%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM388+1 : 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 : 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 12:24:06 PM UTC 2026
% Result : Theorem 0.12s 0.45s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 62 ( 14 unt; 2 def)
% Number of atoms : 169 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 171 ( 64 ~; 62 |; 28 &)
% ( 5 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 85 ( 0 sgn 77 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( ordinal(X0)
=> ( epsilon_transitive(X0)
& epsilon_connected(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_ordinal1) ).
fof(f7,axiom,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( in(X1,X0)
=> subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(f24,conjecture,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ! [X2] :
( epsilon_transitive(X2)
=> ( ( in(X2,X0)
& in(X0,X1) )
=> in(X2,X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_ordinal1) ).
fof(f25,negated_conjecture,
~ ! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ! [X2] :
( epsilon_transitive(X2)
=> ( ( in(X2,X0)
& in(X0,X1) )
=> in(X2,X1) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f24]) ).
fof(f27,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( empty(X1)
| in(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f28,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f29,axiom,
! [X0,X1,X2] :
( ( in(X0,X1)
& element(X1,powerset(X2)) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f32,axiom,
! [X0,X1] :
~ ( in(X0,X1)
& empty(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f43,plain,
! [X0] :
( ( epsilon_transitive(X0)
& epsilon_connected(X0) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f49,plain,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f50,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0)
& in(X0,X1)
& epsilon_transitive(X2) )
& ordinal(X1) )
& ordinal(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f51,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0)
& in(X0,X1)
& epsilon_transitive(X2) )
& ordinal(X1) )
& ordinal(X0) ),
inference(flattening,[],[f50]) ).
fof(f53,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f27]) ).
fof(f54,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f53]) ).
fof(f55,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(ennf_transformation,[],[f29]) ).
fof(f56,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(flattening,[],[f55]) ).
fof(f59,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f61,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) ) )
& ( ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(nnf_transformation,[],[f49]) ).
fof(f62,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(rectify,[],[f61]) ).
fof(f63,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ( ~ subset(sK0(X0),X0)
& in(sK0(X0),X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f62]) ).
fof(f76,plain,
( ~ in(sK15,sK14)
& in(sK15,sK13)
& in(sK13,sK14)
& epsilon_transitive(sK15)
& ordinal(sK14)
& ordinal(sK13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14,sK15]),skolemize(X0,sK13),skolemize(X1,sK14),skolemize(X2,sK15)],[f51]) ).
fof(f77,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f28]) ).
fof(f81,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f86,plain,
! [X2,X0] :
( subset(X2,X0)
| ~ in(X2,X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f118,plain,
ordinal(sK14),
inference(cnf_transformation,[],[f76]) ).
fof(f120,plain,
in(sK13,sK14),
inference(cnf_transformation,[],[f76]) ).
fof(f121,plain,
in(sK15,sK13),
inference(cnf_transformation,[],[f76]) ).
fof(f122,plain,
~ in(sK15,sK14),
inference(cnf_transformation,[],[f76]) ).
fof(f124,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f126,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f127,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(cnf_transformation,[],[f56]) ).
fof(f130,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f140,plain,
! [X2,X0] :
( ~ subset(X2,X0)
| in(X2,X0)
| ~ epsilon_transitive(X0) ),
inference(consistent_polarity_flipping,[],[f86]) ).
fof(f149,plain,
in(sK15,sK14),
inference(consistent_polarity_flipping,[],[f122]) ).
fof(f150,plain,
~ in(sK15,sK13),
inference(consistent_polarity_flipping,[],[f121]) ).
fof(f151,plain,
~ in(sK13,sK14),
inference(consistent_polarity_flipping,[],[f120]) ).
fof(f153,plain,
! [X0,X1] :
( empty(X1)
| ~ in(X0,X1)
| element(X0,X1) ),
inference(consistent_polarity_flipping,[],[f124]) ).
fof(f154,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) ),
inference(consistent_polarity_flipping,[],[f126]) ).
fof(f156,plain,
! [X2,X0,X1] :
( element(X1,powerset(X2))
| in(X0,X1)
| ~ element(X0,X2) ),
inference(consistent_polarity_flipping,[],[f127]) ).
fof(f158,plain,
! [X0,X1] :
( in(X0,X1)
| ~ empty(X1) ),
inference(consistent_polarity_flipping,[],[f130]) ).
fof(f170,plain,
~ empty(sK14),
inference(resolution,[],[f158,f151]) ).
fof(f229,plain,
! [X0] :
( element(X0,sK14)
| ~ in(X0,sK14) ),
inference(resolution,[],[f153,f170]) ).
fof(f284,plain,
! [X2,X0,X1] :
( ~ element(X0,X2)
| in(X0,X1)
| subset(X1,X2) ),
inference(resolution,[],[f156,f154]) ).
fof(f519,plain,
! [X0,X1] :
( subset(X1,sK14)
| in(X0,X1)
| ~ in(X0,sK14) ),
inference(resolution,[],[f284,f229]) ).
fof(f554,plain,
! [X0,X1] :
( in(X0,X1)
| ~ in(X0,sK14)
| in(X1,sK14)
| ~ epsilon_transitive(sK14) ),
inference(resolution,[],[f519,f140]) ).
fof(f556,definition,
( spl16_19
<=> epsilon_transitive(sK14) ),
introduced(definition,[new_symbols(definition,[spl16_19])],[avatar_definition]) ).
fof(f558,plain,
( ~ epsilon_transitive(sK14)
| spl16_19 ),
inference(avatar_component_clause,[],[f556]) ).
fof(f560,definition,
( spl16_20
<=> ! [X0,X1] :
( in(X0,X1)
| in(X1,sK14)
| ~ in(X0,sK14) ) ),
introduced(definition,[new_symbols(definition,[spl16_20])],[avatar_definition]) ).
fof(f561,plain,
( ! [X0,X1] :
( in(X1,sK14)
| in(X0,X1)
| ~ in(X0,sK14) )
| ~ spl16_20 ),
inference(avatar_component_clause,[],[f560]) ).
fof(f562,plain,
( ~ spl16_19
| spl16_20 ),
inference(avatar_split_clause,[],[f554,f560,f556]) ).
fof(f564,plain,
( ~ ordinal(sK14)
| spl16_19 ),
inference(resolution,[],[f558,f81]) ).
fof(f565,plain,
( $false
| spl16_19 ),
inference(resolution,[],[f564,f118]) ).
fof(f566,plain,
spl16_19,
inference(avatar_contradiction_clause,[],[f565]) ).
fof(f643,plain,
( ! [X0] :
( in(X0,sK13)
| ~ in(X0,sK14) )
| ~ spl16_20 ),
inference(resolution,[],[f561,f151]) ).
fof(f659,plain,
( ~ in(sK15,sK14)
| ~ spl16_20 ),
inference(resolution,[],[f643,f150]) ).
fof(f666,plain,
( $false
| ~ spl16_20 ),
inference(resolution,[],[f659,f149]) ).
fof(f670,plain,
~ spl16_20,
inference(avatar_contradiction_clause,[],[f666]) ).
cnf(s25,plain,
( ~ spl16_19
| spl16_20 ),
inference(sat_conversion,[],[f562]) ).
cnf(s26,plain,
spl16_19,
inference(sat_conversion,[],[f566]) ).
cnf(s37,plain,
~ spl16_20,
inference(sat_conversion,[],[f670]) ).
cnf(s38,plain,
$false,
inference(rat,[],[s25,s37,s26]) ).
fof(f671,plain,
$false,
inference(avatar_sat_refutation,[],[s38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM388+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n005.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 19:45:47 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.41 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
% 0.12/0.45 % (125048)Will run a generic schedule for satisfiability detection.
% 0.12/0.45 % (125059)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2970619058:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.12/0.45 % (125054)% WARNING: option uhcvi not known.
% 0.12/0.45 % (125059) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-125048-125059"...
% 0.12/0.45 % (125053)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4040961002_2999 on theBenchmark for (2999ds/0Mi)
% 0.12/0.45 % (125055)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=676537407:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.12/0.45 % (125054)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2497841714:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.12/0.45 % (125056)dis+10_1_sil=32000:sp=arity:random_seed=2934233832:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.12/0.45 % (125057)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2255746369:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.12/0.45 % (125058)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=6267833:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.12/0.45 % (125059)...printing done.
% 0.12/0.45 % (125059)Refutation found. Thanks to Tanya!
% 0.12/0.45 % SZS status Theorem for theBenchmark
% 0.12/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.46 % (125059)------------------------------
% 0.12/0.46 % (125059)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.46 % (125059)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.46 % (125059)CaDiCaL version: 2.1.3
% 0.12/0.46 % (125059)Termination reason: Refutation
% 0.12/0.46 % (125059)Time elapsed: 0.007 s
% 0.12/0.46 % (125059)Peak memory usage: 12 MB
% 0.12/0.46 % (125059)Instructions burned: 13 (million)
% 0.12/0.46 % (125048)Success in time 0.034 s
% 0.12/0.46 % Vampire exiting
%------------------------------------------------------------------------------