%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ITP037^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:23:43 AM UTC 2026
% Result : Theorem 1.26s 0.47s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 16
% Syntax : Number of formulae : 467 ( 85 unt; 0 typ; 0 def)
% Number of atoms : 4335 (1453 equ; 0 cnn)
% Maximal formula atoms : 4 ( 9 avg)
% Number of connectives : 2740 ( 753 ~;1170 |; 6 &; 793 @)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 53 ( 52 usr)
% Number of type conns : 33 ( 33 >; 0 *; 0 +; 0 <<)
% Number of symbols : 146 ( 143 usr; 37 con; 0-10 aty)
% Number of variables : 418 ( 0 ^; 418 !; 0 ?; 418 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_c,type,
c: $tType ).
thf(tp_denota231621370t_unit,type,
denota231621370t_unit: $tType ).
thf(tp_denota610675952t_unit,type,
denota610675952t_unit: $tType ).
thf(tp_finite1398487019real_c,type,
finite1398487019real_c: $tType ).
thf(tp_finite824932053eal_sz,type,
finite824932053eal_sz: $tType ).
thf(tp_formula_sf_sc_sz,type,
formula_sf_sc_sz: $tType ).
thf(tp_frechet_strm_a_c,type,
frechet_strm_a_c: $tType ).
thf(tp_frechet_strm_sf_sz,type,
frechet_strm_sf_sz: $tType ).
thf(tp_list_f1238882004_sc_sz,type,
list_f1238882004_sc_sz: $tType ).
thf(tp_produc1149990247eal_sz,type,
produc1149990247eal_sz: $tType ).
thf(tp_produc1295591296real_c,type,
produc1295591296real_c: $tType ).
thf(tp_produc1299700144real_c,type,
produc1299700144real_c: $tType ).
thf(tp_produc133347448c_real,type,
produc133347448c_real: $tType ).
thf(tp_produc1471603704real_c,type,
produc1471603704real_c: $tType ).
thf(tp_produc1631500469_set_c,type,
produc1631500469_set_c: $tType ).
thf(tp_produc1821101996_sc_sz,type,
produc1821101996_sc_sz: $tType ).
thf(tp_produc189019228set_sz,type,
produc189019228set_sz: $tType ).
thf(tp_produc190496183real_c,type,
produc190496183real_c: $tType ).
thf(tp_produc1952288593real_c,type,
produc1952288593real_c: $tType ).
thf(tp_produc2057661729set_sz,type,
produc2057661729set_sz: $tType ).
thf(tp_produc313687471set_sz,type,
produc313687471set_sz: $tType ).
thf(tp_produc44682460um_c_c,type,
produc44682460um_c_c: $tType ).
thf(tp_produc621499498um_c_c,type,
produc621499498um_c_c: $tType ).
thf(tp_produc640052711real_c,type,
produc640052711real_c: $tType ).
thf(tp_produc729314338real_c,type,
produc729314338real_c: $tType ).
thf(tp_produc756982951_set_c,type,
produc756982951_set_c: $tType ).
thf(tp_produc802386618_set_c,type,
produc802386618_set_c: $tType ).
thf(tp_produc861709536_sz_sz,type,
produc861709536_sz_sz: $tType ).
thf(tp_produc866628903_sc_sz,type,
produc866628903_sc_sz: $tType ).
thf(tp_produc906325778c_real,type,
produc906325778c_real: $tType ).
thf(tp_produc957004601l_real,type,
produc957004601l_real: $tType ).
thf(tp_produc99145217real_c,type,
produc99145217real_c: $tType ).
thf(tp_produc999471430t_unit,type,
produc999471430t_unit: $tType ).
thf(tp_real,type,
real: $tType ).
thf(tp_sc,type,
sc: $tType ).
thf(tp_set_Fi1407883041real_c,type,
set_Fi1407883041real_c: $tType ).
thf(tp_set_Pr1169339874_sc_sz,type,
set_Pr1169339874_sc_sz: $tType ).
thf(tp_set_Pr1389752855real_c,type,
set_Pr1389752855real_c: $tType ).
thf(tp_set_Pr2041213564t_unit,type,
set_Pr2041213564t_unit: $tType ).
thf(tp_set_Sum_sum_c_c,type,
set_Sum_sum_c_c: $tType ).
thf(tp_set_Sum_sum_sz_sz,type,
set_Sum_sum_sz_sz: $tType ).
thf(tp_set_a,type,
set_a: $tType ).
thf(tp_set_c,type,
set_c: $tType ).
thf(tp_set_sf,type,
set_sf: $tType ).
thf(tp_set_sz,type,
set_sz: $tType ).
thf(tp_set_trm_a_c,type,
set_trm_a_c: $tType ).
thf(tp_set_trm_sf_sz,type,
set_trm_sf_sz: $tType ).
thf(tp_sf,type,
sf: $tType ).
thf(tp_sz,type,
sz: $tType ).
thf(tp_trm_a_c,type,
trm_a_c: $tType ).
thf(tp_trm_sf_sz,type,
trm_sf_sz: $tType ).
thf(tp_accp_P529224471_sz_sz,type,
accp_P529224471_sz_sz: ( produc861709536_sz_sz > produc861709536_sz_sz > $o ) > produc861709536_sz_sz > $o ).
thf(tp_args,type,
args: c > trm_a_c ).
thf(tp_collec377961627t_unit,type,
collec377961627t_unit: ( produc999471430t_unit > $o ) > set_Pr2041213564t_unit ).
thf(tp_collect_a,type,
collect_a: ( a > $o ) > set_a ).
thf(tp_collect_sf,type,
collect_sf: ( sf > $o ) > set_sf ).
thf(tp_collect_trm_a_c,type,
collect_trm_a_c: ( trm_a_c > $o ) > set_trm_a_c ).
thf(tp_collect_trm_sf_sz,type,
collect_trm_sf_sz: ( trm_sf_sz > $o ) > set_trm_sf_sz ).
thf(tp_const_a_c,type,
const_a_c: real > trm_a_c ).
thf(tp_const_sf_sz,type,
const_sf_sz: real > trm_sf_sz ).
thf(tp_denota102713844ree_sz,type,
denota102713844ree_sz: produc1149990247eal_sz > produc1149990247eal_sz > set_Sum_sum_sz_sz > $o ).
thf(tp_denota1997846518gree_c,type,
denota1997846518gree_c: produc190496183real_c > produc190496183real_c > set_Sum_sum_c_c > $o ).
thf(tp_denota2112424896_a_b_c,type,
denota2112424896_a_b_c: denota231621370t_unit > trm_a_c > produc190496183real_c > real ).
thf(tp_denota229585092_a_b_c,type,
denota229585092_a_b_c: denota231621370t_unit > trm_a_c > finite1398487019real_c > finite1398487019real_c > real ).
thf(tp_dfree_a_c,type,
dfree_a_c: trm_a_c > $o ).
thf(tp_dfree_sf_sz,type,
dfree_sf_sz: trm_sf_sz > $o ).
thf(tp_diffVar_c_a,type,
diffVar_c_a: c > trm_a_c ).
thf(tp_diffVar_sz_sf,type,
diffVar_sz_sf: sz > trm_sf_sz ).
thf(tp_differential_a_c,type,
differential_a_c: trm_a_c > trm_a_c ).
thf(tp_differential_sf_sz,type,
differential_sf_sz: trm_sf_sz > trm_sf_sz ).
thf(tp_domain2047240575rm_a_c,type,
domain2047240575rm_a_c: ( trm_a_c > frechet_strm_a_c > $o ) > trm_a_c > $o ).
thf(tp_domain512309999_sf_sz,type,
domain512309999_sf_sz: ( trm_sf_sz > frechet_strm_sf_sz > $o ) > trm_sf_sz > $o ).
thf(tp_dsafe_a_c,type,
dsafe_a_c: trm_a_c > $o ).
thf(tp_dsafe_sf_sz,type,
dsafe_sf_sz: trm_sf_sz > $o ).
thf(tp_empty_c_a,type,
empty_c_a: c > trm_a_c ).
thf(tp_empty_sz_sf,type,
empty_sz_sf: sz > trm_sf_sz ).
thf(tp_f0_sf_sz,type,
f0_sf_sz: sf > trm_sf_sz ).
thf(tp_f1_sz_sf,type,
f1_sz_sf: sz > sf > sz > trm_sf_sz ).
thf(tp_ffree_sf_sc_sz,type,
ffree_sf_sc_sz: formula_sf_sc_sz > $o ).
thf(tp_freche1244000341_sf_sz,type,
freche1244000341_sf_sz: trm_sf_sz > frechet_strm_sf_sz > $o ).
thf(tp_frechet_cr_strm_a_c,type,
frechet_cr_strm_a_c: trm_a_c > frechet_strm_a_c > $o ).
thf(tp_function_a_c,type,
function_a_c: a > ( c > trm_a_c ) > trm_a_c ).
thf(tp_function_sf_sz,type,
function_sf_sz: sf > ( sz > trm_sf_sz ) > trm_sf_sz ).
thf(tp_i,type,
i: denota231621370t_unit ).
thf(tp_i2,type,
i2: c ).
thf(tp_ids_sz_sf_sc,type,
ids_sz_sf_sc: sz > sz > sz > sf > sf > sf > sc > sc > sc > sc > $o ).
thf(tp_if_trm_sf_sz,type,
if_trm_sf_sz: $o > trm_sf_sz > trm_sf_sz > trm_sf_sz ).
thf(tp_image_1426741113_sc_sz,type,
image_1426741113_sc_sz: ( produc999471430t_unit > produc1821101996_sc_sz ) > set_Pr2041213564t_unit > set_Pr1169339874_sc_sz ).
thf(tp_image_14429021real_c,type,
image_14429021real_c: ( produc190496183real_c > finite1398487019real_c ) > set_Pr1389752855real_c > set_Fi1407883041real_c ).
thf(tp_image_1726193375_sc_sz,type,
image_1726193375_sc_sz: ( produc1821101996_sc_sz > produc1821101996_sc_sz ) > set_Pr1169339874_sc_sz > set_Pr1169339874_sc_sz ).
thf(tp_image_904562809t_unit,type,
image_904562809t_unit: ( produc1821101996_sc_sz > produc999471430t_unit ) > set_Pr1169339874_sc_sz > set_Pr2041213564t_unit ).
thf(tp_image_c_trm_a_c,type,
image_c_trm_a_c: ( c > trm_a_c ) > set_c > set_trm_a_c ).
thf(tp_image_sz_trm_sf_sz,type,
image_sz_trm_sf_sz: ( sz > trm_sf_sz ) > set_sz > set_trm_sf_sz ).
thf(tp_left_u638806404_sf_sz,type,
left_u638806404_sf_sz: ( trm_sf_sz > frechet_strm_sf_sz > $o ) > $o ).
thf(tp_left_u968903956rm_a_c,type,
left_u968903956rm_a_c: ( trm_a_c > frechet_strm_a_c > $o ) > $o ).
thf(tp_member1057565379_sc_sz,type,
member1057565379_sc_sz: produc1821101996_sc_sz > set_Pr1169339874_sc_sz > $o ).
thf(tp_member235934813t_unit,type,
member235934813t_unit: produc999471430t_unit > set_Pr2041213564t_unit > $o ).
thf(tp_member_a,type,
member_a: a > set_a > $o ).
thf(tp_member_sf,type,
member_sf: sf > set_sf > $o ).
thf(tp_member_trm_a_c,type,
member_trm_a_c: trm_a_c > set_trm_a_c > $o ).
thf(tp_member_trm_sf_sz,type,
member_trm_sf_sz: trm_sf_sz > set_trm_sf_sz > $o ).
thf(tp_nu,type,
nu: produc190496183real_c ).
thf(tp_nu2,type,
nu2: produc190496183real_c ).
thf(tp_p1_sz_sf_sc,type,
p1_sz_sf_sc: sz > sz > sz > formula_sf_sc_sz ).
thf(tp_p_sc_sf_sz,type,
p_sc_sf_sz: sc > formula_sf_sc_sz ).
thf(tp_plus_a_c,type,
plus_a_c: trm_a_c > trm_a_c > trm_a_c ).
thf(tp_plus_sf_sz,type,
plus_sf_sz: trm_sf_sz > trm_sf_sz > trm_sf_sz ).
thf(tp_predic913887884_sf_sz,type,
predic913887884_sf_sz: sc > formula_sf_sc_sz ).
thf(tp_produc116546123real_c,type,
produc116546123real_c: produc190496183real_c > finite1398487019real_c > produc1952288593real_c ).
thf(tp_produc1216682964t_unit,type,
produc1216682964t_unit: produc999471430t_unit > produc866628903_sc_sz ).
thf(tp_produc1251379220set_sz,type,
produc1251379220set_sz: set_Sum_sum_c_c > set_sz > produc189019228set_sz ).
thf(tp_produc1308130519eal_sz,type,
produc1308130519eal_sz: finite824932053eal_sz > finite824932053eal_sz > produc1149990247eal_sz ).
thf(tp_produc1327150128real_c,type,
produc1327150128real_c: real > finite1398487019real_c > produc1471603704real_c ).
thf(tp_produc1503602930_sc_sz,type,
produc1503602930_sc_sz: produc1821101996_sc_sz > denota610675952t_unit ).
thf(tp_produc1519884516um_c_c,type,
produc1519884516um_c_c: set_c > set_Sum_sum_c_c > produc621499498um_c_c ).
thf(tp_produc1563404851real_c,type,
produc1563404851real_c: finite1398487019real_c > produc190496183real_c > produc99145217real_c ).
thf(tp_produc1687028567real_c,type,
produc1687028567real_c: produc190496183real_c > produc190496183real_c > produc640052711real_c ).
thf(tp_produc1715747632c_real,type,
produc1715747632c_real: finite1398487019real_c > real > produc133347448c_real ).
thf(tp_produc171591948c_real,type,
produc171591948c_real: produc190496183real_c > real > produc906325778c_real ).
thf(tp_produc1767696108_set_c,type,
produc1767696108_set_c: set_Sum_sum_c_c > set_c > produc802386618_set_c ).
thf(tp_produc181739436_sz_sz,type,
produc181739436_sz_sz: produc861709536_sz_sz > sz ).
thf(tp_produc1822718231_sc_sz,type,
produc1822718231_sc_sz: list_f1238882004_sc_sz > list_f1238882004_sc_sz > produc866628903_sc_sz ).
thf(tp_produc1915663706real_c,type,
produc1915663706real_c: set_sz > set_Fi1407883041real_c > produc729314338real_c ).
thf(tp_produc2010422875real_c,type,
produc2010422875real_c: produc190496183real_c > finite1398487019real_c ).
thf(tp_produc2039118377set_sz,type,
produc2039118377set_sz: set_c > set_sz > produc313687471set_sz ).
thf(tp_produc2069561454_sz_sz,type,
produc2069561454_sz_sz: produc861709536_sz_sz > trm_sf_sz ).
thf(tp_produc2134005810real_c,type,
produc2134005810real_c: real > produc190496183real_c > produc1295591296real_c ).
thf(tp_produc2156889set_sz,type,
produc2156889set_sz: set_sz > set_sz > produc2057661729set_sz ).
thf(tp_produc245128480t_unit,type,
produc245128480t_unit: produc999471430t_unit > produc1821101996_sc_sz ).
thf(tp_produc280329770real_c,type,
produc280329770real_c: set_c > set_Fi1407883041real_c > produc1299700144real_c ).
thf(tp_produc314122909real_c,type,
produc314122909real_c: produc190496183real_c > finite1398487019real_c ).
thf(tp_produc368345510real_c,type,
produc368345510real_c: ( finite1398487019real_c > finite1398487019real_c ) > ( finite1398487019real_c > finite1398487019real_c ) > produc190496183real_c > produc190496183real_c ).
thf(tp_produc394644079real_c,type,
produc394644079real_c: finite1398487019real_c > finite1398487019real_c > produc190496183real_c ).
thf(tp_produc403791768_sc_sz,type,
produc403791768_sc_sz: ( denota610675952t_unit > denota610675952t_unit ) > ( produc866628903_sc_sz > produc866628903_sc_sz ) > produc1821101996_sc_sz > produc1821101996_sc_sz ).
thf(tp_produc4753477_sc_sz,type,
produc4753477_sc_sz: produc866628903_sc_sz > list_f1238882004_sc_sz ).
thf(tp_produc502616768t_unit,type,
produc502616768t_unit: produc866628903_sc_sz > denota610675952t_unit > produc999471430t_unit ).
thf(tp_produc532048446_sc_sz,type,
produc532048446_sc_sz: produc1821101996_sc_sz > produc999471430t_unit ).
thf(tp_produc548504323_sc_sz,type,
produc548504323_sc_sz: produc866628903_sc_sz > list_f1238882004_sc_sz ).
thf(tp_produc590684180um_c_c,type,
produc590684180um_c_c: set_sz > set_Sum_sum_c_c > produc44682460um_c_c ).
thf(tp_produc687319826t_unit,type,
produc687319826t_unit: produc999471430t_unit > denota610675952t_unit ).
thf(tp_produc704157711real_c,type,
produc704157711real_c: produc190496183real_c > produc190496183real_c ).
thf(tp_produc705216881l_real,type,
produc705216881l_real: real > real > produc957004601l_real ).
thf(tp_produc760013927_set_c,type,
produc760013927_set_c: set_sz > set_c > produc1631500469_set_c ).
thf(tp_produc789536734_sc_sz,type,
produc789536734_sc_sz: denota610675952t_unit > produc866628903_sc_sz > produc1821101996_sc_sz ).
thf(tp_produc792909658_sz_sz,type,
produc792909658_sz_sz: trm_sf_sz > sz > produc861709536_sz_sz ).
thf(tp_produc878845847_set_c,type,
produc878845847_set_c: set_c > set_c > produc756982951_set_c ).
thf(tp_produc974239792_sc_sz,type,
produc974239792_sc_sz: produc1821101996_sc_sz > produc866628903_sc_sz ).
thf(tp_prop_sz_sf_sc,type,
prop_sz_sf_sc: sz > ( sz > trm_sf_sz ) > formula_sf_sc_sz ).
thf(tp_right_1933252621rm_a_c,type,
right_1933252621rm_a_c: ( trm_a_c > frechet_strm_a_c > $o ) > $o ).
thf(tp_right_963419005_sf_sz,type,
right_963419005_sf_sz: ( trm_sf_sz > frechet_strm_sf_sz > $o ) > $o ).
thf(tp_sK1_SY26,type,
sK1_SY26: a > ( c > trm_a_c ) > c ).
thf(tp_sK2_SY31,type,
sK2_SY31: a > ( c > trm_a_c ) > c ).
thf(tp_set1_f989022726_sc_sz,type,
set1_f989022726_sc_sz: formula_sf_sc_sz > set_sf ).
thf(tp_set_trm_a_c2,type,
set_trm_a_c2: trm_a_c > set_a ).
thf(tp_set_trm_sf_sz2,type,
set_trm_sf_sz2: trm_sf_sz > set_sf ).
thf(tp_singleton_rel_sf_sz,type,
singleton_rel_sf_sz: produc861709536_sz_sz > produc861709536_sz_sz > $o ).
thf(tp_singleton_sz_sf,type,
singleton_sz_sf: sz > trm_sf_sz > sz > trm_sf_sz ).
thf(tp_static_FVDiff_a_c,type,
static_FVDiff_a_c: trm_a_c > set_Sum_sum_c_c ).
thf(tp_static_FVDiff_sf_sz,type,
static_FVDiff_sf_sz: trm_sf_sz > set_Sum_sum_sz_sz ).
thf(tp_times_a_c,type,
times_a_c: trm_a_c > trm_a_c > trm_a_c ).
thf(tp_times_sf_sz,type,
times_sf_sz: trm_sf_sz > trm_sf_sz > trm_sf_sz ).
thf(tp_top_to1102260780um_c_c,type,
top_to1102260780um_c_c: produc44682460um_c_c ).
thf(tp_top_to1102487922real_c,type,
top_to1102487922real_c: produc729314338real_c ).
thf(tp_top_to1128637210um_c_c,type,
top_to1128637210um_c_c: produc621499498um_c_c ).
thf(tp_top_to1246370329_sz_sz,type,
top_to1246370329_sz_sz: set_Sum_sum_sz_sz ).
thf(tp_top_to1246597548set_sz,type,
top_to1246597548set_sz: produc189019228set_sz ).
thf(tp_top_to1303770207set_sz,type,
top_to1303770207set_sz: produc313687471set_sz ).
thf(tp_top_to1309524330_set_c,type,
top_to1309524330_set_c: produc802386618_set_c ).
thf(tp_top_to1642137041real_c,type,
top_to1642137041real_c: set_Fi1407883041real_c ).
thf(tp_top_to1660572043um_c_c,type,
top_to1660572043um_c_c: set_Sum_sum_c_c ).
thf(tp_top_to1783191648real_c,type,
top_to1783191648real_c: produc1299700144real_c ).
thf(tp_top_to1999610481set_sz,type,
top_to1999610481set_sz: produc2057661729set_sz ).
thf(tp_top_to226056039real_c,type,
top_to226056039real_c: set_Pr1389752855real_c ).
thf(tp_top_to474099557_set_c,type,
top_to474099557_set_c: produc1631500469_set_c ).
thf(tp_top_to543326711_set_c,type,
top_to543326711_set_c: produc756982951_set_c ).
thf(tp_top_top_set_c,type,
top_top_set_c: set_c ).
thf(tp_top_top_set_sz,type,
top_top_set_sz: set_sz ).
thf(tp_var,type,
var: a ).
thf(tp_var_c_a,type,
var_c_a: c > trm_a_c ).
thf(tp_var_sz_sf,type,
var_sz_sf: sz > trm_sf_sz ).
thf(tp_vid1,type,
vid1: sz ).
thf(tp_vid2,type,
vid2: sz ).
thf(tp_vid3,type,
vid3: sz ).
thf(tp_zero_z109254132real_c,type,
zero_z109254132real_c: finite1398487019real_c ).
thf(tp_zero_z1273814959c_real,type,
zero_z1273814959c_real: produc133347448c_real ).
thf(tp_zero_z1506780526real_c,type,
zero_z1506780526real_c: produc190496183real_c ).
thf(tp_zero_z1830236699c_real,type,
zero_z1830236699c_real: produc906325778c_real ).
thf(tp_zero_z440955354real_c,type,
zero_z440955354real_c: produc1952288593real_c ).
thf(tp_zero_z464587567real_c,type,
zero_z464587567real_c: produc1471603704real_c ).
thf(tp_zero_z659284464l_real,type,
zero_z659284464l_real: produc957004601l_real ).
thf(tp_zero_z72018569real_c,type,
zero_z72018569real_c: produc1295591296real_c ).
thf(tp_zero_z735295626real_c,type,
zero_z735295626real_c: produc99145217real_c ).
thf(tp_zero_z993734942real_c,type,
zero_z993734942real_c: produc640052711real_c ).
thf(tp_zero_zero_real,type,
zero_zero_real: real ).
thf(3,axiom,
! [P: $o] :
( ( P = $true )
| ( P = $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_If_001t__Syntax__Otrm_Itf__sf_Mtf__sz_J_T) ).
thf(181,axiom,
! [Theta3: trm_a_c] :
( ( dfree_a_c @ Theta3 )
=> ( dsafe_a_c @ Theta3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_dfree__is__dsafe) ).
thf(250,axiom,
! [R: real] : ( dfree_a_c @ ( const_a_c @ R ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_dfree__Const) ).
thf(252,axiom,
! [R: real] : ( dfree_a_c @ ( const_a_c @ R ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_dfree__Const__simps) ).
thf(288,axiom,
! [I: c] : ( dfree_a_c @ ( var_c_a @ I ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_dfree__Var) ).
thf(291,axiom,
! [Theta_1: trm_a_c,Theta_2: trm_a_c] :
( ( dfree_a_c @ Theta_1 )
=> ( ( dfree_a_c @ Theta_2 )
=> ( dfree_a_c @ ( times_a_c @ Theta_1 @ Theta_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_dfree__Times) ).
thf(293,axiom,
! [Theta_1: trm_a_c,Theta_2: trm_a_c] :
( ( dfree_a_c @ Theta_1 )
=> ( ( dfree_a_c @ Theta_2 )
=> ( dfree_a_c @ ( plus_a_c @ Theta_1 @ Theta_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_dfree__Plus) ).
thf(295,axiom,
! [Args: c > trm_a_c,I: a] :
( ! [I3: c] : ( dfree_a_c @ ( Args @ I3 ) )
=> ( dfree_a_c @ ( function_a_c @ I @ Args ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_dfree_Odfree__Fun) ).
thf(327,axiom,
! [I: a,Args: c > trm_a_c] :
( ( dfree_a_c @ ( function_a_c @ I @ Args ) )
= ( ! [X2: c] : ( dfree_a_c @ ( Args @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_dfree__Fun__simps) ).
thf(342,axiom,
! [A: trm_a_c,B: trm_a_c] :
( ( dfree_a_c @ ( plus_a_c @ A @ B ) )
= ( ( dfree_a_c @ A )
& ( dfree_a_c @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_dfree__Plus__simps) ).
thf(344,axiom,
! [A: trm_a_c,B: trm_a_c] :
( ( dfree_a_c @ ( times_a_c @ A @ B ) )
= ( ( dfree_a_c @ A )
& ( dfree_a_c @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_dfree__Times__simps) ).
thf(346,axiom,
! [X: c] : ( dfree_a_c @ ( var_c_a @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_dfree__Var__simps) ).
thf(347,axiom,
! [X: trm_a_c] :
~ ( dfree_a_c @ ( differential_a_c @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_dfree__Differential__simps) ).
thf(351,axiom,
! [X: c] :
~ ( dfree_a_c @ ( diffVar_c_a @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_dfree__DiffVar__simps) ).
thf(356,axiom,
! [I: c] : ( dfree_a_c @ ( args @ I ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_free) ).
thf(357,conjecture,
dfree_a_c @ ( args @ i2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(358,negated_conjecture,
( ( dfree_a_c @ ( args @ i2 ) )
= $false ),
inference(negate_conjecture,[status(cth)],[357]) ).
thf(359,plain,
( ( dfree_a_c @ ( args @ i2 ) )
= $false ),
inference(unfold_def,[status(thm)],[358]) ).
thf(360,plain,
( ( ! [P: $o] :
( ( P = $true )
| ( P = $false ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(361,plain,
( ( ! [Theta3: trm_a_c] :
( ( dfree_a_c @ Theta3 )
=> ( dsafe_a_c @ Theta3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[181]) ).
thf(362,plain,
( ( ! [R: real] : ( dfree_a_c @ ( const_a_c @ R ) ) )
= $true ),
inference(unfold_def,[status(thm)],[250]) ).
thf(363,plain,
( ( ! [R: real] : ( dfree_a_c @ ( const_a_c @ R ) ) )
= $true ),
inference(unfold_def,[status(thm)],[252]) ).
thf(364,plain,
( ( ! [I: c] : ( dfree_a_c @ ( var_c_a @ I ) ) )
= $true ),
inference(unfold_def,[status(thm)],[288]) ).
thf(365,plain,
( ( ! [Theta_1: trm_a_c,Theta_2: trm_a_c] :
( ( dfree_a_c @ Theta_1 )
=> ( ( dfree_a_c @ Theta_2 )
=> ( dfree_a_c @ ( times_a_c @ Theta_1 @ Theta_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[291]) ).
thf(366,plain,
( ( ! [Theta_1: trm_a_c,Theta_2: trm_a_c] :
( ( dfree_a_c @ Theta_1 )
=> ( ( dfree_a_c @ Theta_2 )
=> ( dfree_a_c @ ( plus_a_c @ Theta_1 @ Theta_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[293]) ).
thf(367,plain,
( ( ! [Args: c > trm_a_c,I: a] :
( ! [I3: c] : ( dfree_a_c @ ( Args @ I3 ) )
=> ( dfree_a_c @ ( function_a_c @ I @ Args ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[295]) ).
thf(368,plain,
( ( ! [I: a,Args: c > trm_a_c] :
( ( dfree_a_c @ ( function_a_c @ I @ Args ) )
= ( ! [X2: c] : ( dfree_a_c @ ( Args @ X2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[327]) ).
thf(369,plain,
( ( ! [A: trm_a_c,B: trm_a_c] :
( ( dfree_a_c @ ( plus_a_c @ A @ B ) )
= ( ( dfree_a_c @ A )
& ( dfree_a_c @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[342]) ).
thf(370,plain,
( ( ! [A: trm_a_c,B: trm_a_c] :
( ( dfree_a_c @ ( times_a_c @ A @ B ) )
= ( ( dfree_a_c @ A )
& ( dfree_a_c @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[344]) ).
thf(371,plain,
( ( ! [X: c] : ( dfree_a_c @ ( var_c_a @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[346]) ).
thf(372,plain,
( ( ! [X: trm_a_c] :
~ ( dfree_a_c @ ( differential_a_c @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[347]) ).
thf(373,plain,
( ( ! [X: c] :
~ ( dfree_a_c @ ( diffVar_c_a @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[351]) ).
thf(374,plain,
( ( ! [I: c] : ( dfree_a_c @ ( args @ I ) ) )
= $true ),
inference(unfold_def,[status(thm)],[356]) ).
thf(375,plain,
( ( ~ ( dfree_a_c @ ( args @ i2 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[359]) ).
thf(376,plain,
( ( ! [I: c] : ( dfree_a_c @ ( args @ I ) ) )
= $true ),
inference(copy,[status(thm)],[374]) ).
thf(377,plain,
( ( ! [X: c] :
~ ( dfree_a_c @ ( diffVar_c_a @ X ) ) )
= $true ),
inference(copy,[status(thm)],[373]) ).
thf(378,plain,
( ( ! [X: trm_a_c] :
~ ( dfree_a_c @ ( differential_a_c @ X ) ) )
= $true ),
inference(copy,[status(thm)],[372]) ).
thf(379,plain,
( ( ! [X: c] : ( dfree_a_c @ ( var_c_a @ X ) ) )
= $true ),
inference(copy,[status(thm)],[371]) ).
thf(380,plain,
( ( ! [A: trm_a_c,B: trm_a_c] :
( ( dfree_a_c @ ( times_a_c @ A @ B ) )
= ( ( dfree_a_c @ A )
& ( dfree_a_c @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[370]) ).
thf(381,plain,
( ( ! [A: trm_a_c,B: trm_a_c] :
( ( dfree_a_c @ ( plus_a_c @ A @ B ) )
= ( ( dfree_a_c @ A )
& ( dfree_a_c @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[369]) ).
thf(382,plain,
( ( ! [I: a,Args: c > trm_a_c] :
( ( dfree_a_c @ ( function_a_c @ I @ Args ) )
= ( ! [X2: c] : ( dfree_a_c @ ( Args @ X2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[368]) ).
thf(383,plain,
( ( ! [Args: c > trm_a_c,I: a] :
( ! [I3: c] : ( dfree_a_c @ ( Args @ I3 ) )
=> ( dfree_a_c @ ( function_a_c @ I @ Args ) ) ) )
= $true ),
inference(copy,[status(thm)],[367]) ).
thf(384,plain,
( ( ! [Theta_1: trm_a_c,Theta_2: trm_a_c] :
( ( dfree_a_c @ Theta_1 )
=> ( ( dfree_a_c @ Theta_2 )
=> ( dfree_a_c @ ( plus_a_c @ Theta_1 @ Theta_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[366]) ).
thf(385,plain,
( ( ! [Theta_1: trm_a_c,Theta_2: trm_a_c] :
( ( dfree_a_c @ Theta_1 )
=> ( ( dfree_a_c @ Theta_2 )
=> ( dfree_a_c @ ( times_a_c @ Theta_1 @ Theta_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[365]) ).
thf(386,plain,
( ( ! [I: c] : ( dfree_a_c @ ( var_c_a @ I ) ) )
= $true ),
inference(copy,[status(thm)],[364]) ).
thf(387,plain,
( ( ! [R: real] : ( dfree_a_c @ ( const_a_c @ R ) ) )
= $true ),
inference(copy,[status(thm)],[363]) ).
thf(388,plain,
( ( ! [R: real] : ( dfree_a_c @ ( const_a_c @ R ) ) )
= $true ),
inference(copy,[status(thm)],[362]) ).
thf(389,plain,
( ( ! [Theta3: trm_a_c] :
( ( dfree_a_c @ Theta3 )
=> ( dsafe_a_c @ Theta3 ) ) )
= $true ),
inference(copy,[status(thm)],[361]) ).
thf(390,plain,
( ( ! [P: $o] :
( ( P = $true )
| ( P = $false ) ) )
= $true ),
inference(copy,[status(thm)],[360]) ).
thf(391,plain,
( ( ~ ( dfree_a_c @ ( args @ i2 ) ) )
= $true ),
inference(copy,[status(thm)],[375]) ).
thf(392,plain,
( ( ! [SX0: c > trm_a_c,SX1: a] :
( ~ ! [SX2: c] : ( dfree_a_c @ ( SX0 @ SX2 ) )
| ( dfree_a_c @ ( function_a_c @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[383]) ).
thf(393,plain,
( ( ! [SX0: trm_a_c,SX1: trm_a_c] :
( ( dfree_a_c @ ( times_a_c @ SX0 @ SX1 ) )
= ( ~ ( ~ ( dfree_a_c @ SX0 )
| ~ ( dfree_a_c @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[380]) ).
thf(394,plain,
( ( ! [SX0: trm_a_c,SX1: trm_a_c] :
( ~ ( dfree_a_c @ SX0 )
| ~ ( dfree_a_c @ SX1 )
| ( dfree_a_c @ ( plus_a_c @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[384]) ).
thf(395,plain,
( ( ! [SX0: trm_a_c] :
( ~ ( dfree_a_c @ SX0 )
| ( dsafe_a_c @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[389]) ).
thf(396,plain,
( ( ! [SX0: trm_a_c,SX1: trm_a_c] :
( ( dfree_a_c @ ( plus_a_c @ SX0 @ SX1 ) )
= ( ~ ( ~ ( dfree_a_c @ SX0 )
| ~ ( dfree_a_c @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[381]) ).
thf(397,plain,
( ( ! [SX0: trm_a_c,SX1: trm_a_c] :
( ~ ( dfree_a_c @ SX0 )
| ~ ( dfree_a_c @ SX1 )
| ( dfree_a_c @ ( times_a_c @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[385]) ).
thf(398,plain,
! [SV1: c] :
( ( dfree_a_c @ ( args @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[376]) ).
thf(399,plain,
! [SV2: c] :
( ( ~ ( dfree_a_c @ ( diffVar_c_a @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[377]) ).
thf(400,plain,
! [SV3: trm_a_c] :
( ( ~ ( dfree_a_c @ ( differential_a_c @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[378]) ).
thf(401,plain,
! [SV4: c] :
( ( dfree_a_c @ ( var_c_a @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[379]) ).
thf(402,plain,
! [SV5: a] :
( ( ! [SY23: c > trm_a_c] :
( ( dfree_a_c @ ( function_a_c @ SV5 @ SY23 ) )
= ( ! [X2: c] : ( dfree_a_c @ ( SY23 @ X2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[382]) ).
thf(403,plain,
! [SV6: c] :
( ( dfree_a_c @ ( var_c_a @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[386]) ).
thf(404,plain,
! [SV7: real] :
( ( dfree_a_c @ ( const_a_c @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(405,plain,
! [SV8: real] :
( ( dfree_a_c @ ( const_a_c @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[388]) ).
thf(406,plain,
! [SV9: $o] :
( ( ( SV9 = $true )
| ( SV9 = $false ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[390]) ).
thf(407,plain,
( ( ( $true = $true )
| ( $true = $false ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[390]) ).
thf(408,plain,
( ( ( $false = $true )
| ( $false = $false ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[390]) ).
thf(409,plain,
( ( dfree_a_c @ ( args @ i2 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[391]) ).
thf(410,plain,
! [SV10: c > trm_a_c] :
( ( ! [SY25: a] :
( ~ ! [SY26: c] : ( dfree_a_c @ ( SV10 @ SY26 ) )
| ( dfree_a_c @ ( function_a_c @ SY25 @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[392]) ).
thf(411,plain,
! [SV11: trm_a_c] :
( ( ! [SY27: trm_a_c] :
( ( dfree_a_c @ ( times_a_c @ SV11 @ SY27 ) )
= ( ~ ( ~ ( dfree_a_c @ SV11 )
| ~ ( dfree_a_c @ SY27 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[393]) ).
thf(412,plain,
! [SV12: trm_a_c] :
( ( ! [SY28: trm_a_c] :
( ~ ( dfree_a_c @ SV12 )
| ~ ( dfree_a_c @ SY28 )
| ( dfree_a_c @ ( plus_a_c @ SV12 @ SY28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[394]) ).
thf(413,plain,
! [SV13: trm_a_c] :
( ( ~ ( dfree_a_c @ SV13 )
| ( dsafe_a_c @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[395]) ).
thf(414,plain,
! [SV14: trm_a_c] :
( ( ! [SY29: trm_a_c] :
( ( dfree_a_c @ ( plus_a_c @ SV14 @ SY29 ) )
= ( ~ ( ~ ( dfree_a_c @ SV14 )
| ~ ( dfree_a_c @ SY29 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(415,plain,
! [SV15: trm_a_c] :
( ( ! [SY30: trm_a_c] :
( ~ ( dfree_a_c @ SV15 )
| ~ ( dfree_a_c @ SY30 )
| ( dfree_a_c @ ( times_a_c @ SV15 @ SY30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(416,plain,
! [SV2: c] :
( ( dfree_a_c @ ( diffVar_c_a @ SV2 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[399]) ).
thf(417,plain,
! [SV3: trm_a_c] :
( ( dfree_a_c @ ( differential_a_c @ SV3 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[400]) ).
thf(418,plain,
! [SV16: c > trm_a_c,SV5: a] :
( ( ( dfree_a_c @ ( function_a_c @ SV5 @ SV16 ) )
= ( ! [SY31: c] : ( dfree_a_c @ ( SV16 @ SY31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(419,plain,
! [SV9: $o] :
( ( ( SV9 = $true )
= $true )
| ( ( SV9 = $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[406]) ).
thf(420,plain,
( ( ( $true = $true )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[407]) ).
thf(421,plain,
( ( ( $false = $true )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[408]) ).
thf(422,plain,
! [SV17: a,SV10: c > trm_a_c] :
( ( ~ ! [SY26: c] : ( dfree_a_c @ ( SV10 @ SY26 ) )
| ( dfree_a_c @ ( function_a_c @ SV17 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[410]) ).
thf(423,plain,
! [SV18: trm_a_c,SV11: trm_a_c] :
( ( ( dfree_a_c @ ( times_a_c @ SV11 @ SV18 ) )
= ( ~ ( ~ ( dfree_a_c @ SV11 )
| ~ ( dfree_a_c @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[411]) ).
thf(424,plain,
! [SV19: trm_a_c,SV12: trm_a_c] :
( ( ~ ( dfree_a_c @ SV12 )
| ~ ( dfree_a_c @ SV19 )
| ( dfree_a_c @ ( plus_a_c @ SV12 @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(425,plain,
! [SV13: trm_a_c] :
( ( ( ~ ( dfree_a_c @ SV13 ) )
= $true )
| ( ( dsafe_a_c @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[413]) ).
thf(426,plain,
! [SV20: trm_a_c,SV14: trm_a_c] :
( ( ( dfree_a_c @ ( plus_a_c @ SV14 @ SV20 ) )
= ( ~ ( ~ ( dfree_a_c @ SV14 )
| ~ ( dfree_a_c @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[414]) ).
thf(427,plain,
! [SV21: trm_a_c,SV15: trm_a_c] :
( ( ~ ( dfree_a_c @ SV15 )
| ~ ( dfree_a_c @ SV21 )
| ( dfree_a_c @ ( times_a_c @ SV15 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[415]) ).
thf(428,plain,
! [SV16: c > trm_a_c,SV5: a] :
( ( ~ ( ( dfree_a_c @ ( function_a_c @ SV5 @ SV16 ) )
| ! [SY31: c] : ( dfree_a_c @ ( SV16 @ SY31 ) ) )
| ~ ( ~ ( dfree_a_c @ ( function_a_c @ SV5 @ SV16 ) )
| ~ ! [SY31: c] : ( dfree_a_c @ ( SV16 @ SY31 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[418]) ).
thf(429,plain,
! [SV16: c > trm_a_c,SV5: a] :
( ( ( dfree_a_c @ ( function_a_c @ SV5 @ SV16 ) )
= ( ! [SY31: c] : ( dfree_a_c @ ( SV16 @ SY31 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[418]) ).
thf(430,plain,
! [SV9: $o] :
( ( ( ~ ( SV9
| $true )
| ~ ( ~ SV9
| ~ $true ) )
= $true )
| ( ( SV9 = $false )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[419]) ).
thf(431,plain,
! [SV9: $o] :
( ( ( SV9 = $true )
= $true )
| ( ( SV9 = $false )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[419]) ).
thf(432,plain,
( ( ( ~ ( $true
| $true )
| ~ ( ~ $true
| ~ $true ) )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[420]) ).
thf(433,plain,
( ( ( $true = $true )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[420]) ).
thf(434,plain,
( ( ( ~ ( $false
| $true )
| ~ ( ~ $false
| ~ $true ) )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[421]) ).
thf(435,plain,
( ( ( $false = $true )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[421]) ).
thf(436,plain,
! [SV17: a,SV10: c > trm_a_c] :
( ( ( ~ ! [SY26: c] : ( dfree_a_c @ ( SV10 @ SY26 ) ) )
= $true )
| ( ( dfree_a_c @ ( function_a_c @ SV17 @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[422]) ).
thf(437,plain,
! [SV18: trm_a_c,SV11: trm_a_c] :
( ( ~ ( ( dfree_a_c @ ( times_a_c @ SV11 @ SV18 ) )
| ~ ( ~ ( dfree_a_c @ SV11 )
| ~ ( dfree_a_c @ SV18 ) ) )
| ~ ( ~ ( dfree_a_c @ ( times_a_c @ SV11 @ SV18 ) )
| ~ ~ ( ~ ( dfree_a_c @ SV11 )
| ~ ( dfree_a_c @ SV18 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[423]) ).
thf(438,plain,
! [SV18: trm_a_c,SV11: trm_a_c] :
( ( ( dfree_a_c @ ( times_a_c @ SV11 @ SV18 ) )
= ( ~ ( ~ ( dfree_a_c @ SV11 )
| ~ ( dfree_a_c @ SV18 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[423]) ).
thf(439,plain,
! [SV19: trm_a_c,SV12: trm_a_c] :
( ( ( ~ ( dfree_a_c @ SV12 ) )
= $true )
| ( ( ~ ( dfree_a_c @ SV19 )
| ( dfree_a_c @ ( plus_a_c @ SV12 @ SV19 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[424]) ).
thf(440,plain,
! [SV13: trm_a_c] :
( ( ( dfree_a_c @ SV13 )
= $false )
| ( ( dsafe_a_c @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[425]) ).
thf(441,plain,
! [SV20: trm_a_c,SV14: trm_a_c] :
( ( ~ ( ( dfree_a_c @ ( plus_a_c @ SV14 @ SV20 ) )
| ~ ( ~ ( dfree_a_c @ SV14 )
| ~ ( dfree_a_c @ SV20 ) ) )
| ~ ( ~ ( dfree_a_c @ ( plus_a_c @ SV14 @ SV20 ) )
| ~ ~ ( ~ ( dfree_a_c @ SV14 )
| ~ ( dfree_a_c @ SV20 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[426]) ).
thf(442,plain,
! [SV20: trm_a_c,SV14: trm_a_c] :
( ( ( dfree_a_c @ ( plus_a_c @ SV14 @ SV20 ) )
= ( ~ ( ~ ( dfree_a_c @ SV14 )
| ~ ( dfree_a_c @ SV20 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[426]) ).
thf(443,plain,
! [SV21: trm_a_c,SV15: trm_a_c] :
( ( ( ~ ( dfree_a_c @ SV15 ) )
= $true )
| ( ( ~ ( dfree_a_c @ SV21 )
| ( dfree_a_c @ ( times_a_c @ SV15 @ SV21 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[427]) ).
thf(444,plain,
! [SV16: c > trm_a_c,SV5: a] :
( ( ( ~ ( ( dfree_a_c @ ( function_a_c @ SV5 @ SV16 ) )
| ! [SY31: c] : ( dfree_a_c @ ( SV16 @ SY31 ) ) ) )
= $true )
| ( ( ~ ( ~ ( dfree_a_c @ ( function_a_c @ SV5 @ SV16 ) )
| ~ ! [SY31: c] : ( dfree_a_c @ ( SV16 @ SY31 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[428]) ).
thf(445,plain,
! [SV9: $o] :
( ( ( ~ ( SV9
| $true ) )
= $true )
| ( ( ~ ( ~ SV9
| ~ $true ) )
= $true )
| ( ( SV9 = $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[430]) ).
thf(446,plain,
! [SV9: $o] :
( ( ( ~ ( SV9
| $false )
| ~ ( ~ SV9
| ~ $false ) )
= $true )
| ( ( SV9 = $true )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[431]) ).
thf(447,plain,
! [SV9: $o] :
( ( ( SV9 = $false )
= $true )
| ( ( SV9 = $true )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[431]) ).
thf(448,plain,
( ( ( ~ ( $true
| $true ) )
= $true )
| ( ( ~ ( ~ $true
| ~ $true ) )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[432]) ).
thf(449,plain,
( ( ( ~ ( $true
| $false )
| ~ ( ~ $true
| ~ $false ) )
= $true )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[433]) ).
thf(450,plain,
( ( ( $true = $false )
= $true )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[433]) ).
thf(451,plain,
( ( ( ~ ( $false
| $true ) )
= $true )
| ( ( ~ ( ~ $false
| ~ $true ) )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[434]) ).
thf(452,plain,
( ( ( ~ ( $false
| $false )
| ~ ( ~ $false
| ~ $false ) )
= $true )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[435]) ).
thf(453,plain,
( ( ( $false = $false )
= $true )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[435]) ).
thf(454,plain,
! [SV17: a,SV10: c > trm_a_c] :
( ( ( ! [SY26: c] : ( dfree_a_c @ ( SV10 @ SY26 ) ) )
= $false )
| ( ( dfree_a_c @ ( function_a_c @ SV17 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[436]) ).
thf(455,plain,
! [SV18: trm_a_c,SV11: trm_a_c] :
( ( ( ~ ( ( dfree_a_c @ ( times_a_c @ SV11 @ SV18 ) )
| ~ ( ~ ( dfree_a_c @ SV11 )
| ~ ( dfree_a_c @ SV18 ) ) ) )
= $true )
| ( ( ~ ( ~ ( dfree_a_c @ ( times_a_c @ SV11 @ SV18 ) )
| ~ ~ ( ~ ( dfree_a_c @ SV11 )
| ~ ( dfree_a_c @ SV18 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[437]) ).
thf(456,plain,
! [SV19: trm_a_c,SV12: trm_a_c] :
( ( ( dfree_a_c @ SV12 )
= $false )
| ( ( ~ ( dfree_a_c @ SV19 )
| ( dfree_a_c @ ( plus_a_c @ SV12 @ SV19 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[439]) ).
thf(457,plain,
! [SV20: trm_a_c,SV14: trm_a_c] :
( ( ( ~ ( ( dfree_a_c @ ( plus_a_c @ SV14 @ SV20 ) )
| ~ ( ~ ( dfree_a_c @ SV14 )
| ~ ( dfree_a_c @ SV20 ) ) ) )
= $true )
| ( ( ~ ( ~ ( dfree_a_c @ ( plus_a_c @ SV14 @ SV20 ) )
| ~ ~ ( ~ ( dfree_a_c @ SV14 )
| ~ ( dfree_a_c @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[441]) ).
thf(458,plain,
! [SV21: trm_a_c,SV15: trm_a_c] :
( ( ( dfree_a_c @ SV15 )
= $false )
| ( ( ~ ( dfree_a_c @ SV21 )
| ( dfree_a_c @ ( times_a_c @ SV15 @ SV21 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[443]) ).
thf(459,plain,
! [SV16: c > trm_a_c,SV5: a] :
( ( ( ( dfree_a_c @ ( function_a_c @ SV5 @ SV16 ) )
| ! [SY31: c] : ( dfree_a_c @ ( SV16 @ SY31 ) ) )
= $false )
| ( ( ~ ( ~ ( dfree_a_c @ ( function_a_c @ SV5 @ SV16 ) )
| ~ ! [SY31: c] : ( dfree_a_c @ ( SV16 @ SY31 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[444]) ).
thf(460,plain,
! [SV9: $o] :
( ( ( SV9
| $true )
= $false )
| ( ( ~ ( ~ SV9
| ~ $true ) )
= $true )
| ( ( SV9 = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[445]) ).
thf(461,plain,
! [SV9: $o] :
( ( ( ~ ( SV9
| $false ) )
= $true )
| ( ( ~ ( ~ SV9
| ~ $false ) )
= $true )
| ( ( SV9 = $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[446]) ).
thf(462,plain,
( ( ( $true
| $true )
= $false )
| ( ( ~ ( ~ $true
| ~ $true ) )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[448]) ).
thf(463,plain,
( ( ( ~ ( $true
| $false ) )
= $true )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[449]) ).
thf(464,plain,
( ( ( $false
| $true )
= $false )
| ( ( ~ ( ~ $false
| ~ $true ) )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[451]) ).
thf(465,plain,
( ( ( ~ ( $false
| $false ) )
= $true )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[452]) ).
thf(466,plain,
! [SV17: a,SV10: c > trm_a_c] :
( ( ( dfree_a_c @ ( SV10 @ ( sK1_SY26 @ SV17 @ SV10 ) ) )
= $false )
| ( ( dfree_a_c @ ( function_a_c @ SV17 @ SV10 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[454]) ).
thf(467,plain,
! [SV18: trm_a_c,SV11: trm_a_c] :
( ( ( ( dfree_a_c @ ( times_a_c @ SV11 @ SV18 ) )
| ~ ( ~ ( dfree_a_c @ SV11 )
| ~ ( dfree_a_c @ SV18 ) ) )
= $false )
| ( ( ~ ( ~ ( dfree_a_c @ ( times_a_c @ SV11 @ SV18 ) )
| ~ ~ ( ~ ( dfree_a_c @ SV11 )
| ~ ( dfree_a_c @ SV18 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[455]) ).
thf(468,plain,
! [SV12: trm_a_c,SV19: trm_a_c] :
( ( ( ~ ( dfree_a_c @ SV19 ) )
= $true )
| ( ( dfree_a_c @ ( plus_a_c @ SV12 @ SV19 ) )
= $true )
| ( ( dfree_a_c @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[456]) ).
thf(469,plain,
! [SV20: trm_a_c,SV14: trm_a_c] :
( ( ( ( dfree_a_c @ ( plus_a_c @ SV14 @ SV20 ) )
| ~ ( ~ ( dfree_a_c @ SV14 )
| ~ ( dfree_a_c @ SV20 ) ) )
= $false )
| ( ( ~ ( ~ ( dfree_a_c @ ( plus_a_c @ SV14 @ SV20 ) )
| ~ ~ ( ~ ( dfree_a_c @ SV14 )
| ~ ( dfree_a_c @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[457]) ).
thf(470,plain,
! [SV15: trm_a_c,SV21: trm_a_c] :
( ( ( ~ ( dfree_a_c @ SV21 ) )
= $true )
| ( ( dfree_a_c @ ( times_a_c @ SV15 @ SV21 ) )
= $true )
| ( ( dfree_a_c @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[458]) ).
thf(471,plain,
! [SV16: c > trm_a_c,SV5: a] :
( ( ( dfree_a_c @ ( function_a_c @ SV5 @ SV16 ) )
= $false )
| ( ( ~ ( ~ ( dfree_a_c @ ( function_a_c @ SV5 @ SV16 ) )
| ~ ! [SY31: c] : ( dfree_a_c @ ( SV16 @ SY31 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[459]) ).
thf(472,plain,
! [SV5: a,SV16: c > trm_a_c] :
( ( ( ! [SY31: c] : ( dfree_a_c @ ( SV16 @ SY31 ) ) )
= $false )
| ( ( ~ ( ~ ( dfree_a_c @ ( function_a_c @ SV5 @ SV16 ) )
| ~ ! [SY31: c] : ( dfree_a_c @ ( SV16 @ SY31 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[459]) ).
thf(473,plain,
! [SV9: $o] :
( ( SV9 = $false )
| ( ( ~ ( ~ SV9
| ~ $true ) )
= $true )
| ( ( SV9 = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[460]) ).
thf(474,plain,
! [SV9: $o] :
( ( $true = $false )
| ( ( ~ ( ~ SV9
| ~ $true ) )
= $true )
| ( ( SV9 = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[460]) ).
thf(475,plain,
! [SV9: $o] :
( ( ( SV9
| $false )
= $false )
| ( ( ~ ( ~ SV9
| ~ $false ) )
= $true )
| ( ( SV9 = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[461]) ).
thf(476,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $true ) )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[462]) ).
thf(477,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $true ) )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[462]) ).
thf(478,plain,
( ( ( $true
| $false )
= $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[463]) ).
thf(479,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $true ) )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[464]) ).
thf(480,plain,
( ( $true = $false )
| ( ( ~ ( ~ $false
| ~ $true ) )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[464]) ).
thf(481,plain,
( ( ( $false
| $false )
= $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[465]) ).
thf(482,plain,
! [SV18: trm_a_c,SV11: trm_a_c] :
( ( ( dfree_a_c @ ( times_a_c @ SV11 @ SV18 ) )
= $false )
| ( ( ~ ( ~ ( dfree_a_c @ ( times_a_c @ SV11 @ SV18 ) )
| ~ ~ ( ~ ( dfree_a_c @ SV11 )
| ~ ( dfree_a_c @ SV18 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[467]) ).
thf(483,plain,
! [SV18: trm_a_c,SV11: trm_a_c] :
( ( ( ~ ( ~ ( dfree_a_c @ SV11 )
| ~ ( dfree_a_c @ SV18 ) ) )
= $false )
| ( ( ~ ( ~ ( dfree_a_c @ ( times_a_c @ SV11 @ SV18 ) )
| ~ ~ ( ~ ( dfree_a_c @ SV11 )
| ~ ( dfree_a_c @ SV18 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[467]) ).
thf(484,plain,
! [SV12: trm_a_c,SV19: trm_a_c] :
( ( ( dfree_a_c @ SV19 )
= $false )
| ( ( dfree_a_c @ ( plus_a_c @ SV12 @ SV19 ) )
= $true )
| ( ( dfree_a_c @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[468]) ).
thf(485,plain,
! [SV20: trm_a_c,SV14: trm_a_c] :
( ( ( dfree_a_c @ ( plus_a_c @ SV14 @ SV20 ) )
= $false )
| ( ( ~ ( ~ ( dfree_a_c @ ( plus_a_c @ SV14 @ SV20 ) )
| ~ ~ ( ~ ( dfree_a_c @ SV14 )
| ~ ( dfree_a_c @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[469]) ).
thf(486,plain,
! [SV20: trm_a_c,SV14: trm_a_c] :
( ( ( ~ ( ~ ( dfree_a_c @ SV14 )
| ~ ( dfree_a_c @ SV20 ) ) )
= $false )
| ( ( ~ ( ~ ( dfree_a_c @ ( plus_a_c @ SV14 @ SV20 ) )
| ~ ~ ( ~ ( dfree_a_c @ SV14 )
| ~ ( dfree_a_c @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[469]) ).
thf(487,plain,
! [SV15: trm_a_c,SV21: trm_a_c] :
( ( ( dfree_a_c @ SV21 )
= $false )
| ( ( dfree_a_c @ ( times_a_c @ SV15 @ SV21 ) )
= $true )
| ( ( dfree_a_c @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[470]) ).
thf(488,plain,
! [SV16: c > trm_a_c,SV5: a] :
( ( ( ~ ( dfree_a_c @ ( function_a_c @ SV5 @ SV16 ) )
| ~ ! [SY31: c] : ( dfree_a_c @ ( SV16 @ SY31 ) ) )
= $false )
| ( ( dfree_a_c @ ( function_a_c @ SV5 @ SV16 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[471]) ).
thf(489,plain,
! [SV5: a,SV16: c > trm_a_c] :
( ( ( dfree_a_c @ ( SV16 @ ( sK2_SY31 @ SV5 @ SV16 ) ) )
= $false )
| ( ( ~ ( ~ ( dfree_a_c @ ( function_a_c @ SV5 @ SV16 ) )
| ~ ! [SY31: c] : ( dfree_a_c @ ( SV16 @ SY31 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[472]) ).
thf(490,plain,
! [SV9: $o] :
( ( ( ~ SV9
| ~ $true )
= $false )
| ( SV9 = $false )
| ( ( SV9 = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[473]) ).
thf(491,plain,
! [SV9: $o] :
( ( ( ~ SV9
| ~ $true )
= $false )
| ( $true = $false )
| ( ( SV9 = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[474]) ).
thf(492,plain,
! [SV9: $o] :
( ( SV9 = $false )
| ( ( ~ ( ~ SV9
| ~ $false ) )
= $true )
| ( ( SV9 = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[475]) ).
thf(493,plain,
! [SV9: $o] :
( ( $false = $false )
| ( ( ~ ( ~ SV9
| ~ $false ) )
= $true )
| ( ( SV9 = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[475]) ).
thf(494,plain,
( ( ( ~ $true
| ~ $true )
= $false )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[476]) ).
thf(495,plain,
( ( ( ~ $true
| ~ $true )
= $false )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[477]) ).
thf(496,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[478]) ).
thf(497,plain,
( ( $false = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[478]) ).
thf(498,plain,
( ( ( ~ $false
| ~ $true )
= $false )
| ( $false = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[479]) ).
thf(499,plain,
( ( ( ~ $false
| ~ $true )
= $false )
| ( $true = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[480]) ).
thf(500,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[481]) ).
thf(501,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[481]) ).
thf(502,plain,
! [SV18: trm_a_c,SV11: trm_a_c] :
( ( ( ~ ( dfree_a_c @ ( times_a_c @ SV11 @ SV18 ) )
| ~ ~ ( ~ ( dfree_a_c @ SV11 )
| ~ ( dfree_a_c @ SV18 ) ) )
= $false )
| ( ( dfree_a_c @ ( times_a_c @ SV11 @ SV18 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[482]) ).
thf(503,plain,
! [SV18: trm_a_c,SV11: trm_a_c] :
( ( ( ~ ( dfree_a_c @ SV11 )
| ~ ( dfree_a_c @ SV18 ) )
= $true )
| ( ( ~ ( ~ ( dfree_a_c @ ( times_a_c @ SV11 @ SV18 ) )
| ~ ~ ( ~ ( dfree_a_c @ SV11 )
| ~ ( dfree_a_c @ SV18 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[483]) ).
thf(504,plain,
! [SV20: trm_a_c,SV14: trm_a_c] :
( ( ( ~ ( dfree_a_c @ ( plus_a_c @ SV14 @ SV20 ) )
| ~ ~ ( ~ ( dfree_a_c @ SV14 )
| ~ ( dfree_a_c @ SV20 ) ) )
= $false )
| ( ( dfree_a_c @ ( plus_a_c @ SV14 @ SV20 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[485]) ).
thf(505,plain,
! [SV20: trm_a_c,SV14: trm_a_c] :
( ( ( ~ ( dfree_a_c @ SV14 )
| ~ ( dfree_a_c @ SV20 ) )
= $true )
| ( ( ~ ( ~ ( dfree_a_c @ ( plus_a_c @ SV14 @ SV20 ) )
| ~ ~ ( ~ ( dfree_a_c @ SV14 )
| ~ ( dfree_a_c @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[486]) ).
thf(506,plain,
! [SV16: c > trm_a_c,SV5: a] :
( ( ( ~ ( dfree_a_c @ ( function_a_c @ SV5 @ SV16 ) ) )
= $false )
| ( ( dfree_a_c @ ( function_a_c @ SV5 @ SV16 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[488]) ).
thf(507,plain,
! [SV5: a,SV16: c > trm_a_c] :
( ( ( ~ ! [SY31: c] : ( dfree_a_c @ ( SV16 @ SY31 ) ) )
= $false )
| ( ( dfree_a_c @ ( function_a_c @ SV5 @ SV16 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[488]) ).
thf(508,plain,
! [SV16: c > trm_a_c,SV5: a] :
( ( ( ~ ( dfree_a_c @ ( function_a_c @ SV5 @ SV16 ) )
| ~ ! [SY31: c] : ( dfree_a_c @ ( SV16 @ SY31 ) ) )
= $false )
| ( ( dfree_a_c @ ( SV16 @ ( sK2_SY31 @ SV5 @ SV16 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[489]) ).
thf(509,plain,
! [SV9: $o] :
( ( ( ~ SV9 ) = $false )
| ( SV9 = $false )
| ( ( SV9 = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[490]) ).
thf(510,plain,
! [SV9: $o] :
( ( ( ~ $true ) = $false )
| ( SV9 = $false )
| ( ( SV9 = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[490]) ).
thf(511,plain,
! [SV9: $o] :
( ( ( ~ SV9 ) = $false )
| ( $true = $false )
| ( ( SV9 = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[491]) ).
thf(512,plain,
! [SV9: $o] :
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( SV9 = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[491]) ).
thf(513,plain,
! [SV9: $o] :
( ( ( ~ SV9
| ~ $false )
= $false )
| ( SV9 = $false )
| ( ( SV9 = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[492]) ).
thf(514,plain,
! [SV9: $o] :
( ( ( ~ SV9
| ~ $false )
= $false )
| ( $false = $false )
| ( ( SV9 = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[493]) ).
thf(515,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[494]) ).
thf(516,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[494]) ).
thf(517,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[495]) ).
thf(518,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[495]) ).
thf(519,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $true = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[496]) ).
thf(520,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $false = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[497]) ).
thf(521,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[498]) ).
thf(522,plain,
( ( ( ~ $true ) = $false )
| ( $false = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[498]) ).
thf(523,plain,
( ( ( ~ $false ) = $false )
| ( $true = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[499]) ).
thf(524,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[499]) ).
thf(525,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[500]) ).
thf(526,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[501]) ).
thf(527,plain,
! [SV18: trm_a_c,SV11: trm_a_c] :
( ( ( ~ ( dfree_a_c @ ( times_a_c @ SV11 @ SV18 ) ) )
= $false )
| ( ( dfree_a_c @ ( times_a_c @ SV11 @ SV18 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[502]) ).
thf(528,plain,
! [SV18: trm_a_c,SV11: trm_a_c] :
( ( ( ~ ~ ( ~ ( dfree_a_c @ SV11 )
| ~ ( dfree_a_c @ SV18 ) ) )
= $false )
| ( ( dfree_a_c @ ( times_a_c @ SV11 @ SV18 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[502]) ).
thf(529,plain,
! [SV18: trm_a_c,SV11: trm_a_c] :
( ( ( ~ ( dfree_a_c @ SV11 ) )
= $true )
| ( ( ~ ( dfree_a_c @ SV18 ) )
= $true )
| ( ( ~ ( ~ ( dfree_a_c @ ( times_a_c @ SV11 @ SV18 ) )
| ~ ~ ( ~ ( dfree_a_c @ SV11 )
| ~ ( dfree_a_c @ SV18 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[503]) ).
thf(530,plain,
! [SV20: trm_a_c,SV14: trm_a_c] :
( ( ( ~ ( dfree_a_c @ ( plus_a_c @ SV14 @ SV20 ) ) )
= $false )
| ( ( dfree_a_c @ ( plus_a_c @ SV14 @ SV20 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[504]) ).
thf(531,plain,
! [SV20: trm_a_c,SV14: trm_a_c] :
( ( ( ~ ~ ( ~ ( dfree_a_c @ SV14 )
| ~ ( dfree_a_c @ SV20 ) ) )
= $false )
| ( ( dfree_a_c @ ( plus_a_c @ SV14 @ SV20 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[504]) ).
thf(532,plain,
! [SV20: trm_a_c,SV14: trm_a_c] :
( ( ( ~ ( dfree_a_c @ SV14 ) )
= $true )
| ( ( ~ ( dfree_a_c @ SV20 ) )
= $true )
| ( ( ~ ( ~ ( dfree_a_c @ ( plus_a_c @ SV14 @ SV20 ) )
| ~ ~ ( ~ ( dfree_a_c @ SV14 )
| ~ ( dfree_a_c @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[505]) ).
thf(533,plain,
! [SV16: c > trm_a_c,SV5: a] :
( ( ( dfree_a_c @ ( function_a_c @ SV5 @ SV16 ) )
= $true )
| ( ( dfree_a_c @ ( function_a_c @ SV5 @ SV16 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[506]) ).
thf(534,plain,
! [SV5: a,SV16: c > trm_a_c] :
( ( ( ! [SY31: c] : ( dfree_a_c @ ( SV16 @ SY31 ) ) )
= $true )
| ( ( dfree_a_c @ ( function_a_c @ SV5 @ SV16 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[507]) ).
thf(535,plain,
! [SV16: c > trm_a_c,SV5: a] :
( ( ( ~ ( dfree_a_c @ ( function_a_c @ SV5 @ SV16 ) ) )
= $false )
| ( ( dfree_a_c @ ( SV16 @ ( sK2_SY31 @ SV5 @ SV16 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[508]) ).
thf(536,plain,
! [SV5: a,SV16: c > trm_a_c] :
( ( ( ~ ! [SY31: c] : ( dfree_a_c @ ( SV16 @ SY31 ) ) )
= $false )
| ( ( dfree_a_c @ ( SV16 @ ( sK2_SY31 @ SV5 @ SV16 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[508]) ).
thf(537,plain,
! [SV9: $o] :
( ( SV9 = $true )
| ( SV9 = $false )
| ( ( SV9 = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[509]) ).
thf(538,plain,
! [SV9: $o] :
( ( $true = $true )
| ( SV9 = $false )
| ( ( SV9 = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[510]) ).
thf(539,plain,
! [SV9: $o] :
( ( SV9 = $true )
| ( $true = $false )
| ( ( SV9 = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[511]) ).
thf(540,plain,
! [SV9: $o] :
( ( $true = $true )
| ( $true = $false )
| ( ( SV9 = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[512]) ).
thf(541,plain,
! [SV9: $o] :
( ( ( ~ SV9 ) = $false )
| ( SV9 = $false )
| ( ( SV9 = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[513]) ).
thf(542,plain,
! [SV9: $o] :
( ( ( ~ $false ) = $false )
| ( SV9 = $false )
| ( ( SV9 = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[513]) ).
thf(543,plain,
! [SV9: $o] :
( ( ( ~ SV9 ) = $false )
| ( $false = $false )
| ( ( SV9 = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[514]) ).
thf(544,plain,
! [SV9: $o] :
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( SV9 = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[514]) ).
thf(545,plain,
( ( $true = $true )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[515]) ).
thf(546,plain,
( ( $true = $true )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[516]) ).
thf(547,plain,
( ( $true = $true )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[517]) ).
thf(548,plain,
( ( $true = $true )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[518]) ).
thf(549,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[519]) ).
thf(550,plain,
( ( ( ~ $false ) = $false )
| ( $true = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[519]) ).
thf(551,plain,
( ( ( ~ $true ) = $false )
| ( $false = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[520]) ).
thf(552,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[520]) ).
thf(553,plain,
( ( $false = $true )
| ( $false = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[521]) ).
thf(554,plain,
( ( $true = $true )
| ( $false = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[522]) ).
thf(555,plain,
( ( $false = $true )
| ( $true = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[523]) ).
thf(556,plain,
( ( $true = $true )
| ( $true = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[524]) ).
thf(557,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[525]) ).
thf(558,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[525]) ).
thf(559,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[526]) ).
thf(560,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[526]) ).
thf(561,plain,
! [SV18: trm_a_c,SV11: trm_a_c] :
( ( ( dfree_a_c @ ( times_a_c @ SV11 @ SV18 ) )
= $true )
| ( ( dfree_a_c @ ( times_a_c @ SV11 @ SV18 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[527]) ).
thf(562,plain,
! [SV18: trm_a_c,SV11: trm_a_c] :
( ( ( ~ ( ~ ( dfree_a_c @ SV11 )
| ~ ( dfree_a_c @ SV18 ) ) )
= $true )
| ( ( dfree_a_c @ ( times_a_c @ SV11 @ SV18 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[528]) ).
thf(563,plain,
! [SV18: trm_a_c,SV11: trm_a_c] :
( ( ( dfree_a_c @ SV11 )
= $false )
| ( ( ~ ( dfree_a_c @ SV18 ) )
= $true )
| ( ( ~ ( ~ ( dfree_a_c @ ( times_a_c @ SV11 @ SV18 ) )
| ~ ~ ( ~ ( dfree_a_c @ SV11 )
| ~ ( dfree_a_c @ SV18 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[529]) ).
thf(564,plain,
! [SV20: trm_a_c,SV14: trm_a_c] :
( ( ( dfree_a_c @ ( plus_a_c @ SV14 @ SV20 ) )
= $true )
| ( ( dfree_a_c @ ( plus_a_c @ SV14 @ SV20 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[530]) ).
thf(565,plain,
! [SV20: trm_a_c,SV14: trm_a_c] :
( ( ( ~ ( ~ ( dfree_a_c @ SV14 )
| ~ ( dfree_a_c @ SV20 ) ) )
= $true )
| ( ( dfree_a_c @ ( plus_a_c @ SV14 @ SV20 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[531]) ).
thf(566,plain,
! [SV20: trm_a_c,SV14: trm_a_c] :
( ( ( dfree_a_c @ SV14 )
= $false )
| ( ( ~ ( dfree_a_c @ SV20 ) )
= $true )
| ( ( ~ ( ~ ( dfree_a_c @ ( plus_a_c @ SV14 @ SV20 ) )
| ~ ~ ( ~ ( dfree_a_c @ SV14 )
| ~ ( dfree_a_c @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[532]) ).
thf(567,plain,
! [SV5: a,SV22: c,SV16: c > trm_a_c] :
( ( ( dfree_a_c @ ( SV16 @ SV22 ) )
= $true )
| ( ( dfree_a_c @ ( function_a_c @ SV5 @ SV16 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[534]) ).
thf(568,plain,
! [SV16: c > trm_a_c,SV5: a] :
( ( ( dfree_a_c @ ( function_a_c @ SV5 @ SV16 ) )
= $true )
| ( ( dfree_a_c @ ( SV16 @ ( sK2_SY31 @ SV5 @ SV16 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[535]) ).
thf(569,plain,
! [SV5: a,SV16: c > trm_a_c] :
( ( ( ! [SY31: c] : ( dfree_a_c @ ( SV16 @ SY31 ) ) )
= $true )
| ( ( dfree_a_c @ ( SV16 @ ( sK2_SY31 @ SV5 @ SV16 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[536]) ).
thf(570,plain,
! [SV9: $o] :
( ( ( ~ ( SV9
| $false )
| ~ ( ~ SV9
| ~ $false ) )
= $true )
| ( SV9 = $false )
| ( SV9 = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[537]) ).
thf(571,plain,
! [SV9: $o] :
( ( ( SV9 = $false )
= $true )
| ( SV9 = $false )
| ( SV9 = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[537]) ).
thf(572,plain,
! [SV9: $o] :
( ( ( ~ ( SV9
| $false )
| ~ ( ~ SV9
| ~ $false ) )
= $true )
| ( SV9 = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[538]) ).
thf(573,plain,
! [SV9: $o] :
( ( ( SV9 = $false )
= $true )
| ( SV9 = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[538]) ).
thf(574,plain,
! [SV9: $o] :
( ( ( ~ ( SV9
| $false )
| ~ ( ~ SV9
| ~ $false ) )
= $true )
| ( $true = $false )
| ( SV9 = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[539]) ).
thf(575,plain,
! [SV9: $o] :
( ( ( SV9 = $false )
= $true )
| ( $true = $false )
| ( SV9 = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[539]) ).
thf(576,plain,
! [SV9: $o] :
( ( ( ~ ( SV9
| $false )
| ~ ( ~ SV9
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[540]) ).
thf(577,plain,
! [SV9: $o] :
( ( ( SV9 = $false )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[540]) ).
thf(578,plain,
! [SV9: $o] :
( ( SV9 = $true )
| ( SV9 = $false )
| ( ( SV9 = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[541]) ).
thf(579,plain,
! [SV9: $o] :
( ( $false = $true )
| ( SV9 = $false )
| ( ( SV9 = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[542]) ).
thf(580,plain,
! [SV9: $o] :
( ( SV9 = $true )
| ( $false = $false )
| ( ( SV9 = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[543]) ).
thf(581,plain,
! [SV9: $o] :
( ( $false = $true )
| ( $false = $false )
| ( ( SV9 = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[544]) ).
thf(582,plain,
( ( ( ~ ( $true
| $false )
| ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[545]) ).
thf(583,plain,
( ( ( $true = $false )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[545]) ).
thf(584,plain,
( ( ( ~ ( $true
| $false )
| ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[546]) ).
thf(585,plain,
( ( ( $true = $false )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[546]) ).
thf(586,plain,
( ( ( ~ ( $true
| $false )
| ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[547]) ).
thf(587,plain,
( ( ( $true = $false )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[547]) ).
thf(588,plain,
( ( ( ~ ( $true
| $false )
| ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[548]) ).
thf(589,plain,
( ( ( $true = $false )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[548]) ).
thf(590,plain,
( ( $true = $true )
| ( $true = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[549]) ).
thf(591,plain,
( ( $false = $true )
| ( $true = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[550]) ).
thf(592,plain,
( ( $true = $true )
| ( $false = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[551]) ).
thf(593,plain,
( ( $false = $true )
| ( $false = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[552]) ).
thf(594,plain,
( ( ( ~ ( $false
| $false )
| ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[553]) ).
thf(595,plain,
( ( ( $false = $false )
= $true )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[553]) ).
thf(596,plain,
( ( ( ~ ( $false
| $false )
| ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[554]) ).
thf(597,plain,
( ( ( $false = $false )
= $true )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[554]) ).
thf(598,plain,
( ( ( ~ ( $false
| $false )
| ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[555]) ).
thf(599,plain,
( ( ( $false = $false )
= $true )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[555]) ).
thf(600,plain,
( ( ( ~ ( $false
| $false )
| ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[556]) ).
thf(601,plain,
( ( ( $false = $false )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[556]) ).
thf(602,plain,
( ( $false = $true )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[557]) ).
thf(603,plain,
( ( $false = $true )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[558]) ).
thf(604,plain,
( ( $false = $true )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[559]) ).
thf(605,plain,
( ( $false = $true )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[560]) ).
thf(606,plain,
! [SV18: trm_a_c,SV11: trm_a_c] :
( ( ( ~ ( dfree_a_c @ SV11 )
| ~ ( dfree_a_c @ SV18 ) )
= $false )
| ( ( dfree_a_c @ ( times_a_c @ SV11 @ SV18 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[562]) ).
thf(607,plain,
! [SV11: trm_a_c,SV18: trm_a_c] :
( ( ( dfree_a_c @ SV18 )
= $false )
| ( ( dfree_a_c @ SV11 )
= $false )
| ( ( ~ ( ~ ( dfree_a_c @ ( times_a_c @ SV11 @ SV18 ) )
| ~ ~ ( ~ ( dfree_a_c @ SV11 )
| ~ ( dfree_a_c @ SV18 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[563]) ).
thf(608,plain,
! [SV20: trm_a_c,SV14: trm_a_c] :
( ( ( ~ ( dfree_a_c @ SV14 )
| ~ ( dfree_a_c @ SV20 ) )
= $false )
| ( ( dfree_a_c @ ( plus_a_c @ SV14 @ SV20 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[565]) ).
thf(609,plain,
! [SV14: trm_a_c,SV20: trm_a_c] :
( ( ( dfree_a_c @ SV20 )
= $false )
| ( ( dfree_a_c @ SV14 )
= $false )
| ( ( ~ ( ~ ( dfree_a_c @ ( plus_a_c @ SV14 @ SV20 ) )
| ~ ~ ( ~ ( dfree_a_c @ SV14 )
| ~ ( dfree_a_c @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[566]) ).
thf(610,plain,
! [SV5: a,SV23: c,SV16: c > trm_a_c] :
( ( ( dfree_a_c @ ( SV16 @ SV23 ) )
= $true )
| ( ( dfree_a_c @ ( SV16 @ ( sK2_SY31 @ SV5 @ SV16 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[569]) ).
thf(611,plain,
! [SV9: $o] :
( ( ( ~ ( SV9
| $false ) )
= $true )
| ( ( ~ ( ~ SV9
| ~ $false ) )
= $true )
| ( SV9 = $false )
| ( SV9 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[570]) ).
thf(612,plain,
! [SV9: $o] :
( ( ( ~ ( SV9
| $false ) )
= $true )
| ( ( ~ ( ~ SV9
| ~ $false ) )
= $true )
| ( SV9 = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[572]) ).
thf(613,plain,
! [SV9: $o] :
( ( ( ~ ( SV9
| $false ) )
= $true )
| ( ( ~ ( ~ SV9
| ~ $false ) )
= $true )
| ( $true = $false )
| ( SV9 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[574]) ).
thf(614,plain,
! [SV9: $o] :
( ( ( ~ ( SV9
| $false ) )
= $true )
| ( ( ~ ( ~ SV9
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[576]) ).
thf(615,plain,
( ( ( ~ ( $true
| $false ) )
= $true )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[582]) ).
thf(616,plain,
( ( ( ~ ( $true
| $false ) )
= $true )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[584]) ).
thf(617,plain,
( ( ( ~ ( $true
| $false ) )
= $true )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[586]) ).
thf(618,plain,
( ( ( ~ ( $true
| $false ) )
= $true )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[588]) ).
thf(619,plain,
( ( ( ~ ( $false
| $false ) )
= $true )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[594]) ).
thf(620,plain,
( ( ( ~ ( $false
| $false ) )
= $true )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[596]) ).
thf(621,plain,
( ( ( ~ ( $false
| $false ) )
= $true )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[598]) ).
thf(622,plain,
( ( ( ~ ( $false
| $false ) )
= $true )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[600]) ).
thf(623,plain,
! [SV18: trm_a_c,SV11: trm_a_c] :
( ( ( ~ ( dfree_a_c @ SV11 ) )
= $false )
| ( ( dfree_a_c @ ( times_a_c @ SV11 @ SV18 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[606]) ).
thf(624,plain,
! [SV11: trm_a_c,SV18: trm_a_c] :
( ( ( ~ ( dfree_a_c @ SV18 ) )
= $false )
| ( ( dfree_a_c @ ( times_a_c @ SV11 @ SV18 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[606]) ).
thf(625,plain,
! [SV18: trm_a_c,SV11: trm_a_c] :
( ( ( ~ ( dfree_a_c @ ( times_a_c @ SV11 @ SV18 ) )
| ~ ~ ( ~ ( dfree_a_c @ SV11 )
| ~ ( dfree_a_c @ SV18 ) ) )
= $false )
| ( ( dfree_a_c @ SV11 )
= $false )
| ( ( dfree_a_c @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[607]) ).
thf(626,plain,
! [SV20: trm_a_c,SV14: trm_a_c] :
( ( ( ~ ( dfree_a_c @ SV14 ) )
= $false )
| ( ( dfree_a_c @ ( plus_a_c @ SV14 @ SV20 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[608]) ).
thf(627,plain,
! [SV14: trm_a_c,SV20: trm_a_c] :
( ( ( ~ ( dfree_a_c @ SV20 ) )
= $false )
| ( ( dfree_a_c @ ( plus_a_c @ SV14 @ SV20 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[608]) ).
thf(628,plain,
! [SV20: trm_a_c,SV14: trm_a_c] :
( ( ( ~ ( dfree_a_c @ ( plus_a_c @ SV14 @ SV20 ) )
| ~ ~ ( ~ ( dfree_a_c @ SV14 )
| ~ ( dfree_a_c @ SV20 ) ) )
= $false )
| ( ( dfree_a_c @ SV14 )
= $false )
| ( ( dfree_a_c @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[609]) ).
thf(629,plain,
! [SV9: $o] :
( ( ( SV9
| $false )
= $false )
| ( ( ~ ( ~ SV9
| ~ $false ) )
= $true )
| ( SV9 = $false )
| ( SV9 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[611]) ).
thf(630,plain,
! [SV9: $o] :
( ( ( SV9
| $false )
= $false )
| ( ( ~ ( ~ SV9
| ~ $false ) )
= $true )
| ( SV9 = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[612]) ).
thf(631,plain,
! [SV9: $o] :
( ( ( SV9
| $false )
= $false )
| ( ( ~ ( ~ SV9
| ~ $false ) )
= $true )
| ( $true = $false )
| ( SV9 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[613]) ).
thf(632,plain,
! [SV9: $o] :
( ( ( SV9
| $false )
= $false )
| ( ( ~ ( ~ SV9
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[614]) ).
thf(633,plain,
( ( ( $true
| $false )
= $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[615]) ).
thf(634,plain,
( ( ( $true
| $false )
= $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[616]) ).
thf(635,plain,
( ( ( $true
| $false )
= $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[617]) ).
thf(636,plain,
( ( ( $true
| $false )
= $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[618]) ).
thf(637,plain,
( ( ( $false
| $false )
= $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[619]) ).
thf(638,plain,
( ( ( $false
| $false )
= $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[620]) ).
thf(639,plain,
( ( ( $false
| $false )
= $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[621]) ).
thf(640,plain,
( ( ( $false
| $false )
= $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[622]) ).
thf(641,plain,
! [SV18: trm_a_c,SV11: trm_a_c] :
( ( ( dfree_a_c @ SV11 )
= $true )
| ( ( dfree_a_c @ ( times_a_c @ SV11 @ SV18 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[623]) ).
thf(642,plain,
! [SV11: trm_a_c,SV18: trm_a_c] :
( ( ( dfree_a_c @ SV18 )
= $true )
| ( ( dfree_a_c @ ( times_a_c @ SV11 @ SV18 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[624]) ).
thf(643,plain,
! [SV18: trm_a_c,SV11: trm_a_c] :
( ( ( ~ ( dfree_a_c @ ( times_a_c @ SV11 @ SV18 ) ) )
= $false )
| ( ( dfree_a_c @ SV11 )
= $false )
| ( ( dfree_a_c @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[625]) ).
thf(644,plain,
! [SV18: trm_a_c,SV11: trm_a_c] :
( ( ( ~ ~ ( ~ ( dfree_a_c @ SV11 )
| ~ ( dfree_a_c @ SV18 ) ) )
= $false )
| ( ( dfree_a_c @ SV11 )
= $false )
| ( ( dfree_a_c @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[625]) ).
thf(645,plain,
! [SV20: trm_a_c,SV14: trm_a_c] :
( ( ( dfree_a_c @ SV14 )
= $true )
| ( ( dfree_a_c @ ( plus_a_c @ SV14 @ SV20 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[626]) ).
thf(646,plain,
! [SV14: trm_a_c,SV20: trm_a_c] :
( ( ( dfree_a_c @ SV20 )
= $true )
| ( ( dfree_a_c @ ( plus_a_c @ SV14 @ SV20 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[627]) ).
thf(647,plain,
! [SV20: trm_a_c,SV14: trm_a_c] :
( ( ( ~ ( dfree_a_c @ ( plus_a_c @ SV14 @ SV20 ) ) )
= $false )
| ( ( dfree_a_c @ SV14 )
= $false )
| ( ( dfree_a_c @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[628]) ).
thf(648,plain,
! [SV20: trm_a_c,SV14: trm_a_c] :
( ( ( ~ ~ ( ~ ( dfree_a_c @ SV14 )
| ~ ( dfree_a_c @ SV20 ) ) )
= $false )
| ( ( dfree_a_c @ SV14 )
= $false )
| ( ( dfree_a_c @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[628]) ).
thf(649,plain,
! [SV9: $o] :
( ( SV9 = $false )
| ( ( ~ ( ~ SV9
| ~ $false ) )
= $true )
| ( SV9 = $false )
| ( SV9 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[629]) ).
thf(650,plain,
! [SV9: $o] :
( ( $false = $false )
| ( ( ~ ( ~ SV9
| ~ $false ) )
= $true )
| ( SV9 = $false )
| ( SV9 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[629]) ).
thf(651,plain,
! [SV9: $o] :
( ( SV9 = $false )
| ( ( ~ ( ~ SV9
| ~ $false ) )
= $true )
| ( SV9 = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[630]) ).
thf(652,plain,
! [SV9: $o] :
( ( $false = $false )
| ( ( ~ ( ~ SV9
| ~ $false ) )
= $true )
| ( SV9 = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[630]) ).
thf(653,plain,
! [SV9: $o] :
( ( SV9 = $false )
| ( ( ~ ( ~ SV9
| ~ $false ) )
= $true )
| ( $true = $false )
| ( SV9 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[631]) ).
thf(654,plain,
! [SV9: $o] :
( ( $false = $false )
| ( ( ~ ( ~ SV9
| ~ $false ) )
= $true )
| ( $true = $false )
| ( SV9 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[631]) ).
thf(655,plain,
! [SV9: $o] :
( ( SV9 = $false )
| ( ( ~ ( ~ SV9
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[632]) ).
thf(656,plain,
! [SV9: $o] :
( ( $false = $false )
| ( ( ~ ( ~ SV9
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[632]) ).
thf(657,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[633]) ).
thf(658,plain,
( ( $false = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[633]) ).
thf(659,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[634]) ).
thf(660,plain,
( ( $false = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[634]) ).
thf(661,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[635]) ).
thf(662,plain,
( ( $false = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[635]) ).
thf(663,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[636]) ).
thf(664,plain,
( ( $false = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[636]) ).
thf(665,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[637]) ).
thf(666,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[637]) ).
thf(667,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[638]) ).
thf(668,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[638]) ).
thf(669,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[639]) ).
thf(670,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[639]) ).
thf(671,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[640]) ).
thf(672,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[640]) ).
thf(673,plain,
! [SV18: trm_a_c,SV11: trm_a_c] :
( ( ( dfree_a_c @ ( times_a_c @ SV11 @ SV18 ) )
= $true )
| ( ( dfree_a_c @ SV11 )
= $false )
| ( ( dfree_a_c @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[643]) ).
thf(674,plain,
! [SV18: trm_a_c,SV11: trm_a_c] :
( ( ( ~ ( ~ ( dfree_a_c @ SV11 )
| ~ ( dfree_a_c @ SV18 ) ) )
= $true )
| ( ( dfree_a_c @ SV11 )
= $false )
| ( ( dfree_a_c @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[644]) ).
thf(675,plain,
! [SV20: trm_a_c,SV14: trm_a_c] :
( ( ( dfree_a_c @ ( plus_a_c @ SV14 @ SV20 ) )
= $true )
| ( ( dfree_a_c @ SV14 )
= $false )
| ( ( dfree_a_c @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[647]) ).
thf(676,plain,
! [SV20: trm_a_c,SV14: trm_a_c] :
( ( ( ~ ( ~ ( dfree_a_c @ SV14 )
| ~ ( dfree_a_c @ SV20 ) ) )
= $true )
| ( ( dfree_a_c @ SV14 )
= $false )
| ( ( dfree_a_c @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[648]) ).
thf(677,plain,
! [SV9: $o] :
( ( ( ~ SV9
| ~ $false )
= $false )
| ( SV9 = $false )
| ( SV9 = $false )
| ( SV9 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[649]) ).
thf(678,plain,
! [SV9: $o] :
( ( ( ~ SV9
| ~ $false )
= $false )
| ( $false = $false )
| ( SV9 = $false )
| ( SV9 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[650]) ).
thf(679,plain,
! [SV9: $o] :
( ( ( ~ SV9
| ~ $false )
= $false )
| ( SV9 = $false )
| ( SV9 = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[651]) ).
thf(680,plain,
! [SV9: $o] :
( ( ( ~ SV9
| ~ $false )
= $false )
| ( $false = $false )
| ( SV9 = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[652]) ).
thf(681,plain,
! [SV9: $o] :
( ( ( ~ SV9
| ~ $false )
= $false )
| ( SV9 = $false )
| ( $true = $false )
| ( SV9 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[653]) ).
thf(682,plain,
! [SV9: $o] :
( ( ( ~ SV9
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( SV9 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[654]) ).
thf(683,plain,
! [SV9: $o] :
( ( ( ~ SV9
| ~ $false )
= $false )
| ( SV9 = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[655]) ).
thf(684,plain,
! [SV9: $o] :
( ( ( ~ SV9
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[656]) ).
thf(685,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[657]) ).
thf(686,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[658]) ).
thf(687,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[659]) ).
thf(688,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[660]) ).
thf(689,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[661]) ).
thf(690,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[662]) ).
thf(691,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[663]) ).
thf(692,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[664]) ).
thf(693,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[665]) ).
thf(694,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[666]) ).
thf(695,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[667]) ).
thf(696,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[668]) ).
thf(697,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[669]) ).
thf(698,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[670]) ).
thf(699,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[671]) ).
thf(700,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[672]) ).
thf(701,plain,
! [SV18: trm_a_c,SV11: trm_a_c] :
( ( ( ~ ( dfree_a_c @ SV11 )
| ~ ( dfree_a_c @ SV18 ) )
= $false )
| ( ( dfree_a_c @ SV11 )
= $false )
| ( ( dfree_a_c @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[674]) ).
thf(702,plain,
! [SV20: trm_a_c,SV14: trm_a_c] :
( ( ( ~ ( dfree_a_c @ SV14 )
| ~ ( dfree_a_c @ SV20 ) )
= $false )
| ( ( dfree_a_c @ SV14 )
= $false )
| ( ( dfree_a_c @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[676]) ).
thf(703,plain,
! [SV9: $o] :
( ( ( ~ SV9 ) = $false )
| ( SV9 = $false )
| ( SV9 = $false )
| ( SV9 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[677]) ).
thf(704,plain,
! [SV9: $o] :
( ( ( ~ $false ) = $false )
| ( SV9 = $false )
| ( SV9 = $false )
| ( SV9 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[677]) ).
thf(705,plain,
! [SV9: $o] :
( ( ( ~ SV9 ) = $false )
| ( $false = $false )
| ( SV9 = $false )
| ( SV9 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[678]) ).
thf(706,plain,
! [SV9: $o] :
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( SV9 = $false )
| ( SV9 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[678]) ).
thf(707,plain,
! [SV9: $o] :
( ( ( ~ SV9 ) = $false )
| ( SV9 = $false )
| ( SV9 = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[679]) ).
thf(708,plain,
! [SV9: $o] :
( ( ( ~ $false ) = $false )
| ( SV9 = $false )
| ( SV9 = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[679]) ).
thf(709,plain,
! [SV9: $o] :
( ( ( ~ SV9 ) = $false )
| ( $false = $false )
| ( SV9 = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[680]) ).
thf(710,plain,
! [SV9: $o] :
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( SV9 = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[680]) ).
thf(711,plain,
! [SV9: $o] :
( ( ( ~ SV9 ) = $false )
| ( SV9 = $false )
| ( $true = $false )
| ( SV9 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[681]) ).
thf(712,plain,
! [SV9: $o] :
( ( ( ~ $false ) = $false )
| ( SV9 = $false )
| ( $true = $false )
| ( SV9 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[681]) ).
thf(713,plain,
! [SV9: $o] :
( ( ( ~ SV9 ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( SV9 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[682]) ).
thf(714,plain,
! [SV9: $o] :
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( SV9 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[682]) ).
thf(715,plain,
! [SV9: $o] :
( ( ( ~ SV9 ) = $false )
| ( SV9 = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[683]) ).
thf(716,plain,
! [SV9: $o] :
( ( ( ~ $false ) = $false )
| ( SV9 = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[683]) ).
thf(717,plain,
! [SV9: $o] :
( ( ( ~ SV9 ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[684]) ).
thf(718,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[684]) ).
thf(719,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[685]) ).
thf(720,plain,
( ( ( ~ $false ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[685]) ).
thf(721,plain,
( ( ( ~ $true ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[686]) ).
thf(722,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[686]) ).
thf(723,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[687]) ).
thf(724,plain,
( ( ( ~ $false ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[687]) ).
thf(725,plain,
( ( ( ~ $true ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[688]) ).
thf(726,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[688]) ).
thf(727,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[689]) ).
thf(728,plain,
( ( ( ~ $false ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[689]) ).
thf(729,plain,
( ( ( ~ $true ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[690]) ).
thf(730,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[690]) ).
thf(731,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[691]) ).
thf(732,plain,
( ( ( ~ $false ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[691]) ).
thf(733,plain,
( ( ( ~ $true ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[692]) ).
thf(734,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[692]) ).
thf(735,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[693]) ).
thf(736,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[693]) ).
thf(737,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[694]) ).
thf(738,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[694]) ).
thf(739,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[695]) ).
thf(740,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[695]) ).
thf(741,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[696]) ).
thf(742,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[696]) ).
thf(743,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[697]) ).
thf(744,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[697]) ).
thf(745,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[698]) ).
thf(746,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[698]) ).
thf(747,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[699]) ).
thf(748,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[699]) ).
thf(749,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[700]) ).
thf(750,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[700]) ).
thf(751,plain,
! [SV18: trm_a_c,SV11: trm_a_c] :
( ( ( ~ ( dfree_a_c @ SV11 ) )
= $false )
| ( ( dfree_a_c @ SV11 )
= $false )
| ( ( dfree_a_c @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[701]) ).
thf(752,plain,
! [SV11: trm_a_c,SV18: trm_a_c] :
( ( ( ~ ( dfree_a_c @ SV18 ) )
= $false )
| ( ( dfree_a_c @ SV11 )
= $false )
| ( ( dfree_a_c @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[701]) ).
thf(753,plain,
! [SV20: trm_a_c,SV14: trm_a_c] :
( ( ( ~ ( dfree_a_c @ SV14 ) )
= $false )
| ( ( dfree_a_c @ SV14 )
= $false )
| ( ( dfree_a_c @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[702]) ).
thf(754,plain,
! [SV14: trm_a_c,SV20: trm_a_c] :
( ( ( ~ ( dfree_a_c @ SV20 ) )
= $false )
| ( ( dfree_a_c @ SV14 )
= $false )
| ( ( dfree_a_c @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[702]) ).
thf(755,plain,
! [SV9: $o] :
( ( SV9 = $true )
| ( SV9 = $false )
| ( SV9 = $false )
| ( SV9 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[703]) ).
thf(756,plain,
! [SV9: $o] :
( ( $false = $true )
| ( SV9 = $false )
| ( SV9 = $false )
| ( SV9 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[704]) ).
thf(757,plain,
! [SV9: $o] :
( ( SV9 = $true )
| ( $false = $false )
| ( SV9 = $false )
| ( SV9 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[705]) ).
thf(758,plain,
! [SV9: $o] :
( ( $false = $true )
| ( $false = $false )
| ( SV9 = $false )
| ( SV9 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[706]) ).
thf(759,plain,
! [SV9: $o] :
( ( SV9 = $true )
| ( SV9 = $false )
| ( SV9 = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[707]) ).
thf(760,plain,
! [SV9: $o] :
( ( $false = $true )
| ( SV9 = $false )
| ( SV9 = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[708]) ).
thf(761,plain,
! [SV9: $o] :
( ( SV9 = $true )
| ( $false = $false )
| ( SV9 = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[709]) ).
thf(762,plain,
! [SV9: $o] :
( ( $false = $true )
| ( $false = $false )
| ( SV9 = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[710]) ).
thf(763,plain,
! [SV9: $o] :
( ( SV9 = $true )
| ( SV9 = $false )
| ( $true = $false )
| ( SV9 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[711]) ).
thf(764,plain,
! [SV9: $o] :
( ( $false = $true )
| ( SV9 = $false )
| ( $true = $false )
| ( SV9 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[712]) ).
thf(765,plain,
! [SV9: $o] :
( ( SV9 = $true )
| ( $false = $false )
| ( $true = $false )
| ( SV9 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[713]) ).
thf(766,plain,
! [SV9: $o] :
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( SV9 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[714]) ).
thf(767,plain,
! [SV9: $o] :
( ( SV9 = $true )
| ( SV9 = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[715]) ).
thf(768,plain,
! [SV9: $o] :
( ( $false = $true )
| ( SV9 = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[716]) ).
thf(769,plain,
! [SV9: $o] :
( ( SV9 = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[717]) ).
thf(770,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[718]) ).
thf(771,plain,
( ( $true = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[719]) ).
thf(772,plain,
( ( $false = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[720]) ).
thf(773,plain,
( ( $true = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[721]) ).
thf(774,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[722]) ).
thf(775,plain,
( ( $true = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[723]) ).
thf(776,plain,
( ( $false = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[724]) ).
thf(777,plain,
( ( $true = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[725]) ).
thf(778,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[726]) ).
thf(779,plain,
( ( $true = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[727]) ).
thf(780,plain,
( ( $false = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[728]) ).
thf(781,plain,
( ( $true = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[729]) ).
thf(782,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[730]) ).
thf(783,plain,
( ( $true = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[731]) ).
thf(784,plain,
( ( $false = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[732]) ).
thf(785,plain,
( ( $true = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[733]) ).
thf(786,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[734]) ).
thf(787,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[735]) ).
thf(788,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[736]) ).
thf(789,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[737]) ).
thf(790,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[738]) ).
thf(791,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[739]) ).
thf(792,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[740]) ).
thf(793,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[741]) ).
thf(794,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[742]) ).
thf(795,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[743]) ).
thf(796,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[744]) ).
thf(797,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[745]) ).
thf(798,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[746]) ).
thf(799,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[747]) ).
thf(800,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[748]) ).
thf(801,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[749]) ).
thf(802,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[750]) ).
thf(803,plain,
! [SV18: trm_a_c,SV11: trm_a_c] :
( ( ( dfree_a_c @ SV11 )
= $true )
| ( ( dfree_a_c @ SV11 )
= $false )
| ( ( dfree_a_c @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[751]) ).
thf(804,plain,
! [SV11: trm_a_c,SV18: trm_a_c] :
( ( ( dfree_a_c @ SV18 )
= $true )
| ( ( dfree_a_c @ SV11 )
= $false )
| ( ( dfree_a_c @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[752]) ).
thf(805,plain,
! [SV20: trm_a_c,SV14: trm_a_c] :
( ( ( dfree_a_c @ SV14 )
= $true )
| ( ( dfree_a_c @ SV14 )
= $false )
| ( ( dfree_a_c @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[753]) ).
thf(806,plain,
! [SV14: trm_a_c,SV20: trm_a_c] :
( ( ( dfree_a_c @ SV20 )
= $true )
| ( ( dfree_a_c @ SV14 )
= $false )
| ( ( dfree_a_c @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[754]) ).
thf(807,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[398,806,805,804,803,802,801,800,799,798,797,796,795,794,793,792,791,790,789,788,787,786,785,784,783,782,781,780,779,778,777,776,775,774,773,772,771,770,769,768,767,766,765,764,763,762,761,760,759,758,757,756,755,675,673,646,645,642,641,610,605,604,603,602,601,599,597,595,593,592,591,590,589,587,585,583,581,580,579,578,577,575,573,571,568,567,564,561,533,487,484,466,453,450,447,442,440,438,429,417,416,409,405,404,403,401]) ).
thf(808,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[807]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP037^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.05/0.17 % Computer : n011.cluster.edu
% 0.05/0.17 % Model : x86_64 x86_64
% 0.05/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.17 % Memory : 8046.5625MB
% 0.05/0.17 % OS : Linux 6.8.0-71-generic
% 0.05/0.17 % CPULimit : 300
% 0.05/0.17 % WCLimit : 300
% 0.05/0.17 % DateTime : Tue Oct 6 11:14:51 UTC 2026
% 0.05/0.17 % CPUTime :
% 0.05/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.26/0.47 ..
% 1.26/0.47
% 1.26/0.47 No.of.Axioms: 15
% 1.26/0.47
% 1.26/0.47 Length.of.Defs: 0
% 1.26/0.47
% 1.26/0.47 Contains.Choice.Funs: false
% 1.26/0.47 ........
% 1.26/0.47
% 1.26/0.47 ********************************
% 1.26/0.47 * All subproblems solved! *
% 1.26/0.47 ********************************
% 1.26/0.47 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:15,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:807,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.26/0.47
% 1.26/0.47 %**** Beginning of derivation protocol ****
% 1.26/0.47 % SZS output start CNFRefutation
% See solution above
% 1.26/0.47
% 1.26/0.47 %**** End of derivation protocol ****
% 1.26/0.47 %**** no. of clauses in derivation: 467 ****
% 1.26/0.47 %**** clause counter: 807 ****
% 1.26/0.47
% 1.26/0.47 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:15,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:807,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------