%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU146+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 : n015.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 0.47s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 68 ( 10 unt; 3 def)
% Number of atoms : 180 ( 42 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 186 ( 74 ~; 89 |; 13 &)
% ( 8 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 49 ( 1 sgn 43 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f7,axiom,
! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).
fof(f8,axiom,
! [X0,X1,X2] :
( subset(X0,X1)
=> ( in(X2,X0)
| subset(X0,set_difference(X1,singleton(X2))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_zfmisc_1) ).
fof(f9,conjecture,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( X0 = empty_set
| X0 = singleton(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).
fof(f10,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( X0 = empty_set
| X0 = singleton(X1) ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f13,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f14,axiom,
! [X0] : subset(empty_set,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(f15,axiom,
! [X0,X1] :
( set_difference(X0,X1) = empty_set
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
fof(f17,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f13]) ).
fof(f19,plain,
! [X0,X1,X2] :
( in(X2,X0)
| subset(X0,set_difference(X1,singleton(X2)))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f20,plain,
! [X0,X1,X2] :
( in(X2,X0)
| subset(X0,set_difference(X1,singleton(X2)))
| ~ subset(X0,X1) ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
? [X0,X1] :
( subset(X0,singleton(X1))
<~> ( X0 = empty_set
| X0 = singleton(X1) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f23,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f24,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f23]) ).
fof(f25,plain,
! [X0,X1] :
( ( subset(singleton(X0),X1)
| ~ in(X0,X1) )
& ( in(X0,X1)
| ~ subset(singleton(X0),X1) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f26,plain,
? [X0,X1] :
( ( ( empty_set != X0
& singleton(X1) != X0 )
| ~ subset(X0,singleton(X1)) )
& ( X0 = empty_set
| X0 = singleton(X1)
| subset(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f27,plain,
? [X0,X1] :
( ( ( empty_set != X0
& singleton(X1) != X0 )
| ~ subset(X0,singleton(X1)) )
& ( X0 = empty_set
| X0 = singleton(X1)
| subset(X0,singleton(X1)) ) ),
inference(flattening,[],[f26]) ).
fof(f28,plain,
( ( ( empty_set != sK0
& sK0 != singleton(sK1) )
| ~ subset(sK0,singleton(sK1)) )
& ( empty_set = sK0
| sK0 = singleton(sK1)
| subset(sK0,singleton(sK1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f27]) ).
fof(f31,plain,
! [X0,X1] :
( ( set_difference(X0,X1) = empty_set
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| empty_set != set_difference(X0,X1) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f35,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f24]) ).
fof(f38,plain,
! [X0,X1] :
( subset(singleton(X0),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f39,plain,
! [X2,X0,X1] :
( subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f40,plain,
( empty_set = sK0
| sK0 = singleton(sK1)
| subset(sK0,singleton(sK1)) ),
inference(cnf_transformation,[],[f28]) ).
fof(f41,plain,
( sK0 != singleton(sK1)
| ~ subset(sK0,singleton(sK1)) ),
inference(cnf_transformation,[],[f28]) ).
fof(f42,plain,
( empty_set != sK0
| ~ subset(sK0,singleton(sK1)) ),
inference(cnf_transformation,[],[f28]) ).
fof(f45,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f17]) ).
fof(f46,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[],[f14]) ).
fof(f48,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| empty_set = set_difference(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f53,definition,
( spl4_1
<=> subset(sK0,singleton(sK1)) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f54,plain,
( ~ subset(sK0,singleton(sK1))
| spl4_1 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f55,plain,
( subset(sK0,singleton(sK1))
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f57,definition,
( spl4_2
<=> sK0 = singleton(sK1) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f58,plain,
( sK0 != singleton(sK1)
| spl4_2 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f59,plain,
( sK0 = singleton(sK1)
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f61,definition,
( spl4_3
<=> empty_set = sK0 ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
fof(f62,plain,
( empty_set != sK0
| spl4_3 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f63,plain,
( empty_set = sK0
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f64,plain,
( spl4_1
| spl4_2
| spl4_3 ),
inference(avatar_split_clause,[],[f40,f61,f57,f53]) ).
fof(f65,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f41,f57,f53]) ).
fof(f66,plain,
( ~ spl4_1
| ~ spl4_3 ),
inference(avatar_split_clause,[],[f42,f61,f53]) ).
fof(f67,plain,
( ~ subset(sK0,sK0)
| spl4_1
| ~ spl4_2 ),
inference(superposition,[],[f54,f59]) ).
fof(f68,plain,
( $false
| spl4_1
| ~ spl4_2 ),
inference(resolution,[],[f45,f67]) ).
fof(f69,plain,
( spl4_1
| ~ spl4_2 ),
inference(avatar_contradiction_clause,[],[f68]) ).
fof(f70,plain,
( ~ subset(empty_set,singleton(sK1))
| spl4_1
| ~ spl4_3 ),
inference(superposition,[],[f54,f63]) ).
fof(f72,plain,
( $false
| spl4_1
| ~ spl4_3 ),
inference(resolution,[],[f46,f70]) ).
fof(f73,plain,
( spl4_1
| ~ spl4_3 ),
inference(avatar_contradiction_clause,[],[f72]) ).
fof(f82,plain,
( empty_set = set_difference(sK0,singleton(sK1))
| ~ spl4_1 ),
inference(resolution,[],[f48,f55]) ).
fof(f88,plain,
( ~ subset(singleton(sK1),sK0)
| sK0 = singleton(sK1)
| ~ spl4_1 ),
inference(resolution,[],[f35,f55]) ).
fof(f90,plain,
( ~ subset(singleton(sK1),sK0)
| ~ spl4_1
| spl4_2 ),
inference(forward_subsumption_resolution,[],[f88,f58]) ).
fof(f91,plain,
( ~ in(sK1,sK0)
| ~ spl4_1
| spl4_2 ),
inference(resolution,[],[f90,f38]) ).
fof(f95,plain,
( ! [X0] :
( ~ subset(X0,sK0)
| in(sK1,X0)
| subset(X0,empty_set) )
| ~ spl4_1 ),
inference(superposition,[],[f39,f82]) ).
fof(f99,plain,
( in(sK1,sK0)
| subset(sK0,empty_set)
| ~ spl4_1 ),
inference(resolution,[],[f95,f45]) ).
fof(f102,plain,
( subset(sK0,empty_set)
| ~ spl4_1
| spl4_2 ),
inference(forward_subsumption_resolution,[],[f99,f91]) ).
fof(f107,plain,
( ~ subset(empty_set,sK0)
| empty_set = sK0
| ~ spl4_1
| spl4_2 ),
inference(resolution,[],[f102,f35]) ).
fof(f109,plain,
( empty_set = sK0
| ~ spl4_1
| spl4_2 ),
inference(forward_subsumption_resolution,[],[f107,f46]) ).
fof(f112,plain,
( $false
| ~ spl4_1
| spl4_2
| spl4_3 ),
inference(forward_subsumption_resolution,[],[f109,f62]) ).
fof(f113,plain,
( ~ spl4_1
| spl4_2
| spl4_3 ),
inference(avatar_contradiction_clause,[],[f112]) ).
cnf(s1,plain,
( spl4_1
| spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f64]) ).
cnf(s2,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f65]) ).
cnf(s3,plain,
( ~ spl4_1
| ~ spl4_3 ),
inference(sat_conversion,[],[f66]) ).
cnf(s4,plain,
( spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f69]) ).
cnf(s5,plain,
( spl4_1
| ~ spl4_3 ),
inference(sat_conversion,[],[f73]) ).
cnf(s7,plain,
( ~ spl4_1
| spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f113]) ).
cnf(s8,plain,
spl4_1,
inference(rat,[],[s1,s4,s5]) ).
cnf(s9,plain,
~ spl4_3,
inference(rat,[],[s3,s8]) ).
cnf(s10,plain,
~ spl4_2,
inference(rat,[],[s2,s8]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s7,s9,s8,s10]) ).
fof(f114,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU146+1 : 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 : n015.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 03:47:17 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.43 Running first-order model finding
% 0.12/0.43 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
% 0.17/0.47 % (2238131)Will run a generic schedule for satisfiability detection.
% 0.17/0.47 % (2238139)dis+10_1_sil=32000:sp=arity:random_seed=2028021389:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.47 % (2238139) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2238131-2238139"...
% 0.17/0.47 % (2238139)...printing done.
% 0.17/0.47 % (2238137)% WARNING: option uhcvi not known.
% 0.17/0.47 % (2238139)Refutation found. Thanks to Tanya!
% 0.17/0.47 % SZS status Theorem for theBenchmark
% 0.17/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.47 % (2238139)------------------------------
% 0.17/0.47 % (2238139)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.47 % (2238139)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.47 % (2238139)CaDiCaL version: 2.1.3
% 0.17/0.47 % (2238139)Termination reason: Refutation
% 0.17/0.47 % (2238139)Time elapsed: 0.002 s
% 0.17/0.47 % (2238139)Peak memory usage: 12 MB
% 0.17/0.47 % (2238139)Instructions burned: 4 (million)
% 0.17/0.47 % (2238131)Success in time 0.031 s
% 0.17/0.47 % Vampire exiting
%------------------------------------------------------------------------------