%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET002-6 : 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 : n004.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 12:39:27 PM UTC 2026
% Result : Unsatisfiable 3.76s 1.52s
% Output : Refutation 3.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 18
% Syntax : Number of formulae : 67 ( 12 unt; 7 def)
% Number of atoms : 138 ( 6 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 126 ( 55 ~; 64 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 7 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 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(f2,axiom,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_subclass_members1) ).
fof(f3,axiom,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_subclass_members2) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f7,axiom,
! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_implies_equal) ).
fof(f22,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection2) ).
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(f122,negated_conjecture,
union(x,x) != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_idempotency_of_union_1) ).
fof(f123,plain,
x != union(x,x),
inference(reorient_equations,[],[f122]) ).
fof(f135,plain,
x != complement(intersection(complement(x),complement(x))),
inference(definition_unfolding,[],[f123,f26]) ).
fof(f176,definition,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
fof(f177,plain,
~ sQ0_eqProxy(x,complement(intersection(complement(x),complement(x)))),
inference(equality_proxy_replacement,[],[f135,f176]) ).
fof(f178,plain,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(equality_proxy_replacement,[],[f7,f176]) ).
fof(f200,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[],[f1,f4]) ).
fof(f207,plain,
( ~ subclass(complement(intersection(complement(x),complement(x))),x)
| ~ subclass(x,complement(intersection(complement(x),complement(x)))) ),
inference(resolution,[],[f178,f177]) ).
fof(f210,definition,
( spl1_1
<=> subclass(complement(intersection(complement(x),complement(x))),x) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f211,plain,
( ~ subclass(complement(intersection(complement(x),complement(x))),x)
| spl1_1 ),
inference(avatar_component_clause,[],[f210]) ).
fof(f213,definition,
( spl1_2
<=> subclass(x,complement(intersection(complement(x),complement(x)))) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f214,plain,
( ~ subclass(x,complement(intersection(complement(x),complement(x))))
| spl1_2 ),
inference(avatar_component_clause,[],[f213]) ).
fof(f216,plain,
( ~ spl1_2
| ~ spl1_1 ),
inference(avatar_split_clause,[],[f207,f210,f213]) ).
fof(f217,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(x))),x),x)
| spl1_1 ),
inference(resolution,[],[f211,f3]) ).
fof(f218,plain,
( member(not_subclass_element(complement(intersection(complement(x),complement(x))),x),complement(intersection(complement(x),complement(x))))
| spl1_1 ),
inference(resolution,[],[f211,f2]) ).
fof(f219,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(x))),x),intersection(complement(x),complement(x)))
| spl1_1 ),
inference(resolution,[],[f218,f24]) ).
fof(f225,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(x))),x),complement(x))
| ~ member(not_subclass_element(complement(intersection(complement(x),complement(x))),x),complement(x))
| spl1_1 ),
inference(resolution,[],[f23,f219]) ).
fof(f226,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(x))),x),complement(x))
| spl1_1 ),
inference(duplicate_literal_removal,[],[f225]) ).
fof(f227,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(x))),x),universal_class)
| member(not_subclass_element(complement(intersection(complement(x),complement(x))),x),x)
| spl1_1 ),
inference(resolution,[],[f226,f25]) ).
fof(f229,definition,
( spl1_3
<=> member(not_subclass_element(complement(intersection(complement(x),complement(x))),x),x) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f230,plain,
( member(not_subclass_element(complement(intersection(complement(x),complement(x))),x),x)
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f229]) ).
fof(f232,definition,
( spl1_4
<=> member(not_subclass_element(complement(intersection(complement(x),complement(x))),x),universal_class) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f233,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(x))),x),universal_class)
| spl1_4 ),
inference(avatar_component_clause,[],[f232]) ).
fof(f234,plain,
( spl1_3
| ~ spl1_4
| spl1_1 ),
inference(avatar_split_clause,[],[f227,f210,f232,f229]) ).
fof(f235,plain,
( ! [X0] : ~ member(not_subclass_element(complement(intersection(complement(x),complement(x))),x),X0)
| spl1_4 ),
inference(resolution,[],[f233,f200]) ).
fof(f236,plain,
( $false
| spl1_1
| spl1_4 ),
inference(resolution,[],[f235,f218]) ).
fof(f244,plain,
( spl1_1
| spl1_4 ),
inference(avatar_contradiction_clause,[],[f236]) ).
fof(f245,plain,
( $false
| spl1_1
| ~ spl1_3 ),
inference(resolution,[],[f230,f217]) ).
fof(f246,plain,
( spl1_1
| ~ spl1_3 ),
inference(avatar_contradiction_clause,[],[f245]) ).
fof(f247,plain,
( ~ member(not_subclass_element(x,complement(intersection(complement(x),complement(x)))),complement(intersection(complement(x),complement(x))))
| spl1_2 ),
inference(resolution,[],[f214,f3]) ).
fof(f248,plain,
( member(not_subclass_element(x,complement(intersection(complement(x),complement(x)))),x)
| spl1_2 ),
inference(resolution,[],[f214,f2]) ).
fof(f249,plain,
( ~ member(not_subclass_element(x,complement(intersection(complement(x),complement(x)))),universal_class)
| member(not_subclass_element(x,complement(intersection(complement(x),complement(x)))),intersection(complement(x),complement(x)))
| spl1_2 ),
inference(resolution,[],[f247,f25]) ).
fof(f251,definition,
( spl1_5
<=> member(not_subclass_element(x,complement(intersection(complement(x),complement(x)))),intersection(complement(x),complement(x))) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
fof(f252,plain,
( member(not_subclass_element(x,complement(intersection(complement(x),complement(x)))),intersection(complement(x),complement(x)))
| ~ spl1_5 ),
inference(avatar_component_clause,[],[f251]) ).
fof(f254,definition,
( spl1_6
<=> member(not_subclass_element(x,complement(intersection(complement(x),complement(x)))),universal_class) ),
introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition]) ).
fof(f255,plain,
( ~ member(not_subclass_element(x,complement(intersection(complement(x),complement(x)))),universal_class)
| spl1_6 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f256,plain,
( spl1_5
| ~ spl1_6
| spl1_2 ),
inference(avatar_split_clause,[],[f249,f213,f254,f251]) ).
fof(f257,plain,
( ! [X0] : ~ member(not_subclass_element(x,complement(intersection(complement(x),complement(x)))),X0)
| spl1_6 ),
inference(resolution,[],[f255,f200]) ).
fof(f258,plain,
( $false
| spl1_2
| spl1_6 ),
inference(resolution,[],[f257,f248]) ).
fof(f266,plain,
( spl1_2
| spl1_6 ),
inference(avatar_contradiction_clause,[],[f258]) ).
fof(f267,plain,
( member(not_subclass_element(x,complement(intersection(complement(x),complement(x)))),complement(x))
| ~ spl1_5 ),
inference(resolution,[],[f252,f22]) ).
fof(f269,plain,
( ~ member(not_subclass_element(x,complement(intersection(complement(x),complement(x)))),x)
| ~ spl1_5 ),
inference(resolution,[],[f267,f24]) ).
fof(f270,plain,
( $false
| spl1_2
| ~ spl1_5 ),
inference(resolution,[],[f269,f248]) ).
fof(f271,plain,
( spl1_2
| ~ spl1_5 ),
inference(avatar_contradiction_clause,[],[f270]) ).
cnf(s2,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f216]) ).
cnf(s3,plain,
( spl1_1
| spl1_3
| ~ spl1_4 ),
inference(sat_conversion,[],[f234]) ).
cnf(s4,plain,
( spl1_1
| spl1_4 ),
inference(sat_conversion,[],[f244]) ).
cnf(s5,plain,
( spl1_1
| ~ spl1_3 ),
inference(sat_conversion,[],[f246]) ).
cnf(s6,plain,
( spl1_2
| spl1_5
| ~ spl1_6 ),
inference(sat_conversion,[],[f256]) ).
cnf(s7,plain,
( spl1_2
| spl1_6 ),
inference(sat_conversion,[],[f266]) ).
cnf(s8,plain,
( spl1_2
| ~ spl1_5 ),
inference(sat_conversion,[],[f271]) ).
cnf(s9,plain,
spl1_1,
inference(rat,[],[s3,s4,s5]) ).
cnf(s10,plain,
~ spl1_2,
inference(rat,[],[s2,s9]) ).
cnf(s11,plain,
~ spl1_5,
inference(rat,[],[s8,s10]) ).
cnf(s12,plain,
spl1_6,
inference(rat,[],[s7,s10]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s6,s11,s12,s10]) ).
fof(f272,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET002-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n004.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 00:02:37 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 2.66/1.31 % (4018866)Input is clausal, will run a generic CNF schedule.
% 2.66/1.31 % (4018906)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1567234112:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.66/1.31 % (4018902)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1584637090:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.66/1.31 % (4018901)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=632326390:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.66/1.31 % (4018904)lrs+10_1_sil=8000:sp=occurrence:random_seed=3195739281:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.66/1.31 % (4018903)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3272694860:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.66/1.31 % (4018904)Refutation not found, incomplete strategy
% 2.66/1.31 % (4018904)------------------------------
% 2.66/1.31 % (4018904)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.31 % (4018904)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.31 % (4018904)CaDiCaL version: 2.1.3
% 2.66/1.31 % (4018904)Termination reason: Refutation not found, incomplete strategy
% 2.66/1.31 % (4018904)Time elapsed: 0.004 s
% 2.66/1.31 % (4018904)Peak memory usage: 88 MB
% 2.66/1.31 % (4018904)Instructions burned: 4 (million)
% 2.66/1.31 % (4018907)dis-21_1_sil=8000:lcm=predicate:random_seed=1811144552: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)
% 2.66/1.31 % (4018907)First to succeed.
% 2.66/1.31 % (4018907)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4018866"
% 2.66/1.31 % (4018905)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3194315484:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.66/1.31 % (4018906)Instruction limit reached!
% 2.66/1.31 % (4018906)------------------------------
% 2.66/1.31 % (4018906)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.31 % (4018906)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.31 % (4018906)CaDiCaL version: 2.1.3
% 2.66/1.31 % (4018906)Termination reason: Instruction limit
% 2.66/1.31 % (4018906)Termination phase: Saturation
% 2.66/1.31 % (4018906)Time elapsed: 0.075 s
% 2.66/1.31 % (4018906)Peak memory usage: 91 MB
% 2.66/1.31 % (4018906)Instructions burned: 180 (million)
% 2.66/1.31 % (4018905)Instruction limit reached!
% 2.66/1.31 % (4018905)------------------------------
% 2.66/1.31 % (4018905)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.31 % (4018905)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.31 % (4018905)CaDiCaL version: 2.1.3
% 2.66/1.31 % (4018905)Termination reason: Instruction limit
% 2.66/1.31 % (4018905)Termination phase: Saturation
% 2.66/1.31 % (4018905)Time elapsed: 0.069 s
% 2.66/1.31 % (4018905)Peak memory usage: 89 MB
% 2.66/1.31 % (4018905)Instructions burned: 115 (million)
% 2.66/1.31 % (4018952)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=3142470733:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 2.66/1.31 % (4018952)Refutation not found, incomplete strategy
% 2.66/1.31 % (4018952)------------------------------
% 2.66/1.31 % (4018952)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.31 % (4018952)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.31 % (4018952)CaDiCaL version: 2.1.3
% 2.66/1.31 % (4018952)Termination reason: Refutation not found, incomplete strategy
% 2.66/1.31 % (4018952)Time elapsed: 0.001 s
% 2.66/1.31 % (4018952)Peak memory usage: 87 MB
% 2.66/1.31 % (4018952)Instructions burned: 2 (million)
% 2.66/1.31 % (4018904)------------------------------
% 2.66/1.31 % (4018904)------------------------------
% 2.66/1.31 % (4018968)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1854438207:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 2.66/1.31 % (4018968)Refutation not found, incomplete strategy
% 2.66/1.31 % (4018968)------------------------------
% 2.66/1.31 % (4018968)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.76/1.52 % (4018968)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.76/1.52 % (4018968)CaDiCaL version: 2.1.3
% 3.76/1.52 % (4018968)Termination reason: Refutation not found, incomplete strategy
% 3.76/1.52 % (4018968)Time elapsed: 0.004 s
% 3.76/1.52 % (4018968)Peak memory usage: 88 MB
% 3.76/1.52 % (4018968)Instructions burned: 4 (million)
% 3.76/1.52 % (4018907)Refutation found. Thanks to Tanya!
% 3.76/1.52 % SZS status Unsatisfiable for theBenchmark
% 3.76/1.52 % SZS output start Proof for theBenchmark
% See solution above
% 3.76/1.52 % (4018907)------------------------------
% 3.76/1.52 % (4018907)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.76/1.52 % (4018907)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.76/1.52 % (4018907)CaDiCaL version: 2.1.3
% 3.76/1.52 % (4018907)Termination reason: Refutation
% 3.76/1.52 % (4018907)Time elapsed: 0.006 s
% 3.76/1.52 % (4018907)Peak memory usage: 89 MB
% 3.76/1.52 % (4018907)Instructions burned: 8 (million)
% 3.76/1.52 % (4018907)------------------------------
% 3.76/1.52 % (4018907)------------------------------
% 3.76/1.52 % (4018866)Success in time 0.442 s
% 3.76/1.52 % Vampire exiting
%------------------------------------------------------------------------------