%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU144+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 12:52:05 PM UTC 2026
% Result : Theorem 0.17s 0.46s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 51 ( 5 unt; 2 def)
% Number of atoms : 148 ( 28 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 157 ( 60 ~; 70 |; 17 &)
% ( 8 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 60 ( 0 sgn 52 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f3,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f5,conjecture,
! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_zfmisc_1) ).
fof(f6,negated_conjecture,
~ ! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f10,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f11,plain,
? [X0,X1] :
( subset(singleton(X0),X1)
<~> in(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f12,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(f13,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,[],[f12]) ).
fof(f14,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))],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f16,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK1(X0,X1),X1)
& in(sK1(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f16]) ).
fof(f18,plain,
? [X0,X1] :
( ( ~ in(X0,X1)
| ~ subset(singleton(X0),X1) )
& ( in(X0,X1)
| subset(singleton(X0),X1) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f19,plain,
( ( ~ in(sK2,sK3)
| ~ subset(singleton(sK2),sK3) )
& ( in(sK2,sK3)
| subset(singleton(sK2),sK3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f18]) ).
fof(f21,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f14]) ).
fof(f22,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f14]) ).
fof(f25,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f26,plain,
! [X0,X1] :
( in(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f27,plain,
! [X0,X1] :
( ~ in(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f28,plain,
( in(sK2,sK3)
| subset(singleton(sK2),sK3) ),
inference(cnf_transformation,[],[f19]) ).
fof(f29,plain,
( ~ in(sK2,sK3)
| ~ subset(singleton(sK2),sK3) ),
inference(cnf_transformation,[],[f19]) ).
fof(f31,plain,
! [X3,X1] :
( in(X3,X1)
| singleton(X3) != X1 ),
inference(equality_resolution,[],[f22]) ).
fof(f32,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f31]) ).
fof(f33,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f21]) ).
fof(f35,definition,
( spl4_1
<=> subset(singleton(sK2),sK3) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f36,plain,
( subset(singleton(sK2),sK3)
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f35]) ).
fof(f37,plain,
( ~ subset(singleton(sK2),sK3)
| spl4_1 ),
inference(avatar_component_clause,[],[f35]) ).
fof(f39,definition,
( spl4_2
<=> in(sK2,sK3) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f40,plain,
( in(sK2,sK3)
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f41,plain,
( ~ in(sK2,sK3)
| spl4_2 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f42,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f29,f39,f35]) ).
fof(f49,plain,
( in(sK2,sK3)
| spl4_1 ),
inference(forward_subsumption_resolution,[],[f28,f37]) ).
fof(f50,plain,
( spl4_2
| spl4_1 ),
inference(avatar_split_clause,[],[f49,f35,f39]) ).
fof(f110,plain,
! [X0,X1] :
( subset(singleton(X0),X1)
| sK1(singleton(X0),X1) = X0 ),
inference(resolution,[],[f26,f33]) ).
fof(f157,plain,
( ! [X0] :
( ~ in(X0,singleton(sK2))
| in(X0,sK3) )
| ~ spl4_1 ),
inference(resolution,[],[f25,f36]) ).
fof(f174,plain,
( in(sK2,sK3)
| ~ spl4_1 ),
inference(resolution,[],[f157,f32]) ).
fof(f178,plain,
( $false
| ~ spl4_1
| spl4_2 ),
inference(forward_subsumption_resolution,[],[f174,f41]) ).
fof(f179,plain,
( ~ spl4_1
| spl4_2 ),
inference(avatar_contradiction_clause,[],[f178]) ).
fof(f203,plain,
( sK2 = sK1(singleton(sK2),sK3)
| spl4_1 ),
inference(resolution,[],[f110,f37]) ).
fof(f207,plain,
( ~ in(sK2,sK3)
| subset(singleton(sK2),sK3)
| spl4_1 ),
inference(superposition,[],[f27,f203]) ).
fof(f209,plain,
( subset(singleton(sK2),sK3)
| spl4_1
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f207,f40]) ).
fof(f210,plain,
( $false
| spl4_1
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f209,f37]) ).
fof(f211,plain,
( spl4_1
| ~ spl4_2 ),
inference(avatar_contradiction_clause,[],[f210]) ).
cnf(s13,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f42]) ).
cnf(s22,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f50]) ).
cnf(s115,plain,
( ~ spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f179]) ).
cnf(s146,plain,
( spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f211]) ).
cnf(s148,plain,
spl4_1,
inference(rat,[],[s22,s146]) ).
cnf(s149,plain,
spl4_2,
inference(rat,[],[s115,s148]) ).
cnf(s150,plain,
$false,
inference(rat,[],[s13,s149,s148]) ).
fof(f212,plain,
$false,
inference(avatar_sat_refutation,[],[s150]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU144+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 % Computer : n007.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 03:41:55 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 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
% 0.17/0.46 % (2006334)Will run a generic schedule for satisfiability detection.
% 0.17/0.46 % (2006341)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2056032832:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.46 % (2006341) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2006334-2006341"...
% 0.17/0.46 % (2006340)% WARNING: option uhcvi not known.
% 0.17/0.46 % (2006341)...printing done.
% 0.17/0.46 % (2006341)Refutation found. Thanks to Tanya!
% 0.17/0.46 % SZS status Theorem for theBenchmark
% 0.17/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.46 % (2006341)------------------------------
% 0.17/0.46 % (2006341)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.46 % (2006341)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.46 % (2006341)CaDiCaL version: 2.1.3
% 0.17/0.46 % (2006341)Termination reason: Refutation
% 0.17/0.46 % (2006341)Time elapsed: 0.003 s
% 0.17/0.46 % (2006341)Peak memory usage: 12 MB
% 0.17/0.46 % (2006341)Instructions burned: 5 (million)
% 0.17/0.46 % (2006334)Success in time 0.032 s
% 0.17/0.46 % Vampire exiting
%------------------------------------------------------------------------------