%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU245+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 : 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 12:52:34 PM UTC 2026
% Result : Theorem 0.16s 0.46s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 54 ( 7 unt; 3 def)
% Number of atoms : 126 ( 8 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 123 ( 51 ~; 56 |; 5 &)
% ( 7 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 44 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f24,axiom,
! [X0] :
( relation(X0)
=> ! [X1] : relation_restriction(X0,X1) = set_intersection2(X0,cartesian_product2(X1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_wellord1) ).
fof(f25,conjecture,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_restriction(X2,X1))
<=> ( in(X0,X2)
& in(X0,cartesian_product2(X1,X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_wellord1) ).
fof(f26,negated_conjecture,
~ ! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_restriction(X2,X1))
<=> ( in(X0,X2)
& in(X0,cartesian_product2(X1,X1)) ) ) ),
inference(negated_conjecture,[status(cth)],[f25]) ).
fof(f27,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
& in(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f42,plain,
! [X0] :
( ! [X1] : relation_restriction(X0,X1) = set_intersection2(X0,cartesian_product2(X1,X1))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f43,plain,
? [X0,X1,X2] :
( ( in(X0,relation_restriction(X2,X1))
<~> ( in(X0,X2)
& in(X0,cartesian_product2(X1,X1)) ) )
& relation(X2) ),
inference(ennf_transformation,[],[f26]) ).
fof(f66,plain,
! [X0,X1] :
( ~ relation(X0)
| relation_restriction(X0,X1) = set_intersection2(X0,cartesian_product2(X1,X1)) ),
inference(cnf_transformation,[],[f42]) ).
fof(f67,plain,
( ~ in(sK6,cartesian_product2(sK7,sK7))
| ~ in(sK6,sK8)
| ~ in(sK6,relation_restriction(sK8,sK7)) ),
inference(cnf_transformation,[],[f43]) ).
fof(f68,plain,
( in(sK6,cartesian_product2(sK7,sK7))
| in(sK6,relation_restriction(sK8,sK7)) ),
inference(cnf_transformation,[],[f43]) ).
fof(f69,plain,
( in(sK6,sK8)
| in(sK6,relation_restriction(sK8,sK7)) ),
inference(cnf_transformation,[],[f43]) ).
fof(f70,plain,
relation(sK8),
inference(cnf_transformation,[],[f43]) ).
fof(f74,plain,
! [X2,X3,X0,X1] :
( in(X3,X1)
| ~ in(X3,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f27]) ).
fof(f75,plain,
! [X2,X3,X0,X1] :
( in(X3,X0)
| ~ in(X3,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f27]) ).
fof(f76,plain,
! [X2,X3,X0,X1] :
( ~ in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f27]) ).
fof(f77,plain,
! [X3,X0,X1] :
( in(X3,set_intersection2(X0,X1))
| ~ in(X3,X0)
| ~ in(X3,X1) ),
inference(equality_resolution,[],[f76]) ).
fof(f78,plain,
! [X3,X0,X1] :
( ~ in(X3,set_intersection2(X0,X1))
| in(X3,X0) ),
inference(equality_resolution,[],[f75]) ).
fof(f79,plain,
! [X3,X0,X1] :
( ~ in(X3,set_intersection2(X0,X1))
| in(X3,X1) ),
inference(equality_resolution,[],[f74]) ).
fof(f81,definition,
( spl10_1
<=> in(sK6,relation_restriction(sK8,sK7)) ),
introduced(definition,[new_symbols(definition,[spl10_1])],[avatar_definition]) ).
fof(f82,plain,
( in(sK6,relation_restriction(sK8,sK7))
| ~ spl10_1 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f83,plain,
( ~ in(sK6,relation_restriction(sK8,sK7))
| spl10_1 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f85,definition,
( spl10_2
<=> in(sK6,sK8) ),
introduced(definition,[new_symbols(definition,[spl10_2])],[avatar_definition]) ).
fof(f86,plain,
( in(sK6,sK8)
| ~ spl10_2 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f87,plain,
( ~ in(sK6,sK8)
| spl10_2 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f89,definition,
( spl10_3
<=> in(sK6,cartesian_product2(sK7,sK7)) ),
introduced(definition,[new_symbols(definition,[spl10_3])],[avatar_definition]) ).
fof(f90,plain,
( in(sK6,cartesian_product2(sK7,sK7))
| ~ spl10_3 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f91,plain,
( ~ in(sK6,cartesian_product2(sK7,sK7))
| spl10_3 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f92,plain,
( ~ spl10_1
| ~ spl10_2
| ~ spl10_3 ),
inference(avatar_split_clause,[],[f67,f89,f85,f81]) ).
fof(f93,plain,
( spl10_1
| spl10_3 ),
inference(avatar_split_clause,[],[f68,f89,f81]) ).
fof(f94,plain,
( spl10_1
| spl10_2 ),
inference(avatar_split_clause,[],[f69,f85,f81]) ).
fof(f147,plain,
! [X0] : relation_restriction(sK8,X0) = set_intersection2(sK8,cartesian_product2(X0,X0)),
inference(resolution,[],[f66,f70]) ).
fof(f151,plain,
! [X0,X1] :
( in(X1,cartesian_product2(X0,X0))
| ~ in(X1,relation_restriction(sK8,X0)) ),
inference(superposition,[],[f79,f147]) ).
fof(f152,plain,
! [X0,X1] :
( ~ in(X1,relation_restriction(sK8,X0))
| in(X1,sK8) ),
inference(superposition,[],[f78,f147]) ).
fof(f162,plain,
! [X0,X1] :
( ~ in(X1,cartesian_product2(X0,X0))
| ~ in(X1,sK8)
| in(X1,relation_restriction(sK8,X0)) ),
inference(superposition,[],[f77,f147]) ).
fof(f223,plain,
( ~ in(sK6,sK8)
| in(sK6,relation_restriction(sK8,sK7))
| ~ spl10_3 ),
inference(resolution,[],[f162,f90]) ).
fof(f228,plain,
( in(sK6,relation_restriction(sK8,sK7))
| ~ spl10_2
| ~ spl10_3 ),
inference(forward_subsumption_resolution,[],[f223,f86]) ).
fof(f229,plain,
( $false
| spl10_1
| ~ spl10_2
| ~ spl10_3 ),
inference(forward_subsumption_resolution,[],[f228,f83]) ).
fof(f230,plain,
( spl10_1
| ~ spl10_2
| ~ spl10_3 ),
inference(avatar_contradiction_clause,[],[f229]) ).
fof(f231,plain,
( in(sK6,sK8)
| ~ spl10_1 ),
inference(resolution,[],[f82,f152]) ).
fof(f232,plain,
( ~ in(sK6,relation_restriction(sK8,sK7))
| spl10_3 ),
inference(resolution,[],[f91,f151]) ).
fof(f233,plain,
( $false
| ~ spl10_1
| spl10_3 ),
inference(forward_subsumption_resolution,[],[f232,f82]) ).
fof(f234,plain,
( ~ spl10_1
| spl10_3 ),
inference(avatar_contradiction_clause,[],[f233]) ).
fof(f235,plain,
( $false
| ~ spl10_1
| spl10_2 ),
inference(forward_subsumption_resolution,[],[f231,f87]) ).
fof(f236,plain,
( ~ spl10_1
| spl10_2 ),
inference(avatar_contradiction_clause,[],[f235]) ).
cnf(s1,plain,
( ~ spl10_1
| ~ spl10_2
| ~ spl10_3 ),
inference(sat_conversion,[],[f92]) ).
cnf(s2,plain,
( spl10_1
| spl10_3 ),
inference(sat_conversion,[],[f93]) ).
cnf(s3,plain,
( spl10_1
| spl10_2 ),
inference(sat_conversion,[],[f94]) ).
cnf(s4,plain,
( spl10_1
| ~ spl10_2
| ~ spl10_3 ),
inference(sat_conversion,[],[f230]) ).
cnf(s5,plain,
( ~ spl10_1
| spl10_3 ),
inference(sat_conversion,[],[f234]) ).
cnf(s6,plain,
( ~ spl10_1
| spl10_2 ),
inference(sat_conversion,[],[f236]) ).
cnf(s7,plain,
spl10_1,
inference(rat,[],[s4,s2,s3]) ).
cnf(s8,plain,
spl10_2,
inference(rat,[],[s6,s7]) ).
cnf(s9,plain,
spl10_3,
inference(rat,[],[s5,s7]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s1,s8,s9,s7]) ).
fof(f237,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU245+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 : n015.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 04:21:47 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
% 0.16/0.46 % (2255592)Will run a generic schedule for satisfiability detection.
% 0.16/0.46 % (2255601)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4051819087:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.46 % (2255598)% WARNING: option uhcvi not known.
% 0.16/0.46 % (2255601) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2255592-2255601"...
% 0.16/0.46 % (2255601)...printing done.
% 0.16/0.46 % (2255601)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
% 0.16/0.46 % (2255601)------------------------------
% 0.16/0.46 % (2255601)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.46 % (2255601)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.46 % (2255601)CaDiCaL version: 2.1.3
% 0.16/0.46 % (2255601)Termination reason: Refutation
% 0.16/0.46 % (2255601)Time elapsed: 0.004 s
% 0.16/0.46 % (2255601)Peak memory usage: 12 MB
% 0.16/0.46 % (2255601)Instructions burned: 9 (million)
% 0.16/0.46 % (2255592)Success in time 0.034 s
% 0.16/0.46 % Vampire exiting
%------------------------------------------------------------------------------