%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU162+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n020.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 12:52:11 PM UTC 2026
% Result : Theorem 0.09s 0.44s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 50 ( 4 unt; 2 def)
% Number of atoms : 103 ( 23 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 104 ( 51 ~; 41 |; 4 &)
% ( 5 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 44 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
~ ( disjoint(singleton(X0),X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l25_zfmisc_1) ).
fof(f5,axiom,
! [X0,X1] :
( ~ in(X0,X1)
=> disjoint(singleton(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l28_zfmisc_1) ).
fof(f6,axiom,
! [X0,X1] :
( disjoint(X0,X1)
=> disjoint(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(f7,conjecture,
! [X0,X1] :
( set_difference(X0,singleton(X1)) = X0
<=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_zfmisc_1) ).
fof(f8,negated_conjecture,
~ ! [X0,X1] :
( set_difference(X0,singleton(X1)) = X0
<=> ~ in(X1,X0) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_difference(X0,X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_xboole_1) ).
fof(f11,plain,
! [X0,X1] :
( ~ disjoint(singleton(X0),X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f12,plain,
! [X0,X1] :
( disjoint(singleton(X0),X1)
| in(X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f13,plain,
! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f14,plain,
? [X0,X1] :
( set_difference(X0,singleton(X1)) = X0
<~> ~ in(X1,X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f15,plain,
? [X0,X1] :
( ( in(X1,X0)
| set_difference(X0,singleton(X1)) != X0 )
& ( ~ in(X1,X0)
| set_difference(X0,singleton(X1)) = X0 ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f16,plain,
( ( in(sK1,sK0)
| sK0 != set_difference(sK0,singleton(sK1)) )
& ( ~ in(sK1,sK0)
| sK0 = set_difference(sK0,singleton(sK1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| set_difference(X0,X1) != X0 )
& ( set_difference(X0,X1) = X0
| ~ disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f19,plain,
! [X0,X1] :
( ~ disjoint(singleton(X0),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f11]) ).
fof(f20,plain,
! [X0,X1] :
( disjoint(singleton(X0),X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f21,plain,
! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f22,plain,
( ~ in(sK1,sK0)
| sK0 = set_difference(sK0,singleton(sK1)) ),
inference(cnf_transformation,[],[f16]) ).
fof(f23,plain,
( in(sK1,sK0)
| sK0 != set_difference(sK0,singleton(sK1)) ),
inference(cnf_transformation,[],[f16]) ).
fof(f24,plain,
! [X0,X1] :
( set_difference(X0,X1) = X0
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f25,plain,
! [X0,X1] :
( disjoint(X0,X1)
| set_difference(X0,X1) != X0 ),
inference(cnf_transformation,[],[f17]) ).
fof(f27,plain,
! [X0,X1] :
( disjoint(singleton(X0),X1)
| in(X0,X1) ),
inference(consistent_polarity_flipping,[],[f19]) ).
fof(f28,plain,
! [X0,X1] :
( ~ disjoint(singleton(X0),X1)
| ~ in(X0,X1) ),
inference(consistent_polarity_flipping,[],[f20]) ).
fof(f29,plain,
! [X0,X1] :
( disjoint(X0,X1)
| ~ disjoint(X1,X0) ),
inference(consistent_polarity_flipping,[],[f21]) ).
fof(f30,plain,
( ~ in(sK1,sK0)
| sK0 != set_difference(sK0,singleton(sK1)) ),
inference(consistent_polarity_flipping,[],[f23]) ).
fof(f31,plain,
( in(sK1,sK0)
| sK0 = set_difference(sK0,singleton(sK1)) ),
inference(consistent_polarity_flipping,[],[f22]) ).
fof(f32,plain,
! [X0,X1] :
( set_difference(X0,X1) != X0
| ~ disjoint(X0,X1) ),
inference(consistent_polarity_flipping,[],[f25]) ).
fof(f33,plain,
! [X0,X1] :
( disjoint(X0,X1)
| set_difference(X0,X1) = X0 ),
inference(consistent_polarity_flipping,[],[f24]) ).
fof(f35,definition,
( spl2_1
<=> sK0 = set_difference(sK0,singleton(sK1)) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f37,plain,
( sK0 = set_difference(sK0,singleton(sK1))
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f35]) ).
fof(f39,definition,
( spl2_2
<=> in(sK1,sK0) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f41,plain,
( in(sK1,sK0)
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f42,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f31,f39,f35]) ).
fof(f43,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f30,f39,f35]) ).
fof(f45,plain,
! [X0,X1] :
( ~ disjoint(X1,singleton(X0))
| ~ in(X0,X1) ),
inference(resolution,[],[f28,f29]) ).
fof(f49,plain,
! [X0,X1] :
( ~ in(X1,X0)
| set_difference(X0,singleton(X1)) = X0 ),
inference(resolution,[],[f33,f45]) ).
fof(f50,plain,
( sK0 = set_difference(sK0,singleton(sK1))
| ~ spl2_2 ),
inference(resolution,[],[f49,f41]) ).
fof(f53,plain,
( spl2_1
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f50,f39,f35]) ).
fof(f56,plain,
( sK0 != sK0
| ~ disjoint(sK0,singleton(sK1))
| ~ spl2_1 ),
inference(superposition,[],[f32,f37]) ).
fof(f57,plain,
( ~ disjoint(sK0,singleton(sK1))
| ~ spl2_1 ),
inference(trivial_inequality_removal,[],[f56]) ).
fof(f59,plain,
( ~ disjoint(singleton(sK1),sK0)
| ~ spl2_1 ),
inference(resolution,[],[f57,f29]) ).
fof(f60,plain,
( in(sK1,sK0)
| ~ spl2_1 ),
inference(resolution,[],[f59,f27]) ).
fof(f63,plain,
( spl2_2
| ~ spl2_1 ),
inference(avatar_split_clause,[],[f60,f35,f39]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f42]) ).
cnf(s2,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(sat_conversion,[],[f43]) ).
cnf(s3,plain,
( spl2_1
| ~ spl2_2 ),
inference(sat_conversion,[],[f53]) ).
cnf(s4,plain,
( ~ spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f63]) ).
cnf(s5,plain,
spl2_1,
inference(rat,[],[s1,s3]) ).
cnf(s6,plain,
spl2_2,
inference(rat,[],[s4,s5]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s2,s6,s5]) ).
fof(f64,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU162+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.37 % Computer : n020.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 28 03:50:20 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.40 Running first-order model finding
% 0.09/0.40 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
% 0.09/0.44 % (4008091)Will run a generic schedule for satisfiability detection.
% 0.09/0.44 % (4008102)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1052654406:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.44 % (4008102) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4008091-4008102"...
% 0.09/0.44 % (4008102)...printing done.
% 0.09/0.44 % (4008102)Refutation found. Thanks to Tanya!
% 0.09/0.44 % SZS status Theorem for theBenchmark
% 0.09/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.44 % (4008102)------------------------------
% 0.09/0.44 % (4008102)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.44 % (4008102)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.44 % (4008102)CaDiCaL version: 2.1.3
% 0.09/0.44 % (4008102)Termination reason: Refutation
% 0.09/0.44 % (4008102)Time elapsed: 0.002 s
% 0.09/0.44 % (4008102)Peak memory usage: 12 MB
% 0.09/0.44 % (4008102)Instructions burned: 2 (million)
% 0.09/0.44 % (4008091)Success in time 0.027 s
% 0.09/0.44 % Vampire exiting
%------------------------------------------------------------------------------