%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET123-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 12:40:13 PM UTC 2026
% Result : Unsatisfiable 3.66s 1.49s
% Output : Refutation 3.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 18
% Syntax : Number of formulae : 56 ( 22 unt; 6 def)
% Number of atoms : 101 ( 8 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 87 ( 42 ~; 39 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_members) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f8,axiom,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_member) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set) ).
fof(f23,axiom,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection3) ).
fof(f24,axiom,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).
fof(f25,axiom,
! [X0,X1] :
( member(X0,complement(X1))
| ~ member(X0,universal_class)
| member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement2) ).
fof(f26,axiom,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).
fof(f101,axiom,
! [X0,X1] : union(singleton(X0),X1) = set_builder(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_of_set_builder) ).
fof(f102,negated_conjecture,
member(x,set_builder(y,z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_set_builder_alternate_defn1_1) ).
fof(f103,negated_conjecture,
x != y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_set_builder_alternate_defn1_2) ).
fof(f104,negated_conjecture,
~ member(x,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_set_builder_alternate_defn1_3) ).
fof(f110,plain,
! [X0,X1] : set_builder(X0,X1) = complement(intersection(complement(unordered_pair(X0,X0)),complement(X1))),
inference(definition_unfolding,[],[f101,f26,f12]) ).
fof(f114,plain,
member(x,complement(intersection(complement(unordered_pair(y,y)),complement(z)))),
inference(definition_unfolding,[],[f102,f110]) ).
fof(f153,definition,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
fof(f154,plain,
~ sQ0_eqProxy(x,y),
inference(equality_proxy_replacement,[],[f103,f153]) ).
fof(f170,plain,
! [X2,X0,X1] :
( sQ0_eqProxy(X0,X2)
| sQ0_eqProxy(X0,X1)
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(equality_proxy_replacement,[],[f8,f153,f153]) ).
fof(f177,plain,
~ member(x,intersection(complement(unordered_pair(y,y)),complement(z))),
inference(resolution,[],[f24,f114]) ).
fof(f180,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[],[f1,f4]) ).
fof(f200,plain,
( ~ member(x,complement(z))
| ~ member(x,complement(unordered_pair(y,y))) ),
inference(resolution,[],[f23,f177]) ).
fof(f204,definition,
( spl1_3
<=> member(x,complement(unordered_pair(y,y))) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f205,plain,
( ~ member(x,complement(unordered_pair(y,y)))
| spl1_3 ),
inference(avatar_component_clause,[],[f204]) ).
fof(f207,definition,
( spl1_4
<=> member(x,complement(z)) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f208,plain,
( ~ member(x,complement(z))
| spl1_4 ),
inference(avatar_component_clause,[],[f207]) ).
fof(f209,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_split_clause,[],[f200,f207,f204]) ).
fof(f212,definition,
( spl1_5
<=> member(x,unordered_pair(y,y)) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
fof(f213,plain,
( member(x,unordered_pair(y,y))
| ~ spl1_5 ),
inference(avatar_component_clause,[],[f212]) ).
fof(f215,definition,
( spl1_6
<=> member(x,universal_class) ),
introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition]) ).
fof(f216,plain,
( ~ member(x,universal_class)
| spl1_6 ),
inference(avatar_component_clause,[],[f215]) ).
fof(f218,plain,
( ! [X0] : ~ member(x,X0)
| spl1_6 ),
inference(resolution,[],[f216,f180]) ).
fof(f220,plain,
( $false
| spl1_6 ),
inference(resolution,[],[f218,f114]) ).
fof(f229,plain,
spl1_6,
inference(avatar_contradiction_clause,[],[f220]) ).
fof(f232,definition,
( spl1_7
<=> member(x,z) ),
introduced(definition,[new_symbols(definition,[spl1_7])],[avatar_definition]) ).
fof(f233,plain,
( member(x,z)
| ~ spl1_7 ),
inference(avatar_component_clause,[],[f232]) ).
fof(f235,plain,
( ~ member(x,universal_class)
| member(x,unordered_pair(y,y))
| spl1_3 ),
inference(resolution,[],[f205,f25]) ).
fof(f236,plain,
( spl1_5
| ~ spl1_6
| spl1_3 ),
inference(avatar_split_clause,[],[f235,f204,f215,f212]) ).
fof(f239,plain,
! [X0] :
( sQ0_eqProxy(x,X0)
| ~ member(x,unordered_pair(X0,y)) ),
inference(resolution,[],[f170,f154]) ).
fof(f241,plain,
~ member(x,unordered_pair(y,y)),
inference(resolution,[],[f239,f154]) ).
fof(f242,plain,
( $false
| ~ spl1_5 ),
inference(resolution,[],[f241,f213]) ).
fof(f243,plain,
~ spl1_5,
inference(avatar_contradiction_clause,[],[f242]) ).
fof(f244,plain,
( ~ member(x,universal_class)
| member(x,z)
| spl1_4 ),
inference(resolution,[],[f208,f25]) ).
fof(f245,plain,
( spl1_7
| ~ spl1_6
| spl1_4 ),
inference(avatar_split_clause,[],[f244,f207,f215,f232]) ).
fof(f246,plain,
( $false
| ~ spl1_7 ),
inference(resolution,[],[f233,f104]) ).
fof(f247,plain,
~ spl1_7,
inference(avatar_contradiction_clause,[],[f246]) ).
cnf(s3,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(sat_conversion,[],[f209]) ).
cnf(s5,plain,
spl1_6,
inference(sat_conversion,[],[f229]) ).
cnf(s7,plain,
( spl1_3
| spl1_5
| ~ spl1_6 ),
inference(sat_conversion,[],[f236]) ).
cnf(s8,plain,
~ spl1_5,
inference(sat_conversion,[],[f243]) ).
cnf(s9,plain,
( spl1_4
| ~ spl1_6
| spl1_7 ),
inference(sat_conversion,[],[f245]) ).
cnf(s10,plain,
~ spl1_7,
inference(sat_conversion,[],[f247]) ).
cnf(s11,plain,
( spl1_4
| ~ spl1_6 ),
inference(rat,[],[s9,s10]) ).
cnf(s12,plain,
( spl1_3
| ~ spl1_6 ),
inference(rat,[],[s7,s8]) ).
cnf(s14,plain,
spl1_4,
inference(rat,[],[s11,s5]) ).
cnf(s15,plain,
spl1_3,
inference(rat,[],[s12,s5]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s3,s14,s15]) ).
fof(f248,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET123-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n018.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 00:52:39 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.66/1.49 % (2893210)Input is clausal, will run a generic CNF schedule.
% 3.66/1.49 % (2893216)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1770661542:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.66/1.49 % (2893218)lrs+10_1_sil=8000:sp=occurrence:random_seed=1970057270:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.66/1.49 % (2893219)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1347553669:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.66/1.49 % (2893215)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=2840491094:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.66/1.49 % (2893217)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3800085297:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.66/1.49 % (2893221)dis-21_1_sil=8000:lcm=predicate:random_seed=2840607498:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 3.66/1.49 % (2893218)Refutation not found, incomplete strategy
% 3.66/1.49 % (2893218)------------------------------
% 3.66/1.49 % (2893218)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.49 % (2893218)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.49 % (2893218)CaDiCaL version: 2.1.3
% 3.66/1.49 % (2893218)Termination reason: Refutation not found, incomplete strategy
% 3.66/1.49 % (2893218)Time elapsed: 0.003 s
% 3.66/1.49 % (2893218)Peak memory usage: 88 MB
% 3.66/1.49 % (2893218)Instructions burned: 2 (million)
% 3.66/1.49 % (2893221)First to succeed.
% 3.66/1.49 % (2893221)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2893210"
% 3.66/1.49 % (2893220)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=39707905:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.66/1.49 % (2893219)Instruction limit reached!
% 3.66/1.49 % (2893219)------------------------------
% 3.66/1.49 % (2893219)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.49 % (2893219)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.49 % (2893219)CaDiCaL version: 2.1.3
% 3.66/1.49 % (2893219)Termination reason: Instruction limit
% 3.66/1.49 % (2893219)Termination phase: Saturation
% 3.66/1.49 % (2893219)Time elapsed: 0.072 s
% 3.66/1.49 % (2893219)Peak memory usage: 89 MB
% 3.66/1.49 % (2893219)Instructions burned: 114 (million)
% 3.66/1.49 % (2893220)Also succeeded, but the first one will report.
% 3.66/1.49 % (2893218)------------------------------
% 3.66/1.49 % (2893218)------------------------------
% 3.66/1.49 % (2893229)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=3392329444:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.66/1.49 % (2893229)Refutation not found, incomplete strategy
% 3.66/1.49 % (2893229)------------------------------
% 3.66/1.49 % (2893229)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.49 % (2893229)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.49 % (2893229)CaDiCaL version: 2.1.3
% 3.66/1.49 % (2893229)Termination reason: Refutation not found, incomplete strategy
% 3.66/1.49 % (2893229)Time elapsed: 0.002 s
% 3.66/1.49 % (2893229)Peak memory usage: 88 MB
% 3.66/1.49 % (2893229)Instructions burned: 1 (million)
% 3.66/1.49 % (2893221)Refutation found. Thanks to Tanya!
% 3.66/1.49 % SZS status Unsatisfiable for theBenchmark
% 3.66/1.49 % SZS output start Proof for theBenchmark
% See solution above
% 3.66/1.49 % (2893221)------------------------------
% 3.66/1.49 % (2893221)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.49 % (2893221)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.49 % (2893221)CaDiCaL version: 2.1.3
% 3.66/1.49 % (2893221)Termination reason: Refutation
% 3.66/1.49 % (2893221)Time elapsed: 0.006 s
% 3.66/1.49 % (2893221)Peak memory usage: 89 MB
% 3.66/1.49 % (2893221)Instructions burned: 8 (million)
% 3.66/1.49 % (2893221)------------------------------
% 3.66/1.49 % (2893221)------------------------------
% 3.66/1.49 % (2893210)Success in time 0.442 s
% 3.66/1.49 % Vampire exiting
%------------------------------------------------------------------------------