%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV074^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n024.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 09:40:13 AM UTC 2026
% Result : Theorem 1.81s 1.04s
% Output : Refutation 1.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 11
% Syntax : Number of formulae : 76 ( 6 unt; 0 typ; 4 def)
% Number of atoms : 646 ( 207 equ; 0 cnn)
% Maximal formula atoms : 10 ( 8 avg)
% Number of connectives : 907 ( 117 ~; 141 |; 36 &; 588 @)
% ( 10 <=>; 12 =>; 0 <=; 3 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 114 ( 114 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 8 con; 0-5 aty)
% Number of variables : 179 ( 0 ^; 140 !; 39 ?; 179 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_4,type,
sP0: ( a > a > $o ) > a > a > $o ).
thf(func_def_5,type,
sP1: ( a > a > $o ) > a > a > $o ).
thf(func_def_6,type,
sK2: ( a > a > $o ) > a > a > a > a > $o ).
thf(func_def_7,type,
sK3: ( a > a > $o ) > a ).
thf(func_def_8,type,
sK4: ( a > a > $o ) > ( a > a > $o ) > a ).
thf(func_def_9,type,
sK5: ( a > a > $o ) > ( a > a > $o ) > a ).
thf(func_def_10,type,
sK6: a ).
thf(func_def_11,type,
sK7: a ).
thf(func_def_12,type,
sK8: a > a > $o ).
thf(func_def_14,type,
ph10:
!>[X0: $tType] : X0 ).
thf(f321,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f43,f44,f245,f260,f266,f320]) ).
thf(f320,plain,
( spl9_2
| ~ spl9_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f319]) ).
thf(f319,plain,
( $false
| spl9_2
| ~ spl9_3 ),
inference(subsumption_resolution,[status(thm)],[f318,f42]) ).
thf(f42,plain,
( ( $true
!= ( sP1 @ sK8 @ sK7 @ sK6 ) )
| spl9_2 ),
inference(avatar_component_clause,[status(thm)],[f40]) ).
thf(f40,definition,
( spl9_2
<=> ( $true
= ( sP1 @ sK8 @ sK7 @ sK6 ) ) ),
introduced(definition,[new_symbols(naming,[spl9_2])],[avatar_definition]) ).
thf(f318,plain,
( ( $true
= ( sP1 @ sK8 @ sK7 @ sK6 ) )
| ~ spl9_3 ),
inference(trivial_inequality_removal,[status(thm)],[f317]) ).
thf(f317,plain,
( ( $true
= ( sP1 @ sK8 @ sK7 @ sK6 ) )
| ( $true != $true )
| ~ spl9_3 ),
inference(duplicate_literal_removal,[status(thm)],[f312]) ).
thf(f312,plain,
( ( $true != $true )
| ( $true
= ( sP1 @ sK8 @ sK7 @ sK6 ) )
| ( $true
= ( sP1 @ sK8 @ sK7 @ sK6 ) )
| ~ spl9_3 ),
inference(superposition,[status(thm)],[f28,f276]) ).
thf(f276,plain,
( ! [X0: a,X1: a] :
( ( ( sK2 @ sK8 @ X0 @ X1 @ sK7 @ sK6 )
= $true )
| ( $true
= ( sP1 @ sK8 @ X0 @ X1 ) ) )
| ~ spl9_3 ),
inference(trivial_inequality_removal,[status(thm)],[f273]) ).
thf(f273,plain,
( ! [X0: a,X1: a] :
( ( ( sK2 @ sK8 @ X0 @ X1 @ sK7 @ sK6 )
= $true )
| ( $true != $true )
| ( $true
= ( sP1 @ sK8 @ X0 @ X1 ) ) )
| ~ spl9_3 ),
inference(superposition,[status(thm)],[f26,f255]) ).
thf(f255,plain,
( ( ( sK8 @ sK7 @ sK6 )
= $true )
| ~ spl9_3 ),
inference(avatar_component_clause,[status(thm)],[f253]) ).
thf(f253,definition,
( spl9_3
<=> ( ( sK8 @ sK7 @ sK6 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl9_3])],[avatar_definition]) ).
thf(f26,plain,
! [X2: a > a > $o,X0: a,X1: a,X6: a,X5: a] :
( ( ( X2 @ X5 @ X6 )
!= $true )
| ( ( sP1 @ X2 @ X1 @ X0 )
= $true )
| ( $true
= ( sK2 @ X2 @ X1 @ X0 @ X5 @ X6 ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: a,X1: a,X2: a > a > $o] :
( ( ( ( sP1 @ X2 @ X1 @ X0 )
= $true )
| ( ( ( sK2 @ X2 @ X1 @ X0 @ X1 @ X0 )
!= $true )
& ! [X4: a] :
( $true
= ( sK2 @ X2 @ X1 @ X0 @ X4 @ X4 ) )
& ! [X5: a,X6: a] :
( ( ( X2 @ X5 @ X6 )
!= $true )
| ( $true
= ( sK2 @ X2 @ X1 @ X0 @ X5 @ X6 ) ) ) ) )
& ( ! [X7: a > a > $o] :
( ( $true
= ( X7 @ X1 @ X0 ) )
| ( ( X7 @ ( sK3 @ X7 ) @ ( sK3 @ X7 ) )
!= $true )
| ( ( $true
= ( X2 @ ( sK4 @ X7 @ X2 ) @ ( sK5 @ X7 @ X2 ) ) )
& ( $true
!= ( X7 @ ( sK4 @ X7 @ X2 ) @ ( sK5 @ X7 @ X2 ) ) ) ) )
| ( ( sP1 @ X2 @ X1 @ X0 )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f12,f15,f14,f13]) ).
thf(f13,plain,
! [X0: a,X1: a,X2: a > a > $o] :
( ? [X3: a > a > $o] :
( ( $true
!= ( X3 @ X1 @ X0 ) )
& ! [X4: a] :
( ( X3 @ X4 @ X4 )
= $true )
& ! [X5: a,X6: a] :
( ( ( X2 @ X5 @ X6 )
!= $true )
| ( ( X3 @ X5 @ X6 )
= $true ) ) )
=> ( ( ( sK2 @ X2 @ X1 @ X0 @ X1 @ X0 )
!= $true )
& ! [X4: a] :
( $true
= ( sK2 @ X2 @ X1 @ X0 @ X4 @ X4 ) )
& ! [X6: a,X5: a] :
( ( ( X2 @ X5 @ X6 )
!= $true )
| ( $true
= ( sK2 @ X2 @ X1 @ X0 @ X5 @ X6 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
! [X7: a > a > $o] :
( ? [X8: a] :
( $true
!= ( X7 @ X8 @ X8 ) )
=> ( ( X7 @ ( sK3 @ X7 ) @ ( sK3 @ X7 ) )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
! [X2: a > a > $o,X7: a > a > $o] :
( ? [X9: a,X10: a] :
( ( ( X2 @ X9 @ X10 )
= $true )
& ( ( X7 @ X9 @ X10 )
!= $true ) )
=> ( ( $true
= ( X2 @ ( sK4 @ X7 @ X2 ) @ ( sK5 @ X7 @ X2 ) ) )
& ( $true
!= ( X7 @ ( sK4 @ X7 @ X2 ) @ ( sK5 @ X7 @ X2 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
! [X0: a,X1: a,X2: a > a > $o] :
( ( ( ( sP1 @ X2 @ X1 @ X0 )
= $true )
| ? [X3: a > a > $o] :
( ( $true
!= ( X3 @ X1 @ X0 ) )
& ! [X4: a] :
( ( X3 @ X4 @ X4 )
= $true )
& ! [X5: a,X6: a] :
( ( ( X2 @ X5 @ X6 )
!= $true )
| ( ( X3 @ X5 @ X6 )
= $true ) ) ) )
& ( ! [X7: a > a > $o] :
( ( $true
= ( X7 @ X1 @ X0 ) )
| ? [X8: a] :
( $true
!= ( X7 @ X8 @ X8 ) )
| ? [X9: a,X10: a] :
( ( ( X2 @ X9 @ X10 )
= $true )
& ( ( X7 @ X9 @ X10 )
!= $true ) ) )
| ( ( sP1 @ X2 @ X1 @ X0 )
!= $true ) ) ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,plain,
! [X2: a,X0: a,X1: a > a > $o] :
( ( ( $true
= ( sP1 @ X1 @ X0 @ X2 ) )
| ? [X3: a > a > $o] :
( ( ( X3 @ X0 @ X2 )
!= $true )
& ! [X4: a] :
( ( X3 @ X4 @ X4 )
= $true )
& ! [X5: a,X6: a] :
( ( ( X1 @ X5 @ X6 )
!= $true )
| ( ( X3 @ X5 @ X6 )
= $true ) ) ) )
& ( ! [X3: a > a > $o] :
( ( ( X3 @ X0 @ X2 )
= $true )
| ? [X4: a] :
( ( X3 @ X4 @ X4 )
!= $true )
| ? [X5: a,X6: a] :
( ( ( X1 @ X5 @ X6 )
= $true )
& ( ( X3 @ X5 @ X6 )
!= $true ) ) )
| ( $true
!= ( sP1 @ X1 @ X0 @ X2 ) ) ) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X2: a,X0: a,X1: a > a > $o] :
( ( $true
= ( sP1 @ X1 @ X0 @ X2 ) )
<=> ! [X3: a > a > $o] :
( ( ( X3 @ X0 @ X2 )
= $true )
| ? [X4: a] :
( ( X3 @ X4 @ X4 )
!= $true )
| ? [X5: a,X6: a] :
( ( ( X1 @ X5 @ X6 )
= $true )
& ( ( X3 @ X5 @ X6 )
!= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f28,plain,
! [X2: a > a > $o,X0: a,X1: a] :
( ( ( sK2 @ X2 @ X1 @ X0 @ X1 @ X0 )
!= $true )
| ( ( sP1 @ X2 @ X1 @ X0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f266,plain,
( spl9_2
| ~ spl9_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f265]) ).
thf(f265,plain,
( $false
| spl9_2
| ~ spl9_4 ),
inference(subsumption_resolution,[status(thm)],[f264,f66]) ).
thf(f66,plain,
! [X0: a > a > $o,X1: a] :
( ( sP1 @ X0 @ X1 @ X1 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f65]) ).
thf(f65,plain,
! [X0: a > a > $o,X1: a] :
( ( $true != $true )
| ( ( sP1 @ X0 @ X1 @ X1 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f64]) ).
thf(f64,plain,
! [X0: a > a > $o,X1: a] :
( ( ( sP1 @ X0 @ X1 @ X1 )
= $true )
| ( $true != $true )
| ( ( sP1 @ X0 @ X1 @ X1 )
= $true ) ),
inference(superposition,[status(thm)],[f28,f27]) ).
thf(f27,plain,
! [X2: a > a > $o,X0: a,X1: a,X4: a] :
( ( $true
= ( sK2 @ X2 @ X1 @ X0 @ X4 @ X4 ) )
| ( ( sP1 @ X2 @ X1 @ X0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f264,plain,
( ( $true
!= ( sP1 @ sK8 @ sK6 @ sK6 ) )
| spl9_2
| ~ spl9_4 ),
inference(backward_demodulation,[status(thm)],[f42,f259]) ).
thf(f259,plain,
( ( sK6 = sK7 )
| ~ spl9_4 ),
inference(avatar_component_clause,[status(thm)],[f257]) ).
thf(f257,definition,
( spl9_4
<=> ( sK6 = sK7 ) ),
introduced(definition,[new_symbols(naming,[spl9_4])],[avatar_definition]) ).
thf(f260,plain,
( spl9_3
| spl9_4
| ~ spl9_1 ),
inference(avatar_split_clause,[status(thm)],[f249,f36,f257,f253]) ).
thf(f36,definition,
( spl9_1
<=> ( ( sP0 @ sK8 @ sK7 @ sK6 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl9_1])],[avatar_definition]) ).
thf(f249,plain,
( ( ( sK8 @ sK7 @ sK6 )
= $true )
| ( sK6 = sK7 )
| ~ spl9_1 ),
inference(trivial_inequality_removal,[status(thm)],[f246]) ).
thf(f246,plain,
( ( ( sK8 @ sK7 @ sK6 )
= $true )
| ( sK6 = sK7 )
| ( $true != $true )
| ~ spl9_1 ),
inference(superposition,[status(thm)],[f29,f37]) ).
thf(f37,plain,
( ( ( sP0 @ sK8 @ sK7 @ sK6 )
= $true )
| ~ spl9_1 ),
inference(avatar_component_clause,[status(thm)],[f36]) ).
thf(f29,plain,
! [X2: a > a > $o,X0: a,X1: a] :
( ( ( sP0 @ X2 @ X1 @ X0 )
!= $true )
| ( $true
= ( X2 @ X1 @ X0 ) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: a,X1: a,X2: a > a > $o] :
( ( ( ( sP0 @ X2 @ X1 @ X0 )
= $true )
| ( ( X0 != X1 )
& ( $true
!= ( X2 @ X1 @ X0 ) ) ) )
& ( ( X0 = X1 )
| ( $true
= ( X2 @ X1 @ X0 ) )
| ( ( sP0 @ X2 @ X1 @ X0 )
!= $true ) ) ),
inference(rectify,[status(thm)],[f18]) ).
thf(f18,plain,
! [X2: a,X0: a,X1: a > a > $o] :
( ( ( ( sP0 @ X1 @ X0 @ X2 )
= $true )
| ( ( X0 != X2 )
& ( ( X1 @ X0 @ X2 )
!= $true ) ) )
& ( ( X0 = X2 )
| ( ( X1 @ X0 @ X2 )
= $true )
| ( ( sP0 @ X1 @ X0 @ X2 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f17]) ).
thf(f17,plain,
! [X2: a,X0: a,X1: a > a > $o] :
( ( ( ( sP0 @ X1 @ X0 @ X2 )
= $true )
| ( ( X0 != X2 )
& ( ( X1 @ X0 @ X2 )
!= $true ) ) )
& ( ( X0 = X2 )
| ( ( X1 @ X0 @ X2 )
= $true )
| ( ( sP0 @ X1 @ X0 @ X2 )
!= $true ) ) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
! [X2: a,X0: a,X1: a > a > $o] :
( ( ( sP0 @ X1 @ X0 @ X2 )
= $true )
<=> ( ( X0 = X2 )
| ( ( X1 @ X0 @ X2 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f245,plain,
( spl9_1
| ~ spl9_2 ),
inference(avatar_contradiction_clause,[status(thm)],[f244]) ).
thf(f244,plain,
( $false
| spl9_1
| ~ spl9_2 ),
inference(subsumption_resolution,[status(thm)],[f243,f38]) ).
thf(f38,plain,
( ( ( sP0 @ sK8 @ sK7 @ sK6 )
!= $true )
| spl9_1 ),
inference(avatar_component_clause,[status(thm)],[f36]) ).
thf(f243,plain,
( ( ( sP0 @ sK8 @ sK7 @ sK6 )
= $true )
| spl9_1
| ~ spl9_2 ),
inference(trivial_inequality_removal,[status(thm)],[f240]) ).
thf(f240,plain,
( ( ( sP0 @ sK8 @ sK7 @ sK6 )
= $true )
| ( $true != $true )
| spl9_1
| ~ spl9_2 ),
inference(superposition,[status(thm)],[f239,f41]) ).
thf(f41,plain,
( ( $true
= ( sP1 @ sK8 @ sK7 @ sK6 ) )
| ~ spl9_2 ),
inference(avatar_component_clause,[status(thm)],[f40]) ).
thf(f239,plain,
( ! [X0: a,X1: a] :
( ( $true
!= ( sP1 @ sK8 @ X0 @ X1 ) )
| ( $true
= ( sP0 @ sK8 @ X0 @ X1 ) ) )
| spl9_1
| ~ spl9_2 ),
inference(subsumption_resolution,[status(thm)],[f238,f34]) ).
thf(f34,plain,
! [X2: a > a > $o,X1: a] :
( $true
= ( sP0 @ X2 @ X1 @ X1 ) ),
inference(equality_resolution,[status(thm)],[f31]) ).
thf(f31,plain,
! [X2: a > a > $o,X0: a,X1: a] :
( ( ( sP0 @ X2 @ X1 @ X0 )
= $true )
| ( X0 != X1 ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f238,plain,
( ! [X0: a,X1: a] :
( ( $true
= ( sP0 @ sK8 @ X0 @ X1 ) )
| ( $true
!= ( sP1 @ sK8 @ X0 @ X1 ) )
| ( $true
!= ( sP0 @ sK8 @ ( sK3 @ ( sP0 @ sK8 ) ) @ ( sK3 @ ( sP0 @ sK8 ) ) ) ) )
| spl9_1
| ~ spl9_2 ),
inference(subsumption_resolution,[status(thm)],[f235,f38]) ).
thf(f235,plain,
( ! [X0: a,X1: a] :
( ( ( sP0 @ sK8 @ sK7 @ sK6 )
= $true )
| ( $true
!= ( sP1 @ sK8 @ X0 @ X1 ) )
| ( $true
!= ( sP0 @ sK8 @ ( sK3 @ ( sP0 @ sK8 ) ) @ ( sK3 @ ( sP0 @ sK8 ) ) ) )
| ( $true
= ( sP0 @ sK8 @ X0 @ X1 ) ) )
| ~ spl9_2 ),
inference(trivial_inequality_removal,[status(thm)],[f231]) ).
thf(f231,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( $true
!= ( sP0 @ sK8 @ ( sK3 @ ( sP0 @ sK8 ) ) @ ( sK3 @ ( sP0 @ sK8 ) ) ) )
| ( $true
= ( sP0 @ sK8 @ X0 @ X1 ) )
| ( ( sP0 @ sK8 @ sK7 @ sK6 )
= $true )
| ( $true
!= ( sP1 @ sK8 @ X0 @ X1 ) ) )
| ~ spl9_2 ),
inference(superposition,[status(thm)],[f24,f132]) ).
thf(f132,plain,
( ! [X0: a > a > $o] :
( ( $true
= ( sP0 @ sK8 @ ( sK4 @ ( sP0 @ X0 ) @ sK8 ) @ ( sK5 @ ( sP0 @ X0 ) @ sK8 ) ) )
| ( ( sP0 @ X0 @ sK7 @ sK6 )
= $true ) )
| ~ spl9_2 ),
inference(trivial_inequality_removal,[status(thm)],[f131]) ).
thf(f131,plain,
( ! [X0: a > a > $o] :
( ( $true
= ( sP0 @ sK8 @ ( sK4 @ ( sP0 @ X0 ) @ sK8 ) @ ( sK5 @ ( sP0 @ X0 ) @ sK8 ) ) )
| ( ( sP0 @ X0 @ sK7 @ sK6 )
= $true )
| ( $true != $true ) )
| ~ spl9_2 ),
inference(superposition,[status(thm)],[f30,f110]) ).
thf(f110,plain,
( ! [X0: a > a > $o] :
( ( $true
= ( sK8 @ ( sK4 @ ( sP0 @ X0 ) @ sK8 ) @ ( sK5 @ ( sP0 @ X0 ) @ sK8 ) ) )
| ( ( sP0 @ X0 @ sK7 @ sK6 )
= $true ) )
| ~ spl9_2 ),
inference(trivial_inequality_removal,[status(thm)],[f108]) ).
thf(f108,plain,
( ! [X0: a > a > $o] :
( ( $true
= ( sK8 @ ( sK4 @ ( sP0 @ X0 ) @ sK8 ) @ ( sK5 @ ( sP0 @ X0 ) @ sK8 ) ) )
| ( $true != $true )
| ( ( sP0 @ X0 @ sK7 @ sK6 )
= $true ) )
| ~ spl9_2 ),
inference(superposition,[status(thm)],[f99,f41]) ).
thf(f99,plain,
! [X2: a,X3: a,X0: a > a > $o,X1: a > a > $o] :
( ( $true
!= ( sP1 @ X1 @ X2 @ X3 ) )
| ( $true
= ( sP0 @ X0 @ X2 @ X3 ) )
| ( $true
= ( X1 @ ( sK4 @ ( sP0 @ X0 ) @ X1 ) @ ( sK5 @ ( sP0 @ X0 ) @ X1 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f96]) ).
thf(f96,plain,
! [X2: a,X3: a,X0: a > a > $o,X1: a > a > $o] :
( ( $true
= ( X1 @ ( sK4 @ ( sP0 @ X0 ) @ X1 ) @ ( sK5 @ ( sP0 @ X0 ) @ X1 ) ) )
| ( $true
= ( sP0 @ X0 @ X2 @ X3 ) )
| ( $true
!= ( sP1 @ X1 @ X2 @ X3 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f25,f34]) ).
thf(f25,plain,
! [X2: a > a > $o,X0: a,X1: a,X7: a > a > $o] :
( ( ( X7 @ ( sK3 @ X7 ) @ ( sK3 @ X7 ) )
!= $true )
| ( $true
= ( X2 @ ( sK4 @ X7 @ X2 ) @ ( sK5 @ X7 @ X2 ) ) )
| ( ( sP1 @ X2 @ X1 @ X0 )
!= $true )
| ( $true
= ( X7 @ X1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f30,plain,
! [X2: a > a > $o,X0: a,X1: a] :
( ( $true
!= ( X2 @ X1 @ X0 ) )
| ( ( sP0 @ X2 @ X1 @ X0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f24,plain,
! [X2: a > a > $o,X0: a,X1: a,X7: a > a > $o] :
( ( $true
!= ( X7 @ ( sK4 @ X7 @ X2 ) @ ( sK5 @ X7 @ X2 ) ) )
| ( ( X7 @ ( sK3 @ X7 ) @ ( sK3 @ X7 ) )
!= $true )
| ( $true
= ( X7 @ X1 @ X0 ) )
| ( ( sP1 @ X2 @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f44,plain,
( spl9_1
| spl9_2 ),
inference(avatar_split_clause,[status(thm)],[f32,f40,f36]) ).
thf(f32,plain,
( ( ( sP0 @ sK8 @ sK7 @ sK6 )
= $true )
| ( $true
= ( sP1 @ sK8 @ sK7 @ sK6 ) ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ( $true
!= ( sP1 @ sK8 @ sK7 @ sK6 ) )
| ( ( sP0 @ sK8 @ sK7 @ sK6 )
!= $true ) )
& ( ( $true
= ( sP1 @ sK8 @ sK7 @ sK6 ) )
| ( ( sP0 @ sK8 @ sK7 @ sK6 )
= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f21,f22]) ).
thf(f22,plain,
( ? [X0: a,X1: a,X2: a > a > $o] :
( ( ( ( sP1 @ X2 @ X1 @ X0 )
!= $true )
| ( ( sP0 @ X2 @ X1 @ X0 )
!= $true ) )
& ( ( ( sP1 @ X2 @ X1 @ X0 )
= $true )
| ( ( sP0 @ X2 @ X1 @ X0 )
= $true ) ) )
=> ( ( ( $true
!= ( sP1 @ sK8 @ sK7 @ sK6 ) )
| ( ( sP0 @ sK8 @ sK7 @ sK6 )
!= $true ) )
& ( ( $true
= ( sP1 @ sK8 @ sK7 @ sK6 ) )
| ( ( sP0 @ sK8 @ sK7 @ sK6 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f21,plain,
? [X0: a,X1: a,X2: a > a > $o] :
( ( ( ( sP1 @ X2 @ X1 @ X0 )
!= $true )
| ( ( sP0 @ X2 @ X1 @ X0 )
!= $true ) )
& ( ( ( sP1 @ X2 @ X1 @ X0 )
= $true )
| ( ( sP0 @ X2 @ X1 @ X0 )
= $true ) ) ),
inference(rectify,[status(thm)],[f20]) ).
thf(f20,plain,
? [X2: a,X0: a,X1: a > a > $o] :
( ( ( $true
!= ( sP1 @ X1 @ X0 @ X2 ) )
| ( ( sP0 @ X1 @ X0 @ X2 )
!= $true ) )
& ( ( $true
= ( sP1 @ X1 @ X0 @ X2 ) )
| ( ( sP0 @ X1 @ X0 @ X2 )
= $true ) ) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
? [X2: a,X0: a,X1: a > a > $o] :
( ( ( sP0 @ X1 @ X0 @ X2 )
= $true )
<~> ( $true
= ( sP1 @ X1 @ X0 @ X2 ) ) ),
inference(definition_folding,[status(thm)],[f7,f9,f8]) ).
thf(f7,plain,
? [X2: a,X0: a,X1: a > a > $o] :
( ( ( X0 = X2 )
| ( ( X1 @ X0 @ X2 )
= $true ) )
<~> ! [X3: a > a > $o] :
( ( ( X3 @ X0 @ X2 )
= $true )
| ? [X4: a] :
( ( X3 @ X4 @ X4 )
!= $true )
| ? [X5: a,X6: a] :
( ( ( X1 @ X5 @ X6 )
= $true )
& ( ( X3 @ X5 @ X6 )
!= $true ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
? [X1: a > a > $o,X2: a,X0: a] :
( ! [X3: a > a > $o] :
( ( ( X3 @ X0 @ X2 )
= $true )
| ? [X5: a,X6: a] :
( ( ( X1 @ X5 @ X6 )
= $true )
& ( ( X3 @ X5 @ X6 )
!= $true ) )
| ? [X4: a] :
( ( X3 @ X4 @ X4 )
!= $true ) )
<~> ( ( X0 = X2 )
| ( ( X1 @ X0 @ X2 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X1: a > a > $o,X2: a,X0: a] :
( ! [X3: a > a > $o] :
( ( ! [X6: a,X5: a] :
( ( ( X1 @ X5 @ X6 )
= $true )
=> ( ( X3 @ X5 @ X6 )
= $true ) )
& ! [X4: a] :
( ( X3 @ X4 @ X4 )
= $true ) )
=> ( ( X3 @ X0 @ X2 )
= $true ) )
<=> ( ( X0 = X2 )
| ( ( X1 @ X0 @ X2 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a,X1: a > a > $o,X2: a] :
( ! [X3: a > a > $o] :
( ( ! [X4: a] : ( X3 @ X4 @ X4 )
& ! [X5: a,X6: a] :
( ( X1 @ X5 @ X6 )
=> ( X3 @ X5 @ X6 ) ) )
=> ( X3 @ X0 @ X2 ) )
<=> ( ( X1 @ X0 @ X2 )
| ( X0 = X2 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a,X0: a > a > $o,X2: a] :
( ! [X3: a > a > $o] :
( ( ! [X4: a] : ( X3 @ X4 @ X4 )
& ! [X4: a,X5: a] :
( ( X0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) ) )
=> ( X3 @ X1 @ X2 ) )
<=> ( ( X0 @ X1 @ X2 )
| ( X1 = X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: a,X0: a > a > $o,X2: a] :
( ! [X3: a > a > $o] :
( ( ! [X4: a] : ( X3 @ X4 @ X4 )
& ! [X4: a,X5: a] :
( ( X0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) ) )
=> ( X3 @ X1 @ X2 ) )
<=> ( ( X0 @ X1 @ X2 )
| ( X1 = X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.QTwIpeUg66/DTF2THF_31564.p',cTHM523_pme) ).
thf(f43,plain,
( ~ spl9_1
| ~ spl9_2 ),
inference(avatar_split_clause,[status(thm)],[f33,f40,f36]) ).
thf(f33,plain,
( ( ( sP0 @ sK8 @ sK7 @ sK6 )
!= $true )
| ( $true
!= ( sP1 @ sK8 @ sK7 @ sK6 ) ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SEV074^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.25 % Computer : n024.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue Feb 24 07:39:40 EST 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.32 ---- Original DTF file ---
% 0.07/0.32 thf(spec,logic,$$dhol).
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 % File : SEV074^5 : TPTP v9.2.1. Released v4.0.0.
% 0.07/0.32 % Domain : Set Theory (Relations)
% 0.07/0.32 % Problem : TPS problem THM523
% 0.07/0.32 % Version : Especial.
% 0.07/0.32 % English : Theorem about reflexive closure of relations.
% 0.07/0.32
% 0.07/0.32 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.07/0.32 % Source : [Bro09]
% 0.07/0.32 % Names : tps_0522 [Bro09]
% 0.07/0.32 % : THM523 [TPS]
% 0.07/0.32
% 0.07/0.32 % Status : Theorem
% 0.07/0.32 % Rating : 0.67 v9.1.0, 0.62 v9.0.0, 0.60 v8.2.0, 0.69 v8.1.0, 0.73 v7.5.0, 0.57 v7.4.0, 0.78 v7.2.0, 0.88 v7.1.0, 0.75 v7.0.0, 0.71 v6.4.0, 0.67 v6.3.0, 0.60 v6.2.0, 0.71 v5.5.0, 0.83 v5.4.0, 0.80 v4.1.0, 0.67 v4.0.0
% 0.07/0.32 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.07/0.32 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.07/0.32 % Maximal formula atoms : 1 ( 1 avg)
% 0.07/0.32 % Number of connectives : 15 ( 0 ~; 1 |; 1 &; 10 @)
% 0.07/0.32 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.07/0.32 % Maximal formula depth : 13 ( 13 avg)
% 0.07/0.32 % Number of types : 2 ( 1 usr)
% 0.07/0.32 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.07/0.32 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.07/0.32 % Number of variables : 7 ( 0 ^; 7 !; 0 ?; 7 :)
% 0.07/0.32 % SPC : TH0_THM_EQU_NAR
% 0.07/0.32
% 0.07/0.32 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.07/0.32 % project in the Department of Mathematical Sciences at Carnegie
% 0.07/0.32 % Mellon University. Distributed under the Creative Commons copyleft
% 0.07/0.32 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.07/0.32 % : Polymorphic definitions expanded.
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 thf(a_type,type,
% 0.07/0.32 a: $tType ).
% 0.07/0.32
% 0.07/0.32 thf(cTHM523_pme,conjecture,
% 0.07/0.32 ! [Xr: a > a > $o,Xx: a,Xy: a] :
% 0.07/0.32 ( ( ( Xr @ Xx @ Xy )
% 0.07/0.32 | ( Xx = Xy ) )
% 0.07/0.32 <=> ! [Xp: a > a > $o] :
% 0.07/0.32 ( ( ! [Xx0: a,Xy0: a] :
% 0.07/0.32 ( ( Xr @ Xx0 @ Xy0 )
% 0.07/0.32 => ( Xp @ Xx0 @ Xy0 ) )
% 0.07/0.32 & ! [Xx0: a] : ( Xp @ Xx0 @ Xx0 ) )
% 0.07/0.32 => ( Xp @ Xx @ Xy ) ) ) ).
% 0.07/0.32
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 ------------------------
% 0.84/0.88 ---- Embedded in THF ---
% 0.84/0.88 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.84/0.88 %%% Generated on Tue Feb 24 07:39:41 EST 2026
% 0.84/0.88 %%% using '$$dhol' embedding, version 1.3.0.
% 0.84/0.88 %%% Logic specification used:
% 0.84/0.88 %%% thf(spec, logic, $$dhol).
% 0.84/0.88
% 0.84/0.88 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.QTwIpeUg66/DTF2DTF31564.p
% See solution above
% 0.84/0.88 ------------------------
% 0.84/0.88 ---- Cleaned THF ---
% 0.84/0.88 thf(a_type,type,
% 0.84/0.88 a: $tType ).
% 0.84/0.88
% 0.84/0.88 thf(cTHM523_pme,conjecture,
% 0.84/0.88 ! [Xr: a > a > $o,Xx: a,Xy: a] :
% 0.84/0.88 ( ( ( Xr @ Xx @ Xy )
% 0.84/0.88 | ( Xx = Xy ) )
% 0.84/0.88 <=> ! [Xp: a > a > $o] :
% 0.84/0.88 ( ( ! [Xx0: a,Xy0: a] :
% 0.84/0.88 ( ( Xr @ Xx0 @ Xy0 )
% 0.84/0.88 => ( Xp @ Xx0 @ Xy0 ) )
% 0.84/0.88 & ! [Xx0: a] : ( Xp @ Xx0 @ Xx0 ) )
% 0.84/0.88 => ( Xp @ Xx @ Xy ) ) ) ).
% 0.84/0.88 ------------------------
% 1.00/0.90 % (31831)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_31564 for (3000ds/275Mi)
% 1.00/0.90 % (31828)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_31564 for (3000ds/27Mi)
% 1.00/0.90 % (31827)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_31564 for (3000ds/4Mi)
% 1.00/0.90 % (31830)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_31564 for (3000ds/2Mi)
% 1.00/0.90 % (31826)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_31564 for (3000ds/183Mi)
% 1.00/0.90 % (31829)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_31564 for (3000ds/2Mi)
% 1.00/0.90 % (31832)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_31564 for (3000ds/18Mi)
% 1.00/0.90 % (31829)Instruction limit reached!
% 1.00/0.90 % (31829)------------------------------
% 1.00/0.90 % (31829)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.00/0.90 % (31829)Termination reason: Unknown
% 1.00/0.90 % (31829)Termination phase: Saturation
% 1.00/0.90
% 1.00/0.90 % (31829)Memory used [KB]: 5500
% 1.00/0.90 % (31829)Time elapsed: 0.002 s
% 1.00/0.90 % (31829)Instructions burned: 2 (million)
% 1.00/0.90 % (31829)------------------------------
% 1.00/0.90 % (31829)------------------------------
% 1.00/0.90 % (31830)Instruction limit reached!
% 1.00/0.90 % (31830)------------------------------
% 1.00/0.90 % (31830)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.00/0.90 % (31830)Termination reason: Unknown
% 1.00/0.90 % (31830)Termination phase: Saturation
% 1.00/0.90
% 1.00/0.90 % (31830)Memory used [KB]: 5500
% 1.00/0.90 % (31830)Time elapsed: 0.002 s
% 1.00/0.90 % (31830)Instructions burned: 2 (million)
% 1.00/0.90 % (31830)------------------------------
% 1.00/0.90 % (31830)------------------------------
% 1.00/0.90 % (31827)Instruction limit reached!
% 1.00/0.90 % (31827)------------------------------
% 1.00/0.90 % (31827)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.00/0.90 % (31827)Termination reason: Unknown
% 1.00/0.90 % (31827)Termination phase: Saturation
% 1.00/0.90
% 1.00/0.90 % (31827)Memory used [KB]: 5500
% 1.00/0.90 % (31827)Time elapsed: 0.003 s
% 1.00/0.90 % (31827)Instructions burned: 4 (million)
% 1.00/0.90 % (31827)------------------------------
% 1.00/0.90 % (31827)------------------------------
% 1.00/0.90 % (31828)Refutation not found, incomplete strategy
% 1.00/0.90 % (31828)------------------------------
% 1.00/0.90 % (31828)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.00/0.90 % (31828)Termination reason: Refutation not found, incomplete strategy
% 1.00/0.90
% 1.00/0.90
% 1.00/0.90 % (31828)Memory used [KB]: 5500
% 1.00/0.90 % (31828)Time elapsed: 0.004 s
% 1.00/0.90 % (31828)Instructions burned: 7 (million)
% 1.00/0.90 % (31828)------------------------------
% 1.00/0.90 % (31828)------------------------------
% 1.00/0.90 % (31831)Refutation not found, incomplete strategy
% 1.00/0.90 % (31831)------------------------------
% 1.00/0.90 % (31831)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.00/0.90 % (31831)Termination reason: Refutation not found, incomplete strategy
% 1.00/0.90
% 1.00/0.90
% 1.00/0.90 % (31831)Memory used [KB]: 5628
% 1.00/0.90 % (31831)Time elapsed: 0.004 s
% 1.00/0.90 % (31831)Instructions burned: 9 (million)
% 1.00/0.90 % (31831)------------------------------
% 1.00/0.90 % (31831)------------------------------
% 1.00/0.90 % (31832)Instruction limit reached!
% 1.00/0.90 % (31832)------------------------------
% 1.00/0.90 % (31832)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.00/0.90 % (31832)Termination reason: Unknown
% 1.00/0.90 % (31832)Termination phase: Saturation
% 1.00/0.90
% 1.00/0.90 % (31832)Memory used [KB]: 5628
% 1.00/0.90 % (31832)Time elapsed: 0.007 s
% 1.00/0.90 % (31832)Instructions burned: 19 (million)
% 1.00/0.90 % (31832)------------------------------
% 1.00/0.90 % (31832)------------------------------
% 1.00/0.91 % (31833)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_31564 for (2999ds/3Mi)
% 1.00/0.91 % (31834)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_31564 for (2999ds/37Mi)
% 1.00/0.91 % (31835)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_31564 for (2999ds/15Mi)
% 1.00/0.91 % (31833)Instruction limit reached!
% 1.00/0.91 % (31833)------------------------------
% 1.00/0.91 % (31833)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.00/0.91 % (31833)Termination reason: Unknown
% 1.00/0.91 % (31833)Termination phase: Saturation
% 1.00/0.91
% 1.00/0.91 % (31833)Memory used [KB]: 5500
% 1.00/0.91 % (31833)Time elapsed: 0.002 s
% 1.00/0.91 % (31833)Instructions burned: 3 (million)
% 1.00/0.91 % (31833)------------------------------
% 1.00/0.91 % (31833)------------------------------
% 1.00/0.91 % (31836)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_31564 for (2999ds/3Mi)
% 1.00/0.91 % (31837)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_31564 for (2999ds/1041Mi)
% 1.00/0.91 % (31836)Instruction limit reached!
% 1.00/0.91 % (31836)------------------------------
% 1.00/0.91 % (31836)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.00/0.91 % (31836)Termination reason: Unknown
% 1.00/0.91 % (31836)Termination phase: Saturation
% 1.00/0.91
% 1.00/0.91 % (31836)Memory used [KB]: 5500
% 1.00/0.91 % (31836)Time elapsed: 0.002 s
% 1.00/0.91 % (31836)Instructions burned: 3 (million)
% 1.00/0.91 % (31836)------------------------------
% 1.00/0.91 % (31836)------------------------------
% 1.00/0.91 % (31838)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_31564 for (2999ds/7Mi)
% 1.00/0.91 % (31835)Instruction limit reached!
% 1.00/0.91 % (31835)------------------------------
% 1.00/0.91 % (31835)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.00/0.91 % (31835)Termination reason: Unknown
% 1.00/0.91 % (31835)Termination phase: Saturation
% 1.00/0.91
% 1.00/0.91 % (31835)Memory used [KB]: 5628
% 1.00/0.91 % (31835)Time elapsed: 0.006 s
% 1.00/0.91 % (31835)Instructions burned: 15 (million)
% 1.00/0.91 % (31835)------------------------------
% 1.00/0.91 % (31835)------------------------------
% 1.00/0.91 % (31838)Instruction limit reached!
% 1.00/0.91 % (31838)------------------------------
% 1.00/0.91 % (31838)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.00/0.91 % (31838)Termination reason: Unknown
% 1.00/0.91 % (31838)Termination phase: Saturation
% 1.00/0.91
% 1.00/0.91 % (31838)Memory used [KB]: 1023
% 1.00/0.91 % (31838)Time elapsed: 0.003 s
% 1.00/0.91 % (31838)Instructions burned: 7 (million)
% 1.00/0.91 % (31838)------------------------------
% 1.00/0.91 % (31838)------------------------------
% 1.00/0.92 % (31839)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_31564 for (2999ds/16Mi)
% 1.00/0.92 % (31834)Instruction limit reached!
% 1.00/0.92 % (31834)------------------------------
% 1.00/0.92 % (31834)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.00/0.92 % (31834)Termination reason: Unknown
% 1.00/0.92 % (31834)Termination phase: Saturation
% 1.00/0.92
% 1.00/0.92 % (31834)Memory used [KB]: 5884
% 1.00/0.92 % (31834)Time elapsed: 0.013 s
% 1.00/0.92 % (31834)Instructions burned: 40 (million)
% 1.00/0.92 % (31834)------------------------------
% 1.00/0.92 % (31834)------------------------------
% 1.00/0.92 % (31840)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_31564 for (2999ds/3Mi)
% 1.00/0.92 % (31840)Instruction limit reached!
% 1.00/0.92 % (31840)------------------------------
% 1.00/0.92 % (31840)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.00/0.92 % (31840)Termination reason: Unknown
% 1.00/0.92 % (31840)Termination phase: Saturation
% 1.00/0.92
% 1.00/0.92 % (31840)Memory used [KB]: 5500
% 1.00/0.92 % (31840)Time elapsed: 0.002 s
% 1.00/0.92 % (31840)Instructions burned: 4 (million)
% 1.00/0.92 % (31840)------------------------------
% 1.00/0.92 % (31840)------------------------------
% 1.00/0.92 % (31841)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_31564 for (2999ds/3Mi)
% 1.00/0.92 % (31839)Instruction limit reached!
% 1.00/0.92 % (31839)------------------------------
% 1.00/0.92 % (31839)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.00/0.92 % (31839)Termination reason: Unknown
% 1.00/0.92 % (31839)Termination phase: Saturation
% 1.00/0.92
% 1.00/0.92 % (31839)Memory used [KB]: 5628
% 1.00/0.92 % (31839)Time elapsed: 0.006 s
% 1.00/0.92 % (31839)Instructions burned: 16 (million)
% 1.00/0.92 % (31839)------------------------------
% 1.00/0.92 % (31839)------------------------------
% 1.00/0.92 % (31841)Instruction limit reached!
% 1.00/0.92 % (31841)------------------------------
% 1.00/0.92 % (31841)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.00/0.92 % (31841)Termination reason: Unknown
% 1.00/0.92 % (31841)Termination phase: Saturation
% 1.00/0.92
% 1.00/0.92 % (31841)Memory used [KB]: 1023
% 1.00/0.92 % (31841)Time elapsed: 0.002 s
% 1.00/0.92 % (31841)Instructions burned: 4 (million)
% 1.00/0.92 % (31841)------------------------------
% 1.00/0.92 % (31841)------------------------------
% 1.00/0.92 % (31842)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_31564 for (2999ds/7Mi)
% 1.00/0.92 % (31842)Instruction limit reached!
% 1.00/0.92 % (31842)------------------------------
% 1.00/0.92 % (31842)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.00/0.92 % (31842)Termination reason: Unknown
% 1.00/0.92 % (31842)Termination phase: Saturation
% 1.00/0.92
% 1.00/0.92 % (31842)Memory used [KB]: 5500
% 1.00/0.92 % (31842)Time elapsed: 0.003 s
% 1.00/0.92 % (31842)Instructions burned: 7 (million)
% 1.00/0.92 % (31842)------------------------------
% 1.00/0.92 % (31842)------------------------------
% 1.00/0.93 % (31843)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_31564 for (2999ds/3Mi)
% 1.00/0.93 % (31843)Instruction limit reached!
% 1.00/0.93 % (31843)------------------------------
% 1.00/0.93 % (31843)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.00/0.93 % (31843)Termination reason: Unknown
% 1.00/0.93 % (31843)Termination phase: Saturation
% 1.00/0.93
% 1.00/0.93 % (31843)Memory used [KB]: 5500
% 1.00/0.93 % (31843)Time elapsed: 0.002 s
% 1.00/0.93 % (31843)Instructions burned: 4 (million)
% 1.00/0.93 % (31843)------------------------------
% 1.00/0.93 % (31843)------------------------------
% 1.00/0.93 % (31844)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_31564 for (2999ds/4Mi)
% 1.00/0.93 % (31845)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_31564 for (2999ds/18Mi)
% 1.00/0.93 % (31844)Instruction limit reached!
% 1.00/0.93 % (31844)------------------------------
% 1.00/0.93 % (31844)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.00/0.93 % (31844)Termination reason: Unknown
% 1.00/0.93 % (31844)Termination phase: Saturation
% 1.00/0.93
% 1.00/0.93 % (31844)Memory used [KB]: 5500
% 1.00/0.93 % (31844)Time elapsed: 0.003 s
% 1.00/0.93 % (31844)Instructions burned: 6 (million)
% 1.00/0.93 % (31844)------------------------------
% 1.00/0.93 % (31844)------------------------------
% 1.00/0.93 % (31846)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_31564 for (2999ds/710Mi)
% 1.00/0.93 % (31845)Refutation not found, incomplete strategy
% 1.00/0.93 % (31845)------------------------------
% 1.00/0.93 % (31845)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.00/0.93 % (31845)Termination reason: Refutation not found, incomplete strategy
% 1.00/0.93
% 1.00/0.93
% 1.00/0.93 % (31845)Memory used [KB]: 5500
% 1.00/0.93 % (31845)Time elapsed: 0.003 s
% 1.00/0.93 % (31845)Instructions burned: 6 (million)
% 1.00/0.93 % (31845)------------------------------
% 1.00/0.93 % (31845)------------------------------
% 1.00/0.93 % (31847)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_31564 for (2999ds/6Mi)
% 1.00/0.94 % (31847)Instruction limit reached!
% 1.00/0.94 % (31847)------------------------------
% 1.00/0.94 % (31847)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.00/0.94 % (31847)Termination reason: Unknown
% 1.00/0.94 % (31847)Termination phase: Saturation
% 1.00/0.94
% 1.00/0.94 % (31847)Memory used [KB]: 5500
% 1.00/0.94 % (31847)Time elapsed: 0.003 s
% 1.00/0.94 % (31847)Instructions burned: 6 (million)
% 1.00/0.94 % (31847)------------------------------
% 1.00/0.94 % (31847)------------------------------
% 1.00/0.94 % (31848)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_31564 for (2999ds/902Mi)
% 1.00/0.94 % (31849)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_31564 for (2999ds/21Mi)
% 1.00/0.94 % (31850)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_31564 for (2999ds/5Mi)
% 1.00/0.95 % (31851)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_31564 for (2999ds/6Mi)
% 1.00/0.95 % (31850)Instruction limit reached!
% 1.00/0.95 % (31850)------------------------------
% 1.00/0.95 % (31850)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.00/0.95 % (31850)Termination reason: Unknown
% 1.00/0.95 % (31850)Termination phase: Saturation
% 1.00/0.95
% 1.00/0.95 % (31850)Memory used [KB]: 5500
% 1.00/0.95 % (31850)Time elapsed: 0.003 s
% 1.00/0.95 % (31850)Instructions burned: 6 (million)
% 1.00/0.95 % (31850)------------------------------
% 1.00/0.95 % (31850)------------------------------
% 1.00/0.95 % (31826)Instruction limit reached!
% 1.00/0.95 % (31826)------------------------------
% 1.00/0.95 % (31826)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.00/0.95 % (31826)Termination reason: Unknown
% 1.00/0.95 % (31826)Termination phase: Saturation
% 1.00/0.95
% 1.00/0.95 % (31826)Memory used [KB]: 6396
% 1.00/0.95 % (31826)Time elapsed: 0.052 s
% 1.00/0.95 % (31826)Instructions burned: 185 (million)
% 1.00/0.95 % (31826)------------------------------
% 1.00/0.95 % (31826)------------------------------
% 1.00/0.95 % (31851)Instruction limit reached!
% 1.00/0.95 % (31851)------------------------------
% 1.00/0.95 % (31851)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.00/0.95 % (31851)Termination reason: Unknown
% 1.00/0.95 % (31851)Termination phase: Saturation
% 1.00/0.95
% 1.00/0.95 % (31851)Memory used [KB]: 5500
% 1.00/0.95 % (31851)Time elapsed: 0.003 s
% 1.00/0.95 % (31851)Instructions burned: 8 (million)
% 1.00/0.95 % (31851)------------------------------
% 1.00/0.95 % (31851)------------------------------
% 1.00/0.95 % (31849)Instruction limit reached!
% 1.00/0.95 % (31849)------------------------------
% 1.00/0.95 % (31849)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.00/0.95 % (31849)Termination reason: Unknown
% 1.00/0.95 % (31849)Termination phase: Saturation
% 1.00/0.95
% 1.00/0.95 % (31849)Memory used [KB]: 5756
% 1.00/0.95 % (31849)Time elapsed: 0.009 s
% 1.00/0.95 % (31849)Instructions burned: 23 (million)
% 1.00/0.95 % (31849)------------------------------
% 1.00/0.95 % (31849)------------------------------
% 1.00/0.95 % (31837)Refutation not found, incomplete strategy
% 1.00/0.95 % (31837)------------------------------
% 1.00/0.95 % (31837)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.00/0.95 % (31837)Termination reason: Refutation not found, incomplete strategy
% 1.00/0.95
% 1.00/0.95
% 1.00/0.95 % (31837)Memory used [KB]: 5884
% 1.00/0.95 % (31837)Time elapsed: 0.044 s
% 1.00/0.95 % (31837)Instructions burned: 142 (million)
% 1.00/0.95 % (31837)------------------------------
% 1.00/0.95 % (31837)------------------------------
% 1.00/0.95 % (31852)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_31564 for (2999ds/377Mi)
% 1.00/0.96 % (31853)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_31564 for (2999ds/779Mi)
% 1.00/0.96 % (31854)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_31564 for (2999ds/19Mi)
% 1.00/0.96 % (31855)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_31564 for (2999ds/879Mi)
% 1.00/0.96 % (31854)Refutation not found, incomplete strategy
% 1.00/0.96 % (31854)------------------------------
% 1.00/0.96 % (31854)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.00/0.96 % (31854)Termination reason: Refutation not found, incomplete strategy
% 1.00/0.96
% 1.00/0.96
% 1.00/0.96 % (31854)Memory used [KB]: 5500
% 1.00/0.96 % (31854)Time elapsed: 0.004 s
% 1.00/0.96 % (31854)Instructions burned: 10 (million)
% 1.00/0.96 % (31854)------------------------------
% 1.00/0.96 % (31854)------------------------------
% 1.00/0.96 % (31856)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_31564 for (2999ds/17Mi)
% 1.00/0.96 % (31855)Refutation not found, incomplete strategy
% 1.00/0.96 % (31855)------------------------------
% 1.00/0.96 % (31855)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.00/0.96 % (31855)Termination reason: Refutation not found, incomplete strategy
% 1.00/0.96
% 1.00/0.96
% 1.00/0.96 % (31855)Memory used [KB]: 5628
% 1.00/0.96 % (31855)Time elapsed: 0.007 s
% 1.00/0.96 % (31855)Instructions burned: 19 (million)
% 1.00/0.96 % (31855)------------------------------
% 1.00/0.96 % (31855)------------------------------
% 1.00/0.97 % (31856)Instruction limit reached!
% 1.00/0.97 % (31856)------------------------------
% 1.00/0.97 % (31856)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.00/0.97 % (31856)Termination reason: Unknown
% 1.00/0.97 % (31856)Termination phase: Saturation
% 1.00/0.97
% 1.00/0.97 % (31856)Memory used [KB]: 5628
% 1.00/0.97 % (31856)Time elapsed: 0.007 s
% 1.00/0.97 % (31856)Instructions burned: 20 (million)
% 1.00/0.97 % (31856)------------------------------
% 1.00/0.97 % (31856)------------------------------
% 1.00/0.97 % (31857)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_31564 for (2999ds/3Mi)
% 1.00/0.97 % (31857)Instruction limit reached!
% 1.00/0.97 % (31857)------------------------------
% 1.00/0.97 % (31857)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.00/0.97 % (31857)Termination reason: Unknown
% 1.00/0.97 % (31857)Termination phase: Saturation
% 1.00/0.97
% 1.00/0.97 % (31857)Memory used [KB]: 5500
% 1.00/0.97 % (31857)Time elapsed: 0.002 s
% 1.00/0.97 % (31857)Instructions burned: 4 (million)
% 1.00/0.97 % (31857)------------------------------
% 1.00/0.97 % (31857)------------------------------
% 1.00/0.97 % (31858)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_31564 for (2999ds/30Mi)
% 1.00/0.98 % (31859)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_31564 for (2999ds/127Mi)
% 1.00/0.98 % (31860)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_31564 for (2999ds/100Mi)
% 1.00/0.98 % (31860)Refutation not found, incomplete strategy
% 1.00/0.98 % (31860)------------------------------
% 1.00/0.98 % (31860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.00/0.98 % (31860)Termination reason: Refutation not found, incomplete strategy
% 1.00/0.98
% 1.00/0.98
% 1.00/0.98 % (31860)Memory used [KB]: 5500
% 1.00/0.98 % (31860)Time elapsed: 0.002 s
% 1.00/0.98 % (31860)Instructions burned: 3 (million)
% 1.00/0.98 % (31860)------------------------------
% 1.00/0.98 % (31860)------------------------------
% 1.00/0.98 % (31858)Instruction limit reached!
% 1.00/0.98 % (31858)------------------------------
% 1.00/0.98 % (31858)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.00/0.98 % (31858)Termination reason: Unknown
% 1.00/0.98 % (31858)Termination phase: Saturation
% 1.00/0.98
% 1.00/0.98 % (31858)Memory used [KB]: 5756
% 1.00/0.98 % (31858)Time elapsed: 0.010 s
% 1.00/0.98 % (31858)Instructions burned: 30 (million)
% 1.00/0.98 % (31858)------------------------------
% 1.00/0.98 % (31858)------------------------------
% 1.00/0.99 % (31861)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_31564 for (2999ds/3Mi)
% 1.00/0.99 % (31861)Instruction limit reached!
% 1.00/0.99 % (31861)------------------------------
% 1.00/0.99 % (31861)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.00/0.99 % (31861)Termination reason: Unknown
% 1.00/0.99 % (31861)Termination phase: Saturation
% 1.00/0.99
% 1.00/0.99 % (31861)Memory used [KB]: 5500
% 1.00/0.99 % (31861)Time elapsed: 0.002 s
% 1.00/0.99 % (31861)Instructions burned: 3 (million)
% 1.00/0.99 % (31861)------------------------------
% 1.00/0.99 % (31861)------------------------------
% 1.00/0.99 % (31862)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_31564 for (2999ds/20Mi)
% 1.00/1.00 % (31862)Instruction limit reached!
% 1.00/1.00 % (31862)------------------------------
% 1.00/1.00 % (31862)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.00/1.00 % (31862)Termination reason: Unknown
% 1.00/1.00 % (31862)Termination phase: Saturation
% 1.00/1.00
% 1.00/1.00 % (31862)Memory used [KB]: 5628
% 1.00/1.00 % (31862)Time elapsed: 0.008 s
% 1.00/1.00 % (31862)Instructions burned: 22 (million)
% 1.00/1.00 % (31862)------------------------------
% 1.00/1.00 % (31862)------------------------------
% 1.00/1.00 % (31863)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_31564 for (2999ds/86Mi)
% 1.00/1.01 % (31864)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_31564 for (2999ds/107Mi)
% 1.81/1.01 % (31859)Instruction limit reached!
% 1.81/1.01 % (31859)------------------------------
% 1.81/1.01 % (31859)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.01 % (31859)Termination reason: Unknown
% 1.81/1.01 % (31859)Termination phase: Saturation
% 1.81/1.01
% 1.81/1.01 % (31859)Memory used [KB]: 5884
% 1.81/1.01 % (31859)Time elapsed: 0.036 s
% 1.81/1.01 % (31859)Instructions burned: 129 (million)
% 1.81/1.01 % (31859)------------------------------
% 1.81/1.01 % (31859)------------------------------
% 1.81/1.02 % (31865)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_31564 for (2998ds/39Mi)
% 1.81/1.03 % (31863)Instruction limit reached!
% 1.81/1.03 % (31863)------------------------------
% 1.81/1.03 % (31863)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.03 % (31863)Termination reason: Unknown
% 1.81/1.03 % (31863)Termination phase: Saturation
% 1.81/1.03
% 1.81/1.03 % (31863)Memory used [KB]: 5884
% 1.81/1.03 % (31863)Time elapsed: 0.027 s
% 1.81/1.03 % (31863)Instructions burned: 88 (million)
% 1.81/1.03 % (31863)------------------------------
% 1.81/1.03 % (31863)------------------------------
% 1.81/1.03 % (31865)Instruction limit reached!
% 1.81/1.03 % (31865)------------------------------
% 1.81/1.03 % (31865)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.03 % (31865)Termination reason: Unknown
% 1.81/1.03 % (31865)Termination phase: Saturation
% 1.81/1.03
% 1.81/1.03 % (31865)Memory used [KB]: 6012
% 1.81/1.03 % (31865)Time elapsed: 0.034 s
% 1.81/1.03 % (31865)Instructions burned: 39 (million)
% 1.81/1.03 % (31865)------------------------------
% 1.81/1.03 % (31865)------------------------------
% 1.81/1.04 % (31866)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_31564 for (2998ds/448Mi)
% 1.81/1.04 % (31864)First to succeed.
% 1.81/1.04 % (31864)Refutation found. Thanks to Tanya!
% 1.81/1.04 % SZS status Theorem for DTF2THF_31564
% 1.81/1.04 % SZS output start Proof for DTF2THF_31564
% 1.81/1.04 thf(type_def_5, type, a: $tType).
% 1.81/1.04 thf(func_def_0, type, a: $tType).
% 1.81/1.04 thf(func_def_4, type, sP0: (a > a > $o) > a > a > $o).
% 1.81/1.04 thf(func_def_5, type, sP1: (a > a > $o) > a > a > $o).
% 1.81/1.04 thf(func_def_6, type, sK2: (a > a > $o) > a > a > a > a > $o).
% 1.81/1.04 thf(func_def_7, type, sK3: (a > a > $o) > a).
% 1.81/1.04 thf(func_def_8, type, sK4: (a > a > $o) > (a > a > $o) > a).
% 1.81/1.04 thf(func_def_9, type, sK5: (a > a > $o) > (a > a > $o) > a).
% 1.81/1.04 thf(func_def_10, type, sK6: a).
% 1.81/1.04 thf(func_def_11, type, sK7: a).
% 1.81/1.04 thf(func_def_12, type, sK8: a > a > $o).
% 1.81/1.04 thf(func_def_14, type, ph10: !>[X0: $tType]:(X0)).
% 1.81/1.04 thf(f321,plain,(
% 1.81/1.04 $false),
% 1.81/1.04 inference(avatar_sat_refutation,[status(thm)],[f43,f44,f245,f260,f266,f320])).
% 1.81/1.04 thf(f320,plain,(
% 1.81/1.04 spl9_2 | ~spl9_3),
% 1.81/1.04 inference(avatar_contradiction_clause,[status(thm)],[f319])).
% 1.81/1.04 thf(f319,plain,(
% 1.81/1.04 $false | (spl9_2 | ~spl9_3)),
% 1.81/1.04 inference(subsumption_resolution,[status(thm)],[f318,f42])).
% 1.81/1.04 thf(f42,plain,(
% 1.81/1.04 ($true != (sP1 @ sK8 @ sK7 @ sK6)) | spl9_2),
% 1.81/1.04 inference(avatar_component_clause,[status(thm)],[f40])).
% 1.81/1.04 thf(f40,definition,(
% 1.81/1.04 spl9_2 <=> ($true = (sP1 @ sK8 @ sK7 @ sK6))),
% 1.81/1.04 introduced(definition,[new_symbols(naming,[spl9_2])],[avatar_definition])).
% 1.81/1.04 thf(f318,plain,(
% 1.81/1.04 ($true = (sP1 @ sK8 @ sK7 @ sK6)) | ~spl9_3),
% 1.81/1.04 inference(trivial_inequality_removal,[status(thm)],[f317])).
% 1.81/1.04 thf(f317,plain,(
% 1.81/1.04 ($true = (sP1 @ sK8 @ sK7 @ sK6)) | ($true != $true) | ~spl9_3),
% 1.81/1.04 inference(duplicate_literal_removal,[status(thm)],[f312])).
% 1.81/1.04 thf(f312,plain,(
% 1.81/1.04 ($true != $true) | ($true = (sP1 @ sK8 @ sK7 @ sK6)) | ($true = (sP1 @ sK8 @ sK7 @ sK6)) | ~spl9_3),
% 1.81/1.04 inference(superposition,[status(thm)],[f28,f276])).
% 1.81/1.04 thf(f276,plain,(
% 1.81/1.04 ( ! [X0 : a,X1 : a] : (((sK2 @ sK8 @ X0 @ X1 @ sK7 @ sK6) = $true) | ($true = (sP1 @ sK8 @ X0 @ X1))) ) | ~spl9_3),
% 1.81/1.04 inference(trivial_inequality_removal,[status(thm)],[f273])).
% 1.81/1.04 thf(f273,plain,(
% 1.81/1.04 ( ! [X0 : a,X1 : a] : (((sK2 @ sK8 @ X0 @ X1 @ sK7 @ sK6) = $true) | ($true != $true) | ($true = (sP1 @ sK8 @ X0 @ X1))) ) | ~spl9_3),
% 1.81/1.04 inference(superposition,[status(thm)],[f26,f255])).
% 1.81/1.04 thf(f255,plain,(
% 1.81/1.04 ((sK8 @ sK7 @ sK6) = $true) | ~spl9_3),
% 1.81/1.04 inference(avatar_component_clause,[status(thm)],[f253])).
% 1.81/1.04 thf(f253,definition,(
% 1.81/1.04 spl9_3 <=> ((sK8 @ sK7 @ sK6) = $true)),
% 1.81/1.04 introduced(definition,[new_symbols(naming,[spl9_3])],[avatar_definition])).
% 1.81/1.04 thf(f26,plain,(
% 1.81/1.04 ( ! [X2 : a > a > $o,X0 : a,X1 : a,X6 : a,X5 : a] : (((X2 @ X5 @ X6) != $true) | ((sP1 @ X2 @ X1 @ X0) = $true) | ($true = (sK2 @ X2 @ X1 @ X0 @ X5 @ X6))) )),
% 1.81/1.04 inference(cnf_transformation,[status(thm)],[f16])).
% 1.81/1.04 thf(f16,plain,(
% 1.81/1.04 ! [X0 : a,X1 : a,X2 : a > a > $o] : ((((sP1 @ X2 @ X1 @ X0) = $true) | (((sK2 @ X2 @ X1 @ X0 @ X1 @ X0) != $true) & ! [X4 : a] : ($true = (sK2 @ X2 @ X1 @ X0 @ X4 @ X4)) & ! [X5 : a,X6 : a] : (((X2 @ X5 @ X6) != $true) | ($true = (sK2 @ X2 @ X1 @ X0 @ X5 @ X6))))) & (! [X7 : a > a > $o] : (($true = (X7 @ X1 @ X0)) | ((X7 @ (sK3 @ X7) @ (sK3 @ X7)) != $true) | (($true = (X2 @ (sK4 @ X7 @ X2) @ (sK5 @ X7 @ X2))) & ($true != (X7 @ (sK4 @ X7 @ X2) @ (sK5 @ X7 @ X2))))) | ((sP1 @ X2 @ X1 @ X0) != $true)))),
% 1.81/1.04 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f12,f15,f14,f13])).
% 1.81/1.04 thf(f13,plain,(
% 1.81/1.04 ! [X0 : a,X1 : a,X2 : a > a > $o] : (? [X3 : a > a > $o] : (($true != (X3 @ X1 @ X0)) & ! [X4 : a] : ((X3 @ X4 @ X4) = $true) & ! [X5 : a,X6 : a] : (((X2 @ X5 @ X6) != $true) | ((X3 @ X5 @ X6) = $true))) => (((sK2 @ X2 @ X1 @ X0 @ X1 @ X0) != $true) & ! [X4 : a] : ($true = (sK2 @ X2 @ X1 @ X0 @ X4 @ X4)) & ! [X6 : a,X5 : a] : (((X2 @ X5 @ X6) != $true) | ($true = (sK2 @ X2 @ X1 @ X0 @ X5 @ X6)))))),
% 1.81/1.04 introduced(definition,[],[choice_axiom])).
% 1.81/1.04 thf(f14,plain,(
% 1.81/1.04 ! [X7 : a > a > $o] : (? [X8 : a] : ($true != (X7 @ X8 @ X8)) => ((X7 @ (sK3 @ X7) @ (sK3 @ X7)) != $true))),
% 1.81/1.04 introduced(definition,[],[choice_axiom])).
% 1.81/1.04 thf(f15,plain,(
% 1.81/1.04 ! [X2 : a > a > $o,X7 : a > a > $o] : (? [X9 : a,X10 : a] : (((X2 @ X9 @ X10) = $true) & ((X7 @ X9 @ X10) != $true)) => (($true = (X2 @ (sK4 @ X7 @ X2) @ (sK5 @ X7 @ X2))) & ($true != (X7 @ (sK4 @ X7 @ X2) @ (sK5 @ X7 @ X2)))))),
% 1.81/1.04 introduced(definition,[],[choice_axiom])).
% 1.81/1.04 thf(f12,plain,(
% 1.81/1.04 ! [X0 : a,X1 : a,X2 : a > a > $o] : ((((sP1 @ X2 @ X1 @ X0) = $true) | ? [X3 : a > a > $o] : (($true != (X3 @ X1 @ X0)) & ! [X4 : a] : ((X3 @ X4 @ X4) = $true) & ! [X5 : a,X6 : a] : (((X2 @ X5 @ X6) != $true) | ((X3 @ X5 @ X6) = $true)))) & (! [X7 : a > a > $o] : (($true = (X7 @ X1 @ X0)) | ? [X8 : a] : ($true != (X7 @ X8 @ X8)) | ? [X9 : a,X10 : a] : (((X2 @ X9 @ X10) = $true) & ((X7 @ X9 @ X10) != $true))) | ((sP1 @ X2 @ X1 @ X0) != $true)))),
% 1.81/1.04 inference(rectify,[status(thm)],[f11])).
% 1.81/1.04 thf(f11,plain,(
% 1.81/1.04 ! [X2 : a,X0 : a,X1 : a > a > $o] : ((($true = (sP1 @ X1 @ X0 @ X2)) | ? [X3 : a > a > $o] : (((X3 @ X0 @ X2) != $true) & ! [X4 : a] : ((X3 @ X4 @ X4) = $true) & ! [X5 : a,X6 : a] : (((X1 @ X5 @ X6) != $true) | ((X3 @ X5 @ X6) = $true)))) & (! [X3 : a > a > $o] : (((X3 @ X0 @ X2) = $true) | ? [X4 : a] : ((X3 @ X4 @ X4) != $true) | ? [X5 : a,X6 : a] : (((X1 @ X5 @ X6) = $true) & ((X3 @ X5 @ X6) != $true))) | ($true != (sP1 @ X1 @ X0 @ X2))))),
% 1.81/1.04 inference(nnf_transformation,[status(thm)],[f9])).
% 1.81/1.04 thf(f9,plain,(
% 1.81/1.04 ! [X2 : a,X0 : a,X1 : a > a > $o] : (($true = (sP1 @ X1 @ X0 @ X2)) <=> ! [X3 : a > a > $o] : (((X3 @ X0 @ X2) = $true) | ? [X4 : a] : ((X3 @ X4 @ X4) != $true) | ? [X5 : a,X6 : a] : (((X1 @ X5 @ X6) = $true) & ((X3 @ X5 @ X6) != $true))))),
% 1.81/1.04 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.81/1.04 thf(f28,plain,(
% 1.81/1.04 ( ! [X2 : a > a > $o,X0 : a,X1 : a] : (((sK2 @ X2 @ X1 @ X0 @ X1 @ X0) != $true) | ((sP1 @ X2 @ X1 @ X0) = $true)) )),
% 1.81/1.04 inference(cnf_transformation,[status(thm)],[f16])).
% 1.81/1.04 thf(f266,plain,(
% 1.81/1.04 spl9_2 | ~spl9_4),
% 1.81/1.04 inference(avatar_contradiction_clause,[status(thm)],[f265])).
% 1.81/1.04 thf(f265,plain,(
% 1.81/1.04 $false | (spl9_2 | ~spl9_4)),
% 1.81/1.04 inference(subsumption_resolution,[status(thm)],[f264,f66])).
% 1.81/1.04 thf(f66,plain,(
% 1.81/1.04 ( ! [X0 : a > a > $o,X1 : a] : (((sP1 @ X0 @ X1 @ X1) = $true)) )),
% 1.81/1.04 inference(trivial_inequality_removal,[status(thm)],[f65])).
% 1.81/1.04 thf(f65,plain,(
% 1.81/1.04 ( ! [X0 : a > a > $o,X1 : a] : (($true != $true) | ((sP1 @ X0 @ X1 @ X1) = $true)) )),
% 1.81/1.04 inference(duplicate_literal_removal,[status(thm)],[f64])).
% 1.81/1.04 thf(f64,plain,(
% 1.81/1.04 ( ! [X0 : a > a > $o,X1 : a] : (((sP1 @ X0 @ X1 @ X1) = $true) | ($true != $true) | ((sP1 @ X0 @ X1 @ X1) = $true)) )),
% 1.81/1.04 inference(superposition,[status(thm)],[f28,f27])).
% 1.81/1.04 thf(f27,plain,(
% 1.81/1.04 ( ! [X2 : a > a > $o,X0 : a,X1 : a,X4 : a] : (($true = (sK2 @ X2 @ X1 @ X0 @ X4 @ X4)) | ((sP1 @ X2 @ X1 @ X0) = $true)) )),
% 1.81/1.04 inference(cnf_transformation,[status(thm)],[f16])).
% 1.81/1.04 thf(f264,plain,(
% 1.81/1.04 ($true != (sP1 @ sK8 @ sK6 @ sK6)) | (spl9_2 | ~spl9_4)),
% 1.81/1.04 inference(backward_demodulation,[status(thm)],[f42,f259])).
% 1.81/1.04 thf(f259,plain,(
% 1.81/1.04 (sK6 = sK7) | ~spl9_4),
% 1.81/1.04 inference(avatar_component_clause,[status(thm)],[f257])).
% 1.81/1.04 thf(f257,definition,(
% 1.81/1.04 spl9_4 <=> (sK6 = sK7)),
% 1.81/1.04 introduced(definition,[new_symbols(naming,[spl9_4])],[avatar_definition])).
% 1.81/1.04 thf(f260,plain,(
% 1.81/1.04 spl9_3 | spl9_4 | ~spl9_1),
% 1.81/1.04 inference(avatar_split_clause,[status(thm)],[f249,f36,f257,f253])).
% 1.81/1.04 thf(f36,definition,(
% 1.81/1.04 spl9_1 <=> ((sP0 @ sK8 @ sK7 @ sK6) = $true)),
% 1.81/1.04 introduced(definition,[new_symbols(naming,[spl9_1])],[avatar_definition])).
% 1.81/1.04 thf(f249,plain,(
% 1.81/1.04 ((sK8 @ sK7 @ sK6) = $true) | (sK6 = sK7) | ~spl9_1),
% 1.81/1.04 inference(trivial_inequality_removal,[status(thm)],[f246])).
% 1.81/1.04 thf(f246,plain,(
% 1.81/1.04 ((sK8 @ sK7 @ sK6) = $true) | (sK6 = sK7) | ($true != $true) | ~spl9_1),
% 1.81/1.04 inference(superposition,[status(thm)],[f29,f37])).
% 1.81/1.04 thf(f37,plain,(
% 1.81/1.04 ((sP0 @ sK8 @ sK7 @ sK6) = $true) | ~spl9_1),
% 1.81/1.04 inference(avatar_component_clause,[status(thm)],[f36])).
% 1.81/1.04 thf(f29,plain,(
% 1.81/1.04 ( ! [X2 : a > a > $o,X0 : a,X1 : a] : (((sP0 @ X2 @ X1 @ X0) != $true) | ($true = (X2 @ X1 @ X0)) | (X0 = X1)) )),
% 1.81/1.04 inference(cnf_transformation,[status(thm)],[f19])).
% 1.81/1.04 thf(f19,plain,(
% 1.81/1.04 ! [X0 : a,X1 : a,X2 : a > a > $o] : ((((sP0 @ X2 @ X1 @ X0) = $true) | ((X0 != X1) & ($true != (X2 @ X1 @ X0)))) & ((X0 = X1) | ($true = (X2 @ X1 @ X0)) | ((sP0 @ X2 @ X1 @ X0) != $true)))),
% 1.81/1.04 inference(rectify,[status(thm)],[f18])).
% 1.81/1.04 thf(f18,plain,(
% 1.81/1.04 ! [X2 : a,X0 : a,X1 : a > a > $o] : ((((sP0 @ X1 @ X0 @ X2) = $true) | ((X0 != X2) & ((X1 @ X0 @ X2) != $true))) & ((X0 = X2) | ((X1 @ X0 @ X2) = $true) | ((sP0 @ X1 @ X0 @ X2) != $true)))),
% 1.81/1.04 inference(flattening,[status(thm)],[f17])).
% 1.81/1.04 thf(f17,plain,(
% 1.81/1.04 ! [X2 : a,X0 : a,X1 : a > a > $o] : ((((sP0 @ X1 @ X0 @ X2) = $true) | ((X0 != X2) & ((X1 @ X0 @ X2) != $true))) & (((X0 = X2) | ((X1 @ X0 @ X2) = $true)) | ((sP0 @ X1 @ X0 @ X2) != $true)))),
% 1.81/1.04 inference(nnf_transformation,[status(thm)],[f8])).
% 1.81/1.04 thf(f8,plain,(
% 1.81/1.04 ! [X2 : a,X0 : a,X1 : a > a > $o] : (((sP0 @ X1 @ X0 @ X2) = $true) <=> ((X0 = X2) | ((X1 @ X0 @ X2) = $true)))),
% 1.81/1.04 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.81/1.04 thf(f245,plain,(
% 1.81/1.04 spl9_1 | ~spl9_2),
% 1.81/1.04 inference(avatar_contradiction_clause,[status(thm)],[f244])).
% 1.81/1.04 thf(f244,plain,(
% 1.81/1.04 $false | (spl9_1 | ~spl9_2)),
% 1.81/1.04 inference(subsumption_resolution,[status(thm)],[f243,f38])).
% 1.81/1.04 thf(f38,plain,(
% 1.81/1.04 ((sP0 @ sK8 @ sK7 @ sK6) != $true) | spl9_1),
% 1.81/1.04 inference(avatar_component_clause,[status(thm)],[f36])).
% 1.81/1.04 thf(f243,plain,(
% 1.81/1.04 ((sP0 @ sK8 @ sK7 @ sK6) = $true) | (spl9_1 | ~spl9_2)),
% 1.81/1.04 inference(trivial_inequality_removal,[status(thm)],[f240])).
% 1.81/1.04 thf(f240,plain,(
% 1.81/1.04 ((sP0 @ sK8 @ sK7 @ sK6) = $true) | ($true != $true) | (spl9_1 | ~spl9_2)),
% 1.81/1.04 inference(superposition,[status(thm)],[f239,f41])).
% 1.81/1.04 thf(f41,plain,(
% 1.81/1.04 ($true = (sP1 @ sK8 @ sK7 @ sK6)) | ~spl9_2),
% 1.81/1.04 inference(avatar_component_clause,[status(thm)],[f40])).
% 1.81/1.04 thf(f239,plain,(
% 1.81/1.04 ( ! [X0 : a,X1 : a] : (($true != (sP1 @ sK8 @ X0 @ X1)) | ($true = (sP0 @ sK8 @ X0 @ X1))) ) | (spl9_1 | ~spl9_2)),
% 1.81/1.04 inference(subsumption_resolution,[status(thm)],[f238,f34])).
% 1.81/1.04 thf(f34,plain,(
% 1.81/1.04 ( ! [X2 : a > a > $o,X1 : a] : (($true = (sP0 @ X2 @ X1 @ X1))) )),
% 1.81/1.04 inference(equality_resolution,[status(thm)],[f31])).
% 1.81/1.04 thf(f31,plain,(
% 1.81/1.04 ( ! [X2 : a > a > $o,X0 : a,X1 : a] : (((sP0 @ X2 @ X1 @ X0) = $true) | (X0 != X1)) )),
% 1.81/1.04 inference(cnf_transformation,[status(thm)],[f19])).
% 1.81/1.04 thf(f238,plain,(
% 1.81/1.04 ( ! [X0 : a,X1 : a] : (($true = (sP0 @ sK8 @ X0 @ X1)) | ($true != (sP1 @ sK8 @ X0 @ X1)) | ($true != (sP0 @ sK8 @ (sK3 @ (sP0 @ sK8)) @ (sK3 @ (sP0 @ sK8))))) ) | (spl9_1 | ~spl9_2)),
% 1.81/1.04 inference(subsumption_resolution,[status(thm)],[f235,f38])).
% 1.81/1.04 thf(f235,plain,(
% 1.81/1.04 ( ! [X0 : a,X1 : a] : (((sP0 @ sK8 @ sK7 @ sK6) = $true) | ($true != (sP1 @ sK8 @ X0 @ X1)) | ($true != (sP0 @ sK8 @ (sK3 @ (sP0 @ sK8)) @ (sK3 @ (sP0 @ sK8)))) | ($true = (sP0 @ sK8 @ X0 @ X1))) ) | ~spl9_2),
% 1.81/1.04 inference(trivial_inequality_removal,[status(thm)],[f231])).
% 1.81/1.04 thf(f231,plain,(
% 1.81/1.04 ( ! [X0 : a,X1 : a] : (($true != $true) | ($true != (sP0 @ sK8 @ (sK3 @ (sP0 @ sK8)) @ (sK3 @ (sP0 @ sK8)))) | ($true = (sP0 @ sK8 @ X0 @ X1)) | ((sP0 @ sK8 @ sK7 @ sK6) = $true) | ($true != (sP1 @ sK8 @ X0 @ X1))) ) | ~spl9_2),
% 1.81/1.04 inference(superposition,[status(thm)],[f24,f132])).
% 1.81/1.04 thf(f132,plain,(
% 1.81/1.04 ( ! [X0 : a > a > $o] : (($true = (sP0 @ sK8 @ (sK4 @ (sP0 @ X0) @ sK8) @ (sK5 @ (sP0 @ X0) @ sK8))) | ((sP0 @ X0 @ sK7 @ sK6) = $true)) ) | ~spl9_2),
% 1.81/1.04 inference(trivial_inequality_removal,[status(thm)],[f131])).
% 1.81/1.04 thf(f131,plain,(
% 1.81/1.04 ( ! [X0 : a > a > $o] : (($true = (sP0 @ sK8 @ (sK4 @ (sP0 @ X0) @ sK8) @ (sK5 @ (sP0 @ X0) @ sK8))) | ((sP0 @ X0 @ sK7 @ sK6) = $true) | ($true != $true)) ) | ~spl9_2),
% 1.81/1.04 inference(superposition,[status(thm)],[f30,f110])).
% 1.81/1.04 thf(f110,plain,(
% 1.81/1.04 ( ! [X0 : a > a > $o] : (($true = (sK8 @ (sK4 @ (sP0 @ X0) @ sK8) @ (sK5 @ (sP0 @ X0) @ sK8))) | ((sP0 @ X0 @ sK7 @ sK6) = $true)) ) | ~spl9_2),
% 1.81/1.04 inference(trivial_inequality_removal,[status(thm)],[f108])).
% 1.81/1.04 thf(f108,plain,(
% 1.81/1.04 ( ! [X0 : a > a > $o] : (($true = (sK8 @ (sK4 @ (sP0 @ X0) @ sK8) @ (sK5 @ (sP0 @ X0) @ sK8))) | ($true != $true) | ((sP0 @ X0 @ sK7 @ sK6) = $true)) ) | ~spl9_2),
% 1.81/1.04 inference(superposition,[status(thm)],[f99,f41])).
% 1.81/1.04 thf(f99,plain,(
% 1.81/1.04 ( ! [X2 : a,X3 : a,X0 : a > a > $o,X1 : a > a > $o] : (($true != (sP1 @ X1 @ X2 @ X3)) | ($true = (sP0 @ X0 @ X2 @ X3)) | ($true = (X1 @ (sK4 @ (sP0 @ X0) @ X1) @ (sK5 @ (sP0 @ X0) @ X1)))) )),
% 1.81/1.04 inference(trivial_inequality_removal,[status(thm)],[f96])).
% 1.81/1.04 thf(f96,plain,(
% 1.81/1.04 ( ! [X2 : a,X3 : a,X0 : a > a > $o,X1 : a > a > $o] : (($true = (X1 @ (sK4 @ (sP0 @ X0) @ X1) @ (sK5 @ (sP0 @ X0) @ X1))) | ($true = (sP0 @ X0 @ X2 @ X3)) | ($true != (sP1 @ X1 @ X2 @ X3)) | ($true != $true)) )),
% 1.81/1.04 inference(superposition,[status(thm)],[f25,f34])).
% 1.81/1.04 thf(f25,plain,(
% 1.81/1.04 ( ! [X2 : a > a > $o,X0 : a,X1 : a,X7 : a > a > $o] : (((X7 @ (sK3 @ X7) @ (sK3 @ X7)) != $true) | ($true = (X2 @ (sK4 @ X7 @ X2) @ (sK5 @ X7 @ X2))) | ((sP1 @ X2 @ X1 @ X0) != $true) | ($true = (X7 @ X1 @ X0))) )),
% 1.81/1.04 inference(cnf_transformation,[status(thm)],[f16])).
% 1.81/1.04 thf(f30,plain,(
% 1.81/1.04 ( ! [X2 : a > a > $o,X0 : a,X1 : a] : (($true != (X2 @ X1 @ X0)) | ((sP0 @ X2 @ X1 @ X0) = $true)) )),
% 1.81/1.04 inference(cnf_transformation,[status(thm)],[f19])).
% 1.81/1.04 thf(f24,plain,(
% 1.81/1.04 ( ! [X2 : a > a > $o,X0 : a,X1 : a,X7 : a > a > $o] : (($true != (X7 @ (sK4 @ X7 @ X2) @ (sK5 @ X7 @ X2))) | ((X7 @ (sK3 @ X7) @ (sK3 @ X7)) != $true) | ($true = (X7 @ X1 @ X0)) | ((sP1 @ X2 @ X1 @ X0) != $true)) )),
% 1.81/1.04 inference(cnf_transformation,[status(thm)],[f16])).
% 1.81/1.04 thf(f44,plain,(
% 1.81/1.04 spl9_1 | spl9_2),
% 1.81/1.04 inference(avatar_split_clause,[status(thm)],[f32,f40,f36])).
% 1.81/1.04 thf(f32,plain,(
% 1.81/1.04 ((sP0 @ sK8 @ sK7 @ sK6) = $true) | ($true = (sP1 @ sK8 @ sK7 @ sK6))),
% 1.81/1.04 inference(cnf_transformation,[status(thm)],[f23])).
% 1.81/1.04 thf(f23,plain,(
% 1.81/1.04 (($true != (sP1 @ sK8 @ sK7 @ sK6)) | ((sP0 @ sK8 @ sK7 @ sK6) != $true)) & (($true = (sP1 @ sK8 @ sK7 @ sK6)) | ((sP0 @ sK8 @ sK7 @ sK6) = $true))),
% 1.81/1.04 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f21,f22])).
% 1.81/1.04 thf(f22,plain,(
% 1.81/1.04 ? [X0 : a,X1 : a,X2 : a > a > $o] : ((((sP1 @ X2 @ X1 @ X0) != $true) | ((sP0 @ X2 @ X1 @ X0) != $true)) & (((sP1 @ X2 @ X1 @ X0) = $true) | ((sP0 @ X2 @ X1 @ X0) = $true))) => ((($true != (sP1 @ sK8 @ sK7 @ sK6)) | ((sP0 @ sK8 @ sK7 @ sK6) != $true)) & (($true = (sP1 @ sK8 @ sK7 @ sK6)) | ((sP0 @ sK8 @ sK7 @ sK6) = $true)))),
% 1.81/1.04 introduced(definition,[],[choice_axiom])).
% 1.81/1.04 thf(f21,plain,(
% 1.81/1.04 ? [X0 : a,X1 : a,X2 : a > a > $o] : ((((sP1 @ X2 @ X1 @ X0) != $true) | ((sP0 @ X2 @ X1 @ X0) != $true)) & (((sP1 @ X2 @ X1 @ X0) = $true) | ((sP0 @ X2 @ X1 @ X0) = $true)))),
% 1.81/1.04 inference(rectify,[status(thm)],[f20])).
% 1.81/1.04 thf(f20,plain,(
% 1.81/1.04 ? [X2 : a,X0 : a,X1 : a > a > $o] : ((($true != (sP1 @ X1 @ X0 @ X2)) | ((sP0 @ X1 @ X0 @ X2) != $true)) & (($true = (sP1 @ X1 @ X0 @ X2)) | ((sP0 @ X1 @ X0 @ X2) = $true)))),
% 1.81/1.04 inference(nnf_transformation,[status(thm)],[f10])).
% 1.81/1.04 thf(f10,plain,(
% 1.81/1.04 ? [X2 : a,X0 : a,X1 : a > a > $o] : (((sP0 @ X1 @ X0 @ X2) = $true) <~> ($true = (sP1 @ X1 @ X0 @ X2)))),
% 1.81/1.04 inference(definition_folding,[status(thm)],[f7,f9,f8])).
% 1.81/1.04 thf(f7,plain,(
% 1.81/1.04 ? [X2 : a,X0 : a,X1 : a > a > $o] : (((X0 = X2) | ((X1 @ X0 @ X2) = $true)) <~> ! [X3 : a > a > $o] : (((X3 @ X0 @ X2) = $true) | ? [X4 : a] : ((X3 @ X4 @ X4) != $true) | ? [X5 : a,X6 : a] : (((X1 @ X5 @ X6) = $true) & ((X3 @ X5 @ X6) != $true))))),
% 1.81/1.04 inference(flattening,[status(thm)],[f6])).
% 1.81/1.04 thf(f6,plain,(
% 1.81/1.04 ? [X1 : a > a > $o,X2 : a,X0 : a] : (! [X3 : a > a > $o] : (((X3 @ X0 @ X2) = $true) | (? [X5 : a,X6 : a] : (((X1 @ X5 @ X6) = $true) & ((X3 @ X5 @ X6) != $true)) | ? [X4 : a] : ((X3 @ X4 @ X4) != $true))) <~> ((X0 = X2) | ((X1 @ X0 @ X2) = $true)))),
% 1.81/1.04 inference(ennf_transformation,[status(thm)],[f5])).
% 1.81/1.04 thf(f5,plain,(
% 1.81/1.04 ~! [X1 : a > a > $o,X2 : a,X0 : a] : (! [X3 : a > a > $o] : ((! [X6 : a,X5 : a] : (((X1 @ X5 @ X6) = $true) => ((X3 @ X5 @ X6) = $true)) & ! [X4 : a] : ((X3 @ X4 @ X4) = $true)) => ((X3 @ X0 @ X2) = $true)) <=> ((X0 = X2) | ((X1 @ X0 @ X2) = $true)))),
% 1.81/1.04 inference(fool_elimination,[status(thm)],[f4])).
% 1.81/1.04 thf(f4,plain,(
% 1.81/1.04 ~! [X0 : a,X1 : a > a > $o,X2 : a] : (! [X3 : a > a > $o] : ((! [X4 : a] : (X3 @ X4 @ X4) & ! [X5 : a,X6 : a] : ((X1 @ X5 @ X6) => (X3 @ X5 @ X6))) => (X3 @ X0 @ X2)) <=> ((X1 @ X0 @ X2) | (X0 = X2)))),
% 1.81/1.04 inference(rectify,[status(thm)],[f2])).
% 1.81/1.04 thf(f2,negated_conjecture,(
% 1.81/1.04 ~! [X1 : a,X0 : a > a > $o,X2 : a] : (! [X3 : a > a > $o] : ((! [X4 : a] : (X3 @ X4 @ X4) & ! [X4 : a,X5 : a] : ((X0 @ X4 @ X5) => (X3 @ X4 @ X5))) => (X3 @ X1 @ X2)) <=> ((X0 @ X1 @ X2) | (X1 = X2)))),
% 1.81/1.04 inference(negated_conjecture,[status(cth)],[f1])).
% 1.81/1.04 thf(f1,conjecture,(
% 1.81/1.04 ! [X1 : a,X0 : a > a > $o,X2 : a] : (! [X3 : a > a > $o] : ((! [X4 : a] : (X3 @ X4 @ X4) & ! [X4 : a,X5 : a] : ((X0 @ X4 @ X5) => (X3 @ X4 @ X5))) => (X3 @ X1 @ X2)) <=> ((X0 @ X1 @ X2) | (X1 = X2)))),
% 1.81/1.04 file('/export/starexec/sandbox/tmp/tmp.QTwIpeUg66/DTF2THF_31564.p',cTHM523_pme)).
% 1.81/1.04 thf(f43,plain,(
% 1.81/1.04 ~spl9_1 | ~spl9_2),
% 1.81/1.04 inference(avatar_split_clause,[status(thm)],[f33,f40,f36])).
% 1.81/1.04 thf(f33,plain,(
% 1.81/1.04 ((sP0 @ sK8 @ sK7 @ sK6) != $true) | ($true != (sP1 @ sK8 @ sK7 @ sK6))),
% 1.81/1.04 inference(cnf_transformation,[status(thm)],[f23])).
% 1.81/1.04 % SZS output end Proof for DTF2THF_31564
% 1.81/1.04 % (31864)------------------------------
% 1.81/1.04 % (31864)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.04 % (31864)Termination reason: Refutation
% 1.81/1.04
% 1.81/1.04 % (31864)Memory used [KB]: 6012
% 1.81/1.04 % (31864)Time elapsed: 0.055 s
% 1.81/1.04 % (31864)Instructions burned: 99 (million)
% 1.81/1.04 % (31864)------------------------------
% 1.81/1.04 % (31864)------------------------------
% 1.81/1.04 % (31825)Success in time 0.135 s
%------------------------------------------------------------------------------