%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO555^1 : TPTP v9.2.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n001.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 09:54:32 AM UTC 2026
% Result : Theorem 2.08s 1.79s
% Output : Refutation 2.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 9
% Syntax : Number of formulae : 97 ( 30 unt; 0 typ; 4 def)
% Number of atoms : 465 ( 291 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 606 ( 109 ~; 142 |; 99 &; 246 @)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 9 con; 0-3 aty)
% Number of variables : 270 ( 66 ^; 198 !; 6 ?; 270 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
eps1: ( $i > $o ) > $i ).
thf(func_def_2,type,
if1: $o > $i > $i > $i ).
thf(func_def_3,type,
eps2: ( $i > $o ) > $i ).
thf(func_def_4,type,
if2: $o > $i > $i > $i ).
thf(func_def_17,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f200,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f125,f137,f157,f160,f199]) ).
thf(f199,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[status(thm)],[f198]) ).
thf(f198,plain,
( $false
| ~ spl0_4 ),
inference(equality_resolution,[status(thm)],[f136]) ).
thf(f136,plain,
( ! [X0: $i] : ( sK3 != X0 )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f135]) ).
thf(f135,definition,
( spl0_4
<=> ! [X0: $i] : ( sK3 != X0 ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f160,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f159]) ).
thf(f159,plain,
( $false
| ~ spl0_1
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f158]) ).
thf(f158,plain,
( ( $false = $true )
| ~ spl0_1
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f121,f133]) ).
thf(f133,plain,
( ( sK2 = $false )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f131]) ).
thf(f131,definition,
( spl0_3
<=> ( sK2 = $false ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f121,plain,
( ( sK2 = $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f119]) ).
thf(f119,definition,
( spl0_1
<=> ( sK2 = $true ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f157,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f156]) ).
thf(f156,plain,
( $false
| ~ spl0_2 ),
inference(equality_resolution,[status(thm)],[f124]) ).
thf(f124,plain,
( ! [X0: $i] : ( sK4 != X0 )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f123]) ).
thf(f123,definition,
( spl0_2
<=> ! [X0: $i] : ( sK4 != X0 ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f137,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f129,f135,f131]) ).
thf(f129,plain,
! [X0: $i] :
( ( sK3 != X0 )
| ( sK2 = $false ) ),
inference(subsumption_resolution,[status(thm)],[f127,f64]) ).
thf(f64,plain,
! [X2: $i,X3: $i,X0: $i,X1: $o] :
( ( ( if1 @ X1 @ X2 @ X0 )
= X2 )
| ( $false = X1 )
| ( X2 != X3 ) ),
inference(equality_proxy_clausification,[status(thm)],[f63]) ).
thf(f63,plain,
! [X2: $i,X3: $i,X0: $i,X1: $o] :
( ( ( if1 @ X1 @ X2 @ X0 )
= X2 )
| ( $false = X1 )
| ( ( X2 = X3 )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f62]) ).
thf(f62,plain,
! [X2: $i,X3: $i,X0: $i,X1: $o] :
( ( $false = X1 )
| ( $false = X1 )
| ( ( if1 @ X1 @ X2 @ X0 )
= X2 )
| ( ( X2 = X3 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f61]) ).
thf(f61,plain,
! [X2: $i,X3: $i,X0: $i,X1: $o] :
( ( ( if1 @ X1 @ X2 @ X0 )
= X2 )
| ( ( ( X2 = X3 )
& X1 )
= $false )
| ( $false = X1 ) ),
inference(not_proxy_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
! [X2: $i,X3: $i,X0: $i,X1: $o] :
( ( ( if1 @ X1 @ X2 @ X0 )
= X2 )
| ( ( ~ X1 ) = $true )
| ( ( ( X2 = X3 )
& X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
! [X2: $i,X3: $i,X0: $i,X1: $o] :
( ( ( if1 @ X1 @ X2 @ X0 )
= X2 )
| ( ( ( X0
= ( if1 @ X1 @ X2 @ X0 ) )
& ~ X1 )
= $true )
| ( ( ( X2 = X3 )
& X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
! [X2: $i,X3: $i,X0: $i,X1: $o] :
( ( ( ( ( X0 = X3 )
& ~ X1 )
| ( ( X2 = X3 )
& X1 ) )
!= $true )
| ( ( if1 @ X1 @ X2 @ X0 )
= X2 )
| ( ( ( X0
= ( if1 @ X1 @ X2 @ X0 ) )
& ~ X1 )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
! [X2: $i,X3: $i,X0: $i,X1: $o] :
( ( $true
= ( X2
= ( if1 @ X1 @ X2 @ X0 ) ) )
| ( ( ( ( X0 = X3 )
& ~ X1 )
| ( ( X2 = X3 )
& X1 ) )
!= $true )
| ( ( ( X0
= ( if1 @ X1 @ X2 @ X0 ) )
& ~ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
! [X2: $i,X3: $i,X0: $i,X1: $o] :
( ( ( ( X2
= ( if1 @ X1 @ X2 @ X0 ) )
& X1 )
= $true )
| ( ( ( ( X0 = X3 )
& ~ X1 )
| ( ( X2 = X3 )
& X1 ) )
!= $true )
| ( ( ( X0
= ( if1 @ X1 @ X2 @ X0 ) )
& ~ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
! [X2: $i,X3: $i,X0: $i,X1: $o] :
( ( ( ( ( X0
= ( if1 @ X1 @ X2 @ X0 ) )
& ~ X1 )
| ( ( X2
= ( if1 @ X1 @ X2 @ X0 ) )
& X1 ) )
= $true )
| ( ( ( ( X0 = X3 )
& ~ X1 )
| ( ( X2 = X3 )
& X1 ) )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f39]) ).
thf(f39,plain,
! [X2: $i,X3: $i,X0: $i,X1: $o] :
( ( ( ^ [Y0: $i] :
( ( ( X0 = Y0 )
& ~ X1 )
| ( ( X2 = Y0 )
& X1 ) )
@ ( if1 @ X1 @ X2 @ X0 ) )
= $true )
| ( ( ^ [Y0: $i] :
( ( ( X0 = Y0 )
& ~ X1 )
| ( ( X2 = Y0 )
& X1 ) )
@ X3 )
!= $true ) ),
inference(superposition,[status(thm)],[f22,f36]) ).
thf(f36,plain,
! [X2: $i,X3: $i,X1: $o] :
( ( eps1
@ ^ [Y0: $i] :
( ( ( X3 = Y0 )
& ~ X1 )
| ( ( X2 = Y0 )
& X1 ) ) )
= ( if1 @ X1 @ X2 @ X3 ) ),
inference(beta_eta_normalization,[status(thm)],[f35]) ).
thf(f35,plain,
! [X2: $i,X3: $i,X1: $o] :
( ( if1 @ X1 @ X2 @ X3 )
= ( ^ [Y0: $i] :
( eps1
@ ^ [Y1: $i] :
( ( ( Y0 = Y1 )
& ~ X1 )
| ( ( X2 = Y1 )
& X1 ) ) )
@ X3 ) ),
inference(argument_congruence,[status(thm)],[f32]) ).
thf(f32,plain,
! [X2: $i,X1: $o] :
( ( ^ [Y0: $i] :
( eps1
@ ^ [Y1: $i] :
( ( ( Y0 = Y1 )
& ~ X1 )
| ( ( X2 = Y1 )
& X1 ) ) ) )
= ( if1 @ X1 @ X2 ) ),
inference(beta_eta_normalization,[status(thm)],[f31]) ).
thf(f31,plain,
! [X2: $i,X1: $o] :
( ( if1 @ X1 @ X2 )
= ( ^ [Y0: $i,Y1: $i] :
( eps1
@ ^ [Y2: $i] :
( ( ( Y1 = Y2 )
& ~ X1 )
| ( ( Y0 = Y2 )
& X1 ) ) )
@ X2 ) ),
inference(argument_congruence,[status(thm)],[f26]) ).
thf(f26,plain,
! [X1: $o] :
( ( ^ [Y0: $i,Y1: $i] :
( eps1
@ ^ [Y2: $i] :
( ( ( Y1 = Y2 )
& ~ X1 )
| ( ( Y0 = Y2 )
& X1 ) ) ) )
= ( if1 @ X1 ) ),
inference(beta_eta_normalization,[status(thm)],[f25]) ).
thf(f25,plain,
! [X1: $o] :
( ( ^ [Y0: $o,Y1: $i,Y2: $i] :
( eps1
@ ^ [Y3: $i] :
( ( ( Y2 = Y3 )
& ~ Y0 )
| ( ( Y1 = Y3 )
& Y0 ) ) )
@ X1 )
= ( if1 @ X1 ) ),
inference(argument_congruence,[status(thm)],[f19]) ).
thf(f19,plain,
( if1
= ( ^ [Y0: $o,Y1: $i,Y2: $i] :
( eps1
@ ^ [Y3: $i] :
( ( ( Y2 = Y3 )
& ~ Y0 )
| ( ( Y1 = Y3 )
& Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( if1
= ( ^ [Y0: $o,Y1: $i,Y2: $i] :
( eps1
@ ^ [Y3: $i] :
( ( ( Y2 = Y3 )
& ~ Y0 )
| ( ( Y1 = Y3 )
& Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
( if1
= ( ^ [X0: $o,X1: $i,X2: $i] :
( eps1
@ ^ [X3: $i] :
( ( X0
& ( X1 = X3 ) )
| ( ~ X0
& ( X2 = X3 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( if1
= ( ^ [X2: $o,X1: $i,X3: $i] :
( eps1
@ ^ [X4: $i] :
( ( X2
& ( X1 = X4 ) )
| ( ~ X2
& ( X3 = X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.DKzUbxh46v/DTF2THF_8786.p',if1d) ).
thf(f22,plain,
! [X0: $i > $o,X1: $i] :
( ( ( X0 @ ( eps1 @ X0 ) )
= $true )
| ( ( X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: $i > $o] :
( ! [X1: $i] :
( ( X0 @ X1 )
!= $true )
| ( ( X0 @ ( eps1 @ X0 ) )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: $i > $o] :
( ? [X1: $i] :
( ( X0 @ X1 )
= $true )
=> ( ( X0 @ ( eps1 @ X0 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: $i > $o] :
( ? [X1: $i] : ( X0 @ X1 )
=> ( X0 @ ( eps1 @ X0 ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i > $o] :
( ? [X1: $i] : ( X0 @ X1 )
=> ( X0 @ ( eps1 @ X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.DKzUbxh46v/DTF2THF_8786.p',choiceax1) ).
thf(f127,plain,
! [X0: $i] :
( ( sK3 != X0 )
| ( ( if1 @ sK2 @ sK3 @ sK4 )
!= sK3 )
| ( sK2 = $false ) ),
inference(superposition,[status(thm)],[f30,f113]) ).
thf(f113,plain,
! [X2: $i,X3: $i,X0: $i,X1: $o] :
( ( ( if2 @ X1 @ X2 @ X0 )
= X2 )
| ( $false = X1 )
| ( X2 != X3 ) ),
inference(equality_proxy_clausification,[status(thm)],[f112]) ).
thf(f112,plain,
! [X2: $i,X3: $i,X0: $i,X1: $o] :
( ( $false = X1 )
| ( ( X2 = X3 )
= $false )
| ( ( if2 @ X1 @ X2 @ X0 )
= X2 ) ),
inference(duplicate_literal_removal,[status(thm)],[f111]) ).
thf(f111,plain,
! [X2: $i,X3: $i,X0: $i,X1: $o] :
( ( ( if2 @ X1 @ X2 @ X0 )
= X2 )
| ( $false = X1 )
| ( ( X2 = X3 )
= $false )
| ( $false = X1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f110]) ).
thf(f110,plain,
! [X2: $i,X3: $i,X0: $i,X1: $o] :
( ( ( X1
& ( X2 = X3 ) )
= $false )
| ( ( if2 @ X1 @ X2 @ X0 )
= X2 )
| ( $false = X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f106]) ).
thf(f106,plain,
! [X2: $i,X3: $i,X0: $i,X1: $o] :
( ( $false = X1 )
| ( ( X2
= ( if2 @ X1 @ X2 @ X0 ) )
= $true )
| ( ( X1
& ( X2 = X3 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f104]) ).
thf(f104,plain,
! [X2: $i,X3: $i,X0: $i,X1: $o] :
( ( ( ( ( X0 = X3 )
& ~ X1 )
| ( X1
& ( X2 = X3 ) ) )
!= $true )
| ( ( X2
= ( if2 @ X1 @ X2 @ X0 ) )
= $true )
| ( $false = X1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f103]) ).
thf(f103,plain,
! [X2: $i,X3: $i,X0: $i,X1: $o] :
( ( ( X1
& ( X2
= ( if2 @ X1 @ X2 @ X0 ) ) )
= $true )
| ( ( ( ( X0 = X3 )
& ~ X1 )
| ( X1
& ( X2 = X3 ) ) )
!= $true )
| ( $false = X1 ) ),
inference(not_proxy_clausification,[status(thm)],[f83]) ).
thf(f83,plain,
! [X2: $i,X3: $i,X0: $i,X1: $o] :
( ( ( ~ X1 ) = $true )
| ( ( ( ( X0 = X3 )
& ~ X1 )
| ( X1
& ( X2 = X3 ) ) )
!= $true )
| ( ( X1
& ( X2
= ( if2 @ X1 @ X2 @ X0 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f82]) ).
thf(f82,plain,
! [X2: $i,X3: $i,X0: $i,X1: $o] :
( ( ( ( X0
= ( if2 @ X1 @ X2 @ X0 ) )
& ~ X1 )
= $true )
| ( ( ( ( X0 = X3 )
& ~ X1 )
| ( X1
& ( X2 = X3 ) ) )
!= $true )
| ( ( X1
& ( X2
= ( if2 @ X1 @ X2 @ X0 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f81]) ).
thf(f81,plain,
! [X2: $i,X3: $i,X0: $i,X1: $o] :
( ( ( ( ( X0
= ( if2 @ X1 @ X2 @ X0 ) )
& ~ X1 )
| ( X1
& ( X2
= ( if2 @ X1 @ X2 @ X0 ) ) ) )
= $true )
| ( ( ( ( X0 = X3 )
& ~ X1 )
| ( X1
& ( X2 = X3 ) ) )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f80]) ).
thf(f80,plain,
! [X2: $i,X3: $i,X0: $i,X1: $o] :
( ( ( ^ [Y0: $i] :
( ( ( X0 = Y0 )
& ~ X1 )
| ( X1
& ( X2 = Y0 ) ) )
@ X3 )
!= $true )
| ( ( ^ [Y0: $i] :
( ( ( X0 = Y0 )
& ~ X1 )
| ( X1
& ( X2 = Y0 ) ) )
@ ( if2 @ X1 @ X2 @ X0 ) )
= $true ) ),
inference(superposition,[status(thm)],[f20,f38]) ).
thf(f38,plain,
! [X2: $i,X3: $i,X1: $o] :
( ( if2 @ X1 @ X2 @ X3 )
= ( eps2
@ ^ [Y0: $i] :
( ( ( X3 = Y0 )
& ~ X1 )
| ( X1
& ( X2 = Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f37]) ).
thf(f37,plain,
! [X2: $i,X3: $i,X1: $o] :
( ( ^ [Y0: $i] :
( eps2
@ ^ [Y1: $i] :
( ( ( Y0 = Y1 )
& ~ X1 )
| ( X1
& ( X2 = Y1 ) ) ) )
@ X3 )
= ( if2 @ X1 @ X2 @ X3 ) ),
inference(argument_congruence,[status(thm)],[f34]) ).
thf(f34,plain,
! [X2: $i,X1: $o] :
( ( ^ [Y0: $i] :
( eps2
@ ^ [Y1: $i] :
( ( ( Y0 = Y1 )
& ~ X1 )
| ( X1
& ( X2 = Y1 ) ) ) ) )
= ( if2 @ X1 @ X2 ) ),
inference(beta_eta_normalization,[status(thm)],[f33]) ).
thf(f33,plain,
! [X2: $i,X1: $o] :
( ( ^ [Y0: $i,Y1: $i] :
( eps2
@ ^ [Y2: $i] :
( ( ( Y1 = Y2 )
& ~ X1 )
| ( X1
& ( Y0 = Y2 ) ) ) )
@ X2 )
= ( if2 @ X1 @ X2 ) ),
inference(argument_congruence,[status(thm)],[f29]) ).
thf(f29,plain,
! [X1: $o] :
( ( if2 @ X1 )
= ( ^ [Y0: $i,Y1: $i] :
( eps2
@ ^ [Y2: $i] :
( ( ( Y1 = Y2 )
& ~ X1 )
| ( X1
& ( Y0 = Y2 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f28]) ).
thf(f28,plain,
! [X1: $o] :
( ( if2 @ X1 )
= ( ^ [Y0: $o,Y1: $i,Y2: $i] :
( eps2
@ ^ [Y3: $i] :
( ( ( Y2 = Y3 )
& ~ Y0 )
| ( Y0
& ( Y1 = Y3 ) ) ) )
@ X1 ) ),
inference(argument_congruence,[status(thm)],[f23]) ).
thf(f23,plain,
( if2
= ( ^ [Y0: $o,Y1: $i,Y2: $i] :
( eps2
@ ^ [Y3: $i] :
( ( ( Y2 = Y3 )
& ~ Y0 )
| ( Y0
& ( Y1 = Y3 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( if2
= ( ^ [Y0: $o,Y1: $i,Y2: $i] :
( eps2
@ ^ [Y3: $i] :
( ( ( Y2 = Y3 )
& ~ Y0 )
| ( Y0
& ( Y1 = Y3 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( if2
= ( ^ [X0: $o,X1: $i,X2: $i] :
( eps2
@ ^ [X3: $i] :
( ( ( X1 = X3 )
& X0 )
| ( ~ X0
& ( X2 = X3 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( if2
= ( ^ [X2: $o,X1: $i,X3: $i] :
( eps2
@ ^ [X4: $i] :
( ( ( X1 = X4 )
& X2 )
| ( ~ X2
& ( X3 = X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.DKzUbxh46v/DTF2THF_8786.p',if2d) ).
thf(f20,plain,
! [X0: $i > $o,X1: $i] :
( ( ( X0 @ ( eps2 @ X0 ) )
= $true )
| ( ( X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: $i > $o] :
( ( ( X0 @ ( eps2 @ X0 ) )
= $true )
| ! [X1: $i] :
( ( X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $i > $o] :
( ? [X1: $i] :
( ( X0 @ X1 )
= $true )
=> ( ( X0 @ ( eps2 @ X0 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i > $o] :
( ? [X1: $i] : ( X0 @ X1 )
=> ( X0 @ ( eps2 @ X0 ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: $i > $o] :
( ? [X1: $i] : ( X0 @ X1 )
=> ( X0 @ ( eps2 @ X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.DKzUbxh46v/DTF2THF_8786.p',choiceax2) ).
thf(f30,plain,
( ( if1 @ sK2 @ sK3 @ sK4 )
!= ( if2 @ sK2 @ sK3 @ sK4 ) ),
inference(negative_extensionality,[status(thm)],[f27]) ).
thf(f27,plain,
( ( if1 @ sK2 @ sK3 )
!= ( if2 @ sK2 @ sK3 ) ),
inference(negative_extensionality,[status(thm)],[f24]) ).
thf(f24,plain,
( ( if2 @ sK2 )
!= ( if1 @ sK2 ) ),
inference(negative_extensionality,[status(thm)],[f21]) ).
thf(f21,plain,
if1 != if2,
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
if1 != if2,
inference(flattening,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
if1 != if2,
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
if1 = if2,
file('/export/starexec/sandbox/tmp/tmp.DKzUbxh46v/DTF2THF_8786.p',conj) ).
thf(f125,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f117,f123,f119]) ).
thf(f117,plain,
! [X0: $i] :
( ( sK4 != X0 )
| ( sK2 = $true ) ),
inference(subsumption_resolution,[status(thm)],[f116,f73]) ).
thf(f73,plain,
! [X2: $i,X3: $i,X0: $i,X1: $o] :
( ( ( if1 @ X1 @ X2 @ X0 )
= X0 )
| ( $true = X1 )
| ( X0 != X3 ) ),
inference(duplicate_literal_removal,[status(thm)],[f72]) ).
thf(f72,plain,
! [X2: $i,X3: $i,X0: $i,X1: $o] :
( ( $true = X1 )
| ( ( if1 @ X1 @ X2 @ X0 )
= X0 )
| ( $true = X1 )
| ( X0 != X3 ) ),
inference(not_proxy_clausification,[status(thm)],[f71]) ).
thf(f71,plain,
! [X2: $i,X3: $i,X0: $i,X1: $o] :
( ( ( ~ X1 ) = $false )
| ( X0 != X3 )
| ( $true = X1 )
| ( ( if1 @ X1 @ X2 @ X0 )
= X0 ) ),
inference(equality_proxy_clausification,[status(thm)],[f70]) ).
thf(f70,plain,
! [X2: $i,X3: $i,X0: $i,X1: $o] :
( ( ( X0 = X3 )
= $false )
| ( $true = X1 )
| ( ( if1 @ X1 @ X2 @ X0 )
= X0 )
| ( ( ~ X1 ) = $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f69]) ).
thf(f69,plain,
! [X2: $i,X3: $i,X0: $i,X1: $o] :
( ( ( X0
= ( if1 @ X1 @ X2 @ X0 ) )
= $true )
| ( ( X0 = X3 )
= $false )
| ( $true = X1 )
| ( ( ~ X1 ) = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f68]) ).
thf(f68,plain,
! [X2: $i,X3: $i,X0: $i,X1: $o] :
( ( ( ( X0 = X3 )
& ~ X1 )
= $false )
| ( $true = X1 )
| ( ( X0
= ( if1 @ X1 @ X2 @ X0 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f66]) ).
thf(f66,plain,
! [X2: $i,X3: $i,X0: $i,X1: $o] :
( ( $true = X1 )
| ( ( ( ( X0 = X3 )
& ~ X1 )
| ( ( X2 = X3 )
& X1 ) )
!= $true )
| ( ( X0
= ( if1 @ X1 @ X2 @ X0 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
! [X2: $i,X3: $i,X0: $i,X1: $o] :
( ( ( ( X0
= ( if1 @ X1 @ X2 @ X0 ) )
& ~ X1 )
= $true )
| ( $true = X1 )
| ( ( ( ( X0 = X3 )
& ~ X1 )
| ( ( X2 = X3 )
& X1 ) )
!= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f41]) ).
thf(f116,plain,
! [X0: $i] :
( ( sK4 != X0 )
| ( sK2 = $true )
| ( ( if1 @ sK2 @ sK3 @ sK4 )
!= sK4 ) ),
inference(superposition,[status(thm)],[f30,f93]) ).
thf(f93,plain,
! [X2: $i,X3: $i,X0: $i,X1: $o] :
( ( ( if2 @ X1 @ X2 @ X0 )
= X0 )
| ( $true = X1 )
| ( X0 != X3 ) ),
inference(equality_proxy_clausification,[status(thm)],[f92]) ).
thf(f92,plain,
! [X2: $i,X3: $i,X0: $i,X1: $o] :
( ( ( X0 = X3 )
= $false )
| ( $true = X1 )
| ( ( if2 @ X1 @ X2 @ X0 )
= X0 ) ),
inference(duplicate_literal_removal,[status(thm)],[f91]) ).
thf(f91,plain,
! [X2: $i,X3: $i,X0: $i,X1: $o] :
( ( ( X0 = X3 )
= $false )
| ( ( if2 @ X1 @ X2 @ X0 )
= X0 )
| ( $true = X1 )
| ( $true = X1 ) ),
inference(not_proxy_clausification,[status(thm)],[f90]) ).
thf(f90,plain,
! [X2: $i,X3: $i,X0: $i,X1: $o] :
( ( $true = X1 )
| ( ( ~ X1 ) = $false )
| ( ( if2 @ X1 @ X2 @ X0 )
= X0 )
| ( ( X0 = X3 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f89]) ).
thf(f89,plain,
! [X2: $i,X3: $i,X0: $i,X1: $o] :
( ( ( if2 @ X1 @ X2 @ X0 )
= X0 )
| ( ( ( X0 = X3 )
& ~ X1 )
= $false )
| ( $true = X1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f87]) ).
thf(f87,plain,
! [X2: $i,X3: $i,X0: $i,X1: $o] :
( ( ( X1
& ( X2
= ( if2 @ X1 @ X2 @ X0 ) ) )
= $true )
| ( ( if2 @ X1 @ X2 @ X0 )
= X0 )
| ( ( ( X0 = X3 )
& ~ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f85]) ).
thf(f85,plain,
! [X2: $i,X3: $i,X0: $i,X1: $o] :
( ( ( ( ( X0 = X3 )
& ~ X1 )
| ( X1
& ( X2 = X3 ) ) )
!= $true )
| ( ( X1
& ( X2
= ( if2 @ X1 @ X2 @ X0 ) ) )
= $true )
| ( ( if2 @ X1 @ X2 @ X0 )
= X0 ) ),
inference(equality_proxy_clausification,[status(thm)],[f84]) ).
thf(f84,plain,
! [X2: $i,X3: $i,X0: $i,X1: $o] :
( ( ( X0
= ( if2 @ X1 @ X2 @ X0 ) )
= $true )
| ( ( X1
& ( X2
= ( if2 @ X1 @ X2 @ X0 ) ) )
= $true )
| ( ( ( ( X0 = X3 )
& ~ X1 )
| ( X1
& ( X2 = X3 ) ) )
!= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO555^1 : TPTP v9.2.1. Released v5.2.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.35 % Computer : n001.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Tue Feb 24 14:34:35 EST 2026
% 0.17/0.35 % CPUTime :
% 0.17/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.50 ---- Original DTF file ---
% 0.30/0.50 thf(spec,logic,$$dhol).
% 0.30/0.50 %------------------------------------------------------------------------------
% 0.30/0.50 % File : SYO555^1 : TPTP v9.2.1. Released v5.2.0.
% 0.30/0.50 % Domain : Syntactic
% 0.30/0.50 % Problem : If-then-else defined from choice is independent of choice
% 0.30/0.50 % Version : Especial.
% 0.30/0.50 % English :
% 0.30/0.50
% 0.30/0.50 % Refs : [Bro11] Brown (2011), Email to Geoff Sutcliffe
% 0.30/0.50 % Source : [Bro11]
% 0.30/0.50 % Names : CHOICE27 [Bro11]
% 0.30/0.50
% 0.30/0.50 % Status : Theorem
% 0.30/0.50 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.62 v8.1.0, 0.55 v7.5.0, 0.29 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.57 v6.1.0, 0.71 v5.5.0, 0.83 v5.4.0, 0.80 v5.2.0
% 0.30/0.50 % Syntax : Number of formulae : 9 ( 3 unt; 4 typ; 2 def)
% 0.30/0.50 % Number of atoms : 7 ( 7 equ; 0 cnn)
% 0.30/0.50 % Maximal formula atoms : 1 ( 1 avg)
% 0.30/0.50 % Number of connectives : 18 ( 2 ~; 2 |; 4 &; 8 @)
% 0.30/0.50 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.30/0.50 % Maximal formula depth : 5 ( 3 avg)
% 0.30/0.50 % Number of types : 2 ( 0 usr)
% 0.30/0.50 % Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% 0.30/0.50 % Number of symbols : 5 ( 4 usr; 0 con; 1-3 aty)
% 0.30/0.50 % Number of variables : 12 ( 8 ^; 2 !; 2 ?; 12 :)
% 0.30/0.50 % SPC : TH0_THM_EQU_NAR
% 0.30/0.50
% 0.30/0.50 % Comments : Two choice operators on $i are used to define two if-then-else
% 0.30/0.50 % operators at $i. Check that the two if-then-else operators are
% 0.30/0.50 % the same.
% 0.30/0.50 %------------------------------------------------------------------------------
% 0.30/0.50 thf(eps1,type,
% 0.30/0.50 eps1: ( $i > $o ) > $i ).
% 0.30/0.50
% 0.30/0.50 thf(choiceax1,axiom,
% 0.30/0.50 ! [P: $i > $o] :
% 0.30/0.50 ( ? [X: $i] : ( P @ X )
% 0.30/0.50 => ( P @ ( eps1 @ P ) ) ) ).
% 0.30/0.50
% 0.30/0.50 thf(if1,type,
% 0.30/0.50 if1: $o > $i > $i > $i ).
% 0.30/0.50
% 0.30/0.50 thf(if1d,definition,
% 0.30/0.50 ( if1
% 0.30/0.50 = ( ^ [B: $o,X: $i,Y: $i] :
% 0.30/0.50 ( eps1
% 0.30/0.50 @ ^ [Z: $i] :
% 0.30/0.50 ( ( B
% 0.30/0.50 & ( Z = X ) )
% 0.30/0.50 | ( ~ B
% 0.30/0.50 & ( Z = Y ) ) ) ) ) ) ).
% 0.30/0.50
% 0.30/0.50 thf(eps2,type,
% 0.30/0.50 eps2: ( $i > $o ) > $i ).
% 0.30/0.50
% 0.30/0.50 thf(choiceax2,axiom,
% 0.30/0.50 ! [P: $i > $o] :
% 0.30/0.50 ( ? [X: $i] : ( P @ X )
% 0.30/0.50 => ( P @ ( eps2 @ P ) ) ) ).
% 0.30/0.50
% 0.30/0.50 thf(if2,type,
% 0.30/0.50 if2: $o > $i > $i > $i ).
% 0.30/0.50
% 0.30/0.50 thf(if2d,definition,
% 0.30/0.50 ( if2
% 0.30/0.50 = ( ^ [B: $o,X: $i,Y: $i] :
% 0.30/0.50 ( eps2
% 0.30/0.50 @ ^ [Z: $i] :
% 0.30/0.50 ( ( B
% 0.30/0.50 & ( Z = X ) )
% 0.30/0.50 | ( ~ B
% 0.30/0.50 & ( Z = Y ) ) ) ) ) ) ).
% 0.30/0.50
% 0.30/0.50 thf(conj,conjecture,
% 0.30/0.50 if1 = if2 ).
% 0.30/0.50
% 0.30/0.50 %------------------------------------------------------------------------------
% 0.30/0.50 ------------------------
% 1.91/1.67 ---- Embedded in THF ---
% 1.91/1.67 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.91/1.67 %%% Generated on Tue Feb 24 14:34:36 EST 2026
% 1.91/1.67 %%% using '$$dhol' embedding, version 1.3.0.
% 1.91/1.67 %%% Logic specification used:
% 1.91/1.67 %%% thf(spec, logic, $$dhol).
% 1.91/1.67
% 1.91/1.67 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.DKzUbxh46v/DTF2DTF8786.p
% See solution above
% 1.91/1.67 ------------------------
% 1.91/1.68 ---- Cleaned THF ---
% 1.91/1.69 thf(eps1,type,
% 1.91/1.69 eps1: ( $i > $o ) > $i ).
% 1.91/1.69
% 1.91/1.69 thf(choiceax1,axiom,
% 1.91/1.69 ! [P: $i > $o] :
% 1.91/1.69 ( ? [X: $i] : ( P @ X )
% 1.91/1.69 => ( P @ ( eps1 @ P ) ) ) ).
% 1.91/1.69
% 1.91/1.69 thf(if1,type,
% 1.91/1.69 if1: $o > $i > $i > $i ).
% 1.91/1.69
% 1.91/1.69 thf(if1d,definition,
% 1.91/1.69 ( if1
% 1.91/1.69 = ( ^ [B: $o,X: $i,Y: $i] :
% 1.91/1.69 ( eps1
% 1.91/1.69 @ ^ [Z: $i] :
% 1.91/1.69 ( ( B
% 1.91/1.69 & ( Z = X ) )
% 1.91/1.69 | ( ~ B
% 1.91/1.69 & ( Z = Y ) ) ) ) ) ) ).
% 1.91/1.69
% 1.91/1.69 thf(eps2,type,
% 1.91/1.69 eps2: ( $i > $o ) > $i ).
% 1.91/1.69
% 1.91/1.69 thf(choiceax2,axiom,
% 1.91/1.69 ! [P: $i > $o] :
% 1.91/1.69 ( ? [X: $i] : ( P @ X )
% 1.91/1.69 => ( P @ ( eps2 @ P ) ) ) ).
% 1.91/1.69
% 1.91/1.69 thf(if2,type,
% 1.91/1.69 if2: $o > $i > $i > $i ).
% 1.91/1.69
% 1.91/1.69 thf(if2d,definition,
% 1.91/1.69 ( if2
% 1.91/1.69 = ( ^ [B: $o,X: $i,Y: $i] :
% 1.91/1.69 ( eps2
% 1.91/1.69 @ ^ [Z: $i] :
% 1.91/1.69 ( ( B
% 1.91/1.69 & ( Z = X ) )
% 1.91/1.69 | ( ~ B
% 1.91/1.69 & ( Z = Y ) ) ) ) ) ) ).
% 1.91/1.69
% 1.91/1.69 thf(conj,conjecture,
% 1.91/1.69 if1 = if2 ).
% 1.91/1.69 ------------------------
% 2.08/1.70 % (8884)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_8786 for (3000ds/183Mi)
% 2.08/1.71 % (8889)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_8786 for (3000ds/275Mi)
% 2.08/1.71 % (8888)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_8786 for (3000ds/2Mi)
% 2.08/1.71 % (8885)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_8786 for (3000ds/4Mi)
% 2.08/1.71 % (8886)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_8786 for (3000ds/27Mi)
% 2.08/1.71 % (8890)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_8786 for (3000ds/18Mi)
% 2.08/1.71 % (8887)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_8786 for (3000ds/2Mi)
% 2.08/1.71 % (8888)Instruction limit reached!
% 2.08/1.71 % (8888)------------------------------
% 2.08/1.71 % (8888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.08/1.71 % (8888)Termination reason: Unknown
% 2.08/1.71 % (8888)Termination phase: Property scanning
% 2.08/1.71
% 2.08/1.71 % (8888)Memory used [KB]: 895
% 2.08/1.71 % (8888)Time elapsed: 0.003 s
% 2.08/1.71 % (8888)Instructions burned: 2 (million)
% 2.08/1.71 % (8888)------------------------------
% 2.08/1.71 % (8888)------------------------------
% 2.08/1.71 % (8887)Instruction limit reached!
% 2.08/1.71 % (8887)------------------------------
% 2.08/1.71 % (8887)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.08/1.71 % (8887)Termination reason: Unknown
% 2.08/1.71 % (8887)Termination phase: Saturation
% 2.08/1.71
% 2.08/1.71 % (8887)Memory used [KB]: 895
% 2.08/1.71 % (8887)Time elapsed: 0.003 s
% 2.08/1.71 % (8887)Instructions burned: 2 (million)
% 2.08/1.71 % (8887)------------------------------
% 2.08/1.71 % (8887)------------------------------
% 2.08/1.71 % (8889)Refutation not found, incomplete strategy
% 2.08/1.71 % (8889)------------------------------
% 2.08/1.71 % (8889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.08/1.71 % (8889)Termination reason: Refutation not found, incomplete strategy
% 2.08/1.71
% 2.08/1.71
% 2.08/1.71 % (8889)Memory used [KB]: 5500
% 2.08/1.71 % (8889)Time elapsed: 0.004 s
% 2.08/1.71 % (8889)Instructions burned: 3 (million)
% 2.08/1.71 % (8889)------------------------------
% 2.08/1.71 % (8889)------------------------------
% 2.08/1.71 % (8885)Instruction limit reached!
% 2.08/1.71 % (8885)------------------------------
% 2.08/1.71 % (8885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.08/1.71 % (8885)Termination reason: Unknown
% 2.08/1.71 % (8885)Termination phase: Saturation
% 2.08/1.71
% 2.08/1.71 % (8885)Memory used [KB]: 5500
% 2.08/1.71 % (8885)Time elapsed: 0.004 s
% 2.08/1.71 % (8885)Instructions burned: 4 (million)
% 2.08/1.71 % (8885)------------------------------
% 2.08/1.71 % (8885)------------------------------
% 2.08/1.72 % (8890)Instruction limit reached!
% 2.08/1.72 % (8890)------------------------------
% 2.08/1.72 % (8890)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.08/1.72 % (8890)Termination reason: Unknown
% 2.08/1.72 % (8890)Termination phase: Saturation
% 2.08/1.72
% 2.08/1.72 % (8890)Memory used [KB]: 5500
% 2.08/1.72 % (8890)Time elapsed: 0.012 s
% 2.08/1.72 % (8890)Instructions burned: 18 (million)
% 2.08/1.72 % (8890)------------------------------
% 2.08/1.72 % (8890)------------------------------
% 2.08/1.72 % (8886)Instruction limit reached!
% 2.08/1.72 % (8886)------------------------------
% 2.08/1.72 % (8886)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.08/1.72 % (8886)Termination reason: Unknown
% 2.08/1.72 % (8886)Termination phase: Saturation
% 2.08/1.72
% 2.08/1.72 % (8886)Memory used [KB]: 5628
% 2.08/1.72 % (8886)Time elapsed: 0.018 s
% 2.08/1.72 % (8886)Instructions burned: 27 (million)
% 2.08/1.72 % (8886)------------------------------
% 2.08/1.72 % (8886)------------------------------
% 2.08/1.73 % (8892)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_8786 for (2999ds/37Mi)
% 2.08/1.73 % (8893)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_8786 for (2999ds/15Mi)
% 2.08/1.73 % (8891)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_8786 for (2999ds/3Mi)
% 2.08/1.73 % (8891)Instruction limit reached!
% 2.08/1.73 % (8891)------------------------------
% 2.08/1.73 % (8891)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.08/1.73 % (8891)Termination reason: Unknown
% 2.08/1.73 % (8891)Termination phase: Saturation
% 2.08/1.73
% 2.08/1.73 % (8891)Memory used [KB]: 5500
% 2.08/1.73 % (8893)Refutation not found, incomplete strategy
% 2.08/1.73 % (8893)------------------------------
% 2.08/1.73 % (8893)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.08/1.73 % (8891)Time elapsed: 0.004 s
% 2.08/1.73 % (8891)Instructions burned: 4 (million)
% 2.08/1.73 % (8891)------------------------------
% 2.08/1.73 % (8891)------------------------------
% 2.08/1.73 % (8893)Termination reason: Refutation not found, incomplete strategy
% 2.08/1.73
% 2.08/1.73
% 2.08/1.73 % (8893)Memory used [KB]: 5628
% 2.08/1.73 % (8893)Time elapsed: 0.004 s
% 2.08/1.73 % (8893)Instructions burned: 4 (million)
% 2.08/1.73 % (8893)------------------------------
% 2.08/1.73 % (8893)------------------------------
% 2.08/1.74 % (8895)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_8786 for (2999ds/1041Mi)
% 2.08/1.74 % (8894)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_8786 for (2999ds/3Mi)
% 2.08/1.74 % (8896)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_8786 for (2999ds/7Mi)
% 2.08/1.74 % (8894)Instruction limit reached!
% 2.08/1.74 % (8894)------------------------------
% 2.08/1.74 % (8894)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.08/1.74 % (8894)Termination reason: Unknown
% 2.08/1.74 % (8894)Termination phase: Saturation
% 2.08/1.74
% 2.08/1.74 % (8894)Memory used [KB]: 5500
% 2.08/1.74 % (8894)Time elapsed: 0.028 s
% 2.08/1.74 % (8894)Instructions burned: 3 (million)
% 2.08/1.74 % (8894)------------------------------
% 2.08/1.74 % (8894)------------------------------
% 2.08/1.74 % (8896)Instruction limit reached!
% 2.08/1.74 % (8896)------------------------------
% 2.08/1.74 % (8896)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.08/1.74 % (8896)Termination reason: Unknown
% 2.08/1.74 % (8896)Termination phase: Saturation
% 2.08/1.74
% 2.08/1.74 % (8896)Memory used [KB]: 1023
% 2.08/1.74 % (8896)Time elapsed: 0.006 s
% 2.08/1.74 % (8896)Instructions burned: 7 (million)
% 2.08/1.74 % (8896)------------------------------
% 2.08/1.74 % (8896)------------------------------
% 2.08/1.75 % (8892)Instruction limit reached!
% 2.08/1.75 % (8892)------------------------------
% 2.08/1.75 % (8892)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.08/1.75 % (8892)Termination reason: Unknown
% 2.08/1.75 % (8892)Termination phase: Saturation
% 2.08/1.75
% 2.08/1.75 % (8892)Memory used [KB]: 5756
% 2.08/1.75 % (8892)Time elapsed: 0.022 s
% 2.08/1.75 % (8892)Instructions burned: 38 (million)
% 2.08/1.75 % (8892)------------------------------
% 2.08/1.75 % (8892)------------------------------
% 2.08/1.75 % (8897)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_8786 for (2999ds/16Mi)
% 2.08/1.75 % (8898)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_8786 for (2999ds/3Mi)
% 2.08/1.76 % (8898)Instruction limit reached!
% 2.08/1.76 % (8898)------------------------------
% 2.08/1.76 % (8898)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.08/1.76 % (8898)Termination reason: Unknown
% 2.08/1.76 % (8898)Termination phase: Saturation
% 2.08/1.76
% 2.08/1.76 % (8898)Memory used [KB]: 5500
% 2.08/1.76 % (8898)Time elapsed: 0.004 s
% 2.08/1.76 % (8898)Instructions burned: 3 (million)
% 2.08/1.76 % (8898)------------------------------
% 2.08/1.76 % (8898)------------------------------
% 2.08/1.76 % (8884)Instruction limit reached!
% 2.08/1.76 % (8884)------------------------------
% 2.08/1.76 % (8884)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.08/1.76 % (8884)Termination reason: Unknown
% 2.08/1.76 % (8884)Termination phase: Saturation
% 2.08/1.76
% 2.08/1.76 % (8884)Memory used [KB]: 5884
% 2.08/1.76 % (8884)Time elapsed: 0.060 s
% 2.08/1.76 % (8884)Instructions burned: 185 (million)
% 2.08/1.76 % (8884)------------------------------
% 2.08/1.76 % (8884)------------------------------
% 2.08/1.76 % (8895)Refutation not found, incomplete strategy
% 2.08/1.76 % (8895)------------------------------
% 2.08/1.76 % (8895)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.08/1.76 % (8895)Termination reason: Refutation not found, incomplete strategy
% 2.08/1.76
% 2.08/1.76
% 2.08/1.76 % (8895)Memory used [KB]: 5628
% 2.08/1.76 % (8895)Time elapsed: 0.026 s
% 2.08/1.76 % (8895)Instructions burned: 40 (million)
% 2.08/1.76 % (8895)------------------------------
% 2.08/1.76 % (8895)------------------------------
% 2.08/1.76 % (8897)Instruction limit reached!
% 2.08/1.76 % (8897)------------------------------
% 2.08/1.76 % (8897)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.08/1.76 % (8897)Termination reason: Unknown
% 2.08/1.76 % (8897)Termination phase: Saturation
% 2.08/1.76
% 2.08/1.76 % (8897)Memory used [KB]: 5628
% 2.08/1.76 % (8897)Time elapsed: 0.013 s
% 2.08/1.76 % (8897)Instructions burned: 16 (million)
% 2.08/1.76 % (8897)------------------------------
% 2.08/1.76 % (8897)------------------------------
% 2.08/1.76 % (8901)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_8786 for (2999ds/7Mi)
% 2.08/1.76 % (8900)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_8786 for (2999ds/3Mi)
% 2.08/1.77 % (8900)Instruction limit reached!
% 2.08/1.77 % (8900)------------------------------
% 2.08/1.77 % (8900)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.08/1.77 % (8900)Termination reason: Unknown
% 2.08/1.77 % (8900)Termination phase: Saturation
% 2.08/1.77
% 2.08/1.77 % (8900)Memory used [KB]: 1023
% 2.08/1.77 % (8900)Time elapsed: 0.004 s
% 2.08/1.77 % (8900)Instructions burned: 3 (million)
% 2.08/1.77 % (8900)------------------------------
% 2.08/1.77 % (8900)------------------------------
% 2.08/1.77 % (8902)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_8786 for (2999ds/3Mi)
% 2.08/1.77 % (8903)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_8786 for (2999ds/4Mi)
% 2.08/1.77 % (8902)Instruction limit reached!
% 2.08/1.77 % (8902)------------------------------
% 2.08/1.77 % (8902)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.08/1.77 % (8902)Termination reason: Unknown
% 2.08/1.77 % (8902)Termination phase: Saturation
% 2.08/1.77
% 2.08/1.77 % (8902)Memory used [KB]: 5500
% 2.08/1.77 % (8902)Time elapsed: 0.004 s
% 2.08/1.77 % (8902)Instructions burned: 3 (million)
% 2.08/1.77 % (8902)------------------------------
% 2.08/1.77 % (8902)------------------------------
% 2.08/1.77 % (8901)Instruction limit reached!
% 2.08/1.77 % (8901)------------------------------
% 2.08/1.77 % (8901)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.08/1.77 % (8901)Termination reason: Unknown
% 2.08/1.77 % (8901)Termination phase: Saturation
% 2.08/1.77
% 2.08/1.77 % (8901)Memory used [KB]: 5500
% 2.08/1.77 % (8901)Time elapsed: 0.006 s
% 2.08/1.77 % (8901)Instructions burned: 7 (million)
% 2.08/1.77 % (8901)------------------------------
% 2.08/1.77 % (8901)------------------------------
% 2.08/1.77 % (8903)Instruction limit reached!
% 2.08/1.77 % (8903)------------------------------
% 2.08/1.77 % (8903)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.08/1.77 % (8903)Termination reason: Unknown
% 2.08/1.77 % (8903)Termination phase: Saturation
% 2.08/1.77
% 2.08/1.77 % (8903)Memory used [KB]: 5500
% 2.08/1.77 % (8903)Time elapsed: 0.003 s
% 2.08/1.77 % (8903)Instructions burned: 4 (million)
% 2.08/1.77 % (8903)------------------------------
% 2.08/1.77 % (8903)------------------------------
% 2.08/1.77 % (8904)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_8786 for (2999ds/18Mi)
% 2.08/1.78 % (8910)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_8786 for (2999ds/6Mi)
% 2.08/1.78 % (8906)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_8786 for (2999ds/6Mi)
% 2.08/1.78 % (8905)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_8786 for (2999ds/710Mi)
% 2.08/1.78 % (8910)Instruction limit reached!
% 2.08/1.78 % (8910)------------------------------
% 2.08/1.78 % (8910)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.08/1.78 % (8910)Termination reason: Unknown
% 2.08/1.78 % (8910)Termination phase: Saturation
% 2.08/1.78
% 2.08/1.78 % (8910)Memory used [KB]: 5500
% 2.08/1.78 % (8910)Time elapsed: 0.004 s
% 2.08/1.78 % (8910)Instructions burned: 7 (million)
% 2.08/1.78 % (8910)------------------------------
% 2.08/1.78 % (8910)------------------------------
% 2.08/1.78 % (8906)Instruction limit reached!
% 2.08/1.78 % (8906)------------------------------
% 2.08/1.78 % (8906)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.08/1.78 % (8906)Termination reason: Unknown
% 2.08/1.78 % (8906)Termination phase: Saturation
% 2.08/1.78
% 2.08/1.78 % (8906)Memory used [KB]: 5500
% 2.08/1.78 % (8906)Time elapsed: 0.006 s
% 2.08/1.78 % (8906)Instructions burned: 7 (million)
% 2.08/1.78 % (8906)------------------------------
% 2.08/1.78 % (8906)------------------------------
% 2.08/1.79 % (8904)First to succeed.
% 2.08/1.79 % (8909)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_8786 for (2999ds/5Mi)
% 2.08/1.79 % (8908)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_8786 for (2999ds/21Mi)
% 2.08/1.79 % (8907)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_8786 for (2999ds/902Mi)
% 2.08/1.79 % (8907)Refutation not found, incomplete strategy
% 2.08/1.79 % (8907)------------------------------
% 2.08/1.79 % (8907)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.08/1.79 % (8907)Termination reason: Refutation not found, incomplete strategy
% 2.08/1.79
% 2.08/1.79
% 2.08/1.79 % (8907)Memory used [KB]: 5500
% 2.08/1.79 % (8907)Time elapsed: 0.003 s
% 2.08/1.79 % (8907)Instructions burned: 2 (million)
% 2.08/1.79 % (8907)------------------------------
% 2.08/1.79 % (8907)------------------------------
% 2.08/1.79 % (8909)Instruction limit reached!
% 2.08/1.79 % (8909)------------------------------
% 2.08/1.79 % (8909)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.08/1.79 % (8909)Termination reason: Unknown
% 2.08/1.79 % (8909)Termination phase: Saturation
% 2.08/1.79
% 2.08/1.79 % (8909)Memory used [KB]: 5500
% 2.08/1.79 % (8909)Time elapsed: 0.005 s
% 2.08/1.79 % (8909)Instructions burned: 5 (million)
% 2.08/1.79 % (8909)------------------------------
% 2.08/1.79 % (8909)------------------------------
% 2.08/1.79 % (8904)Refutation found. Thanks to Tanya!
% 2.08/1.79 % SZS status Theorem for DTF2THF_8786
% 2.08/1.79 % SZS output start Proof for DTF2THF_8786
% 2.08/1.79 thf(func_def_0, type, eps1: ($i > $o) > $i).
% 2.08/1.79 thf(func_def_2, type, if1: $o > $i > $i > $i).
% 2.08/1.79 thf(func_def_3, type, eps2: ($i > $o) > $i).
% 2.08/1.79 thf(func_def_4, type, if2: $o > $i > $i > $i).
% 2.08/1.79 thf(func_def_17, type, ph1: !>[X0: $tType]:(X0)).
% 2.08/1.79 thf(f200,plain,(
% 2.08/1.79 $false),
% 2.08/1.79 inference(avatar_sat_refutation,[status(thm)],[f125,f137,f157,f160,f199])).
% 2.08/1.79 thf(f199,plain,(
% 2.08/1.79 ~spl0_4),
% 2.08/1.79 inference(avatar_contradiction_clause,[status(thm)],[f198])).
% 2.08/1.79 thf(f198,plain,(
% 2.08/1.79 $false | ~spl0_4),
% 2.08/1.79 inference(equality_resolution,[status(thm)],[f136])).
% 2.08/1.79 thf(f136,plain,(
% 2.08/1.79 ( ! [X0 : $i] : ((sK3 != X0)) ) | ~spl0_4),
% 2.08/1.79 inference(avatar_component_clause,[status(thm)],[f135])).
% 2.08/1.79 thf(f135,definition,(
% 2.08/1.79 spl0_4 <=> ! [X0 : $i] : (sK3 != X0)),
% 2.08/1.79 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 2.08/1.79 thf(f160,plain,(
% 2.08/1.79 ~spl0_1 | ~spl0_3),
% 2.08/1.79 inference(avatar_contradiction_clause,[status(thm)],[f159])).
% 2.08/1.79 thf(f159,plain,(
% 2.08/1.79 $false | (~spl0_1 | ~spl0_3)),
% 2.08/1.79 inference(trivial_inequality_removal,[status(thm)],[f158])).
% 2.08/1.79 thf(f158,plain,(
% 2.08/1.79 ($false = $true) | (~spl0_1 | ~spl0_3)),
% 2.08/1.79 inference(forward_demodulation,[status(thm)],[f121,f133])).
% 2.08/1.79 thf(f133,plain,(
% 2.08/1.79 (sK2 = $false) | ~spl0_3),
% 2.08/1.79 inference(avatar_component_clause,[status(thm)],[f131])).
% 2.08/1.79 thf(f131,definition,(
% 2.08/1.79 spl0_3 <=> (sK2 = $false)),
% 2.08/1.79 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 2.08/1.79 thf(f121,plain,(
% 2.08/1.79 (sK2 = $true) | ~spl0_1),
% 2.08/1.79 inference(avatar_component_clause,[status(thm)],[f119])).
% 2.08/1.79 thf(f119,definition,(
% 2.08/1.79 spl0_1 <=> (sK2 = $true)),
% 2.08/1.79 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 2.08/1.79 thf(f157,plain,(
% 2.08/1.79 ~spl0_2),
% 2.08/1.79 inference(avatar_contradiction_clause,[status(thm)],[f156])).
% 2.08/1.79 thf(f156,plain,(
% 2.08/1.79 $false | ~spl0_2),
% 2.08/1.79 inference(equality_resolution,[status(thm)],[f124])).
% 2.08/1.79 thf(f124,plain,(
% 2.08/1.79 ( ! [X0 : $i] : ((sK4 != X0)) ) | ~spl0_2),
% 2.08/1.79 inference(avatar_component_clause,[status(thm)],[f123])).
% 2.08/1.79 thf(f123,definition,(
% 2.08/1.79 spl0_2 <=> ! [X0 : $i] : (sK4 != X0)),
% 2.08/1.79 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 2.08/1.79 thf(f137,plain,(
% 2.08/1.79 spl0_3 | spl0_4),
% 2.08/1.79 inference(avatar_split_clause,[status(thm)],[f129,f135,f131])).
% 2.08/1.79 thf(f129,plain,(
% 2.08/1.79 ( ! [X0 : $i] : ((sK3 != X0) | (sK2 = $false)) )),
% 2.08/1.79 inference(subsumption_resolution,[status(thm)],[f127,f64])).
% 2.08/1.79 thf(f64,plain,(
% 2.08/1.79 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $o] : (((if1 @ X1 @ X2 @ X0) = X2) | ($false = X1) | (X2 != X3)) )),
% 2.08/1.79 inference(equality_proxy_clausification,[status(thm)],[f63])).
% 2.08/1.79 thf(f63,plain,(
% 2.08/1.79 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $o] : (((if1 @ X1 @ X2 @ X0) = X2) | ($false = X1) | ((X2 = X3) = $false)) )),
% 2.08/1.79 inference(duplicate_literal_removal,[status(thm)],[f62])).
% 2.08/1.79 thf(f62,plain,(
% 2.08/1.79 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $o] : (($false = X1) | ($false = X1) | ((if1 @ X1 @ X2 @ X0) = X2) | ((X2 = X3) = $false)) )),
% 2.08/1.79 inference(binary_proxy_clausification,[status(thm)],[f61])).
% 2.08/1.79 thf(f61,plain,(
% 2.08/1.79 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $o] : (((if1 @ X1 @ X2 @ X0) = X2) | (((X2 = X3) & X1) = $false) | ($false = X1)) )),
% 2.08/1.79 inference(not_proxy_clausification,[status(thm)],[f56])).
% 2.08/1.79 thf(f56,plain,(
% 2.08/1.79 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $o] : (((if1 @ X1 @ X2 @ X0) = X2) | ((~ X1) = $true) | (((X2 = X3) & X1) = $false)) )),
% 2.08/1.79 inference(binary_proxy_clausification,[status(thm)],[f45])).
% 2.08/1.79 thf(f45,plain,(
% 2.08/1.79 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $o] : (((if1 @ X1 @ X2 @ X0) = X2) | (((X0 = (if1 @ X1 @ X2 @ X0)) & (~ X1)) = $true) | (((X2 = X3) & X1) = $false)) )),
% 2.08/1.79 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 2.08/1.79 thf(f44,plain,(
% 2.08/1.79 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $o] : (((((X0 = X3) & (~ X1)) | ((X2 = X3) & X1)) != $true) | ((if1 @ X1 @ X2 @ X0) = X2) | (((X0 = (if1 @ X1 @ X2 @ X0)) & (~ X1)) = $true)) )),
% 2.08/1.79 inference(equality_proxy_clausification,[status(thm)],[f43])).
% 2.08/1.79 thf(f43,plain,(
% 2.08/1.79 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $o] : (($true = (X2 = (if1 @ X1 @ X2 @ X0))) | ((((X0 = X3) & (~ X1)) | ((X2 = X3) & X1)) != $true) | (((X0 = (if1 @ X1 @ X2 @ X0)) & (~ X1)) = $true)) )),
% 2.08/1.79 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 2.08/1.79 thf(f41,plain,(
% 2.08/1.79 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $o] : ((((X2 = (if1 @ X1 @ X2 @ X0)) & X1) = $true) | ((((X0 = X3) & (~ X1)) | ((X2 = X3) & X1)) != $true) | (((X0 = (if1 @ X1 @ X2 @ X0)) & (~ X1)) = $true)) )),
% 2.08/1.79 inference(binary_proxy_clausification,[status(thm)],[f40])).
% 2.08/1.79 thf(f40,plain,(
% 2.08/1.79 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $o] : (((((X0 = (if1 @ X1 @ X2 @ X0)) & (~ X1)) | ((X2 = (if1 @ X1 @ X2 @ X0)) & X1)) = $true) | ((((X0 = X3) & (~ X1)) | ((X2 = X3) & X1)) != $true)) )),
% 2.08/1.79 inference(beta_eta_normalization,[status(thm)],[f39])).
% 2.08/1.79 thf(f39,plain,(
% 2.08/1.79 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $o] : ((((^[Y0 : $i]: (((X0 = Y0) & (~ X1)) | ((X2 = Y0) & X1))) @ (if1 @ X1 @ X2 @ X0)) = $true) | (((^[Y0 : $i]: (((X0 = Y0) & (~ X1)) | ((X2 = Y0) & X1))) @ X3) != $true)) )),
% 2.08/1.79 inference(superposition,[status(thm)],[f22,f36])).
% 2.08/1.79 thf(f36,plain,(
% 2.08/1.79 ( ! [X2 : $i,X3 : $i,X1 : $o] : (((eps1 @ (^[Y0 : $i]: (((X3 = Y0) & (~ X1)) | ((X2 = Y0) & X1)))) = (if1 @ X1 @ X2 @ X3))) )),
% 2.08/1.79 inference(beta_eta_normalization,[status(thm)],[f35])).
% 2.08/1.79 thf(f35,plain,(
% 2.08/1.79 ( ! [X2 : $i,X3 : $i,X1 : $o] : (((if1 @ X1 @ X2 @ X3) = ((^[Y0 : $i]: (eps1 @ (^[Y1 : $i]: (((Y0 = Y1) & (~ X1)) | ((X2 = Y1) & X1))))) @ X3))) )),
% 2.08/1.79 inference(argument_congruence,[status(thm)],[f32])).
% 2.08/1.79 thf(f32,plain,(
% 2.08/1.79 ( ! [X2 : $i,X1 : $o] : (((^[Y0 : $i]: (eps1 @ (^[Y1 : $i]: (((Y0 = Y1) & (~ X1)) | ((X2 = Y1) & X1))))) = (if1 @ X1 @ X2))) )),
% 2.08/1.79 inference(beta_eta_normalization,[status(thm)],[f31])).
% 2.08/1.79 thf(f31,plain,(
% 2.08/1.79 ( ! [X2 : $i,X1 : $o] : (((if1 @ X1 @ X2) = ((^[Y0 : $i]: ((^[Y1 : $i]: (eps1 @ (^[Y2 : $i]: (((Y1 = Y2) & (~ X1)) | ((Y0 = Y2) & X1))))))) @ X2))) )),
% 2.08/1.79 inference(argument_congruence,[status(thm)],[f26])).
% 2.08/1.79 thf(f26,plain,(
% 2.08/1.79 ( ! [X1 : $o] : (((^[Y0 : $i]: ((^[Y1 : $i]: (eps1 @ (^[Y2 : $i]: (((Y1 = Y2) & (~ X1)) | ((Y0 = Y2) & X1))))))) = (if1 @ X1))) )),
% 2.08/1.79 inference(beta_eta_normalization,[status(thm)],[f25])).
% 2.08/1.79 thf(f25,plain,(
% 2.08/1.79 ( ! [X1 : $o] : ((((^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (eps1 @ (^[Y3 : $i]: (((Y2 = Y3) & (~ Y0)) | ((Y1 = Y3) & Y0))))))))) @ X1) = (if1 @ X1))) )),
% 2.08/1.79 inference(argument_congruence,[status(thm)],[f19])).
% 2.08/1.79 thf(f19,plain,(
% 2.08/1.79 (if1 = (^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (eps1 @ (^[Y3 : $i]: (((Y2 = Y3) & (~ Y0)) | ((Y1 = Y3) & Y0))))))))))),
% 2.08/1.79 inference(cnf_transformation,[status(thm)],[f15])).
% 2.08/1.79 thf(f15,plain,(
% 2.08/1.79 (if1 = (^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (eps1 @ (^[Y3 : $i]: (((Y2 = Y3) & (~ Y0)) | ((Y1 = Y3) & Y0))))))))))),
% 2.08/1.79 inference(fool_elimination,[status(thm)],[f14])).
% 2.08/1.79 thf(f14,plain,(
% 2.08/1.79 (if1 = (^[X0 : $o, X1 : $i, X2 : $i] : (eps1 @ (^[X3 : $i] : ((X0 & (X1 = X3)) | (~X0 & (X2 = X3)))))))),
% 2.08/1.79 inference(rectify,[status(thm)],[f2])).
% 2.08/1.79 thf(f2,axiom,(
% 2.08/1.79 (if1 = (^[X2 : $o, X1 : $i, X3 : $i] : (eps1 @ (^[X4 : $i] : ((X2 & (X1 = X4)) | (~X2 & (X3 = X4)))))))),
% 2.08/1.79 file('/export/starexec/sandbox/tmp/tmp.DKzUbxh46v/DTF2THF_8786.p',if1d)).
% 2.08/1.79 thf(f22,plain,(
% 2.08/1.79 ( ! [X0 : $i > $o,X1 : $i] : (((X0 @ (eps1 @ X0)) = $true) | ((X0 @ X1) != $true)) )),
% 2.08/1.79 inference(cnf_transformation,[status(thm)],[f18])).
% 2.08/1.79 thf(f18,plain,(
% 2.08/1.79 ! [X0 : $i > $o] : (! [X1 : $i] : ((X0 @ X1) != $true) | ((X0 @ (eps1 @ X0)) = $true))),
% 2.08/1.79 inference(ennf_transformation,[status(thm)],[f13])).
% 2.08/1.79 thf(f13,plain,(
% 2.08/1.79 ! [X0 : $i > $o] : (? [X1 : $i] : ((X0 @ X1) = $true) => ((X0 @ (eps1 @ X0)) = $true))),
% 2.08/1.79 inference(fool_elimination,[status(thm)],[f12])).
% 2.08/1.79 thf(f12,plain,(
% 2.08/1.79 ! [X0 : $i > $o] : (? [X1 : $i] : (X0 @ X1) => (X0 @ (eps1 @ X0)))),
% 2.08/1.79 inference(rectify,[status(thm)],[f1])).
% 2.08/1.79 thf(f1,axiom,(
% 2.08/1.79 ! [X0 : $i > $o] : (? [X1 : $i] : (X0 @ X1) => (X0 @ (eps1 @ X0)))),
% 2.08/1.79 file('/export/starexec/sandbox/tmp/tmp.DKzUbxh46v/DTF2THF_8786.p',choiceax1)).
% 2.08/1.79 thf(f127,plain,(
% 2.08/1.79 ( ! [X0 : $i] : ((sK3 != X0) | ((if1 @ sK2 @ sK3 @ sK4) != sK3) | (sK2 = $false)) )),
% 2.08/1.79 inference(superposition,[status(thm)],[f30,f113])).
% 2.08/1.79 thf(f113,plain,(
% 2.08/1.79 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $o] : (((if2 @ X1 @ X2 @ X0) = X2) | ($false = X1) | (X2 != X3)) )),
% 2.08/1.79 inference(equality_proxy_clausification,[status(thm)],[f112])).
% 2.08/1.79 thf(f112,plain,(
% 2.08/1.79 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $o] : (($false = X1) | ((X2 = X3) = $false) | ((if2 @ X1 @ X2 @ X0) = X2)) )),
% 2.08/1.79 inference(duplicate_literal_removal,[status(thm)],[f111])).
% 2.08/1.79 thf(f111,plain,(
% 2.08/1.79 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $o] : (((if2 @ X1 @ X2 @ X0) = X2) | ($false = X1) | ((X2 = X3) = $false) | ($false = X1)) )),
% 2.08/1.79 inference(binary_proxy_clausification,[status(thm)],[f110])).
% 2.08/1.79 thf(f110,plain,(
% 2.08/1.79 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $o] : (((X1 & (X2 = X3)) = $false) | ((if2 @ X1 @ X2 @ X0) = X2) | ($false = X1)) )),
% 2.08/1.79 inference(equality_proxy_clausification,[status(thm)],[f106])).
% 2.08/1.79 thf(f106,plain,(
% 2.08/1.79 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $o] : (($false = X1) | ((X2 = (if2 @ X1 @ X2 @ X0)) = $true) | ((X1 & (X2 = X3)) = $false)) )),
% 2.08/1.79 inference(binary_proxy_clausification,[status(thm)],[f104])).
% 2.08/1.79 thf(f104,plain,(
% 2.08/1.79 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $o] : (((((X0 = X3) & (~ X1)) | (X1 & (X2 = X3))) != $true) | ((X2 = (if2 @ X1 @ X2 @ X0)) = $true) | ($false = X1)) )),
% 2.08/1.79 inference(binary_proxy_clausification,[status(thm)],[f103])).
% 2.08/1.79 thf(f103,plain,(
% 2.08/1.79 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $o] : (((X1 & (X2 = (if2 @ X1 @ X2 @ X0))) = $true) | ((((X0 = X3) & (~ X1)) | (X1 & (X2 = X3))) != $true) | ($false = X1)) )),
% 2.08/1.79 inference(not_proxy_clausification,[status(thm)],[f83])).
% 2.08/1.79 thf(f83,plain,(
% 2.08/1.79 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $o] : (((~ X1) = $true) | ((((X0 = X3) & (~ X1)) | (X1 & (X2 = X3))) != $true) | ((X1 & (X2 = (if2 @ X1 @ X2 @ X0))) = $true)) )),
% 2.08/1.79 inference(binary_proxy_clausification,[status(thm)],[f82])).
% 2.08/1.79 thf(f82,plain,(
% 2.08/1.79 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $o] : ((((X0 = (if2 @ X1 @ X2 @ X0)) & (~ X1)) = $true) | ((((X0 = X3) & (~ X1)) | (X1 & (X2 = X3))) != $true) | ((X1 & (X2 = (if2 @ X1 @ X2 @ X0))) = $true)) )),
% 2.08/1.79 inference(binary_proxy_clausification,[status(thm)],[f81])).
% 2.08/1.79 thf(f81,plain,(
% 2.08/1.79 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $o] : (((((X0 = (if2 @ X1 @ X2 @ X0)) & (~ X1)) | (X1 & (X2 = (if2 @ X1 @ X2 @ X0)))) = $true) | ((((X0 = X3) & (~ X1)) | (X1 & (X2 = X3))) != $true)) )),
% 2.08/1.79 inference(beta_eta_normalization,[status(thm)],[f80])).
% 2.08/1.79 thf(f80,plain,(
% 2.08/1.79 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $o] : ((((^[Y0 : $i]: (((X0 = Y0) & (~ X1)) | (X1 & (X2 = Y0)))) @ X3) != $true) | (((^[Y0 : $i]: (((X0 = Y0) & (~ X1)) | (X1 & (X2 = Y0)))) @ (if2 @ X1 @ X2 @ X0)) = $true)) )),
% 2.08/1.79 inference(superposition,[status(thm)],[f20,f38])).
% 2.08/1.79 thf(f38,plain,(
% 2.08/1.79 ( ! [X2 : $i,X3 : $i,X1 : $o] : (((if2 @ X1 @ X2 @ X3) = (eps2 @ (^[Y0 : $i]: (((X3 = Y0) & (~ X1)) | (X1 & (X2 = Y0))))))) )),
% 2.08/1.79 inference(beta_eta_normalization,[status(thm)],[f37])).
% 2.08/1.79 thf(f37,plain,(
% 2.08/1.79 ( ! [X2 : $i,X3 : $i,X1 : $o] : ((((^[Y0 : $i]: (eps2 @ (^[Y1 : $i]: (((Y0 = Y1) & (~ X1)) | (X1 & (X2 = Y1)))))) @ X3) = (if2 @ X1 @ X2 @ X3))) )),
% 2.08/1.79 inference(argument_congruence,[status(thm)],[f34])).
% 2.08/1.79 thf(f34,plain,(
% 2.08/1.79 ( ! [X2 : $i,X1 : $o] : (((^[Y0 : $i]: (eps2 @ (^[Y1 : $i]: (((Y0 = Y1) & (~ X1)) | (X1 & (X2 = Y1)))))) = (if2 @ X1 @ X2))) )),
% 2.08/1.79 inference(beta_eta_normalization,[status(thm)],[f33])).
% 2.08/1.79 thf(f33,plain,(
% 2.08/1.79 ( ! [X2 : $i,X1 : $o] : ((((^[Y0 : $i]: ((^[Y1 : $i]: (eps2 @ (^[Y2 : $i]: (((Y1 = Y2) & (~ X1)) | (X1 & (Y0 = Y2)))))))) @ X2) = (if2 @ X1 @ X2))) )),
% 2.08/1.79 inference(argument_congruence,[status(thm)],[f29])).
% 2.08/1.79 thf(f29,plain,(
% 2.08/1.79 ( ! [X1 : $o] : (((if2 @ X1) = (^[Y0 : $i]: ((^[Y1 : $i]: (eps2 @ (^[Y2 : $i]: (((Y1 = Y2) & (~ X1)) | (X1 & (Y0 = Y2)))))))))) )),
% 2.08/1.79 inference(beta_eta_normalization,[status(thm)],[f28])).
% 2.08/1.79 thf(f28,plain,(
% 2.08/1.79 ( ! [X1 : $o] : (((if2 @ X1) = ((^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (eps2 @ (^[Y3 : $i]: (((Y2 = Y3) & (~ Y0)) | (Y0 & (Y1 = Y3)))))))))) @ X1))) )),
% 2.08/1.79 inference(argument_congruence,[status(thm)],[f23])).
% 2.08/1.79 thf(f23,plain,(
% 2.08/1.79 (if2 = (^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (eps2 @ (^[Y3 : $i]: (((Y2 = Y3) & (~ Y0)) | (Y0 & (Y1 = Y3)))))))))))),
% 2.08/1.79 inference(cnf_transformation,[status(thm)],[f11])).
% 2.08/1.79 thf(f11,plain,(
% 2.08/1.79 (if2 = (^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (eps2 @ (^[Y3 : $i]: (((Y2 = Y3) & (~ Y0)) | (Y0 & (Y1 = Y3)))))))))))),
% 2.08/1.79 inference(fool_elimination,[status(thm)],[f10])).
% 2.08/1.79 thf(f10,plain,(
% 2.08/1.79 (if2 = (^[X0 : $o, X1 : $i, X2 : $i] : (eps2 @ (^[X3 : $i] : (((X1 = X3) & X0) | (~X0 & (X2 = X3)))))))),
% 2.08/1.79 inference(rectify,[status(thm)],[f4])).
% 2.08/1.79 thf(f4,axiom,(
% 2.08/1.79 (if2 = (^[X2 : $o, X1 : $i, X3 : $i] : (eps2 @ (^[X4 : $i] : (((X1 = X4) & X2) | (~X2 & (X3 = X4)))))))),
% 2.08/1.79 file('/export/starexec/sandbox/tmp/tmp.DKzUbxh46v/DTF2THF_8786.p',if2d)).
% 2.08/1.79 thf(f20,plain,(
% 2.08/1.79 ( ! [X0 : $i > $o,X1 : $i] : (((X0 @ (eps2 @ X0)) = $true) | ((X0 @ X1) != $true)) )),
% 2.08/1.79 inference(cnf_transformation,[status(thm)],[f17])).
% 2.08/1.79 thf(f17,plain,(
% 2.08/1.79 ! [X0 : $i > $o] : (((X0 @ (eps2 @ X0)) = $true) | ! [X1 : $i] : ((X0 @ X1) != $true))),
% 2.08/1.79 inference(ennf_transformation,[status(thm)],[f9])).
% 2.08/1.79 thf(f9,plain,(
% 2.08/1.79 ! [X0 : $i > $o] : (? [X1 : $i] : ((X0 @ X1) = $true) => ((X0 @ (eps2 @ X0)) = $true))),
% 2.08/1.79 inference(fool_elimination,[status(thm)],[f8])).
% 2.08/1.79 thf(f8,plain,(
% 2.08/1.79 ! [X0 : $i > $o] : (? [X1 : $i] : (X0 @ X1) => (X0 @ (eps2 @ X0)))),
% 2.08/1.79 inference(rectify,[status(thm)],[f3])).
% 2.08/1.79 thf(f3,axiom,(
% 2.08/1.79 ! [X0 : $i > $o] : (? [X1 : $i] : (X0 @ X1) => (X0 @ (eps2 @ X0)))),
% 2.08/1.79 file('/export/starexec/sandbox/tmp/tmp.DKzUbxh46v/DTF2THF_8786.p',choiceax2)).
% 2.08/1.79 thf(f30,plain,(
% 2.08/1.79 ((if1 @ sK2 @ sK3 @ sK4) != (if2 @ sK2 @ sK3 @ sK4))),
% 2.08/1.79 inference(negative_extensionality,[status(thm)],[f27])).
% 2.08/1.79 thf(f27,plain,(
% 2.08/1.79 ((if1 @ sK2 @ sK3) != (if2 @ sK2 @ sK3))),
% 2.08/1.79 inference(negative_extensionality,[status(thm)],[f24])).
% 2.08/1.79 thf(f24,plain,(
% 2.08/1.79 ((if2 @ sK2) != (if1 @ sK2))),
% 2.08/1.79 inference(negative_extensionality,[status(thm)],[f21])).
% 2.08/1.79 thf(f21,plain,(
% 2.08/1.79 (if1 != if2)),
% 2.08/1.79 inference(cnf_transformation,[status(thm)],[f16])).
% 2.08/1.79 thf(f16,plain,(
% 2.08/1.79 (if1 != if2)),
% 2.08/1.79 inference(flattening,[status(thm)],[f6])).
% 2.08/1.79 thf(f6,negated_conjecture,(
% 2.08/1.79 ~(if1 = if2)),
% 2.08/1.79 inference(negated_conjecture,[status(cth)],[f5])).
% 2.08/1.79 thf(f5,conjecture,(
% 2.08/1.79 (if1 = if2)),
% 2.08/1.79 file('/export/starexec/sandbox/tmp/tmp.DKzUbxh46v/DTF2THF_8786.p',conj)).
% 2.08/1.79 thf(f125,plain,(
% 2.08/1.79 spl0_1 | spl0_2),
% 2.08/1.79 inference(avatar_split_clause,[status(thm)],[f117,f123,f119])).
% 2.08/1.79 thf(f117,plain,(
% 2.08/1.79 ( ! [X0 : $i] : ((sK4 != X0) | (sK2 = $true)) )),
% 2.08/1.79 inference(subsumption_resolution,[status(thm)],[f116,f73])).
% 2.08/1.79 thf(f73,plain,(
% 2.08/1.79 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $o] : (((if1 @ X1 @ X2 @ X0) = X0) | ($true = X1) | (X0 != X3)) )),
% 2.08/1.79 inference(duplicate_literal_removal,[status(thm)],[f72])).
% 2.08/1.79 thf(f72,plain,(
% 2.08/1.79 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $o] : (($true = X1) | ((if1 @ X1 @ X2 @ X0) = X0) | ($true = X1) | (X0 != X3)) )),
% 2.08/1.79 inference(not_proxy_clausification,[status(thm)],[f71])).
% 2.08/1.79 thf(f71,plain,(
% 2.08/1.79 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $o] : (((~ X1) = $false) | (X0 != X3) | ($true = X1) | ((if1 @ X1 @ X2 @ X0) = X0)) )),
% 2.08/1.79 inference(equality_proxy_clausification,[status(thm)],[f70])).
% 2.08/1.79 thf(f70,plain,(
% 2.08/1.79 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $o] : (((X0 = X3) = $false) | ($true = X1) | ((if1 @ X1 @ X2 @ X0) = X0) | ((~ X1) = $false)) )),
% 2.08/1.79 inference(equality_proxy_clausification,[status(thm)],[f69])).
% 2.08/1.79 thf(f69,plain,(
% 2.08/1.79 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $o] : (((X0 = (if1 @ X1 @ X2 @ X0)) = $true) | ((X0 = X3) = $false) | ($true = X1) | ((~ X1) = $false)) )),
% 2.08/1.79 inference(binary_proxy_clausification,[status(thm)],[f68])).
% 2.08/1.79 thf(f68,plain,(
% 2.08/1.79 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $o] : ((((X0 = X3) & (~ X1)) = $false) | ($true = X1) | ((X0 = (if1 @ X1 @ X2 @ X0)) = $true)) )),
% 2.08/1.79 inference(binary_proxy_clausification,[status(thm)],[f66])).
% 2.08/1.79 thf(f66,plain,(
% 2.08/1.79 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $o] : (($true = X1) | ((((X0 = X3) & (~ X1)) | ((X2 = X3) & X1)) != $true) | ((X0 = (if1 @ X1 @ X2 @ X0)) = $true)) )),
% 2.08/1.79 inference(binary_proxy_clausification,[status(thm)],[f42])).
% 2.08/1.79 thf(f42,plain,(
% 2.08/1.79 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $o] : ((((X0 = (if1 @ X1 @ X2 @ X0)) & (~ X1)) = $true) | ($true = X1) | ((((X0 = X3) & (~ X1)) | ((X2 = X3) & X1)) != $true)) )),
% 2.08/1.79 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 2.08/1.79 thf(f116,plain,(
% 2.08/1.79 ( ! [X0 : $i] : ((sK4 != X0) | (sK2 = $true) | ((if1 @ sK2 @ sK3 @ sK4) != sK4)) )),
% 2.08/1.79 inference(superposition,[status(thm)],[f30,f93])).
% 2.08/1.79 thf(f93,plain,(
% 2.08/1.79 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $o] : (((if2 @ X1 @ X2 @ X0) = X0) | ($true = X1) | (X0 != X3)) )),
% 2.08/1.79 inference(equality_proxy_clausification,[status(thm)],[f92])).
% 2.08/1.79 thf(f92,plain,(
% 2.08/1.79 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $o] : (((X0 = X3) = $false) | ($true = X1) | ((if2 @ X1 @ X2 @ X0) = X0)) )),
% 2.08/1.79 inference(duplicate_literal_removal,[status(thm)],[f91])).
% 2.08/1.79 thf(f91,plain,(
% 2.08/1.79 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $o] : (((X0 = X3) = $false) | ((if2 @ X1 @ X2 @ X0) = X0) | ($true = X1) | ($true = X1)) )),
% 2.08/1.79 inference(not_proxy_clausification,[status(thm)],[f90])).
% 2.08/1.79 thf(f90,plain,(
% 2.08/1.79 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $o] : (($true = X1) | ((~ X1) = $false) | ((if2 @ X1 @ X2 @ X0) = X0) | ((X0 = X3) = $false)) )),
% 2.08/1.79 inference(binary_proxy_clausification,[status(thm)],[f89])).
% 2.08/1.79 thf(f89,plain,(
% 2.08/1.79 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $o] : (((if2 @ X1 @ X2 @ X0) = X0) | (((X0 = X3) & (~ X1)) = $false) | ($true = X1)) )),
% 2.08/1.79 inference(binary_proxy_clausification,[status(thm)],[f87])).
% 2.08/1.79 thf(f87,plain,(
% 2.08/1.79 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $o] : (((X1 & (X2 = (if2 @ X1 @ X2 @ X0))) = $true) | ((if2 @ X1 @ X2 @ X0) = X0) | (((X0 = X3) & (~ X1)) = $false)) )),
% 2.08/1.79 inference(binary_proxy_clausification,[status(thm)],[f85])).
% 2.08/1.79 thf(f85,plain,(
% 2.08/1.79 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $o] : (((((X0 = X3) & (~ X1)) | (X1 & (X2 = X3))) != $true) | ((X1 & (X2 = (if2 @ X1 @ X2 @ X0))) = $true) | ((if2 @ X1 @ X2 @ X0) = X0)) )),
% 2.08/1.79 inference(equality_proxy_clausification,[status(thm)],[f84])).
% 2.08/1.79 thf(f84,plain,(
% 2.08/1.79 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $o] : (((X0 = (if2 @ X1 @ X2 @ X0)) = $true) | ((X1 & (X2 = (if2 @ X1 @ X2 @ X0))) = $true) | ((((X0 = X3) & (~ X1)) | (X1 & (X2 = X3))) != $true)) )),
% 2.08/1.79 inference(binary_proxy_clausification,[status(thm)],[f82])).
% 2.08/1.79 % SZS output end Proof for DTF2THF_8786
% 2.08/1.79 % (8904)------------------------------
% 2.08/1.79 % (8904)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.08/1.79 % (8904)Termination reason: Refutation
% 2.08/1.79
% 2.08/1.79 % (8904)Memory used [KB]: 5628
% 2.08/1.79 % (8904)Time elapsed: 0.015 s
% 2.08/1.79 % (8904)Instructions burned: 15 (million)
% 2.08/1.79 % (8904)------------------------------
% 2.08/1.79 % (8904)------------------------------
% 2.08/1.79 % (8883)Success in time 0.091 s
%------------------------------------------------------------------------------