15(sK16,X0) != apply(X0,sK14(sK16,X0))
| ~ in(sK14(sK16,X0),relation_rng(sK16))
| sK14(sK16,X0) != apply(sK16,sK15(sK16,X0))
| ~ in(sK15(sK16,X0),relation_dom(sK16))
| relation_dom(X0) != relation_rng(sK16)
| function_inverse(sK16) = X0 ),
inference(resolution,[],[f126,f141]) ).
fof(f680,plain,
! [X0] :
( ~ function(sK16)
| ~ function(X0)
| ~ relation(X0)
| sK15(sK16,X0) != apply(X0,sK14(sK16,X0))
| ~ in(sK14(sK16,X0),relation_rng(sK16))
| sK14(sK16,X0) != apply(sK16,sK15(sK16,X0))
| ~ in(sK15(sK16,X0),relation_dom(sK16))
| relation_dom(X0) != relation_rng(sK16)
| function_inverse(sK16) = X0 ),
inference(forward_subsumption_resolution,[],[f675,f144]) ).
fof(f682,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| sK15(sK16,X0) != apply(X0,sK14(sK16,X0))
| ~ in(sK14(sK16,X0),relation_rng(sK16))
| sK14(sK16,X0) != apply(sK16,sK15(sK16,X0))
| ~ in(sK15(sK16,X0),relation_dom(sK16))
| relation_dom(X0) != relation_rng(sK16)
| function_inverse(sK16) = X0 ),
inference(forward_subsumption_resolution,[],[f680,f143]) ).
fof(f683,plain,
! [X0] :
( ~ in(sK14(sK16,X0),relation_dom(sK17))
| ~ function(X0)
| ~ relation(X0)
| sK15(sK16,X0) != apply(X0,sK14(sK16,X0))
| sK14(sK16,X0) != apply(sK16,sK15(sK16,X0))
| ~ in(sK15(sK16,X0),relation_dom(sK16))
| relation_dom(X0) != relation_rng(sK16)
| function_inverse(sK16) = X0 ),
inference(forward_demodulation,[],[f682,f139]) ).
fof(f684,plain,
! [X0] :
( ~ in(sK15(sK16,X0),relation_dom(sK16))
| ~ in(sK14(sK16,X0),relation_dom(sK17))
| ~ function(X0)
| ~ relation(X0)
| sK15(sK16,X0) != apply(X0,sK14(sK16,X0))
| sK14(sK16,X0) != apply(sK16,sK15(sK16,X0))
| relation_dom(X0) != relation_dom(sK17)
| function_inverse(sK16) = X0 ),
inference(forward_demodulation,[],[f683,f139]) ).
fof(f978,plain,
( relation_dom(sK17) != relation_dom(sK17)
| ~ relation(sK17)
| sK14(sK16,sK17) = apply(sK16,sK15(sK16,sK17))
| sK15(sK16,sK17) = apply(sK17,sK14(sK16,sK17))
| sK17 = function_inverse(sK16) ),
inference(resolution,[],[f661,f137]) ).
fof(f979,plain,
( ~ relation(sK17)
| sK14(sK16,sK17) = apply(sK16,sK15(sK16,sK17))
| sK15(sK16,sK17) = apply(sK17,sK14(sK16,sK17))
| sK17 = function_inverse(sK16) ),
inference(trivial_inequality_removal,[],[f978]) ).
fof(f980,plain,
( sK14(sK16,sK17) = apply(sK16,sK15(sK16,sK17))
| sK15(sK16,sK17) = apply(sK17,sK14(sK16,sK17))
| sK17 = function_inverse(sK16) ),
inference(forward_subsumption_resolution,[],[f979,f138]) ).
fof(f986,plain,
( sK14(sK16,sK17) = apply(sK16,sK15(sK16,sK17))
| sK15(sK16,sK17) = apply(sK17,sK14(sK16,sK17)) ),
inference(forward_subsumption_resolution,[],[f980,f142]) ).
fof(f992,definition,
( spl19_31
<=> sK15(sK16,sK17) = apply(sK17,sK14(sK16,sK17)) ),
introduced(definition,[new_symbols(definition,[spl19_31])],[avatar_definition]) ).
fof(f993,plain,
( sK15(sK16,sK17) != apply(sK17,sK14(sK16,sK17))
| spl19_31 ),
inference(avatar_component_clause,[],[f992]) ).
fof(f994,plain,
( sK15(sK16,sK17) = apply(sK17,sK14(sK16,sK17))
| ~ spl19_31 ),
inference(avatar_component_clause,[],[f992]) ).
fof(f996,definition,
( spl19_32
<=> sK14(sK16,sK17) = apply(sK16,sK15(sK16,sK17)) ),
introduced(definition,[new_symbols(definition,[spl19_32])],[avatar_definition]) ).
fof(f998,plain,
( sK14(sK16,sK17) = apply(sK16,sK15(sK16,sK17))
| ~ spl19_32 ),
inference(avatar_component_clause,[],[f996]) ).
fof(f999,plain,
( spl19_31
| spl19_32 ),
inference(avatar_split_clause,[],[f986,f996,f992]) ).
fof(f1002,plain,
( ~ in(sK15(sK16,sK17),relation_dom(sK16))
| ~ in(sK14(sK16,sK17),relation_dom(sK17))
| sK14(sK16,sK17) = apply(sK16,sK15(sK16,sK17))
| ~ spl19_31 ),
inference(superposition,[],[f164,f994]) ).
fof(f1003,plain,
( in(sK15(sK16,sK17),relation_rng(sK17))
| ~ relation(sK17)
| ~ in(sK14(sK16,sK17),relation_dom(sK17))
| ~ function(sK17)
| ~ spl19_31 ),
inference(superposition,[],[f151,f994]) ).
fof(f1004,plain,
( in(sK15(sK16,sK17),relation_rng(sK17))
| ~ in(sK14(sK16,sK17),relation_dom(sK17))
| ~ function(sK17)
| ~ spl19_31 ),
inference(forward_subsumption_resolution,[],[f1003,f138]) ).
fof(f1006,definition,
( spl19_33
<=> in(sK14(sK16,sK17),relation_dom(sK17)) ),
introduced(definition,[new_symbols(definition,[spl19_33])],[avatar_definition]) ).
fof(f1007,plain,
( in(sK14(sK16,sK17),relation_dom(sK17))
| ~ spl19_33 ),
inference(avatar_component_clause,[],[f1006]) ).
fof(f1008,plain,
( ~ in(sK14(sK16,sK17),relation_dom(sK17))
| spl19_33 ),
inference(avatar_component_clause,[],[f1006]) ).
fof(f1010,definition,
( spl19_34
<=> in(sK15(sK16,sK17),relation_dom(sK16)) ),
introduced(definition,[new_symbols(definition,[spl19_34])],[avatar_definition]) ).
fof(f1011,plain,
( in(sK15(sK16,sK17),relation_dom(sK16))
| ~ spl19_34 ),
inference(avatar_component_clause,[],[f1010]) ).
fof(f1012,plain,
( ~ in(sK15(sK16,sK17),relation_dom(sK16))
| spl19_34 ),
inference(avatar_component_clause,[],[f1010]) ).
fof(f1013,plain,
( spl19_32
| ~ spl19_33
| ~ spl19_34
| ~ spl19_31 ),
inference(avatar_split_clause,[],[f1002,f992,f1010,f1006,f996]) ).
fof(f1020,plain,
( in(sK15(sK16,sK17),relation_rng(sK17))
| ~ in(sK14(sK16,sK17),relation_dom(sK17))
| ~ spl19_31 ),
inference(forward_subsumption_resolution,[],[f1004,f137]) ).
fof(f1021,plain,
( in(sK15(sK16,sK17),relation_dom(sK16))
| ~ in(sK14(sK16,sK17),relation_dom(sK17))
| ~ spl19_31 ),
inference(forward_demodulation,[],[f1020,f140]) ).
fof(f1022,plain,
( ~ spl19_33
| spl19_34
| ~ spl19_31 ),
inference(avatar_split_clause,[],[f1021,f992,f1010,f1006]) ).
fof(f1023,plain,
( relation_dom(sK17) != relation_dom(sK17)
| ~ function(sK17)
| ~ relation(sK17)
| sK14(sK16,sK17) = apply(sK16,sK15(sK16,sK17))
| sK17 = function_inverse(sK16)
| spl19_33 ),
inference(resolution,[],[f1008,f638]) ).
fof(f1024,plain,
( ~ function(sK17)
| ~ relation(sK17)
| sK14(sK16,sK17) = apply(sK16,sK15(sK16,sK17))
| sK17 = function_inverse(sK16)
| spl19_33 ),
inference(trivial_inequality_removal,[],[f1023]) ).
fof(f1025,plain,
( ~ relation(sK17)
| sK14(sK16,sK17) = apply(sK16,sK15(sK16,sK17))
| sK17 = function_inverse(sK16)
| spl19_33 ),
inference(forward_subsumption_resolution,[],[f1024,f137]) ).
fof(f1026,plain,
( sK14(sK16,sK17) = apply(sK16,sK15(sK16,sK17))
| sK17 = function_inverse(sK16)
| spl19_33 ),
inference(forward_subsumption_resolution,[],[f1025,f138]) ).
fof(f1027,plain,
( sK14(sK16,sK17) = apply(sK16,sK15(sK16,sK17))
| spl19_33 ),
inference(forward_subsumption_resolution,[],[f1026,f142]) ).
fof(f1028,plain,
( spl19_32
| spl19_33 ),
inference(avatar_split_clause,[],[f1027,f1006,f996]) ).
fof(f1030,plain,
( in(sK14(sK16,sK17),relation_dom(sK17))
| ~ in(sK15(sK16,sK17),relation_dom(sK16))
| ~ spl19_32 ),
inference(superposition,[],[f334,f998]) ).
fof(f1031,plain,
( ~ in(sK14(sK16,sK17),relation_dom(sK17))
| ~ in(sK15(sK16,sK17),relation_dom(sK16))
| sK15(sK16,sK17) = apply(sK17,sK14(sK16,sK17))
| ~ spl19_32 ),
inference(superposition,[],[f163,f998]) ).
fof(f1034,plain,
( ~ in(sK15(sK16,sK17),relation_dom(sK16))
| ~ spl19_32
| spl19_33 ),
inference(forward_subsumption_resolution,[],[f1030,f1008]) ).
fof(f1041,plain,
( ~ spl19_34
| ~ spl19_32
| spl19_33 ),
inference(avatar_split_clause,[],[f1034,f1006,f996,f1010]) ).
fof(f1050,plain,
( ~ function(sK17)
| ~ relation(sK17)
| relation_dom(sK17) != relation_dom(sK17)
| sK15(sK16,sK17) = apply(sK17,sK14(sK16,sK17))
| sK17 = function_inverse(sK16)
| spl19_34 ),
inference(resolution,[],[f1012,f628]) ).
fof(f1051,plain,
( in(sK14(sK16,sK17),relation_dom(sK17))
| ~ function(sK17)
| ~ relation(sK17)
| relation_dom(sK17) != relation_dom(sK17)
| sK17 = function_inverse(sK16)
| spl19_34 ),
inference(resolution,[],[f1012,f605]) ).
fof(f1052,plain,
( in(sK14(sK16,sK17),relation_dom(sK17))
| ~ function(sK17)
| ~ relation(sK17)
| sK17 = function_inverse(sK16)
| spl19_34 ),
inference(trivial_inequality_removal,[],[f1051]) ).
fof(f1053,plain,
( ~ function(sK17)
| ~ relation(sK17)
| sK15(sK16,sK17) = apply(sK17,sK14(sK16,sK17))
| sK17 = function_inverse(sK16)
| spl19_34 ),
inference(trivial_inequality_removal,[],[f1050]) ).
fof(f1054,plain,
( ~ function(sK17)
| ~ relation(sK17)
| sK17 = function_inverse(sK16)
| spl19_33
| spl19_34 ),
inference(forward_subsumption_resolution,[],[f1052,f1008]) ).
fof(f1055,plain,
( ~ relation(sK17)
| sK17 = function_inverse(sK16)
| spl19_33
| spl19_34 ),
inference(forward_subsumption_resolution,[],[f1054,f137]) ).
fof(f1056,plain,
( sK17 = function_inverse(sK16)
| spl19_33
| spl19_34 ),
inference(forward_subsumption_resolution,[],[f1055,f138]) ).
fof(f1057,plain,
( $false
| spl19_33
| spl19_34 ),
inference(forward_subsumption_resolution,[],[f1056,f142]) ).
fof(f1058,plain,
( spl19_33
| spl19_34 ),
inference(avatar_contradiction_clause,[],[f1057]) ).
fof(f1059,plain,
( ~ relation(sK17)
| sK15(sK16,sK17) = apply(sK17,sK14(sK16,sK17))
| sK17 = function_inverse(sK16)
| spl19_34 ),
inference(forward_subsumption_resolution,[],[f1053,f137]) ).
fof(f1060,plain,
( sK15(sK16,sK17) = apply(sK17,sK14(sK16,sK17))
| sK17 = function_inverse(sK16)
| spl19_34 ),
inference(forward_subsumption_resolution,[],[f1059,f138]) ).
fof(f1061,plain,
( sK17 = function_inverse(sK16)
| spl19_31
| spl19_34 ),
inference(forward_subsumption_resolution,[],[f1060,f993]) ).
fof(f1062,plain,
( $false
| spl19_31
| spl19_34 ),
inference(forward_subsumption_resolution,[],[f1061,f142]) ).
fof(f1063,plain,
( spl19_31
| spl19_34 ),
inference(avatar_contradiction_clause,[],[f1062]) ).
fof(f1064,plain,
( ~ in(sK15(sK16,sK17),relation_dom(sK16))
| sK15(sK16,sK17) = apply(sK17,sK14(sK16,sK17))
| ~ spl19_32
| ~ spl19_33 ),
inference(forward_subsumption_resolution,[],[f1031,f1007]) ).
fof(f1065,plain,
( sK15(sK16,sK17) = apply(sK17,sK14(sK16,sK17))
| ~ spl19_32
| ~ spl19_33
| ~ spl19_34 ),
inference(forward_subsumption_resolution,[],[f1064,f1011]) ).
fof(f1066,plain,
( spl19_31
| ~ spl19_32
| ~ spl19_33
| ~ spl19_34 ),
inference(avatar_split_clause,[],[f1065,f1010,f1006,f996,f992]) ).
fof(f1096,plain,
( ~ in(sK14(sK16,sK17),relation_dom(sK17))
| ~ function(sK17)
| ~ relation(sK17)
| sK15(sK16,sK17) != apply(sK17,sK14(sK16,sK17))
| sK14(sK16,sK17) != apply(sK16,sK15(sK16,sK17))
| relation_dom(sK17) != relation_dom(sK17)
| sK17 = function_inverse(sK16)
| ~ spl19_34 ),
inference(resolution,[],[f684,f1011]) ).
fof(f1097,plain,
( ~ in(sK14(sK16,sK17),relation_dom(sK17))
| ~ function(sK17)
| ~ relation(sK17)
| sK15(sK16,sK17) != apply(sK17,sK14(sK16,sK17))
| sK14(sK16,sK17) != apply(sK16,sK15(sK16,sK17))
| sK17 = function_inverse(sK16)
| ~ spl19_34 ),
inference(trivial_inequality_removal,[],[f1096]) ).
fof(f1100,plain,
( ~ function(sK17)
| ~ relation(sK17)
| sK15(sK16,sK17) != apply(sK17,sK14(sK16,sK17))
| sK14(sK16,sK17) != apply(sK16,sK15(sK16,sK17))
| sK17 = function_inverse(sK16)
| ~ spl19_33
| ~ spl19_34 ),
inference(forward_subsumption_resolution,[],[f1097,f1007]) ).
fof(f1101,plain,
( ~ relation(sK17)
| sK15(sK16,sK17) != apply(sK17,sK14(sK16,sK17))
| sK14(sK16,sK17) != apply(sK16,sK15(sK16,sK17))
| sK17 = function_inverse(sK16)
| ~ spl19_33
| ~ spl19_34 ),
inference(forward_subsumption_resolution,[],[f1100,f137]) ).
fof(f1102,plain,
( sK15(sK16,sK17) != apply(sK17,sK14(sK16,sK17))
| sK14(sK16,sK17) != apply(sK16,sK15(sK16,sK17))
| sK17 = function_inverse(sK16)
| ~ spl19_33
| ~ spl19_34 ),
inference(forward_subsumption_resolution,[],[f1101,f138]) ).
fof(f1103,plain,
( sK14(sK16,sK17) != apply(sK16,sK15(sK16,sK17))
| sK17 = function_inverse(sK16)
| ~ spl19_31
| ~ spl19_33
| ~ spl19_34 ),
inference(forward_subsumption_resolution,[],[f1102,f994]) ).
fof(f1104,plain,
( sK17 = function_inverse(sK16)
| ~ spl19_31
| ~ spl19_32
| ~ spl19_33
| ~ spl19_34 ),
inference(forward_subsumption_resolution,[],[f1103,f998]) ).
fof(f1105,plain,
( $false
| ~ spl19_31
| ~ spl19_32
| ~ spl19_33
| ~ spl19_34 ),
inference(forward_subsumption_resolution,[],[f1104,f142]) ).
fof(f1106,plain,
( ~ spl19_31
| ~ spl19_32
| ~ spl19_33
| ~ spl19_34 ),
inference(avatar_contradiction_clause,[],[f1105]) ).
cnf(s29,plain,
( spl19_31
| spl19_32 ),
inference(sat_conversion,[],[f999]) ).
cnf(s30,plain,
( ~ spl19_31
| spl19_32
| ~ spl19_33
| ~ spl19_34 ),
inference(sat_conversion,[],[f1013]) ).
cnf(s33,plain,
( ~ spl19_31
| ~ spl19_33
| spl19_34 ),
inference(sat_conversion,[],[f1022]) ).
cnf(s34,plain,
( spl19_32
| spl19_33 ),
inference(sat_conversion,[],[f1028]) ).
cnf(s36,plain,
( ~ spl19_32
| spl19_33
| ~ spl19_34 ),
inference(sat_conversion,[],[f1041]) ).
cnf(s38,plain,
( spl19_33
| spl19_34 ),
inference(sat_conversion,[],[f1058]) ).
cnf(s39,plain,
( spl19_31
| spl19_34 ),
inference(sat_conversion,[],[f1063]) ).
cnf(s40,plain,
( spl19_31
| ~ spl19_32
| ~ spl19_33
| ~ spl19_34 ),
inference(sat_conversion,[],[f1066]) ).
cnf(s41,plain,
( ~ spl19_31
| ~ spl19_32
| ~ spl19_33
| ~ spl19_34 ),
inference(sat_conversion,[],[f1106]) ).
cnf(s43,plain,
( ~ spl19_32
| ~ spl19_34
| spl19_31 ),
inference(rat,[],[s36,s40]) ).
cnf(s44,plain,
spl19_31,
inference(rat,[],[s43,s29,s39]) ).
cnf(s45,plain,
( spl19_33
| ~ spl19_32 ),
inference(rat,[],[s36,s38]) ).
cnf(s46,plain,
~ spl19_32,
inference(rat,[],[s41,s33,s45,s44]) ).
cnf(s47,plain,
spl19_33,
inference(rat,[],[s34,s46]) ).
cnf(s48,plain,
spl19_34,
inference(rat,[],[s33,s44,s47]) ).
cnf(s50,plain,
$false,
inference(rat,[],[s30,s46,s44,s48,s47]) ).
fof(f1107,plain,
$false,
inference(avatar_sat_refutation,[],[s50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU027+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n019.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 03:23:04 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.47 % (3632967)Will run a generic schedule for satisfiability detection.
% 0.15/0.47 % (3632976)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4111297736:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.47 % (3632973)% WARNING: option uhcvi not known.
% 0.15/0.47 % (3632972)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3428514029_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.47 % (3632973)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=564587414:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.47 % (3632977)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=58941983:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.47 % (3632974)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3994166244:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.47 % (3632975)dis+10_1_sil=32000:sp=arity:random_seed=1864721264:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.47 % (3632978)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2423312007:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.47 % TRYING [1]
% 0.15/0.47 % TRYING [2]
% 0.15/0.47 % (3632976) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3632967-3632976"...
% 0.15/0.47 % TRYING [3]
% 0.15/0.47 % (3632976)...printing done.
% 0.15/0.47 % (3632976)Refutation found. Thanks to Tanya!
% 0.15/0.47 % SZS status Theorem for theBenchmark
% 0.15/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.47 % (3632976)------------------------------
% 0.15/0.47 % (3632976)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.47 % (3632976)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.47 % (3632976)CaDiCaL version: 2.1.3
% 0.15/0.47 % (3632976)Termination reason: Refutation
% 0.15/0.47 % (3632976)Time elapsed: 0.016 s
% 0.15/0.47 % (3632976)Peak memory usage: 13 MB
% 0.15/0.47 % (3632976)Instructions burned: 50 (million)
% 0.15/0.47 % (3632967)Success in time 0.044 s
% 0.15/0.47 % Vampire exiting
%------------------------------------------------------------------------------