%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM549+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 12:24:46 PM UTC 2026
% Result : Theorem 0.10s 0.45s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 40 ( 13 unt; 2 def)
% Number of atoms : 79 ( 21 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 71 ( 32 ~; 22 |; 8 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-1 aty)
% Number of variables : 23 ( 0 sgn 20 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(f5,axiom,
! [X0] :
( X0 = slcrc0
<=> ( aSet0(X0)
& ~ ? [X1] : aElementOf0(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
fof(f42,axiom,
! [X0] :
( aSet0(X0)
=> ( sbrdtbr0(X0) = sz00
<=> X0 = slcrc0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardEmpty) ).
fof(f62,axiom,
( aSet0(xS)
& aSet0(xT)
& xk != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2202_02) ).
fof(f66,axiom,
( aSet0(xQ)
& isFinite0(xQ)
& sbrdtbr0(xQ) = xk ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2291) ).
fof(f67,conjecture,
? [X0] :
( aElement0(X0)
& aElementOf0(X0,xQ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f68,negated_conjecture,
~ ? [X0] :
( aElement0(X0)
& aElementOf0(X0,xQ) ),
inference(negated_conjecture,[status(cth)],[f67]) ).
fof(f72,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f75,plain,
! [X0] :
( X0 = slcrc0
<=> ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f130,plain,
! [X0] :
( ( sbrdtbr0(X0) = sz00
<=> X0 = slcrc0 )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f165,plain,
! [X0] :
( ~ aElement0(X0)
| ~ aElementOf0(X0,xQ) ),
inference(ennf_transformation,[],[f68]) ).
fof(f166,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f168,plain,
! [X0] :
( aSet0(X0)
| slcrc0 != X0 ),
inference(cnf_transformation,[],[f75]) ).
fof(f169,plain,
! [X0] :
( ~ aSet0(X0)
| aElementOf0(sK0(X0),X0)
| slcrc0 = X0 ),
inference(cnf_transformation,[],[f75]) ).
fof(f227,plain,
! [X0] :
( ~ aSet0(X0)
| slcrc0 != X0
| sz00 = sbrdtbr0(X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f271,plain,
sz00 != xk,
inference(cnf_transformation,[],[f62]) ).
fof(f307,plain,
xk = sbrdtbr0(xQ),
inference(cnf_transformation,[],[f66]) ).
fof(f309,plain,
aSet0(xQ),
inference(cnf_transformation,[],[f66]) ).
fof(f310,plain,
! [X0] :
( ~ aElement0(X0)
| ~ aElementOf0(X0,xQ) ),
inference(cnf_transformation,[],[f165]) ).
fof(f311,plain,
aSet0(slcrc0),
inference(equality_resolution,[],[f168]) ).
fof(f326,plain,
( ~ aSet0(slcrc0)
| sz00 = sbrdtbr0(slcrc0) ),
inference(equality_resolution,[],[f227]) ).
fof(f344,definition,
( spl15_1
<=> sz00 = sbrdtbr0(slcrc0) ),
introduced(definition,[new_symbols(definition,[spl15_1])],[avatar_definition]) ).
fof(f346,plain,
( sz00 = sbrdtbr0(slcrc0)
| ~ spl15_1 ),
inference(avatar_component_clause,[],[f344]) ).
fof(f348,definition,
( spl15_2
<=> aSet0(slcrc0) ),
introduced(definition,[new_symbols(definition,[spl15_2])],[avatar_definition]) ).
fof(f351,plain,
( spl15_1
| ~ spl15_2 ),
inference(avatar_split_clause,[],[f326,f348,f344]) ).
fof(f357,plain,
spl15_2,
inference(avatar_split_clause,[],[f311,f348]) ).
fof(f385,plain,
! [X0,X1] :
( ~ aSet0(X1)
| ~ aElementOf0(X0,X1)
| ~ aElementOf0(X0,xQ) ),
inference(resolution,[],[f166,f310]) ).
fof(f399,plain,
! [X0] :
( ~ aElementOf0(X0,xQ)
| ~ aElementOf0(X0,xQ) ),
inference(resolution,[],[f385,f309]) ).
fof(f400,plain,
! [X0] : ~ aElementOf0(X0,xQ),
inference(duplicate_literal_removal,[],[f399]) ).
fof(f462,plain,
( aElementOf0(sK0(xQ),xQ)
| slcrc0 = xQ ),
inference(resolution,[],[f169,f309]) ).
fof(f463,plain,
slcrc0 = xQ,
inference(forward_subsumption_resolution,[],[f462,f400]) ).
fof(f505,plain,
xk = sbrdtbr0(slcrc0),
inference(superposition,[],[f307,f463]) ).
fof(f679,plain,
( sz00 = xk
| ~ spl15_1 ),
inference(superposition,[],[f505,f346]) ).
fof(f684,plain,
( $false
| ~ spl15_1 ),
inference(forward_subsumption_resolution,[],[f679,f271]) ).
fof(f685,plain,
~ spl15_1,
inference(avatar_contradiction_clause,[],[f684]) ).
cnf(s1,plain,
( spl15_1
| ~ spl15_2 ),
inference(sat_conversion,[],[f351]) ).
cnf(s3,plain,
spl15_2,
inference(sat_conversion,[],[f357]) ).
cnf(s18,plain,
~ spl15_1,
inference(sat_conversion,[],[f685]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s1,s3,s18]) ).
fof(f686,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM549+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n009.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 20:27:15 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.45 % (2371925)Will run a generic schedule for satisfiability detection.
% 0.10/0.45 % (2371934)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4234431140:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.45 % (2371930)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3655255620_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.45 % (2371932)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1956789577:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.45 % (2371933)dis+10_1_sil=32000:sp=arity:random_seed=195175163:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.45 % (2371935)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1731289173:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.45 % (2371936)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2045275875:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.45 % (2371934) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2371925-2371934"...
% 0.10/0.45 % (2371934)...printing done.
% 0.10/0.45 % (2371934)Refutation found. Thanks to Tanya!
% 0.10/0.45 % SZS status Theorem for theBenchmark
% 0.10/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.45 % (2371934)------------------------------
% 0.10/0.45 % (2371934)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.45 % (2371934)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.45 % (2371934)CaDiCaL version: 2.1.3
% 0.10/0.45 % (2371934)Termination reason: Refutation
% 0.10/0.45 % (2371934)Time elapsed: 0.009 s
% 0.10/0.45 % (2371934)Peak memory usage: 13 MB
% 0.10/0.45 % (2371934)Instructions burned: 23 (million)
% 0.10/0.45 % (2371925)Success in time 0.04 s
% 0.10/0.45 % Vampire exiting
%------------------------------------------------------------------------------