%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET812+4 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n005.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 12:44:40 PM UTC 2026
% Result : Theorem 0.53s 0.62s
% Output : Refutation 0.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 47 ( 8 unt; 2 def)
% Number of atoms : 105 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 94 ( 36 ~; 36 |; 8 &)
% ( 9 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn 43 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).
fof(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',equal_set) ).
fof(f3,axiom,
! [X0,X1] :
( member(X0,power_set(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',power_set) ).
fof(f4,axiom,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
<=> ( member(X0,X1)
& member(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',intersection) ).
fof(f12,axiom,
! [X0] :
( member(X0,on)
<=> ( set(X0)
& strict_well_order(member_predicate,X0)
& ! [X1] :
( member(X1,X0)
=> subset(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+4.ax',ordinal_number) ).
fof(f20,conjecture,
! [X0] :
( member(X0,on)
=> equal_set(X0,intersection(X0,power_set(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thV10) ).
fof(f21,negated_conjecture,
~ ! [X0] :
( member(X0,on)
=> equal_set(X0,intersection(X0,power_set(X0))) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f23,plain,
! [X0,X1] :
( ( subset(X0,X1)
& subset(X1,X0) )
=> equal_set(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f24,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f25,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f26,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(flattening,[],[f25]) ).
fof(f28,plain,
! [X0] :
( member(X0,on)
<=> ( set(X0)
& strict_well_order(member_predicate,X0)
& ! [X1] :
( subset(X1,X0)
| ~ member(X1,X0) ) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f36,plain,
? [X0] :
( ~ equal_set(X0,intersection(X0,power_set(X0)))
& member(X0,on) ),
inference(ennf_transformation,[],[f21]) ).
fof(f38,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f39,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f40,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f26]) ).
fof(f41,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f3]) ).
fof(f44,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[],[f4]) ).
fof(f45,plain,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f4]) ).
fof(f66,plain,
! [X0,X1] :
( subset(X1,X0)
| ~ member(X1,X0)
| ~ member(X0,on) ),
inference(cnf_transformation,[],[f28]) ).
fof(f113,plain,
member(sK13,on),
inference(cnf_transformation,[],[f36]) ).
fof(f114,plain,
~ equal_set(sK13,intersection(sK13,power_set(sK13))),
inference(cnf_transformation,[],[f36]) ).
fof(f131,plain,
( ~ subset(sK13,intersection(sK13,power_set(sK13)))
| ~ subset(intersection(sK13,power_set(sK13)),sK13) ),
inference(resolution,[],[f40,f114]) ).
fof(f133,definition,
( spl14_1
<=> subset(intersection(sK13,power_set(sK13)),sK13) ),
introduced(definition,[new_symbols(definition,[spl14_1])],[avatar_definition]) ).
fof(f135,plain,
( ~ subset(intersection(sK13,power_set(sK13)),sK13)
| spl14_1 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f137,definition,
( spl14_2
<=> subset(sK13,intersection(sK13,power_set(sK13))) ),
introduced(definition,[new_symbols(definition,[spl14_2])],[avatar_definition]) ).
fof(f139,plain,
( ~ subset(sK13,intersection(sK13,power_set(sK13)))
| spl14_2 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f140,plain,
( ~ spl14_1
| ~ spl14_2 ),
inference(avatar_split_clause,[],[f131,f137,f133]) ).
fof(f141,plain,
( ~ member(sK0(intersection(sK13,power_set(sK13)),sK13),sK13)
| spl14_1 ),
inference(resolution,[],[f135,f39]) ).
fof(f142,plain,
( member(sK0(intersection(sK13,power_set(sK13)),sK13),intersection(sK13,power_set(sK13)))
| spl14_1 ),
inference(resolution,[],[f135,f38]) ).
fof(f156,plain,
( member(sK0(intersection(sK13,power_set(sK13)),sK13),sK13)
| spl14_1 ),
inference(resolution,[],[f142,f44]) ).
fof(f158,plain,
( $false
| spl14_1 ),
inference(forward_subsumption_resolution,[],[f156,f141]) ).
fof(f159,plain,
spl14_1,
inference(avatar_contradiction_clause,[],[f158]) ).
fof(f163,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ member(X1,on)
| ~ member(X0,X1) ),
inference(resolution,[],[f66,f41]) ).
fof(f165,plain,
( ~ member(sK0(sK13,intersection(sK13,power_set(sK13))),intersection(sK13,power_set(sK13)))
| spl14_2 ),
inference(resolution,[],[f139,f39]) ).
fof(f166,plain,
( member(sK0(sK13,intersection(sK13,power_set(sK13))),sK13)
| spl14_2 ),
inference(resolution,[],[f139,f38]) ).
fof(f247,plain,
( ~ member(sK0(sK13,intersection(sK13,power_set(sK13))),sK13)
| ~ member(sK0(sK13,intersection(sK13,power_set(sK13))),power_set(sK13))
| spl14_2 ),
inference(resolution,[],[f45,f165]) ).
fof(f248,plain,
( ~ member(sK0(sK13,intersection(sK13,power_set(sK13))),power_set(sK13))
| spl14_2 ),
inference(forward_subsumption_resolution,[],[f247,f166]) ).
fof(f959,plain,
( ~ member(sK13,on)
| ~ member(sK0(sK13,intersection(sK13,power_set(sK13))),sK13)
| spl14_2 ),
inference(resolution,[],[f163,f248]) ).
fof(f962,plain,
( ~ member(sK0(sK13,intersection(sK13,power_set(sK13))),sK13)
| spl14_2 ),
inference(forward_subsumption_resolution,[],[f959,f113]) ).
fof(f967,plain,
( $false
| spl14_2 ),
inference(forward_subsumption_resolution,[],[f962,f166]) ).
fof(f968,plain,
spl14_2,
inference(avatar_contradiction_clause,[],[f967]) ).
cnf(s1,plain,
( ~ spl14_1
| ~ spl14_2 ),
inference(sat_conversion,[],[f140]) ).
cnf(s2,plain,
spl14_1,
inference(sat_conversion,[],[f159]) ).
cnf(s16,plain,
spl14_2,
inference(sat_conversion,[],[f968]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s1,s16,s2]) ).
fof(f973,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET812+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.18/0.45 % Computer : n005.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Mon Sep 28 02:51:37 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.46 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.24/0.51 Running first-order model finding
% 0.24/0.51 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.53/0.62 % (384113)Will run a generic schedule for satisfiability detection.
% 0.53/0.62 % (384120)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2190347305:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.53/0.62 % (384119)% WARNING: option uhcvi not known.
% 0.53/0.62 % (384118)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3901159414_2999 on theBenchmark for (2999ds/0Mi)
% 0.53/0.62 % (384119)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2526597212:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.53/0.62 % (384121)dis+10_1_sil=32000:sp=arity:random_seed=4036511114:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.53/0.62 % (384122)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2872533673:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.53/0.62 % (384123)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2947236798:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.53/0.62 % (384124)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4053701457:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.53/0.62 % TRYING [1]
% 0.53/0.62 % TRYING [2]
% 0.53/0.62 % TRYING [3]
% 0.53/0.62 % TRYING [4]
% 0.53/0.62 % TRYING [5]
% 0.53/0.62 % (384122) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-384113-384122"...
% 0.53/0.62 % (384122)...printing done.
% 0.53/0.62 % (384122)Refutation found. Thanks to Tanya!
% 0.53/0.62 % SZS status Theorem for theBenchmark
% 0.53/0.62 % SZS output start Proof for theBenchmark
% See solution above
% 0.53/0.62 % (384122)------------------------------
% 0.53/0.62 % (384122)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.62 % (384122)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.62 % (384122)CaDiCaL version: 2.1.3
% 0.53/0.62 % (384122)Termination reason: Refutation
% 0.53/0.62 % (384122)Time elapsed: 0.058 s
% 0.53/0.62 % (384122)Peak memory usage: 13 MB
% 0.53/0.62 % (384122)Instructions burned: 55 (million)
% 0.53/0.62 % (384113)Success in time 0.103 s
% 0.53/0.62 % Vampire exiting
%------------------------------------------------------------------------------