%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET921+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n007.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 12:44:59 PM UTC 2026
% Result : Theorem 0.21s 0.51s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 61 ( 8 unt; 3 def)
% Number of atoms : 225 ( 54 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 273 ( 109 ~; 115 |; 39 &)
% ( 9 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 84 ( 0 sgn 70 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f3,axiom,
! [X0,X1,X2] :
( X2 = set_difference(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
& ~ in(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f6,conjecture,
! [X0,X1,X2] :
( in(X0,set_difference(X1,singleton(X2)))
<=> ( in(X0,X1)
& X0 != X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_zfmisc_1) ).
fof(f7,negated_conjecture,
~ ! [X0,X1,X2] :
( in(X0,set_difference(X1,singleton(X2)))
<=> ( in(X0,X1)
& X0 != X2 ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f9,plain,
? [X0,X1,X2] :
( in(X0,set_difference(X1,singleton(X2)))
<~> ( in(X0,X1)
& X0 != X2 ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f10,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X2 = X0
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X2 = X0
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f11,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X2 = X0
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f10]) ).
fof(f12,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ( ( sK0(X0,X1) != X0
| ~ in(sK0(X0,X1),X1) )
& ( sK0(X0,X1) = X0
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f11]) ).
fof(f13,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| in(X3,X1) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| in(X3,X1) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(flattening,[],[f13]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| in(X4,X1) )
& ( ( in(X4,X0)
& ~ in(X4,X1) )
| ~ in(X4,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(rectify,[],[f14]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ( ( ~ in(sK1(X0,X1,X2),X0)
| in(sK1(X0,X1,X2),X1)
| ~ in(sK1(X0,X1,X2),X2) )
& ( ( in(sK1(X0,X1,X2),X0)
& ~ in(sK1(X0,X1,X2),X1) )
| in(sK1(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| in(X4,X1) )
& ( ( in(X4,X0)
& ~ in(X4,X1) )
| ~ in(X4,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f15]) ).
fof(f19,plain,
? [X0,X1,X2] :
( ( ~ in(X0,X1)
| X0 = X2
| ~ in(X0,set_difference(X1,singleton(X2))) )
& ( ( in(X0,X1)
& X0 != X2 )
| in(X0,set_difference(X1,singleton(X2))) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f20,plain,
? [X0,X1,X2] :
( ( ~ in(X0,X1)
| X0 = X2
| ~ in(X0,set_difference(X1,singleton(X2))) )
& ( ( in(X0,X1)
& X0 != X2 )
| in(X0,set_difference(X1,singleton(X2))) ) ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
( ( ~ in(sK4,sK5)
| sK4 = sK6
| ~ in(sK4,set_difference(sK5,singleton(sK6))) )
& ( ( in(sK4,sK5)
& sK4 != sK6 )
| in(sK4,set_difference(sK5,singleton(sK6))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6)],[f20]) ).
fof(f23,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f12]) ).
fof(f24,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f12]) ).
fof(f27,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f16]) ).
fof(f28,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f16]) ).
fof(f29,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| in(X4,X1)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f16]) ).
fof(f35,plain,
( sK4 != sK6
| in(sK4,set_difference(sK5,singleton(sK6))) ),
inference(cnf_transformation,[],[f21]) ).
fof(f36,plain,
( in(sK4,sK5)
| in(sK4,set_difference(sK5,singleton(sK6))) ),
inference(cnf_transformation,[],[f21]) ).
fof(f37,plain,
( ~ in(sK4,sK5)
| sK4 = sK6
| ~ in(sK4,set_difference(sK5,singleton(sK6))) ),
inference(cnf_transformation,[],[f21]) ).
fof(f38,plain,
! [X3,X1] :
( in(X3,X1)
| singleton(X3) != X1 ),
inference(equality_resolution,[],[f24]) ).
fof(f39,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f38]) ).
fof(f40,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f23]) ).
fof(f41,plain,
! [X0,X1,X4] :
( in(X4,set_difference(X0,X1))
| ~ in(X4,X0)
| in(X4,X1) ),
inference(equality_resolution,[],[f29]) ).
fof(f42,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f28]) ).
fof(f43,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f27]) ).
fof(f140,definition,
( spl7_6
<=> in(sK4,set_difference(sK5,singleton(sK6))) ),
introduced(definition,[new_symbols(definition,[spl7_6])],[avatar_definition]) ).
fof(f141,plain,
( ~ in(sK4,set_difference(sK5,singleton(sK6)))
| spl7_6 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f142,plain,
( in(sK4,set_difference(sK5,singleton(sK6)))
| ~ spl7_6 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f144,definition,
( spl7_7
<=> sK4 = sK6 ),
introduced(definition,[new_symbols(definition,[spl7_7])],[avatar_definition]) ).
fof(f145,plain,
( sK4 = sK6
| ~ spl7_7 ),
inference(avatar_component_clause,[],[f144]) ).
fof(f146,plain,
( sK4 != sK6
| spl7_7 ),
inference(avatar_component_clause,[],[f144]) ).
fof(f147,plain,
( spl7_6
| ~ spl7_7 ),
inference(avatar_split_clause,[],[f35,f144,f140]) ).
fof(f150,plain,
( ~ in(sK4,sK5)
| sK4 = sK6
| ~ spl7_6 ),
inference(forward_subsumption_resolution,[],[f37,f142]) ).
fof(f152,definition,
( spl7_8
<=> in(sK4,sK5) ),
introduced(definition,[new_symbols(definition,[spl7_8])],[avatar_definition]) ).
fof(f153,plain,
( in(sK4,sK5)
| ~ spl7_8 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f155,plain,
( spl7_7
| ~ spl7_8
| ~ spl7_6 ),
inference(avatar_split_clause,[],[f150,f140,f152,f144]) ).
fof(f174,plain,
in(sK4,sK5),
inference(forward_subsumption_resolution,[],[f36,f42]) ).
fof(f176,plain,
spl7_8,
inference(avatar_split_clause,[],[f174,f152]) ).
fof(f185,plain,
( ~ in(sK4,sK5)
| in(sK4,singleton(sK6))
| spl7_6 ),
inference(resolution,[],[f41,f141]) ).
fof(f186,plain,
( in(sK4,singleton(sK6))
| spl7_6
| ~ spl7_8 ),
inference(forward_subsumption_resolution,[],[f185,f153]) ).
fof(f187,plain,
( sK4 = sK6
| spl7_6
| ~ spl7_8 ),
inference(resolution,[],[f186,f40]) ).
fof(f189,plain,
( $false
| spl7_6
| spl7_7
| ~ spl7_8 ),
inference(forward_subsumption_resolution,[],[f187,f146]) ).
fof(f190,plain,
( spl7_6
| spl7_7
| ~ spl7_8 ),
inference(avatar_contradiction_clause,[],[f189]) ).
fof(f191,plain,
( in(sK4,set_difference(sK5,singleton(sK4)))
| ~ spl7_6
| ~ spl7_7 ),
inference(forward_demodulation,[],[f142,f145]) ).
fof(f193,plain,
( ~ in(sK4,singleton(sK4))
| ~ spl7_6
| ~ spl7_7 ),
inference(resolution,[],[f191,f43]) ).
fof(f195,plain,
( $false
| ~ spl7_6
| ~ spl7_7 ),
inference(forward_subsumption_resolution,[],[f193,f39]) ).
fof(f196,plain,
( ~ spl7_6
| ~ spl7_7 ),
inference(avatar_contradiction_clause,[],[f195]) ).
cnf(s99,plain,
( spl7_6
| ~ spl7_7 ),
inference(sat_conversion,[],[f147]) ).
cnf(s108,plain,
( ~ spl7_6
| spl7_7
| ~ spl7_8 ),
inference(sat_conversion,[],[f155]) ).
cnf(s128,plain,
spl7_8,
inference(sat_conversion,[],[f176]) ).
cnf(s140,plain,
( spl7_6
| spl7_7
| ~ spl7_8 ),
inference(sat_conversion,[],[f190]) ).
cnf(s148,plain,
( ~ spl7_6
| ~ spl7_7 ),
inference(sat_conversion,[],[f196]) ).
cnf(s149,plain,
( ~ spl7_6
| spl7_7 ),
inference(rat,[],[s108,s128]) ).
cnf(s150,plain,
spl7_6,
inference(rat,[],[s99,s140,s128]) ).
cnf(s151,plain,
~ spl7_7,
inference(rat,[],[s148,s150]) ).
cnf(s152,plain,
$false,
inference(rat,[],[s149,s151,s150]) ).
fof(f197,plain,
$false,
inference(avatar_sat_refutation,[],[s152]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET921+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.15/0.42 % Computer : n007.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Mon Sep 28 03:08:10 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.15/0.46 Running first-order model finding
% 0.15/0.46 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
% 0.21/0.51 % (1989636)Will run a generic schedule for satisfiability detection.
% 0.21/0.51 % (1989642)% WARNING: option uhcvi not known.
% 0.21/0.51 % (1989643)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1733468608:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.51 % (1989642)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3810413440:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.51 % (1989643) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1989636-1989643"...
% 0.21/0.51 % (1989642) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1989636-1989642"...
% 0.21/0.51 % (1989643)...printing done.
% 0.21/0.51 % (1989643)Refutation found. Thanks to Tanya!
% 0.21/0.51 % SZS status Theorem for theBenchmark
% 0.21/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.51 % (1989643)------------------------------
% 0.21/0.51 % (1989643)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.51 % (1989643)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.51 % (1989643)CaDiCaL version: 2.1.3
% 0.21/0.51 % (1989643)Termination reason: Refutation
% 0.21/0.51 % (1989643)Time elapsed: 0.005 s
% 0.21/0.51 % (1989643)Peak memory usage: 12 MB
% 0.21/0.51 % (1989643)Instructions burned: 5 (million)
% 0.21/0.51 % (1989636)Success in time 0.028 s
% 0.21/0.51 % Vampire exiting
%------------------------------------------------------------------------------