%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET080-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 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 12:40:00 PM UTC 2026
% Result : Unsatisfiable 3.53s 1.47s
% Output : Refutation 3.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 23 ( 12 unt; 1 def)
% Number of atoms : 36 ( 1 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 15 ~; 12 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 11 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_members) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f9,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair2) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set) ).
fof(f48,axiom,
! [X0] :
( ~ inductive(X0)
| member(null_class,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive1) ).
fof(f51,axiom,
inductive(omega),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_is_inductive1) ).
fof(f101,negated_conjecture,
~ member(null_class,singleton(null_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_null_class_in_its_singleton_1) ).
fof(f105,plain,
member(null_class,omega),
inference(resolution,[],[f48,f51]) ).
fof(f108,plain,
! [X0] :
( member(X0,singleton(X0))
| ~ member(X0,universal_class) ),
inference(superposition,[],[f9,f12]) ).
fof(f163,definition,
( spl0_6
<=> member(null_class,universal_class) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f164,plain,
( member(null_class,universal_class)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f163]) ).
fof(f165,plain,
( ~ member(null_class,universal_class)
| spl0_6 ),
inference(avatar_component_clause,[],[f163]) ).
fof(f170,plain,
( ! [X0] :
( ~ member(null_class,X0)
| ~ subclass(X0,universal_class) )
| spl0_6 ),
inference(resolution,[],[f165,f1]) ).
fof(f171,plain,
( ! [X0] : ~ member(null_class,X0)
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f170,f4]) ).
fof(f176,plain,
( $false
| spl0_6 ),
inference(resolution,[],[f171,f105]) ).
fof(f177,plain,
spl0_6,
inference(avatar_contradiction_clause,[],[f176]) ).
fof(f332,plain,
~ member(null_class,universal_class),
inference(resolution,[],[f108,f101]) ).
fof(f333,plain,
( $false
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f332,f164]) ).
fof(f334,plain,
~ spl0_6,
inference(avatar_contradiction_clause,[],[f333]) ).
cnf(s4,plain,
spl0_6,
inference(sat_conversion,[],[f177]) ).
cnf(s9,plain,
~ spl0_6,
inference(sat_conversion,[],[f334]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s4,s9]) ).
fof(f335,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET080-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n005.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 00:33:47 UTC 2026
% 0.14/0.38 % CPUTime :
% 0.14/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.53/1.47 % (326011)Input is clausal, will run a generic CNF schedule.
% 3.53/1.47 % (326017)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2456385001:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.53/1.47 % (326021)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=647607335:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.53/1.47 % (326016)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=2270886704:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.53/1.47 % (326019)lrs+10_1_sil=8000:sp=occurrence:random_seed=2561014515:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.53/1.47 % (326018)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=533845356:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.53/1.47 % (326020)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1255238294:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.53/1.47 % (326019)Refutation not found, incomplete strategy
% 3.53/1.47 % (326019)------------------------------
% 3.53/1.47 % (326019)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.47 % (326019)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.47 % (326019)CaDiCaL version: 2.1.3
% 3.53/1.47 % (326019)Termination reason: Refutation not found, incomplete strategy
% 3.53/1.47 % (326019)Time elapsed: 0.001 s
% 3.53/1.47 % (326019)Peak memory usage: 86 MB
% 3.53/1.47 % (326022)dis-21_1_sil=8000:lcm=predicate:random_seed=2150547339:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 3.53/1.47 % (326021)First to succeed.
% 3.53/1.47 % (326021)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-326011"
% 3.53/1.47 % (326022)Also succeeded, but the first one will report.
% 3.53/1.47 % (326020)Instruction limit reached!
% 3.53/1.47 % (326020)------------------------------
% 3.53/1.47 % (326020)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.47 % (326020)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.47 % (326020)CaDiCaL version: 2.1.3
% 3.53/1.47 % (326020)Termination reason: Instruction limit
% 3.53/1.47 % (326020)Termination phase: Saturation
% 3.53/1.47 % (326020)Time elapsed: 0.068 s
% 3.53/1.47 % (326020)Peak memory usage: 89 MB
% 3.53/1.47 % (326020)Instructions burned: 114 (million)
% 3.53/1.47 % (326030)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=3162977453:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.53/1.47 % (326030)Refutation not found, incomplete strategy
% 3.53/1.47 % (326030)------------------------------
% 3.53/1.47 % (326030)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.47 % (326030)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.47 % (326030)CaDiCaL version: 2.1.3
% 3.53/1.47 % (326030)Termination reason: Refutation not found, incomplete strategy
% 3.53/1.47 % (326030)Time elapsed: 0.003 s
% 3.53/1.47 % (326030)Peak memory usage: 88 MB
% 3.53/1.47 % (326030)Instructions burned: 3 (million)
% 3.53/1.47 % (326019)------------------------------
% 3.53/1.47 % (326019)------------------------------
% 3.53/1.47 % (326021)Refutation found. Thanks to Tanya!
% 3.53/1.47 % SZS status Unsatisfiable for theBenchmark
% 3.53/1.47 % SZS output start Proof for theBenchmark
% See solution above
% 3.53/1.47 % (326021)------------------------------
% 3.53/1.47 % (326021)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.47 % (326021)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.47 % (326021)CaDiCaL version: 2.1.3
% 3.53/1.47 % (326021)Termination reason: Refutation
% 3.53/1.47 % (326021)Time elapsed: 0.014 s
% 3.53/1.47 % (326021)Peak memory usage: 89 MB
% 3.53/1.47 % (326021)Instructions burned: 15 (million)
% 3.53/1.47 % (326021)------------------------------
% 3.53/1.47 % (326021)------------------------------
% 3.53/1.47 % (326011)Success in time 0.422 s
% 3.53/1.47 % Vampire exiting
%------------------------------------------------------------------------------