%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO245^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n027.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 09:53:45 AM UTC 2026
% Result : Theorem 1.65s 1.35s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 47 ( 2 unt; 0 typ; 2 def)
% Number of atoms : 327 ( 165 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 752 ( 136 ~; 74 |; 62 &; 424 @)
% ( 2 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 177 ( 177 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 15 usr; 5 con; 0-2 aty)
% ( 0 !!; 34 ??; 0 @@+; 0 @@-)
% Number of variables : 170 ( 73 ^; 69 !; 28 ?; 170 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_10,type,
sK0: ( ( $i > $o ) > $i ) > $i > $o ).
thf(func_def_11,type,
sK1: ( $i > $o ) > $i ).
thf(func_def_13,type,
ph3:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
sK4: $i > $i > $o ).
thf(func_def_15,type,
sK5: $i > $o ).
thf(func_def_16,type,
sK6: $i > $o ).
thf(func_def_17,type,
sK7: $i > $o ).
thf(func_def_18,type,
sK8: $i > $i > $o ).
thf(func_def_19,type,
sK9: $i > $o ).
thf(func_def_20,type,
sK10: $i > $o ).
thf(func_def_21,type,
sK11: $i > $i > $o ).
thf(func_def_22,type,
sK12: $i > $o ).
thf(func_def_23,type,
sK13: $i > $o ).
thf(f232,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f25,f192,f231]) ).
thf(f231,plain,
( spl2_1
| ~ spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f226,f22,f19]) ).
thf(f19,definition,
( spl2_1
<=> ! [X1: $i > $o] :
( ( $true
= ( X1 @ ( sK1 @ X1 ) ) )
| ( ( sK1 @ X1 )
!= ( sK1
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK1 @ Y1 ) )
& ( ( sK1 @ Y1 )
= Y0 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f22,definition,
( spl2_2
<=> ! [X0: $i > $o] :
( ( ( sK1 @ X0 )
!= ( sK1 @ ( sK0 @ sK1 ) ) )
| ( ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK1 @ Y1 ) )
& ( ( sK1 @ Y1 )
= Y0 ) ) ) )
= X0 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f226,plain,
( ! [X0: $i > $o] :
( ( ( X0 @ ( sK1 @ X0 ) )
= $true )
| ( ( sK1
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK1 @ Y1 ) )
& ( ( sK1 @ Y1 )
= Y0 ) ) ) )
!= ( sK1 @ X0 ) ) )
| ~ spl2_2 ),
inference(trivial_inequality_removal,[status(thm)],[f224]) ).
thf(f224,plain,
( ! [X0: $i > $o] :
( ( ( sK1
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK1 @ Y1 ) )
& ( ( sK1 @ Y1 )
= Y0 ) ) ) )
!= ( sK1 @ X0 ) )
| ( ( X0 @ ( sK1 @ X0 ) )
= $true )
| ( $true != $true ) )
| ~ spl2_2 ),
inference(superposition,[status(thm)],[f14,f218]) ).
thf(f218,plain,
( ( $true
= ( sK0 @ sK1 @ ( sK1 @ ( sK0 @ sK1 ) ) ) )
| ~ spl2_2 ),
inference(trivial_inequality_removal,[status(thm)],[f214]) ).
thf(f214,plain,
( ( $true
= ( sK0 @ sK1 @ ( sK1 @ ( sK0 @ sK1 ) ) ) )
| ( ( sK1 @ ( sK0 @ sK1 ) )
!= ( sK1 @ ( sK0 @ sK1 ) ) )
| ( $true != $true )
| ~ spl2_2 ),
inference(equality_factoring,[status(thm)],[f93]) ).
thf(f93,plain,
( ! [X0: $i > $o,X1: $i] :
( ( ( sK0 @ sK1 @ X1 )
= $true )
| ( ( sK1 @ X0 )
!= X1 )
| ( ( X0 @ ( sK1 @ X0 ) )
= $true ) )
| ~ spl2_2 ),
inference(equality_resolution,[status(thm)],[f42]) ).
thf(f42,plain,
( ! [X2: $i > $o,X0: $i > $o,X1: $i] :
( ( ( sK1 @ X0 )
!= ( sK1 @ ( sK0 @ sK1 ) ) )
| ( ( sK1 @ X2 )
!= X1 )
| ( $true
= ( X2 @ ( sK1 @ X2 ) ) )
| ( $true
= ( X0 @ X1 ) ) )
| ~ spl2_2 ),
inference(not_proxy_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
( ! [X2: $i > $o,X0: $i > $o,X1: $i] :
( ( ( sK1 @ X2 )
!= X1 )
| ( $true
= ( X0 @ X1 ) )
| ( ( sK1 @ X0 )
!= ( sK1 @ ( sK0 @ sK1 ) ) )
| ( ( ~ ( X2 @ ( sK1 @ X2 ) ) )
= $false ) )
| ~ spl2_2 ),
inference(equality_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
( ! [X2: $i > $o,X0: $i > $o,X1: $i] :
( ( $true
= ( X0 @ X1 ) )
| ( ( sK1 @ X0 )
!= ( sK1 @ ( sK0 @ sK1 ) ) )
| ( $false
= ( ( sK1 @ X2 )
= X1 ) )
| ( ( ~ ( X2 @ ( sK1 @ X2 ) ) )
= $false ) )
| ~ spl2_2 ),
inference(binary_proxy_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
( ! [X2: $i > $o,X0: $i > $o,X1: $i] :
( ( ( sK1 @ X0 )
!= ( sK1 @ ( sK0 @ sK1 ) ) )
| ( $true
= ( X0 @ X1 ) )
| ( $false
= ( ~ ( X2 @ ( sK1 @ X2 ) )
& ( ( sK1 @ X2 )
= X1 ) ) ) )
| ~ spl2_2 ),
inference(beta_eta_normalization,[status(thm)],[f38]) ).
thf(f38,plain,
( ! [X2: $i > $o,X0: $i > $o,X1: $i] :
( ( ( sK1 @ X0 )
!= ( sK1 @ ( sK0 @ sK1 ) ) )
| ( $true
= ( X0 @ X1 ) )
| ( $false
= ( ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK1 @ Y0 ) )
& ( ( sK1 @ Y0 )
= X1 ) )
@ X2 ) ) )
| ~ spl2_2 ),
inference(pi_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
( ! [X0: $i > $o,X1: $i] :
( ( ( sK1 @ X0 )
!= ( sK1 @ ( sK0 @ sK1 ) ) )
| ( $false
= ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK1 @ Y0 ) )
& ( ( sK1 @ Y0 )
= X1 ) ) ) )
| ( $true
= ( X0 @ X1 ) ) )
| ~ spl2_2 ),
inference(binary_proxy_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
( ! [X0: $i > $o,X1: $i] :
( ( ( X0 @ X1 )
= ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK1 @ Y0 ) )
& ( ( sK1 @ Y0 )
= X1 ) ) ) )
| ( ( sK1 @ X0 )
!= ( sK1 @ ( sK0 @ sK1 ) ) ) )
| ~ spl2_2 ),
inference(beta_eta_normalization,[status(thm)],[f26]) ).
thf(f26,plain,
( ! [X0: $i > $o,X1: $i] :
( ( ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK1 @ Y1 ) )
& ( ( sK1 @ Y1 )
= Y0 ) ) )
@ X1 )
= ( X0 @ X1 ) )
| ( ( sK1 @ X0 )
!= ( sK1 @ ( sK0 @ sK1 ) ) ) )
| ~ spl2_2 ),
inference(argument_congruence,[status(thm)],[f23]) ).
thf(f23,plain,
( ! [X0: $i > $o] :
( ( ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK1 @ Y1 ) )
& ( ( sK1 @ Y1 )
= Y0 ) ) ) )
= X0 )
| ( ( sK1 @ X0 )
!= ( sK1 @ ( sK0 @ sK1 ) ) ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f22]) ).
thf(f14,plain,
! [X0: ( $i > $o ) > $i,X1: $i > $o] :
( ( ( sK0 @ X0 @ ( X0 @ ( sK0 @ X0 ) ) )
!= $true )
| ( ( X1 @ ( X0 @ X1 ) )
= $true )
| ( ( X0 @ X1 )
!= ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( X0 @ Y1 ) )
& ( ( X0 @ Y1 )
= Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ! [X0: ( $i > $o ) > $i] :
( ! [X1: $i > $o] :
( ( ( X0 @ X1 )
!= ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( X0 @ Y1 ) )
& ( ( X0 @ Y1 )
= Y0 ) ) ) ) )
| ( ( X1 @ ( X0 @ X1 ) )
= $true ) )
| ( ( ( sK0 @ X0 @ ( X0 @ ( sK0 @ X0 ) ) )
!= $true )
& ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( X0 @ Y1 ) )
& ( ( X0 @ Y1 )
= Y0 ) ) ) )
= ( X0 @ ( sK0 @ X0 ) ) ) ) )
& ! [X4: $i > $o,X5: $i > $o] :
( ( ( sK1 @ X4 )
!= ( sK1 @ X5 ) )
| ( X4 = X5 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f8,f10,f9]) ).
thf(f9,plain,
! [X0: ( $i > $o ) > $i] :
( ? [X2: $i > $o] :
( ( $true
!= ( X2 @ ( X0 @ X2 ) ) )
& ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( X0 @ Y1 ) )
& ( ( X0 @ Y1 )
= Y0 ) ) ) )
= ( X0 @ X2 ) ) )
=> ( ( ( sK0 @ X0 @ ( X0 @ ( sK0 @ X0 ) ) )
!= $true )
& ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( X0 @ Y1 ) )
& ( ( X0 @ Y1 )
= Y0 ) ) ) )
= ( X0 @ ( sK0 @ X0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X3: ( $i > $o ) > $i] :
! [X4: $i > $o,X5: $i > $o] :
( ( ( X3 @ X5 )
!= ( X3 @ X4 ) )
| ( X4 = X5 ) )
=> ! [X5: $i > $o,X4: $i > $o] :
( ( ( sK1 @ X4 )
!= ( sK1 @ X5 ) )
| ( X4 = X5 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ! [X0: ( $i > $o ) > $i] :
( ! [X1: $i > $o] :
( ( ( X0 @ X1 )
!= ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( X0 @ Y1 ) )
& ( ( X0 @ Y1 )
= Y0 ) ) ) ) )
| ( ( X1 @ ( X0 @ X1 ) )
= $true ) )
| ? [X2: $i > $o] :
( ( $true
!= ( X2 @ ( X0 @ X2 ) ) )
& ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( X0 @ Y1 ) )
& ( ( X0 @ Y1 )
= Y0 ) ) ) )
= ( X0 @ X2 ) ) ) )
& ? [X3: ( $i > $o ) > $i] :
! [X4: $i > $o,X5: $i > $o] :
( ( ( X3 @ X5 )
!= ( X3 @ X4 ) )
| ( X4 = X5 ) ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( ! [X0: ( $i > $o ) > $i] :
( ? [X1: $i > $o] :
( ( ( X1 @ ( X0 @ X1 ) )
!= $true )
& ( ( X0 @ X1 )
= ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( X0 @ Y1 ) )
& ( ( X0 @ Y1 )
= Y0 ) ) ) ) ) )
=> ? [X2: $i > $o] :
( ( $true
!= ( X2 @ ( X0 @ X2 ) ) )
& ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( X0 @ Y1 ) )
& ( ( X0 @ Y1 )
= Y0 ) ) ) )
= ( X0 @ X2 ) ) ) )
=> ~ ? [X3: ( $i > $o ) > $i] :
! [X4: $i > $o,X5: $i > $o] :
( ( ( X3 @ X5 )
= ( X3 @ X4 ) )
=> ( X4 = X5 ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ! [X0: ( $i > $o ) > $i] :
( ? [X1: $i > $o] :
( ( ( X0 @ X1 )
= ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( X0 @ Y1 ) )
& ( ( X0 @ Y1 )
= Y0 ) ) ) ) )
& ( ( X1 @ ( X0 @ X1 ) )
!= $true ) )
=> ? [X2: $i > $o] :
( ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( X0 @ Y1 ) )
& ( ( X0 @ Y1 )
= Y0 ) ) ) )
= ( X0 @ X2 ) )
& ( $true
!= ( X2 @ ( X0 @ X2 ) ) ) ) )
=> ~ ? [X3: ( $i > $o ) > $i] :
! [X4: $i > $o,X5: $i > $o] :
( ( ( X3 @ X5 )
= ( X3 @ X4 ) )
=> ( X4 = X5 ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ! [X0: ( $i > $o ) > $i] :
( ? [X1: $i > $o] :
( ( ( X0 @ X1 )
= ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( X0 @ Y1 ) )
& ( ( X0 @ Y1 )
= Y0 ) ) ) ) )
& ( ( X1 @ ( X0 @ X1 ) )
!= $true ) )
=> ? [X4: $i > $o] :
( ( ( X0 @ X4 )
= ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( X0 @ Y1 ) )
& ( ( X0 @ Y1 )
= Y0 ) ) ) ) )
& ( $true
!= ( X4 @ ( X0 @ X4 ) ) ) ) )
=> ~ ? [X7: ( $i > $o ) > $i] :
! [X8: $i > $o,X9: $i > $o] :
( ( ( X7 @ X9 )
= ( X7 @ X8 ) )
=> ( X8 = X9 ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: ( $i > $o ) > $i] :
( ? [X1: $i > $o] :
( ( ( X0 @ X1 )
= ( X0
@ ^ [X2: $i] :
? [X3: $i > $o] :
( ( ( X0 @ X3 )
= X2 )
& ~ ( X3 @ ( X0 @ X3 ) ) ) ) )
& ~ ( X1 @ ( X0 @ X1 ) ) )
=> ? [X4: $i > $o] :
( ( ( X0 @ X4 )
= ( X0
@ ^ [X5: $i] :
? [X6: $i > $o] :
( ( ( X0 @ X6 )
= X5 )
& ~ ( X6 @ ( X0 @ X6 ) ) ) ) )
& ~ ( X4 @ ( X0 @ X4 ) ) ) )
=> ~ ? [X7: ( $i > $o ) > $i] :
! [X8: $i > $o,X9: $i > $o] :
( ( ( X7 @ X9 )
= ( X7 @ X8 ) )
=> ( X8 = X9 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: ( $i > $o ) > $i] :
( ? [X1: $i > $o] :
( ( ( X0 @ X1 )
= ( X0
@ ^ [X2: $i] :
? [X3: $i > $o] :
( ( ( X0 @ X3 )
= X2 )
& ~ ( X3 @ ( X0 @ X3 ) ) ) ) )
& ~ ( X1 @ ( X0 @ X1 ) ) )
=> ? [X1: $i > $o] :
( ( ( X0 @ X1 )
= ( X0
@ ^ [X2: $i] :
? [X3: $i > $o] :
( ( ( X0 @ X3 )
= X2 )
& ~ ( X3 @ ( X0 @ X3 ) ) ) ) )
& ~ ( X1 @ ( X0 @ X1 ) ) ) )
=> ~ ? [X0: ( $i > $o ) > $i] :
! [X5: $i > $o,X4: $i > $o] :
( ( ( X0 @ X4 )
= ( X0 @ X5 ) )
=> ( X4 = X5 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X0: ( $i > $o ) > $i] :
( ? [X1: $i > $o] :
( ( ( X0 @ X1 )
= ( X0
@ ^ [X2: $i] :
? [X3: $i > $o] :
( ( ( X0 @ X3 )
= X2 )
& ~ ( X3 @ ( X0 @ X3 ) ) ) ) )
& ~ ( X1 @ ( X0 @ X1 ) ) )
=> ? [X1: $i > $o] :
( ( ( X0 @ X1 )
= ( X0
@ ^ [X2: $i] :
? [X3: $i > $o] :
( ( ( X0 @ X3 )
= X2 )
& ~ ( X3 @ ( X0 @ X3 ) ) ) ) )
& ~ ( X1 @ ( X0 @ X1 ) ) ) )
=> ~ ? [X0: ( $i > $o ) > $i] :
! [X5: $i > $o,X4: $i > $o] :
( ( ( X0 @ X4 )
= ( X0 @ X5 ) )
=> ( X4 = X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.LZbPGbpWMS/DTF2THF_27298.p',cTHM193A) ).
thf(f192,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[status(thm)],[f191]) ).
thf(f191,plain,
( $false
| ~ spl2_1 ),
inference(trivial_inequality_removal,[status(thm)],[f190]) ).
thf(f190,plain,
( ( $true = $false )
| ~ spl2_1 ),
inference(forward_demodulation,[status(thm)],[f174,f65]) ).
thf(f65,plain,
( ( $false
= ( sK5 @ ( sK1 @ sK5 ) ) )
| ~ spl2_1 ),
inference(not_proxy_clausification,[status(thm)],[f64]) ).
thf(f64,plain,
( ( $true
= ( ~ ( sK5 @ ( sK1 @ sK5 ) ) ) )
| ~ spl2_1 ),
inference(binary_proxy_clausification,[status(thm)],[f62]) ).
thf(f62,plain,
( ( $true
= ( ~ ( sK5 @ ( sK1 @ sK5 ) )
& ( ( sK1 @ sK5 )
= ( sK1
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK1 @ Y1 ) )
& ( ( sK1 @ Y1 )
= Y0 ) ) ) ) ) ) )
| ~ spl2_1 ),
inference(beta_eta_normalization,[status(thm)],[f61]) ).
thf(f61,plain,
( ( $true
= ( ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK1 @ Y0 ) )
& ( ( sK1 @ Y0 )
= ( sK1
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( sK1 @ Y2 ) )
& ( ( sK1 @ Y2 )
= Y1 ) ) ) ) ) )
@ sK5 ) )
| ~ spl2_1 ),
inference(sigma_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
( ( $true
= ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK1 @ Y0 ) )
& ( ( sK1 @ Y0 )
= ( sK1
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( sK1 @ Y2 ) )
& ( ( sK1 @ Y2 )
= Y1 ) ) ) ) ) ) ) )
| ~ spl2_1 ),
inference(beta_eta_normalization,[status(thm)],[f59]) ).
thf(f59,plain,
( ( ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK1 @ Y1 ) )
& ( ( sK1 @ Y1 )
= Y0 ) ) )
@ ( sK1
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK1 @ Y1 ) )
& ( ( sK1 @ Y1 )
= Y0 ) ) ) ) )
= $true )
| ~ spl2_1 ),
inference(equality_resolution,[status(thm)],[f20]) ).
thf(f20,plain,
( ! [X1: $i > $o] :
( ( ( sK1 @ X1 )
!= ( sK1
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK1 @ Y1 ) )
& ( ( sK1 @ Y1 )
= Y0 ) ) ) ) )
| ( $true
= ( X1 @ ( sK1 @ X1 ) ) ) )
| ~ spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f19]) ).
thf(f174,plain,
( ( $true
= ( sK5 @ ( sK1 @ sK5 ) ) )
| ~ spl2_1 ),
inference(equality_resolution,[status(thm)],[f118]) ).
thf(f118,plain,
( ! [X0: $i > $o] :
( ( ( sK1 @ sK5 )
!= ( sK1 @ X0 ) )
| ( ( X0 @ ( sK1 @ X0 ) )
= $true ) )
| ~ spl2_1 ),
inference(superposition,[status(thm)],[f20,f66]) ).
thf(f66,plain,
( ( ( sK1 @ sK5 )
= ( sK1
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK1 @ Y1 ) )
& ( ( sK1 @ Y1 )
= Y0 ) ) ) ) )
| ~ spl2_1 ),
inference(equality_proxy_clausification,[status(thm)],[f63]) ).
thf(f63,plain,
( ( ( ( sK1 @ sK5 )
= ( sK1
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK1 @ Y1 ) )
& ( ( sK1 @ Y1 )
= Y0 ) ) ) ) )
= $true )
| ~ spl2_1 ),
inference(binary_proxy_clausification,[status(thm)],[f62]) ).
thf(f25,plain,
( spl2_2
| spl2_1 ),
inference(avatar_split_clause,[status(thm)],[f16,f19,f22]) ).
thf(f16,plain,
! [X0: $i > $o,X1: $i > $o] :
( ( ( sK1 @ X0 )
!= ( sK1 @ ( sK0 @ sK1 ) ) )
| ( ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK1 @ Y1 ) )
& ( ( sK1 @ Y1 )
= Y0 ) ) ) )
= X0 )
| ( ( sK1 @ X1 )
!= ( sK1
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK1 @ Y1 ) )
& ( ( sK1 @ Y1 )
= Y0 ) ) ) ) )
| ( $true
= ( X1 @ ( sK1 @ X1 ) ) ) ),
inference(superposition,[status(thm)],[f12,f13]) ).
thf(f13,plain,
! [X0: ( $i > $o ) > $i,X1: $i > $o] :
( ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( X0 @ Y1 ) )
& ( ( X0 @ Y1 )
= Y0 ) ) ) )
= ( X0 @ ( sK0 @ X0 ) ) )
| ( ( X1 @ ( X0 @ X1 ) )
= $true )
| ( ( X0 @ X1 )
!= ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( X0 @ Y1 ) )
& ( ( X0 @ Y1 )
= Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f12,plain,
! [X4: $i > $o,X5: $i > $o] :
( ( ( sK1 @ X4 )
!= ( sK1 @ X5 ) )
| ( X4 = X5 ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO245^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n027.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 14:27:07 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : SYO245^5 : TPTP v9.2.1. Released v4.0.0.
% 0.29/0.46 % Domain : Syntactic
% 0.29/0.46 % Problem : TPS problem from BASIC-HO-EQ-THMS
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English :
% 0.29/0.46
% 0.29/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.46 % Source : [Bro09]
% 0.29/0.46 % Names : tps_1012 [Bro09]
% 0.29/0.46
% 0.29/0.46 % Status : ContradictoryAxioms
% 0.29/0.46 % Rating : 0.44 v9.1.0, 0.38 v9.0.0, 0.40 v8.2.0, 0.54 v8.1.0, 0.45 v7.5.0, 0.57 v7.4.0, 0.00 v7.3.0, 0.44 v7.2.0, 0.38 v7.1.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.43 v6.1.0, 0.57 v5.5.0, 0.50 v5.4.0, 0.60 v5.2.0, 1.00 v5.0.0, 0.80 v4.1.0, 1.00 v4.0.0
% 0.29/0.46 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.29/0.46 % Number of atoms : 6 ( 6 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 4 ( 6 avg)
% 0.29/0.46 % Number of connectives : 28 ( 5 ~; 0 |; 4 &; 16 @)
% 0.29/0.46 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 9 ( 9 avg)
% 0.29/0.46 % Number of types : 2 ( 0 usr)
% 0.29/0.46 % Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.29/0.46 % Number of variables : 10 ( 2 ^; 3 !; 5 ?; 10 :)
% 0.29/0.46 % SPC : TH0_CAX_EQU_NAR
% 0.29/0.46
% 0.29/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.29/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.29/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.29/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.29/0.46 % : May require description or choice.
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 thf(cTHM193A,conjecture,
% 0.29/0.46 ( ! [Xh: ( $i > $o ) > $i] :
% 0.29/0.46 ( ? [Xt: $i > $o] :
% 0.29/0.46 ( ~ ( Xt @ ( Xh @ Xt ) )
% 0.29/0.46 & ( ( Xh
% 0.29/0.46 @ ^ [Xz: $i] :
% 0.29/0.46 ? [Xt0: $i > $o] :
% 0.29/0.46 ( ~ ( Xt0 @ ( Xh @ Xt0 ) )
% 0.29/0.46 & ( Xz
% 0.29/0.46 = ( Xh @ Xt0 ) ) ) )
% 0.29/0.46 = ( Xh @ Xt ) ) )
% 0.29/0.46 => ? [Xt: $i > $o] :
% 0.29/0.46 ( ~ ( Xt @ ( Xh @ Xt ) )
% 0.29/0.46 & ( ( Xh
% 0.29/0.46 @ ^ [Xz: $i] :
% 0.29/0.46 ? [Xt0: $i > $o] :
% 0.29/0.46 ( ~ ( Xt0 @ ( Xh @ Xt0 ) )
% 0.29/0.46 & ( Xz
% 0.29/0.46 = ( Xh @ Xt0 ) ) ) )
% 0.29/0.46 = ( Xh @ Xt ) ) ) )
% 0.29/0.46 => ~ ? [Xh: ( $i > $o ) > $i] :
% 0.29/0.46 ! [Xx: $i > $o,Xy: $i > $o] :
% 0.29/0.46 ( ( ( Xh @ Xx )
% 0.29/0.46 = ( Xh @ Xy ) )
% 0.29/0.46 => ( Xx = Xy ) ) ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 1.46/1.29 ---- Embedded in THF ---
% 1.46/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.29 %%% Generated on Tue Feb 24 14:27:08 EST 2026
% 1.46/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.29 %%% Logic specification used:
% 1.46/1.29 %%% thf(spec, logic, $$dhol).
% 1.46/1.29
% 1.46/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.LZbPGbpWMS/DTF2DTF27298.p
% See solution above
% 1.46/1.29 ------------------------
% 1.65/1.30 ---- Cleaned THF ---
% 1.65/1.31 thf(cTHM193A,conjecture,
% 1.65/1.31 ( ! [Xh: ( $i > $o ) > $i] :
% 1.65/1.31 ( ? [Xt: $i > $o] :
% 1.65/1.31 ( ~ ( Xt @ ( Xh @ Xt ) )
% 1.65/1.31 & ( ( Xh
% 1.65/1.31 @ ^ [Xz: $i] :
% 1.65/1.31 ? [Xt0: $i > $o] :
% 1.65/1.31 ( ~ ( Xt0 @ ( Xh @ Xt0 ) )
% 1.65/1.31 & ( Xz
% 1.65/1.31 = ( Xh @ Xt0 ) ) ) )
% 1.65/1.31 = ( Xh @ Xt ) ) )
% 1.65/1.31 => ? [Xt: $i > $o] :
% 1.65/1.31 ( ~ ( Xt @ ( Xh @ Xt ) )
% 1.65/1.31 & ( ( Xh
% 1.65/1.31 @ ^ [Xz: $i] :
% 1.65/1.31 ? [Xt0: $i > $o] :
% 1.65/1.31 ( ~ ( Xt0 @ ( Xh @ Xt0 ) )
% 1.65/1.31 & ( Xz
% 1.65/1.31 = ( Xh @ Xt0 ) ) ) )
% 1.65/1.31 = ( Xh @ Xt ) ) ) )
% 1.65/1.31 => ~ ? [Xh: ( $i > $o ) > $i] :
% 1.65/1.31 ! [Xx: $i > $o,Xy: $i > $o] :
% 1.65/1.31 ( ( ( Xh @ Xx )
% 1.65/1.31 = ( Xh @ Xy ) )
% 1.65/1.31 => ( Xx = Xy ) ) ) ).
% 1.65/1.31 ------------------------
% 1.65/1.32 % (27573)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_27298 for (2999ds/2Mi)
% 1.65/1.32 % (27572)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_27298 for (2999ds/2Mi)
% 1.65/1.32 % (27572)Instruction limit reached!
% 1.65/1.32 % (27572)------------------------------
% 1.65/1.32 % (27572)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.32 % (27572)Termination reason: Unknown
% 1.65/1.32 % (27572)Termination phase: Saturation
% 1.65/1.32
% 1.65/1.32 % (27572)Memory used [KB]: 895
% 1.65/1.32 % (27572)Time elapsed: 0.002 s
% 1.65/1.32 % (27572)Instructions burned: 2 (million)
% 1.65/1.32 % (27572)------------------------------
% 1.65/1.32 % (27572)------------------------------
% 1.65/1.32 % (27573)Instruction limit reached!
% 1.65/1.32 % (27573)------------------------------
% 1.65/1.32 % (27573)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.32 % (27573)Termination reason: Unknown
% 1.65/1.32 % (27573)Termination phase: Saturation
% 1.65/1.32
% 1.65/1.32 % (27573)Memory used [KB]: 5500
% 1.65/1.32 % (27573)Time elapsed: 0.003 s
% 1.65/1.32 % (27573)Instructions burned: 3 (million)
% 1.65/1.32 % (27573)------------------------------
% 1.65/1.32 % (27573)------------------------------
% 1.65/1.33 % (27569)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_27298 for (2999ds/183Mi)
% 1.65/1.33 % (27571)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_27298 for (2999ds/27Mi)
% 1.65/1.33 % (27570)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_27298 for (2999ds/4Mi)
% 1.65/1.33 % (27574)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_27298 for (2999ds/275Mi)
% 1.65/1.33 % (27575)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_27298 for (2999ds/18Mi)
% 1.65/1.33 % (27577)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_27298 for (2999ds/37Mi)
% 1.65/1.33 % (27570)Instruction limit reached!
% 1.65/1.33 % (27570)------------------------------
% 1.65/1.33 % (27570)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.33 % (27570)Termination reason: Unknown
% 1.65/1.33 % (27570)Termination phase: Saturation
% 1.65/1.33
% 1.65/1.33 % (27570)Memory used [KB]: 5500
% 1.65/1.33 % (27570)Time elapsed: 0.005 s
% 1.65/1.33 % (27570)Instructions burned: 5 (million)
% 1.65/1.33 % (27570)------------------------------
% 1.65/1.33 % (27570)------------------------------
% 1.65/1.33 % (27576)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_27298 for (2999ds/3Mi)
% 1.65/1.33 % (27576)Instruction limit reached!
% 1.65/1.33 % (27576)------------------------------
% 1.65/1.33 % (27576)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.33 % (27576)Termination reason: Unknown
% 1.65/1.33 % (27576)Termination phase: Saturation
% 1.65/1.33
% 1.65/1.33 % (27576)Memory used [KB]: 5500
% 1.65/1.33 % (27576)Time elapsed: 0.002 s
% 1.65/1.33 % (27576)Instructions burned: 3 (million)
% 1.65/1.33 % (27576)------------------------------
% 1.65/1.33 % (27576)------------------------------
% 1.65/1.34 % (27575)Instruction limit reached!
% 1.65/1.34 % (27575)------------------------------
% 1.65/1.34 % (27575)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.34 % (27575)Termination reason: Unknown
% 1.65/1.34 % (27575)Termination phase: Saturation
% 1.65/1.34
% 1.65/1.34 % (27575)Memory used [KB]: 5628
% 1.65/1.34 % (27575)Time elapsed: 0.013 s
% 1.65/1.34 % (27575)Instructions burned: 18 (million)
% 1.65/1.34 % (27575)------------------------------
% 1.65/1.34 % (27575)------------------------------
% 1.65/1.34 % (27577)Instruction limit reached!
% 1.65/1.34 % (27577)------------------------------
% 1.65/1.34 % (27577)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.34 % (27577)Termination reason: Unknown
% 1.65/1.34 % (27577)Termination phase: Saturation
% 1.65/1.34
% 1.65/1.34 % (27577)Memory used [KB]: 5628
% 1.65/1.34 % (27577)Time elapsed: 0.013 s
% 1.65/1.34 % (27577)Instructions burned: 39 (million)
% 1.65/1.34 % (27577)------------------------------
% 1.65/1.34 % (27577)------------------------------
% 1.65/1.34 % (27579)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_27298 for (2999ds/3Mi)
% 1.65/1.34 % (27579)Instruction limit reached!
% 1.65/1.34 % (27579)------------------------------
% 1.65/1.34 % (27579)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.34 % (27579)Termination reason: Unknown
% 1.65/1.34 % (27579)Termination phase: Saturation
% 1.65/1.34
% 1.65/1.34 % (27579)Memory used [KB]: 5500
% 1.65/1.34 % (27579)Time elapsed: 0.003 s
% 1.65/1.34 % (27579)Instructions burned: 3 (million)
% 1.65/1.34 % (27579)------------------------------
% 1.65/1.34 % (27579)------------------------------
% 1.65/1.34 % (27571)Instruction limit reached!
% 1.65/1.34 % (27571)------------------------------
% 1.65/1.34 % (27571)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.34 % (27571)Termination reason: Unknown
% 1.65/1.34 % (27571)Termination phase: Saturation
% 1.65/1.34
% 1.65/1.34 % (27571)Memory used [KB]: 5628
% 1.65/1.34 % (27571)Time elapsed: 0.020 s
% 1.65/1.34 % (27571)Instructions burned: 27 (million)
% 1.65/1.34 % (27571)------------------------------
% 1.65/1.34 % (27571)------------------------------
% 1.65/1.35 % (27574)First to succeed.
% 1.65/1.35 % (27578)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_27298 for (2999ds/15Mi)
% 1.65/1.35 % (27574)Refutation found. Thanks to Tanya!
% 1.65/1.35 % SZS status Theorem for DTF2THF_27298
% 1.65/1.35 % SZS output start Proof for DTF2THF_27298
% 1.65/1.35 thf(func_def_10, type, sK0: (($i > $o) > $i) > $i > $o).
% 1.65/1.35 thf(func_def_11, type, sK1: ($i > $o) > $i).
% 1.65/1.35 thf(func_def_13, type, ph3: !>[X0: $tType]:(X0)).
% 1.65/1.35 thf(func_def_14, type, sK4: $i > $i > $o).
% 1.65/1.35 thf(func_def_15, type, sK5: $i > $o).
% 1.65/1.35 thf(func_def_16, type, sK6: $i > $o).
% 1.65/1.35 thf(func_def_17, type, sK7: $i > $o).
% 1.65/1.35 thf(func_def_18, type, sK8: $i > $i > $o).
% 1.65/1.35 thf(func_def_19, type, sK9: $i > $o).
% 1.65/1.35 thf(func_def_20, type, sK10: $i > $o).
% 1.65/1.35 thf(func_def_21, type, sK11: $i > $i > $o).
% 1.65/1.35 thf(func_def_22, type, sK12: $i > $o).
% 1.65/1.35 thf(func_def_23, type, sK13: $i > $o).
% 1.65/1.35 thf(f232,plain,(
% 1.65/1.35 $false),
% 1.65/1.35 inference(avatar_sat_refutation,[status(thm)],[f25,f192,f231])).
% 1.65/1.35 thf(f231,plain,(
% 1.65/1.35 spl2_1 | ~spl2_2),
% 1.65/1.35 inference(avatar_split_clause,[status(thm)],[f226,f22,f19])).
% 1.65/1.35 thf(f19,definition,(
% 1.65/1.35 spl2_1 <=> ! [X1 : $i > $o] : (($true = (X1 @ (sK1 @ X1))) | ((sK1 @ X1) != (sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0))))))))),
% 1.65/1.35 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.65/1.35 thf(f22,definition,(
% 1.65/1.35 spl2_2 <=> ! [X0 : $i > $o] : (((sK1 @ X0) != (sK1 @ (sK0 @ sK1))) | ((^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0))))) = X0))),
% 1.65/1.35 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.65/1.35 thf(f226,plain,(
% 1.65/1.35 ( ! [X0 : $i > $o] : (((X0 @ (sK1 @ X0)) = $true) | ((sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0)))))) != (sK1 @ X0))) ) | ~spl2_2),
% 1.65/1.35 inference(trivial_inequality_removal,[status(thm)],[f224])).
% 1.65/1.35 thf(f224,plain,(
% 1.65/1.35 ( ! [X0 : $i > $o] : (((sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0)))))) != (sK1 @ X0)) | ((X0 @ (sK1 @ X0)) = $true) | ($true != $true)) ) | ~spl2_2),
% 1.65/1.35 inference(superposition,[status(thm)],[f14,f218])).
% 1.65/1.35 thf(f218,plain,(
% 1.65/1.35 ($true = (sK0 @ sK1 @ (sK1 @ (sK0 @ sK1)))) | ~spl2_2),
% 1.65/1.35 inference(trivial_inequality_removal,[status(thm)],[f214])).
% 1.65/1.35 thf(f214,plain,(
% 1.65/1.35 ($true = (sK0 @ sK1 @ (sK1 @ (sK0 @ sK1)))) | ((sK1 @ (sK0 @ sK1)) != (sK1 @ (sK0 @ sK1))) | ($true != $true) | ~spl2_2),
% 1.65/1.35 inference(equality_factoring,[status(thm)],[f93])).
% 1.65/1.35 thf(f93,plain,(
% 1.65/1.35 ( ! [X0 : $i > $o,X1 : $i] : (((sK0 @ sK1 @ X1) = $true) | ((sK1 @ X0) != X1) | ((X0 @ (sK1 @ X0)) = $true)) ) | ~spl2_2),
% 1.65/1.35 inference(equality_resolution,[status(thm)],[f42])).
% 1.65/1.35 thf(f42,plain,(
% 1.65/1.35 ( ! [X2 : $i > $o,X0 : $i > $o,X1 : $i] : (((sK1 @ X0) != (sK1 @ (sK0 @ sK1))) | ((sK1 @ X2) != X1) | ($true = (X2 @ (sK1 @ X2))) | ($true = (X0 @ X1))) ) | ~spl2_2),
% 1.65/1.35 inference(not_proxy_clausification,[status(thm)],[f41])).
% 1.65/1.35 thf(f41,plain,(
% 1.65/1.35 ( ! [X2 : $i > $o,X0 : $i > $o,X1 : $i] : (((sK1 @ X2) != X1) | ($true = (X0 @ X1)) | ((sK1 @ X0) != (sK1 @ (sK0 @ sK1))) | ((~ (X2 @ (sK1 @ X2))) = $false)) ) | ~spl2_2),
% 1.65/1.35 inference(equality_proxy_clausification,[status(thm)],[f40])).
% 1.65/1.35 thf(f40,plain,(
% 1.65/1.35 ( ! [X2 : $i > $o,X0 : $i > $o,X1 : $i] : (($true = (X0 @ X1)) | ((sK1 @ X0) != (sK1 @ (sK0 @ sK1))) | ($false = ((sK1 @ X2) = X1)) | ((~ (X2 @ (sK1 @ X2))) = $false)) ) | ~spl2_2),
% 1.65/1.35 inference(binary_proxy_clausification,[status(thm)],[f39])).
% 1.65/1.35 thf(f39,plain,(
% 1.65/1.35 ( ! [X2 : $i > $o,X0 : $i > $o,X1 : $i] : (((sK1 @ X0) != (sK1 @ (sK0 @ sK1))) | ($true = (X0 @ X1)) | ($false = ((~ (X2 @ (sK1 @ X2))) & ((sK1 @ X2) = X1)))) ) | ~spl2_2),
% 1.65/1.35 inference(beta_eta_normalization,[status(thm)],[f38])).
% 1.65/1.35 thf(f38,plain,(
% 1.65/1.35 ( ! [X2 : $i > $o,X0 : $i > $o,X1 : $i] : (((sK1 @ X0) != (sK1 @ (sK0 @ sK1))) | ($true = (X0 @ X1)) | ($false = ((^[Y0 : $i > $o]: ((~ (Y0 @ (sK1 @ Y0))) & ((sK1 @ Y0) = X1))) @ X2))) ) | ~spl2_2),
% 1.65/1.35 inference(pi_clausification,[status(thm)],[f30])).
% 1.65/1.35 thf(f30,plain,(
% 1.65/1.35 ( ! [X0 : $i > $o,X1 : $i] : (((sK1 @ X0) != (sK1 @ (sK0 @ sK1))) | ($false = (?? @ ($i > $o) @ (^[Y0 : $i > $o]: ((~ (Y0 @ (sK1 @ Y0))) & ((sK1 @ Y0) = X1))))) | ($true = (X0 @ X1))) ) | ~spl2_2),
% 1.65/1.35 inference(binary_proxy_clausification,[status(thm)],[f29])).
% 1.65/1.35 thf(f29,plain,(
% 1.65/1.35 ( ! [X0 : $i > $o,X1 : $i] : (((X0 @ X1) = (?? @ ($i > $o) @ (^[Y0 : $i > $o]: ((~ (Y0 @ (sK1 @ Y0))) & ((sK1 @ Y0) = X1))))) | ((sK1 @ X0) != (sK1 @ (sK0 @ sK1)))) ) | ~spl2_2),
% 1.65/1.35 inference(beta_eta_normalization,[status(thm)],[f26])).
% 1.65/1.35 thf(f26,plain,(
% 1.65/1.35 ( ! [X0 : $i > $o,X1 : $i] : ((((^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0))))) @ X1) = (X0 @ X1)) | ((sK1 @ X0) != (sK1 @ (sK0 @ sK1)))) ) | ~spl2_2),
% 1.65/1.35 inference(argument_congruence,[status(thm)],[f23])).
% 1.65/1.35 thf(f23,plain,(
% 1.65/1.35 ( ! [X0 : $i > $o] : (((^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0))))) = X0) | ((sK1 @ X0) != (sK1 @ (sK0 @ sK1)))) ) | ~spl2_2),
% 1.65/1.35 inference(avatar_component_clause,[status(thm)],[f22])).
% 1.65/1.35 thf(f14,plain,(
% 1.65/1.35 ( ! [X0 : ($i > $o) > $i,X1 : $i > $o] : (((sK0 @ X0 @ (X0 @ (sK0 @ X0))) != $true) | ((X1 @ (X0 @ X1)) = $true) | ((X0 @ X1) != (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (X0 @ Y1))) & ((X0 @ Y1) = Y0)))))))) )),
% 1.65/1.35 inference(cnf_transformation,[status(thm)],[f11])).
% 1.65/1.35 thf(f11,plain,(
% 1.65/1.35 ! [X0 : ($i > $o) > $i] : (! [X1 : $i > $o] : (((X0 @ X1) != (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (X0 @ Y1))) & ((X0 @ Y1) = Y0))))))) | ((X1 @ (X0 @ X1)) = $true)) | (((sK0 @ X0 @ (X0 @ (sK0 @ X0))) != $true) & ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (X0 @ Y1))) & ((X0 @ Y1) = Y0)))))) = (X0 @ (sK0 @ X0))))) & ! [X4 : $i > $o,X5 : $i > $o] : (((sK1 @ X4) != (sK1 @ X5)) | (X4 = X5))),
% 1.65/1.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f8,f10,f9])).
% 1.65/1.35 thf(f9,plain,(
% 1.65/1.35 ! [X0 : ($i > $o) > $i] : (? [X2 : $i > $o] : (($true != (X2 @ (X0 @ X2))) & ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (X0 @ Y1))) & ((X0 @ Y1) = Y0)))))) = (X0 @ X2))) => (((sK0 @ X0 @ (X0 @ (sK0 @ X0))) != $true) & ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (X0 @ Y1))) & ((X0 @ Y1) = Y0)))))) = (X0 @ (sK0 @ X0)))))),
% 1.65/1.35 introduced(definition,[],[choice_axiom])).
% 1.65/1.35 thf(f10,plain,(
% 1.65/1.35 ? [X3 : ($i > $o) > $i] : ! [X4 : $i > $o,X5 : $i > $o] : (((X3 @ X5) != (X3 @ X4)) | (X4 = X5)) => ! [X5 : $i > $o,X4 : $i > $o] : (((sK1 @ X4) != (sK1 @ X5)) | (X4 = X5))),
% 1.65/1.35 introduced(definition,[],[choice_axiom])).
% 1.65/1.35 thf(f8,plain,(
% 1.65/1.35 ! [X0 : ($i > $o) > $i] : (! [X1 : $i > $o] : (((X0 @ X1) != (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (X0 @ Y1))) & ((X0 @ Y1) = Y0))))))) | ((X1 @ (X0 @ X1)) = $true)) | ? [X2 : $i > $o] : (($true != (X2 @ (X0 @ X2))) & ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (X0 @ Y1))) & ((X0 @ Y1) = Y0)))))) = (X0 @ X2)))) & ? [X3 : ($i > $o) > $i] : ! [X4 : $i > $o,X5 : $i > $o] : (((X3 @ X5) != (X3 @ X4)) | (X4 = X5))),
% 1.65/1.35 inference(ennf_transformation,[status(thm)],[f7])).
% 1.65/1.35 thf(f7,plain,(
% 1.65/1.35 ~(! [X0 : ($i > $o) > $i] : (? [X1 : $i > $o] : (((X1 @ (X0 @ X1)) != $true) & ((X0 @ X1) = (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (X0 @ Y1))) & ((X0 @ Y1) = Y0)))))))) => ? [X2 : $i > $o] : (($true != (X2 @ (X0 @ X2))) & ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (X0 @ Y1))) & ((X0 @ Y1) = Y0)))))) = (X0 @ X2)))) => ~? [X3 : ($i > $o) > $i] : ! [X4 : $i > $o,X5 : $i > $o] : (((X3 @ X5) = (X3 @ X4)) => (X4 = X5)))),
% 1.65/1.35 inference(flattening,[status(thm)],[f6])).
% 1.65/1.35 thf(f6,plain,(
% 1.65/1.35 ~(! [X0 : ($i > $o) > $i] : (? [X1 : $i > $o] : (((X0 @ X1) = (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (X0 @ Y1))) & ((X0 @ Y1) = Y0))))))) & ~((X1 @ (X0 @ X1)) = $true)) => ? [X2 : $i > $o] : (((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (X0 @ Y1))) & ((X0 @ Y1) = Y0)))))) = (X0 @ X2)) & ~($true = (X2 @ (X0 @ X2))))) => ~? [X3 : ($i > $o) > $i] : ! [X4 : $i > $o,X5 : $i > $o] : (((X3 @ X5) = (X3 @ X4)) => (X4 = X5)))),
% 1.65/1.35 inference(rectify,[status(thm)],[f5])).
% 1.65/1.35 thf(f5,plain,(
% 1.65/1.35 ~(! [X0 : ($i > $o) > $i] : (? [X1 : $i > $o] : (((X0 @ X1) = (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (X0 @ Y1))) & ((X0 @ Y1) = Y0))))))) & ~((X1 @ (X0 @ X1)) = $true)) => ? [X4 : $i > $o] : (((X0 @ X4) = (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (X0 @ Y1))) & ((X0 @ Y1) = Y0))))))) & ~($true = (X4 @ (X0 @ X4))))) => ~? [X7 : ($i > $o) > $i] : ! [X8 : $i > $o,X9 : $i > $o] : (((X7 @ X9) = (X7 @ X8)) => (X8 = X9)))),
% 1.65/1.35 inference(fool_elimination,[status(thm)],[f4])).
% 1.65/1.35 thf(f4,plain,(
% 1.65/1.35 ~(! [X0 : ($i > $o) > $i] : (? [X1 : $i > $o] : (((X0 @ X1) = (X0 @ (^[X2 : $i] : (? [X3 : $i > $o] : (((X0 @ X3) = X2) & ~(X3 @ (X0 @ X3))))))) & ~(X1 @ (X0 @ X1))) => ? [X4 : $i > $o] : (((X0 @ X4) = (X0 @ (^[X5 : $i] : (? [X6 : $i > $o] : (((X0 @ X6) = X5) & ~(X6 @ (X0 @ X6))))))) & ~(X4 @ (X0 @ X4)))) => ~? [X7 : ($i > $o) > $i] : ! [X8 : $i > $o,X9 : $i > $o] : (((X7 @ X9) = (X7 @ X8)) => (X8 = X9)))),
% 1.65/1.35 inference(rectify,[status(thm)],[f2])).
% 1.65/1.35 thf(f2,negated_conjecture,(
% 1.65/1.35 ~(! [X0 : ($i > $o) > $i] : (? [X1 : $i > $o] : (((X0 @ X1) = (X0 @ (^[X2 : $i] : (? [X3 : $i > $o] : (((X0 @ X3) = X2) & ~(X3 @ (X0 @ X3))))))) & ~(X1 @ (X0 @ X1))) => ? [X1 : $i > $o] : (((X0 @ X1) = (X0 @ (^[X2 : $i] : (? [X3 : $i > $o] : (((X0 @ X3) = X2) & ~(X3 @ (X0 @ X3))))))) & ~(X1 @ (X0 @ X1)))) => ~? [X0 : ($i > $o) > $i] : ! [X5 : $i > $o,X4 : $i > $o] : (((X0 @ X4) = (X0 @ X5)) => (X4 = X5)))),
% 1.65/1.35 inference(negated_conjecture,[status(cth)],[f1])).
% 1.65/1.35 thf(f1,conjecture,(
% 1.65/1.35 ! [X0 : ($i > $o) > $i] : (? [X1 : $i > $o] : (((X0 @ X1) = (X0 @ (^[X2 : $i] : (? [X3 : $i > $o] : (((X0 @ X3) = X2) & ~(X3 @ (X0 @ X3))))))) & ~(X1 @ (X0 @ X1))) => ? [X1 : $i > $o] : (((X0 @ X1) = (X0 @ (^[X2 : $i] : (? [X3 : $i > $o] : (((X0 @ X3) = X2) & ~(X3 @ (X0 @ X3))))))) & ~(X1 @ (X0 @ X1)))) => ~? [X0 : ($i > $o) > $i] : ! [X5 : $i > $o,X4 : $i > $o] : (((X0 @ X4) = (X0 @ X5)) => (X4 = X5))),
% 1.65/1.35 file('/export/starexec/sandbox2/tmp/tmp.LZbPGbpWMS/DTF2THF_27298.p',cTHM193A)).
% 1.65/1.35 thf(f192,plain,(
% 1.65/1.35 ~spl2_1),
% 1.65/1.35 inference(avatar_contradiction_clause,[status(thm)],[f191])).
% 1.65/1.35 thf(f191,plain,(
% 1.65/1.35 $false | ~spl2_1),
% 1.65/1.35 inference(trivial_inequality_removal,[status(thm)],[f190])).
% 1.65/1.35 thf(f190,plain,(
% 1.65/1.35 ($true = $false) | ~spl2_1),
% 1.65/1.35 inference(forward_demodulation,[status(thm)],[f174,f65])).
% 1.65/1.35 thf(f65,plain,(
% 1.65/1.35 ($false = (sK5 @ (sK1 @ sK5))) | ~spl2_1),
% 1.65/1.35 inference(not_proxy_clausification,[status(thm)],[f64])).
% 1.65/1.35 thf(f64,plain,(
% 1.65/1.35 ($true = (~ (sK5 @ (sK1 @ sK5)))) | ~spl2_1),
% 1.65/1.35 inference(binary_proxy_clausification,[status(thm)],[f62])).
% 1.65/1.35 thf(f62,plain,(
% 1.65/1.35 ($true = ((~ (sK5 @ (sK1 @ sK5))) & ((sK1 @ sK5) = (sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0))))))))) | ~spl2_1),
% 1.65/1.35 inference(beta_eta_normalization,[status(thm)],[f61])).
% 1.65/1.35 thf(f61,plain,(
% 1.65/1.35 ($true = ((^[Y0 : $i > $o]: ((~ (Y0 @ (sK1 @ Y0))) & ((sK1 @ Y0) = (sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ (sK1 @ Y2))) & ((sK1 @ Y2) = Y1))))))))) @ sK5)) | ~spl2_1),
% 1.65/1.35 inference(sigma_clausification,[status(thm)],[f60])).
% 1.65/1.35 thf(f60,plain,(
% 1.65/1.35 ($true = (?? @ ($i > $o) @ (^[Y0 : $i > $o]: ((~ (Y0 @ (sK1 @ Y0))) & ((sK1 @ Y0) = (sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ (sK1 @ Y2))) & ((sK1 @ Y2) = Y1))))))))))) | ~spl2_1),
% 1.65/1.35 inference(beta_eta_normalization,[status(thm)],[f59])).
% 1.65/1.35 thf(f59,plain,(
% 1.65/1.35 (((^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0))))) @ (sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0))))))) = $true) | ~spl2_1),
% 1.65/1.35 inference(equality_resolution,[status(thm)],[f20])).
% 1.65/1.35 thf(f20,plain,(
% 1.65/1.35 ( ! [X1 : $i > $o] : (((sK1 @ X1) != (sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0))))))) | ($true = (X1 @ (sK1 @ X1)))) ) | ~spl2_1),
% 1.65/1.35 inference(avatar_component_clause,[status(thm)],[f19])).
% 1.65/1.35 thf(f174,plain,(
% 1.65/1.35 ($true = (sK5 @ (sK1 @ sK5))) | ~spl2_1),
% 1.65/1.35 inference(equality_resolution,[status(thm)],[f118])).
% 1.65/1.35 thf(f118,plain,(
% 1.65/1.35 ( ! [X0 : $i > $o] : (((sK1 @ sK5) != (sK1 @ X0)) | ((X0 @ (sK1 @ X0)) = $true)) ) | ~spl2_1),
% 1.65/1.35 inference(superposition,[status(thm)],[f20,f66])).
% 1.65/1.35 thf(f66,plain,(
% 1.65/1.35 ((sK1 @ sK5) = (sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0))))))) | ~spl2_1),
% 1.65/1.35 inference(equality_proxy_clausification,[status(thm)],[f63])).
% 1.65/1.35 thf(f63,plain,(
% 1.65/1.35 (((sK1 @ sK5) = (sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0))))))) = $true) | ~spl2_1),
% 1.65/1.35 inference(binary_proxy_clausification,[status(thm)],[f62])).
% 1.65/1.35 thf(f25,plain,(
% 1.65/1.35 spl2_2 | spl2_1),
% 1.65/1.35 inference(avatar_split_clause,[status(thm)],[f16,f19,f22])).
% 1.65/1.35 thf(f16,plain,(
% 1.65/1.35 ( ! [X0 : $i > $o,X1 : $i > $o] : (((sK1 @ X0) != (sK1 @ (sK0 @ sK1))) | ((^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0))))) = X0) | ((sK1 @ X1) != (sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0))))))) | ($true = (X1 @ (sK1 @ X1)))) )),
% 1.65/1.35 inference(superposition,[status(thm)],[f12,f13])).
% 1.65/1.35 thf(f13,plain,(
% 1.65/1.35 ( ! [X0 : ($i > $o) > $i,X1 : $i > $o] : (((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (X0 @ Y1))) & ((X0 @ Y1) = Y0)))))) = (X0 @ (sK0 @ X0))) | ((X1 @ (X0 @ X1)) = $true) | ((X0 @ X1) != (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (X0 @ Y1))) & ((X0 @ Y1) = Y0)))))))) )),
% 1.65/1.35 inference(cnf_transformation,[status(thm)],[f11])).
% 1.65/1.35 thf(f12,plain,(
% 1.65/1.35 ( ! [X4 : $i > $o,X5 : $i > $o] : (((sK1 @ X4) != (sK1 @ X5)) | (X4 = X5)) )),
% 1.65/1.35 inference(cnf_transformation,[status(thm)],[f11])).
% 1.65/1.35 % SZS output end Proof for DTF2THF_27298
% 1.65/1.35 % (27574)------------------------------
% 1.65/1.35 % (27574)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.35 % (27574)Termination reason: Refutation
% 1.65/1.35
% 1.65/1.35 % (27574)Memory used [KB]: 5628
% 1.65/1.35 % (27574)Time elapsed: 0.024 s
% 1.65/1.35 % (27574)Instructions burned: 31 (million)
% 1.65/1.35 % (27574)------------------------------
% 1.65/1.35 % (27574)------------------------------
% 1.65/1.35 % (27568)Success in time 0.038 s
%------------------------------------------------------------------------------