TSTP Solution File: ALG256^1 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ALG256^1 : TPTP v8.1.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n024.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 : 600s
% DateTime : Thu Jul 14 17:57:46 EDT 2022
% Result : Theorem 187.26s 186.51s
% Output : Proof 187.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 79
% Syntax : Number of formulae : 219 ( 81 unt; 0 typ; 31 def)
% Number of atoms : 1099 ( 170 equ; 0 cnn)
% Maximal formula atoms : 67 ( 5 avg)
% Number of connectives : 1478 ( 207 ~; 141 |; 2 &; 837 @)
% ( 0 <=>; 281 =>; 2 <=; 0 <~>)
% Maximal formula depth : 40 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 96 ( 93 usr; 95 con; 0-2 aty)
% ( 8 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 351 ( 3 ^ 348 !; 0 ?; 351 :)
% Comments :
%------------------------------------------------------------------------------
thf(def_axapp,definition,
( axapp
= ( ! [X1: term,X2: term,X3: subst] :
( ( sub @ ( ap @ X1 @ X2 ) @ X3 )
= ( ap @ ( sub @ X1 @ X3 ) @ ( sub @ X2 @ X3 ) ) ) ) ) ).
thf(def_axvarcons,definition,
( axvarcons
= ( ! [X1: term,X2: subst] :
( ( sub @ one @ ( push @ X1 @ X2 ) )
= X1 ) ) ) ).
thf(def_axvarid,definition,
( axvarid
= ( ! [X1: term] :
( ( sub @ X1 @ id )
= X1 ) ) ) ).
thf(def_axabs,definition,
( axabs
= ( ! [X1: term,X2: subst] :
( ( sub @ ( lam @ X1 ) @ X2 )
= ( lam @ ( sub @ X1 @ ( push @ one @ ( comp @ X2 @ sh ) ) ) ) ) ) ) ).
thf(def_axclos,definition,
( axclos
= ( ! [X1: term,X2: subst,X3: subst] :
( ( sub @ ( sub @ X1 @ X2 ) @ X3 )
= ( sub @ X1 @ ( comp @ X2 @ X3 ) ) ) ) ) ).
thf(def_axidl,definition,
( axidl
= ( ! [X1: subst] :
( ( comp @ id @ X1 )
= X1 ) ) ) ).
thf(def_axshiftcons,definition,
( axshiftcons
= ( ! [X1: term,X2: subst] :
( ( comp @ sh @ ( push @ X1 @ X2 ) )
= X2 ) ) ) ).
thf(def_axassoc,definition,
( axassoc
= ( ! [X1: subst,X2: subst,X3: subst] :
( ( comp @ ( comp @ X1 @ X2 ) @ X3 )
= ( comp @ X1 @ ( comp @ X2 @ X3 ) ) ) ) ) ).
thf(def_axmap,definition,
( axmap
= ( ! [X1: term,X2: subst,X3: subst] :
( ( comp @ ( push @ X1 @ X2 ) @ X3 )
= ( push @ ( sub @ X1 @ X3 ) @ ( comp @ X2 @ X3 ) ) ) ) ) ).
thf(def_axidr,definition,
( axidr
= ( ! [X1: subst] :
( ( comp @ X1 @ id )
= X1 ) ) ) ).
thf(def_axvarshift,definition,
( axvarshift
= ( ( push @ one @ sh )
= id ) ) ).
thf(def_axscons,definition,
( axscons
= ( ! [X1: subst] :
( ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) )
= X1 ) ) ) ).
thf(def_ulamvar1,definition,
( ulamvar1
= ( var @ one ) ) ).
thf(def_ulamvarsh,definition,
( ulamvarsh
= ( ! [X1: term] :
( ( var @ X1 )
=> ( var @ ( sub @ X1 @ sh ) ) ) ) ) ).
thf(def_ulamvarind,definition,
( ulamvarind
= ( ! [X1: term > $o] :
( ( X1 @ one )
=> ( ! [X2: term] :
( ( var @ X2 )
=> ( ( X1 @ X2 )
=> ( X1 @ ( sub @ X2 @ sh ) ) ) )
=> ! [X2: term] :
( ( var @ X2 )
=> ( X1 @ X2 ) ) ) ) ) ) ).
thf(def_apinj1,definition,
( apinj1
= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ) ).
thf(def_apinj2,definition,
( apinj2
= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) ).
thf(def_laminj,definition,
( laminj
= ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) ) ) ) ).
thf(def_shinj,definition,
( shinj
= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) ).
thf(def_lamnotap,definition,
( lamnotap
= ( ! [X1: term,X2: term,X3: term] :
( ( lam @ X1 )
!= ( ap @ X2 @ X3 ) ) ) ) ).
thf(def_apnotvar,definition,
( apnotvar
= ( ! [X1: term,X2: term] :
~ ( var @ ( ap @ X1 @ X2 ) ) ) ) ).
thf(def_lamnotvar,definition,
( lamnotvar
= ( ! [X1: term] :
~ ( var @ ( lam @ X1 ) ) ) ) ).
thf(def_induction,definition,
( induction
= ( ! [X1: term > $o] :
( ! [X2: term] :
( ( var @ X2 )
=> ( X1 @ X2 ) )
=> ( ! [X2: term,X3: term] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X1 @ ( ap @ X2 @ X3 ) ) ) )
=> ( ! [X2: term] :
( ( X1 @ X2 )
=> ( X1 @ ( lam @ X2 ) ) )
=> ( !! @ X1 ) ) ) ) ) ) ).
thf(def_pushprop,definition,
( pushprop
= ( ! [X1: term > $o,X2: term,X3: subst] :
( ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) )
=> ( ( X1 @ X2 )
=> ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ ( push @ X2 @ X3 ) ) ) ) ) ) ) ) ).
thf(def_induction2lem,definition,
( induction2lem
= ( ! [X1: term > $o] :
( ! [X2: term,X3: term] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X1 @ ( ap @ X2 @ X3 ) ) ) )
=> ( ! [X2: term] :
( ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( sub @ X2 @ ( push @ X3 @ id ) ) ) )
=> ( X1 @ ( lam @ X2 ) ) )
=> ! [X2: term,X3: subst] :
( ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ).
thf(def_induction2,definition,
( induction2
= ( ! [X1: term > $o] :
( ! [X2: term] :
( ( var @ X2 )
=> ( X1 @ X2 ) )
=> ( ! [X2: term,X3: term] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X1 @ ( ap @ X2 @ X3 ) ) ) )
=> ( ! [X2: term] :
( ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( sub @ X2 @ ( push @ X3 @ id ) ) ) )
=> ( X1 @ ( lam @ X2 ) ) )
=> ( !! @ X1 ) ) ) ) ) ) ).
thf(def_substmonoid,definition,
( substmonoid
= ( ~ ( ~ ( ! [X1: subst,X2: subst,X3: subst] :
( ( comp @ ( comp @ X1 @ X2 ) @ X3 )
= ( comp @ X1 @ ( comp @ X2 @ X3 ) ) )
=> ~ ! [X1: subst] :
( ( comp @ id @ X1 )
= X1 ) )
=> ~ ! [X1: subst] :
( ( comp @ X1 @ id )
= X1 ) ) ) ) ).
thf(def_termmset,definition,
( termmset
= ( ~ ( ! [X1: term,X2: subst,X3: subst] :
( ( sub @ ( sub @ X1 @ X2 ) @ X3 )
= ( sub @ X1 @ ( comp @ X2 @ X3 ) ) )
=> ~ ! [X1: term] :
( ( sub @ X1 @ id )
= X1 ) ) ) ) ).
thf(def_hoasap,definition,
( hoasap
= ( ^ [X1: subst,X2: term,X3: subst] : ( ap @ ( sub @ X2 @ X3 ) ) ) ) ).
thf(def_hoasapinj1,definition,
( hoasapinj1
= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( hoasap @ id @ X1 @ id @ X3 )
= ( hoasap @ id @ X2 @ id @ X4 ) )
=> ( X1 = X2 ) ) ) ) ).
thf(def_hoasapinj1_gthm,definition,
( hoasapinj1_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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm,conjecture,
( ! [X1: term,X2: term,X3: subst] :
( ( sub @ ( ap @ X1 @ X2 ) @ X3 )
= ( ap @ ( sub @ X1 @ X3 ) @ ( sub @ X2 @ X3 ) ) )
=> ( ! [X1: term,X2: subst] :
( ( sub @ one @ ( push @ X1 @ X2 ) )
= X1 )
=> ( ! [X1: term] :
( ( sub @ X1 @ id )
= X1 )
=> ( ! [X1: term,X2: subst] :
( ( sub @ ( lam @ X1 ) @ X2 )
= ( lam @ ( sub @ X1 @ ( push @ one @ ( comp @ X2 @ sh ) ) ) ) )
=> ( ! [X1: term,X2: subst,X3: subst] :
( ( sub @ ( sub @ X1 @ X2 ) @ X3 )
= ( sub @ X1 @ ( comp @ X2 @ X3 ) ) )
=> ( ! [X1: subst] :
( ( comp @ id @ X1 )
= X1 )
=> ( ! [X1: term,X2: subst] :
( ( comp @ sh @ ( push @ X1 @ X2 ) )
= X2 )
=> ( ! [X1: subst,X2: subst,X3: subst] :
( ( comp @ ( comp @ X1 @ X2 ) @ X3 )
= ( comp @ X1 @ ( comp @ X2 @ X3 ) ) )
=> ( ! [X1: term,X2: subst,X3: subst] :
( ( comp @ ( push @ X1 @ X2 ) @ X3 )
= ( push @ ( sub @ X1 @ X3 ) @ ( comp @ X2 @ X3 ) ) )
=> ( ! [X1: subst] :
( ( comp @ X1 @ id )
= X1 )
=> ( ( ( push @ one @ sh )
= id )
=> ( ! [X1: subst] :
( ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) )
= X1 )
=> ( ( var @ one )
=> ( ! [X1: term] :
( ( var @ X1 )
=> ( var @ ( sub @ X1 @ sh ) ) )
=> ( ! [X1: term > $o] :
( ( X1 @ one )
=> ( ! [X2: term] :
( ( var @ X2 )
=> ( ( X1 @ X2 )
=> ( X1 @ ( sub @ X2 @ sh ) ) ) )
=> ! [X2: term] :
( ( var @ X2 )
=> ( X1 @ X2 ) ) ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) )
=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) )
=> ( ! [X1: term,X2: term,X3: term] :
( ( lam @ X1 )
!= ( ap @ X2 @ X3 ) )
=> ( ! [X1: term,X2: term] :
~ ( var @ ( ap @ X1 @ X2 ) )
=> ( ! [X1: term] :
~ ( var @ ( lam @ X1 ) )
=> ( ! [X1: term > $o] :
( ! [X2: term] :
( ( var @ X2 )
=> ( X1 @ X2 ) )
=> ( ! [X2: term,X3: term] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X1 @ ( ap @ X2 @ X3 ) ) ) )
=> ( ! [X2: term] :
( ( X1 @ X2 )
=> ( X1 @ ( lam @ X2 ) ) )
=> ( !! @ X1 ) ) ) )
=> ( ! [X1: term > $o,X2: term,X3: subst] :
( ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) )
=> ( ( X1 @ X2 )
=> ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ ( push @ X2 @ X3 ) ) ) ) ) )
=> ( ! [X1: term > $o] :
( ! [X2: term,X3: term] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X1 @ ( ap @ X2 @ X3 ) ) ) )
=> ( ! [X2: term] :
( ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( sub @ X2 @ ( push @ X3 @ id ) ) ) )
=> ( X1 @ ( lam @ X2 ) ) )
=> ! [X2: term,X3: subst] :
( ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) )
=> ( ! [X1: term > $o] :
( ! [X2: term] :
( ( var @ X2 )
=> ( X1 @ X2 ) )
=> ( ! [X2: term,X3: term] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X1 @ ( ap @ X2 @ X3 ) ) ) )
=> ( ! [X2: term] :
( ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( sub @ X2 @ ( push @ X3 @ id ) ) ) )
=> ( X1 @ ( lam @ X2 ) ) )
=> ( !! @ X1 ) ) ) )
=> ( ~ ( ~ ( ! [X1: subst,X2: subst,X3: subst] :
( ( comp @ ( comp @ X1 @ X2 ) @ X3 )
= ( comp @ X1 @ ( comp @ X2 @ X3 ) ) )
=> ~ ! [X1: subst] :
( ( comp @ id @ X1 )
= X1 ) )
=> ~ ! [X1: subst] :
( ( comp @ X1 @ id )
= X1 ) )
=> ( ~ ( ! [X1: term,X2: subst,X3: subst] :
( ( sub @ ( sub @ X1 @ X2 ) @ X3 )
= ( sub @ X1 @ ( comp @ X2 @ X3 ) ) )
=> ~ ! [X1: term] :
( ( sub @ X1 @ id )
= X1 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( ! [X1: term,X2: term,X3: subst] :
( ( sub @ ( ap @ X1 @ X2 ) @ X3 )
= ( ap @ ( sub @ X1 @ X3 ) @ ( sub @ X2 @ X3 ) ) )
=> ( ! [X1: term,X2: subst] :
( ( sub @ one @ ( push @ X1 @ X2 ) )
= X1 )
=> ( ! [X1: term] :
( ( sub @ X1 @ id )
= X1 )
=> ( ! [X1: term,X2: subst] :
( ( sub @ ( lam @ X1 ) @ X2 )
= ( lam @ ( sub @ X1 @ ( push @ one @ ( comp @ X2 @ sh ) ) ) ) )
=> ( ! [X1: term,X2: subst,X3: subst] :
( ( sub @ ( sub @ X1 @ X2 ) @ X3 )
= ( sub @ X1 @ ( comp @ X2 @ X3 ) ) )
=> ( ! [X1: subst] :
( ( comp @ id @ X1 )
= X1 )
=> ( ! [X1: term,X2: subst] :
( ( comp @ sh @ ( push @ X1 @ X2 ) )
= X2 )
=> ( ! [X1: subst,X2: subst,X3: subst] :
( ( comp @ ( comp @ X1 @ X2 ) @ X3 )
= ( comp @ X1 @ ( comp @ X2 @ X3 ) ) )
=> ( ! [X1: term,X2: subst,X3: subst] :
( ( comp @ ( push @ X1 @ X2 ) @ X3 )
= ( push @ ( sub @ X1 @ X3 ) @ ( comp @ X2 @ X3 ) ) )
=> ( ! [X1: subst] :
( ( comp @ X1 @ id )
= X1 )
=> ( ( ( push @ one @ sh )
= id )
=> ( ! [X1: subst] :
( ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) )
= X1 )
=> ( ( var @ one )
=> ( ! [X1: term] :
( ( var @ X1 )
=> ( var @ ( sub @ X1 @ sh ) ) )
=> ( ! [X1: term > $o] :
( ( X1 @ one )
=> ( ! [X2: term] :
( ( var @ X2 )
=> ( ( X1 @ X2 )
=> ( X1 @ ( sub @ X2 @ sh ) ) ) )
=> ! [X2: term] :
( ( var @ X2 )
=> ( X1 @ X2 ) ) ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) )
=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) )
=> ( ! [X1: term,X2: term,X3: term] :
( ( lam @ X1 )
!= ( ap @ X2 @ X3 ) )
=> ( ! [X1: term,X2: term] :
~ ( var @ ( ap @ X1 @ X2 ) )
=> ( ! [X1: term] :
~ ( var @ ( lam @ X1 ) )
=> ( ! [X1: term > $o] :
( ! [X2: term] :
( ( var @ X2 )
=> ( X1 @ X2 ) )
=> ( ! [X2: term,X3: term] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X1 @ ( ap @ X2 @ X3 ) ) ) )
=> ( ! [X2: term] :
( ( X1 @ X2 )
=> ( X1 @ ( lam @ X2 ) ) )
=> ( !! @ X1 ) ) ) )
=> ( ! [X1: term > $o,X2: term,X3: subst] :
( ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) )
=> ( ( X1 @ X2 )
=> ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ ( push @ X2 @ X3 ) ) ) ) ) )
=> ( ! [X1: term > $o] :
( ! [X2: term,X3: term] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X1 @ ( ap @ X2 @ X3 ) ) ) )
=> ( ! [X2: term] :
( ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( sub @ X2 @ ( push @ X3 @ id ) ) ) )
=> ( X1 @ ( lam @ X2 ) ) )
=> ! [X2: term,X3: subst] :
( ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) )
=> ( ! [X1: term > $o] :
( ! [X2: term] :
( ( var @ X2 )
=> ( X1 @ X2 ) )
=> ( ! [X2: term,X3: term] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X1 @ ( ap @ X2 @ X3 ) ) ) )
=> ( ! [X2: term] :
( ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( sub @ X2 @ ( push @ X3 @ id ) ) ) )
=> ( X1 @ ( lam @ X2 ) ) )
=> ( !! @ X1 ) ) ) )
=> ( ~ ( ~ ( ! [X1: subst,X2: subst,X3: subst] :
( ( comp @ ( comp @ X1 @ X2 ) @ X3 )
= ( comp @ X1 @ ( comp @ X2 @ X3 ) ) )
=> ~ ! [X1: subst] :
( ( comp @ id @ X1 )
= X1 ) )
=> ~ ! [X1: subst] :
( ( comp @ X1 @ id )
= X1 ) )
=> ( ~ ( ! [X1: term,X2: subst,X3: subst] :
( ( sub @ ( sub @ X1 @ X2 ) @ X3 )
= ( sub @ X1 @ ( comp @ X2 @ X3 ) ) )
=> ~ ! [X1: term] :
( ( sub @ X1 @ id )
= X1 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(ax1532,axiom,
( p1
| ~ p3 ),
file('<stdin>',ax1532) ).
thf(ax1534,axiom,
~ p1,
file('<stdin>',ax1534) ).
thf(ax1530,axiom,
( p3
| ~ p5 ),
file('<stdin>',ax1530) ).
thf(ax1528,axiom,
( p5
| ~ p7 ),
file('<stdin>',ax1528) ).
thf(ax1526,axiom,
( p7
| ~ p9 ),
file('<stdin>',ax1526) ).
thf(ax1524,axiom,
( p9
| ~ p11 ),
file('<stdin>',ax1524) ).
thf(ax1522,axiom,
( p11
| ~ p13 ),
file('<stdin>',ax1522) ).
thf(ax1520,axiom,
( p13
| ~ p15 ),
file('<stdin>',ax1520) ).
thf(ax1518,axiom,
( p15
| ~ p17 ),
file('<stdin>',ax1518) ).
thf(ax1516,axiom,
( p17
| ~ p19 ),
file('<stdin>',ax1516) ).
thf(ax1514,axiom,
( p19
| ~ p21 ),
file('<stdin>',ax1514) ).
thf(ax1512,axiom,
( p21
| ~ p23 ),
file('<stdin>',ax1512) ).
thf(ax1510,axiom,
( p23
| ~ p25 ),
file('<stdin>',ax1510) ).
thf(ax1508,axiom,
( p25
| ~ p27 ),
file('<stdin>',ax1508) ).
thf(ax1506,axiom,
( p27
| ~ p29 ),
file('<stdin>',ax1506) ).
thf(ax1504,axiom,
( p29
| ~ p31 ),
file('<stdin>',ax1504) ).
thf(ax1502,axiom,
( p31
| ~ p33 ),
file('<stdin>',ax1502) ).
thf(ax1500,axiom,
( p33
| ~ p35 ),
file('<stdin>',ax1500) ).
thf(ax1498,axiom,
( p35
| ~ p37 ),
file('<stdin>',ax1498) ).
thf(ax1496,axiom,
( p37
| ~ p39 ),
file('<stdin>',ax1496) ).
thf(ax1494,axiom,
( p39
| ~ p41 ),
file('<stdin>',ax1494) ).
thf(ax1492,axiom,
( p41
| ~ p43 ),
file('<stdin>',ax1492) ).
thf(ax1490,axiom,
( p43
| ~ p45 ),
file('<stdin>',ax1490) ).
thf(ax1488,axiom,
( p45
| ~ p47 ),
file('<stdin>',ax1488) ).
thf(ax1486,axiom,
( p47
| ~ p49 ),
file('<stdin>',ax1486) ).
thf(ax1484,axiom,
( p49
| ~ p51 ),
file('<stdin>',ax1484) ).
thf(ax1482,axiom,
( p51
| ~ p53 ),
file('<stdin>',ax1482) ).
thf(ax1480,axiom,
( p53
| ~ p55 ),
file('<stdin>',ax1480) ).
thf(ax1478,axiom,
( p55
| ~ p57 ),
file('<stdin>',ax1478) ).
thf(ax1477,axiom,
( p57
| ~ p58 ),
file('<stdin>',ax1477) ).
thf(ax1455,axiom,
( ~ p81
| p80 ),
file('<stdin>',ax1455) ).
thf(ax1476,axiom,
( p58
| ~ p59 ),
file('<stdin>',ax1476) ).
thf(ax1388,axiom,
( ~ p80
| p144 ),
file('<stdin>',ax1388) ).
thf(ax1456,axiom,
p81,
file('<stdin>',ax1456) ).
thf(ax1475,axiom,
( p59
| ~ p60 ),
file('<stdin>',ax1475) ).
thf(ax1387,axiom,
( ~ p144
| p61
| p143 ),
file('<stdin>',ax1387) ).
thf(ax1474,axiom,
( p60
| ~ p61 ),
file('<stdin>',ax1474) ).
thf(ax1450,axiom,
( ~ p6
| p76 ),
file('<stdin>',ax1450) ).
thf(ax1529,axiom,
( p5
| p6 ),
file('<stdin>',ax1529) ).
thf(pax6,axiom,
( p6
=> ! [X32: term] :
( ( fsub @ X32 @ fid )
= X32 ) ),
file('<stdin>',pax6) ).
thf(ax1385,axiom,
( ~ p142
| ~ p76
| ~ p141 ),
file('<stdin>',ax1385) ).
thf(ax1386,axiom,
( ~ p143
| p142 ),
file('<stdin>',ax1386) ).
thf(nax141,axiom,
( p141
<= ( ( ( fap @ f__0 @ f__2 )
= ( fap @ ( fsub @ f__1 @ fid ) @ f__3 ) )
=> ( f__0 = f__1 ) ) ),
file('<stdin>',nax141) ).
thf(pax32,axiom,
( p32
=> ! [X22: term,X23: term,X24: term,X4: term] :
( ( ( fap @ X22 @ X24 )
= ( fap @ X23 @ X4 ) )
=> ( X22 = X23 ) ) ),
file('<stdin>',pax32) ).
thf(ax1503,axiom,
( p31
| p32 ),
file('<stdin>',ax1503) ).
thf(nax59,axiom,
( p59
<= ! [X1: term,X2: term] :
( ( ( fap @ ( fsub @ f__0 @ fid ) @ X1 )
= ( fap @ ( fsub @ f__1 @ fid ) @ X2 ) )
=> ( f__0 = f__1 ) ) ),
file('<stdin>',nax59) ).
thf(c_0_46,plain,
( p1
| ~ p3 ),
inference(fof_simplification,[status(thm)],[ax1532]) ).
thf(c_0_47,plain,
~ p1,
inference(fof_simplification,[status(thm)],[ax1534]) ).
thf(c_0_48,plain,
( p3
| ~ p5 ),
inference(fof_simplification,[status(thm)],[ax1530]) ).
thf(c_0_49,plain,
( p1
| ~ p3 ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
thf(c_0_50,plain,
~ p1,
inference(split_conjunct,[status(thm)],[c_0_47]) ).
thf(c_0_51,plain,
( p5
| ~ p7 ),
inference(fof_simplification,[status(thm)],[ax1528]) ).
thf(c_0_52,plain,
( p3
| ~ p5 ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
thf(c_0_53,plain,
~ p3,
inference(sr,[status(thm)],[c_0_49,c_0_50]) ).
thf(c_0_54,plain,
( p7
| ~ p9 ),
inference(fof_simplification,[status(thm)],[ax1526]) ).
thf(c_0_55,plain,
( p5
| ~ p7 ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
thf(c_0_56,plain,
~ p5,
inference(sr,[status(thm)],[c_0_52,c_0_53]) ).
thf(c_0_57,plain,
( p9
| ~ p11 ),
inference(fof_simplification,[status(thm)],[ax1524]) ).
thf(c_0_58,plain,
( p7
| ~ p9 ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
thf(c_0_59,plain,
~ p7,
inference(sr,[status(thm)],[c_0_55,c_0_56]) ).
thf(c_0_60,plain,
( p11
| ~ p13 ),
inference(fof_simplification,[status(thm)],[ax1522]) ).
thf(c_0_61,plain,
( p9
| ~ p11 ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
thf(c_0_62,plain,
~ p9,
inference(sr,[status(thm)],[c_0_58,c_0_59]) ).
thf(c_0_63,plain,
( p13
| ~ p15 ),
inference(fof_simplification,[status(thm)],[ax1520]) ).
thf(c_0_64,plain,
( p11
| ~ p13 ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
thf(c_0_65,plain,
~ p11,
inference(sr,[status(thm)],[c_0_61,c_0_62]) ).
thf(c_0_66,plain,
( p15
| ~ p17 ),
inference(fof_simplification,[status(thm)],[ax1518]) ).
thf(c_0_67,plain,
( p13
| ~ p15 ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
thf(c_0_68,plain,
~ p13,
inference(sr,[status(thm)],[c_0_64,c_0_65]) ).
thf(c_0_69,plain,
( p17
| ~ p19 ),
inference(fof_simplification,[status(thm)],[ax1516]) ).
thf(c_0_70,plain,
( p15
| ~ p17 ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
thf(c_0_71,plain,
~ p15,
inference(sr,[status(thm)],[c_0_67,c_0_68]) ).
thf(c_0_72,plain,
( p19
| ~ p21 ),
inference(fof_simplification,[status(thm)],[ax1514]) ).
thf(c_0_73,plain,
( p17
| ~ p19 ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
thf(c_0_74,plain,
~ p17,
inference(sr,[status(thm)],[c_0_70,c_0_71]) ).
thf(c_0_75,plain,
( p21
| ~ p23 ),
inference(fof_simplification,[status(thm)],[ax1512]) ).
thf(c_0_76,plain,
( p19
| ~ p21 ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
thf(c_0_77,plain,
~ p19,
inference(sr,[status(thm)],[c_0_73,c_0_74]) ).
thf(c_0_78,plain,
( p23
| ~ p25 ),
inference(fof_simplification,[status(thm)],[ax1510]) ).
thf(c_0_79,plain,
( p21
| ~ p23 ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
thf(c_0_80,plain,
~ p21,
inference(sr,[status(thm)],[c_0_76,c_0_77]) ).
thf(c_0_81,plain,
( p25
| ~ p27 ),
inference(fof_simplification,[status(thm)],[ax1508]) ).
thf(c_0_82,plain,
( p23
| ~ p25 ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
thf(c_0_83,plain,
~ p23,
inference(sr,[status(thm)],[c_0_79,c_0_80]) ).
thf(c_0_84,plain,
( p27
| ~ p29 ),
inference(fof_simplification,[status(thm)],[ax1506]) ).
thf(c_0_85,plain,
( p25
| ~ p27 ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
thf(c_0_86,plain,
~ p25,
inference(sr,[status(thm)],[c_0_82,c_0_83]) ).
thf(c_0_87,plain,
( p29
| ~ p31 ),
inference(fof_simplification,[status(thm)],[ax1504]) ).
thf(c_0_88,plain,
( p27
| ~ p29 ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
thf(c_0_89,plain,
~ p27,
inference(sr,[status(thm)],[c_0_85,c_0_86]) ).
thf(c_0_90,plain,
( p31
| ~ p33 ),
inference(fof_simplification,[status(thm)],[ax1502]) ).
thf(c_0_91,plain,
( p29
| ~ p31 ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
thf(c_0_92,plain,
~ p29,
inference(sr,[status(thm)],[c_0_88,c_0_89]) ).
thf(c_0_93,plain,
( p33
| ~ p35 ),
inference(fof_simplification,[status(thm)],[ax1500]) ).
thf(c_0_94,plain,
( p31
| ~ p33 ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
thf(c_0_95,plain,
~ p31,
inference(sr,[status(thm)],[c_0_91,c_0_92]) ).
thf(c_0_96,plain,
( p35
| ~ p37 ),
inference(fof_simplification,[status(thm)],[ax1498]) ).
thf(c_0_97,plain,
( p33
| ~ p35 ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
thf(c_0_98,plain,
~ p33,
inference(sr,[status(thm)],[c_0_94,c_0_95]) ).
thf(c_0_99,plain,
( p37
| ~ p39 ),
inference(fof_simplification,[status(thm)],[ax1496]) ).
thf(c_0_100,plain,
( p35
| ~ p37 ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
thf(c_0_101,plain,
~ p35,
inference(sr,[status(thm)],[c_0_97,c_0_98]) ).
thf(c_0_102,plain,
( p39
| ~ p41 ),
inference(fof_simplification,[status(thm)],[ax1494]) ).
thf(c_0_103,plain,
( p37
| ~ p39 ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
thf(c_0_104,plain,
~ p37,
inference(sr,[status(thm)],[c_0_100,c_0_101]) ).
thf(c_0_105,plain,
( p41
| ~ p43 ),
inference(fof_simplification,[status(thm)],[ax1492]) ).
thf(c_0_106,plain,
( p39
| ~ p41 ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
thf(c_0_107,plain,
~ p39,
inference(sr,[status(thm)],[c_0_103,c_0_104]) ).
thf(c_0_108,plain,
( p43
| ~ p45 ),
inference(fof_simplification,[status(thm)],[ax1490]) ).
thf(c_0_109,plain,
( p41
| ~ p43 ),
inference(split_conjunct,[status(thm)],[c_0_105]) ).
thf(c_0_110,plain,
~ p41,
inference(sr,[status(thm)],[c_0_106,c_0_107]) ).
thf(c_0_111,plain,
( p45
| ~ p47 ),
inference(fof_simplification,[status(thm)],[ax1488]) ).
thf(c_0_112,plain,
( p43
| ~ p45 ),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
thf(c_0_113,plain,
~ p43,
inference(sr,[status(thm)],[c_0_109,c_0_110]) ).
thf(c_0_114,plain,
( p47
| ~ p49 ),
inference(fof_simplification,[status(thm)],[ax1486]) ).
thf(c_0_115,plain,
( p45
| ~ p47 ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
thf(c_0_116,plain,
~ p45,
inference(sr,[status(thm)],[c_0_112,c_0_113]) ).
thf(c_0_117,plain,
( p49
| ~ p51 ),
inference(fof_simplification,[status(thm)],[ax1484]) ).
thf(c_0_118,plain,
( p47
| ~ p49 ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
thf(c_0_119,plain,
~ p47,
inference(sr,[status(thm)],[c_0_115,c_0_116]) ).
thf(c_0_120,plain,
( p51
| ~ p53 ),
inference(fof_simplification,[status(thm)],[ax1482]) ).
thf(c_0_121,plain,
( p49
| ~ p51 ),
inference(split_conjunct,[status(thm)],[c_0_117]) ).
thf(c_0_122,plain,
~ p49,
inference(sr,[status(thm)],[c_0_118,c_0_119]) ).
thf(c_0_123,plain,
( p53
| ~ p55 ),
inference(fof_simplification,[status(thm)],[ax1480]) ).
thf(c_0_124,plain,
( p51
| ~ p53 ),
inference(split_conjunct,[status(thm)],[c_0_120]) ).
thf(c_0_125,plain,
~ p51,
inference(sr,[status(thm)],[c_0_121,c_0_122]) ).
thf(c_0_126,plain,
( p55
| ~ p57 ),
inference(fof_simplification,[status(thm)],[ax1478]) ).
thf(c_0_127,plain,
( p53
| ~ p55 ),
inference(split_conjunct,[status(thm)],[c_0_123]) ).
thf(c_0_128,plain,
~ p53,
inference(sr,[status(thm)],[c_0_124,c_0_125]) ).
thf(c_0_129,plain,
( p57
| ~ p58 ),
inference(fof_simplification,[status(thm)],[ax1477]) ).
thf(c_0_130,plain,
( p55
| ~ p57 ),
inference(split_conjunct,[status(thm)],[c_0_126]) ).
thf(c_0_131,plain,
~ p55,
inference(sr,[status(thm)],[c_0_127,c_0_128]) ).
thf(c_0_132,plain,
( ~ p81
| p80 ),
inference(fof_simplification,[status(thm)],[ax1455]) ).
thf(c_0_133,plain,
( p58
| ~ p59 ),
inference(fof_simplification,[status(thm)],[ax1476]) ).
thf(c_0_134,plain,
( p57
| ~ p58 ),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
thf(c_0_135,plain,
~ p57,
inference(sr,[status(thm)],[c_0_130,c_0_131]) ).
thf(c_0_136,plain,
( ~ p80
| p144 ),
inference(fof_simplification,[status(thm)],[ax1388]) ).
thf(c_0_137,plain,
( p80
| ~ p81 ),
inference(split_conjunct,[status(thm)],[c_0_132]) ).
thf(c_0_138,plain,
p81,
inference(split_conjunct,[status(thm)],[ax1456]) ).
thf(c_0_139,plain,
( p59
| ~ p60 ),
inference(fof_simplification,[status(thm)],[ax1475]) ).
thf(c_0_140,plain,
( p58
| ~ p59 ),
inference(split_conjunct,[status(thm)],[c_0_133]) ).
thf(c_0_141,plain,
~ p58,
inference(sr,[status(thm)],[c_0_134,c_0_135]) ).
thf(c_0_142,plain,
( ~ p144
| p61
| p143 ),
inference(fof_simplification,[status(thm)],[ax1387]) ).
thf(c_0_143,plain,
( p144
| ~ p80 ),
inference(split_conjunct,[status(thm)],[c_0_136]) ).
thf(c_0_144,plain,
p80,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_137,c_0_138])]) ).
thf(c_0_145,plain,
( p60
| ~ p61 ),
inference(fof_simplification,[status(thm)],[ax1474]) ).
thf(c_0_146,plain,
( p59
| ~ p60 ),
inference(split_conjunct,[status(thm)],[c_0_139]) ).
thf(c_0_147,plain,
~ p59,
inference(sr,[status(thm)],[c_0_140,c_0_141]) ).
thf(c_0_148,plain,
( ~ p6
| p76 ),
inference(fof_simplification,[status(thm)],[ax1450]) ).
thf(c_0_149,plain,
( p5
| p6 ),
inference(split_conjunct,[status(thm)],[ax1529]) ).
thf(c_0_150,plain,
( p61
| p143
| ~ p144 ),
inference(split_conjunct,[status(thm)],[c_0_142]) ).
thf(c_0_151,plain,
p144,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_143,c_0_144])]) ).
thf(c_0_152,plain,
( p60
| ~ p61 ),
inference(split_conjunct,[status(thm)],[c_0_145]) ).
thf(c_0_153,plain,
~ p60,
inference(sr,[status(thm)],[c_0_146,c_0_147]) ).
thf(c_0_154,plain,
! [X1770: term] :
( ~ p6
| ( ( fsub @ X1770 @ fid )
= X1770 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax6])])]) ).
thf(c_0_155,plain,
( ~ p142
| ~ p76
| ~ p141 ),
inference(fof_simplification,[status(thm)],[ax1385]) ).
thf(c_0_156,plain,
( p76
| ~ p6 ),
inference(split_conjunct,[status(thm)],[c_0_148]) ).
thf(c_0_157,plain,
p6,
inference(sr,[status(thm)],[c_0_149,c_0_56]) ).
thf(c_0_158,plain,
( ~ p143
| p142 ),
inference(fof_simplification,[status(thm)],[ax1386]) ).
thf(c_0_159,plain,
( p143
| p61 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_150,c_0_151])]) ).
thf(c_0_160,plain,
~ p61,
inference(sr,[status(thm)],[c_0_152,c_0_153]) ).
thf(c_0_161,plain,
( ( ( ( fap @ f__0 @ f__2 )
= ( fap @ ( fsub @ f__1 @ fid ) @ f__3 ) )
| p141 )
& ( ( f__0 != f__1 )
| p141 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax141])])]) ).
thf(c_0_162,plain,
! [X1: term] :
( ( ( fsub @ X1 @ fid )
= X1 )
| ~ p6 ),
inference(split_conjunct,[status(thm)],[c_0_154]) ).
thf(c_0_163,plain,
( ~ p142
| ~ p76
| ~ p141 ),
inference(split_conjunct,[status(thm)],[c_0_155]) ).
thf(c_0_164,plain,
p76,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_156,c_0_157])]) ).
thf(c_0_165,plain,
( p142
| ~ p143 ),
inference(split_conjunct,[status(thm)],[c_0_158]) ).
thf(c_0_166,plain,
p143,
inference(sr,[status(thm)],[c_0_159,c_0_160]) ).
thf(c_0_167,plain,
! [X1728: term,X1729: term,X1730: term,X1731: term] :
( ~ p32
| ( ( fap @ X1728 @ X1730 )
!= ( fap @ X1729 @ X1731 ) )
| ( X1728 = X1729 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax32])])]) ).
thf(c_0_168,plain,
( p31
| p32 ),
inference(split_conjunct,[status(thm)],[ax1503]) ).
thf(c_0_169,plain,
( ( ( fap @ f__0 @ f__2 )
= ( fap @ ( fsub @ f__1 @ fid ) @ f__3 ) )
| p141 ),
inference(split_conjunct,[status(thm)],[c_0_161]) ).
thf(c_0_170,plain,
! [X1: term] :
( ( fsub @ X1 @ fid )
= X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_162,c_0_157])]) ).
thf(c_0_171,plain,
( ~ p141
| ~ p142 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_163,c_0_164])]) ).
thf(c_0_172,plain,
p142,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_165,c_0_166])]) ).
thf(c_0_173,plain,
! [X1: term,X2: term,X3: term,X4: term] :
( ( X1 = X3 )
| ~ p32
| ( ( fap @ X1 @ X2 )
!= ( fap @ X3 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_167]) ).
thf(c_0_174,plain,
p32,
inference(sr,[status(thm)],[c_0_168,c_0_95]) ).
thf(c_0_175,plain,
( ( ( fap @ f__1 @ f__3 )
= ( fap @ f__0 @ f__2 ) )
| p141 ),
inference(rw,[status(thm)],[c_0_169,c_0_170]) ).
thf(c_0_176,plain,
~ p141,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_171,c_0_172])]) ).
thf(c_0_177,plain,
( ( ( ( fap @ ( fsub @ f__0 @ fid ) @ esk795_0 )
= ( fap @ ( fsub @ f__1 @ fid ) @ esk796_0 ) )
| p59 )
& ( ( f__0 != f__1 )
| p59 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax59])])])])]) ).
thf(c_0_178,plain,
! [X1: term,X2: term,X3: term,X4: term] :
( ( X1 = X2 )
| ( ( fap @ X1 @ X3 )
!= ( fap @ X2 @ X4 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_173,c_0_174])]) ).
thf(c_0_179,plain,
( ( fap @ f__1 @ f__3 )
= ( fap @ f__0 @ f__2 ) ),
inference(sr,[status(thm)],[c_0_175,c_0_176]) ).
thf(c_0_180,plain,
( p59
| ( f__0 != f__1 ) ),
inference(split_conjunct,[status(thm)],[c_0_177]) ).
thf(c_0_181,plain,
! [X1: term,X2: term] :
( ( f__1 = X1 )
| ( ( fap @ f__0 @ f__2 )
!= ( fap @ X1 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_178,c_0_179]) ).
thf(c_0_182,plain,
f__1 != f__0,
inference(sr,[status(thm)],[c_0_180,c_0_147]) ).
thf(c_0_183,plain,
$false,
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_181]),c_0_182]),
[proof] ).
thf(1,plain,
$false,
inference(eprover,[status(thm),assumptions([h0])],]) ).
thf(0,theorem,
( ! [X1: term,X2: term,X3: subst] :
( ( sub @ ( ap @ X1 @ X2 ) @ X3 )
= ( ap @ ( sub @ X1 @ X3 ) @ ( sub @ X2 @ X3 ) ) )
=> ( ! [X1: term,X2: subst] :
( ( sub @ one @ ( push @ X1 @ X2 ) )
= X1 )
=> ( ! [X1: term] :
( ( sub @ X1 @ id )
= X1 )
=> ( ! [X1: term,X2: subst] :
( ( sub @ ( lam @ X1 ) @ X2 )
= ( lam @ ( sub @ X1 @ ( push @ one @ ( comp @ X2 @ sh ) ) ) ) )
=> ( ! [X1: term,X2: subst,X3: subst] :
( ( sub @ ( sub @ X1 @ X2 ) @ X3 )
= ( sub @ X1 @ ( comp @ X2 @ X3 ) ) )
=> ( ! [X1: subst] :
( ( comp @ id @ X1 )
= X1 )
=> ( ! [X1: term,X2: subst] :
( ( comp @ sh @ ( push @ X1 @ X2 ) )
= X2 )
=> ( ! [X1: subst,X2: subst,X3: subst] :
( ( comp @ ( comp @ X1 @ X2 ) @ X3 )
= ( comp @ X1 @ ( comp @ X2 @ X3 ) ) )
=> ( ! [X1: term,X2: subst,X3: subst] :
( ( comp @ ( push @ X1 @ X2 ) @ X3 )
= ( push @ ( sub @ X1 @ X3 ) @ ( comp @ X2 @ X3 ) ) )
=> ( ! [X1: subst] :
( ( comp @ X1 @ id )
= X1 )
=> ( ( ( push @ one @ sh )
= id )
=> ( ! [X1: subst] :
( ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) )
= X1 )
=> ( ( var @ one )
=> ( ! [X1: term] :
( ( var @ X1 )
=> ( var @ ( sub @ X1 @ sh ) ) )
=> ( ! [X1: term > $o] :
( ( X1 @ one )
=> ( ! [X2: term] :
( ( var @ X2 )
=> ( ( X1 @ X2 )
=> ( X1 @ ( sub @ X2 @ sh ) ) ) )
=> ! [X2: term] :
( ( var @ X2 )
=> ( X1 @ X2 ) ) ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) )
=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) )
=> ( ! [X1: term,X2: term,X3: term] :
( ( lam @ X1 )
!= ( ap @ X2 @ X3 ) )
=> ( ! [X1: term,X2: term] :
~ ( var @ ( ap @ X1 @ X2 ) )
=> ( ! [X1: term] :
~ ( var @ ( lam @ X1 ) )
=> ( ! [X1: term > $o] :
( ! [X2: term] :
( ( var @ X2 )
=> ( X1 @ X2 ) )
=> ( ! [X2: term,X3: term] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X1 @ ( ap @ X2 @ X3 ) ) ) )
=> ( ! [X2: term] :
( ( X1 @ X2 )
=> ( X1 @ ( lam @ X2 ) ) )
=> ( !! @ X1 ) ) ) )
=> ( ! [X1: term > $o,X2: term,X3: subst] :
( ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) )
=> ( ( X1 @ X2 )
=> ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ ( push @ X2 @ X3 ) ) ) ) ) )
=> ( ! [X1: term > $o] :
( ! [X2: term,X3: term] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X1 @ ( ap @ X2 @ X3 ) ) ) )
=> ( ! [X2: term] :
( ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( sub @ X2 @ ( push @ X3 @ id ) ) ) )
=> ( X1 @ ( lam @ X2 ) ) )
=> ! [X2: term,X3: subst] :
( ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) )
=> ( ! [X1: term > $o] :
( ! [X2: term] :
( ( var @ X2 )
=> ( X1 @ X2 ) )
=> ( ! [X2: term,X3: term] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X1 @ ( ap @ X2 @ X3 ) ) ) )
=> ( ! [X2: term] :
( ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( sub @ X2 @ ( push @ X3 @ id ) ) ) )
=> ( X1 @ ( lam @ X2 ) ) )
=> ( !! @ X1 ) ) ) )
=> ( ~ ( ~ ( ! [X1: subst,X2: subst,X3: subst] :
( ( comp @ ( comp @ X1 @ X2 ) @ X3 )
= ( comp @ X1 @ ( comp @ X2 @ X3 ) ) )
=> ~ ! [X1: subst] :
( ( comp @ id @ X1 )
= X1 ) )
=> ~ ! [X1: subst] :
( ( comp @ X1 @ id )
= X1 ) )
=> ( ~ ( ! [X1: term,X2: subst,X3: subst] :
( ( sub @ ( sub @ X1 @ X2 ) @ X3 )
= ( sub @ X1 @ ( comp @ X2 @ X3 ) ) )
=> ~ ! [X1: term] :
( ( sub @ X1 @ id )
= X1 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12 % Problem : ALG256^1 : TPTP v8.1.0. Bugfixed v5.2.0.
% 0.09/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n024.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jun 9 00:57:04 EDT 2022
% 0.13/0.33 % CPUTime :
% 187.26/186.51 % SZS status Theorem
% 187.26/186.51 % Mode: mode503:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=4.:SINE_DEPTH=0
% 187.26/186.51 % Inferences: 66
% 187.26/186.51 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------