%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET411-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 12:43:45 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.48s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 37 ( 20 unt; 2 def)
% Number of atoms : 57 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 42 ( 22 ~; 18 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_members) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',singleton_set) ).
fof(f13,axiom,
! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',ordered_pair) ).
fof(f19,axiom,
! [X0,X1] :
( ~ member(ordered_pair(X0,X1),element_relation)
| member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',element_relation2) ).
fof(f22,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection2) ).
fof(f113,axiom,
intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation,
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-1.ax',compose_can_define_singleton) ).
fof(f122,negated_conjecture,
member(ordered_pair(x,y),singleton_relation),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_compose_condition_for_singleton_membership1_1) ).
fof(f123,negated_conjecture,
~ member(x,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_compose_condition_for_singleton_membership1_2) ).
fof(f128,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f13,f12,f12]) ).
fof(f141,plain,
! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| member(X0,X1) ),
inference(definition_unfolding,[],[f19,f128]) ).
fof(f186,plain,
member(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))),singleton_relation),
inference(definition_unfolding,[],[f122,f128]) ).
fof(f191,plain,
! [X2,X0,X1] :
( member(X2,X0)
| subclass(X0,X1)
| ~ member(X2,X1) ),
inference(consistent_polarity_flipping,[],[f1]) ).
fof(f194,plain,
! [X0] : ~ subclass(X0,universal_class),
inference(consistent_polarity_flipping,[],[f4]) ).
fof(f207,plain,
! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| ~ member(X0,X1) ),
inference(consistent_polarity_flipping,[],[f141]) ).
fof(f210,plain,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2) ),
inference(consistent_polarity_flipping,[],[f22]) ).
fof(f268,plain,
~ member(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))),singleton_relation),
inference(consistent_polarity_flipping,[],[f186]) ).
fof(f269,plain,
member(x,universal_class),
inference(consistent_polarity_flipping,[],[f123]) ).
fof(f305,plain,
! [X0] :
( member(X0,singleton_relation)
| ~ member(X0,element_relation) ),
inference(superposition,[],[f210,f113]) ).
fof(f308,plain,
~ member(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))),element_relation),
inference(resolution,[],[f305,f268]) ).
fof(f1616,plain,
~ member(x,y),
inference(resolution,[],[f207,f308]) ).
fof(f1624,definition,
( spl0_105
<=> member(x,y) ),
introduced(definition,[new_symbols(definition,[spl0_105])],[avatar_definition]) ).
fof(f1626,plain,
( ~ member(x,y)
| spl0_105 ),
inference(avatar_component_clause,[],[f1624]) ).
fof(f1633,plain,
~ spl0_105,
inference(avatar_split_clause,[],[f1616,f1624]) ).
fof(f1634,plain,
( ! [X0] :
( ~ member(x,X0)
| subclass(y,X0) )
| spl0_105 ),
inference(resolution,[],[f1626,f191]) ).
fof(f1647,plain,
( subclass(y,universal_class)
| spl0_105 ),
inference(resolution,[],[f1634,f269]) ).
fof(f1686,definition,
( spl0_113
<=> subclass(y,universal_class) ),
introduced(definition,[new_symbols(definition,[spl0_113])],[avatar_definition]) ).
fof(f1688,plain,
( subclass(y,universal_class)
| ~ spl0_113 ),
inference(avatar_component_clause,[],[f1686]) ).
fof(f1698,plain,
( spl0_113
| spl0_105 ),
inference(avatar_split_clause,[],[f1647,f1624,f1686]) ).
fof(f1722,plain,
( $false
| ~ spl0_113 ),
inference(resolution,[],[f1688,f194]) ).
fof(f1723,plain,
~ spl0_113,
inference(avatar_contradiction_clause,[],[f1722]) ).
cnf(s117,plain,
~ spl0_105,
inference(sat_conversion,[],[f1633]) ).
cnf(s127,plain,
( spl0_105
| spl0_113 ),
inference(sat_conversion,[],[f1698]) ).
cnf(s130,plain,
~ spl0_113,
inference(sat_conversion,[],[f1723]) ).
cnf(s131,plain,
spl0_105,
inference(rat,[],[s127,s130]) ).
cnf(s132,plain,
$false,
inference(rat,[],[s117,s131]) ).
fof(f1724,plain,
$false,
inference(avatar_sat_refutation,[],[s132]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET411-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.36 % Computer : n018.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 28 01:45:39 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.14/0.41 Running first-order model finding
% 0.14/0.41 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
% 0.14/0.48 % (2912578)Will run a generic schedule for satisfiability detection.
% 0.14/0.48 % (2912589)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2185484930:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.14/0.48 % (2912585)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=286218155:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.14/0.48 % (2912584)% WARNING: option uhcvi not known.
% 0.14/0.48 % (2912583)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=866326523_2999 on theBenchmark for (2999ds/0Mi)
% 0.14/0.48 % (2912584)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3807784008:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.14/0.48 % (2912586)dis+10_1_sil=32000:sp=arity:random_seed=3875238355:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.14/0.48 % (2912588)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1871833548:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.14/0.48 % (2912586) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2912578-2912586"...
% 0.14/0.48 % (2912589) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2912578-2912589"...
% 0.14/0.48 % (2912586)...printing done.
% 0.14/0.48 % (2912589)...printing done.
% 0.14/0.48 % (2912589)Refutation found. Thanks to Tanya!
% 0.14/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.48 % (2912589)------------------------------
% 0.14/0.48 % (2912589)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.14/0.48 % (2912589)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/0.48 % (2912589)CaDiCaL version: 2.1.3
% 0.14/0.48 % (2912589)Termination reason: Refutation
% 0.14/0.48 % (2912589)Time elapsed: 0.031 s
% 0.14/0.48 % (2912589)Peak memory usage: 13 MB
% 0.14/0.48 % (2912589)Instructions burned: 46 (million)
% 0.14/0.48 % (2912578)Success in time 0.058 s
% 0.14/0.48 % Vampire exiting
%------------------------------------------------------------------------------