%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC414+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:03:53 PM UTC 2026
% Result : Theorem 8.59s 2.90s
% Output : Refutation 16.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 23
% Syntax : Number of formulae : 156 ( 22 unt; 18 def)
% Number of atoms : 620 ( 101 equ)
% Maximal formula atoms : 30 ( 3 avg)
% Number of connectives : 796 ( 332 ~; 321 |; 105 &)
% ( 12 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 18 ( 16 usr; 13 prp; 0-4 aty)
% Number of functors : 20 ( 20 usr; 12 con; 0-2 aty)
% Number of variables : 252 ( 0 sgn 191 !; 61 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax84) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ~ ssList(X3)
| X1 != X3
| X0 != X2
| ( ( ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& app(app(app(app(X6,cons(X4,nil)),X7),cons(X5,nil)),X8) = X1
& app(app(app(app(X6,cons(X5,nil)),X7),cons(X4,nil)),X8) = X0 ) ) ) ) )
| ! [X9] :
( ssItem(X9)
=> ! [X10] :
( ssItem(X10)
=> ! [X11] :
( ssList(X11)
=> app(app(cons(X9,nil),cons(X10,nil)),X11) != X1 ) ) )
| ! [X12] :
( ssItem(X12)
=> ! [X13] :
( ssItem(X13)
=> ! [X14] :
( ~ ssList(X14)
| app(app(cons(X12,nil),cons(X13,nil)),X14) != X3
| app(app(cons(X13,nil),cons(X12,nil)),X14) != X2 ) ) ) )
& ( ? [X15] :
( ssItem(X15)
& ? [X16] :
( ssItem(X16)
& ? [X17] :
( ssList(X17)
& app(app(cons(X15,nil),cons(X16,nil)),X17) = X3 ) ) )
| ! [X18] :
( ssItem(X18)
=> ! [X19] :
( ssItem(X19)
=> ! [X20] :
( ssList(X20)
=> app(app(cons(X18,nil),cons(X19,nil)),X20) != X1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ~ ssList(X3)
| X1 != X3
| X0 != X2
| ( ( ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& app(app(app(app(X6,cons(X4,nil)),X7),cons(X5,nil)),X8) = X1
& app(app(app(app(X6,cons(X5,nil)),X7),cons(X4,nil)),X8) = X0 ) ) ) ) )
| ! [X9] :
( ssItem(X9)
=> ! [X10] :
( ssItem(X10)
=> ! [X11] :
( ssList(X11)
=> app(app(cons(X9,nil),cons(X10,nil)),X11) != X1 ) ) )
| ! [X12] :
( ssItem(X12)
=> ! [X13] :
( ssItem(X13)
=> ! [X14] :
( ~ ssList(X14)
| app(app(cons(X12,nil),cons(X13,nil)),X14) != X3
| app(app(cons(X13,nil),cons(X12,nil)),X14) != X2 ) ) ) )
& ( ? [X15] :
( ssItem(X15)
& ? [X16] :
( ssItem(X16)
& ? [X17] :
( ssList(X17)
& app(app(cons(X15,nil),cons(X16,nil)),X17) = X3 ) ) )
| ! [X18] :
( ssItem(X18)
=> ! [X19] :
( ssItem(X19)
=> ! [X20] :
( ssList(X20)
=> app(app(cons(X18,nil),cons(X19,nil)),X20) != X1 ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f119,plain,
! [X0] :
( ! [X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f134,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f201,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& X1 = X3
& X0 = X2
& ( ( ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| ! [X7] :
( ~ ssList(X7)
| ! [X8] :
( ~ ssList(X8)
| app(app(app(app(X6,cons(X4,nil)),X7),cons(X5,nil)),X8) != X1
| app(app(app(app(X6,cons(X5,nil)),X7),cons(X4,nil)),X8) != X0 ) ) ) ) )
& ? [X9] :
( ? [X10] :
( ? [X11] :
( app(app(cons(X9,nil),cons(X10,nil)),X11) = X1
& ssList(X11) )
& ssItem(X10) )
& ssItem(X9) )
& ? [X12] :
( ? [X13] :
( ? [X14] :
( ssList(X14)
& app(app(cons(X12,nil),cons(X13,nil)),X14) = X3
& app(app(cons(X13,nil),cons(X12,nil)),X14) = X2 )
& ssItem(X13) )
& ssItem(X12) ) )
| ( ! [X15] :
( ~ ssItem(X15)
| ! [X16] :
( ~ ssItem(X16)
| ! [X17] :
( ~ ssList(X17)
| app(app(cons(X15,nil),cons(X16,nil)),X17) != X3 ) ) )
& ? [X18] :
( ? [X19] :
( ? [X20] :
( app(app(cons(X18,nil),cons(X19,nil)),X20) = X1
& ssList(X20) )
& ssItem(X19) )
& ssItem(X18) ) ) ) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f231,definition,
! [X3,X2] :
( ? [X12] :
( ? [X13] :
( ? [X14] :
( ssList(X14)
& app(app(cons(X12,nil),cons(X13,nil)),X14) = X3
& app(app(cons(X13,nil),cons(X12,nil)),X14) = X2 )
& ssItem(X13) )
& ssItem(X12) )
| ~ sP6(X3,X2) ),
introduced(definition,[new_symbols(definition,[sP6])],[predicate_definition_introduction]) ).
fof(f232,definition,
! [X1,X0,X2,X3] :
( ( ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| ! [X7] :
( ~ ssList(X7)
| ! [X8] :
( ~ ssList(X8)
| app(app(app(app(X6,cons(X4,nil)),X7),cons(X5,nil)),X8) != X1
| app(app(app(app(X6,cons(X5,nil)),X7),cons(X4,nil)),X8) != X0 ) ) ) ) )
& ? [X9] :
( ? [X10] :
( ? [X11] :
( app(app(cons(X9,nil),cons(X10,nil)),X11) = X1
& ssList(X11) )
& ssItem(X10) )
& ssItem(X9) )
& sP6(X3,X2) )
| ~ sP7(X1,X0,X2,X3) ),
introduced(definition,[new_symbols(definition,[sP7])],[predicate_definition_introduction]) ).
fof(f233,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& X1 = X3
& X0 = X2
& ( sP7(X1,X0,X2,X3)
| ( ! [X15] :
( ~ ssItem(X15)
| ! [X16] :
( ~ ssItem(X16)
| ! [X17] :
( ~ ssList(X17)
| app(app(cons(X15,nil),cons(X16,nil)),X17) != X3 ) ) )
& ? [X18] :
( ? [X19] :
( ? [X20] :
( app(app(cons(X18,nil),cons(X19,nil)),X20) = X1
& ssList(X20) )
& ssItem(X19) )
& ssItem(X18) ) ) ) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(definition_folding,[],[f221,f232,f231]) ).
fof(f298,plain,
! [X1,X0,X2,X3] :
( ( ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| ! [X7] :
( ~ ssList(X7)
| ! [X8] :
( ~ ssList(X8)
| app(app(app(app(X6,cons(X4,nil)),X7),cons(X5,nil)),X8) != X1
| app(app(app(app(X6,cons(X5,nil)),X7),cons(X4,nil)),X8) != X0 ) ) ) ) )
& ? [X9] :
( ? [X10] :
( ? [X11] :
( app(app(cons(X9,nil),cons(X10,nil)),X11) = X1
& ssList(X11) )
& ssItem(X10) )
& ssItem(X9) )
& sP6(X3,X2) )
| ~ sP7(X1,X0,X2,X3) ),
inference(nnf_transformation,[],[f232]) ).
fof(f299,plain,
! [X0,X1,X2,X3] :
( ( ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| ! [X7] :
( ~ ssList(X7)
| ! [X8] :
( ~ ssList(X8)
| app(app(app(app(X6,cons(X4,nil)),X7),cons(X5,nil)),X8) != X0
| app(app(app(app(X6,cons(X5,nil)),X7),cons(X4,nil)),X8) != X1 ) ) ) ) )
& ? [X9] :
( ? [X10] :
( ? [X11] :
( app(app(cons(X9,nil),cons(X10,nil)),X11) = X0
& ssList(X11) )
& ssItem(X10) )
& ssItem(X9) )
& sP6(X3,X2) )
| ~ sP7(X0,X1,X2,X3) ),
inference(rectify,[],[f298]) ).
fof(f300,plain,
! [X0,X1,X2,X3] :
( ( ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| ! [X7] :
( ~ ssList(X7)
| ! [X8] :
( ~ ssList(X8)
| app(app(app(app(X6,cons(X4,nil)),X7),cons(X5,nil)),X8) != X0
| app(app(app(app(X6,cons(X5,nil)),X7),cons(X4,nil)),X8) != X1 ) ) ) ) )
& app(app(cons(sK55(X0),nil),cons(sK56(X0),nil)),sK57(X0)) = X0
& ssList(sK57(X0))
& ssItem(sK56(X0))
& ssItem(sK55(X0))
& sP6(X3,X2) )
| ~ sP7(X0,X1,X2,X3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55,sK56,sK57]),skolemize(X9,sK55(X0)),skolemize(X10,sK56(X0)),skolemize(X11,sK57(X0))],[f299]) ).
fof(f301,plain,
! [X3,X2] :
( ? [X12] :
( ? [X13] :
( ? [X14] :
( ssList(X14)
& app(app(cons(X12,nil),cons(X13,nil)),X14) = X3
& app(app(cons(X13,nil),cons(X12,nil)),X14) = X2 )
& ssItem(X13) )
& ssItem(X12) )
| ~ sP6(X3,X2) ),
inference(nnf_transformation,[],[f231]) ).
fof(f302,plain,
! [X0,X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ssList(X4)
& app(app(cons(X2,nil),cons(X3,nil)),X4) = X0
& app(app(cons(X3,nil),cons(X2,nil)),X4) = X1 )
& ssItem(X3) )
& ssItem(X2) )
| ~ sP6(X0,X1) ),
inference(rectify,[],[f301]) ).
fof(f303,plain,
! [X0,X1] :
( ( ssList(sK60(X0,X1))
& app(app(cons(sK58(X0,X1),nil),cons(sK59(X0,X1),nil)),sK60(X0,X1)) = X0
& app(app(cons(sK59(X0,X1),nil),cons(sK58(X0,X1),nil)),sK60(X0,X1)) = X1
& ssItem(sK59(X0,X1))
& ssItem(sK58(X0,X1)) )
| ~ sP6(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK58,sK59,sK60]),skolemize(X2,sK58(X0,X1)),skolemize(X3,sK59(X0,X1)),skolemize(X4,sK60(X0,X1))],[f302]) ).
fof(f304,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& X1 = X3
& X0 = X2
& ( sP7(X1,X0,X2,X3)
| ( ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(cons(X4,nil),cons(X5,nil)),X6) != X3 ) ) )
& ? [X7] :
( ? [X8] :
( ? [X9] :
( app(app(cons(X7,nil),cons(X8,nil)),X9) = X1
& ssList(X9) )
& ssItem(X8) )
& ssItem(X7) ) ) ) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(rectify,[],[f233]) ).
fof(f305,plain,
( ssList(sK64)
& sK62 = sK64
& sK61 = sK63
& ( sP7(sK62,sK61,sK63,sK64)
| ( ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(cons(X4,nil),cons(X5,nil)),X6) != sK64 ) ) )
& sK62 = app(app(cons(sK65,nil),cons(sK66,nil)),sK67)
& ssList(sK67)
& ssItem(sK66)
& ssItem(sK65) ) )
& ssList(sK63)
& ssList(sK62)
& ssList(sK61) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK61,sK62,sK63,sK64,sK65,sK66,sK67]),skolemize(X0,sK61),skolemize(X1,sK62),skolemize(X2,sK63),skolemize(X3,sK64),skolemize(X7,sK65),skolemize(X8,sK66),skolemize(X9,sK67)],[f304]) ).
fof(f397,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f398,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f412,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f134]) ).
fof(f491,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f201]) ).
fof(f505,plain,
! [X2,X3,X0,X1] :
( ~ sP7(X0,X1,X2,X3)
| sP6(X3,X2) ),
inference(cnf_transformation,[],[f300]) ).
fof(f510,plain,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( ~ ssItem(X4)
| ~ ssItem(X5)
| ~ ssList(X6)
| ~ ssList(X7)
| ~ ssList(X8)
| app(app(app(app(X6,cons(X4,nil)),X7),cons(X5,nil)),X8) != X0
| app(app(app(app(X6,cons(X5,nil)),X7),cons(X4,nil)),X8) != X1
| ~ sP7(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f300]) ).
fof(f511,plain,
! [X0,X1] :
( ssItem(sK58(X0,X1))
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f303]) ).
fof(f512,plain,
! [X0,X1] :
( ssItem(sK59(X0,X1))
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f303]) ).
fof(f513,plain,
! [X0,X1] :
( ~ sP6(X0,X1)
| app(app(cons(sK59(X0,X1),nil),cons(sK58(X0,X1),nil)),sK60(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f303]) ).
fof(f514,plain,
! [X0,X1] :
( ~ sP6(X0,X1)
| app(app(cons(sK58(X0,X1),nil),cons(sK59(X0,X1),nil)),sK60(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f303]) ).
fof(f515,plain,
! [X0,X1] :
( ssList(sK60(X0,X1))
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f303]) ).
fof(f519,plain,
( sP7(sK62,sK61,sK63,sK64)
| ssItem(sK65) ),
inference(cnf_transformation,[],[f305]) ).
fof(f520,plain,
( sP7(sK62,sK61,sK63,sK64)
| ssItem(sK66) ),
inference(cnf_transformation,[],[f305]) ).
fof(f521,plain,
( sP7(sK62,sK61,sK63,sK64)
| ssList(sK67) ),
inference(cnf_transformation,[],[f305]) ).
fof(f522,plain,
( sP7(sK62,sK61,sK63,sK64)
| sK62 = app(app(cons(sK65,nil),cons(sK66,nil)),sK67) ),
inference(cnf_transformation,[],[f305]) ).
fof(f523,plain,
! [X6,X4,X5] :
( sP7(sK62,sK61,sK63,sK64)
| ~ ssItem(X4)
| ~ ssItem(X5)
| ~ ssList(X6)
| app(app(cons(X4,nil),cons(X5,nil)),X6) != sK64 ),
inference(cnf_transformation,[],[f305]) ).
fof(f524,plain,
sK61 = sK63,
inference(cnf_transformation,[],[f305]) ).
fof(f525,plain,
sK62 = sK64,
inference(cnf_transformation,[],[f305]) ).
fof(f527,plain,
! [X6,X4,X5] :
( sP7(sK64,sK63,sK63,sK64)
| ~ ssItem(X4)
| ~ ssItem(X5)
| ~ ssList(X6)
| app(app(cons(X4,nil),cons(X5,nil)),X6) != sK64 ),
inference(definition_unfolding,[],[f523,f525,f524]) ).
fof(f528,plain,
( sP7(sK64,sK63,sK63,sK64)
| sK64 = app(app(cons(sK65,nil),cons(sK66,nil)),sK67) ),
inference(definition_unfolding,[],[f522,f525,f524,f525]) ).
fof(f529,plain,
( sP7(sK64,sK63,sK63,sK64)
| ssList(sK67) ),
inference(definition_unfolding,[],[f521,f525,f524]) ).
fof(f530,plain,
( sP7(sK64,sK63,sK63,sK64)
| ssItem(sK66) ),
inference(definition_unfolding,[],[f520,f525,f524]) ).
fof(f531,plain,
( sP7(sK64,sK63,sK63,sK64)
| ssItem(sK65) ),
inference(definition_unfolding,[],[f519,f525,f524]) ).
fof(f561,plain,
! [X2,X3,X1,X8,X6,X7,X4,X5] :
( ~ ssItem(X4)
| ~ ssItem(X5)
| ~ ssList(X6)
| ~ ssList(X7)
| ~ ssList(X8)
| app(app(app(app(X6,cons(X5,nil)),X7),cons(X4,nil)),X8) != X1
| ~ sP7(app(app(app(app(X6,cons(X4,nil)),X7),cons(X5,nil)),X8),X1,X2,X3) ),
inference(equality_resolution,[],[f510]) ).
fof(f562,plain,
! [X2,X3,X8,X6,X7,X4,X5] :
( ~ sP7(app(app(app(app(X6,cons(X4,nil)),X7),cons(X5,nil)),X8),app(app(app(app(X6,cons(X5,nil)),X7),cons(X4,nil)),X8),X2,X3)
| ~ ssItem(X5)
| ~ ssList(X6)
| ~ ssList(X7)
| ~ ssList(X8)
| ~ ssItem(X4) ),
inference(equality_resolution,[],[f561]) ).
fof(f563,definition,
sF68 = cons(sK65,nil),
introduced(definition,[new_symbols(definition,[sF68])],[function_definition]) ).
fof(f564,plain,
cons(sK65,nil) = sF68,
inference(reorient_equations,[],[f563]) ).
fof(f565,definition,
sF69 = cons(sK66,nil),
introduced(definition,[new_symbols(definition,[sF69])],[function_definition]) ).
fof(f566,plain,
cons(sK66,nil) = sF69,
inference(reorient_equations,[],[f565]) ).
fof(f567,definition,
sF70 = app(sF68,sF69),
introduced(definition,[new_symbols(definition,[sF70])],[function_definition]) ).
fof(f568,plain,
app(sF68,sF69) = sF70,
inference(reorient_equations,[],[f567]) ).
fof(f569,definition,
sF71 = app(sF70,sK67),
introduced(definition,[new_symbols(definition,[sF71])],[function_definition]) ).
fof(f570,plain,
app(sF70,sK67) = sF71,
inference(reorient_equations,[],[f569]) ).
fof(f571,plain,
( sP7(sK64,sK63,sK63,sK64)
| sK64 = sF71 ),
inference(definition_folding,[],[f528,f570,f568,f566,f564]) ).
fof(f580,definition,
( spl72_1
<=> ssItem(sK65) ),
introduced(definition,[new_symbols(definition,[spl72_1])],[avatar_definition]) ).
fof(f582,plain,
( ssItem(sK65)
| ~ spl72_1 ),
inference(avatar_component_clause,[],[f580]) ).
fof(f584,definition,
( spl72_2
<=> sP7(sK64,sK63,sK63,sK64) ),
introduced(definition,[new_symbols(definition,[spl72_2])],[avatar_definition]) ).
fof(f586,plain,
( sP7(sK64,sK63,sK63,sK64)
| ~ spl72_2 ),
inference(avatar_component_clause,[],[f584]) ).
fof(f587,plain,
( spl72_1
| spl72_2 ),
inference(avatar_split_clause,[],[f531,f584,f580]) ).
fof(f589,definition,
( spl72_3
<=> ssItem(sK66) ),
introduced(definition,[new_symbols(definition,[spl72_3])],[avatar_definition]) ).
fof(f591,plain,
( ssItem(sK66)
| ~ spl72_3 ),
inference(avatar_component_clause,[],[f589]) ).
fof(f592,plain,
( spl72_3
| spl72_2 ),
inference(avatar_split_clause,[],[f530,f584,f589]) ).
fof(f594,definition,
( spl72_4
<=> ssList(sK67) ),
introduced(definition,[new_symbols(definition,[spl72_4])],[avatar_definition]) ).
fof(f596,plain,
( ssList(sK67)
| ~ spl72_4 ),
inference(avatar_component_clause,[],[f594]) ).
fof(f597,plain,
( spl72_4
| spl72_2 ),
inference(avatar_split_clause,[],[f529,f584,f594]) ).
fof(f599,definition,
( spl72_5
<=> sK64 = sF71 ),
introduced(definition,[new_symbols(definition,[spl72_5])],[avatar_definition]) ).
fof(f601,plain,
( sK64 = sF71
| ~ spl72_5 ),
inference(avatar_component_clause,[],[f599]) ).
fof(f602,plain,
( spl72_5
| spl72_2 ),
inference(avatar_split_clause,[],[f571,f584,f599]) ).
fof(f604,definition,
( spl72_6
<=> ! [X6,X4,X5] :
( ~ ssItem(X4)
| app(app(cons(X4,nil),cons(X5,nil)),X6) != sK64
| ~ ssList(X6)
| ~ ssItem(X5) ) ),
introduced(definition,[new_symbols(definition,[spl72_6])],[avatar_definition]) ).
fof(f605,plain,
( ! [X6,X4,X5] :
( app(app(cons(X4,nil),cons(X5,nil)),X6) != sK64
| ~ ssItem(X4)
| ~ ssList(X6)
| ~ ssItem(X5) )
| ~ spl72_6 ),
inference(avatar_component_clause,[],[f604]) ).
fof(f606,plain,
( spl72_6
| spl72_2 ),
inference(avatar_split_clause,[],[f527,f584,f604]) ).
fof(f608,definition,
( spl72_7
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl72_7])],[avatar_definition]) ).
fof(f609,plain,
( ssList(nil)
| ~ spl72_7 ),
inference(avatar_component_clause,[],[f608]) ).
fof(f636,plain,
spl72_7,
inference(avatar_split_clause,[],[f398,f608]) ).
fof(f639,plain,
( sP6(sK64,sK63)
| ~ spl72_2 ),
inference(resolution,[],[f586,f505]) ).
fof(f642,plain,
( sK63 = app(app(cons(sK59(sK64,sK63),nil),cons(sK58(sK64,sK63),nil)),sK60(sK64,sK63))
| ~ spl72_2 ),
inference(resolution,[],[f639,f513]) ).
fof(f643,plain,
( sK64 = app(app(cons(sK58(sK64,sK63),nil),cons(sK59(sK64,sK63),nil)),sK60(sK64,sK63))
| ~ spl72_2 ),
inference(resolution,[],[f639,f514]) ).
fof(f665,definition,
( spl72_15
<=> ssList(sK60(sK64,sK63)) ),
introduced(definition,[new_symbols(definition,[spl72_15])],[avatar_definition]) ).
fof(f666,plain,
( ssList(sK60(sK64,sK63))
| ~ spl72_15 ),
inference(avatar_component_clause,[],[f665]) ).
fof(f667,plain,
( ~ ssList(sK60(sK64,sK63))
| spl72_15 ),
inference(avatar_component_clause,[],[f665]) ).
fof(f669,definition,
( spl72_16
<=> ssList(cons(sK59(sK64,sK63),nil)) ),
introduced(definition,[new_symbols(definition,[spl72_16])],[avatar_definition]) ).
fof(f670,plain,
( ssList(cons(sK59(sK64,sK63),nil))
| ~ spl72_16 ),
inference(avatar_component_clause,[],[f669]) ).
fof(f671,plain,
( ~ ssList(cons(sK59(sK64,sK63),nil))
| spl72_16 ),
inference(avatar_component_clause,[],[f669]) ).
fof(f673,definition,
( spl72_17
<=> ssItem(sK58(sK64,sK63)) ),
introduced(definition,[new_symbols(definition,[spl72_17])],[avatar_definition]) ).
fof(f674,plain,
( ssItem(sK58(sK64,sK63))
| ~ spl72_17 ),
inference(avatar_component_clause,[],[f673]) ).
fof(f675,plain,
( ~ ssItem(sK58(sK64,sK63))
| spl72_17 ),
inference(avatar_component_clause,[],[f673]) ).
fof(f681,definition,
( spl72_19
<=> ssList(cons(sK58(sK64,sK63),nil)) ),
introduced(definition,[new_symbols(definition,[spl72_19])],[avatar_definition]) ).
fof(f682,plain,
( ssList(cons(sK58(sK64,sK63),nil))
| ~ spl72_19 ),
inference(avatar_component_clause,[],[f681]) ).
fof(f683,plain,
( ~ ssList(cons(sK58(sK64,sK63),nil))
| spl72_19 ),
inference(avatar_component_clause,[],[f681]) ).
fof(f685,definition,
( spl72_20
<=> ssItem(sK59(sK64,sK63)) ),
introduced(definition,[new_symbols(definition,[spl72_20])],[avatar_definition]) ).
fof(f686,plain,
( ssItem(sK59(sK64,sK63))
| ~ spl72_20 ),
inference(avatar_component_clause,[],[f685]) ).
fof(f687,plain,
( ~ ssItem(sK59(sK64,sK63))
| spl72_20 ),
inference(avatar_component_clause,[],[f685]) ).
fof(f724,plain,
( ~ sP6(sK64,sK63)
| spl72_15 ),
inference(resolution,[],[f667,f515]) ).
fof(f725,plain,
( $false
| ~ spl72_2
| spl72_15 ),
inference(forward_subsumption_resolution,[],[f724,f639]) ).
fof(f726,plain,
( ~ spl72_2
| spl72_15 ),
inference(avatar_contradiction_clause,[],[f725]) ).
fof(f727,plain,
( ~ sP6(sK64,sK63)
| spl72_20 ),
inference(resolution,[],[f687,f512]) ).
fof(f728,plain,
( $false
| ~ spl72_2
| spl72_20 ),
inference(forward_subsumption_resolution,[],[f727,f639]) ).
fof(f729,plain,
( ~ spl72_2
| spl72_20 ),
inference(avatar_contradiction_clause,[],[f728]) ).
fof(f732,plain,
( ~ ssItem(sK59(sK64,sK63))
| ~ ssList(nil)
| spl72_16 ),
inference(resolution,[],[f397,f671]) ).
fof(f733,plain,
( ~ ssItem(sK58(sK64,sK63))
| ~ ssList(nil)
| spl72_19 ),
inference(resolution,[],[f397,f683]) ).
fof(f739,plain,
( ~ ssItem(sK58(sK64,sK63))
| ~ spl72_7
| spl72_19 ),
inference(forward_subsumption_resolution,[],[f733,f609]) ).
fof(f740,plain,
( ~ ssList(nil)
| spl72_16
| ~ spl72_20 ),
inference(forward_subsumption_resolution,[],[f732,f686]) ).
fof(f743,plain,
( ~ spl72_17
| ~ spl72_7
| spl72_19 ),
inference(avatar_split_clause,[],[f739,f681,f608,f673]) ).
fof(f744,plain,
( $false
| ~ spl72_7
| spl72_16
| ~ spl72_20 ),
inference(forward_subsumption_resolution,[],[f740,f609]) ).
fof(f745,plain,
( ~ spl72_7
| spl72_16
| ~ spl72_20 ),
inference(avatar_contradiction_clause,[],[f744]) ).
fof(f746,plain,
( ~ sP6(sK64,sK63)
| spl72_17 ),
inference(resolution,[],[f675,f511]) ).
fof(f747,plain,
( $false
| ~ spl72_2
| spl72_17 ),
inference(forward_subsumption_resolution,[],[f746,f639]) ).
fof(f748,plain,
( ~ spl72_2
| spl72_17 ),
inference(avatar_contradiction_clause,[],[f747]) ).
fof(f800,plain,
( cons(sK58(sK64,sK63),nil) = app(nil,cons(sK58(sK64,sK63),nil))
| ~ spl72_19 ),
inference(resolution,[],[f412,f682]) ).
fof(f801,plain,
( cons(sK59(sK64,sK63),nil) = app(nil,cons(sK59(sK64,sK63),nil))
| ~ spl72_16 ),
inference(resolution,[],[f412,f670]) ).
fof(f814,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ sP7(app(app(app(cons(sK58(sK64,sK63),nil),X0),cons(X1,nil)),X2),app(app(app(app(nil,cons(X1,nil)),X0),cons(sK58(sK64,sK63),nil)),X2),X3,X4)
| ~ ssItem(X1)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssItem(sK58(sK64,sK63)) )
| ~ spl72_19 ),
inference(superposition,[],[f562,f800]) ).
fof(f816,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ sP7(app(app(app(cons(sK58(sK64,sK63),nil),X0),cons(X1,nil)),X2),app(app(app(app(nil,cons(X1,nil)),X0),cons(sK58(sK64,sK63),nil)),X2),X3,X4)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssItem(sK58(sK64,sK63)) )
| ~ spl72_7
| ~ spl72_19 ),
inference(forward_subsumption_resolution,[],[f814,f609]) ).
fof(f818,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ sP7(app(app(app(cons(sK58(sK64,sK63),nil),X0),cons(X1,nil)),X2),app(app(app(app(nil,cons(X1,nil)),X0),cons(sK58(sK64,sK63),nil)),X2),X3,X4)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2) )
| ~ spl72_7
| ~ spl72_17
| ~ spl72_19 ),
inference(forward_subsumption_resolution,[],[f816,f674]) ).
fof(f826,plain,
( cons(sK58(sK64,sK63),nil) = app(cons(sK58(sK64,sK63),nil),nil)
| ~ spl72_19 ),
inference(resolution,[],[f491,f682]) ).
fof(f827,plain,
( cons(sK59(sK64,sK63),nil) = app(cons(sK59(sK64,sK63),nil),nil)
| ~ spl72_16 ),
inference(resolution,[],[f491,f670]) ).
fof(f1793,plain,
( ! [X2,X3,X0,X1] :
( ~ sP7(app(app(cons(sK58(sK64,sK63),nil),cons(X0,nil)),X1),app(app(app(app(nil,cons(X0,nil)),nil),cons(sK58(sK64,sK63),nil)),X1),X2,X3)
| ~ ssItem(X0)
| ~ ssList(nil)
| ~ ssList(X1) )
| ~ spl72_7
| ~ spl72_17
| ~ spl72_19 ),
inference(superposition,[],[f818,f826]) ).
fof(f1799,plain,
( ! [X2,X3,X0,X1] :
( ~ sP7(app(app(cons(sK58(sK64,sK63),nil),cons(X0,nil)),X1),app(app(app(app(nil,cons(X0,nil)),nil),cons(sK58(sK64,sK63),nil)),X1),X2,X3)
| ~ ssItem(X0)
| ~ ssList(X1) )
| ~ spl72_7
| ~ spl72_17
| ~ spl72_19 ),
inference(forward_subsumption_resolution,[],[f1793,f609]) ).
fof(f6265,plain,
( ! [X0,X1] :
( ~ sP7(sK64,app(app(app(app(nil,cons(sK59(sK64,sK63),nil)),nil),cons(sK58(sK64,sK63),nil)),sK60(sK64,sK63)),X0,X1)
| ~ ssItem(sK59(sK64,sK63))
| ~ ssList(sK60(sK64,sK63)) )
| ~ spl72_2
| ~ spl72_7
| ~ spl72_17
| ~ spl72_19 ),
inference(superposition,[],[f1799,f643]) ).
fof(f6274,plain,
( ! [X0,X1] :
( ~ sP7(sK64,app(app(app(app(nil,cons(sK59(sK64,sK63),nil)),nil),cons(sK58(sK64,sK63),nil)),sK60(sK64,sK63)),X0,X1)
| ~ ssList(sK60(sK64,sK63)) )
| ~ spl72_2
| ~ spl72_7
| ~ spl72_17
| ~ spl72_19
| ~ spl72_20 ),
inference(forward_subsumption_resolution,[],[f6265,f686]) ).
fof(f6280,plain,
( ! [X0,X1] : ~ sP7(sK64,app(app(app(app(nil,cons(sK59(sK64,sK63),nil)),nil),cons(sK58(sK64,sK63),nil)),sK60(sK64,sK63)),X0,X1)
| ~ spl72_2
| ~ spl72_7
| ~ spl72_15
| ~ spl72_17
| ~ spl72_19
| ~ spl72_20 ),
inference(forward_subsumption_resolution,[],[f6274,f666]) ).
fof(f6286,plain,
( ! [X0,X1] : ~ sP7(sK64,app(app(app(cons(sK59(sK64,sK63),nil),nil),cons(sK58(sK64,sK63),nil)),sK60(sK64,sK63)),X0,X1)
| ~ spl72_2
| ~ spl72_7
| ~ spl72_15
| ~ spl72_16
| ~ spl72_17
| ~ spl72_19
| ~ spl72_20 ),
inference(forward_demodulation,[],[f6280,f801]) ).
fof(f6291,plain,
( ! [X0,X1] : ~ sP7(sK64,app(app(cons(sK59(sK64,sK63),nil),cons(sK58(sK64,sK63),nil)),sK60(sK64,sK63)),X0,X1)
| ~ spl72_2
| ~ spl72_7
| ~ spl72_15
| ~ spl72_16
| ~ spl72_17
| ~ spl72_19
| ~ spl72_20 ),
inference(forward_demodulation,[],[f6286,f827]) ).
fof(f6294,plain,
( ! [X0,X1] : ~ sP7(sK64,sK63,X0,X1)
| ~ spl72_2
| ~ spl72_7
| ~ spl72_15
| ~ spl72_16
| ~ spl72_17
| ~ spl72_19
| ~ spl72_20 ),
inference(forward_demodulation,[],[f6291,f642]) ).
fof(f6295,plain,
( $false
| ~ spl72_2
| ~ spl72_7
| ~ spl72_15
| ~ spl72_16
| ~ spl72_17
| ~ spl72_19
| ~ spl72_20 ),
inference(resolution,[],[f6294,f586]) ).
fof(f6296,plain,
( ~ spl72_2
| ~ spl72_7
| ~ spl72_15
| ~ spl72_16
| ~ spl72_17
| ~ spl72_19
| ~ spl72_20 ),
inference(avatar_contradiction_clause,[],[f6295]) ).
fof(f6431,plain,
( ! [X0,X1] :
( sK64 != app(app(sF68,cons(X0,nil)),X1)
| ~ ssItem(sK65)
| ~ ssList(X1)
| ~ ssItem(X0) )
| ~ spl72_6 ),
inference(superposition,[],[f605,f564]) ).
fof(f6446,plain,
( ! [X0,X1] :
( sK64 != app(app(sF68,cons(X0,nil)),X1)
| ~ ssList(X1)
| ~ ssItem(X0) )
| ~ spl72_1
| ~ spl72_6 ),
inference(forward_subsumption_resolution,[],[f6431,f582]) ).
fof(f6454,plain,
( ! [X0] :
( sK64 != app(app(sF68,sF69),X0)
| ~ ssList(X0)
| ~ ssItem(sK66) )
| ~ spl72_1
| ~ spl72_6 ),
inference(superposition,[],[f6446,f566]) ).
fof(f6457,plain,
( ! [X0] :
( sK64 != app(app(sF68,sF69),X0)
| ~ ssList(X0) )
| ~ spl72_1
| ~ spl72_3
| ~ spl72_6 ),
inference(forward_subsumption_resolution,[],[f6454,f591]) ).
fof(f6458,plain,
( ! [X0] :
( sK64 != app(sF70,X0)
| ~ ssList(X0) )
| ~ spl72_1
| ~ spl72_3
| ~ spl72_6 ),
inference(forward_demodulation,[],[f6457,f568]) ).
fof(f6459,plain,
( sK64 != sF71
| ~ ssList(sK67)
| ~ spl72_1
| ~ spl72_3
| ~ spl72_6 ),
inference(superposition,[],[f6458,f570]) ).
fof(f6460,plain,
( ~ ssList(sK67)
| ~ spl72_1
| ~ spl72_3
| ~ spl72_5
| ~ spl72_6 ),
inference(forward_subsumption_resolution,[],[f6459,f601]) ).
fof(f6461,plain,
( $false
| ~ spl72_1
| ~ spl72_3
| ~ spl72_4
| ~ spl72_5
| ~ spl72_6 ),
inference(forward_subsumption_resolution,[],[f6460,f596]) ).
fof(f6462,plain,
( ~ spl72_1
| ~ spl72_3
| ~ spl72_4
| ~ spl72_5
| ~ spl72_6 ),
inference(avatar_contradiction_clause,[],[f6461]) ).
cnf(s1,plain,
( spl72_1
| spl72_2 ),
inference(sat_conversion,[],[f587]) ).
cnf(s2,plain,
( spl72_2
| spl72_3 ),
inference(sat_conversion,[],[f592]) ).
cnf(s3,plain,
( spl72_2
| spl72_4 ),
inference(sat_conversion,[],[f597]) ).
cnf(s4,plain,
( spl72_2
| spl72_5 ),
inference(sat_conversion,[],[f602]) ).
cnf(s5,plain,
( spl72_2
| spl72_6 ),
inference(sat_conversion,[],[f606]) ).
cnf(s13,plain,
spl72_7,
inference(sat_conversion,[],[f636]) ).
cnf(s24,plain,
( ~ spl72_2
| spl72_15 ),
inference(sat_conversion,[],[f726]) ).
cnf(s25,plain,
( ~ spl72_2
| spl72_20 ),
inference(sat_conversion,[],[f729]) ).
cnf(s27,plain,
( ~ spl72_7
| ~ spl72_17
| spl72_19 ),
inference(sat_conversion,[],[f743]) ).
cnf(s28,plain,
( ~ spl72_7
| spl72_16
| ~ spl72_20 ),
inference(sat_conversion,[],[f745]) ).
cnf(s29,plain,
( ~ spl72_2
| spl72_17 ),
inference(sat_conversion,[],[f748]) ).
cnf(s80,plain,
( ~ spl72_2
| ~ spl72_7
| ~ spl72_15
| ~ spl72_16
| ~ spl72_17
| ~ spl72_19
| ~ spl72_20 ),
inference(sat_conversion,[],[f6296]) ).
cnf(s91,plain,
( ~ spl72_1
| ~ spl72_3
| ~ spl72_4
| ~ spl72_5
| ~ spl72_6 ),
inference(sat_conversion,[],[f6462]) ).
cnf(s95,plain,
~ spl72_2,
inference(rat,[],[s80,s28,s27,s24,s25,s29,s13]) ).
cnf(s96,plain,
spl72_6,
inference(rat,[],[s5,s95]) ).
cnf(s97,plain,
spl72_5,
inference(rat,[],[s4,s95]) ).
cnf(s98,plain,
spl72_4,
inference(rat,[],[s3,s95]) ).
cnf(s99,plain,
spl72_3,
inference(rat,[],[s2,s95]) ).
cnf(s100,plain,
spl72_1,
inference(rat,[],[s1,s95]) ).
cnf(s101,plain,
$false,
inference(rat,[],[s91,s96,s97,s100,s98,s99]) ).
fof(f6463,plain,
$false,
inference(avatar_sat_refutation,[],[s101]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC414+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n016.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 09:38:10 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.75/2.68 % (3508963)Detected formulas, will run a generic FOF schedule.
% 13.75/2.68 % (3509091)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3043734879:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 13.75/2.68 % (3509094)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=557964045:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 13.75/2.68 % (3509095)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1503276423:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 13.75/2.68 % (3509096)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=267558007:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 13.75/2.68 % (3509098)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3372738730:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 13.75/2.68 % (3509099)dis-21_1_sil=8000:lcm=predicate:random_seed=2551436245:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 13.75/2.68 % (3509095)Refutation not found, incomplete strategy
% 13.75/2.68 % (3509095)------------------------------
% 13.75/2.68 % (3509095)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.75/2.68 % (3509095)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.75/2.68 % (3509095)CaDiCaL version: 2.1.3
% 13.75/2.68 % (3509095)Termination reason: Refutation not found, incomplete strategy
% 13.75/2.68 % (3509095)Time elapsed: 0.004 s
% 13.75/2.68 % (3509095)Peak memory usage: 89 MB
% 13.75/2.68 % (3509095)Instructions burned: 4 (million)
% 13.75/2.68 % (3509092)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=280949619:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 13.75/2.68 % (3509096)Instruction limit reached!
% 13.75/2.68 % (3509096)------------------------------
% 13.75/2.68 % (3509096)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.75/2.68 % (3509096)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.75/2.68 % (3509096)CaDiCaL version: 2.1.3
% 13.75/2.68 % (3509096)Termination reason: Instruction limit
% 13.75/2.68 % (3509096)Termination phase: Saturation
% 13.75/2.68 % (3509096)Time elapsed: 0.067 s
% 13.75/2.68 % (3509096)Peak memory usage: 88 MB
% 13.75/2.68 % (3509096)Instructions burned: 119 (million)
% 13.75/2.68 % (3509099)Instruction limit reached!
% 13.75/2.68 % (3509099)------------------------------
% 13.75/2.68 % (3509099)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.75/2.68 % (3509099)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.75/2.68 % (3509099)CaDiCaL version: 2.1.3
% 13.75/2.68 % (3509099)Termination reason: Instruction limit
% 13.75/2.68 % (3509099)Termination phase: Saturation
% 13.75/2.68 % (3509099)Time elapsed: 0.073 s
% 13.75/2.68 % (3509099)Peak memory usage: 90 MB
% 13.75/2.68 % (3509099)Instructions burned: 131 (million)
% 13.75/2.68 % (3509098)Instruction limit reached!
% 13.75/2.68 % (3509098)------------------------------
% 13.75/2.68 % (3509098)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.75/2.68 % (3509098)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.75/2.68 % (3509098)CaDiCaL version: 2.1.3
% 13.75/2.68 % (3509098)Termination reason: Instruction limit
% 13.75/2.68 % (3509098)Termination phase: Saturation
% 13.75/2.68 % (3509098)Time elapsed: 0.089 s
% 13.75/2.68 % (3509098)Peak memory usage: 90 MB
% 13.75/2.68 % (3509098)Instructions burned: 140 (million)
% 13.75/2.68 % (3509112)lrs+10_1_sil=8000:sp=occurrence:random_seed=2667505934:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 13.75/2.68 % (3509113)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3164548093:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 13.75/2.68 % (3509114)lrs+1011_1_sil=32000:sp=occurrence:random_seed=204292173:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 13.75/2.68 % (3509095)------------------------------
% 13.75/2.68 % (3509095)------------------------------
% 13.75/2.68 % (3509113)Instruction limit reached!
% 13.75/2.68 % (3509113)------------------------------
% 13.75/2.68 % (3509113)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.59/2.90 % (3509113)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.59/2.90 % (3509113)CaDiCaL version: 2.1.3
% 8.59/2.90 % (3509113)Termination reason: Instruction limit
% 8.59/2.90 % (3509113)Termination phase: Saturation
% 8.59/2.90 % (3509113)Time elapsed: 0.075 s
% 8.59/2.90 % (3509113)Peak memory usage: 92 MB
% 8.59/2.90 % (3509113)Instructions burned: 159 (million)
% 8.59/2.90 % (3509118)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=3938329563:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 8.59/2.90 % (3509112)Instruction limit reached!
% 8.59/2.90 % (3509112)------------------------------
% 8.59/2.90 % (3509112)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.59/2.90 % (3509112)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.59/2.90 % (3509112)CaDiCaL version: 2.1.3
% 8.59/2.90 % (3509112)Termination reason: Instruction limit
% 8.59/2.90 % (3509112)Termination phase: Saturation
% 8.59/2.90 % (3509112)Time elapsed: 0.169 s
% 8.59/2.90 % (3509112)Peak memory usage: 92 MB
% 8.59/2.90 % (3509112)Instructions burned: 285 (million)
% 8.59/2.90 % (3509114)Instruction limit reached!
% 8.59/2.90 % (3509114)------------------------------
% 8.59/2.90 % (3509114)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.59/2.90 % (3509114)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.59/2.90 % (3509114)CaDiCaL version: 2.1.3
% 8.59/2.90 % (3509114)Termination reason: Instruction limit
% 8.59/2.90 % (3509114)Termination phase: Saturation
% 8.59/2.90 % (3509114)Time elapsed: 0.199 s
% 8.59/2.90 % (3509114)Peak memory usage: 92 MB
% 8.59/2.90 % (3509114)Instructions burned: 325 (million)
% 8.59/2.90 % (3509119)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3200687668:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 8.59/2.90 % (3509119)Refutation not found, incomplete strategy
% 8.59/2.90 % (3509119)------------------------------
% 8.59/2.90 % (3509119)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.59/2.90 % (3509119)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.59/2.90 % (3509119)CaDiCaL version: 2.1.3
% 8.59/2.90 % (3509119)Termination reason: Refutation not found, incomplete strategy
% 8.59/2.90 % (3509119)Time elapsed: 0.008 s
% 8.59/2.90 % (3509119)Peak memory usage: 89 MB
% 8.59/2.90 % (3509119)Instructions burned: 6 (million)
% 8.59/2.90 % (3509118)Instruction limit reached!
% 8.59/2.90 % (3509118)------------------------------
% 8.59/2.90 % (3509118)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.59/2.90 % (3509118)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.59/2.90 % (3509118)CaDiCaL version: 2.1.3
% 8.59/2.90 % (3509118)Termination reason: Instruction limit
% 8.59/2.90 % (3509118)Termination phase: Saturation
% 8.59/2.90 % (3509118)Time elapsed: 0.159 s
% 8.59/2.90 % (3509118)Peak memory usage: 94 MB
% 8.59/2.90 % (3509118)Instructions burned: 249 (million)
% 8.59/2.90 % (3509121)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2814537039:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 8.59/2.90 % (3509122)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=303199179:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 8.59/2.90 % (3509132)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2958833760:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 8.59/2.90 % (3509122)Instruction limit reached!
% 8.59/2.90 % (3509122)------------------------------
% 8.59/2.90 % (3509122)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.59/2.90 % (3509122)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.59/2.90 % (3509122)CaDiCaL version: 2.1.3
% 8.59/2.90 % (3509122)Termination reason: Instruction limit
% 8.59/2.90 % (3509122)Termination phase: Saturation
% 8.59/2.90 % (3509122)Time elapsed: 0.128 s
% 8.59/2.90 % (3509122)Peak memory usage: 90 MB
% 8.59/2.90 % (3509122)Instructions burned: 113 (million)
% 8.59/2.90 % (3509119)------------------------------
% 8.59/2.90 % (3509119)------------------------------
% 8.59/2.90 % (3509132)Instruction limit reached!
% 8.59/2.90 % (3509132)------------------------------
% 8.59/2.90 % (3509132)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.59/2.90 % (3509132)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.59/2.90 % (3509132)CaDiCaL version: 2.1.3
% 8.59/2.90 % (3509132)Termination reason: Instruction limit
% 8.59/2.90 % (3509132)Termination phase: Saturation
% 8.59/2.90 % (3509132)Time elapsed: 0.111 s
% 8.59/2.90 % (3509132)Peak memory usage: 90 MB
% 8.59/2.90 % (3509132)Instructions burned: 127 (million)
% 8.59/2.90 % (3509145)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=82189383:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2989 on theBenchmark for (2989ds/114Mi)
% 8.59/2.90 % (3509146)lrs+10_1_sil=8000:sp=occurrence:random_seed=1390560723:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2989 on theBenchmark for (2989ds/907Mi)
% 8.59/2.90 % (3509147)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1902801561:i=437:sd=1:aac=none:ss=included_2988 on theBenchmark for (2988ds/437Mi)
% 8.59/2.90 % (3509145)Instruction limit reached!
% 8.59/2.90 % (3509145)------------------------------
% 8.59/2.90 % (3509145)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.59/2.90 % (3509145)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.59/2.90 % (3509145)CaDiCaL version: 2.1.3
% 8.59/2.90 % (3509145)Termination reason: Instruction limit
% 8.59/2.90 % (3509145)Termination phase: Saturation
% 8.59/2.90 % (3509145)Time elapsed: 0.063 s
% 8.59/2.90 % (3509145)Peak memory usage: 89 MB
% 8.59/2.90 % (3509145)Instructions burned: 115 (million)
% 8.59/2.90 % (3509147)Refutation not found, incomplete strategy
% 8.59/2.90 % (3509147)------------------------------
% 8.59/2.90 % (3509147)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.59/2.90 % (3509147)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.59/2.90 % (3509147)CaDiCaL version: 2.1.3
% 8.59/2.90 % (3509147)Termination reason: Refutation not found, incomplete strategy
% 8.59/2.90 % (3509147)Time elapsed: 0.003 s
% 8.59/2.90 % (3509147)Peak memory usage: 89 MB
% 8.59/2.90 % (3509147)Instructions burned: 3 (million)
% 8.59/2.90 % (3509151)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=623150418:i=5202:ss=axioms:sgt=16_2987 on theBenchmark for (2987ds/5202Mi)
% 8.59/2.90 % (3509147)------------------------------
% 8.59/2.90 % (3509147)------------------------------
% 8.59/2.90 % (3509154)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=4148671862:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2984 on theBenchmark for (2984ds/134Mi)
% 8.59/2.90 % (3509154)Instruction limit reached!
% 8.59/2.90 % (3509154)------------------------------
% 8.59/2.90 % (3509154)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.59/2.90 % (3509154)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.59/2.90 % (3509154)CaDiCaL version: 2.1.3
% 8.59/2.90 % (3509154)Termination reason: Instruction limit
% 8.59/2.90 % (3509154)Termination phase: Saturation
% 8.59/2.90 % (3509154)Time elapsed: 0.061 s
% 8.59/2.90 % (3509154)Peak memory usage: 90 MB
% 8.59/2.90 % (3509154)Instructions burned: 136 (million)
% 8.59/2.90 % (3509146)Instruction limit reached!
% 8.59/2.90 % (3509146)------------------------------
% 8.59/2.90 % (3509146)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.59/2.90 % (3509146)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.59/2.90 % (3509146)CaDiCaL version: 2.1.3
% 8.59/2.90 % (3509146)Termination reason: Instruction limit
% 8.59/2.90 % (3509146)Termination phase: Saturation
% 8.59/2.90 % (3509146)Time elapsed: 0.584 s
% 8.59/2.90 % (3509146)Peak memory usage: 101 MB
% 8.59/2.90 % (3509146)Instructions burned: 908 (million)
% 8.59/2.90 % (3509223)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=2826514697:st=8:i=592:sd=3:ep=RST:ss=axioms_2982 on theBenchmark for (2982ds/592Mi)
% 8.59/2.90 % (3509223)Refutation not found, incomplete strategy
% 8.59/2.90 % (3509223)------------------------------
% 8.59/2.90 % (3509223)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.59/2.90 % (3509223)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.59/2.90 % (3509223)CaDiCaL version: 2.1.3
% 8.59/2.90 % (3509223)Termination reason: Refutation not found, incomplete strategy
% 8.59/2.90 % (3509223)Time elapsed: 0.007 s
% 8.59/2.90 % (3509223)Peak memory usage: 89 MB
% 8.59/2.90 % (3509223)Instructions burned: 11 (million)
% 8.59/2.90 % (3509121)First to succeed.
% 8.59/2.90 % (3509121)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3508963"
% 8.59/2.90 % (3509249)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=1534301174:st=3:i=13193:sd=3:ss=axioms_2981 on theBenchmark for (2981ds/13193Mi)
% 8.59/2.90 % (3509223)------------------------------
% 8.59/2.90 % (3509223)------------------------------
% 8.59/2.90 % (3509121)Refutation found. Thanks to Tanya!
% 8.59/2.90 % SZS status Theorem for theBenchmark
% 8.59/2.90 % SZS output start Proof for theBenchmark
% See solution above
% 16.29/3.10 % (3509121)------------------------------
% 16.29/3.10 % (3509121)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.29/3.10 % (3509121)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.29/3.10 % (3509121)CaDiCaL version: 2.1.3
% 16.29/3.10 % (3509121)Termination reason: Refutation
% 16.29/3.10 % (3509121)Time elapsed: 1.115 s
% 16.29/3.10 % (3509121)Peak memory usage: 136 MB
% 16.29/3.10 % (3509121)Instructions burned: 1601 (million)
% 16.29/3.10 % (3509121)------------------------------
% 16.29/3.10 % (3509121)------------------------------
% 16.29/3.10 % (3508963)Success in time 2.222 s
% 16.29/3.10 % Vampire exiting
%------------------------------------------------------------------------------