%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU105+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n019.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 12:51:56 PM UTC 2026
% Result : Theorem 0.18s 0.46s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 61 ( 16 unt; 4 def)
% Number of atoms : 146 ( 4 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 147 ( 62 ~; 56 |; 12 &)
% ( 7 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 49 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f32,axiom,
! [X0,X1] : set_difference(X0,X1) = symmetric_difference(X0,set_intersection2(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t100_xboole_1) ).
fof(f33,axiom,
! [X0] :
( preboolean(X0)
<=> ! [X1,X2] :
( ( in(X1,X0)
& in(X2,X0) )
=> ( in(set_union2(X1,X2),X0)
& in(set_difference(X1,X2),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_finsub_1) ).
fof(f34,conjecture,
! [X0] :
( ~ empty(X0)
=> ( ! [X1] :
( element(X1,X0)
=> ! [X2] :
( element(X2,X0)
=> ( in(symmetric_difference(X1,X2),X0)
& in(set_intersection2(X1,X2),X0) ) ) )
=> preboolean(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_finsub_1) ).
fof(f35,negated_conjecture,
~ ! [X0] :
( ~ empty(X0)
=> ( ! [X1] :
( element(X1,X0)
=> ! [X2] :
( element(X2,X0)
=> ( in(symmetric_difference(X1,X2),X0)
& in(set_intersection2(X1,X2),X0) ) ) )
=> preboolean(X0) ) ),
inference(negated_conjecture,[status(cth)],[f34]) ).
fof(f37,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f49,axiom,
! [X0,X1] : set_union2(X0,X1) = symmetric_difference(symmetric_difference(X0,X1),set_intersection2(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t94_xboole_1) ).
fof(f80,plain,
! [X0] :
( preboolean(X0)
<=> ! [X1,X2] :
( ( in(set_union2(X1,X2),X0)
& in(set_difference(X1,X2),X0) )
| ~ in(X1,X0)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f81,plain,
! [X0] :
( preboolean(X0)
<=> ! [X1,X2] :
( ( in(set_union2(X1,X2),X0)
& in(set_difference(X1,X2),X0) )
| ~ in(X1,X0)
| ~ in(X2,X0) ) ),
inference(flattening,[],[f80]) ).
fof(f82,plain,
? [X0] :
( ~ preboolean(X0)
& ! [X1] :
( ! [X2] :
( ( in(symmetric_difference(X1,X2),X0)
& in(set_intersection2(X1,X2),X0) )
| ~ element(X2,X0) )
| ~ element(X1,X0) )
& ~ empty(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f83,plain,
? [X0] :
( ~ preboolean(X0)
& ! [X1] :
( ! [X2] :
( ( in(symmetric_difference(X1,X2),X0)
& in(set_intersection2(X1,X2),X0) )
| ~ element(X2,X0) )
| ~ element(X1,X0) )
& ~ empty(X0) ),
inference(flattening,[],[f82]) ).
fof(f84,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f138,plain,
! [X0,X1] : set_difference(X0,X1) = symmetric_difference(X0,set_intersection2(X0,X1)),
inference(cnf_transformation,[],[f32]) ).
fof(f139,plain,
! [X0] :
( ~ in(set_difference(sK10(X0),sK11(X0)),X0)
| ~ in(set_union2(sK10(X0),sK11(X0)),X0)
| preboolean(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f142,plain,
! [X0] :
( preboolean(X0)
| in(sK11(X0),X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f143,plain,
! [X0] :
( preboolean(X0)
| in(sK10(X0),X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f144,plain,
! [X2,X1] :
( ~ element(X1,sK12)
| ~ element(X2,sK12)
| in(set_intersection2(X1,X2),sK12) ),
inference(cnf_transformation,[],[f83]) ).
fof(f145,plain,
! [X2,X1] :
( ~ element(X1,sK12)
| ~ element(X2,sK12)
| in(symmetric_difference(X1,X2),sK12) ),
inference(cnf_transformation,[],[f83]) ).
fof(f147,plain,
~ preboolean(sK12),
inference(cnf_transformation,[],[f83]) ).
fof(f149,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f161,plain,
! [X0,X1] : set_union2(X0,X1) = symmetric_difference(symmetric_difference(X0,X1),set_intersection2(X0,X1)),
inference(cnf_transformation,[],[f49]) ).
fof(f171,plain,
! [X0] :
( preboolean(X0)
| ~ in(symmetric_difference(symmetric_difference(sK10(X0),sK11(X0)),set_intersection2(sK10(X0),sK11(X0))),X0)
| ~ in(symmetric_difference(sK10(X0),set_intersection2(sK10(X0),sK11(X0))),X0) ),
inference(definition_unfolding,[],[f139,f138,f161]) ).
fof(f208,plain,
in(sK11(sK12),sK12),
inference(resolution,[],[f142,f147]) ).
fof(f212,plain,
in(sK10(sK12),sK12),
inference(resolution,[],[f143,f147]) ).
fof(f216,plain,
! [X0,X1] :
( ~ element(X1,sK12)
| ~ in(X0,sK12)
| in(set_intersection2(X0,X1),sK12) ),
inference(resolution,[],[f149,f144]) ).
fof(f218,plain,
! [X0,X1] :
( ~ element(X1,sK12)
| ~ in(X0,sK12)
| in(symmetric_difference(X0,X1),sK12) ),
inference(resolution,[],[f149,f145]) ).
fof(f304,plain,
! [X0,X1] :
( in(set_intersection2(X0,X1),sK12)
| ~ in(X0,sK12)
| ~ in(X1,sK12) ),
inference(resolution,[],[f216,f149]) ).
fof(f322,plain,
! [X0,X1] :
( in(symmetric_difference(X0,X1),sK12)
| ~ in(X0,sK12)
| ~ in(X1,sK12) ),
inference(resolution,[],[f218,f149]) ).
fof(f550,plain,
( ~ in(symmetric_difference(symmetric_difference(sK10(sK12),sK11(sK12)),set_intersection2(sK10(sK12),sK11(sK12))),sK12)
| ~ in(symmetric_difference(sK10(sK12),set_intersection2(sK10(sK12),sK11(sK12))),sK12) ),
inference(resolution,[],[f171,f147]) ).
fof(f554,definition,
( spl13_3
<=> in(symmetric_difference(sK10(sK12),set_intersection2(sK10(sK12),sK11(sK12))),sK12) ),
introduced(definition,[new_symbols(definition,[spl13_3])],[avatar_definition]) ).
fof(f556,plain,
( ~ in(symmetric_difference(sK10(sK12),set_intersection2(sK10(sK12),sK11(sK12))),sK12)
| spl13_3 ),
inference(avatar_component_clause,[],[f554]) ).
fof(f558,definition,
( spl13_4
<=> in(symmetric_difference(symmetric_difference(sK10(sK12),sK11(sK12)),set_intersection2(sK10(sK12),sK11(sK12))),sK12) ),
introduced(definition,[new_symbols(definition,[spl13_4])],[avatar_definition]) ).
fof(f560,plain,
( ~ in(symmetric_difference(symmetric_difference(sK10(sK12),sK11(sK12)),set_intersection2(sK10(sK12),sK11(sK12))),sK12)
| spl13_4 ),
inference(avatar_component_clause,[],[f558]) ).
fof(f561,plain,
( ~ spl13_3
| ~ spl13_4 ),
inference(avatar_split_clause,[],[f550,f558,f554]) ).
fof(f562,plain,
( ~ in(sK10(sK12),sK12)
| ~ in(set_intersection2(sK10(sK12),sK11(sK12)),sK12)
| spl13_3 ),
inference(resolution,[],[f556,f322]) ).
fof(f563,plain,
( ~ in(set_intersection2(sK10(sK12),sK11(sK12)),sK12)
| spl13_3 ),
inference(forward_subsumption_resolution,[],[f562,f212]) ).
fof(f626,plain,
( ~ in(sK10(sK12),sK12)
| ~ in(sK11(sK12),sK12)
| spl13_3 ),
inference(resolution,[],[f563,f304]) ).
fof(f627,plain,
( ~ in(sK11(sK12),sK12)
| spl13_3 ),
inference(forward_subsumption_resolution,[],[f626,f212]) ).
fof(f628,plain,
( $false
| spl13_3 ),
inference(forward_subsumption_resolution,[],[f627,f208]) ).
fof(f629,plain,
spl13_3,
inference(avatar_contradiction_clause,[],[f628]) ).
fof(f633,plain,
( ~ in(symmetric_difference(sK10(sK12),sK11(sK12)),sK12)
| ~ in(set_intersection2(sK10(sK12),sK11(sK12)),sK12)
| spl13_4 ),
inference(resolution,[],[f560,f322]) ).
fof(f635,definition,
( spl13_5
<=> in(set_intersection2(sK10(sK12),sK11(sK12)),sK12) ),
introduced(definition,[new_symbols(definition,[spl13_5])],[avatar_definition]) ).
fof(f637,plain,
( ~ in(set_intersection2(sK10(sK12),sK11(sK12)),sK12)
| spl13_5 ),
inference(avatar_component_clause,[],[f635]) ).
fof(f639,definition,
( spl13_6
<=> in(symmetric_difference(sK10(sK12),sK11(sK12)),sK12) ),
introduced(definition,[new_symbols(definition,[spl13_6])],[avatar_definition]) ).
fof(f641,plain,
( ~ in(symmetric_difference(sK10(sK12),sK11(sK12)),sK12)
| spl13_6 ),
inference(avatar_component_clause,[],[f639]) ).
fof(f642,plain,
( ~ spl13_5
| ~ spl13_6
| spl13_4 ),
inference(avatar_split_clause,[],[f633,f558,f639,f635]) ).
fof(f643,plain,
( ~ in(sK10(sK12),sK12)
| ~ in(sK11(sK12),sK12)
| spl13_5 ),
inference(resolution,[],[f637,f304]) ).
fof(f644,plain,
( ~ in(sK11(sK12),sK12)
| spl13_5 ),
inference(forward_subsumption_resolution,[],[f643,f212]) ).
fof(f645,plain,
( $false
| spl13_5 ),
inference(forward_subsumption_resolution,[],[f644,f208]) ).
fof(f646,plain,
spl13_5,
inference(avatar_contradiction_clause,[],[f645]) ).
fof(f682,plain,
( ~ in(sK10(sK12),sK12)
| ~ in(sK11(sK12),sK12)
| spl13_6 ),
inference(resolution,[],[f641,f322]) ).
fof(f683,plain,
( ~ in(sK11(sK12),sK12)
| spl13_6 ),
inference(forward_subsumption_resolution,[],[f682,f212]) ).
fof(f684,plain,
( $false
| spl13_6 ),
inference(forward_subsumption_resolution,[],[f683,f208]) ).
fof(f685,plain,
spl13_6,
inference(avatar_contradiction_clause,[],[f684]) ).
cnf(s3,plain,
( ~ spl13_3
| ~ spl13_4 ),
inference(sat_conversion,[],[f561]) ).
cnf(s4,plain,
spl13_3,
inference(sat_conversion,[],[f629]) ).
cnf(s5,plain,
( spl13_4
| ~ spl13_5
| ~ spl13_6 ),
inference(sat_conversion,[],[f642]) ).
cnf(s6,plain,
spl13_5,
inference(sat_conversion,[],[f646]) ).
cnf(s7,plain,
spl13_6,
inference(sat_conversion,[],[f685]) ).
cnf(s8,plain,
spl13_4,
inference(rat,[],[s5,s7,s6]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s3,s8,s4]) ).
fof(f686,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU105+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n019.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 03:35:03 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.41 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
% 0.18/0.46 % (3636669)Will run a generic schedule for satisfiability detection.
% 0.18/0.46 % (3636678)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2183611794:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.46 % (3636675)% WARNING: option uhcvi not known.
% 0.18/0.46 % (3636674)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3792666247_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.46 % (3636675)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2129045334:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.46 % (3636676)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4057303867:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.46 % (3636677)dis+10_1_sil=32000:sp=arity:random_seed=1033193613:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.46 % (3636680)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=654588165:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.46 % (3636679)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2603137024:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.46 % (3636678) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3636669-3636678"...
% 0.18/0.46 % (3636678)...printing done.
% 0.18/0.46 % (3636678)Refutation found. Thanks to Tanya!
% 0.18/0.46 % SZS status Theorem for theBenchmark
% 0.18/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.46 % (3636678)------------------------------
% 0.18/0.46 % (3636678)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.46 % (3636678)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.46 % (3636678)CaDiCaL version: 2.1.3
% 0.18/0.46 % (3636678)Termination reason: Refutation
% 0.18/0.46 % (3636678)Time elapsed: 0.009 s
% 0.18/0.46 % (3636678)Peak memory usage: 13 MB
% 0.18/0.46 % (3636678)Instructions burned: 22 (million)
% 0.18/0.46 % (3636669)Success in time 0.036 s
% 0.18/0.46 % Vampire exiting
%------------------------------------------------------------------------------