%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : MSC025^2 : TPTP v9.2.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n026.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 09:21:42 AM UTC 2026
% Result : Theorem 1.63s 1.48s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 14
% Syntax : Number of formulae : 140 ( 50 unt; 0 typ; 9 def)
% Number of atoms : 637 ( 237 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 504 ( 140 ~; 118 |; 14 &; 167 @)
% ( 9 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 17 usr; 16 con; 0-2 aty)
% ( 15 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 63 ( 20 ^; 43 !; 0 ?; 63 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_2,type,
b1: $o > $i ).
thf(func_def_4,type,
b2: $o > $i ).
thf(func_def_17,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
sK2: $o > $i ).
thf(f744,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f164,f171,f234,f241,f267,f392,f414,f516,f672,f741,f743]) ).
thf(f743,plain,
( spl0_8
| spl0_6 ),
inference(avatar_split_clause,[status(thm)],[f739,f239,f247]) ).
thf(f247,definition,
( spl0_8
<=> ( one
= ( sK2 @ $false ) ) ),
introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition]) ).
thf(f239,definition,
( spl0_6
<=> ( two
= ( sK2 @ $false ) ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f739,plain,
( ( one
= ( sK2 @ $false ) )
| spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f738]) ).
thf(f738,plain,
( ( two != two )
| ( one
= ( sK2 @ $false ) )
| spl0_6 ),
inference(superposition,[status(thm)],[f240,f187]) ).
thf(f187,plain,
! [X1: $i] :
( ( two = X1 )
| ( one = X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f172]) ).
thf(f172,plain,
! [X1: $i] :
( ( ( one = X1 )
= $true )
| ( two = X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
! [X1: $i] :
( ( ( two = X1 )
= $true )
| ( ( one = X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
! [X1: $i] :
( $true
= ( ( two = X1 )
| ( one = X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f21]) ).
thf(f21,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( two = Y0 )
| ( one = Y0 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( two = Y0 )
| ( one = Y0 ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( two = Y0 )
| ( one = Y0 ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i] :
( ( one = X0 )
| ( two = X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.WUFQl6BPhu/DTF2THF_17668.p',binarity_exhaust) ).
thf(f240,plain,
( ( two
!= ( sK2 @ $false ) )
| spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f239]) ).
thf(f741,plain,
( spl0_6
| spl0_13 ),
inference(avatar_contradiction_clause,[status(thm)],[f740]) ).
thf(f740,plain,
( $false
| spl0_6
| spl0_13 ),
inference(subsumption_resolution,[status(thm)],[f739,f720]) ).
thf(f720,plain,
( ( one
!= ( sK2 @ $false ) )
| spl0_13 ),
inference(backward_demodulation,[status(thm)],[f719,f716]) ).
thf(f716,plain,
( ( $false = sK4 )
| spl0_13 ),
inference(trivial_inequality_removal,[status(thm)],[f714]) ).
thf(f714,plain,
( ( two != two )
| ( $false = sK4 )
| spl0_13 ),
inference(superposition,[status(thm)],[f266,f135]) ).
thf(f135,plain,
! [X1: $o] :
( ( two
= ( b2 @ X1 ) )
| ( $false = X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
! [X1: $o] :
( ( $true
= ( two
= ( b2 @ X1 ) ) )
| ( $false = X1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
! [X1: $o] :
( $true
= ( X1
=> ( two
= ( b2 @ X1 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f36]) ).
thf(f36,plain,
! [X1: $o] :
( $true
= ( ( X1
=> ( two
= ( b2 @ X1 ) ) )
& $true ) ),
inference(backward_demodulation,[status(thm)],[f32,f34]) ).
thf(f34,plain,
! [X1: $o] :
( ( ~ X1
=> ( one
= ( b2 @ X1 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
! [X1: $o] :
( $true
= ( ( X1
=> ( two
= ( b2 @ X1 ) ) )
& ( ~ X1
=> ( one
= ( b2 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f31]) ).
thf(f31,plain,
! [X1: $o] :
( $true
= ( ^ [Y0: $o] :
( ( Y0
=> ( two
= ( b2 @ Y0 ) ) )
& ( ~ Y0
=> ( one
= ( b2 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
( $true
= ( !! @ $o
@ ^ [Y0: $o] :
( ( Y0
=> ( two
= ( b2 @ Y0 ) ) )
& ( ~ Y0
=> ( one
= ( b2 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( $true
= ( !! @ $o
@ ^ [Y0: $o] :
( ( Y0
=> ( two
= ( b2 @ Y0 ) ) )
& ( ~ Y0
=> ( one
= ( b2 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: $o] :
( ( ~ X0
=> ( one
= ( b2 @ X0 ) ) )
& ( X0
=> ( two
= ( b2 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X0: $o] :
( ( ~ X0
=> ( one
= ( b2 @ X0 ) ) )
& ( X0
=> ( two
= ( b2 @ X0 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.WUFQl6BPhu/DTF2THF_17668.p',b2) ).
thf(f266,plain,
( ( two
!= ( b2 @ sK4 ) )
| spl0_13 ),
inference(avatar_component_clause,[status(thm)],[f265]) ).
thf(f265,definition,
( spl0_13
<=> ( two
= ( b2 @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_13])],[avatar_definition]) ).
thf(f719,plain,
( ( one
!= ( sK2 @ sK4 ) )
| spl0_13 ),
inference(backward_demodulation,[status(thm)],[f101,f717]) ).
thf(f717,plain,
( ( one
= ( b2 @ sK4 ) )
| spl0_13 ),
inference(trivial_inequality_removal,[status(thm)],[f715]) ).
thf(f715,plain,
( ( two != two )
| ( one
= ( b2 @ sK4 ) )
| spl0_13 ),
inference(superposition,[status(thm)],[f266,f187]) ).
thf(f101,plain,
( ( b2 @ sK4 )
!= ( sK2 @ sK4 ) ),
inference(negative_extensionality,[status(thm)],[f100]) ).
thf(f100,plain,
b2 != sK2,
inference(equality_proxy_clausification,[status(thm)],[f83]) ).
thf(f83,plain,
( ( b2 = sK2 )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
( $false
= ( ( b2 = sK2 )
| ( b1 = sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
( ( ( !! @ $o
@ ^ [Y0: $o] :
( ( sK2 @ ~ Y0 )
!= ( sK2 @ Y0 ) ) )
=> ( ( b2 = sK2 )
| ( b1 = sK2 ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f52]) ).
thf(f52,plain,
( $false
= ( ^ [Y0: $o > $i] :
( ( !! @ $o
@ ^ [Y1: $o] :
( ( Y0 @ ~ Y1 )
!= ( Y0 @ Y1 ) ) )
=> ( ( b2 = Y0 )
| ( b1 = Y0 ) ) )
@ sK2 ) ),
inference(sigma_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
( ( !! @ ( $o > $i )
@ ^ [Y0: $o > $i] :
( ( !! @ $o
@ ^ [Y1: $o] :
( ( Y0 @ ~ Y1 )
!= ( Y0 @ Y1 ) ) )
=> ( ( b2 = Y0 )
| ( b1 = Y0 ) ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
( $true
= ( ~ ( !! @ ( $o > $i )
@ ^ [Y0: $o > $i] :
( ( !! @ $o
@ ^ [Y1: $o] :
( ( Y0 @ ~ Y1 )
!= ( Y0 @ Y1 ) ) )
=> ( ( b2 = Y0 )
| ( b1 = Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( $true
= ( ~ ( !! @ ( $o > $i )
@ ^ [Y0: $o > $i] :
( ( !! @ $o
@ ^ [Y1: $o] :
( ( Y0 @ ~ Y1 )
!= ( Y0 @ Y1 ) ) )
=> ( ( b2 = Y0 )
| ( b1 = Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
~ ! [X0: $o > $i] :
( ! [X1: $o] :
( ( X0 @ ~ X1 )
!= ( X0 @ X1 ) )
=> ( ( b1 = X0 )
| ( b2 = X0 ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ! [X1: $o > $i] :
( ! [X0: $o] :
( ( X1 @ ~ X0 )
!= ( X1 @ X0 ) )
=> ( ( b1 = X1 )
| ( b2 = X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
! [X1: $o > $i] :
( ! [X0: $o] :
( ( X1 @ ~ X0 )
!= ( X1 @ X0 ) )
=> ( ( b1 = X1 )
| ( b2 = X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.WUFQl6BPhu/DTF2THF_17668.p',goal) ).
thf(f672,plain,
( ~ spl0_1
| ~ spl0_8
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[status(thm)],[f671]) ).
thf(f671,plain,
( $false
| ~ spl0_1
| ~ spl0_8
| ~ spl0_12 ),
inference(subsumption_resolution,[status(thm)],[f670,f86]) ).
thf(f86,plain,
( one
= ( b2 @ $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f74]) ).
thf(f74,plain,
( ( one
= ( b2 @ $false ) )
= $true ),
inference(backward_demodulation,[status(thm)],[f72,f68]) ).
thf(f68,plain,
! [X1: $o] :
( ( ( sK2 @ ~ X1 )
= ( sK2 @ X1 ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f67]) ).
thf(f67,plain,
! [X1: $o] :
( $true
= ( ( sK2 @ ~ X1 )
!= ( sK2 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f66]) ).
thf(f66,plain,
! [X1: $o] :
( $true
= ( ^ [Y0: $o] :
( ( sK2 @ ~ Y0 )
!= ( sK2 @ Y0 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
( $true
= ( !! @ $o
@ ^ [Y0: $o] :
( ( sK2 @ ~ Y0 )
!= ( sK2 @ Y0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f53]) ).
thf(f72,plain,
! [X0: $o] :
( ( one
= ( b2
@ ( ( sK2 @ ~ X0 )
= ( sK2 @ X0 ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f70]) ).
thf(f70,plain,
! [X0: $o] :
( ( $true
=> ( one
= ( b2
@ ( ( sK2 @ ~ X0 )
= ( sK2 @ X0 ) ) ) ) )
= $true ),
inference(superposition,[status(thm)],[f34,f67]) ).
thf(f670,plain,
( ( one
!= ( b2 @ $false ) )
| ~ spl0_1
| ~ spl0_8
| ~ spl0_12 ),
inference(backward_demodulation,[status(thm)],[f528,f668]) ).
thf(f668,plain,
( ( $false = sK4 )
| ~ spl0_1
| ~ spl0_8
| ~ spl0_12 ),
inference(trivial_inequality_removal,[status(thm)],[f665]) ).
thf(f665,plain,
( ( $false = sK4 )
| ( one != one )
| ~ spl0_1
| ~ spl0_8
| ~ spl0_12 ),
inference(superposition,[status(thm)],[f533,f263]) ).
thf(f263,plain,
( ( one
= ( sK2 @ sK4 ) )
| ~ spl0_12 ),
inference(avatar_component_clause,[status(thm)],[f262]) ).
thf(f262,definition,
( spl0_12
<=> ( one
= ( sK2 @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition]) ).
thf(f533,plain,
( ! [X0: $o] :
( ( one
!= ( sK2 @ X0 ) )
| ( $false = X0 ) )
| ~ spl0_1
| ~ spl0_8 ),
inference(backward_demodulation,[status(thm)],[f180,f248]) ).
thf(f248,plain,
( ( one
= ( sK2 @ $false ) )
| ~ spl0_8 ),
inference(avatar_component_clause,[status(thm)],[f247]) ).
thf(f180,plain,
( ! [X0: $o] :
( ( ( sK2 @ $false )
!= ( sK2 @ X0 ) )
| ( $false = X0 ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f81,f160]) ).
thf(f160,plain,
( ! [X0: $o] :
( ( $false = ( ~ X0 ) )
| ( $false = X0 ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f159]) ).
thf(f159,definition,
( spl0_1
<=> ! [X0: $o] :
( ( $false = X0 )
| ( $false = ( ~ X0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f81,plain,
! [X1: $o] :
( ( sK2 @ X1 )
!= ( sK2 @ ~ X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f68]) ).
thf(f528,plain,
( ( one
!= ( b2 @ sK4 ) )
| ~ spl0_12 ),
inference(backward_demodulation,[status(thm)],[f101,f263]) ).
thf(f516,plain,
( spl0_8
| ~ spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f402,f229,f247]) ).
thf(f229,definition,
( spl0_3
<=> ( one
= ( sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f402,plain,
( ( one
= ( sK2 @ $false ) )
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f230,f400]) ).
thf(f400,plain,
( ( $false = sK3 )
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f398]) ).
thf(f398,plain,
( ( one != one )
| ( $false = sK3 )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f397,f120]) ).
thf(f120,plain,
! [X1: $o] :
( ( one
= ( b1 @ X1 ) )
| ( $false = X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
! [X1: $o] :
( ( ( one
= ( b1 @ X1 ) )
= $true )
| ( $false = X1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
! [X1: $o] :
( ( X1
=> ( one
= ( b1 @ X1 ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f28]) ).
thf(f28,plain,
! [X1: $o] :
( $true
= ( $true
& ( X1
=> ( one
= ( b1 @ X1 ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f25,f27]) ).
thf(f27,plain,
! [X1: $o] :
( $true
= ( ~ X1
=> ( two
= ( b1 @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
! [X1: $o] :
( $true
= ( ( ~ X1
=> ( two
= ( b1 @ X1 ) ) )
& ( X1
=> ( one
= ( b1 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f24]) ).
thf(f24,plain,
! [X1: $o] :
( ( ^ [Y0: $o] :
( ( ~ Y0
=> ( two
= ( b1 @ Y0 ) ) )
& ( Y0
=> ( one
= ( b1 @ Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
( $true
= ( !! @ $o
@ ^ [Y0: $o] :
( ( ~ Y0
=> ( two
= ( b1 @ Y0 ) ) )
& ( Y0
=> ( one
= ( b1 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( $true
= ( !! @ $o
@ ^ [Y0: $o] :
( ( ~ Y0
=> ( two
= ( b1 @ Y0 ) ) )
& ( Y0
=> ( one
= ( b1 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $o] :
( ( X0
=> ( one
= ( b1 @ X0 ) ) )
& ( ~ X0
=> ( two
= ( b1 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: $o] :
( ( X0
=> ( one
= ( b1 @ X0 ) ) )
& ( ~ X0
=> ( two
= ( b1 @ X0 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.WUFQl6BPhu/DTF2THF_17668.p',b1) ).
thf(f397,plain,
( ( one
!= ( b1 @ sK3 ) )
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f94,f230]) ).
thf(f94,plain,
( ( sK2 @ sK3 )
!= ( b1 @ sK3 ) ),
inference(negative_extensionality,[status(thm)],[f93]) ).
thf(f93,plain,
b1 != sK2,
inference(equality_proxy_clausification,[status(thm)],[f85]) ).
thf(f85,plain,
( ( b1 = sK2 )
= $false ),
inference(boolean_simplification,[status(thm)],[f84]) ).
thf(f84,plain,
( ( $false
| ( b1 = sK2 ) )
= $false ),
inference(backward_demodulation,[status(thm)],[f59,f83]) ).
thf(f230,plain,
( ( one
= ( sK2 @ sK3 ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f229]) ).
thf(f414,plain,
( ~ spl0_3
| spl0_13 ),
inference(avatar_contradiction_clause,[status(thm)],[f413]) ).
thf(f413,plain,
( $false
| ~ spl0_3
| spl0_13 ),
inference(subsumption_resolution,[status(thm)],[f402,f405]) ).
thf(f405,plain,
( ( one
!= ( sK2 @ $false ) )
| spl0_13 ),
inference(forward_demodulation,[status(thm)],[f347,f86]) ).
thf(f347,plain,
( ( ( b2 @ $false )
!= ( sK2 @ $false ) )
| spl0_13 ),
inference(backward_demodulation,[status(thm)],[f101,f345]) ).
thf(f345,plain,
( ( $false = sK4 )
| spl0_13 ),
inference(trivial_inequality_removal,[status(thm)],[f342]) ).
thf(f342,plain,
( ( $false = sK4 )
| ( two != two )
| spl0_13 ),
inference(superposition,[status(thm)],[f266,f135]) ).
thf(f392,plain,
( spl0_4
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f391]) ).
thf(f391,plain,
( $false
| spl0_4
| ~ spl0_5 ),
inference(subsumption_resolution,[status(thm)],[f389,f237]) ).
thf(f237,plain,
( ( one
= ( sK2 @ $true ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f236]) ).
thf(f236,definition,
( spl0_5
<=> ( one
= ( sK2 @ $true ) ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f389,plain,
( ( one
!= ( sK2 @ $true ) )
| spl0_4
| ~ spl0_5 ),
inference(backward_demodulation,[status(thm)],[f296,f388]) ).
thf(f388,plain,
( ( $true = sK3 )
| spl0_4
| ~ spl0_5 ),
inference(boolean_simplification,[status(thm)],[f387]) ).
thf(f387,plain,
( ( ( ~ ~ sK3 )
= $true )
| spl0_4
| ~ spl0_5 ),
inference(boolean_simplification,[status(thm)],[f386]) ).
thf(f386,plain,
( ( $true
= ( ~ sK3
=> $false ) )
| spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[status(thm)],[f381,f330]) ).
thf(f330,plain,
( ( $false
= ( two = one ) )
| ~ spl0_5 ),
inference(forward_demodulation,[status(thm)],[f329,f306]) ).
thf(f306,plain,
( ( two
= ( sK2 @ $false ) )
| ~ spl0_5 ),
inference(trivial_inequality_removal,[status(thm)],[f301]) ).
thf(f301,plain,
( ( two
= ( sK2 @ $false ) )
| ( $true = $false )
| ~ spl0_5 ),
inference(superposition,[status(thm)],[f275,f172]) ).
thf(f275,plain,
( ( $false
= ( one
= ( sK2 @ $false ) ) )
| ~ spl0_5 ),
inference(backward_demodulation,[status(thm)],[f102,f237]) ).
thf(f102,plain,
( ( ( sK2 @ $true )
= ( sK2 @ $false ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f75]) ).
thf(f75,plain,
( ( ( sK2 @ $true )
!= ( sK2 @ $false ) )
= $true ),
inference(backward_demodulation,[status(thm)],[f69,f68]) ).
thf(f69,plain,
! [X0: $o] :
( $true
= ( ( sK2 @ $true )
!= ( sK2
@ ( ( sK2 @ ~ X0 )
= ( sK2 @ X0 ) ) ) ) ),
inference(superposition,[status(thm)],[f67,f67]) ).
thf(f329,plain,
( ( ( ( sK2 @ $false )
= one )
= $false )
| ~ spl0_5 ),
inference(boolean_simplification,[status(thm)],[f328]) ).
thf(f328,plain,
( ( $false
= ( ( sK2 @ ~ $true )
= one ) )
| ~ spl0_5 ),
inference(superposition,[status(thm)],[f68,f237]) ).
thf(f381,plain,
( ( $true
= ( ~ sK3
=> ( two = one ) ) )
| spl0_4 ),
inference(superposition,[status(thm)],[f27,f294]) ).
thf(f294,plain,
( ( one
= ( b1 @ sK3 ) )
| spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f293]) ).
thf(f293,plain,
( ( one
= ( b1 @ sK3 ) )
| ( two != two )
| spl0_4 ),
inference(superposition,[status(thm)],[f233,f187]) ).
thf(f233,plain,
( ( two
!= ( b1 @ sK3 ) )
| spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f232]) ).
thf(f232,definition,
( spl0_4
<=> ( two
= ( b1 @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f296,plain,
( ( one
!= ( sK2 @ sK3 ) )
| spl0_4 ),
inference(backward_demodulation,[status(thm)],[f94,f294]) ).
thf(f267,plain,
( spl0_12
| ~ spl0_13 ),
inference(avatar_split_clause,[status(thm)],[f215,f265,f262]) ).
thf(f215,plain,
( ( one
= ( sK2 @ sK4 ) )
| ( two
!= ( b2 @ sK4 ) ) ),
inference(superposition,[status(thm)],[f101,f187]) ).
thf(f241,plain,
( spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[status(thm)],[f218,f239,f236]) ).
thf(f218,plain,
( ( one
= ( sK2 @ $true ) )
| ( two
!= ( sK2 @ $false ) ) ),
inference(superposition,[status(thm)],[f112,f187]) ).
thf(f112,plain,
( ( sK2 @ $true )
!= ( sK2 @ $false ) ),
inference(backward_demodulation,[status(thm)],[f103,f102]) ).
thf(f103,plain,
( ( sK2 @ $true )
!= ( sK2
@ ( ( sK2 @ $true )
= ( sK2 @ $false ) ) ) ),
inference(superposition,[status(thm)],[f81,f75]) ).
thf(f234,plain,
( spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f214,f232,f229]) ).
thf(f214,plain,
( ( one
= ( sK2 @ sK3 ) )
| ( two
!= ( b1 @ sK3 ) ) ),
inference(superposition,[status(thm)],[f94,f187]) ).
thf(f171,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f170]) ).
thf(f170,plain,
( $false
| ~ spl0_2 ),
inference(subsumption_resolution,[status(thm)],[f167,f17]) ).
thf(f17,plain,
one != two,
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
one != two,
inference(fool_elimination,[status(thm)],[f2]) ).
thf(f2,axiom,
one != two,
file('/export/starexec/sandbox/tmp/tmp.WUFQl6BPhu/DTF2THF_17668.p',binarity_distinc) ).
thf(f167,plain,
( ( one = two )
| ~ spl0_2 ),
inference(equality_proxy_clausification,[status(thm)],[f163]) ).
thf(f163,plain,
( ( $true
= ( two = one ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f162]) ).
thf(f162,definition,
( spl0_2
<=> ( $true
= ( two = one ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f164,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f152,f162,f159]) ).
thf(f152,plain,
! [X0: $o] :
( ( $false = X0 )
| ( $false = ( ~ X0 ) )
| ( $true
= ( two = one ) ) ),
inference(superposition,[status(thm)],[f33,f120]) ).
thf(f33,plain,
! [X1: $o] :
( ( ( two
= ( b1 @ X1 ) )
= $true )
| ( ( ~ X1 ) = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : MSC025^2 : TPTP v9.2.1. Released v5.5.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.30 % Computer : n026.cluster.edu
% 0.12/0.30 % Model : x86_64 x86_64
% 0.12/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.30 % Memory : 8042.1875MB
% 0.12/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.30 % CPULimit : 300
% 0.12/0.30 % WCLimit : 300
% 0.12/0.30 % DateTime : Tue Feb 24 10:42:55 EST 2026
% 0.12/0.30 % CPUTime :
% 0.12/0.30 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.40 ---- Original DTF file ---
% 0.16/0.40 thf(spec,logic,$$dhol).
% 0.16/0.40 %------------------------------------------------------------------------------
% 0.16/0.40 % File : MSC025^2 : TPTP v9.2.1. Released v5.5.0.
% 0.16/0.40 % Domain : Syntactic
% 0.16/0.40 % Problem : Nik's Challenge
% 0.16/0.40 % Version : Especial.
% 0.16/0.40 % : Theorem formulation : Bijection instantiated.
% 0.16/0.40 % English : Force the $i type to only have two elements, then conjecture the
% 0.16/0.40 % existence of a bijection between $o and $i.
% 0.16/0.40
% 0.16/0.40 % Refs : [Sul13] Sultana (2013), Email to Geoff Sutcliffe
% 0.16/0.40 % Source : [Sul13]
% 0.16/0.40 % Names :
% 0.16/0.40
% 0.16/0.40 % Status : Theorem
% 0.16/0.40 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.38 v8.1.0, 0.36 v7.5.0, 0.29 v7.4.0, 0.44 v7.2.0, 0.38 v7.1.0, 0.62 v7.0.0, 0.57 v6.4.0, 0.67 v6.3.0, 0.60 v6.2.0, 0.57 v5.5.0
% 0.16/0.40 % Syntax : Number of formulae : 9 ( 1 unt; 4 typ; 0 def)
% 0.16/0.40 % Number of atoms : 10 ( 10 equ; 0 cnn)
% 0.16/0.40 % Maximal formula atoms : 3 ( 2 avg)
% 0.16/0.40 % Number of connectives : 20 ( 5 ~; 2 |; 2 &; 6 @)
% 0.16/0.40 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.16/0.40 % Maximal formula depth : 5 ( 4 avg)
% 0.16/0.40 % Number of types : 2 ( 0 usr)
% 0.16/0.40 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.16/0.40 % Number of symbols : 5 ( 4 usr; 2 con; 0-2 aty)
% 0.16/0.40 % Number of variables : 5 ( 0 ^; 5 !; 0 ?; 5 :)
% 0.16/0.40 % SPC : TH0_THM_EQU_NAR
% 0.16/0.40
% 0.16/0.40 % Comments :
% 0.16/0.40 %------------------------------------------------------------------------------
% 0.16/0.40 thf(one,type,
% 0.16/0.40 one: $i ).
% 0.16/0.40
% 0.16/0.40 thf(two,type,
% 0.16/0.40 two: $i ).
% 0.16/0.40
% 0.16/0.40 thf(binarity_exhaust,axiom,
% 0.16/0.40 ! [X: $i] :
% 0.16/0.40 ( ( X = one )
% 0.16/0.40 | ( X = two ) ) ).
% 0.16/0.40
% 0.16/0.40 thf(binarity_distinc,axiom,
% 0.16/0.40 one != two ).
% 0.16/0.40
% 0.16/0.40 thf(b1_ty,type,
% 0.16/0.40 b1: $o > $i ).
% 0.16/0.40
% 0.16/0.40 thf(b1,axiom,
% 0.16/0.40 ! [X: $o] :
% 0.16/0.40 ( ( X
% 0.16/0.40 => ( ( b1 @ X )
% 0.16/0.40 = one ) )
% 0.16/0.40 & ( ~ X
% 0.16/0.40 => ( ( b1 @ X )
% 0.16/0.40 = two ) ) ) ).
% 0.16/0.40
% 0.16/0.40 thf(b2_ty,type,
% 0.16/0.40 b2: $o > $i ).
% 0.16/0.40
% 0.16/0.40 thf(b2,axiom,
% 0.16/0.40 ! [X: $o] :
% 0.16/0.40 ( ( X
% 0.16/0.40 => ( ( b2 @ X )
% 0.16/0.40 = two ) )
% 0.16/0.40 & ( ~ X
% 0.16/0.40 => ( ( b2 @ X )
% 0.16/0.40 = one ) ) ) ).
% 0.16/0.40
% 0.16/0.40 thf(goal,conjecture,
% 0.16/0.40 ! [F: $o > $i] :
% 0.16/0.40 ( ! [X: $o] :
% 0.16/0.40 ( ( F @ X )
% 0.16/0.40 != ( F @ ~ X ) )
% 0.16/0.40 => ( ( F = b1 )
% 0.16/0.40 | ( F = b2 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 %------------------------------------------------------------------------------
% 0.16/0.40 ------------------------
% 1.48/1.36 ---- Embedded in THF ---
% 1.48/1.36 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.36 %%% Generated on Tue Feb 24 10:42:56 EST 2026
% 1.48/1.36 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.36 %%% Logic specification used:
% 1.48/1.36 %%% thf(spec, logic, $$dhol).
% 1.48/1.36
% 1.48/1.36 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.WUFQl6BPhu/DTF2DTF17668.p
% See solution above
% 1.48/1.36 ------------------------
% 1.48/1.37 ---- Cleaned THF ---
% 1.48/1.37 thf(one,type,
% 1.48/1.37 one: $i ).
% 1.48/1.37
% 1.48/1.37 thf(two,type,
% 1.48/1.37 two: $i ).
% 1.48/1.37
% 1.48/1.37 thf(binarity_exhaust,axiom,
% 1.48/1.37 ! [X: $i] :
% 1.48/1.37 ( ( X = one )
% 1.48/1.37 | ( X = two ) ) ).
% 1.48/1.37
% 1.48/1.37 thf(binarity_distinc,axiom,
% 1.48/1.37 one != two ).
% 1.48/1.37
% 1.48/1.37 thf(b1_ty,type,
% 1.48/1.37 b1: $o > $i ).
% 1.48/1.37
% 1.48/1.37 thf(b1,axiom,
% 1.48/1.37 ! [X: $o] :
% 1.48/1.37 ( ( X
% 1.48/1.37 => ( ( b1 @ X )
% 1.48/1.37 = one ) )
% 1.48/1.37 & ( ~ X
% 1.48/1.37 => ( ( b1 @ X )
% 1.48/1.37 = two ) ) ) ).
% 1.48/1.37
% 1.48/1.37 thf(b2_ty,type,
% 1.48/1.37 b2: $o > $i ).
% 1.48/1.37
% 1.48/1.37 thf(b2,axiom,
% 1.48/1.37 ! [X: $o] :
% 1.48/1.37 ( ( X
% 1.48/1.37 => ( ( b2 @ X )
% 1.48/1.37 = two ) )
% 1.48/1.37 & ( ~ X
% 1.48/1.37 => ( ( b2 @ X )
% 1.48/1.37 = one ) ) ) ).
% 1.48/1.37
% 1.48/1.37 thf(goal,conjecture,
% 1.48/1.37 ! [F: $o > $i] :
% 1.48/1.37 ( ! [X: $o] :
% 1.48/1.37 ( ( F @ X )
% 1.48/1.37 != ( F @ ~ X ) )
% 1.48/1.37 => ( ( F = b1 )
% 1.48/1.37 | ( F = b2 ) ) ) ).
% 1.48/1.37 ------------------------
% 1.48/1.39 % (17767)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_17668 for (2999ds/4Mi)
% 1.48/1.39 % (17772)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_17668 for (2999ds/18Mi)
% 1.48/1.39 % (17770)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_17668 for (2999ds/2Mi)
% 1.48/1.39 % (17766)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_17668 for (2999ds/183Mi)
% 1.48/1.39 % (17771)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_17668 for (2999ds/275Mi)
% 1.48/1.39 % (17769)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_17668 for (2999ds/2Mi)
% 1.48/1.39 % (17768)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_17668 for (2999ds/27Mi)
% 1.48/1.40 % (17770)Instruction limit reached!
% 1.48/1.40 % (17770)------------------------------
% 1.48/1.40 % (17770)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.40 % (17770)Termination reason: Unknown
% 1.48/1.40 % (17770)Termination phase: Property scanning
% 1.48/1.40
% 1.48/1.40 % (17770)Memory used [KB]: 895
% 1.48/1.40 % (17770)Time elapsed: 0.003 s
% 1.48/1.40 % (17770)Instructions burned: 2 (million)
% 1.48/1.40 % (17770)------------------------------
% 1.48/1.40 % (17770)------------------------------
% 1.48/1.40 % (17769)Instruction limit reached!
% 1.48/1.40 % (17769)------------------------------
% 1.48/1.40 % (17769)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.40 % (17769)Termination reason: Unknown
% 1.48/1.40 % (17769)Termination phase: Saturation
% 1.48/1.40
% 1.48/1.40 % (17769)Memory used [KB]: 5500
% 1.48/1.40 % (17769)Time elapsed: 0.004 s
% 1.48/1.40 % (17769)Instructions burned: 3 (million)
% 1.48/1.40 % (17769)------------------------------
% 1.48/1.40 % (17769)------------------------------
% 1.63/1.40 % (17767)Instruction limit reached!
% 1.63/1.40 % (17767)------------------------------
% 1.63/1.40 % (17767)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.40 % (17767)Termination reason: Unknown
% 1.63/1.40 % (17767)Termination phase: Saturation
% 1.63/1.40
% 1.63/1.40 % (17767)Memory used [KB]: 5500
% 1.63/1.40 % (17767)Time elapsed: 0.005 s
% 1.63/1.40 % (17767)Instructions burned: 5 (million)
% 1.63/1.40 % (17767)------------------------------
% 1.63/1.40 % (17767)------------------------------
% 1.63/1.40 % (17771)Refutation not found, incomplete strategy
% 1.63/1.40 % (17771)------------------------------
% 1.63/1.40 % (17771)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.40 % (17771)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.40
% 1.63/1.40
% 1.63/1.40 % (17771)Memory used [KB]: 5500
% 1.63/1.40 % (17771)Time elapsed: 0.005 s
% 1.63/1.40 % (17771)Instructions burned: 4 (million)
% 1.63/1.40 % (17771)------------------------------
% 1.63/1.40 % (17771)------------------------------
% 1.63/1.41 % (17772)Instruction limit reached!
% 1.63/1.41 % (17772)------------------------------
% 1.63/1.41 % (17772)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.41 % (17772)Termination reason: Unknown
% 1.63/1.41 % (17772)Termination phase: Saturation
% 1.63/1.41
% 1.63/1.41 % (17772)Memory used [KB]: 5628
% 1.63/1.41 % (17772)Time elapsed: 0.013 s
% 1.63/1.41 % (17772)Instructions burned: 19 (million)
% 1.63/1.41 % (17772)------------------------------
% 1.63/1.41 % (17772)------------------------------
% 1.63/1.41 % (17768)Instruction limit reached!
% 1.63/1.41 % (17768)------------------------------
% 1.63/1.41 % (17768)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.41 % (17773)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_17668 for (2999ds/3Mi)
% 1.63/1.41 % (17768)Termination reason: Unknown
% 1.63/1.41 % (17768)Termination phase: Saturation
% 1.63/1.41 % (17774)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_17668 for (2999ds/37Mi)
% 1.63/1.41
% 1.63/1.41 % (17768)Memory used [KB]: 5628
% 1.63/1.41 % (17768)Time elapsed: 0.019 s
% 1.63/1.41 % (17768)Instructions burned: 27 (million)
% 1.63/1.41 % (17768)------------------------------
% 1.63/1.41 % (17768)------------------------------
% 1.63/1.41 % (17775)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_17668 for (2999ds/15Mi)
% 1.63/1.41 % (17773)Instruction limit reached!
% 1.63/1.41 % (17773)------------------------------
% 1.63/1.41 % (17773)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.41 % (17773)Termination reason: Unknown
% 1.63/1.41 % (17773)Termination phase: Saturation
% 1.63/1.41
% 1.63/1.41 % (17773)Memory used [KB]: 5500
% 1.63/1.41 % (17773)Time elapsed: 0.004 s
% 1.63/1.41 % (17773)Instructions burned: 3 (million)
% 1.63/1.41 % (17773)------------------------------
% 1.63/1.41 % (17773)------------------------------
% 1.63/1.41 % (17776)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_17668 for (2999ds/3Mi)
% 1.63/1.42 % (17776)Instruction limit reached!
% 1.63/1.42 % (17776)------------------------------
% 1.63/1.42 % (17776)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.42 % (17776)Termination reason: Unknown
% 1.63/1.42 % (17776)Termination phase: Saturation
% 1.63/1.42
% 1.63/1.42 % (17776)Memory used [KB]: 5500
% 1.63/1.42 % (17776)Time elapsed: 0.003 s
% 1.63/1.42 % (17776)Instructions burned: 3 (million)
% 1.63/1.42 % (17776)------------------------------
% 1.63/1.42 % (17776)------------------------------
% 1.63/1.42 % (17775)Instruction limit reached!
% 1.63/1.42 % (17775)------------------------------
% 1.63/1.42 % (17775)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.42 % (17775)Termination reason: Unknown
% 1.63/1.42 % (17775)Termination phase: Saturation
% 1.63/1.42
% 1.63/1.42 % (17775)Memory used [KB]: 5628
% 1.63/1.42 % (17775)Time elapsed: 0.010 s
% 1.63/1.42 % (17775)Instructions burned: 15 (million)
% 1.63/1.42 % (17775)------------------------------
% 1.63/1.42 % (17775)------------------------------
% 1.63/1.42 % (17777)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_17668 for (2999ds/1041Mi)
% 1.63/1.43 % (17778)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_17668 for (2999ds/7Mi)
% 1.63/1.43 % (17779)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_17668 for (2999ds/16Mi)
% 1.63/1.43 % (17774)Instruction limit reached!
% 1.63/1.43 % (17774)------------------------------
% 1.63/1.43 % (17774)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.43 % (17774)Termination reason: Unknown
% 1.63/1.43 % (17780)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_17668 for (2999ds/3Mi)
% 1.63/1.43 % (17774)Termination phase: Saturation
% 1.63/1.43
% 1.63/1.43 % (17774)Memory used [KB]: 5628
% 1.63/1.43 % (17774)Time elapsed: 0.021 s
% 1.63/1.43 % (17774)Instructions burned: 37 (million)
% 1.63/1.43 % (17774)------------------------------
% 1.63/1.43 % (17774)------------------------------
% 1.63/1.43 % (17778)Instruction limit reached!
% 1.63/1.43 % (17778)------------------------------
% 1.63/1.43 % (17778)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.43 % (17778)Termination reason: Unknown
% 1.63/1.43 % (17778)Termination phase: Saturation
% 1.63/1.43
% 1.63/1.43 % (17778)Memory used [KB]: 1023
% 1.63/1.43 % (17778)Time elapsed: 0.006 s
% 1.63/1.43 % (17778)Instructions burned: 7 (million)
% 1.63/1.43 % (17778)------------------------------
% 1.63/1.43 % (17778)------------------------------
% 1.63/1.43 % (17780)Instruction limit reached!
% 1.63/1.43 % (17780)------------------------------
% 1.63/1.43 % (17780)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.43 % (17780)Termination reason: Unknown
% 1.63/1.43 % (17780)Termination phase: Saturation
% 1.63/1.43
% 1.63/1.43 % (17780)Memory used [KB]: 5500
% 1.63/1.43 % (17780)Time elapsed: 0.003 s
% 1.63/1.43 % (17780)Instructions burned: 3 (million)
% 1.63/1.43 % (17780)------------------------------
% 1.63/1.43 % (17780)------------------------------
% 1.63/1.44 % (17781)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_17668 for (2999ds/3Mi)
% 1.63/1.44 % (17779)Instruction limit reached!
% 1.63/1.44 % (17779)------------------------------
% 1.63/1.44 % (17779)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.44 % (17779)Termination reason: Unknown
% 1.63/1.44 % (17779)Termination phase: Saturation
% 1.63/1.44
% 1.63/1.44 % (17779)Memory used [KB]: 5628
% 1.63/1.44 % (17779)Time elapsed: 0.010 s
% 1.63/1.44 % (17779)Instructions burned: 16 (million)
% 1.63/1.44 % (17779)------------------------------
% 1.63/1.44 % (17779)------------------------------
% 1.63/1.44 % (17781)Instruction limit reached!
% 1.63/1.44 % (17781)------------------------------
% 1.63/1.44 % (17781)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.44 % (17781)Termination reason: Unknown
% 1.63/1.44 % (17781)Termination phase: Saturation
% 1.63/1.44
% 1.63/1.44 % (17781)Memory used [KB]: 5500
% 1.63/1.44 % (17781)Time elapsed: 0.004 s
% 1.63/1.44 % (17781)Instructions burned: 4 (million)
% 1.63/1.44 % (17781)------------------------------
% 1.63/1.44 % (17781)------------------------------
% 1.63/1.45 % (17782)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_17668 for (2999ds/7Mi)
% 1.63/1.45 % (17783)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_17668 for (2999ds/3Mi)
% 1.63/1.45 % (17784)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_17668 for (2999ds/4Mi)
% 1.63/1.45 % (17783)Instruction limit reached!
% 1.63/1.45 % (17783)------------------------------
% 1.63/1.45 % (17783)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.45 % (17783)Termination reason: Unknown
% 1.63/1.45 % (17783)Termination phase: Saturation
% 1.63/1.45
% 1.63/1.45 % (17783)Memory used [KB]: 5500
% 1.63/1.45 % (17783)Time elapsed: 0.003 s
% 1.63/1.45 % (17783)Instructions burned: 3 (million)
% 1.63/1.45 % (17783)------------------------------
% 1.63/1.45 % (17783)------------------------------
% 1.63/1.45 % (17782)Refutation not found, incomplete strategy
% 1.63/1.45 % (17782)------------------------------
% 1.63/1.45 % (17782)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.45 % (17782)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.45
% 1.63/1.45
% 1.63/1.45 % (17782)Memory used [KB]: 5500
% 1.63/1.45 % (17782)Time elapsed: 0.004 s
% 1.63/1.45 % (17782)Instructions burned: 3 (million)
% 1.63/1.45 % (17782)------------------------------
% 1.63/1.45 % (17782)------------------------------
% 1.63/1.45 % (17784)Instruction limit reached!
% 1.63/1.45 % (17784)------------------------------
% 1.63/1.45 % (17784)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.45 % (17784)Termination reason: Unknown
% 1.63/1.45 % (17784)Termination phase: Saturation
% 1.63/1.45
% 1.63/1.45 % (17784)Memory used [KB]: 5500
% 1.63/1.45 % (17784)Time elapsed: 0.004 s
% 1.63/1.45 % (17784)Instructions burned: 5 (million)
% 1.63/1.45 % (17784)------------------------------
% 1.63/1.45 % (17784)------------------------------
% 1.63/1.45 % (17785)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_17668 for (2999ds/18Mi)
% 1.63/1.46 % (17786)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_17668 for (2999ds/710Mi)
% 1.63/1.47 % (17785)Instruction limit reached!
% 1.63/1.47 % (17785)------------------------------
% 1.63/1.47 % (17785)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.47 % (17785)Termination reason: Unknown
% 1.63/1.47 % (17785)Termination phase: Saturation
% 1.63/1.47
% 1.63/1.47 % (17785)Memory used [KB]: 5628
% 1.63/1.47 % (17785)Time elapsed: 0.012 s
% 1.63/1.47 % (17785)Instructions burned: 19 (million)
% 1.63/1.47 % (17785)------------------------------
% 1.63/1.47 % (17785)------------------------------
% 1.63/1.47 % (17787)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_17668 for (2999ds/6Mi)
% 1.63/1.47 % (17788)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_17668 for (2999ds/902Mi)
% 1.63/1.47 % (17789)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_17668 for (2999ds/21Mi)
% 1.63/1.47 % (17787)Instruction limit reached!
% 1.63/1.47 % (17787)------------------------------
% 1.63/1.47 % (17787)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.47 % (17787)Termination reason: Unknown
% 1.63/1.47 % (17787)Termination phase: Saturation
% 1.63/1.47
% 1.63/1.47 % (17787)Memory used [KB]: 5500
% 1.63/1.47 % (17787)Time elapsed: 0.006 s
% 1.63/1.47 % (17787)Instructions burned: 6 (million)
% 1.63/1.47 % (17787)------------------------------
% 1.63/1.47 % (17787)------------------------------
% 1.63/1.47 % (17788)Refutation not found, incomplete strategy
% 1.63/1.47 % (17788)------------------------------
% 1.63/1.47 % (17788)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.47 % (17788)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.47
% 1.63/1.47
% 1.63/1.47 % (17788)Memory used [KB]: 5500
% 1.63/1.47 % (17788)Time elapsed: 0.005 s
% 1.63/1.47 % (17788)Instructions burned: 6 (million)
% 1.63/1.47 % (17788)------------------------------
% 1.63/1.47 % (17788)------------------------------
% 1.63/1.48 % (17777)First to succeed.
% 1.63/1.48 % (17777)Refutation found. Thanks to Tanya!
% 1.63/1.48 % SZS status Theorem for DTF2THF_17668
% 1.63/1.48 % SZS output start Proof for DTF2THF_17668
% 1.63/1.48 thf(func_def_2, type, b1: $o > $i).
% 1.63/1.48 thf(func_def_4, type, b2: $o > $i).
% 1.63/1.48 thf(func_def_17, type, ph1: !>[X0: $tType]:(X0)).
% 1.63/1.48 thf(func_def_18, type, sK2: $o > $i).
% 1.63/1.48 thf(f744,plain,(
% 1.63/1.48 $false),
% 1.63/1.48 inference(avatar_sat_refutation,[status(thm)],[f164,f171,f234,f241,f267,f392,f414,f516,f672,f741,f743])).
% 1.63/1.48 thf(f743,plain,(
% 1.63/1.48 spl0_8 | spl0_6),
% 1.63/1.48 inference(avatar_split_clause,[status(thm)],[f739,f239,f247])).
% 1.63/1.48 thf(f247,definition,(
% 1.63/1.48 spl0_8 <=> (one = (sK2 @ $false))),
% 1.63/1.48 introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition])).
% 1.63/1.48 thf(f239,definition,(
% 1.63/1.48 spl0_6 <=> (two = (sK2 @ $false))),
% 1.63/1.48 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 1.63/1.48 thf(f739,plain,(
% 1.63/1.48 (one = (sK2 @ $false)) | spl0_6),
% 1.63/1.48 inference(trivial_inequality_removal,[status(thm)],[f738])).
% 1.63/1.48 thf(f738,plain,(
% 1.63/1.48 (two != two) | (one = (sK2 @ $false)) | spl0_6),
% 1.63/1.48 inference(superposition,[status(thm)],[f240,f187])).
% 1.63/1.48 thf(f187,plain,(
% 1.63/1.48 ( ! [X1 : $i] : ((two = X1) | (one = X1)) )),
% 1.63/1.48 inference(equality_proxy_clausification,[status(thm)],[f172])).
% 1.63/1.48 thf(f172,plain,(
% 1.63/1.48 ( ! [X1 : $i] : (((one = X1) = $true) | (two = X1)) )),
% 1.63/1.48 inference(equality_proxy_clausification,[status(thm)],[f23])).
% 1.63/1.48 thf(f23,plain,(
% 1.63/1.48 ( ! [X1 : $i] : (((two = X1) = $true) | ((one = X1) = $true)) )),
% 1.63/1.48 inference(binary_proxy_clausification,[status(thm)],[f22])).
% 1.63/1.48 thf(f22,plain,(
% 1.63/1.48 ( ! [X1 : $i] : (($true = ((two = X1) | (one = X1)))) )),
% 1.63/1.48 inference(beta_eta_normalization,[status(thm)],[f21])).
% 1.63/1.48 thf(f21,plain,(
% 1.63/1.48 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((two = Y0) | (one = Y0))) @ X1))) )),
% 1.63/1.48 inference(pi_clausification,[status(thm)],[f20])).
% 1.63/1.48 thf(f20,plain,(
% 1.63/1.48 ((!! @ $i @ (^[Y0 : $i]: ((two = Y0) | (one = Y0)))) = $true)),
% 1.63/1.48 inference(cnf_transformation,[status(thm)],[f8])).
% 1.63/1.48 thf(f8,plain,(
% 1.63/1.48 ((!! @ $i @ (^[Y0 : $i]: ((two = Y0) | (one = Y0)))) = $true)),
% 1.63/1.48 inference(fool_elimination,[status(thm)],[f1])).
% 1.63/1.48 thf(f1,axiom,(
% 1.63/1.48 ! [X0 : $i] : ((one = X0) | (two = X0))),
% 1.63/1.48 file('/export/starexec/sandbox/tmp/tmp.WUFQl6BPhu/DTF2THF_17668.p',binarity_exhaust)).
% 1.63/1.48 thf(f240,plain,(
% 1.63/1.48 (two != (sK2 @ $false)) | spl0_6),
% 1.63/1.48 inference(avatar_component_clause,[status(thm)],[f239])).
% 1.63/1.48 thf(f741,plain,(
% 1.63/1.48 spl0_6 | spl0_13),
% 1.63/1.48 inference(avatar_contradiction_clause,[status(thm)],[f740])).
% 1.63/1.48 thf(f740,plain,(
% 1.63/1.48 $false | (spl0_6 | spl0_13)),
% 1.63/1.48 inference(subsumption_resolution,[status(thm)],[f739,f720])).
% 1.63/1.48 thf(f720,plain,(
% 1.63/1.48 (one != (sK2 @ $false)) | spl0_13),
% 1.63/1.48 inference(backward_demodulation,[status(thm)],[f719,f716])).
% 1.63/1.48 thf(f716,plain,(
% 1.63/1.48 ($false = sK4) | spl0_13),
% 1.63/1.48 inference(trivial_inequality_removal,[status(thm)],[f714])).
% 1.63/1.48 thf(f714,plain,(
% 1.63/1.48 (two != two) | ($false = sK4) | spl0_13),
% 1.63/1.48 inference(superposition,[status(thm)],[f266,f135])).
% 1.63/1.48 thf(f135,plain,(
% 1.63/1.48 ( ! [X1 : $o] : ((two = (b2 @ X1)) | ($false = X1)) )),
% 1.63/1.48 inference(equality_proxy_clausification,[status(thm)],[f38])).
% 1.63/1.48 thf(f38,plain,(
% 1.63/1.48 ( ! [X1 : $o] : (($true = (two = (b2 @ X1))) | ($false = X1)) )),
% 1.63/1.48 inference(binary_proxy_clausification,[status(thm)],[f37])).
% 1.63/1.48 thf(f37,plain,(
% 1.63/1.48 ( ! [X1 : $o] : (($true = (X1 => (two = (b2 @ X1))))) )),
% 1.63/1.48 inference(boolean_simplification,[status(thm)],[f36])).
% 1.63/1.48 thf(f36,plain,(
% 1.63/1.48 ( ! [X1 : $o] : (($true = ((X1 => (two = (b2 @ X1))) & $true))) )),
% 1.63/1.48 inference(backward_demodulation,[status(thm)],[f32,f34])).
% 1.63/1.48 thf(f34,plain,(
% 1.63/1.48 ( ! [X1 : $o] : ((((~ X1) => (one = (b2 @ X1))) = $true)) )),
% 1.63/1.48 inference(binary_proxy_clausification,[status(thm)],[f32])).
% 1.63/1.48 thf(f32,plain,(
% 1.63/1.48 ( ! [X1 : $o] : (($true = ((X1 => (two = (b2 @ X1))) & ((~ X1) => (one = (b2 @ X1)))))) )),
% 1.63/1.48 inference(beta_eta_normalization,[status(thm)],[f31])).
% 1.63/1.48 thf(f31,plain,(
% 1.63/1.48 ( ! [X1 : $o] : (($true = ((^[Y0 : $o]: ((Y0 => (two = (b2 @ Y0))) & ((~ Y0) => (one = (b2 @ Y0))))) @ X1))) )),
% 1.63/1.48 inference(pi_clausification,[status(thm)],[f19])).
% 1.63/1.48 thf(f19,plain,(
% 1.63/1.48 ($true = (!! @ $o @ (^[Y0 : $o]: ((Y0 => (two = (b2 @ Y0))) & ((~ Y0) => (one = (b2 @ Y0)))))))),
% 1.63/1.48 inference(cnf_transformation,[status(thm)],[f14])).
% 1.63/1.48 thf(f14,plain,(
% 1.63/1.48 ($true = (!! @ $o @ (^[Y0 : $o]: ((Y0 => (two = (b2 @ Y0))) & ((~ Y0) => (one = (b2 @ Y0)))))))),
% 1.63/1.48 inference(fool_elimination,[status(thm)],[f13])).
% 1.63/1.48 thf(f13,plain,(
% 1.63/1.48 ! [X0 : $o] : ((~X0 => (one = (b2 @ X0))) & (X0 => (two = (b2 @ X0))))),
% 1.63/1.48 inference(rectify,[status(thm)],[f4])).
% 1.63/1.48 thf(f4,axiom,(
% 1.63/1.48 ! [X0 : $o] : ((~X0 => (one = (b2 @ X0))) & (X0 => (two = (b2 @ X0))))),
% 1.63/1.48 file('/export/starexec/sandbox/tmp/tmp.WUFQl6BPhu/DTF2THF_17668.p',b2)).
% 1.63/1.48 thf(f266,plain,(
% 1.63/1.48 (two != (b2 @ sK4)) | spl0_13),
% 1.63/1.48 inference(avatar_component_clause,[status(thm)],[f265])).
% 1.63/1.48 thf(f265,definition,(
% 1.63/1.48 spl0_13 <=> (two = (b2 @ sK4))),
% 1.63/1.48 introduced(definition,[new_symbols(naming,[spl0_13])],[avatar_definition])).
% 1.63/1.48 thf(f719,plain,(
% 1.63/1.48 (one != (sK2 @ sK4)) | spl0_13),
% 1.63/1.48 inference(backward_demodulation,[status(thm)],[f101,f717])).
% 1.63/1.48 thf(f717,plain,(
% 1.63/1.48 (one = (b2 @ sK4)) | spl0_13),
% 1.63/1.48 inference(trivial_inequality_removal,[status(thm)],[f715])).
% 1.63/1.48 thf(f715,plain,(
% 1.63/1.48 (two != two) | (one = (b2 @ sK4)) | spl0_13),
% 1.63/1.48 inference(superposition,[status(thm)],[f266,f187])).
% 1.63/1.48 thf(f101,plain,(
% 1.63/1.48 ((b2 @ sK4) != (sK2 @ sK4))),
% 1.63/1.48 inference(negative_extensionality,[status(thm)],[f100])).
% 1.63/1.48 thf(f100,plain,(
% 1.63/1.48 (b2 != sK2)),
% 1.63/1.48 inference(equality_proxy_clausification,[status(thm)],[f83])).
% 1.63/1.48 thf(f83,plain,(
% 1.63/1.48 ((b2 = sK2) = $false)),
% 1.63/1.48 inference(binary_proxy_clausification,[status(thm)],[f59])).
% 1.63/1.48 thf(f59,plain,(
% 1.63/1.48 ($false = ((b2 = sK2) | (b1 = sK2)))),
% 1.63/1.48 inference(binary_proxy_clausification,[status(thm)],[f53])).
% 1.63/1.48 thf(f53,plain,(
% 1.63/1.48 (((!! @ $o @ (^[Y0 : $o]: (~ ((sK2 @ (~ Y0)) = (sK2 @ Y0))))) => ((b2 = sK2) | (b1 = sK2))) = $false)),
% 1.63/1.48 inference(beta_eta_normalization,[status(thm)],[f52])).
% 1.63/1.48 thf(f52,plain,(
% 1.63/1.48 ($false = ((^[Y0 : $o > $i]: ((!! @ $o @ (^[Y1 : $o]: (~ ((Y0 @ (~ Y1)) = (Y0 @ Y1))))) => ((b2 = Y0) | (b1 = Y0)))) @ sK2))),
% 1.63/1.48 inference(sigma_clausification,[status(thm)],[f39])).
% 1.63/1.48 thf(f39,plain,(
% 1.63/1.48 ((!! @ ($o > $i) @ (^[Y0 : $o > $i]: ((!! @ $o @ (^[Y1 : $o]: (~ ((Y0 @ (~ Y1)) = (Y0 @ Y1))))) => ((b2 = Y0) | (b1 = Y0))))) = $false)),
% 1.63/1.48 inference(not_proxy_clausification,[status(thm)],[f16])).
% 1.63/1.48 thf(f16,plain,(
% 1.63/1.48 ($true = (~ (!! @ ($o > $i) @ (^[Y0 : $o > $i]: ((!! @ $o @ (^[Y1 : $o]: (~ ((Y0 @ (~ Y1)) = (Y0 @ Y1))))) => ((b2 = Y0) | (b1 = Y0)))))))),
% 1.63/1.48 inference(cnf_transformation,[status(thm)],[f10])).
% 1.63/1.48 thf(f10,plain,(
% 1.63/1.48 ($true = (~ (!! @ ($o > $i) @ (^[Y0 : $o > $i]: ((!! @ $o @ (^[Y1 : $o]: (~ ((Y0 @ (~ Y1)) = (Y0 @ Y1))))) => ((b2 = Y0) | (b1 = Y0)))))))),
% 1.63/1.48 inference(fool_elimination,[status(thm)],[f9])).
% 1.63/1.48 thf(f9,plain,(
% 1.63/1.48 ~! [X0 : $o > $i] : (! [X1 : $o] : ((X0 @ ~X1) != (X0 @ X1)) => ((b1 = X0) | (b2 = X0)))),
% 1.63/1.48 inference(rectify,[status(thm)],[f6])).
% 1.63/1.48 thf(f6,negated_conjecture,(
% 1.63/1.48 ~! [X1 : $o > $i] : (! [X0 : $o] : ((X1 @ ~X0) != (X1 @ X0)) => ((b1 = X1) | (b2 = X1)))),
% 1.63/1.48 inference(negated_conjecture,[status(cth)],[f5])).
% 1.63/1.48 thf(f5,conjecture,(
% 1.63/1.48 ! [X1 : $o > $i] : (! [X0 : $o] : ((X1 @ ~X0) != (X1 @ X0)) => ((b1 = X1) | (b2 = X1)))),
% 1.63/1.48 file('/export/starexec/sandbox/tmp/tmp.WUFQl6BPhu/DTF2THF_17668.p',goal)).
% 1.63/1.48 thf(f672,plain,(
% 1.63/1.48 ~spl0_1 | ~spl0_8 | ~spl0_12),
% 1.63/1.48 inference(avatar_contradiction_clause,[status(thm)],[f671])).
% 1.63/1.48 thf(f671,plain,(
% 1.63/1.48 $false | (~spl0_1 | ~spl0_8 | ~spl0_12)),
% 1.63/1.48 inference(subsumption_resolution,[status(thm)],[f670,f86])).
% 1.63/1.48 thf(f86,plain,(
% 1.63/1.48 (one = (b2 @ $false))),
% 1.63/1.48 inference(equality_proxy_clausification,[status(thm)],[f74])).
% 1.63/1.48 thf(f74,plain,(
% 1.63/1.48 ((one = (b2 @ $false)) = $true)),
% 1.63/1.48 inference(backward_demodulation,[status(thm)],[f72,f68])).
% 1.63/1.48 thf(f68,plain,(
% 1.63/1.48 ( ! [X1 : $o] : ((((sK2 @ (~ X1)) = (sK2 @ X1)) = $false)) )),
% 1.63/1.48 inference(not_proxy_clausification,[status(thm)],[f67])).
% 1.63/1.48 thf(f67,plain,(
% 1.63/1.48 ( ! [X1 : $o] : (($true = (~ ((sK2 @ (~ X1)) = (sK2 @ X1))))) )),
% 1.63/1.48 inference(beta_eta_normalization,[status(thm)],[f66])).
% 1.63/1.48 thf(f66,plain,(
% 1.63/1.48 ( ! [X1 : $o] : (($true = ((^[Y0 : $o]: (~ ((sK2 @ (~ Y0)) = (sK2 @ Y0)))) @ X1))) )),
% 1.63/1.48 inference(pi_clausification,[status(thm)],[f60])).
% 1.63/1.48 thf(f60,plain,(
% 1.63/1.48 ($true = (!! @ $o @ (^[Y0 : $o]: (~ ((sK2 @ (~ Y0)) = (sK2 @ Y0))))))),
% 1.63/1.48 inference(binary_proxy_clausification,[status(thm)],[f53])).
% 1.63/1.48 thf(f72,plain,(
% 1.63/1.48 ( ! [X0 : $o] : (((one = (b2 @ ((sK2 @ (~ X0)) = (sK2 @ X0)))) = $true)) )),
% 1.63/1.48 inference(boolean_simplification,[status(thm)],[f70])).
% 1.63/1.48 thf(f70,plain,(
% 1.63/1.48 ( ! [X0 : $o] : ((($true => (one = (b2 @ ((sK2 @ (~ X0)) = (sK2 @ X0))))) = $true)) )),
% 1.63/1.48 inference(superposition,[status(thm)],[f34,f67])).
% 1.63/1.48 thf(f670,plain,(
% 1.63/1.48 (one != (b2 @ $false)) | (~spl0_1 | ~spl0_8 | ~spl0_12)),
% 1.63/1.48 inference(backward_demodulation,[status(thm)],[f528,f668])).
% 1.63/1.48 thf(f668,plain,(
% 1.63/1.48 ($false = sK4) | (~spl0_1 | ~spl0_8 | ~spl0_12)),
% 1.63/1.48 inference(trivial_inequality_removal,[status(thm)],[f665])).
% 1.63/1.48 thf(f665,plain,(
% 1.63/1.48 ($false = sK4) | (one != one) | (~spl0_1 | ~spl0_8 | ~spl0_12)),
% 1.63/1.48 inference(superposition,[status(thm)],[f533,f263])).
% 1.63/1.48 thf(f263,plain,(
% 1.63/1.48 (one = (sK2 @ sK4)) | ~spl0_12),
% 1.63/1.48 inference(avatar_component_clause,[status(thm)],[f262])).
% 1.63/1.48 thf(f262,definition,(
% 1.63/1.48 spl0_12 <=> (one = (sK2 @ sK4))),
% 1.63/1.48 introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition])).
% 1.63/1.48 thf(f533,plain,(
% 1.63/1.48 ( ! [X0 : $o] : ((one != (sK2 @ X0)) | ($false = X0)) ) | (~spl0_1 | ~spl0_8)),
% 1.63/1.48 inference(backward_demodulation,[status(thm)],[f180,f248])).
% 1.63/1.48 thf(f248,plain,(
% 1.63/1.48 (one = (sK2 @ $false)) | ~spl0_8),
% 1.63/1.48 inference(avatar_component_clause,[status(thm)],[f247])).
% 1.63/1.48 thf(f180,plain,(
% 1.63/1.48 ( ! [X0 : $o] : (((sK2 @ $false) != (sK2 @ X0)) | ($false = X0)) ) | ~spl0_1),
% 1.63/1.48 inference(superposition,[status(thm)],[f81,f160])).
% 1.63/1.48 thf(f160,plain,(
% 1.63/1.48 ( ! [X0 : $o] : (($false = (~ X0)) | ($false = X0)) ) | ~spl0_1),
% 1.63/1.48 inference(avatar_component_clause,[status(thm)],[f159])).
% 1.63/1.48 thf(f159,definition,(
% 1.63/1.48 spl0_1 <=> ! [X0 : $o] : (($false = X0) | ($false = (~ X0)))),
% 1.63/1.48 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.63/1.48 thf(f81,plain,(
% 1.63/1.48 ( ! [X1 : $o] : (((sK2 @ X1) != (sK2 @ (~ X1)))) )),
% 1.63/1.48 inference(equality_proxy_clausification,[status(thm)],[f68])).
% 1.63/1.48 thf(f528,plain,(
% 1.63/1.48 (one != (b2 @ sK4)) | ~spl0_12),
% 1.63/1.48 inference(backward_demodulation,[status(thm)],[f101,f263])).
% 1.63/1.48 thf(f516,plain,(
% 1.63/1.48 spl0_8 | ~spl0_3),
% 1.63/1.48 inference(avatar_split_clause,[status(thm)],[f402,f229,f247])).
% 1.63/1.48 thf(f229,definition,(
% 1.63/1.48 spl0_3 <=> (one = (sK2 @ sK3))),
% 1.63/1.48 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.63/1.48 thf(f402,plain,(
% 1.63/1.48 (one = (sK2 @ $false)) | ~spl0_3),
% 1.63/1.48 inference(backward_demodulation,[status(thm)],[f230,f400])).
% 1.63/1.48 thf(f400,plain,(
% 1.63/1.48 ($false = sK3) | ~spl0_3),
% 1.63/1.48 inference(trivial_inequality_removal,[status(thm)],[f398])).
% 1.63/1.48 thf(f398,plain,(
% 1.63/1.48 (one != one) | ($false = sK3) | ~spl0_3),
% 1.63/1.48 inference(superposition,[status(thm)],[f397,f120])).
% 1.63/1.48 thf(f120,plain,(
% 1.63/1.48 ( ! [X1 : $o] : ((one = (b1 @ X1)) | ($false = X1)) )),
% 1.63/1.48 inference(equality_proxy_clausification,[status(thm)],[f30])).
% 1.63/1.48 thf(f30,plain,(
% 1.63/1.48 ( ! [X1 : $o] : (((one = (b1 @ X1)) = $true) | ($false = X1)) )),
% 1.63/1.48 inference(binary_proxy_clausification,[status(thm)],[f29])).
% 1.63/1.48 thf(f29,plain,(
% 1.63/1.48 ( ! [X1 : $o] : (((X1 => (one = (b1 @ X1))) = $true)) )),
% 1.63/1.48 inference(boolean_simplification,[status(thm)],[f28])).
% 1.63/1.48 thf(f28,plain,(
% 1.63/1.48 ( ! [X1 : $o] : (($true = ($true & (X1 => (one = (b1 @ X1)))))) )),
% 1.63/1.48 inference(backward_demodulation,[status(thm)],[f25,f27])).
% 1.63/1.48 thf(f27,plain,(
% 1.63/1.48 ( ! [X1 : $o] : (($true = ((~ X1) => (two = (b1 @ X1))))) )),
% 1.63/1.48 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.63/1.48 thf(f25,plain,(
% 1.63/1.48 ( ! [X1 : $o] : (($true = (((~ X1) => (two = (b1 @ X1))) & (X1 => (one = (b1 @ X1)))))) )),
% 1.63/1.48 inference(beta_eta_normalization,[status(thm)],[f24])).
% 1.63/1.48 thf(f24,plain,(
% 1.63/1.48 ( ! [X1 : $o] : ((((^[Y0 : $o]: (((~ Y0) => (two = (b1 @ Y0))) & (Y0 => (one = (b1 @ Y0))))) @ X1) = $true)) )),
% 1.63/1.48 inference(pi_clausification,[status(thm)],[f18])).
% 1.63/1.48 thf(f18,plain,(
% 1.63/1.48 ($true = (!! @ $o @ (^[Y0 : $o]: (((~ Y0) => (two = (b1 @ Y0))) & (Y0 => (one = (b1 @ Y0)))))))),
% 1.63/1.48 inference(cnf_transformation,[status(thm)],[f12])).
% 1.63/1.48 thf(f12,plain,(
% 1.63/1.48 ($true = (!! @ $o @ (^[Y0 : $o]: (((~ Y0) => (two = (b1 @ Y0))) & (Y0 => (one = (b1 @ Y0)))))))),
% 1.63/1.48 inference(fool_elimination,[status(thm)],[f11])).
% 1.63/1.48 thf(f11,plain,(
% 1.63/1.48 ! [X0 : $o] : ((X0 => (one = (b1 @ X0))) & (~X0 => (two = (b1 @ X0))))),
% 1.63/1.48 inference(rectify,[status(thm)],[f3])).
% 1.63/1.48 thf(f3,axiom,(
% 1.63/1.48 ! [X0 : $o] : ((X0 => (one = (b1 @ X0))) & (~X0 => (two = (b1 @ X0))))),
% 1.63/1.48 file('/export/starexec/sandbox/tmp/tmp.WUFQl6BPhu/DTF2THF_17668.p',b1)).
% 1.63/1.48 thf(f397,plain,(
% 1.63/1.48 (one != (b1 @ sK3)) | ~spl0_3),
% 1.63/1.48 inference(forward_demodulation,[status(thm)],[f94,f230])).
% 1.63/1.48 thf(f94,plain,(
% 1.63/1.48 ((sK2 @ sK3) != (b1 @ sK3))),
% 1.63/1.48 inference(negative_extensionality,[status(thm)],[f93])).
% 1.63/1.48 thf(f93,plain,(
% 1.63/1.48 (b1 != sK2)),
% 1.63/1.48 inference(equality_proxy_clausification,[status(thm)],[f85])).
% 1.63/1.48 thf(f85,plain,(
% 1.63/1.48 ((b1 = sK2) = $false)),
% 1.63/1.48 inference(boolean_simplification,[status(thm)],[f84])).
% 1.63/1.48 thf(f84,plain,(
% 1.63/1.48 (($false | (b1 = sK2)) = $false)),
% 1.63/1.48 inference(backward_demodulation,[status(thm)],[f59,f83])).
% 1.63/1.48 thf(f230,plain,(
% 1.63/1.48 (one = (sK2 @ sK3)) | ~spl0_3),
% 1.63/1.48 inference(avatar_component_clause,[status(thm)],[f229])).
% 1.63/1.48 thf(f414,plain,(
% 1.63/1.48 ~spl0_3 | spl0_13),
% 1.63/1.48 inference(avatar_contradiction_clause,[status(thm)],[f413])).
% 1.63/1.48 thf(f413,plain,(
% 1.63/1.48 $false | (~spl0_3 | spl0_13)),
% 1.63/1.48 inference(subsumption_resolution,[status(thm)],[f402,f405])).
% 1.63/1.48 thf(f405,plain,(
% 1.63/1.48 (one != (sK2 @ $false)) | spl0_13),
% 1.63/1.48 inference(forward_demodulation,[status(thm)],[f347,f86])).
% 1.63/1.48 thf(f347,plain,(
% 1.63/1.48 ((b2 @ $false) != (sK2 @ $false)) | spl0_13),
% 1.63/1.48 inference(backward_demodulation,[status(thm)],[f101,f345])).
% 1.63/1.48 thf(f345,plain,(
% 1.63/1.48 ($false = sK4) | spl0_13),
% 1.63/1.48 inference(trivial_inequality_removal,[status(thm)],[f342])).
% 1.63/1.48 thf(f342,plain,(
% 1.63/1.48 ($false = sK4) | (two != two) | spl0_13),
% 1.63/1.48 inference(superposition,[status(thm)],[f266,f135])).
% 1.63/1.48 thf(f392,plain,(
% 1.63/1.48 spl0_4 | ~spl0_5),
% 1.63/1.48 inference(avatar_contradiction_clause,[status(thm)],[f391])).
% 1.63/1.48 thf(f391,plain,(
% 1.63/1.48 $false | (spl0_4 | ~spl0_5)),
% 1.63/1.48 inference(subsumption_resolution,[status(thm)],[f389,f237])).
% 1.63/1.48 thf(f237,plain,(
% 1.63/1.48 (one = (sK2 @ $true)) | ~spl0_5),
% 1.63/1.48 inference(avatar_component_clause,[status(thm)],[f236])).
% 1.63/1.48 thf(f236,definition,(
% 1.63/1.48 spl0_5 <=> (one = (sK2 @ $true))),
% 1.63/1.48 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 1.63/1.48 thf(f389,plain,(
% 1.63/1.48 (one != (sK2 @ $true)) | (spl0_4 | ~spl0_5)),
% 1.63/1.48 inference(backward_demodulation,[status(thm)],[f296,f388])).
% 1.63/1.48 thf(f388,plain,(
% 1.63/1.48 ($true = sK3) | (spl0_4 | ~spl0_5)),
% 1.63/1.48 inference(boolean_simplification,[status(thm)],[f387])).
% 1.63/1.48 thf(f387,plain,(
% 1.63/1.48 ((~ (~ sK3)) = $true) | (spl0_4 | ~spl0_5)),
% 1.63/1.48 inference(boolean_simplification,[status(thm)],[f386])).
% 1.63/1.48 thf(f386,plain,(
% 1.63/1.48 ($true = ((~ sK3) => $false)) | (spl0_4 | ~spl0_5)),
% 1.63/1.48 inference(forward_demodulation,[status(thm)],[f381,f330])).
% 1.63/1.48 thf(f330,plain,(
% 1.63/1.48 ($false = (two = one)) | ~spl0_5),
% 1.63/1.48 inference(forward_demodulation,[status(thm)],[f329,f306])).
% 1.63/1.48 thf(f306,plain,(
% 1.63/1.48 (two = (sK2 @ $false)) | ~spl0_5),
% 1.63/1.48 inference(trivial_inequality_removal,[status(thm)],[f301])).
% 1.63/1.48 thf(f301,plain,(
% 1.63/1.48 (two = (sK2 @ $false)) | ($true = $false) | ~spl0_5),
% 1.63/1.48 inference(superposition,[status(thm)],[f275,f172])).
% 1.63/1.48 thf(f275,plain,(
% 1.63/1.48 ($false = (one = (sK2 @ $false))) | ~spl0_5),
% 1.63/1.48 inference(backward_demodulation,[status(thm)],[f102,f237])).
% 1.63/1.48 thf(f102,plain,(
% 1.63/1.48 (((sK2 @ $true) = (sK2 @ $false)) = $false)),
% 1.63/1.48 inference(not_proxy_clausification,[status(thm)],[f75])).
% 1.63/1.48 thf(f75,plain,(
% 1.63/1.48 ((~ ((sK2 @ $true) = (sK2 @ $false))) = $true)),
% 1.63/1.48 inference(backward_demodulation,[status(thm)],[f69,f68])).
% 1.63/1.48 thf(f69,plain,(
% 1.63/1.48 ( ! [X0 : $o] : (($true = (~ ((sK2 @ $true) = (sK2 @ ((sK2 @ (~ X0)) = (sK2 @ X0))))))) )),
% 1.63/1.48 inference(superposition,[status(thm)],[f67,f67])).
% 1.63/1.48 thf(f329,plain,(
% 1.63/1.48 (((sK2 @ $false) = one) = $false) | ~spl0_5),
% 1.63/1.48 inference(boolean_simplification,[status(thm)],[f328])).
% 1.63/1.48 thf(f328,plain,(
% 1.63/1.48 ($false = ((sK2 @ (~ $true)) = one)) | ~spl0_5),
% 1.63/1.48 inference(superposition,[status(thm)],[f68,f237])).
% 1.63/1.48 thf(f381,plain,(
% 1.63/1.48 ($true = ((~ sK3) => (two = one))) | spl0_4),
% 1.63/1.48 inference(superposition,[status(thm)],[f27,f294])).
% 1.63/1.48 thf(f294,plain,(
% 1.63/1.48 (one = (b1 @ sK3)) | spl0_4),
% 1.63/1.48 inference(trivial_inequality_removal,[status(thm)],[f293])).
% 1.63/1.48 thf(f293,plain,(
% 1.63/1.48 (one = (b1 @ sK3)) | (two != two) | spl0_4),
% 1.63/1.48 inference(superposition,[status(thm)],[f233,f187])).
% 1.63/1.48 thf(f233,plain,(
% 1.63/1.48 (two != (b1 @ sK3)) | spl0_4),
% 1.63/1.48 inference(avatar_component_clause,[status(thm)],[f232])).
% 1.63/1.48 thf(f232,definition,(
% 1.63/1.48 spl0_4 <=> (two = (b1 @ sK3))),
% 1.63/1.48 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.63/1.48 thf(f296,plain,(
% 1.63/1.48 (one != (sK2 @ sK3)) | spl0_4),
% 1.63/1.48 inference(backward_demodulation,[status(thm)],[f94,f294])).
% 1.63/1.48 thf(f267,plain,(
% 1.63/1.48 spl0_12 | ~spl0_13),
% 1.63/1.48 inference(avatar_split_clause,[status(thm)],[f215,f265,f262])).
% 1.63/1.48 thf(f215,plain,(
% 1.63/1.48 (one = (sK2 @ sK4)) | (two != (b2 @ sK4))),
% 1.63/1.48 inference(superposition,[status(thm)],[f101,f187])).
% 1.63/1.48 thf(f241,plain,(
% 1.63/1.48 spl0_5 | ~spl0_6),
% 1.63/1.48 inference(avatar_split_clause,[status(thm)],[f218,f239,f236])).
% 1.63/1.48 thf(f218,plain,(
% 1.63/1.48 (one = (sK2 @ $true)) | (two != (sK2 @ $false))),
% 1.63/1.48 inference(superposition,[status(thm)],[f112,f187])).
% 1.63/1.48 thf(f112,plain,(
% 1.63/1.48 ((sK2 @ $true) != (sK2 @ $false))),
% 1.63/1.48 inference(backward_demodulation,[status(thm)],[f103,f102])).
% 1.63/1.48 thf(f103,plain,(
% 1.63/1.48 ((sK2 @ $true) != (sK2 @ ((sK2 @ $true) = (sK2 @ $false))))),
% 1.63/1.48 inference(superposition,[status(thm)],[f81,f75])).
% 1.63/1.48 thf(f234,plain,(
% 1.63/1.48 spl0_3 | ~spl0_4),
% 1.63/1.48 inference(avatar_split_clause,[status(thm)],[f214,f232,f229])).
% 1.63/1.48 thf(f214,plain,(
% 1.63/1.48 (one = (sK2 @ sK3)) | (two != (b1 @ sK3))),
% 1.63/1.48 inference(superposition,[status(thm)],[f94,f187])).
% 1.63/1.48 thf(f171,plain,(
% 1.63/1.48 ~spl0_2),
% 1.63/1.48 inference(avatar_contradiction_clause,[status(thm)],[f170])).
% 1.63/1.48 thf(f170,plain,(
% 1.63/1.48 $false | ~spl0_2),
% 1.63/1.48 inference(subsumption_resolution,[status(thm)],[f167,f17])).
% 1.63/1.48 thf(f17,plain,(
% 1.63/1.48 (one != two)),
% 1.63/1.48 inference(cnf_transformation,[status(thm)],[f15])).
% 1.63/1.48 thf(f15,plain,(
% 1.63/1.48 (one != two)),
% 1.63/1.48 inference(fool_elimination,[status(thm)],[f2])).
% 1.63/1.48 thf(f2,axiom,(
% 1.63/1.48 (one != two)),
% 1.63/1.48 file('/export/starexec/sandbox/tmp/tmp.WUFQl6BPhu/DTF2THF_17668.p',binarity_distinc)).
% 1.63/1.48 thf(f167,plain,(
% 1.63/1.48 (one = two) | ~spl0_2),
% 1.63/1.48 inference(equality_proxy_clausification,[status(thm)],[f163])).
% 1.63/1.48 thf(f163,plain,(
% 1.63/1.48 ($true = (two = one)) | ~spl0_2),
% 1.63/1.48 inference(avatar_component_clause,[status(thm)],[f162])).
% 1.63/1.48 thf(f162,definition,(
% 1.63/1.48 spl0_2 <=> ($true = (two = one))),
% 1.63/1.48 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.63/1.48 thf(f164,plain,(
% 1.63/1.48 spl0_1 | spl0_2),
% 1.63/1.48 inference(avatar_split_clause,[status(thm)],[f152,f162,f159])).
% 1.63/1.48 thf(f152,plain,(
% 1.63/1.48 ( ! [X0 : $o] : (($false = X0) | ($false = (~ X0)) | ($true = (two = one))) )),
% 1.63/1.48 inference(superposition,[status(thm)],[f33,f120])).
% 1.63/1.48 thf(f33,plain,(
% 1.63/1.48 ( ! [X1 : $o] : (((two = (b1 @ X1)) = $true) | ((~ X1) = $false)) )),
% 1.63/1.48 inference(binary_proxy_clausification,[status(thm)],[f27])).
% 1.63/1.48 % SZS output end Proof for DTF2THF_17668
% 1.63/1.48 % (17777)------------------------------
% 1.63/1.48 % (17777)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.48 % (17777)Termination reason: Refutation
% 1.63/1.48
% 1.63/1.48 % (17777)Memory used [KB]: 5756
% 1.63/1.48 % (17777)Time elapsed: 0.058 s
% 1.63/1.48 % (17777)Instructions burned: 97 (million)
% 1.63/1.48 % (17777)------------------------------
% 1.63/1.48 % (17777)------------------------------
% 1.63/1.48 % (17765)Success in time 0.09 s
%------------------------------------------------------------------------------