%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : CSR150^1 : TPTP v9.2.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n019.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 08:43:14 AM UTC 2026
% Result : Theorem 1.37s 1.16s
% Output : Refutation 1.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of formulae : 77 ( 8 unt; 0 typ; 6 def)
% Number of atoms : 559 ( 127 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 560 ( 100 ~; 91 |; 22 &; 333 @)
% ( 12 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 11 con; 0-2 aty)
% Number of variables : 93 ( 15 ^; 62 !; 16 ?; 93 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
num: $tType ).
thf(func_def_1,type,
grandchild_THFTYPE_IiioI: $i > $i > $o ).
thf(func_def_2,type,
grandparent_THFTYPE_IiioI: $i > $i > $o ).
thf(func_def_3,type,
lCardinalityFn_THFTYPE_IIioIiI: ( $i > $o ) > $i ).
thf(func_def_5,type,
ltet_THFTYPE_IiioI: $i > $i > $o ).
thf(func_def_7,type,
parent_THFTYPE_IiioI: $i > $i > $o ).
thf(func_def_13,type,
sK0: $i > $i > $i ).
thf(func_def_14,type,
sK1: $i > $i > $i ).
thf(func_def_16,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f148,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f42,f55,f64,f70,f85,f87,f147]) ).
thf(f147,plain,
( spl2_3
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f146]) ).
thf(f146,plain,
( $false
| spl2_3
| ~ spl2_4 ),
inference(subsumption_resolution,[status(thm)],[f145,f54]) ).
thf(f54,plain,
( ( ( grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ sK4 )
= $true )
| ~ spl2_4 ),
inference(avatar_component_clause,[status(thm)],[f52]) ).
thf(f52,definition,
( spl2_4
<=> ( ( grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition]) ).
thf(f145,plain,
( ( ( grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ sK4 )
!= $true )
| spl2_3 ),
inference(trivial_inequality_removal,[status(thm)],[f144]) ).
thf(f144,plain,
( ( $true != $true )
| ( ( grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ sK4 )
!= $true )
| spl2_3 ),
inference(duplicate_literal_removal,[status(thm)],[f143]) ).
thf(f143,plain,
( ( $true != $true )
| ( ( grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ sK4 )
!= $true )
| ( ( grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ sK4 )
!= $true )
| spl2_3 ),
inference(superposition,[status(thm)],[f135,f28]) ).
thf(f28,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( parent_THFTYPE_IiioI @ ( sK1 @ X1 @ X0 ) @ X1 ) )
| ( ( grandparent_THFTYPE_IiioI @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
! [X0: $i,X1: $i] :
( ( ( ( $true
= ( parent_THFTYPE_IiioI @ X0 @ ( sK1 @ X1 @ X0 ) ) )
& ( $true
= ( parent_THFTYPE_IiioI @ ( sK1 @ X1 @ X0 ) @ X1 ) ) )
| ( ( grandparent_THFTYPE_IiioI @ X0 @ X1 )
!= $true ) )
& ( ( ( grandparent_THFTYPE_IiioI @ X0 @ X1 )
= $true )
| ! [X3: $i] :
( ( ( parent_THFTYPE_IiioI @ X0 @ X3 )
!= $true )
| ( ( parent_THFTYPE_IiioI @ X3 @ X1 )
!= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f21,f22]) ).
thf(f22,plain,
! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( parent_THFTYPE_IiioI @ X0 @ X2 )
= $true )
& ( ( parent_THFTYPE_IiioI @ X2 @ X1 )
= $true ) )
=> ( ( $true
= ( parent_THFTYPE_IiioI @ X0 @ ( sK1 @ X1 @ X0 ) ) )
& ( $true
= ( parent_THFTYPE_IiioI @ ( sK1 @ X1 @ X0 ) @ X1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f21,plain,
! [X0: $i,X1: $i] :
( ( ? [X2: $i] :
( ( ( parent_THFTYPE_IiioI @ X0 @ X2 )
= $true )
& ( ( parent_THFTYPE_IiioI @ X2 @ X1 )
= $true ) )
| ( ( grandparent_THFTYPE_IiioI @ X0 @ X1 )
!= $true ) )
& ( ( ( grandparent_THFTYPE_IiioI @ X0 @ X1 )
= $true )
| ! [X3: $i] :
( ( ( parent_THFTYPE_IiioI @ X0 @ X3 )
!= $true )
| ( ( parent_THFTYPE_IiioI @ X3 @ X1 )
!= $true ) ) ) ),
inference(rectify,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: $i,X1: $i] :
( ( ? [X2: $i] :
( ( ( parent_THFTYPE_IiioI @ X0 @ X2 )
= $true )
& ( ( parent_THFTYPE_IiioI @ X2 @ X1 )
= $true ) )
| ( ( grandparent_THFTYPE_IiioI @ X0 @ X1 )
!= $true ) )
& ( ( ( grandparent_THFTYPE_IiioI @ X0 @ X1 )
= $true )
| ! [X2: $i] :
( ( ( parent_THFTYPE_IiioI @ X0 @ X2 )
!= $true )
| ( ( parent_THFTYPE_IiioI @ X2 @ X1 )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( parent_THFTYPE_IiioI @ X0 @ X2 )
= $true )
& ( ( parent_THFTYPE_IiioI @ X2 @ X1 )
= $true ) )
<=> ( ( grandparent_THFTYPE_IiioI @ X0 @ X1 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( parent_THFTYPE_IiioI @ X2 @ X1 )
& ( parent_THFTYPE_IiioI @ X0 @ X2 ) )
<=> ( grandparent_THFTYPE_IiioI @ X0 @ X1 ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( parent_THFTYPE_IiioI @ X2 @ X1 )
& ( parent_THFTYPE_IiioI @ X0 @ X2 ) )
<=> ( grandparent_THFTYPE_IiioI @ X0 @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.13RLo8Kl0C/DTF2THF_22518.p',ax) ).
thf(f135,plain,
( ! [X0: $i] :
( ( $true
!= ( parent_THFTYPE_IiioI @ ( sK1 @ X0 @ lJohn_THFTYPE_i ) @ sK4 ) )
| ( ( grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ X0 )
!= $true ) )
| spl2_3 ),
inference(trivial_inequality_removal,[status(thm)],[f133]) ).
thf(f133,plain,
( ! [X0: $i] :
( ( $true
!= ( parent_THFTYPE_IiioI @ ( sK1 @ X0 @ lJohn_THFTYPE_i ) @ sK4 ) )
| ( ( grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ X0 )
!= $true )
| ( $true != $true ) )
| spl2_3 ),
inference(superposition,[status(thm)],[f89,f29]) ).
thf(f29,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( parent_THFTYPE_IiioI @ X0 @ ( sK1 @ X1 @ X0 ) ) )
| ( ( grandparent_THFTYPE_IiioI @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f89,plain,
( ! [X0: $i] :
( ( $true
!= ( parent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ X0 ) )
| ( ( parent_THFTYPE_IiioI @ X0 @ sK4 )
!= $true ) )
| spl2_3 ),
inference(trivial_inequality_removal,[status(thm)],[f88]) ).
thf(f88,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( parent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ X0 ) )
| ( ( parent_THFTYPE_IiioI @ X0 @ sK4 )
!= $true ) )
| spl2_3 ),
inference(superposition,[status(thm)],[f49,f26]) ).
thf(f26,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( grandchild_THFTYPE_IiioI @ X0 @ X1 )
= $true )
| ( ( parent_THFTYPE_IiioI @ X2 @ X0 )
!= $true )
| ( ( parent_THFTYPE_IiioI @ X1 @ X2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: $i,X1: $i] :
( ( ( ( grandchild_THFTYPE_IiioI @ X0 @ X1 )
= $true )
| ! [X2: $i] :
( ( ( parent_THFTYPE_IiioI @ X2 @ X0 )
!= $true )
| ( ( parent_THFTYPE_IiioI @ X1 @ X2 )
!= $true ) ) )
& ( ( ( ( parent_THFTYPE_IiioI @ ( sK0 @ X1 @ X0 ) @ X0 )
= $true )
& ( ( parent_THFTYPE_IiioI @ X1 @ ( sK0 @ X1 @ X0 ) )
= $true ) )
| ( ( grandchild_THFTYPE_IiioI @ X0 @ X1 )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f17,f18]) ).
thf(f18,plain,
! [X0: $i,X1: $i] :
( ? [X3: $i] :
( ( ( parent_THFTYPE_IiioI @ X3 @ X0 )
= $true )
& ( ( parent_THFTYPE_IiioI @ X1 @ X3 )
= $true ) )
=> ( ( ( parent_THFTYPE_IiioI @ ( sK0 @ X1 @ X0 ) @ X0 )
= $true )
& ( ( parent_THFTYPE_IiioI @ X1 @ ( sK0 @ X1 @ X0 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
! [X0: $i,X1: $i] :
( ( ( ( grandchild_THFTYPE_IiioI @ X0 @ X1 )
= $true )
| ! [X2: $i] :
( ( ( parent_THFTYPE_IiioI @ X2 @ X0 )
!= $true )
| ( ( parent_THFTYPE_IiioI @ X1 @ X2 )
!= $true ) ) )
& ( ? [X3: $i] :
( ( ( parent_THFTYPE_IiioI @ X3 @ X0 )
= $true )
& ( ( parent_THFTYPE_IiioI @ X1 @ X3 )
= $true ) )
| ( ( grandchild_THFTYPE_IiioI @ X0 @ X1 )
!= $true ) ) ),
inference(rectify,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: $i,X1: $i] :
( ( ( ( grandchild_THFTYPE_IiioI @ X0 @ X1 )
= $true )
| ! [X2: $i] :
( ( ( parent_THFTYPE_IiioI @ X2 @ X0 )
!= $true )
| ( ( parent_THFTYPE_IiioI @ X1 @ X2 )
!= $true ) ) )
& ( ? [X2: $i] :
( ( ( parent_THFTYPE_IiioI @ X2 @ X0 )
= $true )
& ( ( parent_THFTYPE_IiioI @ X1 @ X2 )
= $true ) )
| ( ( grandchild_THFTYPE_IiioI @ X0 @ X1 )
!= $true ) ) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: $i,X1: $i] :
( ( ( grandchild_THFTYPE_IiioI @ X0 @ X1 )
= $true )
<=> ? [X2: $i] :
( ( ( parent_THFTYPE_IiioI @ X2 @ X0 )
= $true )
& ( ( parent_THFTYPE_IiioI @ X1 @ X2 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $i,X1: $i] :
( ( grandchild_THFTYPE_IiioI @ X0 @ X1 )
<=> ? [X2: $i] :
( ( parent_THFTYPE_IiioI @ X2 @ X0 )
& ( parent_THFTYPE_IiioI @ X1 @ X2 ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: $i,X1: $i] :
( ( grandchild_THFTYPE_IiioI @ X0 @ X1 )
<=> ? [X2: $i] :
( ( parent_THFTYPE_IiioI @ X2 @ X0 )
& ( parent_THFTYPE_IiioI @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.13RLo8Kl0C/DTF2THF_22518.p',ax_002) ).
thf(f49,plain,
( ( $true
!= ( grandchild_THFTYPE_IiioI @ sK4 @ lJohn_THFTYPE_i ) )
| spl2_3 ),
inference(avatar_component_clause,[status(thm)],[f48]) ).
thf(f48,definition,
( spl2_3
<=> ( $true
= ( grandchild_THFTYPE_IiioI @ sK4 @ lJohn_THFTYPE_i ) ) ),
introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition]) ).
thf(f87,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[status(thm)],[f86]) ).
thf(f86,plain,
( $false
| ~ spl2_2 ),
inference(equality_resolution,[status(thm)],[f41]) ).
thf(f41,plain,
( ! [X0: $i] : ( n3_THFTYPE_i != X0 )
| ~ spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f40]) ).
thf(f40,definition,
( spl2_2
<=> ! [X0: $i] : ( n3_THFTYPE_i != X0 ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f85,plain,
( ~ spl2_3
| ~ spl2_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f84]) ).
thf(f84,plain,
( $false
| ~ spl2_3
| ~ spl2_6 ),
inference(subsumption_resolution,[status(thm)],[f83,f50]) ).
thf(f50,plain,
( ( $true
= ( grandchild_THFTYPE_IiioI @ sK4 @ lJohn_THFTYPE_i ) )
| ~ spl2_3 ),
inference(avatar_component_clause,[status(thm)],[f48]) ).
thf(f83,plain,
( ( $true
!= ( grandchild_THFTYPE_IiioI @ sK4 @ lJohn_THFTYPE_i ) )
| ~ spl2_6 ),
inference(trivial_inequality_removal,[status(thm)],[f82]) ).
thf(f82,plain,
( ( $true
!= ( grandchild_THFTYPE_IiioI @ sK4 @ lJohn_THFTYPE_i ) )
| ( $true != $true )
| ~ spl2_6 ),
inference(duplicate_literal_removal,[status(thm)],[f81]) ).
thf(f81,plain,
( ( $true
!= ( grandchild_THFTYPE_IiioI @ sK4 @ lJohn_THFTYPE_i ) )
| ( $true
!= ( grandchild_THFTYPE_IiioI @ sK4 @ lJohn_THFTYPE_i ) )
| ( $true != $true )
| ~ spl2_6 ),
inference(superposition,[status(thm)],[f79,f25]) ).
thf(f25,plain,
! [X0: $i,X1: $i] :
( ( ( parent_THFTYPE_IiioI @ ( sK0 @ X1 @ X0 ) @ X0 )
= $true )
| ( ( grandchild_THFTYPE_IiioI @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f79,plain,
( ! [X0: $i] :
( ( $true
!= ( parent_THFTYPE_IiioI @ ( sK0 @ lJohn_THFTYPE_i @ X0 ) @ sK4 ) )
| ( ( grandchild_THFTYPE_IiioI @ X0 @ lJohn_THFTYPE_i )
!= $true ) )
| ~ spl2_6 ),
inference(trivial_inequality_removal,[status(thm)],[f77]) ).
thf(f77,plain,
( ! [X0: $i] :
( ( $true
!= ( parent_THFTYPE_IiioI @ ( sK0 @ lJohn_THFTYPE_i @ X0 ) @ sK4 ) )
| ( ( grandchild_THFTYPE_IiioI @ X0 @ lJohn_THFTYPE_i )
!= $true )
| ( $true != $true ) )
| ~ spl2_6 ),
inference(superposition,[status(thm)],[f76,f24]) ).
thf(f24,plain,
! [X0: $i,X1: $i] :
( ( ( parent_THFTYPE_IiioI @ X1 @ ( sK0 @ X1 @ X0 ) )
= $true )
| ( ( grandchild_THFTYPE_IiioI @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f76,plain,
( ! [X0: $i] :
( ( $true
!= ( parent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ X0 ) )
| ( ( parent_THFTYPE_IiioI @ X0 @ sK4 )
!= $true ) )
| ~ spl2_6 ),
inference(trivial_inequality_removal,[status(thm)],[f73]) ).
thf(f73,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( $true
!= ( parent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ X0 ) )
| ( ( parent_THFTYPE_IiioI @ X0 @ sK4 )
!= $true ) )
| ~ spl2_6 ),
inference(superposition,[status(thm)],[f27,f63]) ).
thf(f63,plain,
( ( ( grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ sK4 )
= $false )
| ~ spl2_6 ),
inference(avatar_component_clause,[status(thm)],[f61]) ).
thf(f61,definition,
( spl2_6
<=> ( ( grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ sK4 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl2_6])],[avatar_definition]) ).
thf(f27,plain,
! [X3: $i,X0: $i,X1: $i] :
( ( ( grandparent_THFTYPE_IiioI @ X0 @ X1 )
= $true )
| ( ( parent_THFTYPE_IiioI @ X0 @ X3 )
!= $true )
| ( ( parent_THFTYPE_IiioI @ X3 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f70,plain,
( ~ spl2_3
| ~ spl2_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f69]) ).
thf(f69,plain,
( $false
| ~ spl2_3
| ~ spl2_5 ),
inference(trivial_inequality_removal,[status(thm)],[f65]) ).
thf(f65,plain,
( ( $false = $true )
| ~ spl2_3
| ~ spl2_5 ),
inference(superposition,[status(thm)],[f59,f50]) ).
thf(f59,plain,
( ( $false
= ( grandchild_THFTYPE_IiioI @ sK4 @ lJohn_THFTYPE_i ) )
| ~ spl2_5 ),
inference(avatar_component_clause,[status(thm)],[f57]) ).
thf(f57,definition,
( spl2_5
<=> ( $false
= ( grandchild_THFTYPE_IiioI @ sK4 @ lJohn_THFTYPE_i ) ) ),
introduced(definition,[new_symbols(naming,[spl2_5])],[avatar_definition]) ).
thf(f64,plain,
( spl2_5
| spl2_6
| spl2_1 ),
inference(avatar_split_clause,[status(thm)],[f46,f36,f61,f57]) ).
thf(f36,definition,
( spl2_1
<=> ( ( grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i )
= ( ^ [Y0: $i] : ( grandchild_THFTYPE_IiioI @ Y0 @ lJohn_THFTYPE_i ) ) ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f46,plain,
( ( $false
= ( grandchild_THFTYPE_IiioI @ sK4 @ lJohn_THFTYPE_i ) )
| ( ( grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ sK4 )
= $false )
| spl2_1 ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
( ( ( grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ sK4 )
!= ( grandchild_THFTYPE_IiioI @ sK4 @ lJohn_THFTYPE_i ) )
| spl2_1 ),
inference(beta_eta_normalization,[status(thm)],[f43]) ).
thf(f43,plain,
( ( ( grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ sK4 )
!= ( ^ [Y0: $i] : ( grandchild_THFTYPE_IiioI @ Y0 @ lJohn_THFTYPE_i )
@ sK4 ) )
| spl2_1 ),
inference(negative_extensionality,[status(thm)],[f38]) ).
thf(f38,plain,
( ( ( grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i )
!= ( ^ [Y0: $i] : ( grandchild_THFTYPE_IiioI @ Y0 @ lJohn_THFTYPE_i ) ) )
| spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f36]) ).
thf(f55,plain,
( spl2_3
| spl2_4
| spl2_1 ),
inference(avatar_split_clause,[status(thm)],[f45,f36,f52,f48]) ).
thf(f45,plain,
( ( ( grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ sK4 )
= $true )
| ( $true
= ( grandchild_THFTYPE_IiioI @ sK4 @ lJohn_THFTYPE_i ) )
| spl2_1 ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f42,plain,
( ~ spl2_1
| spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f34,f40,f36]) ).
thf(f34,plain,
! [X0: $i] :
( ( ( grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i )
!= ( ^ [Y0: $i] : ( grandchild_THFTYPE_IiioI @ Y0 @ lJohn_THFTYPE_i ) ) )
| ( n3_THFTYPE_i != X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f33]) ).
thf(f33,plain,
! [X0: $i] :
( ( n3_THFTYPE_i != X0 )
| ( ( grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i )
!= ( ^ [Y0: $i] : ( grandchild_THFTYPE_IiioI @ Y0 @ lJohn_THFTYPE_i ) ) )
| ( $true != $true ) ),
inference(constrained_superposition,[status(thm)],[f31,f32]) ).
thf(f32,plain,
( ( ltet_THFTYPE_IiioI @ ( lCardinalityFn_THFTYPE_IIioIiI @ ( grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i ) ) @ n3_THFTYPE_i )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ltet_THFTYPE_IiioI
@ ( lCardinalityFn_THFTYPE_IIioIiI
@ ^ [Y0: $i] : ( grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ Y0 ) )
@ n3_THFTYPE_i )
= $true ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ltet_THFTYPE_IiioI
@ ( lCardinalityFn_THFTYPE_IIioIiI
@ ^ [Y0: $i] : ( grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ Y0 ) )
@ n3_THFTYPE_i )
= $true ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( ltet_THFTYPE_IiioI
@ ( lCardinalityFn_THFTYPE_IIioIiI
@ ^ [X0: $i] : ( grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ X0 ) )
@ n3_THFTYPE_i ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( ltet_THFTYPE_IiioI
@ ( lCardinalityFn_THFTYPE_IIioIiI
@ ^ [X0: $i] : ( grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ X0 ) )
@ n3_THFTYPE_i ),
file('/export/starexec/sandbox/tmp/tmp.13RLo8Kl0C/DTF2THF_22518.p',ax_001) ).
thf(f31,plain,
! [X0: $i] :
( ( ltet_THFTYPE_IiioI
@ ( lCardinalityFn_THFTYPE_IIioIiI
@ ^ [Y0: $i] : ( grandchild_THFTYPE_IiioI @ Y0 @ lJohn_THFTYPE_i ) )
@ X0 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: $i] :
( ( ltet_THFTYPE_IiioI
@ ( lCardinalityFn_THFTYPE_IIioIiI
@ ^ [Y0: $i] : ( grandchild_THFTYPE_IiioI @ Y0 @ lJohn_THFTYPE_i ) )
@ X0 )
!= $true ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
~ ? [X0: $i] :
( ( ltet_THFTYPE_IiioI
@ ( lCardinalityFn_THFTYPE_IIioIiI
@ ^ [Y0: $i] : ( grandchild_THFTYPE_IiioI @ Y0 @ lJohn_THFTYPE_i ) )
@ X0 )
= $true ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
~ ? [X0: $i] :
( ltet_THFTYPE_IiioI
@ ( lCardinalityFn_THFTYPE_IIioIiI
@ ^ [X1: $i] : ( grandchild_THFTYPE_IiioI @ X1 @ lJohn_THFTYPE_i ) )
@ X0 ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ? [X1: $i] :
( ltet_THFTYPE_IiioI
@ ( lCardinalityFn_THFTYPE_IIioIiI
@ ^ [X0: $i] : ( grandchild_THFTYPE_IiioI @ X0 @ lJohn_THFTYPE_i ) )
@ X1 ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
? [X1: $i] :
( ltet_THFTYPE_IiioI
@ ( lCardinalityFn_THFTYPE_IIioIiI
@ ^ [X0: $i] : ( grandchild_THFTYPE_IiioI @ X0 @ lJohn_THFTYPE_i ) )
@ X1 ),
file('/export/starexec/sandbox/tmp/tmp.13RLo8Kl0C/DTF2THF_22518.p',con) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : CSR150^1 : TPTP v9.2.1. Released v4.1.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n019.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 05:54:09 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.26/0.45 ---- Original DTF file ---
% 0.26/0.45 thf(spec,logic,$$dhol).
% 0.26/0.45 %------------------------------------------------------------------------------
% 0.26/0.45 % File : CSR150^1 : TPTP v9.2.1. Released v4.1.0.
% 0.26/0.45 % Domain : Commonsense Reasoning
% 0.26/0.45 % Problem : How many grandchildren does John at most have?
% 0.26/0.45 % Version : Especial > Reduced > Especial.
% 0.26/0.45 % English : The number of persons John is grandparent of is maximally three.
% 0.26/0.45 % How many grandchildren does John at most have?
% 0.26/0.45
% 0.26/0.45 % Refs : [PS07] Pease & Sutcliffe (2007), First Order Reasoning on a L
% 0.26/0.45 % : [BP10] Benzmueller & Pease (2010), Progress in Automating Hig
% 0.26/0.45 % : [Ben10] Benzmueller (2010), Email to Geoff Sutcliffe
% 0.26/0.45 % Source : [Ben10]
% 0.26/0.45 % Names : paar_6.tq_SUMO_local [Ben10]
% 0.26/0.45
% 0.26/0.45 % Status : Theorem
% 0.26/0.45 % Rating : 0.08 v9.1.0, 0.12 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.08 v7.4.0, 0.11 v7.3.0, 0.10 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.2.0, 0.00 v6.1.0, 0.50 v6.0.0, 0.17 v5.5.0, 0.20 v5.4.0, 0.25 v5.3.0, 0.50 v5.1.0, 0.75 v5.0.0, 0.50 v4.1.0
% 0.26/0.45 % Syntax : Number of formulae : 12 ( 0 unt; 8 typ; 0 def)
% 0.26/0.45 % Number of atoms : 10 ( 0 equ; 0 cnn)
% 0.26/0.45 % Maximal formula atoms : 3 ( 2 avg)
% 0.26/0.45 % Number of connectives : 26 ( 0 ~; 0 |; 2 &; 22 @)
% 0.26/0.45 % ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% 0.26/0.45 % Maximal formula depth : 8 ( 8 avg)
% 0.26/0.45 % Number of types : 3 ( 1 usr)
% 0.26/0.45 % Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% 0.26/0.45 % Number of symbols : 7 ( 7 usr; 2 con; 0-2 aty)
% 0.26/0.45 % Number of variables : 9 ( 2 ^; 4 !; 3 ?; 9 :)
% 0.26/0.45 % SPC : TH0_THM_NEQ_NAR
% 0.26/0.45
% 0.26/0.45 % Comments : This is a simple test problem for reasoning in/about SUMO.
% 0.26/0.45 % Initally the problem has been hand generated in KIF syntax in
% 0.26/0.45 % SigmaKEE and then automatically translated by Benzmueller's
% 0.26/0.45 % KIF2TH0 translator into THF syntax.
% 0.26/0.45 % : The translation has been applied in two modes: local and SInE.
% 0.26/0.45 % The local mode only translates the local assumptions and the
% 0.26/0.45 % query. The SInE mode additionally translates the SInE-extract
% 0.26/0.45 % of the loaded knowledge base (usually SUMO).
% 0.26/0.45 % : The examples are selected to illustrate the benefits of
% 0.26/0.45 % higher-order reasoning in ontology reasoning.
% 0.26/0.45 %------------------------------------------------------------------------------
% 0.26/0.45 %----The extracted Signature
% 0.26/0.45 thf(numbers,type,
% 0.26/0.45 num: $tType ).
% 0.26/0.45
% 0.26/0.45 thf(grandchild_THFTYPE_IiioI,type,
% 0.26/0.45 grandchild_THFTYPE_IiioI: $i > $i > $o ).
% 0.26/0.45
% 0.26/0.45 thf(grandparent_THFTYPE_IiioI,type,
% 0.26/0.45 grandparent_THFTYPE_IiioI: $i > $i > $o ).
% 0.26/0.45
% 0.26/0.45 thf(lCardinalityFn_THFTYPE_IIioIiI,type,
% 0.26/0.45 lCardinalityFn_THFTYPE_IIioIiI: ( $i > $o ) > $i ).
% 0.26/0.45
% 0.26/0.45 thf(lJohn_THFTYPE_i,type,
% 0.26/0.45 lJohn_THFTYPE_i: $i ).
% 0.26/0.45
% 0.26/0.45 thf(ltet_THFTYPE_IiioI,type,
% 0.26/0.45 ltet_THFTYPE_IiioI: $i > $i > $o ).
% 0.26/0.45
% 0.26/0.45 thf(n3_THFTYPE_i,type,
% 0.26/0.45 n3_THFTYPE_i: $i ).
% 0.26/0.45
% 0.26/0.45 thf(parent_THFTYPE_IiioI,type,
% 0.26/0.45 parent_THFTYPE_IiioI: $i > $i > $o ).
% 0.26/0.45
% 0.26/0.45 %----The translated axioms
% 0.26/0.45 thf(ax,axiom,
% 0.26/0.45 ! [X: $i,Y: $i] :
% 0.26/0.45 ( ( grandparent_THFTYPE_IiioI @ X @ Y )
% 0.26/0.45 <=> ? [Z: $i] :
% 0.26/0.45 ( ( parent_THFTYPE_IiioI @ X @ Z )
% 0.26/0.45 & ( parent_THFTYPE_IiioI @ Z @ Y ) ) ) ).
% 0.26/0.45
% 0.26/0.45 thf(ax_001,axiom,
% 0.26/0.45 ( ltet_THFTYPE_IiioI
% 0.26/0.45 @ ( lCardinalityFn_THFTYPE_IIioIiI
% 0.26/0.45 @ ^ [X: $i] : ( grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ X ) )
% 0.26/0.45 @ n3_THFTYPE_i ) ).
% 0.26/0.45
% 0.26/0.45 thf(ax_002,axiom,
% 0.26/0.45 ! [X: $i,Y: $i] :
% 0.26/0.45 ( ( grandchild_THFTYPE_IiioI @ X @ Y )
% 0.26/0.45 <=> ? [Z: $i] :
% 0.26/0.45 ( ( parent_THFTYPE_IiioI @ Z @ X )
% 0.26/0.45 & ( parent_THFTYPE_IiioI @ Y @ Z ) ) ) ).
% 0.26/0.45
% 0.26/0.45 %----The translated conjectures
% 0.26/0.45 thf(con,conjecture,
% 0.26/0.45 ? [Y: $i] :
% 0.26/0.45 ( ltet_THFTYPE_IiioI
% 0.26/0.45 @ ( lCardinalityFn_THFTYPE_IIioIiI
% 0.26/0.45 @ ^ [X: $i] : ( grandchild_THFTYPE_IiioI @ X @ lJohn_THFTYPE_i ) )
% 0.26/0.45 @ Y ) ).
% 0.26/0.45
% 0.26/0.45 %------------------------------------------------------------------------------
% 0.26/0.45 ------------------------
% 1.37/1.13 ---- Embedded in THF ---
% 1.37/1.13 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.37/1.13 %%% Generated on Tue Feb 24 05:54:10 EST 2026
% 1.37/1.13 %%% using '$$dhol' embedding, version 1.3.0.
% 1.37/1.13 %%% Logic specification used:
% 1.37/1.13 %%% thf(spec, logic, $$dhol).
% 1.37/1.13
% 1.37/1.13 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.13RLo8Kl0C/DTF2DTF22518.p
% See solution above
% 1.37/1.13 ------------------------
% 1.37/1.13 ---- Cleaned THF ---
% 1.37/1.13 thf(numbers,type,
% 1.37/1.13 num: $tType ).
% 1.37/1.13
% 1.37/1.13 thf(grandchild_THFTYPE_IiioI,type,
% 1.37/1.13 grandchild_THFTYPE_IiioI: $i > $i > $o ).
% 1.37/1.13
% 1.37/1.13 thf(grandparent_THFTYPE_IiioI,type,
% 1.37/1.13 grandparent_THFTYPE_IiioI: $i > $i > $o ).
% 1.37/1.13
% 1.37/1.13 thf(lCardinalityFn_THFTYPE_IIioIiI,type,
% 1.37/1.13 lCardinalityFn_THFTYPE_IIioIiI: ( $i > $o ) > $i ).
% 1.37/1.13
% 1.37/1.13 thf(lJohn_THFTYPE_i,type,
% 1.37/1.13 lJohn_THFTYPE_i: $i ).
% 1.37/1.13
% 1.37/1.13 thf(ltet_THFTYPE_IiioI,type,
% 1.37/1.13 ltet_THFTYPE_IiioI: $i > $i > $o ).
% 1.37/1.13
% 1.37/1.13 thf(n3_THFTYPE_i,type,
% 1.37/1.13 n3_THFTYPE_i: $i ).
% 1.37/1.13
% 1.37/1.13 thf(parent_THFTYPE_IiioI,type,
% 1.37/1.13 parent_THFTYPE_IiioI: $i > $i > $o ).
% 1.37/1.13
% 1.37/1.13 thf(ax,axiom,
% 1.37/1.13 ! [X: $i,Y: $i] :
% 1.37/1.13 ( ( grandparent_THFTYPE_IiioI @ X @ Y )
% 1.37/1.13 <=> ? [Z: $i] :
% 1.37/1.13 ( ( parent_THFTYPE_IiioI @ X @ Z )
% 1.37/1.13 & ( parent_THFTYPE_IiioI @ Z @ Y ) ) ) ).
% 1.37/1.13
% 1.37/1.13 thf(ax_001,axiom,
% 1.37/1.13 ( ltet_THFTYPE_IiioI
% 1.37/1.13 @ ( lCardinalityFn_THFTYPE_IIioIiI
% 1.37/1.13 @ ^ [X: $i] : ( grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ X ) )
% 1.37/1.13 @ n3_THFTYPE_i ) ).
% 1.37/1.13
% 1.37/1.13 thf(ax_002,axiom,
% 1.37/1.13 ! [X: $i,Y: $i] :
% 1.37/1.13 ( ( grandchild_THFTYPE_IiioI @ X @ Y )
% 1.37/1.13 <=> ? [Z: $i] :
% 1.37/1.13 ( ( parent_THFTYPE_IiioI @ Z @ X )
% 1.37/1.13 & ( parent_THFTYPE_IiioI @ Y @ Z ) ) ) ).
% 1.37/1.13
% 1.37/1.13 thf(con,conjecture,
% 1.37/1.13 ? [Y: $i] :
% 1.37/1.13 ( ltet_THFTYPE_IiioI
% 1.37/1.13 @ ( lCardinalityFn_THFTYPE_IIioIiI
% 1.37/1.13 @ ^ [X: $i] : ( grandchild_THFTYPE_IiioI @ X @ lJohn_THFTYPE_i ) )
% 1.37/1.13 @ Y ) ).
% 1.37/1.13 ------------------------
% 1.37/1.15 % (22616)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_22518 for (3000ds/4Mi)
% 1.37/1.15 % (22617)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_22518 for (3000ds/27Mi)
% 1.37/1.15 % (22617)Refutation not found, incomplete strategy
% 1.37/1.15 % (22617)------------------------------
% 1.37/1.15 % (22617)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.37/1.15 % (22617)Termination reason: Refutation not found, incomplete strategy
% 1.37/1.15
% 1.37/1.15
% 1.37/1.15 % (22617)Memory used [KB]: 5500
% 1.37/1.15 % (22617)Time elapsed: 0.003 s
% 1.37/1.15 % (22617)Instructions burned: 2 (million)
% 1.37/1.15 % (22617)------------------------------
% 1.37/1.15 % (22617)------------------------------
% 1.37/1.15 % (22616)Instruction limit reached!
% 1.37/1.15 % (22616)------------------------------
% 1.37/1.15 % (22616)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.37/1.15 % (22616)Termination reason: Unknown
% 1.37/1.15 % (22616)Termination phase: Saturation
% 1.37/1.15
% 1.37/1.15 % (22616)Memory used [KB]: 5500
% 1.37/1.15 % (22616)Time elapsed: 0.005 s
% 1.37/1.15 % (22616)Instructions burned: 4 (million)
% 1.37/1.15 % (22616)------------------------------
% 1.37/1.15 % (22616)------------------------------
% 1.37/1.15 % (22618)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_22518 for (3000ds/2Mi)
% 1.37/1.15 % (22619)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_22518 for (3000ds/2Mi)
% 1.37/1.15 % (22620)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_22518 for (3000ds/275Mi)
% 1.37/1.15 % (22621)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_22518 for (3000ds/18Mi)
% 1.37/1.15 % (22618)Instruction limit reached!
% 1.37/1.15 % (22618)------------------------------
% 1.37/1.15 % (22618)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.37/1.15 % (22618)Termination reason: Unknown
% 1.37/1.15 % (22618)Termination phase: Saturation
% 1.37/1.15
% 1.37/1.15 % (22618)Memory used [KB]: 5500
% 1.37/1.15 % (22618)Time elapsed: 0.003 s
% 1.37/1.15 % (22618)Instructions burned: 3 (million)
% 1.37/1.15 % (22618)------------------------------
% 1.37/1.15 % (22618)------------------------------
% 1.37/1.15 % (22619)Instruction limit reached!
% 1.37/1.15 % (22619)------------------------------
% 1.37/1.15 % (22619)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.37/1.15 % (22619)Termination reason: Unknown
% 1.37/1.15 % (22619)Termination phase: Saturation
% 1.37/1.15
% 1.37/1.15 % (22619)Memory used [KB]: 5500
% 1.37/1.15 % (22619)Time elapsed: 0.003 s
% 1.37/1.15 % (22619)Instructions burned: 3 (million)
% 1.37/1.15 % (22619)------------------------------
% 1.37/1.15 % (22619)------------------------------
% 1.37/1.15 % (22620)Refutation not found, incomplete strategy
% 1.37/1.15 % (22620)------------------------------
% 1.37/1.15 % (22620)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.37/1.15 % (22620)Termination reason: Refutation not found, incomplete strategy
% 1.37/1.15
% 1.37/1.15
% 1.37/1.15 % (22620)Memory used [KB]: 5500
% 1.37/1.15 % (22620)Time elapsed: 0.003 s
% 1.37/1.15 % (22620)Instructions burned: 3 (million)
% 1.37/1.15 % (22620)------------------------------
% 1.37/1.15 % (22620)------------------------------
% 1.37/1.15 % (22615)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_22518 for (3000ds/183Mi)
% 1.37/1.16 % (22622)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_22518 for (2999ds/3Mi)
% 1.37/1.16 % (22615)First to succeed.
% 1.37/1.16 % (22622)Instruction limit reached!
% 1.37/1.16 % (22622)------------------------------
% 1.37/1.16 % (22622)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.37/1.16 % (22622)Termination reason: Unknown
% 1.37/1.16 % (22622)Termination phase: Saturation
% 1.37/1.16
% 1.37/1.16 % (22622)Memory used [KB]: 5500
% 1.37/1.16 % (22622)Time elapsed: 0.003 s
% 1.37/1.16 % (22622)Instructions burned: 3 (million)
% 1.37/1.16 % (22622)------------------------------
% 1.37/1.16 % (22622)------------------------------
% 1.37/1.16 % (22615)Refutation found. Thanks to Tanya!
% 1.37/1.16 % SZS status Theorem for DTF2THF_22518
% 1.37/1.16 % SZS output start Proof for DTF2THF_22518
% 1.37/1.16 thf(func_def_0, type, num: $tType).
% 1.37/1.16 thf(func_def_1, type, grandchild_THFTYPE_IiioI: $i > $i > $o).
% 1.37/1.16 thf(func_def_2, type, grandparent_THFTYPE_IiioI: $i > $i > $o).
% 1.37/1.16 thf(func_def_3, type, lCardinalityFn_THFTYPE_IIioIiI: ($i > $o) > $i).
% 1.37/1.16 thf(func_def_5, type, ltet_THFTYPE_IiioI: $i > $i > $o).
% 1.37/1.16 thf(func_def_7, type, parent_THFTYPE_IiioI: $i > $i > $o).
% 1.37/1.16 thf(func_def_13, type, sK0: $i > $i > $i).
% 1.37/1.16 thf(func_def_14, type, sK1: $i > $i > $i).
% 1.37/1.16 thf(func_def_16, type, ph3: !>[X0: $tType]:(X0)).
% 1.37/1.16 thf(f148,plain,(
% 1.37/1.16 $false),
% 1.37/1.16 inference(avatar_sat_refutation,[status(thm)],[f42,f55,f64,f70,f85,f87,f147])).
% 1.37/1.16 thf(f147,plain,(
% 1.37/1.16 spl2_3 | ~spl2_4),
% 1.37/1.16 inference(avatar_contradiction_clause,[status(thm)],[f146])).
% 1.37/1.16 thf(f146,plain,(
% 1.37/1.16 $false | (spl2_3 | ~spl2_4)),
% 1.37/1.16 inference(subsumption_resolution,[status(thm)],[f145,f54])).
% 1.37/1.16 thf(f54,plain,(
% 1.37/1.16 ((grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ sK4) = $true) | ~spl2_4),
% 1.37/1.16 inference(avatar_component_clause,[status(thm)],[f52])).
% 1.37/1.16 thf(f52,definition,(
% 1.37/1.16 spl2_4 <=> ((grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ sK4) = $true)),
% 1.37/1.16 introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition])).
% 1.37/1.16 thf(f145,plain,(
% 1.37/1.16 ((grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ sK4) != $true) | spl2_3),
% 1.37/1.16 inference(trivial_inequality_removal,[status(thm)],[f144])).
% 1.37/1.16 thf(f144,plain,(
% 1.37/1.16 ($true != $true) | ((grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ sK4) != $true) | spl2_3),
% 1.37/1.16 inference(duplicate_literal_removal,[status(thm)],[f143])).
% 1.37/1.16 thf(f143,plain,(
% 1.37/1.16 ($true != $true) | ((grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ sK4) != $true) | ((grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ sK4) != $true) | spl2_3),
% 1.37/1.16 inference(superposition,[status(thm)],[f135,f28])).
% 1.37/1.16 thf(f28,plain,(
% 1.37/1.16 ( ! [X0 : $i,X1 : $i] : (($true = (parent_THFTYPE_IiioI @ (sK1 @ X1 @ X0) @ X1)) | ((grandparent_THFTYPE_IiioI @ X0 @ X1) != $true)) )),
% 1.37/1.16 inference(cnf_transformation,[status(thm)],[f23])).
% 1.37/1.16 thf(f23,plain,(
% 1.37/1.16 ! [X0 : $i,X1 : $i] : (((($true = (parent_THFTYPE_IiioI @ X0 @ (sK1 @ X1 @ X0))) & ($true = (parent_THFTYPE_IiioI @ (sK1 @ X1 @ X0) @ X1))) | ((grandparent_THFTYPE_IiioI @ X0 @ X1) != $true)) & (((grandparent_THFTYPE_IiioI @ X0 @ X1) = $true) | ! [X3 : $i] : (((parent_THFTYPE_IiioI @ X0 @ X3) != $true) | ((parent_THFTYPE_IiioI @ X3 @ X1) != $true))))),
% 1.37/1.16 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f21,f22])).
% 1.37/1.16 thf(f22,plain,(
% 1.37/1.16 ! [X0 : $i,X1 : $i] : (? [X2 : $i] : (((parent_THFTYPE_IiioI @ X0 @ X2) = $true) & ((parent_THFTYPE_IiioI @ X2 @ X1) = $true)) => (($true = (parent_THFTYPE_IiioI @ X0 @ (sK1 @ X1 @ X0))) & ($true = (parent_THFTYPE_IiioI @ (sK1 @ X1 @ X0) @ X1))))),
% 1.37/1.16 introduced(definition,[],[choice_axiom])).
% 1.37/1.16 thf(f21,plain,(
% 1.37/1.16 ! [X0 : $i,X1 : $i] : ((? [X2 : $i] : (((parent_THFTYPE_IiioI @ X0 @ X2) = $true) & ((parent_THFTYPE_IiioI @ X2 @ X1) = $true)) | ((grandparent_THFTYPE_IiioI @ X0 @ X1) != $true)) & (((grandparent_THFTYPE_IiioI @ X0 @ X1) = $true) | ! [X3 : $i] : (((parent_THFTYPE_IiioI @ X0 @ X3) != $true) | ((parent_THFTYPE_IiioI @ X3 @ X1) != $true))))),
% 1.37/1.16 inference(rectify,[status(thm)],[f20])).
% 1.37/1.16 thf(f20,plain,(
% 1.37/1.16 ! [X0 : $i,X1 : $i] : ((? [X2 : $i] : (((parent_THFTYPE_IiioI @ X0 @ X2) = $true) & ((parent_THFTYPE_IiioI @ X2 @ X1) = $true)) | ((grandparent_THFTYPE_IiioI @ X0 @ X1) != $true)) & (((grandparent_THFTYPE_IiioI @ X0 @ X1) = $true) | ! [X2 : $i] : (((parent_THFTYPE_IiioI @ X0 @ X2) != $true) | ((parent_THFTYPE_IiioI @ X2 @ X1) != $true))))),
% 1.37/1.16 inference(nnf_transformation,[status(thm)],[f14])).
% 1.37/1.16 thf(f14,plain,(
% 1.37/1.16 ! [X0 : $i,X1 : $i] : (? [X2 : $i] : (((parent_THFTYPE_IiioI @ X0 @ X2) = $true) & ((parent_THFTYPE_IiioI @ X2 @ X1) = $true)) <=> ((grandparent_THFTYPE_IiioI @ X0 @ X1) = $true))),
% 1.37/1.16 inference(fool_elimination,[status(thm)],[f13])).
% 1.37/1.16 thf(f13,plain,(
% 1.37/1.16 ! [X0 : $i,X1 : $i] : (? [X2 : $i] : ((parent_THFTYPE_IiioI @ X2 @ X1) & (parent_THFTYPE_IiioI @ X0 @ X2)) <=> (grandparent_THFTYPE_IiioI @ X0 @ X1))),
% 1.37/1.16 inference(rectify,[status(thm)],[f1])).
% 1.37/1.16 thf(f1,axiom,(
% 1.37/1.16 ! [X0 : $i,X1 : $i] : (? [X2 : $i] : ((parent_THFTYPE_IiioI @ X2 @ X1) & (parent_THFTYPE_IiioI @ X0 @ X2)) <=> (grandparent_THFTYPE_IiioI @ X0 @ X1))),
% 1.37/1.16 file('/export/starexec/sandbox/tmp/tmp.13RLo8Kl0C/DTF2THF_22518.p',ax)).
% 1.37/1.16 thf(f135,plain,(
% 1.37/1.16 ( ! [X0 : $i] : (($true != (parent_THFTYPE_IiioI @ (sK1 @ X0 @ lJohn_THFTYPE_i) @ sK4)) | ((grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ X0) != $true)) ) | spl2_3),
% 1.37/1.16 inference(trivial_inequality_removal,[status(thm)],[f133])).
% 1.37/1.16 thf(f133,plain,(
% 1.37/1.16 ( ! [X0 : $i] : (($true != (parent_THFTYPE_IiioI @ (sK1 @ X0 @ lJohn_THFTYPE_i) @ sK4)) | ((grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ X0) != $true) | ($true != $true)) ) | spl2_3),
% 1.37/1.16 inference(superposition,[status(thm)],[f89,f29])).
% 1.37/1.16 thf(f29,plain,(
% 1.37/1.16 ( ! [X0 : $i,X1 : $i] : (($true = (parent_THFTYPE_IiioI @ X0 @ (sK1 @ X1 @ X0))) | ((grandparent_THFTYPE_IiioI @ X0 @ X1) != $true)) )),
% 1.37/1.16 inference(cnf_transformation,[status(thm)],[f23])).
% 1.37/1.16 thf(f89,plain,(
% 1.37/1.16 ( ! [X0 : $i] : (($true != (parent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ X0)) | ((parent_THFTYPE_IiioI @ X0 @ sK4) != $true)) ) | spl2_3),
% 1.37/1.16 inference(trivial_inequality_removal,[status(thm)],[f88])).
% 1.37/1.16 thf(f88,plain,(
% 1.37/1.16 ( ! [X0 : $i] : (($true != $true) | ($true != (parent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ X0)) | ((parent_THFTYPE_IiioI @ X0 @ sK4) != $true)) ) | spl2_3),
% 1.37/1.16 inference(superposition,[status(thm)],[f49,f26])).
% 1.37/1.16 thf(f26,plain,(
% 1.37/1.16 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((grandchild_THFTYPE_IiioI @ X0 @ X1) = $true) | ((parent_THFTYPE_IiioI @ X2 @ X0) != $true) | ((parent_THFTYPE_IiioI @ X1 @ X2) != $true)) )),
% 1.37/1.16 inference(cnf_transformation,[status(thm)],[f19])).
% 1.37/1.16 thf(f19,plain,(
% 1.37/1.16 ! [X0 : $i,X1 : $i] : ((((grandchild_THFTYPE_IiioI @ X0 @ X1) = $true) | ! [X2 : $i] : (((parent_THFTYPE_IiioI @ X2 @ X0) != $true) | ((parent_THFTYPE_IiioI @ X1 @ X2) != $true))) & ((((parent_THFTYPE_IiioI @ (sK0 @ X1 @ X0) @ X0) = $true) & ((parent_THFTYPE_IiioI @ X1 @ (sK0 @ X1 @ X0)) = $true)) | ((grandchild_THFTYPE_IiioI @ X0 @ X1) != $true)))),
% 1.37/1.16 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f17,f18])).
% 1.37/1.16 thf(f18,plain,(
% 1.37/1.16 ! [X0 : $i,X1 : $i] : (? [X3 : $i] : (((parent_THFTYPE_IiioI @ X3 @ X0) = $true) & ((parent_THFTYPE_IiioI @ X1 @ X3) = $true)) => (((parent_THFTYPE_IiioI @ (sK0 @ X1 @ X0) @ X0) = $true) & ((parent_THFTYPE_IiioI @ X1 @ (sK0 @ X1 @ X0)) = $true)))),
% 1.37/1.16 introduced(definition,[],[choice_axiom])).
% 1.37/1.16 thf(f17,plain,(
% 1.37/1.16 ! [X0 : $i,X1 : $i] : ((((grandchild_THFTYPE_IiioI @ X0 @ X1) = $true) | ! [X2 : $i] : (((parent_THFTYPE_IiioI @ X2 @ X0) != $true) | ((parent_THFTYPE_IiioI @ X1 @ X2) != $true))) & (? [X3 : $i] : (((parent_THFTYPE_IiioI @ X3 @ X0) = $true) & ((parent_THFTYPE_IiioI @ X1 @ X3) = $true)) | ((grandchild_THFTYPE_IiioI @ X0 @ X1) != $true)))),
% 1.37/1.16 inference(rectify,[status(thm)],[f16])).
% 1.37/1.16 thf(f16,plain,(
% 1.37/1.16 ! [X0 : $i,X1 : $i] : ((((grandchild_THFTYPE_IiioI @ X0 @ X1) = $true) | ! [X2 : $i] : (((parent_THFTYPE_IiioI @ X2 @ X0) != $true) | ((parent_THFTYPE_IiioI @ X1 @ X2) != $true))) & (? [X2 : $i] : (((parent_THFTYPE_IiioI @ X2 @ X0) = $true) & ((parent_THFTYPE_IiioI @ X1 @ X2) = $true)) | ((grandchild_THFTYPE_IiioI @ X0 @ X1) != $true)))),
% 1.37/1.16 inference(nnf_transformation,[status(thm)],[f12])).
% 1.37/1.16 thf(f12,plain,(
% 1.37/1.16 ! [X0 : $i,X1 : $i] : (((grandchild_THFTYPE_IiioI @ X0 @ X1) = $true) <=> ? [X2 : $i] : (((parent_THFTYPE_IiioI @ X2 @ X0) = $true) & ((parent_THFTYPE_IiioI @ X1 @ X2) = $true)))),
% 1.37/1.16 inference(fool_elimination,[status(thm)],[f11])).
% 1.37/1.16 thf(f11,plain,(
% 1.37/1.16 ! [X0 : $i,X1 : $i] : ((grandchild_THFTYPE_IiioI @ X0 @ X1) <=> ? [X2 : $i] : ((parent_THFTYPE_IiioI @ X2 @ X0) & (parent_THFTYPE_IiioI @ X1 @ X2)))),
% 1.37/1.16 inference(rectify,[status(thm)],[f3])).
% 1.37/1.16 thf(f3,axiom,(
% 1.37/1.16 ! [X0 : $i,X1 : $i] : ((grandchild_THFTYPE_IiioI @ X0 @ X1) <=> ? [X2 : $i] : ((parent_THFTYPE_IiioI @ X2 @ X0) & (parent_THFTYPE_IiioI @ X1 @ X2)))),
% 1.37/1.16 file('/export/starexec/sandbox/tmp/tmp.13RLo8Kl0C/DTF2THF_22518.p',ax_002)).
% 1.37/1.16 thf(f49,plain,(
% 1.37/1.16 ($true != (grandchild_THFTYPE_IiioI @ sK4 @ lJohn_THFTYPE_i)) | spl2_3),
% 1.37/1.16 inference(avatar_component_clause,[status(thm)],[f48])).
% 1.37/1.16 thf(f48,definition,(
% 1.37/1.16 spl2_3 <=> ($true = (grandchild_THFTYPE_IiioI @ sK4 @ lJohn_THFTYPE_i))),
% 1.37/1.16 introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition])).
% 1.37/1.16 thf(f87,plain,(
% 1.37/1.16 ~spl2_2),
% 1.37/1.16 inference(avatar_contradiction_clause,[status(thm)],[f86])).
% 1.37/1.16 thf(f86,plain,(
% 1.37/1.16 $false | ~spl2_2),
% 1.37/1.16 inference(equality_resolution,[status(thm)],[f41])).
% 1.37/1.16 thf(f41,plain,(
% 1.37/1.16 ( ! [X0 : $i] : ((n3_THFTYPE_i != X0)) ) | ~spl2_2),
% 1.37/1.16 inference(avatar_component_clause,[status(thm)],[f40])).
% 1.37/1.16 thf(f40,definition,(
% 1.37/1.16 spl2_2 <=> ! [X0 : $i] : (n3_THFTYPE_i != X0)),
% 1.37/1.16 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.37/1.16 thf(f85,plain,(
% 1.37/1.16 ~spl2_3 | ~spl2_6),
% 1.37/1.16 inference(avatar_contradiction_clause,[status(thm)],[f84])).
% 1.37/1.16 thf(f84,plain,(
% 1.37/1.16 $false | (~spl2_3 | ~spl2_6)),
% 1.37/1.16 inference(subsumption_resolution,[status(thm)],[f83,f50])).
% 1.37/1.16 thf(f50,plain,(
% 1.37/1.16 ($true = (grandchild_THFTYPE_IiioI @ sK4 @ lJohn_THFTYPE_i)) | ~spl2_3),
% 1.37/1.16 inference(avatar_component_clause,[status(thm)],[f48])).
% 1.37/1.16 thf(f83,plain,(
% 1.37/1.16 ($true != (grandchild_THFTYPE_IiioI @ sK4 @ lJohn_THFTYPE_i)) | ~spl2_6),
% 1.37/1.16 inference(trivial_inequality_removal,[status(thm)],[f82])).
% 1.37/1.16 thf(f82,plain,(
% 1.37/1.16 ($true != (grandchild_THFTYPE_IiioI @ sK4 @ lJohn_THFTYPE_i)) | ($true != $true) | ~spl2_6),
% 1.37/1.16 inference(duplicate_literal_removal,[status(thm)],[f81])).
% 1.37/1.16 thf(f81,plain,(
% 1.37/1.16 ($true != (grandchild_THFTYPE_IiioI @ sK4 @ lJohn_THFTYPE_i)) | ($true != (grandchild_THFTYPE_IiioI @ sK4 @ lJohn_THFTYPE_i)) | ($true != $true) | ~spl2_6),
% 1.37/1.16 inference(superposition,[status(thm)],[f79,f25])).
% 1.37/1.16 thf(f25,plain,(
% 1.37/1.16 ( ! [X0 : $i,X1 : $i] : (((parent_THFTYPE_IiioI @ (sK0 @ X1 @ X0) @ X0) = $true) | ((grandchild_THFTYPE_IiioI @ X0 @ X1) != $true)) )),
% 1.37/1.16 inference(cnf_transformation,[status(thm)],[f19])).
% 1.37/1.16 thf(f79,plain,(
% 1.37/1.16 ( ! [X0 : $i] : (($true != (parent_THFTYPE_IiioI @ (sK0 @ lJohn_THFTYPE_i @ X0) @ sK4)) | ((grandchild_THFTYPE_IiioI @ X0 @ lJohn_THFTYPE_i) != $true)) ) | ~spl2_6),
% 1.37/1.16 inference(trivial_inequality_removal,[status(thm)],[f77])).
% 1.37/1.16 thf(f77,plain,(
% 1.37/1.16 ( ! [X0 : $i] : (($true != (parent_THFTYPE_IiioI @ (sK0 @ lJohn_THFTYPE_i @ X0) @ sK4)) | ((grandchild_THFTYPE_IiioI @ X0 @ lJohn_THFTYPE_i) != $true) | ($true != $true)) ) | ~spl2_6),
% 1.37/1.16 inference(superposition,[status(thm)],[f76,f24])).
% 1.37/1.16 thf(f24,plain,(
% 1.37/1.16 ( ! [X0 : $i,X1 : $i] : (((parent_THFTYPE_IiioI @ X1 @ (sK0 @ X1 @ X0)) = $true) | ((grandchild_THFTYPE_IiioI @ X0 @ X1) != $true)) )),
% 1.37/1.16 inference(cnf_transformation,[status(thm)],[f19])).
% 1.37/1.16 thf(f76,plain,(
% 1.37/1.16 ( ! [X0 : $i] : (($true != (parent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ X0)) | ((parent_THFTYPE_IiioI @ X0 @ sK4) != $true)) ) | ~spl2_6),
% 1.37/1.16 inference(trivial_inequality_removal,[status(thm)],[f73])).
% 1.37/1.16 thf(f73,plain,(
% 1.37/1.16 ( ! [X0 : $i] : (($false = $true) | ($true != (parent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ X0)) | ((parent_THFTYPE_IiioI @ X0 @ sK4) != $true)) ) | ~spl2_6),
% 1.37/1.16 inference(superposition,[status(thm)],[f27,f63])).
% 1.37/1.16 thf(f63,plain,(
% 1.37/1.16 ((grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ sK4) = $false) | ~spl2_6),
% 1.37/1.16 inference(avatar_component_clause,[status(thm)],[f61])).
% 1.37/1.16 thf(f61,definition,(
% 1.37/1.16 spl2_6 <=> ((grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ sK4) = $false)),
% 1.37/1.16 introduced(definition,[new_symbols(naming,[spl2_6])],[avatar_definition])).
% 1.37/1.16 thf(f27,plain,(
% 1.37/1.16 ( ! [X3 : $i,X0 : $i,X1 : $i] : (((grandparent_THFTYPE_IiioI @ X0 @ X1) = $true) | ((parent_THFTYPE_IiioI @ X0 @ X3) != $true) | ((parent_THFTYPE_IiioI @ X3 @ X1) != $true)) )),
% 1.37/1.16 inference(cnf_transformation,[status(thm)],[f23])).
% 1.37/1.16 thf(f70,plain,(
% 1.37/1.16 ~spl2_3 | ~spl2_5),
% 1.37/1.16 inference(avatar_contradiction_clause,[status(thm)],[f69])).
% 1.37/1.16 thf(f69,plain,(
% 1.37/1.16 $false | (~spl2_3 | ~spl2_5)),
% 1.37/1.16 inference(trivial_inequality_removal,[status(thm)],[f65])).
% 1.37/1.16 thf(f65,plain,(
% 1.37/1.16 ($false = $true) | (~spl2_3 | ~spl2_5)),
% 1.37/1.16 inference(superposition,[status(thm)],[f59,f50])).
% 1.37/1.16 thf(f59,plain,(
% 1.37/1.16 ($false = (grandchild_THFTYPE_IiioI @ sK4 @ lJohn_THFTYPE_i)) | ~spl2_5),
% 1.37/1.16 inference(avatar_component_clause,[status(thm)],[f57])).
% 1.37/1.16 thf(f57,definition,(
% 1.37/1.16 spl2_5 <=> ($false = (grandchild_THFTYPE_IiioI @ sK4 @ lJohn_THFTYPE_i))),
% 1.37/1.16 introduced(definition,[new_symbols(naming,[spl2_5])],[avatar_definition])).
% 1.37/1.16 thf(f64,plain,(
% 1.37/1.16 spl2_5 | spl2_6 | spl2_1),
% 1.37/1.16 inference(avatar_split_clause,[status(thm)],[f46,f36,f61,f57])).
% 1.37/1.16 thf(f36,definition,(
% 1.37/1.16 spl2_1 <=> ((grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i) = (^[Y0 : $i]: (grandchild_THFTYPE_IiioI @ Y0 @ lJohn_THFTYPE_i)))),
% 1.37/1.16 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.37/1.16 thf(f46,plain,(
% 1.37/1.16 ($false = (grandchild_THFTYPE_IiioI @ sK4 @ lJohn_THFTYPE_i)) | ((grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ sK4) = $false) | spl2_1),
% 1.37/1.16 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 1.37/1.16 thf(f44,plain,(
% 1.37/1.16 ((grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ sK4) != (grandchild_THFTYPE_IiioI @ sK4 @ lJohn_THFTYPE_i)) | spl2_1),
% 1.37/1.16 inference(beta_eta_normalization,[status(thm)],[f43])).
% 1.37/1.16 thf(f43,plain,(
% 1.37/1.16 ((grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ sK4) != ((^[Y0 : $i]: (grandchild_THFTYPE_IiioI @ Y0 @ lJohn_THFTYPE_i)) @ sK4)) | spl2_1),
% 1.37/1.16 inference(negative_extensionality,[status(thm)],[f38])).
% 1.37/1.16 thf(f38,plain,(
% 1.37/1.16 ((grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i) != (^[Y0 : $i]: (grandchild_THFTYPE_IiioI @ Y0 @ lJohn_THFTYPE_i))) | spl2_1),
% 1.37/1.16 inference(avatar_component_clause,[status(thm)],[f36])).
% 1.37/1.16 thf(f55,plain,(
% 1.37/1.16 spl2_3 | spl2_4 | spl2_1),
% 1.37/1.16 inference(avatar_split_clause,[status(thm)],[f45,f36,f52,f48])).
% 1.37/1.16 thf(f45,plain,(
% 1.37/1.16 ((grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ sK4) = $true) | ($true = (grandchild_THFTYPE_IiioI @ sK4 @ lJohn_THFTYPE_i)) | spl2_1),
% 1.37/1.16 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 1.37/1.16 thf(f42,plain,(
% 1.37/1.16 ~spl2_1 | spl2_2),
% 1.37/1.16 inference(avatar_split_clause,[status(thm)],[f34,f40,f36])).
% 1.37/1.16 thf(f34,plain,(
% 1.37/1.16 ( ! [X0 : $i] : (((grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i) != (^[Y0 : $i]: (grandchild_THFTYPE_IiioI @ Y0 @ lJohn_THFTYPE_i))) | (n3_THFTYPE_i != X0)) )),
% 1.37/1.16 inference(trivial_inequality_removal,[status(thm)],[f33])).
% 1.37/1.16 thf(f33,plain,(
% 1.37/1.16 ( ! [X0 : $i] : ((n3_THFTYPE_i != X0) | ((grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i) != (^[Y0 : $i]: (grandchild_THFTYPE_IiioI @ Y0 @ lJohn_THFTYPE_i))) | ($true != $true)) )),
% 1.37/1.16 inference(constrained_superposition,[status(thm)],[f31,f32])).
% 1.37/1.16 thf(f32,plain,(
% 1.37/1.16 ((ltet_THFTYPE_IiioI @ (lCardinalityFn_THFTYPE_IIioIiI @ (grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i)) @ n3_THFTYPE_i) = $true)),
% 1.37/1.16 inference(beta_eta_normalization,[status(thm)],[f30])).
% 1.37/1.16 thf(f30,plain,(
% 1.37/1.16 ((ltet_THFTYPE_IiioI @ (lCardinalityFn_THFTYPE_IIioIiI @ (^[Y0 : $i]: (grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ Y0))) @ n3_THFTYPE_i) = $true)),
% 1.37/1.16 inference(cnf_transformation,[status(thm)],[f8])).
% 1.37/1.16 thf(f8,plain,(
% 1.37/1.16 ((ltet_THFTYPE_IiioI @ (lCardinalityFn_THFTYPE_IIioIiI @ (^[Y0 : $i]: (grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ Y0))) @ n3_THFTYPE_i) = $true)),
% 1.37/1.16 inference(fool_elimination,[status(thm)],[f7])).
% 1.37/1.16 thf(f7,plain,(
% 1.37/1.16 (ltet_THFTYPE_IiioI @ (lCardinalityFn_THFTYPE_IIioIiI @ (^[X0 : $i] : (grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ X0))) @ n3_THFTYPE_i)),
% 1.37/1.16 inference(rectify,[status(thm)],[f2])).
% 1.37/1.16 thf(f2,axiom,(
% 1.37/1.16 (ltet_THFTYPE_IiioI @ (lCardinalityFn_THFTYPE_IIioIiI @ (^[X0 : $i] : (grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ X0))) @ n3_THFTYPE_i)),
% 1.37/1.16 file('/export/starexec/sandbox/tmp/tmp.13RLo8Kl0C/DTF2THF_22518.p',ax_001)).
% 1.37/1.16 thf(f31,plain,(
% 1.37/1.16 ( ! [X0 : $i] : (((ltet_THFTYPE_IiioI @ (lCardinalityFn_THFTYPE_IIioIiI @ (^[Y0 : $i]: (grandchild_THFTYPE_IiioI @ Y0 @ lJohn_THFTYPE_i))) @ X0) != $true)) )),
% 1.37/1.16 inference(cnf_transformation,[status(thm)],[f15])).
% 1.37/1.16 thf(f15,plain,(
% 1.37/1.16 ! [X0 : $i] : ((ltet_THFTYPE_IiioI @ (lCardinalityFn_THFTYPE_IIioIiI @ (^[Y0 : $i]: (grandchild_THFTYPE_IiioI @ Y0 @ lJohn_THFTYPE_i))) @ X0) != $true)),
% 1.37/1.16 inference(ennf_transformation,[status(thm)],[f10])).
% 1.37/1.16 thf(f10,plain,(
% 1.37/1.16 ~? [X0 : $i] : ((ltet_THFTYPE_IiioI @ (lCardinalityFn_THFTYPE_IIioIiI @ (^[Y0 : $i]: (grandchild_THFTYPE_IiioI @ Y0 @ lJohn_THFTYPE_i))) @ X0) = $true)),
% 1.37/1.16 inference(fool_elimination,[status(thm)],[f9])).
% 1.37/1.16 thf(f9,plain,(
% 1.37/1.16 ~? [X0 : $i] : (ltet_THFTYPE_IiioI @ (lCardinalityFn_THFTYPE_IIioIiI @ (^[X1 : $i] : (grandchild_THFTYPE_IiioI @ X1 @ lJohn_THFTYPE_i))) @ X0)),
% 1.37/1.16 inference(rectify,[status(thm)],[f5])).
% 1.37/1.16 thf(f5,negated_conjecture,(
% 1.37/1.16 ~? [X1 : $i] : (ltet_THFTYPE_IiioI @ (lCardinalityFn_THFTYPE_IIioIiI @ (^[X0 : $i] : (grandchild_THFTYPE_IiioI @ X0 @ lJohn_THFTYPE_i))) @ X1)),
% 1.37/1.16 inference(negated_conjecture,[status(cth)],[f4])).
% 1.37/1.16 thf(f4,conjecture,(
% 1.37/1.16 ? [X1 : $i] : (ltet_THFTYPE_IiioI @ (lCardinalityFn_THFTYPE_IIioIiI @ (^[X0 : $i] : (grandchild_THFTYPE_IiioI @ X0 @ lJohn_THFTYPE_i))) @ X1)),
% 1.37/1.16 file('/export/starexec/sandbox/tmp/tmp.13RLo8Kl0C/DTF2THF_22518.p',con)).
% 1.37/1.16 % SZS output end Proof for DTF2THF_22518
% 1.37/1.16 % (22615)------------------------------
% 1.37/1.16 % (22615)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.37/1.16 % (22615)Termination reason: Refutation
% 1.37/1.16
% 1.37/1.16 % (22615)Memory used [KB]: 5628
% 1.37/1.16 % (22615)Time elapsed: 0.007 s
% 1.37/1.16 % (22615)Instructions burned: 10 (million)
% 1.37/1.16 % (22615)------------------------------
% 1.37/1.16 % (22615)------------------------------
% 1.37/1.16 % (22614)Success in time 0.021 s
%------------------------------------------------------------------------------