%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV517+1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 12:59:25 PM UTC 2026
% Result : Theorem 0.24s 0.46s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 50 ( 10 unt; 2 def)
% Number of atoms : 172 ( 15 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 192 ( 70 ~; 61 |; 40 &)
% ( 6 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 103 ( 0 sgn 85 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1,X2] :
( member(X0,difference(X2,X1))
<=> ( member(X0,X2)
& ~ member(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',difference) ).
fof(f8,axiom,
! [X0,X1] :
( member(X0,singleton(X1))
<=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',singleton) ).
fof(f13,axiom,
! [X0,X1] :
( partition(X0,X1)
<=> ( ! [X2] :
( member(X2,X0)
=> subset(X2,X1) )
& ! [X2] :
( member(X2,X1)
=> ? [X3] :
( member(X3,X0)
& member(X2,X3) ) )
& ! [X2,X3] :
( ( member(X2,X0)
& member(X3,X0) )
=> ( ? [X4] :
( member(X4,X2)
& member(X4,X3) )
=> X2 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+2.ax',partition) ).
fof(f20,conjecture,
! [X0,X1,X2,X3] :
( ( member(X0,difference(X1,X2))
& partition(X3,X1) )
=> ? [X4] :
( member(X4,difference(X3,singleton(X2)))
& member(X0,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diff_elem_in_partition) ).
fof(f21,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( member(X0,difference(X1,X2))
& partition(X3,X1) )
=> ? [X4] :
( member(X4,difference(X3,singleton(X2)))
& member(X0,X4) ) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( partition(X0,X1)
<=> ( ! [X2] :
( member(X2,X0)
=> subset(X2,X1) )
& ! [X3] :
( member(X3,X1)
=> ? [X4] :
( member(X4,X0)
& member(X3,X4) ) )
& ! [X5,X6] :
( ( member(X5,X0)
& member(X6,X0) )
=> ( ? [X7] :
( member(X7,X5)
& member(X7,X6) )
=> X5 = X6 ) ) ) ),
inference(rectify,[],[f13]) ).
fof(f25,plain,
! [X0,X1] :
( partition(X0,X1)
=> ( ! [X2] :
( member(X2,X0)
=> subset(X2,X1) )
& ! [X3] :
( member(X3,X1)
=> ? [X4] :
( member(X4,X0)
& member(X3,X4) ) )
& ! [X5,X6] :
( ( member(X5,X0)
& member(X6,X0) )
=> ( ? [X7] :
( member(X7,X5)
& member(X7,X6) )
=> X5 = X6 ) ) ) ),
inference(unused_predicate_definition_removal,[],[f22]) ).
fof(f28,plain,
! [X0,X1] :
( ( ! [X2] :
( subset(X2,X1)
| ~ member(X2,X0) )
& ! [X3] :
( ? [X4] :
( member(X4,X0)
& member(X3,X4) )
| ~ member(X3,X1) )
& ! [X5,X6] :
( X5 = X6
| ! [X7] :
( ~ member(X7,X5)
| ~ member(X7,X6) )
| ~ member(X5,X0)
| ~ member(X6,X0) ) )
| ~ partition(X0,X1) ),
inference(ennf_transformation,[],[f25]) ).
fof(f29,plain,
! [X0,X1] :
( ( ! [X2] :
( subset(X2,X1)
| ~ member(X2,X0) )
& ! [X3] :
( ? [X4] :
( member(X4,X0)
& member(X3,X4) )
| ~ member(X3,X1) )
& ! [X5,X6] :
( X5 = X6
| ! [X7] :
( ~ member(X7,X5)
| ~ member(X7,X6) )
| ~ member(X5,X0)
| ~ member(X6,X0) ) )
| ~ partition(X0,X1) ),
inference(flattening,[],[f28]) ).
fof(f30,plain,
? [X0,X1,X2,X3] :
( ! [X4] :
( ~ member(X4,difference(X3,singleton(X2)))
| ~ member(X0,X4) )
& member(X0,difference(X1,X2))
& partition(X3,X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f31,plain,
? [X0,X1,X2,X3] :
( ! [X4] :
( ~ member(X4,difference(X3,singleton(X2)))
| ~ member(X0,X4) )
& member(X0,difference(X1,X2))
& partition(X3,X1) ),
inference(flattening,[],[f30]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ( member(X0,difference(X2,X1))
| ~ member(X0,X2)
| member(X0,X1) )
& ( ( member(X0,X2)
& ~ member(X0,X1) )
| ~ member(X0,difference(X2,X1)) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ( member(X0,difference(X2,X1))
| ~ member(X0,X2)
| member(X0,X1) )
& ( ( member(X0,X2)
& ~ member(X0,X1) )
| ~ member(X0,difference(X2,X1)) ) ),
inference(flattening,[],[f40]) ).
fof(f42,plain,
! [X0,X1] :
( ( member(X0,singleton(X1))
| X0 != X1 )
& ( X0 = X1
| ~ member(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f51,plain,
! [X0,X1] :
( ( ! [X2] :
( subset(X2,X1)
| ~ member(X2,X0) )
& ! [X3] :
( ( member(sK3(X0,X3),X0)
& member(X3,sK3(X0,X3)) )
| ~ member(X3,X1) )
& ! [X5,X6] :
( X5 = X6
| ! [X7] :
( ~ member(X7,X5)
| ~ member(X7,X6) )
| ~ member(X5,X0)
| ~ member(X6,X0) ) )
| ~ partition(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X4,sK3(X0,X3))],[f29]) ).
fof(f57,plain,
( ! [X4] :
( ~ member(X4,difference(sK10,singleton(sK9)))
| ~ member(sK7,X4) )
& member(sK7,difference(sK8,sK9))
& partition(sK10,sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10]),skolemize(X0,sK7),skolemize(X1,sK8),skolemize(X2,sK9),skolemize(X3,sK10)],[f31]) ).
fof(f70,plain,
! [X2,X0,X1] :
( ~ member(X0,difference(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f71,plain,
! [X2,X0,X1] :
( ~ member(X0,difference(X2,X1))
| member(X0,X2) ),
inference(cnf_transformation,[],[f41]) ).
fof(f72,plain,
! [X2,X0,X1] :
( member(X0,difference(X2,X1))
| ~ member(X0,X2)
| member(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f73,plain,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f42]) ).
fof(f85,plain,
! [X3,X0,X1] :
( ~ partition(X0,X1)
| ~ member(X3,X1)
| member(X3,sK3(X0,X3)) ),
inference(cnf_transformation,[],[f51]) ).
fof(f86,plain,
! [X3,X0,X1] :
( ~ partition(X0,X1)
| ~ member(X3,X1)
| member(sK3(X0,X3),X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f98,plain,
partition(sK10,sK8),
inference(cnf_transformation,[],[f57]) ).
fof(f99,plain,
member(sK7,difference(sK8,sK9)),
inference(cnf_transformation,[],[f57]) ).
fof(f100,plain,
! [X4] :
( ~ member(X4,difference(sK10,singleton(sK9)))
| ~ member(sK7,X4) ),
inference(cnf_transformation,[],[f57]) ).
fof(f120,plain,
~ member(sK7,sK9),
inference(resolution,[],[f70,f99]) ).
fof(f122,plain,
member(sK7,sK8),
inference(resolution,[],[f71,f99]) ).
fof(f240,plain,
! [X0] :
( member(X0,singleton(sK9))
| ~ member(X0,sK10)
| ~ member(sK7,X0) ),
inference(resolution,[],[f72,f100]) ).
fof(f247,plain,
! [X0] :
( ~ member(sK7,X0)
| ~ member(X0,sK10)
| sK9 = X0 ),
inference(resolution,[],[f240,f73]) ).
fof(f355,plain,
! [X0] :
( member(X0,sK3(sK10,X0))
| ~ member(X0,sK8) ),
inference(resolution,[],[f85,f98]) ).
fof(f356,plain,
! [X0] :
( member(sK3(sK10,X0),sK10)
| ~ member(X0,sK8) ),
inference(resolution,[],[f86,f98]) ).
fof(f402,plain,
( ~ member(sK7,sK8)
| ~ member(sK3(sK10,sK7),sK10)
| sK9 = sK3(sK10,sK7) ),
inference(resolution,[],[f355,f247]) ).
fof(f403,plain,
( ~ member(sK3(sK10,sK7),sK10)
| sK9 = sK3(sK10,sK7) ),
inference(forward_subsumption_resolution,[],[f402,f122]) ).
fof(f405,definition,
( spl11_19
<=> sK9 = sK3(sK10,sK7) ),
introduced(definition,[new_symbols(definition,[spl11_19])],[avatar_definition]) ).
fof(f407,plain,
( sK9 = sK3(sK10,sK7)
| ~ spl11_19 ),
inference(avatar_component_clause,[],[f405]) ).
fof(f409,definition,
( spl11_20
<=> member(sK3(sK10,sK7),sK10) ),
introduced(definition,[new_symbols(definition,[spl11_20])],[avatar_definition]) ).
fof(f411,plain,
( ~ member(sK3(sK10,sK7),sK10)
| spl11_20 ),
inference(avatar_component_clause,[],[f409]) ).
fof(f412,plain,
( spl11_19
| ~ spl11_20 ),
inference(avatar_split_clause,[],[f403,f409,f405]) ).
fof(f436,plain,
( ~ member(sK7,sK8)
| spl11_20 ),
inference(resolution,[],[f356,f411]) ).
fof(f441,plain,
( $false
| spl11_20 ),
inference(forward_subsumption_resolution,[],[f436,f122]) ).
fof(f442,plain,
spl11_20,
inference(avatar_contradiction_clause,[],[f441]) ).
fof(f446,plain,
( member(sK7,sK9)
| ~ member(sK7,sK8)
| ~ spl11_19 ),
inference(superposition,[],[f355,f407]) ).
fof(f447,plain,
( ~ member(sK7,sK8)
| ~ spl11_19 ),
inference(forward_subsumption_resolution,[],[f446,f120]) ).
fof(f449,plain,
( $false
| ~ spl11_19 ),
inference(forward_subsumption_resolution,[],[f447,f122]) ).
fof(f450,plain,
~ spl11_19,
inference(avatar_contradiction_clause,[],[f449]) ).
cnf(s9,plain,
( spl11_19
| ~ spl11_20 ),
inference(sat_conversion,[],[f412]) ).
cnf(s10,plain,
spl11_20,
inference(sat_conversion,[],[f442]) ).
cnf(s11,plain,
~ spl11_19,
inference(sat_conversion,[],[f450]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s9,s10,s11]) ).
fof(f451,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV517+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n010.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 06:30:17 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.40 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
% 0.24/0.46 % (1716528)Will run a generic schedule for satisfiability detection.
% 0.24/0.46 % (1716533)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=70678122_2999 on theBenchmark for (2999ds/0Mi)
% 0.24/0.46 % TRYING [1]
% 0.24/0.46 % TRYING [2]
% 0.24/0.46 % TRYING [3]
% 0.24/0.46 % (1716534)% WARNING: option uhcvi not known.
% 0.24/0.46 % TRYING [4]
% 0.24/0.46 % (1716535)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1297490741:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.24/0.46 % (1716536)dis+10_1_sil=32000:sp=arity:random_seed=1687654301:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.24/0.46 % (1716537)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3451766277:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.24/0.46 % (1716538)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2650010522:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.24/0.46 % (1716539)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=77333631:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.24/0.46 % (1716534)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4094428646:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.24/0.46 % TRYING [5]
% 0.24/0.46 % (1716536) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1716528-1716536"...
% 0.24/0.46 % TRYING [6]
% 0.24/0.46 % (1716536)...printing done.
% 0.24/0.46 % (1716536)Refutation found. Thanks to Tanya!
% 0.24/0.46 % SZS status Theorem for theBenchmark
% 0.24/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.46 % (1716536)------------------------------
% 0.24/0.46 % (1716536)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.46 % (1716536)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.46 % (1716536)CaDiCaL version: 2.1.3
% 0.24/0.46 % (1716536)Termination reason: Refutation
% 0.24/0.46 % (1716536)Time elapsed: 0.011 s
% 0.24/0.46 % (1716536)Peak memory usage: 12 MB
% 0.24/0.46 % (1716536)Instructions burned: 14 (million)
% 0.24/0.46 % (1716528)Success in time 0.046 s
% 0.24/0.46 % Vampire exiting
%------------------------------------------------------------------------------