%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO175^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:53:35 AM UTC 2026
% Result : Theorem 1.71s 1.45s
% Output : Refutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 7
% Syntax : Number of formulae : 52 ( 10 unt; 0 typ; 4 def)
% Number of atoms : 551 ( 156 equ; 0 cnn)
% Maximal formula atoms : 16 ( 10 avg)
% Number of connectives : 688 ( 107 ~; 67 |; 104 &; 394 @)
% ( 4 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 14 con; 0-2 aty)
% Number of variables : 108 ( 0 ^; 75 !; 33 ?; 108 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
p: $tType ).
thf(type_def_6,type,
a: $tType ).
thf(func_def_0,type,
p: $tType ).
thf(func_def_1,type,
a: $tType ).
thf(func_def_2,type,
cGRAIN: p ).
thf(func_def_3,type,
cVEG_EATS: a > p > $o ).
thf(func_def_4,type,
cMEAT_EATS: a > a > $o ).
thf(func_def_5,type,
cSNAIL: a ).
thf(func_def_6,type,
cCATERPILLAR: a ).
thf(func_def_7,type,
cBIRD: a ).
thf(func_def_8,type,
cWOLF: a ).
thf(func_def_9,type,
cFOX: a ).
thf(func_def_10,type,
cSMALLER: a > a > $o ).
thf(func_def_14,type,
sK0: p ).
thf(func_def_15,type,
sK1: p ).
thf(f66,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f36,f44,f47,f60,f65]) ).
thf(f65,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[status(thm)],[f64]) ).
thf(f64,plain,
( $false
| ~ spl2_1 ),
inference(trivial_inequality_removal,[status(thm)],[f61]) ).
thf(f61,plain,
( ( $true != $true )
| ~ spl2_1 ),
inference(superposition,[status(thm)],[f22,f32]) ).
thf(f32,plain,
( ! [X0: p] :
( ( cVEG_EATS @ cWOLF @ X0 )
= $true )
| ~ spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f31]) ).
thf(f31,definition,
( spl2_1
<=> ! [X0: p] :
( ( cVEG_EATS @ cWOLF @ X0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f22,plain,
( ( cVEG_EATS @ cWOLF @ cGRAIN )
!= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ( cSMALLER @ cBIRD @ cFOX )
= $true )
& ( ( cMEAT_EATS @ cBIRD @ cCATERPILLAR )
= $true )
& ( ( cVEG_EATS @ cWOLF @ cGRAIN )
!= $true )
& ( ( cMEAT_EATS @ cBIRD @ cSNAIL )
!= $true )
& ( ( cSMALLER @ cCATERPILLAR @ cBIRD )
= $true )
& ( $true
= ( cVEG_EATS @ cSNAIL @ sK0 ) )
& ( ( cSMALLER @ cSNAIL @ cBIRD )
= $true )
& ! [X1: a] :
( ! [X2: p] :
( $true
= ( cVEG_EATS @ X1 @ X2 ) )
| ! [X3: a] :
( ( $true
!= ( cSMALLER @ X3 @ X1 ) )
| ! [X4: p] :
( $true
!= ( cVEG_EATS @ X3 @ X4 ) )
| ( $true
= ( cMEAT_EATS @ X1 @ X3 ) ) ) )
& ( ( cSMALLER @ cFOX @ cWOLF )
= $true )
& ( ( cMEAT_EATS @ cWOLF @ cFOX )
!= $true )
& ( $true
= ( cVEG_EATS @ cCATERPILLAR @ sK1 ) )
& ! [X6: a,X7: a] :
( ( $true
!= ( cVEG_EATS @ X7 @ cGRAIN ) )
| ( ( cMEAT_EATS @ X6 @ X7 )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f9,f11,f10]) ).
thf(f10,plain,
( ? [X0: p] :
( $true
= ( cVEG_EATS @ cSNAIL @ X0 ) )
=> ( $true
= ( cVEG_EATS @ cSNAIL @ sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X5: p] :
( $true
= ( cVEG_EATS @ cCATERPILLAR @ X5 ) )
=> ( $true
= ( cVEG_EATS @ cCATERPILLAR @ sK1 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ( ( cSMALLER @ cBIRD @ cFOX )
= $true )
& ( ( cMEAT_EATS @ cBIRD @ cCATERPILLAR )
= $true )
& ( ( cVEG_EATS @ cWOLF @ cGRAIN )
!= $true )
& ( ( cMEAT_EATS @ cBIRD @ cSNAIL )
!= $true )
& ( ( cSMALLER @ cCATERPILLAR @ cBIRD )
= $true )
& ? [X0: p] :
( $true
= ( cVEG_EATS @ cSNAIL @ X0 ) )
& ( ( cSMALLER @ cSNAIL @ cBIRD )
= $true )
& ! [X1: a] :
( ! [X2: p] :
( $true
= ( cVEG_EATS @ X1 @ X2 ) )
| ! [X3: a] :
( ( $true
!= ( cSMALLER @ X3 @ X1 ) )
| ! [X4: p] :
( $true
!= ( cVEG_EATS @ X3 @ X4 ) )
| ( $true
= ( cMEAT_EATS @ X1 @ X3 ) ) ) )
& ( ( cSMALLER @ cFOX @ cWOLF )
= $true )
& ( ( cMEAT_EATS @ cWOLF @ cFOX )
!= $true )
& ? [X5: p] :
( $true
= ( cVEG_EATS @ cCATERPILLAR @ X5 ) )
& ! [X6: a,X7: a] :
( ( $true
!= ( cVEG_EATS @ X7 @ cGRAIN ) )
| ( ( cMEAT_EATS @ X6 @ X7 )
!= $true ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ( cSMALLER @ cBIRD @ cFOX )
= $true )
& ( ( cMEAT_EATS @ cBIRD @ cCATERPILLAR )
= $true )
& ( ( cVEG_EATS @ cWOLF @ cGRAIN )
!= $true )
& ( ( cMEAT_EATS @ cBIRD @ cSNAIL )
!= $true )
& ( ( cSMALLER @ cCATERPILLAR @ cBIRD )
= $true )
& ? [X5: p] :
( ( cVEG_EATS @ cSNAIL @ X5 )
= $true )
& ( ( cSMALLER @ cSNAIL @ cBIRD )
= $true )
& ! [X1: a] :
( ! [X4: p] :
( ( cVEG_EATS @ X1 @ X4 )
= $true )
| ! [X2: a] :
( ( $true
!= ( cSMALLER @ X2 @ X1 ) )
| ! [X3: p] :
( ( cVEG_EATS @ X2 @ X3 )
!= $true )
| ( ( cMEAT_EATS @ X1 @ X2 )
= $true ) ) )
& ( ( cSMALLER @ cFOX @ cWOLF )
= $true )
& ( ( cMEAT_EATS @ cWOLF @ cFOX )
!= $true )
& ? [X0: p] :
( ( cVEG_EATS @ cCATERPILLAR @ X0 )
= $true )
& ! [X6: a,X7: a] :
( ( $true
!= ( cVEG_EATS @ X7 @ cGRAIN ) )
| ( ( cMEAT_EATS @ X6 @ X7 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X6: a,X7: a] :
( ( $true
!= ( cVEG_EATS @ X7 @ cGRAIN ) )
| ( ( cMEAT_EATS @ X6 @ X7 )
!= $true ) )
& ? [X5: p] :
( ( cVEG_EATS @ cSNAIL @ X5 )
= $true )
& ( ( cSMALLER @ cCATERPILLAR @ cBIRD )
= $true )
& ( ( cMEAT_EATS @ cWOLF @ cFOX )
!= $true )
& ( ( cMEAT_EATS @ cBIRD @ cCATERPILLAR )
= $true )
& ! [X1: a] :
( ! [X4: p] :
( ( cVEG_EATS @ X1 @ X4 )
= $true )
| ! [X2: a] :
( ( ( cMEAT_EATS @ X1 @ X2 )
= $true )
| ( $true
!= ( cSMALLER @ X2 @ X1 ) )
| ! [X3: p] :
( ( cVEG_EATS @ X2 @ X3 )
!= $true ) ) )
& ( ( cSMALLER @ cSNAIL @ cBIRD )
= $true )
& ( ( cVEG_EATS @ cWOLF @ cGRAIN )
!= $true )
& ( ( cSMALLER @ cBIRD @ cFOX )
= $true )
& ? [X0: p] :
( ( cVEG_EATS @ cCATERPILLAR @ X0 )
= $true )
& ( ( cMEAT_EATS @ cBIRD @ cSNAIL )
!= $true )
& ( ( cSMALLER @ cFOX @ cWOLF )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ( ? [X5: p] :
( ( cVEG_EATS @ cSNAIL @ X5 )
= $true )
& ( ( cSMALLER @ cCATERPILLAR @ cBIRD )
= $true )
& ( ( cMEAT_EATS @ cWOLF @ cFOX )
!= $true )
& ( ( cMEAT_EATS @ cBIRD @ cCATERPILLAR )
= $true )
& ! [X1: a] :
( ! [X4: p] :
( ( cVEG_EATS @ X1 @ X4 )
= $true )
| ! [X2: a] :
( ( ( $true
= ( cSMALLER @ X2 @ X1 ) )
& ? [X3: p] :
( ( cVEG_EATS @ X2 @ X3 )
= $true ) )
=> ( ( cMEAT_EATS @ X1 @ X2 )
= $true ) ) )
& ( ( cSMALLER @ cSNAIL @ cBIRD )
= $true )
& ( ( cVEG_EATS @ cWOLF @ cGRAIN )
!= $true )
& ( ( cSMALLER @ cBIRD @ cFOX )
= $true )
& ? [X0: p] :
( ( cVEG_EATS @ cCATERPILLAR @ X0 )
= $true )
& ( ( cMEAT_EATS @ cBIRD @ cSNAIL )
!= $true )
& ( ( cSMALLER @ cFOX @ cWOLF )
= $true ) )
=> ? [X7: a,X6: a] :
( ( ( cMEAT_EATS @ X6 @ X7 )
= $true )
& ( $true
= ( cVEG_EATS @ X7 @ cGRAIN ) ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ( ( cSMALLER @ cBIRD @ cFOX )
= $true )
& ( ( cVEG_EATS @ cWOLF @ cGRAIN )
!= $true )
& ? [X0: p] :
( ( cVEG_EATS @ cCATERPILLAR @ X0 )
= $true )
& ( ( cMEAT_EATS @ cBIRD @ cCATERPILLAR )
= $true )
& ( ( cSMALLER @ cCATERPILLAR @ cBIRD )
= $true )
& ( ( cSMALLER @ cSNAIL @ cBIRD )
= $true )
& ( ( cMEAT_EATS @ cBIRD @ cSNAIL )
!= $true )
& ! [X1: a] :
( ! [X4: p] :
( ( cVEG_EATS @ X1 @ X4 )
= $true )
| ! [X2: a] :
( ( ( $true
= ( cSMALLER @ X2 @ X1 ) )
& ? [X3: p] :
( ( cVEG_EATS @ X2 @ X3 )
= $true ) )
=> ( ( cMEAT_EATS @ X1 @ X2 )
= $true ) ) )
& ( ( cSMALLER @ cFOX @ cWOLF )
= $true )
& ( ( cMEAT_EATS @ cWOLF @ cFOX )
!= $true )
& ? [X5: p] :
( ( cVEG_EATS @ cSNAIL @ X5 )
= $true ) )
=> ? [X7: a,X6: a] :
( ( ( cMEAT_EATS @ X6 @ X7 )
= $true )
& ( $true
= ( cVEG_EATS @ X7 @ cGRAIN ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ( cSMALLER @ cBIRD @ cFOX )
& ~ ( cVEG_EATS @ cWOLF @ cGRAIN )
& ? [X0: p] : ( cVEG_EATS @ cCATERPILLAR @ X0 )
& ( cMEAT_EATS @ cBIRD @ cCATERPILLAR )
& ( cSMALLER @ cCATERPILLAR @ cBIRD )
& ( cSMALLER @ cSNAIL @ cBIRD )
& ~ ( cMEAT_EATS @ cBIRD @ cSNAIL )
& ! [X1: a] :
( ! [X2: a] :
( ( ( cSMALLER @ X2 @ X1 )
& ? [X3: p] : ( cVEG_EATS @ X2 @ X3 ) )
=> ( cMEAT_EATS @ X1 @ X2 ) )
| ! [X4: p] : ( cVEG_EATS @ X1 @ X4 ) )
& ( cSMALLER @ cFOX @ cWOLF )
& ~ ( cMEAT_EATS @ cWOLF @ cFOX )
& ? [X5: p] : ( cVEG_EATS @ cSNAIL @ X5 ) )
=> ? [X6: a,X7: a] :
( ( cVEG_EATS @ X7 @ cGRAIN )
& ( cMEAT_EATS @ X6 @ X7 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ( cSMALLER @ cBIRD @ cFOX )
& ~ ( cVEG_EATS @ cWOLF @ cGRAIN )
& ? [X1: p] : ( cVEG_EATS @ cCATERPILLAR @ X1 )
& ( cMEAT_EATS @ cBIRD @ cCATERPILLAR )
& ( cSMALLER @ cCATERPILLAR @ cBIRD )
& ( cSMALLER @ cSNAIL @ cBIRD )
& ~ ( cMEAT_EATS @ cBIRD @ cSNAIL )
& ! [X0: a] :
( ! [X2: a] :
( ( ( cSMALLER @ X2 @ X0 )
& ? [X3: p] : ( cVEG_EATS @ X2 @ X3 ) )
=> ( cMEAT_EATS @ X0 @ X2 ) )
| ! [X1: p] : ( cVEG_EATS @ X0 @ X1 ) )
& ( cSMALLER @ cFOX @ cWOLF )
& ~ ( cMEAT_EATS @ cWOLF @ cFOX )
& ? [X1: p] : ( cVEG_EATS @ cSNAIL @ X1 ) )
=> ? [X0: a,X1: a] :
( ( cVEG_EATS @ X1 @ cGRAIN )
& ( cMEAT_EATS @ X0 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ( cSMALLER @ cBIRD @ cFOX )
& ~ ( cVEG_EATS @ cWOLF @ cGRAIN )
& ? [X1: p] : ( cVEG_EATS @ cCATERPILLAR @ X1 )
& ( cMEAT_EATS @ cBIRD @ cCATERPILLAR )
& ( cSMALLER @ cCATERPILLAR @ cBIRD )
& ( cSMALLER @ cSNAIL @ cBIRD )
& ~ ( cMEAT_EATS @ cBIRD @ cSNAIL )
& ! [X0: a] :
( ! [X2: a] :
( ( ( cSMALLER @ X2 @ X0 )
& ? [X3: p] : ( cVEG_EATS @ X2 @ X3 ) )
=> ( cMEAT_EATS @ X0 @ X2 ) )
| ! [X1: p] : ( cVEG_EATS @ X0 @ X1 ) )
& ( cSMALLER @ cFOX @ cWOLF )
& ~ ( cMEAT_EATS @ cWOLF @ cFOX )
& ? [X1: p] : ( cVEG_EATS @ cSNAIL @ X1 ) )
=> ? [X0: a,X1: a] :
( ( cVEG_EATS @ X1 @ cGRAIN )
& ( cMEAT_EATS @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.DnTVbJIk6s/DTF2THF_8941.p',cPUZ031_1_HO) ).
thf(f60,plain,
( ~ spl2_2
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f59]) ).
thf(f59,plain,
( $false
| ~ spl2_2
| ~ spl2_4 ),
inference(subsumption_resolution,[status(thm)],[f57,f24]) ).
thf(f24,plain,
( ( cSMALLER @ cBIRD @ cFOX )
= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f57,plain,
( ( ( cSMALLER @ cBIRD @ cFOX )
!= $true )
| ~ spl2_2
| ~ spl2_4 ),
inference(trivial_inequality_removal,[status(thm)],[f55]) ).
thf(f55,plain,
( ( ( cSMALLER @ cBIRD @ cFOX )
!= $true )
| ( $true != $true )
| ~ spl2_2
| ~ spl2_4 ),
inference(superposition,[status(thm)],[f35,f52]) ).
thf(f52,plain,
( ! [X0: a,X1: p] :
( ( ( cVEG_EATS @ X0 @ X1 )
= $true )
| ( $true
!= ( cSMALLER @ cBIRD @ X0 ) ) )
| ~ spl2_4 ),
inference(subsumption_resolution,[status(thm)],[f51,f43]) ).
thf(f43,plain,
( ! [X0: p] :
( $true
= ( cVEG_EATS @ cBIRD @ X0 ) )
| ~ spl2_4 ),
inference(avatar_component_clause,[status(thm)],[f42]) ).
thf(f42,definition,
( spl2_4
<=> ! [X0: p] :
( $true
= ( cVEG_EATS @ cBIRD @ X0 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition]) ).
thf(f51,plain,
( ! [X2: p,X0: a,X1: p] :
( ( ( cVEG_EATS @ X0 @ X1 )
= $true )
| ( $true
!= ( cSMALLER @ cBIRD @ X0 ) )
| ( $true
!= ( cVEG_EATS @ cBIRD @ X2 ) ) )
| ~ spl2_4 ),
inference(trivial_inequality_removal,[status(thm)],[f50]) ).
thf(f50,plain,
( ! [X2: p,X0: a,X1: p] :
( ( $true
!= ( cSMALLER @ cBIRD @ X0 ) )
| ( $true != $true )
| ( ( cVEG_EATS @ X0 @ X1 )
= $true )
| ( $true
!= ( cVEG_EATS @ cBIRD @ X2 ) ) )
| ~ spl2_4 ),
inference(superposition,[status(thm)],[f49,f17]) ).
thf(f17,plain,
! [X2: p,X3: a,X1: a,X4: p] :
( ( $true
= ( cMEAT_EATS @ X1 @ X3 ) )
| ( $true
!= ( cSMALLER @ X3 @ X1 ) )
| ( $true
= ( cVEG_EATS @ X1 @ X2 ) )
| ( $true
!= ( cVEG_EATS @ X3 @ X4 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f49,plain,
( ! [X0: a] :
( ( cMEAT_EATS @ X0 @ cBIRD )
!= $true )
| ~ spl2_4 ),
inference(trivial_inequality_removal,[status(thm)],[f48]) ).
thf(f48,plain,
( ! [X0: a] :
( ( ( cMEAT_EATS @ X0 @ cBIRD )
!= $true )
| ( $true != $true ) )
| ~ spl2_4 ),
inference(superposition,[status(thm)],[f13,f43]) ).
thf(f13,plain,
! [X6: a,X7: a] :
( ( $true
!= ( cVEG_EATS @ X7 @ cGRAIN ) )
| ( ( cMEAT_EATS @ X6 @ X7 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f35,plain,
( ! [X1: p] :
( ( cVEG_EATS @ cFOX @ X1 )
!= $true )
| ~ spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f34]) ).
thf(f34,definition,
( spl2_2
<=> ! [X1: p] :
( ( cVEG_EATS @ cFOX @ X1 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f47,plain,
~ spl2_3,
inference(avatar_contradiction_clause,[status(thm)],[f46]) ).
thf(f46,plain,
( $false
| ~ spl2_3 ),
inference(trivial_inequality_removal,[status(thm)],[f45]) ).
thf(f45,plain,
( ( $true != $true )
| ~ spl2_3 ),
inference(superposition,[status(thm)],[f40,f19]) ).
thf(f19,plain,
( $true
= ( cVEG_EATS @ cSNAIL @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f40,plain,
( ! [X1: p] :
( ( cVEG_EATS @ cSNAIL @ X1 )
!= $true )
| ~ spl2_3 ),
inference(avatar_component_clause,[status(thm)],[f39]) ).
thf(f39,definition,
( spl2_3
<=> ! [X1: p] :
( ( cVEG_EATS @ cSNAIL @ X1 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition]) ).
thf(f44,plain,
( spl2_3
| spl2_4 ),
inference(avatar_split_clause,[status(thm)],[f37,f42,f39]) ).
thf(f37,plain,
! [X0: p,X1: p] :
( ( $true
= ( cVEG_EATS @ cBIRD @ X0 ) )
| ( ( cVEG_EATS @ cSNAIL @ X1 )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f27,f18]) ).
thf(f18,plain,
( ( cSMALLER @ cSNAIL @ cBIRD )
= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f27,plain,
! [X0: p,X1: p] :
( ( ( cSMALLER @ cSNAIL @ cBIRD )
!= $true )
| ( $true
= ( cVEG_EATS @ cBIRD @ X0 ) )
| ( ( cVEG_EATS @ cSNAIL @ X1 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f26]) ).
thf(f26,plain,
! [X0: p,X1: p] :
( ( ( cSMALLER @ cSNAIL @ cBIRD )
!= $true )
| ( ( cVEG_EATS @ cSNAIL @ X1 )
!= $true )
| ( $true != $true )
| ( $true
= ( cVEG_EATS @ cBIRD @ X0 ) ) ),
inference(superposition,[status(thm)],[f21,f17]) ).
thf(f21,plain,
( ( cMEAT_EATS @ cBIRD @ cSNAIL )
!= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f36,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f29,f34,f31]) ).
thf(f29,plain,
! [X0: p,X1: p] :
( ( ( cVEG_EATS @ cFOX @ X1 )
!= $true )
| ( ( cVEG_EATS @ cWOLF @ X0 )
= $true ) ),
inference(subsumption_resolution,[status(thm)],[f28,f16]) ).
thf(f16,plain,
( ( cSMALLER @ cFOX @ cWOLF )
= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f28,plain,
! [X0: p,X1: p] :
( ( ( cVEG_EATS @ cFOX @ X1 )
!= $true )
| ( ( cVEG_EATS @ cWOLF @ X0 )
= $true )
| ( ( cSMALLER @ cFOX @ cWOLF )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f25]) ).
thf(f25,plain,
! [X0: p,X1: p] :
( ( ( cVEG_EATS @ cFOX @ X1 )
!= $true )
| ( ( cVEG_EATS @ cWOLF @ X0 )
= $true )
| ( $true != $true )
| ( ( cSMALLER @ cFOX @ cWOLF )
!= $true ) ),
inference(superposition,[status(thm)],[f15,f17]) ).
thf(f15,plain,
( ( cMEAT_EATS @ cWOLF @ cFOX )
!= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO175^5 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.35 % Computer : n001.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Tue Feb 24 14:26:20 EST 2026
% 0.18/0.35 % CPUTime :
% 0.18/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.47 thf(spec,logic,$$dhol).
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 % File : SYO175^5 : TPTP v9.2.1. Released v4.0.0.
% 0.30/0.47 % Domain : Syntactic
% 0.30/0.47 % Problem : TPS problem from BASIC-FO-THMS
% 0.30/0.47 % Version : Especial.
% 0.30/0.47 % English :
% 0.30/0.47
% 0.30/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.30/0.47 % Source : [Bro09]
% 0.30/0.47 % Names : tps_1060 [Bro09]
% 0.30/0.47
% 0.30/0.47 % Status : Theorem
% 0.30/0.47 % Rating : 0.17 v9.1.0, 0.12 v9.0.0, 0.17 v8.2.0, 0.18 v8.1.0, 0.17 v7.4.0, 0.22 v7.3.0, 0.20 v7.2.0, 0.25 v7.1.0, 0.29 v7.0.0, 0.25 v6.4.0, 0.29 v6.3.0, 0.33 v6.0.0, 0.17 v5.5.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.0
% 0.30/0.47 % Syntax : Number of formulae : 12 ( 0 unt; 11 typ; 0 def)
% 0.30/0.47 % Number of atoms : 16 ( 0 equ; 0 cnn)
% 0.30/0.47 % Maximal formula atoms : 16 ( 16 avg)
% 0.30/0.47 % Number of connectives : 50 ( 3 ~; 1 |; 12 &; 32 @)
% 0.30/0.47 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.30/0.47 % Maximal formula depth : 15 ( 15 avg)
% 0.30/0.47 % Number of types : 3 ( 2 usr)
% 0.30/0.47 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.30/0.47 % Number of symbols : 9 ( 9 usr; 6 con; 0-2 aty)
% 0.30/0.47 % Number of variables : 8 ( 0 ^; 3 !; 5 ?; 8 :)
% 0.30/0.47 % SPC : TH0_THM_NEQ_NAR
% 0.30/0.47
% 0.30/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.30/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.30/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.30/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 thf(p_type,type,
% 0.30/0.47 p: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(a_type,type,
% 0.30/0.47 a: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(cGRAIN,type,
% 0.30/0.47 cGRAIN: p ).
% 0.30/0.47
% 0.30/0.47 thf(cVEG_EATS,type,
% 0.30/0.47 cVEG_EATS: a > p > $o ).
% 0.30/0.47
% 0.30/0.47 thf(cMEAT_EATS,type,
% 0.30/0.47 cMEAT_EATS: a > a > $o ).
% 0.30/0.47
% 0.30/0.47 thf(cSNAIL,type,
% 0.30/0.47 cSNAIL: a ).
% 0.30/0.47
% 0.30/0.47 thf(cCATERPILLAR,type,
% 0.30/0.47 cCATERPILLAR: a ).
% 0.30/0.47
% 0.30/0.47 thf(cBIRD,type,
% 0.30/0.47 cBIRD: a ).
% 0.30/0.47
% 0.30/0.47 thf(cWOLF,type,
% 0.30/0.47 cWOLF: a ).
% 0.30/0.47
% 0.30/0.47 thf(cFOX,type,
% 0.30/0.47 cFOX: a ).
% 0.30/0.47
% 0.30/0.47 thf(cSMALLER,type,
% 0.30/0.47 cSMALLER: a > a > $o ).
% 0.30/0.47
% 0.30/0.47 thf(cPUZ031_1_HO,conjecture,
% 0.30/0.47 ( ( ! [Xx: a] :
% 0.30/0.47 ( ! [Xy: p] : ( cVEG_EATS @ Xx @ Xy )
% 0.30/0.47 | ! [Xz: a] :
% 0.30/0.47 ( ( ( cSMALLER @ Xz @ Xx )
% 0.30/0.47 & ? [Xw: p] : ( cVEG_EATS @ Xz @ Xw ) )
% 0.30/0.47 => ( cMEAT_EATS @ Xx @ Xz ) ) )
% 0.30/0.47 & ( cSMALLER @ cCATERPILLAR @ cBIRD )
% 0.30/0.47 & ( cSMALLER @ cSNAIL @ cBIRD )
% 0.30/0.47 & ( cSMALLER @ cBIRD @ cFOX )
% 0.30/0.47 & ( cSMALLER @ cFOX @ cWOLF )
% 0.30/0.47 & ~ ( cMEAT_EATS @ cWOLF @ cFOX )
% 0.30/0.47 & ~ ( cVEG_EATS @ cWOLF @ cGRAIN )
% 0.30/0.47 & ( cMEAT_EATS @ cBIRD @ cCATERPILLAR )
% 0.30/0.47 & ~ ( cMEAT_EATS @ cBIRD @ cSNAIL )
% 0.30/0.47 & ? [Xy: p] : ( cVEG_EATS @ cCATERPILLAR @ Xy )
% 0.30/0.47 & ? [Xy: p] : ( cVEG_EATS @ cSNAIL @ Xy ) )
% 0.30/0.47 => ? [Xx: a,Xy: a] :
% 0.30/0.47 ( ( cMEAT_EATS @ Xx @ Xy )
% 0.30/0.47 & ( cVEG_EATS @ Xy @ cGRAIN ) ) ) ).
% 0.30/0.47
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 ------------------------
% 1.71/1.41 ---- Embedded in THF ---
% 1.71/1.41 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.71/1.41 %%% Generated on Tue Feb 24 14:26:21 EST 2026
% 1.71/1.41 %%% using '$$dhol' embedding, version 1.3.0.
% 1.71/1.41 %%% Logic specification used:
% 1.71/1.41 %%% thf(spec, logic, $$dhol).
% 1.71/1.41
% 1.71/1.41 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.DnTVbJIk6s/DTF2DTF8941.p
% See solution above
% 1.71/1.41 ------------------------
% 1.71/1.42 ---- Cleaned THF ---
% 1.71/1.42 thf(p_type,type,
% 1.71/1.42 p: $tType ).
% 1.71/1.42
% 1.71/1.42 thf(a_type,type,
% 1.71/1.42 a: $tType ).
% 1.71/1.42
% 1.71/1.42 thf(cGRAIN,type,
% 1.71/1.42 cGRAIN: p ).
% 1.71/1.42
% 1.71/1.42 thf(cVEG_EATS,type,
% 1.71/1.42 cVEG_EATS: a > p > $o ).
% 1.71/1.42
% 1.71/1.42 thf(cMEAT_EATS,type,
% 1.71/1.42 cMEAT_EATS: a > a > $o ).
% 1.71/1.42
% 1.71/1.42 thf(cSNAIL,type,
% 1.71/1.42 cSNAIL: a ).
% 1.71/1.42
% 1.71/1.42 thf(cCATERPILLAR,type,
% 1.71/1.42 cCATERPILLAR: a ).
% 1.71/1.42
% 1.71/1.42 thf(cBIRD,type,
% 1.71/1.42 cBIRD: a ).
% 1.71/1.42
% 1.71/1.42 thf(cWOLF,type,
% 1.71/1.42 cWOLF: a ).
% 1.71/1.42
% 1.71/1.42 thf(cFOX,type,
% 1.71/1.42 cFOX: a ).
% 1.71/1.42
% 1.71/1.42 thf(cSMALLER,type,
% 1.71/1.42 cSMALLER: a > a > $o ).
% 1.71/1.42
% 1.71/1.42 thf(cPUZ031_1_HO,conjecture,
% 1.71/1.42 ( ( ! [Xx: a] :
% 1.71/1.42 ( ! [Xy: p] : ( cVEG_EATS @ Xx @ Xy )
% 1.71/1.42 | ! [Xz: a] :
% 1.71/1.42 ( ( ( cSMALLER @ Xz @ Xx )
% 1.71/1.42 & ? [Xw: p] : ( cVEG_EATS @ Xz @ Xw ) )
% 1.71/1.42 => ( cMEAT_EATS @ Xx @ Xz ) ) )
% 1.71/1.42 & ( cSMALLER @ cCATERPILLAR @ cBIRD )
% 1.71/1.42 & ( cSMALLER @ cSNAIL @ cBIRD )
% 1.71/1.42 & ( cSMALLER @ cBIRD @ cFOX )
% 1.71/1.42 & ( cSMALLER @ cFOX @ cWOLF )
% 1.71/1.42 & ~ ( cMEAT_EATS @ cWOLF @ cFOX )
% 1.71/1.42 & ~ ( cVEG_EATS @ cWOLF @ cGRAIN )
% 1.71/1.42 & ( cMEAT_EATS @ cBIRD @ cCATERPILLAR )
% 1.71/1.42 & ~ ( cMEAT_EATS @ cBIRD @ cSNAIL )
% 1.71/1.42 & ? [Xy: p] : ( cVEG_EATS @ cCATERPILLAR @ Xy )
% 1.71/1.42 & ? [Xy: p] : ( cVEG_EATS @ cSNAIL @ Xy ) )
% 1.71/1.42 => ? [Xx: a,Xy: a] :
% 1.71/1.42 ( ( cMEAT_EATS @ Xx @ Xy )
% 1.71/1.42 & ( cVEG_EATS @ Xy @ cGRAIN ) ) ) ).
% 1.71/1.42 ------------------------
% 1.71/1.44 % (9042)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_8941 for (2999ds/2Mi)
% 1.71/1.44 % (9040)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_8941 for (2999ds/27Mi)
% 1.71/1.44 % (9044)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_8941 for (2999ds/18Mi)
% 1.71/1.44 % (9043)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_8941 for (2999ds/275Mi)
% 1.71/1.44 % (9038)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_8941 for (2999ds/183Mi)
% 1.71/1.44 % (9039)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_8941 for (2999ds/4Mi)
% 1.71/1.44 % (9041)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_8941 for (2999ds/2Mi)
% 1.71/1.45 % (9041)Instruction limit reached!
% 1.71/1.45 % (9041)------------------------------
% 1.71/1.45 % (9041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.45 % (9041)Termination reason: Unknown
% 1.71/1.45 % (9041)Termination phase: Saturation
% 1.71/1.45
% 1.71/1.45 % (9042)Instruction limit reached!
% 1.71/1.45 % (9042)------------------------------
% 1.71/1.45 % (9042)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.45 % (9042)Termination reason: Unknown
% 1.71/1.45 % (9042)Termination phase: Saturation
% 1.71/1.45
% 1.71/1.45 % (9042)Memory used [KB]: 5500
% 1.71/1.45 % (9042)Time elapsed: 0.003 s
% 1.71/1.45 % (9042)Instructions burned: 3 (million)
% 1.71/1.45 % (9042)------------------------------
% 1.71/1.45 % (9042)------------------------------
% 1.71/1.45 % (9041)Memory used [KB]: 5500
% 1.71/1.45 % (9041)Time elapsed: 0.003 s
% 1.71/1.45 % (9041)Instructions burned: 2 (million)
% 1.71/1.45 % (9041)------------------------------
% 1.71/1.45 % (9041)------------------------------
% 1.71/1.45 % (9039)Instruction limit reached!
% 1.71/1.45 % (9039)------------------------------
% 1.71/1.45 % (9039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.45 % (9039)Termination reason: Unknown
% 1.71/1.45 % (9039)Termination phase: Saturation
% 1.71/1.45
% 1.71/1.45 % (9039)Memory used [KB]: 5500
% 1.71/1.45 % (9039)Time elapsed: 0.005 s
% 1.71/1.45 % (9039)Instructions burned: 5 (million)
% 1.71/1.45 % (9039)------------------------------
% 1.71/1.45 % (9039)------------------------------
% 1.71/1.45 % (9038)First to succeed.
% 1.71/1.45 % (9040)Also succeeded, but the first one will report.
% 1.71/1.45 % (9038)Refutation found. Thanks to Tanya!
% 1.71/1.45 % SZS status Theorem for DTF2THF_8941
% 1.71/1.45 % SZS output start Proof for DTF2THF_8941
% 1.71/1.45 thf(type_def_5, type, p: $tType).
% 1.71/1.45 thf(type_def_6, type, a: $tType).
% 1.71/1.45 thf(func_def_0, type, p: $tType).
% 1.71/1.45 thf(func_def_1, type, a: $tType).
% 1.71/1.45 thf(func_def_2, type, cGRAIN: p).
% 1.71/1.45 thf(func_def_3, type, cVEG_EATS: a > p > $o).
% 1.71/1.45 thf(func_def_4, type, cMEAT_EATS: a > a > $o).
% 1.71/1.45 thf(func_def_5, type, cSNAIL: a).
% 1.71/1.45 thf(func_def_6, type, cCATERPILLAR: a).
% 1.71/1.45 thf(func_def_7, type, cBIRD: a).
% 1.71/1.45 thf(func_def_8, type, cWOLF: a).
% 1.71/1.45 thf(func_def_9, type, cFOX: a).
% 1.71/1.45 thf(func_def_10, type, cSMALLER: a > a > $o).
% 1.71/1.45 thf(func_def_14, type, sK0: p).
% 1.71/1.45 thf(func_def_15, type, sK1: p).
% 1.71/1.45 thf(f66,plain,(
% 1.71/1.45 $false),
% 1.71/1.45 inference(avatar_sat_refutation,[status(thm)],[f36,f44,f47,f60,f65])).
% 1.71/1.45 thf(f65,plain,(
% 1.71/1.45 ~spl2_1),
% 1.71/1.45 inference(avatar_contradiction_clause,[status(thm)],[f64])).
% 1.71/1.45 thf(f64,plain,(
% 1.71/1.45 $false | ~spl2_1),
% 1.71/1.45 inference(trivial_inequality_removal,[status(thm)],[f61])).
% 1.71/1.45 thf(f61,plain,(
% 1.71/1.45 ($true != $true) | ~spl2_1),
% 1.71/1.45 inference(superposition,[status(thm)],[f22,f32])).
% 1.71/1.45 thf(f32,plain,(
% 1.71/1.45 ( ! [X0 : p] : (((cVEG_EATS @ cWOLF @ X0) = $true)) ) | ~spl2_1),
% 1.71/1.45 inference(avatar_component_clause,[status(thm)],[f31])).
% 1.71/1.45 thf(f31,definition,(
% 1.71/1.45 spl2_1 <=> ! [X0 : p] : ((cVEG_EATS @ cWOLF @ X0) = $true)),
% 1.71/1.45 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.71/1.45 thf(f22,plain,(
% 1.71/1.45 ((cVEG_EATS @ cWOLF @ cGRAIN) != $true)),
% 1.71/1.45 inference(cnf_transformation,[status(thm)],[f12])).
% 1.71/1.45 thf(f12,plain,(
% 1.71/1.45 ((cSMALLER @ cBIRD @ cFOX) = $true) & ((cMEAT_EATS @ cBIRD @ cCATERPILLAR) = $true) & ((cVEG_EATS @ cWOLF @ cGRAIN) != $true) & ((cMEAT_EATS @ cBIRD @ cSNAIL) != $true) & ((cSMALLER @ cCATERPILLAR @ cBIRD) = $true) & ($true = (cVEG_EATS @ cSNAIL @ sK0)) & ((cSMALLER @ cSNAIL @ cBIRD) = $true) & ! [X1 : a] : (! [X2 : p] : ($true = (cVEG_EATS @ X1 @ X2)) | ! [X3 : a] : (($true != (cSMALLER @ X3 @ X1)) | ! [X4 : p] : ($true != (cVEG_EATS @ X3 @ X4)) | ($true = (cMEAT_EATS @ X1 @ X3)))) & ((cSMALLER @ cFOX @ cWOLF) = $true) & ((cMEAT_EATS @ cWOLF @ cFOX) != $true) & ($true = (cVEG_EATS @ cCATERPILLAR @ sK1)) & ! [X6 : a,X7 : a] : (($true != (cVEG_EATS @ X7 @ cGRAIN)) | ((cMEAT_EATS @ X6 @ X7) != $true))),
% 1.71/1.45 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f9,f11,f10])).
% 1.71/1.45 thf(f10,plain,(
% 1.71/1.45 ? [X0 : p] : ($true = (cVEG_EATS @ cSNAIL @ X0)) => ($true = (cVEG_EATS @ cSNAIL @ sK0))),
% 1.71/1.45 introduced(definition,[],[choice_axiom])).
% 1.71/1.45 thf(f11,plain,(
% 1.71/1.45 ? [X5 : p] : ($true = (cVEG_EATS @ cCATERPILLAR @ X5)) => ($true = (cVEG_EATS @ cCATERPILLAR @ sK1))),
% 1.71/1.45 introduced(definition,[],[choice_axiom])).
% 1.71/1.45 thf(f9,plain,(
% 1.71/1.45 ((cSMALLER @ cBIRD @ cFOX) = $true) & ((cMEAT_EATS @ cBIRD @ cCATERPILLAR) = $true) & ((cVEG_EATS @ cWOLF @ cGRAIN) != $true) & ((cMEAT_EATS @ cBIRD @ cSNAIL) != $true) & ((cSMALLER @ cCATERPILLAR @ cBIRD) = $true) & ? [X0 : p] : ($true = (cVEG_EATS @ cSNAIL @ X0)) & ((cSMALLER @ cSNAIL @ cBIRD) = $true) & ! [X1 : a] : (! [X2 : p] : ($true = (cVEG_EATS @ X1 @ X2)) | ! [X3 : a] : (($true != (cSMALLER @ X3 @ X1)) | ! [X4 : p] : ($true != (cVEG_EATS @ X3 @ X4)) | ($true = (cMEAT_EATS @ X1 @ X3)))) & ((cSMALLER @ cFOX @ cWOLF) = $true) & ((cMEAT_EATS @ cWOLF @ cFOX) != $true) & ? [X5 : p] : ($true = (cVEG_EATS @ cCATERPILLAR @ X5)) & ! [X6 : a,X7 : a] : (($true != (cVEG_EATS @ X7 @ cGRAIN)) | ((cMEAT_EATS @ X6 @ X7) != $true))),
% 1.71/1.45 inference(rectify,[status(thm)],[f8])).
% 1.71/1.45 thf(f8,plain,(
% 1.71/1.45 ((cSMALLER @ cBIRD @ cFOX) = $true) & ((cMEAT_EATS @ cBIRD @ cCATERPILLAR) = $true) & ((cVEG_EATS @ cWOLF @ cGRAIN) != $true) & ((cMEAT_EATS @ cBIRD @ cSNAIL) != $true) & ((cSMALLER @ cCATERPILLAR @ cBIRD) = $true) & ? [X5 : p] : ((cVEG_EATS @ cSNAIL @ X5) = $true) & ((cSMALLER @ cSNAIL @ cBIRD) = $true) & ! [X1 : a] : (! [X4 : p] : ((cVEG_EATS @ X1 @ X4) = $true) | ! [X2 : a] : (($true != (cSMALLER @ X2 @ X1)) | ! [X3 : p] : ((cVEG_EATS @ X2 @ X3) != $true) | ((cMEAT_EATS @ X1 @ X2) = $true))) & ((cSMALLER @ cFOX @ cWOLF) = $true) & ((cMEAT_EATS @ cWOLF @ cFOX) != $true) & ? [X0 : p] : ((cVEG_EATS @ cCATERPILLAR @ X0) = $true) & ! [X6 : a,X7 : a] : (($true != (cVEG_EATS @ X7 @ cGRAIN)) | ((cMEAT_EATS @ X6 @ X7) != $true))),
% 1.71/1.45 inference(flattening,[status(thm)],[f7])).
% 1.71/1.45 thf(f7,plain,(
% 1.71/1.45 ! [X6 : a,X7 : a] : (($true != (cVEG_EATS @ X7 @ cGRAIN)) | ((cMEAT_EATS @ X6 @ X7) != $true)) & (? [X5 : p] : ((cVEG_EATS @ cSNAIL @ X5) = $true) & ((cSMALLER @ cCATERPILLAR @ cBIRD) = $true) & ((cMEAT_EATS @ cWOLF @ cFOX) != $true) & ((cMEAT_EATS @ cBIRD @ cCATERPILLAR) = $true) & ! [X1 : a] : (! [X4 : p] : ((cVEG_EATS @ X1 @ X4) = $true) | ! [X2 : a] : (((cMEAT_EATS @ X1 @ X2) = $true) | (($true != (cSMALLER @ X2 @ X1)) | ! [X3 : p] : ((cVEG_EATS @ X2 @ X3) != $true)))) & ((cSMALLER @ cSNAIL @ cBIRD) = $true) & ((cVEG_EATS @ cWOLF @ cGRAIN) != $true) & ((cSMALLER @ cBIRD @ cFOX) = $true) & ? [X0 : p] : ((cVEG_EATS @ cCATERPILLAR @ X0) = $true) & ((cMEAT_EATS @ cBIRD @ cSNAIL) != $true) & ((cSMALLER @ cFOX @ cWOLF) = $true))),
% 1.71/1.45 inference(ennf_transformation,[status(thm)],[f6])).
% 1.71/1.45 thf(f6,plain,(
% 1.71/1.45 ~((? [X5 : p] : ((cVEG_EATS @ cSNAIL @ X5) = $true) & ((cSMALLER @ cCATERPILLAR @ cBIRD) = $true) & ((cMEAT_EATS @ cWOLF @ cFOX) != $true) & ((cMEAT_EATS @ cBIRD @ cCATERPILLAR) = $true) & ! [X1 : a] : (! [X4 : p] : ((cVEG_EATS @ X1 @ X4) = $true) | ! [X2 : a] : ((($true = (cSMALLER @ X2 @ X1)) & ? [X3 : p] : ((cVEG_EATS @ X2 @ X3) = $true)) => ((cMEAT_EATS @ X1 @ X2) = $true))) & ((cSMALLER @ cSNAIL @ cBIRD) = $true) & ((cVEG_EATS @ cWOLF @ cGRAIN) != $true) & ((cSMALLER @ cBIRD @ cFOX) = $true) & ? [X0 : p] : ((cVEG_EATS @ cCATERPILLAR @ X0) = $true) & ((cMEAT_EATS @ cBIRD @ cSNAIL) != $true) & ((cSMALLER @ cFOX @ cWOLF) = $true)) => ? [X7 : a,X6 : a] : (((cMEAT_EATS @ X6 @ X7) = $true) & ($true = (cVEG_EATS @ X7 @ cGRAIN))))),
% 1.71/1.45 inference(flattening,[status(thm)],[f5])).
% 1.71/1.45 thf(f5,plain,(
% 1.71/1.45 ~((((cSMALLER @ cBIRD @ cFOX) = $true) & ~((cVEG_EATS @ cWOLF @ cGRAIN) = $true) & ? [X0 : p] : ((cVEG_EATS @ cCATERPILLAR @ X0) = $true) & ((cMEAT_EATS @ cBIRD @ cCATERPILLAR) = $true) & ((cSMALLER @ cCATERPILLAR @ cBIRD) = $true) & ((cSMALLER @ cSNAIL @ cBIRD) = $true) & ~((cMEAT_EATS @ cBIRD @ cSNAIL) = $true) & ! [X1 : a] : (! [X4 : p] : ((cVEG_EATS @ X1 @ X4) = $true) | ! [X2 : a] : ((($true = (cSMALLER @ X2 @ X1)) & ? [X3 : p] : ((cVEG_EATS @ X2 @ X3) = $true)) => ((cMEAT_EATS @ X1 @ X2) = $true))) & ((cSMALLER @ cFOX @ cWOLF) = $true) & ~((cMEAT_EATS @ cWOLF @ cFOX) = $true) & ? [X5 : p] : ((cVEG_EATS @ cSNAIL @ X5) = $true)) => ? [X7 : a,X6 : a] : (((cMEAT_EATS @ X6 @ X7) = $true) & ($true = (cVEG_EATS @ X7 @ cGRAIN))))),
% 1.71/1.45 inference(fool_elimination,[status(thm)],[f4])).
% 1.71/1.45 thf(f4,plain,(
% 1.71/1.45 ~(((cSMALLER @ cBIRD @ cFOX) & ~(cVEG_EATS @ cWOLF @ cGRAIN) & ? [X0 : p] : (cVEG_EATS @ cCATERPILLAR @ X0) & (cMEAT_EATS @ cBIRD @ cCATERPILLAR) & (cSMALLER @ cCATERPILLAR @ cBIRD) & (cSMALLER @ cSNAIL @ cBIRD) & ~(cMEAT_EATS @ cBIRD @ cSNAIL) & ! [X1 : a] : (! [X2 : a] : (((cSMALLER @ X2 @ X1) & ? [X3 : p] : (cVEG_EATS @ X2 @ X3)) => (cMEAT_EATS @ X1 @ X2)) | ! [X4 : p] : (cVEG_EATS @ X1 @ X4)) & (cSMALLER @ cFOX @ cWOLF) & ~(cMEAT_EATS @ cWOLF @ cFOX) & ? [X5 : p] : (cVEG_EATS @ cSNAIL @ X5)) => ? [X6 : a,X7 : a] : ((cVEG_EATS @ X7 @ cGRAIN) & (cMEAT_EATS @ X6 @ X7)))),
% 1.71/1.45 inference(rectify,[status(thm)],[f2])).
% 1.71/1.45 thf(f2,negated_conjecture,(
% 1.71/1.45 ~(((cSMALLER @ cBIRD @ cFOX) & ~(cVEG_EATS @ cWOLF @ cGRAIN) & ? [X1 : p] : (cVEG_EATS @ cCATERPILLAR @ X1) & (cMEAT_EATS @ cBIRD @ cCATERPILLAR) & (cSMALLER @ cCATERPILLAR @ cBIRD) & (cSMALLER @ cSNAIL @ cBIRD) & ~(cMEAT_EATS @ cBIRD @ cSNAIL) & ! [X0 : a] : (! [X2 : a] : (((cSMALLER @ X2 @ X0) & ? [X3 : p] : (cVEG_EATS @ X2 @ X3)) => (cMEAT_EATS @ X0 @ X2)) | ! [X1 : p] : (cVEG_EATS @ X0 @ X1)) & (cSMALLER @ cFOX @ cWOLF) & ~(cMEAT_EATS @ cWOLF @ cFOX) & ? [X1 : p] : (cVEG_EATS @ cSNAIL @ X1)) => ? [X0 : a,X1 : a] : ((cVEG_EATS @ X1 @ cGRAIN) & (cMEAT_EATS @ X0 @ X1)))),
% 1.71/1.45 inference(negated_conjecture,[status(cth)],[f1])).
% 1.71/1.45 thf(f1,conjecture,(
% 1.71/1.45 ((cSMALLER @ cBIRD @ cFOX) & ~(cVEG_EATS @ cWOLF @ cGRAIN) & ? [X1 : p] : (cVEG_EATS @ cCATERPILLAR @ X1) & (cMEAT_EATS @ cBIRD @ cCATERPILLAR) & (cSMALLER @ cCATERPILLAR @ cBIRD) & (cSMALLER @ cSNAIL @ cBIRD) & ~(cMEAT_EATS @ cBIRD @ cSNAIL) & ! [X0 : a] : (! [X2 : a] : (((cSMALLER @ X2 @ X0) & ? [X3 : p] : (cVEG_EATS @ X2 @ X3)) => (cMEAT_EATS @ X0 @ X2)) | ! [X1 : p] : (cVEG_EATS @ X0 @ X1)) & (cSMALLER @ cFOX @ cWOLF) & ~(cMEAT_EATS @ cWOLF @ cFOX) & ? [X1 : p] : (cVEG_EATS @ cSNAIL @ X1)) => ? [X0 : a,X1 : a] : ((cVEG_EATS @ X1 @ cGRAIN) & (cMEAT_EATS @ X0 @ X1))),
% 1.71/1.45 file('/export/starexec/sandbox/tmp/tmp.DnTVbJIk6s/DTF2THF_8941.p',cPUZ031_1_HO)).
% 1.71/1.45 thf(f60,plain,(
% 1.71/1.45 ~spl2_2 | ~spl2_4),
% 1.71/1.45 inference(avatar_contradiction_clause,[status(thm)],[f59])).
% 1.71/1.45 thf(f59,plain,(
% 1.71/1.45 $false | (~spl2_2 | ~spl2_4)),
% 1.71/1.45 inference(subsumption_resolution,[status(thm)],[f57,f24])).
% 1.71/1.45 thf(f24,plain,(
% 1.71/1.45 ((cSMALLER @ cBIRD @ cFOX) = $true)),
% 1.71/1.45 inference(cnf_transformation,[status(thm)],[f12])).
% 1.71/1.45 thf(f57,plain,(
% 1.71/1.45 ((cSMALLER @ cBIRD @ cFOX) != $true) | (~spl2_2 | ~spl2_4)),
% 1.71/1.45 inference(trivial_inequality_removal,[status(thm)],[f55])).
% 1.71/1.45 thf(f55,plain,(
% 1.71/1.45 ((cSMALLER @ cBIRD @ cFOX) != $true) | ($true != $true) | (~spl2_2 | ~spl2_4)),
% 1.71/1.45 inference(superposition,[status(thm)],[f35,f52])).
% 1.71/1.45 thf(f52,plain,(
% 1.71/1.45 ( ! [X0 : a,X1 : p] : (((cVEG_EATS @ X0 @ X1) = $true) | ($true != (cSMALLER @ cBIRD @ X0))) ) | ~spl2_4),
% 1.71/1.45 inference(subsumption_resolution,[status(thm)],[f51,f43])).
% 1.71/1.45 thf(f43,plain,(
% 1.71/1.45 ( ! [X0 : p] : (($true = (cVEG_EATS @ cBIRD @ X0))) ) | ~spl2_4),
% 1.71/1.45 inference(avatar_component_clause,[status(thm)],[f42])).
% 1.71/1.45 thf(f42,definition,(
% 1.71/1.45 spl2_4 <=> ! [X0 : p] : ($true = (cVEG_EATS @ cBIRD @ X0))),
% 1.71/1.45 introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition])).
% 1.71/1.45 thf(f51,plain,(
% 1.71/1.45 ( ! [X2 : p,X0 : a,X1 : p] : (((cVEG_EATS @ X0 @ X1) = $true) | ($true != (cSMALLER @ cBIRD @ X0)) | ($true != (cVEG_EATS @ cBIRD @ X2))) ) | ~spl2_4),
% 1.71/1.45 inference(trivial_inequality_removal,[status(thm)],[f50])).
% 1.71/1.45 thf(f50,plain,(
% 1.71/1.45 ( ! [X2 : p,X0 : a,X1 : p] : (($true != (cSMALLER @ cBIRD @ X0)) | ($true != $true) | ((cVEG_EATS @ X0 @ X1) = $true) | ($true != (cVEG_EATS @ cBIRD @ X2))) ) | ~spl2_4),
% 1.71/1.45 inference(superposition,[status(thm)],[f49,f17])).
% 1.71/1.45 thf(f17,plain,(
% 1.71/1.45 ( ! [X2 : p,X3 : a,X1 : a,X4 : p] : (($true = (cMEAT_EATS @ X1 @ X3)) | ($true != (cSMALLER @ X3 @ X1)) | ($true = (cVEG_EATS @ X1 @ X2)) | ($true != (cVEG_EATS @ X3 @ X4))) )),
% 1.71/1.45 inference(cnf_transformation,[status(thm)],[f12])).
% 1.71/1.45 thf(f49,plain,(
% 1.71/1.45 ( ! [X0 : a] : (((cMEAT_EATS @ X0 @ cBIRD) != $true)) ) | ~spl2_4),
% 1.71/1.45 inference(trivial_inequality_removal,[status(thm)],[f48])).
% 1.71/1.45 thf(f48,plain,(
% 1.71/1.45 ( ! [X0 : a] : (((cMEAT_EATS @ X0 @ cBIRD) != $true) | ($true != $true)) ) | ~spl2_4),
% 1.71/1.45 inference(superposition,[status(thm)],[f13,f43])).
% 1.71/1.45 thf(f13,plain,(
% 1.71/1.45 ( ! [X6 : a,X7 : a] : (($true != (cVEG_EATS @ X7 @ cGRAIN)) | ((cMEAT_EATS @ X6 @ X7) != $true)) )),
% 1.71/1.45 inference(cnf_transformation,[status(thm)],[f12])).
% 1.71/1.45 thf(f35,plain,(
% 1.71/1.45 ( ! [X1 : p] : (((cVEG_EATS @ cFOX @ X1) != $true)) ) | ~spl2_2),
% 1.71/1.45 inference(avatar_component_clause,[status(thm)],[f34])).
% 1.71/1.45 thf(f34,definition,(
% 1.71/1.45 spl2_2 <=> ! [X1 : p] : ((cVEG_EATS @ cFOX @ X1) != $true)),
% 1.71/1.45 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.71/1.45 thf(f47,plain,(
% 1.71/1.45 ~spl2_3),
% 1.71/1.45 inference(avatar_contradiction_clause,[status(thm)],[f46])).
% 1.71/1.45 thf(f46,plain,(
% 1.71/1.45 $false | ~spl2_3),
% 1.71/1.45 inference(trivial_inequality_removal,[status(thm)],[f45])).
% 1.71/1.45 thf(f45,plain,(
% 1.71/1.45 ($true != $true) | ~spl2_3),
% 1.71/1.45 inference(superposition,[status(thm)],[f40,f19])).
% 1.71/1.45 thf(f19,plain,(
% 1.71/1.45 ($true = (cVEG_EATS @ cSNAIL @ sK0))),
% 1.71/1.45 inference(cnf_transformation,[status(thm)],[f12])).
% 1.71/1.45 thf(f40,plain,(
% 1.71/1.45 ( ! [X1 : p] : (((cVEG_EATS @ cSNAIL @ X1) != $true)) ) | ~spl2_3),
% 1.71/1.45 inference(avatar_component_clause,[status(thm)],[f39])).
% 1.71/1.45 thf(f39,definition,(
% 1.71/1.45 spl2_3 <=> ! [X1 : p] : ((cVEG_EATS @ cSNAIL @ X1) != $true)),
% 1.71/1.45 introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition])).
% 1.71/1.45 thf(f44,plain,(
% 1.71/1.45 spl2_3 | spl2_4),
% 1.71/1.45 inference(avatar_split_clause,[status(thm)],[f37,f42,f39])).
% 1.71/1.45 thf(f37,plain,(
% 1.71/1.45 ( ! [X0 : p,X1 : p] : (($true = (cVEG_EATS @ cBIRD @ X0)) | ((cVEG_EATS @ cSNAIL @ X1) != $true)) )),
% 1.71/1.45 inference(subsumption_resolution,[status(thm)],[f27,f18])).
% 1.71/1.45 thf(f18,plain,(
% 1.71/1.45 ((cSMALLER @ cSNAIL @ cBIRD) = $true)),
% 1.71/1.45 inference(cnf_transformation,[status(thm)],[f12])).
% 1.71/1.45 thf(f27,plain,(
% 1.71/1.45 ( ! [X0 : p,X1 : p] : (((cSMALLER @ cSNAIL @ cBIRD) != $true) | ($true = (cVEG_EATS @ cBIRD @ X0)) | ((cVEG_EATS @ cSNAIL @ X1) != $true)) )),
% 1.71/1.45 inference(trivial_inequality_removal,[status(thm)],[f26])).
% 1.71/1.45 thf(f26,plain,(
% 1.71/1.45 ( ! [X0 : p,X1 : p] : (((cSMALLER @ cSNAIL @ cBIRD) != $true) | ((cVEG_EATS @ cSNAIL @ X1) != $true) | ($true != $true) | ($true = (cVEG_EATS @ cBIRD @ X0))) )),
% 1.71/1.45 inference(superposition,[status(thm)],[f21,f17])).
% 1.71/1.45 thf(f21,plain,(
% 1.71/1.45 ((cMEAT_EATS @ cBIRD @ cSNAIL) != $true)),
% 1.71/1.45 inference(cnf_transformation,[status(thm)],[f12])).
% 1.71/1.45 thf(f36,plain,(
% 1.71/1.45 spl2_1 | spl2_2),
% 1.71/1.45 inference(avatar_split_clause,[status(thm)],[f29,f34,f31])).
% 1.71/1.45 thf(f29,plain,(
% 1.71/1.45 ( ! [X0 : p,X1 : p] : (((cVEG_EATS @ cFOX @ X1) != $true) | ((cVEG_EATS @ cWOLF @ X0) = $true)) )),
% 1.71/1.45 inference(subsumption_resolution,[status(thm)],[f28,f16])).
% 1.71/1.45 thf(f16,plain,(
% 1.71/1.45 ((cSMALLER @ cFOX @ cWOLF) = $true)),
% 1.71/1.45 inference(cnf_transformation,[status(thm)],[f12])).
% 1.71/1.45 thf(f28,plain,(
% 1.71/1.45 ( ! [X0 : p,X1 : p] : (((cVEG_EATS @ cFOX @ X1) != $true) | ((cVEG_EATS @ cWOLF @ X0) = $true) | ((cSMALLER @ cFOX @ cWOLF) != $true)) )),
% 1.71/1.45 inference(trivial_inequality_removal,[status(thm)],[f25])).
% 1.71/1.45 thf(f25,plain,(
% 1.71/1.45 ( ! [X0 : p,X1 : p] : (((cVEG_EATS @ cFOX @ X1) != $true) | ((cVEG_EATS @ cWOLF @ X0) = $true) | ($true != $true) | ((cSMALLER @ cFOX @ cWOLF) != $true)) )),
% 1.71/1.45 inference(superposition,[status(thm)],[f15,f17])).
% 1.71/1.45 thf(f15,plain,(
% 1.71/1.45 ((cMEAT_EATS @ cWOLF @ cFOX) != $true)),
% 1.71/1.45 inference(cnf_transformation,[status(thm)],[f12])).
% 1.71/1.45 % SZS output end Proof for DTF2THF_8941
% 1.71/1.45 % (9038)------------------------------
% 1.71/1.45 % (9038)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.45 % (9038)Termination reason: Refutation
% 1.71/1.45
% 1.71/1.45 % (9038)Memory used [KB]: 5500
% 1.71/1.45 % (9038)Time elapsed: 0.008 s
% 1.71/1.45 % (9038)Instructions burned: 6 (million)
% 1.71/1.45 % (9038)------------------------------
% 1.71/1.45 % (9038)------------------------------
% 1.71/1.45 % (9037)Success in time 0.023 s
%------------------------------------------------------------------------------