%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM190-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n026.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 12:18:04 PM UTC 2026
% Result : Unsatisfiable 0.17s 0.48s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 26 ( 11 unt; 1 def)
% Number of atoms : 43 ( 14 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 33 ( 16 ~; 16 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f21,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection1) ).
fof(f24,axiom,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement1) ).
fof(f48,axiom,
! [X0] :
( ~ inductive(X0)
| member(null_class,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',inductive1) ).
fof(f51,axiom,
inductive(omega),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',omega_is_inductive1) ).
fof(f69,axiom,
! [X0] :
( X0 = null_class
| intersection(X0,regular(X0)) = null_class ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity2) ).
fof(f70,plain,
! [X0] :
( null_class = X0
| null_class = intersection(X0,regular(X0)) ),
inference(reorient_equations,[],[f69]) ).
fof(f176,negated_conjecture,
omega = null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_omega_is_not_null_1) ).
fof(f177,plain,
null_class = omega,
inference(reorient_equations,[],[f176]) ).
fof(f210,plain,
! [X0] :
( ~ inductive(X0)
| member(omega,X0) ),
inference(definition_unfolding,[],[f48,f177]) ).
fof(f223,plain,
! [X0] :
( omega = intersection(X0,regular(X0))
| omega = X0 ),
inference(definition_unfolding,[],[f70,f177,f177]) ).
fof(f283,plain,
member(omega,omega),
inference(resolution,[],[f51,f210]) ).
fof(f402,definition,
( spl0_22
<=> omega = complement(omega) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f404,plain,
( omega = complement(omega)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f402]) ).
fof(f469,plain,
! [X0,X1] :
( ~ member(X0,omega)
| member(X0,X1)
| omega = X1 ),
inference(superposition,[],[f21,f223]) ).
fof(f474,plain,
! [X0] :
( member(omega,X0)
| omega = X0 ),
inference(resolution,[],[f469,f283]) ).
fof(f609,plain,
! [X0] :
( ~ member(omega,X0)
| complement(X0) = omega ),
inference(resolution,[],[f474,f24]) ).
fof(f655,plain,
omega = complement(omega),
inference(resolution,[],[f609,f283]) ).
fof(f670,plain,
spl0_22,
inference(avatar_split_clause,[],[f655,f402]) ).
fof(f677,plain,
( ! [X0] :
( ~ member(X0,omega)
| ~ member(X0,omega) )
| ~ spl0_22 ),
inference(superposition,[],[f24,f404]) ).
fof(f678,plain,
( ! [X0] : ~ member(X0,omega)
| ~ spl0_22 ),
inference(duplicate_literal_removal,[],[f677]) ).
fof(f689,plain,
( $false
| ~ spl0_22 ),
inference(resolution,[],[f678,f283]) ).
fof(f693,plain,
~ spl0_22,
inference(avatar_contradiction_clause,[],[f689]) ).
cnf(s23,plain,
spl0_22,
inference(sat_conversion,[],[f670]) ).
cnf(s24,plain,
~ spl0_22,
inference(sat_conversion,[],[f693]) ).
cnf(s25,plain,
$false,
inference(rat,[],[s23,s24]) ).
fof(f694,plain,
$false,
inference(avatar_sat_refutation,[],[s25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM190-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n026.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 19:10:42 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.43 Running first-order model finding
% 0.12/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.48 % (3149897)Will run a generic schedule for satisfiability detection.
% 0.17/0.48 % (3149906)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2538860050:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.48 % (3149903)% WARNING: option uhcvi not known.
% 0.17/0.48 % (3149903)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=730759423:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.48 % (3149902)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1063749318_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.48 % (3149904)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4009235923:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.48 % (3149905)dis+10_1_sil=32000:sp=arity:random_seed=33366203:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.48 % (3149907)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1093681997:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.48 % (3149908)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1462071749:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.48 % (3149906) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3149897-3149906"...
% 0.17/0.48 % (3149906)...printing done.
% 0.17/0.48 % (3149906)Refutation found. Thanks to Tanya!
% 0.17/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.48 % (3149906)------------------------------
% 0.17/0.48 % (3149906)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.48 % (3149906)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.48 % (3149906)CaDiCaL version: 2.1.3
% 0.17/0.48 % (3149906)Termination reason: Refutation
% 0.17/0.48 % (3149906)Time elapsed: 0.011 s
% 0.17/0.48 % (3149906)Peak memory usage: 13 MB
% 0.17/0.48 % (3149906)Instructions burned: 28 (million)
% 0.17/0.48 % (3149897)Success in time 0.042 s
% 0.17/0.48 % Vampire exiting
%------------------------------------------------------------------------------