%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET580+3 : TPTP v9.3.1. Released v2.2.0.
% 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 12:43:59 PM UTC 2026
% Result : Theorem 0.12s 0.45s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 88 ( 9 unt; 5 def)
% Number of atoms : 207 ( 2 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 207 ( 88 ~; 105 |; 1 &)
% ( 11 <=>; 0 =>; 0 <=; 2 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 55 ( 0 sgn 52 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X0)
| member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).
fof(f2,axiom,
! [X0,X1,X2] :
( member(X2,difference(X0,X1))
<=> ( member(X2,X0)
& ~ member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).
fof(f3,axiom,
! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric_difference_defn) ).
fof(f7,conjecture,
! [X0,X1,X2] :
( member(X0,symmetric_difference(X1,X2))
<=> ~ ( member(X0,X1)
<=> member(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th23) ).
fof(f8,negated_conjecture,
~ ! [X0,X1,X2] :
( member(X0,symmetric_difference(X1,X2))
<=> ~ ( member(X0,X1)
<=> member(X0,X2) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
? [X0,X1,X2] :
( member(X0,symmetric_difference(X1,X2))
<~> ( member(X0,X1)
<~> member(X0,X2) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f10,plain,
! [X2,X0,X1] :
( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f1]) ).
fof(f11,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f1]) ).
fof(f12,plain,
! [X2,X0,X1] :
( ~ member(X2,X0)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f1]) ).
fof(f13,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[],[f2]) ).
fof(f14,plain,
! [X2,X0,X1] :
( member(X2,X0)
| ~ member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[],[f2]) ).
fof(f15,plain,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[],[f2]) ).
fof(f16,plain,
! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
inference(cnf_transformation,[],[f3]) ).
fof(f23,plain,
( ~ member(sK1,sK3)
| member(sK1,sK2)
| ~ member(sK1,symmetric_difference(sK2,sK3)) ),
inference(cnf_transformation,[],[f9]) ).
fof(f24,plain,
( member(sK1,sK3)
| ~ member(sK1,sK2)
| ~ member(sK1,symmetric_difference(sK2,sK3)) ),
inference(cnf_transformation,[],[f9]) ).
fof(f25,plain,
( member(sK1,sK3)
| member(sK1,sK2)
| member(sK1,symmetric_difference(sK2,sK3)) ),
inference(cnf_transformation,[],[f9]) ).
fof(f26,plain,
( ~ member(sK1,sK3)
| ~ member(sK1,sK2)
| member(sK1,symmetric_difference(sK2,sK3)) ),
inference(cnf_transformation,[],[f9]) ).
fof(f28,plain,
( ~ member(sK1,sK3)
| ~ member(sK1,sK2)
| member(sK1,union(difference(sK2,sK3),difference(sK3,sK2))) ),
inference(definition_unfolding,[],[f26,f16]) ).
fof(f29,plain,
( member(sK1,sK3)
| member(sK1,sK2)
| member(sK1,union(difference(sK2,sK3),difference(sK3,sK2))) ),
inference(definition_unfolding,[],[f25,f16]) ).
fof(f30,plain,
( member(sK1,sK3)
| ~ member(sK1,sK2)
| ~ member(sK1,union(difference(sK2,sK3),difference(sK3,sK2))) ),
inference(definition_unfolding,[],[f24,f16]) ).
fof(f31,plain,
( ~ member(sK1,sK3)
| member(sK1,sK2)
| ~ member(sK1,union(difference(sK2,sK3),difference(sK3,sK2))) ),
inference(definition_unfolding,[],[f23,f16]) ).
fof(f34,plain,
! [X2,X0,X1] :
( ~ member(X2,union(X0,X1))
| member(X2,X0) ),
inference(consistent_polarity_flipping,[],[f12]) ).
fof(f35,plain,
! [X2,X0,X1] :
( ~ member(X2,union(X0,X1))
| member(X2,X1) ),
inference(consistent_polarity_flipping,[],[f11]) ).
fof(f36,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X0)
| ~ member(X2,X1) ),
inference(consistent_polarity_flipping,[],[f10]) ).
fof(f37,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| member(X2,X0)
| ~ member(X2,X1) ),
inference(consistent_polarity_flipping,[],[f15]) ).
fof(f38,plain,
! [X2,X0,X1] :
( member(X2,difference(X0,X1))
| ~ member(X2,X0) ),
inference(consistent_polarity_flipping,[],[f14]) ).
fof(f39,plain,
! [X2,X0,X1] :
( member(X2,difference(X0,X1))
| member(X2,X1) ),
inference(consistent_polarity_flipping,[],[f13]) ).
fof(f44,plain,
( member(sK1,sK3)
| member(sK1,sK2)
| ~ member(sK1,union(difference(sK2,sK3),difference(sK3,sK2))) ),
inference(consistent_polarity_flipping,[],[f28]) ).
fof(f45,plain,
( ~ member(sK1,sK3)
| ~ member(sK1,sK2)
| ~ member(sK1,union(difference(sK2,sK3),difference(sK3,sK2))) ),
inference(consistent_polarity_flipping,[],[f29]) ).
fof(f46,plain,
( ~ member(sK1,sK3)
| member(sK1,sK2)
| member(sK1,union(difference(sK2,sK3),difference(sK3,sK2))) ),
inference(consistent_polarity_flipping,[],[f30]) ).
fof(f47,plain,
( member(sK1,sK3)
| ~ member(sK1,sK2)
| member(sK1,union(difference(sK2,sK3),difference(sK3,sK2))) ),
inference(consistent_polarity_flipping,[],[f31]) ).
fof(f49,definition,
( spl4_1
<=> member(sK1,union(difference(sK2,sK3),difference(sK3,sK2))) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f50,plain,
( ~ member(sK1,union(difference(sK2,sK3),difference(sK3,sK2)))
| spl4_1 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f51,plain,
( member(sK1,union(difference(sK2,sK3),difference(sK3,sK2)))
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f53,definition,
( spl4_2
<=> member(sK1,sK2) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f57,definition,
( spl4_3
<=> member(sK1,sK3) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
fof(f58,plain,
( ~ member(sK1,sK3)
| spl4_3 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f60,plain,
( spl4_1
| ~ spl4_2
| spl4_3 ),
inference(avatar_split_clause,[],[f47,f57,f53,f49]) ).
fof(f61,plain,
( spl4_1
| spl4_2
| ~ spl4_3 ),
inference(avatar_split_clause,[],[f46,f57,f53,f49]) ).
fof(f62,plain,
( ~ spl4_1
| ~ spl4_2
| ~ spl4_3 ),
inference(avatar_split_clause,[],[f45,f57,f53,f49]) ).
fof(f63,plain,
( ~ spl4_1
| spl4_2
| spl4_3 ),
inference(avatar_split_clause,[],[f44,f57,f53,f49]) ).
fof(f68,plain,
( ~ member(sK1,difference(sK2,sK3))
| ~ member(sK1,difference(sK3,sK2))
| spl4_1 ),
inference(resolution,[],[f36,f50]) ).
fof(f74,definition,
( spl4_4
<=> member(sK1,difference(sK3,sK2)) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
fof(f75,plain,
( member(sK1,difference(sK3,sK2))
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f76,plain,
( ~ member(sK1,difference(sK3,sK2))
| spl4_4 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f78,definition,
( spl4_5
<=> member(sK1,difference(sK2,sK3)) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
fof(f79,plain,
( member(sK1,difference(sK2,sK3))
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f80,plain,
( ~ member(sK1,difference(sK2,sK3))
| spl4_5 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f82,plain,
( member(sK1,sK2)
| spl4_4 ),
inference(resolution,[],[f76,f39]) ).
fof(f83,plain,
( ~ member(sK1,sK3)
| spl4_4 ),
inference(resolution,[],[f76,f38]) ).
fof(f100,plain,
( member(sK1,sK3)
| ~ member(sK1,sK2)
| ~ spl4_4 ),
inference(resolution,[],[f75,f37]) ).
fof(f101,plain,
( member(sK1,sK3)
| spl4_5 ),
inference(resolution,[],[f80,f39]) ).
fof(f102,plain,
( ~ member(sK1,sK2)
| spl4_5 ),
inference(resolution,[],[f80,f38]) ).
fof(f103,plain,
( $false
| spl4_3
| spl4_5 ),
inference(forward_subsumption_resolution,[],[f101,f58]) ).
fof(f104,plain,
( spl4_3
| spl4_5 ),
inference(avatar_contradiction_clause,[],[f103]) ).
fof(f106,plain,
( member(sK1,difference(sK3,sK2))
| ~ spl4_1 ),
inference(resolution,[],[f51,f35]) ).
fof(f107,plain,
( member(sK1,difference(sK2,sK3))
| ~ spl4_1 ),
inference(resolution,[],[f51,f34]) ).
fof(f110,plain,
( spl4_5
| ~ spl4_1 ),
inference(avatar_split_clause,[],[f107,f49,f78]) ).
fof(f111,plain,
( member(sK1,sK2)
| ~ member(sK1,sK3)
| ~ spl4_5 ),
inference(resolution,[],[f79,f37]) ).
fof(f115,plain,
( ~ member(sK1,difference(sK2,sK3))
| spl4_1
| ~ spl4_4 ),
inference(forward_subsumption_resolution,[],[f68,f75]) ).
fof(f116,plain,
( ~ spl4_2
| spl4_5 ),
inference(avatar_split_clause,[],[f102,f78,f53]) ).
fof(f117,plain,
( ~ spl4_5
| spl4_1
| ~ spl4_4 ),
inference(avatar_split_clause,[],[f115,f74,f49,f78]) ).
fof(f118,plain,
( ~ spl4_3
| spl4_2
| ~ spl4_5 ),
inference(avatar_split_clause,[],[f111,f78,f53,f57]) ).
fof(f119,plain,
( ~ spl4_2
| spl4_3
| ~ spl4_4 ),
inference(avatar_split_clause,[],[f100,f74,f57,f53]) ).
fof(f120,plain,
( spl4_2
| spl4_4 ),
inference(avatar_split_clause,[],[f82,f74,f53]) ).
fof(f121,plain,
( ~ spl4_3
| spl4_4 ),
inference(avatar_split_clause,[],[f83,f74,f57]) ).
fof(f122,plain,
( spl4_4
| ~ spl4_1 ),
inference(avatar_split_clause,[],[f106,f49,f74]) ).
cnf(s1,plain,
( spl4_1
| ~ spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f60]) ).
cnf(s2,plain,
( spl4_1
| spl4_2
| ~ spl4_3 ),
inference(sat_conversion,[],[f61]) ).
cnf(s3,plain,
( ~ spl4_1
| ~ spl4_2
| ~ spl4_3 ),
inference(sat_conversion,[],[f62]) ).
cnf(s4,plain,
( ~ spl4_1
| spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f63]) ).
cnf(s7,plain,
( spl4_3
| spl4_5 ),
inference(sat_conversion,[],[f104]) ).
cnf(s10,plain,
( ~ spl4_1
| spl4_5 ),
inference(sat_conversion,[],[f110]) ).
cnf(s12,plain,
( ~ spl4_2
| spl4_5 ),
inference(sat_conversion,[],[f116]) ).
cnf(s13,plain,
( spl4_1
| ~ spl4_4
| ~ spl4_5 ),
inference(sat_conversion,[],[f117]) ).
cnf(s15,plain,
( spl4_2
| ~ spl4_3
| ~ spl4_5 ),
inference(sat_conversion,[],[f118]) ).
cnf(s16,plain,
( ~ spl4_2
| spl4_3
| ~ spl4_4 ),
inference(sat_conversion,[],[f119]) ).
cnf(s17,plain,
( spl4_2
| spl4_4 ),
inference(sat_conversion,[],[f120]) ).
cnf(s18,plain,
( ~ spl4_3
| spl4_4 ),
inference(sat_conversion,[],[f121]) ).
cnf(s19,plain,
( ~ spl4_1
| spl4_4 ),
inference(sat_conversion,[],[f122]) ).
cnf(s20,plain,
( spl4_2
| spl4_1 ),
inference(rat,[],[s7,s13,s2,s17]) ).
cnf(s21,plain,
spl4_1,
inference(rat,[],[s18,s13,s1,s12,s20]) ).
cnf(s22,plain,
spl4_4,
inference(rat,[],[s19,s21]) ).
cnf(s23,plain,
spl4_5,
inference(rat,[],[s10,s21]) ).
cnf(s24,plain,
spl4_2,
inference(rat,[],[s15,s4,s23,s21]) ).
cnf(s25,plain,
~ spl4_3,
inference(rat,[],[s3,s21,s24]) ).
cnf(s26,plain,
$false,
inference(rat,[],[s16,s22,s24,s25]) ).
fof(f123,plain,
$false,
inference(avatar_sat_refutation,[],[s26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET580+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n007.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 02:10:40 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
% 0.12/0.45 % (1962259)Will run a generic schedule for satisfiability detection.
% 0.12/0.45 % (1962270)% WARNING: option uhcvi not known.
% 0.12/0.45 % (1962270)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4181498915:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.12/0.45 % (1962270) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1962259-1962270"...
% 0.12/0.45 % (1962270)...printing done.
% 0.12/0.45 % (1962270)Refutation found. Thanks to Tanya!
% 0.12/0.45 % SZS status Theorem for theBenchmark
% 0.12/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.45 % (1962270)------------------------------
% 0.12/0.45 % (1962270)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.45 % (1962270)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.45 % (1962270)CaDiCaL version: 2.1.3
% 0.12/0.45 % (1962270)Termination reason: Refutation
% 0.12/0.45 % (1962270)Time elapsed: 0.002 s
% 0.12/0.45 % (1962270)Peak memory usage: 12 MB
% 0.12/0.45 % (1962270)Instructions burned: 4 (million)
% 0.12/0.45 % (1962259)Success in time 0.029 s
% 0.12/0.45 % Vampire exiting
%------------------------------------------------------------------------------