%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV406+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:09:08 PM UTC 2026
% Result : Theorem 3.06s 1.08s
% Output : Refutation 3.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 20
% Syntax : Number of formulae : 125 ( 9 unt; 14 def)
% Number of atoms : 354 ( 21 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 389 ( 160 ~; 167 |; 26 &)
% ( 24 <=>; 11 =>; 0 <=; 1 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 15 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-3 aty)
% Number of variables : 209 ( 0 sgn 186 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( less_than(X0,X1)
| less_than(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality) ).
fof(f4,axiom,
! [X0,X1] :
( strictly_less_than(X0,X1)
<=> ( less_than(X0,X1)
& ~ less_than(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stricly_smaller_definition) ).
fof(f11,axiom,
! [X0,X1,X2,X3,X4] :
( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
<=> ( pair_in_list(X0,X2,X4)
| ( X1 = X2
& X3 = X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax23) ).
fof(f25,axiom,
! [X0,X1,X2,X3,X4] :
( less_than(X4,X3)
=> ( check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
<=> check_cpq(triple(X0,X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax37) ).
fof(f26,axiom,
! [X0,X1,X2,X3,X4] :
( strictly_less_than(X3,X4)
=> ( check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
<=> $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax38) ).
fof(f42,conjecture,
! [X0] :
( ! [X1,X2] :
( check_cpq(triple(X1,X0,X2))
<=> ! [X3,X4] :
( pair_in_list(X0,X3,X4)
=> less_than(X4,X3) ) )
=> ! [X5,X6,X7,X8] :
( check_cpq(triple(X5,insert_slb(X0,pair(X7,X8)),X6))
<=> ! [X9,X10] :
( pair_in_list(insert_slb(X0,pair(X7,X8)),X9,X10)
=> less_than(X10,X9) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l42_co) ).
fof(f43,negated_conjecture,
~ ! [X0] :
( ! [X1,X2] :
( check_cpq(triple(X1,X0,X2))
<=> ! [X3,X4] :
( pair_in_list(X0,X3,X4)
=> less_than(X4,X3) ) )
=> ! [X5,X6,X7,X8] :
( check_cpq(triple(X5,insert_slb(X0,pair(X7,X8)),X6))
<=> ! [X9,X10] :
( pair_in_list(insert_slb(X0,pair(X7,X8)),X9,X10)
=> less_than(X10,X9) ) ) ),
inference(negated_conjecture,[status(cth)],[f42]) ).
fof(f44,plain,
! [X0,X1,X2,X3,X4] :
( strictly_less_than(X3,X4)
=> ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2)) ),
inference(true_and_false_elimination,[],[f26]) ).
fof(f45,plain,
! [X0,X1,X2,X3,X4] :
( strictly_less_than(X3,X4)
=> ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2)) ),
inference(flattening,[],[f44]) ).
fof(f52,plain,
! [X0,X1] :
( ( less_than(X0,X1)
& ~ less_than(X1,X0) )
=> strictly_less_than(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f55,plain,
! [X0,X1] :
( strictly_less_than(X0,X1)
| ~ less_than(X0,X1)
| less_than(X1,X0) ),
inference(ennf_transformation,[],[f52]) ).
fof(f56,plain,
! [X0,X1] :
( strictly_less_than(X0,X1)
| ~ less_than(X0,X1)
| less_than(X1,X0) ),
inference(flattening,[],[f55]) ).
fof(f67,plain,
! [X0,X1,X2,X3,X4] :
( ( check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
<=> check_cpq(triple(X0,X1,X2)) )
| ~ less_than(X4,X3) ),
inference(ennf_transformation,[],[f25]) ).
fof(f68,plain,
! [X0,X1,X2,X3,X4] :
( ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
| ~ strictly_less_than(X3,X4) ),
inference(ennf_transformation,[],[f45]) ).
fof(f82,plain,
? [X0] :
( ? [X5,X6,X7,X8] :
( check_cpq(triple(X5,insert_slb(X0,pair(X7,X8)),X6))
<~> ! [X9,X10] :
( less_than(X10,X9)
| ~ pair_in_list(insert_slb(X0,pair(X7,X8)),X9,X10) ) )
& ! [X1,X2] :
( check_cpq(triple(X1,X0,X2))
<=> ! [X3,X4] :
( less_than(X4,X3)
| ~ pair_in_list(X0,X3,X4) ) ) ),
inference(ennf_transformation,[],[f43]) ).
fof(f85,plain,
! [X0,X1,X2,X3,X4] :
( ( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
| ( ~ pair_in_list(X0,X2,X4)
& ( X1 != X2
| X3 != X4 ) ) )
& ( pair_in_list(X0,X2,X4)
| ( X1 = X2
& X3 = X4 )
| ~ pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f86,plain,
! [X0,X1,X2,X3,X4] :
( ( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
| ( ~ pair_in_list(X0,X2,X4)
& ( X1 != X2
| X3 != X4 ) ) )
& ( pair_in_list(X0,X2,X4)
| ( X1 = X2
& X3 = X4 )
| ~ pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4) ) ),
inference(flattening,[],[f85]) ).
fof(f87,plain,
! [X0,X1,X2,X3,X4] :
( ( ( check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
| ~ check_cpq(triple(X0,X1,X2)) )
& ( check_cpq(triple(X0,X1,X2))
| ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2)) ) )
| ~ less_than(X4,X3) ),
inference(nnf_transformation,[],[f67]) ).
fof(f89,plain,
? [X0] :
( ? [X5,X6,X7,X8] :
( ( ? [X9,X10] :
( ~ less_than(X10,X9)
& pair_in_list(insert_slb(X0,pair(X7,X8)),X9,X10) )
| ~ check_cpq(triple(X5,insert_slb(X0,pair(X7,X8)),X6)) )
& ( ! [X9,X10] :
( less_than(X10,X9)
| ~ pair_in_list(insert_slb(X0,pair(X7,X8)),X9,X10) )
| check_cpq(triple(X5,insert_slb(X0,pair(X7,X8)),X6)) ) )
& ! [X1,X2] :
( ( check_cpq(triple(X1,X0,X2))
| ? [X3,X4] :
( ~ less_than(X4,X3)
& pair_in_list(X0,X3,X4) ) )
& ( ! [X3,X4] :
( less_than(X4,X3)
| ~ pair_in_list(X0,X3,X4) )
| ~ check_cpq(triple(X1,X0,X2)) ) ) ),
inference(nnf_transformation,[],[f82]) ).
fof(f90,plain,
? [X0] :
( ? [X1,X2,X3,X4] :
( ( ? [X5,X6] :
( ~ less_than(X6,X5)
& pair_in_list(insert_slb(X0,pair(X3,X4)),X5,X6) )
| ~ check_cpq(triple(X1,insert_slb(X0,pair(X3,X4)),X2)) )
& ( ! [X7,X8] :
( less_than(X8,X7)
| ~ pair_in_list(insert_slb(X0,pair(X3,X4)),X7,X8) )
| check_cpq(triple(X1,insert_slb(X0,pair(X3,X4)),X2)) ) )
& ! [X9,X10] :
( ( check_cpq(triple(X9,X0,X10))
| ? [X11,X12] :
( ~ less_than(X12,X11)
& pair_in_list(X0,X11,X12) ) )
& ( ! [X13,X14] :
( less_than(X14,X13)
| ~ pair_in_list(X0,X13,X14) )
| ~ check_cpq(triple(X9,X0,X10)) ) ) ),
inference(rectify,[],[f89]) ).
fof(f91,plain,
( ( ( ~ less_than(sK6,sK5)
& pair_in_list(insert_slb(sK0,pair(sK3,sK4)),sK5,sK6) )
| ~ check_cpq(triple(sK1,insert_slb(sK0,pair(sK3,sK4)),sK2)) )
& ( ! [X7,X8] :
( less_than(X8,X7)
| ~ pair_in_list(insert_slb(sK0,pair(sK3,sK4)),X7,X8) )
| check_cpq(triple(sK1,insert_slb(sK0,pair(sK3,sK4)),sK2)) )
& ! [X9,X10] :
( ( check_cpq(triple(X9,sK0,X10))
| ( ~ less_than(sK8,sK7)
& pair_in_list(sK0,sK7,sK8) ) )
& ( ! [X13,X14] :
( less_than(X14,X13)
| ~ pair_in_list(sK0,X13,X14) )
| ~ check_cpq(triple(X9,sK0,X10)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5),skolemize(X6,sK6),skolemize(X11,sK7),skolemize(X12,sK8)],[f90]) ).
fof(f93,plain,
! [X0,X1] :
( less_than(X0,X1)
| less_than(X1,X0) ),
inference(cnf_transformation,[],[f2]) ).
fof(f95,plain,
! [X0,X1] :
( strictly_less_than(X0,X1)
| ~ less_than(X0,X1)
| less_than(X1,X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f104,plain,
! [X2,X3,X0,X1,X4] :
( ~ pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
| X3 = X4
| pair_in_list(X0,X2,X4) ),
inference(cnf_transformation,[],[f86]) ).
fof(f105,plain,
! [X2,X3,X0,X1,X4] :
( ~ pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
| X1 = X2
| pair_in_list(X0,X2,X4) ),
inference(cnf_transformation,[],[f86]) ).
fof(f106,plain,
! [X2,X3,X0,X1,X4] :
( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
| X1 != X2
| X3 != X4 ),
inference(cnf_transformation,[],[f86]) ).
fof(f107,plain,
! [X2,X3,X0,X1,X4] :
( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
| ~ pair_in_list(X0,X2,X4) ),
inference(cnf_transformation,[],[f86]) ).
fof(f121,plain,
! [X2,X3,X0,X1,X4] :
( ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
| check_cpq(triple(X0,X1,X2))
| ~ less_than(X4,X3) ),
inference(cnf_transformation,[],[f87]) ).
fof(f122,plain,
! [X2,X3,X0,X1,X4] :
( ~ check_cpq(triple(X0,X1,X2))
| check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
| ~ less_than(X4,X3) ),
inference(cnf_transformation,[],[f87]) ).
fof(f123,plain,
! [X2,X3,X0,X1,X4] :
( ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
| ~ strictly_less_than(X3,X4) ),
inference(cnf_transformation,[],[f68]) ).
fof(f140,plain,
! [X10,X9,X14,X13] :
( less_than(X14,X13)
| ~ pair_in_list(sK0,X13,X14)
| ~ check_cpq(triple(X9,sK0,X10)) ),
inference(cnf_transformation,[],[f91]) ).
fof(f141,plain,
! [X10,X9] :
( check_cpq(triple(X9,sK0,X10))
| pair_in_list(sK0,sK7,sK8) ),
inference(cnf_transformation,[],[f91]) ).
fof(f142,plain,
! [X10,X9] :
( check_cpq(triple(X9,sK0,X10))
| ~ less_than(sK8,sK7) ),
inference(cnf_transformation,[],[f91]) ).
fof(f143,plain,
! [X8,X7] :
( less_than(X8,X7)
| ~ pair_in_list(insert_slb(sK0,pair(sK3,sK4)),X7,X8)
| check_cpq(triple(sK1,insert_slb(sK0,pair(sK3,sK4)),sK2)) ),
inference(cnf_transformation,[],[f91]) ).
fof(f144,plain,
( pair_in_list(insert_slb(sK0,pair(sK3,sK4)),sK5,sK6)
| ~ check_cpq(triple(sK1,insert_slb(sK0,pair(sK3,sK4)),sK2)) ),
inference(cnf_transformation,[],[f91]) ).
fof(f145,plain,
( ~ less_than(sK6,sK5)
| ~ check_cpq(triple(sK1,insert_slb(sK0,pair(sK3,sK4)),sK2)) ),
inference(cnf_transformation,[],[f91]) ).
fof(f147,plain,
! [X2,X3,X0,X4] :
( pair_in_list(insert_slb(X0,pair(X2,X3)),X2,X4)
| X3 != X4 ),
inference(equality_resolution,[],[f106]) ).
fof(f148,plain,
! [X2,X0,X4] : pair_in_list(insert_slb(X0,pair(X2,X4)),X2,X4),
inference(equality_resolution,[],[f147]) ).
fof(f150,definition,
( spl9_1
<=> ! [X9,X10] : ~ check_cpq(triple(X9,sK0,X10)) ),
introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition]) ).
fof(f151,plain,
( ! [X10,X9] : ~ check_cpq(triple(X9,sK0,X10))
| ~ spl9_1 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f153,definition,
( spl9_2
<=> ! [X13,X14] :
( less_than(X14,X13)
| ~ pair_in_list(sK0,X13,X14) ) ),
introduced(definition,[new_symbols(definition,[spl9_2])],[avatar_definition]) ).
fof(f154,plain,
( ! [X14,X13] :
( ~ pair_in_list(sK0,X13,X14)
| less_than(X14,X13) )
| ~ spl9_2 ),
inference(avatar_component_clause,[],[f153]) ).
fof(f155,plain,
( spl9_1
| spl9_2 ),
inference(avatar_split_clause,[],[f140,f153,f150]) ).
fof(f157,definition,
( spl9_3
<=> pair_in_list(sK0,sK7,sK8) ),
introduced(definition,[new_symbols(definition,[spl9_3])],[avatar_definition]) ).
fof(f159,plain,
( pair_in_list(sK0,sK7,sK8)
| ~ spl9_3 ),
inference(avatar_component_clause,[],[f157]) ).
fof(f161,definition,
( spl9_4
<=> ! [X9,X10] : check_cpq(triple(X9,sK0,X10)) ),
introduced(definition,[new_symbols(definition,[spl9_4])],[avatar_definition]) ).
fof(f162,plain,
( ! [X10,X9] : check_cpq(triple(X9,sK0,X10))
| ~ spl9_4 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f163,plain,
( spl9_3
| spl9_4 ),
inference(avatar_split_clause,[],[f141,f161,f157]) ).
fof(f165,definition,
( spl9_5
<=> less_than(sK8,sK7) ),
introduced(definition,[new_symbols(definition,[spl9_5])],[avatar_definition]) ).
fof(f168,plain,
( ~ spl9_5
| spl9_4 ),
inference(avatar_split_clause,[],[f142,f161,f165]) ).
fof(f170,definition,
( spl9_6
<=> check_cpq(triple(sK1,insert_slb(sK0,pair(sK3,sK4)),sK2)) ),
introduced(definition,[new_symbols(definition,[spl9_6])],[avatar_definition]) ).
fof(f171,plain,
( ~ check_cpq(triple(sK1,insert_slb(sK0,pair(sK3,sK4)),sK2))
| spl9_6 ),
inference(avatar_component_clause,[],[f170]) ).
fof(f172,plain,
( check_cpq(triple(sK1,insert_slb(sK0,pair(sK3,sK4)),sK2))
| ~ spl9_6 ),
inference(avatar_component_clause,[],[f170]) ).
fof(f174,definition,
( spl9_7
<=> ! [X7,X8] :
( less_than(X8,X7)
| ~ pair_in_list(insert_slb(sK0,pair(sK3,sK4)),X7,X8) ) ),
introduced(definition,[new_symbols(definition,[spl9_7])],[avatar_definition]) ).
fof(f175,plain,
( ! [X8,X7] :
( ~ pair_in_list(insert_slb(sK0,pair(sK3,sK4)),X7,X8)
| less_than(X8,X7) )
| ~ spl9_7 ),
inference(avatar_component_clause,[],[f174]) ).
fof(f176,plain,
( spl9_6
| spl9_7 ),
inference(avatar_split_clause,[],[f143,f174,f170]) ).
fof(f178,definition,
( spl9_8
<=> pair_in_list(insert_slb(sK0,pair(sK3,sK4)),sK5,sK6) ),
introduced(definition,[new_symbols(definition,[spl9_8])],[avatar_definition]) ).
fof(f180,plain,
( pair_in_list(insert_slb(sK0,pair(sK3,sK4)),sK5,sK6)
| ~ spl9_8 ),
inference(avatar_component_clause,[],[f178]) ).
fof(f181,plain,
( ~ spl9_6
| spl9_8 ),
inference(avatar_split_clause,[],[f144,f178,f170]) ).
fof(f183,definition,
( spl9_9
<=> less_than(sK6,sK5) ),
introduced(definition,[new_symbols(definition,[spl9_9])],[avatar_definition]) ).
fof(f185,plain,
( ~ less_than(sK6,sK5)
| spl9_9 ),
inference(avatar_component_clause,[],[f183]) ).
fof(f186,plain,
( ~ spl9_6
| ~ spl9_9 ),
inference(avatar_split_clause,[],[f145,f183,f170]) ).
fof(f187,plain,
( less_than(sK8,sK7)
| ~ spl9_2
| ~ spl9_3 ),
inference(resolution,[],[f154,f159]) ).
fof(f190,plain,
( spl9_5
| ~ spl9_2
| ~ spl9_3 ),
inference(avatar_split_clause,[],[f187,f157,f153,f165]) ).
fof(f192,plain,
( less_than(sK4,sK3)
| ~ spl9_7 ),
inference(resolution,[],[f148,f175]) ).
fof(f193,plain,
! [X0,X1] :
( strictly_less_than(X0,X1)
| less_than(X1,X0) ),
inference(forward_subsumption_resolution,[],[f95,f93]) ).
fof(f201,plain,
( ! [X0,X1] :
( ~ pair_in_list(sK0,X0,X1)
| less_than(X1,X0) )
| ~ spl9_7 ),
inference(resolution,[],[f107,f175]) ).
fof(f229,plain,
( ! [X2,X3,X0,X1] :
( check_cpq(triple(X0,insert_slb(sK0,pair(X1,X2)),X3))
| ~ less_than(X2,X1) )
| ~ spl9_4 ),
inference(resolution,[],[f122,f162]) ).
fof(f231,plain,
( ~ less_than(sK4,sK3)
| ~ spl9_4
| spl9_6 ),
inference(resolution,[],[f229,f171]) ).
fof(f236,plain,
( $false
| ~ spl9_4
| spl9_6
| ~ spl9_7 ),
inference(forward_subsumption_resolution,[],[f231,f192]) ).
fof(f237,plain,
( ~ spl9_4
| spl9_6
| ~ spl9_7 ),
inference(avatar_contradiction_clause,[],[f236]) ).
fof(f238,plain,
( spl9_2
| ~ spl9_7 ),
inference(avatar_split_clause,[],[f201,f174,f153]) ).
fof(f250,plain,
( sK3 = sK5
| pair_in_list(sK0,sK5,sK6)
| ~ spl9_8 ),
inference(resolution,[],[f180,f105]) ).
fof(f251,plain,
( sK4 = sK6
| pair_in_list(sK0,sK5,sK6)
| ~ spl9_8 ),
inference(resolution,[],[f180,f104]) ).
fof(f253,definition,
( spl9_10
<=> pair_in_list(sK0,sK5,sK6) ),
introduced(definition,[new_symbols(definition,[spl9_10])],[avatar_definition]) ).
fof(f255,plain,
( pair_in_list(sK0,sK5,sK6)
| ~ spl9_10 ),
inference(avatar_component_clause,[],[f253]) ).
fof(f257,definition,
( spl9_11
<=> sK4 = sK6 ),
introduced(definition,[new_symbols(definition,[spl9_11])],[avatar_definition]) ).
fof(f259,plain,
( sK4 = sK6
| ~ spl9_11 ),
inference(avatar_component_clause,[],[f257]) ).
fof(f260,plain,
( spl9_10
| spl9_11
| ~ spl9_8 ),
inference(avatar_split_clause,[],[f251,f178,f257,f253]) ).
fof(f262,definition,
( spl9_12
<=> sK3 = sK5 ),
introduced(definition,[new_symbols(definition,[spl9_12])],[avatar_definition]) ).
fof(f264,plain,
( sK3 = sK5
| ~ spl9_12 ),
inference(avatar_component_clause,[],[f262]) ).
fof(f265,plain,
( spl9_10
| spl9_12
| ~ spl9_8 ),
inference(avatar_split_clause,[],[f250,f178,f262,f253]) ).
fof(f268,plain,
( less_than(sK6,sK5)
| ~ spl9_2
| ~ spl9_10 ),
inference(resolution,[],[f255,f154]) ).
fof(f269,plain,
( $false
| ~ spl9_2
| spl9_9
| ~ spl9_10 ),
inference(forward_subsumption_resolution,[],[f268,f185]) ).
fof(f270,plain,
( ~ spl9_2
| spl9_9
| ~ spl9_10 ),
inference(avatar_contradiction_clause,[],[f269]) ).
fof(f271,plain,
( check_cpq(triple(sK1,sK0,sK2))
| ~ less_than(sK4,sK3)
| ~ spl9_6 ),
inference(resolution,[],[f172,f121]) ).
fof(f272,plain,
( ~ strictly_less_than(sK3,sK4)
| ~ spl9_6 ),
inference(resolution,[],[f172,f123]) ).
fof(f290,plain,
( ~ less_than(sK6,sK3)
| spl9_9
| ~ spl9_12 ),
inference(superposition,[],[f185,f264]) ).
fof(f291,plain,
( ~ less_than(sK4,sK3)
| spl9_9
| ~ spl9_11
| ~ spl9_12 ),
inference(forward_demodulation,[],[f290,f259]) ).
fof(f295,plain,
( less_than(sK4,sK3)
| ~ spl9_6 ),
inference(resolution,[],[f272,f193]) ).
fof(f315,plain,
( $false
| ~ spl9_6
| spl9_9
| ~ spl9_11
| ~ spl9_12 ),
inference(forward_subsumption_resolution,[],[f295,f291]) ).
fof(f316,plain,
( ~ spl9_6
| spl9_9
| ~ spl9_11
| ~ spl9_12 ),
inference(avatar_contradiction_clause,[],[f315]) ).
fof(f319,definition,
( spl9_13
<=> less_than(sK4,sK3) ),
introduced(definition,[new_symbols(definition,[spl9_13])],[avatar_definition]) ).
fof(f323,definition,
( spl9_14
<=> check_cpq(triple(sK1,sK0,sK2)) ),
introduced(definition,[new_symbols(definition,[spl9_14])],[avatar_definition]) ).
fof(f325,plain,
( check_cpq(triple(sK1,sK0,sK2))
| ~ spl9_14 ),
inference(avatar_component_clause,[],[f323]) ).
fof(f326,plain,
( ~ spl9_13
| spl9_14
| ~ spl9_6 ),
inference(avatar_split_clause,[],[f271,f170,f323,f319]) ).
fof(f343,plain,
( $false
| ~ spl9_1
| ~ spl9_14 ),
inference(forward_subsumption_resolution,[],[f325,f151]) ).
fof(f344,plain,
( ~ spl9_1
| ~ spl9_14 ),
inference(avatar_contradiction_clause,[],[f343]) ).
fof(f345,plain,
( spl9_13
| ~ spl9_6 ),
inference(avatar_split_clause,[],[f295,f170,f319]) ).
cnf(s1,plain,
( spl9_1
| spl9_2 ),
inference(sat_conversion,[],[f155]) ).
cnf(s2,plain,
( spl9_3
| spl9_4 ),
inference(sat_conversion,[],[f163]) ).
cnf(s3,plain,
( spl9_4
| ~ spl9_5 ),
inference(sat_conversion,[],[f168]) ).
cnf(s4,plain,
( spl9_6
| spl9_7 ),
inference(sat_conversion,[],[f176]) ).
cnf(s5,plain,
( ~ spl9_6
| spl9_8 ),
inference(sat_conversion,[],[f181]) ).
cnf(s6,plain,
( ~ spl9_6
| ~ spl9_9 ),
inference(sat_conversion,[],[f186]) ).
cnf(s8,plain,
( ~ spl9_2
| ~ spl9_3
| spl9_5 ),
inference(sat_conversion,[],[f190]) ).
cnf(s9,plain,
( ~ spl9_4
| spl9_6
| ~ spl9_7 ),
inference(sat_conversion,[],[f237]) ).
cnf(s10,plain,
( spl9_2
| ~ spl9_7 ),
inference(sat_conversion,[],[f238]) ).
cnf(s12,plain,
( ~ spl9_8
| spl9_10
| spl9_11 ),
inference(sat_conversion,[],[f260]) ).
cnf(s13,plain,
( ~ spl9_8
| spl9_10
| spl9_12 ),
inference(sat_conversion,[],[f265]) ).
cnf(s15,plain,
( ~ spl9_2
| spl9_9
| ~ spl9_10 ),
inference(sat_conversion,[],[f270]) ).
cnf(s16,plain,
( ~ spl9_6
| spl9_9
| ~ spl9_11
| ~ spl9_12 ),
inference(sat_conversion,[],[f316]) ).
cnf(s17,plain,
( ~ spl9_6
| ~ spl9_13
| spl9_14 ),
inference(sat_conversion,[],[f326]) ).
cnf(s19,plain,
( ~ spl9_1
| ~ spl9_14 ),
inference(sat_conversion,[],[f344]) ).
cnf(s20,plain,
( ~ spl9_6
| spl9_13 ),
inference(sat_conversion,[],[f345]) ).
cnf(s21,plain,
( spl9_6
| ~ spl9_4 ),
inference(rat,[],[s9,s4]) ).
cnf(s22,plain,
( ~ spl9_6
| ~ spl9_2 ),
inference(rat,[],[s16,s12,s13,s15,s5,s6]) ).
cnf(s23,plain,
~ spl9_2,
inference(rat,[],[s8,s2,s3,s21,s22]) ).
cnf(s24,plain,
~ spl9_7,
inference(rat,[],[s10,s23]) ).
cnf(s25,plain,
spl9_1,
inference(rat,[],[s1,s23]) ).
cnf(s26,plain,
spl9_6,
inference(rat,[],[s4,s24]) ).
cnf(s27,plain,
~ spl9_14,
inference(rat,[],[s19,s25]) ).
cnf(s29,plain,
spl9_13,
inference(rat,[],[s20,s26]) ).
cnf(s30,plain,
$false,
inference(rat,[],[s17,s29,s27,s26]) ).
fof(f346,plain,
$false,
inference(avatar_sat_refutation,[],[s30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV406+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n010.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 10:51:18 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 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
% 3.06/1.08 % (1844769)Detected formulas, will run a generic FOF schedule.
% 3.06/1.08 % (1844774)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=2238346904:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.06/1.08 % (1844779)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3600061386:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.06/1.08 % (1844780)dis-21_1_sil=8000:lcm=predicate:random_seed=1617167826:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.06/1.08 % (1844778)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=278873991:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.06/1.08 % (1844777)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3355217933:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.06/1.08 % (1844776)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3507770824:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.06/1.08 % (1844775)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=328472623:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.06/1.08 % (1844779)First to succeed.
% 3.06/1.08 % (1844779)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1844769"
% 3.06/1.08 % (1844778)Also succeeded, but the first one will report.
% 3.06/1.08 % (1844777)Instruction limit reached!
% 3.06/1.08 % (1844777)------------------------------
% 3.06/1.08 % (1844777)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.06/1.08 % (1844777)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.06/1.08 % (1844777)CaDiCaL version: 2.1.3
% 3.06/1.08 % (1844777)Termination reason: Instruction limit
% 3.06/1.08 % (1844777)Termination phase: Saturation
% 3.06/1.08 % (1844777)Time elapsed: 0.047 s
% 3.06/1.08 % (1844777)Peak memory usage: 88 MB
% 3.06/1.08 % (1844777)Instructions burned: 109 (million)
% 3.06/1.08 % (1844780)Instruction limit reached!
% 3.06/1.08 % (1844780)------------------------------
% 3.06/1.08 % (1844780)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.06/1.08 % (1844780)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.06/1.08 % (1844780)CaDiCaL version: 2.1.3
% 3.06/1.08 % (1844780)Termination reason: Instruction limit
% 3.06/1.08 % (1844780)Termination phase: Saturation
% 3.06/1.08 % (1844780)Time elapsed: 0.062 s
% 3.06/1.08 % (1844780)Peak memory usage: 89 MB
% 3.06/1.08 % (1844780)Instructions burned: 131 (million)
% 3.06/1.08 % (1844788)lrs+10_1_sil=8000:sp=occurrence:random_seed=1221402897:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.06/1.08 % (1844788)Also succeeded, but the first one will report.
% 3.06/1.08 % (1844789)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1853578557:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.06/1.08 % (1844779)Refutation found. Thanks to Tanya!
% 3.06/1.08 % SZS status Theorem for theBenchmark
% 3.06/1.08 % SZS output start Proof for theBenchmark
% See solution above
% 3.51/1.18 % (1844779)------------------------------
% 3.51/1.18 % (1844779)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.18 % (1844779)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.18 % (1844779)CaDiCaL version: 2.1.3
% 3.51/1.18 % (1844779)Termination reason: Refutation
% 3.51/1.18 % (1844779)Time elapsed: 0.013 s
% 3.51/1.18 % (1844779)Peak memory usage: 90 MB
% 3.51/1.18 % (1844779)Instructions burned: 15 (million)
% 3.51/1.18 % (1844779)------------------------------
% 3.51/1.18 % (1844779)------------------------------
% 3.51/1.18 % (1844769)Success in time 0.42 s
% 3.51/1.18 % Vampire exiting
%------------------------------------------------------------------------------