%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM555+1 : 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 : n004.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 12:24:47 PM UTC 2026
% Result : Theorem 0.16s 0.47s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 12 unt; 0 def)
% Number of atoms : 59 ( 8 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 59 ( 22 ~; 17 |; 13 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 22 ( 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f16,axiom,
! [X0,X1] :
( ( aSet0(X0)
& aElement0(X1) )
=> ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
fof(f66,axiom,
( aSet0(xQ)
& isFinite0(xQ)
& sbrdtbr0(xQ) = xk ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2291) ).
fof(f67,axiom,
( aElement0(xy)
& aElementOf0(xy,xQ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2304) ).
fof(f68,axiom,
~ aElementOf0(xx,xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2323) ).
fof(f71,conjecture,
~ aElementOf0(xx,sdtmndt0(xQ,xy)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f72,negated_conjecture,
~ ~ aElementOf0(xx,sdtmndt0(xQ,xy)),
inference(negated_conjecture,[status(cth)],[f71]) ).
fof(f73,plain,
aElementOf0(xx,sdtmndt0(xQ,xy)),
inference(flattening,[],[f72]) ).
fof(f96,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 ) ) ) )
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f16]) ).
fof(f97,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 ) ) ) )
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f96]) ).
fof(f191,plain,
! [X2,X3,X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| aElementOf0(X3,X0)
| ~ aElementOf0(X3,X2)
| sdtmndt0(X0,X1) != X2 ),
inference(cnf_transformation,[],[f97]) ).
fof(f280,plain,
aSet0(xQ),
inference(cnf_transformation,[],[f66]) ).
fof(f282,plain,
aElement0(xy),
inference(cnf_transformation,[],[f67]) ).
fof(f283,plain,
~ aElementOf0(xx,xQ),
inference(cnf_transformation,[],[f68]) ).
fof(f286,plain,
aElementOf0(xx,sdtmndt0(xQ,xy)),
inference(cnf_transformation,[],[f73]) ).
fof(f299,plain,
! [X3,X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| aElementOf0(X3,X0)
| ~ aElementOf0(X3,sdtmndt0(X0,X1)) ),
inference(equality_resolution,[],[f191]) ).
fof(f346,plain,
! [X3,X0,X1] :
( ~ aElementOf0(X3,sdtmndt0(X0,X1))
| aSet0(X0)
| aElementOf0(X3,X0)
| aElement0(X1) ),
inference(consistent_polarity_flipping,[],[f299]) ).
fof(f407,plain,
~ aSet0(xQ),
inference(consistent_polarity_flipping,[],[f280]) ).
fof(f408,plain,
~ aElement0(xy),
inference(consistent_polarity_flipping,[],[f282]) ).
fof(f685,plain,
( aSet0(xQ)
| aElementOf0(xx,xQ)
| aElement0(xy) ),
inference(resolution,[],[f346,f286]) ).
fof(f688,plain,
( aElementOf0(xx,xQ)
| aElement0(xy) ),
inference(forward_subsumption_resolution,[],[f685,f407]) ).
fof(f689,plain,
aElement0(xy),
inference(forward_subsumption_resolution,[],[f688,f283]) ).
fof(f690,plain,
$false,
inference(forward_subsumption_resolution,[],[f689,f408]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM555+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n004.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
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 20:28:07 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 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
% 0.16/0.47 % (3855144)Will run a generic schedule for satisfiability detection.
% 0.16/0.47 % (3855154)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3537670490:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.47 % (3855150)% WARNING: option uhcvi not known.
% 0.16/0.47 % (3855151)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=381826366:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.47 % (3855149)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1303861682_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.47 % (3855150)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3180393311:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.47 % (3855152)dis+10_1_sil=32000:sp=arity:random_seed=1363500505:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.47 % (3855153)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1516073081:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.47 % (3855155)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1892503050:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.47 % TRYING [1]
% 0.16/0.47 % TRYING [2]
% 0.16/0.47 % (3855150) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3855144-3855150"...
% 0.16/0.47 % (3855150)...printing done.
% 0.16/0.47 % TRYING [3]
% 0.16/0.47 % (3855150)Refutation found. Thanks to Tanya!
% 0.16/0.47 % SZS status Theorem for theBenchmark
% 0.16/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.47 % (3855150)------------------------------
% 0.16/0.47 % (3855150)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.47 % (3855150)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.47 % (3855150)CaDiCaL version: 2.1.3
% 0.16/0.47 % (3855150)Termination reason: Refutation
% 0.16/0.47 % (3855150)Time elapsed: 0.011 s
% 0.16/0.47 % (3855150)Peak memory usage: 12 MB
% 0.16/0.47 % (3855150)Instructions burned: 13 (million)
% 0.16/0.47 % (3855144)Success in time 0.049 s
% 0.16/0.47 % Vampire exiting
%------------------------------------------------------------------------------