%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET802+4 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n008.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 12:44:39 PM UTC 2026
% Result : Theorem 0.15s 0.50s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 79 ( 6 unt; 4 def)
% Number of atoms : 225 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 242 ( 96 ~; 111 |; 14 &)
% ( 13 <=>; 7 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 5 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 81 ( 0 sgn 77 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X0,X1,X2] :
( lower_bound(X2,X0,X1)
<=> ! [X3] :
( member(X3,X1)
=> apply(X0,X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+3.ax',lower_bound) ).
fof(f17,axiom,
! [X0,X1,X2] :
( least(X2,X0,X1)
<=> ( member(X2,X1)
& ! [X3] :
( member(X3,X1)
=> apply(X0,X2,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+3.ax',least) ).
fof(f21,axiom,
! [X0,X1,X2,X3] :
( greatest_lower_bound(X0,X1,X2,X3)
<=> ( member(X0,X1)
& lower_bound(X0,X2,X1)
& ! [X4] :
( ( member(X4,X3)
& lower_bound(X4,X2,X1) )
=> apply(X2,X4,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+3.ax',greatest_lower_bound) ).
fof(f22,conjecture,
! [X0,X1] :
( order(X0,X1)
=> ! [X2] :
( subset(X2,X1)
=> ! [X3] :
( least(X3,X0,X2)
<=> ( member(X3,X2)
& greatest_lower_bound(X3,X2,X0,X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIV14) ).
fof(f23,negated_conjecture,
~ ! [X0,X1] :
( order(X0,X1)
=> ! [X2] :
( subset(X2,X1)
=> ! [X3] :
( least(X3,X0,X2)
<=> ( member(X3,X2)
& greatest_lower_bound(X3,X2,X0,X1) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f30,plain,
! [X0,X1,X2] :
( lower_bound(X2,X0,X1)
<=> ! [X3] :
( apply(X0,X2,X3)
| ~ member(X3,X1) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f31,plain,
! [X0,X1,X2] :
( least(X2,X0,X1)
<=> ( member(X2,X1)
& ! [X3] :
( apply(X0,X2,X3)
| ~ member(X3,X1) ) ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f32,plain,
! [X0,X1,X2,X3] :
( greatest_lower_bound(X0,X1,X2,X3)
<=> ( member(X0,X1)
& lower_bound(X0,X2,X1)
& ! [X4] :
( apply(X2,X4,X0)
| ~ member(X4,X3)
| ~ lower_bound(X4,X2,X1) ) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f33,plain,
! [X0,X1,X2,X3] :
( greatest_lower_bound(X0,X1,X2,X3)
<=> ( member(X0,X1)
& lower_bound(X0,X2,X1)
& ! [X4] :
( apply(X2,X4,X0)
| ~ member(X4,X3)
| ~ lower_bound(X4,X2,X1) ) ) ),
inference(flattening,[],[f32]) ).
fof(f34,plain,
? [X0,X1] :
( ? [X2] :
( ? [X3] :
( least(X3,X0,X2)
<~> ( member(X3,X2)
& greatest_lower_bound(X3,X2,X0,X1) ) )
& subset(X2,X1) )
& order(X0,X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f64,plain,
! [X2,X3,X0,X1] :
( ~ lower_bound(X2,X0,X1)
| apply(X0,X2,X3)
| ~ member(X3,X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f65,plain,
! [X2,X0,X1] :
( lower_bound(X2,X0,X1)
| member(sK3(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f66,plain,
! [X2,X0,X1] :
( lower_bound(X2,X0,X1)
| ~ apply(X0,X2,sK3(X0,X1,X2)) ),
inference(cnf_transformation,[],[f30]) ).
fof(f67,plain,
! [X2,X0,X1] :
( least(X2,X0,X1)
| ~ member(X2,X1)
| member(sK4(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f68,plain,
! [X2,X0,X1] :
( least(X2,X0,X1)
| ~ member(X2,X1)
| ~ apply(X0,X2,sK4(X0,X1,X2)) ),
inference(cnf_transformation,[],[f31]) ).
fof(f69,plain,
! [X2,X3,X0,X1] :
( ~ least(X2,X0,X1)
| apply(X0,X2,X3)
| ~ member(X3,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f70,plain,
! [X2,X0,X1] :
( ~ least(X2,X0,X1)
| member(X2,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f71,plain,
! [X2,X3,X0,X1] :
( greatest_lower_bound(X0,X1,X2,X3)
| ~ lower_bound(X0,X2,X1)
| ~ member(X0,X1)
| lower_bound(sK5(X0,X1,X2,X3),X2,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f73,plain,
! [X2,X3,X0,X1] :
( greatest_lower_bound(X0,X1,X2,X3)
| ~ lower_bound(X0,X2,X1)
| ~ member(X0,X1)
| ~ apply(X2,sK5(X0,X1,X2,X3),X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f75,plain,
! [X2,X3,X0,X1] :
( ~ greatest_lower_bound(X0,X1,X2,X3)
| lower_bound(X0,X2,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f77,plain,
( ~ greatest_lower_bound(sK9,sK8,sK6,sK7)
| ~ member(sK9,sK8)
| ~ least(sK9,sK6,sK8) ),
inference(cnf_transformation,[],[f34]) ).
fof(f78,plain,
( greatest_lower_bound(sK9,sK8,sK6,sK7)
| least(sK9,sK6,sK8) ),
inference(cnf_transformation,[],[f34]) ).
fof(f79,plain,
( member(sK9,sK8)
| least(sK9,sK6,sK8) ),
inference(cnf_transformation,[],[f34]) ).
fof(f86,definition,
( spl10_1
<=> least(sK9,sK6,sK8) ),
introduced(definition,[new_symbols(definition,[spl10_1])],[avatar_definition]) ).
fof(f87,plain,
( least(sK9,sK6,sK8)
| ~ spl10_1 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f88,plain,
( ~ least(sK9,sK6,sK8)
| spl10_1 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f90,definition,
( spl10_2
<=> member(sK9,sK8) ),
introduced(definition,[new_symbols(definition,[spl10_2])],[avatar_definition]) ).
fof(f91,plain,
( member(sK9,sK8)
| ~ spl10_2 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f94,definition,
( spl10_3
<=> greatest_lower_bound(sK9,sK8,sK6,sK7) ),
introduced(definition,[new_symbols(definition,[spl10_3])],[avatar_definition]) ).
fof(f95,plain,
( greatest_lower_bound(sK9,sK8,sK6,sK7)
| ~ spl10_3 ),
inference(avatar_component_clause,[],[f94]) ).
fof(f96,plain,
( ~ greatest_lower_bound(sK9,sK8,sK6,sK7)
| spl10_3 ),
inference(avatar_component_clause,[],[f94]) ).
fof(f97,plain,
( ~ spl10_1
| ~ spl10_2
| ~ spl10_3 ),
inference(avatar_split_clause,[],[f77,f94,f90,f86]) ).
fof(f98,plain,
( spl10_1
| spl10_3 ),
inference(avatar_split_clause,[],[f78,f94,f86]) ).
fof(f99,plain,
( spl10_1
| spl10_2 ),
inference(avatar_split_clause,[],[f79,f90,f86]) ).
fof(f124,plain,
( lower_bound(sK9,sK6,sK8)
| ~ spl10_3 ),
inference(resolution,[],[f75,f95]) ).
fof(f258,plain,
( member(sK9,sK8)
| ~ spl10_1 ),
inference(resolution,[],[f87,f70]) ).
fof(f259,plain,
( spl10_2
| ~ spl10_1 ),
inference(avatar_split_clause,[],[f258,f86,f90]) ).
fof(f291,plain,
( ! [X0] :
( apply(sK6,sK9,X0)
| ~ member(X0,sK8) )
| ~ spl10_1 ),
inference(resolution,[],[f69,f87]) ).
fof(f306,definition,
( spl10_10
<=> lower_bound(sK9,sK6,sK8) ),
introduced(definition,[new_symbols(definition,[spl10_10])],[avatar_definition]) ).
fof(f307,plain,
( lower_bound(sK9,sK6,sK8)
| ~ spl10_10 ),
inference(avatar_component_clause,[],[f306]) ).
fof(f308,plain,
( ~ lower_bound(sK9,sK6,sK8)
| spl10_10 ),
inference(avatar_component_clause,[],[f306]) ).
fof(f310,plain,
( ~ apply(sK6,sK9,sK3(sK6,sK8,sK9))
| spl10_10 ),
inference(resolution,[],[f308,f66]) ).
fof(f311,plain,
( member(sK3(sK6,sK8,sK9),sK8)
| spl10_10 ),
inference(resolution,[],[f308,f65]) ).
fof(f320,plain,
( ~ lower_bound(sK9,sK6,sK8)
| ~ member(sK9,sK8)
| lower_bound(sK5(sK9,sK8,sK6,sK7),sK6,sK8)
| spl10_3 ),
inference(resolution,[],[f71,f96]) ).
fof(f321,plain,
( ~ member(sK3(sK6,sK8,sK9),sK8)
| ~ spl10_1
| spl10_10 ),
inference(resolution,[],[f310,f291]) ).
fof(f322,plain,
( $false
| ~ spl10_1
| spl10_10 ),
inference(forward_subsumption_resolution,[],[f321,f311]) ).
fof(f323,plain,
( ~ spl10_1
| spl10_10 ),
inference(avatar_contradiction_clause,[],[f322]) ).
fof(f324,plain,
( ~ member(sK9,sK8)
| lower_bound(sK5(sK9,sK8,sK6,sK7),sK6,sK8)
| spl10_3
| ~ spl10_10 ),
inference(forward_subsumption_resolution,[],[f320,f307]) ).
fof(f325,plain,
( lower_bound(sK5(sK9,sK8,sK6,sK7),sK6,sK8)
| ~ spl10_2
| spl10_3
| ~ spl10_10 ),
inference(forward_subsumption_resolution,[],[f324,f91]) ).
fof(f329,plain,
( ~ lower_bound(sK9,sK6,sK8)
| ~ member(sK9,sK8)
| ~ apply(sK6,sK5(sK9,sK8,sK6,sK7),sK9)
| spl10_3 ),
inference(resolution,[],[f73,f96]) ).
fof(f330,plain,
( ~ member(sK9,sK8)
| ~ apply(sK6,sK5(sK9,sK8,sK6,sK7),sK9)
| spl10_3
| ~ spl10_10 ),
inference(forward_subsumption_resolution,[],[f329,f307]) ).
fof(f331,plain,
( ~ apply(sK6,sK5(sK9,sK8,sK6,sK7),sK9)
| ~ spl10_2
| spl10_3
| ~ spl10_10 ),
inference(forward_subsumption_resolution,[],[f330,f91]) ).
fof(f336,plain,
( ! [X0] :
( apply(sK6,sK5(sK9,sK8,sK6,sK7),X0)
| ~ member(X0,sK8) )
| ~ spl10_2
| spl10_3
| ~ spl10_10 ),
inference(resolution,[],[f325,f64]) ).
fof(f446,plain,
( ~ member(sK9,sK8)
| ~ spl10_2
| spl10_3
| ~ spl10_10 ),
inference(resolution,[],[f336,f331]) ).
fof(f457,plain,
( $false
| ~ spl10_2
| spl10_3
| ~ spl10_10 ),
inference(forward_subsumption_resolution,[],[f446,f91]) ).
fof(f458,plain,
( ~ spl10_2
| spl10_3
| ~ spl10_10 ),
inference(avatar_contradiction_clause,[],[f457]) ).
fof(f472,plain,
( spl10_10
| ~ spl10_3 ),
inference(avatar_split_clause,[],[f124,f94,f306]) ).
fof(f473,plain,
( ~ member(sK9,sK8)
| ~ apply(sK6,sK9,sK4(sK6,sK8,sK9))
| spl10_1 ),
inference(resolution,[],[f88,f68]) ).
fof(f474,plain,
( ~ member(sK9,sK8)
| member(sK4(sK6,sK8,sK9),sK8)
| spl10_1 ),
inference(resolution,[],[f88,f67]) ).
fof(f475,plain,
( member(sK4(sK6,sK8,sK9),sK8)
| spl10_1
| ~ spl10_2 ),
inference(forward_subsumption_resolution,[],[f474,f91]) ).
fof(f476,plain,
( ~ apply(sK6,sK9,sK4(sK6,sK8,sK9))
| spl10_1
| ~ spl10_2 ),
inference(forward_subsumption_resolution,[],[f473,f91]) ).
fof(f477,plain,
( ! [X0] :
( apply(sK6,sK9,X0)
| ~ member(X0,sK8) )
| ~ spl10_10 ),
inference(resolution,[],[f307,f64]) ).
fof(f518,plain,
( ~ member(sK4(sK6,sK8,sK9),sK8)
| spl10_1
| ~ spl10_2
| ~ spl10_10 ),
inference(resolution,[],[f477,f476]) ).
fof(f527,plain,
( $false
| spl10_1
| ~ spl10_2
| ~ spl10_10 ),
inference(forward_subsumption_resolution,[],[f518,f475]) ).
fof(f528,plain,
( spl10_1
| ~ spl10_2
| ~ spl10_10 ),
inference(avatar_contradiction_clause,[],[f527]) ).
cnf(s1,plain,
( ~ spl10_1
| ~ spl10_2
| ~ spl10_3 ),
inference(sat_conversion,[],[f97]) ).
cnf(s2,plain,
( spl10_1
| spl10_3 ),
inference(sat_conversion,[],[f98]) ).
cnf(s3,plain,
( spl10_1
| spl10_2 ),
inference(sat_conversion,[],[f99]) ).
cnf(s9,plain,
( ~ spl10_1
| spl10_2 ),
inference(sat_conversion,[],[f259]) ).
cnf(s12,plain,
( ~ spl10_1
| spl10_10 ),
inference(sat_conversion,[],[f323]) ).
cnf(s16,plain,
( ~ spl10_2
| spl10_3
| ~ spl10_10 ),
inference(sat_conversion,[],[f458]) ).
cnf(s18,plain,
( ~ spl10_3
| spl10_10 ),
inference(sat_conversion,[],[f472]) ).
cnf(s21,plain,
( spl10_1
| ~ spl10_2
| ~ spl10_10 ),
inference(sat_conversion,[],[f528]) ).
cnf(s22,plain,
spl10_1,
inference(rat,[],[s18,s21,s2,s3]) ).
cnf(s23,plain,
spl10_10,
inference(rat,[],[s12,s22]) ).
cnf(s24,plain,
spl10_2,
inference(rat,[],[s9,s22]) ).
cnf(s25,plain,
spl10_3,
inference(rat,[],[s16,s23,s24]) ).
cnf(s28,plain,
$false,
inference(rat,[],[s1,s22,s25,s24]) ).
fof(f531,plain,
$false,
inference(avatar_sat_refutation,[],[s28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET802+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.38 % Computer : n008.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Mon Sep 28 02:51:24 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.15/0.41 Running first-order model finding
% 0.15/0.41 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
% 0.15/0.50 % (1820390)Will run a generic schedule for satisfiability detection.
% 0.15/0.50 % (1820413)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3808022132:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.50 % (1820407)% WARNING: option uhcvi not known.
% 0.15/0.50 % (1820404)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2914011386_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.50 % (1820407)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2232956982:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.50 % (1820410)dis+10_1_sil=32000:sp=arity:random_seed=2648290481:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.50 % (1820408)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1138794087:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.50 % (1820411)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1041746815:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.50 % TRYING [1]
% 0.15/0.50 % (1820414)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3310826600:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.50 % TRYING [2]
% 0.15/0.50 % TRYING [3]
% 0.15/0.50 % TRYING [4]
% 0.15/0.50 % TRYING [5]
% 0.15/0.50 % (1820411) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1820390-1820411"...
% 0.15/0.50 % (1820411)...printing done.
% 0.15/0.50 % (1820411)Refutation found. Thanks to Tanya!
% 0.15/0.50 % SZS status Theorem for theBenchmark
% 0.15/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.50 % (1820411)------------------------------
% 0.15/0.50 % (1820411)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.50 % (1820411)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.50 % (1820411)CaDiCaL version: 2.1.3
% 0.15/0.50 % (1820411)Termination reason: Refutation
% 0.15/0.50 % (1820411)Time elapsed: 0.019 s
% 0.15/0.50 % (1820411)Peak memory usage: 12 MB
% 0.15/0.50 % (1820411)Instructions burned: 25 (million)
% 0.15/0.50 % (1820390)Success in time 0.075 s
% 0.15/0.50 % Vampire exiting
%------------------------------------------------------------------------------