%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC418+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n017.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 01:05:58 PM UTC 2026
% Result : Theorem 2.44s 0.60s
% Output : Refutation 2.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 20
% Syntax : Number of formulae : 133 ( 20 unt; 9 def)
% Number of atoms : 477 ( 122 equ)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 589 ( 245 ~; 259 |; 50 &)
% ( 11 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 10 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 107 ( 0 sgn 85 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f22,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssItem(hd(X0)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax22) ).
fof(f24,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssList(tl(X0)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax24) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(f78,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> cons(hd(X0),tl(X0)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax78) ).
fof(f81,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) = app(cons(X1,nil),X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax81) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ~ neq(X1,nil)
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X5,cons(X4,nil)),X6) = X1
& app(app(X6,cons(X4,nil)),X5) = X0 ) ) )
| ( nil != X2
& nil = X3 )
| ( ? [X7] :
( ssList(X7)
& X2 != X7
& ? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& tl(X3) = X8
& app(X8,X9) = X7
& ? [X10] :
( ssItem(X10)
& cons(X10,nil) = X9
& hd(X3) = X10
& neq(nil,X3) )
& neq(nil,X3) ) ) )
& neq(X3,nil) ) ) ) ) ) ),
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
| ~ neq(X1,nil)
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X5,cons(X4,nil)),X6) = X1
& app(app(X6,cons(X4,nil)),X5) = X0 ) ) )
| ( nil != X2
& nil = X3 )
| ( ? [X7] :
( ssList(X7)
& X2 != X7
& ? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& tl(X3) = X8
& app(X8,X9) = X7
& ? [X10] :
( ssItem(X10)
& cons(X10,nil) = X9
& hd(X3) = X10
& neq(nil,X3) )
& neq(nil,X3) ) ) )
& neq(X3,nil) ) ) ) ) ) ),
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(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(f132,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f134,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
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(f201,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& neq(X1,nil)
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != X1
| app(app(X6,cons(X4,nil)),X5) != X0 ) ) )
& ( nil = X2
| nil != X3 )
& ( ! [X7] :
( ~ ssList(X7)
| X2 = X7
| ! [X8] :
( ~ ssList(X8)
| ! [X9] :
( ~ ssList(X9)
| tl(X3) != X8
| app(X8,X9) != X7
| ! [X10] :
( ~ ssItem(X10)
| cons(X10,nil) != X9
| hd(X3) != X10
| ~ neq(nil,X3) )
| ~ neq(nil,X3) ) ) )
| ~ neq(X3,nil) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& neq(X1,nil)
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != X1
| app(app(X6,cons(X4,nil)),X5) != X0 ) ) )
& ( nil = X2
| nil != X3 )
& ( ! [X7] :
( ~ ssList(X7)
| X2 = X7
| ! [X8] :
( ~ ssList(X8)
| ! [X9] :
( ~ ssList(X9)
| tl(X3) != X8
| app(X8,X9) != X7
| ! [X10] :
( ~ ssItem(X10)
| cons(X10,nil) != X9
| hd(X3) != X10
| ~ neq(nil,X3) )
| ~ neq(nil,X3) ) ) )
| ~ neq(X3,nil) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f303,plain,
! [X0,X1] :
( neq(X0,X1)
| ~ ssList(X1)
| X0 = X1
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f118]) ).
fof(f304,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 != X1
| ~ neq(X0,X1) ),
inference(cnf_transformation,[],[f118]) ).
fof(f305,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f306,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f314,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f316,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f318,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f320,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f134]) ).
fof(f389,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(cnf_transformation,[],[f193]) ).
fof(f392,plain,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssList(X0)
| cons(X1,X0) = app(cons(X1,nil),X0) ),
inference(cnf_transformation,[],[f198]) ).
fof(f397,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f201]) ).
fof(f411,plain,
! [X10,X8,X9,X7] :
( ~ neq(sK50,nil)
| ~ neq(nil,sK50)
| hd(sK50) != X10
| cons(X10,nil) != X9
| ~ ssItem(X10)
| app(X8,X9) != X7
| tl(sK50) != X8
| ~ ssList(X9)
| ~ ssList(X8)
| sK49 = X7
| ~ ssList(X7) ),
inference(cnf_transformation,[],[f222]) ).
fof(f412,plain,
! [X6,X4,X5] :
( app(app(X6,cons(X4,nil)),X5) != sK47
| app(app(X5,cons(X4,nil)),X6) != sK48
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f222]) ).
fof(f414,plain,
ssList(sK50),
inference(cnf_transformation,[],[f222]) ).
fof(f415,plain,
neq(sK48,nil),
inference(cnf_transformation,[],[f222]) ).
fof(f416,plain,
sK47 = sK49,
inference(cnf_transformation,[],[f222]) ).
fof(f417,plain,
sK48 = sK50,
inference(cnf_transformation,[],[f222]) ).
fof(f423,plain,
neq(sK50,nil),
inference(definition_unfolding,[],[f415,f417]) ).
fof(f424,plain,
! [X6,X4,X5] :
( app(app(X6,cons(X4,nil)),X5) != sK49
| app(app(X5,cons(X4,nil)),X6) != sK50
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(definition_unfolding,[],[f412,f416,f417]) ).
fof(f439,plain,
! [X1] :
( ~ ssList(X1)
| ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(equality_resolution,[],[f304]) ).
fof(f450,plain,
! [X8,X9,X7] :
( ~ neq(sK50,nil)
| ~ neq(nil,sK50)
| cons(hd(sK50),nil) != X9
| ~ ssItem(hd(sK50))
| app(X8,X9) != X7
| tl(sK50) != X8
| ~ ssList(X9)
| ~ ssList(X8)
| sK49 = X7
| ~ ssList(X7) ),
inference(equality_resolution,[],[f411]) ).
fof(f451,plain,
! [X8,X7] :
( ~ neq(sK50,nil)
| ~ neq(nil,sK50)
| ~ ssItem(hd(sK50))
| app(X8,cons(hd(sK50),nil)) != X7
| tl(sK50) != X8
| ~ ssList(cons(hd(sK50),nil))
| ~ ssList(X8)
| sK49 = X7
| ~ ssList(X7) ),
inference(equality_resolution,[],[f450]) ).
fof(f452,plain,
! [X8] :
( ~ neq(sK50,nil)
| ~ neq(nil,sK50)
| ~ ssItem(hd(sK50))
| tl(sK50) != X8
| ~ ssList(cons(hd(sK50),nil))
| ~ ssList(X8)
| sK49 = app(X8,cons(hd(sK50),nil))
| ~ ssList(app(X8,cons(hd(sK50),nil))) ),
inference(equality_resolution,[],[f451]) ).
fof(f453,plain,
( ~ neq(sK50,nil)
| ~ neq(nil,sK50)
| ~ ssItem(hd(sK50))
| ~ ssList(cons(hd(sK50),nil))
| ~ ssList(tl(sK50))
| sK49 = app(tl(sK50),cons(hd(sK50),nil))
| ~ ssList(app(tl(sK50),cons(hd(sK50),nil))) ),
inference(equality_resolution,[],[f452]) ).
fof(f458,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(duplicate_literal_removal,[],[f439]) ).
fof(f462,definition,
( spl51_1
<=> ssList(app(tl(sK50),cons(hd(sK50),nil))) ),
introduced(definition,[new_symbols(definition,[spl51_1])],[avatar_definition]) ).
fof(f463,plain,
( ssList(app(tl(sK50),cons(hd(sK50),nil)))
| ~ spl51_1 ),
inference(avatar_component_clause,[],[f462]) ).
fof(f464,plain,
( ~ ssList(app(tl(sK50),cons(hd(sK50),nil)))
| spl51_1 ),
inference(avatar_component_clause,[],[f462]) ).
fof(f466,definition,
( spl51_2
<=> sK49 = app(tl(sK50),cons(hd(sK50),nil)) ),
introduced(definition,[new_symbols(definition,[spl51_2])],[avatar_definition]) ).
fof(f470,definition,
( spl51_3
<=> ssList(tl(sK50)) ),
introduced(definition,[new_symbols(definition,[spl51_3])],[avatar_definition]) ).
fof(f471,plain,
( ssList(tl(sK50))
| ~ spl51_3 ),
inference(avatar_component_clause,[],[f470]) ).
fof(f472,plain,
( ~ ssList(tl(sK50))
| spl51_3 ),
inference(avatar_component_clause,[],[f470]) ).
fof(f474,definition,
( spl51_4
<=> ssList(cons(hd(sK50),nil)) ),
introduced(definition,[new_symbols(definition,[spl51_4])],[avatar_definition]) ).
fof(f475,plain,
( ssList(cons(hd(sK50),nil))
| ~ spl51_4 ),
inference(avatar_component_clause,[],[f474]) ).
fof(f476,plain,
( ~ ssList(cons(hd(sK50),nil))
| spl51_4 ),
inference(avatar_component_clause,[],[f474]) ).
fof(f478,definition,
( spl51_5
<=> ssItem(hd(sK50)) ),
introduced(definition,[new_symbols(definition,[spl51_5])],[avatar_definition]) ).
fof(f479,plain,
( ssItem(hd(sK50))
| ~ spl51_5 ),
inference(avatar_component_clause,[],[f478]) ).
fof(f480,plain,
( ~ ssItem(hd(sK50))
| spl51_5 ),
inference(avatar_component_clause,[],[f478]) ).
fof(f482,definition,
( spl51_6
<=> neq(nil,sK50) ),
introduced(definition,[new_symbols(definition,[spl51_6])],[avatar_definition]) ).
fof(f484,plain,
( ~ neq(nil,sK50)
| spl51_6 ),
inference(avatar_component_clause,[],[f482]) ).
fof(f486,definition,
( spl51_7
<=> neq(sK50,nil) ),
introduced(definition,[new_symbols(definition,[spl51_7])],[avatar_definition]) ).
fof(f488,plain,
( ~ neq(sK50,nil)
| spl51_7 ),
inference(avatar_component_clause,[],[f486]) ).
fof(f489,plain,
( ~ spl51_1
| spl51_2
| ~ spl51_3
| ~ spl51_4
| ~ spl51_5
| ~ spl51_6
| ~ spl51_7 ),
inference(avatar_split_clause,[],[f453,f486,f482,f478,f474,f470,f466,f462]) ).
fof(f495,definition,
( spl51_9
<=> nil = sK50 ),
introduced(definition,[new_symbols(definition,[spl51_9])],[avatar_definition]) ).
fof(f496,plain,
( nil = sK50
| ~ spl51_9 ),
inference(avatar_component_clause,[],[f495]) ).
fof(f497,plain,
( nil != sK50
| spl51_9 ),
inference(avatar_component_clause,[],[f495]) ).
fof(f543,plain,
( nil = sK50
| ~ ssList(sK50)
| spl51_5 ),
inference(resolution,[],[f314,f480]) ).
fof(f544,plain,
( ~ ssList(sK50)
| spl51_5
| spl51_9 ),
inference(forward_subsumption_resolution,[],[f543,f497]) ).
fof(f545,plain,
( $false
| spl51_5
| spl51_9 ),
inference(forward_subsumption_resolution,[],[f544,f414]) ).
fof(f546,plain,
( spl51_5
| spl51_9 ),
inference(avatar_contradiction_clause,[],[f545]) ).
fof(f552,plain,
( neq(nil,nil)
| ~ spl51_9 ),
inference(superposition,[],[f423,f496]) ).
fof(f555,plain,
( ~ ssList(nil)
| ~ spl51_9 ),
inference(resolution,[],[f552,f458]) ).
fof(f556,plain,
( $false
| ~ spl51_9 ),
inference(forward_subsumption_resolution,[],[f555,f306]) ).
fof(f557,plain,
~ spl51_9,
inference(avatar_contradiction_clause,[],[f556]) ).
fof(f560,plain,
( ~ ssList(cons(hd(sK50),nil))
| ~ ssList(tl(sK50))
| spl51_1 ),
inference(resolution,[],[f318,f464]) ).
fof(f569,plain,
( ~ spl51_3
| ~ spl51_4
| spl51_1 ),
inference(avatar_split_clause,[],[f560,f462,f474,f470]) ).
fof(f570,plain,
( nil = sK50
| ~ ssList(sK50)
| spl51_3 ),
inference(resolution,[],[f472,f316]) ).
fof(f571,plain,
( ~ ssList(sK50)
| spl51_3
| spl51_9 ),
inference(forward_subsumption_resolution,[],[f570,f497]) ).
fof(f572,plain,
( $false
| spl51_3
| spl51_9 ),
inference(forward_subsumption_resolution,[],[f571,f414]) ).
fof(f573,plain,
( spl51_3
| spl51_9 ),
inference(avatar_contradiction_clause,[],[f572]) ).
fof(f576,plain,
( ~ ssItem(hd(sK50))
| ~ ssList(nil)
| spl51_4 ),
inference(resolution,[],[f476,f305]) ).
fof(f577,plain,
( ~ ssList(nil)
| spl51_4
| ~ spl51_5 ),
inference(forward_subsumption_resolution,[],[f576,f479]) ).
fof(f578,plain,
( $false
| spl51_4
| ~ spl51_5 ),
inference(forward_subsumption_resolution,[],[f577,f306]) ).
fof(f579,plain,
( spl51_4
| ~ spl51_5 ),
inference(avatar_contradiction_clause,[],[f578]) ).
fof(f581,plain,
( cons(hd(sK50),nil) = app(nil,cons(hd(sK50),nil))
| ~ spl51_4 ),
inference(resolution,[],[f475,f320]) ).
fof(f583,plain,
( app(tl(sK50),cons(hd(sK50),nil)) = app(app(tl(sK50),cons(hd(sK50),nil)),nil)
| ~ spl51_1 ),
inference(resolution,[],[f463,f397]) ).
fof(f591,plain,
( sK49 != app(tl(sK50),cons(hd(sK50),nil))
| sK50 != app(app(nil,cons(hd(sK50),nil)),tl(sK50))
| ~ ssList(tl(sK50))
| ~ ssList(nil)
| ~ ssItem(hd(sK50))
| ~ spl51_1 ),
inference(superposition,[],[f424,f583]) ).
fof(f593,plain,
( sK49 != app(tl(sK50),cons(hd(sK50),nil))
| sK50 != app(app(nil,cons(hd(sK50),nil)),tl(sK50))
| ~ ssList(nil)
| ~ ssItem(hd(sK50))
| ~ spl51_1
| ~ spl51_3 ),
inference(forward_subsumption_resolution,[],[f591,f471]) ).
fof(f594,plain,
( sK49 != app(tl(sK50),cons(hd(sK50),nil))
| sK50 != app(app(nil,cons(hd(sK50),nil)),tl(sK50))
| ~ ssItem(hd(sK50))
| ~ spl51_1
| ~ spl51_3 ),
inference(forward_subsumption_resolution,[],[f593,f306]) ).
fof(f595,plain,
( sK49 != app(tl(sK50),cons(hd(sK50),nil))
| sK50 != app(app(nil,cons(hd(sK50),nil)),tl(sK50))
| ~ spl51_1
| ~ spl51_3
| ~ spl51_5 ),
inference(forward_subsumption_resolution,[],[f594,f479]) ).
fof(f596,plain,
( sK50 != app(cons(hd(sK50),nil),tl(sK50))
| sK49 != app(tl(sK50),cons(hd(sK50),nil))
| ~ spl51_1
| ~ spl51_3
| ~ spl51_4
| ~ spl51_5 ),
inference(forward_demodulation,[],[f595,f581]) ).
fof(f598,definition,
( spl51_17
<=> sK50 = app(cons(hd(sK50),nil),tl(sK50)) ),
introduced(definition,[new_symbols(definition,[spl51_17])],[avatar_definition]) ).
fof(f600,plain,
( sK50 != app(cons(hd(sK50),nil),tl(sK50))
| spl51_17 ),
inference(avatar_component_clause,[],[f598]) ).
fof(f601,plain,
( ~ spl51_2
| ~ spl51_17
| ~ spl51_1
| ~ spl51_3
| ~ spl51_4
| ~ spl51_5 ),
inference(avatar_split_clause,[],[f596,f478,f474,f470,f462,f598,f466]) ).
fof(f652,plain,
( ~ ssList(sK50)
| nil = sK50
| ~ ssList(nil)
| spl51_6 ),
inference(resolution,[],[f303,f484]) ).
fof(f655,plain,
( nil = sK50
| ~ ssList(nil)
| spl51_6 ),
inference(forward_subsumption_resolution,[],[f652,f414]) ).
fof(f656,plain,
( ~ ssList(nil)
| spl51_6
| spl51_9 ),
inference(forward_subsumption_resolution,[],[f655,f497]) ).
fof(f657,plain,
( $false
| spl51_6
| spl51_9 ),
inference(forward_subsumption_resolution,[],[f656,f306]) ).
fof(f658,plain,
( spl51_6
| spl51_9 ),
inference(avatar_contradiction_clause,[],[f657]) ).
fof(f659,plain,
( $false
| spl51_7 ),
inference(forward_subsumption_resolution,[],[f488,f423]) ).
fof(f660,plain,
spl51_7,
inference(avatar_contradiction_clause,[],[f659]) ).
fof(f1196,plain,
( nil = sK50
| sK50 = cons(hd(sK50),tl(sK50)) ),
inference(resolution,[],[f389,f414]) ).
fof(f1197,plain,
( sK50 = cons(hd(sK50),tl(sK50))
| spl51_9 ),
inference(forward_subsumption_resolution,[],[f1196,f497]) ).
fof(f1835,plain,
( ! [X0] :
( ~ ssList(X0)
| app(cons(hd(sK50),nil),X0) = cons(hd(sK50),X0) )
| ~ spl51_5 ),
inference(resolution,[],[f392,f479]) ).
fof(f11200,plain,
( app(cons(hd(sK50),nil),tl(sK50)) = cons(hd(sK50),tl(sK50))
| ~ spl51_3
| ~ spl51_5 ),
inference(resolution,[],[f1835,f471]) ).
fof(f11308,plain,
( sK50 = app(cons(hd(sK50),nil),tl(sK50))
| ~ spl51_3
| ~ spl51_5
| spl51_9 ),
inference(forward_demodulation,[],[f11200,f1197]) ).
fof(f11312,plain,
( $false
| ~ spl51_3
| ~ spl51_5
| spl51_9
| spl51_17 ),
inference(forward_subsumption_resolution,[],[f11308,f600]) ).
fof(f11313,plain,
( ~ spl51_3
| ~ spl51_5
| spl51_9
| spl51_17 ),
inference(avatar_contradiction_clause,[],[f11312]) ).
cnf(s1,plain,
( ~ spl51_1
| spl51_2
| ~ spl51_3
| ~ spl51_4
| ~ spl51_5
| ~ spl51_6
| ~ spl51_7 ),
inference(sat_conversion,[],[f489]) ).
cnf(s10,plain,
( spl51_5
| spl51_9 ),
inference(sat_conversion,[],[f546]) ).
cnf(s11,plain,
~ spl51_9,
inference(sat_conversion,[],[f557]) ).
cnf(s12,plain,
( spl51_1
| ~ spl51_3
| ~ spl51_4 ),
inference(sat_conversion,[],[f569]) ).
cnf(s13,plain,
( spl51_3
| spl51_9 ),
inference(sat_conversion,[],[f573]) ).
cnf(s14,plain,
( spl51_4
| ~ spl51_5 ),
inference(sat_conversion,[],[f579]) ).
cnf(s15,plain,
( ~ spl51_1
| ~ spl51_2
| ~ spl51_3
| ~ spl51_4
| ~ spl51_5
| ~ spl51_17 ),
inference(sat_conversion,[],[f601]) ).
cnf(s19,plain,
( spl51_6
| spl51_9 ),
inference(sat_conversion,[],[f658]) ).
cnf(s20,plain,
spl51_7,
inference(sat_conversion,[],[f660]) ).
cnf(s520,plain,
( ~ spl51_3
| ~ spl51_5
| spl51_9
| spl51_17 ),
inference(sat_conversion,[],[f11313]) ).
cnf(s547,plain,
spl51_6,
inference(rat,[],[s19,s11]) ).
cnf(s548,plain,
spl51_3,
inference(rat,[],[s13,s11]) ).
cnf(s553,plain,
spl51_5,
inference(rat,[],[s10,s11]) ).
cnf(s554,plain,
spl51_17,
inference(rat,[],[s520,s548,s11,s553]) ).
cnf(s560,plain,
spl51_4,
inference(rat,[],[s14,s553]) ).
cnf(s571,plain,
spl51_1,
inference(rat,[],[s12,s548,s560]) ).
cnf(s572,plain,
~ spl51_2,
inference(rat,[],[s15,s554,s553,s560,s548,s571]) ).
cnf(s584,plain,
$false,
inference(rat,[],[s1,s20,s547,s553,s560,s548,s572,s571]) ).
fof(f11314,plain,
$false,
inference(avatar_sat_refutation,[],[s584]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC418+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.06/0.18 % Computer : n017.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Mon Sep 28 09:28:51 UTC 2026
% 0.06/0.19 % CPUTime :
% 0.06/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.06/0.22 Running first-order model finding
% 0.06/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.44/0.60 % (3429649)Will run a generic schedule for satisfiability detection.
% 2.44/0.60 % (3429654)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2830224660_2999 on theBenchmark for (2999ds/0Mi)
% 2.44/0.60 % (3429655)% WARNING: option uhcvi not known.
% 2.44/0.60 % (3429655)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3149230419:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.44/0.60 % (3429656)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3417047642:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.44/0.60 % (3429657)dis+10_1_sil=32000:sp=arity:random_seed=2074729880:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.44/0.60 % TRYING [1]
% 2.44/0.60 % (3429658)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3738475638:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.44/0.60 % (3429660)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1381903494:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.44/0.60 % TRYING [2]
% 2.44/0.60 % (3429659)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3757393047:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.44/0.60 % TRYING [3]
% 2.44/0.60 % TRYING [4]
% 2.44/0.60 % TRYING [5]
% 2.44/0.60 % (3429657)Instruction limit reached!
% 2.44/0.60 % (3429657)------------------------------
% 2.44/0.60 % (3429657)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.44/0.60 % (3429657)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.44/0.60 % (3429657)CaDiCaL version: 2.1.3
% 2.44/0.60 % (3429657)Termination reason: Instruction limit
% 2.44/0.60 % (3429657)Termination phase: Saturation
% 2.44/0.60 % (3429657)Time elapsed: 0.061 s
% 2.44/0.60 % (3429657)Peak memory usage: 13 MB
% 2.44/0.60 % (3429657)Instructions burned: 104 (million)
% 2.44/0.60 % (3429658)Instruction limit reached!
% 2.44/0.60 % (3429658)------------------------------
% 2.44/0.60 % (3429658)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.44/0.60 % (3429658)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.44/0.60 % (3429658)CaDiCaL version: 2.1.3
% 2.44/0.60 % (3429658)Termination reason: Instruction limit
% 2.44/0.60 % (3429658)Termination phase: Saturation
% 2.44/0.60 % (3429658)Time elapsed: 0.067 s
% 2.44/0.60 % (3429658)Peak memory usage: 13 MB
% 2.44/0.60 % (3429658)Instructions burned: 116 (million)
% 2.44/0.60 % (3429659)Instruction limit reached!
% 2.44/0.60 % (3429659)------------------------------
% 2.44/0.60 % (3429659)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.44/0.60 % (3429659)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.44/0.60 % (3429659)CaDiCaL version: 2.1.3
% 2.44/0.60 % (3429659)Termination reason: Instruction limit
% 2.44/0.60 % (3429659)Termination phase: Saturation
% 2.44/0.60 % (3429659)Time elapsed: 0.077 s
% 2.44/0.60 % (3429659)Peak memory usage: 14 MB
% 2.44/0.60 % (3429659)Instructions burned: 132 (million)
% 2.44/0.60 % (3429668)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2822221323:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.44/0.60 % (3429669)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3882178318:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 2.44/0.60 % TRYING [1]
% 2.44/0.60 % TRYING [2]
% 2.44/0.60 % (3429670)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=1491930191:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 2.44/0.60 % TRYING [3]
% 2.44/0.60 % (3429660)Instruction limit reached!
% 2.44/0.60 % (3429660)------------------------------
% 2.44/0.60 % (3429660)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.44/0.60 % (3429660)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.44/0.60 % (3429660)CaDiCaL version: 2.1.3
% 2.44/0.60 % (3429660)Termination reason: Instruction limit
% 2.44/0.60 % (3429660)Termination phase: Saturation
% 2.44/0.60 % (3429660)Time elapsed: 0.104 s
% 2.44/0.60 % (3429660)Peak memory usage: 14 MB
% 2.44/0.60 % (3429660)Instructions burned: 159 (million)
% 2.44/0.60 % TRYING [6]
% 2.44/0.60 % TRYING [4]
% 2.44/0.60 % (3429674)ott-21_1_sil=16000:fs=off:random_seed=434372785:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 2.44/0.60 % (3429669)Instruction limit reached!
% 2.44/0.60 % (3429669)------------------------------
% 2.44/0.60 % (3429669)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.44/0.60 % (3429669)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.44/0.60 % (3429669)CaDiCaL version: 2.1.3
% 2.44/0.60 % (3429669)Termination reason: Instruction limit
% 2.44/0.60 % (3429669)Termination phase: Saturation
% 2.44/0.60 % (3429669)Time elapsed: 0.072 s
% 2.44/0.60 % (3429669)Peak memory usage: 13 MB
% 2.44/0.60 % (3429669)Instructions burned: 131 (million)
% 2.44/0.60 % TRYING [5]
% 2.44/0.60 % (3429676)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=104111381:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 2.44/0.60 % (3429674)Instruction limit reached!
% 2.44/0.60 % (3429674)------------------------------
% 2.44/0.60 % (3429674)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.44/0.60 % (3429674)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.44/0.60 % (3429674)CaDiCaL version: 2.1.3
% 2.44/0.60 % (3429674)Termination reason: Instruction limit
% 2.44/0.60 % (3429674)Termination phase: Saturation
% 2.44/0.60 % (3429674)Time elapsed: 0.092 s
% 2.44/0.60 % (3429674)Peak memory usage: 14 MB
% 2.44/0.60 % (3429674)Instructions burned: 181 (million)
% 2.44/0.60 % (3429678)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=4071319411:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 2.44/0.60 % TRYING [1]
% 2.44/0.60 % TRYING [2]
% 2.44/0.60 % TRYING [3]
% 2.44/0.60 % TRYING [7]
% 2.44/0.60 % TRYING [4]
% 2.44/0.60 % (3429670) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3429649-3429670"...
% 2.44/0.60 % (3429670)...printing done.
% 2.44/0.60 % (3429670)Refutation found. Thanks to Tanya!
% 2.44/0.60 % SZS status Theorem for theBenchmark
% 2.44/0.60 % SZS output start Proof for theBenchmark
% See solution above
% 2.44/0.60 % (3429670)------------------------------
% 2.44/0.60 % (3429670)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.44/0.60 % (3429670)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.44/0.60 % (3429670)CaDiCaL version: 2.1.3
% 2.44/0.60 % (3429670)Termination reason: Refutation
% 2.44/0.60 % (3429670)Time elapsed: 0.240 s
% 2.44/0.60 % (3429670)Peak memory usage: 18 MB
% 2.44/0.60 % (3429670)Instructions burned: 392 (million)
% 2.44/0.60 % (3429649)Success in time 0.376 s
% 2.44/0.60 % Vampire exiting
%------------------------------------------------------------------------------