%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM703+4 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 12:16:36 PM UTC 2026
% Result : Theorem 9.37s 2.59s
% Output : Refutation 11.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 27
% Syntax : Number of formulae : 153 ( 26 unt; 15 def)
% Number of atoms : 383 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 388 ( 158 ~; 170 |; 26 &)
% ( 29 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 19 ( 18 usr; 16 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 13 con; 0-2 aty)
% Number of variables : 90 ( 0 sgn 88 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f28,axiom,
! [X0,X1] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1556555915nd_iii,X0),X1))
<=> pp(aa_fun171081125l_bool(scratc1299938692n_some,aa_TPT43085870d_bool(scratc1730230758ffprop(X1),X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_def__iii) ).
fof(f29,axiom,
! [X0,X1] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1283467021_29_ii,X0),X1))
<=> pp(aa_fun171081125l_bool(scratc1299938692n_some,aa_TPT43085870d_bool(scratc1730230758ffprop(X0),X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_def__d__29__ii) ).
fof(f147,axiom,
! [X0,X1] :
( pp(aa_fun171081125l_bool(scratc1445453242all_of(X0),X1))
<=> ! [X2] :
( gg_TPTP_ind(X2)
=> ( scratc1098423007_is_of(X2,X0)
=> pp(aa_TPTP_ind_bool(X1,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_def__all__of) ).
fof(f150,axiom,
pp(aa_fun171081125l_bool(scratc1445453242all_of(aTP_Lamm_a),aTP_Lamm_bt)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_satz26a) ).
fof(f206,axiom,
pp(aa_fun171081125l_bool(scratc1445453242all_of(aTP_Lamm_a),aTP_Lamm_ho)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_satz14) ).
fof(f339,axiom,
! [X0] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ho,X0))
<=> pp(aa_fun171081125l_bool(scratc1445453242all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hn,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ATP_Olambda__39) ).
fof(f389,axiom,
! [X0] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bt,X0))
<=> pp(aa_fun171081125l_bool(scratc1445453242all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bs,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ATP_Olambda__89) ).
fof(f391,axiom,
! [X0] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ab,X0))
<=> pp(aa_fun171081125l_bool(scratc1445453242all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ATP_Olambda__91) ).
fof(f407,axiom,
! [X0,X1] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,X0),X1))
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1283467021_29_ii,aa_TPTP_ind_TPTP_ind(scratc528079173rdsucc,X1)),X0))
=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc23625117moreis,X1),X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ATP_Olambda__107) ).
fof(f410,axiom,
! [X0,X1] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bs,X0),X1))
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1556555915nd_iii,X1),aa_TPTP_ind_TPTP_ind(scratc528079173rdsucc,X0)))
=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2037125153lessis,X1),X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ATP_Olambda__110) ).
fof(f422,axiom,
! [X0,X1] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hn,X0),X1))
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2037125153lessis,X0),X1))
=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc23625117moreis,X1),X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ATP_Olambda__122) ).
fof(f601,conjecture,
pp(aa_fun171081125l_bool(scratc1445453242all_of(aTP_Lamm_a),aTP_Lamm_ab)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f602,negated_conjecture,
~ pp(aa_fun171081125l_bool(scratc1445453242all_of(aTP_Lamm_a),aTP_Lamm_ab)),
inference(negated_conjecture,[status(cth)],[f601]) ).
fof(f603,plain,
~ pp(aa_fun171081125l_bool(scratc1445453242all_of(aTP_Lamm_a),aTP_Lamm_ab)),
inference(flattening,[],[f602]) ).
fof(f620,plain,
! [X0,X1] :
( pp(aa_fun171081125l_bool(scratc1445453242all_of(X0),X1))
<=> ! [X2] :
( pp(aa_TPTP_ind_bool(X1,X2))
| ~ scratc1098423007_is_of(X2,X0)
| ~ gg_TPTP_ind(X2) ) ),
inference(ennf_transformation,[],[f147]) ).
fof(f621,plain,
! [X0,X1] :
( pp(aa_fun171081125l_bool(scratc1445453242all_of(X0),X1))
<=> ! [X2] :
( pp(aa_TPTP_ind_bool(X1,X2))
| ~ scratc1098423007_is_of(X2,X0)
| ~ gg_TPTP_ind(X2) ) ),
inference(flattening,[],[f620]) ).
fof(f684,plain,
! [X0,X1] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,X0),X1))
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc23625117moreis,X1),X0))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1283467021_29_ii,aa_TPTP_ind_TPTP_ind(scratc528079173rdsucc,X1)),X0)) ) ),
inference(ennf_transformation,[],[f407]) ).
fof(f686,plain,
! [X0,X1] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bs,X0),X1))
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2037125153lessis,X1),X0))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1556555915nd_iii,X1),aa_TPTP_ind_TPTP_ind(scratc528079173rdsucc,X0))) ) ),
inference(ennf_transformation,[],[f410]) ).
fof(f694,plain,
! [X0,X1] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hn,X0),X1))
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc23625117moreis,X1),X0))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2037125153lessis,X0),X1)) ) ),
inference(ennf_transformation,[],[f422]) ).
fof(f784,plain,
! [X0,X1] :
( ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1556555915nd_iii,X0),X1))
| ~ pp(aa_fun171081125l_bool(scratc1299938692n_some,aa_TPT43085870d_bool(scratc1730230758ffprop(X1),X0))) )
& ( pp(aa_fun171081125l_bool(scratc1299938692n_some,aa_TPT43085870d_bool(scratc1730230758ffprop(X1),X0)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1556555915nd_iii,X0),X1)) ) ),
inference(nnf_transformation,[],[f28]) ).
fof(f785,plain,
! [X0,X1] :
( ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1283467021_29_ii,X0),X1))
| ~ pp(aa_fun171081125l_bool(scratc1299938692n_some,aa_TPT43085870d_bool(scratc1730230758ffprop(X0),X1))) )
& ( pp(aa_fun171081125l_bool(scratc1299938692n_some,aa_TPT43085870d_bool(scratc1730230758ffprop(X0),X1)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1283467021_29_ii,X0),X1)) ) ),
inference(nnf_transformation,[],[f29]) ).
fof(f848,plain,
! [X0,X1] :
( ( pp(aa_fun171081125l_bool(scratc1445453242all_of(X0),X1))
| ? [X2] :
( ~ pp(aa_TPTP_ind_bool(X1,X2))
& scratc1098423007_is_of(X2,X0)
& gg_TPTP_ind(X2) ) )
& ( ! [X2] :
( pp(aa_TPTP_ind_bool(X1,X2))
| ~ scratc1098423007_is_of(X2,X0)
| ~ gg_TPTP_ind(X2) )
| ~ pp(aa_fun171081125l_bool(scratc1445453242all_of(X0),X1)) ) ),
inference(nnf_transformation,[],[f621]) ).
fof(f849,plain,
! [X0,X1] :
( ( pp(aa_fun171081125l_bool(scratc1445453242all_of(X0),X1))
| ? [X2] :
( ~ pp(aa_TPTP_ind_bool(X1,X2))
& scratc1098423007_is_of(X2,X0)
& gg_TPTP_ind(X2) ) )
& ( ! [X3] :
( pp(aa_TPTP_ind_bool(X1,X3))
| ~ scratc1098423007_is_of(X3,X0)
| ~ gg_TPTP_ind(X3) )
| ~ pp(aa_fun171081125l_bool(scratc1445453242all_of(X0),X1)) ) ),
inference(rectify,[],[f848]) ).
fof(f850,plain,
! [X0,X1] :
( ( pp(aa_fun171081125l_bool(scratc1445453242all_of(X0),X1))
| ( ~ pp(aa_TPTP_ind_bool(X1,sK12(X0,X1)))
& scratc1098423007_is_of(sK12(X0,X1),X0)
& gg_TPTP_ind(sK12(X0,X1)) ) )
& ( ! [X3] :
( pp(aa_TPTP_ind_bool(X1,X3))
| ~ scratc1098423007_is_of(X3,X0)
| ~ gg_TPTP_ind(X3) )
| ~ pp(aa_fun171081125l_bool(scratc1445453242all_of(X0),X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X2,sK12(X0,X1))],[f849]) ).
fof(f908,plain,
! [X0] :
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_ho,X0))
| ~ pp(aa_fun171081125l_bool(scratc1445453242all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hn,X0))) )
& ( pp(aa_fun171081125l_bool(scratc1445453242all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hn,X0)))
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_ho,X0)) ) ),
inference(nnf_transformation,[],[f339]) ).
fof(f958,plain,
! [X0] :
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_bt,X0))
| ~ pp(aa_fun171081125l_bool(scratc1445453242all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bs,X0))) )
& ( pp(aa_fun171081125l_bool(scratc1445453242all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bs,X0)))
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bt,X0)) ) ),
inference(nnf_transformation,[],[f389]) ).
fof(f960,plain,
! [X0] :
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_ab,X0))
| ~ pp(aa_fun171081125l_bool(scratc1445453242all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,X0))) )
& ( pp(aa_fun171081125l_bool(scratc1445453242all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,X0)))
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_ab,X0)) ) ),
inference(nnf_transformation,[],[f391]) ).
fof(f981,plain,
! [X0,X1] :
( ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,X0),X1))
| ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc23625117moreis,X1),X0))
& pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1283467021_29_ii,aa_TPTP_ind_TPTP_ind(scratc528079173rdsucc,X1)),X0)) ) )
& ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc23625117moreis,X1),X0))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1283467021_29_ii,aa_TPTP_ind_TPTP_ind(scratc528079173rdsucc,X1)),X0))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,X0),X1)) ) ),
inference(nnf_transformation,[],[f684]) ).
fof(f982,plain,
! [X0,X1] :
( ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,X0),X1))
| ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc23625117moreis,X1),X0))
& pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1283467021_29_ii,aa_TPTP_ind_TPTP_ind(scratc528079173rdsucc,X1)),X0)) ) )
& ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc23625117moreis,X1),X0))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1283467021_29_ii,aa_TPTP_ind_TPTP_ind(scratc528079173rdsucc,X1)),X0))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,X0),X1)) ) ),
inference(flattening,[],[f981]) ).
fof(f986,plain,
! [X0,X1] :
( ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bs,X0),X1))
| ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2037125153lessis,X1),X0))
& pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1556555915nd_iii,X1),aa_TPTP_ind_TPTP_ind(scratc528079173rdsucc,X0))) ) )
& ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2037125153lessis,X1),X0))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1556555915nd_iii,X1),aa_TPTP_ind_TPTP_ind(scratc528079173rdsucc,X0)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bs,X0),X1)) ) ),
inference(nnf_transformation,[],[f686]) ).
fof(f987,plain,
! [X0,X1] :
( ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bs,X0),X1))
| ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2037125153lessis,X1),X0))
& pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1556555915nd_iii,X1),aa_TPTP_ind_TPTP_ind(scratc528079173rdsucc,X0))) ) )
& ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2037125153lessis,X1),X0))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1556555915nd_iii,X1),aa_TPTP_ind_TPTP_ind(scratc528079173rdsucc,X0)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bs,X0),X1)) ) ),
inference(flattening,[],[f986]) ).
fof(f1006,plain,
! [X0,X1] :
( ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hn,X0),X1))
| ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc23625117moreis,X1),X0))
& pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2037125153lessis,X0),X1)) ) )
& ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc23625117moreis,X1),X0))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2037125153lessis,X0),X1))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hn,X0),X1)) ) ),
inference(nnf_transformation,[],[f694]) ).
fof(f1007,plain,
! [X0,X1] :
( ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hn,X0),X1))
| ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc23625117moreis,X1),X0))
& pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2037125153lessis,X0),X1)) ) )
& ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc23625117moreis,X1),X0))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2037125153lessis,X0),X1))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hn,X0),X1)) ) ),
inference(flattening,[],[f1006]) ).
fof(f1251,plain,
! [X0,X1] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1556555915nd_iii,X0),X1))
| ~ pp(aa_fun171081125l_bool(scratc1299938692n_some,aa_TPT43085870d_bool(scratc1730230758ffprop(X1),X0))) ),
inference(cnf_transformation,[],[f784]) ).
fof(f1252,plain,
! [X0,X1] :
( pp(aa_fun171081125l_bool(scratc1299938692n_some,aa_TPT43085870d_bool(scratc1730230758ffprop(X0),X1)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1283467021_29_ii,X0),X1)) ),
inference(cnf_transformation,[],[f785]) ).
fof(f1438,plain,
! [X3,X0,X1] :
( pp(aa_TPTP_ind_bool(X1,X3))
| ~ scratc1098423007_is_of(X3,X0)
| ~ gg_TPTP_ind(X3)
| ~ pp(aa_fun171081125l_bool(scratc1445453242all_of(X0),X1)) ),
inference(cnf_transformation,[],[f850]) ).
fof(f1439,plain,
! [X0,X1] :
( pp(aa_fun171081125l_bool(scratc1445453242all_of(X0),X1))
| gg_TPTP_ind(sK12(X0,X1)) ),
inference(cnf_transformation,[],[f850]) ).
fof(f1440,plain,
! [X0,X1] :
( pp(aa_fun171081125l_bool(scratc1445453242all_of(X0),X1))
| scratc1098423007_is_of(sK12(X0,X1),X0) ),
inference(cnf_transformation,[],[f850]) ).
fof(f1441,plain,
! [X0,X1] :
( pp(aa_fun171081125l_bool(scratc1445453242all_of(X0),X1))
| ~ pp(aa_TPTP_ind_bool(X1,sK12(X0,X1))) ),
inference(cnf_transformation,[],[f850]) ).
fof(f1445,plain,
pp(aa_fun171081125l_bool(scratc1445453242all_of(aTP_Lamm_a),aTP_Lamm_bt)),
inference(cnf_transformation,[],[f150]) ).
fof(f1501,plain,
pp(aa_fun171081125l_bool(scratc1445453242all_of(aTP_Lamm_a),aTP_Lamm_ho)),
inference(cnf_transformation,[],[f206]) ).
fof(f1702,plain,
! [X0] :
( pp(aa_fun171081125l_bool(scratc1445453242all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hn,X0)))
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_ho,X0)) ),
inference(cnf_transformation,[],[f908]) ).
fof(f1802,plain,
! [X0] :
( pp(aa_fun171081125l_bool(scratc1445453242all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bs,X0)))
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bt,X0)) ),
inference(cnf_transformation,[],[f958]) ).
fof(f1807,plain,
! [X0] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ab,X0))
| ~ pp(aa_fun171081125l_bool(scratc1445453242all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,X0))) ),
inference(cnf_transformation,[],[f960]) ).
fof(f1842,plain,
! [X0,X1] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,X0),X1))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1283467021_29_ii,aa_TPTP_ind_TPTP_ind(scratc528079173rdsucc,X1)),X0)) ),
inference(cnf_transformation,[],[f982]) ).
fof(f1843,plain,
! [X0,X1] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,X0),X1))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc23625117moreis,X1),X0)) ),
inference(cnf_transformation,[],[f982]) ).
fof(f1849,plain,
! [X0,X1] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2037125153lessis,X1),X0))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1556555915nd_iii,X1),aa_TPTP_ind_TPTP_ind(scratc528079173rdsucc,X0)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bs,X0),X1)) ),
inference(cnf_transformation,[],[f987]) ).
fof(f1881,plain,
! [X0,X1] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc23625117moreis,X1),X0))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2037125153lessis,X0),X1))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hn,X0),X1)) ),
inference(cnf_transformation,[],[f1007]) ).
fof(f2298,plain,
~ pp(aa_fun171081125l_bool(scratc1445453242all_of(aTP_Lamm_a),aTP_Lamm_ab)),
inference(cnf_transformation,[],[f603]) ).
fof(f2522,definition,
( spl29_1
<=> pp(aa_fun171081125l_bool(scratc1445453242all_of(aTP_Lamm_a),aTP_Lamm_ab)) ),
introduced(definition,[new_symbols(definition,[spl29_1])],[avatar_definition]) ).
fof(f2524,plain,
( ~ pp(aa_fun171081125l_bool(scratc1445453242all_of(aTP_Lamm_a),aTP_Lamm_ab))
| spl29_1 ),
inference(avatar_component_clause,[],[f2522]) ).
fof(f2525,plain,
~ spl29_1,
inference(avatar_split_clause,[],[f2298,f2522]) ).
fof(f2526,plain,
( gg_TPTP_ind(sK12(aTP_Lamm_a,aTP_Lamm_ab))
| spl29_1 ),
inference(resolution,[],[f2524,f1439]) ).
fof(f2527,plain,
( scratc1098423007_is_of(sK12(aTP_Lamm_a,aTP_Lamm_ab),aTP_Lamm_a)
| spl29_1 ),
inference(resolution,[],[f2524,f1440]) ).
fof(f2528,plain,
( ~ pp(aa_TPTP_ind_bool(aTP_Lamm_ab,sK12(aTP_Lamm_a,aTP_Lamm_ab)))
| spl29_1 ),
inference(resolution,[],[f2524,f1441]) ).
fof(f2541,definition,
( spl29_2
<=> scratc1098423007_is_of(sK12(aTP_Lamm_a,aTP_Lamm_ab),aTP_Lamm_a) ),
introduced(definition,[new_symbols(definition,[spl29_2])],[avatar_definition]) ).
fof(f2543,plain,
( scratc1098423007_is_of(sK12(aTP_Lamm_a,aTP_Lamm_ab),aTP_Lamm_a)
| ~ spl29_2 ),
inference(avatar_component_clause,[],[f2541]) ).
fof(f2544,plain,
( spl29_2
| spl29_1 ),
inference(avatar_split_clause,[],[f2527,f2522,f2541]) ).
fof(f2546,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(f2548,plain,
( ~ pp(aa_TPTP_ind_bool(aTP_Lamm_ab,sK12(aTP_Lamm_a,aTP_Lamm_ab)))
| spl29_3 ),
inference(avatar_component_clause,[],[f2546]) ).
fof(f2549,plain,
( ~ spl29_3
| spl29_1 ),
inference(avatar_split_clause,[],[f2528,f2522,f2546]) ).
fof(f2550,plain,
( ~ pp(aa_fun171081125l_bool(scratc1445453242all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))
| spl29_3 ),
inference(resolution,[],[f2548,f1807]) ).
fof(f2588,definition,
( spl29_4
<=> gg_TPTP_ind(sK12(aTP_Lamm_a,aTP_Lamm_ab)) ),
introduced(definition,[new_symbols(definition,[spl29_4])],[avatar_definition]) ).
fof(f2590,plain,
( gg_TPTP_ind(sK12(aTP_Lamm_a,aTP_Lamm_ab))
| ~ spl29_4 ),
inference(avatar_component_clause,[],[f2588]) ).
fof(f2591,plain,
( spl29_4
| spl29_1 ),
inference(avatar_split_clause,[],[f2526,f2522,f2588]) ).
fof(f2593,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(scratc1445453242all_of(aTP_Lamm_a),X0)) )
| ~ spl29_2 ),
inference(resolution,[],[f2543,f1438]) ).
fof(f2594,plain,
( ! [X0] :
( pp(aa_TPTP_ind_bool(X0,sK12(aTP_Lamm_a,aTP_Lamm_ab)))
| ~ pp(aa_fun171081125l_bool(scratc1445453242all_of(aTP_Lamm_a),X0)) )
| ~ spl29_2
| ~ spl29_4 ),
inference(forward_subsumption_resolution,[],[f2593,f2590]) ).
fof(f2596,definition,
( spl29_5
<=> ! [X0] :
( pp(aa_TPTP_ind_bool(X0,sK12(aTP_Lamm_a,aTP_Lamm_ab)))
| ~ pp(aa_fun171081125l_bool(scratc1445453242all_of(aTP_Lamm_a),X0)) ) ),
introduced(definition,[new_symbols(definition,[spl29_5])],[avatar_definition]) ).
fof(f2597,plain,
( ! [X0] :
( pp(aa_TPTP_ind_bool(X0,sK12(aTP_Lamm_a,aTP_Lamm_ab)))
| ~ pp(aa_fun171081125l_bool(scratc1445453242all_of(aTP_Lamm_a),X0)) )
| ~ spl29_5 ),
inference(avatar_component_clause,[],[f2596]) ).
fof(f2598,plain,
( spl29_5
| ~ spl29_2
| ~ spl29_4 ),
inference(avatar_split_clause,[],[f2594,f2588,f2541,f2596]) ).
fof(f3060,plain,
( ~ pp(aa_fun171081125l_bool(scratc1445453242all_of(aTP_Lamm_a),aTP_Lamm_ho))
| pp(aa_fun171081125l_bool(scratc1445453242all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hn,sK12(aTP_Lamm_a,aTP_Lamm_ab))))
| ~ spl29_5 ),
inference(resolution,[],[f2597,f1702]) ).
fof(f3140,plain,
( pp(aa_fun171081125l_bool(scratc1445453242all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hn,sK12(aTP_Lamm_a,aTP_Lamm_ab))))
| ~ spl29_5 ),
inference(forward_subsumption_resolution,[],[f3060,f1501]) ).
fof(f3260,definition,
( spl29_6
<=> pp(aa_fun171081125l_bool(scratc1445453242all_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(f3262,plain,
( ~ pp(aa_fun171081125l_bool(scratc1445453242all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))
| spl29_6 ),
inference(avatar_component_clause,[],[f3260]) ).
fof(f3263,plain,
( ~ spl29_6
| spl29_3 ),
inference(avatar_split_clause,[],[f2550,f2546,f3260]) ).
fof(f3265,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,[],[f3262,f1439]) ).
fof(f3266,plain,
( scratc1098423007_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,[],[f3262,f1440]) ).
fof(f3267,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,[],[f3262,f1441]) ).
fof(f3280,definition,
( spl29_7
<=> scratc1098423007_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(f3282,plain,
( scratc1098423007_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,[],[f3280]) ).
fof(f3283,plain,
( spl29_7
| spl29_6 ),
inference(avatar_split_clause,[],[f3266,f3260,f3280]) ).
fof(f3285,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(f3287,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,[],[f3285]) ).
fof(f3288,plain,
( ~ spl29_8
| spl29_6 ),
inference(avatar_split_clause,[],[f3267,f3260,f3285]) ).
fof(f3289,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1283467021_29_ii,aa_TPTP_ind_TPTP_ind(scratc528079173rdsucc,sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))),sK12(aTP_Lamm_a,aTP_Lamm_ab)))
| spl29_8 ),
inference(resolution,[],[f3287,f1842]) ).
fof(f3290,plain,
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc23625117moreis,sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)))),sK12(aTP_Lamm_a,aTP_Lamm_ab)))
| spl29_8 ),
inference(resolution,[],[f3287,f1843]) ).
fof(f3336,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(scratc1445453242all_of(aTP_Lamm_a),X0)) )
| ~ spl29_7 ),
inference(resolution,[],[f3282,f1438]) ).
fof(f3337,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(scratc1445453242all_of(aTP_Lamm_a),X0)) )
| spl29_6
| ~ spl29_7 ),
inference(forward_subsumption_resolution,[],[f3336,f3265]) ).
fof(f3339,definition,
( spl29_9
<=> ! [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(scratc1445453242all_of(aTP_Lamm_a),X0)) ) ),
introduced(definition,[new_symbols(definition,[spl29_9])],[avatar_definition]) ).
fof(f3340,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(scratc1445453242all_of(aTP_Lamm_a),X0)) )
| ~ spl29_9 ),
inference(avatar_component_clause,[],[f3339]) ).
fof(f3341,plain,
( spl29_9
| spl29_6
| ~ spl29_7 ),
inference(avatar_split_clause,[],[f3337,f3280,f3260,f3339]) ).
fof(f3749,plain,
( ~ pp(aa_fun171081125l_bool(scratc1445453242all_of(aTP_Lamm_a),aTP_Lamm_bt))
| pp(aa_fun171081125l_bool(scratc1445453242all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bs,sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))))
| ~ spl29_9 ),
inference(resolution,[],[f3340,f1802]) ).
fof(f3938,plain,
( pp(aa_fun171081125l_bool(scratc1445453242all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bs,sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))))
| ~ spl29_9 ),
inference(forward_subsumption_resolution,[],[f3749,f1445]) ).
fof(f4104,definition,
( spl29_12
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc23625117moreis,sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)))),sK12(aTP_Lamm_a,aTP_Lamm_ab))) ),
introduced(definition,[new_symbols(definition,[spl29_12])],[avatar_definition]) ).
fof(f4106,plain,
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc23625117moreis,sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)))),sK12(aTP_Lamm_a,aTP_Lamm_ab)))
| spl29_12 ),
inference(avatar_component_clause,[],[f4104]) ).
fof(f4107,plain,
( ~ spl29_12
| spl29_8 ),
inference(avatar_split_clause,[],[f3290,f3285,f4104]) ).
fof(f4196,plain,
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2037125153lessis,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_hn,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_12 ),
inference(resolution,[],[f4106,f1881]) ).
fof(f4255,definition,
( spl29_13
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hn,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_13])],[avatar_definition]) ).
fof(f4257,plain,
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hn,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_13 ),
inference(avatar_component_clause,[],[f4255]) ).
fof(f4259,definition,
( spl29_14
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2037125153lessis,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(f4261,plain,
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2037125153lessis,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,[],[f4259]) ).
fof(f4262,plain,
( ~ spl29_13
| ~ spl29_14
| spl29_12 ),
inference(avatar_split_clause,[],[f4196,f4104,f4259,f4255]) ).
fof(f4271,plain,
( ~ pp(aa_fun171081125l_bool(scratc1445453242all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hn,sK12(aTP_Lamm_a,aTP_Lamm_ab))))
| ~ spl29_9
| spl29_13 ),
inference(resolution,[],[f4257,f3340]) ).
fof(f4310,plain,
( $false
| ~ spl29_5
| ~ spl29_9
| spl29_13 ),
inference(forward_subsumption_resolution,[],[f4271,f3140]) ).
fof(f4311,plain,
( ~ spl29_5
| ~ spl29_9
| spl29_13 ),
inference(avatar_contradiction_clause,[],[f4310]) ).
fof(f4312,plain,
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1556555915nd_iii,sK12(aTP_Lamm_a,aTP_Lamm_ab)),aa_TPTP_ind_TPTP_ind(scratc528079173rdsucc,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_bs,sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)))),sK12(aTP_Lamm_a,aTP_Lamm_ab)))
| spl29_14 ),
inference(resolution,[],[f4261,f1849]) ).
fof(f4376,definition,
( spl29_15
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1283467021_29_ii,aa_TPTP_ind_TPTP_ind(scratc528079173rdsucc,sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))),sK12(aTP_Lamm_a,aTP_Lamm_ab))) ),
introduced(definition,[new_symbols(definition,[spl29_15])],[avatar_definition]) ).
fof(f4378,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1283467021_29_ii,aa_TPTP_ind_TPTP_ind(scratc528079173rdsucc,sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))),sK12(aTP_Lamm_a,aTP_Lamm_ab)))
| ~ spl29_15 ),
inference(avatar_component_clause,[],[f4376]) ).
fof(f4379,plain,
( spl29_15
| spl29_8 ),
inference(avatar_split_clause,[],[f3289,f3285,f4376]) ).
fof(f4381,plain,
( pp(aa_fun171081125l_bool(scratc1299938692n_some,aa_TPT43085870d_bool(scratc1730230758ffprop(aa_TPTP_ind_TPTP_ind(scratc528079173rdsucc,sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))),sK12(aTP_Lamm_a,aTP_Lamm_ab))))
| ~ spl29_15 ),
inference(resolution,[],[f4378,f1252]) ).
fof(f4435,definition,
( spl29_16
<=> pp(aa_fun171081125l_bool(scratc1299938692n_some,aa_TPT43085870d_bool(scratc1730230758ffprop(aa_TPTP_ind_TPTP_ind(scratc528079173rdsucc,sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))),sK12(aTP_Lamm_a,aTP_Lamm_ab)))) ),
introduced(definition,[new_symbols(definition,[spl29_16])],[avatar_definition]) ).
fof(f4437,plain,
( pp(aa_fun171081125l_bool(scratc1299938692n_some,aa_TPT43085870d_bool(scratc1730230758ffprop(aa_TPTP_ind_TPTP_ind(scratc528079173rdsucc,sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))),sK12(aTP_Lamm_a,aTP_Lamm_ab))))
| ~ spl29_16 ),
inference(avatar_component_clause,[],[f4435]) ).
fof(f4438,plain,
( spl29_16
| ~ spl29_15 ),
inference(avatar_split_clause,[],[f4381,f4376,f4435]) ).
fof(f4440,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1556555915nd_iii,sK12(aTP_Lamm_a,aTP_Lamm_ab)),aa_TPTP_ind_TPTP_ind(scratc528079173rdsucc,sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))))
| ~ spl29_16 ),
inference(resolution,[],[f4437,f1251]) ).
fof(f4450,plain,
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bs,sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)))),sK12(aTP_Lamm_a,aTP_Lamm_ab)))
| spl29_14
| ~ spl29_16 ),
inference(backward_subsumption_resolution,[],[f4312,f4440]) ).
fof(f4452,definition,
( spl29_17
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bs,sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)))),sK12(aTP_Lamm_a,aTP_Lamm_ab))) ),
introduced(definition,[new_symbols(definition,[spl29_17])],[avatar_definition]) ).
fof(f4454,plain,
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bs,sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)))),sK12(aTP_Lamm_a,aTP_Lamm_ab)))
| spl29_17 ),
inference(avatar_component_clause,[],[f4452]) ).
fof(f4455,plain,
( ~ spl29_17
| spl29_14
| ~ spl29_16 ),
inference(avatar_split_clause,[],[f4450,f4435,f4259,f4452]) ).
fof(f4464,plain,
( ~ pp(aa_fun171081125l_bool(scratc1445453242all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bs,sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))))
| ~ spl29_5
| spl29_17 ),
inference(resolution,[],[f4454,f2597]) ).
fof(f4503,plain,
( $false
| ~ spl29_5
| ~ spl29_9
| spl29_17 ),
inference(forward_subsumption_resolution,[],[f4464,f3938]) ).
fof(f4504,plain,
( ~ spl29_5
| ~ spl29_9
| spl29_17 ),
inference(avatar_contradiction_clause,[],[f4503]) ).
cnf(s1,plain,
~ spl29_1,
inference(sat_conversion,[],[f2525]) ).
cnf(s2,plain,
( spl29_1
| spl29_2 ),
inference(sat_conversion,[],[f2544]) ).
cnf(s3,plain,
( spl29_1
| ~ spl29_3 ),
inference(sat_conversion,[],[f2549]) ).
cnf(s4,plain,
( spl29_1
| spl29_4 ),
inference(sat_conversion,[],[f2591]) ).
cnf(s5,plain,
( ~ spl29_2
| ~ spl29_4
| spl29_5 ),
inference(sat_conversion,[],[f2598]) ).
cnf(s6,plain,
( spl29_3
| ~ spl29_6 ),
inference(sat_conversion,[],[f3263]) ).
cnf(s7,plain,
( spl29_6
| spl29_7 ),
inference(sat_conversion,[],[f3283]) ).
cnf(s8,plain,
( spl29_6
| ~ spl29_8 ),
inference(sat_conversion,[],[f3288]) ).
cnf(s9,plain,
( spl29_6
| ~ spl29_7
| spl29_9 ),
inference(sat_conversion,[],[f3341]) ).
cnf(s12,plain,
( spl29_8
| ~ spl29_12 ),
inference(sat_conversion,[],[f4107]) ).
cnf(s13,plain,
( spl29_12
| ~ spl29_13
| ~ spl29_14 ),
inference(sat_conversion,[],[f4262]) ).
cnf(s14,plain,
( ~ spl29_5
| ~ spl29_9
| spl29_13 ),
inference(sat_conversion,[],[f4311]) ).
cnf(s15,plain,
( spl29_8
| spl29_15 ),
inference(sat_conversion,[],[f4379]) ).
cnf(s16,plain,
( ~ spl29_15
| spl29_16 ),
inference(sat_conversion,[],[f4438]) ).
cnf(s17,plain,
( spl29_14
| ~ spl29_16
| ~ spl29_17 ),
inference(sat_conversion,[],[f4455]) ).
cnf(s18,plain,
( ~ spl29_5
| ~ spl29_9
| spl29_17 ),
inference(sat_conversion,[],[f4504]) ).
cnf(s19,plain,
spl29_4,
inference(rat,[],[s4,s1]) ).
cnf(s20,plain,
~ spl29_3,
inference(rat,[],[s3,s1]) ).
cnf(s21,plain,
spl29_2,
inference(rat,[],[s2,s1]) ).
cnf(s22,plain,
~ spl29_6,
inference(rat,[],[s6,s20]) ).
cnf(s23,plain,
spl29_5,
inference(rat,[],[s5,s19,s21]) ).
cnf(s25,plain,
~ spl29_8,
inference(rat,[],[s8,s22]) ).
cnf(s26,plain,
spl29_7,
inference(rat,[],[s7,s22]) ).
cnf(s27,plain,
spl29_15,
inference(rat,[],[s15,s25]) ).
cnf(s28,plain,
~ spl29_12,
inference(rat,[],[s12,s25]) ).
cnf(s30,plain,
spl29_9,
inference(rat,[],[s9,s22,s26]) ).
cnf(s31,plain,
spl29_16,
inference(rat,[],[s16,s27]) ).
cnf(s32,plain,
spl29_17,
inference(rat,[],[s18,s23,s30]) ).
cnf(s33,plain,
spl29_13,
inference(rat,[],[s14,s23,s30]) ).
cnf(s34,plain,
spl29_14,
inference(rat,[],[s17,s32,s31]) ).
cnf(s35,plain,
$false,
inference(rat,[],[s13,s28,s34,s33]) ).
fof(f4505,plain,
$false,
inference(avatar_sat_refutation,[],[s35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM703+4 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.45 % Computer : n013.cluster.edu
% 0.17/0.45 % Model : x86_64 x86_64
% 0.17/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.45 % Memory : 8046.5625MB
% 0.17/0.45 % OS : Linux 6.8.0-71-generic
% 0.17/0.45 % CPULimit : 300
% 0.17/0.45 % WCLimit : 300
% 0.17/0.45 % DateTime : Sun Sep 27 21:08:36 UTC 2026
% 0.17/0.46 % CPUTime :
% 0.17/0.46 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.51 Running first-order theorem proving
% 0.21/0.51 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.37/2.59 % (552497)Detected formulas, will run a generic FOF schedule.
% 9.37/2.59 % (552510)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=666876560:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 9.37/2.59 % (552509)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=474823420:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 9.37/2.59 % (552511)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3066214955:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 9.37/2.59 % (552512)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1249236734:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 9.37/2.59 % (552513)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3220379643:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 9.37/2.59 % (552508)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=603506864:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 9.37/2.59 % (552514)dis-21_1_sil=8000:lcm=predicate:random_seed=3274412695: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)
% 9.37/2.59 % (552511)Refutation not found, incomplete strategy
% 9.37/2.59 % (552511)------------------------------
% 9.37/2.59 % (552511)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.37/2.59 % (552511)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.37/2.59 % (552511)CaDiCaL version: 2.1.3
% 9.37/2.59 % (552511)Termination reason: Refutation not found, incomplete strategy
% 9.37/2.59 % (552511)Time elapsed: 0.004 s
% 9.37/2.59 % (552511)Peak memory usage: 88 MB
% 9.37/2.59 % (552511)Instructions burned: 2 (million)
% 9.37/2.59 % (552512)Refutation not found, incomplete strategy
% 9.37/2.59 % (552512)------------------------------
% 9.37/2.59 % (552512)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.37/2.59 % (552512)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.37/2.59 % (552512)CaDiCaL version: 2.1.3
% 9.37/2.59 % (552512)Termination reason: Refutation not found, incomplete strategy
% 9.37/2.59 % (552512)Time elapsed: 0.005 s
% 9.37/2.59 % (552512)Peak memory usage: 88 MB
% 9.37/2.59 % (552512)Instructions burned: 3 (million)
% 9.37/2.59 % (552514)Instruction limit reached!
% 9.37/2.59 % (552514)------------------------------
% 9.37/2.59 % (552514)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.37/2.59 % (552514)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.37/2.59 % (552514)CaDiCaL version: 2.1.3
% 9.37/2.59 % (552514)Termination reason: Instruction limit
% 9.37/2.59 % (552514)Termination phase: Saturation
% 9.37/2.59 % (552514)Time elapsed: 0.124 s
% 9.37/2.59 % (552514)Peak memory usage: 90 MB
% 9.37/2.59 % (552514)Instructions burned: 130 (million)
% 9.37/2.59 % (552513)Instruction limit reached!
% 9.37/2.59 % (552513)------------------------------
% 9.37/2.59 % (552513)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.37/2.59 % (552513)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.37/2.59 % (552513)CaDiCaL version: 2.1.3
% 9.37/2.59 % (552513)Termination reason: Instruction limit
% 9.37/2.59 % (552513)Termination phase: Saturation
% 9.37/2.59 % (552513)Time elapsed: 0.140 s
% 9.37/2.59 % (552513)Peak memory usage: 90 MB
% 9.37/2.59 % (552513)Instructions burned: 139 (million)
% 9.37/2.59 % (552522)lrs+10_1_sil=8000:sp=occurrence:random_seed=893248153:i=285:sd=3:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/285Mi)
% 9.37/2.59 % (552522)Refutation not found, incomplete strategy
% 9.37/2.59 % (552522)------------------------------
% 9.37/2.59 % (552522)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.37/2.59 % (552522)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.37/2.59 % (552522)CaDiCaL version: 2.1.3
% 9.37/2.59 % (552522)Termination reason: Refutation not found, incomplete strategy
% 9.37/2.59 % (552522)Time elapsed: 0.003 s
% 9.37/2.59 % (552522)Peak memory usage: 88 MB
% 9.37/2.59 % (552522)Instructions burned: 2 (million)
% 9.37/2.59 % (552512)------------------------------
% 9.37/2.59 % (552512)------------------------------
% 9.37/2.59 % (552511)------------------------------
% 9.37/2.59 % (552511)------------------------------
% 9.37/2.59 % (552523)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1023815111:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/157Mi)
% 9.37/2.59 % (552523)Refutation not found, incomplete strategy
% 9.37/2.59 % (552523)------------------------------
% 9.37/2.59 % (552523)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.37/2.59 % (552523)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.37/2.59 % (552523)CaDiCaL version: 2.1.3
% 9.37/2.59 % (552523)Termination reason: Refutation not found, incomplete strategy
% 9.37/2.59 % (552523)Time elapsed: 0.010 s
% 9.37/2.59 % (552523)Peak memory usage: 88 MB
% 9.37/2.59 % (552523)Instructions burned: 9 (million)
% 9.37/2.59 % (552525)lrs+1011_1_sil=32000:sp=occurrence:random_seed=392807563:i=325:sd=1:ss=axioms:sgt=32_2992 on theBenchmark for (2992ds/325Mi)
% 9.37/2.59 % (552525)Refutation not found, incomplete strategy
% 9.37/2.59 % (552525)------------------------------
% 9.37/2.59 % (552525)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.37/2.59 % (552525)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.37/2.59 % (552525)CaDiCaL version: 2.1.3
% 9.37/2.59 % (552525)Termination reason: Refutation not found, incomplete strategy
% 9.37/2.59 % (552525)Time elapsed: 0.008 s
% 9.37/2.59 % (552525)Peak memory usage: 89 MB
% 9.37/2.59 % (552525)Instructions burned: 5 (million)
% 9.37/2.59 % (552522)------------------------------
% 9.37/2.59 % (552522)------------------------------
% 9.37/2.59 % (552527)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=585764735:s2a=on:i=248:s2at=1.23:gtg=position_2992 on theBenchmark for (2992ds/248Mi)
% 9.37/2.59 % (552523)------------------------------
% 9.37/2.59 % (552523)------------------------------
% 9.37/2.59 % (552527)Instruction limit reached!
% 9.37/2.59 % (552527)------------------------------
% 9.37/2.59 % (552527)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.37/2.59 % (552527)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.37/2.59 % (552527)CaDiCaL version: 2.1.3
% 9.37/2.59 % (552527)Termination reason: Instruction limit
% 9.37/2.59 % (552527)Termination phase: Saturation
% 9.37/2.59 % (552527)Time elapsed: 0.216 s
% 9.37/2.59 % (552527)Peak memory usage: 96 MB
% 9.37/2.59 % (552527)Instructions burned: 249 (million)
% 9.37/2.59 % (552529)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3158904090:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2990 on theBenchmark for (2990ds/294Mi)
% 9.37/2.59 % (552529)Refutation not found, incomplete strategy
% 9.37/2.59 % (552529)------------------------------
% 9.37/2.59 % (552529)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.37/2.59 % (552529)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.37/2.59 % (552529)CaDiCaL version: 2.1.3
% 9.37/2.59 % (552529)Termination reason: Refutation not found, incomplete strategy
% 9.37/2.59 % (552529)Time elapsed: 0.008 s
% 9.37/2.59 % (552529)Peak memory usage: 88 MB
% 9.37/2.59 % (552529)Instructions burned: 7 (million)
% 9.37/2.59 % (552510)First to succeed.
% 9.37/2.59 % (552510)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-552497"
% 9.37/2.59 % (552525)------------------------------
% 9.37/2.59 % (552525)------------------------------
% 9.37/2.59 % (552531)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1714095093:i=2350_2988 on theBenchmark for (2988ds/2350Mi)
% 9.37/2.59 % (552532)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2299980145:cts=off:i=113:fsr=off:ss=included:sgt=4_2987 on theBenchmark for (2987ds/113Mi)
% 9.37/2.59 % (552510)Refutation found. Thanks to Tanya!
% 9.37/2.59 % SZS status Theorem for theBenchmark
% 9.37/2.59 % SZS output start Proof for theBenchmark
% See solution above
% 11.04/2.73 % (552510)------------------------------
% 11.04/2.73 % (552510)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.04/2.73 % (552510)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.04/2.73 % (552510)CaDiCaL version: 2.1.3
% 11.04/2.73 % (552510)Termination reason: Refutation
% 11.04/2.73 % (552510)Time elapsed: 1.030 s
% 11.04/2.73 % (552510)Peak memory usage: 144 MB
% 11.04/2.73 % (552510)Instructions burned: 1953 (million)
% 11.04/2.73 % (552510)------------------------------
% 11.04/2.73 % (552510)------------------------------
% 11.04/2.73 % (552497)Success in time 1.505 s
% 11.04/2.73 % Vampire exiting
%------------------------------------------------------------------------------