%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC413+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n013.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 01:05:56 PM UTC 2026
% Result : Theorem 0.26s 0.37s
% Output : Refutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 175 ( 15 unt; 11 def)
% Number of atoms : 635 ( 139 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 745 ( 285 ~; 348 |; 62 &)
% ( 11 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 15 ( 13 usr; 12 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 191 ( 0 sgn 147 !; 44 ?)
% Comments :
%------------------------------------------------------------------------------
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)
& app(app(cons(X4,nil),cons(X5,nil)),X6) = X1
& app(app(cons(X5,nil),cons(X4,nil)),X6) = X0 ) ) )
| ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> app(app(cons(X7,nil),cons(X8,nil)),X9) != X1 ) ) )
| ! [X10] :
( ssItem(X10)
=> ! [X11] :
( ssItem(X11)
=> ! [X12] :
( ssList(X12)
=> ( app(app(cons(X10,nil),cons(X11,nil)),X12) != X3
| app(app(cons(X11,nil),cons(X10,nil)),X12) != X2 ) ) ) ) )
& ( ? [X13] :
( ssItem(X13)
& ? [X14] :
( ssItem(X14)
& ? [X15] :
( ssList(X15)
& app(app(cons(X13,nil),cons(X14,nil)),X15) = X3 ) ) )
| ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> app(app(cons(X7,nil),cons(X8,nil)),X9) != X1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/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)
& app(app(cons(X4,nil),cons(X5,nil)),X6) = X1
& app(app(cons(X5,nil),cons(X4,nil)),X6) = X0 ) ) )
| ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> app(app(cons(X7,nil),cons(X8,nil)),X9) != X1 ) ) )
| ! [X10] :
( ssItem(X10)
=> ! [X11] :
( ssItem(X11)
=> ! [X12] :
( ssList(X12)
=> ( app(app(cons(X10,nil),cons(X11,nil)),X12) != X3
| app(app(cons(X11,nil),cons(X10,nil)),X12) != X2 ) ) ) ) )
& ( ? [X13] :
( ssItem(X13)
& ? [X14] :
( ssItem(X14)
& ? [X15] :
( ssList(X15)
& app(app(cons(X13,nil),cons(X14,nil)),X15) = X3 ) ) )
| ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> app(app(cons(X7,nil),cons(X8,nil)),X9) != X1 ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
~ ! [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)
& app(app(cons(X4,nil),cons(X5,nil)),X6) = X1
& app(app(cons(X5,nil),cons(X4,nil)),X6) = X0 ) ) )
| ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> app(app(cons(X7,nil),cons(X8,nil)),X9) != X1 ) ) )
| ! [X10] :
( ssItem(X10)
=> ! [X11] :
( ssItem(X11)
=> ! [X12] :
( ssList(X12)
=> ( app(app(cons(X10,nil),cons(X11,nil)),X12) != X3
| app(app(cons(X11,nil),cons(X10,nil)),X12) != X2 ) ) ) ) )
& ( ? [X13] :
( ssItem(X13)
& ? [X14] :
( ssItem(X14)
& ? [X15] :
( ssList(X15)
& app(app(cons(X13,nil),cons(X14,nil)),X15) = X3 ) ) )
| ! [X16] :
( ssItem(X16)
=> ! [X17] :
( ssItem(X17)
=> ! [X18] :
( ssList(X18)
=> app(app(cons(X16,nil),cons(X17,nil)),X18) != X1 ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ( ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(cons(X4,nil),cons(X5,nil)),X6) != X1
| app(app(cons(X5,nil),cons(X4,nil)),X6) != X0 ) ) )
& ? [X7] :
( ? [X8] :
( ? [X9] :
( app(app(cons(X7,nil),cons(X8,nil)),X9) = X1
& ssList(X9) )
& ssItem(X8) )
& ssItem(X7) )
& ? [X10] :
( ? [X11] :
( ? [X12] :
( app(app(cons(X10,nil),cons(X11,nil)),X12) = X3
& app(app(cons(X11,nil),cons(X10,nil)),X12) = X2
& ssList(X12) )
& ssItem(X11) )
& ssItem(X10) ) )
| ( ! [X13] :
( ~ ssItem(X13)
| ! [X14] :
( ~ ssItem(X14)
| ! [X15] :
( ~ ssList(X15)
| app(app(cons(X13,nil),cons(X14,nil)),X15) != X3 ) ) )
& ? [X16] :
( ? [X17] :
( ? [X18] :
( app(app(cons(X16,nil),cons(X17,nil)),X18) = X1
& ssList(X18) )
& ssItem(X17) )
& ssItem(X16) ) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f98]) ).
fof(f223,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ( ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(cons(X4,nil),cons(X5,nil)),X6) != X1
| app(app(cons(X5,nil),cons(X4,nil)),X6) != X0 ) ) )
& ? [X7] :
( ? [X8] :
( ? [X9] :
( app(app(cons(X7,nil),cons(X8,nil)),X9) = X1
& ssList(X9) )
& ssItem(X8) )
& ssItem(X7) )
& ? [X10] :
( ? [X11] :
( ? [X12] :
( app(app(cons(X10,nil),cons(X11,nil)),X12) = X3
& app(app(cons(X11,nil),cons(X10,nil)),X12) = X2
& ssList(X12) )
& ssItem(X11) )
& ssItem(X10) ) )
| ( ! [X13] :
( ~ ssItem(X13)
| ! [X14] :
( ~ ssItem(X14)
| ! [X15] :
( ~ ssList(X15)
| app(app(cons(X13,nil),cons(X14,nil)),X15) != X3 ) ) )
& ? [X16] :
( ? [X17] :
( ? [X18] :
( app(app(cons(X16,nil),cons(X17,nil)),X18) = X1
& ssList(X18) )
& ssItem(X17) )
& ssItem(X16) ) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f222]) ).
fof(f412,plain,
! [X6,X4,X5] :
( ssItem(sK54)
| app(app(cons(X5,nil),cons(X4,nil)),X6) != sK47
| app(app(cons(X4,nil),cons(X5,nil)),X6) != sK48
| ~ ssList(X6)
| ~ ssItem(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f223]) ).
fof(f413,plain,
! [X6,X4,X5] :
( ssItem(sK51)
| app(app(cons(X5,nil),cons(X4,nil)),X6) != sK47
| app(app(cons(X4,nil),cons(X5,nil)),X6) != sK48
| ~ ssList(X6)
| ~ ssItem(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f223]) ).
fof(f414,plain,
! [X6,X4,X5] :
( sK48 = app(app(cons(sK51,nil),cons(sK54,nil)),sK57)
| app(app(cons(X5,nil),cons(X4,nil)),X6) != sK47
| app(app(cons(X4,nil),cons(X5,nil)),X6) != sK48
| ~ ssList(X6)
| ~ ssItem(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f223]) ).
fof(f415,plain,
! [X6,X4,X5] :
( ssList(sK57)
| app(app(cons(X5,nil),cons(X4,nil)),X6) != sK47
| app(app(cons(X4,nil),cons(X5,nil)),X6) != sK48
| ~ ssList(X6)
| ~ ssItem(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f223]) ).
fof(f416,plain,
! [X6,X14,X4,X15,X5,X13] :
( app(app(cons(X13,nil),cons(X14,nil)),X15) != sK50
| ~ ssList(X15)
| ~ ssItem(X14)
| ~ ssItem(X13)
| app(app(cons(X5,nil),cons(X4,nil)),X6) != sK47
| app(app(cons(X4,nil),cons(X5,nil)),X6) != sK48
| ~ ssList(X6)
| ~ ssItem(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f223]) ).
fof(f427,plain,
( ssItem(sK54)
| ssList(sK58) ),
inference(cnf_transformation,[],[f223]) ).
fof(f428,plain,
( ssItem(sK54)
| sK49 = app(app(cons(sK55,nil),cons(sK52,nil)),sK58) ),
inference(cnf_transformation,[],[f223]) ).
fof(f429,plain,
( ssItem(sK54)
| sK50 = app(app(cons(sK52,nil),cons(sK55,nil)),sK58) ),
inference(cnf_transformation,[],[f223]) ).
fof(f430,plain,
( ssItem(sK51)
| ssList(sK58) ),
inference(cnf_transformation,[],[f223]) ).
fof(f431,plain,
( ssItem(sK51)
| sK49 = app(app(cons(sK55,nil),cons(sK52,nil)),sK58) ),
inference(cnf_transformation,[],[f223]) ).
fof(f432,plain,
( ssItem(sK51)
| sK50 = app(app(cons(sK52,nil),cons(sK55,nil)),sK58) ),
inference(cnf_transformation,[],[f223]) ).
fof(f433,plain,
( sK48 = app(app(cons(sK51,nil),cons(sK54,nil)),sK57)
| ssList(sK58) ),
inference(cnf_transformation,[],[f223]) ).
fof(f434,plain,
( sK48 = app(app(cons(sK51,nil),cons(sK54,nil)),sK57)
| sK49 = app(app(cons(sK55,nil),cons(sK52,nil)),sK58) ),
inference(cnf_transformation,[],[f223]) ).
fof(f435,plain,
( sK48 = app(app(cons(sK51,nil),cons(sK54,nil)),sK57)
| sK50 = app(app(cons(sK52,nil),cons(sK55,nil)),sK58) ),
inference(cnf_transformation,[],[f223]) ).
fof(f436,plain,
( ssList(sK57)
| ssList(sK58) ),
inference(cnf_transformation,[],[f223]) ).
fof(f437,plain,
( ssList(sK57)
| sK49 = app(app(cons(sK55,nil),cons(sK52,nil)),sK58) ),
inference(cnf_transformation,[],[f223]) ).
fof(f438,plain,
( ssList(sK57)
| sK50 = app(app(cons(sK52,nil),cons(sK55,nil)),sK58) ),
inference(cnf_transformation,[],[f223]) ).
fof(f439,plain,
! [X14,X15,X13] :
( app(app(cons(X13,nil),cons(X14,nil)),X15) != sK50
| ~ ssList(X15)
| ~ ssItem(X14)
| ~ ssItem(X13)
| ssList(sK58) ),
inference(cnf_transformation,[],[f223]) ).
fof(f440,plain,
! [X14,X15,X13] :
( app(app(cons(X13,nil),cons(X14,nil)),X15) != sK50
| ~ ssList(X15)
| ~ ssItem(X14)
| ~ ssItem(X13)
| sK49 = app(app(cons(sK55,nil),cons(sK52,nil)),sK58) ),
inference(cnf_transformation,[],[f223]) ).
fof(f441,plain,
! [X14,X15,X13] :
( app(app(cons(X13,nil),cons(X14,nil)),X15) != sK50
| ~ ssList(X15)
| ~ ssItem(X14)
| ~ ssItem(X13)
| sK50 = app(app(cons(sK52,nil),cons(sK55,nil)),sK58) ),
inference(cnf_transformation,[],[f223]) ).
fof(f443,plain,
! [X14,X15,X13] :
( app(app(cons(X13,nil),cons(X14,nil)),X15) != sK50
| ~ ssList(X15)
| ~ ssItem(X14)
| ~ ssItem(X13)
| ssItem(sK52) ),
inference(cnf_transformation,[],[f223]) ).
fof(f444,plain,
! [X14,X15,X13] :
( app(app(cons(X13,nil),cons(X14,nil)),X15) != sK50
| ~ ssList(X15)
| ~ ssItem(X14)
| ~ ssItem(X13)
| ssItem(sK55) ),
inference(cnf_transformation,[],[f223]) ).
fof(f448,plain,
( ssList(sK57)
| ssItem(sK52) ),
inference(cnf_transformation,[],[f223]) ).
fof(f449,plain,
( sK48 = app(app(cons(sK51,nil),cons(sK54,nil)),sK57)
| ssItem(sK52) ),
inference(cnf_transformation,[],[f223]) ).
fof(f450,plain,
( ssList(sK57)
| ssItem(sK55) ),
inference(cnf_transformation,[],[f223]) ).
fof(f451,plain,
( sK48 = app(app(cons(sK51,nil),cons(sK54,nil)),sK57)
| ssItem(sK55) ),
inference(cnf_transformation,[],[f223]) ).
fof(f456,plain,
( ssItem(sK51)
| ssItem(sK55) ),
inference(cnf_transformation,[],[f223]) ).
fof(f457,plain,
( ssItem(sK54)
| ssItem(sK55) ),
inference(cnf_transformation,[],[f223]) ).
fof(f458,plain,
( ssItem(sK54)
| ssItem(sK52) ),
inference(cnf_transformation,[],[f223]) ).
fof(f461,plain,
( ssItem(sK51)
| ssItem(sK52) ),
inference(cnf_transformation,[],[f223]) ).
fof(f463,plain,
sK47 = sK49,
inference(cnf_transformation,[],[f223]) ).
fof(f464,plain,
sK48 = sK50,
inference(cnf_transformation,[],[f223]) ).
fof(f471,plain,
( sK50 = app(app(cons(sK51,nil),cons(sK54,nil)),sK57)
| ssItem(sK55) ),
inference(definition_unfolding,[],[f451,f464]) ).
fof(f472,plain,
( sK50 = app(app(cons(sK51,nil),cons(sK54,nil)),sK57)
| ssItem(sK52) ),
inference(definition_unfolding,[],[f449,f464]) ).
fof(f474,plain,
( sK50 = app(app(cons(sK51,nil),cons(sK54,nil)),sK57)
| sK50 = app(app(cons(sK52,nil),cons(sK55,nil)),sK58) ),
inference(definition_unfolding,[],[f435,f464]) ).
fof(f475,plain,
( sK50 = app(app(cons(sK51,nil),cons(sK54,nil)),sK57)
| sK49 = app(app(cons(sK55,nil),cons(sK52,nil)),sK58) ),
inference(definition_unfolding,[],[f434,f464]) ).
fof(f476,plain,
( sK50 = app(app(cons(sK51,nil),cons(sK54,nil)),sK57)
| ssList(sK58) ),
inference(definition_unfolding,[],[f433,f464]) ).
fof(f483,plain,
! [X6,X14,X4,X15,X5,X13] :
( app(app(cons(X13,nil),cons(X14,nil)),X15) != sK50
| ~ ssList(X15)
| ~ ssItem(X14)
| ~ ssItem(X13)
| app(app(cons(X5,nil),cons(X4,nil)),X6) != sK49
| app(app(cons(X4,nil),cons(X5,nil)),X6) != sK50
| ~ ssList(X6)
| ~ ssItem(X5)
| ~ ssItem(X4) ),
inference(definition_unfolding,[],[f416,f463,f464]) ).
fof(f484,plain,
! [X6,X4,X5] :
( ssList(sK57)
| app(app(cons(X5,nil),cons(X4,nil)),X6) != sK49
| app(app(cons(X4,nil),cons(X5,nil)),X6) != sK50
| ~ ssList(X6)
| ~ ssItem(X5)
| ~ ssItem(X4) ),
inference(definition_unfolding,[],[f415,f463,f464]) ).
fof(f485,plain,
! [X6,X4,X5] :
( sK50 = app(app(cons(sK51,nil),cons(sK54,nil)),sK57)
| app(app(cons(X5,nil),cons(X4,nil)),X6) != sK49
| app(app(cons(X4,nil),cons(X5,nil)),X6) != sK50
| ~ ssList(X6)
| ~ ssItem(X5)
| ~ ssItem(X4) ),
inference(definition_unfolding,[],[f414,f464,f463,f464]) ).
fof(f486,plain,
! [X6,X4,X5] :
( ssItem(sK51)
| app(app(cons(X5,nil),cons(X4,nil)),X6) != sK49
| app(app(cons(X4,nil),cons(X5,nil)),X6) != sK50
| ~ ssList(X6)
| ~ ssItem(X5)
| ~ ssItem(X4) ),
inference(definition_unfolding,[],[f413,f463,f464]) ).
fof(f487,plain,
! [X6,X4,X5] :
( ssItem(sK54)
| app(app(cons(X5,nil),cons(X4,nil)),X6) != sK49
| app(app(cons(X4,nil),cons(X5,nil)),X6) != sK50
| ~ ssList(X6)
| ~ ssItem(X5)
| ~ ssItem(X4) ),
inference(definition_unfolding,[],[f412,f463,f464]) ).
fof(f695,plain,
( ~ ssList(sK57)
| ssItem(sK55) ),
inference(consistent_polarity_flipping,[],[f450]) ).
fof(f696,plain,
( ~ ssList(sK57)
| ssItem(sK52) ),
inference(consistent_polarity_flipping,[],[f448]) ).
fof(f699,plain,
! [X14,X15,X13] :
( app(app(cons(X13,nil),cons(X14,nil)),X15) != sK50
| ssList(X15)
| ~ ssItem(X14)
| ~ ssItem(X13)
| ssItem(sK55) ),
inference(consistent_polarity_flipping,[],[f444]) ).
fof(f700,plain,
! [X14,X15,X13] :
( app(app(cons(X13,nil),cons(X14,nil)),X15) != sK50
| ssList(X15)
| ~ ssItem(X14)
| ~ ssItem(X13)
| ssItem(sK52) ),
inference(consistent_polarity_flipping,[],[f443]) ).
fof(f702,plain,
! [X14,X15,X13] :
( app(app(cons(X13,nil),cons(X14,nil)),X15) != sK50
| ssList(X15)
| ~ ssItem(X14)
| ~ ssItem(X13)
| sK50 = app(app(cons(sK52,nil),cons(sK55,nil)),sK58) ),
inference(consistent_polarity_flipping,[],[f441]) ).
fof(f703,plain,
! [X14,X15,X13] :
( app(app(cons(X13,nil),cons(X14,nil)),X15) != sK50
| ssList(X15)
| ~ ssItem(X14)
| ~ ssItem(X13)
| sK49 = app(app(cons(sK55,nil),cons(sK52,nil)),sK58) ),
inference(consistent_polarity_flipping,[],[f440]) ).
fof(f704,plain,
! [X14,X15,X13] :
( app(app(cons(X13,nil),cons(X14,nil)),X15) != sK50
| ssList(X15)
| ~ ssItem(X14)
| ~ ssItem(X13)
| ~ ssList(sK58) ),
inference(consistent_polarity_flipping,[],[f439]) ).
fof(f705,plain,
( ~ ssList(sK57)
| sK50 = app(app(cons(sK52,nil),cons(sK55,nil)),sK58) ),
inference(consistent_polarity_flipping,[],[f438]) ).
fof(f706,plain,
( ~ ssList(sK57)
| sK49 = app(app(cons(sK55,nil),cons(sK52,nil)),sK58) ),
inference(consistent_polarity_flipping,[],[f437]) ).
fof(f707,plain,
( ~ ssList(sK57)
| ~ ssList(sK58) ),
inference(consistent_polarity_flipping,[],[f436]) ).
fof(f708,plain,
( sK50 = app(app(cons(sK51,nil),cons(sK54,nil)),sK57)
| ~ ssList(sK58) ),
inference(consistent_polarity_flipping,[],[f476]) ).
fof(f709,plain,
( ssItem(sK51)
| ~ ssList(sK58) ),
inference(consistent_polarity_flipping,[],[f430]) ).
fof(f710,plain,
( ssItem(sK54)
| ~ ssList(sK58) ),
inference(consistent_polarity_flipping,[],[f427]) ).
fof(f718,plain,
! [X6,X14,X4,X15,X5,X13] :
( app(app(cons(X13,nil),cons(X14,nil)),X15) != sK50
| ssList(X15)
| ~ ssItem(X14)
| ~ ssItem(X13)
| app(app(cons(X5,nil),cons(X4,nil)),X6) != sK49
| app(app(cons(X4,nil),cons(X5,nil)),X6) != sK50
| ssList(X6)
| ~ ssItem(X5)
| ~ ssItem(X4) ),
inference(consistent_polarity_flipping,[],[f483]) ).
fof(f719,plain,
! [X6,X4,X5] :
( ~ ssList(sK57)
| app(app(cons(X5,nil),cons(X4,nil)),X6) != sK49
| app(app(cons(X4,nil),cons(X5,nil)),X6) != sK50
| ssList(X6)
| ~ ssItem(X5)
| ~ ssItem(X4) ),
inference(consistent_polarity_flipping,[],[f484]) ).
fof(f720,plain,
! [X6,X4,X5] :
( sK50 = app(app(cons(sK51,nil),cons(sK54,nil)),sK57)
| app(app(cons(X5,nil),cons(X4,nil)),X6) != sK49
| app(app(cons(X4,nil),cons(X5,nil)),X6) != sK50
| ssList(X6)
| ~ ssItem(X5)
| ~ ssItem(X4) ),
inference(consistent_polarity_flipping,[],[f485]) ).
fof(f721,plain,
! [X6,X4,X5] :
( ssItem(sK51)
| app(app(cons(X5,nil),cons(X4,nil)),X6) != sK49
| app(app(cons(X4,nil),cons(X5,nil)),X6) != sK50
| ssList(X6)
| ~ ssItem(X5)
| ~ ssItem(X4) ),
inference(consistent_polarity_flipping,[],[f486]) ).
fof(f722,plain,
! [X6,X4,X5] :
( ssItem(sK54)
| app(app(cons(X5,nil),cons(X4,nil)),X6) != sK49
| app(app(cons(X4,nil),cons(X5,nil)),X6) != sK50
| ssList(X6)
| ~ ssItem(X5)
| ~ ssItem(X4) ),
inference(consistent_polarity_flipping,[],[f487]) ).
fof(f731,definition,
( spl60_1
<=> ! [X6,X4,X5] :
( app(app(cons(X5,nil),cons(X4,nil)),X6) != sK49
| ~ ssItem(X4)
| ~ ssItem(X5)
| ssList(X6)
| app(app(cons(X4,nil),cons(X5,nil)),X6) != sK50 ) ),
introduced(definition,[new_symbols(definition,[spl60_1])],[avatar_definition]) ).
fof(f732,plain,
( ! [X6,X4,X5] :
( app(app(cons(X5,nil),cons(X4,nil)),X6) != sK49
| ~ ssItem(X4)
| ~ ssItem(X5)
| ssList(X6)
| app(app(cons(X4,nil),cons(X5,nil)),X6) != sK50 )
| ~ spl60_1 ),
inference(avatar_component_clause,[],[f731]) ).
fof(f734,definition,
( spl60_2
<=> ssItem(sK54) ),
introduced(definition,[new_symbols(definition,[spl60_2])],[avatar_definition]) ).
fof(f736,plain,
( ssItem(sK54)
| ~ spl60_2 ),
inference(avatar_component_clause,[],[f734]) ).
fof(f737,plain,
( spl60_1
| spl60_2 ),
inference(avatar_split_clause,[],[f722,f734,f731]) ).
fof(f739,definition,
( spl60_3
<=> ssItem(sK51) ),
introduced(definition,[new_symbols(definition,[spl60_3])],[avatar_definition]) ).
fof(f741,plain,
( ssItem(sK51)
| ~ spl60_3 ),
inference(avatar_component_clause,[],[f739]) ).
fof(f742,plain,
( spl60_1
| spl60_3 ),
inference(avatar_split_clause,[],[f721,f739,f731]) ).
fof(f744,definition,
( spl60_4
<=> sK50 = app(app(cons(sK51,nil),cons(sK54,nil)),sK57) ),
introduced(definition,[new_symbols(definition,[spl60_4])],[avatar_definition]) ).
fof(f746,plain,
( sK50 = app(app(cons(sK51,nil),cons(sK54,nil)),sK57)
| ~ spl60_4 ),
inference(avatar_component_clause,[],[f744]) ).
fof(f747,plain,
( spl60_1
| spl60_4 ),
inference(avatar_split_clause,[],[f720,f744,f731]) ).
fof(f749,definition,
( spl60_5
<=> ssList(sK57) ),
introduced(definition,[new_symbols(definition,[spl60_5])],[avatar_definition]) ).
fof(f751,plain,
( ~ ssList(sK57)
| spl60_5 ),
inference(avatar_component_clause,[],[f749]) ).
fof(f752,plain,
( spl60_1
| ~ spl60_5 ),
inference(avatar_split_clause,[],[f719,f749,f731]) ).
fof(f754,definition,
( spl60_6
<=> ! [X13,X14,X15] :
( app(app(cons(X13,nil),cons(X14,nil)),X15) != sK50
| ~ ssItem(X13)
| ~ ssItem(X14)
| ssList(X15) ) ),
introduced(definition,[new_symbols(definition,[spl60_6])],[avatar_definition]) ).
fof(f755,plain,
( ! [X14,X15,X13] :
( app(app(cons(X13,nil),cons(X14,nil)),X15) != sK50
| ~ ssItem(X13)
| ~ ssItem(X14)
| ssList(X15) )
| ~ spl60_6 ),
inference(avatar_component_clause,[],[f754]) ).
fof(f756,plain,
( spl60_1
| spl60_6 ),
inference(avatar_split_clause,[],[f718,f754,f731]) ).
fof(f776,definition,
( spl60_9
<=> ssList(sK58) ),
introduced(definition,[new_symbols(definition,[spl60_9])],[avatar_definition]) ).
fof(f778,plain,
( ~ ssList(sK58)
| spl60_9 ),
inference(avatar_component_clause,[],[f776]) ).
fof(f779,plain,
( ~ spl60_9
| spl60_2 ),
inference(avatar_split_clause,[],[f710,f734,f776]) ).
fof(f781,definition,
( spl60_10
<=> sK49 = app(app(cons(sK55,nil),cons(sK52,nil)),sK58) ),
introduced(definition,[new_symbols(definition,[spl60_10])],[avatar_definition]) ).
fof(f783,plain,
( sK49 = app(app(cons(sK55,nil),cons(sK52,nil)),sK58)
| ~ spl60_10 ),
inference(avatar_component_clause,[],[f781]) ).
fof(f784,plain,
( spl60_10
| spl60_2 ),
inference(avatar_split_clause,[],[f428,f734,f781]) ).
fof(f786,definition,
( spl60_11
<=> sK50 = app(app(cons(sK52,nil),cons(sK55,nil)),sK58) ),
introduced(definition,[new_symbols(definition,[spl60_11])],[avatar_definition]) ).
fof(f788,plain,
( sK50 = app(app(cons(sK52,nil),cons(sK55,nil)),sK58)
| ~ spl60_11 ),
inference(avatar_component_clause,[],[f786]) ).
fof(f789,plain,
( spl60_11
| spl60_2 ),
inference(avatar_split_clause,[],[f429,f734,f786]) ).
fof(f790,plain,
( ~ spl60_9
| spl60_3 ),
inference(avatar_split_clause,[],[f709,f739,f776]) ).
fof(f791,plain,
( spl60_10
| spl60_3 ),
inference(avatar_split_clause,[],[f431,f739,f781]) ).
fof(f792,plain,
( spl60_11
| spl60_3 ),
inference(avatar_split_clause,[],[f432,f739,f786]) ).
fof(f793,plain,
( ~ spl60_9
| spl60_4 ),
inference(avatar_split_clause,[],[f708,f744,f776]) ).
fof(f794,plain,
( spl60_10
| spl60_4 ),
inference(avatar_split_clause,[],[f475,f744,f781]) ).
fof(f795,plain,
( spl60_11
| spl60_4 ),
inference(avatar_split_clause,[],[f474,f744,f786]) ).
fof(f796,plain,
( ~ spl60_9
| ~ spl60_5 ),
inference(avatar_split_clause,[],[f707,f749,f776]) ).
fof(f797,plain,
( spl60_10
| ~ spl60_5 ),
inference(avatar_split_clause,[],[f706,f749,f781]) ).
fof(f798,plain,
( spl60_11
| ~ spl60_5 ),
inference(avatar_split_clause,[],[f705,f749,f786]) ).
fof(f799,plain,
( ~ spl60_9
| spl60_6 ),
inference(avatar_split_clause,[],[f704,f754,f776]) ).
fof(f800,plain,
( spl60_10
| spl60_6 ),
inference(avatar_split_clause,[],[f703,f754,f781]) ).
fof(f801,plain,
( spl60_11
| spl60_6 ),
inference(avatar_split_clause,[],[f702,f754,f786]) ).
fof(f808,definition,
( spl60_13
<=> ssItem(sK52) ),
introduced(definition,[new_symbols(definition,[spl60_13])],[avatar_definition]) ).
fof(f810,plain,
( ssItem(sK52)
| ~ spl60_13 ),
inference(avatar_component_clause,[],[f808]) ).
fof(f811,plain,
( spl60_13
| spl60_6 ),
inference(avatar_split_clause,[],[f700,f754,f808]) ).
fof(f813,definition,
( spl60_14
<=> ssItem(sK55) ),
introduced(definition,[new_symbols(definition,[spl60_14])],[avatar_definition]) ).
fof(f815,plain,
( ssItem(sK55)
| ~ spl60_14 ),
inference(avatar_component_clause,[],[f813]) ).
fof(f816,plain,
( spl60_14
| spl60_6 ),
inference(avatar_split_clause,[],[f699,f754,f813]) ).
fof(f824,plain,
( spl60_13
| ~ spl60_5 ),
inference(avatar_split_clause,[],[f696,f749,f808]) ).
fof(f825,plain,
( spl60_13
| spl60_4 ),
inference(avatar_split_clause,[],[f472,f744,f808]) ).
fof(f826,plain,
( spl60_14
| ~ spl60_5 ),
inference(avatar_split_clause,[],[f695,f749,f813]) ).
fof(f827,plain,
( spl60_14
| spl60_4 ),
inference(avatar_split_clause,[],[f471,f744,f813]) ).
fof(f832,plain,
( spl60_14
| spl60_3 ),
inference(avatar_split_clause,[],[f456,f739,f813]) ).
fof(f833,plain,
( spl60_14
| spl60_2 ),
inference(avatar_split_clause,[],[f457,f734,f813]) ).
fof(f834,plain,
( spl60_13
| spl60_2 ),
inference(avatar_split_clause,[],[f458,f734,f808]) ).
fof(f837,plain,
( spl60_13
| spl60_3 ),
inference(avatar_split_clause,[],[f461,f739,f808]) ).
fof(f873,plain,
( sK50 != sK50
| ~ ssItem(sK51)
| ~ ssItem(sK54)
| ssList(sK57)
| ~ spl60_4
| ~ spl60_6 ),
inference(superposition,[],[f755,f746]) ).
fof(f874,plain,
( ~ ssItem(sK51)
| ~ ssItem(sK54)
| ssList(sK57)
| ~ spl60_4
| ~ spl60_6 ),
inference(trivial_inequality_removal,[],[f873]) ).
fof(f875,plain,
( ~ ssItem(sK54)
| ssList(sK57)
| ~ spl60_3
| ~ spl60_4
| ~ spl60_6 ),
inference(forward_subsumption_resolution,[],[f874,f741]) ).
fof(f876,plain,
( ssList(sK57)
| ~ spl60_2
| ~ spl60_3
| ~ spl60_4
| ~ spl60_6 ),
inference(forward_subsumption_resolution,[],[f875,f736]) ).
fof(f877,plain,
( $false
| ~ spl60_2
| ~ spl60_3
| ~ spl60_4
| spl60_5
| ~ spl60_6 ),
inference(forward_subsumption_resolution,[],[f876,f751]) ).
fof(f878,plain,
( ~ spl60_2
| ~ spl60_3
| ~ spl60_4
| spl60_5
| ~ spl60_6 ),
inference(avatar_contradiction_clause,[],[f877]) ).
fof(f886,plain,
( sK49 != sK49
| ~ ssItem(sK52)
| ~ ssItem(sK55)
| ssList(sK58)
| sK50 != app(app(cons(sK52,nil),cons(sK55,nil)),sK58)
| ~ spl60_1
| ~ spl60_10 ),
inference(superposition,[],[f732,f783]) ).
fof(f888,plain,
( ~ ssItem(sK52)
| ~ ssItem(sK55)
| ssList(sK58)
| sK50 != app(app(cons(sK52,nil),cons(sK55,nil)),sK58)
| ~ spl60_1
| ~ spl60_10 ),
inference(trivial_inequality_removal,[],[f886]) ).
fof(f890,plain,
( ~ ssItem(sK55)
| ssList(sK58)
| sK50 != app(app(cons(sK52,nil),cons(sK55,nil)),sK58)
| ~ spl60_1
| ~ spl60_10
| ~ spl60_13 ),
inference(forward_subsumption_resolution,[],[f888,f810]) ).
fof(f893,plain,
( ssList(sK58)
| sK50 != app(app(cons(sK52,nil),cons(sK55,nil)),sK58)
| ~ spl60_1
| ~ spl60_10
| ~ spl60_13
| ~ spl60_14 ),
inference(forward_subsumption_resolution,[],[f890,f815]) ).
fof(f896,plain,
( sK50 != app(app(cons(sK52,nil),cons(sK55,nil)),sK58)
| ~ spl60_1
| spl60_9
| ~ spl60_10
| ~ spl60_13
| ~ spl60_14 ),
inference(forward_subsumption_resolution,[],[f893,f778]) ).
fof(f907,plain,
( $false
| ~ spl60_1
| spl60_9
| ~ spl60_10
| ~ spl60_11
| ~ spl60_13
| ~ spl60_14 ),
inference(forward_subsumption_resolution,[],[f896,f788]) ).
fof(f908,plain,
( ~ spl60_1
| spl60_9
| ~ spl60_10
| ~ spl60_11
| ~ spl60_13
| ~ spl60_14 ),
inference(avatar_contradiction_clause,[],[f907]) ).
cnf(s1,plain,
( spl60_1
| spl60_2 ),
inference(sat_conversion,[],[f737]) ).
cnf(s2,plain,
( spl60_1
| spl60_3 ),
inference(sat_conversion,[],[f742]) ).
cnf(s3,plain,
( spl60_1
| spl60_4 ),
inference(sat_conversion,[],[f747]) ).
cnf(s4,plain,
( spl60_1
| ~ spl60_5 ),
inference(sat_conversion,[],[f752]) ).
cnf(s5,plain,
( spl60_1
| spl60_6 ),
inference(sat_conversion,[],[f756]) ).
cnf(s16,plain,
( spl60_2
| ~ spl60_9 ),
inference(sat_conversion,[],[f779]) ).
cnf(s17,plain,
( spl60_2
| spl60_10 ),
inference(sat_conversion,[],[f784]) ).
cnf(s18,plain,
( spl60_2
| spl60_11 ),
inference(sat_conversion,[],[f789]) ).
cnf(s19,plain,
( spl60_3
| ~ spl60_9 ),
inference(sat_conversion,[],[f790]) ).
cnf(s20,plain,
( spl60_3
| spl60_10 ),
inference(sat_conversion,[],[f791]) ).
cnf(s21,plain,
( spl60_3
| spl60_11 ),
inference(sat_conversion,[],[f792]) ).
cnf(s22,plain,
( spl60_4
| ~ spl60_9 ),
inference(sat_conversion,[],[f793]) ).
cnf(s23,plain,
( spl60_4
| spl60_10 ),
inference(sat_conversion,[],[f794]) ).
cnf(s24,plain,
( spl60_4
| spl60_11 ),
inference(sat_conversion,[],[f795]) ).
cnf(s25,plain,
( ~ spl60_5
| ~ spl60_9 ),
inference(sat_conversion,[],[f796]) ).
cnf(s26,plain,
( ~ spl60_5
| spl60_10 ),
inference(sat_conversion,[],[f797]) ).
cnf(s27,plain,
( ~ spl60_5
| spl60_11 ),
inference(sat_conversion,[],[f798]) ).
cnf(s28,plain,
( spl60_6
| ~ spl60_9 ),
inference(sat_conversion,[],[f799]) ).
cnf(s29,plain,
( spl60_6
| spl60_10 ),
inference(sat_conversion,[],[f800]) ).
cnf(s30,plain,
( spl60_6
| spl60_11 ),
inference(sat_conversion,[],[f801]) ).
cnf(s32,plain,
( spl60_6
| spl60_13 ),
inference(sat_conversion,[],[f811]) ).
cnf(s33,plain,
( spl60_6
| spl60_14 ),
inference(sat_conversion,[],[f816]) ).
cnf(s37,plain,
( ~ spl60_5
| spl60_13 ),
inference(sat_conversion,[],[f824]) ).
cnf(s38,plain,
( spl60_4
| spl60_13 ),
inference(sat_conversion,[],[f825]) ).
cnf(s39,plain,
( ~ spl60_5
| spl60_14 ),
inference(sat_conversion,[],[f826]) ).
cnf(s40,plain,
( spl60_4
| spl60_14 ),
inference(sat_conversion,[],[f827]) ).
cnf(s45,plain,
( spl60_3
| spl60_14 ),
inference(sat_conversion,[],[f832]) ).
cnf(s46,plain,
( spl60_2
| spl60_14 ),
inference(sat_conversion,[],[f833]) ).
cnf(s47,plain,
( spl60_2
| spl60_13 ),
inference(sat_conversion,[],[f834]) ).
cnf(s50,plain,
( spl60_3
| spl60_13 ),
inference(sat_conversion,[],[f837]) ).
cnf(s60,plain,
( ~ spl60_2
| ~ spl60_3
| ~ spl60_4
| spl60_5
| ~ spl60_6 ),
inference(sat_conversion,[],[f878]) ).
cnf(s63,plain,
( ~ spl60_1
| spl60_9
| ~ spl60_10
| ~ spl60_11
| ~ spl60_13
| ~ spl60_14 ),
inference(sat_conversion,[],[f908]) ).
cnf(s69,plain,
spl60_1,
inference(rat,[],[s60,s1,s2,s3,s4,s5]) ).
cnf(s70,plain,
spl60_2,
inference(rat,[],[s63,s16,s17,s18,s46,s47,s69]) ).
cnf(s71,plain,
spl60_6,
inference(rat,[],[s63,s28,s29,s30,s32,s33,s69]) ).
cnf(s72,plain,
~ spl60_5,
inference(rat,[],[s63,s25,s26,s27,s37,s39,s69]) ).
cnf(s73,plain,
spl60_4,
inference(rat,[],[s63,s22,s23,s24,s38,s40,s69]) ).
cnf(s74,plain,
~ spl60_3,
inference(rat,[],[s60,s71,s72,s70,s73]) ).
cnf(s75,plain,
spl60_13,
inference(rat,[],[s50,s74]) ).
cnf(s77,plain,
spl60_14,
inference(rat,[],[s45,s74]) ).
cnf(s79,plain,
spl60_11,
inference(rat,[],[s21,s74]) ).
cnf(s80,plain,
spl60_10,
inference(rat,[],[s20,s74]) ).
cnf(s81,plain,
~ spl60_9,
inference(rat,[],[s19,s74]) ).
cnf(s84,plain,
$false,
inference(rat,[],[s63,s77,s75,s79,s69,s80,s81]) ).
fof(f914,plain,
$false,
inference(avatar_sat_refutation,[],[s84]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC413+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.24 % Computer : n013.cluster.edu
% 0.09/0.24 % Model : x86_64 x86_64
% 0.09/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.24 % Memory : 8046.5625MB
% 0.09/0.24 % OS : Linux 6.8.0-71-generic
% 0.09/0.24 % CPULimit : 300
% 0.09/0.24 % WCLimit : 300
% 0.09/0.24 % DateTime : Mon Sep 28 09:31:52 UTC 2026
% 0.09/0.24 % CPUTime :
% 0.09/0.24 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.26/0.30 Running first-order model finding
% 0.26/0.30 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.26/0.37 % (1049235)Will run a generic schedule for satisfiability detection.
% 0.26/0.37 % (1049240)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=92499594_2999 on theBenchmark for (2999ds/0Mi)
% 0.26/0.37 % (1049243)dis+10_1_sil=32000:sp=arity:random_seed=4045609525:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.26/0.37 % (1049241)% WARNING: option uhcvi not known.
% 0.26/0.37 % (1049246)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4123615105:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.26/0.37 % (1049245)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1682226726:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.26/0.37 % (1049242)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3109903681:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.26/0.37 % (1049241)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=831685455:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.26/0.37 % TRYING [1]
% 0.26/0.37 % TRYING [2]
% 0.26/0.37 % (1049244)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2083670456:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.26/0.37 % TRYING [3]
% 0.26/0.37 % (1049241) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1049235-1049241"...
% 0.26/0.37 % TRYING [4]
% 0.26/0.37 % (1049241)...printing done.
% 0.26/0.37 % (1049241)Refutation found. Thanks to Tanya!
% 0.26/0.37 % SZS status Theorem for theBenchmark
% 0.26/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.26/0.38 % (1049241)------------------------------
% 0.26/0.38 % (1049241)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.38 % (1049241)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.38 % (1049241)CaDiCaL version: 2.1.3
% 0.26/0.38 % (1049241)Termination reason: Refutation
% 0.26/0.38 % (1049241)Time elapsed: 0.020 s
% 0.26/0.38 % (1049241)Peak memory usage: 13 MB
% 0.26/0.38 % (1049241)Instructions burned: 19 (million)
% 0.26/0.38 % (1049235)Success in time 0.067 s
% 0.26/0.38 % Vampire exiting
%------------------------------------------------------------------------------