%------------------------------------------------------------------------------
% File : Vampire---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 THM
% 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 12:15:02 PM UTC 2026
% Result : Theorem 3.49s 1.38s
% Output : Refutation 3.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 59 ( 13 unt; 3 def)
% Number of atoms : 162 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 167 ( 64 ~; 57 |; 28 &)
% ( 6 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 74 ( 0 sgn 66 !; 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] :
( ~ ordinal(X0)
| epsilon_transitive(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] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f126,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(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(f138,plain,
epsilon_transitive(sK14),
inference(resolution,[],[f81,f118]) ).
fof(f140,plain,
~ empty(sK14),
inference(resolution,[],[f130,f120]) ).
fof(f151,plain,
! [X0,X1] :
( ~ epsilon_transitive(X1)
| ~ in(X0,X1)
| element(X0,powerset(X1)) ),
inference(resolution,[],[f86,f126]) ).
fof(f161,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| in(X0,X2)
| empty(X2) ),
inference(resolution,[],[f127,f124]) ).
fof(f168,plain,
! [X0] :
( element(X0,powerset(sK14))
| ~ in(X0,sK14) ),
inference(resolution,[],[f151,f138]) ).
fof(f215,plain,
! [X0,X1] :
( ~ in(X0,X1)
| in(X0,sK14)
| empty(sK14)
| ~ in(X1,sK14) ),
inference(resolution,[],[f161,f168]) ).
fof(f219,definition,
( spl17_7
<=> empty(sK14) ),
introduced(definition,[new_symbols(definition,[spl17_7])],[avatar_definition]) ).
fof(f220,plain,
( empty(sK14)
| ~ spl17_7 ),
inference(avatar_component_clause,[],[f219]) ).
fof(f222,definition,
( spl17_8
<=> ! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,sK14)
| in(X0,sK14) ) ),
introduced(definition,[new_symbols(definition,[spl17_8])],[avatar_definition]) ).
fof(f223,plain,
( ! [X0,X1] :
( in(X0,sK14)
| ~ in(X1,sK14)
| ~ in(X0,X1) )
| ~ spl17_8 ),
inference(avatar_component_clause,[],[f222]) ).
fof(f224,plain,
( spl17_7
| spl17_8 ),
inference(avatar_split_clause,[],[f215,f222,f219]) ).
fof(f232,plain,
( $false
| ~ spl17_7 ),
inference(resolution,[],[f220,f140]) ).
fof(f233,plain,
~ spl17_7,
inference(avatar_contradiction_clause,[],[f232]) ).
fof(f242,plain,
( ! [X0] :
( ~ in(X0,sK14)
| ~ in(sK15,X0) )
| ~ spl17_8 ),
inference(resolution,[],[f223,f122]) ).
fof(f277,plain,
( ~ in(sK13,sK14)
| ~ spl17_8 ),
inference(resolution,[],[f242,f121]) ).
fof(f284,definition,
( spl17_18
<=> in(sK13,sK14) ),
introduced(definition,[new_symbols(definition,[spl17_18])],[avatar_definition]) ).
fof(f285,plain,
( ~ in(sK13,sK14)
| spl17_18 ),
inference(avatar_component_clause,[],[f284]) ).
fof(f287,plain,
( ~ spl17_18
| ~ spl17_8 ),
inference(avatar_split_clause,[],[f277,f222,f284]) ).
fof(f292,plain,
( $false
| spl17_18 ),
inference(resolution,[],[f285,f120]) ).
fof(f294,plain,
spl17_18,
inference(avatar_contradiction_clause,[],[f292]) ).
cnf(s6,plain,
( spl17_7
| spl17_8 ),
inference(sat_conversion,[],[f224]) ).
cnf(s8,plain,
~ spl17_7,
inference(sat_conversion,[],[f233]) ).
cnf(s14,plain,
( ~ spl17_8
| ~ spl17_18 ),
inference(sat_conversion,[],[f287]) ).
cnf(s16,plain,
spl17_18,
inference(sat_conversion,[],[f294]) ).
cnf(s17,plain,
~ spl17_8,
inference(rat,[],[s14,s16]) ).
cnf(s19,plain,
$false,
inference(rat,[],[s6,s17,s8]) ).
fof(f295,plain,
$false,
inference(avatar_sat_refutation,[],[s19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM388+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n008.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 19:46:39 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.49/1.38 % (1553123)Detected formulas, will run a generic FOF schedule.
% 3.49/1.38 % (1553129)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2588389957:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.49/1.38 % (1553132)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1888768439:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.49/1.38 % (1553130)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3567534317:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.49/1.38 % (1553131)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2942453002:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.49/1.38 % (1553133)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2400588997:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.49/1.38 % (1553128)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1159828253:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.49/1.38 % (1553134)dis-21_1_sil=8000:lcm=predicate:random_seed=1676100182:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.49/1.38 % (1553131)Refutation not found, incomplete strategy
% 3.49/1.38 % (1553131)------------------------------
% 3.49/1.38 % (1553131)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.38 % (1553132)Refutation not found, incomplete strategy
% 3.49/1.38 % (1553132)------------------------------
% 3.49/1.38 % (1553132)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.38 % (1553132)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.38 % (1553131)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.38 % (1553131)CaDiCaL version: 2.1.3
% 3.49/1.38 % (1553132)CaDiCaL version: 2.1.3
% 3.49/1.38 % (1553131)Termination reason: Refutation not found, incomplete strategy
% 3.49/1.38 % (1553131)Time elapsed: 0.001 s
% 3.49/1.38 % (1553132)Termination reason: Refutation not found, incomplete strategy
% 3.49/1.38 % (1553132)Time elapsed: 0.001 s
% 3.49/1.38 % (1553131)Peak memory usage: 88 MB
% 3.49/1.38 % (1553132)Peak memory usage: 87 MB
% 3.49/1.38 % (1553134)First to succeed.
% 3.49/1.38 % (1553134)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1553123"
% 3.49/1.38 % (1553133)Also succeeded, but the first one will report.
% 3.49/1.38 % (1553131)------------------------------
% 3.49/1.38 % (1553131)------------------------------
% 3.49/1.38 % (1553132)------------------------------
% 3.49/1.38 % (1553132)------------------------------
% 3.49/1.38 % (1553134)Refutation found. Thanks to Tanya!
% 3.49/1.38 % SZS status Theorem for theBenchmark
% 3.49/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 3.49/1.38 % (1553134)------------------------------
% 3.49/1.38 % (1553134)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.38 % (1553134)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.38 % (1553134)CaDiCaL version: 2.1.3
% 3.49/1.38 % (1553134)Termination reason: Refutation
% 3.49/1.38 % (1553134)Time elapsed: 0.005 s
% 3.49/1.38 % (1553134)Peak memory usage: 89 MB
% 3.49/1.38 % (1553134)Instructions burned: 5 (million)
% 3.49/1.38 % (1553134)------------------------------
% 3.49/1.38 % (1553134)------------------------------
% 3.49/1.38 % (1553123)Success in time 0.431 s
% 3.49/1.38 % Vampire exiting
%------------------------------------------------------------------------------