%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM669+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 12:16:21 PM UTC 2026
% Result : Theorem 10.99s 2.45s
% Output : Refutation 11.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 28
% Syntax : Number of formulae : 152 ( 47 unt; 6 def)
% Number of atoms : 341 ( 61 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 314 ( 125 ~; 156 |; 16 &)
% ( 13 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 29 ( 29 usr; 19 con; 0-2 aty)
% Number of variables : 134 ( 0 sgn 132 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
gg_TPTP_ind(scratc98832752nd_n_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Scratch__tptp__translate__45846__17029_ONUM669__thf__4__p_Obnd__n__1) ).
fof(f17,axiom,
! [X0,X1] : gg_bool(aa_TPTP_ind_bool(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_aa_001t__TPTP____Interpret__Oind_001t__HOL__Obool) ).
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(f19,axiom,
! [X0,X1] : gg_bool(aa_fun171081125l_bool(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_aa_001t__fun_It__TPTP____Interpret__Oind_Mt__HOL__Obool_J_001t__HOL__Obool) ).
fof(f28,axiom,
! [X0,X1] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,X0),X1))
<=> pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(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(scratc1728063742_29_ii,X0),X1))
<=> pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(X0),X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__d__29__ii) ).
fof(f35,axiom,
! [X0] : scratc80697981d_n_pl(X0) = aa_TPT1424761345TP_ind(scratc1802143164bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1768849959d_plus,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__n__pl) ).
fof(f53,axiom,
scratc80238795d_n_is = scratc561578434d_e_is(scratc2068492180nd_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__n__is) ).
fof(f100,axiom,
! [X0] : scratc561578434d_e_is(X0) = fequal_TPTP_ind,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__e__is) ).
fof(f147,axiom,
! [X0,X1] :
( pp(aa_fun171081125l_bool(scratc846727211all_of(X0),X1))
<=> ! [X2] :
( gg_TPTP_ind(X2)
=> ( scratc1623311406_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(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bs)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_satz18) ).
fof(f184,axiom,
pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_er)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_satz4e) ).
fof(f198,axiom,
scratc1623311406_is_of(scratc98832752nd_n_1,aTP_Lamm_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__1__p) ).
fof(f266,axiom,
! [X0] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_er,X0))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X0)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(X0),scratc98832752nd_n_1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ATP_Olambda__7) ).
fof(f268,axiom,
! [X0] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X0))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X0)),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ATP_Olambda__9) ).
fof(f310,axiom,
! [X0] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bs,X0))
<=> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_br,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ATP_Olambda__51) ).
fof(f339,axiom,
! [X0,X1] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_br,X0),X1))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(X0),X1)),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ATP_Olambda__80) ).
fof(f429,axiom,
pp(fTrue),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
fof(f433,axiom,
! [X0] :
( gg_bool(X0)
=> ( X0 = fTrue
| X0 = fFalse ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
fof(f434,axiom,
~ pp(fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
fof(f440,axiom,
! [X0,X1] :
( ( gg_TPTP_ind(X0)
& gg_TPTP_ind(X1) )
=> ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X0),X1))
| X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_001t__TPTP____Interpret__Oind_T) ).
fof(f444,conjecture,
pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f445,negated_conjecture,
~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa)),
inference(negated_conjecture,[status(cth)],[f444]) ).
fof(f446,plain,
~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa)),
inference(flattening,[],[f445]) ).
fof(f463,plain,
! [X0,X1] :
( pp(aa_fun171081125l_bool(scratc846727211all_of(X0),X1))
<=> ! [X2] :
( pp(aa_TPTP_ind_bool(X1,X2))
| ~ scratc1623311406_is_of(X2,X0)
| ~ gg_TPTP_ind(X2) ) ),
inference(ennf_transformation,[],[f147]) ).
fof(f464,plain,
! [X0,X1] :
( pp(aa_fun171081125l_bool(scratc846727211all_of(X0),X1))
<=> ! [X2] :
( pp(aa_TPTP_ind_bool(X1,X2))
| ~ scratc1623311406_is_of(X2,X0)
| ~ gg_TPTP_ind(X2) ) ),
inference(flattening,[],[f463]) ).
fof(f572,plain,
! [X0] :
( X0 = fTrue
| X0 = fFalse
| ~ gg_bool(X0) ),
inference(ennf_transformation,[],[f433]) ).
fof(f573,plain,
! [X0] :
( X0 = fTrue
| X0 = fFalse
| ~ gg_bool(X0) ),
inference(flattening,[],[f572]) ).
fof(f574,plain,
! [X0,X1] :
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X0),X1))
| X0 = X1
| ~ gg_TPTP_ind(X0)
| ~ gg_TPTP_ind(X1) ),
inference(ennf_transformation,[],[f440]) ).
fof(f575,plain,
! [X0,X1] :
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X0),X1))
| X0 = X1
| ~ gg_TPTP_ind(X0)
| ~ gg_TPTP_ind(X1) ),
inference(flattening,[],[f574]) ).
fof(f579,plain,
! [X0,X1] :
( ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,X0),X1))
| ~ pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(X1),X0))) )
& ( pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(X1),X0)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,X0),X1)) ) ),
inference(nnf_transformation,[],[f28]) ).
fof(f580,plain,
! [X0,X1] :
( ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,X0),X1))
| ~ pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(X0),X1))) )
& ( pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(X0),X1)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,X0),X1)) ) ),
inference(nnf_transformation,[],[f29]) ).
fof(f643,plain,
! [X0,X1] :
( ( pp(aa_fun171081125l_bool(scratc846727211all_of(X0),X1))
| ? [X2] :
( ~ pp(aa_TPTP_ind_bool(X1,X2))
& scratc1623311406_is_of(X2,X0)
& gg_TPTP_ind(X2) ) )
& ( ! [X2] :
( pp(aa_TPTP_ind_bool(X1,X2))
| ~ scratc1623311406_is_of(X2,X0)
| ~ gg_TPTP_ind(X2) )
| ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X0),X1)) ) ),
inference(nnf_transformation,[],[f464]) ).
fof(f644,plain,
! [X0,X1] :
( ( pp(aa_fun171081125l_bool(scratc846727211all_of(X0),X1))
| ? [X2] :
( ~ pp(aa_TPTP_ind_bool(X1,X2))
& scratc1623311406_is_of(X2,X0)
& gg_TPTP_ind(X2) ) )
& ( ! [X3] :
( pp(aa_TPTP_ind_bool(X1,X3))
| ~ scratc1623311406_is_of(X3,X0)
| ~ gg_TPTP_ind(X3) )
| ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X0),X1)) ) ),
inference(rectify,[],[f643]) ).
fof(f645,plain,
! [X0,X1] :
( ( pp(aa_fun171081125l_bool(scratc846727211all_of(X0),X1))
| ( ~ pp(aa_TPTP_ind_bool(X1,sK12(X0,X1)))
& scratc1623311406_is_of(sK12(X0,X1),X0)
& gg_TPTP_ind(sK12(X0,X1)) ) )
& ( ! [X3] :
( pp(aa_TPTP_ind_bool(X1,X3))
| ~ scratc1623311406_is_of(X3,X0)
| ~ gg_TPTP_ind(X3) )
| ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X0),X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X2,sK12(X0,X1))],[f644]) ).
fof(f671,plain,
! [X0] :
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_er,X0))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X0)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(X0),scratc98832752nd_n_1))) )
& ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X0)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(X0),scratc98832752nd_n_1)))
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_er,X0)) ) ),
inference(nnf_transformation,[],[f266]) ).
fof(f673,plain,
! [X0] :
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X0))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X0)),X0)) )
& ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X0)),X0))
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X0)) ) ),
inference(nnf_transformation,[],[f268]) ).
fof(f715,plain,
! [X0] :
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_bs,X0))
| ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_br,X0))) )
& ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_br,X0)))
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bs,X0)) ) ),
inference(nnf_transformation,[],[f310]) ).
fof(f757,plain,
! [X0,X1] :
( ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_br,X0),X1))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(X0),X1)),X0)) )
& ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(X0),X1)),X0))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_br,X0),X1)) ) ),
inference(nnf_transformation,[],[f339]) ).
fof(f874,plain,
gg_TPTP_ind(scratc98832752nd_n_1),
inference(cnf_transformation,[],[f12]) ).
fof(f879,plain,
! [X0,X1] : gg_bool(aa_TPTP_ind_bool(X0,X1)),
inference(cnf_transformation,[],[f17]) ).
fof(f880,plain,
! [X0,X1] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(X0,X1)),
inference(cnf_transformation,[],[f18]) ).
fof(f881,plain,
! [X0,X1] : gg_bool(aa_fun171081125l_bool(X0,X1)),
inference(cnf_transformation,[],[f19]) ).
fof(f893,plain,
! [X0,X1] :
( pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(X1),X0)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,X0),X1)) ),
inference(cnf_transformation,[],[f579]) ).
fof(f894,plain,
! [X0,X1] :
( ~ pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(X1),X0)))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,X0),X1)) ),
inference(cnf_transformation,[],[f579]) ).
fof(f895,plain,
! [X0,X1] :
( pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(X0),X1)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,X0),X1)) ),
inference(cnf_transformation,[],[f580]) ).
fof(f896,plain,
! [X0,X1] :
( ~ pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(X0),X1)))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,X0),X1)) ),
inference(cnf_transformation,[],[f580]) ).
fof(f907,plain,
! [X0] : scratc80697981d_n_pl(X0) = aa_TPT1424761345TP_ind(scratc1802143164bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1768849959d_plus,X0)),
inference(cnf_transformation,[],[f35]) ).
fof(f933,plain,
scratc80238795d_n_is = scratc561578434d_e_is(scratc2068492180nd_nat),
inference(cnf_transformation,[],[f53]) ).
fof(f997,plain,
! [X0] : scratc561578434d_e_is(X0) = fequal_TPTP_ind,
inference(cnf_transformation,[],[f100]) ).
fof(f1081,plain,
! [X3,X0,X1] :
( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X0),X1))
| ~ scratc1623311406_is_of(X3,X0)
| ~ gg_TPTP_ind(X3)
| pp(aa_TPTP_ind_bool(X1,X3)) ),
inference(cnf_transformation,[],[f645]) ).
fof(f1082,plain,
! [X0,X1] :
( pp(aa_fun171081125l_bool(scratc846727211all_of(X0),X1))
| gg_TPTP_ind(sK12(X0,X1)) ),
inference(cnf_transformation,[],[f645]) ).
fof(f1083,plain,
! [X0,X1] :
( pp(aa_fun171081125l_bool(scratc846727211all_of(X0),X1))
| scratc1623311406_is_of(sK12(X0,X1),X0) ),
inference(cnf_transformation,[],[f645]) ).
fof(f1084,plain,
! [X0,X1] :
( ~ pp(aa_TPTP_ind_bool(X1,sK12(X0,X1)))
| pp(aa_fun171081125l_bool(scratc846727211all_of(X0),X1)) ),
inference(cnf_transformation,[],[f645]) ).
fof(f1088,plain,
pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bs)),
inference(cnf_transformation,[],[f150]) ).
fof(f1122,plain,
pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_er)),
inference(cnf_transformation,[],[f184]) ).
fof(f1136,plain,
scratc1623311406_is_of(scratc98832752nd_n_1,aTP_Lamm_a),
inference(cnf_transformation,[],[f198]) ).
fof(f1240,plain,
! [X0] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X0)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(X0),scratc98832752nd_n_1)))
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_er,X0)) ),
inference(cnf_transformation,[],[f671]) ).
fof(f1245,plain,
! [X0] :
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X0)),X0))
| pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X0)) ),
inference(cnf_transformation,[],[f673]) ).
fof(f1328,plain,
! [X0] :
( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_br,X0)))
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bs,X0)) ),
inference(cnf_transformation,[],[f715]) ).
fof(f1397,plain,
! [X0,X1] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(X0),X1)),X0))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_br,X0),X1)) ),
inference(cnf_transformation,[],[f757]) ).
fof(f1605,plain,
pp(fTrue),
inference(cnf_transformation,[],[f429]) ).
fof(f1609,plain,
! [X0] :
( ~ gg_bool(X0)
| fFalse = X0
| fTrue = X0 ),
inference(cnf_transformation,[],[f573]) ).
fof(f1610,plain,
~ pp(fFalse),
inference(cnf_transformation,[],[f434]) ).
fof(f1616,plain,
! [X0,X1] :
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X0),X1))
| X0 = X1
| ~ gg_TPTP_ind(X0)
| ~ gg_TPTP_ind(X1) ),
inference(cnf_transformation,[],[f575]) ).
fof(f1620,plain,
~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa)),
inference(cnf_transformation,[],[f446]) ).
fof(f1645,plain,
scratc80238795d_n_is = fequal_TPTP_ind,
inference(definition_unfolding,[],[f933,f997]) ).
fof(f1684,plain,
! [X0] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X0)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1802143164bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1768849959d_plus,X0)),scratc98832752nd_n_1)))
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_er,X0)) ),
inference(definition_unfolding,[],[f1240,f907]) ).
fof(f1698,plain,
! [X0,X1] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1802143164bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1768849959d_plus,X0)),X1)),X0))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_br,X0),X1)) ),
inference(definition_unfolding,[],[f1397,f907]) ).
fof(f1769,definition,
sF25 = scratc846727211all_of(aTP_Lamm_a),
introduced(definition,[new_symbols(definition,[sF25])],[function_definition]) ).
fof(f1770,plain,
scratc846727211all_of(aTP_Lamm_a) = sF25,
inference(reorient_equations,[],[f1769]) ).
fof(f1771,definition,
sF26 = aa_fun171081125l_bool(sF25,aTP_Lamm_aa),
introduced(definition,[new_symbols(definition,[sF26])],[function_definition]) ).
fof(f1772,plain,
aa_fun171081125l_bool(sF25,aTP_Lamm_aa) = sF26,
inference(reorient_equations,[],[f1771]) ).
fof(f1773,plain,
~ pp(sF26),
inference(definition_folding,[],[f1620,f1772,f1770]) ).
fof(f1806,plain,
! [X0] :
( pp(aa_fun171081125l_bool(sF25,X0))
| gg_TPTP_ind(sK12(aTP_Lamm_a,X0)) ),
inference(superposition,[],[f1082,f1770]) ).
fof(f1807,plain,
( pp(sF26)
| gg_TPTP_ind(sK12(aTP_Lamm_a,aTP_Lamm_aa)) ),
inference(superposition,[],[f1806,f1772]) ).
fof(f1808,plain,
gg_TPTP_ind(sK12(aTP_Lamm_a,aTP_Lamm_aa)),
inference(forward_subsumption_resolution,[],[f1807,f1773]) ).
fof(f1814,plain,
! [X0] :
( scratc1623311406_is_of(sK12(aTP_Lamm_a,X0),aTP_Lamm_a)
| pp(aa_fun171081125l_bool(sF25,X0)) ),
inference(superposition,[],[f1083,f1770]) ).
fof(f1815,plain,
! [X0,X1] :
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,X0),X1))
| X0 = X1
| ~ gg_TPTP_ind(X0)
| ~ gg_TPTP_ind(X1) ),
inference(superposition,[],[f1616,f1645]) ).
fof(f1826,plain,
! [X0,X1] :
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,X1),X0))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,X0),X1)) ),
inference(resolution,[],[f896,f893]) ).
fof(f1827,plain,
! [X0,X1] :
( aa_fun171081125l_bool(X0,X1) = fTrue
| aa_fun171081125l_bool(X0,X1) = fFalse ),
inference(resolution,[],[f1609,f881]) ).
fof(f1846,plain,
! [X2,X0,X1] :
( ~ pp(fTrue)
| ~ scratc1623311406_is_of(X2,X0)
| ~ gg_TPTP_ind(X2)
| pp(aa_TPTP_ind_bool(X1,X2))
| fFalse = aa_fun171081125l_bool(scratc846727211all_of(X0),X1) ),
inference(superposition,[],[f1081,f1827]) ).
fof(f1862,plain,
! [X2,X0,X1] :
( ~ scratc1623311406_is_of(X2,X0)
| ~ gg_TPTP_ind(X2)
| pp(aa_TPTP_ind_bool(X1,X2))
| fFalse = aa_fun171081125l_bool(scratc846727211all_of(X0),X1) ),
inference(forward_subsumption_resolution,[],[f1846,f1605]) ).
fof(f1890,plain,
! [X0,X1] :
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,X0),X1))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,X1),X0)) ),
inference(resolution,[],[f895,f894]) ).
fof(f1922,plain,
! [X0,X1] :
( aa_TPTP_ind_bool(X0,X1) = fTrue
| aa_TPTP_ind_bool(X0,X1) = fFalse ),
inference(resolution,[],[f879,f1609]) ).
fof(f1923,plain,
! [X0] :
( ~ pp(aa_TPTP_ind_bool(aTP_Lamm_er,X0))
| aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X0) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1802143164bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1768849959d_plus,X0)),scratc98832752nd_n_1)
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X0))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1802143164bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1768849959d_plus,X0)),scratc98832752nd_n_1)) ),
inference(resolution,[],[f1684,f1815]) ).
fof(f1924,plain,
! [X0] :
( ~ pp(aa_TPTP_ind_bool(aTP_Lamm_er,X0))
| aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X0) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1802143164bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1768849959d_plus,X0)),scratc98832752nd_n_1)
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X0)) ),
inference(forward_subsumption_resolution,[],[f1923,f880]) ).
fof(f1925,plain,
! [X0] :
( ~ pp(aa_TPTP_ind_bool(aTP_Lamm_er,X0))
| aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X0) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1802143164bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1768849959d_plus,X0)),scratc98832752nd_n_1) ),
inference(forward_subsumption_resolution,[],[f1924,f880]) ).
fof(f1929,definition,
( spl27_7
<=> fFalse = aa_fun171081125l_bool(sF25,aTP_Lamm_er) ),
introduced(definition,[new_symbols(definition,[spl27_7])],[avatar_definition]) ).
fof(f1930,plain,
( fFalse != aa_fun171081125l_bool(sF25,aTP_Lamm_er)
| spl27_7 ),
inference(avatar_component_clause,[],[f1929]) ).
fof(f1931,plain,
( fFalse = aa_fun171081125l_bool(sF25,aTP_Lamm_er)
| ~ spl27_7 ),
inference(avatar_component_clause,[],[f1929]) ).
fof(f1981,plain,
! [X0,X1] :
( ~ pp(fTrue)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,X1),X0))
| fFalse = aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,X0),X1) ),
inference(superposition,[],[f1826,f1922]) ).
fof(f1983,plain,
! [X0,X1] :
( ~ pp(fTrue)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,X1),X0))
| fFalse = aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,X0),X1) ),
inference(superposition,[],[f1890,f1922]) ).
fof(f1993,plain,
! [X0] :
( ~ pp(fTrue)
| aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X0) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1802143164bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1768849959d_plus,X0)),scratc98832752nd_n_1)
| fFalse = aa_TPTP_ind_bool(aTP_Lamm_er,X0) ),
inference(superposition,[],[f1925,f1922]) ).
fof(f1999,plain,
! [X0] :
( aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X0) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1802143164bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1768849959d_plus,X0)),scratc98832752nd_n_1)
| fFalse = aa_TPTP_ind_bool(aTP_Lamm_er,X0) ),
inference(forward_subsumption_resolution,[],[f1993,f1605]) ).
fof(f2003,plain,
! [X0,X1] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,X1),X0))
| fFalse = aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,X0),X1) ),
inference(forward_subsumption_resolution,[],[f1983,f1605]) ).
fof(f2005,plain,
! [X0,X1] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,X1),X0))
| fFalse = aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,X0),X1) ),
inference(forward_subsumption_resolution,[],[f1981,f1605]) ).
fof(f2030,plain,
! [X0] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X0))
| fFalse = aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,X0),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X0)) ),
inference(resolution,[],[f2005,f1245]) ).
fof(f2048,plain,
! [X0] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X0)),X0))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_br,X0),scratc98832752nd_n_1))
| fFalse = aa_TPTP_ind_bool(aTP_Lamm_er,X0) ),
inference(superposition,[],[f1698,f1999]) ).
fof(f2063,plain,
! [X0] :
( pp(aa_fun171081125l_bool(scratc846727211all_of(X0),aTP_Lamm_aa))
| fFalse = aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,sK12(X0,aTP_Lamm_aa)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,sK12(X0,aTP_Lamm_aa))) ),
inference(resolution,[],[f2030,f1084]) ).
fof(f2066,plain,
( pp(aa_fun171081125l_bool(sF25,aTP_Lamm_aa))
| fFalse = aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,sK12(aTP_Lamm_a,aTP_Lamm_aa)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,sK12(aTP_Lamm_a,aTP_Lamm_aa))) ),
inference(superposition,[],[f2063,f1770]) ).
fof(f2068,plain,
( pp(sF26)
| fFalse = aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,sK12(aTP_Lamm_a,aTP_Lamm_aa)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,sK12(aTP_Lamm_a,aTP_Lamm_aa))) ),
inference(forward_demodulation,[],[f2066,f1772]) ).
fof(f2069,plain,
fFalse = aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,sK12(aTP_Lamm_a,aTP_Lamm_aa)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,sK12(aTP_Lamm_a,aTP_Lamm_aa))),
inference(forward_subsumption_resolution,[],[f2068,f1773]) ).
fof(f2073,plain,
( pp(fFalse)
| fFalse = aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,sK12(aTP_Lamm_a,aTP_Lamm_aa))),sK12(aTP_Lamm_a,aTP_Lamm_aa)) ),
inference(superposition,[],[f2003,f2069]) ).
fof(f2094,plain,
fFalse = aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,sK12(aTP_Lamm_a,aTP_Lamm_aa))),sK12(aTP_Lamm_a,aTP_Lamm_aa)),
inference(forward_subsumption_resolution,[],[f2073,f1610]) ).
fof(f2152,definition,
( spl27_21
<=> scratc1623311406_is_of(sK12(aTP_Lamm_a,aTP_Lamm_aa),aTP_Lamm_a) ),
introduced(definition,[new_symbols(definition,[spl27_21])],[avatar_definition]) ).
fof(f2153,plain,
( scratc1623311406_is_of(sK12(aTP_Lamm_a,aTP_Lamm_aa),aTP_Lamm_a)
| ~ spl27_21 ),
inference(avatar_component_clause,[],[f2152]) ).
fof(f2154,plain,
( ~ scratc1623311406_is_of(sK12(aTP_Lamm_a,aTP_Lamm_aa),aTP_Lamm_a)
| spl27_21 ),
inference(avatar_component_clause,[],[f2152]) ).
fof(f2318,plain,
( pp(aa_fun171081125l_bool(sF25,aTP_Lamm_aa))
| spl27_21 ),
inference(resolution,[],[f2154,f1814]) ).
fof(f2319,plain,
( pp(sF26)
| spl27_21 ),
inference(forward_demodulation,[],[f2318,f1772]) ).
fof(f2320,plain,
( $false
| spl27_21 ),
inference(forward_subsumption_resolution,[],[f2319,f1773]) ).
fof(f2321,plain,
spl27_21,
inference(avatar_contradiction_clause,[],[f2320]) ).
fof(f2341,plain,
! [X0] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bs,X0))
| ~ gg_TPTP_ind(X0)
| ~ scratc1623311406_is_of(X0,aTP_Lamm_a) ),
inference(resolution,[],[f1088,f1081]) ).
fof(f2385,plain,
pp(aa_fun171081125l_bool(sF25,aTP_Lamm_er)),
inference(superposition,[],[f1122,f1770]) ).
fof(f2387,plain,
( pp(fFalse)
| ~ spl27_7 ),
inference(forward_demodulation,[],[f2385,f1931]) ).
fof(f2389,plain,
( $false
| ~ spl27_7 ),
inference(forward_subsumption_resolution,[],[f2387,f1610]) ).
fof(f2390,plain,
~ spl27_7,
inference(avatar_contradiction_clause,[],[f2389]) ).
fof(f2987,plain,
! [X2,X0,X1] :
( ~ gg_TPTP_ind(sK12(X0,X1))
| pp(aa_TPTP_ind_bool(X2,sK12(X0,X1)))
| fFalse = aa_fun171081125l_bool(scratc846727211all_of(X0),X2)
| pp(aa_fun171081125l_bool(scratc846727211all_of(X0),X1)) ),
inference(resolution,[],[f1862,f1083]) ).
fof(f2994,plain,
! [X2,X0,X1] :
( pp(aa_TPTP_ind_bool(X2,sK12(X0,X1)))
| fFalse = aa_fun171081125l_bool(scratc846727211all_of(X0),X2)
| pp(aa_fun171081125l_bool(scratc846727211all_of(X0),X1)) ),
inference(forward_subsumption_resolution,[],[f2987,f1082]) ).
fof(f3522,plain,
( pp(fFalse)
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_br,sK12(aTP_Lamm_a,aTP_Lamm_aa)),scratc98832752nd_n_1))
| fFalse = aa_TPTP_ind_bool(aTP_Lamm_er,sK12(aTP_Lamm_a,aTP_Lamm_aa)) ),
inference(superposition,[],[f2048,f2094]) ).
fof(f3524,plain,
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_br,sK12(aTP_Lamm_a,aTP_Lamm_aa)),scratc98832752nd_n_1))
| fFalse = aa_TPTP_ind_bool(aTP_Lamm_er,sK12(aTP_Lamm_a,aTP_Lamm_aa)) ),
inference(forward_subsumption_resolution,[],[f3522,f1610]) ).
fof(f3526,definition,
( spl27_40
<=> fFalse = aa_TPTP_ind_bool(aTP_Lamm_er,sK12(aTP_Lamm_a,aTP_Lamm_aa)) ),
introduced(definition,[new_symbols(definition,[spl27_40])],[avatar_definition]) ).
fof(f3528,plain,
( fFalse = aa_TPTP_ind_bool(aTP_Lamm_er,sK12(aTP_Lamm_a,aTP_Lamm_aa))
| ~ spl27_40 ),
inference(avatar_component_clause,[],[f3526]) ).
fof(f3530,definition,
( spl27_41
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_br,sK12(aTP_Lamm_a,aTP_Lamm_aa)),scratc98832752nd_n_1)) ),
introduced(definition,[new_symbols(definition,[spl27_41])],[avatar_definition]) ).
fof(f3532,plain,
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_br,sK12(aTP_Lamm_a,aTP_Lamm_aa)),scratc98832752nd_n_1))
| spl27_41 ),
inference(avatar_component_clause,[],[f3530]) ).
fof(f3533,plain,
( spl27_40
| ~ spl27_41 ),
inference(avatar_split_clause,[],[f3524,f3530,f3526]) ).
fof(f4034,plain,
! [X0,X1] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_br,X0),X1))
| ~ scratc1623311406_is_of(X1,aTP_Lamm_a)
| ~ gg_TPTP_ind(X1)
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bs,X0)) ),
inference(resolution,[],[f1328,f1081]) ).
fof(f4040,plain,
( ~ scratc1623311406_is_of(scratc98832752nd_n_1,aTP_Lamm_a)
| ~ gg_TPTP_ind(scratc98832752nd_n_1)
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bs,sK12(aTP_Lamm_a,aTP_Lamm_aa)))
| spl27_41 ),
inference(resolution,[],[f4034,f3532]) ).
fof(f4045,plain,
( ~ gg_TPTP_ind(scratc98832752nd_n_1)
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bs,sK12(aTP_Lamm_a,aTP_Lamm_aa)))
| spl27_41 ),
inference(forward_subsumption_resolution,[],[f4040,f1136]) ).
fof(f4047,plain,
( ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bs,sK12(aTP_Lamm_a,aTP_Lamm_aa)))
| spl27_41 ),
inference(forward_subsumption_resolution,[],[f4045,f874]) ).
fof(f4049,plain,
( ~ gg_TPTP_ind(sK12(aTP_Lamm_a,aTP_Lamm_aa))
| ~ scratc1623311406_is_of(sK12(aTP_Lamm_a,aTP_Lamm_aa),aTP_Lamm_a)
| spl27_41 ),
inference(resolution,[],[f4047,f2341]) ).
fof(f4061,plain,
( ~ scratc1623311406_is_of(sK12(aTP_Lamm_a,aTP_Lamm_aa),aTP_Lamm_a)
| spl27_41 ),
inference(forward_subsumption_resolution,[],[f4049,f1808]) ).
fof(f4062,plain,
( $false
| ~ spl27_21
| spl27_41 ),
inference(forward_subsumption_resolution,[],[f4061,f2153]) ).
fof(f4063,plain,
( ~ spl27_21
| spl27_41 ),
inference(avatar_contradiction_clause,[],[f4062]) ).
fof(f4092,plain,
( pp(fFalse)
| fFalse = aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_er)
| pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ spl27_40 ),
inference(superposition,[],[f2994,f3528]) ).
fof(f4098,plain,
( fFalse = aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_er)
| pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ spl27_40 ),
inference(forward_subsumption_resolution,[],[f4092,f1610]) ).
fof(f4103,plain,
( fFalse = aa_fun171081125l_bool(sF25,aTP_Lamm_er)
| pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ spl27_40 ),
inference(forward_demodulation,[],[f4098,f1770]) ).
fof(f4109,plain,
( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa))
| spl27_7
| ~ spl27_40 ),
inference(forward_subsumption_resolution,[],[f4103,f1930]) ).
fof(f4115,plain,
( pp(aa_fun171081125l_bool(sF25,aTP_Lamm_aa))
| spl27_7
| ~ spl27_40 ),
inference(forward_demodulation,[],[f4109,f1770]) ).
fof(f4118,plain,
( pp(sF26)
| spl27_7
| ~ spl27_40 ),
inference(forward_demodulation,[],[f4115,f1772]) ).
fof(f4119,plain,
( $false
| spl27_7
| ~ spl27_40 ),
inference(forward_subsumption_resolution,[],[f4118,f1773]) ).
fof(f4120,plain,
( spl27_7
| ~ spl27_40 ),
inference(avatar_contradiction_clause,[],[f4119]) ).
cnf(s13,plain,
spl27_21,
inference(sat_conversion,[],[f2321]) ).
cnf(s14,plain,
~ spl27_7,
inference(sat_conversion,[],[f2390]) ).
cnf(s34,plain,
( spl27_40
| ~ spl27_41 ),
inference(sat_conversion,[],[f3533]) ).
cnf(s65,plain,
( ~ spl27_21
| spl27_41 ),
inference(sat_conversion,[],[f4063]) ).
cnf(s73,plain,
( spl27_7
| ~ spl27_40 ),
inference(sat_conversion,[],[f4120]) ).
cnf(s96,plain,
~ spl27_40,
inference(rat,[],[s73,s14]) ).
cnf(s97,plain,
~ spl27_41,
inference(rat,[],[s34,s96]) ).
cnf(s98,plain,
~ spl27_21,
inference(rat,[],[s65,s97]) ).
cnf(s99,plain,
$false,
inference(rat,[],[s13,s98]) ).
fof(f4121,plain,
$false,
inference(avatar_sat_refutation,[],[s99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM669+4 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.43 % Computer : n014.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sun Sep 27 21:02:01 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.47 Running first-order theorem proving
% 0.16/0.47 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
% 10.99/2.45 % (1158732)Detected formulas, will run a generic FOF schedule.
% 10.99/2.45 % (1158738)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=3418532956:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 10.99/2.45 % (1158744)dis-21_1_sil=8000:lcm=predicate:random_seed=1140055016: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)
% 10.99/2.45 % (1158741)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1855330421:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 10.99/2.45 % (1158739)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=1539582588:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 10.99/2.45 % (1158740)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=4258584250:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 10.99/2.45 % (1158741)Refutation not found, incomplete strategy
% 10.99/2.45 % (1158741)------------------------------
% 10.99/2.45 % (1158741)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.99/2.45 % (1158741)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.99/2.45 % (1158741)CaDiCaL version: 2.1.3
% 10.99/2.45 % (1158741)Termination reason: Refutation not found, incomplete strategy
% 10.99/2.45 % (1158741)Time elapsed: 0.004 s
% 10.99/2.45 % (1158741)Peak memory usage: 87 MB
% 10.99/2.45 % (1158741)Instructions burned: 2 (million)
% 10.99/2.45 % (1158742)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=917484889:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 10.99/2.45 % (1158743)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=932373158:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 10.99/2.45 % (1158742)Refutation not found, incomplete strategy
% 10.99/2.45 % (1158742)------------------------------
% 10.99/2.45 % (1158742)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.99/2.45 % (1158742)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.99/2.45 % (1158742)CaDiCaL version: 2.1.3
% 10.99/2.45 % (1158742)Termination reason: Refutation not found, incomplete strategy
% 10.99/2.45 % (1158742)Time elapsed: 0.004 s
% 10.99/2.45 % (1158742)Peak memory usage: 88 MB
% 10.99/2.45 % (1158742)Instructions burned: 2 (million)
% 10.99/2.45 % (1158744)Instruction limit reached!
% 10.99/2.45 % (1158744)------------------------------
% 10.99/2.45 % (1158744)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.99/2.45 % (1158744)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.99/2.45 % (1158744)CaDiCaL version: 2.1.3
% 10.99/2.45 % (1158744)Termination reason: Instruction limit
% 10.99/2.45 % (1158744)Termination phase: Saturation
% 10.99/2.45 % (1158744)Time elapsed: 0.121 s
% 10.99/2.45 % (1158744)Peak memory usage: 90 MB
% 10.99/2.45 % (1158744)Instructions burned: 129 (million)
% 10.99/2.45 % (1158743)Instruction limit reached!
% 10.99/2.45 % (1158743)------------------------------
% 10.99/2.45 % (1158743)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.99/2.45 % (1158743)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.99/2.45 % (1158743)CaDiCaL version: 2.1.3
% 10.99/2.45 % (1158743)Termination reason: Instruction limit
% 10.99/2.45 % (1158743)Termination phase: Saturation
% 10.99/2.45 % (1158743)Time elapsed: 0.145 s
% 10.99/2.45 % (1158743)Peak memory usage: 90 MB
% 10.99/2.45 % (1158743)Instructions burned: 139 (million)
% 10.99/2.45 % (1158755)lrs+10_1_sil=8000:sp=occurrence:random_seed=3443602152:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 10.99/2.45 % (1158755)Refutation not found, incomplete strategy
% 10.99/2.45 % (1158755)------------------------------
% 10.99/2.45 % (1158755)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.99/2.45 % (1158755)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.99/2.45 % (1158755)CaDiCaL version: 2.1.3
% 10.99/2.45 % (1158755)Termination reason: Refutation not found, incomplete strategy
% 10.99/2.45 % (1158755)Time elapsed: 0.004 s
% 10.99/2.45 % (1158755)Peak memory usage: 88 MB
% 10.99/2.45 % (1158755)Instructions burned: 2 (million)
% 10.99/2.45 % (1158756)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2192468855:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/157Mi)
% 10.99/2.45 % (1158756)Refutation not found, incomplete strategy
% 10.99/2.45 % (1158756)------------------------------
% 10.99/2.45 % (1158756)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.99/2.45 % (1158756)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.99/2.45 % (1158756)CaDiCaL version: 2.1.3
% 10.99/2.45 % (1158756)Termination reason: Refutation not found, incomplete strategy
% 10.99/2.45 % (1158756)Time elapsed: 0.006 s
% 10.99/2.45 % (1158756)Peak memory usage: 88 MB
% 10.99/2.45 % (1158756)Instructions burned: 7 (million)
% 10.99/2.45 % (1158741)------------------------------
% 10.99/2.45 % (1158741)------------------------------
% 10.99/2.45 % (1158742)------------------------------
% 10.99/2.45 % (1158742)------------------------------
% 10.99/2.45 % (1158760)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3822281304:i=325:sd=1:ss=axioms:sgt=32_2993 on theBenchmark for (2993ds/325Mi)
% 10.99/2.45 % (1158760)Refutation not found, incomplete strategy
% 10.99/2.45 % (1158760)------------------------------
% 10.99/2.45 % (1158760)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.99/2.45 % (1158760)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.99/2.45 % (1158760)CaDiCaL version: 2.1.3
% 10.99/2.45 % (1158760)Termination reason: Refutation not found, incomplete strategy
% 10.99/2.45 % (1158760)Time elapsed: 0.008 s
% 10.99/2.45 % (1158760)Peak memory usage: 88 MB
% 10.99/2.45 % (1158760)Instructions burned: 5 (million)
% 10.99/2.45 % (1158755)------------------------------
% 10.99/2.45 % (1158755)------------------------------
% 10.99/2.45 % (1158761)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=278136237:s2a=on:i=248:s2at=1.23:gtg=position_2992 on theBenchmark for (2992ds/248Mi)
% 10.99/2.45 % (1158756)------------------------------
% 10.99/2.45 % (1158756)------------------------------
% 10.99/2.45 % (1158764)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2546227:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2989 on theBenchmark for (2989ds/294Mi)
% 10.99/2.45 % (1158761)Instruction limit reached!
% 10.99/2.45 % (1158761)------------------------------
% 10.99/2.45 % (1158761)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.99/2.45 % (1158761)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.99/2.45 % (1158761)CaDiCaL version: 2.1.3
% 10.99/2.45 % (1158761)Termination reason: Instruction limit
% 10.99/2.45 % (1158761)Termination phase: Saturation
% 10.99/2.45 % (1158761)Time elapsed: 0.223 s
% 10.99/2.45 % (1158761)Peak memory usage: 94 MB
% 10.99/2.45 % (1158761)Instructions burned: 248 (million)
% 10.99/2.45 % (1158764)Refutation not found, incomplete strategy
% 10.99/2.45 % (1158764)------------------------------
% 10.99/2.45 % (1158764)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.99/2.45 % (1158764)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.99/2.45 % (1158764)CaDiCaL version: 2.1.3
% 10.99/2.45 % (1158764)Termination reason: Refutation not found, incomplete strategy
% 10.99/2.45 % (1158764)Time elapsed: 0.008 s
% 10.99/2.45 % (1158764)Peak memory usage: 88 MB
% 10.99/2.45 % (1158764)Instructions burned: 6 (million)
% 10.99/2.45 % (1158760)------------------------------
% 10.99/2.45 % (1158760)------------------------------
% 10.99/2.45 % (1158738)First to succeed.
% 10.99/2.45 % (1158738)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1158732"
% 10.99/2.45 % (1158765)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2712498662:i=2350_2989 on theBenchmark for (2989ds/2350Mi)
% 10.99/2.45 % (1158767)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=4278404425:cts=off:i=113:fsr=off:ss=included:sgt=4_2987 on theBenchmark for (2987ds/113Mi)
% 10.99/2.45 % (1158767)Instruction limit reached!
% 10.99/2.45 % (1158767)------------------------------
% 10.99/2.45 % (1158767)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.99/2.45 % (1158767)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.99/2.45 % (1158767)CaDiCaL version: 2.1.3
% 10.99/2.45 % (1158767)Termination reason: Instruction limit
% 10.99/2.45 % (1158767)Termination phase: Saturation
% 10.99/2.45 % (1158767)Time elapsed: 0.067 s
% 10.99/2.45 % (1158767)Peak memory usage: 91 MB
% 10.99/2.45 % (1158767)Instructions burned: 114 (million)
% 10.99/2.45 % (1158768)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=160478818:i=127:av=off:fsr=off:sup=off_2987 on theBenchmark for (2987ds/127Mi)
% 10.99/2.45 % (1158738)Refutation found. Thanks to Tanya!
% 10.99/2.45 % SZS status Theorem for theBenchmark
% 10.99/2.45 % SZS output start Proof for theBenchmark
% See solution above
% 11.80/2.70 % (1158738)------------------------------
% 11.80/2.70 % (1158738)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.80/2.70 % (1158738)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.80/2.70 % (1158738)CaDiCaL version: 2.1.3
% 11.80/2.70 % (1158738)Termination reason: Refutation
% 11.80/2.70 % (1158738)Time elapsed: 1.137 s
% 11.80/2.70 % (1158738)Peak memory usage: 141 MB
% 11.80/2.70 % (1158738)Instructions burned: 1904 (million)
% 11.80/2.70 % (1158738)------------------------------
% 11.80/2.70 % (1158738)------------------------------
% 11.80/2.70 % (1158732)Success in time 1.618 s
% 11.80/2.70 % Vampire exiting
%------------------------------------------------------------------------------