%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYN059^5 : 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 : n013.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 09:50:27 AM UTC 2026
% Result : Theorem 1.49s 1.28s
% Output : Refutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 71 ( 5 unt; 0 typ; 8 def)
% Number of atoms : 754 ( 201 equ; 0 cnn)
% Maximal formula atoms : 16 ( 10 avg)
% Number of connectives : 596 ( 135 ~; 115 |; 83 &; 219 @)
% ( 8 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 16 con; 0-2 aty)
% Number of variables : 103 ( 0 ^; 68 !; 35 ?; 103 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cJ: $i > $o ).
thf(func_def_1,type,
cG: $i > $o ).
thf(func_def_2,type,
cH: $i > $o ).
thf(func_def_3,type,
cF: $i > $o ).
thf(f107,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f38,f46,f51,f59,f66,f92,f99,f101,f106]) ).
thf(f106,plain,
~ spl6_7,
inference(avatar_contradiction_clause,[status(thm)],[f105]) ).
thf(f105,plain,
( $false
| ~ spl6_7 ),
inference(trivial_inequality_removal,[status(thm)],[f103]) ).
thf(f103,plain,
( ( $true != $true )
| ~ spl6_7 ),
inference(superposition,[status(thm)],[f58,f24]) ).
thf(f24,plain,
( ( cF @ sK5 )
= $true ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ( sP0 = $true )
| ( ( $true
= ( cG @ sK3 ) )
& ( $true
!= ( cJ @ sK3 ) )
& ! [X1: $i,X2: $i] :
( ( ( cF @ X2 )
!= $true )
| ( ( cG @ X1 )
!= $true )
| ( ( ( cH @ X2 )
= $true )
& ( ( cJ @ X1 )
= $true ) ) ) ) )
& ( ( cG @ sK4 )
= $true )
& ( ( cF @ sK5 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f14,f17,f16,f15]) ).
thf(f15,plain,
( ? [X0: $i] :
( ( ( cG @ X0 )
= $true )
& ( ( cJ @ X0 )
!= $true ) )
=> ( ( $true
= ( cG @ sK3 ) )
& ( $true
!= ( cJ @ sK3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
( ? [X3: $i] :
( ( cG @ X3 )
= $true )
=> ( ( cG @ sK4 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
( ? [X4: $i] :
( ( cF @ X4 )
= $true )
=> ( ( cF @ sK5 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
( ( ( sP0 = $true )
| ( ? [X0: $i] :
( ( ( cG @ X0 )
= $true )
& ( ( cJ @ X0 )
!= $true ) )
& ! [X1: $i,X2: $i] :
( ( ( cF @ X2 )
!= $true )
| ( ( cG @ X1 )
!= $true )
| ( ( ( cH @ X2 )
= $true )
& ( ( cJ @ X1 )
= $true ) ) ) ) )
& ? [X3: $i] :
( ( cG @ X3 )
= $true )
& ? [X4: $i] :
( ( cF @ X4 )
= $true ) ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ( sP0 = $true )
| ( ? [X4: $i] :
( ( $true
= ( cG @ X4 ) )
& ( ( cJ @ X4 )
!= $true ) )
& ! [X3: $i,X2: $i] :
( ( ( cF @ X2 )
!= $true )
| ( ( cG @ X3 )
!= $true )
| ( ( ( cH @ X2 )
= $true )
& ( ( cJ @ X3 )
= $true ) ) ) ) )
& ? [X0: $i] :
( ( cG @ X0 )
= $true )
& ? [X1: $i] :
( ( cF @ X1 )
= $true ) ),
inference(definition_folding,[status(thm)],[f7,f8]) ).
thf(f8,plain,
( ( ! [X6: $i] :
( ( ( cJ @ X6 )
= $true )
| ( ( cG @ X6 )
!= $true ) )
& ! [X5: $i] :
( ( ( cH @ X5 )
= $true )
| ( $true
!= ( cF @ X5 ) ) )
& ? [X8: $i,X7: $i] :
( ( $true
= ( cF @ X8 ) )
& ( ( ( cJ @ X7 )
!= $true )
| ( ( cH @ X8 )
!= $true ) )
& ( ( cG @ X7 )
= $true ) ) )
| ( sP0 != $true ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f7,plain,
( ( ( ! [X6: $i] :
( ( ( cJ @ X6 )
= $true )
| ( ( cG @ X6 )
!= $true ) )
& ! [X5: $i] :
( ( ( cH @ X5 )
= $true )
| ( $true
!= ( cF @ X5 ) ) )
& ? [X8: $i,X7: $i] :
( ( $true
= ( cF @ X8 ) )
& ( ( ( cJ @ X7 )
!= $true )
| ( ( cH @ X8 )
!= $true ) )
& ( ( cG @ X7 )
= $true ) ) )
| ( ? [X4: $i] :
( ( $true
= ( cG @ X4 ) )
& ( ( cJ @ X4 )
!= $true ) )
& ! [X3: $i,X2: $i] :
( ( ( cF @ X2 )
!= $true )
| ( ( cG @ X3 )
!= $true )
| ( ( ( cH @ X2 )
= $true )
& ( ( cJ @ X3 )
= $true ) ) ) ) )
& ? [X0: $i] :
( ( cG @ X0 )
= $true )
& ? [X1: $i] :
( ( cF @ X1 )
= $true ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ( ? [X7: $i,X8: $i] :
( ( ( ( cJ @ X7 )
!= $true )
| ( ( cH @ X8 )
!= $true ) )
& ( $true
= ( cF @ X8 ) )
& ( ( cG @ X7 )
= $true ) )
& ! [X6: $i] :
( ( ( cJ @ X6 )
= $true )
| ( ( cG @ X6 )
!= $true ) )
& ! [X5: $i] :
( ( ( cH @ X5 )
= $true )
| ( $true
!= ( cF @ X5 ) ) ) )
| ( ? [X4: $i] :
( ( $true
= ( cG @ X4 ) )
& ( ( cJ @ X4 )
!= $true ) )
& ! [X3: $i,X2: $i] :
( ( ( ( cH @ X2 )
= $true )
& ( ( cJ @ X3 )
= $true ) )
| ( ( cG @ X3 )
!= $true )
| ( ( cF @ X2 )
!= $true ) ) ) )
& ? [X0: $i] :
( ( cG @ X0 )
= $true )
& ? [X1: $i] :
( ( cF @ X1 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ? [X0: $i] :
( ( cG @ X0 )
= $true )
& ? [X1: $i] :
( ( cF @ X1 )
= $true ) )
=> ( ( ( ! [X6: $i] :
( ( ( cG @ X6 )
= $true )
=> ( ( cJ @ X6 )
= $true ) )
& ! [X5: $i] :
( ( $true
= ( cF @ X5 ) )
=> ( ( cH @ X5 )
= $true ) ) )
=> ! [X7: $i,X8: $i] :
( ( ( $true
= ( cF @ X8 ) )
& ( ( cG @ X7 )
= $true ) )
=> ( ( ( cH @ X8 )
= $true )
& ( ( cJ @ X7 )
= $true ) ) ) )
& ( ! [X3: $i,X2: $i] :
( ( ( ( cG @ X3 )
= $true )
& ( ( cF @ X2 )
= $true ) )
=> ( ( ( cH @ X2 )
= $true )
& ( ( cJ @ X3 )
= $true ) ) )
=> ! [X4: $i] :
( ( $true
= ( cG @ X4 ) )
=> ( ( cJ @ X4 )
= $true ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ? [X0: $i] : ( cG @ X0 )
& ? [X1: $i] : ( cF @ X1 ) )
=> ( ( ! [X2: $i,X3: $i] :
( ( ( cG @ X3 )
& ( cF @ X2 ) )
=> ( ( cJ @ X3 )
& ( cH @ X2 ) ) )
=> ! [X4: $i] :
( ( cG @ X4 )
=> ( cJ @ X4 ) ) )
& ( ( ! [X5: $i] :
( ( cF @ X5 )
=> ( cH @ X5 ) )
& ! [X6: $i] :
( ( cG @ X6 )
=> ( cJ @ X6 ) ) )
=> ! [X7: $i,X8: $i] :
( ( ( cF @ X8 )
& ( cG @ X7 ) )
=> ( ( cH @ X8 )
& ( cJ @ X7 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ? [X0: $i] : ( cG @ X0 )
& ? [X0: $i] : ( cF @ X0 ) )
=> ( ( ! [X0: $i,X1: $i] :
( ( ( cG @ X1 )
& ( cF @ X0 ) )
=> ( ( cJ @ X1 )
& ( cH @ X0 ) ) )
=> ! [X0: $i] :
( ( cG @ X0 )
=> ( cJ @ X0 ) ) )
& ( ( ! [X0: $i] :
( ( cF @ X0 )
=> ( cH @ X0 ) )
& ! [X0: $i] :
( ( cG @ X0 )
=> ( cJ @ X0 ) ) )
=> ! [X1: $i,X0: $i] :
( ( ( cF @ X0 )
& ( cG @ X1 ) )
=> ( ( cH @ X0 )
& ( cJ @ X1 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ? [X0: $i] : ( cG @ X0 )
& ? [X0: $i] : ( cF @ X0 ) )
=> ( ( ! [X0: $i,X1: $i] :
( ( ( cG @ X1 )
& ( cF @ X0 ) )
=> ( ( cJ @ X1 )
& ( cH @ X0 ) ) )
=> ! [X0: $i] :
( ( cG @ X0 )
=> ( cJ @ X0 ) ) )
& ( ( ! [X0: $i] :
( ( cF @ X0 )
=> ( cH @ X0 ) )
& ! [X0: $i] :
( ( cG @ X0 )
=> ( cJ @ X0 ) ) )
=> ! [X1: $i,X0: $i] :
( ( ( cF @ X0 )
& ( cG @ X1 ) )
=> ( ( cH @ X0 )
& ( cJ @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.OnWfODaFyC/DTF2THF_22879.p',cPELL29) ).
thf(f58,plain,
( ! [X2: $i] :
( ( cF @ X2 )
!= $true )
| ~ spl6_7 ),
inference(avatar_component_clause,[status(thm)],[f57]) ).
thf(f57,definition,
( spl6_7
<=> ! [X2: $i] :
( ( cF @ X2 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[spl6_7])],[avatar_definition]) ).
thf(f101,plain,
( ~ spl6_2
| spl6_5
| ~ spl6_6 ),
inference(avatar_split_clause,[status(thm)],[f73,f54,f48,f35]) ).
thf(f35,definition,
( spl6_2
<=> ( $true
= ( cG @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl6_2])],[avatar_definition]) ).
thf(f48,definition,
( spl6_5
<=> ( $true
= ( cJ @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl6_5])],[avatar_definition]) ).
thf(f54,definition,
( spl6_6
<=> ! [X1: $i] :
( ( ( cJ @ X1 )
= $true )
| ( ( cG @ X1 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl6_6])],[avatar_definition]) ).
thf(f73,plain,
( ( $true
!= ( cG @ sK3 ) )
| spl6_5
| ~ spl6_6 ),
inference(trivial_inequality_removal,[status(thm)],[f72]) ).
thf(f72,plain,
( ( $true
!= ( cG @ sK3 ) )
| ( $true != $true )
| spl6_5
| ~ spl6_6 ),
inference(superposition,[status(thm)],[f50,f55]) ).
thf(f55,plain,
( ! [X1: $i] :
( ( ( cJ @ X1 )
= $true )
| ( ( cG @ X1 )
!= $true ) )
| ~ spl6_6 ),
inference(avatar_component_clause,[status(thm)],[f54]) ).
thf(f50,plain,
( ( $true
!= ( cJ @ sK3 ) )
| spl6_5 ),
inference(avatar_component_clause,[status(thm)],[f48]) ).
thf(f99,plain,
( ~ spl6_1
| ~ spl6_6
| ~ spl6_8 ),
inference(avatar_split_clause,[status(thm)],[f98,f77,f54,f31]) ).
thf(f31,definition,
( spl6_1
<=> ( sP0 = $true ) ),
introduced(definition,[new_symbols(naming,[spl6_1])],[avatar_definition]) ).
thf(f77,definition,
( spl6_8
<=> ( ( cH @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl6_8])],[avatar_definition]) ).
thf(f98,plain,
( ( sP0 != $true )
| ~ spl6_6
| ~ spl6_8 ),
inference(subsumption_resolution,[status(thm)],[f97,f19]) ).
thf(f19,plain,
( ( ( cG @ sK2 )
= $true )
| ( sP0 != $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ! [X0: $i] :
( ( ( cJ @ X0 )
= $true )
| ( ( cG @ X0 )
!= $true ) )
& ! [X1: $i] :
( ( ( cH @ X1 )
= $true )
| ( ( cF @ X1 )
!= $true ) )
& ( ( cF @ sK1 )
= $true )
& ( ( $true
!= ( cJ @ sK2 ) )
| ( ( cH @ sK1 )
!= $true ) )
& ( ( cG @ sK2 )
= $true ) )
| ( sP0 != $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f11,f12]) ).
thf(f12,plain,
( ? [X2: $i,X3: $i] :
( ( ( cF @ X2 )
= $true )
& ( ( ( cJ @ X3 )
!= $true )
| ( ( cH @ X2 )
!= $true ) )
& ( ( cG @ X3 )
= $true ) )
=> ( ( ( cF @ sK1 )
= $true )
& ( ( $true
!= ( cJ @ sK2 ) )
| ( ( cH @ sK1 )
!= $true ) )
& ( ( cG @ sK2 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ( ! [X0: $i] :
( ( ( cJ @ X0 )
= $true )
| ( ( cG @ X0 )
!= $true ) )
& ! [X1: $i] :
( ( ( cH @ X1 )
= $true )
| ( ( cF @ X1 )
!= $true ) )
& ? [X2: $i,X3: $i] :
( ( ( cF @ X2 )
= $true )
& ( ( ( cJ @ X3 )
!= $true )
| ( ( cH @ X2 )
!= $true ) )
& ( ( cG @ X3 )
= $true ) ) )
| ( sP0 != $true ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ! [X6: $i] :
( ( ( cJ @ X6 )
= $true )
| ( ( cG @ X6 )
!= $true ) )
& ! [X5: $i] :
( ( ( cH @ X5 )
= $true )
| ( $true
!= ( cF @ X5 ) ) )
& ? [X8: $i,X7: $i] :
( ( $true
= ( cF @ X8 ) )
& ( ( ( cJ @ X7 )
!= $true )
| ( ( cH @ X8 )
!= $true ) )
& ( ( cG @ X7 )
= $true ) ) )
| ( sP0 != $true ) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
thf(f97,plain,
( ( ( cG @ sK2 )
!= $true )
| ( sP0 != $true )
| ~ spl6_6
| ~ spl6_8 ),
inference(subsumption_resolution,[status(thm)],[f74,f78]) ).
thf(f78,plain,
( ( ( cH @ sK1 )
= $true )
| ~ spl6_8 ),
inference(avatar_component_clause,[status(thm)],[f77]) ).
thf(f74,plain,
( ( ( cH @ sK1 )
!= $true )
| ( sP0 != $true )
| ( ( cG @ sK2 )
!= $true )
| ~ spl6_6 ),
inference(trivial_inequality_removal,[status(thm)],[f71]) ).
thf(f71,plain,
( ( ( cG @ sK2 )
!= $true )
| ( sP0 != $true )
| ( $true != $true )
| ( ( cH @ sK1 )
!= $true )
| ~ spl6_6 ),
inference(superposition,[status(thm)],[f20,f55]) ).
thf(f20,plain,
( ( $true
!= ( cJ @ sK2 ) )
| ( ( cH @ sK1 )
!= $true )
| ( sP0 != $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f92,plain,
( ~ spl6_1
| ~ spl6_4
| spl6_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f91]) ).
thf(f91,plain,
( $false
| ~ spl6_1
| ~ spl6_4
| spl6_8 ),
inference(subsumption_resolution,[status(thm)],[f90,f33]) ).
thf(f33,plain,
( ( sP0 = $true )
| ~ spl6_1 ),
inference(avatar_component_clause,[status(thm)],[f31]) ).
thf(f90,plain,
( ( sP0 != $true )
| ~ spl6_4
| spl6_8 ),
inference(trivial_inequality_removal,[status(thm)],[f89]) ).
thf(f89,plain,
( ( $true != $true )
| ( sP0 != $true )
| ~ spl6_4
| spl6_8 ),
inference(superposition,[status(thm)],[f88,f21]) ).
thf(f21,plain,
( ( ( cF @ sK1 )
= $true )
| ( sP0 != $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f88,plain,
( ( ( cF @ sK1 )
!= $true )
| ~ spl6_4
| spl6_8 ),
inference(trivial_inequality_removal,[status(thm)],[f85]) ).
thf(f85,plain,
( ( $true != $true )
| ( ( cF @ sK1 )
!= $true )
| ~ spl6_4
| spl6_8 ),
inference(superposition,[status(thm)],[f79,f45]) ).
thf(f45,plain,
( ! [X2: $i] :
( ( ( cH @ X2 )
= $true )
| ( ( cF @ X2 )
!= $true ) )
| ~ spl6_4 ),
inference(avatar_component_clause,[status(thm)],[f44]) ).
thf(f44,definition,
( spl6_4
<=> ! [X2: $i] :
( ( ( cF @ X2 )
!= $true )
| ( ( cH @ X2 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl6_4])],[avatar_definition]) ).
thf(f79,plain,
( ( ( cH @ sK1 )
!= $true )
| spl6_8 ),
inference(avatar_component_clause,[status(thm)],[f77]) ).
thf(f66,plain,
~ spl6_3,
inference(avatar_contradiction_clause,[status(thm)],[f65]) ).
thf(f65,plain,
( $false
| ~ spl6_3 ),
inference(trivial_inequality_removal,[status(thm)],[f63]) ).
thf(f63,plain,
( ( $true != $true )
| ~ spl6_3 ),
inference(superposition,[status(thm)],[f42,f25]) ).
thf(f25,plain,
( ( cG @ sK4 )
= $true ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f42,plain,
( ! [X1: $i] :
( ( cG @ X1 )
!= $true )
| ~ spl6_3 ),
inference(avatar_component_clause,[status(thm)],[f41]) ).
thf(f41,definition,
( spl6_3
<=> ! [X1: $i] :
( ( cG @ X1 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[spl6_3])],[avatar_definition]) ).
thf(f59,plain,
( spl6_6
| spl6_7 ),
inference(avatar_split_clause,[status(thm)],[f52,f57,f54]) ).
thf(f52,plain,
! [X2: $i,X1: $i] :
( ( ( cJ @ X1 )
= $true )
| ( ( cF @ X2 )
!= $true )
| ( ( cG @ X1 )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f26,f23]) ).
thf(f23,plain,
! [X0: $i] :
( ( ( cJ @ X0 )
= $true )
| ( ( cG @ X0 )
!= $true )
| ( sP0 != $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f26,plain,
! [X2: $i,X1: $i] :
( ( ( cF @ X2 )
!= $true )
| ( ( cG @ X1 )
!= $true )
| ( sP0 = $true )
| ( ( cJ @ X1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f51,plain,
( spl6_1
| ~ spl6_5 ),
inference(avatar_split_clause,[status(thm)],[f28,f48,f31]) ).
thf(f28,plain,
( ( sP0 = $true )
| ( $true
!= ( cJ @ sK3 ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f46,plain,
( spl6_3
| spl6_4 ),
inference(avatar_split_clause,[status(thm)],[f39,f44,f41]) ).
thf(f39,plain,
! [X2: $i,X1: $i] :
( ( ( cF @ X2 )
!= $true )
| ( ( cH @ X2 )
= $true )
| ( ( cG @ X1 )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f27,f22]) ).
thf(f22,plain,
! [X1: $i] :
( ( ( cH @ X1 )
= $true )
| ( ( cF @ X1 )
!= $true )
| ( sP0 != $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f27,plain,
! [X2: $i,X1: $i] :
( ( ( cH @ X2 )
= $true )
| ( ( cF @ X2 )
!= $true )
| ( ( cG @ X1 )
!= $true )
| ( sP0 = $true ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f38,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[status(thm)],[f29,f35,f31]) ).
thf(f29,plain,
( ( $true
= ( cG @ sK3 ) )
| ( sP0 = $true ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYN059^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n013.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 13:50:23 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.45 ---- Original DTF file ---
% 0.19/0.46 thf(spec,logic,$$dhol).
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % File : SYN059^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.46 % Domain : Syntactic
% 0.19/0.46 % Problem : TPS problem PELL29
% 0.19/0.46 % Version : Especial.
% 0.19/0.46 % English :
% 0.19/0.46
% 0.19/0.46 % Refs : [Pel86] Pelletier (1986), Seventy-five Problems for Testing Au
% 0.19/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.46 % Source : [Bro09]
% 0.19/0.46 % Names : tps_0334 [Bro09]
% 0.19/0.46 % : PELL29 [TPS]
% 0.19/0.46 % : Pelletier 29 [Pel86]
% 0.19/0.46
% 0.19/0.46 % Status : Theorem
% 0.19/0.46 % 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 v6.0.0, 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v4.0.0
% 0.19/0.46 % Syntax : Number of formulae : 5 ( 0 unt; 4 typ; 0 def)
% 0.19/0.46 % Number of atoms : 16 ( 0 equ; 0 cnn)
% 0.19/0.46 % Maximal formula atoms : 16 ( 16 avg)
% 0.19/0.46 % Number of connectives : 31 ( 0 ~; 0 |; 7 &; 16 @)
% 0.19/0.46 % ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% 0.19/0.46 % Maximal formula depth : 9 ( 9 avg)
% 0.19/0.46 % Number of types : 2 ( 0 usr)
% 0.19/0.46 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.19/0.46 % Number of symbols : 4 ( 4 usr; 0 con; 1-1 aty)
% 0.19/0.46 % Number of variables : 9 ( 0 ^; 7 !; 2 ?; 9 :)
% 0.19/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.19/0.46
% 0.19/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.46 % :
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 thf(cJ,type,
% 0.19/0.46 cJ: $i > $o ).
% 0.19/0.46
% 0.19/0.46 thf(cG,type,
% 0.19/0.46 cG: $i > $o ).
% 0.19/0.46
% 0.19/0.46 thf(cH,type,
% 0.19/0.46 cH: $i > $o ).
% 0.19/0.46
% 0.19/0.46 thf(cF,type,
% 0.19/0.46 cF: $i > $o ).
% 0.19/0.46
% 0.19/0.46 thf(cPELL29,conjecture,
% 0.19/0.46 ( ( ? [Xx: $i] : ( cF @ Xx )
% 0.19/0.46 & ? [Xx: $i] : ( cG @ Xx ) )
% 0.19/0.46 => ( ( ( ! [Xx: $i] :
% 0.19/0.46 ( ( cF @ Xx )
% 0.19/0.46 => ( cH @ Xx ) )
% 0.19/0.46 & ! [Xx: $i] :
% 0.19/0.46 ( ( cG @ Xx )
% 0.19/0.46 => ( cJ @ Xx ) ) )
% 0.19/0.46 => ! [Xx: $i,Xy: $i] :
% 0.19/0.46 ( ( ( cF @ Xx )
% 0.19/0.46 & ( cG @ Xy ) )
% 0.19/0.46 => ( ( cH @ Xx )
% 0.19/0.46 & ( cJ @ Xy ) ) ) )
% 0.19/0.46 & ( ! [Xx: $i,Xy: $i] :
% 0.19/0.46 ( ( ( cF @ Xx )
% 0.19/0.46 & ( cG @ Xy ) )
% 0.19/0.46 => ( ( cH @ Xx )
% 0.19/0.46 & ( cJ @ Xy ) ) )
% 0.19/0.46 => ! [Xx: $i] :
% 0.19/0.46 ( ( cG @ Xx )
% 0.19/0.46 => ( cJ @ Xx ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 ------------------------
% 1.49/1.25 ---- Embedded in THF ---
% 1.49/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.25 %%% Generated on Tue Feb 24 13:50:24 EST 2026
% 1.49/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.25 %%% Logic specification used:
% 1.49/1.25 %%% thf(spec, logic, $$dhol).
% 1.49/1.25
% 1.49/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.OnWfODaFyC/DTF2DTF22879.p
% See solution above
% 1.49/1.25 ------------------------
% 1.49/1.26 ---- Cleaned THF ---
% 1.49/1.26 thf(cJ,type,
% 1.49/1.26 cJ: $i > $o ).
% 1.49/1.26
% 1.49/1.26 thf(cG,type,
% 1.49/1.26 cG: $i > $o ).
% 1.49/1.26
% 1.49/1.26 thf(cH,type,
% 1.49/1.26 cH: $i > $o ).
% 1.49/1.26
% 1.49/1.26 thf(cF,type,
% 1.49/1.26 cF: $i > $o ).
% 1.49/1.26
% 1.49/1.26 thf(cPELL29,conjecture,
% 1.49/1.26 ( ( ? [Xx: $i] : ( cF @ Xx )
% 1.49/1.26 & ? [Xx: $i] : ( cG @ Xx ) )
% 1.49/1.26 => ( ( ( ! [Xx: $i] :
% 1.49/1.26 ( ( cF @ Xx )
% 1.49/1.26 => ( cH @ Xx ) )
% 1.49/1.26 & ! [Xx: $i] :
% 1.49/1.26 ( ( cG @ Xx )
% 1.49/1.26 => ( cJ @ Xx ) ) )
% 1.49/1.26 => ! [Xx: $i,Xy: $i] :
% 1.49/1.26 ( ( ( cF @ Xx )
% 1.49/1.26 & ( cG @ Xy ) )
% 1.49/1.26 => ( ( cH @ Xx )
% 1.49/1.26 & ( cJ @ Xy ) ) ) )
% 1.49/1.26 & ( ! [Xx: $i,Xy: $i] :
% 1.49/1.26 ( ( ( cF @ Xx )
% 1.49/1.26 & ( cG @ Xy ) )
% 1.49/1.26 => ( ( cH @ Xx )
% 1.49/1.26 & ( cJ @ Xy ) ) )
% 1.49/1.26 => ! [Xx: $i] :
% 1.49/1.26 ( ( cG @ Xx )
% 1.49/1.26 => ( cJ @ Xx ) ) ) ) ) ).
% 1.49/1.26 ------------------------
% 1.49/1.28 % (23212)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_22879 for (3000ds/275Mi)
% 1.49/1.28 % (23212)First to succeed.
% 1.49/1.28 % (23212)Refutation found. Thanks to Tanya!
% 1.49/1.28 % SZS status Theorem for DTF2THF_22879
% 1.49/1.28 % SZS output start Proof for DTF2THF_22879
% 1.49/1.28 thf(func_def_0, type, cJ: $i > $o).
% 1.49/1.28 thf(func_def_1, type, cG: $i > $o).
% 1.49/1.28 thf(func_def_2, type, cH: $i > $o).
% 1.49/1.28 thf(func_def_3, type, cF: $i > $o).
% 1.49/1.28 thf(f107,plain,(
% 1.49/1.28 $false),
% 1.49/1.28 inference(avatar_sat_refutation,[status(thm)],[f38,f46,f51,f59,f66,f92,f99,f101,f106])).
% 1.49/1.28 thf(f106,plain,(
% 1.49/1.28 ~spl6_7),
% 1.49/1.28 inference(avatar_contradiction_clause,[status(thm)],[f105])).
% 1.49/1.28 thf(f105,plain,(
% 1.49/1.28 $false | ~spl6_7),
% 1.49/1.28 inference(trivial_inequality_removal,[status(thm)],[f103])).
% 1.49/1.28 thf(f103,plain,(
% 1.49/1.28 ($true != $true) | ~spl6_7),
% 1.49/1.28 inference(superposition,[status(thm)],[f58,f24])).
% 1.49/1.28 thf(f24,plain,(
% 1.49/1.28 ((cF @ sK5) = $true)),
% 1.49/1.28 inference(cnf_transformation,[status(thm)],[f18])).
% 1.49/1.28 thf(f18,plain,(
% 1.49/1.28 ((sP0 = $true) | ((($true = (cG @ sK3)) & ($true != (cJ @ sK3))) & ! [X1 : $i,X2 : $i] : (((cF @ X2) != $true) | ((cG @ X1) != $true) | (((cH @ X2) = $true) & ((cJ @ X1) = $true))))) & ((cG @ sK4) = $true) & ((cF @ sK5) = $true)),
% 1.49/1.28 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f14,f17,f16,f15])).
% 1.49/1.28 thf(f15,plain,(
% 1.49/1.28 ? [X0 : $i] : (((cG @ X0) = $true) & ((cJ @ X0) != $true)) => (($true = (cG @ sK3)) & ($true != (cJ @ sK3)))),
% 1.49/1.28 introduced(definition,[],[choice_axiom])).
% 1.49/1.28 thf(f16,plain,(
% 1.49/1.28 ? [X3 : $i] : ((cG @ X3) = $true) => ((cG @ sK4) = $true)),
% 1.49/1.28 introduced(definition,[],[choice_axiom])).
% 1.49/1.28 thf(f17,plain,(
% 1.49/1.28 ? [X4 : $i] : ((cF @ X4) = $true) => ((cF @ sK5) = $true)),
% 1.49/1.28 introduced(definition,[],[choice_axiom])).
% 1.49/1.28 thf(f14,plain,(
% 1.49/1.28 ((sP0 = $true) | (? [X0 : $i] : (((cG @ X0) = $true) & ((cJ @ X0) != $true)) & ! [X1 : $i,X2 : $i] : (((cF @ X2) != $true) | ((cG @ X1) != $true) | (((cH @ X2) = $true) & ((cJ @ X1) = $true))))) & ? [X3 : $i] : ((cG @ X3) = $true) & ? [X4 : $i] : ((cF @ X4) = $true)),
% 1.49/1.28 inference(rectify,[status(thm)],[f9])).
% 1.49/1.28 thf(f9,plain,(
% 1.49/1.28 ((sP0 = $true) | (? [X4 : $i] : (($true = (cG @ X4)) & ((cJ @ X4) != $true)) & ! [X3 : $i,X2 : $i] : (((cF @ X2) != $true) | ((cG @ X3) != $true) | (((cH @ X2) = $true) & ((cJ @ X3) = $true))))) & ? [X0 : $i] : ((cG @ X0) = $true) & ? [X1 : $i] : ((cF @ X1) = $true)),
% 1.49/1.28 inference(definition_folding,[status(thm)],[f7,f8])).
% 1.49/1.28 thf(f8,plain,(
% 1.49/1.28 (! [X6 : $i] : (((cJ @ X6) = $true) | ((cG @ X6) != $true)) & ! [X5 : $i] : (((cH @ X5) = $true) | ($true != (cF @ X5))) & ? [X8 : $i,X7 : $i] : (($true = (cF @ X8)) & (((cJ @ X7) != $true) | ((cH @ X8) != $true)) & ((cG @ X7) = $true))) | ~(sP0 = $true)),
% 1.49/1.28 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.49/1.28 thf(f7,plain,(
% 1.49/1.28 ((! [X6 : $i] : (((cJ @ X6) = $true) | ((cG @ X6) != $true)) & ! [X5 : $i] : (((cH @ X5) = $true) | ($true != (cF @ X5))) & ? [X8 : $i,X7 : $i] : (($true = (cF @ X8)) & (((cJ @ X7) != $true) | ((cH @ X8) != $true)) & ((cG @ X7) = $true))) | (? [X4 : $i] : (($true = (cG @ X4)) & ((cJ @ X4) != $true)) & ! [X3 : $i,X2 : $i] : (((cF @ X2) != $true) | ((cG @ X3) != $true) | (((cH @ X2) = $true) & ((cJ @ X3) = $true))))) & ? [X0 : $i] : ((cG @ X0) = $true) & ? [X1 : $i] : ((cF @ X1) = $true)),
% 1.49/1.28 inference(flattening,[status(thm)],[f6])).
% 1.49/1.28 thf(f6,plain,(
% 1.49/1.28 ((? [X7 : $i,X8 : $i] : ((((cJ @ X7) != $true) | ((cH @ X8) != $true)) & (($true = (cF @ X8)) & ((cG @ X7) = $true))) & (! [X6 : $i] : (((cJ @ X6) = $true) | ((cG @ X6) != $true)) & ! [X5 : $i] : (((cH @ X5) = $true) | ($true != (cF @ X5))))) | (? [X4 : $i] : (($true = (cG @ X4)) & ((cJ @ X4) != $true)) & ! [X3 : $i,X2 : $i] : ((((cH @ X2) = $true) & ((cJ @ X3) = $true)) | (((cG @ X3) != $true) | ((cF @ X2) != $true))))) & (? [X0 : $i] : ((cG @ X0) = $true) & ? [X1 : $i] : ((cF @ X1) = $true))),
% 1.49/1.28 inference(ennf_transformation,[status(thm)],[f5])).
% 1.49/1.28 thf(f5,plain,(
% 1.49/1.28 ~((? [X0 : $i] : ((cG @ X0) = $true) & ? [X1 : $i] : ((cF @ X1) = $true)) => (((! [X6 : $i] : (((cG @ X6) = $true) => ((cJ @ X6) = $true)) & ! [X5 : $i] : (($true = (cF @ X5)) => ((cH @ X5) = $true))) => ! [X7 : $i,X8 : $i] : ((($true = (cF @ X8)) & ((cG @ X7) = $true)) => (((cH @ X8) = $true) & ((cJ @ X7) = $true)))) & (! [X3 : $i,X2 : $i] : ((((cG @ X3) = $true) & ((cF @ X2) = $true)) => (((cH @ X2) = $true) & ((cJ @ X3) = $true))) => ! [X4 : $i] : (($true = (cG @ X4)) => ((cJ @ X4) = $true)))))),
% 1.49/1.28 inference(fool_elimination,[status(thm)],[f4])).
% 1.49/1.28 thf(f4,plain,(
% 1.49/1.28 ~((? [X0 : $i] : (cG @ X0) & ? [X1 : $i] : (cF @ X1)) => ((! [X2 : $i,X3 : $i] : (((cG @ X3) & (cF @ X2)) => ((cJ @ X3) & (cH @ X2))) => ! [X4 : $i] : ((cG @ X4) => (cJ @ X4))) & ((! [X5 : $i] : ((cF @ X5) => (cH @ X5)) & ! [X6 : $i] : ((cG @ X6) => (cJ @ X6))) => ! [X7 : $i,X8 : $i] : (((cF @ X8) & (cG @ X7)) => ((cH @ X8) & (cJ @ X7))))))),
% 1.49/1.28 inference(rectify,[status(thm)],[f2])).
% 1.49/1.28 thf(f2,negated_conjecture,(
% 1.49/1.28 ~((? [X0 : $i] : (cG @ X0) & ? [X0 : $i] : (cF @ X0)) => ((! [X0 : $i,X1 : $i] : (((cG @ X1) & (cF @ X0)) => ((cJ @ X1) & (cH @ X0))) => ! [X0 : $i] : ((cG @ X0) => (cJ @ X0))) & ((! [X0 : $i] : ((cF @ X0) => (cH @ X0)) & ! [X0 : $i] : ((cG @ X0) => (cJ @ X0))) => ! [X1 : $i,X0 : $i] : (((cF @ X0) & (cG @ X1)) => ((cH @ X0) & (cJ @ X1))))))),
% 1.49/1.28 inference(negated_conjecture,[status(cth)],[f1])).
% 1.49/1.28 thf(f1,conjecture,(
% 1.49/1.28 (? [X0 : $i] : (cG @ X0) & ? [X0 : $i] : (cF @ X0)) => ((! [X0 : $i,X1 : $i] : (((cG @ X1) & (cF @ X0)) => ((cJ @ X1) & (cH @ X0))) => ! [X0 : $i] : ((cG @ X0) => (cJ @ X0))) & ((! [X0 : $i] : ((cF @ X0) => (cH @ X0)) & ! [X0 : $i] : ((cG @ X0) => (cJ @ X0))) => ! [X1 : $i,X0 : $i] : (((cF @ X0) & (cG @ X1)) => ((cH @ X0) & (cJ @ X1)))))),
% 1.49/1.28 file('/export/starexec/sandbox/tmp/tmp.OnWfODaFyC/DTF2THF_22879.p',cPELL29)).
% 1.49/1.28 thf(f58,plain,(
% 1.49/1.28 ( ! [X2 : $i] : (((cF @ X2) != $true)) ) | ~spl6_7),
% 1.49/1.28 inference(avatar_component_clause,[status(thm)],[f57])).
% 1.49/1.28 thf(f57,definition,(
% 1.49/1.28 spl6_7 <=> ! [X2 : $i] : ((cF @ X2) != $true)),
% 1.49/1.28 introduced(definition,[new_symbols(naming,[spl6_7])],[avatar_definition])).
% 1.49/1.28 thf(f101,plain,(
% 1.49/1.28 ~spl6_2 | spl6_5 | ~spl6_6),
% 1.49/1.28 inference(avatar_split_clause,[status(thm)],[f73,f54,f48,f35])).
% 1.49/1.28 thf(f35,definition,(
% 1.49/1.28 spl6_2 <=> ($true = (cG @ sK3))),
% 1.49/1.28 introduced(definition,[new_symbols(naming,[spl6_2])],[avatar_definition])).
% 1.49/1.28 thf(f48,definition,(
% 1.49/1.28 spl6_5 <=> ($true = (cJ @ sK3))),
% 1.49/1.28 introduced(definition,[new_symbols(naming,[spl6_5])],[avatar_definition])).
% 1.49/1.28 thf(f54,definition,(
% 1.49/1.28 spl6_6 <=> ! [X1 : $i] : (((cJ @ X1) = $true) | ((cG @ X1) != $true))),
% 1.49/1.28 introduced(definition,[new_symbols(naming,[spl6_6])],[avatar_definition])).
% 1.49/1.28 thf(f73,plain,(
% 1.49/1.28 ($true != (cG @ sK3)) | (spl6_5 | ~spl6_6)),
% 1.49/1.28 inference(trivial_inequality_removal,[status(thm)],[f72])).
% 1.49/1.28 thf(f72,plain,(
% 1.49/1.28 ($true != (cG @ sK3)) | ($true != $true) | (spl6_5 | ~spl6_6)),
% 1.49/1.28 inference(superposition,[status(thm)],[f50,f55])).
% 1.49/1.28 thf(f55,plain,(
% 1.49/1.28 ( ! [X1 : $i] : (((cJ @ X1) = $true) | ((cG @ X1) != $true)) ) | ~spl6_6),
% 1.49/1.28 inference(avatar_component_clause,[status(thm)],[f54])).
% 1.49/1.28 thf(f50,plain,(
% 1.49/1.28 ($true != (cJ @ sK3)) | spl6_5),
% 1.49/1.28 inference(avatar_component_clause,[status(thm)],[f48])).
% 1.49/1.28 thf(f99,plain,(
% 1.49/1.28 ~spl6_1 | ~spl6_6 | ~spl6_8),
% 1.49/1.28 inference(avatar_split_clause,[status(thm)],[f98,f77,f54,f31])).
% 1.49/1.28 thf(f31,definition,(
% 1.49/1.28 spl6_1 <=> (sP0 = $true)),
% 1.49/1.28 introduced(definition,[new_symbols(naming,[spl6_1])],[avatar_definition])).
% 1.49/1.28 thf(f77,definition,(
% 1.49/1.28 spl6_8 <=> ((cH @ sK1) = $true)),
% 1.49/1.28 introduced(definition,[new_symbols(naming,[spl6_8])],[avatar_definition])).
% 1.49/1.28 thf(f98,plain,(
% 1.49/1.28 (sP0 != $true) | (~spl6_6 | ~spl6_8)),
% 1.49/1.28 inference(subsumption_resolution,[status(thm)],[f97,f19])).
% 1.49/1.28 thf(f19,plain,(
% 1.49/1.28 ((cG @ sK2) = $true) | (sP0 != $true)),
% 1.49/1.28 inference(cnf_transformation,[status(thm)],[f13])).
% 1.49/1.28 thf(f13,plain,(
% 1.49/1.28 (! [X0 : $i] : (((cJ @ X0) = $true) | ((cG @ X0) != $true)) & ! [X1 : $i] : (((cH @ X1) = $true) | ((cF @ X1) != $true)) & (((cF @ sK1) = $true) & (($true != (cJ @ sK2)) | ((cH @ sK1) != $true)) & ((cG @ sK2) = $true))) | (sP0 != $true)),
% 1.49/1.28 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f11,f12])).
% 1.49/1.28 thf(f12,plain,(
% 1.49/1.28 ? [X2 : $i,X3 : $i] : (((cF @ X2) = $true) & (((cJ @ X3) != $true) | ((cH @ X2) != $true)) & ((cG @ X3) = $true)) => (((cF @ sK1) = $true) & (($true != (cJ @ sK2)) | ((cH @ sK1) != $true)) & ((cG @ sK2) = $true))),
% 1.49/1.28 introduced(definition,[],[choice_axiom])).
% 1.49/1.28 thf(f11,plain,(
% 1.49/1.28 (! [X0 : $i] : (((cJ @ X0) = $true) | ((cG @ X0) != $true)) & ! [X1 : $i] : (((cH @ X1) = $true) | ((cF @ X1) != $true)) & ? [X2 : $i,X3 : $i] : (((cF @ X2) = $true) & (((cJ @ X3) != $true) | ((cH @ X2) != $true)) & ((cG @ X3) = $true))) | (sP0 != $true)),
% 1.49/1.28 inference(rectify,[status(thm)],[f10])).
% 1.49/1.28 thf(f10,plain,(
% 1.49/1.28 (! [X6 : $i] : (((cJ @ X6) = $true) | ((cG @ X6) != $true)) & ! [X5 : $i] : (((cH @ X5) = $true) | ($true != (cF @ X5))) & ? [X8 : $i,X7 : $i] : (($true = (cF @ X8)) & (((cJ @ X7) != $true) | ((cH @ X8) != $true)) & ((cG @ X7) = $true))) | (sP0 != $true)),
% 1.49/1.28 inference(nnf_transformation,[status(thm)],[f8])).
% 1.49/1.28 thf(f97,plain,(
% 1.49/1.28 ((cG @ sK2) != $true) | (sP0 != $true) | (~spl6_6 | ~spl6_8)),
% 1.49/1.28 inference(subsumption_resolution,[status(thm)],[f74,f78])).
% 1.49/1.28 thf(f78,plain,(
% 1.49/1.28 ((cH @ sK1) = $true) | ~spl6_8),
% 1.49/1.28 inference(avatar_component_clause,[status(thm)],[f77])).
% 1.49/1.28 thf(f74,plain,(
% 1.49/1.28 ((cH @ sK1) != $true) | (sP0 != $true) | ((cG @ sK2) != $true) | ~spl6_6),
% 1.49/1.28 inference(trivial_inequality_removal,[status(thm)],[f71])).
% 1.49/1.28 thf(f71,plain,(
% 1.49/1.28 ((cG @ sK2) != $true) | (sP0 != $true) | ($true != $true) | ((cH @ sK1) != $true) | ~spl6_6),
% 1.49/1.28 inference(superposition,[status(thm)],[f20,f55])).
% 1.49/1.28 thf(f20,plain,(
% 1.49/1.28 ($true != (cJ @ sK2)) | ((cH @ sK1) != $true) | (sP0 != $true)),
% 1.49/1.28 inference(cnf_transformation,[status(thm)],[f13])).
% 1.49/1.28 thf(f92,plain,(
% 1.49/1.28 ~spl6_1 | ~spl6_4 | spl6_8),
% 1.49/1.28 inference(avatar_contradiction_clause,[status(thm)],[f91])).
% 1.49/1.28 thf(f91,plain,(
% 1.49/1.28 $false | (~spl6_1 | ~spl6_4 | spl6_8)),
% 1.49/1.28 inference(subsumption_resolution,[status(thm)],[f90,f33])).
% 1.49/1.28 thf(f33,plain,(
% 1.49/1.28 (sP0 = $true) | ~spl6_1),
% 1.49/1.28 inference(avatar_component_clause,[status(thm)],[f31])).
% 1.49/1.28 thf(f90,plain,(
% 1.49/1.28 (sP0 != $true) | (~spl6_4 | spl6_8)),
% 1.49/1.28 inference(trivial_inequality_removal,[status(thm)],[f89])).
% 1.49/1.28 thf(f89,plain,(
% 1.49/1.28 ($true != $true) | (sP0 != $true) | (~spl6_4 | spl6_8)),
% 1.49/1.28 inference(superposition,[status(thm)],[f88,f21])).
% 1.49/1.28 thf(f21,plain,(
% 1.49/1.28 ((cF @ sK1) = $true) | (sP0 != $true)),
% 1.49/1.28 inference(cnf_transformation,[status(thm)],[f13])).
% 1.49/1.28 thf(f88,plain,(
% 1.49/1.28 ((cF @ sK1) != $true) | (~spl6_4 | spl6_8)),
% 1.49/1.28 inference(trivial_inequality_removal,[status(thm)],[f85])).
% 1.49/1.28 thf(f85,plain,(
% 1.49/1.28 ($true != $true) | ((cF @ sK1) != $true) | (~spl6_4 | spl6_8)),
% 1.49/1.28 inference(superposition,[status(thm)],[f79,f45])).
% 1.49/1.28 thf(f45,plain,(
% 1.49/1.28 ( ! [X2 : $i] : (((cH @ X2) = $true) | ((cF @ X2) != $true)) ) | ~spl6_4),
% 1.49/1.28 inference(avatar_component_clause,[status(thm)],[f44])).
% 1.49/1.28 thf(f44,definition,(
% 1.49/1.28 spl6_4 <=> ! [X2 : $i] : (((cF @ X2) != $true) | ((cH @ X2) = $true))),
% 1.49/1.28 introduced(definition,[new_symbols(naming,[spl6_4])],[avatar_definition])).
% 1.49/1.28 thf(f79,plain,(
% 1.49/1.28 ((cH @ sK1) != $true) | spl6_8),
% 1.49/1.28 inference(avatar_component_clause,[status(thm)],[f77])).
% 1.49/1.28 thf(f66,plain,(
% 1.49/1.28 ~spl6_3),
% 1.49/1.28 inference(avatar_contradiction_clause,[status(thm)],[f65])).
% 1.49/1.28 thf(f65,plain,(
% 1.49/1.28 $false | ~spl6_3),
% 1.49/1.28 inference(trivial_inequality_removal,[status(thm)],[f63])).
% 1.49/1.28 thf(f63,plain,(
% 1.49/1.28 ($true != $true) | ~spl6_3),
% 1.49/1.28 inference(superposition,[status(thm)],[f42,f25])).
% 1.49/1.28 thf(f25,plain,(
% 1.49/1.28 ((cG @ sK4) = $true)),
% 1.49/1.28 inference(cnf_transformation,[status(thm)],[f18])).
% 1.49/1.28 thf(f42,plain,(
% 1.49/1.28 ( ! [X1 : $i] : (((cG @ X1) != $true)) ) | ~spl6_3),
% 1.49/1.28 inference(avatar_component_clause,[status(thm)],[f41])).
% 1.49/1.28 thf(f41,definition,(
% 1.49/1.28 spl6_3 <=> ! [X1 : $i] : ((cG @ X1) != $true)),
% 1.49/1.28 introduced(definition,[new_symbols(naming,[spl6_3])],[avatar_definition])).
% 1.49/1.28 thf(f59,plain,(
% 1.49/1.28 spl6_6 | spl6_7),
% 1.49/1.28 inference(avatar_split_clause,[status(thm)],[f52,f57,f54])).
% 1.49/1.28 thf(f52,plain,(
% 1.49/1.28 ( ! [X2 : $i,X1 : $i] : (((cJ @ X1) = $true) | ((cF @ X2) != $true) | ((cG @ X1) != $true)) )),
% 1.49/1.28 inference(subsumption_resolution,[status(thm)],[f26,f23])).
% 1.49/1.28 thf(f23,plain,(
% 1.49/1.28 ( ! [X0 : $i] : (((cJ @ X0) = $true) | ((cG @ X0) != $true) | (sP0 != $true)) )),
% 1.49/1.28 inference(cnf_transformation,[status(thm)],[f13])).
% 1.49/1.28 thf(f26,plain,(
% 1.49/1.28 ( ! [X2 : $i,X1 : $i] : (((cF @ X2) != $true) | ((cG @ X1) != $true) | (sP0 = $true) | ((cJ @ X1) = $true)) )),
% 1.49/1.28 inference(cnf_transformation,[status(thm)],[f18])).
% 1.49/1.28 thf(f51,plain,(
% 1.49/1.28 spl6_1 | ~spl6_5),
% 1.49/1.28 inference(avatar_split_clause,[status(thm)],[f28,f48,f31])).
% 1.49/1.28 thf(f28,plain,(
% 1.49/1.28 (sP0 = $true) | ($true != (cJ @ sK3))),
% 1.49/1.28 inference(cnf_transformation,[status(thm)],[f18])).
% 1.49/1.28 thf(f46,plain,(
% 1.49/1.28 spl6_3 | spl6_4),
% 1.49/1.28 inference(avatar_split_clause,[status(thm)],[f39,f44,f41])).
% 1.49/1.28 thf(f39,plain,(
% 1.49/1.28 ( ! [X2 : $i,X1 : $i] : (((cF @ X2) != $true) | ((cH @ X2) = $true) | ((cG @ X1) != $true)) )),
% 1.49/1.28 inference(subsumption_resolution,[status(thm)],[f27,f22])).
% 1.49/1.28 thf(f22,plain,(
% 1.49/1.28 ( ! [X1 : $i] : (((cH @ X1) = $true) | ((cF @ X1) != $true) | (sP0 != $true)) )),
% 1.49/1.28 inference(cnf_transformation,[status(thm)],[f13])).
% 1.49/1.28 thf(f27,plain,(
% 1.49/1.28 ( ! [X2 : $i,X1 : $i] : (((cH @ X2) = $true) | ((cF @ X2) != $true) | ((cG @ X1) != $true) | (sP0 = $true)) )),
% 1.49/1.28 inference(cnf_transformation,[status(thm)],[f18])).
% 1.49/1.28 thf(f38,plain,(
% 1.49/1.28 spl6_1 | spl6_2),
% 1.49/1.28 inference(avatar_split_clause,[status(thm)],[f29,f35,f31])).
% 1.49/1.28 thf(f29,plain,(
% 1.49/1.28 ($true = (cG @ sK3)) | (sP0 = $true)),
% 1.49/1.28 inference(cnf_transformation,[status(thm)],[f18])).
% 1.49/1.28 % SZS output end Proof for DTF2THF_22879
% 1.49/1.28 % (23212)------------------------------
% 1.49/1.28 % (23212)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.28 % (23212)Termination reason: Refutation
% 1.49/1.28
% 1.49/1.28 % (23212)Memory used [KB]: 5500
% 1.49/1.28 % (23212)Time elapsed: 0.005 s
% 1.49/1.28 % (23212)Instructions burned: 5 (million)
% 1.49/1.28 % (23212)------------------------------
% 1.49/1.28 % (23212)------------------------------
% 1.49/1.28 % (23206)Success in time 0.014 s
%------------------------------------------------------------------------------