%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC111-1 : 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 : n001.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 01:02:30 PM UTC 2026
% Result : Unsatisfiable 6.58s 1.97s
% Output : Refutation 8.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 35
% Syntax : Number of formulae : 146 ( 18 unt; 12 def)
% Number of atoms : 453 ( 55 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 571 ( 264 ~; 295 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 13 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 45 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
totalorderedP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause4) ).
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause8) ).
fof(f56,axiom,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause56) ).
fof(f67,axiom,
! [X0] :
( ~ ssItem(X0)
| totalorderedP(cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause67) ).
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(f79,axiom,
! [X0] :
( nil != X0
| ~ ssList(X0)
| segmentP(nil,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause79) ).
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(f100,axiom,
! [X0,X1] :
( cons(X0,X1) != X1
| ~ ssItem(X0)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause99) ).
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,
segmentP(sk4,sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
fof(f208,negated_conjecture,
! [X0] :
( ~ neq(sk3,X0)
| ~ ssList(X0)
| ~ segmentP(sk4,X0)
| ~ segmentP(X0,sk3)
| ~ totalorderedP(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
fof(f210,negated_conjecture,
( nil = sk2
| ~ neq(sk1,nil)
| ~ segmentP(sk2,sk1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
fof(f211,negated_conjecture,
( nil != sk1
| neq(sk2,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
fof(f216,plain,
( nil = sk4
| ~ neq(sk3,nil)
| ~ segmentP(sk4,sk3) ),
inference(definition_unfolding,[],[f210,f204,f205,f204,f205]) ).
fof(f217,plain,
( nil != sk3
| neq(sk4,nil) ),
inference(definition_unfolding,[],[f211,f205,f204]) ).
fof(f219,plain,
( ~ ssList(nil)
| segmentP(nil,nil) ),
inference(equality_resolution,[],[f79]) ).
fof(f233,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(f250,definition,
( spl0_1
<=> segmentP(sk4,sk3) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f251,plain,
( segmentP(sk4,sk3)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f254,definition,
( spl0_2
<=> neq(sk3,nil) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f255,plain,
( neq(sk3,nil)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f256,plain,
( ~ neq(sk3,nil)
| spl0_2 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f258,definition,
( spl0_3
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f259,plain,
( nil = sk3
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f258]) ).
fof(f263,definition,
( spl0_4
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f265,plain,
( neq(sk4,nil)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f263]) ).
fof(f266,plain,
( spl0_4
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f217,f258,f263]) ).
fof(f268,definition,
( spl0_5
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f269,plain,
( nil != sk4
| spl0_5 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f270,plain,
( nil = sk4
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f271,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_5 ),
inference(avatar_split_clause,[],[f216,f268,f254,f250]) ).
fof(f273,plain,
spl0_1,
inference(avatar_split_clause,[],[f206,f250]) ).
fof(f279,definition,
( spl0_7
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f280,plain,
( ssList(nil)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f279]) ).
fof(f284,definition,
( spl0_8
<=> ! [X1] :
( ~ ssItem(X1)
| totalorderedP(cons(X1,nil)) ) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f285,plain,
( ! [X1] :
( totalorderedP(cons(X1,nil))
| ~ ssItem(X1) )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f284]) ).
fof(f302,definition,
( spl0_12
<=> segmentP(nil,nil) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f304,plain,
( segmentP(nil,nil)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f302]) ).
fof(f305,plain,
( spl0_12
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f219,f279,f302]) ).
fof(f313,plain,
spl0_8,
inference(avatar_split_clause,[],[f67,f284]) ).
fof(f315,plain,
spl0_7,
inference(avatar_split_clause,[],[f8,f279]) ).
fof(f316,plain,
( ~ ssList(sk3)
| ~ ssList(nil)
| nil = sk3
| spl0_2 ),
inference(resolution,[],[f102,f256]) ).
fof(f317,plain,
( ~ ssList(nil)
| nil = sk3
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f316,f202]) ).
fof(f318,plain,
( nil = sk3
| spl0_2
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f317,f280]) ).
fof(f319,plain,
( spl0_3
| spl0_2
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f318,f279,f254,f258]) ).
fof(f320,plain,
( segmentP(nil,sk3)
| ~ spl0_1
| ~ spl0_5 ),
inference(superposition,[],[f251,f270]) ).
fof(f321,plain,
! [X0] :
( ~ ssList(X0)
| ~ segmentP(sk4,X0)
| ~ segmentP(X0,sk3)
| ~ totalorderedP(X0)
| ~ ssList(sk3)
| ~ ssList(X0)
| sk3 = X0 ),
inference(resolution,[],[f208,f102]) ).
fof(f322,plain,
! [X0] :
( ~ ssList(X0)
| ~ segmentP(sk4,X0)
| ~ segmentP(X0,sk3)
| ~ totalorderedP(X0)
| ~ ssList(sk3)
| sk3 = X0 ),
inference(duplicate_literal_removal,[],[f321]) ).
fof(f323,plain,
! [X0] :
( ~ ssList(X0)
| ~ segmentP(sk4,X0)
| ~ segmentP(X0,sk3)
| ~ totalorderedP(X0)
| sk3 = X0 ),
inference(forward_subsumption_resolution,[],[f322,f202]) ).
fof(f325,plain,
( neq(nil,nil)
| ~ spl0_4
| ~ spl0_5 ),
inference(superposition,[],[f265,f270]) ).
fof(f326,plain,
( ~ ssList(nil)
| ~ segmentP(sk4,nil)
| ~ segmentP(nil,sk3)
| ~ totalorderedP(nil)
| ~ spl0_2 ),
inference(resolution,[],[f255,f208]) ).
fof(f327,plain,
( ~ segmentP(sk4,nil)
| ~ segmentP(nil,sk3)
| ~ totalorderedP(nil)
| ~ spl0_2
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f326,f280]) ).
fof(f328,plain,
( ~ segmentP(sk4,nil)
| ~ totalorderedP(nil)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f327,f320]) ).
fof(f329,plain,
( ~ segmentP(sk4,nil)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f328,f4]) ).
fof(f330,plain,
( ~ segmentP(nil,nil)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f329,f270]) ).
fof(f331,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f330,f304]) ).
fof(f332,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f331]) ).
fof(f334,plain,
( ~ neq(nil,nil)
| spl0_2
| ~ spl0_3 ),
inference(superposition,[],[f256,f259]) ).
fof(f340,plain,
( $false
| spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f334,f325]) ).
fof(f341,plain,
( spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f340]) ).
fof(f343,plain,
( ! [X0] :
( ~ segmentP(X0,nil)
| ~ ssList(X0)
| ~ segmentP(sk4,X0)
| ~ totalorderedP(X0)
| sk3 = X0 )
| ~ spl0_3 ),
inference(forward_demodulation,[],[f323,f259]) ).
fof(f344,plain,
( ! [X0] :
( ~ ssList(X0)
| ~ segmentP(sk4,X0)
| ~ totalorderedP(X0)
| sk3 = X0 )
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f343,f56]) ).
fof(f345,plain,
( ! [X0] :
( ~ segmentP(sk4,X0)
| ~ ssList(X0)
| nil = X0
| ~ totalorderedP(X0) )
| ~ spl0_3 ),
inference(forward_demodulation,[],[f344,f259]) ).
fof(f379,plain,
( sk4 = cons(hd(sk4),tl(sk4))
| nil = sk4 ),
inference(resolution,[],[f107,f203]) ).
fof(f380,plain,
( sk4 = cons(hd(sk4),tl(sk4))
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f379,f269]) ).
fof(f394,definition,
( spl0_15
<=> ssList(tl(sk4)) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f395,plain,
( ssList(tl(sk4))
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f394]) ).
fof(f396,plain,
( ~ ssList(tl(sk4))
| spl0_15 ),
inference(avatar_component_clause,[],[f394]) ).
fof(f406,plain,
( ~ ssList(sk4)
| nil = sk4
| spl0_15 ),
inference(resolution,[],[f77,f396]) ).
fof(f410,plain,
( nil = sk4
| spl0_15 ),
inference(forward_subsumption_resolution,[],[f406,f203]) ).
fof(f411,plain,
( $false
| spl0_5
| spl0_15 ),
inference(forward_subsumption_resolution,[],[f410,f269]) ).
fof(f412,plain,
( spl0_5
| spl0_15 ),
inference(avatar_contradiction_clause,[],[f411]) ).
fof(f444,plain,
! [X0,X1] :
( ~ ssList(X1)
| cons(hd(X1),X0) = app(cons(hd(X1),nil),X0)
| ~ ssList(X0)
| nil = X1 ),
inference(resolution,[],[f126,f78]) ).
fof(f452,plain,
! [X0] :
( cons(hd(sk4),X0) = app(cons(hd(sk4),nil),X0)
| ~ ssList(X0)
| nil = sk4 ),
inference(resolution,[],[f444,f203]) ).
fof(f453,plain,
( ! [X0] :
( ~ ssList(X0)
| cons(hd(sk4),X0) = app(cons(hd(sk4),nil),X0) )
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f452,f269]) ).
fof(f461,plain,
( cons(hd(sk4),tl(sk4)) = app(cons(hd(sk4),nil),tl(sk4))
| spl0_5
| ~ spl0_15 ),
inference(resolution,[],[f453,f395]) ).
fof(f476,definition,
( spl0_20
<=> ssList(cons(hd(sk4),nil)) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f477,plain,
( ssList(cons(hd(sk4),nil))
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f476]) ).
fof(f478,plain,
( ~ ssList(cons(hd(sk4),nil))
| spl0_20 ),
inference(avatar_component_clause,[],[f476]) ).
fof(f487,plain,
( ~ ssList(nil)
| ~ ssItem(hd(sk4))
| spl0_20 ),
inference(resolution,[],[f478,f86]) ).
fof(f488,plain,
( ~ ssItem(hd(sk4))
| ~ spl0_7
| spl0_20 ),
inference(forward_subsumption_resolution,[],[f487,f280]) ).
fof(f492,plain,
( ~ ssList(sk4)
| nil = sk4
| ~ spl0_7
| spl0_20 ),
inference(resolution,[],[f488,f78]) ).
fof(f493,plain,
( nil = sk4
| ~ spl0_7
| spl0_20 ),
inference(forward_subsumption_resolution,[],[f492,f203]) ).
fof(f494,plain,
( $false
| spl0_5
| ~ spl0_7
| spl0_20 ),
inference(forward_subsumption_resolution,[],[f493,f269]) ).
fof(f495,plain,
( spl0_5
| ~ spl0_7
| spl0_20 ),
inference(avatar_contradiction_clause,[],[f494]) ).
fof(f501,plain,
( cons(hd(sk4),nil) = app(nil,cons(hd(sk4),nil))
| ~ spl0_20 ),
inference(resolution,[],[f477,f74]) ).
fof(f503,definition,
( spl0_23
<=> nil = cons(hd(sk4),nil) ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f504,plain,
( nil != cons(hd(sk4),nil)
| spl0_23 ),
inference(avatar_component_clause,[],[f503]) ).
fof(f505,plain,
( nil = cons(hd(sk4),nil)
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f503]) ).
fof(f519,plain,
( nil != nil
| ~ ssItem(hd(sk4))
| ~ ssList(nil)
| ~ spl0_23 ),
inference(superposition,[],[f100,f505]) ).
fof(f522,plain,
( ~ ssItem(hd(sk4))
| ~ ssList(nil)
| ~ spl0_23 ),
inference(trivial_inequality_removal,[],[f519]) ).
fof(f525,plain,
( ~ ssItem(hd(sk4))
| ~ spl0_7
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f522,f280]) ).
fof(f528,definition,
( spl0_26
<=> ssItem(hd(sk4)) ),
introduced(definition,[new_symbols(definition,[spl0_26])],[avatar_definition]) ).
fof(f529,plain,
( ssItem(hd(sk4))
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f528]) ).
fof(f530,plain,
( ~ ssItem(hd(sk4))
| spl0_26 ),
inference(avatar_component_clause,[],[f528]) ).
fof(f539,plain,
( ~ spl0_26
| ~ spl0_7
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f525,f503,f279,f528]) ).
fof(f540,plain,
( ~ ssList(sk4)
| nil = sk4
| spl0_26 ),
inference(resolution,[],[f530,f78]) ).
fof(f541,plain,
( nil = sk4
| spl0_26 ),
inference(forward_subsumption_resolution,[],[f540,f203]) ).
fof(f542,plain,
( $false
| spl0_5
| spl0_26 ),
inference(forward_subsumption_resolution,[],[f541,f269]) ).
fof(f543,plain,
( spl0_5
| spl0_26 ),
inference(avatar_contradiction_clause,[],[f542]) ).
fof(f546,plain,
( ! [X0] :
( segmentP(app(cons(hd(sk4),nil),X0),cons(hd(sk4),nil))
| ~ ssList(nil)
| ~ ssList(cons(hd(sk4),nil))
| ~ ssList(app(cons(hd(sk4),nil),X0))
| ~ ssList(X0) )
| ~ spl0_20 ),
inference(superposition,[],[f233,f501]) ).
fof(f549,plain,
( ! [X0] :
( segmentP(app(cons(hd(sk4),nil),X0),cons(hd(sk4),nil))
| ~ ssList(nil)
| ~ ssList(cons(hd(sk4),nil))
| ~ ssList(X0) )
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f546,f85]) ).
fof(f551,plain,
( ! [X0] :
( segmentP(app(cons(hd(sk4),nil),X0),cons(hd(sk4),nil))
| ~ ssList(cons(hd(sk4),nil))
| ~ ssList(X0) )
| ~ spl0_7
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f549,f280]) ).
fof(f553,plain,
( ! [X0] :
( segmentP(app(cons(hd(sk4),nil),X0),cons(hd(sk4),nil))
| ~ ssList(X0) )
| ~ spl0_7
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f551,f477]) ).
fof(f681,plain,
( sk4 = app(cons(hd(sk4),nil),tl(sk4))
| spl0_5
| ~ spl0_15 ),
inference(forward_demodulation,[],[f461,f380]) ).
fof(f684,plain,
( segmentP(sk4,cons(hd(sk4),nil))
| ~ ssList(tl(sk4))
| spl0_5
| ~ spl0_7
| ~ spl0_15
| ~ spl0_20 ),
inference(superposition,[],[f553,f681]) ).
fof(f688,plain,
( segmentP(sk4,cons(hd(sk4),nil))
| spl0_5
| ~ spl0_7
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f684,f395]) ).
fof(f690,plain,
( ~ ssList(cons(hd(sk4),nil))
| nil = cons(hd(sk4),nil)
| ~ totalorderedP(cons(hd(sk4),nil))
| ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_15
| ~ spl0_20 ),
inference(resolution,[],[f688,f345]) ).
fof(f693,plain,
( nil = cons(hd(sk4),nil)
| ~ totalorderedP(cons(hd(sk4),nil))
| ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f690,f477]) ).
fof(f695,plain,
( ~ totalorderedP(cons(hd(sk4),nil))
| ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_15
| ~ spl0_20
| spl0_23 ),
inference(forward_subsumption_resolution,[],[f693,f504]) ).
fof(f696,plain,
( ~ ssItem(hd(sk4))
| ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_15
| ~ spl0_20
| spl0_23 ),
inference(resolution,[],[f695,f285]) ).
fof(f697,plain,
( $false
| ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_15
| ~ spl0_20
| spl0_23
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f696,f529]) ).
fof(f698,plain,
( ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_15
| ~ spl0_20
| spl0_23
| ~ spl0_26 ),
inference(avatar_contradiction_clause,[],[f697]) ).
cnf(s2,plain,
( ~ spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f266]) ).
cnf(s3,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_5 ),
inference(sat_conversion,[],[f271]) ).
cnf(s5,plain,
spl0_1,
inference(sat_conversion,[],[f273]) ).
cnf(s11,plain,
( ~ spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f305]) ).
cnf(s13,plain,
spl0_8,
inference(sat_conversion,[],[f313]) ).
cnf(s15,plain,
spl0_7,
inference(sat_conversion,[],[f315]) ).
cnf(s16,plain,
( spl0_2
| spl0_3
| ~ spl0_7 ),
inference(sat_conversion,[],[f319]) ).
cnf(s17,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12 ),
inference(sat_conversion,[],[f332]) ).
cnf(s19,plain,
( spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f341]) ).
cnf(s22,plain,
( spl0_5
| spl0_15 ),
inference(sat_conversion,[],[f412]) ).
cnf(s27,plain,
( spl0_5
| ~ spl0_7
| spl0_20 ),
inference(sat_conversion,[],[f495]) ).
cnf(s32,plain,
( ~ spl0_7
| ~ spl0_23
| ~ spl0_26 ),
inference(sat_conversion,[],[f539]) ).
cnf(s33,plain,
( spl0_5
| spl0_26 ),
inference(sat_conversion,[],[f543]) ).
cnf(s39,plain,
( ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_15
| ~ spl0_20
| spl0_23
| ~ spl0_26 ),
inference(sat_conversion,[],[f698]) ).
cnf(s41,plain,
spl0_12,
inference(rat,[],[s11,s15]) ).
cnf(s45,plain,
( ~ spl0_2
| spl0_5 ),
inference(rat,[],[s3,s5]) ).
cnf(s47,plain,
( ~ spl0_4
| ~ spl0_3
| spl0_2 ),
inference(rat,[],[s39,s32,s22,s27,s33,s19,s13,s15]) ).
cnf(s48,plain,
spl0_2,
inference(rat,[],[s47,s2,s16,s15]) ).
cnf(s49,plain,
~ spl0_5,
inference(rat,[],[s17,s41,s15,s5,s48]) ).
cnf(s51,plain,
$false,
inference(rat,[],[s45,s49,s48]) ).
fof(f699,plain,
$false,
inference(avatar_sat_refutation,[],[s51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC111-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n001.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 08:00:47 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 6.58/1.97 % (199405)Input is clausal, will run a generic CNF schedule.
% 6.58/1.97 % (199410)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=3097306333:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 6.58/1.97 % (199413)lrs+10_1_sil=8000:sp=occurrence:random_seed=3696415878:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 6.58/1.97 % (199412)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2118449670:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 6.58/1.97 % (199411)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1299216568:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 6.58/1.97 % (199414)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4118577781:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 6.58/1.97 % (199415)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=426921632:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 6.58/1.97 % (199416)dis-21_1_sil=8000:lcm=predicate:random_seed=2378741093: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)
% 6.58/1.97 % (199416)Instruction limit reached!
% 6.58/1.97 % (199416)------------------------------
% 6.58/1.97 % (199416)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.58/1.97 % (199416)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.58/1.97 % (199416)CaDiCaL version: 2.1.3
% 6.58/1.97 % (199416)Termination reason: Instruction limit
% 6.58/1.97 % (199416)Termination phase: Saturation
% 6.58/1.97 % (199416)Time elapsed: 0.028 s
% 6.58/1.97 % (199416)Peak memory usage: 88 MB
% 6.58/1.97 % (199416)Instructions burned: 120 (million)
% 6.58/1.97 % (199414)Instruction limit reached!
% 6.58/1.97 % (199414)------------------------------
% 6.58/1.97 % (199414)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.58/1.97 % (199414)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.58/1.97 % (199414)CaDiCaL version: 2.1.3
% 6.58/1.97 % (199414)Termination reason: Instruction limit
% 6.58/1.97 % (199414)Termination phase: Saturation
% 6.58/1.97 % (199414)Time elapsed: 0.066 s
% 6.58/1.97 % (199414)Peak memory usage: 88 MB
% 6.58/1.97 % (199414)Instructions burned: 115 (million)
% 6.58/1.97 % (199413)Instruction limit reached!
% 6.58/1.97 % (199413)------------------------------
% 6.58/1.97 % (199413)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.58/1.97 % (199413)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.58/1.97 % (199413)CaDiCaL version: 2.1.3
% 6.58/1.97 % (199413)Termination reason: Instruction limit
% 6.58/1.97 % (199413)Termination phase: Saturation
% 6.58/1.97 % (199413)Time elapsed: 0.066 s
% 6.58/1.97 % (199413)Peak memory usage: 89 MB
% 6.58/1.97 % (199413)Instructions burned: 107 (million)
% 6.58/1.97 % (199415)Instruction limit reached!
% 6.58/1.97 % (199415)------------------------------
% 6.58/1.97 % (199415)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.58/1.97 % (199415)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.58/1.97 % (199415)CaDiCaL version: 2.1.3
% 6.58/1.97 % (199415)Termination reason: Instruction limit
% 6.58/1.97 % (199415)Termination phase: Saturation
% 6.58/1.97 % (199415)Time elapsed: 0.124 s
% 6.58/1.97 % (199415)Peak memory usage: 90 MB
% 6.58/1.97 % (199415)Instructions burned: 181 (million)
% 6.58/1.97 % (199424)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=3439445100:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 6.58/1.97 % (199424)Refutation not found, incomplete strategy
% 6.58/1.97 % (199424)------------------------------
% 6.58/1.97 % (199424)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.58/1.97 % (199424)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.58/1.97 % (199424)CaDiCaL version: 2.1.3
% 6.58/1.97 % (199424)Termination reason: Refutation not found, incomplete strategy
% 6.58/1.97 % (199424)Time elapsed: 0.003 s
% 6.58/1.97 % (199424)Peak memory usage: 88 MB
% 6.58/1.97 % (199424)Instructions burned: 5 (million)
% 6.58/1.97 % (199426)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1056274753:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 6.58/1.97 % (199425)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1641510502: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)
% 6.58/1.97 % (199427)lrs+10_64_to=lpo:sil=8000:random_seed=2420419519:i=126:bd=preordered_2997 on theBenchmark for (2997ds/126Mi)
% 6.58/1.97 % (199424)------------------------------
% 6.58/1.97 % (199424)------------------------------
% 6.58/1.97 % (199426)Instruction limit reached!
% 6.58/1.97 % (199426)------------------------------
% 6.58/1.97 % (199426)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.58/1.97 % (199426)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.58/1.97 % (199426)CaDiCaL version: 2.1.3
% 6.58/1.97 % (199426)Termination reason: Instruction limit
% 6.58/1.97 % (199426)Termination phase: Saturation
% 6.58/1.97 % (199426)Time elapsed: 0.087 s
% 6.58/1.97 % (199426)Peak memory usage: 88 MB
% 6.58/1.97 % (199426)Instructions burned: 219 (million)
% 6.58/1.97 % (199425)Instruction limit reached!
% 6.58/1.97 % (199425)------------------------------
% 6.58/1.97 % (199425)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.58/1.97 % (199425)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.58/1.97 % (199425)CaDiCaL version: 2.1.3
% 6.58/1.97 % (199425)Termination reason: Instruction limit
% 6.58/1.97 % (199425)Termination phase: Saturation
% 6.58/1.97 % (199425)Time elapsed: 0.102 s
% 6.58/1.97 % (199425)Peak memory usage: 91 MB
% 6.58/1.97 % (199425)Instructions burned: 189 (million)
% 6.58/1.97 % (199427)Instruction limit reached!
% 6.58/1.97 % (199427)------------------------------
% 6.58/1.97 % (199427)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.58/1.97 % (199427)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.58/1.97 % (199427)CaDiCaL version: 2.1.3
% 6.58/1.97 % (199427)Termination reason: Instruction limit
% 6.58/1.97 % (199427)Termination phase: Saturation
% 6.58/1.97 % (199427)Time elapsed: 0.069 s
% 6.58/1.97 % (199427)Peak memory usage: 90 MB
% 6.58/1.97 % (199427)Instructions burned: 128 (million)
% 6.58/1.97 % (199432)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=1719549144:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 6.58/1.97 % (199433)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=816220272:i=157:gtg=all_2995 on theBenchmark for (2995ds/157Mi)
% 6.58/1.97 % (199432)Instruction limit reached!
% 6.58/1.97 % (199432)------------------------------
% 6.58/1.97 % (199432)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.58/1.97 % (199432)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.58/1.97 % (199432)CaDiCaL version: 2.1.3
% 6.58/1.97 % (199432)Termination reason: Instruction limit
% 6.58/1.97 % (199432)Termination phase: Saturation
% 6.58/1.97 % (199432)Time elapsed: 0.067 s
% 6.58/1.97 % (199432)Peak memory usage: 90 MB
% 6.58/1.97 % (199432)Instructions burned: 198 (million)
% 6.58/1.97 % (199434)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=1775883466:i=3394:sd=4:ss=included:sgt=64_2994 on theBenchmark for (2994ds/3394Mi)
% 6.58/1.97 % (199435)lrs+1011_5_to=lpo:sil=8000:tgt=full:plsq=on:prc=on:drc=off:plsqr=31,4:sp=occurrence:urr=on:nwc=0.8:s2agt=16:br=off:random_seed=80877723:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2994 on theBenchmark for (2994ds/106Mi)
% 6.58/1.97 % (199433)Instruction limit reached!
% 6.58/1.97 % (199433)------------------------------
% 6.58/1.97 % (199433)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.58/1.97 % (199433)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.58/1.97 % (199433)CaDiCaL version: 2.1.3
% 6.58/1.97 % (199433)Termination reason: Instruction limit
% 6.58/1.97 % (199433)Termination phase: Saturation
% 6.58/1.97 % (199433)Time elapsed: 0.094 s
% 6.58/1.97 % (199433)Peak memory usage: 91 MB
% 6.58/1.97 % (199433)Instructions burned: 158 (million)
% 6.58/1.97 % (199435)Instruction limit reached!
% 6.58/1.97 % (199435)------------------------------
% 6.58/1.97 % (199435)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.58/1.97 % (199435)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.58/1.97 % (199435)CaDiCaL version: 2.1.3
% 6.58/1.97 % (199435)Termination reason: Instruction limit
% 6.58/1.97 % (199435)Termination phase: Saturation
% 6.58/1.97 % (199435)Time elapsed: 0.058 s
% 6.58/1.97 % (199435)Peak memory usage: 91 MB
% 6.58/1.97 % (199435)Instructions burned: 108 (million)
% 6.58/1.97 % (199439)lrs+2_4096_sil=8000:plsq=on:plsqr=12672147,131072:sos=on:spb=goal:lcm=predicate:random_seed=983718247:i=107_2993 on theBenchmark for (2993ds/107Mi)
% 6.58/1.97 % (199439)Instruction limit reached!
% 6.58/1.97 % (199439)------------------------------
% 6.58/1.97 % (199439)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.58/1.97 % (199439)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.58/1.97 % (199439)CaDiCaL version: 2.1.3
% 6.58/1.97 % (199439)Termination reason: Instruction limit
% 6.58/1.97 % (199439)Termination phase: Saturation
% 6.58/1.97 % (199439)Time elapsed: 0.036 s
% 6.58/1.97 % (199439)Peak memory usage: 89 MB
% 6.58/1.97 % (199439)Instructions burned: 108 (million)
% 6.58/1.97 % (199410)First to succeed.
% 6.58/1.97 % (199410)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-199405"
% 6.58/1.97 % (199441)lrs+1011_20_sil=64000:tgt=ground:plsq=on:fde=unused:plsqc=1:plsqr=14,1:plsql=on:nwc=0.6:random_seed=860085186:st=6:i=242:gtgl=5:kws=arity_squared:av=off:gtg=exists_sym:ss=included_2992 on theBenchmark for (2992ds/242Mi)
% 6.58/1.97 % (199442)lrs+1010_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:tgt=ground:npcc=on:sims=off:random_seed=641760615:cond=fast:i=5208:av=off_2992 on theBenchmark for (2992ds/5208Mi)
% 6.58/1.97 % (199444)lrs+1011_16_sil=32000:erd=off:bce=on:random_seed=557890704:i=134:sd=2:doe=on:ss=axioms:sgt=14_2991 on theBenchmark for (2991ds/134Mi)
% 6.58/1.97 % (199444)Instruction limit reached!
% 6.58/1.97 % (199444)------------------------------
% 6.58/1.97 % (199444)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.58/1.97 % (199444)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.58/1.97 % (199444)CaDiCaL version: 2.1.3
% 6.58/1.97 % (199444)Termination reason: Instruction limit
% 6.58/1.97 % (199444)Termination phase: Saturation
% 6.58/1.97 % (199444)Time elapsed: 0.049 s
% 6.58/1.97 % (199444)Peak memory usage: 89 MB
% 6.58/1.97 % (199444)Instructions burned: 135 (million)
% 6.58/1.97 % (199441)Instruction limit reached!
% 6.58/1.97 % (199441)------------------------------
% 6.58/1.97 % (199441)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.58/1.97 % (199441)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.58/1.97 % (199441)CaDiCaL version: 2.1.3
% 6.58/1.97 % (199441)Termination reason: Instruction limit
% 6.58/1.97 % (199441)Termination phase: Saturation
% 6.58/1.97 % (199441)Time elapsed: 0.149 s
% 6.58/1.97 % (199441)Peak memory usage: 89 MB
% 6.58/1.97 % (199441)Instructions burned: 243 (million)
% 6.58/1.97 % (199410)Refutation found. Thanks to Tanya!
% 6.58/1.97 % SZS status Unsatisfiable for theBenchmark
% 6.58/1.97 % SZS output start Proof for theBenchmark
% See solution above
% 8.32/2.07 % (199410)------------------------------
% 8.32/2.07 % (199410)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.32/2.07 % (199410)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.32/2.07 % (199410)CaDiCaL version: 2.1.3
% 8.32/2.07 % (199410)Termination reason: Refutation
% 8.32/2.07 % (199410)Time elapsed: 0.708 s
% 8.32/2.07 % (199410)Peak memory usage: 131 MB
% 8.32/2.07 % (199410)Instructions burned: 1047 (million)
% 8.32/2.07 % (199410)------------------------------
% 8.32/2.07 % (199410)------------------------------
% 8.32/2.07 % (199405)Success in time 1.114 s
% 8.32/2.07 % Vampire exiting
%------------------------------------------------------------------------------