%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET980+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 12:45:07 PM UTC 2026
% Result : Theorem 0.09s 0.47s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 21
% Syntax : Number of formulae : 139 ( 23 unt; 16 def)
% Number of atoms : 342 ( 65 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 353 ( 150 ~; 159 |; 21 &)
% ( 19 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 17 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 132 ( 0 sgn 120 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( X0 = empty_set
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f4,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f7,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X0,X2)
& in(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(f11,conjecture,
! [X0,X1,X2,X3] :
( cartesian_product2(X0,X1) = cartesian_product2(X2,X3)
=> ( X0 = empty_set
| X1 = empty_set
| ( X0 = X2
& X1 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t134_zfmisc_1) ).
fof(f12,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( cartesian_product2(X0,X1) = cartesian_product2(X2,X3)
=> ( X0 = empty_set
| X1 = empty_set
| ( X0 = X2
& X1 = X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
fof(f15,plain,
? [X0,X1,X2,X3] :
( empty_set != X0
& empty_set != X1
& ( X0 != X2
| X1 != X3 )
& cartesian_product2(X0,X1) = cartesian_product2(X2,X3) ),
inference(ennf_transformation,[],[f12]) ).
fof(f16,plain,
? [X0,X1,X2,X3] :
( empty_set != X0
& empty_set != X1
& ( X0 != X2
| X1 != X3 )
& cartesian_product2(X0,X1) = cartesian_product2(X2,X3) ),
inference(flattening,[],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( in(X2,X0)
<~> in(X2,X1) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f18,plain,
! [X0] :
( ( X0 = empty_set
| ? [X1] : in(X1,X0) )
& ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f19,plain,
! [X0] :
( ( X0 = empty_set
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f18]) ).
fof(f20,plain,
! [X0] :
( ( X0 = empty_set
| in(sK0(X0),X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f19]) ).
fof(f21,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) )
& ( ( in(X0,X2)
& in(X1,X3) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f22,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) )
& ( ( in(X0,X2)
& in(X1,X3) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f21]) ).
fof(f27,plain,
( empty_set != sK3
& empty_set != sK4
& ( sK3 != sK5
| sK4 != sK6 )
& cartesian_product2(sK5,sK6) = cartesian_product2(sK3,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5),skolemize(X3,sK6)],[f16]) ).
fof(f28,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f29,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ in(sK7(X0,X1),X1)
| ~ in(sK7(X0,X1),X0) )
& ( in(sK7(X0,X1),X1)
| in(sK7(X0,X1),X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X2,sK7(X0,X1))],[f28]) ).
fof(f33,plain,
! [X0] :
( empty_set = X0
| in(sK0(X0),X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f34,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f4]) ).
fof(f37,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f38,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f39,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) ),
inference(cnf_transformation,[],[f22]) ).
fof(f45,plain,
cartesian_product2(sK5,sK6) = cartesian_product2(sK3,sK4),
inference(cnf_transformation,[],[f27]) ).
fof(f46,plain,
( sK3 != sK5
| sK4 != sK6 ),
inference(cnf_transformation,[],[f27]) ).
fof(f47,plain,
empty_set != sK4,
inference(cnf_transformation,[],[f27]) ).
fof(f48,plain,
empty_set != sK3,
inference(cnf_transformation,[],[f27]) ).
fof(f49,plain,
! [X0,X1] :
( X0 = X1
| in(sK7(X0,X1),X1)
| in(sK7(X0,X1),X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f50,plain,
! [X0,X1] :
( X0 = X1
| ~ in(sK7(X0,X1),X1)
| ~ in(sK7(X0,X1),X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f52,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) ),
inference(definition_unfolding,[],[f39,f34]) ).
fof(f53,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
inference(definition_unfolding,[],[f38,f34]) ).
fof(f54,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
inference(definition_unfolding,[],[f37,f34]) ).
fof(f59,plain,
! [X0] :
( ~ in(sK0(X0),X0)
| empty_set = X0 ),
inference(consistent_polarity_flipping,[],[f33]) ).
fof(f63,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X0,X2)
| in(X1,X3) ),
inference(consistent_polarity_flipping,[],[f52]) ).
fof(f64,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| ~ in(X0,X2) ),
inference(consistent_polarity_flipping,[],[f53]) ).
fof(f65,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| ~ in(X1,X3) ),
inference(consistent_polarity_flipping,[],[f54]) ).
fof(f68,plain,
! [X0,X1] :
( in(sK7(X0,X1),X1)
| X0 = X1
| in(sK7(X0,X1),X0) ),
inference(consistent_polarity_flipping,[],[f50]) ).
fof(f69,plain,
! [X0,X1] :
( ~ in(sK7(X0,X1),X1)
| ~ in(sK7(X0,X1),X0)
| X0 = X1 ),
inference(consistent_polarity_flipping,[],[f49]) ).
fof(f71,definition,
( spl8_1
<=> sK4 = sK6 ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
fof(f72,plain,
( sK4 = sK6
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f75,definition,
( spl8_2
<=> sK3 = sK5 ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
fof(f78,plain,
( ~ spl8_1
| ~ spl8_2 ),
inference(avatar_split_clause,[],[f46,f75,f71]) ).
fof(f111,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(sK3,sK4))
| ~ in(X0,sK5) ),
inference(superposition,[],[f64,f45]) ).
fof(f130,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(sK3,sK4))
| ~ in(X1,sK6) ),
inference(superposition,[],[f65,f45]) ).
fof(f154,plain,
! [X0,X1] :
( in(X0,sK3)
| in(X1,sK4)
| ~ in(X1,sK6) ),
inference(resolution,[],[f63,f130]) ).
fof(f155,plain,
! [X0,X1] :
( in(X0,sK3)
| in(X1,sK4)
| ~ in(X0,sK5) ),
inference(resolution,[],[f63,f111]) ).
fof(f163,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(sK3,sK4))
| in(X0,sK5)
| in(X1,sK6) ),
inference(superposition,[],[f63,f45]) ).
fof(f167,definition,
( spl8_6
<=> ! [X1] : in(X1,sK4) ),
introduced(definition,[new_symbols(definition,[spl8_6])],[avatar_definition]) ).
fof(f168,plain,
( ! [X1] : in(X1,sK4)
| ~ spl8_6 ),
inference(avatar_component_clause,[],[f167]) ).
fof(f170,definition,
( spl8_7
<=> ! [X0] :
( in(X0,sK3)
| ~ in(X0,sK5) ) ),
introduced(definition,[new_symbols(definition,[spl8_7])],[avatar_definition]) ).
fof(f171,plain,
( ! [X0] :
( in(X0,sK3)
| ~ in(X0,sK5) )
| ~ spl8_7 ),
inference(avatar_component_clause,[],[f170]) ).
fof(f172,plain,
( spl8_6
| spl8_7 ),
inference(avatar_split_clause,[],[f155,f170,f167]) ).
fof(f174,definition,
( spl8_8
<=> ! [X1] :
( in(X1,sK4)
| ~ in(X1,sK6) ) ),
introduced(definition,[new_symbols(definition,[spl8_8])],[avatar_definition]) ).
fof(f175,plain,
( ! [X1] :
( in(X1,sK4)
| ~ in(X1,sK6) )
| ~ spl8_8 ),
inference(avatar_component_clause,[],[f174]) ).
fof(f177,definition,
( spl8_9
<=> ! [X0] : in(X0,sK3) ),
introduced(definition,[new_symbols(definition,[spl8_9])],[avatar_definition]) ).
fof(f178,plain,
( ! [X0] : in(X0,sK3)
| ~ spl8_9 ),
inference(avatar_component_clause,[],[f177]) ).
fof(f179,plain,
( spl8_8
| spl8_9 ),
inference(avatar_split_clause,[],[f154,f177,f174]) ).
fof(f180,plain,
( empty_set = sK4
| ~ spl8_6 ),
inference(resolution,[],[f168,f59]) ).
fof(f183,plain,
( empty_set != empty_set
| ~ spl8_6 ),
inference(superposition,[],[f47,f180]) ).
fof(f194,plain,
( $false
| ~ spl8_6 ),
inference(trivial_inequality_removal,[],[f183]) ).
fof(f195,plain,
~ spl8_6,
inference(avatar_contradiction_clause,[],[f194]) ).
fof(f196,plain,
( ~ in(sK0(sK3),sK5)
| empty_set = sK3
| ~ spl8_7 ),
inference(resolution,[],[f171,f59]) ).
fof(f198,plain,
( ! [X0] :
( ~ in(sK7(sK3,X0),sK5)
| ~ in(sK7(sK3,X0),X0)
| sK3 = X0 )
| ~ spl8_7 ),
inference(resolution,[],[f171,f69]) ).
fof(f200,definition,
( spl8_10
<=> empty_set = sK3 ),
introduced(definition,[new_symbols(definition,[spl8_10])],[avatar_definition]) ).
fof(f202,plain,
( empty_set = sK3
| ~ spl8_10 ),
inference(avatar_component_clause,[],[f200]) ).
fof(f204,definition,
( spl8_11
<=> in(sK0(sK3),sK5) ),
introduced(definition,[new_symbols(definition,[spl8_11])],[avatar_definition]) ).
fof(f206,plain,
( ~ in(sK0(sK3),sK5)
| spl8_11 ),
inference(avatar_component_clause,[],[f204]) ).
fof(f207,plain,
( spl8_10
| ~ spl8_11
| ~ spl8_7 ),
inference(avatar_split_clause,[],[f196,f170,f204,f200]) ).
fof(f211,plain,
( ! [X0] :
( ~ in(sK7(sK4,X0),sK6)
| ~ in(sK7(sK4,X0),X0)
| sK4 = X0 )
| ~ spl8_8 ),
inference(resolution,[],[f175,f69]) ).
fof(f237,plain,
( ~ in(sK7(sK3,sK5),sK5)
| sK3 = sK5
| ~ spl8_7 ),
inference(factoring,[],[f198]) ).
fof(f240,definition,
( spl8_15
<=> in(sK7(sK3,sK5),sK5) ),
introduced(definition,[new_symbols(definition,[spl8_15])],[avatar_definition]) ).
fof(f242,plain,
( ~ in(sK7(sK3,sK5),sK5)
| spl8_15 ),
inference(avatar_component_clause,[],[f240]) ).
fof(f243,plain,
( spl8_2
| ~ spl8_15
| ~ spl8_7 ),
inference(avatar_split_clause,[],[f237,f170,f240,f75]) ).
fof(f244,plain,
( sK3 = sK5
| in(sK7(sK3,sK5),sK3)
| spl8_15 ),
inference(resolution,[],[f242,f68]) ).
fof(f247,definition,
( spl8_16
<=> in(sK7(sK3,sK5),sK3) ),
introduced(definition,[new_symbols(definition,[spl8_16])],[avatar_definition]) ).
fof(f250,plain,
( spl8_16
| spl8_2
| spl8_15 ),
inference(avatar_split_clause,[],[f244,f240,f75,f247]) ).
fof(f289,plain,
( ~ in(sK7(sK4,sK6),sK6)
| sK4 = sK6
| ~ spl8_8 ),
inference(factoring,[],[f211]) ).
fof(f292,definition,
( spl8_18
<=> in(sK7(sK4,sK6),sK6) ),
introduced(definition,[new_symbols(definition,[spl8_18])],[avatar_definition]) ).
fof(f294,plain,
( ~ in(sK7(sK4,sK6),sK6)
| spl8_18 ),
inference(avatar_component_clause,[],[f292]) ).
fof(f295,plain,
( spl8_1
| ~ spl8_18
| ~ spl8_8 ),
inference(avatar_split_clause,[],[f289,f174,f292,f71]) ).
fof(f296,plain,
( sK4 = sK6
| in(sK7(sK4,sK6),sK4)
| spl8_18 ),
inference(resolution,[],[f294,f68]) ).
fof(f299,definition,
( spl8_19
<=> in(sK7(sK4,sK6),sK4) ),
introduced(definition,[new_symbols(definition,[spl8_19])],[avatar_definition]) ).
fof(f302,plain,
( spl8_19
| spl8_1
| spl8_18 ),
inference(avatar_split_clause,[],[f296,f292,f71,f299]) ).
fof(f342,plain,
! [X0,X1] :
( in(X0,sK5)
| in(X1,sK6)
| ~ in(X1,sK4) ),
inference(resolution,[],[f163,f65]) ).
fof(f343,plain,
! [X0,X1] :
( in(X0,sK5)
| in(X1,sK6)
| ~ in(X0,sK3) ),
inference(resolution,[],[f163,f64]) ).
fof(f352,definition,
( spl8_20
<=> ! [X1] : in(X1,sK6) ),
introduced(definition,[new_symbols(definition,[spl8_20])],[avatar_definition]) ).
fof(f353,plain,
( ! [X1] : in(X1,sK6)
| ~ spl8_20 ),
inference(avatar_component_clause,[],[f352]) ).
fof(f355,definition,
( spl8_21
<=> ! [X0] :
( in(X0,sK5)
| ~ in(X0,sK3) ) ),
introduced(definition,[new_symbols(definition,[spl8_21])],[avatar_definition]) ).
fof(f356,plain,
( ! [X0] :
( in(X0,sK5)
| ~ in(X0,sK3) )
| ~ spl8_21 ),
inference(avatar_component_clause,[],[f355]) ).
fof(f357,plain,
( spl8_20
| spl8_21 ),
inference(avatar_split_clause,[],[f343,f355,f352]) ).
fof(f359,definition,
( spl8_22
<=> ! [X1] :
( in(X1,sK6)
| ~ in(X1,sK4) ) ),
introduced(definition,[new_symbols(definition,[spl8_22])],[avatar_definition]) ).
fof(f360,plain,
( ! [X1] :
( in(X1,sK6)
| ~ in(X1,sK4) )
| ~ spl8_22 ),
inference(avatar_component_clause,[],[f359]) ).
fof(f362,definition,
( spl8_23
<=> ! [X0] : in(X0,sK5) ),
introduced(definition,[new_symbols(definition,[spl8_23])],[avatar_definition]) ).
fof(f363,plain,
( ! [X0] : in(X0,sK5)
| ~ spl8_23 ),
inference(avatar_component_clause,[],[f362]) ).
fof(f364,plain,
( spl8_22
| spl8_23 ),
inference(avatar_split_clause,[],[f342,f362,f359]) ).
fof(f377,plain,
( ! [X0] : in(X0,sK4)
| ~ spl8_1
| ~ spl8_20 ),
inference(superposition,[],[f353,f72]) ).
fof(f382,plain,
( spl8_6
| ~ spl8_1
| ~ spl8_20 ),
inference(avatar_split_clause,[],[f377,f352,f71,f167]) ).
fof(f413,plain,
( ~ in(sK7(sK3,sK5),sK3)
| spl8_15
| ~ spl8_21 ),
inference(resolution,[],[f356,f242]) ).
fof(f417,plain,
( ~ spl8_16
| spl8_15
| ~ spl8_21 ),
inference(avatar_split_clause,[],[f413,f355,f240,f247]) ).
fof(f440,plain,
( empty_set = sK3
| ~ spl8_9 ),
inference(resolution,[],[f178,f59]) ).
fof(f443,plain,
( spl8_10
| ~ spl8_9 ),
inference(avatar_split_clause,[],[f440,f177,f200]) ).
fof(f444,plain,
( empty_set != empty_set
| ~ spl8_10 ),
inference(superposition,[],[f48,f202]) ).
fof(f471,plain,
( $false
| ~ spl8_10 ),
inference(trivial_inequality_removal,[],[f444]) ).
fof(f472,plain,
~ spl8_10,
inference(avatar_contradiction_clause,[],[f471]) ).
fof(f505,plain,
( ~ in(sK7(sK4,sK6),sK4)
| spl8_18
| ~ spl8_22 ),
inference(resolution,[],[f360,f294]) ).
fof(f507,plain,
( ~ spl8_19
| spl8_18
| ~ spl8_22 ),
inference(avatar_split_clause,[],[f505,f359,f292,f299]) ).
fof(f513,plain,
( $false
| spl8_11
| ~ spl8_23 ),
inference(resolution,[],[f363,f206]) ).
fof(f530,plain,
( spl8_11
| ~ spl8_23 ),
inference(avatar_contradiction_clause,[],[f513]) ).
cnf(s1,plain,
( ~ spl8_1
| ~ spl8_2 ),
inference(sat_conversion,[],[f78]) ).
cnf(s3,plain,
( spl8_6
| spl8_7 ),
inference(sat_conversion,[],[f172]) ).
cnf(s4,plain,
( spl8_8
| spl8_9 ),
inference(sat_conversion,[],[f179]) ).
cnf(s5,plain,
~ spl8_6,
inference(sat_conversion,[],[f195]) ).
cnf(s6,plain,
( ~ spl8_7
| spl8_10
| ~ spl8_11 ),
inference(sat_conversion,[],[f207]) ).
cnf(s9,plain,
( spl8_2
| ~ spl8_7
| ~ spl8_15 ),
inference(sat_conversion,[],[f243]) ).
cnf(s10,plain,
( spl8_2
| spl8_15
| spl8_16 ),
inference(sat_conversion,[],[f250]) ).
cnf(s12,plain,
( spl8_1
| ~ spl8_8
| ~ spl8_18 ),
inference(sat_conversion,[],[f295]) ).
cnf(s13,plain,
( spl8_1
| spl8_18
| spl8_19 ),
inference(sat_conversion,[],[f302]) ).
cnf(s14,plain,
( spl8_20
| spl8_21 ),
inference(sat_conversion,[],[f357]) ).
cnf(s15,plain,
( spl8_22
| spl8_23 ),
inference(sat_conversion,[],[f364]) ).
cnf(s20,plain,
( ~ spl8_1
| spl8_6
| ~ spl8_20 ),
inference(sat_conversion,[],[f382]) ).
cnf(s24,plain,
( spl8_15
| ~ spl8_16
| ~ spl8_21 ),
inference(sat_conversion,[],[f417]) ).
cnf(s26,plain,
( ~ spl8_9
| spl8_10 ),
inference(sat_conversion,[],[f443]) ).
cnf(s27,plain,
~ spl8_10,
inference(sat_conversion,[],[f472]) ).
cnf(s28,plain,
( spl8_18
| ~ spl8_19
| ~ spl8_22 ),
inference(sat_conversion,[],[f507]) ).
cnf(s34,plain,
( spl8_11
| ~ spl8_23 ),
inference(sat_conversion,[],[f530]) ).
cnf(s37,plain,
~ spl8_9,
inference(rat,[],[s26,s27]) ).
cnf(s38,plain,
( ~ spl8_7
| ~ spl8_11 ),
inference(rat,[],[s6,s27]) ).
cnf(s39,plain,
spl8_8,
inference(rat,[],[s4,s37]) ).
cnf(s40,plain,
spl8_7,
inference(rat,[],[s3,s5]) ).
cnf(s41,plain,
~ spl8_11,
inference(rat,[],[s38,s40]) ).
cnf(s42,plain,
~ spl8_23,
inference(rat,[],[s34,s41]) ).
cnf(s43,plain,
spl8_22,
inference(rat,[],[s15,s42]) ).
cnf(s44,plain,
spl8_1,
inference(rat,[],[s13,s28,s12,s43,s39]) ).
cnf(s45,plain,
~ spl8_20,
inference(rat,[],[s20,s5,s44]) ).
cnf(s46,plain,
~ spl8_2,
inference(rat,[],[s1,s44]) ).
cnf(s47,plain,
spl8_21,
inference(rat,[],[s14,s45]) ).
cnf(s48,plain,
~ spl8_15,
inference(rat,[],[s9,s40,s46]) ).
cnf(s50,plain,
~ spl8_16,
inference(rat,[],[s24,s48,s47]) ).
cnf(s51,plain,
$false,
inference(rat,[],[s10,s46,s50,s48]) ).
fof(f533,plain,
$false,
inference(avatar_sat_refutation,[],[s51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET980+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.37 % Computer : n016.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 28 03:23:03 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.41 Running first-order model finding
% 0.09/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.47 % (3227694)Will run a generic schedule for satisfiability detection.
% 0.09/0.47 % (3227699)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2562755949_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.47 % TRYING [1]
% 0.09/0.47 % TRYING [2]
% 0.09/0.47 % TRYING [3]
% 0.09/0.47 % (3227700)% WARNING: option uhcvi not known.
% 0.09/0.47 % TRYING [4]
% 0.09/0.47 % (3227700)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3449313579:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.47 % (3227701)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3862298460:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.47 % (3227702)dis+10_1_sil=32000:sp=arity:random_seed=1566141807:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.47 % (3227703)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3049531341:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.47 % (3227705)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=14032747:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.47 % (3227704)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=455889715:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.47 % (3227705) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3227694-3227705"...
% 0.09/0.47 % (3227705)...printing done.
% 0.09/0.47 % (3227705)Refutation found. Thanks to Tanya!
% 0.09/0.47 % SZS status Theorem for theBenchmark
% 0.09/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.47 % (3227705)------------------------------
% 0.09/0.47 % (3227705)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.47 % (3227705)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.47 % (3227705)CaDiCaL version: 2.1.3
% 0.09/0.47 % (3227705)Termination reason: Refutation
% 0.09/0.47 % (3227705)Time elapsed: 0.015 s
% 0.09/0.47 % (3227705)Peak memory usage: 12 MB
% 0.09/0.47 % (3227705)Instructions burned: 18 (million)
% 0.09/0.47 % (3227694)Success in time 0.052 s
% 0.09/0.47 % Vampire exiting
%------------------------------------------------------------------------------