%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM669+4 : TPTP v9.0.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:21:49 AM UTC 2025
% Result : Theorem 24.95s 25.13s
% Output : Proof 25.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 104
% Syntax : Number of formulae : 275 ( 87 unt; 0 typ; 0 def)
% Number of atoms : 1668 ( 99 equ)
% Maximal formula atoms : 32 ( 6 avg)
% Number of connectives : 2688 (1333 ~;1118 |; 22 &)
% ( 206 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 38 ( 38 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 29 ( 29 usr; 17 con; 0-2 aty)
% Number of variables : 443 ( 416 !; 0 ?; 443 :)
% Comments :
%------------------------------------------------------------------------------
tff(pp_type,type,
pp: $i > $o ).
tff(aa_TPTP_ind_bool_type,type,
aa_TPTP_ind_bool: ( $i * $i ) > $i ).
tff(aa_TPTP_ind_TPTP_ind_type,type,
aa_TPTP_ind_TPTP_ind: ( $i * $i ) > $i ).
tff(scratc2095348162ptyset_type,type,
scratc2095348162ptyset: $i ).
tff(scratc2076836790rdsucc_type,type,
scratc2076836790rdsucc: $i ).
tff(scratc80697981d_n_pl_type,type,
scratc80697981d_n_pl: $i > $i ).
tff(tptp_fun_X2_13_type,type,
tptp_fun_X2_13: ( $i * $i ) > $i ).
tff(aTP_Lamm_a_type,type,
aTP_Lamm_a: $i ).
tff(aTP_Lamm_aa_type,type,
aTP_Lamm_aa: $i ).
tff(aa_TPT43085870d_bool_type,type,
aa_TPT43085870d_bool: ( $i * $i ) > $i ).
tff(scratc2027709436nd_iii_type,type,
scratc2027709436nd_iii: $i ).
tff(scratc2018566726d_Sing_type,type,
scratc2018566726d_Sing: $i ).
tff(scratc1307162165nunion_type,type,
scratc1307162165nunion: $i > $i ).
tff(scratc98832752nd_n_1_type,type,
scratc98832752nd_n_1: $i ).
tff(fequal_TPTP_ind_type,type,
fequal_TPTP_ind: $i ).
tff(scratc80238795d_n_is_type,type,
scratc80238795d_n_is: $i ).
tff(scratc561578434d_e_is_type,type,
scratc561578434d_e_is: $i > $i ).
tff(scratc2068492180nd_nat_type,type,
scratc2068492180nd_nat: $i ).
tff(aa_fun1431113780TP_ind_type,type,
aa_fun1431113780TP_ind: ( $i * $i ) > $i ).
tff(aTP_Lamm_ag_type,type,
aTP_Lamm_ag: $i ).
tff(scratc494515559_d_Sep_type,type,
scratc494515559_d_Sep: $i > $i ).
tff(scratc1460043444_omega_type,type,
scratc1460043444_omega: $i ).
tff(aTP_Lamm_er_type,type,
aTP_Lamm_er: $i ).
tff(gg_TPTP_ind_type,type,
gg_TPTP_ind: $i > $o ).
tff(scratc1623311406_is_of_type,type,
scratc1623311406_is_of: ( $i * $i ) > $o ).
tff(aa_fun171081125l_bool_type,type,
aa_fun171081125l_bool: ( $i * $i ) > $i ).
tff(scratc846727211all_of_type,type,
scratc846727211all_of: $i > $i ).
tff(scratc1229761461ffprop_type,type,
scratc1229761461ffprop: $i > $i ).
tff(scratc701212661n_some_type,type,
scratc701212661n_some: $i ).
tff(scratc1728063742_29_ii_type,type,
scratc1728063742_29_ii: $i ).
tff(aTP_Lamm_bp_type,type,
aTP_Lamm_bp: $i ).
tff(aTP_Lamm_bq_type,type,
aTP_Lamm_bq: $i ).
tff(1,plain,
^ [X: $i] :
refl(( ( aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(X),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,X)) )
<=> ( aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(X),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,X)) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(X),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,X)) )
<=> ! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(X),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,X)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(X),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,X)) )
<=> ! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(X),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,X)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(X),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__ordsucc) ).
tff(5,plain,
! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(X),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,X)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(X),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,X)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(X),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,X)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(X),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,X)) )
| ( aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)) = aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)) = aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) = aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
( ( scratc80238795d_n_is = scratc561578434d_e_is(scratc2068492180nd_nat) )
<=> ( scratc80238795d_n_is = scratc561578434d_e_is(scratc2068492180nd_nat) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
scratc80238795d_n_is = scratc561578434d_e_is(scratc2068492180nd_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__n__is) ).
tff(13,plain,
scratc80238795d_n_is = scratc561578434d_e_is(scratc2068492180nd_nat),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
scratc561578434d_e_is(scratc2068492180nd_nat) = scratc80238795d_n_is,
inference(symmetry,[status(thm)],[13]) ).
tff(15,plain,
( ( scratc2068492180nd_nat = aa_fun1431113780TP_ind(scratc494515559_d_Sep(scratc1460043444_omega),aTP_Lamm_ag) )
<=> ( scratc2068492180nd_nat = aa_fun1431113780TP_ind(scratc494515559_d_Sep(scratc1460043444_omega),aTP_Lamm_ag) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
scratc2068492180nd_nat = aa_fun1431113780TP_ind(scratc494515559_d_Sep(scratc1460043444_omega),aTP_Lamm_ag),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__nat) ).
tff(17,plain,
scratc2068492180nd_nat = aa_fun1431113780TP_ind(scratc494515559_d_Sep(scratc1460043444_omega),aTP_Lamm_ag),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
aa_fun1431113780TP_ind(scratc494515559_d_Sep(scratc1460043444_omega),aTP_Lamm_ag) = scratc2068492180nd_nat,
inference(symmetry,[status(thm)],[17]) ).
tff(19,plain,
scratc561578434d_e_is(aa_fun1431113780TP_ind(scratc494515559_d_Sep(scratc1460043444_omega),aTP_Lamm_ag)) = scratc561578434d_e_is(scratc2068492180nd_nat),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
^ [X: $i] :
refl(( ( scratc561578434d_e_is(X) = fequal_TPTP_ind )
<=> ( scratc561578434d_e_is(X) = fequal_TPTP_ind ) )),
inference(bind,[status(th)],[]) ).
tff(21,plain,
( ! [X: $i] : ( scratc561578434d_e_is(X) = fequal_TPTP_ind )
<=> ! [X: $i] : ( scratc561578434d_e_is(X) = fequal_TPTP_ind ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [X: $i] : ( scratc561578434d_e_is(X) = fequal_TPTP_ind )
<=> ! [X: $i] : ( scratc561578434d_e_is(X) = fequal_TPTP_ind ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
! [X: $i] : ( scratc561578434d_e_is(X) = fequal_TPTP_ind ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__e__is) ).
tff(24,plain,
! [X: $i] : ( scratc561578434d_e_is(X) = fequal_TPTP_ind ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [X: $i] : ( scratc561578434d_e_is(X) = fequal_TPTP_ind ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [X: $i] : ( scratc561578434d_e_is(X) = fequal_TPTP_ind ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
( ~ ! [X: $i] : ( scratc561578434d_e_is(X) = fequal_TPTP_ind )
| ( scratc561578434d_e_is(aa_fun1431113780TP_ind(scratc494515559_d_Sep(scratc1460043444_omega),aTP_Lamm_ag)) = fequal_TPTP_ind ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
scratc561578434d_e_is(aa_fun1431113780TP_ind(scratc494515559_d_Sep(scratc1460043444_omega),aTP_Lamm_ag)) = fequal_TPTP_ind,
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
fequal_TPTP_ind = scratc561578434d_e_is(aa_fun1431113780TP_ind(scratc494515559_d_Sep(scratc1460043444_omega),aTP_Lamm_ag)),
inference(symmetry,[status(thm)],[28]) ).
tff(30,plain,
fequal_TPTP_ind = scratc80238795d_n_is,
inference(transitivity,[status(thm)],[29,19,14]) ).
tff(31,plain,
aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))) = aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),
inference(monotonicity,[status(thm)],[30,10]) ).
tff(32,plain,
aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1)) = aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1)),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1))) ),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1))) ),
inference(symmetry,[status(thm)],[33]) ).
tff(35,plain,
^ [Uu: $i] :
refl(( ( pp(aa_TPTP_ind_bool(aTP_Lamm_er,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),scratc98832752nd_n_1))) )
<=> ( pp(aa_TPTP_ind_bool(aTP_Lamm_er,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),scratc98832752nd_n_1))) ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_er,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),scratc98832752nd_n_1))) )
<=> ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_er,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),scratc98832752nd_n_1))) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
( ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_er,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),scratc98832752nd_n_1))) )
<=> ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_er,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),scratc98832752nd_n_1))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,axiom,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_er,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),scratc98832752nd_n_1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ATP_Olambda__7) ).
tff(39,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_er,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),scratc98832752nd_n_1))) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_er,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),scratc98832752nd_n_1))) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_er,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),scratc98832752nd_n_1))) ),
inference(modus_ponens,[status(thm)],[40,36]) ).
tff(42,plain,
( ~ ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_er,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),scratc98832752nd_n_1))) )
| ( pp(aa_TPTP_ind_bool(aTP_Lamm_er,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
( pp(aa_TPTP_ind_bool(aTP_Lamm_er,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1))) ),
inference(unit_resolution,[status(thm)],[42,41]) ).
tff(44,plain,
^ [X: $i,Xa: $i] :
refl(( ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
<=> ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(45,plain,
( ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
<=> ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,plain,
^ [X: $i,Xa: $i] :
rewrite(( ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
<=> ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(47,plain,
( ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
<=> ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,plain,
( ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
<=> ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) ) ),
inference(transitivity,[status(thm)],[47,45]) ).
tff(49,plain,
^ [X: $i,Xa: $i] :
trans(monotonicity(rewrite(( ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
<=> ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) ) )),
monotonicity(rewrite(( ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) )
<=> ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) )),
( ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) )
<=> ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )),
( ( ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
& ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
<=> ( ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
& ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) ) )),
rewrite(( ( ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
& ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
<=> ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) ) )),
( ( ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
& ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
<=> ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(50,plain,
( ! [X: $i,Xa: $i] :
( ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
& ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
<=> ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
( ! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
<=> ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
<=> ! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
<=> ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,plain,
^ [X: $i,Xa: $i] :
rewrite(( ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
<=> ! [X2: $i] :
( gg_TPTP_ind(X2)
=> ( scratc1623311406_is_of(X2,X)
=> pp(aa_TPTP_ind_bool(Xa,X2)) ) ) )
<=> ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
<=> ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(53,plain,
( ! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
<=> ! [X2: $i] :
( gg_TPTP_ind(X2)
=> ( scratc1623311406_is_of(X2,X)
=> pp(aa_TPTP_ind_bool(Xa,X2)) ) ) )
<=> ! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
<=> ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,axiom,
! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
<=> ! [X2: $i] :
( gg_TPTP_ind(X2)
=> ( scratc1623311406_is_of(X2,X)
=> pp(aa_TPTP_ind_bool(Xa,X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__all__of) ).
tff(55,plain,
! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
<=> ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
<=> ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) ),
inference(modus_ponens,[status(thm)],[55,51]) ).
tff(57,plain,
! [X: $i,Xa: $i] :
( ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
& ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) ),
inference(skolemize,[status(sab)],[56]) ).
tff(58,plain,
! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) ),
inference(modus_ponens,[status(thm)],[57,50]) ).
tff(59,plain,
! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) ),
inference(modus_ponens,[status(thm)],[58,48]) ).
tff(60,plain,
( ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ) ) ) )
<=> ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,plain,
( ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ) ) )
<=> ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(62,plain,
( ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ) ) ) )
<=> ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ) ) ) ) ),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
( ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ) ) ) )
<=> ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ) ) ) ) ),
inference(transitivity,[status(thm)],[62,60]) ).
tff(64,plain,
( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(65,plain,
( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ) ) ) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ) ) ),
inference(unit_resolution,[status(thm)],[65,59]) ).
tff(67,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ) )
| pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(68,plain,
( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(unit_resolution,[status(thm)],[67,66]) ).
tff(69,plain,
( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa))
<=> ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa)) ),
inference(rewrite,[status(thm)],[]) ).
tff(70,axiom,
~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(71,plain,
~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa)),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
( ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ) )
| pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(73,plain,
( ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ) )
| ~ ( ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(unit_resolution,[status(thm)],[72,71]) ).
tff(74,plain,
~ ( ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(unit_resolution,[status(thm)],[73,68]) ).
tff(75,plain,
( ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
| gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)) ),
inference(tautology,[status(thm)],[]) ).
tff(76,plain,
gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),
inference(unit_resolution,[status(thm)],[75,74]) ).
tff(77,plain,
( ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
| scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ),
inference(tautology,[status(thm)],[]) ).
tff(78,plain,
scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a),
inference(unit_resolution,[status(thm)],[77,74]) ).
tff(79,plain,
( ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_er))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_er,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_er))
| ~ ( ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_er,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_er,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_er,tptp_fun_X2_13(aTP_Lamm_er,aTP_Lamm_a))) ) ) ) )
<=> ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_er))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_er,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_er))
| ~ ( ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_er,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_er,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_er,tptp_fun_X2_13(aTP_Lamm_er,aTP_Lamm_a))) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(80,plain,
( ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_er))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_er,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_er))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_er,tptp_fun_X2_13(aTP_Lamm_er,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_er,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_er,aTP_Lamm_a),aTP_Lamm_a) ) ) )
<=> ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_er))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_er,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_er))
| ~ ( ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_er,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_er,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_er,tptp_fun_X2_13(aTP_Lamm_er,aTP_Lamm_a))) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(81,plain,
( ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_er))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_er,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_er))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_er,tptp_fun_X2_13(aTP_Lamm_er,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_er,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_er,aTP_Lamm_a),aTP_Lamm_a) ) ) ) )
<=> ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_er))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_er,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_er))
| ~ ( ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_er,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_er,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_er,tptp_fun_X2_13(aTP_Lamm_er,aTP_Lamm_a))) ) ) ) ) ),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,plain,
( ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_er))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_er,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_er))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_er,tptp_fun_X2_13(aTP_Lamm_er,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_er,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_er,aTP_Lamm_a),aTP_Lamm_a) ) ) ) )
<=> ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_er))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_er,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_er))
| ~ ( ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_er,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_er,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_er,tptp_fun_X2_13(aTP_Lamm_er,aTP_Lamm_a))) ) ) ) ) ),
inference(transitivity,[status(thm)],[81,79]) ).
tff(83,plain,
( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_er))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_er,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_er))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_er,tptp_fun_X2_13(aTP_Lamm_er,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_er,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_er,aTP_Lamm_a),aTP_Lamm_a) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(84,plain,
( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_er))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_er,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_er))
| ~ ( ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_er,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_er,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_er,tptp_fun_X2_13(aTP_Lamm_er,aTP_Lamm_a))) ) ) ) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_er))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_er,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_er))
| ~ ( ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_er,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_er,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_er,tptp_fun_X2_13(aTP_Lamm_er,aTP_Lamm_a))) ) ) ),
inference(unit_resolution,[status(thm)],[84,59]) ).
tff(86,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_er))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_er,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_er))
| ~ ( ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_er,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_er,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_er,tptp_fun_X2_13(aTP_Lamm_er,aTP_Lamm_a))) ) )
| ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_er))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_er,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) ),
inference(tautology,[status(thm)],[]) ).
tff(87,plain,
( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_er))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_er,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) ),
inference(unit_resolution,[status(thm)],[86,85]) ).
tff(88,plain,
( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_er))
<=> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_er)) ),
inference(rewrite,[status(thm)],[]) ).
tff(89,axiom,
pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_er)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_satz4e) ).
tff(90,plain,
pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_er)),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_er))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_er,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_er))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_er,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) ),
inference(tautology,[status(thm)],[]) ).
tff(92,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_er))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_er,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_er,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) ),
inference(unit_resolution,[status(thm)],[91,90]) ).
tff(93,plain,
! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_er,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ),
inference(unit_resolution,[status(thm)],[92,87]) ).
tff(94,plain,
( ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_er,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) )
| ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_er,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) )
<=> ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_er,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) )
| ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_er,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(95,plain,
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_er,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) )
<=> ( ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_er,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(96,plain,
( ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_er,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) )
| pp(aa_TPTP_ind_bool(aTP_Lamm_er,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) )
<=> ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_er,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) )
| ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_er,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(monotonicity,[status(thm)],[95]) ).
tff(97,plain,
( ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_er,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) )
| pp(aa_TPTP_ind_bool(aTP_Lamm_er,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) )
<=> ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_er,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) )
| ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_er,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(transitivity,[status(thm)],[96,94]) ).
tff(98,plain,
( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_er,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) )
| pp(aa_TPTP_ind_bool(aTP_Lamm_er,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(99,plain,
( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_er,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) )
| ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_er,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
pp(aa_TPTP_ind_bool(aTP_Lamm_er,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),
inference(unit_resolution,[status(thm)],[99,93,78,76]) ).
tff(101,plain,
( ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_er,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1))) )
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_er,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1))) ),
inference(tautology,[status(thm)],[]) ).
tff(102,plain,
( ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_er,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1))) )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1))) ),
inference(unit_resolution,[status(thm)],[101,100]) ).
tff(103,plain,
pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1))),
inference(unit_resolution,[status(thm)],[102,43]) ).
tff(104,plain,
pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1))),
inference(modus_ponens,[status(thm)],[103,34]) ).
tff(105,plain,
( gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))))
<=> gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(106,plain,
( gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
<=> gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(symmetry,[status(thm)],[105]) ).
tff(107,plain,
^ [B_1: $i,B_2: $i] :
refl(( gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2))
<=> gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2)) )),
inference(bind,[status(th)],[]) ).
tff(108,plain,
( ! [B_1: $i,B_2: $i] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2))
<=> ! [B_1: $i,B_2: $i] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2)) ),
inference(quant_intro,[status(thm)],[107]) ).
tff(109,plain,
( ! [B_1: $i,B_2: $i] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2))
<=> ! [B_1: $i,B_2: $i] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2)) ),
inference(rewrite,[status(thm)],[]) ).
tff(110,axiom,
! [B_1: $i,B_2: $i] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_aa_001t__TPTP____Interpret__Oind_001t__TPTP____Interpret__Oind) ).
tff(111,plain,
! [B_1: $i,B_2: $i] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2)),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
! [B_1: $i,B_2: $i] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2)),
inference(skolemize,[status(sab)],[111]) ).
tff(113,plain,
! [B_1: $i,B_2: $i] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2)),
inference(modus_ponens,[status(thm)],[112,108]) ).
tff(114,plain,
( ~ ! [B_1: $i,B_2: $i] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2))
| gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(115,plain,
gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),
inference(unit_resolution,[status(thm)],[114,113]) ).
tff(116,plain,
gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))),
inference(modus_ponens,[status(thm)],[115,106]) ).
tff(117,plain,
( ( scratc98832752nd_n_1 = aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset) )
<=> ( scratc98832752nd_n_1 = aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(118,axiom,
scratc98832752nd_n_1 = aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__n__1) ).
tff(119,plain,
scratc98832752nd_n_1 = aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset),
inference(modus_ponens,[status(thm)],[118,117]) ).
tff(120,plain,
aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset) = scratc98832752nd_n_1,
inference(symmetry,[status(thm)],[119]) ).
tff(121,plain,
aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset)) = aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1),
inference(monotonicity,[status(thm)],[120]) ).
tff(122,plain,
( gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset)))
<=> gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1)) ),
inference(monotonicity,[status(thm)],[121]) ).
tff(123,plain,
( ~ ! [B_1: $i,B_2: $i] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2))
| gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(124,plain,
gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))),
inference(unit_resolution,[status(thm)],[123,113]) ).
tff(125,plain,
gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1)),
inference(modus_ponens,[status(thm)],[124,122]) ).
tff(126,plain,
^ [X7: $i,Y: $i] :
refl(( ( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
<=> ( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) ) )),
inference(bind,[status(th)],[]) ).
tff(127,plain,
( ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
<=> ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) ) ),
inference(quant_intro,[status(thm)],[126]) ).
tff(128,plain,
^ [X7: $i,Y: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) )
<=> ~ ( ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) ) )),
( ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) )
<=> ~ ~ ( ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) ) )),
rewrite(( ~ ~ ( ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
<=> ( ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) ) )),
( ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) )
<=> ( ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) ) )),
( ( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) ) )
<=> ( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) ) )),
rewrite(( ( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
<=> ( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) ) )),
( ( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) ) )
<=> ( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) ) )),
inference(bind,[status(th)],[]) ).
tff(129,plain,
( ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) ) )
<=> ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) ) ),
inference(quant_intro,[status(thm)],[128]) ).
tff(130,plain,
( ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) ) )
<=> ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(131,plain,
^ [X7: $i,Y: $i] :
rewrite(( ( ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) )
=> ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ( X7 = Y ) ) )
<=> ( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) ) ) )),
inference(bind,[status(th)],[]) ).
tff(132,plain,
( ! [X7: $i,Y: $i] :
( ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) )
=> ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ( X7 = Y ) ) )
<=> ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) ) ) ),
inference(quant_intro,[status(thm)],[131]) ).
tff(133,axiom,
! [X7: $i,Y: $i] :
( ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) )
=> ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ( X7 = Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_001t__TPTP____Interpret__Oind_T) ).
tff(134,plain,
! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) ) ),
inference(modus_ponens,[status(thm)],[133,132]) ).
tff(135,plain,
! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) ) ),
inference(modus_ponens,[status(thm)],[134,130]) ).
tff(136,plain,
! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) ) ),
inference(skolemize,[status(sab)],[135]) ).
tff(137,plain,
! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) ),
inference(modus_ponens,[status(thm)],[136,129]) ).
tff(138,plain,
! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) ),
inference(modus_ponens,[status(thm)],[137,127]) ).
tff(139,plain,
( ( ~ ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1))
| ( aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) = aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1))) )
<=> ( ~ ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1))
| ( aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) = aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(140,plain,
( ( ( aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) = aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1)))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))) )
<=> ( ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1))
| ( aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) = aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(141,plain,
( ( ~ ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
| ( aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) = aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1)))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))) )
<=> ( ~ ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1))
| ( aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) = aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1))) ) ),
inference(monotonicity,[status(thm)],[140]) ).
tff(142,plain,
( ( ~ ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
| ( aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) = aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1)))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))) )
<=> ( ~ ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1))
| ( aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) = aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1))) ) ),
inference(transitivity,[status(thm)],[141,139]) ).
tff(143,plain,
( ~ ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
| ( aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) = aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1)))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(144,plain,
( ~ ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1))
| ( aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) = aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1))) ),
inference(modus_ponens,[status(thm)],[143,142]) ).
tff(145,plain,
( ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1))
| ( aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) = aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1))) ),
inference(unit_resolution,[status(thm)],[144,138]) ).
tff(146,plain,
aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) = aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1),
inference(unit_resolution,[status(thm)],[145,125,116,104]) ).
tff(147,plain,
aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc98832752nd_n_1) = aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),
inference(symmetry,[status(thm)],[146]) ).
tff(148,plain,
aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset)) = aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),
inference(transitivity,[status(thm)],[121,147,10]) ).
tff(149,plain,
aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))) = aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),
inference(monotonicity,[status(thm)],[148]) ).
tff(150,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(monotonicity,[status(thm)],[149]) ).
tff(151,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset)))) ),
inference(symmetry,[status(thm)],[150]) ).
tff(152,plain,
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))))
<=> ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset)))) ),
inference(monotonicity,[status(thm)],[151]) ).
tff(153,plain,
aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))) = aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),
inference(monotonicity,[status(thm)],[10]) ).
tff(154,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(monotonicity,[status(thm)],[153]) ).
tff(155,plain,
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))))
<=> ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(monotonicity,[status(thm)],[154]) ).
tff(156,plain,
^ [X: $i,Xa: $i] :
refl(( ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(Xa),X))) )
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(Xa),X))) ) )),
inference(bind,[status(th)],[]) ).
tff(157,plain,
( ! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(Xa),X))) )
<=> ! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(Xa),X))) ) ),
inference(quant_intro,[status(thm)],[156]) ).
tff(158,plain,
( ! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(Xa),X))) )
<=> ! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(Xa),X))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(159,axiom,
! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(Xa),X))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__iii) ).
tff(160,plain,
! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(Xa),X))) ),
inference(modus_ponens,[status(thm)],[159,158]) ).
tff(161,plain,
! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(Xa),X))) ),
inference(skolemize,[status(sab)],[160]) ).
tff(162,plain,
! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(Xa),X))) ),
inference(modus_ponens,[status(thm)],[161,157]) ).
tff(163,plain,
( ~ ! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(Xa),X))) )
| ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))))
<=> pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(164,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))))
<=> pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(unit_resolution,[status(thm)],[163,162]) ).
tff(165,plain,
scratc1229761461ffprop(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))) = scratc1229761461ffprop(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),
inference(monotonicity,[status(thm)],[10]) ).
tff(166,plain,
aa_TPT43085870d_bool(scratc1229761461ffprop(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)) = aa_TPT43085870d_bool(scratc1229761461ffprop(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),
inference(monotonicity,[status(thm)],[165]) ).
tff(167,plain,
aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) = aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),
inference(monotonicity,[status(thm)],[166]) ).
tff(168,plain,
( pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))))
<=> pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(monotonicity,[status(thm)],[167]) ).
tff(169,plain,
( pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))))
<=> pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(symmetry,[status(thm)],[168]) ).
tff(170,plain,
( ~ pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))))
<=> ~ pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(monotonicity,[status(thm)],[169]) ).
tff(171,plain,
^ [X: $i,Xa: $i] :
refl(( ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(X),Xa))) )
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(X),Xa))) ) )),
inference(bind,[status(th)],[]) ).
tff(172,plain,
( ! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(X),Xa))) )
<=> ! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(X),Xa))) ) ),
inference(quant_intro,[status(thm)],[171]) ).
tff(173,plain,
( ! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(X),Xa))) )
<=> ! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(X),Xa))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(174,axiom,
! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(X),Xa))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__d__29__ii) ).
tff(175,plain,
! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(X),Xa))) ),
inference(modus_ponens,[status(thm)],[174,173]) ).
tff(176,plain,
! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(X),Xa))) ),
inference(skolemize,[status(sab)],[175]) ).
tff(177,plain,
! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(X),Xa))) ),
inference(modus_ponens,[status(thm)],[176,172]) ).
tff(178,plain,
( ~ ! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(X),Xa))) )
| ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(179,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(unit_resolution,[status(thm)],[178,177]) ).
tff(180,plain,
^ [Uu: $i] :
refl(( ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu)),Uu)) )
<=> ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu)),Uu)) ) )),
inference(bind,[status(th)],[]) ).
tff(181,plain,
( ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu)),Uu)) )
<=> ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu)),Uu)) ) ),
inference(quant_intro,[status(thm)],[180]) ).
tff(182,plain,
( ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu)),Uu)) )
<=> ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu)),Uu)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(183,axiom,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu)),Uu)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ATP_Olambda__9) ).
tff(184,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu)),Uu)) ),
inference(modus_ponens,[status(thm)],[183,182]) ).
tff(185,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu)),Uu)) ),
inference(skolemize,[status(sab)],[184]) ).
tff(186,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu)),Uu)) ),
inference(modus_ponens,[status(thm)],[185,181]) ).
tff(187,plain,
( ~ ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu)),Uu)) )
| ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(188,plain,
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(unit_resolution,[status(thm)],[187,186]) ).
tff(189,plain,
( ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(tautology,[status(thm)],[]) ).
tff(190,plain,
~ pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),
inference(unit_resolution,[status(thm)],[189,74]) ).
tff(191,plain,
( ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) )
| pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(tautology,[status(thm)],[]) ).
tff(192,plain,
( ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(unit_resolution,[status(thm)],[191,190]) ).
tff(193,plain,
~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),
inference(unit_resolution,[status(thm)],[192,188]) ).
tff(194,plain,
( ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))) )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(tautology,[status(thm)],[]) ).
tff(195,plain,
( ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))) )
| ~ pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(unit_resolution,[status(thm)],[194,193]) ).
tff(196,plain,
~ pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))),
inference(unit_resolution,[status(thm)],[195,179]) ).
tff(197,plain,
~ pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))),
inference(modus_ponens,[status(thm)],[196,170]) ).
tff(198,plain,
( ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))))
<=> pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))))
| pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(tautology,[status(thm)],[]) ).
tff(199,plain,
~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))))),
inference(unit_resolution,[status(thm)],[198,197,164]) ).
tff(200,plain,
~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))),
inference(modus_ponens,[status(thm)],[199,155]) ).
tff(201,plain,
~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset)))),
inference(modus_ponens,[status(thm)],[200,152]) ).
tff(202,plain,
^ [Uu: $i,Uua: $i] :
refl(( ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,Uu),Uua))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),Uua))) )
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,Uu),Uua))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),Uua))) ) )),
inference(bind,[status(th)],[]) ).
tff(203,plain,
( ! [Uu: $i,Uua: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,Uu),Uua))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),Uua))) )
<=> ! [Uu: $i,Uua: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,Uu),Uua))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),Uua))) ) ),
inference(quant_intro,[status(thm)],[202]) ).
tff(204,plain,
( ! [Uu: $i,Uua: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,Uu),Uua))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),Uua))) )
<=> ! [Uu: $i,Uua: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,Uu),Uua))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),Uua))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(205,axiom,
! [Uu: $i,Uua: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,Uu),Uua))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),Uua))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ATP_Olambda__91) ).
tff(206,plain,
! [Uu: $i,Uua: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,Uu),Uua))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),Uua))) ),
inference(modus_ponens,[status(thm)],[205,204]) ).
tff(207,plain,
! [Uu: $i,Uua: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,Uu),Uua))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),Uua))) ),
inference(skolemize,[status(sab)],[206]) ).
tff(208,plain,
! [Uu: $i,Uua: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,Uu),Uua))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),Uua))) ),
inference(modus_ponens,[status(thm)],[207,203]) ).
tff(209,plain,
( ~ ! [Uu: $i,Uua: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,Uu),Uua))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),Uua))) )
| ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(210,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset)))) ),
inference(unit_resolution,[status(thm)],[209,208]) ).
tff(211,plain,
( ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))))
| ~ ( ~ scratc1623311406_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a))) ) ) ) )
<=> ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))))
| ~ ( ~ scratc1623311406_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a))) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(212,plain,
( ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ) )
<=> ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))))
| ~ ( ~ scratc1623311406_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a))) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(213,plain,
( ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ) ) )
<=> ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))))
| ~ ( ~ scratc1623311406_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a))) ) ) ) ) ),
inference(monotonicity,[status(thm)],[212]) ).
tff(214,plain,
( ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ) ) )
<=> ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))))
| ~ ( ~ scratc1623311406_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a))) ) ) ) ) ),
inference(transitivity,[status(thm)],[213,211]) ).
tff(215,plain,
( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(216,plain,
( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))))
| ~ ( ~ scratc1623311406_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a))) ) ) ) ),
inference(modus_ponens,[status(thm)],[215,214]) ).
tff(217,plain,
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))))
| ~ ( ~ scratc1623311406_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a))) ) ) ),
inference(unit_resolution,[status(thm)],[216,59]) ).
tff(218,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))))
| ~ ( ~ scratc1623311406_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a))) ) )
| ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),X2)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(219,plain,
( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),X2)) ) ),
inference(unit_resolution,[status(thm)],[218,217]) ).
tff(220,plain,
^ [Uu: $i] :
refl(( ( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,Uu))
<=> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,Uu))) )
<=> ( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,Uu))
<=> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,Uu))) ) )),
inference(bind,[status(th)],[]) ).
tff(221,plain,
( ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,Uu))
<=> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,Uu))) )
<=> ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,Uu))
<=> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,Uu))) ) ),
inference(quant_intro,[status(thm)],[220]) ).
tff(222,plain,
( ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,Uu))
<=> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,Uu))) )
<=> ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,Uu))
<=> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,Uu))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(223,axiom,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,Uu))
<=> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,Uu))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ATP_Olambda__52) ).
tff(224,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,Uu))
<=> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,Uu))) ),
inference(modus_ponens,[status(thm)],[223,222]) ).
tff(225,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,Uu))
<=> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,Uu))) ),
inference(skolemize,[status(sab)],[224]) ).
tff(226,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,Uu))
<=> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,Uu))) ),
inference(modus_ponens,[status(thm)],[225,221]) ).
tff(227,plain,
( ~ ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,Uu))
<=> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,Uu))) )
| ( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(228,plain,
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(unit_resolution,[status(thm)],[227,226]) ).
tff(229,plain,
( ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bq))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bq))
| ~ ( ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_bq,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_bq,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_13(aTP_Lamm_bq,aTP_Lamm_a))) ) ) ) )
<=> ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bq))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bq))
| ~ ( ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_bq,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_bq,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_13(aTP_Lamm_bq,aTP_Lamm_a))) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(230,plain,
( ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bq))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bq))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_13(aTP_Lamm_bq,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_bq,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_bq,aTP_Lamm_a),aTP_Lamm_a) ) ) )
<=> ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bq))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bq))
| ~ ( ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_bq,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_bq,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_13(aTP_Lamm_bq,aTP_Lamm_a))) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(231,plain,
( ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bq))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bq))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_13(aTP_Lamm_bq,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_bq,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_bq,aTP_Lamm_a),aTP_Lamm_a) ) ) ) )
<=> ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bq))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bq))
| ~ ( ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_bq,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_bq,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_13(aTP_Lamm_bq,aTP_Lamm_a))) ) ) ) ) ),
inference(monotonicity,[status(thm)],[230]) ).
tff(232,plain,
( ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bq))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bq))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_13(aTP_Lamm_bq,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_bq,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_bq,aTP_Lamm_a),aTP_Lamm_a) ) ) ) )
<=> ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bq))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bq))
| ~ ( ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_bq,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_bq,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_13(aTP_Lamm_bq,aTP_Lamm_a))) ) ) ) ) ),
inference(transitivity,[status(thm)],[231,229]) ).
tff(233,plain,
( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bq))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bq))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_13(aTP_Lamm_bq,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_bq,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_bq,aTP_Lamm_a),aTP_Lamm_a) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(234,plain,
( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bq))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bq))
| ~ ( ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_bq,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_bq,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_13(aTP_Lamm_bq,aTP_Lamm_a))) ) ) ) ),
inference(modus_ponens,[status(thm)],[233,232]) ).
tff(235,plain,
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bq))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bq))
| ~ ( ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_bq,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_bq,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_13(aTP_Lamm_bq,aTP_Lamm_a))) ) ) ),
inference(unit_resolution,[status(thm)],[234,59]) ).
tff(236,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bq))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bq))
| ~ ( ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_bq,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_bq,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_13(aTP_Lamm_bq,aTP_Lamm_a))) ) )
| ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bq))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) ),
inference(tautology,[status(thm)],[]) ).
tff(237,plain,
( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bq))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) ),
inference(unit_resolution,[status(thm)],[236,235]) ).
tff(238,plain,
( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bq))
<=> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bq)) ),
inference(rewrite,[status(thm)],[]) ).
tff(239,axiom,
pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bq)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_satz18a) ).
tff(240,plain,
pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bq)),
inference(modus_ponens,[status(thm)],[239,238]) ).
tff(241,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bq))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bq))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) ),
inference(tautology,[status(thm)],[]) ).
tff(242,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bq))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) ),
inference(unit_resolution,[status(thm)],[241,240]) ).
tff(243,plain,
! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ),
inference(unit_resolution,[status(thm)],[242,237]) ).
tff(244,plain,
( ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) )
| ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) )
<=> ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) )
| ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(245,plain,
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) )
<=> ( ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(246,plain,
( ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) )
| pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) )
<=> ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) )
| ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(monotonicity,[status(thm)],[245]) ).
tff(247,plain,
( ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) )
| pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) )
<=> ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) )
| ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(transitivity,[status(thm)],[246,244]) ).
tff(248,plain,
( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) )
| pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(249,plain,
( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) )
| ~ scratc1623311406_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(modus_ponens,[status(thm)],[248,247]) ).
tff(250,plain,
pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),
inference(unit_resolution,[status(thm)],[249,243,78,76]) ).
tff(251,plain,
( ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))) )
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
| pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(tautology,[status(thm)],[]) ).
tff(252,plain,
( ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))) )
| pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(unit_resolution,[status(thm)],[251,250]) ).
tff(253,plain,
pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))),
inference(unit_resolution,[status(thm)],[252,228]) ).
tff(254,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),X2)) ) )
| ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),X2)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(255,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),X2)) ) )
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),X2)) ) ),
inference(unit_resolution,[status(thm)],[254,253]) ).
tff(256,plain,
! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),X2)) ),
inference(unit_resolution,[status(thm)],[255,219]) ).
tff(257,plain,
( scratc1623311406_is_of(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset),aTP_Lamm_a)
<=> scratc1623311406_is_of(scratc98832752nd_n_1,aTP_Lamm_a) ),
inference(monotonicity,[status(thm)],[120]) ).
tff(258,plain,
( scratc1623311406_is_of(scratc98832752nd_n_1,aTP_Lamm_a)
<=> scratc1623311406_is_of(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset),aTP_Lamm_a) ),
inference(symmetry,[status(thm)],[257]) ).
tff(259,plain,
( scratc1623311406_is_of(scratc98832752nd_n_1,aTP_Lamm_a)
<=> scratc1623311406_is_of(scratc98832752nd_n_1,aTP_Lamm_a) ),
inference(rewrite,[status(thm)],[]) ).
tff(260,axiom,
scratc1623311406_is_of(scratc98832752nd_n_1,aTP_Lamm_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__1__p) ).
tff(261,plain,
scratc1623311406_is_of(scratc98832752nd_n_1,aTP_Lamm_a),
inference(modus_ponens,[status(thm)],[260,259]) ).
tff(262,plain,
scratc1623311406_is_of(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset),aTP_Lamm_a),
inference(modus_ponens,[status(thm)],[261,258]) ).
tff(263,plain,
( gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))
<=> gg_TPTP_ind(scratc98832752nd_n_1) ),
inference(monotonicity,[status(thm)],[120]) ).
tff(264,plain,
( gg_TPTP_ind(scratc98832752nd_n_1)
<=> gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset)) ),
inference(symmetry,[status(thm)],[263]) ).
tff(265,plain,
( gg_TPTP_ind(scratc98832752nd_n_1)
<=> gg_TPTP_ind(scratc98832752nd_n_1) ),
inference(rewrite,[status(thm)],[]) ).
tff(266,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) ).
tff(267,plain,
gg_TPTP_ind(scratc98832752nd_n_1),
inference(modus_ponens,[status(thm)],[266,265]) ).
tff(268,plain,
gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset)),
inference(modus_ponens,[status(thm)],[267,264]) ).
tff(269,plain,
( ( ~ ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),X2)) )
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))
| ~ scratc1623311406_is_of(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))) )
<=> ( ~ ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),X2)) )
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))
| ~ scratc1623311406_is_of(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(270,plain,
( ~ ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),X2)) )
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))
| ~ scratc1623311406_is_of(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(271,plain,
( ~ ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),X2)) )
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))
| ~ scratc1623311406_is_of(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))) ),
inference(modus_ponens,[status(thm)],[270,269]) ).
tff(272,plain,
pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))),
inference(unit_resolution,[status(thm)],[271,268,262,256]) ).
tff(273,plain,
( ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset)))) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset)))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset)))) ),
inference(tautology,[status(thm)],[]) ).
tff(274,plain,
pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset)))),
inference(unit_resolution,[status(thm)],[273,272,210]) ).
tff(275,plain,
$false,
inference(unit_resolution,[status(thm)],[274,201]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM669+4 : TPTP v9.0.0. Released v7.3.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 01:44:20 EDT 2025
% 0.12/0.33 % CPUTime :
% 24.95/25.13 % SZS status Theorem
% 24.95/25.13 % SZS output start Proof
% See solution above
% 25.02/25.28 % E exiting
%------------------------------------------------------------------------------