TSTP Solution File: NUM708+4 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM708+4 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 13:11:38 EDT 2022
% Result : Theorem 16.49s 10.88s
% Output : Proof 16.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 96
% Syntax : Number of formulae : 194 ( 53 unt; 36 typ; 0 def)
% Number of atoms : 826 ( 104 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 1183 ( 552 ~; 482 |; 22 &)
% ( 118 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of FOOLs : 37 ( 37 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 35 ( 22 >; 13 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 33 ( 33 usr; 14 con; 0-2 aty)
% Number of variables : 257 ( 232 !; 0 ?; 257 :)
% Comments :
%------------------------------------------------------------------------------
tff(tptp_fun_X2_12_type,type,
tptp_fun_X2_12: ( $i * $i ) > $i ).
tff(aTP_Lamm_a_type,type,
aTP_Lamm_a: $i ).
tff(aTP_Lamm_aa_type,type,
aTP_Lamm_aa: $i ).
tff(aa_TPTP_ind_TPTP_ind_type,type,
aa_TPTP_ind_TPTP_ind: ( $i * $i ) > $i ).
tff(scratc1184412276d_n_ts_type,type,
scratc1184412276d_n_ts: $i > $i ).
tff(scratc1098815950ptyset_type,type,
scratc1098815950ptyset: $i ).
tff(scratc2087395498rdsucc_type,type,
scratc2087395498rdsucc: $i ).
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(fequal_TPTP_ind_type,type,
fequal_TPTP_ind: $i ).
tff(scratc1665030326d_e_is_type,type,
scratc1665030326d_e_is: $i > $i ).
tff(aa_fun1431113780TP_ind_type,type,
aa_fun1431113780TP_ind: ( $i * $i ) > $i ).
tff(aTP_Lamm_aj_type,type,
aTP_Lamm_aj: $i ).
tff(scratc603855731_d_Sep_type,type,
scratc603855731_d_Sep: $i > $i ).
tff(scratc1619295784_nat_p_type,type,
scratc1619295784_nat_p: $i ).
tff(scratc2052352566univof_type,type,
scratc2052352566univof: $i ).
tff(scratc303331766bnd_if_type,type,
scratc303331766bnd_if: ( $i * $i ) > $i ).
tff(aa_fun277296641TP_ind_type,type,
aa_fun277296641TP_ind: ( $i * $i ) > $i ).
tff(aa_fun1235454963TP_ind_type,type,
aa_fun1235454963TP_ind: ( $i * $i ) > $i ).
tff(aTP_Lamm_bp_type,type,
aTP_Lamm_bp: $i > $i ).
tff(aa_TPT494704832TP_ind_type,type,
aa_TPT494704832TP_ind: ( $i * $i ) > $i ).
tff(scratc1505124840d_repl_type,type,
scratc1505124840d_repl: $i ).
tff(fEx_TPTP_ind_type,type,
fEx_TPTP_ind: $i > $i ).
tff(cOMBS_2003118649l_bool_type,type,
cOMBS_2003118649l_bool: ( $i * $i ) > $i ).
tff(cOMBB_658106424TP_ind_type,type,
cOMBB_658106424TP_ind: ( $i * $i ) > $i ).
tff(cOMBC_1555011498d_bool_type,type,
cOMBC_1555011498d_bool: $i > $i ).
tff(scratc303331774bnd_in_type,type,
scratc303331774bnd_in: $i ).
tff(fconj_type,type,
fconj: $i ).
tff(scratc479575420nd_n_1_type,type,
scratc479575420nd_n_1: $i ).
tff(scratc1183690687d_n_is_type,type,
scratc1183690687d_n_is: $i ).
tff(scratc1732651578_is_of_type,type,
scratc1732651578_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(scratc857285919all_of_type,type,
scratc857285919all_of: $i > $i ).
tff(aTP_Lamm_bx_type,type,
aTP_Lamm_bx: $i ).
tff(1,plain,
( ( aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) = tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a) )
<=> ( tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a) = aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) ) ),
inference(commutativity,[status(thm)],]) ).
tff(2,plain,
( ( tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a) = aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) )
<=> ( aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) = tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a) ) ),
inference(symmetry,[status(thm)],[1]) ).
tff(3,plain,
( ( tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a) != aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) )
<=> ( aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) != tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a) ) ),
inference(monotonicity,[status(thm)],[2]) ).
tff(4,plain,
^ [X: $i,Xa: $i] :
refl(
( ( aa_fun1431113780TP_ind(scratc603855731_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc303331766bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc303331774bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1505124840d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bp(X),Xa))),scratc1098815950ptyset) )
<=> ( aa_fun1431113780TP_ind(scratc603855731_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc303331766bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc303331774bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1505124840d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bp(X),Xa))),scratc1098815950ptyset) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [X: $i,Xa: $i] : ( aa_fun1431113780TP_ind(scratc603855731_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc303331766bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc303331774bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1505124840d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bp(X),Xa))),scratc1098815950ptyset) )
<=> ! [X: $i,Xa: $i] : ( aa_fun1431113780TP_ind(scratc603855731_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc303331766bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc303331774bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1505124840d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bp(X),Xa))),scratc1098815950ptyset) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [X: $i,Xa: $i] : ( aa_fun1431113780TP_ind(scratc603855731_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc303331766bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc303331774bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1505124840d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bp(X),Xa))),scratc1098815950ptyset) )
<=> ! [X: $i,Xa: $i] : ( aa_fun1431113780TP_ind(scratc603855731_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc303331766bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc303331774bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1505124840d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bp(X),Xa))),scratc1098815950ptyset) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
! [X: $i,Xa: $i] : ( aa_fun1431113780TP_ind(scratc603855731_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc303331766bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc303331774bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1505124840d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bp(X),Xa))),scratc1098815950ptyset) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_def__d__Sep) ).
tff(8,plain,
! [X: $i,Xa: $i] : ( aa_fun1431113780TP_ind(scratc603855731_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc303331766bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc303331774bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1505124840d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bp(X),Xa))),scratc1098815950ptyset) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [X: $i,Xa: $i] : ( aa_fun1431113780TP_ind(scratc603855731_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc303331766bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc303331774bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1505124840d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bp(X),Xa))),scratc1098815950ptyset) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [X: $i,Xa: $i] : ( aa_fun1431113780TP_ind(scratc603855731_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc303331766bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc303331774bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1505124840d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bp(X),Xa))),scratc1098815950ptyset) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ~ ! [X: $i,Xa: $i] : ( aa_fun1431113780TP_ind(scratc603855731_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc303331766bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc303331774bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1505124840d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bp(X),Xa))),scratc1098815950ptyset) )
| ( aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj) = aa_TPTP_ind_TPTP_ind(scratc303331766bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc303331774bnd_in),aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p))),aTP_Lamm_aj)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1505124840d_repl,aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aa_fun1235454963TP_ind(aTP_Lamm_bp(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj))),scratc1098815950ptyset) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(12,plain,
aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj) = aa_TPTP_ind_TPTP_ind(scratc303331766bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc303331774bnd_in),aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p))),aTP_Lamm_aj)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1505124840d_repl,aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aa_fun1235454963TP_ind(aTP_Lamm_bp(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj))),scratc1098815950ptyset),
inference(unit_resolution,[status(thm)],[11,10]) ).
tff(13,plain,
scratc1665030326d_e_is(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj)) = scratc1665030326d_e_is(aa_TPTP_ind_TPTP_ind(scratc303331766bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc303331774bnd_in),aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p))),aTP_Lamm_aj)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1505124840d_repl,aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aa_fun1235454963TP_ind(aTP_Lamm_bp(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj))),scratc1098815950ptyset)),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
scratc1665030326d_e_is(aa_TPTP_ind_TPTP_ind(scratc303331766bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc303331774bnd_in),aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p))),aTP_Lamm_aj)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1505124840d_repl,aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aa_fun1235454963TP_ind(aTP_Lamm_bp(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj))),scratc1098815950ptyset)) = scratc1665030326d_e_is(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj)),
inference(symmetry,[status(thm)],[13]) ).
tff(15,plain,
^ [X: $i] :
refl(
( ( scratc1665030326d_e_is(X) = fequal_TPTP_ind )
<=> ( scratc1665030326d_e_is(X) = fequal_TPTP_ind ) )),
inference(bind,[status(th)],]) ).
tff(16,plain,
( ! [X: $i] : ( scratc1665030326d_e_is(X) = fequal_TPTP_ind )
<=> ! [X: $i] : ( scratc1665030326d_e_is(X) = fequal_TPTP_ind ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [X: $i] : ( scratc1665030326d_e_is(X) = fequal_TPTP_ind )
<=> ! [X: $i] : ( scratc1665030326d_e_is(X) = fequal_TPTP_ind ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,axiom,
! [X: $i] : ( scratc1665030326d_e_is(X) = fequal_TPTP_ind ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_def__e__is) ).
tff(19,plain,
! [X: $i] : ( scratc1665030326d_e_is(X) = fequal_TPTP_ind ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [X: $i] : ( scratc1665030326d_e_is(X) = fequal_TPTP_ind ),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [X: $i] : ( scratc1665030326d_e_is(X) = fequal_TPTP_ind ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
( ~ ! [X: $i] : ( scratc1665030326d_e_is(X) = fequal_TPTP_ind )
| ( scratc1665030326d_e_is(aa_TPTP_ind_TPTP_ind(scratc303331766bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc303331774bnd_in),aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p))),aTP_Lamm_aj)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1505124840d_repl,aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aa_fun1235454963TP_ind(aTP_Lamm_bp(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj))),scratc1098815950ptyset)) = fequal_TPTP_ind ) ),
inference(quant_inst,[status(thm)],]) ).
tff(23,plain,
scratc1665030326d_e_is(aa_TPTP_ind_TPTP_ind(scratc303331766bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc303331774bnd_in),aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p))),aTP_Lamm_aj)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1505124840d_repl,aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aa_fun1235454963TP_ind(aTP_Lamm_bp(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj))),scratc1098815950ptyset)) = fequal_TPTP_ind,
inference(unit_resolution,[status(thm)],[22,21]) ).
tff(24,plain,
fequal_TPTP_ind = scratc1665030326d_e_is(aa_TPTP_ind_TPTP_ind(scratc303331766bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc303331774bnd_in),aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p))),aTP_Lamm_aj)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1505124840d_repl,aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aa_fun1235454963TP_ind(aTP_Lamm_bp(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj))),scratc1098815950ptyset)),
inference(symmetry,[status(thm)],[23]) ).
tff(25,plain,
fequal_TPTP_ind = scratc1665030326d_e_is(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj)),
inference(transitivity,[status(thm)],[24,14]) ).
tff(26,plain,
aa_TPT43085870d_bool(fequal_TPTP_ind,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) = aa_TPT43085870d_bool(scratc1665030326d_e_is(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),
inference(monotonicity,[status(thm)],[25]) ).
tff(27,plain,
aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) = aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1665030326d_e_is(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1665030326d_e_is(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(monotonicity,[status(thm)],[27]) ).
tff(29,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1665030326d_e_is(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(symmetry,[status(thm)],[28]) ).
tff(30,plain,
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1665030326d_e_is(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
<=> ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
^ [Uu: $i] :
refl(
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1665030326d_e_is(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj)),Uu),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),Uu))) )
<=> ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1665030326d_e_is(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj)),Uu),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),Uu))) ) )),
inference(bind,[status(th)],]) ).
tff(32,plain,
( ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1665030326d_e_is(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj)),Uu),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),Uu))) )
<=> ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1665030326d_e_is(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj)),Uu),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),Uu))) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,plain,
^ [Uu: $i] :
rewrite(
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1183690687d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(scratc479575420nd_n_1),Uu))) )
<=> ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1665030326d_e_is(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj)),Uu),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),Uu))) ) )),
inference(bind,[status(th)],]) ).
tff(34,plain,
( ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1183690687d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(scratc479575420nd_n_1),Uu))) )
<=> ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1665030326d_e_is(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj)),Uu),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),Uu))) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,plain,
( ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1183690687d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(scratc479575420nd_n_1),Uu))) )
<=> ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1183690687d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(scratc479575420nd_n_1),Uu))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,axiom,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1183690687d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(scratc479575420nd_n_1),Uu))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ATP_Olambda__18) ).
tff(37,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1183690687d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(scratc479575420nd_n_1),Uu))) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1665030326d_e_is(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj)),Uu),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),Uu))) ),
inference(modus_ponens,[status(thm)],[37,34]) ).
tff(39,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1665030326d_e_is(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj)),Uu),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),Uu))) ),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1665030326d_e_is(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj)),Uu),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),Uu))) ),
inference(modus_ponens,[status(thm)],[39,32]) ).
tff(41,plain,
( ~ ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1665030326d_e_is(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj)),Uu),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),Uu))) )
| ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1665030326d_e_is(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(42,plain,
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1665030326d_e_is(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(unit_resolution,[status(thm)],[41,40]) ).
tff(43,plain,
^ [X: $i,Xa: $i] :
refl(
( ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(44,plain,
( ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,plain,
^ [X: $i,Xa: $i] :
rewrite(
( ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(46,plain,
( ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,plain,
( ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) ),
inference(transitivity,[status(thm)],[46,44]) ).
tff(48,plain,
^ [X: $i,Xa: $i] :
trans(
monotonicity(
rewrite(
( ( ~ pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,X) ) )
<=> ( ~ pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,X) ) ) )),
monotonicity(
rewrite(
( ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(Xa,X),X) )
<=> ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(Xa,X),X) ) )),
( ( pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(Xa,X),X) ) )
<=> ( pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )),
( ( ( ~ pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,X) ) )
& ( pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ( ( ~ pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,X) ) )
& ( pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) )),
rewrite(
( ( ( ~ pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,X) ) )
& ( pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) )),
( ( ( ~ pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,X) ) )
& ( pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(49,plain,
( ! [X: $i,Xa: $i] :
( ( ~ pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,X) ) )
& ( pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,plain,
( ! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
<=> ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,X) ) )
<=> ! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
<=> ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
^ [X: $i,Xa: $i] :
rewrite(
( ( pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
<=> ! [X2: $i] :
( gg_TPTP_ind(X2)
=> ( scratc1732651578_is_of(X2,X)
=> pp(aa_TPTP_ind_bool(Xa,X2)) ) ) )
<=> ( pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
<=> ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,X) ) ) )),
inference(bind,[status(th)],]) ).
tff(52,plain,
( ! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
<=> ! [X2: $i] :
( gg_TPTP_ind(X2)
=> ( scratc1732651578_is_of(X2,X)
=> pp(aa_TPTP_ind_bool(Xa,X2)) ) ) )
<=> ! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
<=> ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,X) ) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,axiom,
! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
<=> ! [X2: $i] :
( gg_TPTP_ind(X2)
=> ( scratc1732651578_is_of(X2,X)
=> pp(aa_TPTP_ind_bool(Xa,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_def__all__of) ).
tff(54,plain,
! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
<=> ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,X) ) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
<=> ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,X) ) ),
inference(modus_ponens,[status(thm)],[54,50]) ).
tff(56,plain,
! [X: $i,Xa: $i] :
( ( ~ pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,X) ) )
& ( pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ),
inference(skolemize,[status(sab)],[55]) ).
tff(57,plain,
! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ),
inference(modus_ponens,[status(thm)],[56,49]) ).
tff(58,plain,
! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ),
inference(modus_ponens,[status(thm)],[57,47]) ).
tff(59,plain,
( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc857285919all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc857285919all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(60,plain,
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc857285919all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc857285919all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ) ) ),
inference(unit_resolution,[status(thm)],[59,58]) ).
tff(61,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc857285919all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc857285919all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ) )
| pp(aa_fun171081125l_bool(scratc857285919all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ) ),
inference(tautology,[status(thm)],]) ).
tff(62,plain,
( pp(aa_fun171081125l_bool(scratc857285919all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ) ),
inference(unit_resolution,[status(thm)],[61,60]) ).
tff(63,plain,
( ~ pp(aa_fun171081125l_bool(scratc857285919all_of(aTP_Lamm_a),aTP_Lamm_aa))
<=> ~ pp(aa_fun171081125l_bool(scratc857285919all_of(aTP_Lamm_a),aTP_Lamm_aa)) ),
inference(rewrite,[status(thm)],]) ).
tff(64,axiom,
~ pp(aa_fun171081125l_bool(scratc857285919all_of(aTP_Lamm_a),aTP_Lamm_aa)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(65,plain,
~ pp(aa_fun171081125l_bool(scratc857285919all_of(aTP_Lamm_a),aTP_Lamm_aa)),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
( ~ ( pp(aa_fun171081125l_bool(scratc857285919all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ) )
| pp(aa_fun171081125l_bool(scratc857285919all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ) ),
inference(tautology,[status(thm)],]) ).
tff(67,plain,
( ~ ( pp(aa_fun171081125l_bool(scratc857285919all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ) )
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ) ),
inference(unit_resolution,[status(thm)],[66,65]) ).
tff(68,plain,
~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ),
inference(unit_resolution,[status(thm)],[67,62]) ).
tff(69,plain,
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(tautology,[status(thm)],]) ).
tff(70,plain,
~ pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),
inference(unit_resolution,[status(thm)],[69,68]) ).
tff(71,plain,
( ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1665030326d_e_is(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) )
| pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1665030326d_e_is(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(tautology,[status(thm)],]) ).
tff(72,plain,
( ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1665030326d_e_is(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1665030326d_e_is(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(unit_resolution,[status(thm)],[71,70]) ).
tff(73,plain,
~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1665030326d_e_is(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))),
inference(unit_resolution,[status(thm)],[72,42]) ).
tff(74,plain,
~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))),
inference(modus_ponens,[status(thm)],[73,30]) ).
tff(75,plain,
^ [X7: $i,Y: $i] :
refl(
( ( ( X7 != Y )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)) )
<=> ( ( X7 != Y )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)) ) )),
inference(bind,[status(th)],]) ).
tff(76,plain,
( ! [X7: $i,Y: $i] :
( ( X7 != Y )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)) )
<=> ! [X7: $i,Y: $i] :
( ( X7 != Y )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)) ) ),
inference(quant_intro,[status(thm)],[75]) ).
tff(77,plain,
( ! [X7: $i,Y: $i] :
( ( X7 != Y )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)) )
<=> ! [X7: $i,Y: $i] :
( ( X7 != Y )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(78,axiom,
! [X7: $i,Y: $i] :
( ( X7 != Y )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_001t__TPTP____Interpret__Oind_T) ).
tff(79,plain,
! [X7: $i,Y: $i] :
( ( X7 != Y )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)) ),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
! [X7: $i,Y: $i] :
( ( X7 != Y )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)) ),
inference(skolemize,[status(sab)],[79]) ).
tff(81,plain,
! [X7: $i,Y: $i] :
( ( X7 != Y )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)) ),
inference(modus_ponens,[status(thm)],[80,76]) ).
tff(82,plain,
( ( ~ ! [X7: $i,Y: $i] :
( ( X7 != Y )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)) )
| ( tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a) != aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) )
<=> ( ~ ! [X7: $i,Y: $i] :
( ( X7 != Y )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)) )
| ( tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a) != aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(83,plain,
( ~ ! [X7: $i,Y: $i] :
( ( X7 != Y )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)) )
| ( tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a) != aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(84,plain,
( ~ ! [X7: $i,Y: $i] :
( ( X7 != Y )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)) )
| ( tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a) != aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
( ( tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a) != aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(unit_resolution,[status(thm)],[84,81]) ).
tff(86,plain,
tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a) != aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),
inference(unit_resolution,[status(thm)],[85,74]) ).
tff(87,plain,
aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) != tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),
inference(modus_ponens,[status(thm)],[86,3]) ).
tff(88,plain,
aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) = aa_TPT43085870d_bool(scratc1665030326d_e_is(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj)),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),
inference(monotonicity,[status(thm)],[25]) ).
tff(89,plain,
aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) = aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1665030326d_e_is(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj)),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),
inference(monotonicity,[status(thm)],[88]) ).
tff(90,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1665030326d_e_is(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj)),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(monotonicity,[status(thm)],[89]) ).
tff(91,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1665030326d_e_is(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj)),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(symmetry,[status(thm)],[90]) ).
tff(92,plain,
^ [Uu: $i] :
refl(
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1665030326d_e_is(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj)),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),Uu)),Uu)) )
<=> ( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1665030326d_e_is(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj)),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),Uu)),Uu)) ) )),
inference(bind,[status(th)],]) ).
tff(93,plain,
( ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1665030326d_e_is(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj)),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),Uu)),Uu)) )
<=> ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1665030326d_e_is(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj)),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),Uu)),Uu)) ) ),
inference(quant_intro,[status(thm)],[92]) ).
tff(94,plain,
^ [Uu: $i] :
rewrite(
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1183690687d_n_is,aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(scratc479575420nd_n_1),Uu)),Uu)) )
<=> ( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1665030326d_e_is(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj)),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),Uu)),Uu)) ) )),
inference(bind,[status(th)],]) ).
tff(95,plain,
( ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1183690687d_n_is,aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(scratc479575420nd_n_1),Uu)),Uu)) )
<=> ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1665030326d_e_is(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj)),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),Uu)),Uu)) ) ),
inference(quant_intro,[status(thm)],[94]) ).
tff(96,plain,
( ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1183690687d_n_is,aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(scratc479575420nd_n_1),Uu)),Uu)) )
<=> ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1183690687d_n_is,aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(scratc479575420nd_n_1),Uu)),Uu)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(97,axiom,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1183690687d_n_is,aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(scratc479575420nd_n_1),Uu)),Uu)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ATP_Olambda__6) ).
tff(98,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1183690687d_n_is,aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(scratc479575420nd_n_1),Uu)),Uu)) ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1665030326d_e_is(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj)),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),Uu)),Uu)) ),
inference(modus_ponens,[status(thm)],[98,95]) ).
tff(100,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1665030326d_e_is(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj)),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),Uu)),Uu)) ),
inference(skolemize,[status(sab)],[99]) ).
tff(101,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1665030326d_e_is(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj)),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),Uu)),Uu)) ),
inference(modus_ponens,[status(thm)],[100,93]) ).
tff(102,plain,
( ~ ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1665030326d_e_is(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj)),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),Uu)),Uu)) )
| ( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1665030326d_e_is(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj)),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(103,plain,
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1665030326d_e_is(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj)),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(unit_resolution,[status(thm)],[102,101]) ).
tff(104,plain,
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| scratc1732651578_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ),
inference(tautology,[status(thm)],]) ).
tff(105,plain,
scratc1732651578_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a),
inference(unit_resolution,[status(thm)],[104,68]) ).
tff(106,plain,
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) ),
inference(tautology,[status(thm)],]) ).
tff(107,plain,
gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),
inference(unit_resolution,[status(thm)],[106,68]) ).
tff(108,plain,
( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc857285919all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc857285919all_of(aTP_Lamm_a),aTP_Lamm_bx))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc857285919all_of(aTP_Lamm_a),aTP_Lamm_bx))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,tptp_fun_X2_12(aTP_Lamm_bx,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_bx,aTP_Lamm_a))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(aTP_Lamm_bx,aTP_Lamm_a),aTP_Lamm_a) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(109,plain,
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc857285919all_of(aTP_Lamm_a),aTP_Lamm_bx))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc857285919all_of(aTP_Lamm_a),aTP_Lamm_bx))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,tptp_fun_X2_12(aTP_Lamm_bx,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_bx,aTP_Lamm_a))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(aTP_Lamm_bx,aTP_Lamm_a),aTP_Lamm_a) ) ) ),
inference(unit_resolution,[status(thm)],[108,58]) ).
tff(110,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc857285919all_of(aTP_Lamm_a),aTP_Lamm_bx))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc857285919all_of(aTP_Lamm_a),aTP_Lamm_bx))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,tptp_fun_X2_12(aTP_Lamm_bx,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_bx,aTP_Lamm_a))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(aTP_Lamm_bx,aTP_Lamm_a),aTP_Lamm_a) ) )
| ~ pp(aa_fun171081125l_bool(scratc857285919all_of(aTP_Lamm_a),aTP_Lamm_bx))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,aTP_Lamm_a) ) ),
inference(tautology,[status(thm)],]) ).
tff(111,plain,
( ~ pp(aa_fun171081125l_bool(scratc857285919all_of(aTP_Lamm_a),aTP_Lamm_bx))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,aTP_Lamm_a) ) ),
inference(unit_resolution,[status(thm)],[110,109]) ).
tff(112,plain,
( pp(aa_fun171081125l_bool(scratc857285919all_of(aTP_Lamm_a),aTP_Lamm_bx))
<=> pp(aa_fun171081125l_bool(scratc857285919all_of(aTP_Lamm_a),aTP_Lamm_bx)) ),
inference(rewrite,[status(thm)],]) ).
tff(113,axiom,
pp(aa_fun171081125l_bool(scratc857285919all_of(aTP_Lamm_a),aTP_Lamm_bx)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_satz28c) ).
tff(114,plain,
pp(aa_fun171081125l_bool(scratc857285919all_of(aTP_Lamm_a),aTP_Lamm_bx)),
inference(modus_ponens,[status(thm)],[113,112]) ).
tff(115,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc857285919all_of(aTP_Lamm_a),aTP_Lamm_bx))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,aTP_Lamm_a) ) )
| ~ pp(aa_fun171081125l_bool(scratc857285919all_of(aTP_Lamm_a),aTP_Lamm_bx))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,aTP_Lamm_a) ) ),
inference(tautology,[status(thm)],]) ).
tff(116,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc857285919all_of(aTP_Lamm_a),aTP_Lamm_bx))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,aTP_Lamm_a) ) )
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,aTP_Lamm_a) ) ),
inference(unit_resolution,[status(thm)],[115,114]) ).
tff(117,plain,
! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,aTP_Lamm_a) ),
inference(unit_resolution,[status(thm)],[116,111]) ).
tff(118,plain,
( ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,aTP_Lamm_a) )
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aTP_Lamm_bx,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) )
<=> ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,aTP_Lamm_a) )
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aTP_Lamm_bx,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(119,plain,
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) )
<=> ( ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aTP_Lamm_bx,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(120,plain,
( ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,aTP_Lamm_a) )
| pp(aa_TPTP_ind_bool(aTP_Lamm_bx,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) )
<=> ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,aTP_Lamm_a) )
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aTP_Lamm_bx,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(monotonicity,[status(thm)],[119]) ).
tff(121,plain,
( ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,aTP_Lamm_a) )
| pp(aa_TPTP_ind_bool(aTP_Lamm_bx,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) )
<=> ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,aTP_Lamm_a) )
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aTP_Lamm_bx,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(transitivity,[status(thm)],[120,118]) ).
tff(122,plain,
( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,aTP_Lamm_a) )
| pp(aa_TPTP_ind_bool(aTP_Lamm_bx,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ),
inference(quant_inst,[status(thm)],]) ).
tff(123,plain,
( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1732651578_is_of(X2,aTP_Lamm_a) )
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1732651578_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aTP_Lamm_bx,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(modus_ponens,[status(thm)],[122,121]) ).
tff(124,plain,
pp(aa_TPTP_ind_bool(aTP_Lamm_bx,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),
inference(unit_resolution,[status(thm)],[123,117,107,105]) ).
tff(125,plain,
( ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1665030326d_e_is(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj)),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) )
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bx,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1665030326d_e_is(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj)),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(tautology,[status(thm)],]) ).
tff(126,plain,
( ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1665030326d_e_is(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj)),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1665030326d_e_is(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj)),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(unit_resolution,[status(thm)],[125,124]) ).
tff(127,plain,
pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1665030326d_e_is(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_fun1431113780TP_ind(scratc603855731_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2052352566univof,scratc1098815950ptyset)),scratc1619295784_nat_p)),aTP_Lamm_aj)),aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),
inference(unit_resolution,[status(thm)],[126,103]) ).
tff(128,plain,
pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),
inference(modus_ponens,[status(thm)],[127,91]) ).
tff(129,plain,
^ [B_1: $i,B_2: $i] :
refl(
( gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2))
<=> gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2)) )),
inference(bind,[status(th)],]) ).
tff(130,plain,
( ! [B_1: $i,B_2: $i] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2))
<=> ! [B_1: $i,B_2: $i] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2)) ),
inference(quant_intro,[status(thm)],[129]) ).
tff(131,plain,
( ! [B_1: $i,B_2: $i] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2))
<=> ! [B_1: $i,B_2: $i] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2)) ),
inference(rewrite,[status(thm)],]) ).
tff(132,axiom,
! [B_1: $i,B_2: $i] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_aa_001t__TPTP____Interpret__Oind_001t__TPTP____Interpret__Oind) ).
tff(133,plain,
! [B_1: $i,B_2: $i] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2)),
inference(modus_ponens,[status(thm)],[132,131]) ).
tff(134,plain,
! [B_1: $i,B_2: $i] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2)),
inference(skolemize,[status(sab)],[133]) ).
tff(135,plain,
! [B_1: $i,B_2: $i] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2)),
inference(modus_ponens,[status(thm)],[134,130]) ).
tff(136,plain,
( ~ ! [B_1: $i,B_2: $i] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2))
| gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(137,plain,
gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),
inference(unit_resolution,[status(thm)],[136,135]) ).
tff(138,plain,
^ [X7: $i,Y: $i] :
refl(
( ( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
<=> ( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) ) )),
inference(bind,[status(th)],]) ).
tff(139,plain,
( ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
<=> ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) ) ),
inference(quant_intro,[status(thm)],[138]) ).
tff(140,plain,
^ [X7: $i,Y: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) )
<=> ~ ( ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) ) )),
( ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) )
<=> ~ ~ ( ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) ) )),
rewrite(
( ~ ~ ( ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
<=> ( ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) ) )),
( ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) )
<=> ( ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) ) )),
( ( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) ) )
<=> ( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) ) )),
rewrite(
( ( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
<=> ( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) ) )),
( ( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) ) )
<=> ( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) ) )),
inference(bind,[status(th)],]) ).
tff(141,plain,
( ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) ) )
<=> ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) ) ),
inference(quant_intro,[status(thm)],[140]) ).
tff(142,plain,
( ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) ) )
<=> ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(143,plain,
^ [X7: $i,Y: $i] :
rewrite(
( ( ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) )
=> ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ( X7 = Y ) ) )
<=> ( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) ) ) )),
inference(bind,[status(th)],]) ).
tff(144,plain,
( ! [X7: $i,Y: $i] :
( ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) )
=> ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ( X7 = Y ) ) )
<=> ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) ) ) ),
inference(quant_intro,[status(thm)],[143]) ).
tff(145,axiom,
! [X7: $i,Y: $i] :
( ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) )
=> ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ( X7 = Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_001t__TPTP____Interpret__Oind_T) ).
tff(146,plain,
! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) ) ),
inference(modus_ponens,[status(thm)],[145,144]) ).
tff(147,plain,
! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) ) ),
inference(modus_ponens,[status(thm)],[146,142]) ).
tff(148,plain,
! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) ) ),
inference(skolemize,[status(sab)],[147]) ).
tff(149,plain,
! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) ),
inference(modus_ponens,[status(thm)],[148,141]) ).
tff(150,plain,
! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) ),
inference(modus_ponens,[status(thm)],[149,139]) ).
tff(151,plain,
( ( ~ ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ( aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) = tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) )
<=> ( ~ ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ( aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) = tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(152,plain,
( ( ( aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) = tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) )
<=> ( ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ( aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) = tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(153,plain,
( ( ~ ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
| ( aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) = tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) )
<=> ( ~ ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ( aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) = tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(monotonicity,[status(thm)],[152]) ).
tff(154,plain,
( ( ~ ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
| ( aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) = tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) )
<=> ( ~ ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ( aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) = tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(transitivity,[status(thm)],[153,151]) ).
tff(155,plain,
( ~ ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
| ( aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) = tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(156,plain,
( ~ ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ( aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) = tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(modus_ponens,[status(thm)],[155,154]) ).
tff(157,plain,
( ( aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) = tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc1184412276d_n_ts(aa_TPTP_ind_TPTP_ind(scratc2087395498rdsucc,scratc1098815950ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(unit_resolution,[status(thm)],[156,150,107,137]) ).
tff(158,plain,
$false,
inference(unit_resolution,[status(thm)],[157,128,87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM708+4 : TPTP v8.1.0. Released v7.3.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 14:03:07 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 16.49/10.88 % SZS status Theorem
% 16.49/10.88 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------