TSTP Solution File: ALG251^1 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : ALG251^1 : TPTP v8.2.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n017.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 18:05:51 EDT 2024
% Result : Theorem 0.54s 0.65s
% Output : CNFRefutation 0.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 71
% Syntax : Number of formulae : 94 ( 12 unt; 45 typ; 0 def)
% Number of atoms : 224 ( 108 equ; 0 cnn)
% Maximal formula atoms : 41 ( 4 avg)
% Number of connectives : 1008 ( 61 ~; 68 |; 39 &; 683 @)
% ( 25 <=>; 132 =>; 0 <=; 0 <~>)
% Maximal formula depth : 91 ( 8 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 45 ( 43 usr; 32 con; 0-2 aty)
% Number of variables : 240 ( 6 ^ 234 !; 0 ?; 240 :)
% 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_41,type,
axvarshift: $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_101,type,
pushprop_gthm: $o ).
thf(decl_102,type,
axabs: $o ).
thf(decl_108,type,
lamnotap: $o ).
thf(decl_111,type,
axidl: $o ).
thf(decl_116,type,
pushprop: $o ).
thf(decl_121,type,
lamnotvar: $o ).
thf(decl_130,type,
ulamvarsh: $o ).
thf(decl_136,type,
axshiftcons: $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,
epred1_0: term > $o ).
thf(decl_150,type,
esk6_0: term ).
thf(decl_151,type,
esk7_0: subst ).
thf(decl_152,type,
esk8_0: term ).
thf(pushprop_gthm,axiom,
( pushprop_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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',pushprop_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(thm,conjecture,
pushprop_gthm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(c_0_26,axiom,
( pushprop_gthm
= ( ! [X2063: term,X2064: term,X2065: subst] :
( ( sub @ ( ap @ X2063 @ X2064 ) @ X2065 )
= ( ap @ ( sub @ X2063 @ X2065 ) @ ( sub @ X2064 @ X2065 ) ) )
=> ( ! [X2066: term,X2067: subst] :
( ( sub @ one @ ( push @ X2066 @ X2067 ) )
= X2066 )
=> ( ! [X2068: term] :
( ( sub @ X2068 @ id )
= X2068 )
=> ( ! [X2069: term,X2070: subst] :
( ( sub @ ( lam @ X2069 ) @ X2070 )
= ( lam @ ( sub @ X2069 @ ( push @ one @ ( comp @ X2070 @ sh ) ) ) ) )
=> ( ! [X2071: term,X2072: subst,X2073: subst] :
( ( sub @ ( sub @ X2071 @ X2072 ) @ X2073 )
= ( sub @ X2071 @ ( comp @ X2072 @ X2073 ) ) )
=> ( ! [X2074: subst] :
( ( comp @ id @ X2074 )
= X2074 )
=> ( ! [X2075: term,X2076: subst] :
( ( comp @ sh @ ( push @ X2075 @ X2076 ) )
= X2076 )
=> ( ! [X2077: subst,X2078: subst,X2079: subst] :
( ( comp @ ( comp @ X2077 @ X2078 ) @ X2079 )
= ( comp @ X2077 @ ( comp @ X2078 @ X2079 ) ) )
=> ( ! [X2080: term,X2081: subst,X2082: subst] :
( ( comp @ ( push @ X2080 @ X2081 ) @ X2082 )
= ( push @ ( sub @ X2080 @ X2082 ) @ ( comp @ X2081 @ X2082 ) ) )
=> ( ! [X2083: subst] :
( ( comp @ X2083 @ id )
= X2083 )
=> ( ( ( push @ one @ sh )
= id )
=> ( ! [X2084: subst] :
( ( push @ ( sub @ one @ X2084 ) @ ( comp @ sh @ X2084 ) )
= X2084 )
=> ( ( var @ one )
=> ( ! [X2085: term] :
( ( var @ X2085 )
=> ( var @ ( sub @ X2085 @ sh ) ) )
=> ( ! [X2086: term > $o] :
( ( X2086 @ one )
=> ( ! [X2087: term] :
( ( var @ X2087 )
=> ( ( X2086 @ X2087 )
=> ( X2086 @ ( sub @ X2087 @ sh ) ) ) )
=> ! [X2088: term] :
( ( var @ X2088 )
=> ( X2086 @ X2088 ) ) ) )
=> ( ! [X2089: term,X2090: term,X2091: term,X2092: term] :
( ( ( ap @ X2089 @ X2091 )
= ( ap @ X2090 @ X2092 ) )
=> ( X2089 = X2090 ) )
=> ( ! [X2093: term,X2094: term,X2095: term,X2096: term] :
( ( ( ap @ X2093 @ X2095 )
= ( ap @ X2094 @ X2096 ) )
=> ( X2095 = X2096 ) )
=> ( ! [X2097: term,X2098: term] :
( ( ( lam @ X2097 )
= ( lam @ X2098 ) )
=> ( X2097 = X2098 ) )
=> ( ! [X2099: term,X2100: term] :
( ( ( sub @ X2099 @ sh )
= ( sub @ X2100 @ sh ) )
=> ( X2099 = X2100 ) )
=> ( ! [X2101: term,X2102: term,X2103: term] :
( ( lam @ X2101 )
!= ( ap @ X2102 @ X2103 ) )
=> ( ! [X2104: term,X2105: term] :
~ ( var @ ( ap @ X2104 @ X2105 ) )
=> ( ! [X2106: term] :
~ ( var @ ( lam @ X2106 ) )
=> ( ! [X2107: term > $o] :
( ! [X2108: term] :
( ( var @ X2108 )
=> ( X2107 @ X2108 ) )
=> ( ! [X2109: term,X2110: term] :
( ( X2107 @ X2109 )
=> ( ( X2107 @ X2110 )
=> ( X2107 @ ( ap @ X2109 @ X2110 ) ) ) )
=> ( ! [X2111: term] :
( ( X2107 @ X2111 )
=> ( X2107 @ ( lam @ X2111 ) ) )
=> ! [X2112: term] : ( X2107 @ X2112 ) ) ) )
=> ! [X2113: term > $o,X2114: term,X2115: subst] :
( ! [X2116: term] :
( ( var @ X2116 )
=> ( X2113 @ ( sub @ X2116 @ X2115 ) ) )
=> ( ( X2113 @ X2114 )
=> ! [X2117: term] :
( ( var @ X2117 )
=> ( X2113 @ ( sub @ X2117 @ ( push @ X2114 @ X2115 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
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)],[pushprop_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]) ).
thf(c_0_27,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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[thm]),c_0_26])]) ).
thf(c_0_28,negated_conjecture,
! [X3440: term,X3441: term,X3442: subst,X3443: term,X3444: subst,X3445: term,X3446: term,X3447: subst,X3448: term,X3449: subst,X3450: subst,X3451: subst,X3452: term,X3453: subst,X3454: subst,X3455: subst,X3456: subst,X3457: term,X3458: subst,X3459: subst,X3460: subst,X3461: subst,X3462: term,X3463: term > $o,X3465: term,X3466: term,X3467: term,X3468: term,X3469: term,X3470: term,X3471: term,X3472: term,X3473: term,X3474: term,X3475: term,X3476: term,X3477: term,X3478: term,X3479: term,X3480: term,X3481: term,X3482: term,X3483: term,X3484: term > $o,X3489: term,X3493: term] :
( ( ( sub @ ( ap @ X3440 @ X3441 ) @ X3442 )
= ( ap @ ( sub @ X3440 @ X3442 ) @ ( sub @ X3441 @ X3442 ) ) )
& ( ( sub @ one @ ( push @ X3443 @ X3444 ) )
= X3443 )
& ( ( sub @ X3445 @ id )
= X3445 )
& ( ( sub @ ( lam @ X3446 ) @ X3447 )
= ( lam @ ( sub @ X3446 @ ( push @ one @ ( comp @ X3447 @ sh ) ) ) ) )
& ( ( sub @ ( sub @ X3448 @ X3449 ) @ X3450 )
= ( sub @ X3448 @ ( comp @ X3449 @ X3450 ) ) )
& ( ( comp @ id @ X3451 )
= X3451 )
& ( ( comp @ sh @ ( push @ X3452 @ X3453 ) )
= X3453 )
& ( ( comp @ ( comp @ X3454 @ X3455 ) @ X3456 )
= ( comp @ X3454 @ ( comp @ X3455 @ X3456 ) ) )
& ( ( comp @ ( push @ X3457 @ X3458 ) @ X3459 )
= ( push @ ( sub @ X3457 @ X3459 ) @ ( comp @ X3458 @ X3459 ) ) )
& ( ( comp @ X3460 @ id )
= X3460 )
& ( ( push @ one @ sh )
= id )
& ( ( push @ ( sub @ one @ X3461 ) @ ( comp @ sh @ X3461 ) )
= X3461 )
& ( var @ one )
& ( ~ ( var @ X3462 )
| ( var @ ( sub @ X3462 @ sh ) ) )
& ( ( var @ ( esk1_1 @ X3463 ) )
| ~ ( var @ X3465 )
| ( X3463 @ X3465 )
| ~ ( X3463 @ one ) )
& ( ( X3463 @ ( esk1_1 @ X3463 ) )
| ~ ( var @ X3465 )
| ( X3463 @ X3465 )
| ~ ( X3463 @ one ) )
& ( ~ ( X3463 @ ( sub @ ( esk1_1 @ X3463 ) @ sh ) )
| ~ ( var @ X3465 )
| ( X3463 @ X3465 )
| ~ ( X3463 @ one ) )
& ( ( ( ap @ X3466 @ X3468 )
!= ( ap @ X3467 @ X3469 ) )
| ( X3466 = X3467 ) )
& ( ( ( ap @ X3470 @ X3472 )
!= ( ap @ X3471 @ X3473 ) )
| ( X3472 = X3473 ) )
& ( ( ( lam @ X3474 )
!= ( lam @ X3475 ) )
| ( X3474 = X3475 ) )
& ( ( ( sub @ X3476 @ sh )
!= ( sub @ X3477 @ sh ) )
| ( X3476 = X3477 ) )
& ( ( lam @ X3478 )
!= ( ap @ X3479 @ X3480 ) )
& ~ ( var @ ( ap @ X3481 @ X3482 ) )
& ~ ( var @ ( lam @ X3483 ) )
& ( ( X3484 @ ( esk5_1 @ X3484 ) )
| ( X3484 @ X3489 )
| ( X3484 @ ( esk3_1 @ X3484 ) )
| ( var @ ( esk2_1 @ X3484 ) ) )
& ( ~ ( X3484 @ ( lam @ ( esk5_1 @ X3484 ) ) )
| ( X3484 @ X3489 )
| ( X3484 @ ( esk3_1 @ X3484 ) )
| ( var @ ( esk2_1 @ X3484 ) ) )
& ( ( X3484 @ ( esk5_1 @ X3484 ) )
| ( X3484 @ X3489 )
| ( X3484 @ ( esk4_1 @ X3484 ) )
| ( var @ ( esk2_1 @ X3484 ) ) )
& ( ~ ( X3484 @ ( lam @ ( esk5_1 @ X3484 ) ) )
| ( X3484 @ X3489 )
| ( X3484 @ ( esk4_1 @ X3484 ) )
| ( var @ ( esk2_1 @ X3484 ) ) )
& ( ( X3484 @ ( esk5_1 @ X3484 ) )
| ( X3484 @ X3489 )
| ~ ( X3484 @ ( ap @ ( esk3_1 @ X3484 ) @ ( esk4_1 @ X3484 ) ) )
| ( var @ ( esk2_1 @ X3484 ) ) )
& ( ~ ( X3484 @ ( lam @ ( esk5_1 @ X3484 ) ) )
| ( X3484 @ X3489 )
| ~ ( X3484 @ ( ap @ ( esk3_1 @ X3484 ) @ ( esk4_1 @ X3484 ) ) )
| ( var @ ( esk2_1 @ X3484 ) ) )
& ( ( X3484 @ ( esk5_1 @ X3484 ) )
| ( X3484 @ X3489 )
| ( X3484 @ ( esk3_1 @ X3484 ) )
| ~ ( X3484 @ ( esk2_1 @ X3484 ) ) )
& ( ~ ( X3484 @ ( lam @ ( esk5_1 @ X3484 ) ) )
| ( X3484 @ X3489 )
| ( X3484 @ ( esk3_1 @ X3484 ) )
| ~ ( X3484 @ ( esk2_1 @ X3484 ) ) )
& ( ( X3484 @ ( esk5_1 @ X3484 ) )
| ( X3484 @ X3489 )
| ( X3484 @ ( esk4_1 @ X3484 ) )
| ~ ( X3484 @ ( esk2_1 @ X3484 ) ) )
& ( ~ ( X3484 @ ( lam @ ( esk5_1 @ X3484 ) ) )
| ( X3484 @ X3489 )
| ( X3484 @ ( esk4_1 @ X3484 ) )
| ~ ( X3484 @ ( esk2_1 @ X3484 ) ) )
& ( ( X3484 @ ( esk5_1 @ X3484 ) )
| ( X3484 @ X3489 )
| ~ ( X3484 @ ( ap @ ( esk3_1 @ X3484 ) @ ( esk4_1 @ X3484 ) ) )
| ~ ( X3484 @ ( esk2_1 @ X3484 ) ) )
& ( ~ ( X3484 @ ( lam @ ( esk5_1 @ X3484 ) ) )
| ( X3484 @ X3489 )
| ~ ( X3484 @ ( ap @ ( esk3_1 @ X3484 ) @ ( esk4_1 @ X3484 ) ) )
| ~ ( X3484 @ ( esk2_1 @ X3484 ) ) )
& ( ~ ( var @ X3493 )
| ( epred1_0 @ ( sub @ X3493 @ esk7_0 ) ) )
& ( epred1_0 @ esk6_0 )
& ( var @ esk8_0 )
& ~ ( epred1_0 @ ( sub @ esk8_0 @ ( push @ esk6_0 @ esk7_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_27])])])])])])]) ).
thf(c_0_29,negated_conjecture,
! [X1: term,X6: term > $o] :
( ( X6 @ X1 )
| ~ ( X6 @ ( sub @ ( esk1_1 @ X6 ) @ sh ) )
| ~ ( var @ X1 )
| ~ ( X6 @ one ) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_30,negated_conjecture,
! [X1: term,X3: subst,X4: subst] :
( ( sub @ ( sub @ X1 @ X3 ) @ X4 )
= ( sub @ X1 @ ( comp @ X3 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_31,negated_conjecture,
! [X1: term,X3: subst] :
( ( comp @ sh @ ( push @ X1 @ X3 ) )
= X3 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_32,negated_conjecture,
! [X1: term] :
( ( ( sub
@ ( esk1_1
@ ^ [Z0: term] : ( Z0 != X1 ) )
@ sh )
= X1 )
| ( one = X1 )
| ~ ( var @ X1 ) ),
inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[]),c_0_29]) ).
thf(c_0_33,negated_conjecture,
var @ esk8_0,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_34,negated_conjecture,
! [X1: term,X2: term,X3: subst] :
( ( sub @ ( sub @ X1 @ sh ) @ ( push @ X2 @ X3 ) )
= ( sub @ X1 @ X3 ) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
thf(c_0_35,negated_conjecture,
( ( ( sub
@ ( esk1_1
@ ^ [Z0: term] : ( Z0 != esk8_0 ) )
@ sh )
= esk8_0 )
| ( esk8_0 = one ) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
thf(c_0_36,negated_conjecture,
! [X1: term,X3: subst] :
( ( ( sub @ esk8_0 @ ( push @ X1 @ X3 ) )
= ( sub
@ ( esk1_1
@ ^ [Z0: term] : ( Z0 != esk8_0 ) )
@ X3 ) )
| ( esk8_0 = one ) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
thf(c_0_37,negated_conjecture,
~ ( epred1_0 @ ( sub @ esk8_0 @ ( push @ esk6_0 @ esk7_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_38,negated_conjecture,
! [X1: term,X2: term,X3: subst] :
( ( ( sub @ esk8_0 @ ( push @ X1 @ X3 ) )
= ( sub @ esk8_0 @ ( push @ X2 @ X3 ) ) )
| ( esk8_0 = one ) ),
inference(spm,[status(thm)],[c_0_36,c_0_36]) ).
thf(c_0_39,negated_conjecture,
! [X1: term] :
( ( esk8_0 = one )
| ~ ( epred1_0 @ ( sub @ esk8_0 @ ( push @ X1 @ esk7_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
thf(c_0_40,negated_conjecture,
( ( esk8_0 = one )
| ~ ( epred1_0
@ ( sub
@ ( esk1_1
@ ^ [Z0: term] : ( Z0 != esk8_0 ) )
@ esk7_0 ) ) ),
inference(spm,[status(thm)],[c_0_39,c_0_36]) ).
thf(c_0_41,negated_conjecture,
! [X1: term] :
( ( epred1_0 @ ( sub @ X1 @ esk7_0 ) )
| ~ ( var @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_42,negated_conjecture,
! [X1: term,X6: term > $o] :
( ( var @ ( esk1_1 @ X6 ) )
| ( X6 @ X1 )
| ~ ( var @ X1 )
| ~ ( X6 @ one ) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_43,negated_conjecture,
( ( esk8_0 = one )
| ~ ( var
@ ( esk1_1
@ ^ [Z0: term] : ( Z0 != esk8_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
thf(c_0_44,negated_conjecture,
! [X1: term] :
( ( one = X1 )
| ( var
@ ( esk1_1
@ ^ [Z0: term] : ( Z0 != X1 ) ) )
| ~ ( var @ X1 ) ),
inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[]),c_0_42]) ).
thf(c_0_45,negated_conjecture,
esk8_0 = one,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_33])]) ).
thf(c_0_46,negated_conjecture,
! [X3: subst,X1: term] :
( ( sub @ one @ ( push @ X1 @ X3 ) )
= X1 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_47,negated_conjecture,
epred1_0 @ esk6_0,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_48,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_45]),c_0_46]),c_0_47])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG251^1 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.03/0.14 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n017.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat May 18 23:14:23 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.22/0.51 Running higher-order theorem proving
% 0.22/0.51 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
% 0.54/0.65 # Version: 3.1.0-ho
% 0.54/0.65 # Preprocessing class: HSMMSLSSLLLNHFA.
% 0.54/0.65 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.54/0.65 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.54/0.65 # Starting post_as_ho1 with 300s (1) cores
% 0.54/0.65 # Starting post_as_ho5 with 300s (1) cores
% 0.54/0.65 # Starting post_as_ho10 with 300s (1) cores
% 0.54/0.65 # new_ho_10_cnf2 with pid 19998 completed with status 0
% 0.54/0.65 # Result found by new_ho_10_cnf2
% 0.54/0.65 # Preprocessing class: HSMMSLSSLLLNHFA.
% 0.54/0.65 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.54/0.65 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.54/0.65 # No SInE strategy applied
% 0.54/0.65 # Search class: HGUSM-FFMS31-MHFMMSBN
% 0.54/0.65 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.54/0.65 # Starting ehoh_best_nonlift with 675s (1) cores
% 0.54/0.65 # Starting new_ho_10_cnf2 with 151s (1) cores
% 0.54/0.65 # Starting post_as_ho7 with 169s (1) cores
% 0.54/0.65 # Starting ehoh_best_sine_rwall with 169s (1) cores
% 0.54/0.65 # Starting sh1l with 169s (1) cores
% 0.54/0.65 # post_as_ho7 with pid 20007 completed with status 0
% 0.54/0.65 # Result found by post_as_ho7
% 0.54/0.65 # Preprocessing class: HSMMSLSSLLLNHFA.
% 0.54/0.65 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.54/0.65 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.54/0.65 # No SInE strategy applied
% 0.54/0.65 # Search class: HGUSM-FFMS31-MHFMMSBN
% 0.54/0.65 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.54/0.65 # Starting ehoh_best_nonlift with 675s (1) cores
% 0.54/0.65 # Starting new_ho_10_cnf2 with 151s (1) cores
% 0.54/0.65 # Starting post_as_ho7 with 169s (1) cores
% 0.54/0.65 # Preprocessing time : 0.004 s
% 0.54/0.65
% 0.54/0.65 # Proof found!
% 0.54/0.65 # SZS status Theorem
% 0.54/0.65 # SZS output start CNFRefutation
% See solution above
% 0.54/0.65 # Parsed axioms : 238
% 0.54/0.65 # Removed by relevancy pruning/SinE : 0
% 0.54/0.65 # Initial clauses : 166
% 0.54/0.65 # Removed in clause preprocessing : 124
% 0.54/0.65 # Initial clauses in saturation : 42
% 0.54/0.65 # Processed clauses : 368
% 0.54/0.65 # ...of these trivial : 4
% 0.54/0.65 # ...subsumed : 182
% 0.54/0.65 # ...remaining for further processing : 182
% 0.54/0.65 # Other redundant clauses eliminated : 0
% 0.54/0.65 # Clauses deleted for lack of memory : 0
% 0.54/0.65 # Backward-subsumed : 16
% 0.54/0.65 # Backward-rewritten : 30
% 0.54/0.65 # Generated clauses : 1701
% 0.54/0.65 # ...of the previous two non-redundant : 1495
% 0.54/0.65 # ...aggressively subsumed : 0
% 0.54/0.65 # Contextual simplify-reflections : 0
% 0.54/0.65 # Paramodulations : 1572
% 0.54/0.65 # Factorizations : 3
% 0.54/0.65 # NegExts : 2
% 0.54/0.65 # Equation resolutions : 14
% 0.54/0.65 # Disequality decompositions : 0
% 0.54/0.65 # Total rewrite steps : 456
% 0.54/0.65 # ...of those cached : 202
% 0.54/0.65 # Propositional unsat checks : 0
% 0.54/0.65 # Propositional check models : 0
% 0.54/0.65 # Propositional check unsatisfiable : 0
% 0.54/0.65 # Propositional clauses : 0
% 0.54/0.65 # Propositional clauses after purity: 0
% 0.54/0.65 # Propositional unsat core size : 0
% 0.54/0.65 # Propositional preprocessing time : 0.000
% 0.54/0.65 # Propositional encoding time : 0.000
% 0.54/0.65 # Propositional solver time : 0.000
% 0.54/0.65 # Success case prop preproc time : 0.000
% 0.54/0.65 # Success case prop encoding time : 0.000
% 0.54/0.65 # Success case prop solver time : 0.000
% 0.54/0.65 # Current number of processed clauses : 131
% 0.54/0.65 # Positive orientable unit clauses : 32
% 0.54/0.65 # Positive unorientable unit clauses: 6
% 0.54/0.65 # Negative unit clauses : 22
% 0.54/0.65 # Non-unit-clauses : 71
% 0.54/0.65 # Current number of unprocessed clauses: 1016
% 0.54/0.65 # ...number of literals in the above : 2789
% 0.54/0.65 # Current number of archived formulas : 0
% 0.54/0.65 # Current number of archived clauses : 51
% 0.54/0.65 # Clause-clause subsumption calls (NU) : 743
% 0.54/0.65 # Rec. Clause-clause subsumption calls : 495
% 0.54/0.65 # Non-unit clause-clause subsumptions : 107
% 0.54/0.65 # Unit Clause-clause subsumption calls : 184
% 0.54/0.65 # Rewrite failures with RHS unbound : 0
% 0.54/0.65 # BW rewrite match attempts : 39
% 0.54/0.65 # BW rewrite match successes : 8
% 0.54/0.65 # Condensation attempts : 0
% 0.54/0.65 # Condensation successes : 0
% 0.54/0.65 # Termbank termtop insertions : 117052
% 0.54/0.65 # Search garbage collected termcells : 2905
% 0.54/0.65
% 0.54/0.65 # -------------------------------------------------
% 0.54/0.65 # User time : 0.100 s
% 0.54/0.65 # System time : 0.013 s
% 0.54/0.65 # Total time : 0.113 s
% 0.54/0.65 # Maximum resident set size: 5924 pages
% 0.54/0.65
% 0.54/0.65 # -------------------------------------------------
% 0.54/0.65 # User time : 0.420 s
% 0.54/0.65 # System time : 0.051 s
% 0.54/0.65 # Total time : 0.471 s
% 0.54/0.65 # Maximum resident set size: 2072 pages
% 0.54/0.65 % E---3.1 exiting
% 0.54/0.65 % E exiting
%------------------------------------------------------------------------------