TSTP Solution File: ALG253^1 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : ALG253^1 : TPTP v8.2.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n006.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 18:05:52 EDT 2024
% Result : Theorem 29.00s 4.15s
% Output : CNFRefutation 29.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 79
% Syntax : Number of formulae : 115 ( 12 unt; 51 typ; 0 def)
% Number of atoms : 290 ( 86 equ; 0 cnn)
% Maximal formula atoms : 55 ( 4 avg)
% Number of connectives : 1836 ( 116 ~; 176 |; 54 &;1277 @)
% ( 27 <=>; 186 =>; 0 <=; 0 <~>)
% Maximal formula depth : 119 ( 10 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 67 ( 67 >; 0 *; 0 +; 0 <<)
% Number of symbols : 51 ( 49 usr; 32 con; 0-3 aty)
% Number of variables : 339 ( 0 ^ 339 !; 0 ?; 339 :)
% 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_39,type,
induction2lem: $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_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_125,type,
induction2_gthm: $o ).
thf(decl_130,type,
ulamvarsh: $o ).
thf(decl_131,type,
induction2: $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,
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,
epred1_0: term > $o ).
thf(decl_155,type,
esk11_1: term > term ).
thf(decl_156,type,
esk12_0: term ).
thf(induction2_gthm,axiom,
( induction2_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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',induction2_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(thm,conjecture,
induction2_gthm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(c_0_28,axiom,
( induction2_gthm
= ( ! [X3068: term,X3069: term,X3070: subst] :
( ( sub @ ( ap @ X3068 @ X3069 ) @ X3070 )
= ( ap @ ( sub @ X3068 @ X3070 ) @ ( sub @ X3069 @ X3070 ) ) )
=> ( ! [X3071: term,X3072: subst] :
( ( sub @ one @ ( push @ X3071 @ X3072 ) )
= X3071 )
=> ( ! [X3073: term] :
( ( sub @ X3073 @ id )
= X3073 )
=> ( ! [X3074: term,X3075: subst] :
( ( sub @ ( lam @ X3074 ) @ X3075 )
= ( lam @ ( sub @ X3074 @ ( push @ one @ ( comp @ X3075 @ sh ) ) ) ) )
=> ( ! [X3076: term,X3077: subst,X3078: subst] :
( ( sub @ ( sub @ X3076 @ X3077 ) @ X3078 )
= ( sub @ X3076 @ ( comp @ X3077 @ X3078 ) ) )
=> ( ! [X3079: subst] :
( ( comp @ id @ X3079 )
= X3079 )
=> ( ! [X3080: term,X3081: subst] :
( ( comp @ sh @ ( push @ X3080 @ X3081 ) )
= X3081 )
=> ( ! [X3082: subst,X3083: subst,X3084: subst] :
( ( comp @ ( comp @ X3082 @ X3083 ) @ X3084 )
= ( comp @ X3082 @ ( comp @ X3083 @ X3084 ) ) )
=> ( ! [X3085: term,X3086: subst,X3087: subst] :
( ( comp @ ( push @ X3085 @ X3086 ) @ X3087 )
= ( push @ ( sub @ X3085 @ X3087 ) @ ( comp @ X3086 @ X3087 ) ) )
=> ( ! [X3088: subst] :
( ( comp @ X3088 @ id )
= X3088 )
=> ( ( ( push @ one @ sh )
= id )
=> ( ! [X3089: subst] :
( ( push @ ( sub @ one @ X3089 ) @ ( comp @ sh @ X3089 ) )
= X3089 )
=> ( ( var @ one )
=> ( ! [X3090: term] :
( ( var @ X3090 )
=> ( var @ ( sub @ X3090 @ sh ) ) )
=> ( ! [X3091: term > $o] :
( ( X3091 @ one )
=> ( ! [X3092: term] :
( ( var @ X3092 )
=> ( ( X3091 @ X3092 )
=> ( X3091 @ ( sub @ X3092 @ sh ) ) ) )
=> ! [X3093: term] :
( ( var @ X3093 )
=> ( X3091 @ X3093 ) ) ) )
=> ( ! [X3094: term,X3095: term,X3096: term,X3097: term] :
( ( ( ap @ X3094 @ X3096 )
= ( ap @ X3095 @ X3097 ) )
=> ( X3094 = X3095 ) )
=> ( ! [X3098: term,X3099: term,X3100: term,X3101: term] :
( ( ( ap @ X3098 @ X3100 )
= ( ap @ X3099 @ X3101 ) )
=> ( X3100 = X3101 ) )
=> ( ! [X3102: term,X3103: term] :
( ( ( lam @ X3102 )
= ( lam @ X3103 ) )
=> ( X3102 = X3103 ) )
=> ( ! [X3104: term,X3105: term] :
( ( ( sub @ X3104 @ sh )
= ( sub @ X3105 @ sh ) )
=> ( X3104 = X3105 ) )
=> ( ! [X3106: term,X3107: term,X3108: term] :
( ( lam @ X3106 )
!= ( ap @ X3107 @ X3108 ) )
=> ( ! [X3109: term,X3110: term] :
~ ( var @ ( ap @ X3109 @ X3110 ) )
=> ( ! [X3111: term] :
~ ( var @ ( lam @ X3111 ) )
=> ( ! [X3112: term > $o] :
( ! [X3113: term] :
( ( var @ X3113 )
=> ( X3112 @ X3113 ) )
=> ( ! [X3114: term,X3115: term] :
( ( X3112 @ X3114 )
=> ( ( X3112 @ X3115 )
=> ( X3112 @ ( ap @ X3114 @ X3115 ) ) ) )
=> ( ! [X3116: term] :
( ( X3112 @ X3116 )
=> ( X3112 @ ( lam @ X3116 ) ) )
=> ! [X3117: term] : ( X3112 @ X3117 ) ) ) )
=> ( ! [X3118: term > $o,X3119: term,X3120: subst] :
( ! [X3121: term] :
( ( var @ X3121 )
=> ( X3118 @ ( sub @ X3121 @ X3120 ) ) )
=> ( ( X3118 @ X3119 )
=> ! [X3122: term] :
( ( var @ X3122 )
=> ( X3118 @ ( sub @ X3122 @ ( push @ X3119 @ X3120 ) ) ) ) ) )
=> ( ! [X3123: term > $o] :
( ! [X3124: term,X3125: term] :
( ( X3123 @ X3124 )
=> ( ( X3123 @ X3125 )
=> ( X3123 @ ( ap @ X3124 @ X3125 ) ) ) )
=> ( ! [X3126: term] :
( ! [X3127: term] :
( ( X3123 @ X3127 )
=> ( X3123 @ ( sub @ X3126 @ ( push @ X3127 @ id ) ) ) )
=> ( X3123 @ ( lam @ X3126 ) ) )
=> ! [X3128: term,X3129: subst] :
( ! [X3130: term] :
( ( var @ X3130 )
=> ( X3123 @ ( sub @ X3130 @ X3129 ) ) )
=> ( X3123 @ ( sub @ X3128 @ X3129 ) ) ) ) )
=> ! [X3131: term > $o] :
( ! [X3132: term] :
( ( var @ X3132 )
=> ( X3131 @ X3132 ) )
=> ( ! [X3133: term,X3134: term] :
( ( X3131 @ X3133 )
=> ( ( X3131 @ X3134 )
=> ( X3131 @ ( ap @ X3133 @ X3134 ) ) ) )
=> ( ! [X3135: term] :
( ! [X3136: term] :
( ( X3131 @ X3136 )
=> ( X3131 @ ( sub @ X3135 @ ( push @ X3136 @ id ) ) ) )
=> ( X3131 @ ( lam @ X3135 ) ) )
=> ! [X3137: term] : ( X3131 @ X3137 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
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)],[induction2_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]) ).
thf(c_0_29,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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[thm]),c_0_28])]) ).
thf(c_0_30,negated_conjecture,
! [X3455: term,X3456: term,X3457: subst,X3458: term,X3459: subst,X3460: term,X3461: term,X3462: subst,X3463: term,X3464: subst,X3465: subst,X3466: subst,X3467: term,X3468: subst,X3469: subst,X3470: subst,X3471: subst,X3472: term,X3473: subst,X3474: subst,X3475: subst,X3476: subst,X3477: term,X3478: term > $o,X3480: term,X3481: term,X3482: term,X3483: term,X3484: term,X3485: term,X3486: term,X3487: term,X3488: term,X3489: term,X3490: term,X3491: term,X3492: term,X3493: term,X3494: term,X3495: term,X3496: term,X3497: term,X3498: term,X3499: term > $o,X3504: term,X3505: term > $o,X3506: term,X3507: subst,X3509: term,X3510: term > $o,X3514: term,X3515: term,X3516: subst,X3519: term,X3520: term,X3521: term,X3522: term] :
( ( ( sub @ ( ap @ X3455 @ X3456 ) @ X3457 )
= ( ap @ ( sub @ X3455 @ X3457 ) @ ( sub @ X3456 @ X3457 ) ) )
& ( ( sub @ one @ ( push @ X3458 @ X3459 ) )
= X3458 )
& ( ( sub @ X3460 @ id )
= X3460 )
& ( ( sub @ ( lam @ X3461 ) @ X3462 )
= ( lam @ ( sub @ X3461 @ ( push @ one @ ( comp @ X3462 @ sh ) ) ) ) )
& ( ( sub @ ( sub @ X3463 @ X3464 ) @ X3465 )
= ( sub @ X3463 @ ( comp @ X3464 @ X3465 ) ) )
& ( ( comp @ id @ X3466 )
= X3466 )
& ( ( comp @ sh @ ( push @ X3467 @ X3468 ) )
= X3468 )
& ( ( comp @ ( comp @ X3469 @ X3470 ) @ X3471 )
= ( comp @ X3469 @ ( comp @ X3470 @ X3471 ) ) )
& ( ( comp @ ( push @ X3472 @ X3473 ) @ X3474 )
= ( push @ ( sub @ X3472 @ X3474 ) @ ( comp @ X3473 @ X3474 ) ) )
& ( ( comp @ X3475 @ id )
= X3475 )
& ( ( push @ one @ sh )
= id )
& ( ( push @ ( sub @ one @ X3476 ) @ ( comp @ sh @ X3476 ) )
= X3476 )
& ( var @ one )
& ( ~ ( var @ X3477 )
| ( var @ ( sub @ X3477 @ sh ) ) )
& ( ( var @ ( esk1_1 @ X3478 ) )
| ~ ( var @ X3480 )
| ( X3478 @ X3480 )
| ~ ( X3478 @ one ) )
& ( ( X3478 @ ( esk1_1 @ X3478 ) )
| ~ ( var @ X3480 )
| ( X3478 @ X3480 )
| ~ ( X3478 @ one ) )
& ( ~ ( X3478 @ ( sub @ ( esk1_1 @ X3478 ) @ sh ) )
| ~ ( var @ X3480 )
| ( X3478 @ X3480 )
| ~ ( X3478 @ one ) )
& ( ( ( ap @ X3481 @ X3483 )
!= ( ap @ X3482 @ X3484 ) )
| ( X3481 = X3482 ) )
& ( ( ( ap @ X3485 @ X3487 )
!= ( ap @ X3486 @ X3488 ) )
| ( X3487 = X3488 ) )
& ( ( ( lam @ X3489 )
!= ( lam @ X3490 ) )
| ( X3489 = X3490 ) )
& ( ( ( sub @ X3491 @ sh )
!= ( sub @ X3492 @ sh ) )
| ( X3491 = X3492 ) )
& ( ( lam @ X3493 )
!= ( ap @ X3494 @ X3495 ) )
& ~ ( var @ ( ap @ X3496 @ X3497 ) )
& ~ ( var @ ( lam @ X3498 ) )
& ( ( X3499 @ ( esk5_1 @ X3499 ) )
| ( X3499 @ X3504 )
| ( X3499 @ ( esk3_1 @ X3499 ) )
| ( var @ ( esk2_1 @ X3499 ) ) )
& ( ~ ( X3499 @ ( lam @ ( esk5_1 @ X3499 ) ) )
| ( X3499 @ X3504 )
| ( X3499 @ ( esk3_1 @ X3499 ) )
| ( var @ ( esk2_1 @ X3499 ) ) )
& ( ( X3499 @ ( esk5_1 @ X3499 ) )
| ( X3499 @ X3504 )
| ( X3499 @ ( esk4_1 @ X3499 ) )
| ( var @ ( esk2_1 @ X3499 ) ) )
& ( ~ ( X3499 @ ( lam @ ( esk5_1 @ X3499 ) ) )
| ( X3499 @ X3504 )
| ( X3499 @ ( esk4_1 @ X3499 ) )
| ( var @ ( esk2_1 @ X3499 ) ) )
& ( ( X3499 @ ( esk5_1 @ X3499 ) )
| ( X3499 @ X3504 )
| ~ ( X3499 @ ( ap @ ( esk3_1 @ X3499 ) @ ( esk4_1 @ X3499 ) ) )
| ( var @ ( esk2_1 @ X3499 ) ) )
& ( ~ ( X3499 @ ( lam @ ( esk5_1 @ X3499 ) ) )
| ( X3499 @ X3504 )
| ~ ( X3499 @ ( ap @ ( esk3_1 @ X3499 ) @ ( esk4_1 @ X3499 ) ) )
| ( var @ ( esk2_1 @ X3499 ) ) )
& ( ( X3499 @ ( esk5_1 @ X3499 ) )
| ( X3499 @ X3504 )
| ( X3499 @ ( esk3_1 @ X3499 ) )
| ~ ( X3499 @ ( esk2_1 @ X3499 ) ) )
& ( ~ ( X3499 @ ( lam @ ( esk5_1 @ X3499 ) ) )
| ( X3499 @ X3504 )
| ( X3499 @ ( esk3_1 @ X3499 ) )
| ~ ( X3499 @ ( esk2_1 @ X3499 ) ) )
& ( ( X3499 @ ( esk5_1 @ X3499 ) )
| ( X3499 @ X3504 )
| ( X3499 @ ( esk4_1 @ X3499 ) )
| ~ ( X3499 @ ( esk2_1 @ X3499 ) ) )
& ( ~ ( X3499 @ ( lam @ ( esk5_1 @ X3499 ) ) )
| ( X3499 @ X3504 )
| ( X3499 @ ( esk4_1 @ X3499 ) )
| ~ ( X3499 @ ( esk2_1 @ X3499 ) ) )
& ( ( X3499 @ ( esk5_1 @ X3499 ) )
| ( X3499 @ X3504 )
| ~ ( X3499 @ ( ap @ ( esk3_1 @ X3499 ) @ ( esk4_1 @ X3499 ) ) )
| ~ ( X3499 @ ( esk2_1 @ X3499 ) ) )
& ( ~ ( X3499 @ ( lam @ ( esk5_1 @ X3499 ) ) )
| ( X3499 @ X3504 )
| ~ ( X3499 @ ( ap @ ( esk3_1 @ X3499 ) @ ( esk4_1 @ X3499 ) ) )
| ~ ( X3499 @ ( esk2_1 @ X3499 ) ) )
& ( ( var @ ( esk6_3 @ X3505 @ X3506 @ X3507 ) )
| ~ ( X3505 @ X3506 )
| ~ ( var @ X3509 )
| ( X3505 @ ( sub @ X3509 @ ( push @ X3506 @ X3507 ) ) ) )
& ( ~ ( X3505 @ ( sub @ ( esk6_3 @ X3505 @ X3506 @ X3507 ) @ X3507 ) )
| ~ ( X3505 @ X3506 )
| ~ ( var @ X3509 )
| ( X3505 @ ( sub @ X3509 @ ( push @ X3506 @ X3507 ) ) ) )
& ( ( var @ ( esk10_3 @ X3510 @ X3515 @ X3516 ) )
| ( X3510 @ ( sub @ X3515 @ X3516 ) )
| ~ ( X3510 @ X3514 )
| ( X3510 @ ( sub @ ( esk9_1 @ X3510 ) @ ( push @ X3514 @ id ) ) )
| ( X3510 @ ( esk7_1 @ X3510 ) ) )
& ( ~ ( X3510 @ ( sub @ ( esk10_3 @ X3510 @ X3515 @ X3516 ) @ X3516 ) )
| ( X3510 @ ( sub @ X3515 @ X3516 ) )
| ~ ( X3510 @ X3514 )
| ( X3510 @ ( sub @ ( esk9_1 @ X3510 ) @ ( push @ X3514 @ id ) ) )
| ( X3510 @ ( esk7_1 @ X3510 ) ) )
& ( ( var @ ( esk10_3 @ X3510 @ X3515 @ X3516 ) )
| ( X3510 @ ( sub @ X3515 @ X3516 ) )
| ~ ( X3510 @ ( lam @ ( esk9_1 @ X3510 ) ) )
| ( X3510 @ ( esk7_1 @ X3510 ) ) )
& ( ~ ( X3510 @ ( sub @ ( esk10_3 @ X3510 @ X3515 @ X3516 ) @ X3516 ) )
| ( X3510 @ ( sub @ X3515 @ X3516 ) )
| ~ ( X3510 @ ( lam @ ( esk9_1 @ X3510 ) ) )
| ( X3510 @ ( esk7_1 @ X3510 ) ) )
& ( ( var @ ( esk10_3 @ X3510 @ X3515 @ X3516 ) )
| ( X3510 @ ( sub @ X3515 @ X3516 ) )
| ~ ( X3510 @ X3514 )
| ( X3510 @ ( sub @ ( esk9_1 @ X3510 ) @ ( push @ X3514 @ id ) ) )
| ( X3510 @ ( esk8_1 @ X3510 ) ) )
& ( ~ ( X3510 @ ( sub @ ( esk10_3 @ X3510 @ X3515 @ X3516 ) @ X3516 ) )
| ( X3510 @ ( sub @ X3515 @ X3516 ) )
| ~ ( X3510 @ X3514 )
| ( X3510 @ ( sub @ ( esk9_1 @ X3510 ) @ ( push @ X3514 @ id ) ) )
| ( X3510 @ ( esk8_1 @ X3510 ) ) )
& ( ( var @ ( esk10_3 @ X3510 @ X3515 @ X3516 ) )
| ( X3510 @ ( sub @ X3515 @ X3516 ) )
| ~ ( X3510 @ ( lam @ ( esk9_1 @ X3510 ) ) )
| ( X3510 @ ( esk8_1 @ X3510 ) ) )
& ( ~ ( X3510 @ ( sub @ ( esk10_3 @ X3510 @ X3515 @ X3516 ) @ X3516 ) )
| ( X3510 @ ( sub @ X3515 @ X3516 ) )
| ~ ( X3510 @ ( lam @ ( esk9_1 @ X3510 ) ) )
| ( X3510 @ ( esk8_1 @ X3510 ) ) )
& ( ( var @ ( esk10_3 @ X3510 @ X3515 @ X3516 ) )
| ( X3510 @ ( sub @ X3515 @ X3516 ) )
| ~ ( X3510 @ X3514 )
| ( X3510 @ ( sub @ ( esk9_1 @ X3510 ) @ ( push @ X3514 @ id ) ) )
| ~ ( X3510 @ ( ap @ ( esk7_1 @ X3510 ) @ ( esk8_1 @ X3510 ) ) ) )
& ( ~ ( X3510 @ ( sub @ ( esk10_3 @ X3510 @ X3515 @ X3516 ) @ X3516 ) )
| ( X3510 @ ( sub @ X3515 @ X3516 ) )
| ~ ( X3510 @ X3514 )
| ( X3510 @ ( sub @ ( esk9_1 @ X3510 ) @ ( push @ X3514 @ id ) ) )
| ~ ( X3510 @ ( ap @ ( esk7_1 @ X3510 ) @ ( esk8_1 @ X3510 ) ) ) )
& ( ( var @ ( esk10_3 @ X3510 @ X3515 @ X3516 ) )
| ( X3510 @ ( sub @ X3515 @ X3516 ) )
| ~ ( X3510 @ ( lam @ ( esk9_1 @ X3510 ) ) )
| ~ ( X3510 @ ( ap @ ( esk7_1 @ X3510 ) @ ( esk8_1 @ X3510 ) ) ) )
& ( ~ ( X3510 @ ( sub @ ( esk10_3 @ X3510 @ X3515 @ X3516 ) @ X3516 ) )
| ( X3510 @ ( sub @ X3515 @ X3516 ) )
| ~ ( X3510 @ ( lam @ ( esk9_1 @ X3510 ) ) )
| ~ ( X3510 @ ( ap @ ( esk7_1 @ X3510 ) @ ( esk8_1 @ X3510 ) ) ) )
& ( ~ ( var @ X3519 )
| ( epred1_0 @ X3519 ) )
& ( ~ ( epred1_0 @ X3520 )
| ~ ( epred1_0 @ X3521 )
| ( epred1_0 @ ( ap @ X3520 @ X3521 ) ) )
& ( ( epred1_0 @ ( esk11_1 @ X3522 ) )
| ( epred1_0 @ ( lam @ X3522 ) ) )
& ( ~ ( epred1_0 @ ( sub @ X3522 @ ( push @ ( esk11_1 @ X3522 ) @ id ) ) )
| ( epred1_0 @ ( lam @ X3522 ) ) )
& ~ ( epred1_0 @ esk12_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_29])])])])])])]) ).
thf(c_0_31,negated_conjecture,
! [X3: subst,X1: term,X6: term > $o] :
( ( X6 @ ( sub @ X1 @ X3 ) )
| ~ ( X6 @ ( sub @ ( esk10_3 @ X6 @ X1 @ X3 ) @ X3 ) )
| ~ ( X6 @ ( lam @ ( esk9_1 @ X6 ) ) )
| ~ ( X6 @ ( ap @ ( esk7_1 @ X6 ) @ ( esk8_1 @ X6 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_32,negated_conjecture,
! [X1: term,X2: term] :
( ( epred1_0 @ ( ap @ X1 @ X2 ) )
| ~ ( epred1_0 @ X1 )
| ~ ( epred1_0 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_33,negated_conjecture,
! [X3: subst,X1: term,X6: term > $o] :
( ( X6 @ ( sub @ X1 @ X3 ) )
| ( X6 @ ( esk7_1 @ X6 ) )
| ~ ( X6 @ ( sub @ ( esk10_3 @ X6 @ X1 @ X3 ) @ X3 ) )
| ~ ( X6 @ ( lam @ ( esk9_1 @ X6 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_34,negated_conjecture,
! [X3: subst,X1: term,X6: term > $o] :
( ( X6 @ ( sub @ X1 @ X3 ) )
| ( X6 @ ( esk8_1 @ X6 ) )
| ~ ( X6 @ ( sub @ ( esk10_3 @ X6 @ X1 @ X3 ) @ X3 ) )
| ~ ( X6 @ ( lam @ ( esk9_1 @ X6 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_35,negated_conjecture,
! [X1: term,X3: subst] :
( ( epred1_0 @ ( sub @ X1 @ X3 ) )
| ~ ( epred1_0 @ ( sub @ ( esk10_3 @ epred1_0 @ X1 @ X3 ) @ X3 ) )
| ~ ( epred1_0 @ ( lam @ ( esk9_1 @ epred1_0 ) ) ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]),c_0_34]) ).
thf(c_0_36,negated_conjecture,
! [X1: term] :
( ( sub @ X1 @ id )
= X1 ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_37,negated_conjecture,
! [X1: term,X3: subst,X2: term,X6: term > $o] :
( ( X6 @ ( sub @ X1 @ X3 ) )
| ( X6 @ ( sub @ ( esk9_1 @ X6 ) @ ( push @ X2 @ id ) ) )
| ~ ( X6 @ ( sub @ ( esk10_3 @ X6 @ X1 @ X3 ) @ X3 ) )
| ~ ( X6 @ X2 )
| ~ ( X6 @ ( ap @ ( esk7_1 @ X6 ) @ ( esk8_1 @ X6 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_38,negated_conjecture,
! [X1: term,X6: term > $o,X3: subst,X2: term] :
( ( X6 @ ( sub @ X1 @ X3 ) )
| ( X6 @ ( sub @ ( esk9_1 @ X6 ) @ ( push @ X2 @ id ) ) )
| ( X6 @ ( esk7_1 @ X6 ) )
| ~ ( X6 @ ( sub @ ( esk10_3 @ X6 @ X1 @ X3 ) @ X3 ) )
| ~ ( X6 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_39,negated_conjecture,
! [X1: term,X6: term > $o,X3: subst,X2: term] :
( ( X6 @ ( sub @ X1 @ X3 ) )
| ( X6 @ ( sub @ ( esk9_1 @ X6 ) @ ( push @ X2 @ id ) ) )
| ( X6 @ ( esk8_1 @ X6 ) )
| ~ ( X6 @ ( sub @ ( esk10_3 @ X6 @ X1 @ X3 ) @ X3 ) )
| ~ ( X6 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_40,negated_conjecture,
! [X3: subst,X2: term,X1: term,X6: term > $o] :
( ( var @ ( esk10_3 @ X6 @ X1 @ X3 ) )
| ( X6 @ ( sub @ X1 @ X3 ) )
| ( X6 @ ( sub @ ( esk9_1 @ X6 ) @ ( push @ X2 @ id ) ) )
| ~ ( X6 @ X2 )
| ~ ( X6 @ ( ap @ ( esk7_1 @ X6 ) @ ( esk8_1 @ X6 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_41,negated_conjecture,
! [X6: term > $o,X1: term,X3: subst,X2: term] :
( ( var @ ( esk10_3 @ X6 @ X1 @ X3 ) )
| ( X6 @ ( sub @ X1 @ X3 ) )
| ( X6 @ ( sub @ ( esk9_1 @ X6 ) @ ( push @ X2 @ id ) ) )
| ( X6 @ ( esk7_1 @ X6 ) )
| ~ ( X6 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_42,negated_conjecture,
! [X6: term > $o,X1: term,X3: subst,X2: term] :
( ( var @ ( esk10_3 @ X6 @ X1 @ X3 ) )
| ( X6 @ ( sub @ X1 @ X3 ) )
| ( X6 @ ( sub @ ( esk9_1 @ X6 ) @ ( push @ X2 @ id ) ) )
| ( X6 @ ( esk8_1 @ X6 ) )
| ~ ( X6 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_43,negated_conjecture,
! [X1: term] :
( ( epred1_0 @ X1 )
| ~ ( epred1_0 @ ( esk10_3 @ epred1_0 @ X1 @ id ) )
| ~ ( epred1_0 @ ( lam @ ( esk9_1 @ epred1_0 ) ) ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_36]) ).
thf(c_0_44,negated_conjecture,
! [X1: term] :
( ( epred1_0 @ X1 )
| ~ ( var @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_45,negated_conjecture,
! [X3: subst,X1: term,X6: term > $o] :
( ( var @ ( esk10_3 @ X6 @ X1 @ X3 ) )
| ( X6 @ ( sub @ X1 @ X3 ) )
| ~ ( X6 @ ( lam @ ( esk9_1 @ X6 ) ) )
| ~ ( X6 @ ( ap @ ( esk7_1 @ X6 ) @ ( esk8_1 @ X6 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_46,negated_conjecture,
! [X3: subst,X1: term,X6: term > $o] :
( ( var @ ( esk10_3 @ X6 @ X1 @ X3 ) )
| ( X6 @ ( sub @ X1 @ X3 ) )
| ( X6 @ ( esk7_1 @ X6 ) )
| ~ ( X6 @ ( lam @ ( esk9_1 @ X6 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_47,negated_conjecture,
! [X3: subst,X1: term,X6: term > $o] :
( ( var @ ( esk10_3 @ X6 @ X1 @ X3 ) )
| ( X6 @ ( sub @ X1 @ X3 ) )
| ( X6 @ ( esk8_1 @ X6 ) )
| ~ ( X6 @ ( lam @ ( esk9_1 @ X6 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_48,negated_conjecture,
! [X3: subst,X2: term,X1: term] :
( ( epred1_0 @ ( sub @ ( esk9_1 @ epred1_0 ) @ ( push @ X1 @ id ) ) )
| ( epred1_0 @ ( sub @ X2 @ X3 ) )
| ~ ( epred1_0 @ ( sub @ ( esk10_3 @ epred1_0 @ X2 @ X3 ) @ X3 ) )
| ~ ( epred1_0 @ X1 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_32]),c_0_38]),c_0_39]) ).
thf(c_0_49,negated_conjecture,
! [X3: subst,X2: term,X1: term] :
( ( epred1_0 @ ( sub @ ( esk9_1 @ epred1_0 ) @ ( push @ X1 @ id ) ) )
| ( var @ ( esk10_3 @ epred1_0 @ X2 @ X3 ) )
| ( epred1_0 @ ( sub @ X2 @ X3 ) )
| ~ ( epred1_0 @ X1 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_32]),c_0_41]),c_0_42]) ).
thf(c_0_50,negated_conjecture,
! [X1: term] :
( ( epred1_0 @ ( esk11_1 @ X1 ) )
| ( epred1_0 @ ( lam @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_51,negated_conjecture,
! [X1: term] :
( ( epred1_0 @ X1 )
| ~ ( var @ ( esk10_3 @ epred1_0 @ X1 @ id ) )
| ~ ( epred1_0 @ ( lam @ ( esk9_1 @ epred1_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
thf(c_0_52,negated_conjecture,
! [X1: term,X3: subst] :
( ( var @ ( esk10_3 @ epred1_0 @ X1 @ X3 ) )
| ( epred1_0 @ ( sub @ X1 @ X3 ) )
| ~ ( epred1_0 @ ( lam @ ( esk9_1 @ epred1_0 ) ) ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_32]),c_0_46]),c_0_47]) ).
thf(c_0_53,negated_conjecture,
! [X2: term,X1: term] :
( ( epred1_0 @ ( sub @ ( esk9_1 @ epred1_0 ) @ ( push @ X1 @ id ) ) )
| ( epred1_0 @ X2 )
| ~ ( epred1_0 @ ( esk10_3 @ epred1_0 @ X2 @ id ) )
| ~ ( epred1_0 @ X1 ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_36]),c_0_36]) ).
thf(c_0_54,negated_conjecture,
! [X1: term] :
( ( epred1_0 @ ( lam @ X1 ) )
| ~ ( epred1_0 @ ( sub @ X1 @ ( push @ ( esk11_1 @ X1 ) @ id ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_55,negated_conjecture,
! [X3: subst,X2: term,X1: term] :
( ( epred1_0 @ ( sub @ ( esk9_1 @ epred1_0 ) @ ( push @ ( esk11_1 @ X1 ) @ id ) ) )
| ( var @ ( esk10_3 @ epred1_0 @ X2 @ X3 ) )
| ( epred1_0 @ ( sub @ X2 @ X3 ) )
| ( epred1_0 @ ( lam @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
thf(c_0_56,negated_conjecture,
! [X1: term] :
( ( epred1_0 @ X1 )
| ~ ( epred1_0 @ ( lam @ ( esk9_1 @ epred1_0 ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_36])]) ).
thf(c_0_57,negated_conjecture,
! [X2: term,X1: term] :
( ( epred1_0 @ ( sub @ ( esk9_1 @ epred1_0 ) @ ( push @ X1 @ id ) ) )
| ( epred1_0 @ X2 )
| ~ ( var @ ( esk10_3 @ epred1_0 @ X2 @ id ) )
| ~ ( epred1_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_53,c_0_44]) ).
thf(c_0_58,negated_conjecture,
! [X1: term,X3: subst] :
( ( var @ ( esk10_3 @ epred1_0 @ X1 @ X3 ) )
| ( epred1_0 @ ( sub @ X1 @ X3 ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56]) ).
thf(c_0_59,negated_conjecture,
! [X1: term] :
( ( epred1_0 @ ( sub @ ( esk9_1 @ epred1_0 ) @ ( push @ X1 @ id ) ) )
| ~ ( epred1_0 @ X1 ) ),
inference(condense,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_36])])]) ).
thf(c_0_60,negated_conjecture,
epred1_0 @ ( lam @ ( esk9_1 @ epred1_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_59]),c_0_50]) ).
thf(c_0_61,negated_conjecture,
~ ( epred1_0 @ esk12_0 ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_62,negated_conjecture,
! [X1: term] : ( epred1_0 @ X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_60])]) ).
thf(c_0_63,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_62])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : ALG253^1 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n006.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 22:54:23 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.21/0.48 Running higher-order theorem proving
% 0.21/0.48 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
% 29.00/4.15 # Version: 3.1.0-ho
% 29.00/4.15 # Preprocessing class: HSMMSLSSLLLNHFA.
% 29.00/4.15 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 29.00/4.15 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 29.00/4.15 # Starting post_as_ho1 with 300s (1) cores
% 29.00/4.15 # Starting post_as_ho5 with 300s (1) cores
% 29.00/4.15 # Starting post_as_ho10 with 300s (1) cores
% 29.00/4.15 # post_as_ho10 with pid 10769 completed with status 0
% 29.00/4.15 # Result found by post_as_ho10
% 29.00/4.15 # Preprocessing class: HSMMSLSSLLLNHFA.
% 29.00/4.15 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 29.00/4.15 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 29.00/4.15 # Starting post_as_ho1 with 300s (1) cores
% 29.00/4.15 # Starting post_as_ho5 with 300s (1) cores
% 29.00/4.15 # Starting post_as_ho10 with 300s (1) cores
% 29.00/4.15 # No SInE strategy applied
% 29.00/4.15 # Search class: HGUSM-FFMF31-MHFMMMBN
% 29.00/4.15 # partial match(1): HGUSM-FFMS31-MHFMMMBN
% 29.00/4.15 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 29.00/4.15 # Starting new_ho_10 with 163s (1) cores
% 29.00/4.15 # new_ho_10 with pid 10776 completed with status 0
% 29.00/4.15 # Result found by new_ho_10
% 29.00/4.15 # Preprocessing class: HSMMSLSSLLLNHFA.
% 29.00/4.15 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 29.00/4.15 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 29.00/4.15 # Starting post_as_ho1 with 300s (1) cores
% 29.00/4.15 # Starting post_as_ho5 with 300s (1) cores
% 29.00/4.15 # Starting post_as_ho10 with 300s (1) cores
% 29.00/4.15 # No SInE strategy applied
% 29.00/4.15 # Search class: HGUSM-FFMF31-MHFMMMBN
% 29.00/4.15 # partial match(1): HGUSM-FFMS31-MHFMMMBN
% 29.00/4.15 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 29.00/4.15 # Starting new_ho_10 with 163s (1) cores
% 29.00/4.15 # Preprocessing time : 0.005 s
% 29.00/4.15 # Presaturation interreduction done
% 29.00/4.15
% 29.00/4.15 # Proof found!
% 29.00/4.15 # SZS status Theorem
% 29.00/4.15 # SZS output start CNFRefutation
% See solution above
% 29.00/4.15 # Parsed axioms : 238
% 29.00/4.15 # Removed by relevancy pruning/SinE : 0
% 29.00/4.15 # Initial clauses : 181
% 29.00/4.15 # Removed in clause preprocessing : 124
% 29.00/4.15 # Initial clauses in saturation : 57
% 29.00/4.15 # Processed clauses : 2877
% 29.00/4.15 # ...of these trivial : 189
% 29.00/4.15 # ...subsumed : 1503
% 29.00/4.15 # ...remaining for further processing : 1185
% 29.00/4.15 # Other redundant clauses eliminated : 0
% 29.00/4.15 # Clauses deleted for lack of memory : 0
% 29.00/4.15 # Backward-subsumed : 100
% 29.00/4.15 # Backward-rewritten : 375
% 29.00/4.15 # Generated clauses : 103558
% 29.00/4.15 # ...of the previous two non-redundant : 96652
% 29.00/4.15 # ...aggressively subsumed : 0
% 29.00/4.15 # Contextual simplify-reflections : 61
% 29.00/4.15 # Paramodulations : 103187
% 29.00/4.15 # Factorizations : 348
% 29.00/4.15 # NegExts : 0
% 29.00/4.15 # Equation resolutions : 19
% 29.00/4.15 # Disequality decompositions : 0
% 29.00/4.15 # Total rewrite steps : 35906
% 29.00/4.15 # ...of those cached : 28480
% 29.00/4.15 # Propositional unsat checks : 0
% 29.00/4.15 # Propositional check models : 0
% 29.00/4.15 # Propositional check unsatisfiable : 0
% 29.00/4.15 # Propositional clauses : 0
% 29.00/4.15 # Propositional clauses after purity: 0
% 29.00/4.15 # Propositional unsat core size : 0
% 29.00/4.15 # Propositional preprocessing time : 0.000
% 29.00/4.15 # Propositional encoding time : 0.000
% 29.00/4.15 # Propositional solver time : 0.000
% 29.00/4.15 # Success case prop preproc time : 0.000
% 29.00/4.15 # Success case prop encoding time : 0.000
% 29.00/4.15 # Success case prop solver time : 0.000
% 29.00/4.15 # Current number of processed clauses : 654
% 29.00/4.15 # Positive orientable unit clauses : 122
% 29.00/4.15 # Positive unorientable unit clauses: 16
% 29.00/4.15 # Negative unit clauses : 9
% 29.00/4.15 # Non-unit-clauses : 507
% 29.00/4.15 # Current number of unprocessed clauses: 93434
% 29.00/4.15 # ...number of literals in the above : 835535
% 29.00/4.15 # Current number of archived formulas : 0
% 29.00/4.15 # Current number of archived clauses : 531
% 29.00/4.15 # Clause-clause subsumption calls (NU) : 167312
% 29.00/4.15 # Rec. Clause-clause subsumption calls : 9664
% 29.00/4.15 # Non-unit clause-clause subsumptions : 1345
% 29.00/4.15 # Unit Clause-clause subsumption calls : 1589
% 29.00/4.15 # Rewrite failures with RHS unbound : 0
% 29.00/4.15 # BW rewrite match attempts : 7129
% 29.00/4.15 # BW rewrite match successes : 323
% 29.00/4.15 # Condensation attempts : 2877
% 29.00/4.15 # Condensation successes : 301
% 29.00/4.15 # Termbank termtop insertions : 4407447
% 29.00/4.15 # Search garbage collected termcells : 3467
% 29.00/4.15
% 29.00/4.15 # -------------------------------------------------
% 29.00/4.15 # User time : 3.479 s
% 29.00/4.15 # System time : 0.089 s
% 29.00/4.15 # Total time : 3.569 s
% 29.00/4.15 # Maximum resident set size: 5976 pages
% 29.00/4.15
% 29.00/4.15 # -------------------------------------------------
% 29.00/4.15 # User time : 3.486 s
% 29.00/4.15 # System time : 0.090 s
% 29.00/4.15 # Total time : 3.575 s
% 29.00/4.15 # Maximum resident set size: 2072 pages
% 29.00/4.15 % E---3.1 exiting
% 29.00/4.15 % E exiting
%------------------------------------------------------------------------------