%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU119+2 : 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 : 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 12:51:58 PM UTC 2026
% Result : Theorem 0.16s 0.46s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 62 ( 7 unt; 4 def)
% Number of atoms : 216 ( 32 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 264 ( 110 ~; 100 |; 46 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 83 ( 0 sgn 72 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( X0 = empty_set
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f4,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
& in(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f5,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_intersection2(X0,X1) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(f13,conjecture,
! [X0,X1] :
( ~ ( ~ disjoint(X0,X1)
& ! [X2] :
~ ( in(X2,X0)
& in(X2,X1) ) )
& ~ ( ? [X2] :
( in(X2,X0)
& in(X2,X1) )
& disjoint(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).
fof(f14,negated_conjecture,
~ ! [X0,X1] :
( ~ ( ~ disjoint(X0,X1)
& ! [X2] :
~ ( in(X2,X0)
& in(X2,X1) ) )
& ~ ( ? [X2] :
( in(X2,X0)
& in(X2,X1) )
& disjoint(X0,X1) ) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f16,plain,
~ ! [X0,X1] :
( ~ ( ~ disjoint(X0,X1)
& ! [X2] :
~ ( in(X2,X0)
& in(X2,X1) ) )
& ~ ( ? [X3] :
( in(X3,X0)
& in(X3,X1) )
& disjoint(X0,X1) ) ),
inference(rectify,[],[f14]) ).
fof(f19,plain,
? [X0,X1] :
( ( ~ disjoint(X0,X1)
& ! [X2] :
( ~ in(X2,X0)
| ~ in(X2,X1) ) )
| ( ? [X3] :
( in(X3,X0)
& in(X3,X1) )
& disjoint(X0,X1) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f20,plain,
! [X0] :
( ( X0 = empty_set
| ? [X1] : in(X1,X0) )
& ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f21,plain,
! [X0] :
( ( X0 = empty_set
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f20]) ).
fof(f22,plain,
! [X0] :
( ( X0 = empty_set
| in(sK0(X0),X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f21]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(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_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(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_intersection2(X0,X1) != X2 ) ),
inference(flattening,[],[f23]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(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_intersection2(X0,X1) != X2 ) ),
inference(rectify,[],[f24]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(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_intersection2(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f25]) ).
fof(f27,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set )
& ( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f30,plain,
( ( ~ disjoint(sK4,sK5)
& ! [X2] :
( ~ in(X2,sK4)
| ~ in(X2,sK5) ) )
| ( in(sK6,sK4)
& in(sK6,sK5)
& disjoint(sK4,sK5) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X3,sK6)],[f19]) ).
fof(f33,plain,
! [X2,X0] :
( ~ in(X2,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f22]) ).
fof(f37,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f26]) ).
fof(f38,plain,
! [X2,X0,X1] :
( in(sK1(X0,X1,X2),X2)
| in(sK1(X0,X1,X2),X1)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f26]) ).
fof(f39,plain,
! [X2,X0,X1] :
( in(sK1(X0,X1,X2),X2)
| in(sK1(X0,X1,X2),X0)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f26]) ).
fof(f41,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| set_intersection2(X0,X1) = empty_set ),
inference(cnf_transformation,[],[f27]) ).
fof(f42,plain,
! [X0,X1] :
( set_intersection2(X0,X1) != empty_set
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f48,plain,
! [X2] :
( ~ in(X2,sK4)
| ~ in(X2,sK5)
| disjoint(sK4,sK5) ),
inference(cnf_transformation,[],[f30]) ).
fof(f52,plain,
( ~ disjoint(sK4,sK5)
| in(sK6,sK5) ),
inference(cnf_transformation,[],[f30]) ).
fof(f53,plain,
( ~ disjoint(sK4,sK5)
| in(sK6,sK4) ),
inference(cnf_transformation,[],[f30]) ).
fof(f54,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f33]) ).
fof(f55,plain,
! [X0,X1,X4] :
( in(X4,set_intersection2(X0,X1))
| ~ in(X4,X0)
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f37]) ).
fof(f59,definition,
( spl7_1
<=> disjoint(sK4,sK5) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
fof(f61,plain,
( disjoint(sK4,sK5)
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f63,definition,
( spl7_2
<=> ! [X2] :
( ~ in(X2,sK4)
| ~ in(X2,sK5) ) ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
fof(f64,plain,
( ! [X2] :
( ~ in(X2,sK5)
| ~ in(X2,sK4) )
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f65,plain,
( spl7_1
| spl7_2 ),
inference(avatar_split_clause,[],[f48,f63,f59]) ).
fof(f67,definition,
( spl7_3
<=> in(sK6,sK5) ),
introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition]) ).
fof(f69,plain,
( in(sK6,sK5)
| ~ spl7_3 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f72,definition,
( spl7_4
<=> in(sK6,sK4) ),
introduced(definition,[new_symbols(definition,[spl7_4])],[avatar_definition]) ).
fof(f76,plain,
( spl7_3
| ~ spl7_1 ),
inference(avatar_split_clause,[],[f52,f59,f67]) ).
fof(f77,plain,
( spl7_4
| ~ spl7_1 ),
inference(avatar_split_clause,[],[f53,f59,f72]) ).
fof(f123,plain,
( ! [X0,X1] :
( ~ in(sK1(X0,sK5,X1),sK4)
| set_intersection2(X0,sK5) = X1
| in(sK1(X0,sK5,X1),X1) )
| ~ spl7_2 ),
inference(resolution,[],[f38,f64]) ).
fof(f137,plain,
( ! [X0] :
( set_intersection2(sK4,sK5) = X0
| in(sK1(sK4,sK5,X0),X0)
| in(sK1(sK4,sK5,X0),X0)
| set_intersection2(sK4,sK5) = X0 )
| ~ spl7_2 ),
inference(resolution,[],[f123,f39]) ).
fof(f138,plain,
( ! [X0] :
( in(sK1(sK4,sK5,X0),X0)
| set_intersection2(sK4,sK5) = X0 )
| ~ spl7_2 ),
inference(duplicate_literal_removal,[],[f137]) ).
fof(f150,plain,
( empty_set = set_intersection2(sK4,sK5)
| ~ spl7_2 ),
inference(resolution,[],[f138,f54]) ).
fof(f163,plain,
( empty_set != empty_set
| disjoint(sK4,sK5)
| ~ spl7_2 ),
inference(superposition,[],[f42,f150]) ).
fof(f169,plain,
( disjoint(sK4,sK5)
| ~ spl7_2 ),
inference(trivial_inequality_removal,[],[f163]) ).
fof(f172,plain,
( spl7_1
| ~ spl7_2 ),
inference(avatar_split_clause,[],[f169,f63,f59]) ).
fof(f173,plain,
( empty_set = set_intersection2(sK4,sK5)
| ~ spl7_1 ),
inference(resolution,[],[f61,f41]) ).
fof(f175,plain,
( ~ in(sK6,sK4)
| ~ spl7_2
| ~ spl7_3 ),
inference(resolution,[],[f69,f64]) ).
fof(f177,plain,
( ~ spl7_4
| ~ spl7_2
| ~ spl7_3 ),
inference(avatar_split_clause,[],[f175,f67,f63,f72]) ).
fof(f183,plain,
( ! [X0] :
( in(X0,empty_set)
| ~ in(X0,sK4)
| ~ in(X0,sK5) )
| ~ spl7_1 ),
inference(superposition,[],[f55,f173]) ).
fof(f189,plain,
( ! [X0] :
( ~ in(X0,sK4)
| ~ in(X0,sK5) )
| ~ spl7_1 ),
inference(forward_subsumption_resolution,[],[f183,f54]) ).
fof(f190,plain,
( spl7_2
| ~ spl7_1 ),
inference(avatar_split_clause,[],[f189,f59,f63]) ).
cnf(s1,plain,
( spl7_1
| spl7_2 ),
inference(sat_conversion,[],[f65]) ).
cnf(s4,plain,
( ~ spl7_1
| spl7_3 ),
inference(sat_conversion,[],[f76]) ).
cnf(s5,plain,
( ~ spl7_1
| spl7_4 ),
inference(sat_conversion,[],[f77]) ).
cnf(s9,plain,
( spl7_1
| ~ spl7_2 ),
inference(sat_conversion,[],[f172]) ).
cnf(s10,plain,
( ~ spl7_2
| ~ spl7_3
| ~ spl7_4 ),
inference(sat_conversion,[],[f177]) ).
cnf(s11,plain,
( ~ spl7_1
| spl7_2 ),
inference(sat_conversion,[],[f190]) ).
cnf(s12,plain,
spl7_1,
inference(rat,[],[s1,s9]) ).
cnf(s13,plain,
spl7_2,
inference(rat,[],[s11,s12]) ).
cnf(s14,plain,
spl7_4,
inference(rat,[],[s5,s12]) ).
cnf(s15,plain,
spl7_3,
inference(rat,[],[s4,s12]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s10,s13,s14,s15]) ).
fof(f191,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU119+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n007.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 03:34:41 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 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
% 0.16/0.46 % (2001383)Will run a generic schedule for satisfiability detection.
% 0.16/0.46 % (2001391)dis+10_1_sil=32000:sp=arity:random_seed=803968004:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.46 % (2001391) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2001383-2001391"...
% 0.16/0.46 % (2001389)% WARNING: option uhcvi not known.
% 0.16/0.46 % (2001391)...printing done.
% 0.16/0.46 % (2001391)Refutation found. Thanks to Tanya!
% 0.16/0.46 % SZS status Theorem for theBenchmark
% 0.16/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.47 % (2001391)------------------------------
% 0.16/0.47 % (2001391)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.47 % (2001391)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.47 % (2001391)CaDiCaL version: 2.1.3
% 0.16/0.47 % (2001391)Termination reason: Refutation
% 0.16/0.47 % (2001391)Time elapsed: 0.003 s
% 0.16/0.47 % (2001391)Peak memory usage: 12 MB
% 0.16/0.47 % (2001391)Instructions burned: 7 (million)
% 0.16/0.47 % (2001383)Success in time 0.036 s
% 0.16/0.47 % Vampire exiting
%------------------------------------------------------------------------------