%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU868^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : 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 09:37:37 AM UTC 2026
% Result : Theorem 1.58s 1.34s
% Output : Refutation 1.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 3
% Syntax : Number of formulae : 62 ( 30 unt; 0 typ; 2 def)
% Number of atoms : 476 ( 137 equ; 0 cnn)
% Maximal formula atoms : 5 ( 7 avg)
% Number of connectives : 875 ( 52 ~; 86 |; 49 &; 478 @)
% ( 5 <=>; 86 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 186 ( 186 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 12 usr; 10 con; 0-2 aty)
% ( 105 !!; 14 ??; 0 @@+; 0 @@-)
% Number of variables : 218 ( 159 ^; 56 !; 3 ?; 218 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
cC: a > $o ).
thf(func_def_19,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
sK2: ( a > $o ) > $o ).
thf(func_def_21,type,
sK3: a ).
thf(func_def_22,type,
sK4: a ).
thf(func_def_23,type,
sK5: a ).
thf(func_def_24,type,
sK6: a > $o ).
thf(func_def_25,type,
sK7: a ).
thf(func_def_26,type,
sK8: a > a ).
thf(func_def_27,type,
sK9: a > a ).
thf(f214,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f40,f92,f213]) ).
thf(f213,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f212]) ).
thf(f212,plain,
( $false
| ~ spl0_1 ),
inference(equality_resolution,[status(thm)],[f208]) ).
thf(f208,plain,
( ! [X0: a] :
( ( ( sK6 @ ( sK9 @ X0 ) )
| ( X0
= ( sK9 @ X0 ) ) )
!= ( ( sK6 @ ( sK9 @ X0 ) )
| ( sK5
= ( sK9 @ X0 ) ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f207]) ).
thf(f207,plain,
( ! [X0: a] :
( $false
= ( ( ( sK6 @ ( sK9 @ X0 ) )
| ( sK5
= ( sK9 @ X0 ) ) )
= ( ( sK6 @ ( sK9 @ X0 ) )
| ( X0
= ( sK9 @ X0 ) ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f205]) ).
thf(f205,plain,
( ! [X0: a] :
( $false
= ( ^ [Y0: a] :
( ( ( sK6 @ Y0 )
| ( sK5 = Y0 ) )
= ( ( sK6 @ Y0 )
| ( X0 = Y0 ) ) )
@ ( sK9 @ X0 ) ) )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f175]) ).
thf(f175,plain,
( ! [X0: a] :
( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ Y0 )
| ( sK5 = Y0 ) )
= ( ( sK6 @ Y0 )
| ( X0 = Y0 ) ) ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f169]) ).
thf(f169,plain,
( ! [X0: a] :
( $false
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ Y0 )
| ( sK5 = Y0 ) )
= ( ( sK6 @ Y0 )
| ( X0 = Y0 ) ) ) ) ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f146,f112]) ).
thf(f112,plain,
( ( $true
= ( sK2 @ sK6 ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f110]) ).
thf(f110,plain,
( ( $false
= ( ( sK2 @ sK6 )
=> ( sK2
@ ^ [Y0: a] :
( ( sK6 @ Y0 )
| ( sK5 = Y0 ) ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f109]) ).
thf(f109,plain,
( ( $false
= ( ^ [Y0: a > $o] :
( ( sK2 @ Y0 )
=> ( sK2
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
| ( sK5 = Y1 ) ) ) )
@ sK6 ) )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f102]) ).
thf(f102,plain,
( ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK2 @ Y0 )
=> ( sK2
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
| ( sK5 = Y1 ) ) ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f98]) ).
thf(f98,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( sK2 @ Y1 )
=> ( sK2
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
| ( Y0 = Y2 ) ) ) ) )
@ sK5 ) )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( sK2 @ Y1 )
=> ( sK2
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
| ( Y0 = Y2 ) ) ) ) ) ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f35]) ).
thf(f35,definition,
( spl0_1
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( sK2 @ Y1 )
=> ( sK2
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
| ( Y0 = Y2 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f146,plain,
( ! [X0: a > $o,X1: a] :
( $false
= ( ( sK2 @ X0 )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ Y0 )
| ( sK5 = Y0 ) )
= ( ( X0 @ Y0 )
| ( X1 = Y0 ) ) ) ) ) )
| ~ spl0_1 ),
inference(not_proxy_clausification,[status(thm)],[f119]) ).
thf(f119,plain,
( ! [X0: a > $o,X1: a] :
( $true
= ( ~ ( ( sK2 @ X0 )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ Y0 )
| ( sK5 = Y0 ) )
= ( ( X0 @ Y0 )
| ( X1 = Y0 ) ) ) ) ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f118]) ).
thf(f118,plain,
( ! [X0: a > $o,X1: a] :
( $true
= ( ( ( sK2 @ X0 )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ Y0 )
| ( sK5 = Y0 ) )
= ( ( X0 @ Y0 )
| ( X1 = Y0 ) ) ) ) )
=> $false ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f116]) ).
thf(f116,plain,
( ! [X0: a > $o,X1: a] :
( $true
= ( ( ( sK2 @ X0 )
& ( !! @ a
@ ^ [Y0: a] :
( ( ^ [Y1: a] :
( ( sK6 @ Y1 )
| ( sK5 = Y1 ) )
@ Y0 )
= ( ( X0 @ Y0 )
| ( X1 = Y0 ) ) ) ) )
=> $false ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f70,f114]) ).
thf(f114,plain,
( ( $false
= ( sK2
@ ^ [Y0: a] :
( ( sK6 @ Y0 )
| ( sK5 = Y0 ) ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f113]) ).
thf(f113,plain,
( ( ( $true
=> ( sK2
@ ^ [Y0: a] :
( ( sK6 @ Y0 )
| ( sK5 = Y0 ) ) ) )
= $false )
| ~ spl0_1 ),
inference(backward_demodulation,[status(thm)],[f110,f112]) ).
thf(f70,plain,
! [X2: a,X3: a > $o,X1: a > $o] :
( ( ( ( sK2 @ X3 )
& ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
= ( ( X3 @ Y0 )
| ( X2 = Y0 ) ) ) ) )
=> ( sK2 @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f69]) ).
thf(f69,plain,
! [X2: a,X3: a > $o,X1: a > $o] :
( $true
= ( ^ [Y0: a > $o] :
( ( ( sK2 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( X1 @ Y1 )
= ( ( Y0 @ Y1 )
| ( X2 = Y1 ) ) ) ) )
=> ( sK2 @ X1 ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f62]) ).
thf(f62,plain,
! [X2: a,X1: a > $o] :
( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( sK2 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( X1 @ Y1 )
= ( ( Y0 @ Y1 )
| ( X2 = Y1 ) ) ) ) )
=> ( sK2 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f61]) ).
thf(f61,plain,
! [X2: a,X1: a > $o] :
( $true
= ( ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( sK2 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( X1 @ Y2 )
= ( ( Y1 @ Y2 )
| ( Y0 = Y2 ) ) ) ) )
=> ( sK2 @ X1 ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
! [X1: a > $o] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( sK2 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( X1 @ Y2 )
= ( ( Y1 @ Y2 )
| ( Y0 = Y2 ) ) ) ) )
=> ( sK2 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f52]) ).
thf(f52,plain,
! [X1: a > $o] :
( $true
= ( ^ [Y0: a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( sK2 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 )
= ( ( Y2 @ Y3 )
| ( Y1 = Y3 ) ) ) ) )
=> ( sK2 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f49]) ).
thf(f49,plain,
( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( sK2 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 )
= ( ( Y2 @ Y3 )
| ( Y1 = Y3 ) ) ) ) )
=> ( sK2 @ Y0 ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f48]) ).
thf(f48,plain,
( $true
= ( $true
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( sK2 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 )
= ( ( Y2 @ Y3 )
| ( Y1 = Y3 ) ) ) ) )
=> ( sK2 @ Y0 ) ) ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f23,f47]) ).
thf(f47,plain,
( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ~ ( ?? @ a @ Y0 )
=> ( sK2 @ Y0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ~ ( ?? @ a @ Y0 )
=> ( sK2 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( sK2 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 )
= ( ( Y2 @ Y3 )
| ( Y1 = Y3 ) ) ) ) )
=> ( sK2 @ Y0 ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( $false
= ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ~ ( ?? @ a @ Y0 )
=> ( sK2 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( sK2 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 )
= ( ( Y2 @ Y3 )
| ( Y1 = Y3 ) ) ) ) )
=> ( sK2 @ Y0 ) ) ) ) ) )
=> ( sK2 @ cC ) ) ),
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,plain,
( $false
= ( ^ [Y0: ( a > $o ) > $o] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ~ ( ?? @ a @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( !! @ a
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y0 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 )
= ( ( Y3 @ Y4 )
| ( Y2 = Y4 ) ) ) ) )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( Y0 @ cC ) )
@ sK2 ) ),
inference(sigma_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( $false
= ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ~ ( ?? @ a @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( !! @ a
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y0 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 )
= ( ( Y3 @ Y4 )
| ( Y2 = Y4 ) ) ) ) )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( Y0 @ cC ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f8]) ).
thf(f8,plain,
( $false
= ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y0 @ Y2 )
=> ( Y0
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
| ( Y1 = Y3 ) ) ) ) ) )
& ( Y0
@ ^ [Y1: a] : $false ) )
=> ( Y0 @ cC ) ) )
=> ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ~ ( ?? @ a @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( !! @ a
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y0 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 )
= ( ( Y3 @ Y4 )
| ( Y2 = Y4 ) ) ) ) )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( Y0 @ cC ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ~ ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y0 @ Y2 )
=> ( Y0
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
| ( Y1 = Y3 ) ) ) ) ) )
& ( Y0
@ ^ [Y1: a] : $false ) )
=> ( Y0 @ cC ) ) )
=> ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ~ ( ?? @ a @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( !! @ a
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y0 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 )
= ( ( Y3 @ Y4 )
| ( Y2 = Y4 ) ) ) ) )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( Y0 @ cC ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y0 @ Y2 )
=> ( Y0
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
| ( Y1 = Y3 ) ) ) ) ) )
& ( Y0
@ ^ [Y1: a] : $false ) )
=> ( Y0 @ cC ) ) )
=> ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ~ ( ?? @ a
@ ^ [Y2: a] : ( Y1 @ Y2 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( !! @ a
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y0 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 )
= ( ( Y3 @ Y4 )
| ( Y2 = Y4 ) ) ) ) )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( Y0 @ cC ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y0 @ Y2 )
=> ( Y0
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
| ( Y1 = Y3 ) ) ) ) ) )
& ( Y0
@ ^ [Y1: a] : $false ) )
=> ( Y0 @ cC ) ) )
=> ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ~ ( ?? @ a
@ ^ [Y2: a] : ( Y1 @ Y2 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( !! @ a
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y0 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 )
= ( ( Y3 @ Y4 )
| ( Y2 = Y4 ) ) ) ) )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( Y0 @ cC ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: ( a > $o ) > $o] :
( ( ( X0
@ ^ [X1: a] : $false )
& ! [X2: a > $o,X3: a] :
( ( X0 @ X2 )
=> ( X0
@ ^ [X4: a] :
( ( X3 = X4 )
| ( X2 @ X4 ) ) ) ) )
=> ( X0 @ cC ) )
=> ! [X5: ( a > $o ) > $o] :
( ( ! [X6: a > $o,X7: a,X8: a > $o] :
( ( ! [X9: a] :
( ( X8 @ X9 )
<=> ( ( X7 = X9 )
| ( X6 @ X9 ) ) )
& ( X5 @ X6 ) )
=> ( X5 @ X8 ) )
& ! [X10: a > $o] :
( ~ ? [X11: a] : ( X10 @ X11 )
=> ( X5 @ X10 ) ) )
=> ( X5 @ cC ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: ( a > $o ) > $o] :
( ( ( X0
@ ^ [X1: a] : $false )
& ! [X2: a > $o,X1: a] :
( ( X0 @ X2 )
=> ( X0
@ ^ [X3: a] :
( ( X1 = X3 )
| ( X2 @ X3 ) ) ) ) )
=> ( X0 @ cC ) )
=> ! [X4: ( a > $o ) > $o] :
( ( ! [X6: a > $o,X1: a,X7: a > $o] :
( ( ! [X8: a] :
( ( X7 @ X8 )
<=> ( ( X1 = X8 )
| ( X6 @ X8 ) ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) )
& ! [X5: a > $o] :
( ~ ? [X3: a] : ( X5 @ X3 )
=> ( X4 @ X5 ) ) )
=> ( X4 @ cC ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X0: ( a > $o ) > $o] :
( ( ( X0
@ ^ [X1: a] : $false )
& ! [X2: a > $o,X1: a] :
( ( X0 @ X2 )
=> ( X0
@ ^ [X3: a] :
( ( X1 = X3 )
| ( X2 @ X3 ) ) ) ) )
=> ( X0 @ cC ) )
=> ! [X4: ( a > $o ) > $o] :
( ( ! [X6: a > $o,X1: a,X7: a > $o] :
( ( ! [X8: a] :
( ( X7 @ X8 )
<=> ( ( X1 = X8 )
| ( X6 @ X8 ) ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) )
& ! [X5: a > $o] :
( ~ ? [X3: a] : ( X5 @ X3 )
=> ( X4 @ X5 ) ) )
=> ( X4 @ cC ) ) ),
file('/export/starexec/sandbox/tmp/tmp.2DbGc2r228/DTF2THF_20552.p',cTHM551_pme) ).
thf(f92,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f91]) ).
thf(f91,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f90]) ).
thf(f90,plain,
( ( $false = $true )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f85]) ).
thf(f85,plain,
( ( $true
= ( ^ [Y0: a] : $false
@ sK4 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
( ( $true
= ( ?? @ a
@ ^ [Y0: a] : $false ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f59]) ).
thf(f59,plain,
( ( ( ~ ~ ( ?? @ a
@ ^ [Y0: a] : $false ) )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f55]) ).
thf(f55,plain,
( ( $true
= ( ~ ( ?? @ a
@ ^ [Y0: a] : $false )
=> $false ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f51,f39]) ).
thf(f39,plain,
( ( $false
= ( sK2
@ ^ [Y0: a] : $false ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f38]) ).
thf(f38,definition,
( spl0_2
<=> ( $false
= ( sK2
@ ^ [Y0: a] : $false ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f51,plain,
! [X1: a > $o] :
( ( ~ ( ?? @ a @ X1 )
=> ( sK2 @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f50]) ).
thf(f50,plain,
! [X1: a > $o] :
( ( ^ [Y0: a > $o] :
( ~ ( ?? @ a @ Y0 )
=> ( sK2 @ Y0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f47]) ).
thf(f40,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f31,f38,f35]) ).
thf(f31,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( sK2 @ Y1 )
=> ( sK2
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
| ( Y0 = Y2 ) ) ) ) ) ) )
| ( $false
= ( sK2
@ ^ [Y0: a] : $false ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( sK2 @ Y1 )
=> ( sK2
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
| ( Y0 = Y2 ) ) ) ) ) )
& ( sK2
@ ^ [Y0: a] : $false ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( sK2 @ Y1 )
=> ( sK2
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
| ( Y0 = Y2 ) ) ) ) ) )
& ( sK2
@ ^ [Y0: a] : $false ) ) ) ),
inference(boolean_simplification,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( sK2 @ Y1 )
=> ( sK2
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
| ( Y0 = Y2 ) ) ) ) ) )
& ( sK2
@ ^ [Y0: a] : $false ) )
=> $false )
= $true ),
inference(superposition,[status(thm)],[f18,f25]) ).
thf(f25,plain,
( ( sK2 @ cC )
= $false ),
inference(boolean_simplification,[status(thm)],[f24]) ).
thf(f24,plain,
( ( $true
=> ( sK2 @ cC ) )
= $false ),
inference(backward_demodulation,[status(thm)],[f21,f23]) ).
thf(f18,plain,
! [X1: ( a > $o ) > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( X1 @ Y1 )
=> ( X1
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
| ( Y0 = Y2 ) ) ) ) ) )
& ( X1
@ ^ [Y0: a] : $false ) )
=> ( X1 @ cC ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f17]) ).
thf(f17,plain,
! [X1: ( a > $o ) > $o] :
( ( ^ [Y0: ( a > $o ) > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y0 @ Y2 )
=> ( Y0
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
| ( Y1 = Y3 ) ) ) ) ) )
& ( Y0
@ ^ [Y1: a] : $false ) )
=> ( Y0 @ cC ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f12]) ).
thf(f12,plain,
( $true
= ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y0 @ Y2 )
=> ( Y0
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
| ( Y1 = Y3 ) ) ) ) ) )
& ( Y0
@ ^ [Y1: a] : $false ) )
=> ( Y0 @ cC ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU868^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n001.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:36:35 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.46 ---- Original DTF file ---
% 0.19/0.46 thf(spec,logic,$$dhol).
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % File : SEU868^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.46 % Domain : Set Theory (Finite sets)
% 0.19/0.46 % Problem : TPS problem from FINITE-SET-THMS
% 0.19/0.46 % Version : Especial.
% 0.19/0.46 % English :
% 0.19/0.46
% 0.19/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.46 % Source : [Bro09]
% 0.19/0.46 % Names : tps_1008 [Bro09]
% 0.19/0.46
% 0.19/0.46 % Status : Theorem
% 0.19/0.46 % Rating : 0.33 v9.1.0, 0.25 v9.0.0, 0.40 v8.2.0, 0.54 v8.1.0, 0.45 v7.5.0, 0.43 v7.4.0, 0.22 v7.2.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.60 v5.2.0, 0.80 v4.1.0, 1.00 v4.0.0
% 0.19/0.46 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.19/0.46 % Number of atoms : 5 ( 2 equ; 0 cnn)
% 0.19/0.46 % Maximal formula atoms : 5 ( 5 avg)
% 0.19/0.46 % Number of connectives : 25 ( 1 ~; 2 |; 3 &; 12 @)
% 0.19/0.46 % ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% 0.19/0.46 % Maximal formula depth : 14 ( 14 avg)
% 0.19/0.46 % Number of types : 2 ( 1 usr)
% 0.19/0.46 % Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% 0.19/0.46 % Number of symbols : 3 ( 1 usr; 1 con; 0-2 aty)
% 0.19/0.46 % Number of variables : 12 ( 2 ^; 9 !; 1 ?; 12 :)
% 0.19/0.46 % SPC : TH0_THM_EQU_NAR
% 0.19/0.46
% 0.19/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 thf(a_type,type,
% 0.19/0.46 a: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(cC,type,
% 0.19/0.46 cC: a > $o ).
% 0.19/0.46
% 0.19/0.46 thf(cTHM551_pme,conjecture,
% 0.19/0.46 ( ! [Xw: ( a > $o ) > $o] :
% 0.19/0.46 ( ( ( Xw
% 0.19/0.46 @ ^ [Xx: a] : $false )
% 0.19/0.46 & ! [Xr: a > $o,Xx: a] :
% 0.19/0.46 ( ( Xw @ Xr )
% 0.19/0.46 => ( Xw
% 0.19/0.46 @ ^ [Xt: a] :
% 0.19/0.46 ( ( Xr @ Xt )
% 0.19/0.46 | ( Xt = Xx ) ) ) ) )
% 0.19/0.46 => ( Xw @ cC ) )
% 0.19/0.46 => ! [P: ( a > $o ) > $o] :
% 0.19/0.46 ( ( ! [E: a > $o] :
% 0.19/0.46 ( ~ ? [Xt: a] : ( E @ Xt )
% 0.19/0.46 => ( P @ E ) )
% 0.19/0.46 & ! [Y: a > $o,Xx: a,Z: a > $o] :
% 0.19/0.46 ( ( ( P @ Y )
% 0.19/0.46 & ! [Xx_16: a] :
% 0.19/0.46 ( ( Z @ Xx_16 )
% 0.19/0.46 <=> ( ( Y @ Xx_16 )
% 0.19/0.46 | ( Xx_16 = Xx ) ) ) )
% 0.19/0.46 => ( P @ Z ) ) )
% 0.19/0.46 => ( P @ cC ) ) ) ).
% 0.19/0.46
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 ------------------------
% 1.47/1.24 ---- Embedded in THF ---
% 1.47/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.25 %%% Generated on Tue Feb 24 12:36:36 EST 2026
% 1.47/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.25 %%% Logic specification used:
% 1.47/1.25 %%% thf(spec, logic, $$dhol).
% 1.47/1.25
% 1.47/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.2DbGc2r228/DTF2DTF20552.p
% See solution above
% 1.47/1.25 ------------------------
% 1.47/1.25 ---- Cleaned THF ---
% 1.47/1.26 thf(a_type,type,
% 1.47/1.26 a: $tType ).
% 1.47/1.26
% 1.47/1.26 thf(cC,type,
% 1.47/1.26 cC: a > $o ).
% 1.47/1.26
% 1.47/1.26 thf(cTHM551_pme,conjecture,
% 1.47/1.26 ( ! [Xw: ( a > $o ) > $o] :
% 1.47/1.26 ( ( ( Xw
% 1.47/1.26 @ ^ [Xx: a] : $false )
% 1.47/1.26 & ! [Xr: a > $o,Xx: a] :
% 1.47/1.26 ( ( Xw @ Xr )
% 1.47/1.26 => ( Xw
% 1.47/1.26 @ ^ [Xt: a] :
% 1.47/1.26 ( ( Xr @ Xt )
% 1.47/1.26 | ( Xt = Xx ) ) ) ) )
% 1.47/1.26 => ( Xw @ cC ) )
% 1.47/1.26 => ! [P: ( a > $o ) > $o] :
% 1.47/1.26 ( ( ! [E: a > $o] :
% 1.47/1.26 ( ~ ? [Xt: a] : ( E @ Xt )
% 1.47/1.26 => ( P @ E ) )
% 1.47/1.26 & ! [Y: a > $o,Xx: a,Z: a > $o] :
% 1.47/1.26 ( ( ( P @ Y )
% 1.47/1.26 & ! [Xx_16: a] :
% 1.47/1.26 ( ( Z @ Xx_16 )
% 1.47/1.26 <=> ( ( Y @ Xx_16 )
% 1.47/1.26 | ( Xx_16 = Xx ) ) ) )
% 1.47/1.26 => ( P @ Z ) ) )
% 1.47/1.26 => ( P @ cC ) ) ) ).
% 1.47/1.26 ------------------------
% 1.47/1.27 % (20742)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_20552 for (2999ds/4Mi)
% 1.47/1.27 % (20741)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_20552 for (2999ds/183Mi)
% 1.47/1.27 % (20745)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_20552 for (2999ds/2Mi)
% 1.47/1.27 % (20742)Instruction limit reached!
% 1.47/1.27 % (20742)------------------------------
% 1.47/1.27 % (20742)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.27 % (20742)Termination reason: Unknown
% 1.47/1.27 % (20742)Termination phase: Saturation
% 1.47/1.27
% 1.47/1.27 % (20742)Memory used [KB]: 5500
% 1.47/1.27 % (20742)Time elapsed: 0.003 s
% 1.47/1.27 % (20742)Instructions burned: 4 (million)
% 1.47/1.27 % (20742)------------------------------
% 1.47/1.27 % (20742)------------------------------
% 1.47/1.27 % (20745)Instruction limit reached!
% 1.47/1.27 % (20745)------------------------------
% 1.47/1.27 % (20745)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.27 % (20745)Termination reason: Unknown
% 1.47/1.27 % (20745)Termination phase: Saturation
% 1.47/1.27
% 1.47/1.27 % (20745)Memory used [KB]: 5500
% 1.47/1.27 % (20745)Time elapsed: 0.002 s
% 1.47/1.27 % (20745)Instructions burned: 2 (million)
% 1.47/1.27 % (20745)------------------------------
% 1.47/1.27 % (20745)------------------------------
% 1.47/1.28 % (20743)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_20552 for (2999ds/27Mi)
% 1.47/1.28 % (20746)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_20552 for (2999ds/275Mi)
% 1.47/1.28 % (20747)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_20552 for (2999ds/18Mi)
% 1.47/1.28 % (20744)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_20552 for (2999ds/2Mi)
% 1.47/1.28 % (20744)Instruction limit reached!
% 1.47/1.28 % (20744)------------------------------
% 1.47/1.28 % (20744)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.28 % (20744)Termination reason: Unknown
% 1.47/1.28 % (20744)Termination phase: Preprocessing 3
% 1.47/1.28
% 1.47/1.28 % (20744)Memory used [KB]: 1023
% 1.47/1.28 % (20744)Time elapsed: 0.004 s
% 1.47/1.28 % (20744)Instructions burned: 2 (million)
% 1.47/1.28 % (20744)------------------------------
% 1.47/1.28 % (20744)------------------------------
% 1.47/1.28 % (20743)Refutation not found, incomplete strategy
% 1.47/1.28 % (20743)------------------------------
% 1.47/1.28 % (20743)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.28 % (20743)Termination reason: Refutation not found, incomplete strategy
% 1.47/1.28
% 1.47/1.28
% 1.47/1.28 % (20743)Memory used [KB]: 5500
% 1.47/1.28 % (20743)Time elapsed: 0.005 s
% 1.47/1.28 % (20743)Instructions burned: 4 (million)
% 1.47/1.28 % (20743)------------------------------
% 1.47/1.28 % (20743)------------------------------
% 1.47/1.28 % (20749)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_20552 for (2999ds/3Mi)
% 1.47/1.28 % (20749)Instruction limit reached!
% 1.47/1.28 % (20749)------------------------------
% 1.47/1.28 % (20749)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.28 % (20749)Termination reason: Unknown
% 1.47/1.28 % (20749)Termination phase: Saturation
% 1.47/1.28
% 1.47/1.28 % (20749)Memory used [KB]: 5500
% 1.47/1.28 % (20749)Time elapsed: 0.002 s
% 1.47/1.28 % (20749)Instructions burned: 3 (million)
% 1.47/1.28 % (20749)------------------------------
% 1.47/1.28 % (20749)------------------------------
% 1.47/1.29 % (20750)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_20552 for (2999ds/37Mi)
% 1.47/1.29 % (20747)Instruction limit reached!
% 1.47/1.29 % (20747)------------------------------
% 1.47/1.29 % (20747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.29 % (20747)Termination reason: Unknown
% 1.47/1.29 % (20747)Termination phase: Saturation
% 1.47/1.29
% 1.47/1.29 % (20747)Memory used [KB]: 5628
% 1.47/1.29 % (20747)Time elapsed: 0.014 s
% 1.47/1.29 % (20747)Instructions burned: 18 (million)
% 1.47/1.29 % (20747)------------------------------
% 1.47/1.29 % (20747)------------------------------
% 1.47/1.29 % (20751)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_20552 for (2999ds/15Mi)
% 1.47/1.30 % (20751)Instruction limit reached!
% 1.47/1.30 % (20751)------------------------------
% 1.47/1.30 % (20751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.30 % (20751)Termination reason: Unknown
% 1.47/1.30 % (20751)Termination phase: Saturation
% 1.47/1.30
% 1.47/1.30 % (20751)Memory used [KB]: 5628
% 1.47/1.30 % (20751)Time elapsed: 0.006 s
% 1.47/1.30 % (20751)Instructions burned: 15 (million)
% 1.47/1.30 % (20751)------------------------------
% 1.47/1.30 % (20751)------------------------------
% 1.58/1.30 % (20752)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_20552 for (2999ds/3Mi)
% 1.58/1.30 % (20752)Instruction limit reached!
% 1.58/1.30 % (20752)------------------------------
% 1.58/1.30 % (20752)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.30 % (20752)Termination reason: Unknown
% 1.58/1.30 % (20752)Termination phase: Saturation
% 1.58/1.30
% 1.58/1.30 % (20752)Memory used [KB]: 5500
% 1.58/1.30 % (20752)Time elapsed: 0.004 s
% 1.58/1.30 % (20752)Instructions burned: 3 (million)
% 1.58/1.30 % (20752)------------------------------
% 1.58/1.30 % (20752)------------------------------
% 1.58/1.30 % (20753)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_20552 for (2999ds/1041Mi)
% 1.58/1.31 % (20755)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_20552 for (2999ds/16Mi)
% 1.58/1.31 % (20750)Instruction limit reached!
% 1.58/1.31 % (20750)------------------------------
% 1.58/1.31 % (20750)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.31 % (20750)Termination reason: Unknown
% 1.58/1.31 % (20750)Termination phase: Saturation
% 1.58/1.31
% 1.58/1.31 % (20750)Memory used [KB]: 5884
% 1.58/1.31 % (20750)Time elapsed: 0.021 s
% 1.58/1.31 % (20750)Instructions burned: 38 (million)
% 1.58/1.31 % (20750)------------------------------
% 1.58/1.31 % (20750)------------------------------
% 1.58/1.31 % (20754)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_20552 for (2999ds/7Mi)
% 1.58/1.31 % (20755)Instruction limit reached!
% 1.58/1.31 % (20755)------------------------------
% 1.58/1.31 % (20755)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.31 % (20755)Termination reason: Unknown
% 1.58/1.31 % (20755)Termination phase: Saturation
% 1.58/1.31
% 1.58/1.31 % (20755)Memory used [KB]: 5628
% 1.58/1.31 % (20755)Time elapsed: 0.007 s
% 1.58/1.31 % (20755)Instructions burned: 18 (million)
% 1.58/1.31 % (20755)------------------------------
% 1.58/1.31 % (20755)------------------------------
% 1.58/1.31 % (20754)Instruction limit reached!
% 1.58/1.31 % (20754)------------------------------
% 1.58/1.31 % (20754)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.31 % (20754)Termination reason: Unknown
% 1.58/1.31 % (20754)Termination phase: Saturation
% 1.58/1.31
% 1.58/1.31 % (20754)Memory used [KB]: 1023
% 1.58/1.31 % (20754)Time elapsed: 0.007 s
% 1.58/1.31 % (20754)Instructions burned: 7 (million)
% 1.58/1.31 % (20754)------------------------------
% 1.58/1.31 % (20754)------------------------------
% 1.58/1.32 % (20756)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_20552 for (2999ds/3Mi)
% 1.58/1.32 % (20757)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_20552 for (2999ds/3Mi)
% 1.58/1.32 % (20756)Instruction limit reached!
% 1.58/1.32 % (20756)------------------------------
% 1.58/1.32 % (20756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.32 % (20756)Termination reason: Unknown
% 1.58/1.32 % (20756)Termination phase: Property scanning
% 1.58/1.32
% 1.58/1.32 % (20756)Memory used [KB]: 1023
% 1.58/1.32 % (20756)Time elapsed: 0.004 s
% 1.58/1.32 % (20756)Instructions burned: 4 (million)
% 1.58/1.32 % (20756)------------------------------
% 1.58/1.32 % (20756)------------------------------
% 1.58/1.32 % (20758)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_20552 for (2999ds/7Mi)
% 1.58/1.32 % (20757)Instruction limit reached!
% 1.58/1.32 % (20757)------------------------------
% 1.58/1.32 % (20757)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.32 % (20757)Termination reason: Unknown
% 1.58/1.32 % (20757)Termination phase: Saturation
% 1.58/1.32
% 1.58/1.32 % (20757)Memory used [KB]: 1023
% 1.58/1.32 % (20757)Time elapsed: 0.003 s
% 1.58/1.32 % (20757)Instructions burned: 4 (million)
% 1.58/1.32 % (20757)------------------------------
% 1.58/1.32 % (20757)------------------------------
% 1.58/1.32 % (20741)Instruction limit reached!
% 1.58/1.32 % (20741)------------------------------
% 1.58/1.32 % (20741)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.32 % (20741)Termination reason: Unknown
% 1.58/1.32 % (20741)Termination phase: Saturation
% 1.58/1.32
% 1.58/1.32 % (20741)Memory used [KB]: 6908
% 1.58/1.32 % (20741)Time elapsed: 0.056 s
% 1.58/1.32 % (20741)Instructions burned: 187 (million)
% 1.58/1.32 % (20741)------------------------------
% 1.58/1.32 % (20741)------------------------------
% 1.58/1.32 % (20758)Instruction limit reached!
% 1.58/1.32 % (20758)------------------------------
% 1.58/1.32 % (20758)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.32 % (20758)Termination reason: Unknown
% 1.58/1.32 % (20758)Termination phase: Saturation
% 1.58/1.32
% 1.58/1.32 % (20758)Memory used [KB]: 5500
% 1.58/1.32 % (20758)Time elapsed: 0.004 s
% 1.58/1.32 % (20758)Instructions burned: 9 (million)
% 1.58/1.32 % (20758)------------------------------
% 1.58/1.32 % (20758)------------------------------
% 1.58/1.33 % (20759)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_20552 for (2999ds/3Mi)
% 1.58/1.33 % (20759)Instruction limit reached!
% 1.58/1.33 % (20759)------------------------------
% 1.58/1.33 % (20759)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.33 % (20759)Termination reason: Unknown
% 1.58/1.33 % (20759)Termination phase: Saturation
% 1.58/1.33
% 1.58/1.33 % (20759)Memory used [KB]: 5500
% 1.58/1.33 % (20759)Time elapsed: 0.004 s
% 1.58/1.33 % (20759)Instructions burned: 4 (million)
% 1.58/1.33 % (20759)------------------------------
% 1.58/1.33 % (20759)------------------------------
% 1.58/1.33 % (20761)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_20552 for (2999ds/18Mi)
% 1.58/1.33 % (20762)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_20552 for (2999ds/710Mi)
% 1.58/1.33 % (20761)Refutation not found, incomplete strategy
% 1.58/1.33 % (20761)------------------------------
% 1.58/1.33 % (20761)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.33 % (20761)Termination reason: Refutation not found, incomplete strategy
% 1.58/1.33
% 1.58/1.33
% 1.58/1.33 % (20761)Memory used [KB]: 5500
% 1.58/1.33 % (20761)Time elapsed: 0.003 s
% 1.58/1.33 % (20761)Instructions burned: 5 (million)
% 1.58/1.33 % (20761)------------------------------
% 1.58/1.33 % (20761)------------------------------
% 1.58/1.33 % (20753)First to succeed.
% 1.58/1.33 % (20763)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_20552 for (2999ds/6Mi)
% 1.58/1.34 % (20763)Instruction limit reached!
% 1.58/1.34 % (20763)------------------------------
% 1.58/1.34 % (20763)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.34 % (20763)Termination reason: Unknown
% 1.58/1.34 % (20763)Termination phase: Saturation
% 1.58/1.34
% 1.58/1.34 % (20763)Memory used [KB]: 5628
% 1.58/1.34 % (20763)Time elapsed: 0.004 s
% 1.58/1.34 % (20763)Instructions burned: 8 (million)
% 1.58/1.34 % (20763)------------------------------
% 1.58/1.34 % (20763)------------------------------
% 1.58/1.34 % (20760)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_20552 for (2999ds/4Mi)
% 1.58/1.34 % (20753)Refutation found. Thanks to Tanya!
% 1.58/1.34 % SZS status Theorem for DTF2THF_20552
% 1.58/1.34 % SZS output start Proof for DTF2THF_20552
% 1.58/1.34 thf(type_def_5, type, a: $tType).
% 1.58/1.34 thf(func_def_0, type, a: $tType).
% 1.58/1.34 thf(func_def_1, type, cC: a > $o).
% 1.58/1.34 thf(func_def_19, type, ph1: !>[X0: $tType]:(X0)).
% 1.58/1.34 thf(func_def_20, type, sK2: (a > $o) > $o).
% 1.58/1.34 thf(func_def_21, type, sK3: a).
% 1.58/1.34 thf(func_def_22, type, sK4: a).
% 1.58/1.34 thf(func_def_23, type, sK5: a).
% 1.58/1.34 thf(func_def_24, type, sK6: a > $o).
% 1.58/1.34 thf(func_def_25, type, sK7: a).
% 1.58/1.34 thf(func_def_26, type, sK8: a > a).
% 1.58/1.34 thf(func_def_27, type, sK9: a > a).
% 1.58/1.34 thf(f214,plain,(
% 1.58/1.34 $false),
% 1.58/1.34 inference(avatar_sat_refutation,[status(thm)],[f40,f92,f213])).
% 1.58/1.34 thf(f213,plain,(
% 1.58/1.34 ~spl0_1),
% 1.58/1.34 inference(avatar_contradiction_clause,[status(thm)],[f212])).
% 1.58/1.34 thf(f212,plain,(
% 1.58/1.34 $false | ~spl0_1),
% 1.58/1.34 inference(equality_resolution,[status(thm)],[f208])).
% 1.58/1.34 thf(f208,plain,(
% 1.58/1.34 ( ! [X0 : a] : ((((sK6 @ (sK9 @ X0)) | (X0 = (sK9 @ X0))) != ((sK6 @ (sK9 @ X0)) | (sK5 = (sK9 @ X0))))) ) | ~spl0_1),
% 1.58/1.34 inference(binary_proxy_clausification,[status(thm)],[f207])).
% 1.58/1.34 thf(f207,plain,(
% 1.58/1.34 ( ! [X0 : a] : (($false = (((sK6 @ (sK9 @ X0)) | (sK5 = (sK9 @ X0))) = ((sK6 @ (sK9 @ X0)) | (X0 = (sK9 @ X0)))))) ) | ~spl0_1),
% 1.58/1.34 inference(beta_eta_normalization,[status(thm)],[f205])).
% 1.58/1.34 thf(f205,plain,(
% 1.58/1.34 ( ! [X0 : a] : (($false = ((^[Y0 : a]: (((sK6 @ Y0) | (sK5 = Y0)) = ((sK6 @ Y0) | (X0 = Y0)))) @ (sK9 @ X0)))) ) | ~spl0_1),
% 1.58/1.34 inference(sigma_clausification,[status(thm)],[f175])).
% 1.58/1.34 thf(f175,plain,(
% 1.58/1.34 ( ! [X0 : a] : (($false = (!! @ a @ (^[Y0 : a]: (((sK6 @ Y0) | (sK5 = Y0)) = ((sK6 @ Y0) | (X0 = Y0))))))) ) | ~spl0_1),
% 1.58/1.34 inference(boolean_simplification,[status(thm)],[f169])).
% 1.58/1.34 thf(f169,plain,(
% 1.58/1.34 ( ! [X0 : a] : (($false = ($true & (!! @ a @ (^[Y0 : a]: (((sK6 @ Y0) | (sK5 = Y0)) = ((sK6 @ Y0) | (X0 = Y0)))))))) ) | ~spl0_1),
% 1.58/1.34 inference(superposition,[status(thm)],[f146,f112])).
% 1.58/1.34 thf(f112,plain,(
% 1.58/1.34 ($true = (sK2 @ sK6)) | ~spl0_1),
% 1.58/1.34 inference(binary_proxy_clausification,[status(thm)],[f110])).
% 1.58/1.34 thf(f110,plain,(
% 1.58/1.34 ($false = ((sK2 @ sK6) => (sK2 @ (^[Y0 : a]: ((sK6 @ Y0) | (sK5 = Y0)))))) | ~spl0_1),
% 1.58/1.34 inference(beta_eta_normalization,[status(thm)],[f109])).
% 1.58/1.34 thf(f109,plain,(
% 1.58/1.34 ($false = ((^[Y0 : a > $o]: ((sK2 @ Y0) => (sK2 @ (^[Y1 : a]: ((Y0 @ Y1) | (sK5 = Y1)))))) @ sK6)) | ~spl0_1),
% 1.58/1.34 inference(sigma_clausification,[status(thm)],[f102])).
% 1.58/1.34 thf(f102,plain,(
% 1.58/1.34 ($false = (!! @ (a > $o) @ (^[Y0 : a > $o]: ((sK2 @ Y0) => (sK2 @ (^[Y1 : a]: ((Y0 @ Y1) | (sK5 = Y1)))))))) | ~spl0_1),
% 1.58/1.34 inference(beta_eta_normalization,[status(thm)],[f98])).
% 1.58/1.34 thf(f98,plain,(
% 1.58/1.34 ($false = ((^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: ((sK2 @ Y1) => (sK2 @ (^[Y2 : a]: ((Y1 @ Y2) | (Y0 = Y2)))))))) @ sK5)) | ~spl0_1),
% 1.58/1.34 inference(sigma_clausification,[status(thm)],[f36])).
% 1.58/1.34 thf(f36,plain,(
% 1.58/1.34 ($false = (!! @ a @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: ((sK2 @ Y1) => (sK2 @ (^[Y2 : a]: ((Y1 @ Y2) | (Y0 = Y2)))))))))) | ~spl0_1),
% 1.58/1.34 inference(avatar_component_clause,[status(thm)],[f35])).
% 1.58/1.34 thf(f35,definition,(
% 1.58/1.34 spl0_1 <=> ($false = (!! @ a @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: ((sK2 @ Y1) => (sK2 @ (^[Y2 : a]: ((Y1 @ Y2) | (Y0 = Y2))))))))))),
% 1.58/1.34 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.58/1.34 thf(f146,plain,(
% 1.58/1.34 ( ! [X0 : a > $o,X1 : a] : (($false = ((sK2 @ X0) & (!! @ a @ (^[Y0 : a]: (((sK6 @ Y0) | (sK5 = Y0)) = ((X0 @ Y0) | (X1 = Y0)))))))) ) | ~spl0_1),
% 1.58/1.34 inference(not_proxy_clausification,[status(thm)],[f119])).
% 1.58/1.34 thf(f119,plain,(
% 1.58/1.34 ( ! [X0 : a > $o,X1 : a] : (($true = (~ ((sK2 @ X0) & (!! @ a @ (^[Y0 : a]: (((sK6 @ Y0) | (sK5 = Y0)) = ((X0 @ Y0) | (X1 = Y0))))))))) ) | ~spl0_1),
% 1.58/1.34 inference(boolean_simplification,[status(thm)],[f118])).
% 1.58/1.34 thf(f118,plain,(
% 1.58/1.34 ( ! [X0 : a > $o,X1 : a] : (($true = (((sK2 @ X0) & (!! @ a @ (^[Y0 : a]: (((sK6 @ Y0) | (sK5 = Y0)) = ((X0 @ Y0) | (X1 = Y0)))))) => $false))) ) | ~spl0_1),
% 1.58/1.34 inference(beta_eta_normalization,[status(thm)],[f116])).
% 1.58/1.34 thf(f116,plain,(
% 1.58/1.34 ( ! [X0 : a > $o,X1 : a] : (($true = (((sK2 @ X0) & (!! @ a @ (^[Y0 : a]: (((^[Y1 : a]: ((sK6 @ Y1) | (sK5 = Y1))) @ Y0) = ((X0 @ Y0) | (X1 = Y0)))))) => $false))) ) | ~spl0_1),
% 1.58/1.34 inference(superposition,[status(thm)],[f70,f114])).
% 1.58/1.34 thf(f114,plain,(
% 1.58/1.34 ($false = (sK2 @ (^[Y0 : a]: ((sK6 @ Y0) | (sK5 = Y0))))) | ~spl0_1),
% 1.58/1.34 inference(boolean_simplification,[status(thm)],[f113])).
% 1.58/1.34 thf(f113,plain,(
% 1.58/1.34 (($true => (sK2 @ (^[Y0 : a]: ((sK6 @ Y0) | (sK5 = Y0))))) = $false) | ~spl0_1),
% 1.58/1.34 inference(backward_demodulation,[status(thm)],[f110,f112])).
% 1.58/1.34 thf(f70,plain,(
% 1.58/1.34 ( ! [X2 : a,X3 : a > $o,X1 : a > $o] : (((((sK2 @ X3) & (!! @ a @ (^[Y0 : a]: ((X1 @ Y0) = ((X3 @ Y0) | (X2 = Y0)))))) => (sK2 @ X1)) = $true)) )),
% 1.58/1.34 inference(beta_eta_normalization,[status(thm)],[f69])).
% 1.58/1.34 thf(f69,plain,(
% 1.58/1.34 ( ! [X2 : a,X3 : a > $o,X1 : a > $o] : (($true = ((^[Y0 : a > $o]: (((sK2 @ Y0) & (!! @ a @ (^[Y1 : a]: ((X1 @ Y1) = ((Y0 @ Y1) | (X2 = Y1)))))) => (sK2 @ X1))) @ X3))) )),
% 1.58/1.34 inference(pi_clausification,[status(thm)],[f62])).
% 1.58/1.34 thf(f62,plain,(
% 1.58/1.34 ( ! [X2 : a,X1 : a > $o] : (($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((sK2 @ Y0) & (!! @ a @ (^[Y1 : a]: ((X1 @ Y1) = ((Y0 @ Y1) | (X2 = Y1)))))) => (sK2 @ X1)))))) )),
% 1.58/1.34 inference(beta_eta_normalization,[status(thm)],[f61])).
% 1.58/1.34 thf(f61,plain,(
% 1.58/1.34 ( ! [X2 : a,X1 : a > $o] : (($true = ((^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((sK2 @ Y1) & (!! @ a @ (^[Y2 : a]: ((X1 @ Y2) = ((Y1 @ Y2) | (Y0 = Y2)))))) => (sK2 @ X1))))) @ X2))) )),
% 1.58/1.34 inference(pi_clausification,[status(thm)],[f53])).
% 1.58/1.34 thf(f53,plain,(
% 1.58/1.34 ( ! [X1 : a > $o] : (($true = (!! @ a @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((sK2 @ Y1) & (!! @ a @ (^[Y2 : a]: ((X1 @ Y2) = ((Y1 @ Y2) | (Y0 = Y2)))))) => (sK2 @ X1)))))))) )),
% 1.58/1.34 inference(beta_eta_normalization,[status(thm)],[f52])).
% 1.58/1.34 thf(f52,plain,(
% 1.58/1.34 ( ! [X1 : a > $o] : (($true = ((^[Y0 : a > $o]: (!! @ a @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((sK2 @ Y2) & (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3) = ((Y2 @ Y3) | (Y1 = Y3)))))) => (sK2 @ Y0))))))) @ X1))) )),
% 1.58/1.34 inference(pi_clausification,[status(thm)],[f49])).
% 1.58/1.34 thf(f49,plain,(
% 1.58/1.34 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (!! @ a @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((sK2 @ Y2) & (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3) = ((Y2 @ Y3) | (Y1 = Y3)))))) => (sK2 @ Y0)))))))) = $true)),
% 1.58/1.34 inference(boolean_simplification,[status(thm)],[f48])).
% 1.58/1.34 thf(f48,plain,(
% 1.58/1.34 ($true = ($true & (!! @ (a > $o) @ (^[Y0 : a > $o]: (!! @ a @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((sK2 @ Y2) & (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3) = ((Y2 @ Y3) | (Y1 = Y3)))))) => (sK2 @ Y0))))))))))),
% 1.58/1.34 inference(backward_demodulation,[status(thm)],[f23,f47])).
% 1.58/1.34 thf(f47,plain,(
% 1.58/1.34 ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: ((~ (?? @ a @ Y0)) => (sK2 @ Y0)))))),
% 1.58/1.34 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 1.58/1.34 thf(f23,plain,(
% 1.58/1.34 (((!! @ (a > $o) @ (^[Y0 : a > $o]: ((~ (?? @ a @ Y0)) => (sK2 @ Y0)))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (!! @ a @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((sK2 @ Y2) & (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3) = ((Y2 @ Y3) | (Y1 = Y3)))))) => (sK2 @ Y0))))))))) = $true)),
% 1.58/1.34 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.58/1.34 thf(f21,plain,(
% 1.58/1.34 ($false = (((!! @ (a > $o) @ (^[Y0 : a > $o]: ((~ (?? @ a @ Y0)) => (sK2 @ Y0)))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (!! @ a @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((sK2 @ Y2) & (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3) = ((Y2 @ Y3) | (Y1 = Y3)))))) => (sK2 @ Y0))))))))) => (sK2 @ cC)))),
% 1.58/1.34 inference(beta_eta_normalization,[status(thm)],[f20])).
% 1.58/1.34 thf(f20,plain,(
% 1.58/1.34 ($false = ((^[Y0 : (a > $o) > $o]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: ((~ (?? @ a @ Y1)) => (Y0 @ Y1)))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: (!! @ a @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y0 @ Y3) & (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4) = ((Y3 @ Y4) | (Y2 = Y4)))))) => (Y0 @ Y1))))))))) => (Y0 @ cC))) @ sK2))),
% 1.58/1.34 inference(sigma_clausification,[status(thm)],[f11])).
% 1.58/1.34 thf(f11,plain,(
% 1.58/1.34 ($false = (!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: ((~ (?? @ a @ Y1)) => (Y0 @ Y1)))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: (!! @ a @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y0 @ Y3) & (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4) = ((Y3 @ Y4) | (Y2 = Y4)))))) => (Y0 @ Y1))))))))) => (Y0 @ cC)))))),
% 1.58/1.34 inference(binary_proxy_clausification,[status(thm)],[f8])).
% 1.58/1.34 thf(f8,plain,(
% 1.58/1.34 ($false = ((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: ((Y0 @ Y2) => (Y0 @ (^[Y3 : a]: ((Y2 @ Y3) | (Y1 = Y3))))))))) & (Y0 @ (^[Y1 : a]: ($false)))) => (Y0 @ cC)))) => (!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: ((~ (?? @ a @ Y1)) => (Y0 @ Y1)))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: (!! @ a @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y0 @ Y3) & (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4) = ((Y3 @ Y4) | (Y2 = Y4)))))) => (Y0 @ Y1))))))))) => (Y0 @ cC))))))),
% 1.58/1.34 inference(not_proxy_clausification,[status(thm)],[f7])).
% 1.58/1.34 thf(f7,plain,(
% 1.58/1.34 ((~ ((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: ((Y0 @ Y2) => (Y0 @ (^[Y3 : a]: ((Y2 @ Y3) | (Y1 = Y3))))))))) & (Y0 @ (^[Y1 : a]: ($false)))) => (Y0 @ cC)))) => (!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: ((~ (?? @ a @ Y1)) => (Y0 @ Y1)))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: (!! @ a @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y0 @ Y3) & (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4) = ((Y3 @ Y4) | (Y2 = Y4)))))) => (Y0 @ Y1))))))))) => (Y0 @ cC)))))) = $true)),
% 1.58/1.34 inference(beta_eta_normalization,[status(thm)],[f6])).
% 1.58/1.34 thf(f6,plain,(
% 1.58/1.34 ($true = (~ ((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: ((Y0 @ Y2) => (Y0 @ (^[Y3 : a]: ((Y2 @ Y3) | (Y1 = Y3))))))))) & (Y0 @ (^[Y1 : a]: ($false)))) => (Y0 @ cC)))) => (!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: ((~ (?? @ a @ (^[Y2 : a]: (Y1 @ Y2)))) => (Y0 @ Y1)))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: (!! @ a @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y0 @ Y3) & (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4) = ((Y3 @ Y4) | (Y2 = Y4)))))) => (Y0 @ Y1))))))))) => (Y0 @ cC)))))))),
% 1.58/1.34 inference(cnf_transformation,[status(thm)],[f5])).
% 1.58/1.34 thf(f5,plain,(
% 1.58/1.34 ($true = (~ ((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: ((Y0 @ Y2) => (Y0 @ (^[Y3 : a]: ((Y2 @ Y3) | (Y1 = Y3))))))))) & (Y0 @ (^[Y1 : a]: ($false)))) => (Y0 @ cC)))) => (!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: ((~ (?? @ a @ (^[Y2 : a]: (Y1 @ Y2)))) => (Y0 @ Y1)))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: (!! @ a @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y0 @ Y3) & (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4) = ((Y3 @ Y4) | (Y2 = Y4)))))) => (Y0 @ Y1))))))))) => (Y0 @ cC)))))))),
% 1.58/1.34 inference(fool_elimination,[status(thm)],[f4])).
% 1.58/1.34 thf(f4,plain,(
% 1.58/1.34 ~(! [X0 : (a > $o) > $o] : (((X0 @ (^[X1 : a] : ($false))) & ! [X2 : a > $o,X3 : a] : ((X0 @ X2) => (X0 @ (^[X4 : a] : ((X3 = X4) | (X2 @ X4)))))) => (X0 @ cC)) => ! [X5 : (a > $o) > $o] : ((! [X6 : a > $o,X7 : a,X8 : a > $o] : ((! [X9 : a] : ((X8 @ X9) <=> ((X7 = X9) | (X6 @ X9))) & (X5 @ X6)) => (X5 @ X8)) & ! [X10 : a > $o] : (~? [X11 : a] : (X10 @ X11) => (X5 @ X10))) => (X5 @ cC)))),
% 1.58/1.34 inference(rectify,[status(thm)],[f2])).
% 1.58/1.34 thf(f2,negated_conjecture,(
% 1.58/1.34 ~(! [X0 : (a > $o) > $o] : (((X0 @ (^[X1 : a] : ($false))) & ! [X2 : a > $o,X1 : a] : ((X0 @ X2) => (X0 @ (^[X3 : a] : ((X1 = X3) | (X2 @ X3)))))) => (X0 @ cC)) => ! [X4 : (a > $o) > $o] : ((! [X6 : a > $o,X1 : a,X7 : a > $o] : ((! [X8 : a] : ((X7 @ X8) <=> ((X1 = X8) | (X6 @ X8))) & (X4 @ X6)) => (X4 @ X7)) & ! [X5 : a > $o] : (~? [X3 : a] : (X5 @ X3) => (X4 @ X5))) => (X4 @ cC)))),
% 1.58/1.34 inference(negated_conjecture,[status(cth)],[f1])).
% 1.58/1.34 thf(f1,conjecture,(
% 1.58/1.34 ! [X0 : (a > $o) > $o] : (((X0 @ (^[X1 : a] : ($false))) & ! [X2 : a > $o,X1 : a] : ((X0 @ X2) => (X0 @ (^[X3 : a] : ((X1 = X3) | (X2 @ X3)))))) => (X0 @ cC)) => ! [X4 : (a > $o) > $o] : ((! [X6 : a > $o,X1 : a,X7 : a > $o] : ((! [X8 : a] : ((X7 @ X8) <=> ((X1 = X8) | (X6 @ X8))) & (X4 @ X6)) => (X4 @ X7)) & ! [X5 : a > $o] : (~? [X3 : a] : (X5 @ X3) => (X4 @ X5))) => (X4 @ cC))),
% 1.58/1.34 file('/export/starexec/sandbox/tmp/tmp.2DbGc2r228/DTF2THF_20552.p',cTHM551_pme)).
% 1.58/1.34 thf(f92,plain,(
% 1.58/1.34 ~spl0_2),
% 1.58/1.34 inference(avatar_contradiction_clause,[status(thm)],[f91])).
% 1.58/1.34 thf(f91,plain,(
% 1.58/1.34 $false | ~spl0_2),
% 1.58/1.34 inference(trivial_inequality_removal,[status(thm)],[f90])).
% 1.58/1.34 thf(f90,plain,(
% 1.58/1.34 ($false = $true) | ~spl0_2),
% 1.58/1.34 inference(beta_eta_normalization,[status(thm)],[f85])).
% 1.58/1.34 thf(f85,plain,(
% 1.58/1.34 ($true = ((^[Y0 : a]: ($false)) @ sK4)) | ~spl0_2),
% 1.58/1.34 inference(sigma_clausification,[status(thm)],[f60])).
% 1.58/1.34 thf(f60,plain,(
% 1.58/1.34 ($true = (?? @ a @ (^[Y0 : a]: ($false)))) | ~spl0_2),
% 1.58/1.34 inference(boolean_simplification,[status(thm)],[f59])).
% 1.58/1.34 thf(f59,plain,(
% 1.58/1.34 ((~ (~ (?? @ a @ (^[Y0 : a]: ($false))))) = $true) | ~spl0_2),
% 1.58/1.34 inference(boolean_simplification,[status(thm)],[f55])).
% 1.58/1.34 thf(f55,plain,(
% 1.58/1.34 ($true = ((~ (?? @ a @ (^[Y0 : a]: ($false)))) => $false)) | ~spl0_2),
% 1.58/1.34 inference(superposition,[status(thm)],[f51,f39])).
% 1.58/1.34 thf(f39,plain,(
% 1.58/1.34 ($false = (sK2 @ (^[Y0 : a]: ($false)))) | ~spl0_2),
% 1.58/1.34 inference(avatar_component_clause,[status(thm)],[f38])).
% 1.58/1.34 thf(f38,definition,(
% 1.58/1.34 spl0_2 <=> ($false = (sK2 @ (^[Y0 : a]: ($false))))),
% 1.58/1.34 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.58/1.34 thf(f51,plain,(
% 1.58/1.34 ( ! [X1 : a > $o] : ((((~ (?? @ a @ X1)) => (sK2 @ X1)) = $true)) )),
% 1.58/1.34 inference(beta_eta_normalization,[status(thm)],[f50])).
% 1.58/1.34 thf(f50,plain,(
% 1.58/1.34 ( ! [X1 : a > $o] : ((((^[Y0 : a > $o]: ((~ (?? @ a @ Y0)) => (sK2 @ Y0))) @ X1) = $true)) )),
% 1.58/1.34 inference(pi_clausification,[status(thm)],[f47])).
% 1.58/1.34 thf(f40,plain,(
% 1.58/1.34 spl0_1 | spl0_2),
% 1.58/1.34 inference(avatar_split_clause,[status(thm)],[f31,f38,f35])).
% 1.58/1.34 thf(f31,plain,(
% 1.58/1.34 ($false = (!! @ a @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: ((sK2 @ Y1) => (sK2 @ (^[Y2 : a]: ((Y1 @ Y2) | (Y0 = Y2)))))))))) | ($false = (sK2 @ (^[Y0 : a]: ($false))))),
% 1.58/1.34 inference(binary_proxy_clausification,[status(thm)],[f28])).
% 1.58/1.34 thf(f28,plain,(
% 1.58/1.34 (((!! @ a @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: ((sK2 @ Y1) => (sK2 @ (^[Y2 : a]: ((Y1 @ Y2) | (Y0 = Y2))))))))) & (sK2 @ (^[Y0 : a]: ($false)))) = $false)),
% 1.58/1.34 inference(not_proxy_clausification,[status(thm)],[f27])).
% 1.58/1.34 thf(f27,plain,(
% 1.58/1.34 ($true = (~ ((!! @ a @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: ((sK2 @ Y1) => (sK2 @ (^[Y2 : a]: ((Y1 @ Y2) | (Y0 = Y2))))))))) & (sK2 @ (^[Y0 : a]: ($false))))))),
% 1.58/1.34 inference(boolean_simplification,[status(thm)],[f26])).
% 1.58/1.34 thf(f26,plain,(
% 1.58/1.34 ((((!! @ a @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: ((sK2 @ Y1) => (sK2 @ (^[Y2 : a]: ((Y1 @ Y2) | (Y0 = Y2))))))))) & (sK2 @ (^[Y0 : a]: ($false)))) => $false) = $true)),
% 1.58/1.34 inference(superposition,[status(thm)],[f18,f25])).
% 1.58/1.34 thf(f25,plain,(
% 1.58/1.34 ((sK2 @ cC) = $false)),
% 1.58/1.34 inference(boolean_simplification,[status(thm)],[f24])).
% 1.58/1.34 thf(f24,plain,(
% 1.58/1.34 (($true => (sK2 @ cC)) = $false)),
% 1.58/1.34 inference(backward_demodulation,[status(thm)],[f21,f23])).
% 1.58/1.34 thf(f18,plain,(
% 1.58/1.34 ( ! [X1 : (a > $o) > $o] : (((((!! @ a @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: ((X1 @ Y1) => (X1 @ (^[Y2 : a]: ((Y1 @ Y2) | (Y0 = Y2))))))))) & (X1 @ (^[Y0 : a]: ($false)))) => (X1 @ cC)) = $true)) )),
% 1.58/1.34 inference(beta_eta_normalization,[status(thm)],[f17])).
% 1.58/1.34 thf(f17,plain,(
% 1.58/1.34 ( ! [X1 : (a > $o) > $o] : ((((^[Y0 : (a > $o) > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: ((Y0 @ Y2) => (Y0 @ (^[Y3 : a]: ((Y2 @ Y3) | (Y1 = Y3))))))))) & (Y0 @ (^[Y1 : a]: ($false)))) => (Y0 @ cC))) @ X1) = $true)) )),
% 1.58/1.34 inference(pi_clausification,[status(thm)],[f12])).
% 1.58/1.34 thf(f12,plain,(
% 1.58/1.34 ($true = (!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: ((Y0 @ Y2) => (Y0 @ (^[Y3 : a]: ((Y2 @ Y3) | (Y1 = Y3))))))))) & (Y0 @ (^[Y1 : a]: ($false)))) => (Y0 @ cC)))))),
% 1.58/1.34 inference(binary_proxy_clausification,[status(thm)],[f8])).
% 1.58/1.34 % SZS output end Proof for DTF2THF_20552
% 1.58/1.34 % (20753)------------------------------
% 1.58/1.34 % (20753)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.34 % (20753)Termination reason: Refutation
% 1.58/1.34
% 1.58/1.34 % (20753)Memory used [KB]: 5756
% 1.58/1.34 % (20753)Time elapsed: 0.036 s
% 1.58/1.34 % (20753)Instructions burned: 38 (million)
% 1.58/1.34 % (20753)------------------------------
% 1.58/1.34 % (20753)------------------------------
% 1.58/1.34 % (20740)Success in time 0.067 s
%------------------------------------------------------------------------------