%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM694+4 : TPTP v9.0.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:21:53 AM UTC 2025
% Result : Theorem 25.02s 25.24s
% Output : Proof 25.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 66
% Syntax : Number of formulae : 162 ( 37 unt; 0 typ; 0 def)
% Number of atoms : 1316 ( 8 equ)
% Maximal formula atoms : 32 ( 8 avg)
% Number of connectives : 2328 (1192 ~; 998 |; 6 &)
% ( 123 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 18 ( 18 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 9 con; 0-2 aty)
% Number of variables : 309 ( 295 !; 0 ?; 309 :)
% 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_13_type,type,
tptp_fun_X2_13: ( $i * $i ) > $i ).
tff(aTP_Lamm_a_type,type,
aTP_Lamm_a: $i ).
tff(scratc2094053556nd_n_1_type,type,
scratc2094053556nd_n_1: $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(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(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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(Xa,X),X) )
<=> ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(Xa,X),X) ) )),
( ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(Xa,X),X) ) )
<=> ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))))
| ~ ( ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))))
| ~ ( ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))))
| ~ ( ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))))
| ~ ( ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))))
| ~ ( ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))))
| ~ ( ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))))
| ~ ( ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))))
| ~ ( ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),tptp_fun_X2_13(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),aTP_Lamm_a))) ) )
| ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)))
<=> pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
( pp(aa_TPTP_ind_bool(aTP_Lamm_gy,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)))
<=> pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1)))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1)))
| ~ ( ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1)))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1)))
| ~ ( ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,plain,
( ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1)))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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,scratc2094053556nd_n_1)))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a),aTP_Lamm_a) ) ) )
<=> ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1)))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1)))
| ~ ( ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1)))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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,scratc2094053556nd_n_1)))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1)))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1)))
| ~ ( ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1)))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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,scratc2094053556nd_n_1)))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1)))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1)))
| ~ ( ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1)))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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,scratc2094053556nd_n_1)))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1)))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1)))
| ~ ( ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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,scratc2094053556nd_n_1)))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1)))
| ~ ( ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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,scratc2094053556nd_n_1)))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1)))
| ~ ( ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))) ) )
| pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1)))
| ~ ( ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(43,plain,
( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1)))
| ~ ( ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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,scratc2094053556nd_n_1))) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,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(46,plain,
~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1))),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
( ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1)))
| ~ ( ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))) ) )
| pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1)))
| ~ ( ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(48,plain,
( ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1)))
| ~ ( ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))) ) )
| ~ ( ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))) ) ),
inference(unit_resolution,[status(thm)],[47,46]) ).
tff(49,plain,
~ ( ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))) ),
inference(unit_resolution,[status(thm)],[48,43]) ).
tff(50,plain,
( ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)))
| gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)) ),
inference(tautology,[status(thm)],[]) ).
tff(51,plain,
gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),
inference(unit_resolution,[status(thm)],[50,49]) ).
tff(52,plain,
( ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)))
| scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a),aTP_Lamm_a) ),
inference(tautology,[status(thm)],[]) ).
tff(53,plain,
scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a),aTP_Lamm_a),
inference(unit_resolution,[status(thm)],[52,49]) ).
tff(54,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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(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))
| ~ ( ~ scratc2135361906_is_of(tptp_fun_X2_13(aTP_Lamm_gy,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_gy,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_gy,tptp_fun_X2_13(aTP_Lamm_gy,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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(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))
| ~ ( ~ scratc2135361906_is_of(tptp_fun_X2_13(aTP_Lamm_gy,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_gy,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_gy,tptp_fun_X2_13(aTP_Lamm_gy,aTP_Lamm_a))) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,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_13(aTP_Lamm_gy,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_gy,aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(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) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_gy))
| ~ ( ~ scratc2135361906_is_of(tptp_fun_X2_13(aTP_Lamm_gy,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_gy,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_gy,tptp_fun_X2_13(aTP_Lamm_gy,aTP_Lamm_a))) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(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_13(aTP_Lamm_gy,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_gy,aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(aTP_Lamm_gy,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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(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))
| ~ ( ~ scratc2135361906_is_of(tptp_fun_X2_13(aTP_Lamm_gy,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_gy,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_gy,tptp_fun_X2_13(aTP_Lamm_gy,aTP_Lamm_a))) ) ) ) ) ),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(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_13(aTP_Lamm_gy,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_gy,aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(aTP_Lamm_gy,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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(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))
| ~ ( ~ scratc2135361906_is_of(tptp_fun_X2_13(aTP_Lamm_gy,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_gy,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_gy,tptp_fun_X2_13(aTP_Lamm_gy,aTP_Lamm_a))) ) ) ) ) ),
inference(transitivity,[status(thm)],[56,54]) ).
tff(58,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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(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_13(aTP_Lamm_gy,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_gy,aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(aTP_Lamm_gy,aTP_Lamm_a),aTP_Lamm_a) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(59,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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(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))
| ~ ( ~ scratc2135361906_is_of(tptp_fun_X2_13(aTP_Lamm_gy,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_gy,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_gy,tptp_fun_X2_13(aTP_Lamm_gy,aTP_Lamm_a))) ) ) ) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,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))
| ~ ( ~ scratc2135361906_is_of(tptp_fun_X2_13(aTP_Lamm_gy,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_gy,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_gy,tptp_fun_X2_13(aTP_Lamm_gy,aTP_Lamm_a))) ) ) ),
inference(unit_resolution,[status(thm)],[59,16]) ).
tff(61,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))
| ~ ( ~ scratc2135361906_is_of(tptp_fun_X2_13(aTP_Lamm_gy,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_gy,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_gy,tptp_fun_X2_13(aTP_Lamm_gy,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(62,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)],[61,60]) ).
tff(63,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(64,axiom,
pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_gy)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_satz13) ).
tff(65,plain,
pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_gy)),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,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(67,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)],[66,65]) ).
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) ),
inference(unit_resolution,[status(thm)],[67,62]) ).
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) )
| ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_gy,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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) )
| ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_gy,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(70,plain,
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_gy,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a),aTP_Lamm_a) )
<=> ( ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_gy,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))) ) ),
inference(rewrite,[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) )
| pp(aa_TPTP_ind_bool(aTP_Lamm_gy,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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) )
| ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_gy,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))) ) ),
inference(monotonicity,[status(thm)],[70]) ).
tff(72,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_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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) )
| ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_gy,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))) ) ),
inference(transitivity,[status(thm)],[71,69]) ).
tff(73,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_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a),aTP_Lamm_a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(74,plain,
( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_gy,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a) )
| ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_gy,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))) ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
pp(aa_TPTP_ind_bool(aTP_Lamm_gy,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))),
inference(unit_resolution,[status(thm)],[74,68,53,51]) ).
tff(76,plain,
( ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_gy,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)))
<=> pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)))) )
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_gy,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)))
| pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)))) ),
inference(tautology,[status(thm)],[]) ).
tff(77,plain,
( ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_gy,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)))
<=> pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)))) )
| pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)))) ),
inference(unit_resolution,[status(thm)],[76,75]) ).
tff(78,plain,
pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)))),
inference(unit_resolution,[status(thm)],[77,34]) ).
tff(79,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),X2)) ) )
| ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),X2)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(80,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),X2)) ) ),
inference(unit_resolution,[status(thm)],[79,78]) ).
tff(81,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_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),X2)) ),
inference(unit_resolution,[status(thm)],[80,25]) ).
tff(82,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(83,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)],[82]) ).
tff(84,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(85,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(86,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)],[85]) ).
tff(87,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(88,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)],[87,86]) ).
tff(89,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)],[88,84]) ).
tff(90,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)],[89]) ).
tff(91,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)],[90,83]) ).
tff(92,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_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),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_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(93,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),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_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))) ) ),
inference(unit_resolution,[status(thm)],[92,91]) ).
tff(94,plain,
( ( scratc2094053556nd_n_1 = aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset) )
<=> ( scratc2094053556nd_n_1 = aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(95,axiom,
scratc2094053556nd_n_1 = aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__n__1) ).
tff(96,plain,
scratc2094053556nd_n_1 = aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset),
inference(modus_ponens,[status(thm)],[95,94]) ).
tff(97,plain,
aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset) = scratc2094053556nd_n_1,
inference(symmetry,[status(thm)],[96]) ).
tff(98,plain,
aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)) = aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),
inference(monotonicity,[status(thm)],[97]) ).
tff(99,plain,
aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)) = aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),
inference(monotonicity,[status(thm)],[98]) ).
tff(100,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))) ),
inference(monotonicity,[status(thm)],[99]) ).
tff(101,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))) ),
inference(symmetry,[status(thm)],[100]) ).
tff(102,plain,
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)))
<=> ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))) ),
inference(monotonicity,[status(thm)],[101]) ).
tff(103,plain,
( ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))) ),
inference(tautology,[status(thm)],[]) ).
tff(104,plain,
~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))),
inference(unit_resolution,[status(thm)],[103,49]) ).
tff(105,plain,
~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))),
inference(modus_ponens,[status(thm)],[104,102]) ).
tff(106,plain,
aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),scratc2094053556nd_n_1) = aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),
inference(monotonicity,[status(thm)],[96]) ).
tff(107,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),scratc2094053556nd_n_1))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))) ),
inference(monotonicity,[status(thm)],[106]) ).
tff(108,plain,
^ [Uu: $i] :
refl(( ( 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),scratc2094053556nd_n_1)) ) )),
inference(bind,[status(th)],[]) ).
tff(109,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(quant_intro,[status(thm)],[108]) ).
tff(110,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(111,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(112,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)],[111,110]) ).
tff(113,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(skolemize,[status(sab)],[112]) ).
tff(114,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)],[113,109]) ).
tff(115,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)) )
| ( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),scratc2094053556nd_n_1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(116,plain,
( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),scratc2094053556nd_n_1)) ),
inference(unit_resolution,[status(thm)],[115,114]) ).
tff(117,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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(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))
| ~ ( ~ scratc2135361906_is_of(tptp_fun_X2_13(aTP_Lamm_bo,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_bo,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_bo,tptp_fun_X2_13(aTP_Lamm_bo,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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(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))
| ~ ( ~ scratc2135361906_is_of(tptp_fun_X2_13(aTP_Lamm_bo,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_bo,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_bo,tptp_fun_X2_13(aTP_Lamm_bo,aTP_Lamm_a))) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(118,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_13(aTP_Lamm_bo,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_bo,aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(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) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_bo))
| ~ ( ~ scratc2135361906_is_of(tptp_fun_X2_13(aTP_Lamm_bo,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_bo,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_bo,tptp_fun_X2_13(aTP_Lamm_bo,aTP_Lamm_a))) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(119,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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(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_13(aTP_Lamm_bo,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_bo,aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(aTP_Lamm_bo,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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(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))
| ~ ( ~ scratc2135361906_is_of(tptp_fun_X2_13(aTP_Lamm_bo,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_bo,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_bo,tptp_fun_X2_13(aTP_Lamm_bo,aTP_Lamm_a))) ) ) ) ) ),
inference(monotonicity,[status(thm)],[118]) ).
tff(120,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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(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_13(aTP_Lamm_bo,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_bo,aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(aTP_Lamm_bo,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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(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))
| ~ ( ~ scratc2135361906_is_of(tptp_fun_X2_13(aTP_Lamm_bo,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_bo,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_bo,tptp_fun_X2_13(aTP_Lamm_bo,aTP_Lamm_a))) ) ) ) ) ),
inference(transitivity,[status(thm)],[119,117]) ).
tff(121,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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(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_13(aTP_Lamm_bo,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_bo,aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(aTP_Lamm_bo,aTP_Lamm_a),aTP_Lamm_a) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(122,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_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(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))
| ~ ( ~ scratc2135361906_is_of(tptp_fun_X2_13(aTP_Lamm_bo,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_bo,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_bo,tptp_fun_X2_13(aTP_Lamm_bo,aTP_Lamm_a))) ) ) ) ),
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,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))
| ~ ( ~ scratc2135361906_is_of(tptp_fun_X2_13(aTP_Lamm_bo,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_bo,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_bo,tptp_fun_X2_13(aTP_Lamm_bo,aTP_Lamm_a))) ) ) ),
inference(unit_resolution,[status(thm)],[122,16]) ).
tff(124,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))
| ~ ( ~ scratc2135361906_is_of(tptp_fun_X2_13(aTP_Lamm_bo,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_bo,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_bo,tptp_fun_X2_13(aTP_Lamm_bo,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(125,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)],[124,123]) ).
tff(126,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(127,axiom,
pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_bo)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_satz24) ).
tff(128,plain,
pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_bo)),
inference(modus_ponens,[status(thm)],[127,126]) ).
tff(129,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(130,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)],[129,128]) ).
tff(131,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)],[130,125]) ).
tff(132,plain,
( ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a) )
| ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_bo,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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) )
| ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_bo,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(133,plain,
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a),aTP_Lamm_a) )
<=> ( ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_bo,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(134,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_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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) )
| ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_bo,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))) ) ),
inference(monotonicity,[status(thm)],[133]) ).
tff(135,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_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),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) )
| ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_bo,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))) ) ),
inference(transitivity,[status(thm)],[134,132]) ).
tff(136,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_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))
| ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a),aTP_Lamm_a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(137,plain,
( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc2135361906_is_of(X2,aTP_Lamm_a) )
| ~ scratc2135361906_is_of(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_bo,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))) ),
inference(modus_ponens,[status(thm)],[136,135]) ).
tff(138,plain,
pp(aa_TPTP_ind_bool(aTP_Lamm_bo,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a))),
inference(unit_resolution,[status(thm)],[137,131,53,51]) ).
tff(139,plain,
( ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),scratc2094053556nd_n_1)) )
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bo,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),scratc2094053556nd_n_1)) ),
inference(tautology,[status(thm)],[]) ).
tff(140,plain,
( ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),scratc2094053556nd_n_1)) )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),scratc2094053556nd_n_1)) ),
inference(unit_resolution,[status(thm)],[139,138]) ).
tff(141,plain,
pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),scratc2094053556nd_n_1)),
inference(unit_resolution,[status(thm)],[140,116]) ).
tff(142,plain,
pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))),
inference(modus_ponens,[status(thm)],[141,107]) ).
tff(143,plain,
( ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),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_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))) ),
inference(tautology,[status(thm)],[]) ).
tff(144,plain,
~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))) ),
inference(unit_resolution,[status(thm)],[143,142,105]) ).
tff(145,plain,
( ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),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_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))) ) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),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_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))) ),
inference(tautology,[status(thm)],[]) ).
tff(146,plain,
~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))),
inference(unit_resolution,[status(thm)],[145,144,93]) ).
tff(147,plain,
( scratc2135361906_is_of(aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset),aTP_Lamm_a)
<=> scratc2135361906_is_of(scratc2094053556nd_n_1,aTP_Lamm_a) ),
inference(monotonicity,[status(thm)],[97]) ).
tff(148,plain,
( scratc2135361906_is_of(scratc2094053556nd_n_1,aTP_Lamm_a)
<=> scratc2135361906_is_of(aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset),aTP_Lamm_a) ),
inference(symmetry,[status(thm)],[147]) ).
tff(149,plain,
( scratc2135361906_is_of(scratc2094053556nd_n_1,aTP_Lamm_a)
<=> scratc2135361906_is_of(scratc2094053556nd_n_1,aTP_Lamm_a) ),
inference(rewrite,[status(thm)],[]) ).
tff(150,axiom,
scratc2135361906_is_of(scratc2094053556nd_n_1,aTP_Lamm_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__1__p) ).
tff(151,plain,
scratc2135361906_is_of(scratc2094053556nd_n_1,aTP_Lamm_a),
inference(modus_ponens,[status(thm)],[150,149]) ).
tff(152,plain,
scratc2135361906_is_of(aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset),aTP_Lamm_a),
inference(modus_ponens,[status(thm)],[151,148]) ).
tff(153,plain,
( gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))
<=> gg_TPTP_ind(scratc2094053556nd_n_1) ),
inference(monotonicity,[status(thm)],[97]) ).
tff(154,plain,
( gg_TPTP_ind(scratc2094053556nd_n_1)
<=> gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)) ),
inference(symmetry,[status(thm)],[153]) ).
tff(155,plain,
( gg_TPTP_ind(scratc2094053556nd_n_1)
<=> gg_TPTP_ind(scratc2094053556nd_n_1) ),
inference(rewrite,[status(thm)],[]) ).
tff(156,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(157,plain,
gg_TPTP_ind(scratc2094053556nd_n_1),
inference(modus_ponens,[status(thm)],[156,155]) ).
tff(158,plain,
gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset)),
inference(modus_ponens,[status(thm)],[157,154]) ).
tff(159,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_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),X2)) )
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))
| ~ scratc2135361906_is_of(aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),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(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),X2)) )
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))
| ~ scratc2135361906_is_of(aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(160,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_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),X2)) )
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))
| ~ scratc2135361906_is_of(aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(161,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_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),X2)) )
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))
| ~ scratc2135361906_is_of(aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,tptp_fun_X2_13(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset))) ),
inference(modus_ponens,[status(thm)],[160,159]) ).
tff(162,plain,
$false,
inference(unit_resolution,[status(thm)],[161,158,152,146,81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM694+4 : TPTP v9.0.0. Released v7.3.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n015.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % 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 Jun 20 01:47:10 EDT 2025
% 0.13/0.35 % CPUTime :
% 25.02/25.24 % SZS status Theorem
% 25.02/25.24 % SZS output start Proof
% See solution above
% 25.26/25.43 % E exiting
%------------------------------------------------------------------------------