%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM394+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 : n020.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 12:15:03 PM UTC 2026
% Result : Theorem 2.03s 1.30s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 74 ( 17 unt; 5 def)
% Number of atoms : 197 ( 9 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 214 ( 91 ~; 83 |; 21 &)
% ( 10 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 6 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 52 ( 1 sgn 46 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( ordinal(X0)
=> ( epsilon_transitive(X0)
& epsilon_connected(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_ordinal1) ).
fof(f8,axiom,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( in(X1,X0)
=> subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(f24,axiom,
! [X0,X1] :
( ( ordinal(X0)
& ordinal(X1) )
=> ( ordinal_subset(X0,X1)
<=> subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
fof(f26,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f28,axiom,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ~ ( ~ in(X0,X1)
& X0 != X1
& ~ in(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_ordinal1) ).
fof(f29,conjecture,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ( ordinal_subset(X0,X1)
| in(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_ordinal1) ).
fof(f30,negated_conjecture,
~ ! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ( ordinal_subset(X0,X1)
| in(X1,X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f38,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f26]) ).
fof(f47,plain,
! [X0] :
( ( epsilon_transitive(X0)
& epsilon_connected(X0) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f55,plain,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f56,plain,
! [X0,X1] :
( ( ordinal_subset(X0,X1)
<=> subset(X0,X1) )
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(ennf_transformation,[],[f24]) ).
fof(f57,plain,
! [X0,X1] :
( ( ordinal_subset(X0,X1)
<=> subset(X0,X1) )
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(flattening,[],[f56]) ).
fof(f61,plain,
! [X0] :
( ! [X1] :
( in(X0,X1)
| X0 = X1
| in(X1,X0)
| ~ ordinal(X1) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f62,plain,
! [X0] :
( ! [X1] :
( in(X0,X1)
| X0 = X1
| in(X1,X0)
| ~ ordinal(X1) )
| ~ ordinal(X0) ),
inference(flattening,[],[f61]) ).
fof(f63,plain,
? [X0] :
( ? [X1] :
( ~ ordinal_subset(X0,X1)
& ~ in(X1,X0)
& ordinal(X1) )
& ordinal(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f64,plain,
? [X0] :
( ? [X1] :
( ~ ordinal_subset(X0,X1)
& ~ in(X1,X0)
& ordinal(X1) )
& ordinal(X0) ),
inference(flattening,[],[f63]) ).
fof(f73,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,[],[f55]) ).
fof(f74,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(rectify,[],[f73]) ).
fof(f75,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))],[f74]) ).
fof(f88,plain,
! [X0,X1] :
( ( ( ordinal_subset(X0,X1)
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ ordinal_subset(X0,X1) ) )
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(nnf_transformation,[],[f57]) ).
fof(f89,plain,
( ~ ordinal_subset(sK13,sK14)
& ~ in(sK14,sK13)
& ordinal(sK14)
& ordinal(sK13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14]),skolemize(X0,sK13),skolemize(X1,sK14)],[f64]) ).
fof(f94,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f100,plain,
! [X2,X0] :
( ~ in(X2,X0)
| subset(X2,X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f131,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ordinal_subset(X0,X1)
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f88]) ).
fof(f133,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f38]) ).
fof(f135,plain,
! [X0,X1] :
( ~ ordinal(X0)
| X0 = X1
| in(X1,X0)
| ~ ordinal(X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f136,plain,
ordinal(sK13),
inference(cnf_transformation,[],[f89]) ).
fof(f137,plain,
ordinal(sK14),
inference(cnf_transformation,[],[f89]) ).
fof(f138,plain,
~ in(sK14,sK13),
inference(cnf_transformation,[],[f89]) ).
fof(f139,plain,
~ ordinal_subset(sK13,sK14),
inference(cnf_transformation,[],[f89]) ).
fof(f152,definition,
( spl15_2
<=> ! [X0] :
( ordinal_subset(X0,X0)
| ~ ordinal(X0) ) ),
introduced(definition,[new_symbols(definition,[spl15_2])],[avatar_definition]) ).
fof(f153,plain,
( ! [X0] :
( ordinal_subset(X0,X0)
| ~ ordinal(X0) )
| ~ spl15_2 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f167,plain,
! [X0] :
( ~ ordinal(X0)
| in(X0,sK14)
| sK14 = X0
| in(sK14,X0) ),
inference(resolution,[],[f135,f137]) ).
fof(f190,definition,
( spl15_6
<=> in(sK13,sK14) ),
introduced(definition,[new_symbols(definition,[spl15_6])],[avatar_definition]) ).
fof(f192,plain,
( in(sK13,sK14)
| ~ spl15_6 ),
inference(avatar_component_clause,[],[f190]) ).
fof(f194,definition,
( spl15_7
<=> sK13 = sK14 ),
introduced(definition,[new_symbols(definition,[spl15_7])],[avatar_definition]) ).
fof(f196,plain,
( sK13 = sK14
| ~ spl15_7 ),
inference(avatar_component_clause,[],[f194]) ).
fof(f200,plain,
( in(sK13,sK14)
| sK13 = sK14
| in(sK14,sK13) ),
inference(resolution,[],[f167,f136]) ).
fof(f203,plain,
( in(sK13,sK14)
| sK13 = sK14 ),
inference(forward_subsumption_resolution,[],[f200,f138]) ).
fof(f217,plain,
( spl15_7
| spl15_6 ),
inference(avatar_split_clause,[],[f203,f190,f194]) ).
fof(f224,plain,
! [X0] :
( ordinal_subset(X0,X0)
| ~ ordinal(X0)
| ~ ordinal(X0) ),
inference(resolution,[],[f133,f131]) ).
fof(f225,plain,
! [X0] :
( ordinal_subset(X0,X0)
| ~ ordinal(X0) ),
inference(duplicate_literal_removal,[],[f224]) ).
fof(f232,definition,
( spl15_11
<=> epsilon_transitive(sK14) ),
introduced(definition,[new_symbols(definition,[spl15_11])],[avatar_definition]) ).
fof(f233,plain,
( epsilon_transitive(sK14)
| ~ spl15_11 ),
inference(avatar_component_clause,[],[f232]) ).
fof(f234,plain,
( ~ epsilon_transitive(sK14)
| spl15_11 ),
inference(avatar_component_clause,[],[f232]) ).
fof(f236,definition,
( spl15_12
<=> subset(sK13,sK14) ),
introduced(definition,[new_symbols(definition,[spl15_12])],[avatar_definition]) ).
fof(f238,plain,
( subset(sK13,sK14)
| ~ spl15_12 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f242,plain,
( ~ ordinal(sK14)
| spl15_11 ),
inference(resolution,[],[f234,f94]) ).
fof(f243,plain,
( $false
| spl15_11 ),
inference(forward_subsumption_resolution,[],[f242,f137]) ).
fof(f244,plain,
spl15_11,
inference(avatar_contradiction_clause,[],[f243]) ).
fof(f254,plain,
( ~ ordinal_subset(sK13,sK13)
| ~ spl15_7 ),
inference(superposition,[],[f139,f196]) ).
fof(f278,plain,
( ~ ordinal(sK13)
| ~ spl15_2
| ~ spl15_7 ),
inference(resolution,[],[f254,f153]) ).
fof(f281,plain,
( $false
| ~ spl15_2
| ~ spl15_7 ),
inference(forward_subsumption_resolution,[],[f278,f136]) ).
fof(f282,plain,
( ~ spl15_2
| ~ spl15_7 ),
inference(avatar_contradiction_clause,[],[f281]) ).
fof(f285,plain,
( subset(sK13,sK14)
| ~ epsilon_transitive(sK14)
| ~ spl15_6 ),
inference(resolution,[],[f192,f100]) ).
fof(f288,plain,
( subset(sK13,sK14)
| ~ spl15_6
| ~ spl15_11 ),
inference(forward_subsumption_resolution,[],[f285,f233]) ).
fof(f289,plain,
( spl15_12
| ~ spl15_6
| ~ spl15_11 ),
inference(avatar_split_clause,[],[f288,f232,f190,f236]) ).
fof(f299,plain,
( ordinal_subset(sK13,sK14)
| ~ ordinal(sK13)
| ~ ordinal(sK14)
| ~ spl15_12 ),
inference(resolution,[],[f238,f131]) ).
fof(f300,plain,
( ~ ordinal(sK13)
| ~ ordinal(sK14)
| ~ spl15_12 ),
inference(forward_subsumption_resolution,[],[f299,f139]) ).
fof(f301,plain,
( ~ ordinal(sK14)
| ~ spl15_12 ),
inference(forward_subsumption_resolution,[],[f300,f136]) ).
fof(f302,plain,
( $false
| ~ spl15_12 ),
inference(forward_subsumption_resolution,[],[f301,f137]) ).
fof(f303,plain,
~ spl15_12,
inference(avatar_contradiction_clause,[],[f302]) ).
fof(f304,plain,
spl15_2,
inference(avatar_split_clause,[],[f225,f152]) ).
cnf(s5,plain,
( spl15_6
| spl15_7 ),
inference(sat_conversion,[],[f217]) ).
cnf(s8,plain,
spl15_11,
inference(sat_conversion,[],[f244]) ).
cnf(s9,plain,
( ~ spl15_2
| ~ spl15_7 ),
inference(sat_conversion,[],[f282]) ).
cnf(s11,plain,
( ~ spl15_6
| ~ spl15_11
| spl15_12 ),
inference(sat_conversion,[],[f289]) ).
cnf(s13,plain,
~ spl15_12,
inference(sat_conversion,[],[f303]) ).
cnf(s14,plain,
spl15_2,
inference(sat_conversion,[],[f304]) ).
cnf(s15,plain,
( ~ spl15_6
| ~ spl15_11 ),
inference(rat,[],[s11,s13]) ).
cnf(s16,plain,
~ spl15_7,
inference(rat,[],[s9,s14]) ).
cnf(s17,plain,
~ spl15_6,
inference(rat,[],[s15,s8]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s5,s16,s17]) ).
fof(f305,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM394+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n020.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 19:47:04 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
% 2.03/1.30 % (3702726)Detected formulas, will run a generic FOF schedule.
% 2.03/1.30 % (3702737)dis-21_1_sil=8000:lcm=predicate:random_seed=602444398: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)
% 2.03/1.30 % (3702731)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=3141172376:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.03/1.30 % (3702733)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=2283007289:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.03/1.30 % (3702734)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=628722235:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.03/1.30 % (3702732)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=2463409406:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.03/1.30 % (3702734)Refutation not found, incomplete strategy
% 2.03/1.30 % (3702734)------------------------------
% 2.03/1.30 % (3702734)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.03/1.30 % (3702734)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/1.30 % (3702734)CaDiCaL version: 2.1.3
% 2.03/1.30 % (3702734)Termination reason: Refutation not found, incomplete strategy
% 2.03/1.30 % (3702734)Time elapsed: 0.001 s
% 2.03/1.30 % (3702734)Peak memory usage: 88 MB
% 2.03/1.30 % (3702737)Instruction limit reached!
% 2.03/1.30 % (3702737)------------------------------
% 2.03/1.30 % (3702737)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.03/1.30 % (3702737)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/1.30 % (3702737)CaDiCaL version: 2.1.3
% 2.03/1.30 % (3702737)Termination reason: Instruction limit
% 2.03/1.30 % (3702737)Termination phase: Saturation
% 2.03/1.30 % (3702737)Time elapsed: 0.039 s
% 2.03/1.30 % (3702737)Peak memory usage: 89 MB
% 2.03/1.30 % (3702737)Instructions burned: 130 (million)
% 2.03/1.30 % (3702736)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3377967577:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.03/1.30 % (3702735)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3031743573:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.03/1.30 % (3702735)Refutation not found, incomplete strategy
% 2.03/1.30 % (3702735)------------------------------
% 2.03/1.30 % (3702735)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.03/1.30 % (3702735)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/1.30 % (3702735)CaDiCaL version: 2.1.3
% 2.03/1.30 % (3702735)Termination reason: Refutation not found, incomplete strategy
% 2.03/1.30 % (3702735)Time elapsed: 0.001 s
% 2.03/1.30 % (3702735)Peak memory usage: 88 MB
% 2.03/1.30 % (3702736)First to succeed.
% 2.03/1.30 % (3702736)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3702726"
% 2.03/1.30 % (3702743)lrs+10_1_sil=8000:sp=occurrence:random_seed=2910195319:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.03/1.30 % (3702743)Also succeeded, but the first one will report.
% 2.03/1.30 % (3702734)------------------------------
% 2.03/1.30 % (3702734)------------------------------
% 2.03/1.30 % (3702735)------------------------------
% 2.03/1.30 % (3702735)------------------------------
% 2.03/1.30 % (3702736)Refutation found. Thanks to Tanya!
% 2.03/1.30 % SZS status Theorem for theBenchmark
% 2.03/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/1.50 % (3702736)------------------------------
% 0.18/1.50 % (3702736)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.50 % (3702736)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.50 % (3702736)CaDiCaL version: 2.1.3
% 0.18/1.50 % (3702736)Termination reason: Refutation
% 0.18/1.50 % (3702736)Time elapsed: 0.007 s
% 0.18/1.50 % (3702736)Peak memory usage: 89 MB
% 0.18/1.50 % (3702736)Instructions burned: 7 (million)
% 0.18/1.50 % (3702736)------------------------------
% 0.18/1.50 % (3702736)------------------------------
% 0.18/1.50 % (3702726)Success in time 0.444 s
% 0.18/1.50 % Vampire exiting
%------------------------------------------------------------------------------