%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC314+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 01:03:25 PM UTC 2026
% Result : Theorem 3.03s 1.11s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 27
% Syntax : Number of formulae : 168 ( 15 unt; 16 def)
% Number of atoms : 593 ( 142 equ)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 727 ( 302 ~; 330 |; 51 &)
% ( 18 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 17 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 96 ( 0 sgn 82 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
fof(f21,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> nil != cons(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax21) ).
fof(f22,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssItem(hd(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax22) ).
fof(f23,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> hd(cons(X1,X0)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax23) ).
fof(f24,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssList(tl(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax24) ).
fof(f25,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> tl(cons(X1,X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax25) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).
fof(f81,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) = app(cons(X1,nil),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax81) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ~ ssList(X3)
| X1 != X3
| X0 != X2
| ( nil != X2
& nil = X3 )
| ( ? [X4] :
( ssList(X4)
& X2 != X4
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& tl(X3) = X5
& app(X5,X6) = X4
& ? [X7] :
( ssItem(X7)
& cons(X7,nil) = X6
& hd(X3) = X7
& neq(nil,X3) )
& neq(nil,X3) ) ) )
& neq(X3,nil) )
| ( ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ~ ssList(X9)
| app(cons(X8,nil),X9) != X1
| app(X9,cons(X8,nil)) = X0 ) )
& ( nil != X1
| nil = X0 ) ) ) ) ) ),
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
| ( nil != X2
& nil = X3 )
| ( ? [X4] :
( ssList(X4)
& X2 != X4
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& tl(X3) = X5
& app(X5,X6) = X4
& ? [X7] :
( ssItem(X7)
& cons(X7,nil) = X6
& hd(X3) = X7
& neq(nil,X3) )
& neq(nil,X3) ) ) )
& neq(X3,nil) )
| ( ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ~ ssList(X9)
| app(cons(X8,nil),X9) != X1
| app(X9,cons(X8,nil)) = X0 ) )
& ( nil != X1
| nil = X0 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f118,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f119,plain,
! [X0] :
( ! [X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f125,plain,
! [X0] :
( ! [X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f126,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f127,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f126]) ).
fof(f128,plain,
! [X0] :
( ! [X1] :
( hd(cons(X1,X0)) = X1
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f129,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f130,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f129]) ).
fof(f131,plain,
! [X0] :
( ! [X1] :
( tl(cons(X1,X0)) = X0
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f132,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f198,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f81]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& X1 = X3
& X0 = X2
& ( nil = X2
| nil != X3 )
& ( ! [X4] :
( ~ ssList(X4)
| X2 = X4
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| tl(X3) != X5
| app(X5,X6) != X4
| ! [X7] :
( ~ ssItem(X7)
| cons(X7,nil) != X6
| hd(X3) != X7
| ~ neq(nil,X3) )
| ~ neq(nil,X3) ) ) )
| ~ neq(X3,nil) )
& ( ? [X8] :
( ? [X9] :
( ssList(X9)
& app(cons(X8,nil),X9) = X1
& app(X9,cons(X8,nil)) != X0 )
& ssItem(X8) )
| ( nil = X1
& nil != X0 ) ) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f272,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f118]) ).
fof(f295,plain,
( ssList(sK56)
& sK54 = sK56
& sK53 = sK55
& ( nil = sK55
| nil != sK56 )
& ( ! [X4] :
( ~ ssList(X4)
| sK55 = X4
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| tl(sK56) != X5
| app(X5,X6) != X4
| ! [X7] :
( ~ ssItem(X7)
| cons(X7,nil) != X6
| hd(sK56) != X7
| ~ neq(nil,sK56) )
| ~ neq(nil,sK56) ) ) )
| ~ neq(sK56,nil) )
& ( ( ssList(sK58)
& sK54 = app(cons(sK57,nil),sK58)
& sK53 != app(sK58,cons(sK57,nil))
& ssItem(sK57) )
| ( nil = sK54
& nil != sK53 ) )
& ssList(sK55)
& ssList(sK54)
& ssList(sK53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57,sK58]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X8,sK57),skolemize(X9,sK58)],[f221]) ).
fof(f386,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f272]) ).
fof(f387,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f388,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f395,plain,
! [X0,X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f396,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f397,plain,
! [X0,X1] :
( hd(cons(X1,X0)) = X1
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f398,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f399,plain,
! [X0,X1] :
( tl(cons(X1,X0)) = X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f400,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f476,plain,
! [X0,X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f198]) ).
fof(f498,plain,
( ssItem(sK57)
| nil != sK53 ),
inference(cnf_transformation,[],[f295]) ).
fof(f499,plain,
( ssItem(sK57)
| nil = sK54 ),
inference(cnf_transformation,[],[f295]) ).
fof(f501,plain,
( sK53 != app(sK58,cons(sK57,nil))
| nil = sK54 ),
inference(cnf_transformation,[],[f295]) ).
fof(f502,plain,
( sK54 = app(cons(sK57,nil),sK58)
| nil != sK53 ),
inference(cnf_transformation,[],[f295]) ).
fof(f503,plain,
( sK54 = app(cons(sK57,nil),sK58)
| nil = sK54 ),
inference(cnf_transformation,[],[f295]) ).
fof(f504,plain,
( ssList(sK58)
| nil != sK53 ),
inference(cnf_transformation,[],[f295]) ).
fof(f505,plain,
( ssList(sK58)
| nil = sK54 ),
inference(cnf_transformation,[],[f295]) ).
fof(f506,plain,
! [X6,X7,X4,X5] :
( ~ ssList(X4)
| sK55 = X4
| ~ ssList(X5)
| ~ ssList(X6)
| tl(sK56) != X5
| app(X5,X6) != X4
| ~ ssItem(X7)
| cons(X7,nil) != X6
| hd(sK56) != X7
| ~ neq(nil,sK56)
| ~ neq(nil,sK56)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f295]) ).
fof(f507,plain,
( nil = sK55
| nil != sK56 ),
inference(cnf_transformation,[],[f295]) ).
fof(f508,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f295]) ).
fof(f509,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f295]) ).
fof(f510,plain,
ssList(sK56),
inference(cnf_transformation,[],[f295]) ).
fof(f538,plain,
! [X6,X7,X4] :
( ~ ssList(X4)
| sK55 = X4
| ~ ssList(tl(sK56))
| ~ ssList(X6)
| app(tl(sK56),X6) != X4
| ~ ssItem(X7)
| cons(X7,nil) != X6
| hd(sK56) != X7
| ~ neq(nil,sK56)
| ~ neq(nil,sK56)
| ~ neq(sK56,nil) ),
inference(equality_resolution,[],[f506]) ).
fof(f539,plain,
! [X6,X7] :
( ~ ssList(app(tl(sK56),X6))
| sK55 = app(tl(sK56),X6)
| ~ ssList(tl(sK56))
| ~ ssList(X6)
| ~ ssItem(X7)
| cons(X7,nil) != X6
| hd(sK56) != X7
| ~ neq(nil,sK56)
| ~ neq(nil,sK56)
| ~ neq(sK56,nil) ),
inference(equality_resolution,[],[f538]) ).
fof(f540,plain,
! [X7] :
( ~ ssList(app(tl(sK56),cons(X7,nil)))
| sK55 = app(tl(sK56),cons(X7,nil))
| ~ ssList(tl(sK56))
| ~ ssList(cons(X7,nil))
| ~ ssItem(X7)
| hd(sK56) != X7
| ~ neq(nil,sK56)
| ~ neq(nil,sK56)
| ~ neq(sK56,nil) ),
inference(equality_resolution,[],[f539]) ).
fof(f541,plain,
( ~ ssList(app(tl(sK56),cons(hd(sK56),nil)))
| sK55 = app(tl(sK56),cons(hd(sK56),nil))
| ~ ssList(tl(sK56))
| ~ ssList(cons(hd(sK56),nil))
| ~ ssItem(hd(sK56))
| ~ neq(nil,sK56)
| ~ neq(nil,sK56)
| ~ neq(sK56,nil) ),
inference(equality_resolution,[],[f540]) ).
fof(f542,plain,
( ~ ssList(app(tl(sK56),cons(hd(sK56),nil)))
| sK55 = app(tl(sK56),cons(hd(sK56),nil))
| ~ ssList(tl(sK56))
| ~ ssList(cons(hd(sK56),nil))
| ~ ssItem(hd(sK56))
| ~ neq(nil,sK56)
| ~ neq(sK56,nil) ),
inference(duplicate_literal_removal,[],[f541]) ).
fof(f551,definition,
( spl59_1
<=> nil = sK53 ),
introduced(definition,[new_symbols(definition,[spl59_1])],[avatar_definition]) ).
fof(f555,definition,
( spl59_2
<=> ssItem(sK57) ),
introduced(definition,[new_symbols(definition,[spl59_2])],[avatar_definition]) ).
fof(f557,plain,
( ssItem(sK57)
| ~ spl59_2 ),
inference(avatar_component_clause,[],[f555]) ).
fof(f558,plain,
( ~ spl59_1
| spl59_2 ),
inference(avatar_split_clause,[],[f498,f555,f551]) ).
fof(f560,definition,
( spl59_3
<=> nil = sK54 ),
introduced(definition,[new_symbols(definition,[spl59_3])],[avatar_definition]) ).
fof(f562,plain,
( nil = sK54
| ~ spl59_3 ),
inference(avatar_component_clause,[],[f560]) ).
fof(f563,plain,
( spl59_3
| spl59_2 ),
inference(avatar_split_clause,[],[f499,f555,f560]) ).
fof(f565,definition,
( spl59_4
<=> sK53 = app(sK58,cons(sK57,nil)) ),
introduced(definition,[new_symbols(definition,[spl59_4])],[avatar_definition]) ).
fof(f567,plain,
( sK53 != app(sK58,cons(sK57,nil))
| spl59_4 ),
inference(avatar_component_clause,[],[f565]) ).
fof(f569,plain,
( spl59_3
| ~ spl59_4 ),
inference(avatar_split_clause,[],[f501,f565,f560]) ).
fof(f571,definition,
( spl59_5
<=> sK54 = app(cons(sK57,nil),sK58) ),
introduced(definition,[new_symbols(definition,[spl59_5])],[avatar_definition]) ).
fof(f573,plain,
( sK54 = app(cons(sK57,nil),sK58)
| ~ spl59_5 ),
inference(avatar_component_clause,[],[f571]) ).
fof(f574,plain,
( ~ spl59_1
| spl59_5 ),
inference(avatar_split_clause,[],[f502,f571,f551]) ).
fof(f575,plain,
( spl59_3
| spl59_5 ),
inference(avatar_split_clause,[],[f503,f571,f560]) ).
fof(f577,definition,
( spl59_6
<=> ssList(sK58) ),
introduced(definition,[new_symbols(definition,[spl59_6])],[avatar_definition]) ).
fof(f579,plain,
( ssList(sK58)
| ~ spl59_6 ),
inference(avatar_component_clause,[],[f577]) ).
fof(f580,plain,
( ~ spl59_1
| spl59_6 ),
inference(avatar_split_clause,[],[f504,f577,f551]) ).
fof(f581,plain,
( spl59_3
| spl59_6 ),
inference(avatar_split_clause,[],[f505,f577,f560]) ).
fof(f583,definition,
( spl59_7
<=> neq(sK56,nil) ),
introduced(definition,[new_symbols(definition,[spl59_7])],[avatar_definition]) ).
fof(f585,plain,
( ~ neq(sK56,nil)
| spl59_7 ),
inference(avatar_component_clause,[],[f583]) ).
fof(f587,definition,
( spl59_8
<=> neq(nil,sK56) ),
introduced(definition,[new_symbols(definition,[spl59_8])],[avatar_definition]) ).
fof(f589,plain,
( ~ neq(nil,sK56)
| spl59_8 ),
inference(avatar_component_clause,[],[f587]) ).
fof(f591,definition,
( spl59_9
<=> ssItem(hd(sK56)) ),
introduced(definition,[new_symbols(definition,[spl59_9])],[avatar_definition]) ).
fof(f593,plain,
( ~ ssItem(hd(sK56))
| spl59_9 ),
inference(avatar_component_clause,[],[f591]) ).
fof(f595,definition,
( spl59_10
<=> ssList(cons(hd(sK56),nil)) ),
introduced(definition,[new_symbols(definition,[spl59_10])],[avatar_definition]) ).
fof(f597,plain,
( ~ ssList(cons(hd(sK56),nil))
| spl59_10 ),
inference(avatar_component_clause,[],[f595]) ).
fof(f599,definition,
( spl59_11
<=> ssList(tl(sK56)) ),
introduced(definition,[new_symbols(definition,[spl59_11])],[avatar_definition]) ).
fof(f601,plain,
( ~ ssList(tl(sK56))
| spl59_11 ),
inference(avatar_component_clause,[],[f599]) ).
fof(f603,definition,
( spl59_12
<=> sK55 = app(tl(sK56),cons(hd(sK56),nil)) ),
introduced(definition,[new_symbols(definition,[spl59_12])],[avatar_definition]) ).
fof(f605,plain,
( sK55 = app(tl(sK56),cons(hd(sK56),nil))
| ~ spl59_12 ),
inference(avatar_component_clause,[],[f603]) ).
fof(f607,definition,
( spl59_13
<=> ssList(app(tl(sK56),cons(hd(sK56),nil))) ),
introduced(definition,[new_symbols(definition,[spl59_13])],[avatar_definition]) ).
fof(f609,plain,
( ~ ssList(app(tl(sK56),cons(hd(sK56),nil)))
| spl59_13 ),
inference(avatar_component_clause,[],[f607]) ).
fof(f610,plain,
( ~ spl59_7
| ~ spl59_8
| ~ spl59_9
| ~ spl59_10
| ~ spl59_11
| spl59_12
| ~ spl59_13 ),
inference(avatar_split_clause,[],[f542,f607,f603,f599,f595,f591,f587,f583]) ).
fof(f612,definition,
( spl59_14
<=> nil = sK56 ),
introduced(definition,[new_symbols(definition,[spl59_14])],[avatar_definition]) ).
fof(f614,plain,
( nil != sK56
| spl59_14 ),
inference(avatar_component_clause,[],[f612]) ).
fof(f616,definition,
( spl59_15
<=> nil = sK55 ),
introduced(definition,[new_symbols(definition,[spl59_15])],[avatar_definition]) ).
fof(f618,plain,
( nil = sK55
| ~ spl59_15 ),
inference(avatar_component_clause,[],[f616]) ).
fof(f619,plain,
( ~ spl59_14
| spl59_15 ),
inference(avatar_split_clause,[],[f507,f616,f612]) ).
fof(f621,definition,
( spl59_16
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl59_16])],[avatar_definition]) ).
fof(f622,plain,
( ssList(nil)
| ~ spl59_16 ),
inference(avatar_component_clause,[],[f621]) ).
fof(f654,plain,
spl59_16,
inference(avatar_split_clause,[],[f388,f621]) ).
fof(f658,plain,
( nil = sK56
| ~ spl59_3 ),
inference(superposition,[],[f509,f562]) ).
fof(f661,plain,
( spl59_14
| ~ spl59_3 ),
inference(avatar_split_clause,[],[f658,f560,f612]) ).
fof(f664,plain,
( nil = sK53
| ~ spl59_15 ),
inference(superposition,[],[f618,f508]) ).
fof(f673,plain,
( sK56 = app(cons(sK57,nil),sK58)
| ~ spl59_5 ),
inference(forward_demodulation,[],[f573,f509]) ).
fof(f676,plain,
( ~ ssList(cons(hd(sK56),nil))
| ~ ssList(tl(sK56))
| spl59_13 ),
inference(resolution,[],[f400,f609]) ).
fof(f684,plain,
( ~ spl59_11
| ~ spl59_10
| spl59_13 ),
inference(avatar_split_clause,[],[f676,f607,f595,f599]) ).
fof(f685,plain,
( ~ ssItem(hd(sK56))
| ~ ssList(nil)
| spl59_10 ),
inference(resolution,[],[f597,f387]) ).
fof(f686,plain,
( ~ ssItem(hd(sK56))
| spl59_10
| ~ spl59_16 ),
inference(forward_subsumption_resolution,[],[f685,f622]) ).
fof(f687,plain,
( ~ spl59_9
| spl59_10
| ~ spl59_16 ),
inference(avatar_split_clause,[],[f686,f621,f595,f591]) ).
fof(f688,plain,
( nil = sK56
| ~ ssList(sK56)
| spl59_9 ),
inference(resolution,[],[f593,f396]) ).
fof(f689,plain,
( ~ ssList(sK56)
| spl59_9
| spl59_14 ),
inference(forward_subsumption_resolution,[],[f688,f614]) ).
fof(f690,plain,
( $false
| spl59_9
| spl59_14 ),
inference(forward_subsumption_resolution,[],[f689,f510]) ).
fof(f691,plain,
( spl59_9
| spl59_14 ),
inference(avatar_contradiction_clause,[],[f690]) ).
fof(f692,plain,
( nil = sK56
| ~ ssList(sK56)
| spl59_11 ),
inference(resolution,[],[f601,f398]) ).
fof(f693,plain,
( ~ ssList(sK56)
| spl59_11
| spl59_14 ),
inference(forward_subsumption_resolution,[],[f692,f614]) ).
fof(f694,plain,
( $false
| spl59_11
| spl59_14 ),
inference(forward_subsumption_resolution,[],[f693,f510]) ).
fof(f695,plain,
( spl59_11
| spl59_14 ),
inference(avatar_contradiction_clause,[],[f694]) ).
fof(f728,plain,
( nil = sK56
| ~ ssList(nil)
| ~ ssList(sK56)
| spl59_7 ),
inference(resolution,[],[f386,f585]) ).
fof(f731,plain,
( ~ ssList(nil)
| ~ ssList(sK56)
| spl59_7
| spl59_14 ),
inference(forward_subsumption_resolution,[],[f728,f614]) ).
fof(f732,plain,
( ~ ssList(sK56)
| spl59_7
| spl59_14
| ~ spl59_16 ),
inference(forward_subsumption_resolution,[],[f731,f622]) ).
fof(f733,plain,
( $false
| spl59_7
| spl59_14
| ~ spl59_16 ),
inference(forward_subsumption_resolution,[],[f732,f510]) ).
fof(f734,plain,
( spl59_7
| spl59_14
| ~ spl59_16 ),
inference(avatar_contradiction_clause,[],[f733]) ).
fof(f735,plain,
( nil = sK56
| ~ ssList(sK56)
| ~ ssList(nil)
| spl59_8 ),
inference(resolution,[],[f589,f386]) ).
fof(f737,plain,
( ~ ssList(sK56)
| ~ ssList(nil)
| spl59_8
| spl59_14 ),
inference(forward_subsumption_resolution,[],[f735,f614]) ).
fof(f738,plain,
( ~ ssList(nil)
| spl59_8
| spl59_14 ),
inference(forward_subsumption_resolution,[],[f737,f510]) ).
fof(f739,plain,
( $false
| spl59_8
| spl59_14
| ~ spl59_16 ),
inference(forward_subsumption_resolution,[],[f738,f622]) ).
fof(f740,plain,
( spl59_8
| spl59_14
| ~ spl59_16 ),
inference(avatar_contradiction_clause,[],[f739]) ).
fof(f741,plain,
( sK53 = app(tl(sK56),cons(hd(sK56),nil))
| ~ spl59_12 ),
inference(forward_demodulation,[],[f605,f508]) ).
fof(f869,plain,
( sK56 = cons(sK57,sK58)
| ~ ssItem(sK57)
| ~ ssList(sK58)
| ~ spl59_5 ),
inference(superposition,[],[f673,f476]) ).
fof(f876,plain,
( sK56 = cons(sK57,sK58)
| ~ ssList(sK58)
| ~ spl59_2
| ~ spl59_5 ),
inference(forward_subsumption_resolution,[],[f869,f557]) ).
fof(f878,plain,
( sK56 = cons(sK57,sK58)
| ~ spl59_2
| ~ spl59_5
| ~ spl59_6 ),
inference(forward_subsumption_resolution,[],[f876,f579]) ).
fof(f880,plain,
( tl(sK56) = sK58
| ~ ssItem(sK57)
| ~ ssList(sK58)
| ~ spl59_2
| ~ spl59_5
| ~ spl59_6 ),
inference(superposition,[],[f399,f878]) ).
fof(f881,plain,
( hd(sK56) = sK57
| ~ ssItem(sK57)
| ~ ssList(sK58)
| ~ spl59_2
| ~ spl59_5
| ~ spl59_6 ),
inference(superposition,[],[f397,f878]) ).
fof(f883,plain,
( nil != sK56
| ~ ssItem(sK57)
| ~ ssList(sK58)
| ~ spl59_2
| ~ spl59_5
| ~ spl59_6 ),
inference(superposition,[],[f395,f878]) ).
fof(f888,plain,
( hd(sK56) = sK57
| ~ ssList(sK58)
| ~ spl59_2
| ~ spl59_5
| ~ spl59_6 ),
inference(forward_subsumption_resolution,[],[f881,f557]) ).
fof(f889,plain,
( tl(sK56) = sK58
| ~ ssList(sK58)
| ~ spl59_2
| ~ spl59_5
| ~ spl59_6 ),
inference(forward_subsumption_resolution,[],[f880,f557]) ).
fof(f892,plain,
( hd(sK56) = sK57
| ~ spl59_2
| ~ spl59_5
| ~ spl59_6 ),
inference(forward_subsumption_resolution,[],[f888,f579]) ).
fof(f893,plain,
( tl(sK56) = sK58
| ~ spl59_2
| ~ spl59_5
| ~ spl59_6 ),
inference(forward_subsumption_resolution,[],[f889,f579]) ).
fof(f917,plain,
( sK53 = app(sK58,cons(hd(sK56),nil))
| ~ spl59_2
| ~ spl59_5
| ~ spl59_6
| ~ spl59_12 ),
inference(superposition,[],[f741,f893]) ).
fof(f927,plain,
( sK53 = app(sK58,cons(sK57,nil))
| ~ spl59_2
| ~ spl59_5
| ~ spl59_6
| ~ spl59_12 ),
inference(forward_demodulation,[],[f917,f892]) ).
fof(f930,plain,
( $false
| ~ spl59_2
| spl59_4
| ~ spl59_5
| ~ spl59_6
| ~ spl59_12 ),
inference(forward_subsumption_resolution,[],[f927,f567]) ).
fof(f931,plain,
( ~ spl59_2
| spl59_4
| ~ spl59_5
| ~ spl59_6
| ~ spl59_12 ),
inference(avatar_contradiction_clause,[],[f930]) ).
fof(f935,plain,
( spl59_1
| ~ spl59_15 ),
inference(avatar_split_clause,[],[f664,f616,f551]) ).
fof(f938,plain,
( nil != sK56
| ~ ssList(sK58)
| ~ spl59_2
| ~ spl59_5
| ~ spl59_6 ),
inference(forward_subsumption_resolution,[],[f883,f557]) ).
fof(f960,plain,
( nil != sK56
| ~ spl59_2
| ~ spl59_5
| ~ spl59_6 ),
inference(forward_subsumption_resolution,[],[f938,f579]) ).
fof(f974,plain,
( ~ spl59_14
| ~ spl59_2
| ~ spl59_5
| ~ spl59_6 ),
inference(avatar_split_clause,[],[f960,f577,f571,f555,f612]) ).
cnf(s1,plain,
( ~ spl59_1
| spl59_2 ),
inference(sat_conversion,[],[f558]) ).
cnf(s2,plain,
( spl59_2
| spl59_3 ),
inference(sat_conversion,[],[f563]) ).
cnf(s4,plain,
( spl59_3
| ~ spl59_4 ),
inference(sat_conversion,[],[f569]) ).
cnf(s5,plain,
( ~ spl59_1
| spl59_5 ),
inference(sat_conversion,[],[f574]) ).
cnf(s6,plain,
( spl59_3
| spl59_5 ),
inference(sat_conversion,[],[f575]) ).
cnf(s7,plain,
( ~ spl59_1
| spl59_6 ),
inference(sat_conversion,[],[f580]) ).
cnf(s8,plain,
( spl59_3
| spl59_6 ),
inference(sat_conversion,[],[f581]) ).
cnf(s9,plain,
( ~ spl59_7
| ~ spl59_8
| ~ spl59_9
| ~ spl59_10
| ~ spl59_11
| spl59_12
| ~ spl59_13 ),
inference(sat_conversion,[],[f610]) ).
cnf(s10,plain,
( ~ spl59_14
| spl59_15 ),
inference(sat_conversion,[],[f619]) ).
cnf(s19,plain,
spl59_16,
inference(sat_conversion,[],[f654]) ).
cnf(s21,plain,
( ~ spl59_3
| spl59_14 ),
inference(sat_conversion,[],[f661]) ).
cnf(s28,plain,
( ~ spl59_10
| ~ spl59_11
| spl59_13 ),
inference(sat_conversion,[],[f684]) ).
cnf(s29,plain,
( ~ spl59_9
| spl59_10
| ~ spl59_16 ),
inference(sat_conversion,[],[f687]) ).
cnf(s30,plain,
( spl59_9
| spl59_14 ),
inference(sat_conversion,[],[f691]) ).
cnf(s31,plain,
( spl59_11
| spl59_14 ),
inference(sat_conversion,[],[f695]) ).
cnf(s33,plain,
( spl59_7
| spl59_14
| ~ spl59_16 ),
inference(sat_conversion,[],[f734]) ).
cnf(s34,plain,
( spl59_8
| spl59_14
| ~ spl59_16 ),
inference(sat_conversion,[],[f740]) ).
cnf(s35,plain,
( ~ spl59_2
| spl59_4
| ~ spl59_5
| ~ spl59_6
| ~ spl59_12 ),
inference(sat_conversion,[],[f931]) ).
cnf(s38,plain,
( spl59_1
| ~ spl59_15 ),
inference(sat_conversion,[],[f935]) ).
cnf(s45,plain,
( ~ spl59_2
| ~ spl59_5
| ~ spl59_6
| ~ spl59_14 ),
inference(sat_conversion,[],[f974]) ).
cnf(s50,plain,
spl59_14,
inference(rat,[],[s9,s35,s28,s2,s4,s6,s8,s29,s21,s30,s31,s33,s34,s19]) ).
cnf(s52,plain,
spl59_15,
inference(rat,[],[s10,s50]) ).
cnf(s53,plain,
spl59_1,
inference(rat,[],[s38,s52]) ).
cnf(s54,plain,
spl59_6,
inference(rat,[],[s7,s53]) ).
cnf(s55,plain,
spl59_5,
inference(rat,[],[s5,s53]) ).
cnf(s57,plain,
spl59_2,
inference(rat,[],[s1,s53]) ).
cnf(s58,plain,
$false,
inference(rat,[],[s45,s50,s54,s55,s57]) ).
fof(f975,plain,
$false,
inference(avatar_sat_refutation,[],[s58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC314+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n011.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Mon Sep 28 09:01:15 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running first-order theorem proving
% 0.07/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.03/1.11 % (3260062)Detected formulas, will run a generic FOF schedule.
% 3.03/1.11 % (3260071)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=348663460:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.03/1.11 % (3260069)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=3305217878:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.03/1.11 % (3260071)Instruction limit reached!
% 3.03/1.11 % (3260071)------------------------------
% 3.03/1.11 % (3260071)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.03/1.11 % (3260071)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.03/1.11 % (3260071)CaDiCaL version: 2.1.3
% 3.03/1.11 % (3260071)Termination reason: Instruction limit
% 3.03/1.11 % (3260071)Termination phase: Saturation
% 3.03/1.11 % (3260071)Time elapsed: 0.036 s
% 3.03/1.11 % (3260071)Peak memory usage: 88 MB
% 3.03/1.11 % (3260071)Instructions burned: 120 (million)
% 3.03/1.11 % (3260068)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=1977748111:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.03/1.11 % (3260067)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=2132838285:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.03/1.11 % (3260070)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=391326249:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.03/1.11 % (3260072)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1701918541:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.03/1.11 % (3260073)dis-21_1_sil=8000:lcm=predicate:random_seed=786209699: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)
% 3.03/1.11 % (3260072)First to succeed.
% 3.03/1.11 % (3260072)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3260062"
% 3.03/1.11 % (3260070)Also succeeded, but the first one will report.
% 3.03/1.11 % (3260073)Instruction limit reached!
% 3.03/1.11 % (3260073)------------------------------
% 3.03/1.11 % (3260073)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.03/1.11 % (3260073)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.03/1.11 % (3260073)CaDiCaL version: 2.1.3
% 3.03/1.11 % (3260073)Termination reason: Instruction limit
% 3.03/1.11 % (3260073)Termination phase: Saturation
% 3.03/1.11 % (3260073)Time elapsed: 0.073 s
% 3.03/1.11 % (3260073)Peak memory usage: 90 MB
% 3.03/1.11 % (3260073)Instructions burned: 130 (million)
% 3.03/1.11 % (3260076)lrs+10_1_sil=8000:sp=occurrence:random_seed=3761575697:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.03/1.11 % (3260076)Also succeeded, but the first one will report.
% 3.03/1.11 % (3260083)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2326033054:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.03/1.11 % (3260072)Refutation found. Thanks to Tanya!
% 3.03/1.11 % SZS status Theorem for theBenchmark
% 3.03/1.11 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/1.30 % (3260072)------------------------------
% 0.20/1.30 % (3260072)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.30 % (3260072)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.30 % (3260072)CaDiCaL version: 2.1.3
% 0.20/1.30 % (3260072)Termination reason: Refutation
% 0.20/1.30 % (3260072)Time elapsed: 0.020 s
% 0.20/1.30 % (3260072)Peak memory usage: 90 MB
% 0.20/1.30 % (3260072)Instructions burned: 28 (million)
% 0.20/1.30 % (3260072)------------------------------
% 0.20/1.30 % (3260072)------------------------------
% 0.20/1.30 % (3260062)Success in time 0.441 s
% 0.20/1.30 % Vampire exiting
%------------------------------------------------------------------------------