TSTP Solution File: ALG257^1 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : ALG257^1 : TPTP v8.2.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 18:05:53 EDT 2024
% Result : Theorem 0.20s 0.55s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 94
% Syntax : Number of formulae : 107 ( 11 unt; 61 typ; 0 def)
% Number of atoms : 263 ( 133 equ; 0 cnn)
% Maximal formula atoms : 60 ( 5 avg)
% Number of connectives : 1798 ( 95 ~; 143 |; 78 &;1247 @)
% ( 31 <=>; 204 =>; 0 <=; 0 <~>)
% Maximal formula depth : 140 ( 10 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 66 ( 66 >; 0 *; 0 +; 0 <<)
% Number of symbols : 61 ( 59 usr; 39 con; 0-4 aty)
% Number of variables : 353 ( 4 ^ 349 !; 0 ?; 353 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
term: $tType ).
thf(decl_sort2,type,
subst: $tType ).
thf(decl_22,type,
one: term ).
thf(decl_23,type,
ap: term > term > term ).
thf(decl_24,type,
lam: term > term ).
thf(decl_25,type,
sub: term > subst > term ).
thf(decl_26,type,
id: subst ).
thf(decl_27,type,
sh: subst ).
thf(decl_28,type,
push: term > subst > subst ).
thf(decl_29,type,
comp: subst > subst > subst ).
thf(decl_30,type,
var: term > $o ).
thf(decl_33,type,
axmap: $o ).
thf(decl_35,type,
shinj: $o ).
thf(decl_38,type,
hoasap: subst > term > subst > term > term ).
thf(decl_39,type,
induction2lem: $o ).
thf(decl_41,type,
axvarshift: $o ).
thf(decl_42,type,
hoasapinj2: $o ).
thf(decl_44,type,
hoasapinj1: $o ).
thf(decl_45,type,
ulamvar1: $o ).
thf(decl_48,type,
apnotvar: $o ).
thf(decl_67,type,
axapp: $o ).
thf(decl_71,type,
ulamvarind: $o ).
thf(decl_72,type,
induction: $o ).
thf(decl_82,type,
axclos: $o ).
thf(decl_83,type,
axassoc: $o ).
thf(decl_86,type,
apinj2: $o ).
thf(decl_87,type,
apinj1: $o ).
thf(decl_92,type,
axvarcons: $o ).
thf(decl_94,type,
axscons: $o ).
thf(decl_96,type,
axidr: $o ).
thf(decl_98,type,
laminj: $o ).
thf(decl_102,type,
axabs: $o ).
thf(decl_105,type,
hoasapinj2_gthm: $o ).
thf(decl_108,type,
lamnotap: $o ).
thf(decl_111,type,
axidl: $o ).
thf(decl_116,type,
pushprop: $o ).
thf(decl_120,type,
substmonoid: $o ).
thf(decl_121,type,
lamnotvar: $o ).
thf(decl_130,type,
ulamvarsh: $o ).
thf(decl_131,type,
induction2: $o ).
thf(decl_136,type,
axshiftcons: $o ).
thf(decl_137,type,
termmset: $o ).
thf(decl_142,type,
axvarid: $o ).
thf(decl_144,type,
esk1_1: ( term > $o ) > term ).
thf(decl_145,type,
esk2_1: ( term > $o ) > term ).
thf(decl_146,type,
esk3_1: ( term > $o ) > term ).
thf(decl_147,type,
esk4_1: ( term > $o ) > term ).
thf(decl_148,type,
esk5_1: ( term > $o ) > term ).
thf(decl_149,type,
esk6_3: ( term > $o ) > term > subst > term ).
thf(decl_150,type,
esk7_1: ( term > $o ) > term ).
thf(decl_151,type,
esk8_1: ( term > $o ) > term ).
thf(decl_152,type,
esk9_1: ( term > $o ) > term ).
thf(decl_153,type,
esk10_3: ( term > $o ) > term > subst > term ).
thf(decl_154,type,
esk11_1: ( term > $o ) > term ).
thf(decl_155,type,
esk12_1: ( term > $o ) > term ).
thf(decl_156,type,
esk13_1: ( term > $o ) > term ).
thf(decl_157,type,
esk14_1: ( term > $o ) > term ).
thf(decl_158,type,
esk15_0: term ).
thf(decl_159,type,
esk16_0: term ).
thf(decl_160,type,
esk17_0: term ).
thf(decl_161,type,
esk18_0: term ).
thf(hoasapinj2_gthm,axiom,
( hoasapinj2_gthm
<=> ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> hoasapinj2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',hoasapinj2_gthm) ).
thf(axapp,axiom,
( axapp
<=> ! [X1: term,X2: term,X3: subst] :
( ( sub @ ( ap @ X1 @ X2 ) @ X3 )
= ( ap @ ( sub @ X1 @ X3 ) @ ( sub @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axapp) ).
thf(axvarcons,axiom,
( axvarcons
<=> ! [X1: term,X3: subst] :
( ( sub @ one @ ( push @ X1 @ X3 ) )
= X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axvarcons) ).
thf(axvarid,axiom,
( axvarid
<=> ! [X1: term] :
( ( sub @ X1 @ id )
= X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axvarid) ).
thf(axabs,axiom,
( axabs
<=> ! [X1: term,X3: subst] :
( ( sub @ ( lam @ X1 ) @ X3 )
= ( lam @ ( sub @ X1 @ ( push @ one @ ( comp @ X3 @ sh ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axabs) ).
thf(axclos,axiom,
( axclos
<=> ! [X1: term,X3: subst,X4: subst] :
( ( sub @ ( sub @ X1 @ X3 ) @ X4 )
= ( sub @ X1 @ ( comp @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axclos) ).
thf(axidl,axiom,
( axidl
<=> ! [X3: subst] :
( ( comp @ id @ X3 )
= X3 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axidl) ).
thf(axshiftcons,axiom,
( axshiftcons
<=> ! [X1: term,X3: subst] :
( ( comp @ sh @ ( push @ X1 @ X3 ) )
= X3 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axshiftcons) ).
thf(axassoc,axiom,
( axassoc
<=> ! [X3: subst,X4: subst,X5: subst] :
( ( comp @ ( comp @ X3 @ X4 ) @ X5 )
= ( comp @ X3 @ ( comp @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axassoc) ).
thf(axmap,axiom,
( axmap
<=> ! [X1: term,X3: subst,X4: subst] :
( ( comp @ ( push @ X1 @ X3 ) @ X4 )
= ( push @ ( sub @ X1 @ X4 ) @ ( comp @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axmap) ).
thf(axidr,axiom,
( axidr
<=> ! [X3: subst] :
( ( comp @ X3 @ id )
= X3 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axidr) ).
thf(axvarshift,axiom,
( axvarshift
<=> ( ( push @ one @ sh )
= id ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axvarshift) ).
thf(axscons,axiom,
( axscons
<=> ! [X3: subst] :
( ( push @ ( sub @ one @ X3 ) @ ( comp @ sh @ X3 ) )
= X3 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axscons) ).
thf(ulamvar1,axiom,
( ulamvar1
<=> ( var @ one ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',ulamvar1) ).
thf(ulamvarsh,axiom,
( ulamvarsh
<=> ! [X1: term] :
( ( var @ X1 )
=> ( var @ ( sub @ X1 @ sh ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',ulamvarsh) ).
thf(ulamvarind,axiom,
( ulamvarind
<=> ! [X6: term > $o] :
( ( X6 @ one )
=> ( ! [X1: term] :
( ( var @ X1 )
=> ( ( X6 @ X1 )
=> ( X6 @ ( sub @ X1 @ sh ) ) ) )
=> ! [X1: term] :
( ( var @ X1 )
=> ( X6 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',ulamvarind) ).
thf(apinj1,axiom,
( apinj1
<=> ! [X1: term,X2: term,X7: term,X8: term] :
( ( ( ap @ X1 @ X7 )
= ( ap @ X2 @ X8 ) )
=> ( X1 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',apinj1) ).
thf(apinj2,axiom,
( apinj2
<=> ! [X1: term,X2: term,X7: term,X8: term] :
( ( ( ap @ X1 @ X7 )
= ( ap @ X2 @ X8 ) )
=> ( X7 = X8 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',apinj2) ).
thf(laminj,axiom,
( laminj
<=> ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',laminj) ).
thf(shinj,axiom,
( shinj
<=> ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',shinj) ).
thf(lamnotap,axiom,
( lamnotap
<=> ! [X1: term,X2: term,X7: term] :
( ( lam @ X1 )
!= ( ap @ X2 @ X7 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',lamnotap) ).
thf(apnotvar,axiom,
( apnotvar
<=> ! [X1: term,X2: term] :
~ ( var @ ( ap @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',apnotvar) ).
thf(lamnotvar,axiom,
( lamnotvar
<=> ! [X1: term] :
~ ( var @ ( lam @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',lamnotvar) ).
thf(induction,axiom,
( induction
<=> ! [X6: term > $o] :
( ! [X1: term] :
( ( var @ X1 )
=> ( X6 @ X1 ) )
=> ( ! [X1: term,X2: term] :
( ( X6 @ X1 )
=> ( ( X6 @ X2 )
=> ( X6 @ ( ap @ X1 @ X2 ) ) ) )
=> ( ! [X1: term] :
( ( X6 @ X1 )
=> ( X6 @ ( lam @ X1 ) ) )
=> ! [X1: term] : ( X6 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',induction) ).
thf(pushprop,axiom,
( pushprop
<=> ! [X6: term > $o,X1: term,X3: subst] :
( ! [X2: term] :
( ( var @ X2 )
=> ( X6 @ ( sub @ X2 @ X3 ) ) )
=> ( ( X6 @ X1 )
=> ! [X2: term] :
( ( var @ X2 )
=> ( X6 @ ( sub @ X2 @ ( push @ X1 @ X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',pushprop) ).
thf(induction2lem,axiom,
( induction2lem
<=> ! [X6: term > $o] :
( ! [X1: term,X2: term] :
( ( X6 @ X1 )
=> ( ( X6 @ X2 )
=> ( X6 @ ( ap @ X1 @ X2 ) ) ) )
=> ( ! [X1: term] :
( ! [X2: term] :
( ( X6 @ X2 )
=> ( X6 @ ( sub @ X1 @ ( push @ X2 @ id ) ) ) )
=> ( X6 @ ( lam @ X1 ) ) )
=> ! [X1: term,X3: subst] :
( ! [X2: term] :
( ( var @ X2 )
=> ( X6 @ ( sub @ X2 @ X3 ) ) )
=> ( X6 @ ( sub @ X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',induction2lem) ).
thf(induction2,axiom,
( induction2
<=> ! [X6: term > $o] :
( ! [X1: term] :
( ( var @ X1 )
=> ( X6 @ X1 ) )
=> ( ! [X1: term,X2: term] :
( ( X6 @ X1 )
=> ( ( X6 @ X2 )
=> ( X6 @ ( ap @ X1 @ X2 ) ) ) )
=> ( ! [X1: term] :
( ! [X2: term] :
( ( X6 @ X2 )
=> ( X6 @ ( sub @ X1 @ ( push @ X2 @ id ) ) ) )
=> ( X6 @ ( lam @ X1 ) ) )
=> ! [X1: term] : ( X6 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',induction2) ).
thf(substmonoid,axiom,
( substmonoid
<=> ( ! [X3: subst,X4: subst,X5: subst] :
( ( comp @ ( comp @ X3 @ X4 ) @ X5 )
= ( comp @ X3 @ ( comp @ X4 @ X5 ) ) )
& ! [X3: subst] :
( ( comp @ id @ X3 )
= X3 )
& ! [X3: subst] :
( ( comp @ X3 @ id )
= X3 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',substmonoid) ).
thf(termmset,axiom,
( termmset
<=> ( ! [X1: term,X3: subst,X4: subst] :
( ( sub @ ( sub @ X1 @ X3 ) @ X4 )
= ( sub @ X1 @ ( comp @ X3 @ X4 ) ) )
& ! [X1: term] :
( ( sub @ X1 @ id )
= X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',termmset) ).
thf(hoasapinj1,axiom,
( hoasapinj1
<=> ! [X1: term,X2: term,X7: term,X8: term] :
( ( ( hoasap @ id @ X1 @ id @ X7 )
= ( hoasap @ id @ X2 @ id @ X8 ) )
=> ( X1 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',hoasapinj1) ).
thf(hoasapinj2,axiom,
( hoasapinj2
<=> ! [X1: term,X2: term,X7: term,X8: term] :
( ( ( hoasap @ id @ X1 @ id @ X7 )
= ( hoasap @ id @ X2 @ id @ X8 ) )
=> ( X7 = X8 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',hoasapinj2) ).
thf(thm,conjecture,
hoasapinj2_gthm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(hoasap,axiom,
( hoasap
= ( ^ [X3: subst,X1: term,X4: subst,X2: term] : ( ap @ ( sub @ X1 @ X4 ) @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',hoasap) ).
thf(c_0_33,axiom,
( hoasapinj2_gthm
= ( ! [X2261: term,X2262: term,X2263: subst] :
( ( sub @ ( ap @ X2261 @ X2262 ) @ X2263 )
= ( ap @ ( sub @ X2261 @ X2263 ) @ ( sub @ X2262 @ X2263 ) ) )
=> ( ! [X2264: term,X2265: subst] :
( ( sub @ one @ ( push @ X2264 @ X2265 ) )
= X2264 )
=> ( ! [X2266: term] :
( ( sub @ X2266 @ id )
= X2266 )
=> ( ! [X2267: term,X2268: subst] :
( ( sub @ ( lam @ X2267 ) @ X2268 )
= ( lam @ ( sub @ X2267 @ ( push @ one @ ( comp @ X2268 @ sh ) ) ) ) )
=> ( ! [X2269: term,X2270: subst,X2271: subst] :
( ( sub @ ( sub @ X2269 @ X2270 ) @ X2271 )
= ( sub @ X2269 @ ( comp @ X2270 @ X2271 ) ) )
=> ( ! [X2272: subst] :
( ( comp @ id @ X2272 )
= X2272 )
=> ( ! [X2273: term,X2274: subst] :
( ( comp @ sh @ ( push @ X2273 @ X2274 ) )
= X2274 )
=> ( ! [X2275: subst,X2276: subst,X2277: subst] :
( ( comp @ ( comp @ X2275 @ X2276 ) @ X2277 )
= ( comp @ X2275 @ ( comp @ X2276 @ X2277 ) ) )
=> ( ! [X2278: term,X2279: subst,X2280: subst] :
( ( comp @ ( push @ X2278 @ X2279 ) @ X2280 )
= ( push @ ( sub @ X2278 @ X2280 ) @ ( comp @ X2279 @ X2280 ) ) )
=> ( ! [X2281: subst] :
( ( comp @ X2281 @ id )
= X2281 )
=> ( ( ( push @ one @ sh )
= id )
=> ( ! [X2282: subst] :
( ( push @ ( sub @ one @ X2282 ) @ ( comp @ sh @ X2282 ) )
= X2282 )
=> ( ( var @ one )
=> ( ! [X2283: term] :
( ( var @ X2283 )
=> ( var @ ( sub @ X2283 @ sh ) ) )
=> ( ! [X2284: term > $o] :
( ( X2284 @ one )
=> ( ! [X2285: term] :
( ( var @ X2285 )
=> ( ( X2284 @ X2285 )
=> ( X2284 @ ( sub @ X2285 @ sh ) ) ) )
=> ! [X2286: term] :
( ( var @ X2286 )
=> ( X2284 @ X2286 ) ) ) )
=> ( ! [X2287: term,X2288: term,X2289: term,X2290: term] :
( ( ( ap @ X2287 @ X2289 )
= ( ap @ X2288 @ X2290 ) )
=> ( X2287 = X2288 ) )
=> ( ! [X2291: term,X2292: term,X2293: term,X2294: term] :
( ( ( ap @ X2291 @ X2293 )
= ( ap @ X2292 @ X2294 ) )
=> ( X2293 = X2294 ) )
=> ( ! [X2295: term,X2296: term] :
( ( ( lam @ X2295 )
= ( lam @ X2296 ) )
=> ( X2295 = X2296 ) )
=> ( ! [X2297: term,X2298: term] :
( ( ( sub @ X2297 @ sh )
= ( sub @ X2298 @ sh ) )
=> ( X2297 = X2298 ) )
=> ( ! [X2299: term,X2300: term,X2301: term] :
( ( lam @ X2299 )
!= ( ap @ X2300 @ X2301 ) )
=> ( ! [X2302: term,X2303: term] :
~ ( var @ ( ap @ X2302 @ X2303 ) )
=> ( ! [X2304: term] :
~ ( var @ ( lam @ X2304 ) )
=> ( ! [X2305: term > $o] :
( ! [X2306: term] :
( ( var @ X2306 )
=> ( X2305 @ X2306 ) )
=> ( ! [X2307: term,X2308: term] :
( ( X2305 @ X2307 )
=> ( ( X2305 @ X2308 )
=> ( X2305 @ ( ap @ X2307 @ X2308 ) ) ) )
=> ( ! [X2309: term] :
( ( X2305 @ X2309 )
=> ( X2305 @ ( lam @ X2309 ) ) )
=> ! [X2310: term] : ( X2305 @ X2310 ) ) ) )
=> ( ! [X2311: term > $o,X2312: term,X2313: subst] :
( ! [X2314: term] :
( ( var @ X2314 )
=> ( X2311 @ ( sub @ X2314 @ X2313 ) ) )
=> ( ( X2311 @ X2312 )
=> ! [X2315: term] :
( ( var @ X2315 )
=> ( X2311 @ ( sub @ X2315 @ ( push @ X2312 @ X2313 ) ) ) ) ) )
=> ( ! [X2316: term > $o] :
( ! [X2317: term,X2318: term] :
( ( X2316 @ X2317 )
=> ( ( X2316 @ X2318 )
=> ( X2316 @ ( ap @ X2317 @ X2318 ) ) ) )
=> ( ! [X2319: term] :
( ! [X2320: term] :
( ( X2316 @ X2320 )
=> ( X2316 @ ( sub @ X2319 @ ( push @ X2320 @ id ) ) ) )
=> ( X2316 @ ( lam @ X2319 ) ) )
=> ! [X2321: term,X2322: subst] :
( ! [X2323: term] :
( ( var @ X2323 )
=> ( X2316 @ ( sub @ X2323 @ X2322 ) ) )
=> ( X2316 @ ( sub @ X2321 @ X2322 ) ) ) ) )
=> ( ! [X2324: term > $o] :
( ! [X2325: term] :
( ( var @ X2325 )
=> ( X2324 @ X2325 ) )
=> ( ! [X2326: term,X2327: term] :
( ( X2324 @ X2326 )
=> ( ( X2324 @ X2327 )
=> ( X2324 @ ( ap @ X2326 @ X2327 ) ) ) )
=> ( ! [X2328: term] :
( ! [X2329: term] :
( ( X2324 @ X2329 )
=> ( X2324 @ ( sub @ X2328 @ ( push @ X2329 @ id ) ) ) )
=> ( X2324 @ ( lam @ X2328 ) ) )
=> ! [X2330: term] : ( X2324 @ X2330 ) ) ) )
=> ( ( ! [X2331: subst,X2332: subst,X2333: subst] :
( ( comp @ ( comp @ X2331 @ X2332 ) @ X2333 )
= ( comp @ X2331 @ ( comp @ X2332 @ X2333 ) ) )
& ! [X2334: subst] :
( ( comp @ id @ X2334 )
= X2334 )
& ! [X2335: subst] :
( ( comp @ X2335 @ id )
= X2335 ) )
=> ( ( ! [X2336: term,X2337: subst,X2338: subst] :
( ( sub @ ( sub @ X2336 @ X2337 ) @ X2338 )
= ( sub @ X2336 @ ( comp @ X2337 @ X2338 ) ) )
& ! [X2339: term] :
( ( sub @ X2339 @ id )
= X2339 ) )
=> ( ! [X2340: term,X2341: term,X2342: term,X2343: term] :
( ( ( hoasap @ id @ X2340 @ id @ X2342 )
= ( hoasap @ id @ X2341 @ id @ X2343 ) )
=> ( X2340 = X2341 ) )
=> ! [X2344: term,X2345: term,X2346: term,X2347: term] :
( ( ( hoasap @ id @ X2344 @ id @ X2346 )
= ( hoasap @ id @ X2345 @ id @ X2347 ) )
=> ( X2346 = X2347 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[hoasapinj2_gthm,axapp]),axvarcons]),axvarid]),axabs]),axclos]),axidl]),axshiftcons]),axassoc]),axmap]),axidr]),axvarshift]),axscons]),ulamvar1]),ulamvarsh]),ulamvarind]),apinj1]),apinj2]),laminj]),shinj]),lamnotap]),apnotvar]),lamnotvar]),induction]),pushprop]),induction2lem]),induction2]),substmonoid]),termmset]),hoasapinj1]),hoasapinj2]) ).
thf(c_0_34,negated_conjecture,
~ ( ! [X3373: term,X3374: term,X3375: subst] :
( ( sub @ ( ap @ X3373 @ X3374 ) @ X3375 )
= ( ap @ ( sub @ X3373 @ X3375 ) @ ( sub @ X3374 @ X3375 ) ) )
=> ( ! [X3376: term,X3377: subst] :
( ( sub @ one @ ( push @ X3376 @ X3377 ) )
= X3376 )
=> ( ! [X3378: term] :
( ( sub @ X3378 @ id )
= X3378 )
=> ( ! [X3379: term,X3380: subst] :
( ( sub @ ( lam @ X3379 ) @ X3380 )
= ( lam @ ( sub @ X3379 @ ( push @ one @ ( comp @ X3380 @ sh ) ) ) ) )
=> ( ! [X3381: term,X3382: subst,X3383: subst] :
( ( sub @ ( sub @ X3381 @ X3382 ) @ X3383 )
= ( sub @ X3381 @ ( comp @ X3382 @ X3383 ) ) )
=> ( ! [X3384: subst] :
( ( comp @ id @ X3384 )
= X3384 )
=> ( ! [X3385: term,X3386: subst] :
( ( comp @ sh @ ( push @ X3385 @ X3386 ) )
= X3386 )
=> ( ! [X3387: subst,X3388: subst,X3389: subst] :
( ( comp @ ( comp @ X3387 @ X3388 ) @ X3389 )
= ( comp @ X3387 @ ( comp @ X3388 @ X3389 ) ) )
=> ( ! [X3390: term,X3391: subst,X3392: subst] :
( ( comp @ ( push @ X3390 @ X3391 ) @ X3392 )
= ( push @ ( sub @ X3390 @ X3392 ) @ ( comp @ X3391 @ X3392 ) ) )
=> ( ! [X3393: subst] :
( ( comp @ X3393 @ id )
= X3393 )
=> ( ( ( push @ one @ sh )
= id )
=> ( ! [X3394: subst] :
( ( push @ ( sub @ one @ X3394 ) @ ( comp @ sh @ X3394 ) )
= X3394 )
=> ( ( var @ one )
=> ( ! [X3395: term] :
( ( var @ X3395 )
=> ( var @ ( sub @ X3395 @ sh ) ) )
=> ( ! [X3396: term > $o] :
( ( X3396 @ one )
=> ( ! [X3397: term] :
( ( var @ X3397 )
=> ( ( X3396 @ X3397 )
=> ( X3396 @ ( sub @ X3397 @ sh ) ) ) )
=> ! [X3398: term] :
( ( var @ X3398 )
=> ( X3396 @ X3398 ) ) ) )
=> ( ! [X3399: term,X3400: term,X3401: term,X3402: term] :
( ( ( ap @ X3399 @ X3401 )
= ( ap @ X3400 @ X3402 ) )
=> ( X3399 = X3400 ) )
=> ( ! [X3403: term,X3404: term,X3405: term,X3406: term] :
( ( ( ap @ X3403 @ X3405 )
= ( ap @ X3404 @ X3406 ) )
=> ( X3405 = X3406 ) )
=> ( ! [X3407: term,X3408: term] :
( ( ( lam @ X3407 )
= ( lam @ X3408 ) )
=> ( X3407 = X3408 ) )
=> ( ! [X3409: term,X3410: term] :
( ( ( sub @ X3409 @ sh )
= ( sub @ X3410 @ sh ) )
=> ( X3409 = X3410 ) )
=> ( ! [X3411: term,X3412: term,X3413: term] :
( ( lam @ X3411 )
!= ( ap @ X3412 @ X3413 ) )
=> ( ! [X3414: term,X3415: term] :
~ ( var @ ( ap @ X3414 @ X3415 ) )
=> ( ! [X3416: term] :
~ ( var @ ( lam @ X3416 ) )
=> ( ! [X3417: term > $o] :
( ! [X3418: term] :
( ( var @ X3418 )
=> ( X3417 @ X3418 ) )
=> ( ! [X3419: term,X3420: term] :
( ( X3417 @ X3419 )
=> ( ( X3417 @ X3420 )
=> ( X3417 @ ( ap @ X3419 @ X3420 ) ) ) )
=> ( ! [X3421: term] :
( ( X3417 @ X3421 )
=> ( X3417 @ ( lam @ X3421 ) ) )
=> ! [X3422: term] : ( X3417 @ X3422 ) ) ) )
=> ( ! [X3423: term > $o,X3424: term,X3425: subst] :
( ! [X3426: term] :
( ( var @ X3426 )
=> ( X3423 @ ( sub @ X3426 @ X3425 ) ) )
=> ( ( X3423 @ X3424 )
=> ! [X3427: term] :
( ( var @ X3427 )
=> ( X3423 @ ( sub @ X3427 @ ( push @ X3424 @ X3425 ) ) ) ) ) )
=> ( ! [X3428: term > $o] :
( ! [X3429: term,X3430: term] :
( ( X3428 @ X3429 )
=> ( ( X3428 @ X3430 )
=> ( X3428 @ ( ap @ X3429 @ X3430 ) ) ) )
=> ( ! [X3431: term] :
( ! [X3432: term] :
( ( X3428 @ X3432 )
=> ( X3428 @ ( sub @ X3431 @ ( push @ X3432 @ id ) ) ) )
=> ( X3428 @ ( lam @ X3431 ) ) )
=> ! [X3433: term,X3434: subst] :
( ! [X3435: term] :
( ( var @ X3435 )
=> ( X3428 @ ( sub @ X3435 @ X3434 ) ) )
=> ( X3428 @ ( sub @ X3433 @ X3434 ) ) ) ) )
=> ( ! [X3436: term > $o] :
( ! [X3437: term] :
( ( var @ X3437 )
=> ( X3436 @ X3437 ) )
=> ( ! [X3438: term,X3439: term] :
( ( X3436 @ X3438 )
=> ( ( X3436 @ X3439 )
=> ( X3436 @ ( ap @ X3438 @ X3439 ) ) ) )
=> ( ! [X3440: term] :
( ! [X3441: term] :
( ( X3436 @ X3441 )
=> ( X3436 @ ( sub @ X3440 @ ( push @ X3441 @ id ) ) ) )
=> ( X3436 @ ( lam @ X3440 ) ) )
=> ! [X3442: term] : ( X3436 @ X3442 ) ) ) )
=> ( ( ! [X3443: subst,X3444: subst,X3445: subst] :
( ( comp @ ( comp @ X3443 @ X3444 ) @ X3445 )
= ( comp @ X3443 @ ( comp @ X3444 @ X3445 ) ) )
& ! [X3446: subst] :
( ( comp @ id @ X3446 )
= X3446 )
& ! [X3447: subst] :
( ( comp @ X3447 @ id )
= X3447 ) )
=> ( ( ! [X3448: term,X3449: subst,X3450: subst] :
( ( sub @ ( sub @ X3448 @ X3449 ) @ X3450 )
= ( sub @ X3448 @ ( comp @ X3449 @ X3450 ) ) )
& ! [X3451: term] :
( ( sub @ X3451 @ id )
= X3451 ) )
=> ( ! [X3452: term,X3453: term,X3454: term,X3455: term] :
( ( ( hoasap @ id @ X3452 @ id @ X3454 )
= ( hoasap @ id @ X3453 @ id @ X3455 ) )
=> ( X3452 = X3453 ) )
=> ! [X3456: term,X3457: term,X3458: term,X3459: term] :
( ( ( hoasap @ id @ X3456 @ id @ X3458 )
= ( hoasap @ id @ X3457 @ id @ X3459 ) )
=> ( X3458 = X3459 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[thm]),c_0_33])]) ).
thf(c_0_35,plain,
! [X3460: subst,X3461: term,X3462: subst,X3463: term] :
( ( hoasap @ X3460 @ X3461 @ X3462 @ X3463 )
= ( ap @ ( sub @ X3461 @ X3462 ) @ X3463 ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[hoasap])]) ).
thf(c_0_36,negated_conjecture,
! [X3472: term,X3473: term,X3474: subst,X3475: term,X3476: subst,X3477: term,X3478: term,X3479: subst,X3480: term,X3481: subst,X3482: subst,X3483: subst,X3484: term,X3485: subst,X3486: subst,X3487: subst,X3488: subst,X3489: term,X3490: subst,X3491: subst,X3492: subst,X3493: subst,X3494: term,X3495: term > $o,X3497: term,X3498: term,X3499: term,X3500: term,X3501: term,X3502: term,X3503: term,X3504: term,X3505: term,X3506: term,X3507: term,X3508: term,X3509: term,X3510: term,X3511: term,X3512: term,X3513: term,X3514: term,X3515: term,X3516: term > $o,X3521: term,X3522: term > $o,X3523: term,X3524: subst,X3526: term,X3527: term > $o,X3531: term,X3532: term,X3533: subst,X3535: term > $o,X3540: term,X3541: term,X3542: subst,X3543: subst,X3544: subst,X3545: subst,X3546: subst,X3547: term,X3548: subst,X3549: subst,X3550: term,X3551: term,X3552: term,X3553: term,X3554: term] :
( ( ( sub @ ( ap @ X3472 @ X3473 ) @ X3474 )
= ( ap @ ( sub @ X3472 @ X3474 ) @ ( sub @ X3473 @ X3474 ) ) )
& ( ( sub @ one @ ( push @ X3475 @ X3476 ) )
= X3475 )
& ( ( sub @ X3477 @ id )
= X3477 )
& ( ( sub @ ( lam @ X3478 ) @ X3479 )
= ( lam @ ( sub @ X3478 @ ( push @ one @ ( comp @ X3479 @ sh ) ) ) ) )
& ( ( sub @ ( sub @ X3480 @ X3481 ) @ X3482 )
= ( sub @ X3480 @ ( comp @ X3481 @ X3482 ) ) )
& ( ( comp @ id @ X3483 )
= X3483 )
& ( ( comp @ sh @ ( push @ X3484 @ X3485 ) )
= X3485 )
& ( ( comp @ ( comp @ X3486 @ X3487 ) @ X3488 )
= ( comp @ X3486 @ ( comp @ X3487 @ X3488 ) ) )
& ( ( comp @ ( push @ X3489 @ X3490 ) @ X3491 )
= ( push @ ( sub @ X3489 @ X3491 ) @ ( comp @ X3490 @ X3491 ) ) )
& ( ( comp @ X3492 @ id )
= X3492 )
& ( ( push @ one @ sh )
= id )
& ( ( push @ ( sub @ one @ X3493 ) @ ( comp @ sh @ X3493 ) )
= X3493 )
& ( var @ one )
& ( ~ ( var @ X3494 )
| ( var @ ( sub @ X3494 @ sh ) ) )
& ( ( var @ ( esk1_1 @ X3495 ) )
| ~ ( var @ X3497 )
| ( X3495 @ X3497 )
| ~ ( X3495 @ one ) )
& ( ( X3495 @ ( esk1_1 @ X3495 ) )
| ~ ( var @ X3497 )
| ( X3495 @ X3497 )
| ~ ( X3495 @ one ) )
& ( ~ ( X3495 @ ( sub @ ( esk1_1 @ X3495 ) @ sh ) )
| ~ ( var @ X3497 )
| ( X3495 @ X3497 )
| ~ ( X3495 @ one ) )
& ( ( ( ap @ X3498 @ X3500 )
!= ( ap @ X3499 @ X3501 ) )
| ( X3498 = X3499 ) )
& ( ( ( ap @ X3502 @ X3504 )
!= ( ap @ X3503 @ X3505 ) )
| ( X3504 = X3505 ) )
& ( ( ( lam @ X3506 )
!= ( lam @ X3507 ) )
| ( X3506 = X3507 ) )
& ( ( ( sub @ X3508 @ sh )
!= ( sub @ X3509 @ sh ) )
| ( X3508 = X3509 ) )
& ( ( lam @ X3510 )
!= ( ap @ X3511 @ X3512 ) )
& ~ ( var @ ( ap @ X3513 @ X3514 ) )
& ~ ( var @ ( lam @ X3515 ) )
& ( ( X3516 @ ( esk5_1 @ X3516 ) )
| ( X3516 @ X3521 )
| ( X3516 @ ( esk3_1 @ X3516 ) )
| ( var @ ( esk2_1 @ X3516 ) ) )
& ( ~ ( X3516 @ ( lam @ ( esk5_1 @ X3516 ) ) )
| ( X3516 @ X3521 )
| ( X3516 @ ( esk3_1 @ X3516 ) )
| ( var @ ( esk2_1 @ X3516 ) ) )
& ( ( X3516 @ ( esk5_1 @ X3516 ) )
| ( X3516 @ X3521 )
| ( X3516 @ ( esk4_1 @ X3516 ) )
| ( var @ ( esk2_1 @ X3516 ) ) )
& ( ~ ( X3516 @ ( lam @ ( esk5_1 @ X3516 ) ) )
| ( X3516 @ X3521 )
| ( X3516 @ ( esk4_1 @ X3516 ) )
| ( var @ ( esk2_1 @ X3516 ) ) )
& ( ( X3516 @ ( esk5_1 @ X3516 ) )
| ( X3516 @ X3521 )
| ~ ( X3516 @ ( ap @ ( esk3_1 @ X3516 ) @ ( esk4_1 @ X3516 ) ) )
| ( var @ ( esk2_1 @ X3516 ) ) )
& ( ~ ( X3516 @ ( lam @ ( esk5_1 @ X3516 ) ) )
| ( X3516 @ X3521 )
| ~ ( X3516 @ ( ap @ ( esk3_1 @ X3516 ) @ ( esk4_1 @ X3516 ) ) )
| ( var @ ( esk2_1 @ X3516 ) ) )
& ( ( X3516 @ ( esk5_1 @ X3516 ) )
| ( X3516 @ X3521 )
| ( X3516 @ ( esk3_1 @ X3516 ) )
| ~ ( X3516 @ ( esk2_1 @ X3516 ) ) )
& ( ~ ( X3516 @ ( lam @ ( esk5_1 @ X3516 ) ) )
| ( X3516 @ X3521 )
| ( X3516 @ ( esk3_1 @ X3516 ) )
| ~ ( X3516 @ ( esk2_1 @ X3516 ) ) )
& ( ( X3516 @ ( esk5_1 @ X3516 ) )
| ( X3516 @ X3521 )
| ( X3516 @ ( esk4_1 @ X3516 ) )
| ~ ( X3516 @ ( esk2_1 @ X3516 ) ) )
& ( ~ ( X3516 @ ( lam @ ( esk5_1 @ X3516 ) ) )
| ( X3516 @ X3521 )
| ( X3516 @ ( esk4_1 @ X3516 ) )
| ~ ( X3516 @ ( esk2_1 @ X3516 ) ) )
& ( ( X3516 @ ( esk5_1 @ X3516 ) )
| ( X3516 @ X3521 )
| ~ ( X3516 @ ( ap @ ( esk3_1 @ X3516 ) @ ( esk4_1 @ X3516 ) ) )
| ~ ( X3516 @ ( esk2_1 @ X3516 ) ) )
& ( ~ ( X3516 @ ( lam @ ( esk5_1 @ X3516 ) ) )
| ( X3516 @ X3521 )
| ~ ( X3516 @ ( ap @ ( esk3_1 @ X3516 ) @ ( esk4_1 @ X3516 ) ) )
| ~ ( X3516 @ ( esk2_1 @ X3516 ) ) )
& ( ( var @ ( esk6_3 @ X3522 @ X3523 @ X3524 ) )
| ~ ( X3522 @ X3523 )
| ~ ( var @ X3526 )
| ( X3522 @ ( sub @ X3526 @ ( push @ X3523 @ X3524 ) ) ) )
& ( ~ ( X3522 @ ( sub @ ( esk6_3 @ X3522 @ X3523 @ X3524 ) @ X3524 ) )
| ~ ( X3522 @ X3523 )
| ~ ( var @ X3526 )
| ( X3522 @ ( sub @ X3526 @ ( push @ X3523 @ X3524 ) ) ) )
& ( ( var @ ( esk10_3 @ X3527 @ X3532 @ X3533 ) )
| ( X3527 @ ( sub @ X3532 @ X3533 ) )
| ~ ( X3527 @ X3531 )
| ( X3527 @ ( sub @ ( esk9_1 @ X3527 ) @ ( push @ X3531 @ id ) ) )
| ( X3527 @ ( esk7_1 @ X3527 ) ) )
& ( ~ ( X3527 @ ( sub @ ( esk10_3 @ X3527 @ X3532 @ X3533 ) @ X3533 ) )
| ( X3527 @ ( sub @ X3532 @ X3533 ) )
| ~ ( X3527 @ X3531 )
| ( X3527 @ ( sub @ ( esk9_1 @ X3527 ) @ ( push @ X3531 @ id ) ) )
| ( X3527 @ ( esk7_1 @ X3527 ) ) )
& ( ( var @ ( esk10_3 @ X3527 @ X3532 @ X3533 ) )
| ( X3527 @ ( sub @ X3532 @ X3533 ) )
| ~ ( X3527 @ ( lam @ ( esk9_1 @ X3527 ) ) )
| ( X3527 @ ( esk7_1 @ X3527 ) ) )
& ( ~ ( X3527 @ ( sub @ ( esk10_3 @ X3527 @ X3532 @ X3533 ) @ X3533 ) )
| ( X3527 @ ( sub @ X3532 @ X3533 ) )
| ~ ( X3527 @ ( lam @ ( esk9_1 @ X3527 ) ) )
| ( X3527 @ ( esk7_1 @ X3527 ) ) )
& ( ( var @ ( esk10_3 @ X3527 @ X3532 @ X3533 ) )
| ( X3527 @ ( sub @ X3532 @ X3533 ) )
| ~ ( X3527 @ X3531 )
| ( X3527 @ ( sub @ ( esk9_1 @ X3527 ) @ ( push @ X3531 @ id ) ) )
| ( X3527 @ ( esk8_1 @ X3527 ) ) )
& ( ~ ( X3527 @ ( sub @ ( esk10_3 @ X3527 @ X3532 @ X3533 ) @ X3533 ) )
| ( X3527 @ ( sub @ X3532 @ X3533 ) )
| ~ ( X3527 @ X3531 )
| ( X3527 @ ( sub @ ( esk9_1 @ X3527 ) @ ( push @ X3531 @ id ) ) )
| ( X3527 @ ( esk8_1 @ X3527 ) ) )
& ( ( var @ ( esk10_3 @ X3527 @ X3532 @ X3533 ) )
| ( X3527 @ ( sub @ X3532 @ X3533 ) )
| ~ ( X3527 @ ( lam @ ( esk9_1 @ X3527 ) ) )
| ( X3527 @ ( esk8_1 @ X3527 ) ) )
& ( ~ ( X3527 @ ( sub @ ( esk10_3 @ X3527 @ X3532 @ X3533 ) @ X3533 ) )
| ( X3527 @ ( sub @ X3532 @ X3533 ) )
| ~ ( X3527 @ ( lam @ ( esk9_1 @ X3527 ) ) )
| ( X3527 @ ( esk8_1 @ X3527 ) ) )
& ( ( var @ ( esk10_3 @ X3527 @ X3532 @ X3533 ) )
| ( X3527 @ ( sub @ X3532 @ X3533 ) )
| ~ ( X3527 @ X3531 )
| ( X3527 @ ( sub @ ( esk9_1 @ X3527 ) @ ( push @ X3531 @ id ) ) )
| ~ ( X3527 @ ( ap @ ( esk7_1 @ X3527 ) @ ( esk8_1 @ X3527 ) ) ) )
& ( ~ ( X3527 @ ( sub @ ( esk10_3 @ X3527 @ X3532 @ X3533 ) @ X3533 ) )
| ( X3527 @ ( sub @ X3532 @ X3533 ) )
| ~ ( X3527 @ X3531 )
| ( X3527 @ ( sub @ ( esk9_1 @ X3527 ) @ ( push @ X3531 @ id ) ) )
| ~ ( X3527 @ ( ap @ ( esk7_1 @ X3527 ) @ ( esk8_1 @ X3527 ) ) ) )
& ( ( var @ ( esk10_3 @ X3527 @ X3532 @ X3533 ) )
| ( X3527 @ ( sub @ X3532 @ X3533 ) )
| ~ ( X3527 @ ( lam @ ( esk9_1 @ X3527 ) ) )
| ~ ( X3527 @ ( ap @ ( esk7_1 @ X3527 ) @ ( esk8_1 @ X3527 ) ) ) )
& ( ~ ( X3527 @ ( sub @ ( esk10_3 @ X3527 @ X3532 @ X3533 ) @ X3533 ) )
| ( X3527 @ ( sub @ X3532 @ X3533 ) )
| ~ ( X3527 @ ( lam @ ( esk9_1 @ X3527 ) ) )
| ~ ( X3527 @ ( ap @ ( esk7_1 @ X3527 ) @ ( esk8_1 @ X3527 ) ) ) )
& ( ~ ( X3535 @ X3540 )
| ( X3535 @ ( sub @ ( esk14_1 @ X3535 ) @ ( push @ X3540 @ id ) ) )
| ( X3535 @ X3541 )
| ( X3535 @ ( esk12_1 @ X3535 ) )
| ( var @ ( esk11_1 @ X3535 ) ) )
& ( ~ ( X3535 @ ( lam @ ( esk14_1 @ X3535 ) ) )
| ( X3535 @ X3541 )
| ( X3535 @ ( esk12_1 @ X3535 ) )
| ( var @ ( esk11_1 @ X3535 ) ) )
& ( ~ ( X3535 @ X3540 )
| ( X3535 @ ( sub @ ( esk14_1 @ X3535 ) @ ( push @ X3540 @ id ) ) )
| ( X3535 @ X3541 )
| ( X3535 @ ( esk13_1 @ X3535 ) )
| ( var @ ( esk11_1 @ X3535 ) ) )
& ( ~ ( X3535 @ ( lam @ ( esk14_1 @ X3535 ) ) )
| ( X3535 @ X3541 )
| ( X3535 @ ( esk13_1 @ X3535 ) )
| ( var @ ( esk11_1 @ X3535 ) ) )
& ( ~ ( X3535 @ X3540 )
| ( X3535 @ ( sub @ ( esk14_1 @ X3535 ) @ ( push @ X3540 @ id ) ) )
| ( X3535 @ X3541 )
| ~ ( X3535 @ ( ap @ ( esk12_1 @ X3535 ) @ ( esk13_1 @ X3535 ) ) )
| ( var @ ( esk11_1 @ X3535 ) ) )
& ( ~ ( X3535 @ ( lam @ ( esk14_1 @ X3535 ) ) )
| ( X3535 @ X3541 )
| ~ ( X3535 @ ( ap @ ( esk12_1 @ X3535 ) @ ( esk13_1 @ X3535 ) ) )
| ( var @ ( esk11_1 @ X3535 ) ) )
& ( ~ ( X3535 @ X3540 )
| ( X3535 @ ( sub @ ( esk14_1 @ X3535 ) @ ( push @ X3540 @ id ) ) )
| ( X3535 @ X3541 )
| ( X3535 @ ( esk12_1 @ X3535 ) )
| ~ ( X3535 @ ( esk11_1 @ X3535 ) ) )
& ( ~ ( X3535 @ ( lam @ ( esk14_1 @ X3535 ) ) )
| ( X3535 @ X3541 )
| ( X3535 @ ( esk12_1 @ X3535 ) )
| ~ ( X3535 @ ( esk11_1 @ X3535 ) ) )
& ( ~ ( X3535 @ X3540 )
| ( X3535 @ ( sub @ ( esk14_1 @ X3535 ) @ ( push @ X3540 @ id ) ) )
| ( X3535 @ X3541 )
| ( X3535 @ ( esk13_1 @ X3535 ) )
| ~ ( X3535 @ ( esk11_1 @ X3535 ) ) )
& ( ~ ( X3535 @ ( lam @ ( esk14_1 @ X3535 ) ) )
| ( X3535 @ X3541 )
| ( X3535 @ ( esk13_1 @ X3535 ) )
| ~ ( X3535 @ ( esk11_1 @ X3535 ) ) )
& ( ~ ( X3535 @ X3540 )
| ( X3535 @ ( sub @ ( esk14_1 @ X3535 ) @ ( push @ X3540 @ id ) ) )
| ( X3535 @ X3541 )
| ~ ( X3535 @ ( ap @ ( esk12_1 @ X3535 ) @ ( esk13_1 @ X3535 ) ) )
| ~ ( X3535 @ ( esk11_1 @ X3535 ) ) )
& ( ~ ( X3535 @ ( lam @ ( esk14_1 @ X3535 ) ) )
| ( X3535 @ X3541 )
| ~ ( X3535 @ ( ap @ ( esk12_1 @ X3535 ) @ ( esk13_1 @ X3535 ) ) )
| ~ ( X3535 @ ( esk11_1 @ X3535 ) ) )
& ( ( comp @ ( comp @ X3542 @ X3543 ) @ X3544 )
= ( comp @ X3542 @ ( comp @ X3543 @ X3544 ) ) )
& ( ( comp @ id @ X3545 )
= X3545 )
& ( ( comp @ X3546 @ id )
= X3546 )
& ( ( sub @ ( sub @ X3547 @ X3548 ) @ X3549 )
= ( sub @ X3547 @ ( comp @ X3548 @ X3549 ) ) )
& ( ( sub @ X3550 @ id )
= X3550 )
& ( ( ( hoasap @ id @ X3551 @ id @ X3553 )
!= ( hoasap @ id @ X3552 @ id @ X3554 ) )
| ( X3551 = X3552 ) )
& ( ( hoasap @ id @ esk15_0 @ id @ esk17_0 )
= ( hoasap @ id @ esk16_0 @ id @ esk18_0 ) )
& ( esk17_0 != esk18_0 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_34])])])])])])]) ).
thf(c_0_37,plain,
! [X3466: subst,X3467: term,X3468: subst,X3469: term] :
( ( hoasap @ X3466 @ X3467 @ X3468 @ X3469 )
= ( ap @ ( sub @ X3467 @ X3468 ) @ X3469 ) ),
inference(variable_rename,[status(thm)],[c_0_35]) ).
thf(c_0_38,negated_conjecture,
( ( hoasap @ id @ esk15_0 @ id @ esk17_0 )
= ( hoasap @ id @ esk16_0 @ id @ esk18_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
thf(c_0_39,plain,
! [X1: term,X3: subst,X4: subst,X2: term] :
( ( hoasap @ X3 @ X1 @ X4 @ X2 )
= ( ap @ ( sub @ X1 @ X4 ) @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_40,negated_conjecture,
! [X1: term] :
( ( sub @ X1 @ id )
= X1 ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
thf(c_0_41,negated_conjecture,
! [X1: term,X2: term,X7: term,X8: term] :
( ( X2 = X8 )
| ( ( ap @ X1 @ X2 )
!= ( ap @ X7 @ X8 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
thf(c_0_42,negated_conjecture,
( ( ap @ esk15_0 @ esk17_0 )
= ( ap @ esk16_0 @ esk18_0 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39]),c_0_40]),c_0_39]),c_0_40]) ).
thf(c_0_43,negated_conjecture,
! [X2: term,X1: term] :
( ( X1 = esk17_0 )
| ( ( ap @ X2 @ X1 )
!= ( ap @ esk16_0 @ esk18_0 ) ) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
thf(c_0_44,negated_conjecture,
esk17_0 != esk18_0,
inference(split_conjunct,[status(thm)],[c_0_36]) ).
thf(c_0_45,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_43]),c_0_44]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : ALG257^1 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat May 18 22:58:53 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.20/0.48 Running higher-order theorem proving
% 0.20/0.48 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.55 # Version: 3.1.0-ho
% 0.20/0.55 # Preprocessing class: HSMMSLSSLLLNHFA.
% 0.20/0.55 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.55 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.20/0.55 # Starting post_as_ho1 with 300s (1) cores
% 0.20/0.55 # Starting post_as_ho5 with 300s (1) cores
% 0.20/0.55 # Starting post_as_ho10 with 300s (1) cores
% 0.20/0.55 # post_as_ho10 with pid 27284 completed with status 0
% 0.20/0.55 # Result found by post_as_ho10
% 0.20/0.55 # Preprocessing class: HSMMSLSSLLLNHFA.
% 0.20/0.55 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.55 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.20/0.55 # Starting post_as_ho1 with 300s (1) cores
% 0.20/0.55 # Starting post_as_ho5 with 300s (1) cores
% 0.20/0.55 # Starting post_as_ho10 with 300s (1) cores
% 0.20/0.55 # No SInE strategy applied
% 0.20/0.55 # Search class: HGUSM-FFMS31-MHFMMMBN
% 0.20/0.55 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.55 # Starting new_ho_10 with 163s (1) cores
% 0.20/0.55 # new_ho_10 with pid 27289 completed with status 0
% 0.20/0.55 # Result found by new_ho_10
% 0.20/0.55 # Preprocessing class: HSMMSLSSLLLNHFA.
% 0.20/0.55 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.55 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.20/0.55 # Starting post_as_ho1 with 300s (1) cores
% 0.20/0.55 # Starting post_as_ho5 with 300s (1) cores
% 0.20/0.55 # Starting post_as_ho10 with 300s (1) cores
% 0.20/0.55 # No SInE strategy applied
% 0.20/0.55 # Search class: HGUSM-FFMS31-MHFMMMBN
% 0.20/0.55 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.55 # Starting new_ho_10 with 163s (1) cores
% 0.20/0.55 # Preprocessing time : 0.003 s
% 0.20/0.55 # Presaturation interreduction done
% 0.20/0.55
% 0.20/0.55 # Proof found!
% 0.20/0.55 # SZS status Theorem
% 0.20/0.55 # SZS output start CNFRefutation
% See solution above
% 0.20/0.55 # Parsed axioms : 238
% 0.20/0.55 # Removed by relevancy pruning/SinE : 0
% 0.20/0.55 # Initial clauses : 196
% 0.20/0.55 # Removed in clause preprocessing : 124
% 0.20/0.55 # Initial clauses in saturation : 72
% 0.20/0.55 # Processed clauses : 96
% 0.20/0.55 # ...of these trivial : 5
% 0.20/0.55 # ...subsumed : 3
% 0.20/0.55 # ...remaining for further processing : 88
% 0.20/0.55 # Other redundant clauses eliminated : 0
% 0.20/0.55 # Clauses deleted for lack of memory : 0
% 0.20/0.55 # Backward-subsumed : 0
% 0.20/0.55 # Backward-rewritten : 3
% 0.20/0.55 # Generated clauses : 20
% 0.20/0.55 # ...of the previous two non-redundant : 12
% 0.20/0.55 # ...aggressively subsumed : 0
% 0.20/0.55 # Contextual simplify-reflections : 0
% 0.20/0.55 # Paramodulations : 15
% 0.20/0.55 # Factorizations : 0
% 0.20/0.55 # NegExts : 0
% 0.20/0.55 # Equation resolutions : 5
% 0.20/0.55 # Disequality decompositions : 0
% 0.20/0.55 # Total rewrite steps : 23
% 0.20/0.55 # ...of those cached : 5
% 0.20/0.55 # Propositional unsat checks : 0
% 0.20/0.55 # Propositional check models : 0
% 0.20/0.55 # Propositional check unsatisfiable : 0
% 0.20/0.55 # Propositional clauses : 0
% 0.20/0.55 # Propositional clauses after purity: 0
% 0.20/0.55 # Propositional unsat core size : 0
% 0.20/0.55 # Propositional preprocessing time : 0.000
% 0.20/0.55 # Propositional encoding time : 0.000
% 0.20/0.55 # Propositional solver time : 0.000
% 0.20/0.55 # Success case prop preproc time : 0.000
% 0.20/0.55 # Success case prop encoding time : 0.000
% 0.20/0.55 # Success case prop solver time : 0.000
% 0.20/0.55 # Current number of processed clauses : 20
% 0.20/0.55 # Positive orientable unit clauses : 10
% 0.20/0.55 # Positive unorientable unit clauses: 0
% 0.20/0.55 # Negative unit clauses : 4
% 0.20/0.55 # Non-unit-clauses : 6
% 0.20/0.55 # Current number of unprocessed clauses: 53
% 0.20/0.55 # ...number of literals in the above : 194
% 0.20/0.55 # Current number of archived formulas : 0
% 0.20/0.55 # Current number of archived clauses : 68
% 0.20/0.55 # Clause-clause subsumption calls (NU) : 104
% 0.20/0.55 # Rec. Clause-clause subsumption calls : 35
% 0.20/0.55 # Non-unit clause-clause subsumptions : 1
% 0.20/0.55 # Unit Clause-clause subsumption calls : 5
% 0.20/0.55 # Rewrite failures with RHS unbound : 0
% 0.20/0.55 # BW rewrite match attempts : 5
% 0.20/0.55 # BW rewrite match successes : 5
% 0.20/0.55 # Condensation attempts : 96
% 0.20/0.55 # Condensation successes : 0
% 0.20/0.55 # Termbank termtop insertions : 33165
% 0.20/0.55 # Search garbage collected termcells : 3757
% 0.20/0.55
% 0.20/0.55 # -------------------------------------------------
% 0.20/0.55 # User time : 0.039 s
% 0.20/0.55 # System time : 0.012 s
% 0.20/0.55 # Total time : 0.051 s
% 0.20/0.55 # Maximum resident set size: 6028 pages
% 0.20/0.55
% 0.20/0.55 # -------------------------------------------------
% 0.20/0.55 # User time : 0.047 s
% 0.20/0.55 # System time : 0.016 s
% 0.20/0.55 # Total time : 0.063 s
% 0.20/0.55 # Maximum resident set size: 2072 pages
% 0.20/0.55 % E---3.1 exiting
% 0.20/0.55 % E exiting
%------------------------------------------------------------------------------