%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM656+4 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 12:16:15 PM UTC 2026
% Result : Theorem 6.70s 2.51s
% Output : Refutation 12.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 28
% Syntax : Number of formulae : 154 ( 29 unt; 16 def)
% Number of atoms : 362 ( 2 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 356 ( 148 ~; 158 |; 20 &)
% ( 26 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 21 ( 19 usr; 17 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 10 con; 0-2 aty)
% Number of variables : 79 ( 0 sgn 77 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f115,axiom,
! [X0] :
( pp(scratc424593673_d_not(X0))
<=> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1168780466nd_imp,X0),fFalse)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__d__not) ).
fof(f116,axiom,
scratc1168780466nd_imp = fimplies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__imp) ).
fof(f147,axiom,
! [X0,X1] :
( pp(aa_fun171081125l_bool(scratc1382104286all_of(X0),X1))
<=> ! [X2] :
( gg_TPTP_ind(X2)
=> ( scratc1329672891_is_of(X2,X0)
=> pp(aa_TPTP_ind_bool(X1,X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__all__of) ).
fof(f151,axiom,
pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aTP_Lamm_bv)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_satz10d) ).
fof(f284,axiom,
! [X0] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bv,X0))
<=> pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bu,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ATP_Olambda__37) ).
fof(f287,axiom,
! [X0] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ab,X0))
<=> pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ATP_Olambda__40) ).
fof(f311,axiom,
! [X0,X1] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,X0),X1))
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc364131377_29_ii,X0),X1))
=> pp(scratc424593673_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc120891389lessis,X0),X1))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ATP_Olambda__64) ).
fof(f313,axiom,
! [X0,X1] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bu,X0),X1))
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc120891389lessis,X0),X1))
=> pp(scratc424593673_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc364131377_29_ii,X0),X1))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ATP_Olambda__66) ).
fof(f393,axiom,
~ pp(fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
fof(f394,axiom,
! [X0,X1] :
( ~ pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,X0),X1))
| ~ pp(X0)
| pp(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_3_1_U) ).
fof(f396,axiom,
! [X0,X1] :
( pp(X0)
| pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,X0),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_1_1_U) ).
fof(f403,conjecture,
pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aTP_Lamm_ab)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f404,negated_conjecture,
~ pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aTP_Lamm_ab)),
inference(negated_conjecture,[status(cth)],[f403]) ).
fof(f405,plain,
~ pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aTP_Lamm_ab)),
inference(flattening,[],[f404]) ).
fof(f422,plain,
! [X0,X1] :
( pp(aa_fun171081125l_bool(scratc1382104286all_of(X0),X1))
<=> ! [X2] :
( pp(aa_TPTP_ind_bool(X1,X2))
| ~ scratc1329672891_is_of(X2,X0)
| ~ gg_TPTP_ind(X2) ) ),
inference(ennf_transformation,[],[f147]) ).
fof(f423,plain,
! [X0,X1] :
( pp(aa_fun171081125l_bool(scratc1382104286all_of(X0),X1))
<=> ! [X2] :
( pp(aa_TPTP_ind_bool(X1,X2))
| ~ scratc1329672891_is_of(X2,X0)
| ~ gg_TPTP_ind(X2) ) ),
inference(flattening,[],[f422]) ).
fof(f490,plain,
! [X0,X1] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,X0),X1))
<=> ( pp(scratc424593673_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc120891389lessis,X0),X1)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc364131377_29_ii,X0),X1)) ) ),
inference(ennf_transformation,[],[f311]) ).
fof(f492,plain,
! [X0,X1] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bu,X0),X1))
<=> ( pp(scratc424593673_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc364131377_29_ii,X0),X1)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc120891389lessis,X0),X1)) ) ),
inference(ennf_transformation,[],[f313]) ).
fof(f564,plain,
! [X0] :
( ( pp(scratc424593673_d_not(X0))
| ~ pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1168780466nd_imp,X0),fFalse)) )
& ( pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1168780466nd_imp,X0),fFalse))
| ~ pp(scratc424593673_d_not(X0)) ) ),
inference(nnf_transformation,[],[f115]) ).
fof(f587,plain,
! [X0,X1] :
( ( pp(aa_fun171081125l_bool(scratc1382104286all_of(X0),X1))
| ? [X2] :
( ~ pp(aa_TPTP_ind_bool(X1,X2))
& scratc1329672891_is_of(X2,X0)
& gg_TPTP_ind(X2) ) )
& ( ! [X2] :
( pp(aa_TPTP_ind_bool(X1,X2))
| ~ scratc1329672891_is_of(X2,X0)
| ~ gg_TPTP_ind(X2) )
| ~ pp(aa_fun171081125l_bool(scratc1382104286all_of(X0),X1)) ) ),
inference(nnf_transformation,[],[f423]) ).
fof(f588,plain,
! [X0,X1] :
( ( pp(aa_fun171081125l_bool(scratc1382104286all_of(X0),X1))
| ? [X2] :
( ~ pp(aa_TPTP_ind_bool(X1,X2))
& scratc1329672891_is_of(X2,X0)
& gg_TPTP_ind(X2) ) )
& ( ! [X3] :
( pp(aa_TPTP_ind_bool(X1,X3))
| ~ scratc1329672891_is_of(X3,X0)
| ~ gg_TPTP_ind(X3) )
| ~ pp(aa_fun171081125l_bool(scratc1382104286all_of(X0),X1)) ) ),
inference(rectify,[],[f587]) ).
fof(f589,plain,
! [X0,X1] :
( ( pp(aa_fun171081125l_bool(scratc1382104286all_of(X0),X1))
| ( ~ pp(aa_TPTP_ind_bool(X1,sK12(X0,X1)))
& scratc1329672891_is_of(sK12(X0,X1),X0)
& gg_TPTP_ind(sK12(X0,X1)) ) )
& ( ! [X3] :
( pp(aa_TPTP_ind_bool(X1,X3))
| ~ scratc1329672891_is_of(X3,X0)
| ~ gg_TPTP_ind(X3) )
| ~ pp(aa_fun171081125l_bool(scratc1382104286all_of(X0),X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X2,sK12(X0,X1))],[f588]) ).
fof(f645,plain,
! [X0] :
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_bv,X0))
| ~ pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bu,X0))) )
& ( pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bu,X0)))
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bv,X0)) ) ),
inference(nnf_transformation,[],[f284]) ).
fof(f648,plain,
! [X0] :
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_ab,X0))
| ~ pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,X0))) )
& ( pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,X0)))
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_ab,X0)) ) ),
inference(nnf_transformation,[],[f287]) ).
fof(f681,plain,
! [X0,X1] :
( ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,X0),X1))
| ( ~ pp(scratc424593673_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc120891389lessis,X0),X1)))
& pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc364131377_29_ii,X0),X1)) ) )
& ( pp(scratc424593673_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc120891389lessis,X0),X1)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc364131377_29_ii,X0),X1))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,X0),X1)) ) ),
inference(nnf_transformation,[],[f490]) ).
fof(f682,plain,
! [X0,X1] :
( ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,X0),X1))
| ( ~ pp(scratc424593673_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc120891389lessis,X0),X1)))
& pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc364131377_29_ii,X0),X1)) ) )
& ( pp(scratc424593673_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc120891389lessis,X0),X1)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc364131377_29_ii,X0),X1))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,X0),X1)) ) ),
inference(flattening,[],[f681]) ).
fof(f685,plain,
! [X0,X1] :
( ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bu,X0),X1))
| ( ~ pp(scratc424593673_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc364131377_29_ii,X0),X1)))
& pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc120891389lessis,X0),X1)) ) )
& ( pp(scratc424593673_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc364131377_29_ii,X0),X1)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc120891389lessis,X0),X1))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bu,X0),X1)) ) ),
inference(nnf_transformation,[],[f492]) ).
fof(f686,plain,
! [X0,X1] :
( ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bu,X0),X1))
| ( ~ pp(scratc424593673_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc364131377_29_ii,X0),X1)))
& pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc120891389lessis,X0),X1)) ) )
& ( pp(scratc424593673_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc364131377_29_ii,X0),X1)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc120891389lessis,X0),X1))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bu,X0),X1)) ) ),
inference(flattening,[],[f685]) ).
fof(f923,plain,
! [X0] :
( pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1168780466nd_imp,X0),fFalse))
| ~ pp(scratc424593673_d_not(X0)) ),
inference(cnf_transformation,[],[f564]) ).
fof(f924,plain,
! [X0] :
( pp(scratc424593673_d_not(X0))
| ~ pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1168780466nd_imp,X0),fFalse)) ),
inference(cnf_transformation,[],[f564]) ).
fof(f925,plain,
scratc1168780466nd_imp = fimplies,
inference(cnf_transformation,[],[f116]) ).
fof(f987,plain,
! [X3,X0,X1] :
( pp(aa_TPTP_ind_bool(X1,X3))
| ~ scratc1329672891_is_of(X3,X0)
| ~ gg_TPTP_ind(X3)
| ~ pp(aa_fun171081125l_bool(scratc1382104286all_of(X0),X1)) ),
inference(cnf_transformation,[],[f589]) ).
fof(f988,plain,
! [X0,X1] :
( pp(aa_fun171081125l_bool(scratc1382104286all_of(X0),X1))
| gg_TPTP_ind(sK12(X0,X1)) ),
inference(cnf_transformation,[],[f589]) ).
fof(f989,plain,
! [X0,X1] :
( pp(aa_fun171081125l_bool(scratc1382104286all_of(X0),X1))
| scratc1329672891_is_of(sK12(X0,X1),X0) ),
inference(cnf_transformation,[],[f589]) ).
fof(f990,plain,
! [X0,X1] :
( pp(aa_fun171081125l_bool(scratc1382104286all_of(X0),X1))
| ~ pp(aa_TPTP_ind_bool(X1,sK12(X0,X1))) ),
inference(cnf_transformation,[],[f589]) ).
fof(f995,plain,
pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aTP_Lamm_bv)),
inference(cnf_transformation,[],[f151]) ).
fof(f1194,plain,
! [X0] :
( pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bu,X0)))
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bv,X0)) ),
inference(cnf_transformation,[],[f645]) ).
fof(f1201,plain,
! [X0] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ab,X0))
| ~ pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,X0))) ),
inference(cnf_transformation,[],[f648]) ).
fof(f1256,plain,
! [X0,X1] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,X0),X1))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc364131377_29_ii,X0),X1)) ),
inference(cnf_transformation,[],[f682]) ).
fof(f1257,plain,
! [X0,X1] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,X0),X1))
| ~ pp(scratc424593673_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc120891389lessis,X0),X1))) ),
inference(cnf_transformation,[],[f682]) ).
fof(f1261,plain,
! [X0,X1] :
( pp(scratc424593673_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc364131377_29_ii,X0),X1)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc120891389lessis,X0),X1))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bu,X0),X1)) ),
inference(cnf_transformation,[],[f686]) ).
fof(f1431,plain,
~ pp(fFalse),
inference(cnf_transformation,[],[f393]) ).
fof(f1432,plain,
! [X0,X1] :
( ~ pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,X0),X1))
| ~ pp(X0)
| pp(X1) ),
inference(cnf_transformation,[],[f394]) ).
fof(f1434,plain,
! [X0,X1] :
( pp(X0)
| pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,X0),X1)) ),
inference(cnf_transformation,[],[f396]) ).
fof(f1441,plain,
~ pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aTP_Lamm_ab)),
inference(cnf_transformation,[],[f405]) ).
fof(f1493,plain,
! [X0] :
( pp(scratc424593673_d_not(X0))
| ~ pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,X0),fFalse)) ),
inference(definition_unfolding,[],[f924,f925]) ).
fof(f1494,plain,
! [X0] :
( pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,X0),fFalse))
| ~ pp(scratc424593673_d_not(X0)) ),
inference(definition_unfolding,[],[f923,f925]) ).
fof(f1597,definition,
( spl29_1
<=> pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aTP_Lamm_ab)) ),
introduced(definition,[new_symbols(definition,[spl29_1])],[avatar_definition]) ).
fof(f1599,plain,
( ~ pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aTP_Lamm_ab))
| spl29_1 ),
inference(avatar_component_clause,[],[f1597]) ).
fof(f1600,plain,
~ spl29_1,
inference(avatar_split_clause,[],[f1441,f1597]) ).
fof(f1601,plain,
( gg_TPTP_ind(sK12(aTP_Lamm_a,aTP_Lamm_ab))
| spl29_1 ),
inference(resolution,[],[f1599,f988]) ).
fof(f1602,plain,
( scratc1329672891_is_of(sK12(aTP_Lamm_a,aTP_Lamm_ab),aTP_Lamm_a)
| spl29_1 ),
inference(resolution,[],[f1599,f989]) ).
fof(f1603,plain,
( ~ pp(aa_TPTP_ind_bool(aTP_Lamm_ab,sK12(aTP_Lamm_a,aTP_Lamm_ab)))
| spl29_1 ),
inference(resolution,[],[f1599,f990]) ).
fof(f1616,definition,
( spl29_2
<=> scratc1329672891_is_of(sK12(aTP_Lamm_a,aTP_Lamm_ab),aTP_Lamm_a) ),
introduced(definition,[new_symbols(definition,[spl29_2])],[avatar_definition]) ).
fof(f1618,plain,
( scratc1329672891_is_of(sK12(aTP_Lamm_a,aTP_Lamm_ab),aTP_Lamm_a)
| ~ spl29_2 ),
inference(avatar_component_clause,[],[f1616]) ).
fof(f1619,plain,
( spl29_2
| spl29_1 ),
inference(avatar_split_clause,[],[f1602,f1597,f1616]) ).
fof(f1621,definition,
( spl29_3
<=> pp(aa_TPTP_ind_bool(aTP_Lamm_ab,sK12(aTP_Lamm_a,aTP_Lamm_ab))) ),
introduced(definition,[new_symbols(definition,[spl29_3])],[avatar_definition]) ).
fof(f1623,plain,
( ~ pp(aa_TPTP_ind_bool(aTP_Lamm_ab,sK12(aTP_Lamm_a,aTP_Lamm_ab)))
| spl29_3 ),
inference(avatar_component_clause,[],[f1621]) ).
fof(f1624,plain,
( ~ spl29_3
| spl29_1 ),
inference(avatar_split_clause,[],[f1603,f1597,f1621]) ).
fof(f1625,plain,
( ~ pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))
| spl29_3 ),
inference(resolution,[],[f1623,f1201]) ).
fof(f1663,plain,
( ! [X0] :
( pp(aa_TPTP_ind_bool(X0,sK12(aTP_Lamm_a,aTP_Lamm_ab)))
| ~ gg_TPTP_ind(sK12(aTP_Lamm_a,aTP_Lamm_ab))
| ~ pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),X0)) )
| ~ spl29_2 ),
inference(resolution,[],[f1618,f987]) ).
fof(f1664,plain,
( ! [X0] :
( pp(aa_TPTP_ind_bool(X0,sK12(aTP_Lamm_a,aTP_Lamm_ab)))
| ~ pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),X0)) )
| spl29_1
| ~ spl29_2 ),
inference(forward_subsumption_resolution,[],[f1663,f1601]) ).
fof(f1666,definition,
( spl29_4
<=> ! [X0] :
( pp(aa_TPTP_ind_bool(X0,sK12(aTP_Lamm_a,aTP_Lamm_ab)))
| ~ pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),X0)) ) ),
introduced(definition,[new_symbols(definition,[spl29_4])],[avatar_definition]) ).
fof(f1667,plain,
( ! [X0] :
( pp(aa_TPTP_ind_bool(X0,sK12(aTP_Lamm_a,aTP_Lamm_ab)))
| ~ pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),X0)) )
| ~ spl29_4 ),
inference(avatar_component_clause,[],[f1666]) ).
fof(f1668,plain,
( spl29_4
| spl29_1
| ~ spl29_2 ),
inference(avatar_split_clause,[],[f1664,f1616,f1597,f1666]) ).
fof(f1908,plain,
( ~ pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aTP_Lamm_bv))
| pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bu,sK12(aTP_Lamm_a,aTP_Lamm_ab))))
| ~ spl29_4 ),
inference(resolution,[],[f1667,f1194]) ).
fof(f1992,plain,
( pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bu,sK12(aTP_Lamm_a,aTP_Lamm_ab))))
| ~ spl29_4 ),
inference(forward_subsumption_resolution,[],[f1908,f995]) ).
fof(f2063,definition,
( spl29_6
<=> pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)))) ),
introduced(definition,[new_symbols(definition,[spl29_6])],[avatar_definition]) ).
fof(f2065,plain,
( ~ pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))
| spl29_6 ),
inference(avatar_component_clause,[],[f2063]) ).
fof(f2066,plain,
( ~ spl29_6
| spl29_3 ),
inference(avatar_split_clause,[],[f1625,f1621,f2063]) ).
fof(f2068,plain,
( gg_TPTP_ind(sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))
| spl29_6 ),
inference(resolution,[],[f2065,f988]) ).
fof(f2069,plain,
( scratc1329672891_is_of(sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))),aTP_Lamm_a)
| spl29_6 ),
inference(resolution,[],[f2065,f989]) ).
fof(f2070,plain,
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)),sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)))))
| spl29_6 ),
inference(resolution,[],[f2065,f990]) ).
fof(f2083,definition,
( spl29_7
<=> scratc1329672891_is_of(sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))),aTP_Lamm_a) ),
introduced(definition,[new_symbols(definition,[spl29_7])],[avatar_definition]) ).
fof(f2085,plain,
( scratc1329672891_is_of(sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))),aTP_Lamm_a)
| ~ spl29_7 ),
inference(avatar_component_clause,[],[f2083]) ).
fof(f2086,plain,
( spl29_7
| spl29_6 ),
inference(avatar_split_clause,[],[f2069,f2063,f2083]) ).
fof(f2088,definition,
( spl29_8
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)),sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))) ),
introduced(definition,[new_symbols(definition,[spl29_8])],[avatar_definition]) ).
fof(f2090,plain,
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)),sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)))))
| spl29_8 ),
inference(avatar_component_clause,[],[f2088]) ).
fof(f2091,plain,
( ~ spl29_8
| spl29_6 ),
inference(avatar_split_clause,[],[f2070,f2063,f2088]) ).
fof(f2092,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc364131377_29_ii,sK12(aTP_Lamm_a,aTP_Lamm_ab)),sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)))))
| spl29_8 ),
inference(resolution,[],[f2090,f1256]) ).
fof(f2093,plain,
( ~ pp(scratc424593673_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc120891389lessis,sK12(aTP_Lamm_a,aTP_Lamm_ab)),sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))))
| spl29_8 ),
inference(resolution,[],[f2090,f1257]) ).
fof(f2139,definition,
( spl29_9
<=> pp(scratc424593673_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc120891389lessis,sK12(aTP_Lamm_a,aTP_Lamm_ab)),sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)))))) ),
introduced(definition,[new_symbols(definition,[spl29_9])],[avatar_definition]) ).
fof(f2141,plain,
( ~ pp(scratc424593673_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc120891389lessis,sK12(aTP_Lamm_a,aTP_Lamm_ab)),sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))))
| spl29_9 ),
inference(avatar_component_clause,[],[f2139]) ).
fof(f2142,plain,
( ~ spl29_9
| spl29_8 ),
inference(avatar_split_clause,[],[f2093,f2088,f2139]) ).
fof(f2145,plain,
( ~ pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc120891389lessis,sK12(aTP_Lamm_a,aTP_Lamm_ab)),sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))),fFalse))
| spl29_9 ),
inference(resolution,[],[f2141,f1493]) ).
fof(f2158,definition,
( spl29_10
<=> pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc120891389lessis,sK12(aTP_Lamm_a,aTP_Lamm_ab)),sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))),fFalse)) ),
introduced(definition,[new_symbols(definition,[spl29_10])],[avatar_definition]) ).
fof(f2160,plain,
( ~ pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc120891389lessis,sK12(aTP_Lamm_a,aTP_Lamm_ab)),sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))),fFalse))
| spl29_10 ),
inference(avatar_component_clause,[],[f2158]) ).
fof(f2161,plain,
( ~ spl29_10
| spl29_9 ),
inference(avatar_split_clause,[],[f2145,f2139,f2158]) ).
fof(f2163,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc120891389lessis,sK12(aTP_Lamm_a,aTP_Lamm_ab)),sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)))))
| spl29_10 ),
inference(resolution,[],[f2160,f1434]) ).
fof(f2178,plain,
( ! [X0] :
( pp(aa_TPTP_ind_bool(X0,sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)))))
| ~ gg_TPTP_ind(sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))
| ~ pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),X0)) )
| ~ spl29_7 ),
inference(resolution,[],[f2085,f987]) ).
fof(f2179,plain,
( ! [X0] :
( pp(aa_TPTP_ind_bool(X0,sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)))))
| ~ pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),X0)) )
| spl29_6
| ~ spl29_7 ),
inference(forward_subsumption_resolution,[],[f2178,f2068]) ).
fof(f2181,definition,
( spl29_11
<=> ! [X0] :
( pp(aa_TPTP_ind_bool(X0,sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)))))
| ~ pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),X0)) ) ),
introduced(definition,[new_symbols(definition,[spl29_11])],[avatar_definition]) ).
fof(f2182,plain,
( ! [X0] :
( pp(aa_TPTP_ind_bool(X0,sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)))))
| ~ pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),X0)) )
| ~ spl29_11 ),
inference(avatar_component_clause,[],[f2181]) ).
fof(f2183,plain,
( spl29_11
| spl29_6
| ~ spl29_7 ),
inference(avatar_split_clause,[],[f2179,f2083,f2063,f2181]) ).
fof(f2582,definition,
( spl29_14
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc364131377_29_ii,sK12(aTP_Lamm_a,aTP_Lamm_ab)),sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))) ),
introduced(definition,[new_symbols(definition,[spl29_14])],[avatar_definition]) ).
fof(f2584,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc364131377_29_ii,sK12(aTP_Lamm_a,aTP_Lamm_ab)),sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)))))
| ~ spl29_14 ),
inference(avatar_component_clause,[],[f2582]) ).
fof(f2585,plain,
( spl29_14
| spl29_8 ),
inference(avatar_split_clause,[],[f2092,f2088,f2582]) ).
fof(f2919,definition,
( spl29_20
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc120891389lessis,sK12(aTP_Lamm_a,aTP_Lamm_ab)),sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))) ),
introduced(definition,[new_symbols(definition,[spl29_20])],[avatar_definition]) ).
fof(f2921,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc120891389lessis,sK12(aTP_Lamm_a,aTP_Lamm_ab)),sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)))))
| ~ spl29_20 ),
inference(avatar_component_clause,[],[f2919]) ).
fof(f2922,plain,
( spl29_20
| spl29_10 ),
inference(avatar_split_clause,[],[f2163,f2158,f2919]) ).
fof(f3151,definition,
( spl29_39
<=> pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bu,sK12(aTP_Lamm_a,aTP_Lamm_ab)))) ),
introduced(definition,[new_symbols(definition,[spl29_39])],[avatar_definition]) ).
fof(f3153,plain,
( pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bu,sK12(aTP_Lamm_a,aTP_Lamm_ab))))
| ~ spl29_39 ),
inference(avatar_component_clause,[],[f3151]) ).
fof(f3154,plain,
( spl29_39
| ~ spl29_4 ),
inference(avatar_split_clause,[],[f1992,f1666,f3151]) ).
fof(f3383,plain,
( pp(scratc424593673_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc364131377_29_ii,sK12(aTP_Lamm_a,aTP_Lamm_ab)),sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bu,sK12(aTP_Lamm_a,aTP_Lamm_ab)),sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)))))
| ~ spl29_20 ),
inference(resolution,[],[f2921,f1261]) ).
fof(f3738,definition,
( spl29_63
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bu,sK12(aTP_Lamm_a,aTP_Lamm_ab)),sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))) ),
introduced(definition,[new_symbols(definition,[spl29_63])],[avatar_definition]) ).
fof(f3740,plain,
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bu,sK12(aTP_Lamm_a,aTP_Lamm_ab)),sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)))))
| spl29_63 ),
inference(avatar_component_clause,[],[f3738]) ).
fof(f3742,definition,
( spl29_64
<=> pp(scratc424593673_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc364131377_29_ii,sK12(aTP_Lamm_a,aTP_Lamm_ab)),sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)))))) ),
introduced(definition,[new_symbols(definition,[spl29_64])],[avatar_definition]) ).
fof(f3744,plain,
( pp(scratc424593673_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc364131377_29_ii,sK12(aTP_Lamm_a,aTP_Lamm_ab)),sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))))
| ~ spl29_64 ),
inference(avatar_component_clause,[],[f3742]) ).
fof(f3745,plain,
( ~ spl29_63
| spl29_64
| ~ spl29_20 ),
inference(avatar_split_clause,[],[f3383,f2919,f3742,f3738]) ).
fof(f3754,plain,
( ~ pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bu,sK12(aTP_Lamm_a,aTP_Lamm_ab))))
| ~ spl29_11
| spl29_63 ),
inference(resolution,[],[f3740,f2182]) ).
fof(f3793,plain,
( $false
| ~ spl29_11
| ~ spl29_39
| spl29_63 ),
inference(forward_subsumption_resolution,[],[f3754,f3153]) ).
fof(f3794,plain,
( ~ spl29_11
| ~ spl29_39
| spl29_63 ),
inference(avatar_contradiction_clause,[],[f3793]) ).
fof(f3798,plain,
( pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc364131377_29_ii,sK12(aTP_Lamm_a,aTP_Lamm_ab)),sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))),fFalse))
| ~ spl29_64 ),
inference(resolution,[],[f3744,f1494]) ).
fof(f3809,definition,
( spl29_65
<=> pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc364131377_29_ii,sK12(aTP_Lamm_a,aTP_Lamm_ab)),sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))),fFalse)) ),
introduced(definition,[new_symbols(definition,[spl29_65])],[avatar_definition]) ).
fof(f3811,plain,
( pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc364131377_29_ii,sK12(aTP_Lamm_a,aTP_Lamm_ab)),sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))),fFalse))
| ~ spl29_65 ),
inference(avatar_component_clause,[],[f3809]) ).
fof(f3812,plain,
( spl29_65
| ~ spl29_64 ),
inference(avatar_split_clause,[],[f3798,f3742,f3809]) ).
fof(f3814,plain,
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc364131377_29_ii,sK12(aTP_Lamm_a,aTP_Lamm_ab)),sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)))))
| pp(fFalse)
| ~ spl29_65 ),
inference(resolution,[],[f3811,f1432]) ).
fof(f3825,plain,
( pp(fFalse)
| ~ spl29_14
| ~ spl29_65 ),
inference(forward_subsumption_resolution,[],[f3814,f2584]) ).
fof(f3826,plain,
( $false
| ~ spl29_14
| ~ spl29_65 ),
inference(forward_subsumption_resolution,[],[f3825,f1431]) ).
fof(f3827,plain,
( ~ spl29_14
| ~ spl29_65 ),
inference(avatar_contradiction_clause,[],[f3826]) ).
cnf(s1,plain,
~ spl29_1,
inference(sat_conversion,[],[f1600]) ).
cnf(s2,plain,
( spl29_1
| spl29_2 ),
inference(sat_conversion,[],[f1619]) ).
cnf(s3,plain,
( spl29_1
| ~ spl29_3 ),
inference(sat_conversion,[],[f1624]) ).
cnf(s4,plain,
( spl29_1
| ~ spl29_2
| spl29_4 ),
inference(sat_conversion,[],[f1668]) ).
cnf(s6,plain,
( spl29_3
| ~ spl29_6 ),
inference(sat_conversion,[],[f2066]) ).
cnf(s7,plain,
( spl29_6
| spl29_7 ),
inference(sat_conversion,[],[f2086]) ).
cnf(s8,plain,
( spl29_6
| ~ spl29_8 ),
inference(sat_conversion,[],[f2091]) ).
cnf(s9,plain,
( spl29_8
| ~ spl29_9 ),
inference(sat_conversion,[],[f2142]) ).
cnf(s10,plain,
( spl29_9
| ~ spl29_10 ),
inference(sat_conversion,[],[f2161]) ).
cnf(s11,plain,
( spl29_6
| ~ spl29_7
| spl29_11 ),
inference(sat_conversion,[],[f2183]) ).
cnf(s14,plain,
( spl29_8
| spl29_14 ),
inference(sat_conversion,[],[f2585]) ).
cnf(s20,plain,
( spl29_10
| spl29_20 ),
inference(sat_conversion,[],[f2922]) ).
cnf(s39,plain,
( ~ spl29_4
| spl29_39 ),
inference(sat_conversion,[],[f3154]) ).
cnf(s63,plain,
( ~ spl29_20
| ~ spl29_63
| spl29_64 ),
inference(sat_conversion,[],[f3745]) ).
cnf(s64,plain,
( ~ spl29_11
| ~ spl29_39
| spl29_63 ),
inference(sat_conversion,[],[f3794]) ).
cnf(s65,plain,
( ~ spl29_64
| spl29_65 ),
inference(sat_conversion,[],[f3812]) ).
cnf(s66,plain,
( ~ spl29_14
| ~ spl29_65 ),
inference(sat_conversion,[],[f3827]) ).
cnf(s68,plain,
~ spl29_3,
inference(rat,[],[s3,s1]) ).
cnf(s69,plain,
spl29_2,
inference(rat,[],[s2,s1]) ).
cnf(s75,plain,
~ spl29_6,
inference(rat,[],[s6,s68]) ).
cnf(s76,plain,
spl29_4,
inference(rat,[],[s4,s1,s69]) ).
cnf(s78,plain,
~ spl29_8,
inference(rat,[],[s8,s75]) ).
cnf(s79,plain,
spl29_7,
inference(rat,[],[s7,s75]) ).
cnf(s95,plain,
spl29_39,
inference(rat,[],[s39,s76]) ).
cnf(s111,plain,
spl29_14,
inference(rat,[],[s14,s78]) ).
cnf(s113,plain,
~ spl29_9,
inference(rat,[],[s9,s78]) ).
cnf(s114,plain,
spl29_11,
inference(rat,[],[s11,s75,s79]) ).
cnf(s115,plain,
~ spl29_65,
inference(rat,[],[s66,s111]) ).
cnf(s118,plain,
~ spl29_10,
inference(rat,[],[s10,s113]) ).
cnf(s119,plain,
spl29_63,
inference(rat,[],[s64,s95,s114]) ).
cnf(s127,plain,
~ spl29_64,
inference(rat,[],[s65,s115]) ).
cnf(s129,plain,
spl29_20,
inference(rat,[],[s20,s118]) ).
cnf(s130,plain,
$false,
inference(rat,[],[s63,s127,s119,s129]) ).
fof(f3828,plain,
$false,
inference(avatar_sat_refutation,[],[s130]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM656+4 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n016.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 21:03:17 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.70/2.51 % (2984614)Detected formulas, will run a generic FOF schedule.
% 6.70/2.51 % (2984620)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=4240455056:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.70/2.51 % (2984623)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1421142016:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.70/2.51 % (2984622)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1781722309:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.70/2.51 % (2984619)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=2068515338:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.70/2.51 % (2984625)dis-21_1_sil=8000:lcm=predicate:random_seed=2575479291:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 6.70/2.51 % (2984621)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=1666831631:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.70/2.51 % (2984622)Refutation not found, incomplete strategy
% 6.70/2.51 % (2984622)------------------------------
% 6.70/2.51 % (2984622)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.70/2.51 % (2984622)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.70/2.51 % (2984622)CaDiCaL version: 2.1.3
% 6.70/2.51 % (2984622)Termination reason: Refutation not found, incomplete strategy
% 6.70/2.51 % (2984622)Time elapsed: 0.002 s
% 6.70/2.51 % (2984622)Peak memory usage: 88 MB
% 6.70/2.51 % (2984622)Instructions burned: 1 (million)
% 6.70/2.51 % (2984623)Refutation not found, incomplete strategy
% 6.70/2.51 % (2984623)------------------------------
% 6.70/2.51 % (2984623)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.70/2.51 % (2984623)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.70/2.51 % (2984623)CaDiCaL version: 2.1.3
% 6.70/2.51 % (2984623)Termination reason: Refutation not found, incomplete strategy
% 6.70/2.51 % (2984623)Time elapsed: 0.003 s
% 6.70/2.51 % (2984623)Peak memory usage: 88 MB
% 6.70/2.51 % (2984623)Instructions burned: 2 (million)
% 6.70/2.51 % (2984624)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3079171445:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.70/2.51 % (2984625)Instruction limit reached!
% 6.70/2.51 % (2984625)------------------------------
% 6.70/2.51 % (2984625)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.70/2.51 % (2984625)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.70/2.51 % (2984625)CaDiCaL version: 2.1.3
% 6.70/2.51 % (2984625)Termination reason: Instruction limit
% 6.70/2.51 % (2984625)Termination phase: Saturation
% 6.70/2.51 % (2984625)Time elapsed: 0.078 s
% 6.70/2.51 % (2984625)Peak memory usage: 90 MB
% 6.70/2.51 % (2984625)Instructions burned: 130 (million)
% 6.70/2.51 % (2984624)Instruction limit reached!
% 6.70/2.51 % (2984624)------------------------------
% 6.70/2.51 % (2984624)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.70/2.51 % (2984624)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.70/2.51 % (2984624)CaDiCaL version: 2.1.3
% 6.70/2.51 % (2984624)Termination reason: Instruction limit
% 6.70/2.51 % (2984624)Termination phase: Saturation
% 6.70/2.51 % (2984624)Time elapsed: 0.090 s
% 6.70/2.51 % (2984624)Peak memory usage: 90 MB
% 6.70/2.51 % (2984624)Instructions burned: 140 (million)
% 6.70/2.51 % (2984622)------------------------------
% 6.70/2.51 % (2984622)------------------------------
% 6.70/2.51 % (2984623)------------------------------
% 6.70/2.51 % (2984623)------------------------------
% 6.70/2.51 % (2984633)lrs+10_1_sil=8000:sp=occurrence:random_seed=2073874767:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 6.70/2.51 % (2984633)Refutation not found, incomplete strategy
% 6.70/2.51 % (2984633)------------------------------
% 6.70/2.51 % (2984633)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.70/2.51 % (2984633)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.70/2.51 % (2984633)CaDiCaL version: 2.1.3
% 6.70/2.51 % (2984633)Termination reason: Refutation not found, incomplete strategy
% 6.70/2.51 % (2984633)Time elapsed: 0.003 s
% 6.70/2.51 % (2984633)Peak memory usage: 88 MB
% 6.70/2.51 % (2984633)Instructions burned: 3 (million)
% 6.70/2.51 % (2984634)lrs+10_1_sil=32000:urr=on:br=off:random_seed=428663579:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.70/2.51 % (2984634)Refutation not found, incomplete strategy
% 6.70/2.51 % (2984634)------------------------------
% 6.70/2.51 % (2984634)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.70/2.51 % (2984634)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.70/2.51 % (2984634)CaDiCaL version: 2.1.3
% 6.70/2.51 % (2984634)Termination reason: Refutation not found, incomplete strategy
% 6.70/2.51 % (2984634)Time elapsed: 0.004 s
% 6.70/2.51 % (2984634)Peak memory usage: 88 MB
% 6.70/2.51 % (2984634)Instructions burned: 6 (million)
% 6.70/2.51 % (2984637)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=4027911331:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 6.70/2.51 % (2984636)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3940639305:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 6.70/2.51 % (2984636)Refutation not found, incomplete strategy
% 6.70/2.51 % (2984636)------------------------------
% 6.70/2.51 % (2984636)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.70/2.51 % (2984636)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.70/2.51 % (2984636)CaDiCaL version: 2.1.3
% 6.70/2.51 % (2984636)Termination reason: Refutation not found, incomplete strategy
% 6.70/2.51 % (2984636)Time elapsed: 0.005 s
% 6.70/2.51 % (2984636)Peak memory usage: 89 MB
% 6.70/2.51 % (2984636)Instructions burned: 4 (million)
% 6.70/2.51 % (2984633)------------------------------
% 6.70/2.51 % (2984633)------------------------------
% 6.70/2.51 % (2984634)------------------------------
% 6.70/2.51 % (2984634)------------------------------
% 6.70/2.51 % (2984637)Instruction limit reached!
% 6.70/2.51 % (2984637)------------------------------
% 6.70/2.51 % (2984637)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.70/2.51 % (2984637)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.70/2.51 % (2984637)CaDiCaL version: 2.1.3
% 6.70/2.51 % (2984637)Termination reason: Instruction limit
% 6.70/2.51 % (2984637)Termination phase: Saturation
% 6.70/2.51 % (2984637)Time elapsed: 0.147 s
% 6.70/2.51 % (2984637)Peak memory usage: 93 MB
% 6.70/2.51 % (2984637)Instructions burned: 248 (million)
% 6.70/2.51 % (2984641)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2942939716:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2993 on theBenchmark for (2993ds/294Mi)
% 6.70/2.51 % (2984641)Refutation not found, incomplete strategy
% 6.70/2.51 % (2984641)------------------------------
% 6.70/2.51 % (2984641)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.70/2.51 % (2984641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.70/2.51 % (2984641)CaDiCaL version: 2.1.3
% 6.70/2.51 % (2984641)Termination reason: Refutation not found, incomplete strategy
% 6.70/2.51 % (2984641)Time elapsed: 0.004 s
% 6.70/2.51 % (2984641)Peak memory usage: 88 MB
% 6.70/2.51 % (2984641)Instructions burned: 5 (million)
% 6.70/2.51 % (2984642)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=250176330:i=2350_2992 on theBenchmark for (2992ds/2350Mi)
% 6.70/2.51 % (2984636)------------------------------
% 6.70/2.51 % (2984636)------------------------------
% 6.70/2.51 % (2984643)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=722500862:cts=off:i=113:fsr=off:ss=included:sgt=4_2992 on theBenchmark for (2992ds/113Mi)
% 6.70/2.51 % (2984643)Instruction limit reached!
% 6.70/2.51 % (2984643)------------------------------
% 6.70/2.51 % (2984643)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.70/2.51 % (2984643)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.70/2.51 % (2984643)CaDiCaL version: 2.1.3
% 6.70/2.51 % (2984643)Termination reason: Instruction limit
% 6.70/2.51 % (2984643)Termination phase: Saturation
% 6.70/2.51 % (2984643)Time elapsed: 0.066 s
% 6.70/2.51 % (2984643)Peak memory usage: 90 MB
% 6.70/2.51 % (2984643)Instructions burned: 114 (million)
% 6.70/2.51 % (2984646)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3146807276:i=127:av=off:fsr=off:sup=off_2991 on theBenchmark for (2991ds/127Mi)
% 6.70/2.51 % (2984641)------------------------------
% 6.70/2.51 % (2984641)------------------------------
% 6.70/2.51 % (2984646)Instruction limit reached!
% 6.70/2.51 % (2984646)------------------------------
% 6.70/2.51 % (2984646)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.70/2.51 % (2984646)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.70/2.51 % (2984646)CaDiCaL version: 2.1.3
% 6.70/2.51 % (2984646)Termination reason: Instruction limit
% 6.70/2.51 % (2984646)Termination phase: Saturation
% 6.70/2.51 % (2984646)Time elapsed: 0.063 s
% 6.70/2.51 % (2984646)Peak memory usage: 89 MB
% 6.70/2.51 % (2984646)Instructions burned: 128 (million)
% 6.70/2.51 % (2984648)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3055512760:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2989 on theBenchmark for (2989ds/114Mi)
% 6.70/2.51 % (2984648)Instruction limit reached!
% 6.70/2.51 % (2984648)------------------------------
% 6.70/2.51 % (2984648)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.70/2.51 % (2984648)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.70/2.51 % (2984648)CaDiCaL version: 2.1.3
% 6.70/2.51 % (2984648)Termination reason: Instruction limit
% 6.70/2.51 % (2984648)Termination phase: Saturation
% 6.70/2.51 % (2984648)Time elapsed: 0.063 s
% 6.70/2.51 % (2984648)Peak memory usage: 89 MB
% 6.70/2.51 % (2984648)Instructions burned: 115 (million)
% 6.70/2.51 % (2984650)lrs+10_1_sil=8000:sp=occurrence:random_seed=5129683:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2989 on theBenchmark for (2989ds/907Mi)
% 6.70/2.51 % (2984651)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1792134132:i=437:sd=1:aac=none:ss=included_2988 on theBenchmark for (2988ds/437Mi)
% 6.70/2.51 % (2984651)Refutation not found, incomplete strategy
% 6.70/2.51 % (2984651)------------------------------
% 6.70/2.51 % (2984651)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.70/2.51 % (2984651)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.70/2.51 % (2984651)CaDiCaL version: 2.1.3
% 6.70/2.51 % (2984651)Termination reason: Refutation not found, incomplete strategy
% 6.70/2.51 % (2984651)Time elapsed: 0.029 s
% 6.70/2.51 % (2984651)Peak memory usage: 90 MB
% 6.70/2.51 % (2984651)Instructions burned: 54 (million)
% 6.70/2.51 % (2984621)First to succeed.
% 6.70/2.51 % (2984621)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2984614"
% 6.70/2.51 % (2984619)Also succeeded, but the first one will report.
% 6.70/2.51 % (2984654)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1564049516:i=5202:ss=axioms:sgt=16_2987 on theBenchmark for (2987ds/5202Mi)
% 6.70/2.51 % (2984651)------------------------------
% 6.70/2.51 % (2984651)------------------------------
% 6.70/2.51 % (2984621)Refutation found. Thanks to Tanya!
% 6.70/2.51 % SZS status Theorem for theBenchmark
% 6.70/2.51 % SZS output start Proof for theBenchmark
% See solution above
% 12.10/2.72 % (2984621)------------------------------
% 12.10/2.72 % (2984621)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.10/2.72 % (2984621)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.10/2.72 % (2984621)CaDiCaL version: 2.1.3
% 12.10/2.72 % (2984621)Termination reason: Refutation
% 12.10/2.72 % (2984621)Time elapsed: 1.181 s
% 12.10/2.72 % (2984621)Peak memory usage: 141 MB
% 12.10/2.72 % (2984621)Instructions burned: 1913 (million)
% 12.10/2.72 % (2984621)------------------------------
% 12.10/2.72 % (2984621)------------------------------
% 12.10/2.72 % (2984614)Success in time 1.641 s
% 12.10/2.72 % Vampire exiting
%------------------------------------------------------------------------------