%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC224+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 : n010.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 01:03:00 PM UTC 2026
% Result : Theorem 6.82s 2.04s
% Output : Refutation 8.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 19
% Syntax : Number of formulae : 117 ( 25 unt; 10 def)
% Number of atoms : 439 ( 115 equ)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 529 ( 207 ~; 226 |; 66 &)
% ( 6 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 7 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-3 aty)
% Number of variables : 138 ( 0 sgn 114 !; 24 ?)
% 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(f22,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssItem(hd(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax22) ).
fof(f24,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssList(tl(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax24) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax38) ).
fof(f78,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> cons(hd(X0),tl(X0)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax78) ).
fof(f81,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) = app(cons(X1,nil),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax81) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| nil = X0
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X5,cons(X4,nil)),X6) = X0
& ! [X7] :
( ssItem(X7)
=> ( ~ memberP(X5,X7)
| ~ memberP(X6,X7)
| ~ leq(X4,X7)
| leq(X7,X4) ) ) ) ) )
| ! [X8] :
( ssList(X8)
=> ( app(X2,X8) != X3
| ~ equalelemsP(X2)
| ? [X9] :
( ssItem(X9)
& ? [X10] :
( ssList(X10)
& app(cons(X9,nil),X10) = X8
& ? [X11] :
( ssList(X11)
& app(X11,cons(X9,nil)) = X2 ) ) ) ) )
| ( nil != X3
& nil = X2 ) ) ) ) ) ),
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
| nil = X0
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X5,cons(X4,nil)),X6) = X0
& ! [X7] :
( ssItem(X7)
=> ( ~ memberP(X5,X7)
| ~ memberP(X6,X7)
| ~ leq(X4,X7)
| leq(X7,X4) ) ) ) ) )
| ! [X8] :
( ssList(X8)
=> ( app(X2,X8) != X3
| ~ equalelemsP(X2)
| ? [X9] :
( ssItem(X9)
& ? [X10] :
( ssList(X10)
& app(cons(X9,nil),X10) = X8
& ? [X11] :
( ssList(X11)
& app(X11,cons(X9,nil)) = X2 ) ) ) ) )
| ( nil != X3
& nil = X2 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f119,plain,
! [X0] :
( ! [X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f16]) ).
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(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(f134,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f148,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f192,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f78]) ).
fof(f193,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f192]) ).
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] :
( X1 = X3
& X0 = X2
& nil != X0
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != X0
| ? [X7] :
( memberP(X5,X7)
& memberP(X6,X7)
& leq(X4,X7)
& ~ leq(X7,X4)
& ssItem(X7) ) ) ) )
& ? [X8] :
( app(X2,X8) = X3
& equalelemsP(X2)
& ! [X9] :
( ~ ssItem(X9)
| ! [X10] :
( ~ ssList(X10)
| app(cons(X9,nil),X10) != X8
| ! [X11] :
( ~ ssList(X11)
| app(X11,cons(X9,nil)) != X2 ) ) )
& ssList(X8) )
& ( nil = X3
| nil != X2 )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& nil != X0
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != X0
| ? [X7] :
( memberP(X5,X7)
& memberP(X6,X7)
& leq(X4,X7)
& ~ leq(X7,X4)
& ssItem(X7) ) ) ) )
& ? [X8] :
( app(X2,X8) = X3
& equalelemsP(X2)
& ! [X9] :
( ~ ssItem(X9)
| ! [X10] :
( ~ ssList(X10)
| app(cons(X9,nil),X10) != X8
| ! [X11] :
( ~ ssList(X11)
| app(X11,cons(X9,nil)) != X2 ) ) )
& ssList(X8) )
& ( nil = X3
| nil != X2 )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f296,plain,
( sK54 = sK56
& sK53 = sK55
& nil != sK53
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK53
| ( memberP(X5,sK57(X4,X5,X6))
& memberP(X6,sK57(X4,X5,X6))
& leq(X4,sK57(X4,X5,X6))
& ~ leq(sK57(X4,X5,X6),X4)
& ssItem(sK57(X4,X5,X6)) ) ) ) )
& sK56 = app(sK55,sK58)
& equalelemsP(sK55)
& ! [X9] :
( ~ ssItem(X9)
| ! [X10] :
( ~ ssList(X10)
| app(cons(X9,nil),X10) != sK58
| ! [X11] :
( ~ ssList(X11)
| app(X11,cons(X9,nil)) != sK55 ) ) )
& ssList(sK58)
& ( nil = sK56
| nil != sK55 )
& ssList(sK56)
& 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(X7,sK57(X4,X5,X6)),skolemize(X8,sK58)],[f222]) ).
fof(f388,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f389,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f397,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f399,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f403,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f134]) ).
fof(f419,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f474,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(cnf_transformation,[],[f193]) ).
fof(f477,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ),
inference(cnf_transformation,[],[f198]) ).
fof(f496,plain,
ssList(sK53),
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
! [X6,X4,X5] :
( ~ ssItem(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK53
| ssItem(sK57(X4,X5,X6)) ),
inference(cnf_transformation,[],[f296]) ).
fof(f509,plain,
! [X6,X4,X5] :
( ~ ssItem(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK53
| memberP(X5,sK57(X4,X5,X6)) ),
inference(cnf_transformation,[],[f296]) ).
fof(f510,plain,
nil != sK53,
inference(cnf_transformation,[],[f296]) ).
fof(f511,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f513,plain,
nil != sK55,
inference(definition_unfolding,[],[f510,f511]) ).
fof(f514,plain,
! [X6,X4,X5] :
( ~ ssItem(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK55
| memberP(X5,sK57(X4,X5,X6)) ),
inference(definition_unfolding,[],[f509,f511]) ).
fof(f518,plain,
! [X6,X4,X5] :
( ~ ssItem(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK55
| ssItem(sK57(X4,X5,X6)) ),
inference(definition_unfolding,[],[f505,f511]) ).
fof(f520,plain,
ssList(sK55),
inference(definition_unfolding,[],[f496,f511]) ).
fof(f548,definition,
! [X4] : sF59(X4) = cons(X4,nil),
introduced(definition,[new_symbols(definition,[sF59])],[function_definition]) ).
fof(f549,plain,
! [X4] : cons(X4,nil) = sF59(X4),
inference(reorient_equations,[],[f548]) ).
fof(f550,definition,
! [X4,X5] : sF60(X5,X4) = app(X5,sF59(X4)),
introduced(definition,[new_symbols(definition,[sF60])],[function_definition]) ).
fof(f551,plain,
! [X4,X5] : app(X5,sF59(X4)) = sF60(X5,X4),
inference(reorient_equations,[],[f550]) ).
fof(f552,definition,
! [X6,X4,X5] : sF61(X5,X4,X6) = app(sF60(X5,X4),X6),
introduced(definition,[new_symbols(definition,[sF61])],[function_definition]) ).
fof(f553,plain,
! [X6,X4,X5] : app(sF60(X5,X4),X6) = sF61(X5,X4,X6),
inference(reorient_equations,[],[f552]) ).
fof(f554,plain,
! [X6,X4,X5] :
( sK55 != sF61(X5,X4,X6)
| ~ ssList(X5)
| ~ ssList(X6)
| ~ ssItem(X4)
| memberP(X5,sK57(X4,X5,X6)) ),
inference(definition_folding,[],[f514,f553,f551,f549]) ).
fof(f558,plain,
! [X6,X4,X5] :
( sK55 != sF61(X5,X4,X6)
| ~ ssList(X5)
| ~ ssList(X6)
| ~ ssItem(X4)
| ssItem(sK57(X4,X5,X6)) ),
inference(definition_folding,[],[f518,f553,f551,f549]) ).
fof(f562,definition,
! [X10,X9] : sF63(X9,X10) = app(sF59(X9),X10),
introduced(definition,[new_symbols(definition,[sF63])],[function_definition]) ).
fof(f563,plain,
! [X10,X9] : app(sF59(X9),X10) = sF63(X9,X10),
inference(reorient_equations,[],[f562]) ).
fof(f573,definition,
( spl64_1
<=> nil = sK55 ),
introduced(definition,[new_symbols(definition,[spl64_1])],[avatar_definition]) ).
fof(f575,plain,
( nil != sK55
| spl64_1 ),
inference(avatar_component_clause,[],[f573]) ).
fof(f581,plain,
~ spl64_1,
inference(avatar_split_clause,[],[f513,f573]) ).
fof(f583,definition,
( spl64_3
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl64_3])],[avatar_definition]) ).
fof(f584,plain,
( ssList(nil)
| ~ spl64_3 ),
inference(avatar_component_clause,[],[f583]) ).
fof(f611,plain,
spl64_3,
inference(avatar_split_clause,[],[f389,f583]) ).
fof(f639,plain,
( nil = sK55
| sK55 = cons(hd(sK55),tl(sK55)) ),
inference(resolution,[],[f474,f520]) ).
fof(f650,plain,
( sK55 = cons(hd(sK55),tl(sK55))
| spl64_1 ),
inference(forward_subsumption_resolution,[],[f639,f575]) ).
fof(f656,plain,
! [X0] :
( ssList(sF59(X0))
| ~ ssItem(X0)
| ~ ssList(nil) ),
inference(superposition,[],[f388,f549]) ).
fof(f657,plain,
( ! [X0] :
( ssList(sF59(X0))
| ~ ssItem(X0) )
| ~ spl64_3 ),
inference(forward_subsumption_resolution,[],[f656,f584]) ).
fof(f660,plain,
! [X0,X1] :
( nil = X0
| ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,tl(X0)) = app(cons(X1,nil),tl(X0)) ),
inference(resolution,[],[f399,f477]) ).
fof(f662,plain,
! [X0,X1] :
( cons(X1,tl(X0)) = app(sF59(X1),tl(X0))
| nil = X0
| ~ ssList(X0)
| ~ ssItem(X1) ),
inference(forward_demodulation,[],[f660,f549]) ).
fof(f663,plain,
! [X0,X1] :
( ~ ssList(X0)
| nil = X0
| cons(X1,tl(X0)) = sF63(X1,tl(X0))
| ~ ssItem(X1) ),
inference(forward_demodulation,[],[f662,f563]) ).
fof(f668,plain,
( ! [X0] :
( ~ ssItem(X0)
| sF59(X0) = app(nil,sF59(X0)) )
| ~ spl64_3 ),
inference(resolution,[],[f657,f403]) ).
fof(f669,plain,
( ! [X0] :
( ~ ssItem(X0)
| sF59(X0) = sF60(nil,X0) )
| ~ spl64_3 ),
inference(forward_demodulation,[],[f668,f551]) ).
fof(f772,definition,
( spl64_15
<=> ssItem(hd(sK55)) ),
introduced(definition,[new_symbols(definition,[spl64_15])],[avatar_definition]) ).
fof(f773,plain,
( ssItem(hd(sK55))
| ~ spl64_15 ),
inference(avatar_component_clause,[],[f772]) ).
fof(f774,plain,
( ~ ssItem(hd(sK55))
| spl64_15 ),
inference(avatar_component_clause,[],[f772]) ).
fof(f780,plain,
( nil = sK55
| ~ ssList(sK55)
| spl64_15 ),
inference(resolution,[],[f774,f397]) ).
fof(f781,plain,
( ~ ssList(sK55)
| spl64_1
| spl64_15 ),
inference(forward_subsumption_resolution,[],[f780,f575]) ).
fof(f782,plain,
( $false
| spl64_1
| spl64_15 ),
inference(forward_subsumption_resolution,[],[f781,f520]) ).
fof(f783,plain,
( spl64_1
| spl64_15 ),
inference(avatar_contradiction_clause,[],[f782]) ).
fof(f786,plain,
( sF59(hd(sK55)) = sF60(nil,hd(sK55))
| ~ spl64_3
| ~ spl64_15 ),
inference(resolution,[],[f773,f669]) ).
fof(f789,plain,
( ! [X0] : sF61(nil,hd(sK55),X0) = app(sF59(hd(sK55)),X0)
| ~ spl64_3
| ~ spl64_15 ),
inference(superposition,[],[f553,f786]) ).
fof(f790,plain,
( ! [X0] : sF61(nil,hd(sK55),X0) = sF63(hd(sK55),X0)
| ~ spl64_3
| ~ spl64_15 ),
inference(forward_demodulation,[],[f789,f563]) ).
fof(f793,plain,
( ! [X0] :
( sK55 != sF63(hd(sK55),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(hd(sK55))
| ssItem(sK57(hd(sK55),nil,X0)) )
| ~ spl64_3
| ~ spl64_15 ),
inference(superposition,[],[f558,f790]) ).
fof(f794,plain,
( ! [X0] :
( sK55 != sF63(hd(sK55),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(hd(sK55))
| memberP(nil,sK57(hd(sK55),nil,X0)) )
| ~ spl64_3
| ~ spl64_15 ),
inference(superposition,[],[f554,f790]) ).
fof(f797,plain,
( ! [X0] :
( sK55 != sF63(hd(sK55),X0)
| ~ ssList(X0)
| ~ ssItem(hd(sK55))
| memberP(nil,sK57(hd(sK55),nil,X0)) )
| ~ spl64_3
| ~ spl64_15 ),
inference(forward_subsumption_resolution,[],[f794,f584]) ).
fof(f798,plain,
( ! [X0] :
( sK55 != sF63(hd(sK55),X0)
| ~ ssList(X0)
| ~ ssItem(hd(sK55))
| ssItem(sK57(hd(sK55),nil,X0)) )
| ~ spl64_3
| ~ spl64_15 ),
inference(forward_subsumption_resolution,[],[f793,f584]) ).
fof(f802,plain,
( ! [X0] :
( sK55 != sF63(hd(sK55),X0)
| ~ ssList(X0)
| memberP(nil,sK57(hd(sK55),nil,X0)) )
| ~ spl64_3
| ~ spl64_15 ),
inference(forward_subsumption_resolution,[],[f797,f773]) ).
fof(f803,plain,
( ! [X0] :
( sK55 != sF63(hd(sK55),X0)
| ~ ssList(X0)
| ssItem(sK57(hd(sK55),nil,X0)) )
| ~ spl64_3
| ~ spl64_15 ),
inference(forward_subsumption_resolution,[],[f798,f773]) ).
fof(f834,plain,
! [X0] :
( nil = sK55
| cons(X0,tl(sK55)) = sF63(X0,tl(sK55))
| ~ ssItem(X0) ),
inference(resolution,[],[f663,f520]) ).
fof(f839,plain,
( ! [X0] :
( ~ ssItem(X0)
| cons(X0,tl(sK55)) = sF63(X0,tl(sK55)) )
| spl64_1 ),
inference(forward_subsumption_resolution,[],[f834,f575]) ).
fof(f842,plain,
( cons(hd(sK55),tl(sK55)) = sF63(hd(sK55),tl(sK55))
| spl64_1
| ~ spl64_15 ),
inference(resolution,[],[f839,f773]) ).
fof(f844,plain,
( sK55 = sF63(hd(sK55),tl(sK55))
| spl64_1
| ~ spl64_15 ),
inference(forward_demodulation,[],[f842,f650]) ).
fof(f847,plain,
( sK55 != sK55
| ~ ssList(tl(sK55))
| ssItem(sK57(hd(sK55),nil,tl(sK55)))
| spl64_1
| ~ spl64_3
| ~ spl64_15 ),
inference(superposition,[],[f803,f844]) ).
fof(f848,plain,
( sK55 != sK55
| ~ ssList(tl(sK55))
| memberP(nil,sK57(hd(sK55),nil,tl(sK55)))
| spl64_1
| ~ spl64_3
| ~ spl64_15 ),
inference(superposition,[],[f802,f844]) ).
fof(f850,plain,
( ~ ssList(tl(sK55))
| memberP(nil,sK57(hd(sK55),nil,tl(sK55)))
| spl64_1
| ~ spl64_3
| ~ spl64_15 ),
inference(trivial_inequality_removal,[],[f848]) ).
fof(f851,plain,
( ~ ssList(tl(sK55))
| ssItem(sK57(hd(sK55),nil,tl(sK55)))
| spl64_1
| ~ spl64_3
| ~ spl64_15 ),
inference(trivial_inequality_removal,[],[f847]) ).
fof(f856,definition,
( spl64_19
<=> memberP(nil,sK57(hd(sK55),nil,tl(sK55))) ),
introduced(definition,[new_symbols(definition,[spl64_19])],[avatar_definition]) ).
fof(f858,plain,
( memberP(nil,sK57(hd(sK55),nil,tl(sK55)))
| ~ spl64_19 ),
inference(avatar_component_clause,[],[f856]) ).
fof(f860,definition,
( spl64_20
<=> ssList(tl(sK55)) ),
introduced(definition,[new_symbols(definition,[spl64_20])],[avatar_definition]) ).
fof(f862,plain,
( ~ ssList(tl(sK55))
| spl64_20 ),
inference(avatar_component_clause,[],[f860]) ).
fof(f863,plain,
( spl64_19
| ~ spl64_20
| spl64_1
| ~ spl64_3
| ~ spl64_15 ),
inference(avatar_split_clause,[],[f850,f772,f583,f573,f860,f856]) ).
fof(f865,definition,
( spl64_21
<=> ssItem(sK57(hd(sK55),nil,tl(sK55))) ),
introduced(definition,[new_symbols(definition,[spl64_21])],[avatar_definition]) ).
fof(f867,plain,
( ssItem(sK57(hd(sK55),nil,tl(sK55)))
| ~ spl64_21 ),
inference(avatar_component_clause,[],[f865]) ).
fof(f868,plain,
( spl64_21
| ~ spl64_20
| spl64_1
| ~ spl64_3
| ~ spl64_15 ),
inference(avatar_split_clause,[],[f851,f772,f583,f573,f860,f865]) ).
fof(f884,plain,
( nil = sK55
| ~ ssList(sK55)
| spl64_20 ),
inference(resolution,[],[f862,f399]) ).
fof(f885,plain,
( ~ ssList(sK55)
| spl64_1
| spl64_20 ),
inference(forward_subsumption_resolution,[],[f884,f575]) ).
fof(f886,plain,
( $false
| spl64_1
| spl64_20 ),
inference(forward_subsumption_resolution,[],[f885,f520]) ).
fof(f887,plain,
( spl64_1
| spl64_20 ),
inference(avatar_contradiction_clause,[],[f886]) ).
fof(f888,plain,
( ~ ssItem(sK57(hd(sK55),nil,tl(sK55)))
| ~ spl64_19 ),
inference(resolution,[],[f858,f419]) ).
fof(f889,plain,
( $false
| ~ spl64_19
| ~ spl64_21 ),
inference(forward_subsumption_resolution,[],[f888,f867]) ).
fof(f890,plain,
( ~ spl64_19
| ~ spl64_21 ),
inference(avatar_contradiction_clause,[],[f889]) ).
cnf(s2,plain,
~ spl64_1,
inference(sat_conversion,[],[f581]) ).
cnf(s10,plain,
spl64_3,
inference(sat_conversion,[],[f611]) ).
cnf(s17,plain,
( spl64_1
| spl64_15 ),
inference(sat_conversion,[],[f783]) ).
cnf(s19,plain,
( spl64_1
| ~ spl64_3
| ~ spl64_15
| spl64_19
| ~ spl64_20 ),
inference(sat_conversion,[],[f863]) ).
cnf(s20,plain,
( spl64_1
| ~ spl64_3
| ~ spl64_15
| ~ spl64_20
| spl64_21 ),
inference(sat_conversion,[],[f868]) ).
cnf(s24,plain,
( spl64_1
| spl64_20 ),
inference(sat_conversion,[],[f887]) ).
cnf(s25,plain,
( ~ spl64_19
| ~ spl64_21 ),
inference(sat_conversion,[],[f890]) ).
cnf(s29,plain,
spl64_20,
inference(rat,[],[s24,s2]) ).
cnf(s30,plain,
spl64_15,
inference(rat,[],[s17,s2]) ).
cnf(s33,plain,
spl64_21,
inference(rat,[],[s20,s2,s29,s10,s30]) ).
cnf(s34,plain,
spl64_19,
inference(rat,[],[s19,s29,s2,s10,s30]) ).
cnf(s35,plain,
$false,
inference(rat,[],[s25,s33,s34]) ).
fof(f891,plain,
$false,
inference(avatar_sat_refutation,[],[s35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC224+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 % Computer : n010.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Mon Sep 28 08:33:17 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.28 Running first-order theorem proving
% 0.10/0.28 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
% 6.82/2.04 % (1771556)Detected formulas, will run a generic FOF schedule.
% 6.82/2.04 % (1771563)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=2435311765:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.82/2.04 % (1771567)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2990534427:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.82/2.04 % (1771566)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1307039942:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.82/2.04 % (1771568)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2556254352:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.82/2.04 % (1771564)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=3851772818:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.82/2.04 % (1771569)dis-21_1_sil=8000:lcm=predicate:random_seed=3225952213: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)
% 6.82/2.04 % (1771565)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=2075916282:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.82/2.04 % (1771566)Instruction limit reached!
% 6.82/2.04 % (1771566)------------------------------
% 6.82/2.04 % (1771566)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.82/2.04 % (1771566)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.82/2.04 % (1771566)CaDiCaL version: 2.1.3
% 6.82/2.04 % (1771566)Termination reason: Instruction limit
% 6.82/2.04 % (1771566)Termination phase: Saturation
% 6.82/2.04 % (1771566)Time elapsed: 0.108 s
% 6.82/2.04 % (1771566)Peak memory usage: 89 MB
% 6.82/2.04 % (1771566)Instructions burned: 109 (million)
% 6.82/2.04 % (1771569)Instruction limit reached!
% 6.82/2.04 % (1771569)------------------------------
% 6.82/2.04 % (1771569)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.82/2.04 % (1771569)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.82/2.04 % (1771569)CaDiCaL version: 2.1.3
% 6.82/2.04 % (1771569)Termination reason: Instruction limit
% 6.82/2.04 % (1771569)Termination phase: Saturation
% 6.82/2.04 % (1771569)Time elapsed: 0.122 s
% 6.82/2.04 % (1771569)Peak memory usage: 91 MB
% 6.82/2.04 % (1771569)Instructions burned: 129 (million)
% 6.82/2.04 % (1771567)Instruction limit reached!
% 6.82/2.04 % (1771567)------------------------------
% 6.82/2.04 % (1771567)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.82/2.04 % (1771567)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.82/2.04 % (1771567)CaDiCaL version: 2.1.3
% 6.82/2.04 % (1771567)Termination reason: Instruction limit
% 6.82/2.04 % (1771567)Termination phase: Saturation
% 6.82/2.04 % (1771567)Time elapsed: 0.122 s
% 6.82/2.04 % (1771567)Peak memory usage: 89 MB
% 6.82/2.04 % (1771567)Instructions burned: 121 (million)
% 6.82/2.04 % (1771568)Instruction limit reached!
% 6.82/2.04 % (1771568)------------------------------
% 6.82/2.04 % (1771568)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.82/2.04 % (1771568)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.82/2.04 % (1771568)CaDiCaL version: 2.1.3
% 6.82/2.04 % (1771568)Termination reason: Instruction limit
% 6.82/2.04 % (1771568)Termination phase: Saturation
% 6.82/2.04 % (1771568)Time elapsed: 0.144 s
% 6.82/2.04 % (1771568)Peak memory usage: 90 MB
% 6.82/2.04 % (1771568)Instructions burned: 139 (million)
% 6.82/2.04 % (1771578)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3595966637:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 6.82/2.04 % (1771577)lrs+10_1_sil=8000:sp=occurrence:random_seed=724533733:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 6.82/2.04 % (1771579)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1385220583:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 6.82/2.04 % (1771580)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=1386168973:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 6.82/2.04 % (1771578)Instruction limit reached!
% 6.82/2.04 % (1771578)------------------------------
% 6.82/2.04 % (1771578)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.82/2.04 % (1771578)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.82/2.04 % (1771578)CaDiCaL version: 2.1.3
% 6.82/2.04 % (1771578)Termination reason: Instruction limit
% 6.82/2.04 % (1771578)Termination phase: Saturation
% 6.82/2.04 % (1771578)Time elapsed: 0.136 s
% 6.82/2.04 % (1771578)Peak memory usage: 94 MB
% 6.82/2.04 % (1771578)Instructions burned: 157 (million)
% 6.82/2.04 % (1771563)First to succeed.
% 6.82/2.04 % (1771563)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1771556"
% 6.82/2.04 % (1771580)Instruction limit reached!
% 6.82/2.04 % (1771580)------------------------------
% 6.82/2.04 % (1771580)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.82/2.04 % (1771580)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.82/2.04 % (1771580)CaDiCaL version: 2.1.3
% 6.82/2.04 % (1771580)Termination reason: Instruction limit
% 6.82/2.04 % (1771580)Termination phase: Saturation
% 6.82/2.04 % (1771580)Time elapsed: 0.205 s
% 6.82/2.04 % (1771580)Peak memory usage: 94 MB
% 6.82/2.04 % (1771580)Instructions burned: 248 (million)
% 6.82/2.04 % (1771577)Instruction limit reached!
% 6.82/2.04 % (1771577)------------------------------
% 6.82/2.04 % (1771577)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.82/2.04 % (1771577)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.82/2.04 % (1771577)CaDiCaL version: 2.1.3
% 6.82/2.04 % (1771577)Termination reason: Instruction limit
% 6.82/2.04 % (1771577)Termination phase: Saturation
% 6.82/2.04 % (1771577)Time elapsed: 0.281 s
% 6.82/2.04 % (1771577)Peak memory usage: 92 MB
% 6.82/2.04 % (1771577)Instructions burned: 285 (million)
% 6.82/2.04 % (1771579)Instruction limit reached!
% 6.82/2.04 % (1771579)------------------------------
% 6.82/2.04 % (1771579)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.82/2.04 % (1771579)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.82/2.04 % (1771579)CaDiCaL version: 2.1.3
% 6.82/2.04 % (1771579)Termination reason: Instruction limit
% 6.82/2.04 % (1771579)Termination phase: Saturation
% 6.82/2.04 % (1771579)Time elapsed: 0.304 s
% 6.82/2.04 % (1771579)Peak memory usage: 92 MB
% 6.82/2.04 % (1771579)Instructions burned: 326 (million)
% 6.82/2.04 % (1771585)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=4164298971:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2992 on theBenchmark for (2992ds/294Mi)
% 6.82/2.04 % (1771563)Refutation found. Thanks to Tanya!
% 6.82/2.04 % SZS status Theorem for theBenchmark
% 6.82/2.04 % SZS output start Proof for theBenchmark
% See solution above
% 8.77/2.30 % (1771563)------------------------------
% 8.77/2.30 % (1771563)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.77/2.30 % (1771563)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.77/2.30 % (1771563)CaDiCaL version: 2.1.3
% 8.77/2.30 % (1771563)Termination reason: Refutation
% 8.77/2.30 % (1771563)Time elapsed: 0.641 s
% 8.77/2.30 % (1771563)Peak memory usage: 131 MB
% 8.77/2.30 % (1771563)Instructions burned: 1046 (million)
% 8.77/2.30 % (1771563)------------------------------
% 8.77/2.30 % (1771563)------------------------------
% 8.77/2.30 % (1771556)Success in time 1.107 s
% 8.77/2.30 % Vampire exiting
%------------------------------------------------------------------------------