TSTP Solution File: NUM694+4 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM694+4 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 : Sun Sep 18 13:11:30 EDT 2022
% Result : Theorem 9.15s 6.12s
% Output : Proof 9.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 88
% Syntax : Number of formulae : 187 ( 45 unt; 20 typ; 0 def)
% Number of atoms : 1090 ( 17 equ)
% Maximal formula atoms : 32 ( 6 avg)
% Number of connectives : 1797 ( 894 ~; 761 |; 6 &)
% ( 127 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 20 ( 20 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 10 >; 6 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 10 con; 0-2 aty)
% Number of variables : 263 ( 247 !; 0 ?; 263 :)
% Comments :
%------------------------------------------------------------------------------
tff(pp_type,type,
pp: $i > $o ).
tff(aa_TPTP_ind_bool_type,type,
aa_TPTP_ind_bool: ( $i * $i ) > $i ).
tff(aa_TPT43085870d_bool_type,type,
aa_TPT43085870d_bool: ( $i * $i ) > $i ).
tff(tptp_fun_X2_12_type,type,
tptp_fun_X2_12: ( $i * $i ) > $i ).
tff(aTP_Lamm_a_type,type,
aTP_Lamm_a: $i ).
tff(aa_TPTP_ind_TPTP_ind_type,type,
aa_TPTP_ind_TPTP_ind: ( $i * $i ) > $i ).
tff(scratc1150508294ptyset_type,type,
scratc1150508294ptyset: $i ).
tff(scratc1138364274rdsucc_type,type,
scratc1138364274rdsucc: $i ).
tff(scratc926580404lessis_type,type,
scratc926580404lessis: $i ).
tff(aTP_Lamm_gx_type,type,
aTP_Lamm_gx: $i ).
tff(scratc2135361906_is_of_type,type,
scratc2135361906_is_of: ( $i * $i ) > $o ).
tff(gg_TPTP_ind_type,type,
gg_TPTP_ind: $i > $o ).
tff(aa_fun171081125l_bool_type,type,
aa_fun171081125l_bool: ( $i * $i ) > $i ).
tff(scratc2055738343all_of_type,type,
scratc2055738343all_of: $i > $i ).
tff(aTP_Lamm_gy_type,type,
aTP_Lamm_gy: $i ).
tff(scratc2094053556nd_n_1_type,type,
scratc2094053556nd_n_1: $i ).
tff(scratc1080094210d_Sing_type,type,
scratc1080094210d_Sing: $i ).
tff(scratc362322297nunion_type,type,
scratc362322297nunion: $i > $i ).
tff(scratc1060564016moreis_type,type,
scratc1060564016moreis: $i ).
tff(aTP_Lamm_bo_type,type,
aTP_Lamm_bo: $i ).
tff(1,plain,
^ [X: $i,Xa: $i] :
refl(
( ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $i,Xa: $i] :
rewrite(
( ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(4,plain,
( ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) ),
inference(transitivity,[status(thm)],[4,2]) ).
tff(6,plain,
^ [X: $i,Xa: $i] :
trans(
monotonicity(
rewrite(
( ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,X) ) )
<=> ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,X) ) ) )),
monotonicity(
rewrite(
( ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(Xa,X),X) )
<=> ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(Xa,X),X) ) )),
( ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(Xa,X),X) ) )
<=> ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )),
( ( ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,X) ) )
& ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ( ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,X) ) )
& ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) )),
rewrite(
( ( ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,X) ) )
& ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) )),
( ( ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,X) ) )
& ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(7,plain,
( ! [X: $i,Xa: $i] :
( ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,X) ) )
& ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
( ! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
<=> ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,X) ) )
<=> ! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
<=> ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(9,plain,
^ [X: $i,Xa: $i] :
rewrite(
( ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
<=> ! [X2: $i] :
( gg_TPTP_ind(X2)
=> ( scratc2135361906_is_of(X2,X)
=> pp(aa_TPTP_ind_bool(Xa,X2)) ) ) )
<=> ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
<=> ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,X) ) ) )),
inference(bind,[status(th)],]) ).
tff(10,plain,
( ! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
<=> ! [X2: $i] :
( gg_TPTP_ind(X2)
=> ( scratc2135361906_is_of(X2,X)
=> pp(aa_TPTP_ind_bool(Xa,X2)) ) ) )
<=> ! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
<=> ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,X) ) ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,axiom,
! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
<=> ! [X2: $i] :
( gg_TPTP_ind(X2)
=> ( scratc2135361906_is_of(X2,X)
=> pp(aa_TPTP_ind_bool(Xa,X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__all__of) ).
tff(12,plain,
! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
<=> ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,X) ) ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
<=> ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,X) ) ),
inference(modus_ponens,[status(thm)],[12,8]) ).
tff(14,plain,
! [X: $i,Xa: $i] :
( ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,X) ) )
& ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ),
inference(skolemize,[status(sab)],[13]) ).
tff(15,plain,
! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ),
inference(modus_ponens,[status(thm)],[14,7]) ).
tff(16,plain,
! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ),
inference(modus_ponens,[status(thm)],[15,5]) ).
tff(17,plain,
( ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ) ) )
<=> ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ) )
<=> ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
( ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ) ) )
<=> ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ) ) ) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ) ) )
<=> ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ) ) ) ),
inference(transitivity,[status(thm)],[19,17]) ).
tff(21,plain,
( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(22,plain,
( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ) ) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ) ),
inference(unit_resolution,[status(thm)],[22,16]) ).
tff(24,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) )
| ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),X2)) ) ),
inference(tautology,[status(thm)],]) ).
tff(25,plain,
( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),X2)) ) ),
inference(unit_resolution,[status(thm)],[24,23]) ).
tff(26,plain,
^ [Uu: $i] :
refl(
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_gy,Uu))
<=> pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,Uu))) )
<=> ( pp(aa_TPTP_ind_bool(aTP_Lamm_gy,Uu))
<=> pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,Uu))) ) )),
inference(bind,[status(th)],]) ).
tff(27,plain,
( ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_gy,Uu))
<=> pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,Uu))) )
<=> ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_gy,Uu))
<=> pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,Uu))) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
( ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_gy,Uu))
<=> pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,Uu))) )
<=> ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_gy,Uu))
<=> pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,Uu))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,axiom,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_gy,Uu))
<=> pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,Uu))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ATP_Olambda__37) ).
tff(30,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_gy,Uu))
<=> pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,Uu))) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_gy,Uu))
<=> pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,Uu))) ),
inference(skolemize,[status(sab)],[30]) ).
tff(32,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_gy,Uu))
<=> pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,Uu))) ),
inference(modus_ponens,[status(thm)],[31,27]) ).
tff(33,plain,
( ~ ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_gy,Uu))
<=> pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,Uu))) )
| ( pp(aa_TPTP_ind_bool(aTP_Lamm_gy,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
<=> pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(34,plain,
( pp(aa_TPTP_ind_bool(aTP_Lamm_gy,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
<=> pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))) ),
inference(unit_resolution,[status(thm)],[33,32]) ).
tff(35,plain,
( ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a),aTP_Lamm_a) ) ) ) )
<=> ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a),aTP_Lamm_a) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
( ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a),aTP_Lamm_a) ) ) )
<=> ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a),aTP_Lamm_a) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(37,plain,
( ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a),aTP_Lamm_a) ) ) ) )
<=> ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a),aTP_Lamm_a) ) ) ) ) ),
inference(monotonicity,[status(thm)],[36]) ).
tff(38,plain,
( ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a),aTP_Lamm_a) ) ) ) )
<=> ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a),aTP_Lamm_a) ) ) ) ) ),
inference(transitivity,[status(thm)],[37,35]) ).
tff(39,plain,
( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a),aTP_Lamm_a) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(40,plain,
( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a),aTP_Lamm_a) ) ) ) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a),aTP_Lamm_a) ) ) ),
inference(unit_resolution,[status(thm)],[40,16]) ).
tff(42,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a),aTP_Lamm_a) ) )
| pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a),aTP_Lamm_a) ) ),
inference(tautology,[status(thm)],]) ).
tff(43,plain,
( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a),aTP_Lamm_a) ) ),
inference(unit_resolution,[status(thm)],[42,41]) ).
tff(44,plain,
( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1)))
<=> ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)))) ),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1)))
<=> ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1))) ),
inference(rewrite,[status(thm)],]) ).
tff(46,axiom,
~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(47,plain,
~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1))),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)))),
inference(modus_ponens,[status(thm)],[47,44]) ).
tff(49,plain,
( ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a),aTP_Lamm_a) ) )
| pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a),aTP_Lamm_a) ) ),
inference(tautology,[status(thm)],]) ).
tff(50,plain,
( ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a),aTP_Lamm_a) ) )
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a),aTP_Lamm_a) ) ),
inference(unit_resolution,[status(thm)],[49,48]) ).
tff(51,plain,
~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a),aTP_Lamm_a) ),
inference(unit_resolution,[status(thm)],[50,43]) ).
tff(52,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a),aTP_Lamm_a)
| scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a),aTP_Lamm_a) ),
inference(tautology,[status(thm)],]) ).
tff(53,plain,
scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a),aTP_Lamm_a),
inference(unit_resolution,[status(thm)],[52,51]) ).
tff(54,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a),aTP_Lamm_a)
| gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)) ),
inference(tautology,[status(thm)],]) ).
tff(55,plain,
gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),
inference(unit_resolution,[status(thm)],[54,51]) ).
tff(56,plain,
( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_gy))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_gy,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_gy))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_gy,tptp_fun_X2_12(aTP_Lamm_gy,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_gy,aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aTP_Lamm_gy,aTP_Lamm_a),aTP_Lamm_a) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(57,plain,
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_gy))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_gy,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_gy))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_gy,tptp_fun_X2_12(aTP_Lamm_gy,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_gy,aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aTP_Lamm_gy,aTP_Lamm_a),aTP_Lamm_a) ) ) ),
inference(unit_resolution,[status(thm)],[56,16]) ).
tff(58,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_gy))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_gy,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_gy))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_gy,tptp_fun_X2_12(aTP_Lamm_gy,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_gy,aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aTP_Lamm_gy,aTP_Lamm_a),aTP_Lamm_a) ) )
| ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_gy))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_gy,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a) ) ),
inference(tautology,[status(thm)],]) ).
tff(59,plain,
( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_gy))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_gy,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a) ) ),
inference(unit_resolution,[status(thm)],[58,57]) ).
tff(60,plain,
( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_gy))
<=> pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_gy)) ),
inference(rewrite,[status(thm)],]) ).
tff(61,axiom,
pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_gy)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_satz13) ).
tff(62,plain,
pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_gy)),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_gy))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_gy,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a) ) )
| ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_gy))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_gy,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a) ) ),
inference(tautology,[status(thm)],]) ).
tff(64,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_gy))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_gy,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a) ) )
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_gy,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a) ) ),
inference(unit_resolution,[status(thm)],[63,62]) ).
tff(65,plain,
! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_gy,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a) ),
inference(unit_resolution,[status(thm)],[64,59]) ).
tff(66,plain,
( ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_gy,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a) )
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aTP_Lamm_gy,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))) )
<=> ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_gy,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a) )
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aTP_Lamm_gy,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(67,plain,
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_gy,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a),aTP_Lamm_a) )
<=> ( ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aTP_Lamm_gy,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(68,plain,
( ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_gy,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a) )
| pp(aa_TPTP_ind_bool(aTP_Lamm_gy,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a),aTP_Lamm_a) )
<=> ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_gy,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a) )
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aTP_Lamm_gy,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))) ) ),
inference(monotonicity,[status(thm)],[67]) ).
tff(69,plain,
( ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_gy,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a) )
| pp(aa_TPTP_ind_bool(aTP_Lamm_gy,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a),aTP_Lamm_a) )
<=> ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_gy,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a) )
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aTP_Lamm_gy,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))) ) ),
inference(transitivity,[status(thm)],[68,66]) ).
tff(70,plain,
( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_gy,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a) )
| pp(aa_TPTP_ind_bool(aTP_Lamm_gy,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a),aTP_Lamm_a) ),
inference(quant_inst,[status(thm)],]) ).
tff(71,plain,
( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_gy,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a) )
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aTP_Lamm_gy,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
pp(aa_TPTP_ind_bool(aTP_Lamm_gy,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))),
inference(unit_resolution,[status(thm)],[71,65,55,53]) ).
tff(73,plain,
( ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_gy,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
<=> pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))) )
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_gy,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
| pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))) ),
inference(tautology,[status(thm)],]) ).
tff(74,plain,
( ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_gy,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
<=> pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))) )
| pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))) ),
inference(unit_resolution,[status(thm)],[73,72]) ).
tff(75,plain,
pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))),
inference(unit_resolution,[status(thm)],[74,34]) ).
tff(76,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),X2)) ) )
| ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),X2)) ) ),
inference(tautology,[status(thm)],]) ).
tff(77,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),X2)) ) )
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),X2)) ) ),
inference(unit_resolution,[status(thm)],[76,75]) ).
tff(78,plain,
! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),X2)) ),
inference(unit_resolution,[status(thm)],[77,25]) ).
tff(79,plain,
^ [X: $i] :
refl(
( ( aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc362322297nunion(X),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,X)) )
<=> ( aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc362322297nunion(X),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,X)) ) )),
inference(bind,[status(th)],]) ).
tff(80,plain,
( ! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc362322297nunion(X),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,X)) )
<=> ! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc362322297nunion(X),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,X)) ) ),
inference(quant_intro,[status(thm)],[79]) ).
tff(81,plain,
( ! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc362322297nunion(X),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,X)) )
<=> ! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc362322297nunion(X),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,X)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(82,axiom,
! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc362322297nunion(X),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__ordsucc) ).
tff(83,plain,
! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc362322297nunion(X),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,X)) ),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc362322297nunion(X),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,X)) ),
inference(skolemize,[status(sab)],[83]) ).
tff(85,plain,
! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc362322297nunion(X),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,X)) ),
inference(modus_ponens,[status(thm)],[84,80]) ).
tff(86,plain,
( ~ ! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc362322297nunion(X),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,X)) )
| ( aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset) = aa_TPTP_ind_TPTP_ind(scratc362322297nunion(scratc1150508294ptyset),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,scratc1150508294ptyset)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(87,plain,
aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset) = aa_TPTP_ind_TPTP_ind(scratc362322297nunion(scratc1150508294ptyset),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,scratc1150508294ptyset)),
inference(unit_resolution,[status(thm)],[86,85]) ).
tff(88,plain,
aa_TPTP_ind_TPTP_ind(scratc362322297nunion(scratc1150508294ptyset),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,scratc1150508294ptyset)) = aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset),
inference(symmetry,[status(thm)],[87]) ).
tff(89,plain,
( scratc2135361906_is_of(aa_TPTP_ind_TPTP_ind(scratc362322297nunion(scratc1150508294ptyset),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,scratc1150508294ptyset)),aTP_Lamm_a)
<=> scratc2135361906_is_of(aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset),aTP_Lamm_a) ),
inference(monotonicity,[status(thm)],[88]) ).
tff(90,plain,
( scratc2135361906_is_of(aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset),aTP_Lamm_a)
<=> scratc2135361906_is_of(aa_TPTP_ind_TPTP_ind(scratc362322297nunion(scratc1150508294ptyset),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,scratc1150508294ptyset)),aTP_Lamm_a) ),
inference(symmetry,[status(thm)],[89]) ).
tff(91,plain,
( scratc2135361906_is_of(scratc2094053556nd_n_1,aTP_Lamm_a)
<=> scratc2135361906_is_of(aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset),aTP_Lamm_a) ),
inference(rewrite,[status(thm)],]) ).
tff(92,plain,
( scratc2135361906_is_of(scratc2094053556nd_n_1,aTP_Lamm_a)
<=> scratc2135361906_is_of(scratc2094053556nd_n_1,aTP_Lamm_a) ),
inference(rewrite,[status(thm)],]) ).
tff(93,axiom,
scratc2135361906_is_of(scratc2094053556nd_n_1,aTP_Lamm_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__1__p) ).
tff(94,plain,
scratc2135361906_is_of(scratc2094053556nd_n_1,aTP_Lamm_a),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
scratc2135361906_is_of(aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset),aTP_Lamm_a),
inference(modus_ponens,[status(thm)],[94,91]) ).
tff(96,plain,
scratc2135361906_is_of(aa_TPTP_ind_TPTP_ind(scratc362322297nunion(scratc1150508294ptyset),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,scratc1150508294ptyset)),aTP_Lamm_a),
inference(modus_ponens,[status(thm)],[95,90]) ).
tff(97,plain,
( gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc362322297nunion(scratc1150508294ptyset),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,scratc1150508294ptyset)))
<=> gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)) ),
inference(monotonicity,[status(thm)],[88]) ).
tff(98,plain,
( gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))
<=> gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc362322297nunion(scratc1150508294ptyset),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,scratc1150508294ptyset))) ),
inference(symmetry,[status(thm)],[97]) ).
tff(99,plain,
( gg_TPTP_ind(scratc2094053556nd_n_1)
<=> gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)) ),
inference(rewrite,[status(thm)],]) ).
tff(100,plain,
( gg_TPTP_ind(scratc2094053556nd_n_1)
<=> gg_TPTP_ind(scratc2094053556nd_n_1) ),
inference(rewrite,[status(thm)],]) ).
tff(101,axiom,
gg_TPTP_ind(scratc2094053556nd_n_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Scratch__tptp__translate__50151__9814_ONUM694__thf__4__p_Obnd__n__1) ).
tff(102,plain,
gg_TPTP_ind(scratc2094053556nd_n_1),
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,plain,
gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),
inference(modus_ponens,[status(thm)],[102,99]) ).
tff(104,plain,
gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc362322297nunion(scratc1150508294ptyset),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,scratc1150508294ptyset))),
inference(modus_ponens,[status(thm)],[103,98]) ).
tff(105,plain,
^ [Uu: $i,Uua: $i] :
refl(
( ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,Uu),Uua))
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,Uua),Uu))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,Uu),Uua)) ) )
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,Uu),Uua))
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,Uua),Uu))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,Uu),Uua)) ) ) )),
inference(bind,[status(th)],]) ).
tff(106,plain,
( ! [Uu: $i,Uua: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,Uu),Uua))
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,Uua),Uu))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,Uu),Uua)) ) )
<=> ! [Uu: $i,Uua: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,Uu),Uua))
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,Uua),Uu))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,Uu),Uua)) ) ) ),
inference(quant_intro,[status(thm)],[105]) ).
tff(107,plain,
( ! [Uu: $i,Uua: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,Uu),Uua))
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,Uua),Uu))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,Uu),Uua)) ) )
<=> ! [Uu: $i,Uua: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,Uu),Uua))
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,Uua),Uu))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,Uu),Uua)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(108,plain,
^ [Uu: $i,Uua: $i] :
rewrite(
( ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,Uu),Uua))
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,Uu),Uua))
=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,Uua),Uu)) ) )
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,Uu),Uua))
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,Uua),Uu))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,Uu),Uua)) ) ) )),
inference(bind,[status(th)],]) ).
tff(109,plain,
( ! [Uu: $i,Uua: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,Uu),Uua))
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,Uu),Uua))
=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,Uua),Uu)) ) )
<=> ! [Uu: $i,Uua: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,Uu),Uua))
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,Uua),Uu))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,Uu),Uua)) ) ) ),
inference(quant_intro,[status(thm)],[108]) ).
tff(110,axiom,
! [Uu: $i,Uua: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,Uu),Uua))
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,Uu),Uua))
=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,Uua),Uu)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ATP_Olambda__103) ).
tff(111,plain,
! [Uu: $i,Uua: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,Uu),Uua))
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,Uua),Uu))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,Uu),Uua)) ) ),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
! [Uu: $i,Uua: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,Uu),Uua))
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,Uua),Uu))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,Uu),Uua)) ) ),
inference(modus_ponens,[status(thm)],[111,107]) ).
tff(113,plain,
! [Uu: $i,Uua: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,Uu),Uua))
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,Uua),Uu))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,Uu),Uua)) ) ),
inference(skolemize,[status(sab)],[112]) ).
tff(114,plain,
! [Uu: $i,Uua: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,Uu),Uua))
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,Uua),Uu))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,Uu),Uua)) ) ),
inference(modus_ponens,[status(thm)],[113,106]) ).
tff(115,plain,
( ~ ! [Uu: $i,Uua: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,Uu),Uua))
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,Uua),Uu))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,Uu),Uua)) ) )
| ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc362322297nunion(scratc1150508294ptyset),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,scratc1150508294ptyset))))
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc362322297nunion(scratc1150508294ptyset),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,scratc1150508294ptyset))),tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc362322297nunion(scratc1150508294ptyset),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,scratc1150508294ptyset)))) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(116,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc362322297nunion(scratc1150508294ptyset),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,scratc1150508294ptyset))))
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc362322297nunion(scratc1150508294ptyset),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,scratc1150508294ptyset))),tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc362322297nunion(scratc1150508294ptyset),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,scratc1150508294ptyset)))) ) ),
inference(unit_resolution,[status(thm)],[115,114]) ).
tff(117,plain,
aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc362322297nunion(scratc1150508294ptyset),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,scratc1150508294ptyset))) = aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),
inference(monotonicity,[status(thm)],[88]) ).
tff(118,plain,
aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc362322297nunion(scratc1150508294ptyset),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,scratc1150508294ptyset))),tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)) = aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),
inference(monotonicity,[status(thm)],[117]) ).
tff(119,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc362322297nunion(scratc1150508294ptyset),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,scratc1150508294ptyset))),tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))) ),
inference(monotonicity,[status(thm)],[118]) ).
tff(120,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc362322297nunion(scratc1150508294ptyset),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,scratc1150508294ptyset))),tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))) ),
inference(symmetry,[status(thm)],[119]) ).
tff(121,plain,
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
<=> ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc362322297nunion(scratc1150508294ptyset),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,scratc1150508294ptyset))),tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))) ),
inference(monotonicity,[status(thm)],[120]) ).
tff(122,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a),aTP_Lamm_a)
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))) ),
inference(tautology,[status(thm)],]) ).
tff(123,plain,
~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))),
inference(unit_resolution,[status(thm)],[122,51]) ).
tff(124,plain,
~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc362322297nunion(scratc1150508294ptyset),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,scratc1150508294ptyset))),tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))),
inference(modus_ponens,[status(thm)],[123,121]) ).
tff(125,plain,
aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)) = aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc362322297nunion(scratc1150508294ptyset),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,scratc1150508294ptyset))),
inference(monotonicity,[status(thm)],[87]) ).
tff(126,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc362322297nunion(scratc1150508294ptyset),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,scratc1150508294ptyset)))) ),
inference(monotonicity,[status(thm)],[125]) ).
tff(127,plain,
^ [Uu: $i] :
refl(
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,Uu),aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))) )
<=> ( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,Uu),aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))) ) )),
inference(bind,[status(th)],]) ).
tff(128,plain,
( ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,Uu),aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))) )
<=> ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,Uu),aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))) ) ),
inference(quant_intro,[status(thm)],[127]) ).
tff(129,plain,
^ [Uu: $i] :
rewrite(
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,Uu),scratc2094053556nd_n_1)) )
<=> ( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,Uu),aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))) ) )),
inference(bind,[status(th)],]) ).
tff(130,plain,
( ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,Uu),scratc2094053556nd_n_1)) )
<=> ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,Uu),aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))) ) ),
inference(quant_intro,[status(thm)],[129]) ).
tff(131,plain,
( ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,Uu),scratc2094053556nd_n_1)) )
<=> ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,Uu),scratc2094053556nd_n_1)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(132,axiom,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,Uu),scratc2094053556nd_n_1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ATP_Olambda__15) ).
tff(133,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,Uu),scratc2094053556nd_n_1)) ),
inference(modus_ponens,[status(thm)],[132,131]) ).
tff(134,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,Uu),aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))) ),
inference(modus_ponens,[status(thm)],[133,130]) ).
tff(135,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,Uu),aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))) ),
inference(skolemize,[status(sab)],[134]) ).
tff(136,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,Uu),aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))) ),
inference(modus_ponens,[status(thm)],[135,128]) ).
tff(137,plain,
( ~ ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,Uu),aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))) )
| ( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(138,plain,
( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))) ),
inference(unit_resolution,[status(thm)],[137,136]) ).
tff(139,plain,
( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_bo))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_bo))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,tptp_fun_X2_12(aTP_Lamm_bo,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_bo,aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aTP_Lamm_bo,aTP_Lamm_a),aTP_Lamm_a) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(140,plain,
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_bo))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_bo))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,tptp_fun_X2_12(aTP_Lamm_bo,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_bo,aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aTP_Lamm_bo,aTP_Lamm_a),aTP_Lamm_a) ) ) ),
inference(unit_resolution,[status(thm)],[139,16]) ).
tff(141,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_bo))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_bo))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,tptp_fun_X2_12(aTP_Lamm_bo,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_bo,aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aTP_Lamm_bo,aTP_Lamm_a),aTP_Lamm_a) ) )
| ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_bo))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a) ) ),
inference(tautology,[status(thm)],]) ).
tff(142,plain,
( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_bo))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a) ) ),
inference(unit_resolution,[status(thm)],[141,140]) ).
tff(143,plain,
( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_bo))
<=> pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_bo)) ),
inference(rewrite,[status(thm)],]) ).
tff(144,axiom,
pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_bo)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_satz24) ).
tff(145,plain,
pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_bo)),
inference(modus_ponens,[status(thm)],[144,143]) ).
tff(146,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_bo))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a) ) )
| ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_bo))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a) ) ),
inference(tautology,[status(thm)],]) ).
tff(147,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_bo))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a) ) )
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a) ) ),
inference(unit_resolution,[status(thm)],[146,145]) ).
tff(148,plain,
! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a) ),
inference(unit_resolution,[status(thm)],[147,142]) ).
tff(149,plain,
( ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a) )
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aTP_Lamm_bo,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))) )
<=> ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a) )
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aTP_Lamm_bo,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(150,plain,
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a),aTP_Lamm_a) )
<=> ( ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aTP_Lamm_bo,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(151,plain,
( ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a) )
| pp(aa_TPTP_ind_bool(aTP_Lamm_bo,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a),aTP_Lamm_a) )
<=> ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a) )
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aTP_Lamm_bo,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))) ) ),
inference(monotonicity,[status(thm)],[150]) ).
tff(152,plain,
( ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a) )
| pp(aa_TPTP_ind_bool(aTP_Lamm_bo,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a),aTP_Lamm_a) )
<=> ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a) )
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aTP_Lamm_bo,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))) ) ),
inference(transitivity,[status(thm)],[151,149]) ).
tff(153,plain,
( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a) )
| pp(aa_TPTP_ind_bool(aTP_Lamm_bo,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a),aTP_Lamm_a) ),
inference(quant_inst,[status(thm)],]) ).
tff(154,plain,
( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a) )
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aTP_Lamm_bo,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))) ),
inference(modus_ponens,[status(thm)],[153,152]) ).
tff(155,plain,
pp(aa_TPTP_ind_bool(aTP_Lamm_bo,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a))),
inference(unit_resolution,[status(thm)],[154,148,55,53]) ).
tff(156,plain,
( ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))) )
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bo,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))) ),
inference(tautology,[status(thm)],]) ).
tff(157,plain,
( ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))) )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))) ),
inference(unit_resolution,[status(thm)],[156,155]) ).
tff(158,plain,
pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))),
inference(unit_resolution,[status(thm)],[157,138]) ).
tff(159,plain,
pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc362322297nunion(scratc1150508294ptyset),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,scratc1150508294ptyset)))),
inference(modus_ponens,[status(thm)],[158,126]) ).
tff(160,plain,
( ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc362322297nunion(scratc1150508294ptyset),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,scratc1150508294ptyset))),tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc362322297nunion(scratc1150508294ptyset),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,scratc1150508294ptyset)))) )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc362322297nunion(scratc1150508294ptyset),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,scratc1150508294ptyset))),tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc362322297nunion(scratc1150508294ptyset),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,scratc1150508294ptyset)))) ),
inference(tautology,[status(thm)],]) ).
tff(161,plain,
~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc362322297nunion(scratc1150508294ptyset),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,scratc1150508294ptyset))),tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc362322297nunion(scratc1150508294ptyset),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,scratc1150508294ptyset)))) ),
inference(unit_resolution,[status(thm)],[160,159,124]) ).
tff(162,plain,
( ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc362322297nunion(scratc1150508294ptyset),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,scratc1150508294ptyset))))
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc362322297nunion(scratc1150508294ptyset),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,scratc1150508294ptyset))),tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc362322297nunion(scratc1150508294ptyset),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,scratc1150508294ptyset)))) ) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc362322297nunion(scratc1150508294ptyset),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,scratc1150508294ptyset))))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc362322297nunion(scratc1150508294ptyset),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,scratc1150508294ptyset))),tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc362322297nunion(scratc1150508294ptyset),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,scratc1150508294ptyset)))) ),
inference(tautology,[status(thm)],]) ).
tff(163,plain,
~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc362322297nunion(scratc1150508294ptyset),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,scratc1150508294ptyset)))),
inference(unit_resolution,[status(thm)],[162,161,116]) ).
tff(164,plain,
( ( ~ ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),X2)) )
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc362322297nunion(scratc1150508294ptyset),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,scratc1150508294ptyset)))
| ~ scratc2135361906_is_of(aa_TPTP_ind_TPTP_ind(scratc362322297nunion(scratc1150508294ptyset),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,scratc1150508294ptyset)),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc362322297nunion(scratc1150508294ptyset),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,scratc1150508294ptyset)))) )
<=> ( ~ ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),X2)) )
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc362322297nunion(scratc1150508294ptyset),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,scratc1150508294ptyset)))
| ~ scratc2135361906_is_of(aa_TPTP_ind_TPTP_ind(scratc362322297nunion(scratc1150508294ptyset),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,scratc1150508294ptyset)),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc362322297nunion(scratc1150508294ptyset),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,scratc1150508294ptyset)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(165,plain,
( ~ ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),X2)) )
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc362322297nunion(scratc1150508294ptyset),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,scratc1150508294ptyset)))
| ~ scratc2135361906_is_of(aa_TPTP_ind_TPTP_ind(scratc362322297nunion(scratc1150508294ptyset),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,scratc1150508294ptyset)),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc362322297nunion(scratc1150508294ptyset),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,scratc1150508294ptyset)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(166,plain,
( ~ ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),X2)) )
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc362322297nunion(scratc1150508294ptyset),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,scratc1150508294ptyset)))
| ~ scratc2135361906_is_of(aa_TPTP_ind_TPTP_ind(scratc362322297nunion(scratc1150508294ptyset),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,scratc1150508294ptyset)),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_12(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc362322297nunion(scratc1150508294ptyset),aa_TPTP_ind_TPTP_ind(scratc1080094210d_Sing,scratc1150508294ptyset)))) ),
inference(modus_ponens,[status(thm)],[165,164]) ).
tff(167,plain,
$false,
inference(unit_resolution,[status(thm)],[166,163,104,96,78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM694+4 : TPTP v8.1.0. Released v7.3.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Sep 2 13:34:34 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 9.15/6.12 % SZS status Theorem
% 9.15/6.12 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------