%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n020.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 12:41:12 PM UTC 2026
% Result : Theorem 0.33s 0.99s
% Output : Refutation 3.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of formulae : 91 ( 12 unt; 5 def)
% Number of atoms : 242 ( 5 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 255 ( 104 ~; 123 |; 15 &)
% ( 11 <=>; 0 =>; 0 <=; 2 <~>)
% Maximal formula depth : 9 ( 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 : 66 ( 0 sgn 60 !; 6 ?)
% 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(f4,axiom,
! [X0,X1] : union(X0,X1) = union(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
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,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X0)
& ~ member(X2,X1) ) )
& ( member(X2,X0)
| member(X2,X1)
| ~ member(X2,union(X0,X1)) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f11,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X0)
& ~ member(X2,X1) ) )
& ( member(X2,X0)
| member(X2,X1)
| ~ member(X2,union(X0,X1)) ) ),
inference(flattening,[],[f10]) ).
fof(f12,plain,
! [X0,X1,X2] :
( ( member(X2,difference(X0,X1))
| ~ member(X2,X0)
| member(X2,X1) )
& ( ( member(X2,X0)
& ~ member(X2,X1) )
| ~ member(X2,difference(X0,X1)) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f13,plain,
! [X0,X1,X2] :
( ( member(X2,difference(X0,X1))
| ~ member(X2,X0)
| member(X2,X1) )
& ( ( member(X2,X0)
& ~ member(X2,X1) )
| ~ member(X2,difference(X0,X1)) ) ),
inference(flattening,[],[f12]) ).
fof(f17,plain,
? [X0,X1,X2] :
( ( ( ( member(X0,X1)
| ~ member(X0,X2) )
& ( member(X0,X2)
| ~ member(X0,X1) ) )
| ~ member(X0,symmetric_difference(X1,X2)) )
& ( ( ( ~ member(X0,X2)
| ~ member(X0,X1) )
& ( member(X0,X2)
| member(X0,X1) ) )
| member(X0,symmetric_difference(X1,X2)) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f18,plain,
( ( ( ( member(sK1,sK2)
| ~ member(sK1,sK3) )
& ( member(sK1,sK3)
| ~ member(sK1,sK2) ) )
| ~ member(sK1,symmetric_difference(sK2,sK3)) )
& ( ( ( ~ member(sK1,sK3)
| ~ member(sK1,sK2) )
& ( member(sK1,sK3)
| member(sK1,sK2) ) )
| member(sK1,symmetric_difference(sK2,sK3)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f17]) ).
fof(f19,plain,
! [X2,X0,X1] :
( ~ member(X2,union(X0,X1))
| member(X2,X1)
| member(X2,X0) ),
inference(cnf_transformation,[],[f11]) ).
fof(f21,plain,
! [X2,X0,X1] :
( ~ member(X2,X0)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f11]) ).
fof(f22,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f23,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f13]) ).
fof(f24,plain,
! [X2,X0,X1] :
( member(X2,difference(X0,X1))
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f25,plain,
! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
inference(cnf_transformation,[],[f3]) ).
fof(f26,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f32,plain,
( member(sK1,sK3)
| member(sK1,sK2)
| member(sK1,symmetric_difference(sK2,sK3)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f33,plain,
( ~ member(sK1,sK3)
| ~ member(sK1,sK2)
| member(sK1,symmetric_difference(sK2,sK3)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f34,plain,
( member(sK1,sK3)
| ~ member(sK1,sK2)
| ~ member(sK1,symmetric_difference(sK2,sK3)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f35,plain,
( member(sK1,sK2)
| ~ member(sK1,sK3)
| ~ member(sK1,symmetric_difference(sK2,sK3)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f39,definition,
( spl4_1
<=> member(sK1,symmetric_difference(sK2,sK3)) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f40,plain,
( ~ member(sK1,symmetric_difference(sK2,sK3))
| spl4_1 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f41,plain,
( member(sK1,symmetric_difference(sK2,sK3))
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f43,definition,
( spl4_2
<=> member(sK1,sK2) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f44,plain,
( ~ member(sK1,sK2)
| spl4_2 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f45,plain,
( member(sK1,sK2)
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f47,definition,
( spl4_3
<=> member(sK1,sK3) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
fof(f48,plain,
( ~ member(sK1,sK3)
| spl4_3 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f49,plain,
( member(sK1,sK3)
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f50,plain,
( spl4_1
| spl4_2
| spl4_3 ),
inference(avatar_split_clause,[],[f32,f47,f43,f39]) ).
fof(f51,plain,
( spl4_1
| ~ spl4_2
| ~ spl4_3 ),
inference(avatar_split_clause,[],[f33,f47,f43,f39]) ).
fof(f52,plain,
( ~ spl4_1
| ~ spl4_2
| spl4_3 ),
inference(avatar_split_clause,[],[f34,f47,f43,f39]) ).
fof(f53,plain,
( ~ spl4_1
| ~ spl4_3
| spl4_2 ),
inference(avatar_split_clause,[],[f35,f43,f47,f39]) ).
fof(f77,plain,
! [X2,X3,X0,X1] :
( member(X0,union(difference(X1,X2),X3))
| member(X0,X2)
| ~ member(X0,X1) ),
inference(resolution,[],[f24,f21]) ).
fof(f86,plain,
! [X0,X1] : union(difference(X0,X1),difference(X1,X0)) = symmetric_difference(X1,X0),
inference(superposition,[],[f25,f26]) ).
fof(f88,plain,
! [X2,X0,X1] :
( ~ member(X2,symmetric_difference(X0,X1))
| member(X2,difference(X1,X0))
| member(X2,difference(X0,X1)) ),
inference(superposition,[],[f19,f25]) ).
fof(f118,plain,
! [X2,X0,X1] :
( member(X2,symmetric_difference(X0,X1))
| member(X2,X1)
| ~ member(X2,X0) ),
inference(superposition,[],[f77,f25]) ).
fof(f235,plain,
( member(sK1,sK3)
| ~ member(sK1,sK2)
| spl4_1 ),
inference(resolution,[],[f118,f40]) ).
fof(f244,plain,
( ~ member(sK1,sK2)
| spl4_1
| spl4_3 ),
inference(forward_subsumption_resolution,[],[f235,f48]) ).
fof(f245,plain,
( $false
| spl4_1
| ~ spl4_2
| spl4_3 ),
inference(forward_subsumption_resolution,[],[f244,f45]) ).
fof(f246,plain,
( spl4_1
| ~ spl4_2
| spl4_3 ),
inference(avatar_contradiction_clause,[],[f245]) ).
fof(f249,plain,
( member(sK1,difference(sK3,sK2))
| member(sK1,difference(sK2,sK3))
| ~ spl4_1 ),
inference(resolution,[],[f41,f88]) ).
fof(f253,definition,
( spl4_4
<=> member(sK1,difference(sK2,sK3)) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
fof(f255,plain,
( member(sK1,difference(sK2,sK3))
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f253]) ).
fof(f257,definition,
( spl4_5
<=> member(sK1,difference(sK3,sK2)) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
fof(f258,plain,
( ~ member(sK1,difference(sK3,sK2))
| spl4_5 ),
inference(avatar_component_clause,[],[f257]) ).
fof(f259,plain,
( member(sK1,difference(sK3,sK2))
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f257]) ).
fof(f260,plain,
( spl4_4
| spl4_5
| ~ spl4_1 ),
inference(avatar_split_clause,[],[f249,f39,f257,f253]) ).
fof(f271,plain,
( member(sK1,sK3)
| ~ spl4_5 ),
inference(resolution,[],[f259,f23]) ).
fof(f272,plain,
( ~ member(sK1,sK2)
| ~ spl4_5 ),
inference(resolution,[],[f259,f22]) ).
fof(f275,plain,
( $false
| ~ spl4_2
| ~ spl4_5 ),
inference(forward_subsumption_resolution,[],[f272,f45]) ).
fof(f276,plain,
( ~ spl4_2
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f275]) ).
fof(f282,plain,
( member(sK1,sK2)
| ~ spl4_4 ),
inference(resolution,[],[f255,f23]) ).
fof(f283,plain,
( ~ member(sK1,sK3)
| ~ spl4_4 ),
inference(resolution,[],[f255,f22]) ).
fof(f286,plain,
( $false
| ~ spl4_3
| ~ spl4_4 ),
inference(forward_subsumption_resolution,[],[f283,f49]) ).
fof(f287,plain,
( ~ spl4_3
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f286]) ).
fof(f290,plain,
( ~ member(sK1,sK3)
| member(sK1,sK2)
| spl4_5 ),
inference(resolution,[],[f258,f24]) ).
fof(f291,plain,
( member(sK1,sK2)
| ~ spl4_3
| spl4_5 ),
inference(forward_subsumption_resolution,[],[f290,f49]) ).
fof(f292,plain,
( $false
| spl4_2
| ~ spl4_3
| spl4_5 ),
inference(forward_subsumption_resolution,[],[f291,f44]) ).
fof(f293,plain,
( spl4_2
| ~ spl4_3
| spl4_5 ),
inference(avatar_contradiction_clause,[],[f292]) ).
fof(f296,plain,
( ! [X0] : member(sK1,union(difference(sK3,sK2),X0))
| ~ spl4_5 ),
inference(resolution,[],[f259,f21]) ).
fof(f329,plain,
( member(sK1,symmetric_difference(sK2,sK3))
| ~ spl4_5 ),
inference(superposition,[],[f296,f86]) ).
fof(f338,plain,
( $false
| spl4_2
| ~ spl4_4 ),
inference(forward_subsumption_resolution,[],[f282,f44]) ).
fof(f339,plain,
( spl4_2
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f338]) ).
fof(f341,plain,
( spl4_3
| ~ spl4_5 ),
inference(avatar_split_clause,[],[f271,f257,f47]) ).
fof(f342,plain,
( spl4_1
| ~ spl4_5 ),
inference(avatar_split_clause,[],[f329,f257,f39]) ).
cnf(s1,plain,
( spl4_1
| spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f50]) ).
cnf(s2,plain,
( spl4_1
| ~ spl4_2
| ~ spl4_3 ),
inference(sat_conversion,[],[f51]) ).
cnf(s3,plain,
( ~ spl4_1
| ~ spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f52]) ).
cnf(s4,plain,
( ~ spl4_1
| spl4_2
| ~ spl4_3 ),
inference(sat_conversion,[],[f53]) ).
cnf(s5,plain,
( spl4_1
| ~ spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f246]) ).
cnf(s6,plain,
( ~ spl4_1
| spl4_4
| spl4_5 ),
inference(sat_conversion,[],[f260]) ).
cnf(s7,plain,
( ~ spl4_2
| ~ spl4_5 ),
inference(sat_conversion,[],[f276]) ).
cnf(s8,plain,
( ~ spl4_3
| ~ spl4_4 ),
inference(sat_conversion,[],[f287]) ).
cnf(s9,plain,
( spl4_2
| ~ spl4_3
| spl4_5 ),
inference(sat_conversion,[],[f293]) ).
cnf(s12,plain,
( spl4_2
| ~ spl4_4 ),
inference(sat_conversion,[],[f339]) ).
cnf(s14,plain,
( spl4_3
| ~ spl4_5 ),
inference(sat_conversion,[],[f341]) ).
cnf(s16,plain,
( spl4_1
| ~ spl4_5 ),
inference(sat_conversion,[],[f342]) ).
cnf(s18,plain,
( spl4_2
| spl4_1 ),
inference(rat,[],[s1,s9,s16]) ).
cnf(s19,plain,
( ~ spl4_2
| spl4_1 ),
inference(rat,[],[s2,s5]) ).
cnf(s20,plain,
spl4_1,
inference(rat,[],[s19,s18]) ).
cnf(s21,plain,
spl4_2,
inference(rat,[],[s14,s6,s4,s12,s20]) ).
cnf(s22,plain,
~ spl4_5,
inference(rat,[],[s7,s21]) ).
cnf(s23,plain,
spl4_3,
inference(rat,[],[s3,s20,s21]) ).
cnf(s24,plain,
spl4_4,
inference(rat,[],[s6,s20,s22]) ).
cnf(s25,plain,
$false,
inference(rat,[],[s8,s24,s23]) ).
fof(f343,plain,
$false,
inference(avatar_sat_refutation,[],[s25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET580+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.34 % Computer : n020.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8046.5625MB
% 0.10/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/0.34 % CPULimit : 300
% 0.10/0.34 % WCLimit : 300
% 0.10/0.34 % DateTime : Mon Sep 28 02:13:34 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 Running first-order theorem proving
% 0.12/0.38 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.33/0.99 % (3965884)Detected formulas, will run a generic FOF schedule.
% 0.33/0.99 % (3965898)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4039143234:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.33/0.99 % (3965896)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1205831419:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.33/0.99 % (3965898)First to succeed.
% 0.33/0.99 % (3965898)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3965884"
% 0.33/0.99 % (3965896)Refutation not found, incomplete strategy
% 0.33/0.99 % (3965896)------------------------------
% 0.33/0.99 % (3965896)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.33/0.99 % (3965896)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.99 % (3965896)CaDiCaL version: 2.1.3
% 0.33/0.99 % (3965896)Termination reason: Refutation not found, incomplete strategy
% 0.33/0.99 % (3965896)Time elapsed: 0.002 s
% 0.33/0.99 % (3965896)Peak memory usage: 88 MB
% 0.33/0.99 % (3965896)Instructions burned: 1 (million)
% 0.33/0.99 % (3965899)dis-21_1_sil=8000:lcm=predicate:random_seed=472709848:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 0.33/0.99 % (3965899)Also succeeded, but the first one will report.
% 0.33/0.99 % (3965895)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1743820073:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.33/0.99 % (3965894)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3612183948:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.33/0.99 % (3965893)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1217761955:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.33/0.99 % (3965897)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3037856667:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.33/0.99 % (3965897)Refutation not found, incomplete strategy
% 0.33/0.99 % (3965897)------------------------------
% 0.33/0.99 % (3965897)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.33/0.99 % (3965897)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.99 % (3965897)CaDiCaL version: 2.1.3
% 0.33/0.99 % (3965897)Termination reason: Refutation not found, incomplete strategy
% 0.33/0.99 % (3965897)Time elapsed: 0.003 s
% 0.33/0.99 % (3965897)Peak memory usage: 87 MB
% 0.33/0.99 % (3965897)Instructions burned: 1 (million)
% 0.33/0.99 % (3965898)Refutation found. Thanks to Tanya!
% 0.33/0.99 % SZS status Theorem for theBenchmark
% 0.33/0.99 % SZS output start Proof for theBenchmark
% See solution above
% 3.09/1.11 % (3965898)------------------------------
% 3.09/1.11 % (3965898)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.09/1.11 % (3965898)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.09/1.11 % (3965898)CaDiCaL version: 2.1.3
% 3.09/1.11 % (3965898)Termination reason: Refutation
% 3.09/1.11 % (3965898)Time elapsed: 0.007 s
% 3.09/1.11 % (3965898)Peak memory usage: 90 MB
% 3.09/1.11 % (3965898)Instructions burned: 14 (million)
% 3.09/1.11 % (3965898)------------------------------
% 3.09/1.11 % (3965898)------------------------------
% 3.09/1.11 % (3965884)Success in time 0.405 s
% 3.09/1.11 % Vampire exiting
%------------------------------------------------------------------------------