TSTP Solution File: SYO175^5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SYO175^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n025.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 : Tue May 21 09:10:29 EDT 2024
% Result : Theorem 0.13s 0.38s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 31
% Syntax : Number of formulae : 87 ( 15 unt; 23 typ; 0 def)
% Number of atoms : 1053 ( 183 equ; 0 cnn)
% Maximal formula atoms : 16 ( 16 avg)
% Number of connectives : 280 ( 85 ~; 75 |; 104 &; 0 @)
% ( 4 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 24 ( 23 >; 1 *; 0 +; 0 <<)
% Number of symbols : 27 ( 24 usr; 14 con; 0-6 aty)
% Number of variables : 125 ( 0 ^ 86 !; 33 ?; 125 :)
% ( 6 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
p: $tType ).
thf(type_def_6,type,
a: $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $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(func_def_17,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_18,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_19,type,
vAND: $o > $o > $o ).
thf(func_def_20,type,
vOR: $o > $o > $o ).
thf(func_def_21,type,
vIMP: $o > $o > $o ).
thf(func_def_22,type,
vNOT: $o > $o ).
thf(func_def_23,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f169,plain,
$false,
inference(avatar_sat_refutation,[],[f122,f131,f142,f149,f168]) ).
thf(f168,plain,
~ spl2_4,
inference(avatar_contradiction_clause,[],[f167]) ).
thf(f167,plain,
( $false
| ~ spl2_4 ),
inference(trivial_inequality_removal,[],[f159]) ).
thf(f159,plain,
( ( $true = $false )
| ~ spl2_4 ),
inference(superposition,[],[f130,f57]) ).
thf(f57,plain,
vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cWOLF),cGRAIN) = $false,
inference(trivial_inequality_removal,[],[f56]) ).
thf(f56,plain,
( ( $true != $true )
| ( vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cWOLF),cGRAIN) = $false ) ),
inference(superposition,[],[f20,f4]) ).
thf(f4,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f20,plain,
vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cWOLF),cGRAIN) != $true,
inference(cnf_transformation,[],[f13]) ).
thf(f13,plain,
( ! [X0: a,X1: a] :
( ( vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X1),cGRAIN) != $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X0),X1) != $true ) )
& ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cSNAIL),sK0) )
& ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cCATERPILLAR),sK1) )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cBIRD),cSNAIL) != $true )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cBIRD),cCATERPILLAR) = $true )
& ( vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cWOLF),cGRAIN) != $true )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cWOLF),cFOX) != $true )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cFOX),cWOLF) = $true )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cBIRD),cFOX) = $true )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cSNAIL),cBIRD) = $true )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cCATERPILLAR),cBIRD) = $true )
& ! [X4: a] :
( ! [X5: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X4),X5) )
| ! [X6: p] : ( $true != vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X5),X6) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,X5),X4) ) )
| ! [X7: p] : ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X4),X7) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f10,f12,f11]) ).
thf(f11,plain,
( ? [X2: p] : ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cSNAIL),X2) )
=> ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cSNAIL),sK0) ) ),
introduced(choice_axiom,[]) ).
thf(f12,plain,
( ? [X3: p] : ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cCATERPILLAR),X3) )
=> ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cCATERPILLAR),sK1) ) ),
introduced(choice_axiom,[]) ).
thf(f10,plain,
( ! [X0: a,X1: a] :
( ( vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X1),cGRAIN) != $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X0),X1) != $true ) )
& ? [X2: p] : ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cSNAIL),X2) )
& ? [X3: p] : ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cCATERPILLAR),X3) )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cBIRD),cSNAIL) != $true )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cBIRD),cCATERPILLAR) = $true )
& ( vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cWOLF),cGRAIN) != $true )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cWOLF),cFOX) != $true )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cFOX),cWOLF) = $true )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cBIRD),cFOX) = $true )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cSNAIL),cBIRD) = $true )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cCATERPILLAR),cBIRD) = $true )
& ! [X4: a] :
( ! [X5: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X4),X5) )
| ! [X6: p] : ( $true != vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X5),X6) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,X5),X4) ) )
| ! [X7: p] : ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X4),X7) ) ) ),
inference(rectify,[],[f9]) ).
thf(f9,plain,
( ! [X6: a,X7: a] :
( ( $true != vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X7),cGRAIN) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X6),X7) ) )
& ? [X0: p] : ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cSNAIL),X0) )
& ? [X1: p] : ( vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cCATERPILLAR),X1) = $true )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cBIRD),cSNAIL) != $true )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cBIRD),cCATERPILLAR) = $true )
& ( vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cWOLF),cGRAIN) != $true )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cWOLF),cFOX) != $true )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cFOX),cWOLF) = $true )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cBIRD),cFOX) = $true )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cSNAIL),cBIRD) = $true )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cCATERPILLAR),cBIRD) = $true )
& ! [X2: a] :
( ! [X3: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X2),X3) )
| ! [X4: p] : ( $true != vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X3),X4) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,X3),X2) ) )
| ! [X5: p] : ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X2),X5) ) ) ),
inference(flattening,[],[f8]) ).
thf(f8,plain,
( ! [X6: a,X7: a] :
( ( $true != vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X7),cGRAIN) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X6),X7) ) )
& ? [X0: p] : ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cSNAIL),X0) )
& ? [X1: p] : ( vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cCATERPILLAR),X1) = $true )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cBIRD),cSNAIL) != $true )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cBIRD),cCATERPILLAR) = $true )
& ( vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cWOLF),cGRAIN) != $true )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cWOLF),cFOX) != $true )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cFOX),cWOLF) = $true )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cBIRD),cFOX) = $true )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cSNAIL),cBIRD) = $true )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cCATERPILLAR),cBIRD) = $true )
& ! [X2: a] :
( ! [X3: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X2),X3) )
| ! [X4: p] : ( $true != vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X3),X4) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,X3),X2) ) )
| ! [X5: p] : ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X2),X5) ) ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f7,plain,
~ ( ( ? [X0: p] : ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cSNAIL),X0) )
& ? [X1: p] : ( vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cCATERPILLAR),X1) = $true )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cBIRD),cSNAIL) != $true )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cBIRD),cCATERPILLAR) = $true )
& ( vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cWOLF),cGRAIN) != $true )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cWOLF),cFOX) != $true )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cFOX),cWOLF) = $true )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cBIRD),cFOX) = $true )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cSNAIL),cBIRD) = $true )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cCATERPILLAR),cBIRD) = $true )
& ! [X2: a] :
( ! [X3: a] :
( ( ? [X4: p] : ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X3),X4) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,X3),X2) ) )
=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X2),X3) ) )
| ! [X5: p] : ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X2),X5) ) ) )
=> ? [X6: a,X7: a] :
( ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X7),cGRAIN) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X6),X7) ) ) ),
inference(flattening,[],[f6]) ).
thf(f6,plain,
~ ( ( ? [X0: p] : ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cSNAIL),X0) )
& ? [X1: p] : ( vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cCATERPILLAR),X1) = $true )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cBIRD),cSNAIL) != $true )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cBIRD),cCATERPILLAR) = $true )
& ( vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cWOLF),cGRAIN) != $true )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cWOLF),cFOX) != $true )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cFOX),cWOLF) = $true )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cBIRD),cFOX) = $true )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cSNAIL),cBIRD) = $true )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cCATERPILLAR),cBIRD) = $true )
& ! [X2: a] :
( ! [X3: a] :
( ( ? [X4: p] : ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X3),X4) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,X3),X2) ) )
=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X2),X3) ) )
| ! [X5: p] : ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X2),X5) ) ) )
=> ? [X6: a,X7: a] :
( ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X7),cGRAIN) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X6),X7) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f5,plain,
~ ( ( ? [X0: p] : vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cSNAIL),X0)
& ? [X1: p] : vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cCATERPILLAR),X1)
& ~ vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cBIRD),cSNAIL)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cBIRD),cCATERPILLAR)
& ~ vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cWOLF),cGRAIN)
& ~ vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cWOLF),cFOX)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cFOX),cWOLF)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cBIRD),cFOX)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cSNAIL),cBIRD)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cCATERPILLAR),cBIRD)
& ! [X2: a] :
( ! [X3: a] :
( ( ? [X4: p] : vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X3),X4)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,X3),X2) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X2),X3) )
| ! [X5: p] : vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X2),X5) ) )
=> ? [X6: a,X7: a] :
( vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X7),cGRAIN)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X6),X7) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ? [X1: p] : vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cSNAIL),X1)
& ? [X1: p] : vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cCATERPILLAR),X1)
& ~ vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cBIRD),cSNAIL)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cBIRD),cCATERPILLAR)
& ~ vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cWOLF),cGRAIN)
& ~ vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cWOLF),cFOX)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cFOX),cWOLF)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cBIRD),cFOX)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cSNAIL),cBIRD)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cCATERPILLAR),cBIRD)
& ! [X0: a] :
( ! [X2: a] :
( ( ? [X3: p] : vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X2),X3)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,X2),X0) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X0),X2) )
| ! [X1: p] : vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X0),X1) ) )
=> ? [X0: a,X1: a] :
( vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X1),cGRAIN)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X0),X1) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
( ( ? [X1: p] : vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cSNAIL),X1)
& ? [X1: p] : vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cCATERPILLAR),X1)
& ~ vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cBIRD),cSNAIL)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cBIRD),cCATERPILLAR)
& ~ vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cWOLF),cGRAIN)
& ~ vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cWOLF),cFOX)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cFOX),cWOLF)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cBIRD),cFOX)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cSNAIL),cBIRD)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cCATERPILLAR),cBIRD)
& ! [X0: a] :
( ! [X2: a] :
( ( ? [X3: p] : vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X2),X3)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,X2),X0) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X0),X2) )
| ! [X1: p] : vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X0),X1) ) )
=> ? [X0: a,X1: a] :
( vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X1),cGRAIN)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X0),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cPUZ031_1_HO) ).
thf(f130,plain,
( ! [X0: p] : ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cWOLF),X0) )
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f129]) ).
thf(f129,plain,
( spl2_4
<=> ! [X0: p] : ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cWOLF),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_4])]) ).
thf(f149,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[],[f148]) ).
thf(f148,plain,
( $false
| ~ spl2_1 ),
inference(trivial_inequality_removal,[],[f143]) ).
thf(f143,plain,
( ( $true = $false )
| ~ spl2_1 ),
inference(backward_demodulation,[],[f94,f118]) ).
thf(f118,plain,
( ! [X1: p] : ( $false = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cBIRD),X1) )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f117]) ).
thf(f117,plain,
( spl2_1
<=> ! [X1: p] : ( $false = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cBIRD),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).
thf(f94,plain,
! [X0: p] : ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cBIRD),X0) ),
inference(trivial_inequality_removal,[],[f93]) ).
thf(f93,plain,
! [X0: p] :
( ( $true = $false )
| ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cBIRD),X0) ) ),
inference(forward_demodulation,[],[f92,f59]) ).
thf(f59,plain,
vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cBIRD),cSNAIL) = $false,
inference(trivial_inequality_removal,[],[f58]) ).
thf(f58,plain,
( ( $true != $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cBIRD),cSNAIL) = $false ) ),
inference(superposition,[],[f22,f4]) ).
thf(f22,plain,
vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cBIRD),cSNAIL) != $true,
inference(cnf_transformation,[],[f13]) ).
thf(f92,plain,
! [X0: p] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cBIRD),cSNAIL) = $true )
| ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cBIRD),X0) ) ),
inference(trivial_inequality_removal,[],[f89]) ).
thf(f89,plain,
! [X0: p] :
( ( $true != $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cBIRD),cSNAIL) = $true )
| ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cBIRD),X0) ) ),
inference(superposition,[],[f69,f16]) ).
thf(f16,plain,
vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cSNAIL),cBIRD) = $true,
inference(cnf_transformation,[],[f13]) ).
thf(f69,plain,
! [X0: a,X1: p] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cSNAIL),X0) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X0),cSNAIL) )
| ( vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X0),X1) = $true ) ),
inference(trivial_inequality_removal,[],[f66]) ).
thf(f66,plain,
! [X0: a,X1: p] :
( ( $true != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X0),cSNAIL) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cSNAIL),X0) )
| ( vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X0),X1) = $true ) ),
inference(superposition,[],[f14,f24]) ).
thf(f24,plain,
$true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cSNAIL),sK0),
inference(cnf_transformation,[],[f13]) ).
thf(f14,plain,
! [X6: p,X7: p,X4: a,X5: a] :
( ( $true != vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X5),X6) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X4),X5) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,X5),X4) )
| ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X4),X7) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f142,plain,
( ~ spl2_2
| ~ spl2_3 ),
inference(avatar_contradiction_clause,[],[f141]) ).
thf(f141,plain,
( $false
| ~ spl2_2
| ~ spl2_3 ),
inference(trivial_inequality_removal,[],[f136]) ).
thf(f136,plain,
( ( $true = $false )
| ~ spl2_2
| ~ spl2_3 ),
inference(backward_demodulation,[],[f121,f127]) ).
thf(f127,plain,
( ! [X1: p] : ( $false = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cFOX),X1) )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f126]) ).
thf(f126,plain,
( spl2_3
<=> ! [X1: p] : ( $false = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cFOX),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).
thf(f121,plain,
( ! [X0: p] : ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cFOX),X0) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f120]) ).
thf(f120,plain,
( spl2_2
<=> ! [X0: p] : ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cFOX),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).
thf(f131,plain,
( spl2_3
| spl2_4 ),
inference(avatar_split_clause,[],[f124,f129,f126]) ).
thf(f124,plain,
! [X0: p,X1: p] :
( ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cWOLF),X0) )
| ( $false = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cFOX),X1) ) ),
inference(trivial_inequality_removal,[],[f123]) ).
thf(f123,plain,
! [X0: p,X1: p] :
( ( $true = $false )
| ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cWOLF),X0) )
| ( $false = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cFOX),X1) ) ),
inference(forward_demodulation,[],[f111,f55]) ).
thf(f55,plain,
vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cWOLF),cFOX) = $false,
inference(trivial_inequality_removal,[],[f54]) ).
thf(f54,plain,
( ( $true != $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cWOLF),cFOX) = $false ) ),
inference(superposition,[],[f19,f4]) ).
thf(f19,plain,
vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cWOLF),cFOX) != $true,
inference(cnf_transformation,[],[f13]) ).
thf(f111,plain,
! [X0: p,X1: p] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cWOLF),cFOX) = $true )
| ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cWOLF),X0) )
| ( $false = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cFOX),X1) ) ),
inference(trivial_inequality_removal,[],[f108]) ).
thf(f108,plain,
! [X0: p,X1: p] :
( ( $true != $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cWOLF),cFOX) = $true )
| ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cWOLF),X0) )
| ( $false = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cFOX),X1) ) ),
inference(superposition,[],[f68,f18]) ).
thf(f18,plain,
vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cFOX),cWOLF) = $true,
inference(cnf_transformation,[],[f13]) ).
thf(f68,plain,
! [X2: a,X3: p,X0: a,X1: p] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,X0),X2) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X2),X0) )
| ( vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X2),X3) = $true )
| ( vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X0),X1) = $false ) ),
inference(trivial_inequality_removal,[],[f67]) ).
thf(f67,plain,
! [X2: a,X3: p,X0: a,X1: p] :
( ( $true != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X2),X0) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,X0),X2) )
| ( vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X2),X3) = $true )
| ( vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X0),X1) = $false ) ),
inference(superposition,[],[f14,f4]) ).
thf(f122,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f115,f120,f117]) ).
thf(f115,plain,
! [X0: p,X1: p] :
( ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cFOX),X0) )
| ( $false = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cBIRD),X1) ) ),
inference(subsumption_resolution,[],[f112,f97]) ).
thf(f97,plain,
! [X0: a] : ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X0),cBIRD) ),
inference(trivial_inequality_removal,[],[f96]) ).
thf(f96,plain,
! [X0: a] :
( ( $true != $true )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X0),cBIRD) ) ),
inference(superposition,[],[f25,f94]) ).
thf(f25,plain,
! [X0: a,X1: a] :
( ( vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X1),cGRAIN) != $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X0),X1) != $true ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f112,plain,
! [X0: p,X1: p] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cFOX),cBIRD) )
| ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cFOX),X0) )
| ( $false = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cBIRD),X1) ) ),
inference(trivial_inequality_removal,[],[f107]) ).
thf(f107,plain,
! [X0: p,X1: p] :
( ( $true != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cFOX),cBIRD) )
| ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cFOX),X0) )
| ( $false = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cBIRD),X1) ) ),
inference(superposition,[],[f68,f17]) ).
thf(f17,plain,
vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cBIRD),cFOX) = $true,
inference(cnf_transformation,[],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO175^5 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon May 20 09:33:23 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % (6906)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.37 % (6908)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.13/0.37 % (6913)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.13/0.37 % (6911)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.13/0.37 % (6907)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.13/0.37 % (6910)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.13/0.37 % Exception at run slice level
% 0.13/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.37 % Exception at run slice level% (6912)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.13/0.37
% 0.13/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.37 % Exception at run slice level
% 0.13/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.37 % (6910)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.13/0.37 % Exception at run slice level
% 0.13/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.37 % (6909)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.13/0.37 % (6909)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.13/0.37 % (6912)First to succeed.
% 0.13/0.38 % (6909)Also succeeded, but the first one will report.
% 0.13/0.38 % (6912)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-6906"
% 0.13/0.38 % (6911)Also succeeded, but the first one will report.
% 0.13/0.38 % (6912)Refutation found. Thanks to Tanya!
% 0.13/0.38 % SZS status Theorem for theBenchmark
% 0.13/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.38 % (6912)------------------------------
% 0.13/0.38 % (6912)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.38 % (6912)Termination reason: Refutation
% 0.13/0.38
% 0.13/0.38 % (6912)Memory used [KB]: 856
% 0.13/0.38 % (6912)Time elapsed: 0.012 s
% 0.13/0.38 % (6912)Instructions burned: 18 (million)
% 0.13/0.38 % (6906)Success in time 0.04 s
%------------------------------------------------------------------------------