%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV203^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n013.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 : Wed Feb 25 09:40:32 AM UTC 2026
% Result : Theorem 1.63s 1.53s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 81
% Number of leaves : 7
% Syntax : Number of formulae : 149 ( 25 unt; 0 typ; 6 def)
% Number of atoms : 1779 ( 673 equ; 0 cnn)
% Maximal formula atoms : 12 ( 11 avg)
% Number of connectives : 4420 ( 221 ~; 403 |; 253 &;3195 @)
% ( 6 <=>; 79 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 112 ( 112 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 14 usr; 13 con; 0-3 aty)
% ( 125 !!; 138 ??; 0 @@+; 0 @@-)
% Number of variables : 1111 ( 642 ^; 451 !; 18 ?;1111 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
iS: $tType ).
thf(func_def_0,type,
iS: $tType ).
thf(func_def_1,type,
y: iS ).
thf(func_def_2,type,
x: iS ).
thf(func_def_3,type,
cP: iS > iS > iS ).
thf(func_def_4,type,
c0: iS ).
thf(func_def_27,type,
sK1: ( iS > $o ) > iS ).
thf(func_def_28,type,
sK2: ( iS > $o ) > iS ).
thf(func_def_29,type,
sK3: iS > iS > iS > $o ).
thf(func_def_30,type,
ph4:
!>[X0: $tType] : X0 ).
thf(f999,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f197,f255,f257,f312,f337,f866,f986]) ).
thf(f986,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f985]) ).
thf(f985,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f948]) ).
thf(f948,plain,
( ( $true = $false )
| ( x != x )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f191,f95]) ).
thf(f95,plain,
! [X0: iS,X1: iS] :
( ( $true
= ( sK3 @ c0 @ X0 @ X1 ) )
| ( X0 != X1 ) ),
inference(equality_resolution,[status(thm)],[f88]) ).
thf(f88,plain,
! [X2: iS,X3: iS,X1: iS] :
( ( c0 != X1 )
| ( $true
= ( sK3 @ X1 @ X3 @ X2 ) )
| ( X2 != X3 ) ),
inference(equality_proxy_clausification,[status(thm)],[f87]) ).
thf(f87,plain,
! [X2: iS,X3: iS,X1: iS] :
( ( c0 != X1 )
| ( ( X3 = X2 )
= $false )
| ( $true
= ( sK3 @ X1 @ X3 @ X2 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f86]) ).
thf(f86,plain,
! [X2: iS,X3: iS,X1: iS] :
( ( ( c0 = X1 )
= $false )
| ( ( X3 = X2 )
= $false )
| ( $true
= ( sK3 @ X1 @ X3 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f65]) ).
thf(f65,plain,
! [X2: iS,X3: iS,X1: iS] :
( ( ( ( X3 = X2 )
& ( c0 = X1 ) )
= $false )
| ( $true
= ( sK3 @ X1 @ X3 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f61]) ).
thf(f61,plain,
! [X2: iS,X3: iS,X1: iS] :
( ( ( ( ?? @ iS
@ ^ [Y0: iS] :
( ?? @ iS
@ ^ [Y1: iS] :
( ?? @ iS
@ ^ [Y2: iS] :
( ?? @ iS
@ ^ [Y3: iS] :
( ?? @ iS
@ ^ [Y4: iS] :
( ?? @ iS
@ ^ [Y5: iS] :
( ( sK3 @ Y0 @ Y3 @ Y1 )
& ( ( cP @ Y5 @ Y0 )
= X1 )
& ( sK3 @ Y5 @ Y2 @ Y4 )
& ( ( cP @ Y2 @ Y3 )
= X3 )
& ( ( cP @ Y4 @ Y1 )
= X2 ) ) ) ) ) ) ) )
| ( ( X3 = X2 )
& ( c0 = X1 ) ) )
= $false )
| ( $true
= ( sK3 @ X1 @ X3 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
! [X2: iS,X3: iS,X1: iS] :
( ( ( ( ?? @ iS
@ ^ [Y0: iS] :
( ?? @ iS
@ ^ [Y1: iS] :
( ?? @ iS
@ ^ [Y2: iS] :
( ?? @ iS
@ ^ [Y3: iS] :
( ?? @ iS
@ ^ [Y4: iS] :
( ?? @ iS
@ ^ [Y5: iS] :
( ( sK3 @ Y0 @ Y3 @ Y1 )
& ( ( cP @ Y5 @ Y0 )
= X1 )
& ( sK3 @ Y5 @ Y2 @ Y4 )
& ( ( cP @ Y2 @ Y3 )
= X3 )
& ( ( cP @ Y4 @ Y1 )
= X2 ) ) ) ) ) ) ) )
| ( ( X3 = X2 )
& ( c0 = X1 ) )
| ( ( c0 = X3 )
& ( X2 = X1 ) ) )
= $false )
| ( $true
= ( sK3 @ X1 @ X3 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f58]) ).
thf(f58,plain,
! [X2: iS,X3: iS,X1: iS] :
( $true
= ( ( ( ?? @ iS
@ ^ [Y0: iS] :
( ?? @ iS
@ ^ [Y1: iS] :
( ?? @ iS
@ ^ [Y2: iS] :
( ?? @ iS
@ ^ [Y3: iS] :
( ?? @ iS
@ ^ [Y4: iS] :
( ?? @ iS
@ ^ [Y5: iS] :
( ( sK3 @ Y0 @ Y3 @ Y1 )
& ( ( cP @ Y5 @ Y0 )
= X1 )
& ( sK3 @ Y5 @ Y2 @ Y4 )
& ( ( cP @ Y2 @ Y3 )
= X3 )
& ( ( cP @ Y4 @ Y1 )
= X2 ) ) ) ) ) ) ) )
| ( ( X3 = X2 )
& ( c0 = X1 ) )
| ( ( c0 = X3 )
& ( X2 = X1 ) ) )
=> ( sK3 @ X1 @ X3 @ X2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f57]) ).
thf(f57,plain,
! [X2: iS,X3: iS,X1: iS] :
( $true
= ( ^ [Y0: iS] :
( ( ( ?? @ iS
@ ^ [Y1: iS] :
( ?? @ iS
@ ^ [Y2: iS] :
( ?? @ iS
@ ^ [Y3: iS] :
( ?? @ iS
@ ^ [Y4: iS] :
( ?? @ iS
@ ^ [Y5: iS] :
( ?? @ iS
@ ^ [Y6: iS] :
( ( sK3 @ Y1 @ Y4 @ Y2 )
& ( ( cP @ Y6 @ Y1 )
= X1 )
& ( sK3 @ Y6 @ Y3 @ Y5 )
& ( ( cP @ Y3 @ Y4 )
= Y0 )
& ( ( cP @ Y5 @ Y2 )
= X2 ) ) ) ) ) ) ) )
| ( ( Y0 = X2 )
& ( c0 = X1 ) )
| ( ( c0 = Y0 )
& ( X2 = X1 ) ) )
=> ( sK3 @ X1 @ Y0 @ X2 ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
! [X2: iS,X1: iS] :
( $true
= ( !! @ iS
@ ^ [Y0: iS] :
( ( ( ?? @ iS
@ ^ [Y1: iS] :
( ?? @ iS
@ ^ [Y2: iS] :
( ?? @ iS
@ ^ [Y3: iS] :
( ?? @ iS
@ ^ [Y4: iS] :
( ?? @ iS
@ ^ [Y5: iS] :
( ?? @ iS
@ ^ [Y6: iS] :
( ( sK3 @ Y1 @ Y4 @ Y2 )
& ( ( cP @ Y6 @ Y1 )
= X1 )
& ( sK3 @ Y6 @ Y3 @ Y5 )
& ( ( cP @ Y3 @ Y4 )
= Y0 )
& ( ( cP @ Y5 @ Y2 )
= X2 ) ) ) ) ) ) ) )
| ( ( Y0 = X2 )
& ( c0 = X1 ) )
| ( ( c0 = Y0 )
& ( X2 = X1 ) ) )
=> ( sK3 @ X1 @ Y0 @ X2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f55]) ).
thf(f55,plain,
! [X2: iS,X1: iS] :
( ( ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( ( ( ?? @ iS
@ ^ [Y2: iS] :
( ?? @ iS
@ ^ [Y3: iS] :
( ?? @ iS
@ ^ [Y4: iS] :
( ?? @ iS
@ ^ [Y5: iS] :
( ?? @ iS
@ ^ [Y6: iS] :
( ?? @ iS
@ ^ [Y7: iS] :
( ( sK3 @ Y2 @ Y5 @ Y3 )
& ( ( cP @ Y7 @ Y2 )
= X1 )
& ( sK3 @ Y7 @ Y4 @ Y6 )
& ( ( cP @ Y4 @ Y5 )
= Y1 )
& ( ( cP @ Y6 @ Y3 )
= Y0 ) ) ) ) ) ) ) )
| ( ( Y1 = Y0 )
& ( c0 = X1 ) )
| ( ( c0 = Y1 )
& ( Y0 = X1 ) ) )
=> ( sK3 @ X1 @ Y1 @ Y0 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
! [X1: iS] :
( ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( ( ( ?? @ iS
@ ^ [Y2: iS] :
( ?? @ iS
@ ^ [Y3: iS] :
( ?? @ iS
@ ^ [Y4: iS] :
( ?? @ iS
@ ^ [Y5: iS] :
( ?? @ iS
@ ^ [Y6: iS] :
( ?? @ iS
@ ^ [Y7: iS] :
( ( sK3 @ Y2 @ Y5 @ Y3 )
& ( ( cP @ Y7 @ Y2 )
= X1 )
& ( sK3 @ Y7 @ Y4 @ Y6 )
& ( ( cP @ Y4 @ Y5 )
= Y1 )
& ( ( cP @ Y6 @ Y3 )
= Y0 ) ) ) ) ) ) ) )
| ( ( Y1 = Y0 )
& ( c0 = X1 ) )
| ( ( c0 = Y1 )
& ( Y0 = X1 ) ) )
=> ( sK3 @ X1 @ Y1 @ Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f53]) ).
thf(f53,plain,
! [X1: iS] :
( $true
= ( ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( ( ( ?? @ iS
@ ^ [Y3: iS] :
( ?? @ iS
@ ^ [Y4: iS] :
( ?? @ iS
@ ^ [Y5: iS] :
( ?? @ iS
@ ^ [Y6: iS] :
( ?? @ iS
@ ^ [Y7: iS] :
( ?? @ iS
@ ^ [Y8: iS] :
( ( sK3 @ Y3 @ Y6 @ Y4 )
& ( ( cP @ Y8 @ Y3 )
= Y0 )
& ( sK3 @ Y8 @ Y5 @ Y7 )
& ( ( cP @ Y5 @ Y6 )
= Y2 )
& ( ( cP @ Y7 @ Y4 )
= Y1 ) ) ) ) ) ) ) )
| ( ( Y2 = Y1 )
& ( c0 = Y0 ) )
| ( ( c0 = Y2 )
& ( Y1 = Y0 ) ) )
=> ( sK3 @ Y0 @ Y2 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
( $true
= ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( ( ( ?? @ iS
@ ^ [Y3: iS] :
( ?? @ iS
@ ^ [Y4: iS] :
( ?? @ iS
@ ^ [Y5: iS] :
( ?? @ iS
@ ^ [Y6: iS] :
( ?? @ iS
@ ^ [Y7: iS] :
( ?? @ iS
@ ^ [Y8: iS] :
( ( sK3 @ Y3 @ Y6 @ Y4 )
& ( ( cP @ Y8 @ Y3 )
= Y0 )
& ( sK3 @ Y8 @ Y5 @ Y7 )
& ( ( cP @ Y5 @ Y6 )
= Y2 )
& ( ( cP @ Y7 @ Y4 )
= Y1 ) ) ) ) ) ) ) )
| ( ( Y2 = Y1 )
& ( c0 = Y0 ) )
| ( ( c0 = Y2 )
& ( Y1 = Y0 ) ) )
=> ( sK3 @ Y0 @ Y2 @ Y1 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f50]) ).
thf(f50,plain,
( $false
= ( ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( ( ( ?? @ iS
@ ^ [Y3: iS] :
( ?? @ iS
@ ^ [Y4: iS] :
( ?? @ iS
@ ^ [Y5: iS] :
( ?? @ iS
@ ^ [Y6: iS] :
( ?? @ iS
@ ^ [Y7: iS] :
( ?? @ iS
@ ^ [Y8: iS] :
( ( sK3 @ Y3 @ Y6 @ Y4 )
& ( ( cP @ Y8 @ Y3 )
= Y0 )
& ( sK3 @ Y8 @ Y5 @ Y7 )
& ( ( cP @ Y5 @ Y6 )
= Y2 )
& ( ( cP @ Y7 @ Y4 )
= Y1 ) ) ) ) ) ) ) )
| ( ( Y2 = Y1 )
& ( c0 = Y0 ) )
| ( ( c0 = Y2 )
& ( Y1 = Y0 ) ) )
=> ( sK3 @ Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( sK3 @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) @ ( cP @ x @ y ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f49]) ).
thf(f49,plain,
( ( ^ [Y0: iS > iS > iS > $o] :
( ( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( !! @ iS
@ ^ [Y3: iS] :
( ( ( ?? @ iS
@ ^ [Y4: iS] :
( ?? @ iS
@ ^ [Y5: iS] :
( ?? @ iS
@ ^ [Y6: iS] :
( ?? @ iS
@ ^ [Y7: iS] :
( ?? @ iS
@ ^ [Y8: iS] :
( ?? @ iS
@ ^ [Y9: iS] :
( ( Y0 @ Y4 @ Y7 @ Y5 )
& ( ( cP @ Y9 @ Y4 )
= Y1 )
& ( Y0 @ Y9 @ Y6 @ Y8 )
& ( ( cP @ Y6 @ Y7 )
= Y3 )
& ( ( cP @ Y8 @ Y5 )
= Y2 ) ) ) ) ) ) ) )
| ( ( Y3 = Y2 )
& ( c0 = Y1 ) )
| ( ( c0 = Y3 )
& ( Y2 = Y1 ) ) )
=> ( Y0 @ Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y0 @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) @ ( cP @ x @ y ) ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[status(thm)],[f10]) ).
thf(f10,plain,
( ( !! @ ( iS > iS > iS > $o )
@ ^ [Y0: iS > iS > iS > $o] :
( ( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( !! @ iS
@ ^ [Y3: iS] :
( ( ( ?? @ iS
@ ^ [Y4: iS] :
( ?? @ iS
@ ^ [Y5: iS] :
( ?? @ iS
@ ^ [Y6: iS] :
( ?? @ iS
@ ^ [Y7: iS] :
( ?? @ iS
@ ^ [Y8: iS] :
( ?? @ iS
@ ^ [Y9: iS] :
( ( Y0 @ Y4 @ Y7 @ Y5 )
& ( ( cP @ Y9 @ Y4 )
= Y1 )
& ( Y0 @ Y9 @ Y6 @ Y8 )
& ( ( cP @ Y6 @ Y7 )
= Y3 )
& ( ( cP @ Y8 @ Y5 )
= Y2 ) ) ) ) ) ) ) )
| ( ( Y3 = Y2 )
& ( c0 = Y1 ) )
| ( ( c0 = Y3 )
& ( Y2 = Y1 ) ) )
=> ( Y0 @ Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y0 @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) @ ( cP @ x @ y ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ( ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( c0
!= ( cP @ Y1 @ Y0 ) ) ) )
& ( !! @ ( iS > $o )
@ ^ [Y0: iS > $o] :
( ( ( Y0 @ c0 )
& ( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( ( ( Y0 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ ( cP @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ iS @ Y0 ) ) )
& ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( !! @ iS
@ ^ [Y3: iS] :
( ( ( cP @ Y3 @ Y2 )
= ( cP @ Y1 @ Y0 ) )
=> ( ( Y3 = Y1 )
& ( Y2 = Y0 ) ) ) ) ) ) ) )
=> ( !! @ ( iS > iS > iS > $o )
@ ^ [Y0: iS > iS > iS > $o] :
( ( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( !! @ iS
@ ^ [Y3: iS] :
( ( ( ?? @ iS
@ ^ [Y4: iS] :
( ?? @ iS
@ ^ [Y5: iS] :
( ?? @ iS
@ ^ [Y6: iS] :
( ?? @ iS
@ ^ [Y7: iS] :
( ?? @ iS
@ ^ [Y8: iS] :
( ?? @ iS
@ ^ [Y9: iS] :
( ( Y0 @ Y4 @ Y7 @ Y5 )
& ( ( cP @ Y9 @ Y4 )
= Y1 )
& ( Y0 @ Y9 @ Y6 @ Y8 )
& ( ( cP @ Y6 @ Y7 )
= Y3 )
& ( ( cP @ Y8 @ Y5 )
= Y2 ) ) ) ) ) ) ) )
| ( ( Y3 = Y2 )
& ( c0 = Y1 ) )
| ( ( c0 = Y3 )
& ( Y2 = Y1 ) ) )
=> ( Y0 @ Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y0 @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) @ ( cP @ x @ y ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f8]) ).
thf(f8,plain,
( $true
= ( ~ ( ( ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( c0
!= ( cP @ Y1 @ Y0 ) ) ) )
& ( !! @ ( iS > $o )
@ ^ [Y0: iS > $o] :
( ( ( Y0 @ c0 )
& ( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( ( ( Y0 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ ( cP @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ iS @ Y0 ) ) )
& ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( !! @ iS
@ ^ [Y3: iS] :
( ( ( cP @ Y3 @ Y2 )
= ( cP @ Y1 @ Y0 ) )
=> ( ( Y3 = Y1 )
& ( Y2 = Y0 ) ) ) ) ) ) ) )
=> ( !! @ ( iS > iS > iS > $o )
@ ^ [Y0: iS > iS > iS > $o] :
( ( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( !! @ iS
@ ^ [Y3: iS] :
( ( ( ?? @ iS
@ ^ [Y4: iS] :
( ?? @ iS
@ ^ [Y5: iS] :
( ?? @ iS
@ ^ [Y6: iS] :
( ?? @ iS
@ ^ [Y7: iS] :
( ?? @ iS
@ ^ [Y8: iS] :
( ?? @ iS
@ ^ [Y9: iS] :
( ( Y0 @ Y4 @ Y7 @ Y5 )
& ( ( cP @ Y9 @ Y4 )
= Y1 )
& ( Y0 @ Y9 @ Y6 @ Y8 )
& ( ( cP @ Y6 @ Y7 )
= Y3 )
& ( ( cP @ Y8 @ Y5 )
= Y2 ) ) ) ) ) ) ) )
| ( ( Y3 = Y2 )
& ( c0 = Y1 ) )
| ( ( c0 = Y3 )
& ( Y2 = Y1 ) ) )
=> ( Y0 @ Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y0 @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) @ ( cP @ x @ y ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f7]) ).
thf(f7,plain,
( $true
= ( ~ ( ( ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( c0
!= ( cP @ Y1 @ Y0 ) ) ) )
& ( !! @ ( iS > $o )
@ ^ [Y0: iS > $o] :
( ( ( Y0 @ c0 )
& ( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( ( ( Y0 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ ( cP @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ iS @ Y0 ) ) )
& ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( !! @ iS
@ ^ [Y3: iS] :
( ( ( cP @ Y3 @ Y2 )
= ( cP @ Y1 @ Y0 ) )
=> ( ( Y3 = Y1 )
& ( Y2 = Y0 ) ) ) ) ) ) ) )
=> ( !! @ ( iS > iS > iS > $o )
@ ^ [Y0: iS > iS > iS > $o] :
( ( ( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( !! @ iS
@ ^ [Y3: iS] :
( ( ( ?? @ iS
@ ^ [Y4: iS] :
( ?? @ iS
@ ^ [Y5: iS] :
( ?? @ iS
@ ^ [Y6: iS] :
( ?? @ iS
@ ^ [Y7: iS] :
( ?? @ iS
@ ^ [Y8: iS] :
( ?? @ iS
@ ^ [Y9: iS] :
( ( Y0 @ Y4 @ Y7 @ Y5 )
& ( ( cP @ Y9 @ Y4 )
= Y1 )
& ( Y0 @ Y9 @ Y6 @ Y8 )
& ( ( cP @ Y6 @ Y7 )
= Y3 )
& ( ( cP @ Y8 @ Y5 )
= Y2 ) ) ) ) ) ) ) )
| ( ( Y3 = Y2 )
& ( c0 = Y1 ) )
| ( ( c0 = Y3 )
& ( Y2 = Y1 ) ) )
=> ( Y0 @ Y1 @ Y3 @ Y2 ) ) ) ) )
& $true )
=> ( Y0 @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) @ ( cP @ x @ y ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( ( ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( c0
!= ( cP @ Y1 @ Y0 ) ) ) )
& ( !! @ ( iS > $o )
@ ^ [Y0: iS > $o] :
( ( ( Y0 @ c0 )
& ( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( ( ( Y0 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ ( cP @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ iS
@ ^ [Y1: iS] : ( Y0 @ Y1 ) ) ) )
& ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( !! @ iS
@ ^ [Y3: iS] :
( ( ( cP @ Y3 @ Y2 )
= ( cP @ Y1 @ Y0 ) )
=> ( ( Y3 = Y1 )
& ( Y2 = Y0 ) ) ) ) ) ) ) )
=> ( !! @ ( iS > iS > iS > $o )
@ ^ [Y0: iS > iS > iS > $o] :
( ( ( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( !! @ iS
@ ^ [Y3: iS] :
( ( ( ?? @ iS
@ ^ [Y4: iS] :
( ?? @ iS
@ ^ [Y5: iS] :
( ?? @ iS
@ ^ [Y6: iS] :
( ?? @ iS
@ ^ [Y7: iS] :
( ?? @ iS
@ ^ [Y8: iS] :
( ?? @ iS
@ ^ [Y9: iS] :
( ( Y0 @ Y4 @ Y7 @ Y5 )
& ( ( cP @ Y9 @ Y4 )
= Y1 )
& ( Y0 @ Y9 @ Y6 @ Y8 )
& ( ( cP @ Y6 @ Y7 )
= Y3 )
& ( ( cP @ Y8 @ Y5 )
= Y2 ) ) ) ) ) ) ) )
| ( ( Y3 = Y2 )
& ( c0 = Y1 ) )
| ( ( c0 = Y3 )
& ( Y2 = Y1 ) ) )
=> ( Y0 @ Y1 @ Y3 @ Y2 ) ) ) ) )
& $true )
=> ( Y0 @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) @ ( cP @ x @ y ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( ( ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( c0
!= ( cP @ Y1 @ Y0 ) ) ) )
& ( !! @ ( iS > $o )
@ ^ [Y0: iS > $o] :
( ( ( Y0 @ c0 )
& ( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( ( ( Y0 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ ( cP @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ iS
@ ^ [Y1: iS] : ( Y0 @ Y1 ) ) ) )
& ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( !! @ iS
@ ^ [Y3: iS] :
( ( ( cP @ Y3 @ Y2 )
= ( cP @ Y1 @ Y0 ) )
=> ( ( Y3 = Y1 )
& ( Y2 = Y0 ) ) ) ) ) ) ) )
=> ( !! @ ( iS > iS > iS > $o )
@ ^ [Y0: iS > iS > iS > $o] :
( ( ( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( !! @ iS
@ ^ [Y3: iS] :
( ( ( ?? @ iS
@ ^ [Y4: iS] :
( ?? @ iS
@ ^ [Y5: iS] :
( ?? @ iS
@ ^ [Y6: iS] :
( ?? @ iS
@ ^ [Y7: iS] :
( ?? @ iS
@ ^ [Y8: iS] :
( ?? @ iS
@ ^ [Y9: iS] :
( ( Y0 @ Y4 @ Y7 @ Y5 )
& ( ( cP @ Y9 @ Y4 )
= Y1 )
& ( Y0 @ Y9 @ Y6 @ Y8 )
& ( ( cP @ Y6 @ Y7 )
= Y3 )
& ( ( cP @ Y8 @ Y5 )
= Y2 ) ) ) ) ) ) ) )
| ( ( Y3 = Y2 )
& ( c0 = Y1 ) )
| ( ( c0 = Y3 )
& ( Y2 = Y1 ) ) )
=> ( Y0 @ Y1 @ Y3 @ Y2 ) ) ) ) )
& $true )
=> ( Y0 @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) @ ( cP @ x @ y ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: iS,X1: iS,X2: iS,X3: iS] :
( ( ( cP @ X0 @ X1 )
= ( cP @ X2 @ X3 ) )
=> ( ( X1 = X3 )
& ( X0 = X2 ) ) )
& ! [X4: iS > $o] :
( ( ! [X5: iS,X6: iS] :
( ( ( X4 @ X6 )
& ( X4 @ X5 ) )
=> ( X4 @ ( cP @ X5 @ X6 ) ) )
& ( X4 @ c0 ) )
=> ! [X7: iS] : ( X4 @ X7 ) )
& ! [X8: iS,X9: iS] :
( c0
!= ( cP @ X8 @ X9 ) ) )
=> ! [X10: iS > iS > iS > $o] :
( ( $true
& ! [X11: iS,X12: iS,X13: iS] :
( ( ( ( X12 = X13 )
& ( c0 = X11 ) )
| ( ( c0 = X13 )
& ( X11 = X12 ) )
| ? [X14: iS,X15: iS,X16: iS,X17: iS,X18: iS,X19: iS] :
( ( ( cP @ X15 @ X18 )
= X12 )
& ( ( cP @ X17 @ X16 )
= X11 )
& ( X10 @ X14 @ X17 @ X15 )
& ( ( cP @ X14 @ X19 )
= X13 )
& ( X10 @ X19 @ X16 @ X18 ) ) )
=> ( X10 @ X13 @ X11 @ X12 ) ) )
=> ( X10 @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) @ ( cP @ x @ y ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X1: iS,X3: iS,X0: iS,X2: iS] :
( ( ( cP @ X0 @ X2 )
= ( cP @ X1 @ X3 ) )
=> ( ( X2 = X3 )
& ( X0 = X1 ) ) )
& ! [X4: iS > $o] :
( ( ! [X0: iS,X1: iS] :
( ( ( X4 @ X1 )
& ( X4 @ X0 ) )
=> ( X4 @ ( cP @ X0 @ X1 ) ) )
& ( X4 @ c0 ) )
=> ! [X0: iS] : ( X4 @ X0 ) )
& ! [X0: iS,X1: iS] :
( ( cP @ X0 @ X1 )
!= c0 ) )
=> ! [X5: iS > iS > iS > $o] :
( ( $true
& ! [X7: iS,X8: iS,X6: iS] :
( ( ( ( X6 = X8 )
& ( c0 = X7 ) )
| ( ( c0 = X6 )
& ( X7 = X8 ) )
| ? [X9: iS,X13: iS,X12: iS,X11: iS,X14: iS,X10: iS] :
( ( ( cP @ X13 @ X14 )
= X8 )
& ( ( cP @ X11 @ X12 )
= X7 )
& ( X5 @ X9 @ X11 @ X13 )
& ( ( cP @ X9 @ X10 )
= X6 )
& ( X5 @ X10 @ X12 @ X14 ) ) )
=> ( X5 @ X6 @ X7 @ X8 ) ) )
=> ( X5 @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) @ ( cP @ x @ y ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X1: iS,X3: iS,X0: iS,X2: iS] :
( ( ( cP @ X0 @ X2 )
= ( cP @ X1 @ X3 ) )
=> ( ( X2 = X3 )
& ( X0 = X1 ) ) )
& ! [X4: iS > $o] :
( ( ! [X0: iS,X1: iS] :
( ( ( X4 @ X1 )
& ( X4 @ X0 ) )
=> ( X4 @ ( cP @ X0 @ X1 ) ) )
& ( X4 @ c0 ) )
=> ! [X0: iS] : ( X4 @ X0 ) )
& ! [X0: iS,X1: iS] :
( ( cP @ X0 @ X1 )
!= c0 ) )
=> ! [X5: iS > iS > iS > $o] :
( ( $true
& ! [X7: iS,X8: iS,X6: iS] :
( ( ( ( X6 = X8 )
& ( c0 = X7 ) )
| ( ( c0 = X6 )
& ( X7 = X8 ) )
| ? [X9: iS,X13: iS,X12: iS,X11: iS,X14: iS,X10: iS] :
( ( ( cP @ X13 @ X14 )
= X8 )
& ( ( cP @ X11 @ X12 )
= X7 )
& ( X5 @ X9 @ X11 @ X13 )
& ( ( cP @ X9 @ X10 )
= X6 )
& ( X5 @ X10 @ X12 @ X14 ) ) )
=> ( X5 @ X6 @ X7 @ X8 ) ) )
=> ( X5 @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) @ ( cP @ x @ y ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.siZw90THh0/DTF2THF_7046.p',cS_INCL_LEM5_pme) ).
thf(f191,plain,
( ( $false
= ( sK3 @ c0 @ x @ x ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f189]) ).
thf(f189,definition,
( spl0_1
<=> ( $false
= ( sK3 @ c0 @ x @ x ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f866,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[status(thm)],[f865]) ).
thf(f865,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_10 ),
inference(trivial_inequality_removal,[status(thm)],[f749]) ).
thf(f749,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_10 ),
inference(superposition,[status(thm)],[f308,f688]) ).
thf(f688,plain,
( ( $false
= ( sK3 @ c0 @ c0 @ c0 ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f664]) ).
thf(f664,plain,
( ( $false
= ( sK3 @ c0 @ c0 @ c0 ) )
| ( $true = $false )
| ~ spl0_2
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f652,f195]) ).
thf(f195,plain,
( ( ( sK3 @ y @ y @ y )
= $false )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f193]) ).
thf(f193,definition,
( spl0_2
<=> ( ( sK3 @ y @ y @ y )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f652,plain,
( ! [X0: iS] :
( ( $true
= ( sK3 @ X0 @ X0 @ X0 ) )
| ( $false
= ( sK3 @ c0 @ c0 @ c0 ) ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f622]) ).
thf(f622,plain,
( ! [X0: iS] :
( ( $false
= ( sK3 @ c0 @ c0 @ c0 ) )
| ( $true
= ( sK3 @ X0 @ X0 @ X0 ) )
| ( $true = $false ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f594,f195]) ).
thf(f594,plain,
( ! [X0: iS,X1: iS] :
( ( $true
= ( sK3 @ X0 @ X0 @ X0 ) )
| ( ( sK3 @ X1 @ X1 @ X1 )
= $true )
| ( $false
= ( sK3 @ c0 @ c0 @ c0 ) ) )
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f592]) ).
thf(f592,plain,
( ! [X0: iS,X1: iS] :
( ( $true != $true )
| ( $false
= ( sK3 @ c0 @ c0 @ c0 ) )
| ( $true
= ( sK3 @ X0 @ X0 @ X0 ) )
| ( ( sK3 @ X1 @ X1 @ X1 )
= $true ) )
| ~ spl0_4 ),
inference(equality_factoring,[status(thm)],[f569]) ).
thf(f569,plain,
( ! [X2: iS,X0: iS,X1: iS] :
( ( $true
= ( sK3 @ X2 @ X2 @ X2 ) )
| ( $false
= ( sK3 @ c0 @ c0 @ c0 ) )
| ( $true
= ( sK3 @ X0 @ X0 @ X0 ) )
| ( ( sK3 @ X1 @ X1 @ X1 )
= $true ) )
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f568]) ).
thf(f568,plain,
( ! [X2: iS,X0: iS,X1: iS] :
( ( $true
= ( sK3 @ X0 @ X0 @ X0 ) )
| ( ( sK3 @ X1 @ X1 @ X1 )
= $true )
| ( ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
!= ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) ) )
| ( $true
= ( sK3 @ X2 @ X2 @ X2 ) )
| ( $false
= ( sK3 @ c0 @ c0 @ c0 ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f567]) ).
thf(f567,plain,
( ! [X2: iS,X0: iS,X1: iS] :
( ( ( sK3 @ X1 @ X1 @ X1 )
= $true )
| ( $true
= ( sK3 @ X0 @ X0 @ X0 ) )
| ( ( sK3
@ ( ^ [Y0: iS] : Y0
@ X2 )
@ X2
@ ( ^ [Y0: iS] : Y0
@ X2 ) )
= $true )
| ( ( ^ [Y0: iS] : Y0
@ ( sK1
@ ^ [Y0: iS] :
( sK3
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ Y0
@ ( ^ [Y1: iS] : Y1
@ Y0 ) ) ) )
!= ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) ) )
| ( ( sK3
@ ( ^ [Y0: iS] : Y0
@ c0 )
@ c0
@ ( ^ [Y0: iS] : Y0
@ c0 ) )
= $false ) )
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f566]) ).
thf(f566,plain,
( ! [X2: iS,X0: iS,X1: iS] :
( ( ( sK3
@ ( ^ [Y0: iS] : Y0
@ c0 )
@ c0
@ ( ^ [Y0: iS] : Y0
@ c0 ) )
= $false )
| ( $true
= ( sK3 @ X0 @ X0 @ X0 ) )
| ( ( sK3
@ ( ^ [Y0: iS] : Y0
@ X2 )
@ X2
@ ( ^ [Y0: iS] : Y0
@ X2 ) )
= $true )
| ( ( ^ [Y0: iS] : Y0 )
!= ( ^ [Y0: iS] : Y0 ) )
| ( ( ^ [Y0: iS] : Y0
@ ( sK1
@ ^ [Y0: iS] :
( sK3
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ Y0
@ ( ^ [Y1: iS] : Y1
@ Y0 ) ) ) )
!= ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) ) )
| ( ( sK3 @ X1 @ X1 @ X1 )
= $true ) )
| ~ spl0_4 ),
inference(duplicate_literal_removal,[status(thm)],[f564]) ).
thf(f564,plain,
( ! [X2: iS,X0: iS,X1: iS] :
( ( ( sK3 @ X1 @ X1 @ X1 )
= $true )
| ( ( sK3
@ ( ^ [Y0: iS] : Y0
@ X2 )
@ X2
@ ( ^ [Y0: iS] : Y0
@ X2 ) )
= $true )
| ( $true
= ( sK3 @ X0 @ X0 @ X0 ) )
| ( ( ^ [Y0: iS] : Y0 )
!= ( ^ [Y0: iS] : Y0 ) )
| ( ( sK3
@ ( ^ [Y0: iS] : Y0
@ c0 )
@ c0
@ ( ^ [Y0: iS] : Y0
@ c0 ) )
= $false )
| ( ( ^ [Y0: iS] : Y0
@ ( sK1
@ ^ [Y0: iS] :
( sK3
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ Y0
@ ( ^ [Y1: iS] : Y1
@ Y0 ) ) ) )
!= ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) ) )
| ( ( ^ [Y0: iS] : Y0 )
!= ( ^ [Y0: iS] : Y0 ) ) )
| ~ spl0_4 ),
inference(equality_resolution,[status(thm)],[f553]) ).
thf(f553,plain,
( ! [X2: iS,X3: iS,X0: iS > iS,X1: iS > iS,X4: iS] :
( ( ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
!= ( X1
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ ( X0 @ Y0 ) @ Y0 @ ( X1 @ Y0 ) ) ) ) )
| ( ( X0
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ ( X0 @ Y0 ) @ Y0 @ ( X1 @ Y0 ) ) ) )
!= ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) ) )
| ( ( ^ [Y0: iS] : Y0 )
!= X0 )
| ( ( sK3 @ ( X0 @ c0 ) @ c0 @ ( X1 @ c0 ) )
= $false )
| ( $true
= ( sK3 @ X3 @ X3 @ X3 ) )
| ( ( sK3 @ X4 @ X4 @ X4 )
= $true )
| ( $true
= ( sK3 @ ( X0 @ X2 ) @ X2 @ ( X1 @ X2 ) ) )
| ( ( ^ [Y0: iS] : Y0 )
!= X1 ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f552]) ).
thf(f552,plain,
( ! [X2: iS,X3: iS,X0: iS > iS,X1: iS > iS,X4: iS] :
( ( ( sK3 @ X4 @ X4 @ X4 )
= $true )
| ( $false
= ( ^ [Y0: iS] :
( sK3 @ ( X0 @ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X1 @ Y0 ) )
@ c0 ) )
| ( ( X1
@ ( sK1
@ ^ [Y0: iS] :
( sK3 @ ( X0 @ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X1 @ Y0 ) ) ) )
!= ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) ) )
| ( $true
= ( sK3 @ X3 @ X3 @ X3 ) )
| ( ( ^ [Y0: iS] :
( sK3 @ ( X0 @ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X1 @ Y0 ) )
@ X2 )
= $true )
| ( ( ^ [Y0: iS] : ( X1 @ Y0 ) )
!= ( ^ [Y0: iS] : Y0 ) )
| ( ( ^ [Y0: iS] : ( X0 @ Y0 ) )
!= ( ^ [Y0: iS] : Y0 ) )
| ( ( X0
@ ( sK1
@ ^ [Y0: iS] :
( sK3 @ ( X0 @ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X1 @ Y0 ) ) ) )
!= ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) ) ) )
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f547]) ).
thf(f547,plain,
( ! [X2: iS,X3: iS,X0: iS > iS,X1: iS > iS,X4: iS] :
( ( ( X0
@ ( sK1
@ ^ [Y0: iS] :
( sK3 @ ( X0 @ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X1 @ Y0 ) ) ) )
!= ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) ) )
| ( ( ^ [Y0: iS] : ( X0 @ Y0 ) )
!= ( ^ [Y0: iS] : Y0 ) )
| ( $true
= ( sK3 @ X3 @ X3 @ X3 ) )
| ( ( ^ [Y0: iS] :
( sK3 @ ( X0 @ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X1 @ Y0 ) )
@ X2 )
= $true )
| ( ( ^ [Y0: iS] : ( X1 @ Y0 ) )
!= ( ^ [Y0: iS] : Y0 ) )
| ( ( X1
@ ( sK1
@ ^ [Y0: iS] :
( sK3 @ ( X0 @ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X1 @ Y0 ) ) ) )
!= ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) ) )
| ( $true = $false )
| ( ( sK3 @ X4 @ X4 @ X4 )
= $true )
| ( $false
= ( ^ [Y0: iS] :
( sK3 @ ( X0 @ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X1 @ Y0 ) )
@ c0 ) ) )
| ~ spl0_4 ),
inference(constrained_superposition,[status(thm)],[f47,f541]) ).
thf(f541,plain,
( ! [X0: iS,X1: iS] :
( ( ( sK3
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) ) )
= $false )
| ( ( sK3 @ X1 @ X1 @ X1 )
= $true )
| ( $true
= ( sK3 @ X0 @ X0 @ X0 ) ) )
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f540]) ).
thf(f540,plain,
( ! [X0: iS,X1: iS] :
( ( $true = $false )
| ( ( sK3 @ X1 @ X1 @ X1 )
= $true )
| ( $true
= ( sK3 @ X0 @ X0 @ X0 ) )
| ( ( sK3
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) ) )
= $false ) )
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f539,f254]) ).
thf(f254,plain,
( ( $true
= ( sK3 @ c0 @ c0 @ c0 ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f252]) ).
thf(f252,definition,
( spl0_4
<=> ( $true
= ( sK3 @ c0 @ c0 @ c0 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f539,plain,
( ! [X0: iS,X1: iS] :
( ( ( sK3
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) ) )
= $false )
| ( $true
= ( sK3 @ X0 @ X0 @ X0 ) )
| ( $false
= ( sK3 @ c0 @ c0 @ c0 ) )
| ( ( sK3 @ X1 @ X1 @ X1 )
= $true ) )
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f538]) ).
thf(f538,plain,
( ! [X0: iS,X1: iS] :
( ( $false
= ( sK3 @ c0 @ c0 @ c0 ) )
| ( $true
= ( sK3 @ X0 @ X0 @ X0 ) )
| ( ( sK3 @ X1 @ X1 @ X1 )
= $true )
| ( ( sK2
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
!= ( sK2
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) ) )
| ( ( sK3
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) ) )
= $false ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f537]) ).
thf(f537,plain,
( ! [X0: iS,X1: iS] :
( ( ( sK3 @ X1 @ X1 @ X1 )
= $true )
| ( $true
= ( sK3 @ X0
@ ( ^ [Y0: iS] : Y0
@ X0 )
@ ( ^ [Y0: iS] : Y0
@ X0 ) ) )
| ( ( sK3
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) ) )
= $false )
| ( $false
= ( sK3 @ c0
@ ( ^ [Y0: iS] : Y0
@ c0 )
@ ( ^ [Y0: iS] : Y0
@ c0 ) ) )
| ( ( sK2
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
!= ( ^ [Y0: iS] : Y0
@ ( sK2
@ ^ [Y0: iS] :
( sK3 @ Y0
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 ) ) ) ) ) )
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f536]) ).
thf(f536,plain,
( ! [X0: iS,X1: iS] :
( ( $true
= ( sK3 @ X0
@ ( ^ [Y0: iS] : Y0
@ X0 )
@ ( ^ [Y0: iS] : Y0
@ X0 ) ) )
| ( $false
= ( sK3 @ c0
@ ( ^ [Y0: iS] : Y0
@ c0 )
@ ( ^ [Y0: iS] : Y0
@ c0 ) ) )
| ( ( sK3 @ X1 @ X1 @ X1 )
= $true )
| ( ( sK3
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) ) )
= $false )
| ( ( ^ [Y0: iS] : Y0 )
!= ( ^ [Y0: iS] : Y0 ) )
| ( ( sK2
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
!= ( ^ [Y0: iS] : Y0
@ ( sK2
@ ^ [Y0: iS] :
( sK3 @ Y0
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 ) ) ) ) ) )
| ~ spl0_4 ),
inference(duplicate_literal_removal,[status(thm)],[f533]) ).
thf(f533,plain,
( ! [X0: iS,X1: iS] :
( ( ( sK3 @ X1 @ X1 @ X1 )
= $true )
| ( ( sK3
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) ) )
= $false )
| ( $false
= ( sK3 @ c0
@ ( ^ [Y0: iS] : Y0
@ c0 )
@ ( ^ [Y0: iS] : Y0
@ c0 ) ) )
| ( $true
= ( sK3 @ X0
@ ( ^ [Y0: iS] : Y0
@ X0 )
@ ( ^ [Y0: iS] : Y0
@ X0 ) ) )
| ( ( ^ [Y0: iS] : Y0 )
!= ( ^ [Y0: iS] : Y0 ) )
| ( ( sK2
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
!= ( ^ [Y0: iS] : Y0
@ ( sK2
@ ^ [Y0: iS] :
( sK3 @ Y0
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 ) ) ) ) )
| ( ( ^ [Y0: iS] : Y0 )
!= ( ^ [Y0: iS] : Y0 ) ) )
| ~ spl0_4 ),
inference(equality_resolution,[status(thm)],[f524]) ).
thf(f524,plain,
( ! [X2: iS,X3: iS,X0: iS > iS,X1: iS > iS] :
( ( ( sK2
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
!= ( X1
@ ( sK2
@ ^ [Y0: iS] : ( sK3 @ Y0 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) ) ) )
| ( ( sK3 @ c0 @ ( X0 @ c0 ) @ ( X1 @ c0 ) )
= $false )
| ( $true
= ( sK3 @ X3 @ ( X0 @ X3 ) @ ( X1 @ X3 ) ) )
| ( ( sK3
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) ) )
= $false )
| ( ( sK2
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
!= ( X0
@ ( sK2
@ ^ [Y0: iS] : ( sK3 @ Y0 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) ) ) )
| ( $true
= ( sK3 @ X2 @ X2 @ X2 ) )
| ( ( ^ [Y0: iS] : Y0 )
!= X1 )
| ( ( ^ [Y0: iS] : Y0 )
!= X0 ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f523]) ).
thf(f523,plain,
( ! [X2: iS,X3: iS,X0: iS > iS,X1: iS > iS] :
( ( $true
= ( ^ [Y0: iS] :
( sK3
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X0 @ Y0 )
@ ( X1 @ Y0 ) )
@ X3 ) )
| ( ( ^ [Y0: iS] : ( X0 @ Y0 ) )
!= ( ^ [Y0: iS] : Y0 ) )
| ( ( ^ [Y0: iS] :
( sK3
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X0 @ Y0 )
@ ( X1 @ Y0 ) )
@ c0 )
= $false )
| ( $true
= ( sK3 @ X2 @ X2 @ X2 ) )
| ( ( ^ [Y0: iS] : ( X1 @ Y0 ) )
!= ( ^ [Y0: iS] : Y0 ) )
| ( ( sK2
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
!= ( X0
@ ( sK2
@ ^ [Y0: iS] :
( sK3
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X0 @ Y0 )
@ ( X1 @ Y0 ) ) ) ) )
| ( ( sK2
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
!= ( X1
@ ( sK2
@ ^ [Y0: iS] :
( sK3
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X0 @ Y0 )
@ ( X1 @ Y0 ) ) ) ) )
| ( ( sK3
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) ) )
= $false ) )
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f513]) ).
thf(f513,plain,
( ! [X2: iS,X3: iS,X0: iS > iS,X1: iS > iS] :
( ( $true = $false )
| ( ( sK3
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) ) )
= $false )
| ( $true
= ( sK3 @ X2 @ X2 @ X2 ) )
| ( ( ^ [Y0: iS] : ( X0 @ Y0 ) )
!= ( ^ [Y0: iS] : Y0 ) )
| ( ( ^ [Y0: iS] :
( sK3
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X0 @ Y0 )
@ ( X1 @ Y0 ) )
@ c0 )
= $false )
| ( $true
= ( ^ [Y0: iS] :
( sK3
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X0 @ Y0 )
@ ( X1 @ Y0 ) )
@ X3 ) )
| ( ( ^ [Y0: iS] : ( X1 @ Y0 ) )
!= ( ^ [Y0: iS] : Y0 ) )
| ( ( sK2
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
!= ( X1
@ ( sK2
@ ^ [Y0: iS] :
( sK3
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X0 @ Y0 )
@ ( X1 @ Y0 ) ) ) ) )
| ( ( sK2
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
!= ( X0
@ ( sK2
@ ^ [Y0: iS] :
( sK3
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X0 @ Y0 )
@ ( X1 @ Y0 ) ) ) ) ) )
| ~ spl0_4 ),
inference(constrained_superposition,[status(thm)],[f509,f48]) ).
thf(f48,plain,
! [X2: iS,X1: iS > $o] :
( ( $true
= ( X1 @ ( sK2 @ X1 ) ) )
| ( $true
= ( X1 @ X2 ) )
| ( ( X1 @ c0 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
! [X2: iS,X1: iS > $o] :
( ( $true
= ( X1 @ X2 ) )
| ( $true
= ( ( X1 @ ( sK2 @ X1 ) )
& ( X1 @ ( sK1 @ X1 ) ) ) )
| ( ( X1 @ c0 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
! [X2: iS,X1: iS > $o] :
( ( $true
= ( X1 @ X2 ) )
| ( ( X1 @ c0 )
= $false )
| ( $false
= ( ( ( X1 @ ( sK2 @ X1 ) )
& ( X1 @ ( sK1 @ X1 ) ) )
=> ( X1 @ ( cP @ ( sK2 @ X1 ) @ ( sK1 @ X1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f43]) ).
thf(f43,plain,
! [X2: iS,X1: iS > $o] :
( ( $true
= ( X1 @ X2 ) )
| ( $false
= ( ^ [Y0: iS] :
( ( ( X1 @ Y0 )
& ( X1 @ ( sK1 @ X1 ) ) )
=> ( X1 @ ( cP @ Y0 @ ( sK1 @ X1 ) ) ) )
@ ( sK2 @ X1 ) ) )
| ( ( X1 @ c0 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
! [X2: iS,X1: iS > $o] :
( ( ( X1 @ c0 )
= $false )
| ( $true
= ( X1 @ X2 ) )
| ( ( !! @ iS
@ ^ [Y0: iS] :
( ( ( X1 @ Y0 )
& ( X1 @ ( sK1 @ X1 ) ) )
=> ( X1 @ ( cP @ Y0 @ ( sK1 @ X1 ) ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f41]) ).
thf(f41,plain,
! [X2: iS,X1: iS > $o] :
( ( $true
= ( X1 @ X2 ) )
| ( ( X1 @ c0 )
= $false )
| ( $false
= ( ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( ( ( X1 @ Y1 )
& ( X1 @ Y0 ) )
=> ( X1 @ ( cP @ Y1 @ Y0 ) ) ) )
@ ( sK1 @ X1 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
! [X2: iS,X1: iS > $o] :
( ( ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( ( ( X1 @ Y1 )
& ( X1 @ Y0 ) )
=> ( X1 @ ( cP @ Y1 @ Y0 ) ) ) ) )
= $false )
| ( ( X1 @ c0 )
= $false )
| ( $true
= ( X1 @ X2 ) ) ),
inference(pi_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
! [X1: iS > $o] :
( ( $true
= ( !! @ iS @ X1 ) )
| ( ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( ( ( X1 @ Y1 )
& ( X1 @ Y0 ) )
=> ( X1 @ ( cP @ Y1 @ Y0 ) ) ) ) )
= $false )
| ( ( X1 @ c0 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
! [X1: iS > $o] :
( ( ( ( X1 @ c0 )
& ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( ( ( X1 @ Y1 )
& ( X1 @ Y0 ) )
=> ( X1 @ ( cP @ Y1 @ Y0 ) ) ) ) ) )
= $false )
| ( $true
= ( !! @ iS @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
! [X1: iS > $o] :
( ( ( ( X1 @ c0 )
& ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( ( ( X1 @ Y1 )
& ( X1 @ Y0 ) )
=> ( X1 @ ( cP @ Y1 @ Y0 ) ) ) ) ) )
=> ( !! @ iS @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f36]) ).
thf(f36,plain,
! [X1: iS > $o] :
( $true
= ( ^ [Y0: iS > $o] :
( ( ( Y0 @ c0 )
& ( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( ( ( Y0 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ ( cP @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ iS @ Y0 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
( $true
= ( !! @ ( iS > $o )
@ ^ [Y0: iS > $o] :
( ( ( Y0 @ c0 )
& ( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( ( ( Y0 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ ( cP @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ iS @ Y0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( $true
= ( ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( c0
!= ( cP @ Y1 @ Y0 ) ) ) )
& ( !! @ ( iS > $o )
@ ^ [Y0: iS > $o] :
( ( ( Y0 @ c0 )
& ( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( ( ( Y0 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ ( cP @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ iS @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( $true
= ( ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( c0
!= ( cP @ Y1 @ Y0 ) ) ) )
& ( !! @ ( iS > $o )
@ ^ [Y0: iS > $o] :
( ( ( Y0 @ c0 )
& ( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( ( ( Y0 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ ( cP @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ iS @ Y0 ) ) )
& ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( !! @ iS
@ ^ [Y3: iS] :
( ( ( cP @ Y3 @ Y2 )
= ( cP @ Y1 @ Y0 ) )
=> ( ( Y3 = Y1 )
& ( Y2 = Y0 ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f9]) ).
thf(f509,plain,
( ! [X0: iS] :
( ( ( sK3
@ ( sK2
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
@ ( sK2
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
@ ( sK2
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) ) )
= $false )
| ( $true
= ( sK3 @ X0 @ X0 @ X0 ) )
| ( ( sK3
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) ) )
= $false ) )
| ~ spl0_4 ),
inference(equality_resolution,[status(thm)],[f508]) ).
thf(f508,plain,
( ! [X0: iS,X1: iS] :
( ( ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
!= X1 )
| ( $true
= ( sK3 @ X0 @ X0 @ X0 ) )
| ( ( sK3
@ ( sK2
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
@ ( sK2
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
@ ( sK2
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) ) )
= $false )
| ( ( sK3
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
@ X1
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) ) )
= $false ) )
| ~ spl0_4 ),
inference(equality_resolution,[status(thm)],[f507]) ).
thf(f507,plain,
( ! [X2: iS,X0: iS,X1: iS] :
( ( ( sK2
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
!= X1 )
| ( $true
= ( sK3 @ X2 @ X2 @ X2 ) )
| ( ( sK3
@ ( sK2
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
@ X1
@ ( sK2
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) ) )
= $false )
| ( ( sK3
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
@ X0
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) ) )
= $false )
| ( ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
!= X0 ) )
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f506]) ).
thf(f506,plain,
( ! [X2: iS,X0: iS,X1: iS] :
( ( ( sK3
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
@ X0
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) ) )
= $false )
| ( $true
= ( sK3 @ X2 @ X2 @ X2 ) )
| ( ( sK3
@ ( sK2
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
@ X1
@ ( sK2
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) ) )
= $false )
| ( ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
!= X0 )
| ( $true = $false )
| ( ( sK2
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
!= X1 ) )
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f504,f254]) ).
thf(f504,plain,
! [X2: iS,X0: iS,X1: iS] :
( ( ( sK2
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
!= X1 )
| ( $true
= ( sK3 @ X2 @ X2 @ X2 ) )
| ( ( sK3
@ ( sK2
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
@ X1
@ ( sK2
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) ) )
= $false )
| ( ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
!= X0 )
| ( ( sK3
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) )
@ X0
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ Y0 @ Y0 ) ) )
= $false )
| ( $false
= ( sK3 @ c0 @ c0 @ c0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f502]) ).
thf(f502,plain,
! [X2: iS,X0: iS,X1: iS] :
( ( ( sK3
@ ( ^ [Y0: iS] : Y0
@ c0 )
@ c0
@ c0 )
= $false )
| ( ( sK2
@ ^ [Y0: iS] :
( sK3
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ Y0
@ Y0 ) )
!= X1 )
| ( ( sK3
@ ( ^ [Y0: iS] : Y0
@ X2 )
@ X2
@ X2 )
= $true )
| ( $false
= ( sK3
@ ( sK2
@ ^ [Y0: iS] :
( sK3
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ Y0
@ Y0 ) )
@ X1
@ ( sK2
@ ^ [Y0: iS] :
( sK3
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ Y0
@ Y0 ) ) ) )
| ( ( sK3
@ ( sK1
@ ^ [Y0: iS] :
( sK3
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ Y0
@ Y0 ) )
@ X0
@ ( sK1
@ ^ [Y0: iS] :
( sK3
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ Y0
@ Y0 ) ) )
= $false )
| ( ( sK1
@ ^ [Y0: iS] :
( sK3
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ Y0
@ Y0 ) )
!= X0 ) ),
inference(equality_resolution,[status(thm)],[f501]) ).
thf(f501,plain,
! [X2: iS,X3: iS,X0: iS > iS,X1: iS,X4: iS,X5: iS] :
( ( ( cP @ X2 @ X4 )
!= ( X0
@ ( cP
@ ( sK2
@ ^ [Y0: iS] : ( sK3 @ ( X0 @ Y0 ) @ Y0 @ Y0 ) )
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ ( X0 @ Y0 ) @ Y0 @ Y0 ) ) ) ) )
| ( ( sK3 @ ( X0 @ c0 ) @ c0 @ c0 )
= $false )
| ( ( sK1
@ ^ [Y0: iS] : ( sK3 @ ( X0 @ Y0 ) @ Y0 @ Y0 ) )
!= X1 )
| ( $false
= ( sK3 @ X4 @ X1
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ ( X0 @ Y0 ) @ Y0 @ Y0 ) ) ) )
| ( ( sK2
@ ^ [Y0: iS] : ( sK3 @ ( X0 @ Y0 ) @ Y0 @ Y0 ) )
!= X3 )
| ( $false
= ( sK3 @ X2 @ X3
@ ( sK2
@ ^ [Y0: iS] : ( sK3 @ ( X0 @ Y0 ) @ Y0 @ Y0 ) ) ) )
| ( $true
= ( sK3 @ ( X0 @ X5 ) @ X5 @ X5 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f498]) ).
thf(f498,plain,
! [X2: iS,X3: iS,X0: iS > iS,X1: iS,X4: iS,X5: iS] :
( ( ( sK1
@ ^ [Y0: iS] :
( sK3 @ ( X0 @ Y0 ) @ Y0
@ ( ^ [Y1: iS] : Y1
@ Y0 ) ) )
!= X1 )
| ( $false
= ( sK3 @ ( X0 @ c0 ) @ c0
@ ( ^ [Y0: iS] : Y0
@ c0 ) ) )
| ( ( sK2
@ ^ [Y0: iS] :
( sK3 @ ( X0 @ Y0 ) @ Y0
@ ( ^ [Y1: iS] : Y1
@ Y0 ) ) )
!= X3 )
| ( ( sK3 @ X4 @ X1
@ ( sK1
@ ^ [Y0: iS] :
( sK3 @ ( X0 @ Y0 ) @ Y0
@ ( ^ [Y1: iS] : Y1
@ Y0 ) ) ) )
= $false )
| ( ( sK3 @ X2 @ X3
@ ( sK2
@ ^ [Y0: iS] :
( sK3 @ ( X0 @ Y0 ) @ Y0
@ ( ^ [Y1: iS] : Y1
@ Y0 ) ) ) )
= $false )
| ( $true
= ( sK3 @ ( X0 @ X5 ) @ X5
@ ( ^ [Y0: iS] : Y0
@ X5 ) ) )
| ( ( X0
@ ( cP
@ ( sK2
@ ^ [Y0: iS] :
( sK3 @ ( X0 @ Y0 ) @ Y0
@ ( ^ [Y1: iS] : Y1
@ Y0 ) ) )
@ ( sK1
@ ^ [Y0: iS] :
( sK3 @ ( X0 @ Y0 ) @ Y0
@ ( ^ [Y1: iS] : Y1
@ Y0 ) ) ) ) )
!= ( cP @ X2 @ X4 ) ) ),
inference(equality_resolution,[status(thm)],[f182]) ).
thf(f182,plain,
! [X2: iS > iS,X3: iS > iS,X0: iS,X1: iS,X8: iS,X6: iS,X7: iS,X4: iS,X5: iS] :
( ( ( cP @ X4 @ X5 )
!= ( X3
@ ( cP
@ ( sK2
@ ^ [Y0: iS] : ( sK3 @ ( X2 @ Y0 ) @ Y0 @ ( X3 @ Y0 ) ) )
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ ( X2 @ Y0 ) @ Y0 @ ( X3 @ Y0 ) ) ) ) ) )
| ( ( sK1
@ ^ [Y0: iS] : ( sK3 @ ( X2 @ Y0 ) @ Y0 @ ( X3 @ Y0 ) ) )
!= X6 )
| ( $false
= ( sK3 @ X0 @ X7 @ X4 ) )
| ( ( sK3 @ X1 @ X6 @ X5 )
= $false )
| ( ( cP @ X0 @ X1 )
!= ( X2
@ ( cP
@ ( sK2
@ ^ [Y0: iS] : ( sK3 @ ( X2 @ Y0 ) @ Y0 @ ( X3 @ Y0 ) ) )
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ ( X2 @ Y0 ) @ Y0 @ ( X3 @ Y0 ) ) ) ) ) )
| ( ( sK2
@ ^ [Y0: iS] : ( sK3 @ ( X2 @ Y0 ) @ Y0 @ ( X3 @ Y0 ) ) )
!= X7 )
| ( $true
= ( sK3 @ ( X2 @ X8 ) @ X8 @ ( X3 @ X8 ) ) )
| ( ( sK3 @ ( X2 @ c0 ) @ c0 @ ( X3 @ c0 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f181]) ).
thf(f181,plain,
! [X2: iS > iS,X3: iS > iS,X0: iS,X1: iS,X8: iS,X6: iS,X7: iS,X4: iS,X5: iS] :
( ( ( ^ [Y0: iS] :
( sK3 @ ( X2 @ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X3 @ Y0 ) )
@ c0 )
= $false )
| ( $false
= ( sK3 @ X0 @ X7 @ X4 ) )
| ( ( sK1
@ ^ [Y0: iS] :
( sK3 @ ( X2 @ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X3 @ Y0 ) ) )
!= X6 )
| ( ( sK3 @ X1 @ X6 @ X5 )
= $false )
| ( ( sK2
@ ^ [Y0: iS] :
( sK3 @ ( X2 @ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X3 @ Y0 ) ) )
!= X7 )
| ( ( cP @ X4 @ X5 )
!= ( X3
@ ( cP
@ ( sK2
@ ^ [Y0: iS] :
( sK3 @ ( X2 @ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X3 @ Y0 ) ) )
@ ( sK1
@ ^ [Y0: iS] :
( sK3 @ ( X2 @ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X3 @ Y0 ) ) ) ) ) )
| ( ( cP @ X0 @ X1 )
!= ( X2
@ ( cP
@ ( sK2
@ ^ [Y0: iS] :
( sK3 @ ( X2 @ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X3 @ Y0 ) ) )
@ ( sK1
@ ^ [Y0: iS] :
( sK3 @ ( X2 @ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X3 @ Y0 ) ) ) ) ) )
| ( $true
= ( ^ [Y0: iS] :
( sK3 @ ( X2 @ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X3 @ Y0 ) )
@ X8 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f176]) ).
thf(f176,plain,
! [X2: iS > iS,X3: iS > iS,X0: iS,X1: iS,X8: iS,X6: iS,X7: iS,X4: iS,X5: iS] :
( ( ( ^ [Y0: iS] :
( sK3 @ ( X2 @ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X3 @ Y0 ) )
@ c0 )
= $false )
| ( $true
= ( ^ [Y0: iS] :
( sK3 @ ( X2 @ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X3 @ Y0 ) )
@ X8 ) )
| ( $false
= ( sK3 @ X0 @ X7 @ X4 ) )
| ( $true = $false )
| ( ( sK2
@ ^ [Y0: iS] :
( sK3 @ ( X2 @ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X3 @ Y0 ) ) )
!= X7 )
| ( ( cP @ X4 @ X5 )
!= ( X3
@ ( cP
@ ( sK2
@ ^ [Y0: iS] :
( sK3 @ ( X2 @ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X3 @ Y0 ) ) )
@ ( sK1
@ ^ [Y0: iS] :
( sK3 @ ( X2 @ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X3 @ Y0 ) ) ) ) ) )
| ( ( sK3 @ X1 @ X6 @ X5 )
= $false )
| ( ( sK1
@ ^ [Y0: iS] :
( sK3 @ ( X2 @ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X3 @ Y0 ) ) )
!= X6 )
| ( ( cP @ X0 @ X1 )
!= ( X2
@ ( cP
@ ( sK2
@ ^ [Y0: iS] :
( sK3 @ ( X2 @ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X3 @ Y0 ) ) )
@ ( sK1
@ ^ [Y0: iS] :
( sK3 @ ( X2 @ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X3 @ Y0 ) ) ) ) ) ) ),
inference(constrained_superposition,[status(thm)],[f45,f170]) ).
thf(f170,plain,
! [X2: iS,X3: iS,X0: iS,X1: iS,X4: iS,X5: iS] :
( ( $true
= ( sK3 @ ( cP @ X0 @ X1 ) @ ( cP @ X2 @ X3 ) @ ( cP @ X4 @ X5 ) ) )
| ( $false
= ( sK3 @ X0 @ X2 @ X4 ) )
| ( ( sK3 @ X1 @ X3 @ X5 )
= $false ) ),
inference(equality_resolution,[status(thm)],[f169]) ).
thf(f169,plain,
! [X2: iS,X3: iS,X0: iS,X1: iS,X6: iS,X4: iS,X5: iS] :
( ( ( cP @ X1 @ X3 )
!= X4 )
| ( $true
= ( sK3 @ ( cP @ X0 @ X5 ) @ X4 @ ( cP @ X2 @ X6 ) ) )
| ( ( sK3 @ X0 @ X1 @ X2 )
= $false )
| ( ( sK3 @ X5 @ X3 @ X6 )
= $false ) ),
inference(equality_resolution,[status(thm)],[f168]) ).
thf(f168,plain,
! [X2: iS,X3: iS,X0: iS,X1: iS,X6: iS,X7: iS,X4: iS,X5: iS] :
( ( ( cP @ X7 @ X5 )
!= X3 )
| ( ( sK3 @ X0 @ X6 @ X7 )
= $false )
| ( ( cP @ X6 @ X4 )
!= X2 )
| ( $false
= ( sK3 @ X1 @ X4 @ X5 ) )
| ( $true
= ( sK3 @ ( cP @ X0 @ X1 ) @ X2 @ X3 ) ) ),
inference(equality_resolution,[status(thm)],[f85]) ).
thf(f85,plain,
! [X2: iS,X3: iS,X1: iS,X8: iS,X6: iS,X9: iS,X7: iS,X4: iS,X5: iS] :
( ( ( cP @ X9 @ X4 )
!= X1 )
| ( $true
= ( sK3 @ X1 @ X3 @ X2 ) )
| ( $false
= ( sK3 @ X4 @ X7 @ X5 ) )
| ( ( cP @ X6 @ X7 )
!= X3 )
| ( $false
= ( sK3 @ X9 @ X6 @ X8 ) )
| ( ( cP @ X8 @ X5 )
!= X2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f84]) ).
thf(f84,plain,
! [X2: iS,X3: iS,X1: iS,X8: iS,X6: iS,X9: iS,X7: iS,X4: iS,X5: iS] :
( ( $false
= ( sK3 @ X9 @ X6 @ X8 ) )
| ( ( ( cP @ X9 @ X4 )
= X1 )
= $false )
| ( $true
= ( sK3 @ X1 @ X3 @ X2 ) )
| ( ( cP @ X6 @ X7 )
!= X3 )
| ( $false
= ( sK3 @ X4 @ X7 @ X5 ) )
| ( ( cP @ X8 @ X5 )
!= X2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f83]) ).
thf(f83,plain,
! [X2: iS,X3: iS,X1: iS,X8: iS,X6: iS,X9: iS,X7: iS,X4: iS,X5: iS] :
( ( ( cP @ X8 @ X5 )
!= X2 )
| ( ( ( sK3 @ X4 @ X7 @ X5 )
& ( ( cP @ X9 @ X4 )
= X1 ) )
= $false )
| ( $false
= ( sK3 @ X9 @ X6 @ X8 ) )
| ( ( cP @ X6 @ X7 )
!= X3 )
| ( $true
= ( sK3 @ X1 @ X3 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f82]) ).
thf(f82,plain,
! [X2: iS,X3: iS,X1: iS,X8: iS,X6: iS,X9: iS,X7: iS,X4: iS,X5: iS] :
( ( $false
= ( ( sK3 @ X4 @ X7 @ X5 )
& ( ( cP @ X9 @ X4 )
= X1 )
& ( sK3 @ X9 @ X6 @ X8 ) ) )
| ( $true
= ( sK3 @ X1 @ X3 @ X2 ) )
| ( ( cP @ X8 @ X5 )
!= X2 )
| ( ( cP @ X6 @ X7 )
!= X3 ) ),
inference(equality_proxy_clausification,[status(thm)],[f81]) ).
thf(f81,plain,
! [X2: iS,X3: iS,X1: iS,X8: iS,X6: iS,X9: iS,X7: iS,X4: iS,X5: iS] :
( ( ( ( cP @ X6 @ X7 )
= X3 )
= $false )
| ( $false
= ( ( sK3 @ X4 @ X7 @ X5 )
& ( ( cP @ X9 @ X4 )
= X1 )
& ( sK3 @ X9 @ X6 @ X8 ) ) )
| ( ( cP @ X8 @ X5 )
!= X2 )
| ( $true
= ( sK3 @ X1 @ X3 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f80]) ).
thf(f80,plain,
! [X2: iS,X3: iS,X1: iS,X8: iS,X6: iS,X9: iS,X7: iS,X4: iS,X5: iS] :
( ( $false
= ( ( sK3 @ X4 @ X7 @ X5 )
& ( ( cP @ X9 @ X4 )
= X1 )
& ( sK3 @ X9 @ X6 @ X8 )
& ( ( cP @ X6 @ X7 )
= X3 ) ) )
| ( ( cP @ X8 @ X5 )
!= X2 )
| ( $true
= ( sK3 @ X1 @ X3 @ X2 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f79]) ).
thf(f79,plain,
! [X2: iS,X3: iS,X1: iS,X8: iS,X6: iS,X9: iS,X7: iS,X4: iS,X5: iS] :
( ( ( ( cP @ X8 @ X5 )
= X2 )
= $false )
| ( $true
= ( sK3 @ X1 @ X3 @ X2 ) )
| ( $false
= ( ( sK3 @ X4 @ X7 @ X5 )
& ( ( cP @ X9 @ X4 )
= X1 )
& ( sK3 @ X9 @ X6 @ X8 )
& ( ( cP @ X6 @ X7 )
= X3 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f78]) ).
thf(f78,plain,
! [X2: iS,X3: iS,X1: iS,X8: iS,X6: iS,X9: iS,X7: iS,X4: iS,X5: iS] :
( ( ( ( sK3 @ X4 @ X7 @ X5 )
& ( ( cP @ X9 @ X4 )
= X1 )
& ( sK3 @ X9 @ X6 @ X8 )
& ( ( cP @ X6 @ X7 )
= X3 )
& ( ( cP @ X8 @ X5 )
= X2 ) )
= $false )
| ( $true
= ( sK3 @ X1 @ X3 @ X2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f77]) ).
thf(f77,plain,
! [X2: iS,X3: iS,X1: iS,X8: iS,X6: iS,X9: iS,X7: iS,X4: iS,X5: iS] :
( ( $true
= ( sK3 @ X1 @ X3 @ X2 ) )
| ( ( ^ [Y0: iS] :
( ( sK3 @ X4 @ X7 @ X5 )
& ( ( cP @ Y0 @ X4 )
= X1 )
& ( sK3 @ Y0 @ X6 @ X8 )
& ( ( cP @ X6 @ X7 )
= X3 )
& ( ( cP @ X8 @ X5 )
= X2 ) )
@ X9 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f76]) ).
thf(f76,plain,
! [X2: iS,X3: iS,X1: iS,X8: iS,X6: iS,X7: iS,X4: iS,X5: iS] :
( ( ( ?? @ iS
@ ^ [Y0: iS] :
( ( sK3 @ X4 @ X7 @ X5 )
& ( ( cP @ Y0 @ X4 )
= X1 )
& ( sK3 @ Y0 @ X6 @ X8 )
& ( ( cP @ X6 @ X7 )
= X3 )
& ( ( cP @ X8 @ X5 )
= X2 ) ) )
= $false )
| ( $true
= ( sK3 @ X1 @ X3 @ X2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f75]) ).
thf(f75,plain,
! [X2: iS,X3: iS,X1: iS,X8: iS,X6: iS,X7: iS,X4: iS,X5: iS] :
( ( $true
= ( sK3 @ X1 @ X3 @ X2 ) )
| ( $false
= ( ^ [Y0: iS] :
( ?? @ iS
@ ^ [Y1: iS] :
( ( sK3 @ X4 @ X7 @ X5 )
& ( ( cP @ Y1 @ X4 )
= X1 )
& ( sK3 @ Y1 @ X6 @ Y0 )
& ( ( cP @ X6 @ X7 )
= X3 )
& ( ( cP @ Y0 @ X5 )
= X2 ) ) )
@ X8 ) ) ),
inference(pi_clausification,[status(thm)],[f74]) ).
thf(f74,plain,
! [X2: iS,X3: iS,X1: iS,X6: iS,X7: iS,X4: iS,X5: iS] :
( ( $true
= ( sK3 @ X1 @ X3 @ X2 ) )
| ( ( ?? @ iS
@ ^ [Y0: iS] :
( ?? @ iS
@ ^ [Y1: iS] :
( ( sK3 @ X4 @ X7 @ X5 )
& ( ( cP @ Y1 @ X4 )
= X1 )
& ( sK3 @ Y1 @ X6 @ Y0 )
& ( ( cP @ X6 @ X7 )
= X3 )
& ( ( cP @ Y0 @ X5 )
= X2 ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f73]) ).
thf(f73,plain,
! [X2: iS,X3: iS,X1: iS,X6: iS,X7: iS,X4: iS,X5: iS] :
( ( $false
= ( ^ [Y0: iS] :
( ?? @ iS
@ ^ [Y1: iS] :
( ?? @ iS
@ ^ [Y2: iS] :
( ( sK3 @ X4 @ Y0 @ X5 )
& ( ( cP @ Y2 @ X4 )
= X1 )
& ( sK3 @ Y2 @ X6 @ Y1 )
& ( ( cP @ X6 @ Y0 )
= X3 )
& ( ( cP @ Y1 @ X5 )
= X2 ) ) ) )
@ X7 ) )
| ( $true
= ( sK3 @ X1 @ X3 @ X2 ) ) ),
inference(pi_clausification,[status(thm)],[f72]) ).
thf(f72,plain,
! [X2: iS,X3: iS,X1: iS,X6: iS,X4: iS,X5: iS] :
( ( $true
= ( sK3 @ X1 @ X3 @ X2 ) )
| ( ( ?? @ iS
@ ^ [Y0: iS] :
( ?? @ iS
@ ^ [Y1: iS] :
( ?? @ iS
@ ^ [Y2: iS] :
( ( sK3 @ X4 @ Y0 @ X5 )
& ( ( cP @ Y2 @ X4 )
= X1 )
& ( sK3 @ Y2 @ X6 @ Y1 )
& ( ( cP @ X6 @ Y0 )
= X3 )
& ( ( cP @ Y1 @ X5 )
= X2 ) ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f71]) ).
thf(f71,plain,
! [X2: iS,X3: iS,X1: iS,X6: iS,X4: iS,X5: iS] :
( ( $false
= ( ^ [Y0: iS] :
( ?? @ iS
@ ^ [Y1: iS] :
( ?? @ iS
@ ^ [Y2: iS] :
( ?? @ iS
@ ^ [Y3: iS] :
( ( sK3 @ X4 @ Y1 @ X5 )
& ( ( cP @ Y3 @ X4 )
= X1 )
& ( sK3 @ Y3 @ Y0 @ Y2 )
& ( ( cP @ Y0 @ Y1 )
= X3 )
& ( ( cP @ Y2 @ X5 )
= X2 ) ) ) ) )
@ X6 ) )
| ( $true
= ( sK3 @ X1 @ X3 @ X2 ) ) ),
inference(pi_clausification,[status(thm)],[f70]) ).
thf(f70,plain,
! [X2: iS,X3: iS,X1: iS,X4: iS,X5: iS] :
( ( ( ?? @ iS
@ ^ [Y0: iS] :
( ?? @ iS
@ ^ [Y1: iS] :
( ?? @ iS
@ ^ [Y2: iS] :
( ?? @ iS
@ ^ [Y3: iS] :
( ( sK3 @ X4 @ Y1 @ X5 )
& ( ( cP @ Y3 @ X4 )
= X1 )
& ( sK3 @ Y3 @ Y0 @ Y2 )
& ( ( cP @ Y0 @ Y1 )
= X3 )
& ( ( cP @ Y2 @ X5 )
= X2 ) ) ) ) ) )
= $false )
| ( $true
= ( sK3 @ X1 @ X3 @ X2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f69]) ).
thf(f69,plain,
! [X2: iS,X3: iS,X1: iS,X4: iS,X5: iS] :
( ( ( ^ [Y0: iS] :
( ?? @ iS
@ ^ [Y1: iS] :
( ?? @ iS
@ ^ [Y2: iS] :
( ?? @ iS
@ ^ [Y3: iS] :
( ?? @ iS
@ ^ [Y4: iS] :
( ( sK3 @ X4 @ Y2 @ Y0 )
& ( ( cP @ Y4 @ X4 )
= X1 )
& ( sK3 @ Y4 @ Y1 @ Y3 )
& ( ( cP @ Y1 @ Y2 )
= X3 )
& ( ( cP @ Y3 @ Y0 )
= X2 ) ) ) ) ) )
@ X5 )
= $false )
| ( $true
= ( sK3 @ X1 @ X3 @ X2 ) ) ),
inference(pi_clausification,[status(thm)],[f68]) ).
thf(f68,plain,
! [X2: iS,X3: iS,X1: iS,X4: iS] :
( ( ( ?? @ iS
@ ^ [Y0: iS] :
( ?? @ iS
@ ^ [Y1: iS] :
( ?? @ iS
@ ^ [Y2: iS] :
( ?? @ iS
@ ^ [Y3: iS] :
( ?? @ iS
@ ^ [Y4: iS] :
( ( sK3 @ X4 @ Y2 @ Y0 )
& ( ( cP @ Y4 @ X4 )
= X1 )
& ( sK3 @ Y4 @ Y1 @ Y3 )
& ( ( cP @ Y1 @ Y2 )
= X3 )
& ( ( cP @ Y3 @ Y0 )
= X2 ) ) ) ) ) ) )
= $false )
| ( $true
= ( sK3 @ X1 @ X3 @ X2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f67]) ).
thf(f67,plain,
! [X2: iS,X3: iS,X1: iS,X4: iS] :
( ( ( ^ [Y0: iS] :
( ?? @ iS
@ ^ [Y1: iS] :
( ?? @ iS
@ ^ [Y2: iS] :
( ?? @ iS
@ ^ [Y3: iS] :
( ?? @ iS
@ ^ [Y4: iS] :
( ?? @ iS
@ ^ [Y5: iS] :
( ( sK3 @ Y0 @ Y3 @ Y1 )
& ( ( cP @ Y5 @ Y0 )
= X1 )
& ( sK3 @ Y5 @ Y2 @ Y4 )
& ( ( cP @ Y2 @ Y3 )
= X3 )
& ( ( cP @ Y4 @ Y1 )
= X2 ) ) ) ) ) ) )
@ X4 )
= $false )
| ( $true
= ( sK3 @ X1 @ X3 @ X2 ) ) ),
inference(pi_clausification,[status(thm)],[f66]) ).
thf(f66,plain,
! [X2: iS,X3: iS,X1: iS] :
( ( ( ?? @ iS
@ ^ [Y0: iS] :
( ?? @ iS
@ ^ [Y1: iS] :
( ?? @ iS
@ ^ [Y2: iS] :
( ?? @ iS
@ ^ [Y3: iS] :
( ?? @ iS
@ ^ [Y4: iS] :
( ?? @ iS
@ ^ [Y5: iS] :
( ( sK3 @ Y0 @ Y3 @ Y1 )
& ( ( cP @ Y5 @ Y0 )
= X1 )
& ( sK3 @ Y5 @ Y2 @ Y4 )
& ( ( cP @ Y2 @ Y3 )
= X3 )
& ( ( cP @ Y4 @ Y1 )
= X2 ) ) ) ) ) ) ) )
= $false )
| ( $true
= ( sK3 @ X1 @ X3 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f61]) ).
thf(f45,plain,
! [X2: iS,X1: iS > $o] :
( ( $false
= ( X1 @ ( cP @ ( sK2 @ X1 ) @ ( sK1 @ X1 ) ) ) )
| ( $true
= ( X1 @ X2 ) )
| ( ( X1 @ c0 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f47,plain,
! [X2: iS,X1: iS > $o] :
( ( $true
= ( X1 @ ( sK1 @ X1 ) ) )
| ( $true
= ( X1 @ X2 ) )
| ( ( X1 @ c0 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f46]) ).
thf(f308,plain,
( ! [X0: iS] :
( ( sK3 @ X0 @ c0 @ X0 )
= $true )
| ~ spl0_10 ),
inference(avatar_component_clause,[status(thm)],[f307]) ).
thf(f307,definition,
( spl0_10
<=> ! [X0: iS] :
( ( sK3 @ X0 @ c0 @ X0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition]) ).
thf(f337,plain,
~ spl0_9,
inference(avatar_contradiction_clause,[status(thm)],[f336]) ).
thf(f336,plain,
( $false
| ~ spl0_9 ),
inference(equality_resolution,[status(thm)],[f335]) ).
thf(f335,plain,
( ! [X0: iS] :
( ( cP
@ ( sK2
@ ^ [Y0: iS] : ( sK3 @ Y0 @ c0 @ Y0 ) )
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ c0 @ Y0 ) ) )
!= X0 )
| ~ spl0_9 ),
inference(duplicate_literal_removal,[status(thm)],[f334]) ).
thf(f334,plain,
( ! [X0: iS] :
( ( ( cP
@ ( sK2
@ ^ [Y0: iS] : ( sK3 @ Y0 @ c0 @ Y0 ) )
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ c0 @ Y0 ) ) )
!= X0 )
| ( ( cP
@ ( sK2
@ ^ [Y0: iS] : ( sK3 @ Y0 @ c0 @ Y0 ) )
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ c0 @ Y0 ) ) )
!= X0 ) )
| ~ spl0_9 ),
inference(equality_resolution,[status(thm)],[f305]) ).
thf(f305,plain,
( ! [X2: iS,X1: iS] :
( ( ( cP
@ ( sK2
@ ^ [Y0: iS] : ( sK3 @ Y0 @ c0 @ Y0 ) )
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ c0 @ Y0 ) ) )
!= X2 )
| ( ( cP
@ ( sK2
@ ^ [Y0: iS] : ( sK3 @ Y0 @ c0 @ Y0 ) )
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ c0 @ Y0 ) ) )
!= X1 )
| ( X1 != X2 ) )
| ~ spl0_9 ),
inference(avatar_component_clause,[status(thm)],[f304]) ).
thf(f304,definition,
( spl0_9
<=> ! [X2: iS,X1: iS] :
( ( X1 != X2 )
| ( ( cP
@ ( sK2
@ ^ [Y0: iS] : ( sK3 @ Y0 @ c0 @ Y0 ) )
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ c0 @ Y0 ) ) )
!= X2 )
| ( ( cP
@ ( sK2
@ ^ [Y0: iS] : ( sK3 @ Y0 @ c0 @ Y0 ) )
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ c0 @ Y0 ) ) )
!= X1 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition]) ).
thf(f312,plain,
( spl0_9
| spl0_10
| ~ spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f270,f252,f307,f304]) ).
thf(f270,plain,
( ! [X2: iS,X0: iS,X1: iS] :
( ( ( cP
@ ( sK2
@ ^ [Y0: iS] : ( sK3 @ Y0 @ c0 @ Y0 ) )
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ c0 @ Y0 ) ) )
!= X2 )
| ( ( sK3 @ X0 @ c0 @ X0 )
= $true )
| ( X1 != X2 )
| ( ( cP
@ ( sK2
@ ^ [Y0: iS] : ( sK3 @ Y0 @ c0 @ Y0 ) )
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ Y0 @ c0 @ Y0 ) ) )
!= X1 ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f269]) ).
thf(f269,plain,
( ! [X2: iS,X0: iS,X1: iS] :
( ( ( ^ [Y0: iS] : Y0
@ ( cP
@ ( sK2
@ ^ [Y0: iS] :
( sK3
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ c0
@ ( ^ [Y1: iS] : Y1
@ Y0 ) ) )
@ ( sK1
@ ^ [Y0: iS] :
( sK3
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ c0
@ ( ^ [Y1: iS] : Y1
@ Y0 ) ) ) ) )
!= X2 )
| ( ( ^ [Y0: iS] : Y0
@ ( cP
@ ( sK2
@ ^ [Y0: iS] :
( sK3
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ c0
@ ( ^ [Y1: iS] : Y1
@ Y0 ) ) )
@ ( sK1
@ ^ [Y0: iS] :
( sK3
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ c0
@ ( ^ [Y1: iS] : Y1
@ Y0 ) ) ) ) )
!= X1 )
| ( ( sK3
@ ( ^ [Y0: iS] : Y0
@ X0 )
@ c0
@ ( ^ [Y0: iS] : Y0
@ X0 ) )
= $true )
| ( X1 != X2 ) )
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f264]) ).
thf(f264,plain,
( ! [X2: iS,X0: iS,X1: iS] :
( ( $true = $false )
| ( ( sK3
@ ( ^ [Y0: iS] : Y0
@ X0 )
@ c0
@ ( ^ [Y0: iS] : Y0
@ X0 ) )
= $true )
| ( X1 != X2 )
| ( ( ^ [Y0: iS] : Y0
@ ( cP
@ ( sK2
@ ^ [Y0: iS] :
( sK3
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ c0
@ ( ^ [Y1: iS] : Y1
@ Y0 ) ) )
@ ( sK1
@ ^ [Y0: iS] :
( sK3
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ c0
@ ( ^ [Y1: iS] : Y1
@ Y0 ) ) ) ) )
!= X2 )
| ( ( ^ [Y0: iS] : Y0
@ ( cP
@ ( sK2
@ ^ [Y0: iS] :
( sK3
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ c0
@ ( ^ [Y1: iS] : Y1
@ Y0 ) ) )
@ ( sK1
@ ^ [Y0: iS] :
( sK3
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ c0
@ ( ^ [Y1: iS] : Y1
@ Y0 ) ) ) ) )
!= X1 ) )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f143,f254]) ).
thf(f143,plain,
! [X2: iS,X3: iS,X0: iS > iS,X1: iS > iS,X4: iS] :
( ( ( sK3 @ ( X0 @ c0 ) @ c0 @ ( X1 @ c0 ) )
= $false )
| ( ( sK3 @ ( X0 @ X4 ) @ c0 @ ( X1 @ X4 ) )
= $true )
| ( ( X0
@ ( cP
@ ( sK2
@ ^ [Y0: iS] : ( sK3 @ ( X0 @ Y0 ) @ c0 @ ( X1 @ Y0 ) ) )
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ ( X0 @ Y0 ) @ c0 @ ( X1 @ Y0 ) ) ) ) )
!= X2 )
| ( ( X1
@ ( cP
@ ( sK2
@ ^ [Y0: iS] : ( sK3 @ ( X0 @ Y0 ) @ c0 @ ( X1 @ Y0 ) ) )
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ ( X0 @ Y0 ) @ c0 @ ( X1 @ Y0 ) ) ) ) )
!= X3 )
| ( X2 != X3 ) ),
inference(beta_eta_normalization,[status(thm)],[f142]) ).
thf(f142,plain,
! [X2: iS,X3: iS,X0: iS > iS,X1: iS > iS,X4: iS] :
( ( ( X1
@ ( cP
@ ( sK2
@ ^ [Y0: iS] :
( sK3 @ ( X0 @ Y0 )
@ ( ^ [Y1: iS] : c0
@ Y0 )
@ ( X1 @ Y0 ) ) )
@ ( sK1
@ ^ [Y0: iS] :
( sK3 @ ( X0 @ Y0 )
@ ( ^ [Y1: iS] : c0
@ Y0 )
@ ( X1 @ Y0 ) ) ) ) )
!= X3 )
| ( $true
= ( ^ [Y0: iS] :
( sK3 @ ( X0 @ Y0 )
@ ( ^ [Y1: iS] : c0
@ Y0 )
@ ( X1 @ Y0 ) )
@ X4 ) )
| ( ( X0
@ ( cP
@ ( sK2
@ ^ [Y0: iS] :
( sK3 @ ( X0 @ Y0 )
@ ( ^ [Y1: iS] : c0
@ Y0 )
@ ( X1 @ Y0 ) ) )
@ ( sK1
@ ^ [Y0: iS] :
( sK3 @ ( X0 @ Y0 )
@ ( ^ [Y1: iS] : c0
@ Y0 )
@ ( X1 @ Y0 ) ) ) ) )
!= X2 )
| ( $false
= ( ^ [Y0: iS] :
( sK3 @ ( X0 @ Y0 )
@ ( ^ [Y1: iS] : c0
@ Y0 )
@ ( X1 @ Y0 ) )
@ c0 ) )
| ( X2 != X3 ) ),
inference(trivial_inequality_removal,[status(thm)],[f130]) ).
thf(f130,plain,
! [X2: iS,X3: iS,X0: iS > iS,X1: iS > iS,X4: iS] :
( ( $true
= ( ^ [Y0: iS] :
( sK3 @ ( X0 @ Y0 )
@ ( ^ [Y1: iS] : c0
@ Y0 )
@ ( X1 @ Y0 ) )
@ X4 ) )
| ( $false
= ( ^ [Y0: iS] :
( sK3 @ ( X0 @ Y0 )
@ ( ^ [Y1: iS] : c0
@ Y0 )
@ ( X1 @ Y0 ) )
@ c0 ) )
| ( X2 != X3 )
| ( ( X0
@ ( cP
@ ( sK2
@ ^ [Y0: iS] :
( sK3 @ ( X0 @ Y0 )
@ ( ^ [Y1: iS] : c0
@ Y0 )
@ ( X1 @ Y0 ) ) )
@ ( sK1
@ ^ [Y0: iS] :
( sK3 @ ( X0 @ Y0 )
@ ( ^ [Y1: iS] : c0
@ Y0 )
@ ( X1 @ Y0 ) ) ) ) )
!= X2 )
| ( ( X1
@ ( cP
@ ( sK2
@ ^ [Y0: iS] :
( sK3 @ ( X0 @ Y0 )
@ ( ^ [Y1: iS] : c0
@ Y0 )
@ ( X1 @ Y0 ) ) )
@ ( sK1
@ ^ [Y0: iS] :
( sK3 @ ( X0 @ Y0 )
@ ( ^ [Y1: iS] : c0
@ Y0 )
@ ( X1 @ Y0 ) ) ) ) )
!= X3 )
| ( $true = $false ) ),
inference(constrained_superposition,[status(thm)],[f45,f93]) ).
thf(f93,plain,
! [X0: iS,X1: iS] :
( ( $true
= ( sK3 @ X0 @ c0 @ X1 ) )
| ( X0 != X1 ) ),
inference(equality_resolution,[status(thm)],[f64]) ).
thf(f64,plain,
! [X2: iS,X3: iS,X1: iS] :
( ( c0 != X3 )
| ( $true
= ( sK3 @ X1 @ X3 @ X2 ) )
| ( X1 != X2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f63]) ).
thf(f63,plain,
! [X2: iS,X3: iS,X1: iS] :
( ( ( c0 = X3 )
= $false )
| ( $true
= ( sK3 @ X1 @ X3 @ X2 ) )
| ( X1 != X2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f62]) ).
thf(f62,plain,
! [X2: iS,X3: iS,X1: iS] :
( ( $true
= ( sK3 @ X1 @ X3 @ X2 ) )
| ( $false
= ( X2 = X1 ) )
| ( ( c0 = X3 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
! [X2: iS,X3: iS,X1: iS] :
( ( $false
= ( ( c0 = X3 )
& ( X2 = X1 ) ) )
| ( $true
= ( sK3 @ X1 @ X3 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f59]) ).
thf(f257,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[status(thm)],[f256]) ).
thf(f256,plain,
( $false
| ~ spl0_3 ),
inference(equality_resolution,[status(thm)],[f250]) ).
thf(f250,plain,
( ! [X1: iS] : ( c0 != X1 )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f249]) ).
thf(f249,definition,
( spl0_3
<=> ! [X1: iS] : ( c0 != X1 ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f255,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f247,f252,f249]) ).
thf(f247,plain,
! [X1: iS] :
( ( $true
= ( sK3 @ c0 @ c0 @ c0 ) )
| ( c0 != X1 ) ),
inference(duplicate_literal_removal,[status(thm)],[f246]) ).
thf(f246,plain,
! [X1: iS] :
( ( $true
= ( sK3 @ c0 @ c0 @ c0 ) )
| ( c0 != X1 )
| ( c0 != X1 ) ),
inference(beta_eta_normalization,[status(thm)],[f245]) ).
thf(f245,plain,
! [X0: iS,X1: iS] :
( ( $true
= ( sK3 @ c0 @ c0
@ ( ^ [Y0: iS] : c0
@ X0 ) ) )
| ( c0 != X1 )
| ( ( ^ [Y0: iS] : c0
@ c0 )
!= X1 ) ),
inference(equality_resolution,[status(thm)],[f244]) ).
thf(f244,plain,
! [X2: iS,X0: iS,X1: iS > iS] :
( ( c0
!= ( X1
@ ( cP
@ ( sK2
@ ^ [Y0: iS] : ( sK3 @ c0 @ c0 @ ( X1 @ Y0 ) ) )
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ c0 @ c0 @ ( X1 @ Y0 ) ) ) ) ) )
| ( ( sK3 @ c0 @ c0 @ ( X1 @ X2 ) )
= $true )
| ( c0 != X0 )
| ( ( X1 @ c0 )
!= X0 ) ),
inference(equality_resolution,[status(thm)],[f243]) ).
thf(f243,plain,
! [X2: iS,X3: iS,X0: iS,X1: iS > iS] :
( ( c0 != X3 )
| ( c0 != X0 )
| ( ( sK3 @ c0 @ c0 @ ( X1 @ X2 ) )
= $true )
| ( ( X1 @ c0 )
!= X0 )
| ( ( X1
@ ( cP
@ ( sK2
@ ^ [Y0: iS] : ( sK3 @ c0 @ c0 @ ( X1 @ Y0 ) ) )
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ c0 @ c0 @ ( X1 @ Y0 ) ) ) ) )
!= X3 ) ),
inference(equality_resolution,[status(thm)],[f225]) ).
thf(f225,plain,
! [X8: iS,X6: iS,X9: iS,X7: iS,X5: iS > iS] :
( ( c0 != X8 )
| ( c0 != X6 )
| ( $true
= ( sK3 @ c0 @ c0 @ ( X5 @ X7 ) ) )
| ( ( X5
@ ( cP
@ ( sK2
@ ^ [Y0: iS] : ( sK3 @ c0 @ c0 @ ( X5 @ Y0 ) ) )
@ ( sK1
@ ^ [Y0: iS] : ( sK3 @ c0 @ c0 @ ( X5 @ Y0 ) ) ) ) )
!= X9 )
| ( X8 != X9 )
| ( ( X5 @ c0 )
!= X6 ) ),
inference(beta_eta_normalization,[status(thm)],[f224]) ).
thf(f224,plain,
! [X8: iS,X6: iS,X9: iS,X7: iS,X5: iS > iS] :
( ( $true
= ( sK3
@ ( ^ [Y0: iS] : c0
@ X7 )
@ c0
@ ( X5 @ X7 ) ) )
| ( c0 != X6 )
| ( X8 != X9 )
| ( ( X5 @ c0 )
!= X6 )
| ( ( ^ [Y0: iS] : c0
@ ( cP
@ ( sK2
@ ^ [Y0: iS] :
( sK3
@ ( ^ [Y1: iS] : c0
@ Y0 )
@ c0
@ ( X5 @ Y0 ) ) )
@ ( sK1
@ ^ [Y0: iS] :
( sK3
@ ( ^ [Y1: iS] : c0
@ Y0 )
@ c0
@ ( X5 @ Y0 ) ) ) ) )
!= X8 )
| ( ( X5
@ ( cP
@ ( sK2
@ ^ [Y0: iS] :
( sK3
@ ( ^ [Y1: iS] : c0
@ Y0 )
@ c0
@ ( X5 @ Y0 ) ) )
@ ( sK1
@ ^ [Y0: iS] :
( sK3
@ ( ^ [Y1: iS] : c0
@ Y0 )
@ c0
@ ( X5 @ Y0 ) ) ) ) )
!= X9 ) ),
inference(trivial_inequality_removal,[status(thm)],[f220]) ).
thf(f220,plain,
! [X8: iS,X6: iS,X9: iS,X7: iS,X5: iS > iS] :
( ( ( X5
@ ( cP
@ ( sK2
@ ^ [Y0: iS] :
( sK3
@ ( ^ [Y1: iS] : c0
@ Y0 )
@ c0
@ ( X5 @ Y0 ) ) )
@ ( sK1
@ ^ [Y0: iS] :
( sK3
@ ( ^ [Y1: iS] : c0
@ Y0 )
@ c0
@ ( X5 @ Y0 ) ) ) ) )
!= X9 )
| ( c0 != X6 )
| ( $true
= ( sK3
@ ( ^ [Y0: iS] : c0
@ X7 )
@ c0
@ ( X5 @ X7 ) ) )
| ( ( X5 @ c0 )
!= X6 )
| ( X8 != X9 )
| ( ( ^ [Y0: iS] : c0
@ ( cP
@ ( sK2
@ ^ [Y0: iS] :
( sK3
@ ( ^ [Y1: iS] : c0
@ Y0 )
@ c0
@ ( X5 @ Y0 ) ) )
@ ( sK1
@ ^ [Y0: iS] :
( sK3
@ ( ^ [Y1: iS] : c0
@ Y0 )
@ c0
@ ( X5 @ Y0 ) ) ) ) )
!= X8 )
| ( $true = $false ) ),
inference(constrained_superposition,[status(thm)],[f95,f143]) ).
thf(f197,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f178,f193,f189]) ).
thf(f178,plain,
( ( $false
= ( sK3 @ c0 @ x @ x ) )
| ( ( sK3 @ y @ y @ y )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f172]) ).
thf(f172,plain,
( ( $true = $false )
| ( $false
= ( sK3 @ c0 @ x @ x ) )
| ( ( sK3 @ y @ y @ y )
= $false ) ),
inference(superposition,[status(thm)],[f170,f51]) ).
thf(f51,plain,
( ( sK3 @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) @ ( cP @ x @ y ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV203^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n013.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:41:38 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.46 thf(spec,logic,$$dhol).
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % File : SEV203^5 : TPTP v9.2.1. Released v4.0.0.
% 0.31/0.46 % Domain : Set Theory (Sets of sets)
% 0.31/0.46 % Problem : TPS problem from S-THMS
% 0.31/0.46 % Version : Especial.
% 0.31/0.46 % English :
% 0.31/0.46
% 0.31/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.31/0.46 % Source : [Bro09]
% 0.31/0.46 % Names : tps_1156 [Bro09]
% 0.31/0.46
% 0.31/0.46 % Status : Theorem
% 0.31/0.46 % Rating : 0.56 v9.1.0, 0.50 v9.0.0, 0.60 v8.2.0, 0.77 v8.1.0, 0.73 v7.5.0, 0.71 v7.4.0, 0.89 v7.2.0, 0.88 v7.0.0, 0.86 v6.4.0, 0.83 v6.3.0, 0.80 v6.2.0, 0.86 v5.5.0, 1.00 v4.0.0
% 0.31/0.46 % Syntax : Number of formulae : 6 ( 0 unt; 5 typ; 0 def)
% 0.31/0.46 % Number of atoms : 12 ( 11 equ; 0 cnn)
% 0.31/0.46 % Maximal formula atoms : 12 ( 12 avg)
% 0.31/0.46 % Number of connectives : 58 ( 1 ~; 2 |; 12 &; 37 @)
% 0.31/0.46 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 0.31/0.46 % Maximal formula depth : 24 ( 24 avg)
% 0.31/0.46 % Number of types : 2 ( 1 usr)
% 0.31/0.46 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.31/0.46 % Number of symbols : 6 ( 4 usr; 4 con; 0-2 aty)
% 0.31/0.46 % Number of variables : 20 ( 0 ^; 14 !; 6 ?; 20 :)
% 0.31/0.46 % SPC : TH0_THM_EQU_NAR
% 0.31/0.46
% 0.31/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.31/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.31/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.31/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 thf(iS_type,type,
% 0.31/0.46 iS: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(y,type,
% 0.31/0.46 y: iS ).
% 0.31/0.46
% 0.31/0.46 thf(x,type,
% 0.31/0.46 x: iS ).
% 0.31/0.46
% 0.31/0.46 thf(cP,type,
% 0.31/0.46 cP: iS > iS > iS ).
% 0.31/0.46
% 0.31/0.46 thf(c0,type,
% 0.31/0.46 c0: iS ).
% 0.31/0.46
% 0.31/0.46 thf(cS_INCL_LEM5_pme,conjecture,
% 0.31/0.46 ( ( ! [Xx0: iS,Xy0: iS] :
% 0.31/0.46 ( ( cP @ Xx0 @ Xy0 )
% 0.31/0.46 != c0 )
% 0.31/0.46 & ! [Xx0: iS,Xy0: iS,Xu: iS,Xv: iS] :
% 0.31/0.46 ( ( ( cP @ Xx0 @ Xu )
% 0.31/0.46 = ( cP @ Xy0 @ Xv ) )
% 0.31/0.46 => ( ( Xx0 = Xy0 )
% 0.31/0.46 & ( Xu = Xv ) ) )
% 0.31/0.46 & ! [X: iS > $o] :
% 0.31/0.46 ( ( ( X @ c0 )
% 0.31/0.46 & ! [Xx0: iS,Xy0: iS] :
% 0.31/0.46 ( ( ( X @ Xx0 )
% 0.31/0.46 & ( X @ Xy0 ) )
% 0.31/0.46 => ( X @ ( cP @ Xx0 @ Xy0 ) ) ) )
% 0.31/0.46 => ! [Xx0: iS] : ( X @ Xx0 ) ) )
% 0.31/0.46 => ! [R: iS > iS > iS > $o] :
% 0.31/0.46 ( ( $true
% 0.31/0.46 & ! [Xa: iS,Xb: iS,Xc: iS] :
% 0.31/0.46 ( ( ( ( Xa = c0 )
% 0.31/0.46 & ( Xb = Xc ) )
% 0.31/0.46 | ( ( Xb = c0 )
% 0.31/0.46 & ( Xa = Xc ) )
% 0.31/0.46 | ? [Xx1: iS,Xx2: iS,Xy1: iS,Xy2: iS,Xz1: iS,Xz2: iS] :
% 0.31/0.46 ( ( Xa
% 0.31/0.46 = ( cP @ Xx1 @ Xx2 ) )
% 0.31/0.46 & ( Xb
% 0.31/0.46 = ( cP @ Xy1 @ Xy2 ) )
% 0.31/0.46 & ( Xc
% 0.31/0.46 = ( cP @ Xz1 @ Xz2 ) )
% 0.31/0.46 & ( R @ Xx1 @ Xy1 @ Xz1 )
% 0.31/0.46 & ( R @ Xx2 @ Xy2 @ Xz2 ) ) )
% 0.31/0.46 => ( R @ Xa @ Xb @ Xc ) ) )
% 0.31/0.46 => ( R @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) @ ( cP @ x @ y ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 ------------------------
% 1.54/1.24 ---- Embedded in THF ---
% 1.54/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.54/1.24 %%% Generated on Tue Feb 24 12:41:39 EST 2026
% 1.54/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.54/1.24 %%% Logic specification used:
% 1.54/1.24 %%% thf(spec, logic, $$dhol).
% 1.54/1.24
% 1.54/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.siZw90THh0/DTF2DTF7046.p
% See solution above
% 1.54/1.24 ------------------------
% 1.54/1.25 ---- Cleaned THF ---
% 1.54/1.25 thf(iS_type,type,
% 1.54/1.25 iS: $tType ).
% 1.54/1.25
% 1.54/1.25 thf(y,type,
% 1.54/1.25 y: iS ).
% 1.54/1.25
% 1.54/1.25 thf(x,type,
% 1.54/1.25 x: iS ).
% 1.54/1.25
% 1.54/1.25 thf(cP,type,
% 1.54/1.25 cP: iS > iS > iS ).
% 1.54/1.25
% 1.54/1.25 thf(c0,type,
% 1.54/1.25 c0: iS ).
% 1.54/1.25
% 1.54/1.25 thf(cS_INCL_LEM5_pme,conjecture,
% 1.54/1.25 ( ( ! [Xx0: iS,Xy0: iS] :
% 1.54/1.25 ( ( cP @ Xx0 @ Xy0 )
% 1.54/1.25 != c0 )
% 1.54/1.25 & ! [Xx0: iS,Xy0: iS,Xu: iS,Xv: iS] :
% 1.54/1.25 ( ( ( cP @ Xx0 @ Xu )
% 1.54/1.25 = ( cP @ Xy0 @ Xv ) )
% 1.54/1.25 => ( ( Xx0 = Xy0 )
% 1.54/1.25 & ( Xu = Xv ) ) )
% 1.54/1.25 & ! [X: iS > $o] :
% 1.54/1.25 ( ( ( X @ c0 )
% 1.54/1.25 & ! [Xx0: iS,Xy0: iS] :
% 1.54/1.25 ( ( ( X @ Xx0 )
% 1.54/1.25 & ( X @ Xy0 ) )
% 1.54/1.25 => ( X @ ( cP @ Xx0 @ Xy0 ) ) ) )
% 1.54/1.25 => ! [Xx0: iS] : ( X @ Xx0 ) ) )
% 1.54/1.25 => ! [R: iS > iS > iS > $o] :
% 1.54/1.25 ( ( $true
% 1.54/1.25 & ! [Xa: iS,Xb: iS,Xc: iS] :
% 1.54/1.25 ( ( ( ( Xa = c0 )
% 1.54/1.25 & ( Xb = Xc ) )
% 1.54/1.25 | ( ( Xb = c0 )
% 1.54/1.25 & ( Xa = Xc ) )
% 1.54/1.25 | ? [Xx1: iS,Xx2: iS,Xy1: iS,Xy2: iS,Xz1: iS,Xz2: iS] :
% 1.54/1.25 ( ( Xa
% 1.54/1.25 = ( cP @ Xx1 @ Xx2 ) )
% 1.54/1.25 & ( Xb
% 1.54/1.25 = ( cP @ Xy1 @ Xy2 ) )
% 1.54/1.25 & ( Xc
% 1.54/1.25 = ( cP @ Xz1 @ Xz2 ) )
% 1.54/1.25 & ( R @ Xx1 @ Xy1 @ Xz1 )
% 1.54/1.25 & ( R @ Xx2 @ Xy2 @ Xz2 ) ) )
% 1.54/1.25 => ( R @ Xa @ Xb @ Xc ) ) )
% 1.54/1.25 => ( R @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) @ ( cP @ x @ y ) ) ) ) ).
% 1.54/1.25 ------------------------
% 1.54/1.27 % (7328)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7046 for (2999ds/2Mi)
% 1.54/1.27 % (7328)Instruction limit reached!
% 1.54/1.27 % (7328)------------------------------
% 1.54/1.27 % (7328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.27 % (7328)Termination reason: Unknown
% 1.54/1.27 % (7328)Termination phase: Preprocessing 3
% 1.54/1.27
% 1.54/1.27 % (7328)Memory used [KB]: 1023
% 1.54/1.27 % (7328)Time elapsed: 0.002 s
% 1.54/1.27 % (7328)Instructions burned: 2 (million)
% 1.54/1.27 % (7328)------------------------------
% 1.54/1.27 % (7328)------------------------------
% 1.54/1.28 % (7325)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7046 for (2999ds/183Mi)
% 1.54/1.28 % (7326)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_7046 for (2999ds/4Mi)
% 1.54/1.28 % (7327)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_7046 for (2999ds/27Mi)
% 1.54/1.28 % (7329)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_7046 for (2999ds/2Mi)
% 1.54/1.28 % (7330)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_7046 for (2999ds/275Mi)
% 1.54/1.28 % (7331)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7046 for (2999ds/18Mi)
% 1.54/1.28 % (7329)Instruction limit reached!
% 1.54/1.28 % (7329)------------------------------
% 1.54/1.28 % (7329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.28 % (7329)Termination reason: Unknown
% 1.54/1.28 % (7329)Termination phase: shuffling
% 1.54/1.28
% 1.54/1.28 % (7329)Memory used [KB]: 1023
% 1.54/1.28 % (7329)Time elapsed: 0.003 s
% 1.54/1.28 % (7329)Instructions burned: 2 (million)
% 1.54/1.28 % (7329)------------------------------
% 1.54/1.28 % (7329)------------------------------
% 1.54/1.28 % (7332)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_7046 for (2999ds/3Mi)
% 1.54/1.28 % (7326)Instruction limit reached!
% 1.54/1.28 % (7326)------------------------------
% 1.54/1.28 % (7326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.28 % (7326)Termination reason: Unknown
% 1.54/1.28 % (7326)Termination phase: Saturation
% 1.54/1.28
% 1.54/1.28 % (7326)Memory used [KB]: 5500
% 1.54/1.28 % (7326)Time elapsed: 0.005 s
% 1.54/1.28 % (7326)Instructions burned: 4 (million)
% 1.54/1.28 % (7326)------------------------------
% 1.54/1.28 % (7326)------------------------------
% 1.54/1.28 % (7332)Instruction limit reached!
% 1.54/1.28 % (7332)------------------------------
% 1.54/1.28 % (7332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.28 % (7332)Termination reason: Unknown
% 1.54/1.28 % (7332)Termination phase: Saturation
% 1.54/1.28
% 1.54/1.28 % (7332)Memory used [KB]: 5500
% 1.54/1.28 % (7332)Time elapsed: 0.002 s
% 1.54/1.28 % (7332)Instructions burned: 3 (million)
% 1.54/1.28 % (7332)------------------------------
% 1.54/1.28 % (7332)------------------------------
% 1.54/1.29 % (7331)Instruction limit reached!
% 1.54/1.29 % (7331)------------------------------
% 1.54/1.29 % (7331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.29 % (7331)Termination reason: Unknown
% 1.54/1.29 % (7331)Termination phase: Saturation
% 1.54/1.29
% 1.54/1.29 % (7331)Memory used [KB]: 5628
% 1.54/1.29 % (7331)Time elapsed: 0.014 s
% 1.54/1.29 % (7331)Instructions burned: 19 (million)
% 1.54/1.29 % (7331)------------------------------
% 1.54/1.29 % (7331)------------------------------
% 1.54/1.29 % (7335)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_7046 for (2999ds/3Mi)
% 1.54/1.29 % (7335)Instruction limit reached!
% 1.54/1.29 % (7335)------------------------------
% 1.54/1.29 % (7335)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.29 % (7335)Termination reason: Unknown
% 1.54/1.29 % (7335)Termination phase: Equality resolution with deletion
% 1.54/1.29
% 1.54/1.29 % (7335)Memory used [KB]: 1023
% 1.54/1.29 % (7335)Time elapsed: 0.002 s
% 1.54/1.29 % (7335)Instructions burned: 3 (million)
% 1.54/1.29 % (7335)------------------------------
% 1.54/1.29 % (7335)------------------------------
% 1.54/1.29 % (7327)Instruction limit reached!
% 1.54/1.29 % (7327)------------------------------
% 1.54/1.29 % (7327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.29 % (7327)Termination reason: Unknown
% 1.54/1.29 % (7327)Termination phase: Saturation
% 1.54/1.29
% 1.54/1.29 % (7327)Memory used [KB]: 5628
% 1.54/1.29 % (7327)Time elapsed: 0.019 s
% 1.54/1.29 % (7327)Instructions burned: 27 (million)
% 1.54/1.29 % (7327)------------------------------
% 1.54/1.29 % (7327)------------------------------
% 1.54/1.29 % (7333)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_7046 for (2999ds/37Mi)
% 1.54/1.30 % (7334)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_7046 for (2999ds/15Mi)
% 1.63/1.30 % (7337)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_7046 for (2999ds/7Mi)
% 1.63/1.30 % (7337)Instruction limit reached!
% 1.63/1.30 % (7337)------------------------------
% 1.63/1.30 % (7337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.30 % (7337)Termination reason: Unknown
% 1.63/1.30 % (7337)Termination phase: Saturation
% 1.63/1.30
% 1.63/1.30 % (7337)Memory used [KB]: 1151
% 1.63/1.30 % (7337)Time elapsed: 0.004 s
% 1.63/1.30 % (7337)Instructions burned: 9 (million)
% 1.63/1.30 % (7337)------------------------------
% 1.63/1.30 % (7337)------------------------------
% 1.63/1.31 % (7334)Instruction limit reached!
% 1.63/1.31 % (7334)------------------------------
% 1.63/1.31 % (7334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.31 % (7334)Termination reason: Unknown
% 1.63/1.31 % (7334)Termination phase: Saturation
% 1.63/1.31
% 1.63/1.31 % (7334)Memory used [KB]: 5628
% 1.63/1.31 % (7334)Time elapsed: 0.011 s
% 1.63/1.31 % (7334)Instructions burned: 15 (million)
% 1.63/1.31 % (7334)------------------------------
% 1.63/1.31 % (7334)------------------------------
% 1.63/1.31 % (7336)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_7046 for (2999ds/1041Mi)
% 1.63/1.31 % (7338)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_7046 for (2999ds/16Mi)
% 1.63/1.31 % (7339)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_7046 for (2999ds/3Mi)
% 1.63/1.31 % (7339)Instruction limit reached!
% 1.63/1.31 % (7339)------------------------------
% 1.63/1.31 % (7339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.31 % (7339)Termination reason: Unknown
% 1.63/1.31 % (7339)Termination phase: Twee Goal Transformation
% 1.63/1.31
% 1.63/1.31 % (7339)Memory used [KB]: 1023
% 1.63/1.31 % (7339)Time elapsed: 0.002 s
% 1.63/1.31 % (7339)Instructions burned: 3 (million)
% 1.63/1.31 % (7339)------------------------------
% 1.63/1.31 % (7339)------------------------------
% 1.63/1.32 % (7333)Instruction limit reached!
% 1.63/1.32 % (7333)------------------------------
% 1.63/1.32 % (7333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.32 % (7333)Termination reason: Unknown
% 1.63/1.32 % (7333)Termination phase: Saturation
% 1.63/1.32
% 1.63/1.32 % (7333)Memory used [KB]: 5756
% 1.63/1.32 % (7333)Time elapsed: 0.023 s
% 1.63/1.32 % (7333)Instructions burned: 37 (million)
% 1.63/1.32 % (7333)------------------------------
% 1.63/1.32 % (7333)------------------------------
% 1.63/1.32 % (7340)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_7046 for (2999ds/3Mi)
% 1.63/1.32 % (7340)Instruction limit reached!
% 1.63/1.32 % (7340)------------------------------
% 1.63/1.32 % (7340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.32 % (7340)Termination reason: Unknown
% 1.63/1.32 % (7340)Termination phase: Property scanning
% 1.63/1.32
% 1.63/1.32 % (7340)Memory used [KB]: 1023
% 1.63/1.32 % (7340)Time elapsed: 0.002 s
% 1.63/1.32 % (7340)Instructions burned: 3 (million)
% 1.63/1.32 % (7340)------------------------------
% 1.63/1.32 % (7340)------------------------------
% 1.63/1.32 % (7338)Instruction limit reached!
% 1.63/1.32 % (7338)------------------------------
% 1.63/1.32 % (7338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.32 % (7338)Termination reason: Unknown
% 1.63/1.32 % (7338)Termination phase: Saturation
% 1.63/1.32
% 1.63/1.32 % (7338)Memory used [KB]: 5628
% 1.63/1.32 % (7338)Time elapsed: 0.012 s
% 1.63/1.32 % (7338)Instructions burned: 16 (million)
% 1.63/1.32 % (7338)------------------------------
% 1.63/1.32 % (7338)------------------------------
% 1.63/1.32 % (7341)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_7046 for (2999ds/7Mi)
% 1.63/1.32 % (7341)Instruction limit reached!
% 1.63/1.32 % (7341)------------------------------
% 1.63/1.32 % (7341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.32 % (7341)Termination reason: Unknown
% 1.63/1.32 % (7341)Termination phase: Saturation
% 1.63/1.32
% 1.63/1.32 % (7341)Memory used [KB]: 5500
% 1.63/1.32 % (7341)Time elapsed: 0.004 s
% 1.63/1.32 % (7341)Instructions burned: 9 (million)
% 1.63/1.32 % (7341)------------------------------
% 1.63/1.32 % (7341)------------------------------
% 1.63/1.33 % (7343)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_7046 for (2999ds/4Mi)
% 1.63/1.33 % (7343)Instruction limit reached!
% 1.63/1.33 % (7343)------------------------------
% 1.63/1.33 % (7343)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.33 % (7343)Termination reason: Unknown
% 1.63/1.33 % (7343)Termination phase: Saturation
% 1.63/1.33
% 1.63/1.33 % (7343)Memory used [KB]: 5500
% 1.63/1.33 % (7343)Time elapsed: 0.003 s
% 1.63/1.33 % (7343)Instructions burned: 4 (million)
% 1.63/1.33 % (7343)------------------------------
% 1.63/1.33 % (7343)------------------------------
% 1.63/1.33 % (7342)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_7046 for (2999ds/3Mi)
% 1.63/1.33 % (7345)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_7046 for (2999ds/710Mi)
% 1.63/1.33 % (7342)Instruction limit reached!
% 1.63/1.33 % (7342)------------------------------
% 1.63/1.33 % (7342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.33 % (7342)Termination reason: Unknown
% 1.63/1.33 % (7342)Termination phase: Property scanning
% 1.63/1.33
% 1.63/1.33 % (7342)Memory used [KB]: 1023
% 1.63/1.33 % (7342)Time elapsed: 0.003 s
% 1.63/1.33 % (7342)Instructions burned: 3 (million)
% 1.63/1.33 % (7342)------------------------------
% 1.63/1.33 % (7342)------------------------------
% 1.63/1.34 % (7344)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_7046 for (2999ds/18Mi)
% 1.63/1.34 % (7346)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_7046 for (2999ds/6Mi)
% 1.63/1.34 % (7346)Instruction limit reached!
% 1.63/1.34 % (7346)------------------------------
% 1.63/1.34 % (7346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.34 % (7346)Termination reason: Unknown
% 1.63/1.34 % (7346)Termination phase: Saturation
% 1.63/1.34
% 1.63/1.34 % (7346)Memory used [KB]: 5500
% 1.63/1.34 % (7346)Time elapsed: 0.004 s
% 1.63/1.34 % (7346)Instructions burned: 6 (million)
% 1.63/1.34 % (7346)------------------------------
% 1.63/1.34 % (7346)------------------------------
% 1.63/1.34 % (7344)Refutation not found, incomplete strategy
% 1.63/1.34 % (7344)------------------------------
% 1.63/1.34 % (7344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.34 % (7344)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.34
% 1.63/1.34
% 1.63/1.34 % (7344)Memory used [KB]: 5500
% 1.63/1.34 % (7344)Time elapsed: 0.007 s
% 1.63/1.34 % (7344)Instructions burned: 9 (million)
% 1.63/1.34 % (7344)------------------------------
% 1.63/1.34 % (7344)------------------------------
% 1.63/1.35 % (7325)Instruction limit reached!
% 1.63/1.35 % (7325)------------------------------
% 1.63/1.35 % (7325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.35 % (7325)Termination reason: Unknown
% 1.63/1.35 % (7325)Termination phase: Saturation
% 1.63/1.35
% 1.63/1.35 % (7325)Memory used [KB]: 6396
% 1.63/1.35 % (7325)Time elapsed: 0.074 s
% 1.63/1.35 % (7325)Instructions burned: 185 (million)
% 1.63/1.35 % (7325)------------------------------
% 1.63/1.35 % (7325)------------------------------
% 1.63/1.35 % (7347)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_7046 for (2999ds/902Mi)
% 1.63/1.35 % (7348)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_7046 for (2999ds/21Mi)
% 1.63/1.35 % (7349)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_7046 for (2999ds/5Mi)
% 1.63/1.36 % (7349)Instruction limit reached!
% 1.63/1.36 % (7349)------------------------------
% 1.63/1.36 % (7349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.36 % (7349)Termination reason: Unknown
% 1.63/1.36 % (7349)Termination phase: Saturation
% 1.63/1.36
% 1.63/1.36 % (7349)Memory used [KB]: 5500
% 1.63/1.36 % (7349)Time elapsed: 0.003 s
% 1.63/1.36 % (7349)Instructions burned: 6 (million)
% 1.63/1.36 % (7349)------------------------------
% 1.63/1.36 % (7349)------------------------------
% 1.63/1.36 % (7350)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_7046 for (2999ds/6Mi)
% 1.63/1.36 % (7348)Instruction limit reached!
% 1.63/1.36 % (7348)------------------------------
% 1.63/1.36 % (7348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.36 % (7348)Termination reason: Unknown
% 1.63/1.36 % (7348)Termination phase: Saturation
% 1.63/1.36
% 1.63/1.36 % (7348)Memory used [KB]: 5628
% 1.63/1.36 % (7348)Time elapsed: 0.009 s
% 1.63/1.36 % (7348)Instructions burned: 21 (million)
% 1.63/1.36 % (7348)------------------------------
% 1.63/1.36 % (7348)------------------------------
% 1.63/1.36 % (7350)Instruction limit reached!
% 1.63/1.36 % (7350)------------------------------
% 1.63/1.36 % (7350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.36 % (7350)Termination reason: Unknown
% 1.63/1.36 % (7350)Termination phase: Saturation
% 1.63/1.36
% 1.63/1.36 % (7350)Memory used [KB]: 5500
% 1.63/1.36 % (7350)Time elapsed: 0.004 s
% 1.63/1.36 % (7350)Instructions burned: 8 (million)
% 1.63/1.36 % (7350)------------------------------
% 1.63/1.36 % (7350)------------------------------
% 1.63/1.37 % (7351)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_7046 for (2999ds/377Mi)
% 1.63/1.37 % (7352)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_7046 for (2999ds/779Mi)
% 1.63/1.37 % (7353)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_7046 for (2999ds/19Mi)
% 1.63/1.38 % (7353)Instruction limit reached!
% 1.63/1.38 % (7353)------------------------------
% 1.63/1.38 % (7353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.38 % (7353)Termination reason: Unknown
% 1.63/1.38 % (7353)Termination phase: Saturation
% 1.63/1.38
% 1.63/1.38 % (7353)Memory used [KB]: 5628
% 1.63/1.38 % (7353)Time elapsed: 0.008 s
% 1.63/1.38 % (7353)Instructions burned: 20 (million)
% 1.63/1.38 % (7353)------------------------------
% 1.63/1.38 % (7353)------------------------------
% 1.63/1.39 % (7354)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_7046 for (2998ds/879Mi)
% 1.63/1.40 % (7330)Instruction limit reached!
% 1.63/1.40 % (7330)------------------------------
% 1.63/1.40 % (7330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.40 % (7330)Termination reason: Unknown
% 1.63/1.40 % (7330)Termination phase: Saturation
% 1.63/1.40
% 1.63/1.40 % (7330)Memory used [KB]: 6140
% 1.63/1.40 % (7330)Time elapsed: 0.130 s
% 1.63/1.40 % (7330)Instructions burned: 275 (million)
% 1.63/1.40 % (7330)------------------------------
% 1.63/1.40 % (7330)------------------------------
% 1.63/1.41 % (7355)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_7046 for (2998ds/17Mi)
% 1.63/1.42 % (7355)Instruction limit reached!
% 1.63/1.42 % (7355)------------------------------
% 1.63/1.42 % (7355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.42 % (7355)Termination reason: Unknown
% 1.63/1.42 % (7355)Termination phase: Saturation
% 1.63/1.42
% 1.63/1.42 % (7355)Memory used [KB]: 5628
% 1.63/1.42 % (7355)Time elapsed: 0.008 s
% 1.63/1.42 % (7355)Instructions burned: 17 (million)
% 1.63/1.42 % (7355)------------------------------
% 1.63/1.42 % (7355)------------------------------
% 1.63/1.43 % (7356)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_7046 for (2998ds/3Mi)
% 1.63/1.43 % (7356)Instruction limit reached!
% 1.63/1.43 % (7356)------------------------------
% 1.63/1.43 % (7356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.43 % (7356)Termination reason: Unknown
% 1.63/1.43 % (7356)Termination phase: Saturation
% 1.63/1.43
% 1.63/1.43 % (7356)Memory used [KB]: 1023
% 1.63/1.43 % (7356)Time elapsed: 0.003 s
% 1.63/1.43 % (7356)Instructions burned: 4 (million)
% 1.63/1.43 % (7356)------------------------------
% 1.63/1.43 % (7356)------------------------------
% 1.63/1.44 % (7357)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_7046 for (2998ds/30Mi)
% 1.63/1.45 % (7357)Instruction limit reached!
% 1.63/1.45 % (7357)------------------------------
% 1.63/1.45 % (7357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.45 % (7357)Termination reason: Unknown
% 1.63/1.45 % (7357)Termination phase: Saturation
% 1.63/1.45
% 1.63/1.45 % (7357)Memory used [KB]: 5628
% 1.63/1.45 % (7357)Time elapsed: 0.012 s
% 1.63/1.45 % (7357)Instructions burned: 31 (million)
% 1.63/1.45 % (7357)------------------------------
% 1.63/1.45 % (7357)------------------------------
% 1.63/1.46 % (7358)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_7046 for (2998ds/127Mi)
% 1.63/1.49 % (7351)Instruction limit reached!
% 1.63/1.49 % (7351)------------------------------
% 1.63/1.49 % (7351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.49 % (7351)Termination reason: Unknown
% 1.63/1.49 % (7351)Termination phase: Saturation
% 1.63/1.49
% 1.63/1.49 % (7351)Memory used [KB]: 6012
% 1.63/1.49 % (7351)Time elapsed: 0.126 s
% 1.63/1.49 % (7351)Instructions burned: 379 (million)
% 1.63/1.49 % (7351)------------------------------
% 1.63/1.49 % (7351)------------------------------
% 1.63/1.50 % (7359)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_7046 for (2997ds/100Mi)
% 1.63/1.50 % (7359)Refutation not found, incomplete strategy
% 1.63/1.50 % (7359)------------------------------
% 1.63/1.50 % (7359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.50 % (7359)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.50
% 1.63/1.50
% 1.63/1.50 % (7359)Memory used [KB]: 5500
% 1.63/1.50 % (7359)Time elapsed: 0.005 s
% 1.63/1.50 % (7359)Instructions burned: 6 (million)
% 1.63/1.50 % (7359)------------------------------
% 1.63/1.50 % (7359)------------------------------
% 1.63/1.51 % (7358)Instruction limit reached!
% 1.63/1.51 % (7358)------------------------------
% 1.63/1.51 % (7358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.51 % (7358)Termination reason: Unknown
% 1.63/1.51 % (7358)Termination phase: Saturation
% 1.63/1.51
% 1.63/1.51 % (7358)Memory used [KB]: 6012
% 1.63/1.51 % (7358)Time elapsed: 0.045 s
% 1.63/1.51 % (7358)Instructions burned: 129 (million)
% 1.63/1.51 % (7358)------------------------------
% 1.63/1.51 % (7358)------------------------------
% 1.63/1.51 % (7360)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_7046 for (2997ds/3Mi)
% 1.63/1.52 % (7361)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_7046 for (2997ds/20Mi)
% 1.63/1.52 % (7360)Instruction limit reached!
% 1.63/1.52 % (7360)------------------------------
% 1.63/1.52 % (7360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.52 % (7360)Termination reason: Unknown
% 1.63/1.52 % (7360)Termination phase: Saturation
% 1.63/1.52
% 1.63/1.52 % (7360)Memory used [KB]: 5500
% 1.63/1.52 % (7360)Time elapsed: 0.003 s
% 1.63/1.52 % (7360)Instructions burned: 4 (million)
% 1.63/1.52 % (7360)------------------------------
% 1.63/1.52 % (7360)------------------------------
% 1.63/1.52 % (7361)Instruction limit reached!
% 1.63/1.52 % (7361)------------------------------
% 1.63/1.52 % (7361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.52 % (7361)Termination reason: Unknown
% 1.63/1.52 % (7361)Termination phase: Saturation
% 1.63/1.52
% 1.63/1.52 % (7361)Memory used [KB]: 5628
% 1.63/1.52 % (7361)Time elapsed: 0.010 s
% 1.63/1.52 % (7361)Instructions burned: 22 (million)
% 1.63/1.52 % (7361)------------------------------
% 1.63/1.52 % (7361)------------------------------
% 1.63/1.53 % (7362)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_7046 for (2997ds/86Mi)
% 1.63/1.53 % (7352)First to succeed.
% 1.63/1.53 % (7352)Refutation found. Thanks to Tanya!
% 1.63/1.53 % SZS status Theorem for DTF2THF_7046
% 1.63/1.53 % SZS output start Proof for DTF2THF_7046
% 1.63/1.53 thf(type_def_5, type, iS: $tType).
% 1.63/1.53 thf(func_def_0, type, iS: $tType).
% 1.63/1.53 thf(func_def_1, type, y: iS).
% 1.63/1.53 thf(func_def_2, type, x: iS).
% 1.63/1.53 thf(func_def_3, type, cP: iS > iS > iS).
% 1.63/1.53 thf(func_def_4, type, c0: iS).
% 1.63/1.53 thf(func_def_27, type, sK1: (iS > $o) > iS).
% 1.63/1.53 thf(func_def_28, type, sK2: (iS > $o) > iS).
% 1.63/1.53 thf(func_def_29, type, sK3: iS > iS > iS > $o).
% 1.63/1.53 thf(func_def_30, type, ph4: !>[X0: $tType]:(X0)).
% 1.63/1.53 thf(f999,plain,(
% 1.63/1.53 $false),
% 1.63/1.53 inference(avatar_sat_refutation,[status(thm)],[f197,f255,f257,f312,f337,f866,f986])).
% 1.63/1.53 thf(f986,plain,(
% 1.63/1.53 ~spl0_1),
% 1.63/1.53 inference(avatar_contradiction_clause,[status(thm)],[f985])).
% 1.63/1.53 thf(f985,plain,(
% 1.63/1.53 $false | ~spl0_1),
% 1.63/1.53 inference(trivial_inequality_removal,[status(thm)],[f948])).
% 1.63/1.53 thf(f948,plain,(
% 1.63/1.53 ($true = $false) | (x != x) | ~spl0_1),
% 1.63/1.53 inference(superposition,[status(thm)],[f191,f95])).
% 1.63/1.53 thf(f95,plain,(
% 1.63/1.53 ( ! [X0 : iS,X1 : iS] : (($true = (sK3 @ c0 @ X0 @ X1)) | (X0 != X1)) )),
% 1.63/1.53 inference(equality_resolution,[status(thm)],[f88])).
% 1.63/1.53 thf(f88,plain,(
% 1.63/1.53 ( ! [X2 : iS,X3 : iS,X1 : iS] : ((c0 != X1) | ($true = (sK3 @ X1 @ X3 @ X2)) | (X2 != X3)) )),
% 1.63/1.53 inference(equality_proxy_clausification,[status(thm)],[f87])).
% 1.63/1.53 thf(f87,plain,(
% 1.63/1.53 ( ! [X2 : iS,X3 : iS,X1 : iS] : ((c0 != X1) | ((X3 = X2) = $false) | ($true = (sK3 @ X1 @ X3 @ X2))) )),
% 1.63/1.53 inference(equality_proxy_clausification,[status(thm)],[f86])).
% 1.63/1.53 thf(f86,plain,(
% 1.63/1.53 ( ! [X2 : iS,X3 : iS,X1 : iS] : (((c0 = X1) = $false) | ((X3 = X2) = $false) | ($true = (sK3 @ X1 @ X3 @ X2))) )),
% 1.63/1.53 inference(binary_proxy_clausification,[status(thm)],[f65])).
% 1.63/1.53 thf(f65,plain,(
% 1.63/1.53 ( ! [X2 : iS,X3 : iS,X1 : iS] : ((((X3 = X2) & (c0 = X1)) = $false) | ($true = (sK3 @ X1 @ X3 @ X2))) )),
% 1.63/1.53 inference(binary_proxy_clausification,[status(thm)],[f61])).
% 1.63/1.53 thf(f61,plain,(
% 1.63/1.53 ( ! [X2 : iS,X3 : iS,X1 : iS] : ((((?? @ iS @ (^[Y0 : iS]: (?? @ iS @ (^[Y1 : iS]: (?? @ iS @ (^[Y2 : iS]: (?? @ iS @ (^[Y3 : iS]: (?? @ iS @ (^[Y4 : iS]: (?? @ iS @ (^[Y5 : iS]: (((((sK3 @ Y0 @ Y3 @ Y1) & ((cP @ Y5 @ Y0) = X1)) & (sK3 @ Y5 @ Y2 @ Y4)) & ((cP @ Y2 @ Y3) = X3)) & ((cP @ Y4 @ Y1) = X2)))))))))))))) | ((X3 = X2) & (c0 = X1))) = $false) | ($true = (sK3 @ X1 @ X3 @ X2))) )),
% 1.63/1.53 inference(binary_proxy_clausification,[status(thm)],[f59])).
% 1.63/1.53 thf(f59,plain,(
% 1.63/1.53 ( ! [X2 : iS,X3 : iS,X1 : iS] : (((((?? @ iS @ (^[Y0 : iS]: (?? @ iS @ (^[Y1 : iS]: (?? @ iS @ (^[Y2 : iS]: (?? @ iS @ (^[Y3 : iS]: (?? @ iS @ (^[Y4 : iS]: (?? @ iS @ (^[Y5 : iS]: (((((sK3 @ Y0 @ Y3 @ Y1) & ((cP @ Y5 @ Y0) = X1)) & (sK3 @ Y5 @ Y2 @ Y4)) & ((cP @ Y2 @ Y3) = X3)) & ((cP @ Y4 @ Y1) = X2)))))))))))))) | ((X3 = X2) & (c0 = X1))) | ((c0 = X3) & (X2 = X1))) = $false) | ($true = (sK3 @ X1 @ X3 @ X2))) )),
% 1.63/1.53 inference(binary_proxy_clausification,[status(thm)],[f58])).
% 1.63/1.53 thf(f58,plain,(
% 1.63/1.53 ( ! [X2 : iS,X3 : iS,X1 : iS] : (($true = ((((?? @ iS @ (^[Y0 : iS]: (?? @ iS @ (^[Y1 : iS]: (?? @ iS @ (^[Y2 : iS]: (?? @ iS @ (^[Y3 : iS]: (?? @ iS @ (^[Y4 : iS]: (?? @ iS @ (^[Y5 : iS]: (((((sK3 @ Y0 @ Y3 @ Y1) & ((cP @ Y5 @ Y0) = X1)) & (sK3 @ Y5 @ Y2 @ Y4)) & ((cP @ Y2 @ Y3) = X3)) & ((cP @ Y4 @ Y1) = X2)))))))))))))) | ((X3 = X2) & (c0 = X1))) | ((c0 = X3) & (X2 = X1))) => (sK3 @ X1 @ X3 @ X2)))) )),
% 1.63/1.53 inference(beta_eta_normalization,[status(thm)],[f57])).
% 1.63/1.53 thf(f57,plain,(
% 1.63/1.53 ( ! [X2 : iS,X3 : iS,X1 : iS] : (($true = ((^[Y0 : iS]: ((((?? @ iS @ (^[Y1 : iS]: (?? @ iS @ (^[Y2 : iS]: (?? @ iS @ (^[Y3 : iS]: (?? @ iS @ (^[Y4 : iS]: (?? @ iS @ (^[Y5 : iS]: (?? @ iS @ (^[Y6 : iS]: (((((sK3 @ Y1 @ Y4 @ Y2) & ((cP @ Y6 @ Y1) = X1)) & (sK3 @ Y6 @ Y3 @ Y5)) & ((cP @ Y3 @ Y4) = Y0)) & ((cP @ Y5 @ Y2) = X2)))))))))))))) | ((Y0 = X2) & (c0 = X1))) | ((c0 = Y0) & (X2 = X1))) => (sK3 @ X1 @ Y0 @ X2))) @ X3))) )),
% 1.63/1.53 inference(pi_clausification,[status(thm)],[f56])).
% 1.63/1.53 thf(f56,plain,(
% 1.63/1.53 ( ! [X2 : iS,X1 : iS] : (($true = (!! @ iS @ (^[Y0 : iS]: ((((?? @ iS @ (^[Y1 : iS]: (?? @ iS @ (^[Y2 : iS]: (?? @ iS @ (^[Y3 : iS]: (?? @ iS @ (^[Y4 : iS]: (?? @ iS @ (^[Y5 : iS]: (?? @ iS @ (^[Y6 : iS]: (((((sK3 @ Y1 @ Y4 @ Y2) & ((cP @ Y6 @ Y1) = X1)) & (sK3 @ Y6 @ Y3 @ Y5)) & ((cP @ Y3 @ Y4) = Y0)) & ((cP @ Y5 @ Y2) = X2)))))))))))))) | ((Y0 = X2) & (c0 = X1))) | ((c0 = Y0) & (X2 = X1))) => (sK3 @ X1 @ Y0 @ X2)))))) )),
% 1.63/1.53 inference(beta_eta_normalization,[status(thm)],[f55])).
% 1.63/1.53 thf(f55,plain,(
% 1.63/1.53 ( ! [X2 : iS,X1 : iS] : ((((^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: ((((?? @ iS @ (^[Y2 : iS]: (?? @ iS @ (^[Y3 : iS]: (?? @ iS @ (^[Y4 : iS]: (?? @ iS @ (^[Y5 : iS]: (?? @ iS @ (^[Y6 : iS]: (?? @ iS @ (^[Y7 : iS]: (((((sK3 @ Y2 @ Y5 @ Y3) & ((cP @ Y7 @ Y2) = X1)) & (sK3 @ Y7 @ Y4 @ Y6)) & ((cP @ Y4 @ Y5) = Y1)) & ((cP @ Y6 @ Y3) = Y0)))))))))))))) | ((Y1 = Y0) & (c0 = X1))) | ((c0 = Y1) & (Y0 = X1))) => (sK3 @ X1 @ Y1 @ Y0))))) @ X2) = $true)) )),
% 1.63/1.53 inference(pi_clausification,[status(thm)],[f54])).
% 1.63/1.53 thf(f54,plain,(
% 1.63/1.53 ( ! [X1 : iS] : (((!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: ((((?? @ iS @ (^[Y2 : iS]: (?? @ iS @ (^[Y3 : iS]: (?? @ iS @ (^[Y4 : iS]: (?? @ iS @ (^[Y5 : iS]: (?? @ iS @ (^[Y6 : iS]: (?? @ iS @ (^[Y7 : iS]: (((((sK3 @ Y2 @ Y5 @ Y3) & ((cP @ Y7 @ Y2) = X1)) & (sK3 @ Y7 @ Y4 @ Y6)) & ((cP @ Y4 @ Y5) = Y1)) & ((cP @ Y6 @ Y3) = Y0)))))))))))))) | ((Y1 = Y0) & (c0 = X1))) | ((c0 = Y1) & (Y0 = X1))) => (sK3 @ X1 @ Y1 @ Y0)))))) = $true)) )),
% 1.63/1.53 inference(beta_eta_normalization,[status(thm)],[f53])).
% 1.63/1.53 thf(f53,plain,(
% 1.63/1.53 ( ! [X1 : iS] : (($true = ((^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: ((((?? @ iS @ (^[Y3 : iS]: (?? @ iS @ (^[Y4 : iS]: (?? @ iS @ (^[Y5 : iS]: (?? @ iS @ (^[Y6 : iS]: (?? @ iS @ (^[Y7 : iS]: (?? @ iS @ (^[Y8 : iS]: (((((sK3 @ Y3 @ Y6 @ Y4) & ((cP @ Y8 @ Y3) = Y0)) & (sK3 @ Y8 @ Y5 @ Y7)) & ((cP @ Y5 @ Y6) = Y2)) & ((cP @ Y7 @ Y4) = Y1)))))))))))))) | ((Y2 = Y1) & (c0 = Y0))) | ((c0 = Y2) & (Y1 = Y0))) => (sK3 @ Y0 @ Y2 @ Y1))))))) @ X1))) )),
% 1.63/1.53 inference(pi_clausification,[status(thm)],[f52])).
% 1.63/1.53 thf(f52,plain,(
% 1.63/1.53 ($true = (!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: ((((?? @ iS @ (^[Y3 : iS]: (?? @ iS @ (^[Y4 : iS]: (?? @ iS @ (^[Y5 : iS]: (?? @ iS @ (^[Y6 : iS]: (?? @ iS @ (^[Y7 : iS]: (?? @ iS @ (^[Y8 : iS]: (((((sK3 @ Y3 @ Y6 @ Y4) & ((cP @ Y8 @ Y3) = Y0)) & (sK3 @ Y8 @ Y5 @ Y7)) & ((cP @ Y5 @ Y6) = Y2)) & ((cP @ Y7 @ Y4) = Y1)))))))))))))) | ((Y2 = Y1) & (c0 = Y0))) | ((c0 = Y2) & (Y1 = Y0))) => (sK3 @ Y0 @ Y2 @ Y1)))))))))),
% 1.63/1.53 inference(binary_proxy_clausification,[status(thm)],[f50])).
% 1.63/1.53 thf(f50,plain,(
% 1.63/1.53 ($false = ((!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: ((((?? @ iS @ (^[Y3 : iS]: (?? @ iS @ (^[Y4 : iS]: (?? @ iS @ (^[Y5 : iS]: (?? @ iS @ (^[Y6 : iS]: (?? @ iS @ (^[Y7 : iS]: (?? @ iS @ (^[Y8 : iS]: (((((sK3 @ Y3 @ Y6 @ Y4) & ((cP @ Y8 @ Y3) = Y0)) & (sK3 @ Y8 @ Y5 @ Y7)) & ((cP @ Y5 @ Y6) = Y2)) & ((cP @ Y7 @ Y4) = Y1)))))))))))))) | ((Y2 = Y1) & (c0 = Y0))) | ((c0 = Y2) & (Y1 = Y0))) => (sK3 @ Y0 @ Y2 @ Y1)))))))) => (sK3 @ (cP @ c0 @ y) @ (cP @ x @ y) @ (cP @ x @ y))))),
% 1.63/1.53 inference(beta_eta_normalization,[status(thm)],[f49])).
% 1.63/1.53 thf(f49,plain,(
% 1.63/1.53 (((^[Y0 : iS > iS > iS > $o]: ((!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (!! @ iS @ (^[Y3 : iS]: ((((?? @ iS @ (^[Y4 : iS]: (?? @ iS @ (^[Y5 : iS]: (?? @ iS @ (^[Y6 : iS]: (?? @ iS @ (^[Y7 : iS]: (?? @ iS @ (^[Y8 : iS]: (?? @ iS @ (^[Y9 : iS]: (((((Y0 @ Y4 @ Y7 @ Y5) & ((cP @ Y9 @ Y4) = Y1)) & (Y0 @ Y9 @ Y6 @ Y8)) & ((cP @ Y6 @ Y7) = Y3)) & ((cP @ Y8 @ Y5) = Y2)))))))))))))) | ((Y3 = Y2) & (c0 = Y1))) | ((c0 = Y3) & (Y2 = Y1))) => (Y0 @ Y1 @ Y3 @ Y2)))))))) => (Y0 @ (cP @ c0 @ y) @ (cP @ x @ y) @ (cP @ x @ y)))) @ sK3) = $false)),
% 1.63/1.53 inference(sigma_clausification,[status(thm)],[f10])).
% 1.63/1.53 thf(f10,plain,(
% 1.63/1.53 ((!! @ (iS > iS > iS > $o) @ (^[Y0 : iS > iS > iS > $o]: ((!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (!! @ iS @ (^[Y3 : iS]: ((((?? @ iS @ (^[Y4 : iS]: (?? @ iS @ (^[Y5 : iS]: (?? @ iS @ (^[Y6 : iS]: (?? @ iS @ (^[Y7 : iS]: (?? @ iS @ (^[Y8 : iS]: (?? @ iS @ (^[Y9 : iS]: (((((Y0 @ Y4 @ Y7 @ Y5) & ((cP @ Y9 @ Y4) = Y1)) & (Y0 @ Y9 @ Y6 @ Y8)) & ((cP @ Y6 @ Y7) = Y3)) & ((cP @ Y8 @ Y5) = Y2)))))))))))))) | ((Y3 = Y2) & (c0 = Y1))) | ((c0 = Y3) & (Y2 = Y1))) => (Y0 @ Y1 @ Y3 @ Y2)))))))) => (Y0 @ (cP @ c0 @ y) @ (cP @ x @ y) @ (cP @ x @ y))))) = $false)),
% 1.63/1.53 inference(binary_proxy_clausification,[status(thm)],[f9])).
% 1.63/1.53 thf(f9,plain,(
% 1.63/1.53 (((((!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (~ (c0 = (cP @ Y1 @ Y0))))))) & (!! @ (iS > $o) @ (^[Y0 : iS > $o]: (((Y0 @ c0) & (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (((Y0 @ Y2) & (Y0 @ Y1)) => (Y0 @ (cP @ Y2 @ Y1)))))))) => (!! @ iS @ Y0))))) & (!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (!! @ iS @ (^[Y3 : iS]: (((cP @ Y3 @ Y2) = (cP @ Y1 @ Y0)) => ((Y3 = Y1) & (Y2 = Y0)))))))))))) => (!! @ (iS > iS > iS > $o) @ (^[Y0 : iS > iS > iS > $o]: ((!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (!! @ iS @ (^[Y3 : iS]: ((((?? @ iS @ (^[Y4 : iS]: (?? @ iS @ (^[Y5 : iS]: (?? @ iS @ (^[Y6 : iS]: (?? @ iS @ (^[Y7 : iS]: (?? @ iS @ (^[Y8 : iS]: (?? @ iS @ (^[Y9 : iS]: (((((Y0 @ Y4 @ Y7 @ Y5) & ((cP @ Y9 @ Y4) = Y1)) & (Y0 @ Y9 @ Y6 @ Y8)) & ((cP @ Y6 @ Y7) = Y3)) & ((cP @ Y8 @ Y5) = Y2)))))))))))))) | ((Y3 = Y2) & (c0 = Y1))) | ((c0 = Y3) & (Y2 = Y1))) => (Y0 @ Y1 @ Y3 @ Y2)))))))) => (Y0 @ (cP @ c0 @ y) @ (cP @ x @ y) @ (cP @ x @ y)))))) = $false)),
% 1.63/1.53 inference(not_proxy_clausification,[status(thm)],[f8])).
% 1.63/1.53 thf(f8,plain,(
% 1.63/1.53 ($true = (~ ((((!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (~ (c0 = (cP @ Y1 @ Y0))))))) & (!! @ (iS > $o) @ (^[Y0 : iS > $o]: (((Y0 @ c0) & (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (((Y0 @ Y2) & (Y0 @ Y1)) => (Y0 @ (cP @ Y2 @ Y1)))))))) => (!! @ iS @ Y0))))) & (!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (!! @ iS @ (^[Y3 : iS]: (((cP @ Y3 @ Y2) = (cP @ Y1 @ Y0)) => ((Y3 = Y1) & (Y2 = Y0)))))))))))) => (!! @ (iS > iS > iS > $o) @ (^[Y0 : iS > iS > iS > $o]: ((!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (!! @ iS @ (^[Y3 : iS]: ((((?? @ iS @ (^[Y4 : iS]: (?? @ iS @ (^[Y5 : iS]: (?? @ iS @ (^[Y6 : iS]: (?? @ iS @ (^[Y7 : iS]: (?? @ iS @ (^[Y8 : iS]: (?? @ iS @ (^[Y9 : iS]: (((((Y0 @ Y4 @ Y7 @ Y5) & ((cP @ Y9 @ Y4) = Y1)) & (Y0 @ Y9 @ Y6 @ Y8)) & ((cP @ Y6 @ Y7) = Y3)) & ((cP @ Y8 @ Y5) = Y2)))))))))))))) | ((Y3 = Y2) & (c0 = Y1))) | ((c0 = Y3) & (Y2 = Y1))) => (Y0 @ Y1 @ Y3 @ Y2)))))))) => (Y0 @ (cP @ c0 @ y) @ (cP @ x @ y) @ (cP @ x @ y))))))))),
% 1.63/1.53 inference(boolean_simplification,[status(thm)],[f7])).
% 1.63/1.53 thf(f7,plain,(
% 1.63/1.53 ($true = (~ ((((!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (~ (c0 = (cP @ Y1 @ Y0))))))) & (!! @ (iS > $o) @ (^[Y0 : iS > $o]: (((Y0 @ c0) & (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (((Y0 @ Y2) & (Y0 @ Y1)) => (Y0 @ (cP @ Y2 @ Y1)))))))) => (!! @ iS @ Y0))))) & (!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (!! @ iS @ (^[Y3 : iS]: (((cP @ Y3 @ Y2) = (cP @ Y1 @ Y0)) => ((Y3 = Y1) & (Y2 = Y0)))))))))))) => (!! @ (iS > iS > iS > $o) @ (^[Y0 : iS > iS > iS > $o]: (((!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (!! @ iS @ (^[Y3 : iS]: ((((?? @ iS @ (^[Y4 : iS]: (?? @ iS @ (^[Y5 : iS]: (?? @ iS @ (^[Y6 : iS]: (?? @ iS @ (^[Y7 : iS]: (?? @ iS @ (^[Y8 : iS]: (?? @ iS @ (^[Y9 : iS]: (((((Y0 @ Y4 @ Y7 @ Y5) & ((cP @ Y9 @ Y4) = Y1)) & (Y0 @ Y9 @ Y6 @ Y8)) & ((cP @ Y6 @ Y7) = Y3)) & ((cP @ Y8 @ Y5) = Y2)))))))))))))) | ((Y3 = Y2) & (c0 = Y1))) | ((c0 = Y3) & (Y2 = Y1))) => (Y0 @ Y1 @ Y3 @ Y2)))))))) & $true) => (Y0 @ (cP @ c0 @ y) @ (cP @ x @ y) @ (cP @ x @ y))))))))),
% 1.63/1.53 inference(beta_eta_normalization,[status(thm)],[f6])).
% 1.63/1.53 thf(f6,plain,(
% 1.63/1.53 ($true = (~ ((((!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (~ (c0 = (cP @ Y1 @ Y0))))))) & (!! @ (iS > $o) @ (^[Y0 : iS > $o]: (((Y0 @ c0) & (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (((Y0 @ Y2) & (Y0 @ Y1)) => (Y0 @ (cP @ Y2 @ Y1)))))))) => (!! @ iS @ (^[Y1 : iS]: (Y0 @ Y1))))))) & (!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (!! @ iS @ (^[Y3 : iS]: (((cP @ Y3 @ Y2) = (cP @ Y1 @ Y0)) => ((Y3 = Y1) & (Y2 = Y0)))))))))))) => (!! @ (iS > iS > iS > $o) @ (^[Y0 : iS > iS > iS > $o]: (((!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (!! @ iS @ (^[Y3 : iS]: ((((?? @ iS @ (^[Y4 : iS]: (?? @ iS @ (^[Y5 : iS]: (?? @ iS @ (^[Y6 : iS]: (?? @ iS @ (^[Y7 : iS]: (?? @ iS @ (^[Y8 : iS]: (?? @ iS @ (^[Y9 : iS]: (((((Y0 @ Y4 @ Y7 @ Y5) & ((cP @ Y9 @ Y4) = Y1)) & (Y0 @ Y9 @ Y6 @ Y8)) & ((cP @ Y6 @ Y7) = Y3)) & ((cP @ Y8 @ Y5) = Y2)))))))))))))) | ((Y3 = Y2) & (c0 = Y1))) | ((c0 = Y3) & (Y2 = Y1))) => (Y0 @ Y1 @ Y3 @ Y2)))))))) & $true) => (Y0 @ (cP @ c0 @ y) @ (cP @ x @ y) @ (cP @ x @ y))))))))),
% 1.63/1.53 inference(cnf_transformation,[status(thm)],[f5])).
% 1.63/1.53 thf(f5,plain,(
% 1.63/1.53 ($true = (~ ((((!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (~ (c0 = (cP @ Y1 @ Y0))))))) & (!! @ (iS > $o) @ (^[Y0 : iS > $o]: (((Y0 @ c0) & (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (((Y0 @ Y2) & (Y0 @ Y1)) => (Y0 @ (cP @ Y2 @ Y1)))))))) => (!! @ iS @ (^[Y1 : iS]: (Y0 @ Y1))))))) & (!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (!! @ iS @ (^[Y3 : iS]: (((cP @ Y3 @ Y2) = (cP @ Y1 @ Y0)) => ((Y3 = Y1) & (Y2 = Y0)))))))))))) => (!! @ (iS > iS > iS > $o) @ (^[Y0 : iS > iS > iS > $o]: (((!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (!! @ iS @ (^[Y3 : iS]: ((((?? @ iS @ (^[Y4 : iS]: (?? @ iS @ (^[Y5 : iS]: (?? @ iS @ (^[Y6 : iS]: (?? @ iS @ (^[Y7 : iS]: (?? @ iS @ (^[Y8 : iS]: (?? @ iS @ (^[Y9 : iS]: (((((Y0 @ Y4 @ Y7 @ Y5) & ((cP @ Y9 @ Y4) = Y1)) & (Y0 @ Y9 @ Y6 @ Y8)) & ((cP @ Y6 @ Y7) = Y3)) & ((cP @ Y8 @ Y5) = Y2)))))))))))))) | ((Y3 = Y2) & (c0 = Y1))) | ((c0 = Y3) & (Y2 = Y1))) => (Y0 @ Y1 @ Y3 @ Y2)))))))) & $true) => (Y0 @ (cP @ c0 @ y) @ (cP @ x @ y) @ (cP @ x @ y))))))))),
% 1.63/1.53 inference(fool_elimination,[status(thm)],[f4])).
% 1.63/1.53 thf(f4,plain,(
% 1.63/1.53 ~((! [X0 : iS,X1 : iS,X2 : iS,X3 : iS] : (((cP @ X0 @ X1) = (cP @ X2 @ X3)) => ((X1 = X3) & (X0 = X2))) & ! [X4 : iS > $o] : ((! [X5 : iS,X6 : iS] : (((X4 @ X6) & (X4 @ X5)) => (X4 @ (cP @ X5 @ X6))) & (X4 @ c0)) => ! [X7 : iS] : (X4 @ X7)) & ! [X8 : iS,X9 : iS] : (c0 != (cP @ X8 @ X9))) => ! [X10 : iS > iS > iS > $o] : (($true & ! [X11 : iS,X12 : iS,X13 : iS] : ((((X12 = X13) & (c0 = X11)) | ((c0 = X13) & (X11 = X12)) | ? [X14 : iS,X15 : iS,X16 : iS,X17 : iS,X18 : iS,X19 : iS] : (((cP @ X15 @ X18) = X12) & ((cP @ X17 @ X16) = X11) & (X10 @ X14 @ X17 @ X15) & ((cP @ X14 @ X19) = X13) & (X10 @ X19 @ X16 @ X18))) => (X10 @ X13 @ X11 @ X12))) => (X10 @ (cP @ c0 @ y) @ (cP @ x @ y) @ (cP @ x @ y))))),
% 1.63/1.53 inference(rectify,[status(thm)],[f2])).
% 1.63/1.53 thf(f2,negated_conjecture,(
% 1.63/1.53 ~((! [X1 : iS,X3 : iS,X0 : iS,X2 : iS] : (((cP @ X0 @ X2) = (cP @ X1 @ X3)) => ((X2 = X3) & (X0 = X1))) & ! [X4 : iS > $o] : ((! [X0 : iS,X1 : iS] : (((X4 @ X1) & (X4 @ X0)) => (X4 @ (cP @ X0 @ X1))) & (X4 @ c0)) => ! [X0 : iS] : (X4 @ X0)) & ! [X0 : iS,X1 : iS] : ((cP @ X0 @ X1) != c0)) => ! [X5 : iS > iS > iS > $o] : (($true & ! [X7 : iS,X8 : iS,X6 : iS] : ((((X6 = X8) & (c0 = X7)) | ((c0 = X6) & (X7 = X8)) | ? [X9 : iS,X13 : iS,X12 : iS,X11 : iS,X14 : iS,X10 : iS] : (((cP @ X13 @ X14) = X8) & ((cP @ X11 @ X12) = X7) & (X5 @ X9 @ X11 @ X13) & ((cP @ X9 @ X10) = X6) & (X5 @ X10 @ X12 @ X14))) => (X5 @ X6 @ X7 @ X8))) => (X5 @ (cP @ c0 @ y) @ (cP @ x @ y) @ (cP @ x @ y))))),
% 1.63/1.53 inference(negated_conjecture,[status(cth)],[f1])).
% 1.63/1.53 thf(f1,conjecture,(
% 1.63/1.53 (! [X1 : iS,X3 : iS,X0 : iS,X2 : iS] : (((cP @ X0 @ X2) = (cP @ X1 @ X3)) => ((X2 = X3) & (X0 = X1))) & ! [X4 : iS > $o] : ((! [X0 : iS,X1 : iS] : (((X4 @ X1) & (X4 @ X0)) => (X4 @ (cP @ X0 @ X1))) & (X4 @ c0)) => ! [X0 : iS] : (X4 @ X0)) & ! [X0 : iS,X1 : iS] : ((cP @ X0 @ X1) != c0)) => ! [X5 : iS > iS > iS > $o] : (($true & ! [X7 : iS,X8 : iS,X6 : iS] : ((((X6 = X8) & (c0 = X7)) | ((c0 = X6) & (X7 = X8)) | ? [X9 : iS,X13 : iS,X12 : iS,X11 : iS,X14 : iS,X10 : iS] : (((cP @ X13 @ X14) = X8) & ((cP @ X11 @ X12) = X7) & (X5 @ X9 @ X11 @ X13) & ((cP @ X9 @ X10) = X6) & (X5 @ X10 @ X12 @ X14))) => (X5 @ X6 @ X7 @ X8))) => (X5 @ (cP @ c0 @ y) @ (cP @ x @ y) @ (cP @ x @ y)))),
% 1.63/1.53 file('/export/starexec/sandbox/tmp/tmp.siZw90THh0/DTF2THF_7046.p',cS_INCL_LEM5_pme)).
% 1.63/1.53 thf(f191,plain,(
% 1.63/1.53 ($false = (sK3 @ c0 @ x @ x)) | ~spl0_1),
% 1.63/1.53 inference(avatar_component_clause,[status(thm)],[f189])).
% 1.63/1.53 thf(f189,definition,(
% 1.63/1.53 spl0_1 <=> ($false = (sK3 @ c0 @ x @ x))),
% 1.63/1.53 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.63/1.53 thf(f866,plain,(
% 1.63/1.53 ~spl0_2 | ~spl0_4 | ~spl0_10),
% 1.63/1.53 inference(avatar_contradiction_clause,[status(thm)],[f865])).
% 1.63/1.53 thf(f865,plain,(
% 1.63/1.53 $false | (~spl0_2 | ~spl0_4 | ~spl0_10)),
% 1.63/1.53 inference(trivial_inequality_removal,[status(thm)],[f749])).
% 1.63/1.53 thf(f749,plain,(
% 1.63/1.53 ($true = $false) | (~spl0_2 | ~spl0_4 | ~spl0_10)),
% 1.63/1.53 inference(superposition,[status(thm)],[f308,f688])).
% 1.63/1.53 thf(f688,plain,(
% 1.63/1.53 ($false = (sK3 @ c0 @ c0 @ c0)) | (~spl0_2 | ~spl0_4)),
% 1.63/1.53 inference(trivial_inequality_removal,[status(thm)],[f664])).
% 1.63/1.53 thf(f664,plain,(
% 1.63/1.53 ($false = (sK3 @ c0 @ c0 @ c0)) | ($true = $false) | (~spl0_2 | ~spl0_4)),
% 1.63/1.53 inference(superposition,[status(thm)],[f652,f195])).
% 1.63/1.53 thf(f195,plain,(
% 1.63/1.53 ((sK3 @ y @ y @ y) = $false) | ~spl0_2),
% 1.63/1.53 inference(avatar_component_clause,[status(thm)],[f193])).
% 1.63/1.53 thf(f193,definition,(
% 1.63/1.53 spl0_2 <=> ((sK3 @ y @ y @ y) = $false)),
% 1.63/1.53 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.63/1.53 thf(f652,plain,(
% 1.63/1.53 ( ! [X0 : iS] : (($true = (sK3 @ X0 @ X0 @ X0)) | ($false = (sK3 @ c0 @ c0 @ c0))) ) | (~spl0_2 | ~spl0_4)),
% 1.63/1.53 inference(trivial_inequality_removal,[status(thm)],[f622])).
% 1.63/1.53 thf(f622,plain,(
% 1.63/1.53 ( ! [X0 : iS] : (($false = (sK3 @ c0 @ c0 @ c0)) | ($true = (sK3 @ X0 @ X0 @ X0)) | ($true = $false)) ) | (~spl0_2 | ~spl0_4)),
% 1.63/1.53 inference(superposition,[status(thm)],[f594,f195])).
% 1.63/1.53 thf(f594,plain,(
% 1.63/1.53 ( ! [X0 : iS,X1 : iS] : (($true = (sK3 @ X0 @ X0 @ X0)) | ((sK3 @ X1 @ X1 @ X1) = $true) | ($false = (sK3 @ c0 @ c0 @ c0))) ) | ~spl0_4),
% 1.63/1.53 inference(trivial_inequality_removal,[status(thm)],[f592])).
% 1.63/1.53 thf(f592,plain,(
% 1.63/1.53 ( ! [X0 : iS,X1 : iS] : (($true != $true) | ($false = (sK3 @ c0 @ c0 @ c0)) | ($true = (sK3 @ X0 @ X0 @ X0)) | ((sK3 @ X1 @ X1 @ X1) = $true)) ) | ~spl0_4),
% 1.63/1.53 inference(equality_factoring,[status(thm)],[f569])).
% 1.63/1.53 thf(f569,plain,(
% 1.63/1.53 ( ! [X2 : iS,X0 : iS,X1 : iS] : (($true = (sK3 @ X2 @ X2 @ X2)) | ($false = (sK3 @ c0 @ c0 @ c0)) | ($true = (sK3 @ X0 @ X0 @ X0)) | ((sK3 @ X1 @ X1 @ X1) = $true)) ) | ~spl0_4),
% 1.63/1.53 inference(trivial_inequality_removal,[status(thm)],[f568])).
% 1.63/1.53 thf(f568,plain,(
% 1.63/1.53 ( ! [X2 : iS,X0 : iS,X1 : iS] : (($true = (sK3 @ X0 @ X0 @ X0)) | ((sK3 @ X1 @ X1 @ X1) = $true) | ((sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) != (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0)))) | ($true = (sK3 @ X2 @ X2 @ X2)) | ($false = (sK3 @ c0 @ c0 @ c0))) ) | ~spl0_4),
% 1.63/1.53 inference(beta_eta_normalization,[status(thm)],[f567])).
% 1.63/1.53 thf(f567,plain,(
% 1.63/1.53 ( ! [X2 : iS,X0 : iS,X1 : iS] : (((sK3 @ X1 @ X1 @ X1) = $true) | ($true = (sK3 @ X0 @ X0 @ X0)) | ((sK3 @ ((^[Y0 : iS]: (Y0)) @ X2) @ X2 @ ((^[Y0 : iS]: (Y0)) @ X2)) = $true) | (((^[Y0 : iS]: (Y0)) @ (sK1 @ (^[Y0 : iS]: (sK3 @ ((^[Y1 : iS]: (Y1)) @ Y0) @ Y0 @ ((^[Y1 : iS]: (Y1)) @ Y0))))) != (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0)))) | ((sK3 @ ((^[Y0 : iS]: (Y0)) @ c0) @ c0 @ ((^[Y0 : iS]: (Y0)) @ c0)) = $false)) ) | ~spl0_4),
% 1.63/1.53 inference(trivial_inequality_removal,[status(thm)],[f566])).
% 1.63/1.53 thf(f566,plain,(
% 1.63/1.53 ( ! [X2 : iS,X0 : iS,X1 : iS] : (((sK3 @ ((^[Y0 : iS]: (Y0)) @ c0) @ c0 @ ((^[Y0 : iS]: (Y0)) @ c0)) = $false) | ($true = (sK3 @ X0 @ X0 @ X0)) | ((sK3 @ ((^[Y0 : iS]: (Y0)) @ X2) @ X2 @ ((^[Y0 : iS]: (Y0)) @ X2)) = $true) | ((^[Y0 : iS]: (Y0)) != (^[Y0 : iS]: (Y0))) | (((^[Y0 : iS]: (Y0)) @ (sK1 @ (^[Y0 : iS]: (sK3 @ ((^[Y1 : iS]: (Y1)) @ Y0) @ Y0 @ ((^[Y1 : iS]: (Y1)) @ Y0))))) != (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0)))) | ((sK3 @ X1 @ X1 @ X1) = $true)) ) | ~spl0_4),
% 1.63/1.53 inference(duplicate_literal_removal,[status(thm)],[f564])).
% 1.63/1.53 thf(f564,plain,(
% 1.63/1.53 ( ! [X2 : iS,X0 : iS,X1 : iS] : (((sK3 @ X1 @ X1 @ X1) = $true) | ((sK3 @ ((^[Y0 : iS]: (Y0)) @ X2) @ X2 @ ((^[Y0 : iS]: (Y0)) @ X2)) = $true) | ($true = (sK3 @ X0 @ X0 @ X0)) | ((^[Y0 : iS]: (Y0)) != (^[Y0 : iS]: (Y0))) | ((sK3 @ ((^[Y0 : iS]: (Y0)) @ c0) @ c0 @ ((^[Y0 : iS]: (Y0)) @ c0)) = $false) | (((^[Y0 : iS]: (Y0)) @ (sK1 @ (^[Y0 : iS]: (sK3 @ ((^[Y1 : iS]: (Y1)) @ Y0) @ Y0 @ ((^[Y1 : iS]: (Y1)) @ Y0))))) != (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0)))) | ((^[Y0 : iS]: (Y0)) != (^[Y0 : iS]: (Y0)))) ) | ~spl0_4),
% 1.63/1.53 inference(equality_resolution,[status(thm)],[f553])).
% 1.63/1.53 thf(f553,plain,(
% 1.63/1.53 ( ! [X2 : iS,X3 : iS,X0 : iS > iS,X1 : iS > iS,X4 : iS] : (((sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) != (X1 @ (sK1 @ (^[Y0 : iS]: (sK3 @ (X0 @ Y0) @ Y0 @ (X1 @ Y0)))))) | ((X0 @ (sK1 @ (^[Y0 : iS]: (sK3 @ (X0 @ Y0) @ Y0 @ (X1 @ Y0))))) != (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0)))) | ((^[Y0 : iS]: (Y0)) != X0) | ((sK3 @ (X0 @ c0) @ c0 @ (X1 @ c0)) = $false) | ($true = (sK3 @ X3 @ X3 @ X3)) | ((sK3 @ X4 @ X4 @ X4) = $true) | ($true = (sK3 @ (X0 @ X2) @ X2 @ (X1 @ X2))) | ((^[Y0 : iS]: (Y0)) != X1)) ) | ~spl0_4),
% 1.63/1.53 inference(beta_eta_normalization,[status(thm)],[f552])).
% 1.63/1.53 thf(f552,plain,(
% 1.63/1.53 ( ! [X2 : iS,X3 : iS,X0 : iS > iS,X1 : iS > iS,X4 : iS] : (((sK3 @ X4 @ X4 @ X4) = $true) | ($false = ((^[Y0 : iS]: (sK3 @ (X0 @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X1 @ Y0))) @ c0)) | ((X1 @ (sK1 @ (^[Y0 : iS]: (sK3 @ (X0 @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X1 @ Y0))))) != (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0)))) | ($true = (sK3 @ X3 @ X3 @ X3)) | (((^[Y0 : iS]: (sK3 @ (X0 @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X1 @ Y0))) @ X2) = $true) | ((^[Y0 : iS]: (X1 @ Y0)) != (^[Y0 : iS]: (Y0))) | ((^[Y0 : iS]: (X0 @ Y0)) != (^[Y0 : iS]: (Y0))) | ((X0 @ (sK1 @ (^[Y0 : iS]: (sK3 @ (X0 @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X1 @ Y0))))) != (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))))) ) | ~spl0_4),
% 1.63/1.53 inference(trivial_inequality_removal,[status(thm)],[f547])).
% 1.63/1.53 thf(f547,plain,(
% 1.63/1.53 ( ! [X2 : iS,X3 : iS,X0 : iS > iS,X1 : iS > iS,X4 : iS] : (((X0 @ (sK1 @ (^[Y0 : iS]: (sK3 @ (X0 @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X1 @ Y0))))) != (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0)))) | ((^[Y0 : iS]: (X0 @ Y0)) != (^[Y0 : iS]: (Y0))) | ($true = (sK3 @ X3 @ X3 @ X3)) | (((^[Y0 : iS]: (sK3 @ (X0 @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X1 @ Y0))) @ X2) = $true) | ((^[Y0 : iS]: (X1 @ Y0)) != (^[Y0 : iS]: (Y0))) | ((X1 @ (sK1 @ (^[Y0 : iS]: (sK3 @ (X0 @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X1 @ Y0))))) != (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0)))) | ($true = $false) | ((sK3 @ X4 @ X4 @ X4) = $true) | ($false = ((^[Y0 : iS]: (sK3 @ (X0 @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X1 @ Y0))) @ c0))) ) | ~spl0_4),
% 1.63/1.53 inference(constrained_superposition,[status(thm)],[f47,f541])).
% 1.63/1.53 thf(f541,plain,(
% 1.63/1.53 ( ! [X0 : iS,X1 : iS] : (((sK3 @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0)))) = $false) | ((sK3 @ X1 @ X1 @ X1) = $true) | ($true = (sK3 @ X0 @ X0 @ X0))) ) | ~spl0_4),
% 1.63/1.53 inference(trivial_inequality_removal,[status(thm)],[f540])).
% 1.63/1.53 thf(f540,plain,(
% 1.63/1.53 ( ! [X0 : iS,X1 : iS] : (($true = $false) | ((sK3 @ X1 @ X1 @ X1) = $true) | ($true = (sK3 @ X0 @ X0 @ X0)) | ((sK3 @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0)))) = $false)) ) | ~spl0_4),
% 1.63/1.53 inference(forward_demodulation,[status(thm)],[f539,f254])).
% 1.63/1.53 thf(f254,plain,(
% 1.63/1.53 ($true = (sK3 @ c0 @ c0 @ c0)) | ~spl0_4),
% 1.63/1.53 inference(avatar_component_clause,[status(thm)],[f252])).
% 1.63/1.53 thf(f252,definition,(
% 1.63/1.53 spl0_4 <=> ($true = (sK3 @ c0 @ c0 @ c0))),
% 1.63/1.53 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.63/1.53 thf(f539,plain,(
% 1.63/1.53 ( ! [X0 : iS,X1 : iS] : (((sK3 @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0)))) = $false) | ($true = (sK3 @ X0 @ X0 @ X0)) | ($false = (sK3 @ c0 @ c0 @ c0)) | ((sK3 @ X1 @ X1 @ X1) = $true)) ) | ~spl0_4),
% 1.63/1.53 inference(trivial_inequality_removal,[status(thm)],[f538])).
% 1.63/1.53 thf(f538,plain,(
% 1.63/1.53 ( ! [X0 : iS,X1 : iS] : (($false = (sK3 @ c0 @ c0 @ c0)) | ($true = (sK3 @ X0 @ X0 @ X0)) | ((sK3 @ X1 @ X1 @ X1) = $true) | ((sK2 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) != (sK2 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0)))) | ((sK3 @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0)))) = $false)) ) | ~spl0_4),
% 1.63/1.53 inference(beta_eta_normalization,[status(thm)],[f537])).
% 1.63/1.53 thf(f537,plain,(
% 1.63/1.53 ( ! [X0 : iS,X1 : iS] : (((sK3 @ X1 @ X1 @ X1) = $true) | ($true = (sK3 @ X0 @ ((^[Y0 : iS]: (Y0)) @ X0) @ ((^[Y0 : iS]: (Y0)) @ X0))) | ((sK3 @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0)))) = $false) | ($false = (sK3 @ c0 @ ((^[Y0 : iS]: (Y0)) @ c0) @ ((^[Y0 : iS]: (Y0)) @ c0))) | ((sK2 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) != ((^[Y0 : iS]: (Y0)) @ (sK2 @ (^[Y0 : iS]: (sK3 @ Y0 @ ((^[Y1 : iS]: (Y1)) @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0))))))) ) | ~spl0_4),
% 1.63/1.53 inference(trivial_inequality_removal,[status(thm)],[f536])).
% 1.63/1.53 thf(f536,plain,(
% 1.63/1.53 ( ! [X0 : iS,X1 : iS] : (($true = (sK3 @ X0 @ ((^[Y0 : iS]: (Y0)) @ X0) @ ((^[Y0 : iS]: (Y0)) @ X0))) | ($false = (sK3 @ c0 @ ((^[Y0 : iS]: (Y0)) @ c0) @ ((^[Y0 : iS]: (Y0)) @ c0))) | ((sK3 @ X1 @ X1 @ X1) = $true) | ((sK3 @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0)))) = $false) | ((^[Y0 : iS]: (Y0)) != (^[Y0 : iS]: (Y0))) | ((sK2 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) != ((^[Y0 : iS]: (Y0)) @ (sK2 @ (^[Y0 : iS]: (sK3 @ Y0 @ ((^[Y1 : iS]: (Y1)) @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0))))))) ) | ~spl0_4),
% 1.63/1.53 inference(duplicate_literal_removal,[status(thm)],[f533])).
% 1.63/1.53 thf(f533,plain,(
% 1.63/1.53 ( ! [X0 : iS,X1 : iS] : (((sK3 @ X1 @ X1 @ X1) = $true) | ((sK3 @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0)))) = $false) | ($false = (sK3 @ c0 @ ((^[Y0 : iS]: (Y0)) @ c0) @ ((^[Y0 : iS]: (Y0)) @ c0))) | ($true = (sK3 @ X0 @ ((^[Y0 : iS]: (Y0)) @ X0) @ ((^[Y0 : iS]: (Y0)) @ X0))) | ((^[Y0 : iS]: (Y0)) != (^[Y0 : iS]: (Y0))) | ((sK2 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) != ((^[Y0 : iS]: (Y0)) @ (sK2 @ (^[Y0 : iS]: (sK3 @ Y0 @ ((^[Y1 : iS]: (Y1)) @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0)))))) | ((^[Y0 : iS]: (Y0)) != (^[Y0 : iS]: (Y0)))) ) | ~spl0_4),
% 1.63/1.53 inference(equality_resolution,[status(thm)],[f524])).
% 1.63/1.53 thf(f524,plain,(
% 1.63/1.53 ( ! [X2 : iS,X3 : iS,X0 : iS > iS,X1 : iS > iS] : (((sK2 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) != (X1 @ (sK2 @ (^[Y0 : iS]: (sK3 @ Y0 @ (X0 @ Y0) @ (X1 @ Y0)))))) | ((sK3 @ c0 @ (X0 @ c0) @ (X1 @ c0)) = $false) | ($true = (sK3 @ X3 @ (X0 @ X3) @ (X1 @ X3))) | ((sK3 @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0)))) = $false) | ((sK2 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) != (X0 @ (sK2 @ (^[Y0 : iS]: (sK3 @ Y0 @ (X0 @ Y0) @ (X1 @ Y0)))))) | ($true = (sK3 @ X2 @ X2 @ X2)) | ((^[Y0 : iS]: (Y0)) != X1) | ((^[Y0 : iS]: (Y0)) != X0)) ) | ~spl0_4),
% 1.63/1.53 inference(beta_eta_normalization,[status(thm)],[f523])).
% 1.63/1.53 thf(f523,plain,(
% 1.63/1.53 ( ! [X2 : iS,X3 : iS,X0 : iS > iS,X1 : iS > iS] : (($true = ((^[Y0 : iS]: (sK3 @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X0 @ Y0) @ (X1 @ Y0))) @ X3)) | ((^[Y0 : iS]: (X0 @ Y0)) != (^[Y0 : iS]: (Y0))) | (((^[Y0 : iS]: (sK3 @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X0 @ Y0) @ (X1 @ Y0))) @ c0) = $false) | ($true = (sK3 @ X2 @ X2 @ X2)) | ((^[Y0 : iS]: (X1 @ Y0)) != (^[Y0 : iS]: (Y0))) | ((sK2 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) != (X0 @ (sK2 @ (^[Y0 : iS]: (sK3 @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X0 @ Y0) @ (X1 @ Y0)))))) | ((sK2 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) != (X1 @ (sK2 @ (^[Y0 : iS]: (sK3 @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X0 @ Y0) @ (X1 @ Y0)))))) | ((sK3 @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0)))) = $false)) ) | ~spl0_4),
% 1.63/1.53 inference(trivial_inequality_removal,[status(thm)],[f513])).
% 1.63/1.53 thf(f513,plain,(
% 1.63/1.53 ( ! [X2 : iS,X3 : iS,X0 : iS > iS,X1 : iS > iS] : (($true = $false) | ((sK3 @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0)))) = $false) | ($true = (sK3 @ X2 @ X2 @ X2)) | ((^[Y0 : iS]: (X0 @ Y0)) != (^[Y0 : iS]: (Y0))) | (((^[Y0 : iS]: (sK3 @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X0 @ Y0) @ (X1 @ Y0))) @ c0) = $false) | ($true = ((^[Y0 : iS]: (sK3 @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X0 @ Y0) @ (X1 @ Y0))) @ X3)) | ((^[Y0 : iS]: (X1 @ Y0)) != (^[Y0 : iS]: (Y0))) | ((sK2 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) != (X1 @ (sK2 @ (^[Y0 : iS]: (sK3 @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X0 @ Y0) @ (X1 @ Y0)))))) | ((sK2 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) != (X0 @ (sK2 @ (^[Y0 : iS]: (sK3 @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X0 @ Y0) @ (X1 @ Y0))))))) ) | ~spl0_4),
% 1.63/1.53 inference(constrained_superposition,[status(thm)],[f509,f48])).
% 1.63/1.53 thf(f48,plain,(
% 1.63/1.53 ( ! [X2 : iS,X1 : iS > $o] : (($true = (X1 @ (sK2 @ X1))) | ($true = (X1 @ X2)) | ((X1 @ c0) = $false)) )),
% 1.63/1.53 inference(binary_proxy_clausification,[status(thm)],[f46])).
% 1.63/1.53 thf(f46,plain,(
% 1.63/1.53 ( ! [X2 : iS,X1 : iS > $o] : (($true = (X1 @ X2)) | ($true = ((X1 @ (sK2 @ X1)) & (X1 @ (sK1 @ X1)))) | ((X1 @ c0) = $false)) )),
% 1.63/1.53 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 1.63/1.53 thf(f44,plain,(
% 1.63/1.53 ( ! [X2 : iS,X1 : iS > $o] : (($true = (X1 @ X2)) | ((X1 @ c0) = $false) | ($false = (((X1 @ (sK2 @ X1)) & (X1 @ (sK1 @ X1))) => (X1 @ (cP @ (sK2 @ X1) @ (sK1 @ X1)))))) )),
% 1.63/1.53 inference(beta_eta_normalization,[status(thm)],[f43])).
% 1.63/1.53 thf(f43,plain,(
% 1.63/1.53 ( ! [X2 : iS,X1 : iS > $o] : (($true = (X1 @ X2)) | ($false = ((^[Y0 : iS]: (((X1 @ Y0) & (X1 @ (sK1 @ X1))) => (X1 @ (cP @ Y0 @ (sK1 @ X1))))) @ (sK2 @ X1))) | ((X1 @ c0) = $false)) )),
% 1.63/1.53 inference(sigma_clausification,[status(thm)],[f42])).
% 1.63/1.53 thf(f42,plain,(
% 1.63/1.53 ( ! [X2 : iS,X1 : iS > $o] : (((X1 @ c0) = $false) | ($true = (X1 @ X2)) | ((!! @ iS @ (^[Y0 : iS]: (((X1 @ Y0) & (X1 @ (sK1 @ X1))) => (X1 @ (cP @ Y0 @ (sK1 @ X1)))))) = $false)) )),
% 1.63/1.53 inference(beta_eta_normalization,[status(thm)],[f41])).
% 1.63/1.53 thf(f41,plain,(
% 1.63/1.53 ( ! [X2 : iS,X1 : iS > $o] : (($true = (X1 @ X2)) | ((X1 @ c0) = $false) | ($false = ((^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (((X1 @ Y1) & (X1 @ Y0)) => (X1 @ (cP @ Y1 @ Y0)))))) @ (sK1 @ X1)))) )),
% 1.63/1.53 inference(sigma_clausification,[status(thm)],[f40])).
% 1.63/1.53 thf(f40,plain,(
% 1.63/1.53 ( ! [X2 : iS,X1 : iS > $o] : (((!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (((X1 @ Y1) & (X1 @ Y0)) => (X1 @ (cP @ Y1 @ Y0))))))) = $false) | ((X1 @ c0) = $false) | ($true = (X1 @ X2))) )),
% 1.63/1.53 inference(pi_clausification,[status(thm)],[f39])).
% 1.63/1.53 thf(f39,plain,(
% 1.63/1.53 ( ! [X1 : iS > $o] : (($true = (!! @ iS @ X1)) | ((!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (((X1 @ Y1) & (X1 @ Y0)) => (X1 @ (cP @ Y1 @ Y0))))))) = $false) | ((X1 @ c0) = $false)) )),
% 1.63/1.53 inference(binary_proxy_clausification,[status(thm)],[f38])).
% 1.63/1.53 thf(f38,plain,(
% 1.63/1.53 ( ! [X1 : iS > $o] : ((((X1 @ c0) & (!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (((X1 @ Y1) & (X1 @ Y0)) => (X1 @ (cP @ Y1 @ Y0)))))))) = $false) | ($true = (!! @ iS @ X1))) )),
% 1.63/1.53 inference(binary_proxy_clausification,[status(thm)],[f37])).
% 1.63/1.53 thf(f37,plain,(
% 1.63/1.53 ( ! [X1 : iS > $o] : (((((X1 @ c0) & (!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (((X1 @ Y1) & (X1 @ Y0)) => (X1 @ (cP @ Y1 @ Y0)))))))) => (!! @ iS @ X1)) = $true)) )),
% 1.63/1.53 inference(beta_eta_normalization,[status(thm)],[f36])).
% 1.63/1.53 thf(f36,plain,(
% 1.63/1.53 ( ! [X1 : iS > $o] : (($true = ((^[Y0 : iS > $o]: (((Y0 @ c0) & (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (((Y0 @ Y2) & (Y0 @ Y1)) => (Y0 @ (cP @ Y2 @ Y1)))))))) => (!! @ iS @ Y0))) @ X1))) )),
% 1.63/1.53 inference(pi_clausification,[status(thm)],[f28])).
% 1.63/1.53 thf(f28,plain,(
% 1.63/1.53 ($true = (!! @ (iS > $o) @ (^[Y0 : iS > $o]: (((Y0 @ c0) & (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (((Y0 @ Y2) & (Y0 @ Y1)) => (Y0 @ (cP @ Y2 @ Y1)))))))) => (!! @ iS @ Y0)))))),
% 1.63/1.53 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.63/1.53 thf(f13,plain,(
% 1.63/1.53 ($true = ((!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (~ (c0 = (cP @ Y1 @ Y0))))))) & (!! @ (iS > $o) @ (^[Y0 : iS > $o]: (((Y0 @ c0) & (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (((Y0 @ Y2) & (Y0 @ Y1)) => (Y0 @ (cP @ Y2 @ Y1)))))))) => (!! @ iS @ Y0))))))),
% 1.63/1.53 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.63/1.53 thf(f11,plain,(
% 1.63/1.53 ($true = (((!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (~ (c0 = (cP @ Y1 @ Y0))))))) & (!! @ (iS > $o) @ (^[Y0 : iS > $o]: (((Y0 @ c0) & (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (((Y0 @ Y2) & (Y0 @ Y1)) => (Y0 @ (cP @ Y2 @ Y1)))))))) => (!! @ iS @ Y0))))) & (!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (!! @ iS @ (^[Y3 : iS]: (((cP @ Y3 @ Y2) = (cP @ Y1 @ Y0)) => ((Y3 = Y1) & (Y2 = Y0)))))))))))))),
% 1.63/1.53 inference(binary_proxy_clausification,[status(thm)],[f9])).
% 1.63/1.53 thf(f509,plain,(
% 1.63/1.53 ( ! [X0 : iS] : (((sK3 @ (sK2 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) @ (sK2 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) @ (sK2 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0)))) = $false) | ($true = (sK3 @ X0 @ X0 @ X0)) | ((sK3 @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0)))) = $false)) ) | ~spl0_4),
% 1.63/1.53 inference(equality_resolution,[status(thm)],[f508])).
% 1.63/1.53 thf(f508,plain,(
% 1.63/1.53 ( ! [X0 : iS,X1 : iS] : (((sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) != X1) | ($true = (sK3 @ X0 @ X0 @ X0)) | ((sK3 @ (sK2 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) @ (sK2 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) @ (sK2 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0)))) = $false) | ((sK3 @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) @ X1 @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0)))) = $false)) ) | ~spl0_4),
% 1.63/1.53 inference(equality_resolution,[status(thm)],[f507])).
% 1.63/1.53 thf(f507,plain,(
% 1.63/1.53 ( ! [X2 : iS,X0 : iS,X1 : iS] : (((sK2 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) != X1) | ($true = (sK3 @ X2 @ X2 @ X2)) | ((sK3 @ (sK2 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) @ X1 @ (sK2 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0)))) = $false) | ((sK3 @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) @ X0 @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0)))) = $false) | ((sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) != X0)) ) | ~spl0_4),
% 1.63/1.53 inference(trivial_inequality_removal,[status(thm)],[f506])).
% 1.63/1.53 thf(f506,plain,(
% 1.63/1.53 ( ! [X2 : iS,X0 : iS,X1 : iS] : (((sK3 @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) @ X0 @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0)))) = $false) | ($true = (sK3 @ X2 @ X2 @ X2)) | ((sK3 @ (sK2 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) @ X1 @ (sK2 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0)))) = $false) | ((sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) != X0) | ($true = $false) | ((sK2 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) != X1)) ) | ~spl0_4),
% 1.63/1.53 inference(forward_demodulation,[status(thm)],[f504,f254])).
% 1.63/1.53 thf(f504,plain,(
% 1.63/1.53 ( ! [X2 : iS,X0 : iS,X1 : iS] : (((sK2 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) != X1) | ($true = (sK3 @ X2 @ X2 @ X2)) | ((sK3 @ (sK2 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) @ X1 @ (sK2 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0)))) = $false) | ((sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) != X0) | ((sK3 @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0))) @ X0 @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ Y0 @ Y0)))) = $false) | ($false = (sK3 @ c0 @ c0 @ c0))) )),
% 1.63/1.53 inference(beta_eta_normalization,[status(thm)],[f502])).
% 1.63/1.53 thf(f502,plain,(
% 1.63/1.53 ( ! [X2 : iS,X0 : iS,X1 : iS] : (((sK3 @ ((^[Y0 : iS]: (Y0)) @ c0) @ c0 @ c0) = $false) | ((sK2 @ (^[Y0 : iS]: (sK3 @ ((^[Y1 : iS]: (Y1)) @ Y0) @ Y0 @ Y0))) != X1) | ((sK3 @ ((^[Y0 : iS]: (Y0)) @ X2) @ X2 @ X2) = $true) | ($false = (sK3 @ (sK2 @ (^[Y0 : iS]: (sK3 @ ((^[Y1 : iS]: (Y1)) @ Y0) @ Y0 @ Y0))) @ X1 @ (sK2 @ (^[Y0 : iS]: (sK3 @ ((^[Y1 : iS]: (Y1)) @ Y0) @ Y0 @ Y0))))) | ((sK3 @ (sK1 @ (^[Y0 : iS]: (sK3 @ ((^[Y1 : iS]: (Y1)) @ Y0) @ Y0 @ Y0))) @ X0 @ (sK1 @ (^[Y0 : iS]: (sK3 @ ((^[Y1 : iS]: (Y1)) @ Y0) @ Y0 @ Y0)))) = $false) | ((sK1 @ (^[Y0 : iS]: (sK3 @ ((^[Y1 : iS]: (Y1)) @ Y0) @ Y0 @ Y0))) != X0)) )),
% 1.63/1.53 inference(equality_resolution,[status(thm)],[f501])).
% 1.63/1.53 thf(f501,plain,(
% 1.63/1.53 ( ! [X2 : iS,X3 : iS,X0 : iS > iS,X1 : iS,X4 : iS,X5 : iS] : (((cP @ X2 @ X4) != (X0 @ (cP @ (sK2 @ (^[Y0 : iS]: (sK3 @ (X0 @ Y0) @ Y0 @ Y0))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ (X0 @ Y0) @ Y0 @ Y0)))))) | ((sK3 @ (X0 @ c0) @ c0 @ c0) = $false) | ((sK1 @ (^[Y0 : iS]: (sK3 @ (X0 @ Y0) @ Y0 @ Y0))) != X1) | ($false = (sK3 @ X4 @ X1 @ (sK1 @ (^[Y0 : iS]: (sK3 @ (X0 @ Y0) @ Y0 @ Y0))))) | ((sK2 @ (^[Y0 : iS]: (sK3 @ (X0 @ Y0) @ Y0 @ Y0))) != X3) | ($false = (sK3 @ X2 @ X3 @ (sK2 @ (^[Y0 : iS]: (sK3 @ (X0 @ Y0) @ Y0 @ Y0))))) | ($true = (sK3 @ (X0 @ X5) @ X5 @ X5))) )),
% 1.63/1.53 inference(beta_eta_normalization,[status(thm)],[f498])).
% 1.63/1.53 thf(f498,plain,(
% 1.63/1.53 ( ! [X2 : iS,X3 : iS,X0 : iS > iS,X1 : iS,X4 : iS,X5 : iS] : (((sK1 @ (^[Y0 : iS]: (sK3 @ (X0 @ Y0) @ Y0 @ ((^[Y1 : iS]: (Y1)) @ Y0)))) != X1) | ($false = (sK3 @ (X0 @ c0) @ c0 @ ((^[Y0 : iS]: (Y0)) @ c0))) | ((sK2 @ (^[Y0 : iS]: (sK3 @ (X0 @ Y0) @ Y0 @ ((^[Y1 : iS]: (Y1)) @ Y0)))) != X3) | ((sK3 @ X4 @ X1 @ (sK1 @ (^[Y0 : iS]: (sK3 @ (X0 @ Y0) @ Y0 @ ((^[Y1 : iS]: (Y1)) @ Y0))))) = $false) | ((sK3 @ X2 @ X3 @ (sK2 @ (^[Y0 : iS]: (sK3 @ (X0 @ Y0) @ Y0 @ ((^[Y1 : iS]: (Y1)) @ Y0))))) = $false) | ($true = (sK3 @ (X0 @ X5) @ X5 @ ((^[Y0 : iS]: (Y0)) @ X5))) | ((X0 @ (cP @ (sK2 @ (^[Y0 : iS]: (sK3 @ (X0 @ Y0) @ Y0 @ ((^[Y1 : iS]: (Y1)) @ Y0)))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ (X0 @ Y0) @ Y0 @ ((^[Y1 : iS]: (Y1)) @ Y0)))))) != (cP @ X2 @ X4))) )),
% 1.63/1.53 inference(equality_resolution,[status(thm)],[f182])).
% 1.63/1.53 thf(f182,plain,(
% 1.63/1.53 ( ! [X2 : iS > iS,X3 : iS > iS,X0 : iS,X1 : iS,X8 : iS,X6 : iS,X7 : iS,X4 : iS,X5 : iS] : (((cP @ X4 @ X5) != (X3 @ (cP @ (sK2 @ (^[Y0 : iS]: (sK3 @ (X2 @ Y0) @ Y0 @ (X3 @ Y0)))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ (X2 @ Y0) @ Y0 @ (X3 @ Y0))))))) | ((sK1 @ (^[Y0 : iS]: (sK3 @ (X2 @ Y0) @ Y0 @ (X3 @ Y0)))) != X6) | ($false = (sK3 @ X0 @ X7 @ X4)) | ((sK3 @ X1 @ X6 @ X5) = $false) | ((cP @ X0 @ X1) != (X2 @ (cP @ (sK2 @ (^[Y0 : iS]: (sK3 @ (X2 @ Y0) @ Y0 @ (X3 @ Y0)))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ (X2 @ Y0) @ Y0 @ (X3 @ Y0))))))) | ((sK2 @ (^[Y0 : iS]: (sK3 @ (X2 @ Y0) @ Y0 @ (X3 @ Y0)))) != X7) | ($true = (sK3 @ (X2 @ X8) @ X8 @ (X3 @ X8))) | ((sK3 @ (X2 @ c0) @ c0 @ (X3 @ c0)) = $false)) )),
% 1.63/1.53 inference(beta_eta_normalization,[status(thm)],[f181])).
% 1.63/1.53 thf(f181,plain,(
% 1.63/1.53 ( ! [X2 : iS > iS,X3 : iS > iS,X0 : iS,X1 : iS,X8 : iS,X6 : iS,X7 : iS,X4 : iS,X5 : iS] : ((((^[Y0 : iS]: (sK3 @ (X2 @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X3 @ Y0))) @ c0) = $false) | ($false = (sK3 @ X0 @ X7 @ X4)) | ((sK1 @ (^[Y0 : iS]: (sK3 @ (X2 @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X3 @ Y0)))) != X6) | ((sK3 @ X1 @ X6 @ X5) = $false) | ((sK2 @ (^[Y0 : iS]: (sK3 @ (X2 @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X3 @ Y0)))) != X7) | ((cP @ X4 @ X5) != (X3 @ (cP @ (sK2 @ (^[Y0 : iS]: (sK3 @ (X2 @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X3 @ Y0)))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ (X2 @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X3 @ Y0))))))) | ((cP @ X0 @ X1) != (X2 @ (cP @ (sK2 @ (^[Y0 : iS]: (sK3 @ (X2 @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X3 @ Y0)))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ (X2 @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X3 @ Y0))))))) | ($true = ((^[Y0 : iS]: (sK3 @ (X2 @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X3 @ Y0))) @ X8))) )),
% 1.63/1.53 inference(trivial_inequality_removal,[status(thm)],[f176])).
% 1.63/1.53 thf(f176,plain,(
% 1.63/1.53 ( ! [X2 : iS > iS,X3 : iS > iS,X0 : iS,X1 : iS,X8 : iS,X6 : iS,X7 : iS,X4 : iS,X5 : iS] : ((((^[Y0 : iS]: (sK3 @ (X2 @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X3 @ Y0))) @ c0) = $false) | ($true = ((^[Y0 : iS]: (sK3 @ (X2 @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X3 @ Y0))) @ X8)) | ($false = (sK3 @ X0 @ X7 @ X4)) | ($true = $false) | ((sK2 @ (^[Y0 : iS]: (sK3 @ (X2 @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X3 @ Y0)))) != X7) | ((cP @ X4 @ X5) != (X3 @ (cP @ (sK2 @ (^[Y0 : iS]: (sK3 @ (X2 @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X3 @ Y0)))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ (X2 @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X3 @ Y0))))))) | ((sK3 @ X1 @ X6 @ X5) = $false) | ((sK1 @ (^[Y0 : iS]: (sK3 @ (X2 @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X3 @ Y0)))) != X6) | ((cP @ X0 @ X1) != (X2 @ (cP @ (sK2 @ (^[Y0 : iS]: (sK3 @ (X2 @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X3 @ Y0)))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ (X2 @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X3 @ Y0)))))))) )),
% 1.63/1.53 inference(constrained_superposition,[status(thm)],[f45,f170])).
% 1.63/1.53 thf(f170,plain,(
% 1.63/1.53 ( ! [X2 : iS,X3 : iS,X0 : iS,X1 : iS,X4 : iS,X5 : iS] : (($true = (sK3 @ (cP @ X0 @ X1) @ (cP @ X2 @ X3) @ (cP @ X4 @ X5))) | ($false = (sK3 @ X0 @ X2 @ X4)) | ((sK3 @ X1 @ X3 @ X5) = $false)) )),
% 1.63/1.53 inference(equality_resolution,[status(thm)],[f169])).
% 1.63/1.53 thf(f169,plain,(
% 1.63/1.53 ( ! [X2 : iS,X3 : iS,X0 : iS,X1 : iS,X6 : iS,X4 : iS,X5 : iS] : (((cP @ X1 @ X3) != X4) | ($true = (sK3 @ (cP @ X0 @ X5) @ X4 @ (cP @ X2 @ X6))) | ((sK3 @ X0 @ X1 @ X2) = $false) | ((sK3 @ X5 @ X3 @ X6) = $false)) )),
% 1.63/1.53 inference(equality_resolution,[status(thm)],[f168])).
% 1.63/1.53 thf(f168,plain,(
% 1.63/1.53 ( ! [X2 : iS,X3 : iS,X0 : iS,X1 : iS,X6 : iS,X7 : iS,X4 : iS,X5 : iS] : (((cP @ X7 @ X5) != X3) | ((sK3 @ X0 @ X6 @ X7) = $false) | ((cP @ X6 @ X4) != X2) | ($false = (sK3 @ X1 @ X4 @ X5)) | ($true = (sK3 @ (cP @ X0 @ X1) @ X2 @ X3))) )),
% 1.63/1.53 inference(equality_resolution,[status(thm)],[f85])).
% 1.63/1.53 thf(f85,plain,(
% 1.63/1.53 ( ! [X2 : iS,X3 : iS,X1 : iS,X8 : iS,X6 : iS,X9 : iS,X7 : iS,X4 : iS,X5 : iS] : (((cP @ X9 @ X4) != X1) | ($true = (sK3 @ X1 @ X3 @ X2)) | ($false = (sK3 @ X4 @ X7 @ X5)) | ((cP @ X6 @ X7) != X3) | ($false = (sK3 @ X9 @ X6 @ X8)) | ((cP @ X8 @ X5) != X2)) )),
% 1.63/1.53 inference(equality_proxy_clausification,[status(thm)],[f84])).
% 1.63/1.53 thf(f84,plain,(
% 1.63/1.53 ( ! [X2 : iS,X3 : iS,X1 : iS,X8 : iS,X6 : iS,X9 : iS,X7 : iS,X4 : iS,X5 : iS] : (($false = (sK3 @ X9 @ X6 @ X8)) | (((cP @ X9 @ X4) = X1) = $false) | ($true = (sK3 @ X1 @ X3 @ X2)) | ((cP @ X6 @ X7) != X3) | ($false = (sK3 @ X4 @ X7 @ X5)) | ((cP @ X8 @ X5) != X2)) )),
% 1.63/1.53 inference(binary_proxy_clausification,[status(thm)],[f83])).
% 1.63/1.53 thf(f83,plain,(
% 1.63/1.53 ( ! [X2 : iS,X3 : iS,X1 : iS,X8 : iS,X6 : iS,X9 : iS,X7 : iS,X4 : iS,X5 : iS] : (((cP @ X8 @ X5) != X2) | (((sK3 @ X4 @ X7 @ X5) & ((cP @ X9 @ X4) = X1)) = $false) | ($false = (sK3 @ X9 @ X6 @ X8)) | ((cP @ X6 @ X7) != X3) | ($true = (sK3 @ X1 @ X3 @ X2))) )),
% 1.63/1.53 inference(binary_proxy_clausification,[status(thm)],[f82])).
% 1.63/1.53 thf(f82,plain,(
% 1.63/1.53 ( ! [X2 : iS,X3 : iS,X1 : iS,X8 : iS,X6 : iS,X9 : iS,X7 : iS,X4 : iS,X5 : iS] : (($false = (((sK3 @ X4 @ X7 @ X5) & ((cP @ X9 @ X4) = X1)) & (sK3 @ X9 @ X6 @ X8))) | ($true = (sK3 @ X1 @ X3 @ X2)) | ((cP @ X8 @ X5) != X2) | ((cP @ X6 @ X7) != X3)) )),
% 1.63/1.53 inference(equality_proxy_clausification,[status(thm)],[f81])).
% 1.63/1.53 thf(f81,plain,(
% 1.63/1.53 ( ! [X2 : iS,X3 : iS,X1 : iS,X8 : iS,X6 : iS,X9 : iS,X7 : iS,X4 : iS,X5 : iS] : ((((cP @ X6 @ X7) = X3) = $false) | ($false = (((sK3 @ X4 @ X7 @ X5) & ((cP @ X9 @ X4) = X1)) & (sK3 @ X9 @ X6 @ X8))) | ((cP @ X8 @ X5) != X2) | ($true = (sK3 @ X1 @ X3 @ X2))) )),
% 1.63/1.53 inference(binary_proxy_clausification,[status(thm)],[f80])).
% 1.63/1.53 thf(f80,plain,(
% 1.63/1.53 ( ! [X2 : iS,X3 : iS,X1 : iS,X8 : iS,X6 : iS,X9 : iS,X7 : iS,X4 : iS,X5 : iS] : (($false = ((((sK3 @ X4 @ X7 @ X5) & ((cP @ X9 @ X4) = X1)) & (sK3 @ X9 @ X6 @ X8)) & ((cP @ X6 @ X7) = X3))) | ((cP @ X8 @ X5) != X2) | ($true = (sK3 @ X1 @ X3 @ X2))) )),
% 1.63/1.53 inference(equality_proxy_clausification,[status(thm)],[f79])).
% 1.63/1.53 thf(f79,plain,(
% 1.63/1.53 ( ! [X2 : iS,X3 : iS,X1 : iS,X8 : iS,X6 : iS,X9 : iS,X7 : iS,X4 : iS,X5 : iS] : ((((cP @ X8 @ X5) = X2) = $false) | ($true = (sK3 @ X1 @ X3 @ X2)) | ($false = ((((sK3 @ X4 @ X7 @ X5) & ((cP @ X9 @ X4) = X1)) & (sK3 @ X9 @ X6 @ X8)) & ((cP @ X6 @ X7) = X3)))) )),
% 1.63/1.53 inference(binary_proxy_clausification,[status(thm)],[f78])).
% 1.63/1.53 thf(f78,plain,(
% 1.63/1.53 ( ! [X2 : iS,X3 : iS,X1 : iS,X8 : iS,X6 : iS,X9 : iS,X7 : iS,X4 : iS,X5 : iS] : (((((((sK3 @ X4 @ X7 @ X5) & ((cP @ X9 @ X4) = X1)) & (sK3 @ X9 @ X6 @ X8)) & ((cP @ X6 @ X7) = X3)) & ((cP @ X8 @ X5) = X2)) = $false) | ($true = (sK3 @ X1 @ X3 @ X2))) )),
% 1.63/1.53 inference(beta_eta_normalization,[status(thm)],[f77])).
% 1.63/1.53 thf(f77,plain,(
% 1.63/1.53 ( ! [X2 : iS,X3 : iS,X1 : iS,X8 : iS,X6 : iS,X9 : iS,X7 : iS,X4 : iS,X5 : iS] : (($true = (sK3 @ X1 @ X3 @ X2)) | (((^[Y0 : iS]: (((((sK3 @ X4 @ X7 @ X5) & ((cP @ Y0 @ X4) = X1)) & (sK3 @ Y0 @ X6 @ X8)) & ((cP @ X6 @ X7) = X3)) & ((cP @ X8 @ X5) = X2))) @ X9) = $false)) )),
% 1.63/1.53 inference(pi_clausification,[status(thm)],[f76])).
% 1.63/1.53 thf(f76,plain,(
% 1.63/1.53 ( ! [X2 : iS,X3 : iS,X1 : iS,X8 : iS,X6 : iS,X7 : iS,X4 : iS,X5 : iS] : (((?? @ iS @ (^[Y0 : iS]: (((((sK3 @ X4 @ X7 @ X5) & ((cP @ Y0 @ X4) = X1)) & (sK3 @ Y0 @ X6 @ X8)) & ((cP @ X6 @ X7) = X3)) & ((cP @ X8 @ X5) = X2)))) = $false) | ($true = (sK3 @ X1 @ X3 @ X2))) )),
% 1.63/1.53 inference(beta_eta_normalization,[status(thm)],[f75])).
% 1.63/1.53 thf(f75,plain,(
% 1.63/1.53 ( ! [X2 : iS,X3 : iS,X1 : iS,X8 : iS,X6 : iS,X7 : iS,X4 : iS,X5 : iS] : (($true = (sK3 @ X1 @ X3 @ X2)) | ($false = ((^[Y0 : iS]: (?? @ iS @ (^[Y1 : iS]: (((((sK3 @ X4 @ X7 @ X5) & ((cP @ Y1 @ X4) = X1)) & (sK3 @ Y1 @ X6 @ Y0)) & ((cP @ X6 @ X7) = X3)) & ((cP @ Y0 @ X5) = X2))))) @ X8))) )),
% 1.63/1.53 inference(pi_clausification,[status(thm)],[f74])).
% 1.63/1.53 thf(f74,plain,(
% 1.63/1.53 ( ! [X2 : iS,X3 : iS,X1 : iS,X6 : iS,X7 : iS,X4 : iS,X5 : iS] : (($true = (sK3 @ X1 @ X3 @ X2)) | ((?? @ iS @ (^[Y0 : iS]: (?? @ iS @ (^[Y1 : iS]: (((((sK3 @ X4 @ X7 @ X5) & ((cP @ Y1 @ X4) = X1)) & (sK3 @ Y1 @ X6 @ Y0)) & ((cP @ X6 @ X7) = X3)) & ((cP @ Y0 @ X5) = X2)))))) = $false)) )),
% 1.63/1.53 inference(beta_eta_normalization,[status(thm)],[f73])).
% 1.63/1.53 thf(f73,plain,(
% 1.63/1.53 ( ! [X2 : iS,X3 : iS,X1 : iS,X6 : iS,X7 : iS,X4 : iS,X5 : iS] : (($false = ((^[Y0 : iS]: (?? @ iS @ (^[Y1 : iS]: (?? @ iS @ (^[Y2 : iS]: (((((sK3 @ X4 @ Y0 @ X5) & ((cP @ Y2 @ X4) = X1)) & (sK3 @ Y2 @ X6 @ Y1)) & ((cP @ X6 @ Y0) = X3)) & ((cP @ Y1 @ X5) = X2))))))) @ X7)) | ($true = (sK3 @ X1 @ X3 @ X2))) )),
% 1.63/1.53 inference(pi_clausification,[status(thm)],[f72])).
% 1.63/1.53 thf(f72,plain,(
% 1.63/1.53 ( ! [X2 : iS,X3 : iS,X1 : iS,X6 : iS,X4 : iS,X5 : iS] : (($true = (sK3 @ X1 @ X3 @ X2)) | ((?? @ iS @ (^[Y0 : iS]: (?? @ iS @ (^[Y1 : iS]: (?? @ iS @ (^[Y2 : iS]: (((((sK3 @ X4 @ Y0 @ X5) & ((cP @ Y2 @ X4) = X1)) & (sK3 @ Y2 @ X6 @ Y1)) & ((cP @ X6 @ Y0) = X3)) & ((cP @ Y1 @ X5) = X2)))))))) = $false)) )),
% 1.63/1.53 inference(beta_eta_normalization,[status(thm)],[f71])).
% 1.63/1.53 thf(f71,plain,(
% 1.63/1.53 ( ! [X2 : iS,X3 : iS,X1 : iS,X6 : iS,X4 : iS,X5 : iS] : (($false = ((^[Y0 : iS]: (?? @ iS @ (^[Y1 : iS]: (?? @ iS @ (^[Y2 : iS]: (?? @ iS @ (^[Y3 : iS]: (((((sK3 @ X4 @ Y1 @ X5) & ((cP @ Y3 @ X4) = X1)) & (sK3 @ Y3 @ Y0 @ Y2)) & ((cP @ Y0 @ Y1) = X3)) & ((cP @ Y2 @ X5) = X2))))))))) @ X6)) | ($true = (sK3 @ X1 @ X3 @ X2))) )),
% 1.63/1.53 inference(pi_clausification,[status(thm)],[f70])).
% 1.63/1.53 thf(f70,plain,(
% 1.63/1.53 ( ! [X2 : iS,X3 : iS,X1 : iS,X4 : iS,X5 : iS] : (((?? @ iS @ (^[Y0 : iS]: (?? @ iS @ (^[Y1 : iS]: (?? @ iS @ (^[Y2 : iS]: (?? @ iS @ (^[Y3 : iS]: (((((sK3 @ X4 @ Y1 @ X5) & ((cP @ Y3 @ X4) = X1)) & (sK3 @ Y3 @ Y0 @ Y2)) & ((cP @ Y0 @ Y1) = X3)) & ((cP @ Y2 @ X5) = X2)))))))))) = $false) | ($true = (sK3 @ X1 @ X3 @ X2))) )),
% 1.63/1.53 inference(beta_eta_normalization,[status(thm)],[f69])).
% 1.63/1.53 thf(f69,plain,(
% 1.63/1.53 ( ! [X2 : iS,X3 : iS,X1 : iS,X4 : iS,X5 : iS] : ((((^[Y0 : iS]: (?? @ iS @ (^[Y1 : iS]: (?? @ iS @ (^[Y2 : iS]: (?? @ iS @ (^[Y3 : iS]: (?? @ iS @ (^[Y4 : iS]: (((((sK3 @ X4 @ Y2 @ Y0) & ((cP @ Y4 @ X4) = X1)) & (sK3 @ Y4 @ Y1 @ Y3)) & ((cP @ Y1 @ Y2) = X3)) & ((cP @ Y3 @ Y0) = X2))))))))))) @ X5) = $false) | ($true = (sK3 @ X1 @ X3 @ X2))) )),
% 1.63/1.53 inference(pi_clausification,[status(thm)],[f68])).
% 1.63/1.53 thf(f68,plain,(
% 1.63/1.53 ( ! [X2 : iS,X3 : iS,X1 : iS,X4 : iS] : (((?? @ iS @ (^[Y0 : iS]: (?? @ iS @ (^[Y1 : iS]: (?? @ iS @ (^[Y2 : iS]: (?? @ iS @ (^[Y3 : iS]: (?? @ iS @ (^[Y4 : iS]: (((((sK3 @ X4 @ Y2 @ Y0) & ((cP @ Y4 @ X4) = X1)) & (sK3 @ Y4 @ Y1 @ Y3)) & ((cP @ Y1 @ Y2) = X3)) & ((cP @ Y3 @ Y0) = X2)))))))))))) = $false) | ($true = (sK3 @ X1 @ X3 @ X2))) )),
% 1.63/1.53 inference(beta_eta_normalization,[status(thm)],[f67])).
% 1.63/1.53 thf(f67,plain,(
% 1.63/1.53 ( ! [X2 : iS,X3 : iS,X1 : iS,X4 : iS] : ((((^[Y0 : iS]: (?? @ iS @ (^[Y1 : iS]: (?? @ iS @ (^[Y2 : iS]: (?? @ iS @ (^[Y3 : iS]: (?? @ iS @ (^[Y4 : iS]: (?? @ iS @ (^[Y5 : iS]: (((((sK3 @ Y0 @ Y3 @ Y1) & ((cP @ Y5 @ Y0) = X1)) & (sK3 @ Y5 @ Y2 @ Y4)) & ((cP @ Y2 @ Y3) = X3)) & ((cP @ Y4 @ Y1) = X2))))))))))))) @ X4) = $false) | ($true = (sK3 @ X1 @ X3 @ X2))) )),
% 1.63/1.53 inference(pi_clausification,[status(thm)],[f66])).
% 1.63/1.53 thf(f66,plain,(
% 1.63/1.53 ( ! [X2 : iS,X3 : iS,X1 : iS] : (((?? @ iS @ (^[Y0 : iS]: (?? @ iS @ (^[Y1 : iS]: (?? @ iS @ (^[Y2 : iS]: (?? @ iS @ (^[Y3 : iS]: (?? @ iS @ (^[Y4 : iS]: (?? @ iS @ (^[Y5 : iS]: (((((sK3 @ Y0 @ Y3 @ Y1) & ((cP @ Y5 @ Y0) = X1)) & (sK3 @ Y5 @ Y2 @ Y4)) & ((cP @ Y2 @ Y3) = X3)) & ((cP @ Y4 @ Y1) = X2)))))))))))))) = $false) | ($true = (sK3 @ X1 @ X3 @ X2))) )),
% 1.63/1.53 inference(binary_proxy_clausification,[status(thm)],[f61])).
% 1.63/1.53 thf(f45,plain,(
% 1.63/1.53 ( ! [X2 : iS,X1 : iS > $o] : (($false = (X1 @ (cP @ (sK2 @ X1) @ (sK1 @ X1)))) | ($true = (X1 @ X2)) | ((X1 @ c0) = $false)) )),
% 1.63/1.53 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 1.63/1.53 thf(f47,plain,(
% 1.63/1.53 ( ! [X2 : iS,X1 : iS > $o] : (($true = (X1 @ (sK1 @ X1))) | ($true = (X1 @ X2)) | ((X1 @ c0) = $false)) )),
% 1.63/1.53 inference(binary_proxy_clausification,[status(thm)],[f46])).
% 1.63/1.53 thf(f308,plain,(
% 1.63/1.53 ( ! [X0 : iS] : (((sK3 @ X0 @ c0 @ X0) = $true)) ) | ~spl0_10),
% 1.63/1.53 inference(avatar_component_clause,[status(thm)],[f307])).
% 1.63/1.53 thf(f307,definition,(
% 1.63/1.53 spl0_10 <=> ! [X0 : iS] : ((sK3 @ X0 @ c0 @ X0) = $true)),
% 1.63/1.53 introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition])).
% 1.63/1.53 thf(f337,plain,(
% 1.63/1.53 ~spl0_9),
% 1.63/1.53 inference(avatar_contradiction_clause,[status(thm)],[f336])).
% 1.63/1.53 thf(f336,plain,(
% 1.63/1.53 $false | ~spl0_9),
% 1.63/1.53 inference(equality_resolution,[status(thm)],[f335])).
% 1.63/1.53 thf(f335,plain,(
% 1.63/1.53 ( ! [X0 : iS] : (((cP @ (sK2 @ (^[Y0 : iS]: (sK3 @ Y0 @ c0 @ Y0))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ c0 @ Y0)))) != X0)) ) | ~spl0_9),
% 1.63/1.53 inference(duplicate_literal_removal,[status(thm)],[f334])).
% 1.63/1.53 thf(f334,plain,(
% 1.63/1.53 ( ! [X0 : iS] : (((cP @ (sK2 @ (^[Y0 : iS]: (sK3 @ Y0 @ c0 @ Y0))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ c0 @ Y0)))) != X0) | ((cP @ (sK2 @ (^[Y0 : iS]: (sK3 @ Y0 @ c0 @ Y0))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ c0 @ Y0)))) != X0)) ) | ~spl0_9),
% 1.63/1.53 inference(equality_resolution,[status(thm)],[f305])).
% 1.63/1.53 thf(f305,plain,(
% 1.63/1.53 ( ! [X2 : iS,X1 : iS] : (((cP @ (sK2 @ (^[Y0 : iS]: (sK3 @ Y0 @ c0 @ Y0))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ c0 @ Y0)))) != X2) | ((cP @ (sK2 @ (^[Y0 : iS]: (sK3 @ Y0 @ c0 @ Y0))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ c0 @ Y0)))) != X1) | (X1 != X2)) ) | ~spl0_9),
% 1.63/1.53 inference(avatar_component_clause,[status(thm)],[f304])).
% 1.63/1.53 thf(f304,definition,(
% 1.63/1.53 spl0_9 <=> ! [X2 : iS,X1 : iS] : ((X1 != X2) | ((cP @ (sK2 @ (^[Y0 : iS]: (sK3 @ Y0 @ c0 @ Y0))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ c0 @ Y0)))) != X2) | ((cP @ (sK2 @ (^[Y0 : iS]: (sK3 @ Y0 @ c0 @ Y0))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ c0 @ Y0)))) != X1))),
% 1.63/1.53 introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition])).
% 1.63/1.53 thf(f312,plain,(
% 1.63/1.53 spl0_9 | spl0_10 | ~spl0_4),
% 1.63/1.53 inference(avatar_split_clause,[status(thm)],[f270,f252,f307,f304])).
% 1.63/1.53 thf(f270,plain,(
% 1.63/1.53 ( ! [X2 : iS,X0 : iS,X1 : iS] : (((cP @ (sK2 @ (^[Y0 : iS]: (sK3 @ Y0 @ c0 @ Y0))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ c0 @ Y0)))) != X2) | ((sK3 @ X0 @ c0 @ X0) = $true) | (X1 != X2) | ((cP @ (sK2 @ (^[Y0 : iS]: (sK3 @ Y0 @ c0 @ Y0))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ Y0 @ c0 @ Y0)))) != X1)) ) | ~spl0_4),
% 1.63/1.53 inference(beta_eta_normalization,[status(thm)],[f269])).
% 1.63/1.53 thf(f269,plain,(
% 1.63/1.53 ( ! [X2 : iS,X0 : iS,X1 : iS] : ((((^[Y0 : iS]: (Y0)) @ (cP @ (sK2 @ (^[Y0 : iS]: (sK3 @ ((^[Y1 : iS]: (Y1)) @ Y0) @ c0 @ ((^[Y1 : iS]: (Y1)) @ Y0)))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ ((^[Y1 : iS]: (Y1)) @ Y0) @ c0 @ ((^[Y1 : iS]: (Y1)) @ Y0)))))) != X2) | (((^[Y0 : iS]: (Y0)) @ (cP @ (sK2 @ (^[Y0 : iS]: (sK3 @ ((^[Y1 : iS]: (Y1)) @ Y0) @ c0 @ ((^[Y1 : iS]: (Y1)) @ Y0)))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ ((^[Y1 : iS]: (Y1)) @ Y0) @ c0 @ ((^[Y1 : iS]: (Y1)) @ Y0)))))) != X1) | ((sK3 @ ((^[Y0 : iS]: (Y0)) @ X0) @ c0 @ ((^[Y0 : iS]: (Y0)) @ X0)) = $true) | (X1 != X2)) ) | ~spl0_4),
% 1.63/1.53 inference(trivial_inequality_removal,[status(thm)],[f264])).
% 1.63/1.53 thf(f264,plain,(
% 1.63/1.53 ( ! [X2 : iS,X0 : iS,X1 : iS] : (($true = $false) | ((sK3 @ ((^[Y0 : iS]: (Y0)) @ X0) @ c0 @ ((^[Y0 : iS]: (Y0)) @ X0)) = $true) | (X1 != X2) | (((^[Y0 : iS]: (Y0)) @ (cP @ (sK2 @ (^[Y0 : iS]: (sK3 @ ((^[Y1 : iS]: (Y1)) @ Y0) @ c0 @ ((^[Y1 : iS]: (Y1)) @ Y0)))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ ((^[Y1 : iS]: (Y1)) @ Y0) @ c0 @ ((^[Y1 : iS]: (Y1)) @ Y0)))))) != X2) | (((^[Y0 : iS]: (Y0)) @ (cP @ (sK2 @ (^[Y0 : iS]: (sK3 @ ((^[Y1 : iS]: (Y1)) @ Y0) @ c0 @ ((^[Y1 : iS]: (Y1)) @ Y0)))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ ((^[Y1 : iS]: (Y1)) @ Y0) @ c0 @ ((^[Y1 : iS]: (Y1)) @ Y0)))))) != X1)) ) | ~spl0_4),
% 1.63/1.53 inference(superposition,[status(thm)],[f143,f254])).
% 1.63/1.53 thf(f143,plain,(
% 1.63/1.53 ( ! [X2 : iS,X3 : iS,X0 : iS > iS,X1 : iS > iS,X4 : iS] : (((sK3 @ (X0 @ c0) @ c0 @ (X1 @ c0)) = $false) | ((sK3 @ (X0 @ X4) @ c0 @ (X1 @ X4)) = $true) | ((X0 @ (cP @ (sK2 @ (^[Y0 : iS]: (sK3 @ (X0 @ Y0) @ c0 @ (X1 @ Y0)))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ (X0 @ Y0) @ c0 @ (X1 @ Y0)))))) != X2) | ((X1 @ (cP @ (sK2 @ (^[Y0 : iS]: (sK3 @ (X0 @ Y0) @ c0 @ (X1 @ Y0)))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ (X0 @ Y0) @ c0 @ (X1 @ Y0)))))) != X3) | (X2 != X3)) )),
% 1.63/1.53 inference(beta_eta_normalization,[status(thm)],[f142])).
% 1.63/1.53 thf(f142,plain,(
% 1.63/1.53 ( ! [X2 : iS,X3 : iS,X0 : iS > iS,X1 : iS > iS,X4 : iS] : (((X1 @ (cP @ (sK2 @ (^[Y0 : iS]: (sK3 @ (X0 @ Y0) @ ((^[Y1 : iS]: (c0)) @ Y0) @ (X1 @ Y0)))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ (X0 @ Y0) @ ((^[Y1 : iS]: (c0)) @ Y0) @ (X1 @ Y0)))))) != X3) | ($true = ((^[Y0 : iS]: (sK3 @ (X0 @ Y0) @ ((^[Y1 : iS]: (c0)) @ Y0) @ (X1 @ Y0))) @ X4)) | ((X0 @ (cP @ (sK2 @ (^[Y0 : iS]: (sK3 @ (X0 @ Y0) @ ((^[Y1 : iS]: (c0)) @ Y0) @ (X1 @ Y0)))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ (X0 @ Y0) @ ((^[Y1 : iS]: (c0)) @ Y0) @ (X1 @ Y0)))))) != X2) | ($false = ((^[Y0 : iS]: (sK3 @ (X0 @ Y0) @ ((^[Y1 : iS]: (c0)) @ Y0) @ (X1 @ Y0))) @ c0)) | (X2 != X3)) )),
% 1.63/1.53 inference(trivial_inequality_removal,[status(thm)],[f130])).
% 1.63/1.53 thf(f130,plain,(
% 1.63/1.53 ( ! [X2 : iS,X3 : iS,X0 : iS > iS,X1 : iS > iS,X4 : iS] : (($true = ((^[Y0 : iS]: (sK3 @ (X0 @ Y0) @ ((^[Y1 : iS]: (c0)) @ Y0) @ (X1 @ Y0))) @ X4)) | ($false = ((^[Y0 : iS]: (sK3 @ (X0 @ Y0) @ ((^[Y1 : iS]: (c0)) @ Y0) @ (X1 @ Y0))) @ c0)) | (X2 != X3) | ((X0 @ (cP @ (sK2 @ (^[Y0 : iS]: (sK3 @ (X0 @ Y0) @ ((^[Y1 : iS]: (c0)) @ Y0) @ (X1 @ Y0)))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ (X0 @ Y0) @ ((^[Y1 : iS]: (c0)) @ Y0) @ (X1 @ Y0)))))) != X2) | ((X1 @ (cP @ (sK2 @ (^[Y0 : iS]: (sK3 @ (X0 @ Y0) @ ((^[Y1 : iS]: (c0)) @ Y0) @ (X1 @ Y0)))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ (X0 @ Y0) @ ((^[Y1 : iS]: (c0)) @ Y0) @ (X1 @ Y0)))))) != X3) | ($true = $false)) )),
% 1.63/1.53 inference(constrained_superposition,[status(thm)],[f45,f93])).
% 1.63/1.53 thf(f93,plain,(
% 1.63/1.53 ( ! [X0 : iS,X1 : iS] : (($true = (sK3 @ X0 @ c0 @ X1)) | (X0 != X1)) )),
% 1.63/1.53 inference(equality_resolution,[status(thm)],[f64])).
% 1.63/1.53 thf(f64,plain,(
% 1.63/1.53 ( ! [X2 : iS,X3 : iS,X1 : iS] : ((c0 != X3) | ($true = (sK3 @ X1 @ X3 @ X2)) | (X1 != X2)) )),
% 1.63/1.53 inference(equality_proxy_clausification,[status(thm)],[f63])).
% 1.63/1.53 thf(f63,plain,(
% 1.63/1.53 ( ! [X2 : iS,X3 : iS,X1 : iS] : (((c0 = X3) = $false) | ($true = (sK3 @ X1 @ X3 @ X2)) | (X1 != X2)) )),
% 1.63/1.53 inference(equality_proxy_clausification,[status(thm)],[f62])).
% 1.63/1.53 thf(f62,plain,(
% 1.63/1.53 ( ! [X2 : iS,X3 : iS,X1 : iS] : (($true = (sK3 @ X1 @ X3 @ X2)) | ($false = (X2 = X1)) | ((c0 = X3) = $false)) )),
% 1.63/1.53 inference(binary_proxy_clausification,[status(thm)],[f60])).
% 1.63/1.53 thf(f60,plain,(
% 1.63/1.53 ( ! [X2 : iS,X3 : iS,X1 : iS] : (($false = ((c0 = X3) & (X2 = X1))) | ($true = (sK3 @ X1 @ X3 @ X2))) )),
% 1.63/1.53 inference(binary_proxy_clausification,[status(thm)],[f59])).
% 1.63/1.53 thf(f257,plain,(
% 1.63/1.53 ~spl0_3),
% 1.63/1.53 inference(avatar_contradiction_clause,[status(thm)],[f256])).
% 1.63/1.53 thf(f256,plain,(
% 1.63/1.53 $false | ~spl0_3),
% 1.63/1.53 inference(equality_resolution,[status(thm)],[f250])).
% 1.63/1.53 thf(f250,plain,(
% 1.63/1.53 ( ! [X1 : iS] : ((c0 != X1)) ) | ~spl0_3),
% 1.63/1.53 inference(avatar_component_clause,[status(thm)],[f249])).
% 1.63/1.53 thf(f249,definition,(
% 1.63/1.53 spl0_3 <=> ! [X1 : iS] : (c0 != X1)),
% 1.63/1.53 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.63/1.53 thf(f255,plain,(
% 1.63/1.53 spl0_3 | spl0_4),
% 1.63/1.53 inference(avatar_split_clause,[status(thm)],[f247,f252,f249])).
% 1.63/1.53 thf(f247,plain,(
% 1.63/1.53 ( ! [X1 : iS] : (($true = (sK3 @ c0 @ c0 @ c0)) | (c0 != X1)) )),
% 1.63/1.53 inference(duplicate_literal_removal,[status(thm)],[f246])).
% 1.63/1.53 thf(f246,plain,(
% 1.63/1.53 ( ! [X1 : iS] : (($true = (sK3 @ c0 @ c0 @ c0)) | (c0 != X1) | (c0 != X1)) )),
% 1.63/1.53 inference(beta_eta_normalization,[status(thm)],[f245])).
% 1.63/1.53 thf(f245,plain,(
% 1.63/1.53 ( ! [X0 : iS,X1 : iS] : (($true = (sK3 @ c0 @ c0 @ ((^[Y0 : iS]: (c0)) @ X0))) | (c0 != X1) | (((^[Y0 : iS]: (c0)) @ c0) != X1)) )),
% 1.63/1.53 inference(equality_resolution,[status(thm)],[f244])).
% 1.63/1.53 thf(f244,plain,(
% 1.63/1.53 ( ! [X2 : iS,X0 : iS,X1 : iS > iS] : ((c0 != (X1 @ (cP @ (sK2 @ (^[Y0 : iS]: (sK3 @ c0 @ c0 @ (X1 @ Y0)))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ c0 @ c0 @ (X1 @ Y0))))))) | ((sK3 @ c0 @ c0 @ (X1 @ X2)) = $true) | (c0 != X0) | ((X1 @ c0) != X0)) )),
% 1.63/1.53 inference(equality_resolution,[status(thm)],[f243])).
% 1.63/1.53 thf(f243,plain,(
% 1.63/1.53 ( ! [X2 : iS,X3 : iS,X0 : iS,X1 : iS > iS] : ((c0 != X3) | (c0 != X0) | ((sK3 @ c0 @ c0 @ (X1 @ X2)) = $true) | ((X1 @ c0) != X0) | ((X1 @ (cP @ (sK2 @ (^[Y0 : iS]: (sK3 @ c0 @ c0 @ (X1 @ Y0)))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ c0 @ c0 @ (X1 @ Y0)))))) != X3)) )),
% 1.63/1.53 inference(equality_resolution,[status(thm)],[f225])).
% 1.63/1.53 thf(f225,plain,(
% 1.63/1.53 ( ! [X8 : iS,X6 : iS,X9 : iS,X7 : iS,X5 : iS > iS] : ((c0 != X8) | (c0 != X6) | ($true = (sK3 @ c0 @ c0 @ (X5 @ X7))) | ((X5 @ (cP @ (sK2 @ (^[Y0 : iS]: (sK3 @ c0 @ c0 @ (X5 @ Y0)))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ c0 @ c0 @ (X5 @ Y0)))))) != X9) | (X8 != X9) | ((X5 @ c0) != X6)) )),
% 1.63/1.53 inference(beta_eta_normalization,[status(thm)],[f224])).
% 1.63/1.53 thf(f224,plain,(
% 1.63/1.53 ( ! [X8 : iS,X6 : iS,X9 : iS,X7 : iS,X5 : iS > iS] : (($true = (sK3 @ ((^[Y0 : iS]: (c0)) @ X7) @ c0 @ (X5 @ X7))) | (c0 != X6) | (X8 != X9) | ((X5 @ c0) != X6) | (((^[Y0 : iS]: (c0)) @ (cP @ (sK2 @ (^[Y0 : iS]: (sK3 @ ((^[Y1 : iS]: (c0)) @ Y0) @ c0 @ (X5 @ Y0)))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ ((^[Y1 : iS]: (c0)) @ Y0) @ c0 @ (X5 @ Y0)))))) != X8) | ((X5 @ (cP @ (sK2 @ (^[Y0 : iS]: (sK3 @ ((^[Y1 : iS]: (c0)) @ Y0) @ c0 @ (X5 @ Y0)))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ ((^[Y1 : iS]: (c0)) @ Y0) @ c0 @ (X5 @ Y0)))))) != X9)) )),
% 1.63/1.53 inference(trivial_inequality_removal,[status(thm)],[f220])).
% 1.63/1.53 thf(f220,plain,(
% 1.63/1.53 ( ! [X8 : iS,X6 : iS,X9 : iS,X7 : iS,X5 : iS > iS] : (((X5 @ (cP @ (sK2 @ (^[Y0 : iS]: (sK3 @ ((^[Y1 : iS]: (c0)) @ Y0) @ c0 @ (X5 @ Y0)))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ ((^[Y1 : iS]: (c0)) @ Y0) @ c0 @ (X5 @ Y0)))))) != X9) | (c0 != X6) | ($true = (sK3 @ ((^[Y0 : iS]: (c0)) @ X7) @ c0 @ (X5 @ X7))) | ((X5 @ c0) != X6) | (X8 != X9) | (((^[Y0 : iS]: (c0)) @ (cP @ (sK2 @ (^[Y0 : iS]: (sK3 @ ((^[Y1 : iS]: (c0)) @ Y0) @ c0 @ (X5 @ Y0)))) @ (sK1 @ (^[Y0 : iS]: (sK3 @ ((^[Y1 : iS]: (c0)) @ Y0) @ c0 @ (X5 @ Y0)))))) != X8) | ($true = $false)) )),
% 1.63/1.53 inference(constrained_superposition,[status(thm)],[f95,f143])).
% 1.63/1.53 thf(f197,plain,(
% 1.63/1.53 spl0_1 | spl0_2),
% 1.63/1.53 inference(avatar_split_clause,[status(thm)],[f178,f193,f189])).
% 1.63/1.53 thf(f178,plain,(
% 1.63/1.53 ($false = (sK3 @ c0 @ x @ x)) | ((sK3 @ y @ y @ y) = $false)),
% 1.63/1.53 inference(trivial_inequality_removal,[status(thm)],[f172])).
% 1.63/1.53 thf(f172,plain,(
% 1.63/1.53 ($true = $false) | ($false = (sK3 @ c0 @ x @ x)) | ((sK3 @ y @ y @ y) = $false)),
% 1.63/1.53 inference(superposition,[status(thm)],[f170,f51])).
% 1.63/1.53 thf(f51,plain,(
% 1.63/1.53 ((sK3 @ (cP @ c0 @ y) @ (cP @ x @ y) @ (cP @ x @ y)) = $false)),
% 1.63/1.53 inference(binary_proxy_clausification,[status(thm)],[f50])).
% 1.63/1.53 % SZS output end Proof for DTF2THF_7046
% 1.63/1.53 % (7352)------------------------------
% 1.63/1.53 % (7352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.53 % (7352)Termination reason: Refutation
% 1.63/1.53
% 1.63/1.53 % (7352)Memory used [KB]: 6780
% 1.63/1.53 % (7352)Time elapsed: 0.165 s
% 1.63/1.53 % (7352)Instructions burned: 492 (million)
% 1.63/1.53 % (7352)------------------------------
% 1.63/1.53 % (7352)------------------------------
% 1.63/1.53 % (7324)Success in time 0.259 s
%------------------------------------------------------------------------------