%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU297+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n012.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 : Fri Sep 25 02:56:31 PM UTC 2026
% Result : Theorem 3.85s 1.13s
% Output : CNFRefutation 3.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 7
% Syntax : Number of formulae : 101 ( 20 unt; 5 def)
% Number of atoms : 469 ( 71 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 506 ( 176 ~; 231 |; 82 &)
% ( 7 <=>; 8 =>; 0 <=; 2 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 5 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 194 ( 0 sgn 147 !; 47 ?; 55 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2)
& element(X1,powerset(powerset(X0))) )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ( in(relation_image(X2,X4),X1)
& in(X4,powerset(relation_dom(X2))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e6_27__finset_1) ).
fof(f2,negated_conjecture,
~ ! [X0,X1,X2] :
( ( function(X2)
& relation(X2)
& element(X1,powerset(powerset(X0))) )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ( in(relation_image(X2,X4),X1)
& in(X4,powerset(relation_dom(X2))) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f38,axiom,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2)
& element(X1,powerset(powerset(X0))) )
=> ( ! [X3,X4,X5] :
( ( in(relation_image(X2,X5),X1)
& X3 = X5
& in(relation_image(X2,X4),X1)
& X3 = X4 )
=> X4 = X5 )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(relation_image(X2,X4),X1)
& X5 = X4
& in(X5,powerset(relation_dom(X2))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e6_27__finset_1__1) ).
fof(f39,plain,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2)
& element(X1,powerset(powerset(X0))) )
=> ( ! [X3,X4,X5] :
( ( in(relation_image(X2,X5),X1)
& X3 = X5
& in(relation_image(X2,X4),X1)
& X3 = X4 )
=> X4 = X5 )
=> ? [X6] :
! [X7] :
( in(X7,X6)
<=> ? [X8] :
( in(relation_image(X2,X7),X1)
& X7 = X8
& in(X8,powerset(relation_dom(X2))) ) ) ) ),
inference(rectify,[],[f38]) ).
fof(f47,plain,
? [X0,X1,X2] :
( function(X2)
& relation(X2)
& element(X1,powerset(powerset(X0)))
& ! [X3] :
? [X4] :
( in(X4,X3)
<~> ( in(relation_image(X2,X4),X1)
& in(X4,powerset(relation_dom(X2))) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f48,plain,
? [X0,X1,X2] :
( function(X2)
& relation(X2)
& element(X1,powerset(powerset(X0)))
& ! [X3] :
? [X4] :
( in(X4,X3)
<~> ( in(relation_image(X2,X4),X1)
& in(X4,powerset(relation_dom(X2))) ) ) ),
inference(flattening,[],[f47]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0)))
| ? [X3,X4,X5] :
( in(relation_image(X2,X5),X1)
& X3 = X5
& in(relation_image(X2,X4),X1)
& X3 = X4
& X4 != X5 )
| ? [X6] :
! [X7] :
( in(X7,X6)
<=> ? [X8] :
( in(relation_image(X2,X7),X1)
& X7 = X8
& in(X8,powerset(relation_dom(X2))) ) ) ),
inference(ennf_transformation,[],[f39]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0)))
| ? [X3,X4,X5] :
( in(relation_image(X2,X5),X1)
& X3 = X5
& in(relation_image(X2,X4),X1)
& X3 = X4
& X4 != X5 )
| ? [X6] :
! [X7] :
( in(X7,X6)
<=> ? [X8] :
( in(relation_image(X2,X7),X1)
& X7 = X8
& in(X8,powerset(relation_dom(X2))) ) ) ),
inference(flattening,[],[f70]) ).
fof(f74,plain,
? [X0,X1,X2] :
( function(X2)
& relation(X2)
& element(X1,powerset(powerset(X0)))
& ! [X3] :
? [X4] :
( ( in(X4,X3)
| ( in(relation_image(X2,X4),X1)
& in(X4,powerset(relation_dom(X2))) ) )
& ( ~ in(X4,X3)
| ~ in(relation_image(X2,X4),X1)
| ~ in(X4,powerset(relation_dom(X2))) ) ) ),
inference(nnf_transformation,[],[f48]) ).
fof(f75,plain,
? [X0,X1,X2] :
( function(X2)
& relation(X2)
& element(X1,powerset(powerset(X0)))
& ! [X3] :
? [X4] :
( ( in(X4,X3)
| ( in(relation_image(X2,X4),X1)
& in(X4,powerset(relation_dom(X2))) ) )
& ( ~ in(X4,X3)
| ~ in(relation_image(X2,X4),X1)
| ~ in(X4,powerset(relation_dom(X2))) ) ) ),
inference(flattening,[],[f74]) ).
fof(f76,plain,
( function(sK3)
& relation(sK3)
& element(sK2,powerset(powerset(sK1)))
& ! [X3] :
( ( in(sK4(X3),X3)
| ( in(relation_image(sK3,sK4(X3)),sK2)
& in(sK4(X3),powerset(relation_dom(sK3))) ) )
& ( ~ in(sK4(X3),X3)
| ~ in(relation_image(sK3,sK4(X3)),sK2)
| ~ in(sK4(X3),powerset(relation_dom(sK3))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3),skolemize(X4,sK4(X3))],[f75]) ).
fof(f96,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0)))
| sP0(X1,X2)
| ? [X6] :
! [X7] :
( ( ~ in(X7,X6)
| ? [X8] :
( in(relation_image(X2,X7),X1)
& X7 = X8
& in(X8,powerset(relation_dom(X2))) ) )
& ( ! [X8] :
( ~ in(relation_image(X2,X7),X1)
| X7 != X8
| ~ in(X8,powerset(relation_dom(X2))) )
| in(X7,X6) ) ) ),
inference(nnf_transformation,[],[f73]) ).
fof(f97,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0)))
| sP0(X1,X2)
| ? [X3] :
! [X4] :
( ( ~ in(X4,X3)
| ? [X6] :
( in(relation_image(X2,X4),X1)
& X4 = X6
& in(X6,powerset(relation_dom(X2))) ) )
& ( ! [X5] :
( ~ in(relation_image(X2,X4),X1)
| X4 != X5
| ~ in(X5,powerset(relation_dom(X2))) )
| in(X4,X3) ) ) ),
inference(rectify,[],[f96]) ).
fof(f98,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0)))
| sP0(X1,X2)
| ! [X4] :
( ( ~ in(X4,sK24(X1,X2))
| ( in(relation_image(X2,X4),X1)
& sK25(X1,X2,X4) = X4
& in(sK25(X1,X2,X4),powerset(relation_dom(X2))) ) )
& ( ! [X5] :
( ~ in(relation_image(X2,X4),X1)
| X4 != X5
| ~ in(X5,powerset(relation_dom(X2))) )
| in(X4,sK24(X1,X2)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24,sK25]),skolemize(X3,sK24(X1,X2)),skolemize(X6,sK25(X1,X2,X4))],[f97]) ).
fof(f99,plain,
function(sK3),
inference(cnf_transformation,[],[f76]) ).
fof(f100,plain,
relation(sK3),
inference(cnf_transformation,[],[f76]) ).
fof(f101,plain,
element(sK2,powerset(powerset(sK1))),
inference(cnf_transformation,[],[f76]) ).
fof(f102,plain,
! [X3] :
( in(sK4(X3),X3)
| in(relation_image(sK3,sK4(X3)),sK2) ),
inference(cnf_transformation,[],[f76]) ).
fof(f103,plain,
! [X3] :
( in(sK4(X3),X3)
| in(sK4(X3),powerset(relation_dom(sK3))) ),
inference(cnf_transformation,[],[f76]) ).
fof(f104,plain,
! [X3] :
( ~ in(sK4(X3),X3)
| ~ in(relation_image(sK3,sK4(X3)),sK2)
| ~ in(sK4(X3),powerset(relation_dom(sK3))) ),
inference(cnf_transformation,[],[f76]) ).
fof(f181,plain,
! [X2,X0,X1,X4] :
( ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0)))
| sP0(X1,X2)
| ~ in(X4,sK24(X1,X2))
| in(relation_image(X2,X4),X1) ),
inference(cnf_transformation,[],[f98]) ).
fof(f182,plain,
! [X2,X0,X1,X4] :
( ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0)))
| sP0(X1,X2)
| ~ in(X4,sK24(X1,X2))
| sK25(X1,X2,X4) = X4 ),
inference(cnf_transformation,[],[f98]) ).
fof(f183,plain,
! [X2,X0,X1,X4] :
( ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0)))
| sP0(X1,X2)
| ~ in(X4,sK24(X1,X2))
| in(sK25(X1,X2,X4),powerset(relation_dom(X2))) ),
inference(cnf_transformation,[],[f98]) ).
fof(f184,plain,
! [X2,X0,X1,X4,X5] :
( ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0)))
| sP0(X1,X2)
| ~ in(relation_image(X2,X4),X1)
| X4 != X5
| ~ in(X5,powerset(relation_dom(X2)))
| in(X4,sK24(X1,X2)) ),
inference(cnf_transformation,[],[f98]) ).
fof(f185,plain,
! [X2,X0,X1,X5] :
( ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0)))
| sP0(X1,X2)
| ~ in(relation_image(X2,X5),X1)
| ~ in(X5,powerset(relation_dom(X2)))
| in(X5,sK24(X1,X2)) ),
inference(equality_resolution,[],[f184]) ).
tcf(c_49,negated_conjecture,
! [X0: $i] :
( ~ in(sK4(X0),X0)
| ~ in(sK4(X0),powerset(relation_dom(sK3)))
| ~ in(relation_image(sK3,sK4(X0)),sK2) ),
inference(cnf_transformation,[],[f104]) ).
tcf(c_50,negated_conjecture,
! [X0: $i] :
( in(sK4(X0),X0)
| in(sK4(X0),powerset(relation_dom(sK3))) ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_51,negated_conjecture,
! [X0: $i] :
( in(sK4(X0),X0)
| in(relation_image(sK3,sK4(X0)),sK2) ),
inference(cnf_transformation,[],[f102]) ).
tcf(c_52,negated_conjecture,
element(sK2,powerset(powerset(sK1))),
inference(cnf_transformation,[],[f101]) ).
tcf(c_53,negated_conjecture,
relation(sK3),
inference(cnf_transformation,[],[f100]) ).
tcf(c_54,negated_conjecture,
function(sK3),
inference(cnf_transformation,[],[f99]) ).
tcf(c_128,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP0(X2,X0)
| in(X1,sK24(X2,X0))
| ~ function(X0)
| ~ relation(X0)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X1,powerset(relation_dom(X0)))
| ~ in(relation_image(X0,X1),X2) ),
inference(cnf_transformation,[],[f185]) ).
tcf(c_129,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP0(X1,X2)
| in(sK25(X1,X2,X0),powerset(relation_dom(X2)))
| ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X3)))
| ~ in(X0,sK24(X1,X2)) ),
inference(cnf_transformation,[],[f183]) ).
tcf(c_130,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP0(X1,X2)
| ( sK25(X1,X2,X0) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X3)))
| ~ in(X0,sK24(X1,X2)) ),
inference(cnf_transformation,[],[f182]) ).
tcf(c_131,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP0(X1,X2)
| in(relation_image(X2,X0),X1)
| ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X3)))
| ~ in(X0,sK24(X1,X2)) ),
inference(cnf_transformation,[],[f181]) ).
tcf(c_6402,definition,
iPr_def_10 = powerset(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_6403,definition,
iPr_def_11 = powerset(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_6404,definition,
iPr_def_12 = relation_dom(sK3),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_6405,definition,
iPr_def_13 = powerset(iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_6406,negated_conjecture,
function(sK3),
inference(demodulation,[status(thm)],[c_54]) ).
tcf(c_6407,negated_conjecture,
relation(sK3),
inference(demodulation,[status(thm)],[c_53]) ).
tcf(c_6408,negated_conjecture,
element(sK2,iPr_def_11),
inference(demodulation,[status(thm)],[c_52,c_6402,c_6403]) ).
tcf(c_6409,negated_conjecture,
! [X0: $i] :
( in(sK4(X0),X0)
| in(relation_image(sK3,sK4(X0)),sK2) ),
inference(demodulation,[status(thm)],[c_51]) ).
tcf(c_6410,negated_conjecture,
! [X0: $i] :
( in(sK4(X0),iPr_def_13)
| in(sK4(X0),X0) ),
inference(demodulation,[status(thm)],[c_50,c_6404,c_6405]) ).
tcf(c_6411,negated_conjecture,
! [X0: $i] :
( ~ in(sK4(X0),iPr_def_13)
| ~ in(sK4(X0),X0)
| ~ in(relation_image(sK3,sK4(X0)),sK2) ),
inference(demodulation,[status(thm)],[c_49]) ).
tcf(c_7512,plain,
! [X0: $i,X1: $i] :
( sP0(sK2,sK3)
| in(sK4(X0),X0)
| in(sK4(X0),sK24(sK2,sK3))
| ~ function(sK3)
| ~ relation(sK3)
| ~ element(sK2,powerset(powerset(X1)))
| ~ in(sK4(X0),powerset(relation_dom(sK3))) ),
inference(superposition,[status(thm)],[c_6409,c_128]) ).
tcf(c_7520,plain,
! [X0: $i,X1: $i] :
( sP0(sK2,sK3)
| in(sK4(X1),X1)
| in(sK4(X1),sK24(sK2,sK3))
| ~ function(sK3)
| ~ relation(sK3)
| ~ in(sK4(X1),iPr_def_13)
| ~ element(sK2,powerset(powerset(X0))) ),
inference(light_normalisation,[status(thm)],[c_7512,c_6404,c_6405]) ).
tcf(c_7521,plain,
! [X0: $i,X1: $i] :
( sP0(sK2,sK3)
| in(sK4(X1),X1)
| in(sK4(X1),sK24(sK2,sK3))
| ~ in(sK4(X1),iPr_def_13)
| ~ element(sK2,powerset(powerset(X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7520,c_6406,c_6407]) ).
tcf(c_7691,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X1,X2)
| in(sK25(X1,X2,X0),powerset(relation_dom(X2)))
| ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(iPr_def_10))
| ~ in(X0,sK24(X1,X2)) ),
inference(superposition,[status(thm)],[c_6402,c_129]) ).
tcf(c_7706,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X1,X2)
| in(sK25(X1,X2,X0),powerset(relation_dom(X2)))
| ~ function(X2)
| ~ relation(X2)
| ~ element(X1,iPr_def_11)
| ~ in(X0,sK24(X1,X2)) ),
inference(light_normalisation,[status(thm)],[c_7691,c_6403]) ).
tcf(c_7770,plain,
! [X0: $i,X1: $i] :
( sP0(sK2,sK3)
| in(sK4(X1),X1)
| in(sK4(X1),sK24(sK2,sK3))
| ~ element(sK2,powerset(powerset(X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7521,c_6410]) ).
tcf(c_7783,plain,
! [X0: $i] :
( sP0(sK2,sK3)
| in(sK4(X0),X0)
| in(sK4(X0),sK24(sK2,sK3))
| ~ element(sK2,powerset(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_6402,c_7770]) ).
tcf(c_7794,plain,
! [X0: $i] :
( sP0(sK2,sK3)
| in(sK4(X0),X0)
| in(sK4(X0),sK24(sK2,sK3))
| ~ element(sK2,iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_7783,c_6403]) ).
tcf(c_7795,plain,
! [X0: $i] :
( sP0(sK2,sK3)
| in(sK4(X0),X0)
| in(sK4(X0),sK24(sK2,sK3)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7794,c_6408]) ).
tcf(c_7819,plain,
( sP0(sK2,sK3)
| in(sK4(sK24(sK2,sK3)),sK24(sK2,sK3)) ),
inference(equality_factoring,[status(thm)],[c_7795]) ).
tcf(c_7878,plain,
! [X0: $i] :
( sP0(sK2,sK3)
| ( sK25(sK2,sK3,sK4(sK24(sK2,sK3))) = sK4(sK24(sK2,sK3)) )
| ~ function(sK3)
| ~ relation(sK3)
| ~ element(sK2,powerset(powerset(X0))) ),
inference(superposition,[status(thm)],[c_7819,c_130]) ).
tcf(c_7879,plain,
! [X0: $i] :
( sP0(sK2,sK3)
| in(relation_image(sK3,sK4(sK24(sK2,sK3))),sK2)
| ~ function(sK3)
| ~ relation(sK3)
| ~ element(sK2,powerset(powerset(X0))) ),
inference(superposition,[status(thm)],[c_7819,c_131]) ).
tcf(c_7883,plain,
! [X0: $i] :
( sP0(sK2,sK3)
| in(relation_image(sK3,sK4(sK24(sK2,sK3))),sK2)
| ~ element(sK2,powerset(powerset(X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7879,c_6406,c_6407]) ).
tcf(c_7887,plain,
! [X0: $i] :
( sP0(sK2,sK3)
| ( sK25(sK2,sK3,sK4(sK24(sK2,sK3))) = sK4(sK24(sK2,sK3)) )
| ~ element(sK2,powerset(powerset(X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7878,c_6406,c_6407]) ).
tcf(c_7912,plain,
( sP0(sK2,sK3)
| in(relation_image(sK3,sK4(sK24(sK2,sK3))),sK2)
| ~ element(sK2,powerset(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_6402,c_7883]) ).
tcf(c_7918,plain,
( sP0(sK2,sK3)
| in(relation_image(sK3,sK4(sK24(sK2,sK3))),sK2)
| ~ element(sK2,iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_7912,c_6403]) ).
tcf(c_7919,plain,
( sP0(sK2,sK3)
| in(relation_image(sK3,sK4(sK24(sK2,sK3))),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7918,c_6408]) ).
tcf(c_7928,plain,
( sP0(sK2,sK3)
| ~ in(sK4(sK24(sK2,sK3)),iPr_def_13)
| ~ in(sK4(sK24(sK2,sK3)),sK24(sK2,sK3)) ),
inference(superposition,[status(thm)],[c_7919,c_6411]) ).
tcf(c_7936,plain,
( sP0(sK2,sK3)
| ~ in(sK4(sK24(sK2,sK3)),iPr_def_13) ),
inference(global_subsumption_just,[status(thm)],[c_7928,c_7819,c_7928]) ).
tcf(c_8018,plain,
( sP0(sK2,sK3)
| ( sK25(sK2,sK3,sK4(sK24(sK2,sK3))) = sK4(sK24(sK2,sK3)) )
| ~ element(sK2,powerset(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_6402,c_7887]) ).
tcf(c_8027,plain,
( sP0(sK2,sK3)
| ( sK25(sK2,sK3,sK4(sK24(sK2,sK3))) = sK4(sK24(sK2,sK3)) )
| ~ element(sK2,iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_8018,c_6403]) ).
tcf(c_8028,plain,
( sP0(sK2,sK3)
| ( sK25(sK2,sK3,sK4(sK24(sK2,sK3))) = sK4(sK24(sK2,sK3)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8027,c_6408]) ).
tcf(c_8141,plain,
! [X0: $i,X1: $i] :
( sP0(X1,sK3)
| in(sK25(X1,sK3,X0),powerset(iPr_def_12))
| ~ function(sK3)
| ~ relation(sK3)
| ~ element(X1,iPr_def_11)
| ~ in(X0,sK24(X1,sK3)) ),
inference(superposition,[status(thm)],[c_6404,c_7706]) ).
tcf(c_8143,plain,
! [X0: $i,X1: $i] :
( sP0(X1,sK3)
| in(sK25(X1,sK3,X0),iPr_def_13)
| ~ function(sK3)
| ~ relation(sK3)
| ~ element(X1,iPr_def_11)
| ~ in(X0,sK24(X1,sK3)) ),
inference(light_normalisation,[status(thm)],[c_8141,c_6405]) ).
tcf(c_8144,plain,
! [X0: $i,X1: $i] :
( sP0(X1,sK3)
| in(sK25(X1,sK3,X0),iPr_def_13)
| ~ element(X1,iPr_def_11)
| ~ in(X0,sK24(X1,sK3)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8143,c_6406,c_6407]) ).
fof(f72,definition,
! [X1,X2] :
( ~ sP0(X1,X2)
| ? [X3,X4,X5] :
( in(relation_image(X2,X5),X1)
& X3 = X5
& in(relation_image(X2,X4),X1)
& X3 = X4
& X4 != X5 ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0)))
| sP0(X1,X2)
| ? [X6] :
! [X7] :
( in(X7,X6)
<=> ? [X8] :
( in(relation_image(X2,X7),X1)
& X7 = X8
& in(X8,powerset(relation_dom(X2))) ) ) ),
inference(definition_folding,[],[f71,f72]) ).
fof(f93,plain,
! [X1,X2] :
( ~ sP0(X1,X2)
| ? [X3,X4,X5] :
( in(relation_image(X2,X5),X1)
& X3 = X5
& in(relation_image(X2,X4),X1)
& X3 = X4
& X4 != X5 ) ),
inference(nnf_transformation,[],[f72]) ).
fof(f94,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ? [X2,X3,X4] :
( in(relation_image(X1,X4),X0)
& X2 = X4
& in(relation_image(X1,X3),X0)
& X2 = X3
& X3 != X4 ) ),
inference(rectify,[],[f93]) ).
fof(f95,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ( in(relation_image(X1,sK23(X0,X1)),X0)
& sK21(X0,X1) = sK23(X0,X1)
& in(relation_image(X1,sK22(X0,X1)),X0)
& sK21(X0,X1) = sK22(X0,X1)
& sK22(X0,X1) != sK23(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21,sK22,sK23]),skolemize(X2,sK21(X0,X1)),skolemize(X3,sK22(X0,X1)),skolemize(X4,sK23(X0,X1))],[f94]) ).
fof(f177,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| sK21(X0,X1) = sK23(X0,X1) ),
inference(cnf_transformation,[],[f95]) ).
fof(f179,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| sK21(X0,X1) = sK22(X0,X1) ),
inference(cnf_transformation,[],[f95]) ).
fof(f180,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| sK22(X0,X1) != sK23(X0,X1) ),
inference(cnf_transformation,[],[f95]) ).
tcf(c_123,plain,
! [X0: $i,X1: $i] :
( ~ sP0(X0,X1)
| ( sK22(X0,X1) != sK23(X0,X1) ) ),
inference(cnf_transformation,[],[f180]) ).
tcf(c_124,plain,
! [X0: $i,X1: $i] :
( ( sK22(X0,X1) = sK21(X0,X1) )
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f179]) ).
tcf(c_126,plain,
! [X0: $i,X1: $i] :
( ( sK23(X0,X1) = sK21(X0,X1) )
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f177]) ).
tcf(c_8037,plain,
( ( sK23(sK2,sK3) = sK21(sK2,sK3) )
| ( sK25(sK2,sK3,sK4(sK24(sK2,sK3))) = sK4(sK24(sK2,sK3)) ) ),
inference(superposition,[status(thm)],[c_8028,c_126]) ).
tcf(c_8038,plain,
( ( sK22(sK2,sK3) = sK21(sK2,sK3) )
| ( sK25(sK2,sK3,sK4(sK24(sK2,sK3))) = sK4(sK24(sK2,sK3)) ) ),
inference(superposition,[status(thm)],[c_8028,c_124]) ).
tcf(c_8139,plain,
( sP0(sK2,sK3)
| in(sK4(sK24(sK2,sK3)),powerset(relation_dom(sK3)))
| ( sK22(sK2,sK3) = sK21(sK2,sK3) )
| ~ function(sK3)
| ~ relation(sK3)
| ~ element(sK2,iPr_def_11)
| ~ in(sK4(sK24(sK2,sK3)),sK24(sK2,sK3)) ),
inference(superposition,[status(thm)],[c_8038,c_7706]) ).
tcf(c_8140,plain,
( sP0(sK2,sK3)
| in(sK4(sK24(sK2,sK3)),powerset(relation_dom(sK3)))
| ( sK23(sK2,sK3) = sK21(sK2,sK3) )
| ~ function(sK3)
| ~ relation(sK3)
| ~ element(sK2,iPr_def_11)
| ~ in(sK4(sK24(sK2,sK3)),sK24(sK2,sK3)) ),
inference(superposition,[status(thm)],[c_8037,c_7706]) ).
tcf(c_8155,plain,
( sP0(sK2,sK3)
| in(sK4(sK24(sK2,sK3)),iPr_def_13)
| ( sK23(sK2,sK3) = sK21(sK2,sK3) )
| ~ function(sK3)
| ~ relation(sK3)
| ~ element(sK2,iPr_def_11)
| ~ in(sK4(sK24(sK2,sK3)),sK24(sK2,sK3)) ),
inference(light_normalisation,[status(thm)],[c_8140,c_6404,c_6405]) ).
tcf(c_8156,plain,
( sP0(sK2,sK3)
| in(sK4(sK24(sK2,sK3)),iPr_def_13)
| ( sK23(sK2,sK3) = sK21(sK2,sK3) )
| ~ in(sK4(sK24(sK2,sK3)),sK24(sK2,sK3)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8155,c_6406,c_6407,c_6408]) ).
tcf(c_8161,plain,
( sP0(sK2,sK3)
| in(sK4(sK24(sK2,sK3)),iPr_def_13)
| ( sK22(sK2,sK3) = sK21(sK2,sK3) )
| ~ function(sK3)
| ~ relation(sK3)
| ~ element(sK2,iPr_def_11)
| ~ in(sK4(sK24(sK2,sK3)),sK24(sK2,sK3)) ),
inference(light_normalisation,[status(thm)],[c_8139,c_6404,c_6405]) ).
tcf(c_8162,plain,
( sP0(sK2,sK3)
| in(sK4(sK24(sK2,sK3)),iPr_def_13)
| ( sK22(sK2,sK3) = sK21(sK2,sK3) )
| ~ in(sK4(sK24(sK2,sK3)),sK24(sK2,sK3)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8161,c_6406,c_6407,c_6408]) ).
tcf(c_8194,plain,
( sP0(sK2,sK3)
| ( sK23(sK2,sK3) = sK21(sK2,sK3) ) ),
inference(global_subsumption_just,[status(thm)],[c_8156,c_7819,c_7936,c_8156]) ).
tcf(c_8198,plain,
sK23(sK2,sK3) = sK21(sK2,sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_8194,c_126]) ).
tcf(c_8203,plain,
( sP0(sK2,sK3)
| ( sK22(sK2,sK3) = sK21(sK2,sK3) ) ),
inference(global_subsumption_just,[status(thm)],[c_8162,c_7819,c_7936,c_8162]) ).
tcf(c_8205,plain,
( sP0(sK2,sK3)
| ( sK22(sK2,sK3) = sK23(sK2,sK3) ) ),
inference(light_normalisation,[status(thm)],[c_8203,c_8198]) ).
tcf(c_8213,plain,
( ( sK22(sK2,sK3) = sK21(sK2,sK3) )
| ( sK22(sK2,sK3) = sK23(sK2,sK3) ) ),
inference(superposition,[status(thm)],[c_8205,c_124]) ).
tcf(c_8214,plain,
sK22(sK2,sK3) = sK23(sK2,sK3),
inference(light_normalisation,[status(thm)],[c_8213,c_8198]) ).
tcf(c_8566,plain,
~ sP0(sK2,sK3),
inference(superposition,[status(thm)],[c_8214,c_123]) ).
tcf(c_8568,plain,
sK25(sK2,sK3,sK4(sK24(sK2,sK3))) = sK4(sK24(sK2,sK3)),
inference(backward_subsumption_resolution,[status(thm)],[c_8028,c_8566]) ).
tcf(c_8571,plain,
~ in(sK4(sK24(sK2,sK3)),iPr_def_13),
inference(backward_subsumption_resolution,[status(thm)],[c_7936,c_8566]) ).
tcf(c_8786,plain,
( sP0(sK2,sK3)
| in(sK4(sK24(sK2,sK3)),iPr_def_13)
| ~ element(sK2,iPr_def_11)
| ~ in(sK4(sK24(sK2,sK3)),sK24(sK2,sK3)) ),
inference(superposition,[status(thm)],[c_8568,c_8144]) ).
tcf(c_8789,plain,
~ in(sK4(sK24(sK2,sK3)),sK24(sK2,sK3)),
inference(forward_subsumption_resolution,[status(thm)],[c_8786,c_8566,c_8571,c_6408]) ).
tcf(c_8790,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_8789,c_8566,c_7819]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU297+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n012.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 13:35:07 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.38 Running first-order theorem proving
% 0.11/0.38 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.39
% 0.11/0.39 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.39
% 0.11/0.39 % Detected problem language: tptp
% 0.11/0.40 % Proving...
% 3.85/1.13 % SZS status Started for theBenchmark.p
% 3.85/1.13 % SZS status Theorem for theBenchmark.p
% 3.85/1.13
% 3.85/1.13 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.85/1.13
% 3.85/1.13 % ------ iProver source info
% 3.85/1.13
% 3.85/1.13 % git: date: 2026-07-19 20:42:38 +0200
% 3.85/1.13 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.85/1.13 % git: non_committed_changes: false
% 3.85/1.13
% 3.85/1.13 % ------ Parsing...
% 3.85/1.13 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.85/1.13
% 3.85/1.13 % ------ Preprocessing... sup_sim: 0 sf_s rm: 35 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 5 0s sf_e pe_s pe_e %
% 3.85/1.13
% 3.85/1.13 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.85/1.13
% 3.85/1.13 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.85/1.13 % ------ Proving...
% 3.85/1.13 % ------ Problem Properties
% 3.85/1.13
% 3.85/1.13 %
% 3.85/1.13 % clauses 55
% 3.85/1.13 % conjectures 6
% 3.85/1.13 % EPR 25
% 3.85/1.13 % Horn 47
% 3.85/1.13 % unary 33
% 3.85/1.13 % binary 16
% 3.85/1.13 % lits 96
% 3.85/1.13 % lits eq 8
% 3.85/1.13 % fd_pure 0
% 3.85/1.13 % fd_pseudo 0
% 3.85/1.13 % fd_cond 0
% 3.85/1.13 % fd_pseudo_cond 0
% 3.85/1.13 % AC symbols 0
% 3.85/1.13
% 3.85/1.13 % ------ Schedule dynamic 5 is on
% 3.85/1.13
% 3.85/1.13 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.85/1.13
% 3.85/1.13
% 3.85/1.13 % ------
% 3.85/1.13 % Current options:
% 3.85/1.13 % ------
% 3.85/1.13
% 3.85/1.13
% 3.85/1.13 %
% 3.85/1.13
% 3.85/1.13 % ------ Proving...
% 3.85/1.13 %
% 3.85/1.13
% 3.85/1.13 % SZS status Theorem for theBenchmark.p
% 3.85/1.13
% 3.85/1.13 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.85/1.13
% 3.85/1.13
%------------------------------------------------------------------------------