%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC072-1 : 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 : 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 01:02:18 PM UTC 2026
% Result : Unsatisfiable 5.71s 1.74s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 35
% Syntax : Number of formulae : 167 ( 28 unt; 15 def)
% Number of atoms : 571 ( 82 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 754 ( 350 ~; 393 |; 0 &)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 12 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 54 ( 0 sgn 54 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause8) ).
fof(f57,axiom,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause57) ).
fof(f73,axiom,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause73) ).
fof(f74,axiom,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause74) ).
fof(f77,axiom,
! [X0] :
( ssList(tl(X0))
| ~ ssList(X0)
| nil = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause77) ).
fof(f78,axiom,
! [X0] :
( ssItem(hd(X0))
| ~ ssList(X0)
| nil = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause78) ).
fof(f85,axiom,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause85) ).
fof(f86,axiom,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause86) ).
fof(f101,axiom,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| neq(X1,X0)
| X1 = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause100) ).
fof(f102,plain,
! [X0,X1] :
( neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0)
| X0 = X1 ),
inference(reorient_equations,[],[f101]) ).
fof(f107,axiom,
! [X0] :
( ~ ssList(X0)
| cons(hd(X0),tl(X0)) = X0
| nil = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause104) ).
fof(f125,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| app(cons(X0,nil),X1) = cons(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause120) ).
fof(f126,plain,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| cons(X0,X1) = app(cons(X0,nil),X1) ),
inference(reorient_equations,[],[f125]) ).
fof(f187,axiom,
! [X2,X3,X0,X1] :
( app(app(X0,X1),X2) != X3
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| segmentP(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause173) ).
fof(f202,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
fof(f203,negated_conjecture,
ssList(sk4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_4) ).
fof(f204,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
fof(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
fof(f206,negated_conjecture,
! [X0] :
( ~ ssList(X0)
| ~ neq(X0,nil)
| ~ segmentP(sk2,X0)
| ~ segmentP(sk1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
( nil = sk3
| nil != sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
fof(f208,negated_conjecture,
( nil != sk2
| nil != sk1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
fof(f209,negated_conjecture,
! [X2,X3,X0,X1] :
( ~ ssList(X0)
| sk3 = X0
| ~ ssList(X1)
| ~ ssList(X2)
| tl(sk4) != X1
| app(X1,X2) != X0
| ~ ssItem(X3)
| cons(X3,nil) != X2
| hd(sk4) != X3
| ~ neq(nil,sk4)
| ~ neq(nil,sk4)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
fof(f212,plain,
! [X0] :
( ~ neq(X0,nil)
| ~ ssList(X0)
| ~ segmentP(sk4,X0)
| ~ segmentP(sk3,X0) ),
inference(definition_unfolding,[],[f206,f204,f205]) ).
fof(f213,plain,
( nil != sk4
| nil != sk3 ),
inference(definition_unfolding,[],[f208,f204,f205]) ).
fof(f228,plain,
! [X2,X0,X1] :
( segmentP(app(app(X0,X1),X2),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(app(app(X0,X1),X2))
| ~ ssList(X2) ),
inference(equality_resolution,[],[f187]) ).
fof(f238,plain,
! [X2,X3,X0] :
( ~ ssList(X0)
| sk3 = X0
| ~ ssList(tl(sk4))
| ~ ssList(X2)
| app(tl(sk4),X2) != X0
| ~ ssItem(X3)
| cons(X3,nil) != X2
| hd(sk4) != X3
| ~ neq(nil,sk4)
| ~ neq(nil,sk4)
| ~ neq(sk4,nil) ),
inference(equality_resolution,[],[f209]) ).
fof(f239,plain,
! [X2,X3] :
( ~ ssList(app(tl(sk4),X2))
| sk3 = app(tl(sk4),X2)
| ~ ssList(tl(sk4))
| ~ ssList(X2)
| ~ ssItem(X3)
| cons(X3,nil) != X2
| hd(sk4) != X3
| ~ neq(nil,sk4)
| ~ neq(nil,sk4)
| ~ neq(sk4,nil) ),
inference(equality_resolution,[],[f238]) ).
fof(f240,plain,
! [X3] :
( ~ ssList(app(tl(sk4),cons(X3,nil)))
| sk3 = app(tl(sk4),cons(X3,nil))
| ~ ssList(tl(sk4))
| ~ ssList(cons(X3,nil))
| ~ ssItem(X3)
| hd(sk4) != X3
| ~ neq(nil,sk4)
| ~ neq(nil,sk4)
| ~ neq(sk4,nil) ),
inference(equality_resolution,[],[f239]) ).
fof(f241,plain,
( ~ ssList(app(tl(sk4),cons(hd(sk4),nil)))
| sk3 = app(tl(sk4),cons(hd(sk4),nil))
| ~ ssList(tl(sk4))
| ~ ssList(cons(hd(sk4),nil))
| ~ ssItem(hd(sk4))
| ~ neq(nil,sk4)
| ~ neq(nil,sk4)
| ~ neq(sk4,nil) ),
inference(equality_resolution,[],[f240]) ).
fof(f242,definition,
sF0 = tl(sk4),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f243,plain,
tl(sk4) = sF0,
inference(reorient_equations,[],[f242]) ).
fof(f244,definition,
sF1 = hd(sk4),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f245,plain,
hd(sk4) = sF1,
inference(reorient_equations,[],[f244]) ).
fof(f246,definition,
sF2 = cons(sF1,nil),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f247,plain,
cons(sF1,nil) = sF2,
inference(reorient_equations,[],[f246]) ).
fof(f248,definition,
sF3 = app(sF0,sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f249,plain,
app(sF0,sF2) = sF3,
inference(reorient_equations,[],[f248]) ).
fof(f250,plain,
( ~ ssList(sF3)
| sk3 = sF3
| ~ ssList(sF0)
| ~ ssList(sF2)
| ~ ssItem(sF1)
| ~ neq(nil,sk4)
| ~ neq(nil,sk4)
| ~ neq(sk4,nil) ),
inference(definition_folding,[],[f241,f245,f247,f245,f243,f249,f247,f245,f243,f249,f247,f245,f243]) ).
fof(f251,plain,
( ~ ssList(sF3)
| sk3 = sF3
| ~ ssList(sF0)
| ~ ssList(sF2)
| ~ ssItem(sF1)
| ~ neq(nil,sk4)
| ~ neq(sk4,nil) ),
inference(duplicate_literal_removal,[],[f250]) ).
fof(f259,definition,
( spl4_1
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f260,plain,
( neq(sk4,nil)
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f261,plain,
( ~ neq(sk4,nil)
| spl4_1 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f263,definition,
( spl4_2
<=> neq(nil,sk4) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f265,plain,
( ~ neq(nil,sk4)
| spl4_2 ),
inference(avatar_component_clause,[],[f263]) ).
fof(f267,definition,
( spl4_3
<=> ssItem(sF1) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
fof(f268,plain,
( ssItem(sF1)
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f267]) ).
fof(f269,plain,
( ~ ssItem(sF1)
| spl4_3 ),
inference(avatar_component_clause,[],[f267]) ).
fof(f271,definition,
( spl4_4
<=> ssList(sF2) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
fof(f272,plain,
( ssList(sF2)
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f271]) ).
fof(f273,plain,
( ~ ssList(sF2)
| spl4_4 ),
inference(avatar_component_clause,[],[f271]) ).
fof(f275,definition,
( spl4_5
<=> ssList(sF0) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
fof(f276,plain,
( ssList(sF0)
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f275]) ).
fof(f279,definition,
( spl4_6
<=> sk3 = sF3 ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
fof(f281,plain,
( sk3 = sF3
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f279]) ).
fof(f283,definition,
( spl4_7
<=> ssList(sF3) ),
introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition]) ).
fof(f285,plain,
( ~ ssList(sF3)
| spl4_7 ),
inference(avatar_component_clause,[],[f283]) ).
fof(f286,plain,
( ~ spl4_1
| ~ spl4_2
| ~ spl4_3
| ~ spl4_4
| ~ spl4_5
| spl4_6
| ~ spl4_7 ),
inference(avatar_split_clause,[],[f251,f283,f279,f275,f271,f267,f263,f259]) ).
fof(f288,definition,
( spl4_8
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[spl4_8])],[avatar_definition]) ).
fof(f292,definition,
( spl4_9
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[spl4_9])],[avatar_definition]) ).
fof(f294,plain,
( nil != sk4
| spl4_9 ),
inference(avatar_component_clause,[],[f292]) ).
fof(f295,plain,
( ~ spl4_8
| ~ spl4_9 ),
inference(avatar_split_clause,[],[f213,f292,f288]) ).
fof(f296,plain,
( ~ spl4_9
| spl4_8 ),
inference(avatar_split_clause,[],[f207,f288,f292]) ).
fof(f302,definition,
( spl4_11
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl4_11])],[avatar_definition]) ).
fof(f303,plain,
( ssList(nil)
| ~ spl4_11 ),
inference(avatar_component_clause,[],[f302]) ).
fof(f338,plain,
spl4_11,
inference(avatar_split_clause,[],[f8,f302]) ).
fof(f339,plain,
( sk4 = cons(hd(sk4),tl(sk4))
| nil = sk4 ),
inference(resolution,[],[f107,f203]) ).
fof(f347,plain,
( sk4 = cons(hd(sk4),tl(sk4))
| spl4_9 ),
inference(forward_subsumption_resolution,[],[f339,f294]) ).
fof(f348,plain,
( sk4 = cons(hd(sk4),sF0)
| spl4_9 ),
inference(forward_demodulation,[],[f347,f243]) ).
fof(f349,plain,
( sk4 = cons(sF1,sF0)
| spl4_9 ),
inference(forward_demodulation,[],[f348,f245]) ).
fof(f352,plain,
( ssList(sF0)
| ~ ssList(sk4)
| nil = sk4 ),
inference(superposition,[],[f77,f243]) ).
fof(f353,plain,
( ssList(sF0)
| nil = sk4 ),
inference(forward_subsumption_resolution,[],[f352,f203]) ).
fof(f354,plain,
( ssList(sF0)
| spl4_9 ),
inference(forward_subsumption_resolution,[],[f353,f294]) ).
fof(f355,plain,
( spl4_5
| spl4_9 ),
inference(avatar_split_clause,[],[f354,f292,f275]) ).
fof(f358,definition,
( spl4_20
<=> nil = sF0 ),
introduced(definition,[new_symbols(definition,[spl4_20])],[avatar_definition]) ).
fof(f359,plain,
( nil != sF0
| spl4_20 ),
inference(avatar_component_clause,[],[f358]) ).
fof(f360,plain,
( nil = sF0
| ~ spl4_20 ),
inference(avatar_component_clause,[],[f358]) ).
fof(f366,plain,
! [X0] :
( ~ ssList(X0)
| ~ segmentP(sk4,X0)
| ~ segmentP(sk3,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| nil = X0 ),
inference(resolution,[],[f212,f102]) ).
fof(f367,plain,
! [X0] :
( ~ ssList(X0)
| ~ segmentP(sk4,X0)
| ~ segmentP(sk3,X0)
| ~ ssList(nil)
| nil = X0 ),
inference(duplicate_literal_removal,[],[f366]) ).
fof(f368,plain,
( ! [X0] :
( ~ segmentP(sk4,X0)
| ~ ssList(X0)
| ~ segmentP(sk3,X0)
| nil = X0 )
| ~ spl4_11 ),
inference(forward_subsumption_resolution,[],[f367,f303]) ).
fof(f370,plain,
( ssList(sF2)
| ~ ssList(nil)
| ~ ssItem(sF1) ),
inference(superposition,[],[f86,f247]) ).
fof(f372,plain,
( ~ ssList(nil)
| ~ ssItem(sF1)
| spl4_4 ),
inference(forward_subsumption_resolution,[],[f370,f273]) ).
fof(f374,plain,
( ~ ssItem(sF1)
| spl4_4
| ~ spl4_11 ),
inference(forward_subsumption_resolution,[],[f372,f303]) ).
fof(f378,plain,
( ~ ssList(sk4)
| ~ ssList(nil)
| nil = sk4
| spl4_1 ),
inference(resolution,[],[f261,f102]) ).
fof(f379,plain,
( ~ ssList(nil)
| nil = sk4
| spl4_1 ),
inference(forward_subsumption_resolution,[],[f378,f203]) ).
fof(f380,plain,
( nil = sk4
| spl4_1
| ~ spl4_11 ),
inference(forward_subsumption_resolution,[],[f379,f303]) ).
fof(f381,plain,
( $false
| spl4_1
| spl4_9
| ~ spl4_11 ),
inference(forward_subsumption_resolution,[],[f380,f294]) ).
fof(f382,plain,
( spl4_1
| spl4_9
| ~ spl4_11 ),
inference(avatar_contradiction_clause,[],[f381]) ).
fof(f393,plain,
( ~ spl4_3
| spl4_4
| ~ spl4_11 ),
inference(avatar_split_clause,[],[f374,f302,f271,f267]) ).
fof(f396,plain,
( ~ ssList(nil)
| ~ ssList(sk4)
| nil = sk4
| spl4_2 ),
inference(resolution,[],[f265,f102]) ).
fof(f397,plain,
( ~ ssList(sk4)
| nil = sk4
| spl4_2
| ~ spl4_11 ),
inference(forward_subsumption_resolution,[],[f396,f303]) ).
fof(f398,plain,
( nil = sk4
| spl4_2
| ~ spl4_11 ),
inference(forward_subsumption_resolution,[],[f397,f203]) ).
fof(f399,plain,
( $false
| spl4_2
| spl4_9
| ~ spl4_11 ),
inference(forward_subsumption_resolution,[],[f398,f294]) ).
fof(f400,plain,
( spl4_2
| spl4_9
| ~ spl4_11 ),
inference(avatar_contradiction_clause,[],[f399]) ).
fof(f401,plain,
( ssItem(sF1)
| ~ ssList(sk4)
| nil = sk4 ),
inference(superposition,[],[f78,f245]) ).
fof(f402,plain,
( ~ ssList(sk4)
| nil = sk4
| spl4_3 ),
inference(forward_subsumption_resolution,[],[f401,f269]) ).
fof(f403,plain,
( nil = sk4
| spl4_3 ),
inference(forward_subsumption_resolution,[],[f402,f203]) ).
fof(f404,plain,
( $false
| spl4_3
| spl4_9 ),
inference(forward_subsumption_resolution,[],[f403,f294]) ).
fof(f405,plain,
( spl4_3
| spl4_9 ),
inference(avatar_contradiction_clause,[],[f404]) ).
fof(f412,plain,
( sF0 = app(nil,sF0)
| ~ spl4_5 ),
inference(resolution,[],[f74,f276]) ).
fof(f418,plain,
( ssList(sF3)
| ~ ssList(sF0)
| ~ ssList(sF2) ),
inference(superposition,[],[f85,f249]) ).
fof(f419,plain,
( ~ ssList(sF0)
| ~ ssList(sF2)
| spl4_7 ),
inference(forward_subsumption_resolution,[],[f418,f285]) ).
fof(f420,plain,
( ~ ssList(sF2)
| ~ spl4_5
| spl4_7 ),
inference(forward_subsumption_resolution,[],[f419,f276]) ).
fof(f421,plain,
( $false
| ~ spl4_4
| ~ spl4_5
| spl4_7 ),
inference(forward_subsumption_resolution,[],[f420,f272]) ).
fof(f422,plain,
( ~ spl4_4
| ~ spl4_5
| spl4_7 ),
inference(avatar_contradiction_clause,[],[f421]) ).
fof(f431,plain,
sk3 = app(sk3,nil),
inference(resolution,[],[f73,f202]) ).
fof(f432,plain,
sk4 = app(sk4,nil),
inference(resolution,[],[f73,f203]) ).
fof(f438,plain,
( ~ ssList(sk4)
| ~ segmentP(sk4,sk4)
| ~ segmentP(sk3,sk4)
| ~ spl4_1 ),
inference(resolution,[],[f260,f212]) ).
fof(f439,plain,
( ~ ssList(sk4)
| ~ segmentP(sk3,sk4)
| ~ spl4_1 ),
inference(forward_subsumption_resolution,[],[f438,f57]) ).
fof(f440,plain,
( ~ segmentP(sk3,sk4)
| ~ spl4_1 ),
inference(forward_subsumption_resolution,[],[f439,f203]) ).
fof(f443,plain,
! [X0] :
( segmentP(app(sF3,X0),sF2)
| ~ ssList(sF0)
| ~ ssList(sF2)
| ~ ssList(app(sF3,X0))
| ~ ssList(X0) ),
inference(superposition,[],[f228,f249]) ).
fof(f446,plain,
( ! [X0] :
( segmentP(app(sF3,X0),sF2)
| ~ ssList(sF2)
| ~ ssList(app(sF3,X0))
| ~ ssList(X0) )
| ~ spl4_5 ),
inference(forward_subsumption_resolution,[],[f443,f276]) ).
fof(f448,plain,
( ! [X0] :
( segmentP(app(sF3,X0),sF2)
| ~ ssList(app(sF3,X0))
| ~ ssList(X0) )
| ~ spl4_4
| ~ spl4_5 ),
inference(forward_subsumption_resolution,[],[f446,f272]) ).
fof(f462,plain,
( ! [X0] :
( segmentP(app(sk3,X0),sF2)
| ~ ssList(app(sF3,X0))
| ~ ssList(X0) )
| ~ spl4_4
| ~ spl4_5
| ~ spl4_6 ),
inference(forward_demodulation,[],[f448,f281]) ).
fof(f463,plain,
( ! [X0] :
( segmentP(app(sk3,X0),sF2)
| ~ ssList(app(sk3,X0))
| ~ ssList(X0) )
| ~ spl4_4
| ~ spl4_5
| ~ spl4_6 ),
inference(forward_demodulation,[],[f462,f281]) ).
fof(f464,plain,
( segmentP(sk3,sF2)
| ~ ssList(sk3)
| ~ ssList(nil)
| ~ spl4_4
| ~ spl4_5
| ~ spl4_6 ),
inference(superposition,[],[f463,f431]) ).
fof(f465,plain,
( segmentP(sk3,sF2)
| ~ ssList(nil)
| ~ spl4_4
| ~ spl4_5
| ~ spl4_6 ),
inference(forward_subsumption_resolution,[],[f464,f202]) ).
fof(f466,plain,
( segmentP(sk3,sF2)
| ~ spl4_4
| ~ spl4_5
| ~ spl4_6
| ~ spl4_11 ),
inference(forward_subsumption_resolution,[],[f465,f303]) ).
fof(f479,plain,
( ! [X0] :
( ~ ssList(X0)
| cons(sF1,X0) = app(cons(sF1,nil),X0) )
| ~ spl4_3 ),
inference(resolution,[],[f126,f268]) ).
fof(f480,plain,
( ! [X0] :
( ~ ssList(X0)
| cons(sF1,X0) = app(sF2,X0) )
| ~ spl4_3 ),
inference(forward_demodulation,[],[f479,f247]) ).
fof(f487,plain,
( cons(sF1,sF0) = app(sF2,sF0)
| ~ spl4_3
| ~ spl4_5 ),
inference(resolution,[],[f480,f276]) ).
fof(f519,plain,
( sk4 = cons(sF1,nil)
| spl4_9
| ~ spl4_20 ),
inference(superposition,[],[f349,f360]) ).
fof(f522,plain,
( sk4 = sF2
| spl4_9
| ~ spl4_20 ),
inference(forward_demodulation,[],[f519,f247]) ).
fof(f528,plain,
( segmentP(sk3,sk4)
| ~ spl4_4
| ~ spl4_5
| ~ spl4_6
| spl4_9
| ~ spl4_11
| ~ spl4_20 ),
inference(superposition,[],[f466,f522]) ).
fof(f531,plain,
( $false
| ~ spl4_1
| ~ spl4_4
| ~ spl4_5
| ~ spl4_6
| spl4_9
| ~ spl4_11
| ~ spl4_20 ),
inference(forward_subsumption_resolution,[],[f528,f440]) ).
fof(f532,plain,
( ~ spl4_1
| ~ spl4_4
| ~ spl4_5
| ~ spl4_6
| spl4_9
| ~ spl4_11
| ~ spl4_20 ),
inference(avatar_contradiction_clause,[],[f531]) ).
fof(f537,plain,
( sk4 = app(sF2,sF0)
| ~ spl4_3
| ~ spl4_5
| spl4_9 ),
inference(forward_demodulation,[],[f487,f349]) ).
fof(f538,plain,
( ! [X0] :
( segmentP(app(sk4,X0),sF0)
| ~ ssList(sF2)
| ~ ssList(sF0)
| ~ ssList(app(sk4,X0))
| ~ ssList(X0) )
| ~ spl4_3
| ~ spl4_5
| spl4_9 ),
inference(superposition,[],[f228,f537]) ).
fof(f540,plain,
( ! [X0] :
( segmentP(app(sk4,X0),sF0)
| ~ ssList(sF0)
| ~ ssList(app(sk4,X0))
| ~ ssList(X0) )
| ~ spl4_3
| ~ spl4_4
| ~ spl4_5
| spl4_9 ),
inference(forward_subsumption_resolution,[],[f538,f272]) ).
fof(f541,plain,
( ! [X0] :
( segmentP(app(sk4,X0),sF0)
| ~ ssList(app(sk4,X0))
| ~ ssList(X0) )
| ~ spl4_3
| ~ spl4_4
| ~ spl4_5
| spl4_9 ),
inference(forward_subsumption_resolution,[],[f540,f276]) ).
fof(f542,plain,
( segmentP(sk4,sF0)
| ~ ssList(sk4)
| ~ ssList(nil)
| ~ spl4_3
| ~ spl4_4
| ~ spl4_5
| spl4_9 ),
inference(superposition,[],[f541,f432]) ).
fof(f543,plain,
( segmentP(sk4,sF0)
| ~ ssList(nil)
| ~ spl4_3
| ~ spl4_4
| ~ spl4_5
| spl4_9 ),
inference(forward_subsumption_resolution,[],[f542,f203]) ).
fof(f544,plain,
( segmentP(sk4,sF0)
| ~ spl4_3
| ~ spl4_4
| ~ spl4_5
| spl4_9
| ~ spl4_11 ),
inference(forward_subsumption_resolution,[],[f543,f303]) ).
fof(f545,plain,
( ~ ssList(sF0)
| ~ segmentP(sk3,sF0)
| nil = sF0
| ~ spl4_3
| ~ spl4_4
| ~ spl4_5
| spl4_9
| ~ spl4_11 ),
inference(resolution,[],[f544,f368]) ).
fof(f546,plain,
( ~ segmentP(sk3,sF0)
| nil = sF0
| ~ spl4_3
| ~ spl4_4
| ~ spl4_5
| spl4_9
| ~ spl4_11 ),
inference(forward_subsumption_resolution,[],[f545,f276]) ).
fof(f547,plain,
( ~ segmentP(sk3,sF0)
| ~ spl4_3
| ~ spl4_4
| ~ spl4_5
| spl4_9
| ~ spl4_11
| spl4_20 ),
inference(forward_subsumption_resolution,[],[f546,f359]) ).
fof(f583,plain,
( ! [X0] :
( segmentP(app(sF0,X0),sF0)
| ~ ssList(nil)
| ~ ssList(sF0)
| ~ ssList(app(sF0,X0))
| ~ ssList(X0) )
| ~ spl4_5 ),
inference(superposition,[],[f228,f412]) ).
fof(f585,plain,
( ! [X0] :
( segmentP(app(sF0,X0),sF0)
| ~ ssList(nil)
| ~ ssList(sF0)
| ~ ssList(X0) )
| ~ spl4_5 ),
inference(forward_subsumption_resolution,[],[f583,f85]) ).
fof(f586,plain,
( ! [X0] :
( segmentP(app(sF0,X0),sF0)
| ~ ssList(sF0)
| ~ ssList(X0) )
| ~ spl4_5
| ~ spl4_11 ),
inference(forward_subsumption_resolution,[],[f585,f303]) ).
fof(f587,plain,
( ! [X0] :
( segmentP(app(sF0,X0),sF0)
| ~ ssList(X0) )
| ~ spl4_5
| ~ spl4_11 ),
inference(forward_subsumption_resolution,[],[f586,f276]) ).
fof(f588,plain,
( segmentP(sF3,sF0)
| ~ ssList(sF2)
| ~ spl4_5
| ~ spl4_11 ),
inference(superposition,[],[f587,f249]) ).
fof(f589,plain,
( segmentP(sF3,sF0)
| ~ spl4_4
| ~ spl4_5
| ~ spl4_11 ),
inference(forward_subsumption_resolution,[],[f588,f272]) ).
fof(f590,plain,
( segmentP(sk3,sF0)
| ~ spl4_4
| ~ spl4_5
| ~ spl4_6
| ~ spl4_11 ),
inference(forward_demodulation,[],[f589,f281]) ).
fof(f591,plain,
( $false
| ~ spl4_3
| ~ spl4_4
| ~ spl4_5
| ~ spl4_6
| spl4_9
| ~ spl4_11
| spl4_20 ),
inference(forward_subsumption_resolution,[],[f590,f547]) ).
fof(f592,plain,
( ~ spl4_3
| ~ spl4_4
| ~ spl4_5
| ~ spl4_6
| spl4_9
| ~ spl4_11
| spl4_20 ),
inference(avatar_contradiction_clause,[],[f591]) ).
cnf(s1,plain,
( ~ spl4_1
| ~ spl4_2
| ~ spl4_3
| ~ spl4_4
| ~ spl4_5
| spl4_6
| ~ spl4_7 ),
inference(sat_conversion,[],[f286]) ).
cnf(s2,plain,
( ~ spl4_8
| ~ spl4_9 ),
inference(sat_conversion,[],[f295]) ).
cnf(s3,plain,
( spl4_8
| ~ spl4_9 ),
inference(sat_conversion,[],[f296]) ).
cnf(s13,plain,
spl4_11,
inference(sat_conversion,[],[f338]) ).
cnf(s15,plain,
( spl4_5
| spl4_9 ),
inference(sat_conversion,[],[f355]) ).
cnf(s18,plain,
( spl4_1
| spl4_9
| ~ spl4_11 ),
inference(sat_conversion,[],[f382]) ).
cnf(s20,plain,
( ~ spl4_3
| spl4_4
| ~ spl4_11 ),
inference(sat_conversion,[],[f393]) ).
cnf(s22,plain,
( spl4_2
| spl4_9
| ~ spl4_11 ),
inference(sat_conversion,[],[f400]) ).
cnf(s23,plain,
( spl4_3
| spl4_9 ),
inference(sat_conversion,[],[f405]) ).
cnf(s24,plain,
( ~ spl4_4
| ~ spl4_5
| spl4_7 ),
inference(sat_conversion,[],[f422]) ).
cnf(s27,plain,
( ~ spl4_1
| ~ spl4_4
| ~ spl4_5
| ~ spl4_6
| spl4_9
| ~ spl4_11
| ~ spl4_20 ),
inference(sat_conversion,[],[f532]) ).
cnf(s28,plain,
( ~ spl4_3
| ~ spl4_4
| ~ spl4_5
| ~ spl4_6
| spl4_9
| ~ spl4_11
| spl4_20 ),
inference(sat_conversion,[],[f592]) ).
cnf(s33,plain,
~ spl4_9,
inference(rat,[],[s2,s3]) ).
cnf(s34,plain,
spl4_3,
inference(rat,[],[s23,s33]) ).
cnf(s35,plain,
spl4_2,
inference(rat,[],[s22,s13,s33]) ).
cnf(s36,plain,
spl4_1,
inference(rat,[],[s18,s13,s33]) ).
cnf(s37,plain,
spl4_5,
inference(rat,[],[s15,s33]) ).
cnf(s39,plain,
spl4_4,
inference(rat,[],[s20,s13,s34]) ).
cnf(s40,plain,
spl4_7,
inference(rat,[],[s24,s39,s37]) ).
cnf(s41,plain,
spl4_6,
inference(rat,[],[s1,s40,s39,s34,s35,s36,s37]) ).
cnf(s43,plain,
~ spl4_20,
inference(rat,[],[s27,s33,s13,s37,s39,s36,s41]) ).
cnf(s44,plain,
$false,
inference(rat,[],[s28,s33,s13,s37,s39,s34,s41,s43]) ).
fof(f593,plain,
$false,
inference(avatar_sat_refutation,[],[s44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC072-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n017.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 07:39:06 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 5.71/1.74 % (3379779)Input is clausal, will run a generic CNF schedule.
% 5.71/1.74 % (3379885)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=2200368357:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.71/1.74 % (3379886)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1056271092:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.71/1.74 % (3379890)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=359347385:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.71/1.74 % (3379891)dis-21_1_sil=8000:lcm=predicate:random_seed=95944977:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 5.71/1.74 % (3379889)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3620428026:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.71/1.74 % (3379887)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1449646426:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.71/1.74 % (3379888)lrs+10_1_sil=8000:sp=occurrence:random_seed=3807744915:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.71/1.74 % (3379891)Instruction limit reached!
% 5.71/1.74 % (3379891)------------------------------
% 5.71/1.74 % (3379891)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.71/1.74 % (3379891)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.71/1.74 % (3379891)CaDiCaL version: 2.1.3
% 5.71/1.74 % (3379891)Termination reason: Instruction limit
% 5.71/1.74 % (3379891)Termination phase: Saturation
% 5.71/1.74 % (3379891)Time elapsed: 0.071 s
% 5.71/1.74 % (3379891)Peak memory usage: 89 MB
% 5.71/1.74 % (3379891)Instructions burned: 118 (million)
% 5.71/1.74 % (3379889)Instruction limit reached!
% 5.71/1.74 % (3379889)------------------------------
% 5.71/1.74 % (3379889)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.71/1.74 % (3379889)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.71/1.74 % (3379889)CaDiCaL version: 2.1.3
% 5.71/1.74 % (3379889)Termination reason: Instruction limit
% 5.71/1.74 % (3379889)Termination phase: Saturation
% 5.71/1.74 % (3379889)Time elapsed: 0.072 s
% 5.71/1.74 % (3379889)Peak memory usage: 88 MB
% 5.71/1.74 % (3379889)Instructions burned: 115 (million)
% 5.71/1.74 % (3379888)Instruction limit reached!
% 5.71/1.74 % (3379888)------------------------------
% 5.71/1.74 % (3379888)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.71/1.74 % (3379888)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.71/1.74 % (3379888)CaDiCaL version: 2.1.3
% 5.71/1.74 % (3379888)Termination reason: Instruction limit
% 5.71/1.74 % (3379888)Termination phase: Saturation
% 5.71/1.74 % (3379888)Time elapsed: 0.074 s
% 5.71/1.74 % (3379888)Peak memory usage: 89 MB
% 5.71/1.74 % (3379888)Instructions burned: 107 (million)
% 5.71/1.74 % (3379890)Instruction limit reached!
% 5.71/1.74 % (3379890)------------------------------
% 5.71/1.74 % (3379890)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.71/1.74 % (3379890)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.71/1.74 % (3379890)CaDiCaL version: 2.1.3
% 5.71/1.74 % (3379890)Termination reason: Instruction limit
% 5.71/1.74 % (3379890)Termination phase: Saturation
% 5.71/1.74 % (3379890)Time elapsed: 0.167 s
% 5.71/1.74 % (3379890)Peak memory usage: 90 MB
% 5.71/1.74 % (3379890)Instructions burned: 180 (million)
% 5.71/1.74 % (3379912)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=22427307:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 5.71/1.74 % (3379917)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=821347148:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 5.71/1.74 % (3379925)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3046396807:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 5.71/1.74 % (3379929)lrs+10_64_to=lpo:sil=8000:random_seed=635691576:i=126:bd=preordered_2996 on theBenchmark for (2996ds/126Mi)
% 5.71/1.74 % (3379885)First to succeed.
% 5.71/1.74 % (3379885)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3379779"
% 5.71/1.74 % (3379912)Instruction limit reached!
% 5.71/1.74 % (3379912)------------------------------
% 5.71/1.74 % (3379912)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.71/1.74 % (3379912)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.71/1.74 % (3379912)CaDiCaL version: 2.1.3
% 5.71/1.74 % (3379912)Termination reason: Instruction limit
% 5.71/1.74 % (3379912)Termination phase: Saturation
% 5.71/1.74 % (3379912)Time elapsed: 0.141 s
% 5.71/1.74 % (3379912)Peak memory usage: 89 MB
% 5.71/1.74 % (3379912)Instructions burned: 144 (million)
% 5.71/1.74 % (3379917)Instruction limit reached!
% 5.71/1.74 % (3379917)------------------------------
% 5.71/1.74 % (3379917)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.71/1.74 % (3379917)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.71/1.74 % (3379917)CaDiCaL version: 2.1.3
% 5.71/1.74 % (3379917)Termination reason: Instruction limit
% 5.71/1.74 % (3379917)Termination phase: Saturation
% 5.71/1.74 % (3379917)Time elapsed: 0.181 s
% 5.71/1.74 % (3379917)Peak memory usage: 91 MB
% 5.71/1.74 % (3379917)Instructions burned: 190 (million)
% 5.71/1.74 % (3379925)Instruction limit reached!
% 5.71/1.74 % (3379925)------------------------------
% 5.71/1.74 % (3379925)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.71/1.74 % (3379925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.71/1.74 % (3379925)CaDiCaL version: 2.1.3
% 5.71/1.74 % (3379925)Termination reason: Instruction limit
% 5.71/1.74 % (3379925)Termination phase: Saturation
% 5.71/1.74 % (3379925)Time elapsed: 0.201 s
% 5.71/1.74 % (3379925)Peak memory usage: 90 MB
% 5.71/1.74 % (3379925)Instructions burned: 219 (million)
% 5.71/1.74 % (3379929)Instruction limit reached!
% 5.71/1.74 % (3379929)------------------------------
% 5.71/1.74 % (3379929)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.71/1.74 % (3379929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.71/1.74 % (3379929)CaDiCaL version: 2.1.3
% 5.71/1.74 % (3379929)Termination reason: Instruction limit
% 5.71/1.74 % (3379929)Termination phase: Saturation
% 5.71/1.74 % (3379929)Time elapsed: 0.119 s
% 5.71/1.74 % (3379929)Peak memory usage: 90 MB
% 5.71/1.74 % (3379929)Instructions burned: 126 (million)
% 5.71/1.74 % (3379946)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=3714634256:avsq=on:i=194:fgj=on:bd=preordered_2993 on theBenchmark for (2993ds/194Mi)
% 5.71/1.74 % (3379885)Refutation found. Thanks to Tanya!
% 5.71/1.74 % SZS status Unsatisfiable for theBenchmark
% 5.71/1.74 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/2.07 % (3379885)------------------------------
% 0.17/2.07 % (3379885)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/2.07 % (3379885)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/2.07 % (3379885)CaDiCaL version: 2.1.3
% 0.17/2.07 % (3379885)Termination reason: Refutation
% 0.17/2.07 % (3379885)Time elapsed: 0.497 s
% 0.17/2.07 % (3379885)Peak memory usage: 132 MB
% 0.17/2.07 % (3379885)Instructions burned: 1015 (million)
% 0.17/2.07 % (3379885)------------------------------
% 0.17/2.07 % (3379885)------------------------------
% 0.17/2.07 % (3379779)Success in time 0.868 s
% 0.17/2.07 % Vampire exiting
%------------------------------------------------------------------------------