%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM699+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 : n014.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 12:16:34 PM UTC 2026
% Result : Theorem 23.74s 4.30s
% Output : Refutation 24.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 34
% Syntax : Number of formulae : 184 ( 34 unt; 19 def)
% Number of atoms : 445 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 444 ( 183 ~; 195 |; 27 &)
% ( 34 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 23 ( 22 usr; 20 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 14 con; 0-2 aty)
% Number of variables : 101 ( 0 sgn 99 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f18,axiom,
! [X0,X1] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_aa_001t__TPTP____Interpret__Oind_001t__TPTP____Interpret__Oind) ).
fof(f28,axiom,
! [X0,X1] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,X0),X1))
<=> pp(aa_fun171081125l_bool(scratc93448950n_some,aa_TPT43085870d_bool(scratc572008692ffprop(X1),X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__iii) ).
fof(f29,axiom,
! [X0,X1] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,X0),X1))
<=> pp(aa_fun171081125l_bool(scratc93448950n_some,aa_TPT43085870d_bool(scratc572008692ffprop(X0),X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__d__29__ii) ).
fof(f147,axiom,
! [X0,X1] :
( pp(aa_fun171081125l_bool(scratc238963500all_of(X0),X1))
<=> ! [X2] :
( gg_TPTP_ind(X2)
=> ( scratc1857401069_is_of(X2,X0)
=> pp(aa_TPTP_ind_bool(X1,X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__all__of) ).
fof(f150,axiom,
pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aTP_Lamm_bt)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_satz25a) ).
fof(f203,axiom,
pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aTP_Lamm_hi)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_satz13) ).
fof(f234,axiom,
pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aTP_Lamm_jp)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_suc__p) ).
fof(f307,axiom,
! [X0] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_jp,X0))
<=> scratc1857401069_is_of(aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,X0),aTP_Lamm_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ATP_Olambda__11) ).
fof(f334,axiom,
! [X0] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_hi,X0))
<=> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hh,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ATP_Olambda__38) ).
fof(f381,axiom,
! [X0] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bt,X0))
<=> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bs,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ATP_Olambda__85) ).
fof(f383,axiom,
! [X0] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ab,X0))
<=> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ATP_Olambda__87) ).
fof(f404,axiom,
! [X0,X1] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,X0),X1))
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,X1),X0))
=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc648619567lessis,aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,X1)),X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ATP_Olambda__108) ).
fof(f406,axiom,
! [X0,X1] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bs,X0),X1))
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,X1),X0))
=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc782603179moreis,X1),aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,X0))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ATP_Olambda__110) ).
fof(f409,axiom,
! [X0,X1] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hh,X0),X1))
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc782603179moreis,X0),X1))
=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc648619567lessis,X1),X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ATP_Olambda__113) ).
fof(f589,conjecture,
pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aTP_Lamm_ab)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f590,negated_conjecture,
~ pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aTP_Lamm_ab)),
inference(negated_conjecture,[status(cth)],[f589]) ).
fof(f591,plain,
~ pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aTP_Lamm_ab)),
inference(flattening,[],[f590]) ).
fof(f608,plain,
! [X0,X1] :
( pp(aa_fun171081125l_bool(scratc238963500all_of(X0),X1))
<=> ! [X2] :
( pp(aa_TPTP_ind_bool(X1,X2))
| ~ scratc1857401069_is_of(X2,X0)
| ~ gg_TPTP_ind(X2) ) ),
inference(ennf_transformation,[],[f147]) ).
fof(f609,plain,
! [X0,X1] :
( pp(aa_fun171081125l_bool(scratc238963500all_of(X0),X1))
<=> ! [X2] :
( pp(aa_TPTP_ind_bool(X1,X2))
| ~ scratc1857401069_is_of(X2,X0)
| ~ gg_TPTP_ind(X2) ) ),
inference(flattening,[],[f608]) ).
fof(f673,plain,
! [X0,X1] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,X0),X1))
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc648619567lessis,aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,X1)),X0))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,X1),X0)) ) ),
inference(ennf_transformation,[],[f404]) ).
fof(f675,plain,
! [X0,X1] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bs,X0),X1))
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc782603179moreis,X1),aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,X0)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,X1),X0)) ) ),
inference(ennf_transformation,[],[f406]) ).
fof(f677,plain,
! [X0,X1] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hh,X0),X1))
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc648619567lessis,X1),X0))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc782603179moreis,X0),X1)) ) ),
inference(ennf_transformation,[],[f409]) ).
fof(f768,plain,
! [X0,X1] :
( ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,X0),X1))
| ~ pp(aa_fun171081125l_bool(scratc93448950n_some,aa_TPT43085870d_bool(scratc572008692ffprop(X1),X0))) )
& ( pp(aa_fun171081125l_bool(scratc93448950n_some,aa_TPT43085870d_bool(scratc572008692ffprop(X1),X0)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,X0),X1)) ) ),
inference(nnf_transformation,[],[f28]) ).
fof(f769,plain,
! [X0,X1] :
( ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,X0),X1))
| ~ pp(aa_fun171081125l_bool(scratc93448950n_some,aa_TPT43085870d_bool(scratc572008692ffprop(X0),X1))) )
& ( pp(aa_fun171081125l_bool(scratc93448950n_some,aa_TPT43085870d_bool(scratc572008692ffprop(X0),X1)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,X0),X1)) ) ),
inference(nnf_transformation,[],[f29]) ).
fof(f832,plain,
! [X0,X1] :
( ( pp(aa_fun171081125l_bool(scratc238963500all_of(X0),X1))
| ? [X2] :
( ~ pp(aa_TPTP_ind_bool(X1,X2))
& scratc1857401069_is_of(X2,X0)
& gg_TPTP_ind(X2) ) )
& ( ! [X2] :
( pp(aa_TPTP_ind_bool(X1,X2))
| ~ scratc1857401069_is_of(X2,X0)
| ~ gg_TPTP_ind(X2) )
| ~ pp(aa_fun171081125l_bool(scratc238963500all_of(X0),X1)) ) ),
inference(nnf_transformation,[],[f609]) ).
fof(f833,plain,
! [X0,X1] :
( ( pp(aa_fun171081125l_bool(scratc238963500all_of(X0),X1))
| ? [X2] :
( ~ pp(aa_TPTP_ind_bool(X1,X2))
& scratc1857401069_is_of(X2,X0)
& gg_TPTP_ind(X2) ) )
& ( ! [X3] :
( pp(aa_TPTP_ind_bool(X1,X3))
| ~ scratc1857401069_is_of(X3,X0)
| ~ gg_TPTP_ind(X3) )
| ~ pp(aa_fun171081125l_bool(scratc238963500all_of(X0),X1)) ) ),
inference(rectify,[],[f832]) ).
fof(f834,plain,
! [X0,X1] :
( ( pp(aa_fun171081125l_bool(scratc238963500all_of(X0),X1))
| ( ~ pp(aa_TPTP_ind_bool(X1,sK12(X0,X1)))
& scratc1857401069_is_of(sK12(X0,X1),X0)
& gg_TPTP_ind(sK12(X0,X1)) ) )
& ( ! [X3] :
( pp(aa_TPTP_ind_bool(X1,X3))
| ~ scratc1857401069_is_of(X3,X0)
| ~ gg_TPTP_ind(X3) )
| ~ pp(aa_fun171081125l_bool(scratc238963500all_of(X0),X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X2,sK12(X0,X1))],[f833]) ).
fof(f864,plain,
! [X0] :
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_jp,X0))
| ~ scratc1857401069_is_of(aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,X0),aTP_Lamm_a) )
& ( scratc1857401069_is_of(aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,X0),aTP_Lamm_a)
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_jp,X0)) ) ),
inference(nnf_transformation,[],[f307]) ).
fof(f891,plain,
! [X0] :
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_hi,X0))
| ~ pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hh,X0))) )
& ( pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hh,X0)))
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_hi,X0)) ) ),
inference(nnf_transformation,[],[f334]) ).
fof(f938,plain,
! [X0] :
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_bt,X0))
| ~ pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bs,X0))) )
& ( pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bs,X0)))
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bt,X0)) ) ),
inference(nnf_transformation,[],[f381]) ).
fof(f940,plain,
! [X0] :
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_ab,X0))
| ~ pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,X0))) )
& ( pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,X0)))
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_ab,X0)) ) ),
inference(nnf_transformation,[],[f383]) ).
fof(f967,plain,
! [X0,X1] :
( ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,X0),X1))
| ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc648619567lessis,aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,X1)),X0))
& pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,X1),X0)) ) )
& ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc648619567lessis,aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,X1)),X0))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,X1),X0))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,X0),X1)) ) ),
inference(nnf_transformation,[],[f673]) ).
fof(f968,plain,
! [X0,X1] :
( ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,X0),X1))
| ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc648619567lessis,aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,X1)),X0))
& pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,X1),X0)) ) )
& ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc648619567lessis,aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,X1)),X0))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,X1),X0))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,X0),X1)) ) ),
inference(flattening,[],[f967]) ).
fof(f971,plain,
! [X0,X1] :
( ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bs,X0),X1))
| ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc782603179moreis,X1),aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,X0)))
& pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,X1),X0)) ) )
& ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc782603179moreis,X1),aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,X0)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,X1),X0))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bs,X0),X1)) ) ),
inference(nnf_transformation,[],[f675]) ).
fof(f972,plain,
! [X0,X1] :
( ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bs,X0),X1))
| ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc782603179moreis,X1),aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,X0)))
& pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,X1),X0)) ) )
& ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc782603179moreis,X1),aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,X0)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,X1),X0))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bs,X0),X1)) ) ),
inference(flattening,[],[f971]) ).
fof(f976,plain,
! [X0,X1] :
( ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hh,X0),X1))
| ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc648619567lessis,X1),X0))
& pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc782603179moreis,X0),X1)) ) )
& ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc648619567lessis,X1),X0))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc782603179moreis,X0),X1))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hh,X0),X1)) ) ),
inference(nnf_transformation,[],[f677]) ).
fof(f977,plain,
! [X0,X1] :
( ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hh,X0),X1))
| ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc648619567lessis,X1),X0))
& pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc782603179moreis,X0),X1)) ) )
& ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc648619567lessis,X1),X0))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc782603179moreis,X0),X1))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hh,X0),X1)) ) ),
inference(flattening,[],[f976]) ).
fof(f1209,plain,
! [X0,X1] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(X0,X1)),
inference(cnf_transformation,[],[f18]) ).
fof(f1222,plain,
! [X0,X1] :
( pp(aa_fun171081125l_bool(scratc93448950n_some,aa_TPT43085870d_bool(scratc572008692ffprop(X1),X0)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,X0),X1)) ),
inference(cnf_transformation,[],[f768]) ).
fof(f1225,plain,
! [X0,X1] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,X0),X1))
| ~ pp(aa_fun171081125l_bool(scratc93448950n_some,aa_TPT43085870d_bool(scratc572008692ffprop(X0),X1))) ),
inference(cnf_transformation,[],[f769]) ).
fof(f1410,plain,
! [X3,X0,X1] :
( pp(aa_TPTP_ind_bool(X1,X3))
| ~ scratc1857401069_is_of(X3,X0)
| ~ gg_TPTP_ind(X3)
| ~ pp(aa_fun171081125l_bool(scratc238963500all_of(X0),X1)) ),
inference(cnf_transformation,[],[f834]) ).
fof(f1411,plain,
! [X0,X1] :
( pp(aa_fun171081125l_bool(scratc238963500all_of(X0),X1))
| gg_TPTP_ind(sK12(X0,X1)) ),
inference(cnf_transformation,[],[f834]) ).
fof(f1412,plain,
! [X0,X1] :
( pp(aa_fun171081125l_bool(scratc238963500all_of(X0),X1))
| scratc1857401069_is_of(sK12(X0,X1),X0) ),
inference(cnf_transformation,[],[f834]) ).
fof(f1413,plain,
! [X0,X1] :
( pp(aa_fun171081125l_bool(scratc238963500all_of(X0),X1))
| ~ pp(aa_TPTP_ind_bool(X1,sK12(X0,X1))) ),
inference(cnf_transformation,[],[f834]) ).
fof(f1417,plain,
pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aTP_Lamm_bt)),
inference(cnf_transformation,[],[f150]) ).
fof(f1470,plain,
pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aTP_Lamm_hi)),
inference(cnf_transformation,[],[f203]) ).
fof(f1501,plain,
pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aTP_Lamm_jp)),
inference(cnf_transformation,[],[f234]) ).
fof(f1614,plain,
! [X0] :
( scratc1857401069_is_of(aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,X0),aTP_Lamm_a)
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_jp,X0)) ),
inference(cnf_transformation,[],[f864]) ).
fof(f1668,plain,
! [X0] :
( pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hh,X0)))
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_hi,X0)) ),
inference(cnf_transformation,[],[f891]) ).
fof(f1762,plain,
! [X0] :
( pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bs,X0)))
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bt,X0)) ),
inference(cnf_transformation,[],[f938]) ).
fof(f1767,plain,
! [X0] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ab,X0))
| ~ pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,X0))) ),
inference(cnf_transformation,[],[f940]) ).
fof(f1813,plain,
! [X0,X1] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,X0),X1))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,X1),X0)) ),
inference(cnf_transformation,[],[f968]) ).
fof(f1814,plain,
! [X0,X1] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,X0),X1))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc648619567lessis,aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,X1)),X0)) ),
inference(cnf_transformation,[],[f968]) ).
fof(f1818,plain,
! [X0,X1] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc782603179moreis,X1),aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,X0)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,X1),X0))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bs,X0),X1)) ),
inference(cnf_transformation,[],[f972]) ).
fof(f1826,plain,
! [X0,X1] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc648619567lessis,X1),X0))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc782603179moreis,X0),X1))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hh,X0),X1)) ),
inference(cnf_transformation,[],[f977]) ).
fof(f2246,plain,
~ pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aTP_Lamm_ab)),
inference(cnf_transformation,[],[f591]) ).
fof(f2466,definition,
( spl29_1
<=> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aTP_Lamm_ab)) ),
introduced(definition,[new_symbols(definition,[spl29_1])],[avatar_definition]) ).
fof(f2468,plain,
( ~ pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aTP_Lamm_ab))
| spl29_1 ),
inference(avatar_component_clause,[],[f2466]) ).
fof(f2469,plain,
~ spl29_1,
inference(avatar_split_clause,[],[f2246,f2466]) ).
fof(f2470,plain,
( gg_TPTP_ind(sK12(aTP_Lamm_a,aTP_Lamm_ab))
| spl29_1 ),
inference(resolution,[],[f2468,f1411]) ).
fof(f2471,plain,
( scratc1857401069_is_of(sK12(aTP_Lamm_a,aTP_Lamm_ab),aTP_Lamm_a)
| spl29_1 ),
inference(resolution,[],[f2468,f1412]) ).
fof(f2472,plain,
( ~ pp(aa_TPTP_ind_bool(aTP_Lamm_ab,sK12(aTP_Lamm_a,aTP_Lamm_ab)))
| spl29_1 ),
inference(resolution,[],[f2468,f1413]) ).
fof(f2485,definition,
( spl29_2
<=> scratc1857401069_is_of(sK12(aTP_Lamm_a,aTP_Lamm_ab),aTP_Lamm_a) ),
introduced(definition,[new_symbols(definition,[spl29_2])],[avatar_definition]) ).
fof(f2487,plain,
( scratc1857401069_is_of(sK12(aTP_Lamm_a,aTP_Lamm_ab),aTP_Lamm_a)
| ~ spl29_2 ),
inference(avatar_component_clause,[],[f2485]) ).
fof(f2488,plain,
( spl29_2
| spl29_1 ),
inference(avatar_split_clause,[],[f2471,f2466,f2485]) ).
fof(f2490,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(f2492,plain,
( ~ pp(aa_TPTP_ind_bool(aTP_Lamm_ab,sK12(aTP_Lamm_a,aTP_Lamm_ab)))
| spl29_3 ),
inference(avatar_component_clause,[],[f2490]) ).
fof(f2493,plain,
( ~ spl29_3
| spl29_1 ),
inference(avatar_split_clause,[],[f2472,f2466,f2490]) ).
fof(f2494,plain,
( ~ pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))
| spl29_3 ),
inference(resolution,[],[f2492,f1767]) ).
fof(f2532,definition,
( spl29_4
<=> gg_TPTP_ind(sK12(aTP_Lamm_a,aTP_Lamm_ab)) ),
introduced(definition,[new_symbols(definition,[spl29_4])],[avatar_definition]) ).
fof(f2534,plain,
( gg_TPTP_ind(sK12(aTP_Lamm_a,aTP_Lamm_ab))
| ~ spl29_4 ),
inference(avatar_component_clause,[],[f2532]) ).
fof(f2535,plain,
( spl29_4
| spl29_1 ),
inference(avatar_split_clause,[],[f2470,f2466,f2532]) ).
fof(f2537,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(scratc238963500all_of(aTP_Lamm_a),X0)) )
| ~ spl29_2 ),
inference(resolution,[],[f2487,f1410]) ).
fof(f2538,plain,
( ! [X0] :
( pp(aa_TPTP_ind_bool(X0,sK12(aTP_Lamm_a,aTP_Lamm_ab)))
| ~ pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),X0)) )
| ~ spl29_2
| ~ spl29_4 ),
inference(forward_subsumption_resolution,[],[f2537,f2534]) ).
fof(f2540,definition,
( spl29_5
<=> ! [X0] :
( pp(aa_TPTP_ind_bool(X0,sK12(aTP_Lamm_a,aTP_Lamm_ab)))
| ~ pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),X0)) ) ),
introduced(definition,[new_symbols(definition,[spl29_5])],[avatar_definition]) ).
fof(f2541,plain,
( ! [X0] :
( pp(aa_TPTP_ind_bool(X0,sK12(aTP_Lamm_a,aTP_Lamm_ab)))
| ~ pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),X0)) )
| ~ spl29_5 ),
inference(avatar_component_clause,[],[f2540]) ).
fof(f2542,plain,
( spl29_5
| ~ spl29_2
| ~ spl29_4 ),
inference(avatar_split_clause,[],[f2538,f2532,f2485,f2540]) ).
fof(f2991,plain,
( ~ pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aTP_Lamm_hi))
| pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hh,sK12(aTP_Lamm_a,aTP_Lamm_ab))))
| ~ spl29_5 ),
inference(resolution,[],[f2541,f1668]) ).
fof(f3069,plain,
( pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hh,sK12(aTP_Lamm_a,aTP_Lamm_ab))))
| ~ spl29_5 ),
inference(forward_subsumption_resolution,[],[f2991,f1470]) ).
fof(f3186,definition,
( spl29_6
<=> pp(aa_fun171081125l_bool(scratc238963500all_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(f3188,plain,
( ~ pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))
| spl29_6 ),
inference(avatar_component_clause,[],[f3186]) ).
fof(f3189,plain,
( ~ spl29_6
| spl29_3 ),
inference(avatar_split_clause,[],[f2494,f2490,f3186]) ).
fof(f3191,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,[],[f3188,f1411]) ).
fof(f3192,plain,
( scratc1857401069_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,[],[f3188,f1412]) ).
fof(f3193,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,[],[f3188,f1413]) ).
fof(f3206,definition,
( spl29_7
<=> scratc1857401069_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(f3208,plain,
( scratc1857401069_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,[],[f3206]) ).
fof(f3209,plain,
( spl29_7
| spl29_6 ),
inference(avatar_split_clause,[],[f3192,f3186,f3206]) ).
fof(f3211,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(f3213,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,[],[f3211]) ).
fof(f3214,plain,
( ~ spl29_8
| spl29_6 ),
inference(avatar_split_clause,[],[f3193,f3186,f3211]) ).
fof(f3215,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,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,[],[f3213,f1813]) ).
fof(f3216,plain,
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc648619567lessis,aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,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,[],[f3213,f1814]) ).
fof(f3262,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(scratc238963500all_of(aTP_Lamm_a),X0)) )
| ~ spl29_7 ),
inference(resolution,[],[f3208,f1410]) ).
fof(f3263,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(scratc238963500all_of(aTP_Lamm_a),X0)) )
| spl29_6
| ~ spl29_7 ),
inference(forward_subsumption_resolution,[],[f3262,f3191]) ).
fof(f3265,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(scratc238963500all_of(aTP_Lamm_a),X0)) ) ),
introduced(definition,[new_symbols(definition,[spl29_9])],[avatar_definition]) ).
fof(f3266,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(scratc238963500all_of(aTP_Lamm_a),X0)) )
| ~ spl29_9 ),
inference(avatar_component_clause,[],[f3265]) ).
fof(f3267,plain,
( spl29_9
| spl29_6
| ~ spl29_7 ),
inference(avatar_split_clause,[],[f3263,f3206,f3186,f3265]) ).
fof(f3665,plain,
( ~ pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aTP_Lamm_bt))
| pp(aa_fun171081125l_bool(scratc238963500all_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,[],[f3266,f1762]) ).
fof(f3749,plain,
( ~ pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aTP_Lamm_jp))
| scratc1857401069_is_of(aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)))),aTP_Lamm_a)
| ~ spl29_9 ),
inference(resolution,[],[f3266,f1614]) ).
fof(f3764,plain,
( scratc1857401069_is_of(aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)))),aTP_Lamm_a)
| ~ spl29_9 ),
inference(forward_subsumption_resolution,[],[f3749,f1501]) ).
fof(f3846,plain,
( pp(aa_fun171081125l_bool(scratc238963500all_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,[],[f3665,f1417]) ).
fof(f3920,definition,
( spl29_12
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,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(f3922,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,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,[],[f3920]) ).
fof(f3923,plain,
( spl29_12
| spl29_8 ),
inference(avatar_split_clause,[],[f3215,f3211,f3920]) ).
fof(f3924,plain,
( pp(aa_fun171081125l_bool(scratc93448950n_some,aa_TPT43085870d_bool(scratc572008692ffprop(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,[],[f3922,f1222]) ).
fof(f3981,definition,
( spl29_13
<=> pp(aa_fun171081125l_bool(scratc93448950n_some,aa_TPT43085870d_bool(scratc572008692ffprop(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(f3983,plain,
( pp(aa_fun171081125l_bool(scratc93448950n_some,aa_TPT43085870d_bool(scratc572008692ffprop(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,[],[f3981]) ).
fof(f3984,plain,
( spl29_13
| ~ spl29_12 ),
inference(avatar_split_clause,[],[f3924,f3920,f3981]) ).
fof(f3985,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_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_13 ),
inference(resolution,[],[f3983,f1225]) ).
fof(f4175,definition,
( spl29_14
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc648619567lessis,aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,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_14])],[avatar_definition]) ).
fof(f4177,plain,
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc648619567lessis,aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,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(avatar_component_clause,[],[f4175]) ).
fof(f4178,plain,
( ~ spl29_14
| spl29_8 ),
inference(avatar_split_clause,[],[f3216,f3211,f4175]) ).
fof(f4180,plain,
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc782603179moreis,sK12(aTP_Lamm_a,aTP_Lamm_ab)),aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,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_hh,sK12(aTP_Lamm_a,aTP_Lamm_ab)),aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))))
| spl29_14 ),
inference(resolution,[],[f4177,f1826]) ).
fof(f4242,definition,
( spl29_15
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_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_15])],[avatar_definition]) ).
fof(f4244,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_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_15 ),
inference(avatar_component_clause,[],[f4242]) ).
fof(f4245,plain,
( spl29_15
| ~ spl29_13 ),
inference(avatar_split_clause,[],[f3985,f3981,f4242]) ).
fof(f4247,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc782603179moreis,sK12(aTP_Lamm_a,aTP_Lamm_ab)),aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,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_15 ),
inference(resolution,[],[f4244,f1818]) ).
fof(f5240,definition,
( spl29_39
<=> scratc1857401069_is_of(aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,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_39])],[avatar_definition]) ).
fof(f5242,plain,
( scratc1857401069_is_of(aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)))),aTP_Lamm_a)
| ~ spl29_39 ),
inference(avatar_component_clause,[],[f5240]) ).
fof(f5243,plain,
( spl29_39
| ~ spl29_9 ),
inference(avatar_split_clause,[],[f3764,f3265,f5240]) ).
fof(f5246,plain,
( ! [X0] :
( pp(aa_TPTP_ind_bool(X0,aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)))))
| ~ pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),X0)) )
| ~ spl29_39 ),
inference(resolution,[],[f5242,f1410]) ).
fof(f5247,plain,
( ! [X0] :
( pp(aa_TPTP_ind_bool(X0,aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))))
| ~ pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),X0)) )
| ~ spl29_39 ),
inference(forward_subsumption_resolution,[],[f5246,f1209]) ).
fof(f5262,definition,
( spl29_42
<=> 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_42])],[avatar_definition]) ).
fof(f5264,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_42 ),
inference(avatar_component_clause,[],[f5262]) ).
fof(f5266,definition,
( spl29_43
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc782603179moreis,sK12(aTP_Lamm_a,aTP_Lamm_ab)),aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)))))) ),
introduced(definition,[new_symbols(definition,[spl29_43])],[avatar_definition]) ).
fof(f5268,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc782603179moreis,sK12(aTP_Lamm_a,aTP_Lamm_ab)),aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))))
| ~ spl29_43 ),
inference(avatar_component_clause,[],[f5266]) ).
fof(f5269,plain,
( ~ spl29_42
| spl29_43
| ~ spl29_15 ),
inference(avatar_split_clause,[],[f4247,f4242,f5266,f5262]) ).
fof(f5278,plain,
( ~ pp(aa_fun171081125l_bool(scratc238963500all_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_42 ),
inference(resolution,[],[f5264,f2541]) ).
fof(f5317,plain,
( $false
| ~ spl29_5
| ~ spl29_9
| spl29_42 ),
inference(forward_subsumption_resolution,[],[f5278,f3846]) ).
fof(f5318,plain,
( ~ spl29_5
| ~ spl29_9
| spl29_42 ),
inference(avatar_contradiction_clause,[],[f5317]) ).
fof(f5319,plain,
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hh,sK12(aTP_Lamm_a,aTP_Lamm_ab)),aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))))
| spl29_14
| ~ spl29_43 ),
inference(backward_subsumption_resolution,[],[f4180,f5268]) ).
fof(f5321,definition,
( spl29_44
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hh,sK12(aTP_Lamm_a,aTP_Lamm_ab)),aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)))))) ),
introduced(definition,[new_symbols(definition,[spl29_44])],[avatar_definition]) ).
fof(f5323,plain,
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hh,sK12(aTP_Lamm_a,aTP_Lamm_ab)),aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))))
| spl29_44 ),
inference(avatar_component_clause,[],[f5321]) ).
fof(f5324,plain,
( ~ spl29_44
| spl29_14
| ~ spl29_43 ),
inference(avatar_split_clause,[],[f5319,f5266,f4175,f5321]) ).
fof(f8052,definition,
( spl29_174
<=> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hh,sK12(aTP_Lamm_a,aTP_Lamm_ab)))) ),
introduced(definition,[new_symbols(definition,[spl29_174])],[avatar_definition]) ).
fof(f8054,plain,
( pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hh,sK12(aTP_Lamm_a,aTP_Lamm_ab))))
| ~ spl29_174 ),
inference(avatar_component_clause,[],[f8052]) ).
fof(f8055,plain,
( spl29_174
| ~ spl29_5 ),
inference(avatar_split_clause,[],[f3069,f2540,f8052]) ).
fof(f11638,definition,
( spl29_299
<=> ! [X0] :
( pp(aa_TPTP_ind_bool(X0,aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))))
| ~ pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),X0)) ) ),
introduced(definition,[new_symbols(definition,[spl29_299])],[avatar_definition]) ).
fof(f11639,plain,
( ! [X0] :
( pp(aa_TPTP_ind_bool(X0,aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))))
| ~ pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),X0)) )
| ~ spl29_299 ),
inference(avatar_component_clause,[],[f11638]) ).
fof(f11640,plain,
( spl29_299
| ~ spl29_39 ),
inference(avatar_split_clause,[],[f5247,f5240,f11638]) ).
fof(f11905,plain,
( ~ pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hh,sK12(aTP_Lamm_a,aTP_Lamm_ab))))
| spl29_44
| ~ spl29_299 ),
inference(resolution,[],[f11639,f5323]) ).
fof(f12247,plain,
( $false
| spl29_44
| ~ spl29_174
| ~ spl29_299 ),
inference(forward_subsumption_resolution,[],[f11905,f8054]) ).
fof(f12248,plain,
( spl29_44
| ~ spl29_174
| ~ spl29_299 ),
inference(avatar_contradiction_clause,[],[f12247]) ).
cnf(s1,plain,
~ spl29_1,
inference(sat_conversion,[],[f2469]) ).
cnf(s2,plain,
( spl29_1
| spl29_2 ),
inference(sat_conversion,[],[f2488]) ).
cnf(s3,plain,
( spl29_1
| ~ spl29_3 ),
inference(sat_conversion,[],[f2493]) ).
cnf(s4,plain,
( spl29_1
| spl29_4 ),
inference(sat_conversion,[],[f2535]) ).
cnf(s5,plain,
( ~ spl29_2
| ~ spl29_4
| spl29_5 ),
inference(sat_conversion,[],[f2542]) ).
cnf(s6,plain,
( spl29_3
| ~ spl29_6 ),
inference(sat_conversion,[],[f3189]) ).
cnf(s7,plain,
( spl29_6
| spl29_7 ),
inference(sat_conversion,[],[f3209]) ).
cnf(s8,plain,
( spl29_6
| ~ spl29_8 ),
inference(sat_conversion,[],[f3214]) ).
cnf(s9,plain,
( spl29_6
| ~ spl29_7
| spl29_9 ),
inference(sat_conversion,[],[f3267]) ).
cnf(s12,plain,
( spl29_8
| spl29_12 ),
inference(sat_conversion,[],[f3923]) ).
cnf(s13,plain,
( ~ spl29_12
| spl29_13 ),
inference(sat_conversion,[],[f3984]) ).
cnf(s14,plain,
( spl29_8
| ~ spl29_14 ),
inference(sat_conversion,[],[f4178]) ).
cnf(s15,plain,
( ~ spl29_13
| spl29_15 ),
inference(sat_conversion,[],[f4245]) ).
cnf(s38,plain,
( ~ spl29_9
| spl29_39 ),
inference(sat_conversion,[],[f5243]) ).
cnf(s41,plain,
( ~ spl29_15
| ~ spl29_42
| spl29_43 ),
inference(sat_conversion,[],[f5269]) ).
cnf(s42,plain,
( ~ spl29_5
| ~ spl29_9
| spl29_42 ),
inference(sat_conversion,[],[f5318]) ).
cnf(s43,plain,
( spl29_14
| ~ spl29_43
| ~ spl29_44 ),
inference(sat_conversion,[],[f5324]) ).
cnf(s173,plain,
( ~ spl29_5
| spl29_174 ),
inference(sat_conversion,[],[f8055]) ).
cnf(s298,plain,
( ~ spl29_39
| spl29_299 ),
inference(sat_conversion,[],[f11640]) ).
cnf(s300,plain,
( spl29_44
| ~ spl29_174
| ~ spl29_299 ),
inference(sat_conversion,[],[f12248]) ).
cnf(s303,plain,
spl29_4,
inference(rat,[],[s4,s1]) ).
cnf(s304,plain,
~ spl29_3,
inference(rat,[],[s3,s1]) ).
cnf(s305,plain,
spl29_2,
inference(rat,[],[s2,s1]) ).
cnf(s315,plain,
~ spl29_6,
inference(rat,[],[s6,s304]) ).
cnf(s316,plain,
spl29_5,
inference(rat,[],[s5,s303,s305]) ).
cnf(s322,plain,
~ spl29_8,
inference(rat,[],[s8,s315]) ).
cnf(s323,plain,
spl29_7,
inference(rat,[],[s7,s315]) ).
cnf(s353,plain,
spl29_174,
inference(rat,[],[s173,s316]) ).
cnf(s401,plain,
~ spl29_14,
inference(rat,[],[s14,s322]) ).
cnf(s402,plain,
spl29_12,
inference(rat,[],[s12,s322]) ).
cnf(s404,plain,
spl29_9,
inference(rat,[],[s9,s315,s323]) ).
cnf(s414,plain,
spl29_13,
inference(rat,[],[s13,s402]) ).
cnf(s489,plain,
spl29_42,
inference(rat,[],[s42,s316,s404]) ).
cnf(s490,plain,
spl29_39,
inference(rat,[],[s38,s404]) ).
cnf(s499,plain,
spl29_15,
inference(rat,[],[s15,s414]) ).
cnf(s554,plain,
spl29_299,
inference(rat,[],[s298,s490]) ).
cnf(s563,plain,
spl29_43,
inference(rat,[],[s41,s489,s499]) ).
cnf(s569,plain,
spl29_44,
inference(rat,[],[s300,s353,s554]) ).
cnf(s576,plain,
$false,
inference(rat,[],[s43,s401,s569,s563]) ).
fof(f12307,plain,
$false,
inference(avatar_sat_refutation,[],[s576]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM699+4 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n014.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 21:07:46 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 11.37/2.53 % (1169059)Detected formulas, will run a generic FOF schedule.
% 11.37/2.53 % (1169169)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2256133450:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 11.37/2.53 % (1169169)Refutation not found, incomplete strategy
% 11.37/2.53 % (1169169)------------------------------
% 11.37/2.53 % (1169169)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.37/2.53 % (1169169)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.37/2.53 % (1169169)CaDiCaL version: 2.1.3
% 11.37/2.53 % (1169169)Termination reason: Refutation not found, incomplete strategy
% 11.37/2.53 % (1169169)Time elapsed: 0.002 s
% 11.37/2.53 % (1169169)Peak memory usage: 88 MB
% 11.37/2.53 % (1169169)Instructions burned: 3 (million)
% 11.37/2.53 % (1169168)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1384278020:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 11.37/2.53 % (1169165)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=3601680424:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 11.37/2.53 % (1169166)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=4017608688:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 11.37/2.53 % (1169167)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=3757318817:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 11.37/2.53 % (1169168)Refutation not found, incomplete strategy
% 11.37/2.53 % (1169168)------------------------------
% 11.37/2.53 % (1169168)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.37/2.53 % (1169168)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.37/2.53 % (1169168)CaDiCaL version: 2.1.3
% 11.37/2.53 % (1169168)Termination reason: Refutation not found, incomplete strategy
% 11.37/2.53 % (1169168)Time elapsed: 0.003 s
% 11.37/2.53 % (1169168)Peak memory usage: 88 MB
% 11.37/2.53 % (1169168)Instructions burned: 2 (million)
% 11.37/2.53 % (1169171)dis-21_1_sil=8000:lcm=predicate:random_seed=3179920234: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)
% 11.37/2.53 % (1169170)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3256660170:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 11.37/2.53 % (1169171)Instruction limit reached!
% 11.37/2.53 % (1169171)------------------------------
% 11.37/2.53 % (1169171)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.37/2.53 % (1169171)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.37/2.53 % (1169171)CaDiCaL version: 2.1.3
% 11.37/2.53 % (1169171)Termination reason: Instruction limit
% 11.37/2.53 % (1169171)Termination phase: Saturation
% 11.37/2.53 % (1169171)Time elapsed: 0.082 s
% 11.37/2.53 % (1169171)Peak memory usage: 90 MB
% 11.37/2.53 % (1169171)Instructions burned: 129 (million)
% 11.37/2.53 % (1169169)------------------------------
% 11.37/2.53 % (1169169)------------------------------
% 11.37/2.53 % (1169170)Instruction limit reached!
% 11.37/2.53 % (1169170)------------------------------
% 11.37/2.53 % (1169170)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.37/2.53 % (1169170)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.37/2.53 % (1169170)CaDiCaL version: 2.1.3
% 11.37/2.53 % (1169170)Termination reason: Instruction limit
% 11.37/2.53 % (1169170)Termination phase: Saturation
% 11.37/2.53 % (1169170)Time elapsed: 0.094 s
% 11.37/2.53 % (1169170)Peak memory usage: 90 MB
% 11.37/2.53 % (1169170)Instructions burned: 139 (million)
% 11.37/2.53 % (1169203)lrs+10_1_sil=8000:sp=occurrence:random_seed=2174259818:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 11.37/2.53 % (1169203)Refutation not found, incomplete strategy
% 11.37/2.53 % (1169203)------------------------------
% 11.37/2.53 % (1169203)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.37/2.53 % (1169203)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.37/2.53 % (1169203)CaDiCaL version: 2.1.3
% 11.37/2.53 % (1169203)Termination reason: Refutation not found, incomplete strategy
% 11.37/2.53 % (1169203)Time elapsed: 0.003 s
% 11.37/2.53 % (1169203)Peak memory usage: 88 MB
% 18.51/3.51 % (1169203)Instructions burned: 2 (million)
% 18.51/3.51 % (1169204)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2266545016:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 18.51/3.51 % (1169204)Refutation not found, incomplete strategy
% 18.51/3.51 % (1169204)------------------------------
% 18.51/3.51 % (1169204)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 18.51/3.51 % (1169204)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.51/3.51 % (1169204)CaDiCaL version: 2.1.3
% 18.51/3.51 % (1169204)Termination reason: Refutation not found, incomplete strategy
% 18.51/3.51 % (1169204)Time elapsed: 0.003 s
% 18.51/3.51 % (1169204)Peak memory usage: 88 MB
% 18.51/3.51 % (1169204)Instructions burned: 9 (million)
% 18.51/3.51 % (1169168)------------------------------
% 18.51/3.51 % (1169168)------------------------------
% 18.51/3.51 % (1169205)lrs+1011_1_sil=32000:sp=occurrence:random_seed=15668981:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 18.51/3.51 % (1169205)Refutation not found, incomplete strategy
% 18.51/3.51 % (1169205)------------------------------
% 18.51/3.51 % (1169205)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 18.51/3.51 % (1169205)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.51/3.51 % (1169205)CaDiCaL version: 2.1.3
% 18.51/3.51 % (1169205)Termination reason: Refutation not found, incomplete strategy
% 18.51/3.51 % (1169205)Time elapsed: 0.005 s
% 18.51/3.51 % (1169205)Peak memory usage: 89 MB
% 18.51/3.51 % (1169205)Instructions burned: 5 (million)
% 18.51/3.51 % (1169204)------------------------------
% 18.51/3.51 % (1169204)------------------------------
% 18.51/3.51 % (1169232)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=1576069758:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 18.51/3.51 % (1169203)------------------------------
% 18.51/3.51 % (1169203)------------------------------
% 18.51/3.51 % (1169291)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2797337389:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 18.51/3.51 % (1169291)Refutation not found, incomplete strategy
% 18.51/3.51 % (1169291)------------------------------
% 18.51/3.51 % (1169291)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 18.51/3.51 % (1169291)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.51/3.51 % (1169291)CaDiCaL version: 2.1.3
% 18.51/3.51 % (1169291)Termination reason: Refutation not found, incomplete strategy
% 18.51/3.51 % (1169291)Time elapsed: 0.003 s
% 18.51/3.51 % (1169291)Peak memory usage: 89 MB
% 18.51/3.51 % (1169291)Instructions burned: 7 (million)
% 18.51/3.51 % (1169232)Instruction limit reached!
% 18.51/3.51 % (1169232)------------------------------
% 18.51/3.51 % (1169232)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 18.51/3.51 % (1169232)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.51/3.51 % (1169232)CaDiCaL version: 2.1.3
% 18.51/3.51 % (1169232)Termination reason: Instruction limit
% 18.51/3.51 % (1169232)Termination phase: Saturation
% 18.51/3.51 % (1169232)Time elapsed: 0.119 s
% 18.51/3.51 % (1169232)Peak memory usage: 90 MB
% 18.51/3.51 % (1169232)Instructions burned: 249 (million)
% 18.51/3.51 % (1169205)------------------------------
% 18.51/3.51 % (1169205)------------------------------
% 18.51/3.51 % (1169317)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=679449731:i=2350_2993 on theBenchmark for (2993ds/2350Mi)
% 18.51/3.51 % (1169291)------------------------------
% 18.51/3.51 % (1169291)------------------------------
% 18.51/3.51 % (1169319)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3334275198:cts=off:i=113:fsr=off:ss=included:sgt=4_2992 on theBenchmark for (2992ds/113Mi)
% 18.51/3.51 % (1169320)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=574032745:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 18.51/3.51 % (1169319)Instruction limit reached!
% 18.51/3.51 % (1169319)------------------------------
% 18.51/3.51 % (1169319)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 18.51/3.51 % (1169319)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.51/3.51 % (1169319)CaDiCaL version: 2.1.3
% 18.51/3.51 % (1169319)Termination reason: Instruction limit
% 18.51/3.51 % (1169319)Termination phase: Saturation
% 18.51/3.51 % (1169319)Time elapsed: 0.060 s
% 23.74/4.30 % (1169319)Peak memory usage: 91 MB
% 23.74/4.30 % (1169319)Instructions burned: 113 (million)
% 23.74/4.30 % (1169354)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3004541587:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 23.74/4.30 % (1169320)Instruction limit reached!
% 23.74/4.30 % (1169320)------------------------------
% 23.74/4.30 % (1169320)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.74/4.30 % (1169320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.74/4.30 % (1169320)CaDiCaL version: 2.1.3
% 23.74/4.30 % (1169320)Termination reason: Instruction limit
% 23.74/4.30 % (1169320)Termination phase: Saturation
% 23.74/4.30 % (1169320)Time elapsed: 0.061 s
% 23.74/4.30 % (1169320)Peak memory usage: 89 MB
% 23.74/4.30 % (1169320)Instructions burned: 128 (million)
% 23.74/4.30 % (1169354)Instruction limit reached!
% 23.74/4.30 % (1169354)------------------------------
% 23.74/4.30 % (1169354)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.74/4.30 % (1169354)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.74/4.30 % (1169354)CaDiCaL version: 2.1.3
% 23.74/4.30 % (1169354)Termination reason: Instruction limit
% 23.74/4.30 % (1169354)Termination phase: Saturation
% 23.74/4.30 % (1169354)Time elapsed: 0.033 s
% 23.74/4.30 % (1169354)Peak memory usage: 90 MB
% 23.74/4.30 % (1169354)Instructions burned: 114 (million)
% 23.74/4.30 % (1169372)lrs+10_1_sil=8000:sp=occurrence:random_seed=2184593529:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2990 on theBenchmark for (2990ds/907Mi)
% 23.74/4.30 % (1169375)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2791850563:i=5202:ss=axioms:sgt=16_2989 on theBenchmark for (2989ds/5202Mi)
% 23.74/4.30 % (1169374)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1802654243:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 23.74/4.30 % (1169374)Refutation not found, incomplete strategy
% 23.74/4.30 % (1169374)------------------------------
% 23.74/4.30 % (1169374)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.74/4.30 % (1169374)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.74/4.30 % (1169374)CaDiCaL version: 2.1.3
% 23.74/4.30 % (1169374)Termination reason: Refutation not found, incomplete strategy
% 23.74/4.30 % (1169374)Time elapsed: 0.042 s
% 23.74/4.30 % (1169374)Peak memory usage: 90 MB
% 23.74/4.30 % (1169374)Instructions burned: 83 (million)
% 23.74/4.30 % (1169374)------------------------------
% 23.74/4.30 % (1169374)------------------------------
% 23.74/4.30 % (1169372)Instruction limit reached!
% 23.74/4.30 % (1169372)------------------------------
% 23.74/4.30 % (1169372)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.74/4.30 % (1169372)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.74/4.30 % (1169372)CaDiCaL version: 2.1.3
% 23.74/4.30 % (1169372)Termination reason: Instruction limit
% 23.74/4.30 % (1169372)Termination phase: Saturation
% 23.74/4.30 % (1169372)Time elapsed: 0.380 s
% 23.74/4.30 % (1169372)Peak memory usage: 95 MB
% 23.74/4.30 % (1169372)Instructions burned: 909 (million)
% 23.74/4.30 % (1169379)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=1992563005:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2985 on theBenchmark for (2985ds/134Mi)
% 23.74/4.30 % (1169380)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=4096197176:st=8:i=592:sd=3:ep=RST:ss=axioms_2985 on theBenchmark for (2985ds/592Mi)
% 23.74/4.30 % (1169380)Refutation not found, incomplete strategy
% 23.74/4.30 % (1169380)------------------------------
% 23.74/4.30 % (1169380)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.74/4.30 % (1169380)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.74/4.30 % (1169380)CaDiCaL version: 2.1.3
% 23.74/4.30 % (1169380)Termination reason: Refutation not found, incomplete strategy
% 23.74/4.30 % (1169380)Time elapsed: 0.007 s
% 23.74/4.30 % (1169380)Peak memory usage: 89 MB
% 23.74/4.30 % (1169380)Instructions burned: 23 (million)
% 23.74/4.30 % (1169379)Instruction limit reached!
% 23.74/4.30 % (1169379)------------------------------
% 23.74/4.30 % (1169379)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.74/4.30 % (1169379)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.74/4.30 % (1169379)CaDiCaL version: 2.1.3
% 23.74/4.30 % (1169379)Termination reason: Instruction limit
% 23.74/4.30 % (1169379)Termination phase: Saturation
% 23.74/4.30 % (1169379)Time elapsed: 0.075 s
% 23.74/4.30 % (1169379)Peak memory usage: 94 MB
% 23.74/4.30 % (1169379)Instructions burned: 135 (million)
% 23.74/4.30 % (1169380)------------------------------
% 23.74/4.30 % (1169380)------------------------------
% 23.74/4.30 % (1169383)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=843164206:st=3:i=13193:sd=3:ss=axioms_2983 on theBenchmark for (2983ds/13193Mi)
% 23.74/4.30 % (1169384)lrs+1666_7_slsqr=4,1:sil=8000:plsq=on:plsqc=1:sos=on:urr=on:plsql=on:rp=on:alpa=false:sac=on:slsq=on:random_seed=1898706038:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2982 on theBenchmark for (2982ds/125Mi)
% 23.74/4.30 % (1169384)Refutation not found, incomplete strategy
% 23.74/4.30 % (1169384)------------------------------
% 23.74/4.30 % (1169384)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.74/4.30 % (1169384)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.74/4.30 % (1169384)CaDiCaL version: 2.1.3
% 23.74/4.30 % (1169384)Termination reason: Refutation not found, incomplete strategy
% 23.74/4.30 % (1169384)Time elapsed: 0.004 s
% 23.74/4.30 % (1169384)Peak memory usage: 89 MB
% 23.74/4.30 % (1169384)Instructions burned: 12 (million)
% 23.74/4.30 % (1169384)------------------------------
% 23.74/4.30 % (1169384)------------------------------
% 23.74/4.30 % (1169387)lrs+10_1024_to=lpo:sil=8000:tgt=full:sp=arity:slsq=on:random_seed=3374769999:i=134:gtgl=5:slsql=off:gtg=exists_sym_2979 on theBenchmark for (2979ds/134Mi)
% 23.74/4.30 % (1169387)Instruction limit reached!
% 23.74/4.30 % (1169387)------------------------------
% 23.74/4.30 % (1169387)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.74/4.30 % (1169387)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.74/4.30 % (1169387)CaDiCaL version: 2.1.3
% 23.74/4.30 % (1169387)Termination reason: Instruction limit
% 23.74/4.30 % (1169387)Termination phase: Saturation
% 23.74/4.30 % (1169387)Time elapsed: 0.035 s
% 23.74/4.30 % (1169387)Peak memory usage: 92 MB
% 23.74/4.30 % (1169387)Instructions burned: 137 (million)
% 23.74/4.30 % (1169389)lrs+10_1_sil=16000:plsq=on:plsqc=1:plsqr=32,1:sos=on:lcm=reverse:fd=off:newcnf=on:random_seed=3369744491:i=141:sd=1:gsp=on:sup=off:ss=axioms:sgt=8_2977 on theBenchmark for (2977ds/141Mi)
% 23.74/4.30 % (1169389)Refutation not found, incomplete strategy
% 23.74/4.30 % (1169389)------------------------------
% 23.74/4.30 % (1169389)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.74/4.30 % (1169389)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.74/4.30 % (1169389)CaDiCaL version: 2.1.3
% 23.74/4.30 % (1169389)Termination reason: Refutation not found, incomplete strategy
% 23.74/4.30 % (1169389)Time elapsed: 0.002 s
% 23.74/4.30 % (1169389)Peak memory usage: 88 MB
% 23.74/4.30 % (1169389)Instructions burned: 2 (million)
% 23.74/4.30 % (1169317)Instruction limit reached!
% 23.74/4.30 % (1169317)------------------------------
% 23.74/4.30 % (1169317)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.74/4.30 % (1169317)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.74/4.30 % (1169317)CaDiCaL version: 2.1.3
% 23.74/4.30 % (1169317)Termination reason: Instruction limit
% 23.74/4.30 % (1169317)Termination phase: Saturation
% 23.74/4.30 % (1169317)Time elapsed: 1.567 s
% 23.74/4.30 % (1169317)Peak memory usage: 145 MB
% 23.74/4.30 % (1169317)Instructions burned: 2350 (million)
% 23.74/4.30 % (1169389)------------------------------
% 23.74/4.30 % (1169389)------------------------------
% 23.74/4.30 % (1169391)lrs+1011_1_sil=8000:plsq=on:sp=occurrence:fs=off:random_seed=1171356811:i=431:sd=1:fsr=off:sup=off:ss=axioms:sgt=64_2975 on theBenchmark for (2975ds/431Mi)
% 23.74/4.30 % (1169391)Refutation not found, incomplete strategy
% 23.74/4.30 % (1169391)------------------------------
% 23.74/4.30 % (1169391)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.74/4.30 % (1169391)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.74/4.30 % (1169391)CaDiCaL version: 2.1.3
% 23.74/4.30 % (1169391)Termination reason: Refutation not found, incomplete strategy
% 23.74/4.30 % (1169391)Time elapsed: 0.003 s
% 23.74/4.30 % (1169391)Peak memory usage: 89 MB
% 23.74/4.30 % (1169391)Instructions burned: 2 (million)
% 23.74/4.30 % (1169392)lrs+1010_1_ncem=casc2026/models/loop6.pt:sil=64000:tgt=full:npcc=on:prc=on:urr=ec_only:bsr=on:fd=preordered:gs=on:sac=on:newcnf=on:random_seed=3265035272:i=6060:aac=none:ins=25_2974 on theBenchmark for (2974ds/6060Mi)
% 23.74/4.30 % (1169391)------------------------------
% 23.74/4.30 % (1169391)------------------------------
% 23.74/4.30 % (1169395)lrs+10_16_anc=all:slsqr=32,1:sil=8000:avsql=on:sp=unary_frequency:lcm=predicate:urr=full:rp=on:br=off:slsqc=4:flr=on:sac=on:slsq=on:avsqc=1:random_seed=1911743175:avsq=on:s2a=on:i=150:kws=precedence:nicw=on:gsp=on:rawr=on_2971 on theBenchmark for (2971ds/150Mi)
% 23.74/4.30 % (1169395)Instruction limit reached!
% 23.74/4.30 % (1169395)------------------------------
% 23.74/4.30 % (1169395)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.74/4.30 % (1169395)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.74/4.30 % (1169395)CaDiCaL version: 2.1.3
% 23.74/4.30 % (1169395)Termination reason: Instruction limit
% 23.74/4.30 % (1169395)Termination phase: Saturation
% 23.74/4.30 % (1169395)Time elapsed: 0.078 s
% 23.74/4.30 % (1169395)Peak memory usage: 91 MB
% 23.74/4.30 % (1169395)Instructions burned: 152 (million)
% 23.74/4.30 % (1169167)First to succeed.
% 23.74/4.30 % (1169167)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1169059"
% 23.74/4.30 % (1169397)lrs+1010_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=ground:npcc=on:sp=arity:urr=on:random_seed=1385848043:i=14155:bd=all_2969 on theBenchmark for (2969ds/14155Mi)
% 23.74/4.30 % (1169167)Refutation found. Thanks to Tanya!
% 23.74/4.30 % SZS status Theorem for theBenchmark
% 23.74/4.30 % SZS output start Proof for theBenchmark
% See solution above
% 24.55/4.49 % (1169167)------------------------------
% 24.55/4.49 % (1169167)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 24.55/4.49 % (1169167)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.55/4.49 % (1169167)CaDiCaL version: 2.1.3
% 24.55/4.49 % (1169167)Termination reason: Refutation
% 24.55/4.49 % (1169167)Time elapsed: 2.951 s
% 24.55/4.49 % (1169167)Peak memory usage: 167 MB
% 24.55/4.49 % (1169167)Instructions burned: 4776 (million)
% 24.55/4.49 % (1169167)------------------------------
% 24.55/4.49 % (1169167)------------------------------
% 24.55/4.49 % (1169059)Success in time 3.422 s
% 24.55/4.49 % Vampire exiting
%------------------------------------------------------------------------------