%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM395+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 : n018.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 4.68s 1.74s
% Output : Refutation 4.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 12 unt; 2 def)
% Number of atoms : 44 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 35 ( 17 ~; 13 |; 2 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-1 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 4 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
! [X0] :
( ( epsilon_transitive(X0)
& epsilon_connected(X0) )
=> ordinal(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_ordinal1) ).
fof(f27,conjecture,
ordinal(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_ordinal1) ).
fof(f28,negated_conjecture,
~ ordinal(empty_set),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f30,axiom,
( epsilon_transitive(empty_set)
& epsilon_connected(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l18_ordinal1) ).
fof(f31,plain,
~ ordinal(empty_set),
inference(flattening,[],[f28]) ).
fof(f49,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_transitive(X0)
| ~ epsilon_connected(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f50,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_transitive(X0)
| ~ epsilon_connected(X0) ),
inference(flattening,[],[f49]) ).
fof(f78,plain,
! [X0] :
( ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0)
| ordinal(X0) ),
inference(cnf_transformation,[],[f50]) ).
fof(f106,plain,
~ ordinal(empty_set),
inference(cnf_transformation,[],[f31]) ).
fof(f110,plain,
epsilon_connected(empty_set),
inference(cnf_transformation,[],[f30]) ).
fof(f111,plain,
epsilon_transitive(empty_set),
inference(cnf_transformation,[],[f30]) ).
fof(f119,plain,
( ~ epsilon_transitive(empty_set)
| ordinal(empty_set) ),
inference(resolution,[],[f78,f110]) ).
fof(f122,definition,
( spl13_1
<=> ordinal(empty_set) ),
introduced(definition,[new_symbols(definition,[spl13_1])],[avatar_definition]) ).
fof(f123,plain,
( ordinal(empty_set)
| ~ spl13_1 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f125,definition,
( spl13_2
<=> epsilon_transitive(empty_set) ),
introduced(definition,[new_symbols(definition,[spl13_2])],[avatar_definition]) ).
fof(f126,plain,
( ~ epsilon_transitive(empty_set)
| spl13_2 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f127,plain,
( spl13_1
| ~ spl13_2 ),
inference(avatar_split_clause,[],[f119,f125,f122]) ).
fof(f128,plain,
( $false
| spl13_2 ),
inference(resolution,[],[f126,f111]) ).
fof(f130,plain,
spl13_2,
inference(avatar_contradiction_clause,[],[f128]) ).
fof(f131,plain,
( $false
| ~ spl13_1 ),
inference(resolution,[],[f123,f106]) ).
fof(f132,plain,
~ spl13_1,
inference(avatar_contradiction_clause,[],[f131]) ).
cnf(s1,plain,
( spl13_1
| ~ spl13_2 ),
inference(sat_conversion,[],[f127]) ).
cnf(s2,plain,
spl13_2,
inference(sat_conversion,[],[f130]) ).
cnf(s3,plain,
~ spl13_1,
inference(sat_conversion,[],[f132]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f133,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM395+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 : n018.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 19:48:39 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.43 Running first-order theorem proving
% 0.15/0.43 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
% 4.68/1.74 % (2683288)Detected formulas, will run a generic FOF schedule.
% 4.68/1.74 % (2683303)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=1613945120:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.68/1.74 % (2683308)dis-21_1_sil=8000:lcm=predicate:random_seed=588103707: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)
% 4.68/1.74 % (2683308)First to succeed.
% 4.68/1.74 % (2683308)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2683288"
% 4.68/1.74 % (2683304)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=3331880466:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.68/1.74 % (2683306)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1335708191:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.68/1.74 % (2683307)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4266374139:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.68/1.74 % (2683305)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2925225895:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.68/1.74 % (2683302)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=3516506983:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.68/1.74 % (2683306)Also succeeded, but the first one will report.
% 4.68/1.74 % (2683305)Refutation not found, incomplete strategy
% 4.68/1.74 % (2683305)------------------------------
% 4.68/1.74 % (2683305)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.68/1.74 % (2683305)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.68/1.74 % (2683305)CaDiCaL version: 2.1.3
% 4.68/1.74 % (2683305)Termination reason: Refutation not found, incomplete strategy
% 4.68/1.74 % (2683305)Time elapsed: 0.001 s
% 4.68/1.74 % (2683305)Peak memory usage: 88 MB
% 4.68/1.74 % (2683307)Also succeeded, but the first one will report.
% 4.68/1.74 % (2683308)Refutation found. Thanks to Tanya!
% 4.68/1.74 % SZS status Theorem for theBenchmark
% 4.68/1.74 % SZS output start Proof for theBenchmark
% See solution above
% 4.68/1.74 % (2683308)------------------------------
% 4.68/1.74 % (2683308)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.68/1.74 % (2683308)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.68/1.74 % (2683308)CaDiCaL version: 2.1.3
% 4.68/1.74 % (2683308)Termination reason: Refutation
% 4.68/1.74 % (2683308)Time elapsed: 0.003 s
% 4.68/1.74 % (2683308)Peak memory usage: 89 MB
% 4.68/1.74 % (2683308)Instructions burned: 1 (million)
% 4.68/1.74 % (2683308)------------------------------
% 4.68/1.74 % (2683308)------------------------------
% 4.68/1.74 % (2683288)Success in time 0.553 s
% 4.68/1.74 % Vampire exiting
%------------------------------------------------------------------------------