%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM815^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:24:50 AM UTC 2026
% Result : Theorem 1.64s 1.40s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 5
% Syntax : Number of formulae : 91 ( 45 unt; 0 typ; 2 def)
% Number of atoms : 665 ( 204 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 1446 ( 53 ~; 41 |; 54 &;1052 @)
% ( 2 <=>; 54 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 14 usr; 12 con; 0-3 aty)
% ( 124 !!; 66 ??; 0 @@+; 0 @@-)
% Number of variables : 265 ( 217 ^; 45 !; 3 ?; 265 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
cPSI: $i > $i > $i ).
thf(func_def_2,type,
cS: $i > $i ).
thf(func_def_4,type,
cPETER_INDEQS: $i > ( $i > $i ) > ( $i > $i > $i ) > $o ).
thf(func_def_20,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_29,type,
sK10: $i > $i ).
thf(func_def_30,type,
sK11: $i > $i ).
thf(f623,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f180,f194,f621]) ).
thf(f621,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[status(thm)],[f620]) ).
thf(f620,plain,
( $false
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f616]) ).
thf(f616,plain,
( ( $false = $true )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f584,f261]) ).
thf(f261,plain,
( ! [X1: $i] :
( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( cS @ ( sK10 @ X1 ) )
= ( cS @ Y0 ) ) ) )
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f250,f257]) ).
thf(f257,plain,
( ! [X1: $i] :
( ( cPSI @ sK7 @ X1 )
= ( cS @ ( sK10 @ X1 ) ) )
| ~ spl0_4 ),
inference(equality_proxy_clausification,[status(thm)],[f256]) ).
thf(f256,plain,
( ! [X1: $i] :
( ( ( cPSI @ sK7 @ X1 )
= ( cS @ ( sK10 @ X1 ) ) )
= $true )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f255]) ).
thf(f255,plain,
( ! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( cPSI @ sK7 @ X1 )
= ( cS @ Y0 ) )
@ ( sK10 @ X1 ) ) )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f250]) ).
thf(f250,plain,
( ! [X1: $i] :
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( cPSI @ sK7 @ X1 )
= ( cS @ Y0 ) ) )
= $true )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f248]) ).
thf(f248,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( cPSI @ sK7 @ Y0 )
= ( cS @ Y1 ) ) )
@ X1 )
= $true )
| ~ spl0_4 ),
inference(pi_clausification,[status(thm)],[f205]) ).
thf(f205,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( cPSI @ sK7 @ Y0 )
= ( cS @ Y1 ) ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f199]) ).
thf(f199,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( cPSI @ sK7 @ Y0 )
= ( cS @ Y1 ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( cPSI @ ( cS @ sK7 ) @ Y0 )
= ( cS @ Y1 ) ) ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f197]) ).
thf(f197,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( cPSI @ Y0 @ Y1 )
= ( cS @ Y2 ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( cPSI @ ( cS @ Y0 ) @ Y1 )
= ( cS @ Y2 ) ) ) ) )
@ sK7 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f179]) ).
thf(f179,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( cPSI @ Y0 @ Y1 )
= ( cS @ Y2 ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( cPSI @ ( cS @ Y0 ) @ Y1 )
= ( cS @ Y2 ) ) ) ) ) ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f178]) ).
thf(f178,definition,
( spl0_4
<=> ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( cPSI @ Y0 @ Y1 )
= ( cS @ Y2 ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( cPSI @ ( cS @ Y0 ) @ Y1 )
= ( cS @ Y2 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f584,plain,
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( cS @ ( sK10 @ ( cS @ sK16 ) ) )
= ( cS @ Y0 ) ) ) )
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f383,f583]) ).
thf(f583,plain,
( ( ( cPSI @ ( cS @ sK7 ) @ ( cS @ sK12 ) )
= ( cS @ ( sK10 @ ( cS @ sK16 ) ) ) )
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f582,f257]) ).
thf(f582,plain,
( ( ( cPSI @ ( cS @ sK7 ) @ ( cS @ sK12 ) )
= ( cPSI @ sK7 @ ( cS @ sK16 ) ) )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f61,f577]) ).
thf(f577,plain,
( ( ( cPSI @ ( cS @ sK7 ) @ sK12 )
= ( cS @ sK16 ) )
| ~ spl0_4 ),
inference(equality_proxy_clausification,[status(thm)],[f576]) ).
thf(f576,plain,
( ( $true
= ( ( cPSI @ ( cS @ sK7 ) @ sK12 )
= ( cS @ sK16 ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f575]) ).
thf(f575,plain,
( ( ( ^ [Y0: $i] :
( ( cPSI @ ( cS @ sK7 ) @ sK12 )
= ( cS @ Y0 ) )
@ sK16 )
= $true )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f384]) ).
thf(f384,plain,
( ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( cPSI @ ( cS @ sK7 ) @ sK12 )
= ( cS @ Y0 ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f376]) ).
thf(f376,plain,
( ( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( cPSI @ ( cS @ sK7 ) @ sK12 )
= ( cS @ Y0 ) ) )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( cPSI @ ( cS @ sK7 ) @ ( cS @ sK12 ) )
= ( cS @ Y0 ) ) ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f374]) ).
thf(f374,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( cPSI @ ( cS @ sK7 ) @ Y0 )
= ( cS @ Y1 ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( cPSI @ ( cS @ sK7 ) @ ( cS @ Y0 ) )
= ( cS @ Y1 ) ) ) )
@ sK12 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f371]) ).
thf(f371,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( cPSI @ ( cS @ sK7 ) @ Y0 )
= ( cS @ Y1 ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( cPSI @ ( cS @ sK7 ) @ ( cS @ Y0 ) )
= ( cS @ Y1 ) ) ) ) )
= $false )
| ~ spl0_4 ),
inference(not_proxy_clausification,[status(thm)],[f254]) ).
thf(f254,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( cPSI @ ( cS @ sK7 ) @ Y0 )
= ( cS @ Y1 ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( cPSI @ ( cS @ sK7 ) @ ( cS @ Y0 ) )
= ( cS @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f253]) ).
thf(f253,plain,
( ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( cPSI @ ( cS @ sK7 ) @ Y0 )
= ( cS @ Y1 ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( cPSI @ ( cS @ sK7 ) @ ( cS @ Y0 ) )
= ( cS @ Y1 ) ) ) ) )
& $true ) ) )
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f216,f250]) ).
thf(f216,plain,
( ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( cPSI @ ( cS @ sK7 ) @ Y0 )
= ( cS @ Y1 ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( cPSI @ ( cS @ sK7 ) @ ( cS @ Y0 ) )
= ( cS @ Y1 ) ) ) ) )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( cPSI @ sK7 @ ( cS @ c0 ) )
= ( cS @ Y0 ) ) ) ) ) )
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f214,f52]) ).
thf(f52,plain,
! [X1: $i] :
( ( cPSI @ ( cS @ X1 ) @ c0 )
= ( cPSI @ X1 @ ( cS @ c0 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
! [X1: $i] :
( ( ( cPSI @ ( cS @ X1 ) @ c0 )
= ( cPSI @ X1 @ ( cS @ c0 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f50]) ).
thf(f50,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( cPSI @ ( cS @ Y0 ) @ c0 )
= ( cPSI @ Y0 @ ( cS @ c0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( cPSI @ ( cS @ Y0 ) @ c0 )
= ( cPSI @ Y0 @ ( cS @ c0 ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( cS @ Y0 )
= ( cPSI @ c0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( cPSI @ ( cS @ Y0 ) @ c0 )
= ( cPSI @ Y0 @ ( cS @ c0 ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f37]) ).
thf(f37,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( cS @ Y0 )
= ( cPSI @ c0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( cPSI @ ( cS @ Y0 ) @ c0 )
= ( cPSI @ Y0 @ ( cS @ c0 ) ) ) )
& $true )
= $true ),
inference(backward_demodulation,[status(thm)],[f34,f35]) ).
thf(f35,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cPSI @ Y1 @ ( cPSI @ ( cS @ Y1 ) @ Y0 ) )
= ( cPSI @ ( cS @ Y1 ) @ ( cS @ Y0 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( cS @ Y0 )
= ( cPSI @ c0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( cPSI @ ( cS @ Y0 ) @ c0 )
= ( cPSI @ Y0 @ ( cS @ c0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cPSI @ Y1 @ ( cPSI @ ( cS @ Y1 ) @ Y0 ) )
= ( cPSI @ ( cS @ Y1 ) @ ( cS @ Y0 ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f33]) ).
thf(f33,plain,
( $true
= ( $true
& ( !! @ $i
@ ^ [Y0: $i] :
( ( cS @ Y0 )
= ( cPSI @ c0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( cPSI @ ( cS @ Y0 ) @ c0 )
= ( cPSI @ Y0 @ ( cS @ c0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cPSI @ Y1 @ ( cPSI @ ( cS @ Y1 ) @ Y0 ) )
= ( cPSI @ ( cS @ Y1 ) @ ( cS @ Y0 ) ) ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f21,f32]) ).
thf(f32,plain,
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ Y1 ) ) ) )
& ( Y0 @ c0 ) )
=> ( !! @ $i @ Y0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ Y1 ) ) ) )
& ( Y0 @ c0 ) )
=> ( !! @ $i @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( cS @ Y0 )
= ( cPSI @ c0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( cPSI @ ( cS @ Y0 ) @ c0 )
= ( cPSI @ Y0 @ ( cS @ c0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cPSI @ Y1 @ ( cPSI @ ( cS @ Y1 ) @ Y0 ) )
= ( cPSI @ ( cS @ Y1 ) @ ( cS @ Y0 ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( $false
= ( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ Y1 ) ) ) )
& ( Y0 @ c0 ) )
=> ( !! @ $i @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( cS @ Y0 )
= ( cPSI @ c0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( cPSI @ ( cS @ Y0 ) @ c0 )
= ( cPSI @ Y0 @ ( cS @ c0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cPSI @ Y1 @ ( cPSI @ ( cS @ Y1 ) @ Y0 ) )
= ( cPSI @ ( cS @ Y1 ) @ ( cS @ Y0 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( cPSI @ Y0 @ Y1 )
= ( cS @ Y2 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ~ ( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ Y1 ) ) ) )
& ( Y0 @ c0 ) )
=> ( !! @ $i @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( cS @ Y0 )
= ( cPSI @ c0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( cPSI @ ( cS @ Y0 ) @ c0 )
= ( cPSI @ Y0 @ ( cS @ c0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cPSI @ Y1 @ ( cPSI @ ( cS @ Y1 ) @ Y0 ) )
= ( cPSI @ ( cS @ Y1 ) @ ( cS @ Y0 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( cPSI @ Y0 @ Y1 )
= ( cS @ Y2 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ~ ( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ Y1 ) ) ) )
& ( Y0 @ c0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( ^ [Y0: $i,Y1: $i > $i,Y2: $i > $i > $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
= ( Y2 @ Y0 @ Y3 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ ( Y1 @ Y3 ) @ Y0 )
= ( Y2 @ Y3 @ ( Y1 @ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ ( Y2 @ ( Y1 @ Y4 ) @ Y3 ) )
= ( Y2 @ ( Y1 @ Y4 ) @ ( Y1 @ Y3 ) ) ) ) ) )
@ c0
@ cS
@ cPSI ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( cPSI @ Y0 @ Y1 )
= ( cS @ Y2 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f14,f13,f12]) ).
thf(f12,plain,
( cPETER_INDEQS
= ( ^ [Y0: $i,Y1: $i > $i,Y2: $i > $i > $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
= ( Y2 @ Y0 @ Y3 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ ( Y1 @ Y3 ) @ Y0 )
= ( Y2 @ Y3 @ ( Y1 @ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ ( Y2 @ ( Y1 @ Y4 ) @ Y3 ) )
= ( Y2 @ ( Y1 @ Y4 ) @ ( Y1 @ Y3 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( cPETER_INDEQS
= ( ^ [Y0: $i,Y1: $i > $i,Y2: $i > $i > $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
= ( Y2 @ Y0 @ Y3 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ ( Y1 @ Y3 ) @ Y0 )
= ( Y2 @ Y3 @ ( Y1 @ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ ( Y2 @ ( Y1 @ Y4 ) @ Y3 ) )
= ( Y2 @ ( Y1 @ Y4 ) @ ( Y1 @ Y3 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ^ [X0: $i,X1: $i > $i,X2: $i > $i > $i] :
( ! [X3: $i,X4: $i] :
( ( X2 @ X3 @ ( X2 @ ( X1 @ X3 ) @ X4 ) )
= ( X2 @ ( X1 @ X3 ) @ ( X1 @ X4 ) ) )
& ! [X5: $i] :
( ( X2 @ ( X1 @ X5 ) @ X0 )
= ( X2 @ X5 @ ( X1 @ X0 ) ) )
& ! [X6: $i] :
( ( X1 @ X6 )
= ( X2 @ X0 @ X6 ) ) ) )
= cPETER_INDEQS ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( ( ^ [X2: $i,X3: $i > $i,X4: $i > $i > $i] :
( ! [X6: $i,X5: $i] :
( ( X4 @ ( X3 @ X6 ) @ ( X3 @ X5 ) )
= ( X4 @ X6 @ ( X4 @ ( X3 @ X6 ) @ X5 ) ) )
& ! [X6: $i] :
( ( X4 @ ( X3 @ X6 ) @ X2 )
= ( X4 @ X6 @ ( X3 @ X2 ) ) )
& ! [X5: $i] :
( ( X4 @ X2 @ X5 )
= ( X3 @ X5 ) ) ) )
= cPETER_INDEQS ),
file('/export/starexec/sandbox2/tmp/tmp.3GJoy61PLV/DTF2THF_23352.p',cPETER_INDEQS_def) ).
thf(f13,plain,
( cIND
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ Y1 ) ) ) )
& ( Y0 @ c0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( cIND
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ Y1 ) ) ) )
& ( Y0 @ c0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
( cIND
= ( ! [X0: $i > $o] :
( ( ( X0 @ c0 )
& ! [X1: $i] :
( ( X0 @ X1 )
=> ( X0 @ ( cS @ X1 ) ) ) )
=> ! [X2: $i] : ( X0 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( cIND
= ( ! [X0: $i > $o] :
( ( ( X0 @ c0 )
& ! [X1: $i] :
( ( X0 @ X1 )
=> ( X0 @ ( cS @ X1 ) ) ) )
=> ! [X1: $i] : ( X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.3GJoy61PLV/DTF2THF_23352.p',cIND_def) ).
thf(f14,plain,
( $true
= ( ~ ( ( cIND
& ( cPETER_INDEQS @ c0 @ cS @ cPSI ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( cPSI @ Y0 @ Y1 )
= ( cS @ Y2 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( $true
= ( ~ ( ( cIND
& ( cPETER_INDEQS @ c0 @ cS @ cPSI ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( cPSI @ Y0 @ Y1 )
= ( cS @ Y2 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( ( ( cPETER_INDEQS @ c0 @ cS @ cPSI )
& cIND )
=> ! [X0: $i,X1: $i] :
? [X2: $i] :
( ( cPSI @ X1 @ X0 )
= ( cS @ X2 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( ( ( cPETER_INDEQS @ c0 @ cS @ cPSI )
& cIND )
=> ! [X5: $i,X6: $i] :
? [X7: $i] :
( ( cPSI @ X6 @ X5 )
= ( cS @ X7 ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( ( ( cPETER_INDEQS @ c0 @ cS @ cPSI )
& cIND )
=> ! [X5: $i,X6: $i] :
? [X7: $i] :
( ( cPSI @ X6 @ X5 )
= ( cS @ X7 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.3GJoy61PLV/DTF2THF_23352.p',cTHM585) ).
thf(f214,plain,
( ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( cPSI @ ( cS @ sK7 ) @ Y0 )
= ( cS @ Y1 ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( cPSI @ ( cS @ sK7 ) @ ( cS @ Y0 ) )
= ( cS @ Y1 ) ) ) ) )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( cPSI @ ( cS @ sK7 ) @ c0 )
= ( cS @ Y0 ) ) ) ) )
= $true )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f213]) ).
thf(f213,plain,
( ( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( cPSI @ ( cS @ sK7 ) @ Y0 )
= ( cS @ Y1 ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( cPSI @ ( cS @ sK7 ) @ ( cS @ Y0 ) )
= ( cS @ Y1 ) ) ) ) )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( cPSI @ ( cS @ sK7 ) @ c0 )
= ( cS @ Y0 ) ) ) )
=> $false )
= $true )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f212]) ).
thf(f212,plain,
( ( $true
= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( cPSI @ ( cS @ sK7 ) @ Y1 )
= ( cS @ Y2 ) ) )
@ Y0 )
=> ( ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( cPSI @ ( cS @ sK7 ) @ Y1 )
= ( cS @ Y2 ) ) )
@ ( cS @ Y0 ) ) ) )
& ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( cPSI @ ( cS @ sK7 ) @ Y0 )
= ( cS @ Y1 ) ) )
@ c0 ) )
=> $false ) )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f75,f207]) ).
thf(f207,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( cPSI @ ( cS @ sK7 ) @ Y0 )
= ( cS @ Y1 ) ) ) ) )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f206]) ).
thf(f206,plain,
( ( ( $true
=> ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( cPSI @ ( cS @ sK7 ) @ Y0 )
= ( cS @ Y1 ) ) ) ) )
= $false )
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f199,f205]) ).
thf(f75,plain,
! [X1: $i > $o] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( cS @ Y0 ) ) ) )
& ( X1 @ c0 ) )
=> ( !! @ $i @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f74]) ).
thf(f74,plain,
! [X1: $i > $o] :
( ( ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ Y1 ) ) ) )
& ( Y0 @ c0 ) )
=> ( !! @ $i @ Y0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f32]) ).
thf(f61,plain,
! [X2: $i,X1: $i] :
( ( cPSI @ X2 @ ( cPSI @ ( cS @ X2 ) @ X1 ) )
= ( cPSI @ ( cS @ X2 ) @ ( cS @ X1 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( cPSI @ X2 @ ( cPSI @ ( cS @ X2 ) @ X1 ) )
= ( cPSI @ ( cS @ X2 ) @ ( cS @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f59]) ).
thf(f59,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( cPSI @ Y0 @ ( cPSI @ ( cS @ Y0 ) @ X1 ) )
= ( cPSI @ ( cS @ Y0 ) @ ( cS @ X1 ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( cPSI @ Y0 @ ( cPSI @ ( cS @ Y0 ) @ X1 ) )
= ( cPSI @ ( cS @ Y0 ) @ ( cS @ X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f39]) ).
thf(f39,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cPSI @ Y1 @ ( cPSI @ ( cS @ Y1 ) @ Y0 ) )
= ( cPSI @ ( cS @ Y1 ) @ ( cS @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f35]) ).
thf(f383,plain,
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( cPSI @ ( cS @ sK7 ) @ ( cS @ sK12 ) )
= ( cS @ Y0 ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f376]) ).
thf(f194,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[status(thm)],[f193]) ).
thf(f193,plain,
( $false
| ~ spl0_3 ),
inference(equality_resolution,[status(thm)],[f192]) ).
thf(f192,plain,
( ! [X1: $i] :
( ( cS @ X1 )
!= ( cS @ sK6 ) )
| ~ spl0_3 ),
inference(equality_proxy_clausification,[status(thm)],[f191]) ).
thf(f191,plain,
( ! [X1: $i] :
( ( ( cS @ sK6 )
= ( cS @ X1 ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f190]) ).
thf(f190,plain,
( ! [X1: $i] :
( $false
= ( ^ [Y0: $i] :
( ( cS @ sK6 )
= ( cS @ Y0 ) )
@ X1 ) )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f188]) ).
thf(f188,plain,
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( cS @ sK6 )
= ( cS @ Y0 ) ) ) )
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f187,f47]) ).
thf(f47,plain,
! [X1: $i] :
( ( cS @ X1 )
= ( cPSI @ c0 @ X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
! [X1: $i] :
( $true
= ( ( cS @ X1 )
= ( cPSI @ c0 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f45]) ).
thf(f45,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( cS @ Y0 )
= ( cPSI @ c0 @ Y0 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( cS @ Y0 )
= ( cPSI @ c0 @ Y0 ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f43]) ).
thf(f43,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( cS @ Y0 )
= ( cPSI @ c0 @ Y0 ) ) )
& $true ) ),
inference(backward_demodulation,[status(thm)],[f38,f41]) ).
thf(f187,plain,
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( cPSI @ c0 @ sK6 )
= ( cS @ Y0 ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f183]) ).
thf(f183,plain,
( ( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( cPSI @ c0 @ Y0 )
= ( cS @ Y1 ) ) )
@ sK6 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f176]) ).
thf(f176,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( cPSI @ c0 @ Y0 )
= ( cS @ Y1 ) ) ) ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f175]) ).
thf(f175,definition,
( spl0_3
<=> ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( cPSI @ c0 @ Y0 )
= ( cS @ Y1 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f180,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f173,f178,f175]) ).
thf(f173,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( cPSI @ c0 @ Y0 )
= ( cS @ Y1 ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( cPSI @ Y0 @ Y1 )
= ( cS @ Y2 ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( cPSI @ ( cS @ Y0 ) @ Y1 )
= ( cS @ Y2 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f166]) ).
thf(f166,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( cPSI @ Y0 @ Y1 )
= ( cS @ Y2 ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( cPSI @ ( cS @ Y0 ) @ Y1 )
= ( cS @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( cPSI @ c0 @ Y0 )
= ( cS @ Y1 ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f89]) ).
thf(f89,plain,
( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( cPSI @ Y0 @ Y1 )
= ( cS @ Y2 ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( cPSI @ ( cS @ Y0 ) @ Y1 )
= ( cS @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( cPSI @ c0 @ Y0 )
= ( cS @ Y1 ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f88]) ).
thf(f88,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( cPSI @ Y0 @ Y1 )
= ( cS @ Y2 ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( cPSI @ ( cS @ Y0 ) @ Y1 )
= ( cS @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( cPSI @ c0 @ Y0 )
= ( cS @ Y1 ) ) ) ) )
=> $false )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f85]) ).
thf(f85,plain,
( $true
= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( cPSI @ Y1 @ Y2 )
= ( cS @ Y3 ) ) ) )
@ Y0 )
=> ( ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( cPSI @ Y1 @ Y2 )
= ( cS @ Y3 ) ) ) )
@ ( cS @ Y0 ) ) ) )
& ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( cPSI @ Y0 @ Y1 )
= ( cS @ Y2 ) ) ) )
@ c0 ) )
=> $false ) ),
inference(superposition,[status(thm)],[f75,f23]) ).
thf(f23,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( cPSI @ Y0 @ Y1 )
= ( cS @ Y2 ) ) ) ) )
= $false ),
inference(boolean_simplification,[status(thm)],[f22]) ).
thf(f22,plain,
( $false
= ( $true
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( cPSI @ Y0 @ Y1 )
= ( cS @ Y2 ) ) ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f17,f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM815^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n021.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 11:15:39 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.46 ---- Original DTF file ---
% 0.19/0.46 thf(spec,logic,$$dhol).
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % File : NUM815^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% 0.19/0.46 % Domain : Number Theory (Induction on naturals)
% 0.19/0.46 % Problem : TPS problem from IND-THMS
% 0.19/0.46 % Version : Especial.
% 0.19/0.46 % English :
% 0.19/0.46
% 0.19/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.46 % Source : [Bro09]
% 0.19/0.46 % Names : tps_0773 [Bro09]
% 0.19/0.46
% 0.19/0.46 % Status : Theorem
% 0.19/0.46 % Rating : 0.89 v9.1.0, 0.88 v9.0.0, 1.00 v5.2.0
% 0.19/0.46 % Syntax : Number of formulae : 8 ( 2 unt; 5 typ; 2 def)
% 0.19/0.46 % Number of atoms : 10 ( 6 equ; 0 cnn)
% 0.19/0.46 % Maximal formula atoms : 3 ( 3 avg)
% 0.19/0.46 % Number of connectives : 36 ( 0 ~; 0 |; 4 &; 29 @)
% 0.19/0.46 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.19/0.46 % Maximal formula depth : 6 ( 3 avg)
% 0.19/0.46 % Number of types : 2 ( 0 usr)
% 0.19/0.46 % Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% 0.19/0.46 % Number of symbols : 6 ( 5 usr; 2 con; 0-3 aty)
% 0.19/0.46 % Number of variables : 13 ( 3 ^; 9 !; 1 ?; 13 :)
% 0.19/0.46 % SPC : TH0_THM_EQU_NAR
% 0.19/0.46
% 0.19/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.46 % :
% 0.19/0.46 % Bugfixes : v5.2.0 - Added missing type declarations.
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 thf(c0_type,type,
% 0.19/0.46 c0: $i ).
% 0.19/0.46
% 0.19/0.46 thf(cPSI_type,type,
% 0.19/0.46 cPSI: $i > $i > $i ).
% 0.19/0.46
% 0.19/0.46 thf(cS_type,type,
% 0.19/0.46 cS: $i > $i ).
% 0.19/0.46
% 0.19/0.46 thf(cIND_type,type,
% 0.19/0.46 cIND: $o ).
% 0.19/0.46
% 0.19/0.46 thf(cPETER_INDEQS_type,type,
% 0.19/0.46 cPETER_INDEQS: $i > ( $i > $i ) > ( $i > $i > $i ) > $o ).
% 0.19/0.46
% 0.19/0.46 thf(cIND_def,definition,
% 0.19/0.46 ( cIND
% 0.19/0.46 = ( ! [Xp: $i > $o] :
% 0.19/0.46 ( ( ( Xp @ c0 )
% 0.19/0.46 & ! [Xx: $i] :
% 0.19/0.46 ( ( Xp @ Xx )
% 0.19/0.46 => ( Xp @ ( cS @ Xx ) ) ) )
% 0.19/0.46 => ! [Xx: $i] : ( Xp @ Xx ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(cPETER_INDEQS_def,definition,
% 0.19/0.46 ( cPETER_INDEQS
% 0.19/0.46 = ( ^ [X0: $i,S: $i > $i,PSI: $i > $i > $i] :
% 0.19/0.46 ( ! [Xn: $i] :
% 0.19/0.46 ( ( PSI @ X0 @ Xn )
% 0.19/0.46 = ( S @ Xn ) )
% 0.19/0.46 & ! [Xm: $i] :
% 0.19/0.46 ( ( PSI @ ( S @ Xm ) @ X0 )
% 0.19/0.46 = ( PSI @ Xm @ ( S @ X0 ) ) )
% 0.19/0.46 & ! [Xm: $i,Xn: $i] :
% 0.19/0.46 ( ( PSI @ ( S @ Xm ) @ ( S @ Xn ) )
% 0.19/0.46 = ( PSI @ Xm @ ( PSI @ ( S @ Xm ) @ Xn ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(cTHM585,conjecture,
% 0.19/0.46 ( ( cIND
% 0.19/0.46 & ( cPETER_INDEQS @ c0 @ cS @ cPSI ) )
% 0.19/0.46 => ! [Xm: $i,Xn: $i] :
% 0.19/0.46 ? [Xk: $i] :
% 0.19/0.46 ( ( cPSI @ Xm @ Xn )
% 0.19/0.46 = ( cS @ Xk ) ) ) ).
% 0.19/0.46
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 ------------------------
% 1.52/1.26 ---- Embedded in THF ---
% 1.52/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.52/1.26 %%% Generated on Tue Feb 24 11:15:39 EST 2026
% 1.52/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.52/1.26 %%% Logic specification used:
% 1.52/1.26 %%% thf(spec, logic, $$dhol).
% 1.52/1.26
% 1.52/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.3GJoy61PLV/DTF2DTF23352.p
% See solution above
% 1.52/1.26 ------------------------
% 1.52/1.27 ---- Cleaned THF ---
% 1.52/1.27 thf(c0_type,type,
% 1.52/1.27 c0: $i ).
% 1.52/1.27
% 1.52/1.27 thf(cPSI_type,type,
% 1.52/1.27 cPSI: $i > $i > $i ).
% 1.52/1.27
% 1.52/1.27 thf(cS_type,type,
% 1.52/1.27 cS: $i > $i ).
% 1.52/1.27
% 1.52/1.27 thf(cIND_type,type,
% 1.52/1.27 cIND: $o ).
% 1.52/1.27
% 1.52/1.27 thf(cPETER_INDEQS_type,type,
% 1.52/1.27 cPETER_INDEQS: $i > ( $i > $i ) > ( $i > $i > $i ) > $o ).
% 1.52/1.27
% 1.52/1.27 thf(cIND_def,definition,
% 1.52/1.27 ( cIND
% 1.52/1.27 = ( ! [Xp: $i > $o] :
% 1.52/1.27 ( ( ( Xp @ c0 )
% 1.52/1.27 & ! [Xx: $i] :
% 1.52/1.27 ( ( Xp @ Xx )
% 1.52/1.27 => ( Xp @ ( cS @ Xx ) ) ) )
% 1.52/1.27 => ! [Xx: $i] : ( Xp @ Xx ) ) ) ) ).
% 1.52/1.27
% 1.52/1.27 thf(cPETER_INDEQS_def,definition,
% 1.52/1.27 ( cPETER_INDEQS
% 1.52/1.27 = ( ^ [X0: $i,S: $i > $i,PSI: $i > $i > $i] :
% 1.52/1.27 ( ! [Xn: $i] :
% 1.52/1.27 ( ( PSI @ X0 @ Xn )
% 1.52/1.27 = ( S @ Xn ) )
% 1.52/1.27 & ! [Xm: $i] :
% 1.52/1.27 ( ( PSI @ ( S @ Xm ) @ X0 )
% 1.52/1.27 = ( PSI @ Xm @ ( S @ X0 ) ) )
% 1.52/1.27 & ! [Xm: $i,Xn: $i] :
% 1.52/1.27 ( ( PSI @ ( S @ Xm ) @ ( S @ Xn ) )
% 1.52/1.27 = ( PSI @ Xm @ ( PSI @ ( S @ Xm ) @ Xn ) ) ) ) ) ) ).
% 1.52/1.27
% 1.52/1.27 thf(cTHM585,conjecture,
% 1.52/1.27 ( ( cIND
% 1.52/1.27 & ( cPETER_INDEQS @ c0 @ cS @ cPSI ) )
% 1.52/1.27 => ! [Xm: $i,Xn: $i] :
% 1.52/1.27 ? [Xk: $i] :
% 1.52/1.27 ( ( cPSI @ Xm @ Xn )
% 1.52/1.27 = ( cS @ Xk ) ) ) ).
% 1.52/1.27 ------------------------
% 1.52/1.28 % (23462)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_23352 for (3000ds/4Mi)
% 1.52/1.28 % (23462)Instruction limit reached!
% 1.52/1.28 % (23462)------------------------------
% 1.52/1.28 % (23462)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.28 % (23462)Termination reason: Unknown
% 1.52/1.28 % (23462)Termination phase: Saturation
% 1.52/1.28
% 1.52/1.28 % (23462)Memory used [KB]: 5500
% 1.52/1.28 % (23462)Time elapsed: 0.003 s
% 1.52/1.28 % (23462)Instructions burned: 4 (million)
% 1.52/1.28 % (23462)------------------------------
% 1.52/1.28 % (23462)------------------------------
% 1.52/1.29 % (23461)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_23352 for (3000ds/183Mi)
% 1.52/1.29 % (23463)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_23352 for (3000ds/27Mi)
% 1.52/1.29 % (23464)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_23352 for (3000ds/2Mi)
% 1.52/1.29 % (23467)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_23352 for (3000ds/18Mi)
% 1.52/1.29 % (23466)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_23352 for (3000ds/275Mi)
% 1.52/1.29 % (23464)Instruction limit reached!
% 1.52/1.29 % (23464)------------------------------
% 1.52/1.29 % (23464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.29 % (23464)Termination reason: Unknown
% 1.52/1.29 % (23464)Termination phase: shuffling
% 1.52/1.29
% 1.52/1.29 % (23464)Memory used [KB]: 895
% 1.52/1.29 % (23464)Time elapsed: 0.003 s
% 1.52/1.29 % (23464)Instructions burned: 2 (million)
% 1.52/1.29 % (23464)------------------------------
% 1.52/1.29 % (23464)------------------------------
% 1.52/1.29 % (23465)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_23352 for (3000ds/2Mi)
% 1.52/1.29 % (23465)Instruction limit reached!
% 1.52/1.29 % (23465)------------------------------
% 1.52/1.29 % (23465)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.29 % (23465)Termination reason: Unknown
% 1.52/1.29 % (23465)Termination phase: Property scanning
% 1.52/1.29
% 1.52/1.29 % (23465)Memory used [KB]: 895
% 1.52/1.29 % (23465)Time elapsed: 0.004 s
% 1.52/1.29 % (23465)Instructions burned: 2 (million)
% 1.52/1.29 % (23465)------------------------------
% 1.52/1.29 % (23465)------------------------------
% 1.52/1.29 % (23468)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_23352 for (2999ds/3Mi)
% 1.52/1.29 % (23468)Instruction limit reached!
% 1.52/1.29 % (23468)------------------------------
% 1.52/1.29 % (23468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.29 % (23468)Termination reason: Unknown
% 1.52/1.29 % (23468)Termination phase: Property scanning
% 1.52/1.29
% 1.52/1.29 % (23468)Memory used [KB]: 1023
% 1.52/1.29 % (23468)Time elapsed: 0.002 s
% 1.52/1.29 % (23468)Instructions burned: 3 (million)
% 1.52/1.29 % (23468)------------------------------
% 1.52/1.29 % (23468)------------------------------
% 1.64/1.30 % (23466)Refutation not found, incomplete strategy
% 1.64/1.30 % (23466)------------------------------
% 1.64/1.30 % (23466)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.30 % (23466)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.30
% 1.64/1.30
% 1.64/1.30 % (23466)Memory used [KB]: 5628
% 1.64/1.30 % (23466)Time elapsed: 0.012 s
% 1.64/1.30 % (23466)Instructions burned: 15 (million)
% 1.64/1.30 % (23466)------------------------------
% 1.64/1.30 % (23466)------------------------------
% 1.64/1.30 % (23467)Instruction limit reached!
% 1.64/1.30 % (23467)------------------------------
% 1.64/1.30 % (23467)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.30 % (23467)Termination reason: Unknown
% 1.64/1.30 % (23467)Termination phase: Saturation
% 1.64/1.30
% 1.64/1.30 % (23467)Memory used [KB]: 5628
% 1.64/1.30 % (23467)Time elapsed: 0.014 s
% 1.64/1.30 % (23467)Instructions burned: 18 (million)
% 1.64/1.30 % (23467)------------------------------
% 1.64/1.30 % (23467)------------------------------
% 1.64/1.30 % (23471)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_23352 for (2999ds/3Mi)
% 1.64/1.30 % (23471)Instruction limit reached!
% 1.64/1.30 % (23471)------------------------------
% 1.64/1.30 % (23471)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.30 % (23471)Termination reason: Unknown
% 1.64/1.30 % (23471)Termination phase: Saturation
% 1.64/1.30
% 1.64/1.30 % (23471)Memory used [KB]: 5500
% 1.64/1.30 % (23471)Time elapsed: 0.002 s
% 1.64/1.30 % (23471)Instructions burned: 3 (million)
% 1.64/1.30 % (23471)------------------------------
% 1.64/1.30 % (23471)------------------------------
% 1.64/1.30 % (23463)Instruction limit reached!
% 1.64/1.30 % (23463)------------------------------
% 1.64/1.30 % (23463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.30 % (23463)Termination reason: Unknown
% 1.64/1.30 % (23463)Termination phase: Saturation
% 1.64/1.30
% 1.64/1.30 % (23463)Memory used [KB]: 5628
% 1.64/1.30 % (23463)Time elapsed: 0.019 s
% 1.64/1.30 % (23463)Instructions burned: 27 (million)
% 1.64/1.30 % (23463)------------------------------
% 1.64/1.30 % (23463)------------------------------
% 1.64/1.31 % (23469)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_23352 for (2999ds/37Mi)
% 1.64/1.31 % (23474)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_23352 for (2999ds/16Mi)
% 1.64/1.32 % (23474)Instruction limit reached!
% 1.64/1.32 % (23474)------------------------------
% 1.64/1.32 % (23474)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.32 % (23474)Termination reason: Unknown
% 1.64/1.32 % (23474)Termination phase: Saturation
% 1.64/1.32
% 1.64/1.32 % (23474)Memory used [KB]: 5756
% 1.64/1.32 % (23474)Time elapsed: 0.007 s
% 1.64/1.32 % (23474)Instructions burned: 16 (million)
% 1.64/1.32 % (23474)------------------------------
% 1.64/1.32 % (23474)------------------------------
% 1.64/1.32 % (23472)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_23352 for (2999ds/1041Mi)
% 1.64/1.32 % (23473)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_23352 for (2999ds/7Mi)
% 1.64/1.32 % (23470)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_23352 for (2999ds/15Mi)
% 1.64/1.32 % (23475)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_23352 for (2999ds/3Mi)
% 1.64/1.32 % (23473)Instruction limit reached!
% 1.64/1.32 % (23473)------------------------------
% 1.64/1.32 % (23473)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.32 % (23473)Termination reason: Unknown
% 1.64/1.32 % (23473)Termination phase: Saturation
% 1.64/1.32
% 1.64/1.32 % (23473)Memory used [KB]: 1023
% 1.64/1.32 % (23473)Time elapsed: 0.007 s
% 1.64/1.32 % (23473)Instructions burned: 8 (million)
% 1.64/1.32 % (23473)------------------------------
% 1.64/1.32 % (23473)------------------------------
% 1.64/1.32 % (23475)Instruction limit reached!
% 1.64/1.32 % (23475)------------------------------
% 1.64/1.32 % (23475)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.32 % (23475)Termination reason: Unknown
% 1.64/1.32 % (23475)Termination phase: Saturation
% 1.64/1.32
% 1.64/1.32 % (23475)Memory used [KB]: 1023
% 1.64/1.32 % (23475)Time elapsed: 0.004 s
% 1.64/1.32 % (23475)Instructions burned: 4 (million)
% 1.64/1.32 % (23475)------------------------------
% 1.64/1.32 % (23475)------------------------------
% 1.64/1.33 % (23469)Instruction limit reached!
% 1.64/1.33 % (23469)------------------------------
% 1.64/1.33 % (23469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.33 % (23469)Termination reason: Unknown
% 1.64/1.33 % (23469)Termination phase: Saturation
% 1.64/1.33
% 1.64/1.33 % (23469)Memory used [KB]: 5756
% 1.64/1.33 % (23469)Time elapsed: 0.022 s
% 1.64/1.33 % (23469)Instructions burned: 37 (million)
% 1.64/1.33 % (23469)------------------------------
% 1.64/1.33 % (23469)------------------------------
% 1.64/1.33 % (23476)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_23352 for (2999ds/3Mi)
% 1.64/1.33 % (23476)Instruction limit reached!
% 1.64/1.33 % (23476)------------------------------
% 1.64/1.33 % (23476)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.33 % (23476)Termination reason: Unknown
% 1.64/1.33 % (23476)Termination phase: Property scanning
% 1.64/1.33
% 1.64/1.33 % (23476)Memory used [KB]: 1023
% 1.64/1.33 % (23476)Time elapsed: 0.002 s
% 1.64/1.33 % (23476)Instructions burned: 3 (million)
% 1.64/1.33 % (23476)------------------------------
% 1.64/1.33 % (23476)------------------------------
% 1.64/1.34 % (23470)Instruction limit reached!
% 1.64/1.34 % (23470)------------------------------
% 1.64/1.34 % (23470)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.34 % (23470)Termination reason: Unknown
% 1.64/1.34 % (23470)Termination phase: Saturation
% 1.64/1.34
% 1.64/1.34 % (23470)Memory used [KB]: 5628
% 1.64/1.34 % (23470)Time elapsed: 0.018 s
% 1.64/1.34 % (23470)Instructions burned: 15 (million)
% 1.64/1.34 % (23470)------------------------------
% 1.64/1.34 % (23470)------------------------------
% 1.64/1.34 % (23480)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_23352 for (2999ds/18Mi)
% 1.64/1.34 % (23477)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_23352 for (2999ds/7Mi)
% 1.64/1.34 % (23478)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_23352 for (2999ds/3Mi)
% 1.64/1.34 % (23480)Instruction limit reached!
% 1.64/1.34 % (23480)------------------------------
% 1.64/1.34 % (23480)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.34 % (23480)Termination reason: Unknown
% 1.64/1.34 % (23480)Termination phase: Saturation
% 1.64/1.34
% 1.64/1.34 % (23480)Memory used [KB]: 5628
% 1.64/1.34 % (23480)Time elapsed: 0.007 s
% 1.64/1.34 % (23480)Instructions burned: 18 (million)
% 1.64/1.34 % (23480)------------------------------
% 1.64/1.34 % (23480)------------------------------
% 1.64/1.34 % (23478)Instruction limit reached!
% 1.64/1.34 % (23478)------------------------------
% 1.64/1.34 % (23478)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.34 % (23478)Termination reason: Unknown
% 1.64/1.34 % (23478)Termination phase: Saturation
% 1.64/1.34
% 1.64/1.34 % (23478)Memory used [KB]: 5500
% 1.64/1.34 % (23478)Time elapsed: 0.004 s
% 1.64/1.34 % (23478)Instructions burned: 4 (million)
% 1.64/1.34 % (23478)------------------------------
% 1.64/1.34 % (23478)------------------------------
% 1.64/1.34 % (23479)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_23352 for (2999ds/4Mi)
% 1.64/1.34 % (23477)Instruction limit reached!
% 1.64/1.34 % (23477)------------------------------
% 1.64/1.34 % (23477)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.34 % (23477)Termination reason: Unknown
% 1.64/1.34 % (23477)Termination phase: Saturation
% 1.64/1.34
% 1.64/1.34 % (23477)Memory used [KB]: 5500
% 1.64/1.34 % (23477)Time elapsed: 0.006 s
% 1.64/1.34 % (23477)Instructions burned: 7 (million)
% 1.64/1.34 % (23477)------------------------------
% 1.64/1.34 % (23477)------------------------------
% 1.64/1.35 % (23479)Instruction limit reached!
% 1.64/1.35 % (23479)------------------------------
% 1.64/1.35 % (23479)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.35 % (23479)Termination reason: Unknown
% 1.64/1.35 % (23479)Termination phase: Saturation
% 1.64/1.35
% 1.64/1.35 % (23479)Memory used [KB]: 5500
% 1.64/1.35 % (23479)Time elapsed: 0.004 s
% 1.64/1.35 % (23479)Instructions burned: 4 (million)
% 1.64/1.35 % (23479)------------------------------
% 1.64/1.35 % (23479)------------------------------
% 1.64/1.35 % (23482)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_23352 for (2999ds/6Mi)
% 1.64/1.35 % (23482)Instruction limit reached!
% 1.64/1.35 % (23482)------------------------------
% 1.64/1.35 % (23482)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.35 % (23482)Termination reason: Unknown
% 1.64/1.35 % (23482)Termination phase: Saturation
% 1.64/1.35
% 1.64/1.35 % (23482)Memory used [KB]: 5500
% 1.64/1.35 % (23482)Time elapsed: 0.003 s
% 1.64/1.35 % (23482)Instructions burned: 6 (million)
% 1.64/1.35 % (23482)------------------------------
% 1.64/1.35 % (23482)------------------------------
% 1.64/1.36 % (23481)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_23352 for (2999ds/710Mi)
% 1.64/1.36 % (23483)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_23352 for (2999ds/902Mi)
% 1.64/1.36 % (23484)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_23352 for (2999ds/21Mi)
% 1.64/1.36 % (23485)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_23352 for (2999ds/5Mi)
% 1.64/1.36 % (23483)Refutation not found, incomplete strategy
% 1.64/1.36 % (23483)------------------------------
% 1.64/1.36 % (23483)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.36 % (23483)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.36
% 1.64/1.36
% 1.64/1.36 % (23483)Memory used [KB]: 5500
% 1.64/1.36 % (23483)Time elapsed: 0.004 s
% 1.64/1.36 % (23483)Instructions burned: 3 (million)
% 1.64/1.36 % (23483)------------------------------
% 1.64/1.36 % (23483)------------------------------
% 1.64/1.36 % (23486)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_23352 for (2999ds/6Mi)
% 1.64/1.37 % (23486)Instruction limit reached!
% 1.64/1.37 % (23486)------------------------------
% 1.64/1.37 % (23486)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.37 % (23486)Termination reason: Unknown
% 1.64/1.37 % (23486)Termination phase: Saturation
% 1.64/1.37
% 1.64/1.37 % (23486)Memory used [KB]: 5500
% 1.64/1.37 % (23486)Time elapsed: 0.003 s
% 1.64/1.37 % (23486)Instructions burned: 7 (million)
% 1.64/1.37 % (23486)------------------------------
% 1.64/1.37 % (23486)------------------------------
% 1.64/1.37 % (23485)Instruction limit reached!
% 1.64/1.37 % (23485)------------------------------
% 1.64/1.37 % (23485)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.37 % (23485)Termination reason: Unknown
% 1.64/1.37 % (23485)Termination phase: Saturation
% 1.64/1.37
% 1.64/1.37 % (23485)Memory used [KB]: 5500
% 1.64/1.37 % (23485)Time elapsed: 0.005 s
% 1.64/1.37 % (23485)Instructions burned: 6 (million)
% 1.64/1.37 % (23485)------------------------------
% 1.64/1.37 % (23485)------------------------------
% 1.64/1.38 % (23488)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_23352 for (2999ds/779Mi)
% 1.64/1.38 % (23484)Instruction limit reached!
% 1.64/1.38 % (23484)------------------------------
% 1.64/1.38 % (23484)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.38 % (23484)Termination reason: Unknown
% 1.64/1.38 % (23484)Termination phase: Saturation
% 1.64/1.38
% 1.64/1.38 % (23484)Memory used [KB]: 5628
% 1.64/1.38 % (23484)Time elapsed: 0.016 s
% 1.64/1.38 % (23484)Instructions burned: 21 (million)
% 1.64/1.38 % (23484)------------------------------
% 1.64/1.38 % (23484)------------------------------
% 1.64/1.38 % (23487)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_23352 for (2999ds/377Mi)
% 1.64/1.38 % (23489)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_23352 for (2999ds/19Mi)
% 1.64/1.39 % (23489)Instruction limit reached!
% 1.64/1.39 % (23489)------------------------------
% 1.64/1.39 % (23489)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.39 % (23489)Termination reason: Unknown
% 1.64/1.39 % (23489)Termination phase: Saturation
% 1.64/1.39
% 1.64/1.39 % (23489)Memory used [KB]: 5628
% 1.64/1.39 % (23489)Time elapsed: 0.011 s
% 1.64/1.39 % (23489)Instructions burned: 21 (million)
% 1.64/1.39 % (23489)------------------------------
% 1.64/1.39 % (23489)------------------------------
% 1.64/1.39 % (23490)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_23352 for (2999ds/879Mi)
% 1.64/1.39 % (23472)First to succeed.
% 1.64/1.40 % (23472)Refutation found. Thanks to Tanya!
% 1.64/1.40 % SZS status Theorem for DTF2THF_23352
% 1.64/1.40 % SZS output start Proof for DTF2THF_23352
% 1.64/1.40 thf(func_def_1, type, cPSI: $i > $i > $i).
% 1.64/1.40 thf(func_def_2, type, cS: $i > $i).
% 1.64/1.40 thf(func_def_4, type, cPETER_INDEQS: $i > ($i > $i) > ($i > $i > $i) > $o).
% 1.64/1.40 thf(func_def_20, type, ph1: !>[X0: $tType]:(X0)).
% 1.64/1.40 thf(func_def_29, type, sK10: $i > $i).
% 1.64/1.40 thf(func_def_30, type, sK11: $i > $i).
% 1.64/1.40 thf(f623,plain,(
% 1.64/1.40 $false),
% 1.64/1.40 inference(avatar_sat_refutation,[status(thm)],[f180,f194,f621])).
% 1.64/1.40 thf(f621,plain,(
% 1.64/1.40 ~spl0_4),
% 1.64/1.40 inference(avatar_contradiction_clause,[status(thm)],[f620])).
% 1.64/1.40 thf(f620,plain,(
% 1.64/1.40 $false | ~spl0_4),
% 1.64/1.40 inference(trivial_inequality_removal,[status(thm)],[f616])).
% 1.64/1.40 thf(f616,plain,(
% 1.64/1.40 ($false = $true) | ~spl0_4),
% 1.64/1.40 inference(superposition,[status(thm)],[f584,f261])).
% 1.64/1.40 thf(f261,plain,(
% 1.64/1.40 ( ! [X1 : $i] : (($true = (?? @ $i @ (^[Y0 : $i]: ((cS @ (sK10 @ X1)) = (cS @ Y0)))))) ) | ~spl0_4),
% 1.64/1.40 inference(backward_demodulation,[status(thm)],[f250,f257])).
% 1.64/1.40 thf(f257,plain,(
% 1.64/1.40 ( ! [X1 : $i] : (((cPSI @ sK7 @ X1) = (cS @ (sK10 @ X1)))) ) | ~spl0_4),
% 1.64/1.40 inference(equality_proxy_clausification,[status(thm)],[f256])).
% 1.64/1.40 thf(f256,plain,(
% 1.64/1.40 ( ! [X1 : $i] : ((((cPSI @ sK7 @ X1) = (cS @ (sK10 @ X1))) = $true)) ) | ~spl0_4),
% 1.64/1.40 inference(beta_eta_normalization,[status(thm)],[f255])).
% 1.64/1.40 thf(f255,plain,(
% 1.64/1.40 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((cPSI @ sK7 @ X1) = (cS @ Y0))) @ (sK10 @ X1)))) ) | ~spl0_4),
% 1.64/1.40 inference(sigma_clausification,[status(thm)],[f250])).
% 1.64/1.40 thf(f250,plain,(
% 1.64/1.40 ( ! [X1 : $i] : (((?? @ $i @ (^[Y0 : $i]: ((cPSI @ sK7 @ X1) = (cS @ Y0)))) = $true)) ) | ~spl0_4),
% 1.64/1.40 inference(beta_eta_normalization,[status(thm)],[f248])).
% 1.64/1.40 thf(f248,plain,(
% 1.64/1.40 ( ! [X1 : $i] : ((((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((cPSI @ sK7 @ Y0) = (cS @ Y1))))) @ X1) = $true)) ) | ~spl0_4),
% 1.64/1.40 inference(pi_clausification,[status(thm)],[f205])).
% 1.64/1.40 thf(f205,plain,(
% 1.64/1.40 ($true = (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((cPSI @ sK7 @ Y0) = (cS @ Y1))))))) | ~spl0_4),
% 1.64/1.40 inference(binary_proxy_clausification,[status(thm)],[f199])).
% 1.64/1.40 thf(f199,plain,(
% 1.64/1.40 ($false = ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((cPSI @ sK7 @ Y0) = (cS @ Y1)))))) => (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((cPSI @ (cS @ sK7) @ Y0) = (cS @ Y1)))))))) | ~spl0_4),
% 1.64/1.40 inference(beta_eta_normalization,[status(thm)],[f197])).
% 1.64/1.40 thf(f197,plain,(
% 1.64/1.40 ($false = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((cPSI @ Y0 @ Y1) = (cS @ Y2)))))) => (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((cPSI @ (cS @ Y0) @ Y1) = (cS @ Y2)))))))) @ sK7)) | ~spl0_4),
% 1.64/1.40 inference(sigma_clausification,[status(thm)],[f179])).
% 1.64/1.40 thf(f179,plain,(
% 1.64/1.40 ($false = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((cPSI @ Y0 @ Y1) = (cS @ Y2)))))) => (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((cPSI @ (cS @ Y0) @ Y1) = (cS @ Y2)))))))))) | ~spl0_4),
% 1.64/1.40 inference(avatar_component_clause,[status(thm)],[f178])).
% 1.64/1.40 thf(f178,definition,(
% 1.64/1.40 spl0_4 <=> ($false = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((cPSI @ Y0 @ Y1) = (cS @ Y2)))))) => (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((cPSI @ (cS @ Y0) @ Y1) = (cS @ Y2))))))))))),
% 1.64/1.40 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.64/1.40 thf(f584,plain,(
% 1.64/1.40 ($false = (?? @ $i @ (^[Y0 : $i]: ((cS @ (sK10 @ (cS @ sK16))) = (cS @ Y0))))) | ~spl0_4),
% 1.64/1.40 inference(backward_demodulation,[status(thm)],[f383,f583])).
% 1.64/1.40 thf(f583,plain,(
% 1.64/1.40 ((cPSI @ (cS @ sK7) @ (cS @ sK12)) = (cS @ (sK10 @ (cS @ sK16)))) | ~spl0_4),
% 1.64/1.40 inference(forward_demodulation,[status(thm)],[f582,f257])).
% 1.64/1.40 thf(f582,plain,(
% 1.64/1.40 ((cPSI @ (cS @ sK7) @ (cS @ sK12)) = (cPSI @ sK7 @ (cS @ sK16))) | ~spl0_4),
% 1.64/1.40 inference(superposition,[status(thm)],[f61,f577])).
% 1.64/1.40 thf(f577,plain,(
% 1.64/1.40 ((cPSI @ (cS @ sK7) @ sK12) = (cS @ sK16)) | ~spl0_4),
% 1.64/1.40 inference(equality_proxy_clausification,[status(thm)],[f576])).
% 1.64/1.40 thf(f576,plain,(
% 1.64/1.40 ($true = ((cPSI @ (cS @ sK7) @ sK12) = (cS @ sK16))) | ~spl0_4),
% 1.64/1.40 inference(beta_eta_normalization,[status(thm)],[f575])).
% 1.64/1.40 thf(f575,plain,(
% 1.64/1.40 (((^[Y0 : $i]: ((cPSI @ (cS @ sK7) @ sK12) = (cS @ Y0))) @ sK16) = $true) | ~spl0_4),
% 1.64/1.40 inference(sigma_clausification,[status(thm)],[f384])).
% 1.64/1.40 thf(f384,plain,(
% 1.64/1.40 ($true = (?? @ $i @ (^[Y0 : $i]: ((cPSI @ (cS @ sK7) @ sK12) = (cS @ Y0))))) | ~spl0_4),
% 1.64/1.40 inference(binary_proxy_clausification,[status(thm)],[f376])).
% 1.64/1.40 thf(f376,plain,(
% 1.64/1.40 (((?? @ $i @ (^[Y0 : $i]: ((cPSI @ (cS @ sK7) @ sK12) = (cS @ Y0)))) => (?? @ $i @ (^[Y0 : $i]: ((cPSI @ (cS @ sK7) @ (cS @ sK12)) = (cS @ Y0))))) = $false) | ~spl0_4),
% 1.64/1.40 inference(beta_eta_normalization,[status(thm)],[f374])).
% 1.64/1.40 thf(f374,plain,(
% 1.64/1.40 ($false = ((^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((cPSI @ (cS @ sK7) @ Y0) = (cS @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((cPSI @ (cS @ sK7) @ (cS @ Y0)) = (cS @ Y1)))))) @ sK12)) | ~spl0_4),
% 1.64/1.40 inference(sigma_clausification,[status(thm)],[f371])).
% 1.64/1.40 thf(f371,plain,(
% 1.64/1.40 ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((cPSI @ (cS @ sK7) @ Y0) = (cS @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((cPSI @ (cS @ sK7) @ (cS @ Y0)) = (cS @ Y1))))))) = $false) | ~spl0_4),
% 1.64/1.40 inference(not_proxy_clausification,[status(thm)],[f254])).
% 1.64/1.40 thf(f254,plain,(
% 1.64/1.40 ((~ (!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((cPSI @ (cS @ sK7) @ Y0) = (cS @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((cPSI @ (cS @ sK7) @ (cS @ Y0)) = (cS @ Y1)))))))) = $true) | ~spl0_4),
% 1.64/1.40 inference(boolean_simplification,[status(thm)],[f253])).
% 1.64/1.40 thf(f253,plain,(
% 1.64/1.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((cPSI @ (cS @ sK7) @ Y0) = (cS @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((cPSI @ (cS @ sK7) @ (cS @ Y0)) = (cS @ Y1))))))) & $true))) | ~spl0_4),
% 1.64/1.40 inference(backward_demodulation,[status(thm)],[f216,f250])).
% 1.64/1.40 thf(f216,plain,(
% 1.64/1.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((cPSI @ (cS @ sK7) @ Y0) = (cS @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((cPSI @ (cS @ sK7) @ (cS @ Y0)) = (cS @ Y1))))))) & (?? @ $i @ (^[Y0 : $i]: ((cPSI @ sK7 @ (cS @ c0)) = (cS @ Y0))))))) | ~spl0_4),
% 1.64/1.40 inference(forward_demodulation,[status(thm)],[f214,f52])).
% 1.64/1.40 thf(f52,plain,(
% 1.64/1.40 ( ! [X1 : $i] : (((cPSI @ (cS @ X1) @ c0) = (cPSI @ X1 @ (cS @ c0)))) )),
% 1.64/1.40 inference(equality_proxy_clausification,[status(thm)],[f51])).
% 1.64/1.40 thf(f51,plain,(
% 1.64/1.40 ( ! [X1 : $i] : ((((cPSI @ (cS @ X1) @ c0) = (cPSI @ X1 @ (cS @ c0))) = $true)) )),
% 1.64/1.40 inference(beta_eta_normalization,[status(thm)],[f50])).
% 1.64/1.40 thf(f50,plain,(
% 1.64/1.40 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((cPSI @ (cS @ Y0) @ c0) = (cPSI @ Y0 @ (cS @ c0)))) @ X1))) )),
% 1.64/1.40 inference(pi_clausification,[status(thm)],[f41])).
% 1.64/1.40 thf(f41,plain,(
% 1.64/1.40 ((!! @ $i @ (^[Y0 : $i]: ((cPSI @ (cS @ Y0) @ c0) = (cPSI @ Y0 @ (cS @ c0))))) = $true)),
% 1.64/1.40 inference(binary_proxy_clausification,[status(thm)],[f38])).
% 1.64/1.40 thf(f38,plain,(
% 1.64/1.40 (((!! @ $i @ (^[Y0 : $i]: ((cS @ Y0) = (cPSI @ c0 @ Y0)))) & (!! @ $i @ (^[Y0 : $i]: ((cPSI @ (cS @ Y0) @ c0) = (cPSI @ Y0 @ (cS @ c0)))))) = $true)),
% 1.64/1.40 inference(boolean_simplification,[status(thm)],[f37])).
% 1.64/1.40 thf(f37,plain,(
% 1.64/1.40 ((((!! @ $i @ (^[Y0 : $i]: ((cS @ Y0) = (cPSI @ c0 @ Y0)))) & (!! @ $i @ (^[Y0 : $i]: ((cPSI @ (cS @ Y0) @ c0) = (cPSI @ Y0 @ (cS @ c0)))))) & $true) = $true)),
% 1.64/1.40 inference(backward_demodulation,[status(thm)],[f34,f35])).
% 1.64/1.40 thf(f35,plain,(
% 1.64/1.40 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cPSI @ Y1 @ (cPSI @ (cS @ Y1) @ Y0)) = (cPSI @ (cS @ Y1) @ (cS @ Y0))))))) = $true)),
% 1.64/1.40 inference(binary_proxy_clausification,[status(thm)],[f34])).
% 1.64/1.40 thf(f34,plain,(
% 1.64/1.40 ($true = (((!! @ $i @ (^[Y0 : $i]: ((cS @ Y0) = (cPSI @ c0 @ Y0)))) & (!! @ $i @ (^[Y0 : $i]: ((cPSI @ (cS @ Y0) @ c0) = (cPSI @ Y0 @ (cS @ c0)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cPSI @ Y1 @ (cPSI @ (cS @ Y1) @ Y0)) = (cPSI @ (cS @ Y1) @ (cS @ Y0)))))))))),
% 1.64/1.40 inference(boolean_simplification,[status(thm)],[f33])).
% 1.64/1.40 thf(f33,plain,(
% 1.64/1.40 ($true = ($true & (((!! @ $i @ (^[Y0 : $i]: ((cS @ Y0) = (cPSI @ c0 @ Y0)))) & (!! @ $i @ (^[Y0 : $i]: ((cPSI @ (cS @ Y0) @ c0) = (cPSI @ Y0 @ (cS @ c0)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cPSI @ Y1 @ (cPSI @ (cS @ Y1) @ Y0)) = (cPSI @ (cS @ Y1) @ (cS @ Y0))))))))))),
% 1.64/1.40 inference(backward_demodulation,[status(thm)],[f21,f32])).
% 1.64/1.40 thf(f32,plain,(
% 1.64/1.40 ($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1))))) & (Y0 @ c0)) => (!! @ $i @ Y0)))))),
% 1.64/1.40 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.64/1.40 thf(f21,plain,(
% 1.64/1.40 (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1))))) & (Y0 @ c0)) => (!! @ $i @ Y0)))) & (((!! @ $i @ (^[Y0 : $i]: ((cS @ Y0) = (cPSI @ c0 @ Y0)))) & (!! @ $i @ (^[Y0 : $i]: ((cPSI @ (cS @ Y0) @ c0) = (cPSI @ Y0 @ (cS @ c0)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cPSI @ Y1 @ (cPSI @ (cS @ Y1) @ Y0)) = (cPSI @ (cS @ Y1) @ (cS @ Y0))))))))) = $true)),
% 1.64/1.40 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.64/1.40 thf(f17,plain,(
% 1.64/1.40 ($false = (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1))))) & (Y0 @ c0)) => (!! @ $i @ Y0)))) & (((!! @ $i @ (^[Y0 : $i]: ((cS @ Y0) = (cPSI @ c0 @ Y0)))) & (!! @ $i @ (^[Y0 : $i]: ((cPSI @ (cS @ Y0) @ c0) = (cPSI @ Y0 @ (cS @ c0)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cPSI @ Y1 @ (cPSI @ (cS @ Y1) @ Y0)) = (cPSI @ (cS @ Y1) @ (cS @ Y0))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((cPSI @ Y0 @ Y1) = (cS @ Y2))))))))))),
% 1.64/1.40 inference(not_proxy_clausification,[status(thm)],[f16])).
% 1.64/1.40 thf(f16,plain,(
% 1.64/1.40 ((~ (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1))))) & (Y0 @ c0)) => (!! @ $i @ Y0)))) & (((!! @ $i @ (^[Y0 : $i]: ((cS @ Y0) = (cPSI @ c0 @ Y0)))) & (!! @ $i @ (^[Y0 : $i]: ((cPSI @ (cS @ Y0) @ c0) = (cPSI @ Y0 @ (cS @ c0)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cPSI @ Y1 @ (cPSI @ (cS @ Y1) @ Y0)) = (cPSI @ (cS @ Y1) @ (cS @ Y0))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((cPSI @ Y0 @ Y1) = (cS @ Y2)))))))))) = $true)),
% 1.64/1.40 inference(beta_eta_normalization,[status(thm)],[f15])).
% 1.64/1.40 thf(f15,plain,(
% 1.64/1.40 ((~ (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1))))) & (Y0 @ c0)) => (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & ((^[Y0 : $i]: ((^[Y1 : $i > $i]: ((^[Y2 : $i > $i > $i]: (((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) = (Y2 @ Y0 @ Y3)))) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ (Y1 @ Y3) @ Y0) = (Y2 @ Y3 @ (Y1 @ Y0)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ (Y2 @ (Y1 @ Y4) @ Y3)) = (Y2 @ (Y1 @ Y4) @ (Y1 @ Y3))))))))))))) @ c0 @ cS @ cPSI)) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((cPSI @ Y0 @ Y1) = (cS @ Y2)))))))))) = $true)),
% 1.64/1.40 inference(definition_unfolding,[status(thm)],[f14,f13,f12])).
% 1.64/1.40 thf(f12,plain,(
% 1.64/1.40 (cPETER_INDEQS = (^[Y0 : $i]: ((^[Y1 : $i > $i]: ((^[Y2 : $i > $i > $i]: (((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) = (Y2 @ Y0 @ Y3)))) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ (Y1 @ Y3) @ Y0) = (Y2 @ Y3 @ (Y1 @ Y0)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ (Y2 @ (Y1 @ Y4) @ Y3)) = (Y2 @ (Y1 @ Y4) @ (Y1 @ Y3))))))))))))))),
% 1.64/1.40 inference(cnf_transformation,[status(thm)],[f7])).
% 1.64/1.40 thf(f7,plain,(
% 1.64/1.40 (cPETER_INDEQS = (^[Y0 : $i]: ((^[Y1 : $i > $i]: ((^[Y2 : $i > $i > $i]: (((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) = (Y2 @ Y0 @ Y3)))) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ (Y1 @ Y3) @ Y0) = (Y2 @ Y3 @ (Y1 @ Y0)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ (Y2 @ (Y1 @ Y4) @ Y3)) = (Y2 @ (Y1 @ Y4) @ (Y1 @ Y3))))))))))))))),
% 1.64/1.40 inference(fool_elimination,[status(thm)],[f6])).
% 1.64/1.40 thf(f6,plain,(
% 1.64/1.40 ((^[X0 : $i, X1 : $i > $i, X2 : $i > $i > $i] : (! [X3 : $i,X4 : $i] : ((X2 @ X3 @ (X2 @ (X1 @ X3) @ X4)) = (X2 @ (X1 @ X3) @ (X1 @ X4))) & ! [X5 : $i] : ((X2 @ (X1 @ X5) @ X0) = (X2 @ X5 @ (X1 @ X0))) & ! [X6 : $i] : ((X1 @ X6) = (X2 @ X0 @ X6)))) = cPETER_INDEQS)),
% 1.64/1.40 inference(rectify,[status(thm)],[f2])).
% 1.64/1.40 thf(f2,axiom,(
% 1.64/1.40 ((^[X2 : $i, X3 : $i > $i, X4 : $i > $i > $i] : (! [X6 : $i,X5 : $i] : ((X4 @ (X3 @ X6) @ (X3 @ X5)) = (X4 @ X6 @ (X4 @ (X3 @ X6) @ X5))) & ! [X6 : $i] : ((X4 @ (X3 @ X6) @ X2) = (X4 @ X6 @ (X3 @ X2))) & ! [X5 : $i] : ((X4 @ X2 @ X5) = (X3 @ X5)))) = cPETER_INDEQS)),
% 1.64/1.40 file('/export/starexec/sandbox2/tmp/tmp.3GJoy61PLV/DTF2THF_23352.p',cPETER_INDEQS_def)).
% 1.64/1.40 thf(f13,plain,(
% 1.64/1.40 (cIND = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1))))) & (Y0 @ c0)) => (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))))),
% 1.64/1.40 inference(cnf_transformation,[status(thm)],[f9])).
% 1.64/1.40 thf(f9,plain,(
% 1.64/1.40 (cIND = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1))))) & (Y0 @ c0)) => (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))))),
% 1.64/1.40 inference(fool_elimination,[status(thm)],[f8])).
% 1.64/1.40 thf(f8,plain,(
% 1.64/1.40 (cIND = ! [X0 : $i > $o] : (((X0 @ c0) & ! [X1 : $i] : ((X0 @ X1) => (X0 @ (cS @ X1)))) => ! [X2 : $i] : (X0 @ X2)))),
% 1.64/1.40 inference(rectify,[status(thm)],[f1])).
% 1.64/1.40 thf(f1,axiom,(
% 1.64/1.40 (cIND = ! [X0 : $i > $o] : (((X0 @ c0) & ! [X1 : $i] : ((X0 @ X1) => (X0 @ (cS @ X1)))) => ! [X1 : $i] : (X0 @ X1)))),
% 1.64/1.40 file('/export/starexec/sandbox2/tmp/tmp.3GJoy61PLV/DTF2THF_23352.p',cIND_def)).
% 1.64/1.40 thf(f14,plain,(
% 1.64/1.40 ($true = (~ ((cIND & (cPETER_INDEQS @ c0 @ cS @ cPSI)) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((cPSI @ Y0 @ Y1) = (cS @ Y2)))))))))))),
% 1.64/1.40 inference(cnf_transformation,[status(thm)],[f11])).
% 1.64/1.40 thf(f11,plain,(
% 1.64/1.40 ($true = (~ ((cIND & (cPETER_INDEQS @ c0 @ cS @ cPSI)) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((cPSI @ Y0 @ Y1) = (cS @ Y2)))))))))))),
% 1.64/1.40 inference(fool_elimination,[status(thm)],[f10])).
% 1.64/1.40 thf(f10,plain,(
% 1.64/1.40 ~(((cPETER_INDEQS @ c0 @ cS @ cPSI) & cIND) => ! [X0 : $i,X1 : $i] : ? [X2 : $i] : ((cPSI @ X1 @ X0) = (cS @ X2)))),
% 1.64/1.40 inference(rectify,[status(thm)],[f4])).
% 1.64/1.40 thf(f4,negated_conjecture,(
% 1.64/1.40 ~(((cPETER_INDEQS @ c0 @ cS @ cPSI) & cIND) => ! [X5 : $i,X6 : $i] : ? [X7 : $i] : ((cPSI @ X6 @ X5) = (cS @ X7)))),
% 1.64/1.40 inference(negated_conjecture,[status(cth)],[f3])).
% 1.64/1.40 thf(f3,conjecture,(
% 1.64/1.40 ((cPETER_INDEQS @ c0 @ cS @ cPSI) & cIND) => ! [X5 : $i,X6 : $i] : ? [X7 : $i] : ((cPSI @ X6 @ X5) = (cS @ X7))),
% 1.64/1.40 file('/export/starexec/sandbox2/tmp/tmp.3GJoy61PLV/DTF2THF_23352.p',cTHM585)).
% 1.64/1.40 thf(f214,plain,(
% 1.64/1.40 ((~ ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((cPSI @ (cS @ sK7) @ Y0) = (cS @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((cPSI @ (cS @ sK7) @ (cS @ Y0)) = (cS @ Y1))))))) & (?? @ $i @ (^[Y0 : $i]: ((cPSI @ (cS @ sK7) @ c0) = (cS @ Y0)))))) = $true) | ~spl0_4),
% 1.64/1.40 inference(boolean_simplification,[status(thm)],[f213])).
% 1.64/1.40 thf(f213,plain,(
% 1.64/1.40 ((((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((cPSI @ (cS @ sK7) @ Y0) = (cS @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((cPSI @ (cS @ sK7) @ (cS @ Y0)) = (cS @ Y1))))))) & (?? @ $i @ (^[Y0 : $i]: ((cPSI @ (cS @ sK7) @ c0) = (cS @ Y0))))) => $false) = $true) | ~spl0_4),
% 1.64/1.40 inference(beta_eta_normalization,[status(thm)],[f212])).
% 1.64/1.40 thf(f212,plain,(
% 1.64/1.40 ($true = (((!! @ $i @ (^[Y0 : $i]: (((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((cPSI @ (cS @ sK7) @ Y1) = (cS @ Y2))))) @ Y0) => ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((cPSI @ (cS @ sK7) @ Y1) = (cS @ Y2))))) @ (cS @ Y0))))) & ((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((cPSI @ (cS @ sK7) @ Y0) = (cS @ Y1))))) @ c0)) => $false)) | ~spl0_4),
% 1.64/1.40 inference(superposition,[status(thm)],[f75,f207])).
% 1.64/1.40 thf(f207,plain,(
% 1.64/1.40 ($false = (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((cPSI @ (cS @ sK7) @ Y0) = (cS @ Y1))))))) | ~spl0_4),
% 1.64/1.40 inference(boolean_simplification,[status(thm)],[f206])).
% 1.64/1.40 thf(f206,plain,(
% 1.64/1.40 (($true => (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((cPSI @ (cS @ sK7) @ Y0) = (cS @ Y1))))))) = $false) | ~spl0_4),
% 1.64/1.40 inference(backward_demodulation,[status(thm)],[f199,f205])).
% 1.64/1.40 thf(f75,plain,(
% 1.64/1.40 ( ! [X1 : $i > $o] : (((((!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (cS @ Y0))))) & (X1 @ c0)) => (!! @ $i @ X1)) = $true)) )),
% 1.64/1.40 inference(beta_eta_normalization,[status(thm)],[f74])).
% 1.64/1.40 thf(f74,plain,(
% 1.64/1.40 ( ! [X1 : $i > $o] : ((((^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1))))) & (Y0 @ c0)) => (!! @ $i @ Y0))) @ X1) = $true)) )),
% 1.64/1.40 inference(pi_clausification,[status(thm)],[f32])).
% 1.64/1.40 thf(f61,plain,(
% 1.64/1.40 ( ! [X2 : $i,X1 : $i] : (((cPSI @ X2 @ (cPSI @ (cS @ X2) @ X1)) = (cPSI @ (cS @ X2) @ (cS @ X1)))) )),
% 1.64/1.40 inference(equality_proxy_clausification,[status(thm)],[f60])).
% 1.64/1.40 thf(f60,plain,(
% 1.64/1.40 ( ! [X2 : $i,X1 : $i] : (($true = ((cPSI @ X2 @ (cPSI @ (cS @ X2) @ X1)) = (cPSI @ (cS @ X2) @ (cS @ X1))))) )),
% 1.64/1.40 inference(beta_eta_normalization,[status(thm)],[f59])).
% 1.64/1.40 thf(f59,plain,(
% 1.64/1.40 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((cPSI @ Y0 @ (cPSI @ (cS @ Y0) @ X1)) = (cPSI @ (cS @ Y0) @ (cS @ X1)))) @ X2))) )),
% 1.64/1.40 inference(pi_clausification,[status(thm)],[f40])).
% 1.64/1.40 thf(f40,plain,(
% 1.64/1.40 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((cPSI @ Y0 @ (cPSI @ (cS @ Y0) @ X1)) = (cPSI @ (cS @ Y0) @ (cS @ X1))))) = $true)) )),
% 1.64/1.40 inference(beta_eta_normalization,[status(thm)],[f39])).
% 1.64/1.40 thf(f39,plain,(
% 1.64/1.40 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cPSI @ Y1 @ (cPSI @ (cS @ Y1) @ Y0)) = (cPSI @ (cS @ Y1) @ (cS @ Y0)))))) @ X1))) )),
% 1.64/1.40 inference(pi_clausification,[status(thm)],[f35])).
% 1.64/1.40 thf(f383,plain,(
% 1.64/1.40 ($false = (?? @ $i @ (^[Y0 : $i]: ((cPSI @ (cS @ sK7) @ (cS @ sK12)) = (cS @ Y0))))) | ~spl0_4),
% 1.64/1.40 inference(binary_proxy_clausification,[status(thm)],[f376])).
% 1.64/1.40 thf(f194,plain,(
% 1.64/1.40 ~spl0_3),
% 1.64/1.40 inference(avatar_contradiction_clause,[status(thm)],[f193])).
% 1.64/1.40 thf(f193,plain,(
% 1.64/1.40 $false | ~spl0_3),
% 1.64/1.40 inference(equality_resolution,[status(thm)],[f192])).
% 1.64/1.40 thf(f192,plain,(
% 1.64/1.40 ( ! [X1 : $i] : (((cS @ X1) != (cS @ sK6))) ) | ~spl0_3),
% 1.64/1.40 inference(equality_proxy_clausification,[status(thm)],[f191])).
% 1.64/1.40 thf(f191,plain,(
% 1.64/1.40 ( ! [X1 : $i] : ((((cS @ sK6) = (cS @ X1)) = $false)) ) | ~spl0_3),
% 1.64/1.40 inference(beta_eta_normalization,[status(thm)],[f190])).
% 1.64/1.40 thf(f190,plain,(
% 1.64/1.40 ( ! [X1 : $i] : (($false = ((^[Y0 : $i]: ((cS @ sK6) = (cS @ Y0))) @ X1))) ) | ~spl0_3),
% 1.64/1.40 inference(pi_clausification,[status(thm)],[f188])).
% 1.64/1.40 thf(f188,plain,(
% 1.64/1.40 ($false = (?? @ $i @ (^[Y0 : $i]: ((cS @ sK6) = (cS @ Y0))))) | ~spl0_3),
% 1.64/1.40 inference(forward_demodulation,[status(thm)],[f187,f47])).
% 1.64/1.40 thf(f47,plain,(
% 1.64/1.40 ( ! [X1 : $i] : (((cS @ X1) = (cPSI @ c0 @ X1))) )),
% 1.64/1.40 inference(equality_proxy_clausification,[status(thm)],[f46])).
% 1.64/1.40 thf(f46,plain,(
% 1.64/1.40 ( ! [X1 : $i] : (($true = ((cS @ X1) = (cPSI @ c0 @ X1)))) )),
% 1.64/1.40 inference(beta_eta_normalization,[status(thm)],[f45])).
% 1.64/1.40 thf(f45,plain,(
% 1.64/1.40 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((cS @ Y0) = (cPSI @ c0 @ Y0))) @ X1))) )),
% 1.64/1.40 inference(pi_clausification,[status(thm)],[f44])).
% 1.64/1.40 thf(f44,plain,(
% 1.64/1.40 ((!! @ $i @ (^[Y0 : $i]: ((cS @ Y0) = (cPSI @ c0 @ Y0)))) = $true)),
% 1.64/1.40 inference(boolean_simplification,[status(thm)],[f43])).
% 1.64/1.40 thf(f43,plain,(
% 1.64/1.40 ($true = ((!! @ $i @ (^[Y0 : $i]: ((cS @ Y0) = (cPSI @ c0 @ Y0)))) & $true))),
% 1.64/1.40 inference(backward_demodulation,[status(thm)],[f38,f41])).
% 1.64/1.40 thf(f187,plain,(
% 1.64/1.40 ($false = (?? @ $i @ (^[Y0 : $i]: ((cPSI @ c0 @ sK6) = (cS @ Y0))))) | ~spl0_3),
% 1.64/1.40 inference(beta_eta_normalization,[status(thm)],[f183])).
% 1.64/1.40 thf(f183,plain,(
% 1.64/1.40 (((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((cPSI @ c0 @ Y0) = (cS @ Y1))))) @ sK6) = $false) | ~spl0_3),
% 1.64/1.40 inference(sigma_clausification,[status(thm)],[f176])).
% 1.64/1.40 thf(f176,plain,(
% 1.64/1.40 ($false = (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((cPSI @ c0 @ Y0) = (cS @ Y1))))))) | ~spl0_3),
% 1.64/1.40 inference(avatar_component_clause,[status(thm)],[f175])).
% 1.64/1.40 thf(f175,definition,(
% 1.64/1.40 spl0_3 <=> ($false = (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((cPSI @ c0 @ Y0) = (cS @ Y1)))))))),
% 1.64/1.40 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.64/1.40 thf(f180,plain,(
% 1.64/1.40 spl0_3 | spl0_4),
% 1.64/1.40 inference(avatar_split_clause,[status(thm)],[f173,f178,f175])).
% 1.64/1.40 thf(f173,plain,(
% 1.64/1.40 ($false = (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((cPSI @ c0 @ Y0) = (cS @ Y1))))))) | ($false = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((cPSI @ Y0 @ Y1) = (cS @ Y2)))))) => (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((cPSI @ (cS @ Y0) @ Y1) = (cS @ Y2))))))))))),
% 1.64/1.40 inference(binary_proxy_clausification,[status(thm)],[f166])).
% 1.64/1.40 thf(f166,plain,(
% 1.64/1.40 ($false = ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((cPSI @ Y0 @ Y1) = (cS @ Y2)))))) => (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((cPSI @ (cS @ Y0) @ Y1) = (cS @ Y2))))))))) & (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((cPSI @ c0 @ Y0) = (cS @ Y1))))))))),
% 1.64/1.40 inference(not_proxy_clausification,[status(thm)],[f89])).
% 1.64/1.40 thf(f89,plain,(
% 1.64/1.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((cPSI @ Y0 @ Y1) = (cS @ Y2)))))) => (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((cPSI @ (cS @ Y0) @ Y1) = (cS @ Y2))))))))) & (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((cPSI @ c0 @ Y0) = (cS @ Y1)))))))))),
% 1.64/1.40 inference(boolean_simplification,[status(thm)],[f88])).
% 1.64/1.40 thf(f88,plain,(
% 1.64/1.40 ((((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((cPSI @ Y0 @ Y1) = (cS @ Y2)))))) => (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((cPSI @ (cS @ Y0) @ Y1) = (cS @ Y2))))))))) & (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((cPSI @ c0 @ Y0) = (cS @ Y1))))))) => $false) = $true)),
% 1.64/1.40 inference(beta_eta_normalization,[status(thm)],[f85])).
% 1.64/1.40 thf(f85,plain,(
% 1.64/1.40 ($true = (((!! @ $i @ (^[Y0 : $i]: (((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((cPSI @ Y1 @ Y2) = (cS @ Y3))))))) @ Y0) => ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((cPSI @ Y1 @ Y2) = (cS @ Y3))))))) @ (cS @ Y0))))) & ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((cPSI @ Y0 @ Y1) = (cS @ Y2))))))) @ c0)) => $false))),
% 1.64/1.40 inference(superposition,[status(thm)],[f75,f23])).
% 1.64/1.40 thf(f23,plain,(
% 1.64/1.40 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((cPSI @ Y0 @ Y1) = (cS @ Y2)))))))) = $false)),
% 1.64/1.40 inference(boolean_simplification,[status(thm)],[f22])).
% 1.64/1.40 thf(f22,plain,(
% 1.64/1.40 ($false = ($true => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((cPSI @ Y0 @ Y1) = (cS @ Y2))))))))))),
% 1.64/1.40 inference(backward_demodulation,[status(thm)],[f17,f21])).
% 1.64/1.40 % SZS output end Proof for DTF2THF_23352
% 1.64/1.40 % (23472)------------------------------
% 1.64/1.40 % (23472)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.40 % (23472)Termination reason: Refutation
% 1.64/1.40
% 1.64/1.40 % (23472)Memory used [KB]: 6524
% 1.64/1.40 % (23472)Time elapsed: 0.081 s
% 1.64/1.40 % (23472)Instructions burned: 200 (million)
% 1.64/1.40 % (23472)------------------------------
% 1.64/1.40 % (23472)------------------------------
% 1.64/1.40 % (23460)Success in time 0.115 s
%------------------------------------------------------------------------------