%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC421+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 : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:05:59 PM UTC 2026
% Result : Theorem 3.35s 0.72s
% Output : Refutation 3.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 21
% Syntax : Number of formulae : 151 ( 20 unt; 10 def)
% Number of atoms : 524 ( 127 equ)
% Maximal formula atoms : 27 ( 3 avg)
% Number of connectives : 648 ( 275 ~; 285 |; 52 &)
% ( 12 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 11 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 110 ( 0 sgn 88 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f22,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssItem(hd(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax22) ).
fof(f24,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssList(tl(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax24) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(f78,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> cons(hd(X0),tl(X0)) = X0 ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/SWC001+0.ax',ax81) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox2/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 )
| ( neq(X3,nil)
& ( ~ neq(X2,nil)
| ? [X7] :
( ssList(X7)
& X3 != X7
& ? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& tl(X2) = X8
& app(X8,X9) = X7
& ? [X10] :
( ssItem(X10)
& cons(X10,nil) = X9
& hd(X2) = X10
& neq(nil,X2) )
& neq(nil,X2) ) ) ) ) ) ) ) ) ) ),
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
| ~ 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 )
| ( neq(X3,nil)
& ( ~ neq(X2,nil)
| ? [X7] :
( ssList(X7)
& X3 != X7
& ? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& tl(X2) = X8
& app(X8,X9) = X7
& ? [X10] :
( ssItem(X10)
& cons(X10,nil) = X9
& hd(X2) = X10
& neq(nil,X2) )
& neq(nil,X2) ) ) ) ) ) ) ) ) ) ),
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 )
& ( ~ neq(X3,nil)
| ( neq(X2,nil)
& ! [X7] :
( ~ ssList(X7)
| X3 = X7
| ! [X8] :
( ~ ssList(X8)
| ! [X9] :
( ~ ssList(X9)
| tl(X2) != X8
| app(X8,X9) != X7
| ! [X10] :
( ~ ssItem(X10)
| cons(X10,nil) != X9
| hd(X2) != X10
| ~ neq(nil,X2) )
| ~ neq(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
& 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 )
& ( ~ neq(X3,nil)
| ( neq(X2,nil)
& ! [X7] :
( ~ ssList(X7)
| X3 = X7
| ! [X8] :
( ~ ssList(X8)
| ! [X9] :
( ~ ssList(X9)
| tl(X2) != X8
| app(X8,X9) != X7
| ! [X10] :
( ~ ssItem(X10)
| cons(X10,nil) != X9
| hd(X2) != X10
| ~ neq(nil,X2) )
| ~ neq(nil,X2) ) ) ) ) )
& 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(nil,sK49)
| hd(sK49) != X10
| cons(X10,nil) != X9
| ~ ssItem(X10)
| app(X8,X9) != X7
| tl(sK49) != X8
| ~ ssList(X9)
| ~ ssList(X8)
| sK50 = X7
| ~ ssList(X7)
| ~ neq(sK50,nil) ),
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(f413,plain,
( neq(sK49,nil)
| ~ neq(sK50,nil) ),
inference(cnf_transformation,[],[f222]) ).
fof(f416,plain,
neq(sK48,nil),
inference(cnf_transformation,[],[f222]) ).
fof(f417,plain,
sK47 = sK49,
inference(cnf_transformation,[],[f222]) ).
fof(f418,plain,
sK48 = sK50,
inference(cnf_transformation,[],[f222]) ).
fof(f419,plain,
ssList(sK49),
inference(cnf_transformation,[],[f222]) ).
fof(f424,plain,
neq(sK50,nil),
inference(definition_unfolding,[],[f416,f418]) ).
fof(f425,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,f417,f418]) ).
fof(f440,plain,
! [X1] :
( ~ ssList(X1)
| ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(equality_resolution,[],[f304]) ).
fof(f451,plain,
! [X8,X9,X7] :
( ~ neq(nil,sK49)
| cons(hd(sK49),nil) != X9
| ~ ssItem(hd(sK49))
| app(X8,X9) != X7
| tl(sK49) != X8
| ~ ssList(X9)
| ~ ssList(X8)
| sK50 = X7
| ~ ssList(X7)
| ~ neq(sK50,nil) ),
inference(equality_resolution,[],[f411]) ).
fof(f452,plain,
! [X8,X7] :
( ~ neq(nil,sK49)
| ~ ssItem(hd(sK49))
| app(X8,cons(hd(sK49),nil)) != X7
| tl(sK49) != X8
| ~ ssList(cons(hd(sK49),nil))
| ~ ssList(X8)
| sK50 = X7
| ~ ssList(X7)
| ~ neq(sK50,nil) ),
inference(equality_resolution,[],[f451]) ).
fof(f453,plain,
! [X8] :
( ~ neq(nil,sK49)
| ~ ssItem(hd(sK49))
| tl(sK49) != X8
| ~ ssList(cons(hd(sK49),nil))
| ~ ssList(X8)
| sK50 = app(X8,cons(hd(sK49),nil))
| ~ ssList(app(X8,cons(hd(sK49),nil)))
| ~ neq(sK50,nil) ),
inference(equality_resolution,[],[f452]) ).
fof(f454,plain,
( ~ neq(nil,sK49)
| ~ ssItem(hd(sK49))
| ~ ssList(cons(hd(sK49),nil))
| ~ ssList(tl(sK49))
| sK50 = app(tl(sK49),cons(hd(sK49),nil))
| ~ ssList(app(tl(sK49),cons(hd(sK49),nil)))
| ~ neq(sK50,nil) ),
inference(equality_resolution,[],[f453]) ).
fof(f459,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(duplicate_literal_removal,[],[f440]) ).
fof(f463,definition,
( spl51_1
<=> neq(sK50,nil) ),
introduced(definition,[new_symbols(definition,[spl51_1])],[avatar_definition]) ).
fof(f465,plain,
( ~ neq(sK50,nil)
| spl51_1 ),
inference(avatar_component_clause,[],[f463]) ).
fof(f467,definition,
( spl51_2
<=> ssList(app(tl(sK49),cons(hd(sK49),nil))) ),
introduced(definition,[new_symbols(definition,[spl51_2])],[avatar_definition]) ).
fof(f468,plain,
( ssList(app(tl(sK49),cons(hd(sK49),nil)))
| ~ spl51_2 ),
inference(avatar_component_clause,[],[f467]) ).
fof(f469,plain,
( ~ ssList(app(tl(sK49),cons(hd(sK49),nil)))
| spl51_2 ),
inference(avatar_component_clause,[],[f467]) ).
fof(f471,definition,
( spl51_3
<=> sK50 = app(tl(sK49),cons(hd(sK49),nil)) ),
introduced(definition,[new_symbols(definition,[spl51_3])],[avatar_definition]) ).
fof(f475,definition,
( spl51_4
<=> ssList(tl(sK49)) ),
introduced(definition,[new_symbols(definition,[spl51_4])],[avatar_definition]) ).
fof(f476,plain,
( ssList(tl(sK49))
| ~ spl51_4 ),
inference(avatar_component_clause,[],[f475]) ).
fof(f477,plain,
( ~ ssList(tl(sK49))
| spl51_4 ),
inference(avatar_component_clause,[],[f475]) ).
fof(f479,definition,
( spl51_5
<=> ssList(cons(hd(sK49),nil)) ),
introduced(definition,[new_symbols(definition,[spl51_5])],[avatar_definition]) ).
fof(f480,plain,
( ssList(cons(hd(sK49),nil))
| ~ spl51_5 ),
inference(avatar_component_clause,[],[f479]) ).
fof(f481,plain,
( ~ ssList(cons(hd(sK49),nil))
| spl51_5 ),
inference(avatar_component_clause,[],[f479]) ).
fof(f483,definition,
( spl51_6
<=> ssItem(hd(sK49)) ),
introduced(definition,[new_symbols(definition,[spl51_6])],[avatar_definition]) ).
fof(f484,plain,
( ssItem(hd(sK49))
| ~ spl51_6 ),
inference(avatar_component_clause,[],[f483]) ).
fof(f485,plain,
( ~ ssItem(hd(sK49))
| spl51_6 ),
inference(avatar_component_clause,[],[f483]) ).
fof(f487,definition,
( spl51_7
<=> neq(nil,sK49) ),
introduced(definition,[new_symbols(definition,[spl51_7])],[avatar_definition]) ).
fof(f488,plain,
( neq(nil,sK49)
| ~ spl51_7 ),
inference(avatar_component_clause,[],[f487]) ).
fof(f489,plain,
( ~ neq(nil,sK49)
| spl51_7 ),
inference(avatar_component_clause,[],[f487]) ).
fof(f490,plain,
( ~ spl51_1
| ~ spl51_2
| spl51_3
| ~ spl51_4
| ~ spl51_5
| ~ spl51_6
| ~ spl51_7 ),
inference(avatar_split_clause,[],[f454,f487,f483,f479,f475,f471,f467,f463]) ).
fof(f492,definition,
( spl51_8
<=> neq(sK49,nil) ),
introduced(definition,[new_symbols(definition,[spl51_8])],[avatar_definition]) ).
fof(f494,plain,
( neq(sK49,nil)
| ~ spl51_8 ),
inference(avatar_component_clause,[],[f492]) ).
fof(f495,plain,
( ~ spl51_1
| spl51_8 ),
inference(avatar_split_clause,[],[f413,f492,f463]) ).
fof(f497,definition,
( spl51_9
<=> nil = sK49 ),
introduced(definition,[new_symbols(definition,[spl51_9])],[avatar_definition]) ).
fof(f498,plain,
( nil != sK49
| spl51_9 ),
inference(avatar_component_clause,[],[f497]) ).
fof(f499,plain,
( nil = sK49
| ~ spl51_9 ),
inference(avatar_component_clause,[],[f497]) ).
fof(f537,plain,
( $false
| spl51_1 ),
inference(forward_subsumption_resolution,[],[f465,f424]) ).
fof(f538,plain,
spl51_1,
inference(avatar_contradiction_clause,[],[f537]) ).
fof(f553,plain,
( ~ ssList(cons(hd(sK49),nil))
| ~ ssList(tl(sK49))
| spl51_2 ),
inference(resolution,[],[f318,f469]) ).
fof(f562,plain,
( ~ spl51_4
| ~ spl51_5
| spl51_2 ),
inference(avatar_split_clause,[],[f553,f467,f479,f475]) ).
fof(f563,plain,
( nil = sK49
| ~ ssList(sK49)
| spl51_4 ),
inference(resolution,[],[f477,f316]) ).
fof(f564,plain,
( nil = sK49
| spl51_4 ),
inference(forward_subsumption_resolution,[],[f563,f419]) ).
fof(f568,plain,
( neq(nil,nil)
| spl51_4
| ~ spl51_8 ),
inference(superposition,[],[f494,f564]) ).
fof(f573,plain,
( ~ ssList(nil)
| spl51_4
| ~ spl51_8 ),
inference(resolution,[],[f568,f459]) ).
fof(f574,plain,
( $false
| spl51_4
| ~ spl51_8 ),
inference(forward_subsumption_resolution,[],[f573,f306]) ).
fof(f575,plain,
( spl51_4
| ~ spl51_8 ),
inference(avatar_contradiction_clause,[],[f574]) ).
fof(f578,plain,
( ~ ssItem(hd(sK49))
| ~ ssList(nil)
| spl51_5 ),
inference(resolution,[],[f481,f305]) ).
fof(f579,plain,
( ~ ssItem(hd(sK49))
| spl51_5 ),
inference(forward_subsumption_resolution,[],[f578,f306]) ).
fof(f580,plain,
( nil = sK49
| ~ ssList(sK49)
| spl51_5 ),
inference(resolution,[],[f579,f314]) ).
fof(f581,plain,
( nil = sK49
| spl51_5 ),
inference(forward_subsumption_resolution,[],[f580,f419]) ).
fof(f586,plain,
( neq(nil,nil)
| spl51_5
| ~ spl51_8 ),
inference(superposition,[],[f494,f581]) ).
fof(f594,plain,
( ~ ssList(nil)
| spl51_5
| ~ spl51_8 ),
inference(resolution,[],[f586,f459]) ).
fof(f595,plain,
( $false
| spl51_5
| ~ spl51_8 ),
inference(forward_subsumption_resolution,[],[f594,f306]) ).
fof(f596,plain,
( spl51_5
| ~ spl51_8 ),
inference(avatar_contradiction_clause,[],[f595]) ).
fof(f597,plain,
( nil = sK49
| ~ ssList(sK49)
| spl51_6 ),
inference(resolution,[],[f485,f314]) ).
fof(f598,plain,
( nil = sK49
| spl51_6 ),
inference(forward_subsumption_resolution,[],[f597,f419]) ).
fof(f602,plain,
( neq(nil,nil)
| spl51_6
| ~ spl51_8 ),
inference(superposition,[],[f494,f598]) ).
fof(f609,plain,
( ~ ssList(nil)
| spl51_6
| ~ spl51_8 ),
inference(resolution,[],[f602,f459]) ).
fof(f610,plain,
( $false
| spl51_6
| ~ spl51_8 ),
inference(forward_subsumption_resolution,[],[f609,f306]) ).
fof(f611,plain,
( spl51_6
| ~ spl51_8 ),
inference(avatar_contradiction_clause,[],[f610]) ).
fof(f613,plain,
( cons(hd(sK49),nil) = app(nil,cons(hd(sK49),nil))
| ~ spl51_5 ),
inference(resolution,[],[f480,f320]) ).
fof(f616,plain,
( app(tl(sK49),cons(hd(sK49),nil)) = app(app(tl(sK49),cons(hd(sK49),nil)),nil)
| ~ spl51_2 ),
inference(resolution,[],[f468,f397]) ).
fof(f619,plain,
( ! [X0] :
( sK49 != app(cons(hd(sK49),nil),X0)
| sK50 != app(app(X0,cons(hd(sK49),nil)),nil)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(hd(sK49)) )
| ~ spl51_5 ),
inference(superposition,[],[f425,f613]) ).
fof(f621,plain,
( ! [X0] :
( sK49 != app(cons(hd(sK49),nil),X0)
| sK50 != app(app(X0,cons(hd(sK49),nil)),nil)
| ~ ssList(X0)
| ~ ssItem(hd(sK49)) )
| ~ spl51_5 ),
inference(forward_subsumption_resolution,[],[f619,f306]) ).
fof(f622,plain,
( ! [X0] :
( sK50 != app(app(X0,cons(hd(sK49),nil)),nil)
| sK49 != app(cons(hd(sK49),nil),X0)
| ~ ssList(X0) )
| ~ spl51_5
| ~ spl51_6 ),
inference(forward_subsumption_resolution,[],[f621,f484]) ).
fof(f640,plain,
( sK50 != app(tl(sK49),cons(hd(sK49),nil))
| sK49 != app(cons(hd(sK49),nil),tl(sK49))
| ~ ssList(tl(sK49))
| ~ spl51_2
| ~ spl51_5
| ~ spl51_6 ),
inference(superposition,[],[f622,f616]) ).
fof(f641,plain,
( sK50 != app(tl(sK49),cons(hd(sK49),nil))
| sK49 != app(cons(hd(sK49),nil),tl(sK49))
| ~ spl51_2
| ~ spl51_4
| ~ spl51_5
| ~ spl51_6 ),
inference(forward_subsumption_resolution,[],[f640,f476]) ).
fof(f644,definition,
( spl51_20
<=> sK49 = app(cons(hd(sK49),nil),tl(sK49)) ),
introduced(definition,[new_symbols(definition,[spl51_20])],[avatar_definition]) ).
fof(f646,plain,
( sK49 != app(cons(hd(sK49),nil),tl(sK49))
| spl51_20 ),
inference(avatar_component_clause,[],[f644]) ).
fof(f647,plain,
( ~ spl51_20
| ~ spl51_3
| ~ spl51_2
| ~ spl51_4
| ~ spl51_5
| ~ spl51_6 ),
inference(avatar_split_clause,[],[f641,f483,f479,f475,f467,f471,f644]) ).
fof(f683,plain,
( ~ ssList(sK49)
| nil = sK49
| ~ ssList(nil)
| spl51_7 ),
inference(resolution,[],[f303,f489]) ).
fof(f686,plain,
( nil = sK49
| ~ ssList(nil)
| spl51_7 ),
inference(forward_subsumption_resolution,[],[f683,f419]) ).
fof(f687,plain,
( nil = sK49
| spl51_7 ),
inference(forward_subsumption_resolution,[],[f686,f306]) ).
fof(f694,plain,
( ~ neq(nil,nil)
| spl51_7 ),
inference(superposition,[],[f489,f687]) ).
fof(f695,plain,
( neq(nil,nil)
| spl51_7
| ~ spl51_8 ),
inference(superposition,[],[f494,f687]) ).
fof(f717,plain,
( $false
| spl51_7
| ~ spl51_8 ),
inference(forward_subsumption_resolution,[],[f695,f694]) ).
fof(f718,plain,
( spl51_7
| ~ spl51_8 ),
inference(avatar_contradiction_clause,[],[f717]) ).
fof(f988,plain,
( neq(nil,nil)
| ~ spl51_7
| ~ spl51_9 ),
inference(superposition,[],[f488,f499]) ).
fof(f1043,plain,
( ~ ssList(nil)
| ~ spl51_7
| ~ spl51_9 ),
inference(resolution,[],[f988,f459]) ).
fof(f1044,plain,
( $false
| ~ spl51_7
| ~ spl51_9 ),
inference(forward_subsumption_resolution,[],[f1043,f306]) ).
fof(f1045,plain,
( ~ spl51_7
| ~ spl51_9 ),
inference(avatar_contradiction_clause,[],[f1044]) ).
fof(f1233,plain,
( nil = sK49
| sK49 = cons(hd(sK49),tl(sK49)) ),
inference(resolution,[],[f389,f419]) ).
fof(f1236,plain,
( sK49 = cons(hd(sK49),tl(sK49))
| spl51_9 ),
inference(forward_subsumption_resolution,[],[f1233,f498]) ).
fof(f3882,plain,
( ! [X0] :
( ~ ssList(X0)
| app(cons(hd(sK49),nil),X0) = cons(hd(sK49),X0) )
| ~ spl51_6 ),
inference(resolution,[],[f392,f484]) ).
fof(f17074,plain,
( app(cons(hd(sK49),nil),tl(sK49)) = cons(hd(sK49),tl(sK49))
| ~ spl51_4
| ~ spl51_6 ),
inference(resolution,[],[f3882,f476]) ).
fof(f17215,plain,
( sK49 = app(cons(hd(sK49),nil),tl(sK49))
| ~ spl51_4
| ~ spl51_6
| spl51_9 ),
inference(forward_demodulation,[],[f17074,f1236]) ).
fof(f17219,plain,
( $false
| ~ spl51_4
| ~ spl51_6
| spl51_9
| spl51_20 ),
inference(forward_subsumption_resolution,[],[f17215,f646]) ).
fof(f17220,plain,
( ~ spl51_4
| ~ spl51_6
| spl51_9
| spl51_20 ),
inference(avatar_contradiction_clause,[],[f17219]) ).
cnf(s1,plain,
( ~ spl51_1
| ~ spl51_2
| spl51_3
| ~ spl51_4
| ~ spl51_5
| ~ spl51_6
| ~ spl51_7 ),
inference(sat_conversion,[],[f490]) ).
cnf(s2,plain,
( ~ spl51_1
| spl51_8 ),
inference(sat_conversion,[],[f495]) ).
cnf(s10,plain,
spl51_1,
inference(sat_conversion,[],[f538]) ).
cnf(s12,plain,
( spl51_2
| ~ spl51_4
| ~ spl51_5 ),
inference(sat_conversion,[],[f562]) ).
cnf(s13,plain,
( spl51_4
| ~ spl51_8 ),
inference(sat_conversion,[],[f575]) ).
cnf(s14,plain,
( spl51_5
| ~ spl51_8 ),
inference(sat_conversion,[],[f596]) ).
cnf(s15,plain,
( spl51_6
| ~ spl51_8 ),
inference(sat_conversion,[],[f611]) ).
cnf(s17,plain,
( ~ spl51_2
| ~ spl51_3
| ~ spl51_4
| ~ spl51_5
| ~ spl51_6
| ~ spl51_20 ),
inference(sat_conversion,[],[f647]) ).
cnf(s20,plain,
( spl51_7
| ~ spl51_8 ),
inference(sat_conversion,[],[f718]) ).
cnf(s30,plain,
( ~ spl51_7
| ~ spl51_9 ),
inference(sat_conversion,[],[f1045]) ).
cnf(s666,plain,
( ~ spl51_4
| ~ spl51_6
| spl51_9
| spl51_20 ),
inference(sat_conversion,[],[f17220]) ).
cnf(s747,plain,
spl51_8,
inference(rat,[],[s2,s10]) ).
cnf(s748,plain,
spl51_7,
inference(rat,[],[s20,s747]) ).
cnf(s749,plain,
spl51_6,
inference(rat,[],[s15,s747]) ).
cnf(s750,plain,
spl51_5,
inference(rat,[],[s14,s747]) ).
cnf(s751,plain,
spl51_4,
inference(rat,[],[s13,s747]) ).
cnf(s752,plain,
~ spl51_9,
inference(rat,[],[s30,s748]) ).
cnf(s760,plain,
spl51_20,
inference(rat,[],[s666,s749,s752,s751]) ).
cnf(s761,plain,
spl51_2,
inference(rat,[],[s12,s750,s751]) ).
cnf(s776,plain,
~ spl51_3,
inference(rat,[],[s17,s760,s749,s750,s751,s761]) ).
cnf(s799,plain,
$false,
inference(rat,[],[s1,s748,s749,s750,s751,s776,s761,s10]) ).
fof(f17221,plain,
$false,
inference(avatar_sat_refutation,[],[s799]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC421+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.17 % Computer : n016.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Mon Sep 28 09:39:48 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.21 Running first-order model finding
% 0.07/0.21 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
% 3.35/0.72 % (3511769)Will run a generic schedule for satisfiability detection.
% 3.35/0.72 % (3511774)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2991285874_2999 on theBenchmark for (2999ds/0Mi)
% 3.35/0.72 % (3511776)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2574176432:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 3.35/0.72 % (3511777)dis+10_1_sil=32000:sp=arity:random_seed=4042318159:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 3.35/0.72 % (3511778)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=615540414:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 3.35/0.72 % (3511779)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3805533993:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 3.35/0.72 % TRYING [1]
% 3.35/0.72 % (3511780)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=31993427:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 3.35/0.72 % TRYING [2]
% 3.35/0.72 % (3511775)% WARNING: option uhcvi not known.
% 3.35/0.72 % TRYING [3]
% 3.35/0.72 % (3511775)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2280647710:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 3.35/0.72 % TRYING [4]
% 3.35/0.72 % TRYING [5]
% 3.35/0.72 % (3511777)Instruction limit reached!
% 3.35/0.72 % (3511777)------------------------------
% 3.35/0.72 % (3511777)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.35/0.72 % (3511777)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/0.72 % (3511777)CaDiCaL version: 2.1.3
% 3.35/0.72 % (3511777)Termination reason: Instruction limit
% 3.35/0.72 % (3511777)Termination phase: Saturation
% 3.35/0.72 % (3511777)Time elapsed: 0.062 s
% 3.35/0.72 % (3511777)Peak memory usage: 13 MB
% 3.35/0.72 % (3511777)Instructions burned: 103 (million)
% 3.35/0.72 % (3511778)Instruction limit reached!
% 3.35/0.72 % (3511778)------------------------------
% 3.35/0.72 % (3511778)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.35/0.72 % (3511778)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/0.72 % (3511778)CaDiCaL version: 2.1.3
% 3.35/0.72 % (3511778)Termination reason: Instruction limit
% 3.35/0.72 % (3511778)Termination phase: Saturation
% 3.35/0.72 % (3511778)Time elapsed: 0.069 s
% 3.35/0.72 % (3511778)Peak memory usage: 14 MB
% 3.35/0.72 % (3511778)Instructions burned: 117 (million)
% 3.35/0.72 % (3511779)Instruction limit reached!
% 3.35/0.72 % (3511779)------------------------------
% 3.35/0.72 % (3511779)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.35/0.72 % (3511779)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/0.72 % (3511779)CaDiCaL version: 2.1.3
% 3.35/0.72 % (3511779)Termination reason: Instruction limit
% 3.35/0.72 % (3511779)Termination phase: Saturation
% 3.35/0.72 % (3511779)Time elapsed: 0.078 s
% 3.35/0.72 % (3511779)Peak memory usage: 14 MB
% 3.35/0.72 % (3511779)Instructions burned: 132 (million)
% 3.35/0.72 % (3511788)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1311260102:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 3.35/0.72 % (3511789)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1261896185:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 3.35/0.72 % TRYING [1]
% 3.35/0.72 % (3511790)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=3611493216:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 3.35/0.72 % TRYING [2]
% 3.35/0.72 % (3511780)Instruction limit reached!
% 3.35/0.72 % (3511780)------------------------------
% 3.35/0.72 % (3511780)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.35/0.72 % (3511780)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/0.72 % (3511780)CaDiCaL version: 2.1.3
% 3.35/0.72 % (3511780)Termination reason: Instruction limit
% 3.35/0.72 % (3511780)Termination phase: Saturation
% 3.35/0.72 % (3511780)Time elapsed: 0.101 s
% 3.35/0.72 % (3511780)Peak memory usage: 14 MB
% 3.35/0.72 % (3511780)Instructions burned: 159 (million)
% 3.35/0.72 % TRYING [3]
% 3.35/0.72 % TRYING [6]
% 3.35/0.72 % TRYING [4]
% 3.35/0.72 % (3511794)ott-21_1_sil=16000:fs=off:random_seed=4118428069:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 3.35/0.72 % (3511789)Instruction limit reached!
% 3.35/0.72 % (3511789)------------------------------
% 3.35/0.72 % (3511789)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.35/0.72 % (3511789)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/0.72 % (3511789)CaDiCaL version: 2.1.3
% 3.35/0.72 % (3511789)Termination reason: Instruction limit
% 3.35/0.72 % (3511789)Termination phase: Saturation
% 3.35/0.72 % (3511789)Time elapsed: 0.073 s
% 3.35/0.72 % (3511789)Peak memory usage: 13 MB
% 3.35/0.72 % (3511789)Instructions burned: 132 (million)
% 3.35/0.72 % TRYING [5]
% 3.35/0.72 % (3511796)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1201984427:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 3.35/0.72 % (3511794)Instruction limit reached!
% 3.35/0.72 % (3511794)------------------------------
% 3.35/0.72 % (3511794)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.35/0.72 % (3511794)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/0.72 % (3511794)CaDiCaL version: 2.1.3
% 3.35/0.72 % (3511794)Termination reason: Instruction limit
% 3.35/0.72 % (3511794)Termination phase: Saturation
% 3.35/0.72 % (3511794)Time elapsed: 0.093 s
% 3.35/0.72 % (3511794)Peak memory usage: 14 MB
% 3.35/0.72 % (3511794)Instructions burned: 181 (million)
% 3.35/0.72 % (3511798)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=337952210:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 3.35/0.72 % TRYING [1]
% 3.35/0.72 % TRYING [2]
% 3.35/0.72 % TRYING [3]
% 3.35/0.72 % TRYING [7]
% 3.35/0.72 % TRYING [4]
% 3.35/0.72 % TRYING [6]
% 3.35/0.72 % (3511788)Instruction limit reached!
% 3.35/0.72 % (3511788)------------------------------
% 3.35/0.72 % (3511788)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.35/0.72 % (3511788)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/0.72 % (3511788)CaDiCaL version: 2.1.3
% 3.35/0.72 % (3511788)Termination reason: Instruction limit
% 3.35/0.72 % (3511788)Termination phase: Finite model building constraint generation
% 3.35/0.72 % (3511788)Time elapsed: 0.289 s
% 3.35/0.72 % (3511788)Peak memory usage: 28 MB
% 3.35/0.72 % (3511788)Instructions burned: 716 (million)
% 3.35/0.72 % (3511800)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3736908908:i=1179_2995 on theBenchmark for (2995ds/1179Mi)
% 3.35/0.72 % TRYING [5]
% 3.35/0.72 % (3511790) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3511769-3511790"...
% 3.35/0.72 % (3511790)...printing done.
% 3.35/0.72 % (3511790)Refutation found. Thanks to Tanya!
% 3.35/0.72 % SZS status Theorem for theBenchmark
% 3.35/0.72 % SZS output start Proof for theBenchmark
% See solution above
% 3.35/0.72 % (3511790)------------------------------
% 3.35/0.72 % (3511790)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.35/0.72 % (3511790)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/0.72 % (3511790)CaDiCaL version: 2.1.3
% 3.35/0.72 % (3511790)Termination reason: Refutation
% 3.35/0.72 % (3511790)Time elapsed: 0.360 s
% 3.35/0.72 % (3511790)Peak memory usage: 20 MB
% 3.35/0.72 % (3511790)Instructions burned: 632 (million)
% 3.35/0.72 % (3511769)Success in time 0.501 s
% 3.35/0.72 % Vampire exiting
%------------------------------------------------------------------------------