%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET591+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 12:44:02 PM UTC 2026
% Result : Theorem 0.10s 0.43s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 40 ( 12 unt; 1 def)
% Number of atoms : 105 ( 13 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 111 ( 46 ~; 39 |; 18 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn 64 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f2,axiom,
! [X0,X1,X2] :
( member(X2,difference(X0,X1))
<=> ( member(X2,X0)
& ~ member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
fof(f3,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f4,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(f7,conjecture,
! [X0,X1] :
( subset(X0,difference(X1,X0))
=> X0 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th50) ).
fof(f8,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,difference(X1,X0))
=> X0 = empty_set ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f10,plain,
? [X0,X1] :
( empty_set != X0
& subset(X0,difference(X1,X0)) ),
inference(ennf_transformation,[],[f8]) ).
fof(f11,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f12,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f11]) ).
fof(f13,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f12]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( member(X2,difference(X0,X1))
| ~ member(X2,X0)
| member(X2,X1) )
& ( ( member(X2,X0)
& ~ member(X2,X1) )
| ~ member(X2,difference(X0,X1)) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ( member(X2,difference(X0,X1))
| ~ member(X2,X0)
| member(X2,X1) )
& ( ( member(X2,X0)
& ~ member(X2,X1) )
| ~ member(X2,difference(X0,X1)) ) ),
inference(flattening,[],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f17,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
( empty_set != sK1
& subset(sK1,difference(sK2,sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f10]) ).
fof(f19,plain,
! [X3,X0,X1] :
( ~ member(X3,X0)
| member(X3,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f20,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f22,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f25,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f3]) ).
fof(f28,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f17]) ).
fof(f30,plain,
subset(sK1,difference(sK2,sK1)),
inference(cnf_transformation,[],[f18]) ).
fof(f31,plain,
empty_set != sK1,
inference(cnf_transformation,[],[f18]) ).
fof(f65,plain,
! [X0] : subset(empty_set,X0),
inference(resolution,[],[f20,f25]) ).
fof(f119,plain,
! [X2,X0,X1] :
( member(sK0(X0,X1),X2)
| ~ subset(X0,X2)
| subset(X0,X1) ),
inference(resolution,[],[f19,f20]) ).
fof(f133,plain,
! [X0] :
( ~ subset(X0,empty_set)
| empty_set = X0 ),
inference(resolution,[],[f28,f65]) ).
fof(f295,plain,
! [X2,X3,X0,X1] :
( ~ member(sK0(X0,X3),X2)
| subset(X0,X3)
| ~ subset(X0,difference(X1,X2)) ),
inference(resolution,[],[f119,f22]) ).
fof(f477,definition,
( spl3_24
<=> ! [X0] : subset(sK1,X0) ),
introduced(definition,[new_symbols(definition,[spl3_24])],[avatar_definition]) ).
fof(f478,plain,
( ! [X0] : subset(sK1,X0)
| ~ spl3_24 ),
inference(avatar_component_clause,[],[f477]) ).
fof(f487,plain,
( empty_set = sK1
| ~ spl3_24 ),
inference(resolution,[],[f478,f133]) ).
fof(f490,plain,
( $false
| ~ spl3_24 ),
inference(forward_subsumption_resolution,[],[f487,f31]) ).
fof(f491,plain,
~ spl3_24,
inference(avatar_contradiction_clause,[],[f490]) ).
fof(f562,plain,
! [X2,X0,X1] :
( subset(X0,X1)
| ~ subset(X0,difference(X2,X0))
| subset(X0,X1) ),
inference(resolution,[],[f295,f20]) ).
fof(f572,plain,
! [X2,X0,X1] :
( ~ subset(X0,difference(X2,X0))
| subset(X0,X1) ),
inference(duplicate_literal_removal,[],[f562]) ).
fof(f607,plain,
! [X0] : subset(sK1,X0),
inference(resolution,[],[f572,f30]) ).
fof(f620,plain,
spl3_24,
inference(avatar_split_clause,[],[f607,f477]) ).
cnf(s311,plain,
~ spl3_24,
inference(sat_conversion,[],[f491]) ).
cnf(s402,plain,
spl3_24,
inference(sat_conversion,[],[f620]) ).
cnf(s403,plain,
$false,
inference(rat,[],[s311,s402]) ).
fof(f621,plain,
$false,
inference(avatar_sat_refutation,[],[s403]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET591+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.36 % Computer : n005.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 02:16:47 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.39 Running first-order model finding
% 0.10/0.39 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
% 0.10/0.43 % (365692)Will run a generic schedule for satisfiability detection.
% 0.10/0.43 % (365699)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2621866671:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.43 % (365698)% WARNING: option uhcvi not known.
% 0.10/0.43 % (365697)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=776615056_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.43 % (365699) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-365692-365699"...
% 0.10/0.43 % (365701)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2664247018:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.43 % (365700)dis+10_1_sil=32000:sp=arity:random_seed=1999090649:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.43 % (365698)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3687249731:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/0.43 % (365702)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1945297028:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.43 % (365699)...printing done.
% 0.10/0.43 % (365703)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1973629880:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.43 % TRYING [1]
% 0.10/0.43 % (365699)Refutation found. Thanks to Tanya!
% 0.10/0.43 % SZS status Theorem for theBenchmark
% 0.10/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.43 % (365699)------------------------------
% 0.10/0.43 % (365699)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.43 % (365699)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.43 % (365699)CaDiCaL version: 2.1.3
% 0.10/0.43 % (365699)Termination reason: Refutation
% 0.10/0.43 % (365699)Time elapsed: 0.008 s
% 0.10/0.43 % (365699)Peak memory usage: 12 MB
% 0.10/0.43 % (365699)Instructions burned: 14 (million)
% 0.10/0.43 % (365692)Success in time 0.034 s
% 0.10/0.43 % Vampire exiting
%------------------------------------------------------------------------------