%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET507-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 12:43:53 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.45s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 17
% Syntax : Number of formulae : 56 ( 16 unt; 2 def)
% Number of atoms : 111 ( 45 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 89 ( 34 ~; 53 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 62 ( 0 sgn 62 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',subclass_members) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
fof(f7,axiom,
! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',subclass_implies_equal) ).
fof(f8,axiom,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair_member) ).
fof(f11,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pairs_in_universal) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/SET004-0.ax',element_relation2) ).
fof(f22,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection2) ).
fof(f24,axiom,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).
fof(f48,axiom,
! [X0] :
( ~ inductive(X0)
| member(null_class,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',inductive1) ).
fof(f51,axiom,
inductive(omega),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',omega_is_inductive1) ).
fof(f67,axiom,
! [X0] :
( X0 = null_class
| member(regular(X0),X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity1) ).
fof(f68,plain,
! [X0] :
( member(regular(X0),X0)
| null_class = X0 ),
inference(reorient_equations,[],[f67]) ).
fof(f69,axiom,
! [X0] :
( X0 = null_class
| intersection(X0,regular(X0)) = null_class ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity2) ).
fof(f70,plain,
! [X0] :
( null_class = intersection(X0,regular(X0))
| null_class = X0 ),
inference(reorient_equations,[],[f69]) ).
fof(f122,negated_conjecture,
subclass(universal_class,null_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_universal_class_not_subclass_of_null_class_1) ).
fof(f127,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(f140,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,f127]) ).
fof(f189,plain,
member(null_class,omega),
inference(resolution,[],[f48,f51]) ).
fof(f195,plain,
! [X0,X1] :
( ~ member(X0,X1)
| member(X0,universal_class) ),
inference(resolution,[],[f1,f4]) ).
fof(f218,plain,
! [X0] :
( ~ subclass(universal_class,X0)
| universal_class = X0 ),
inference(resolution,[],[f7,f4]) ).
fof(f230,plain,
member(null_class,universal_class),
inference(resolution,[],[f195,f189]) ).
fof(f235,plain,
universal_class = null_class,
inference(resolution,[],[f218,f122]) ).
fof(f242,plain,
member(universal_class,universal_class),
inference(superposition,[],[f230,f235]) ).
fof(f250,plain,
! [X0,X1] :
( regular(unordered_pair(X0,X1)) = X0
| regular(unordered_pair(X0,X1)) = X1
| unordered_pair(X0,X1) = null_class ),
inference(resolution,[],[f8,f68]) ).
fof(f251,plain,
! [X0,X1] :
( regular(unordered_pair(X0,X1)) = X0
| regular(unordered_pair(X0,X1)) = X1
| universal_class = unordered_pair(X0,X1) ),
inference(forward_demodulation,[],[f250,f235]) ).
fof(f264,plain,
! [X0,X1] :
( X0 != X1
| regular(unordered_pair(X0,X1)) = X1
| universal_class = unordered_pair(X0,X1) ),
inference(equality_factoring,[],[f251]) ).
fof(f282,plain,
! [X0] :
( regular(unordered_pair(X0,X0)) = X0
| universal_class = unordered_pair(X0,X0) ),
inference(equality_resolution,[],[f264]) ).
fof(f283,plain,
! [X0] :
( null_class = intersection(unordered_pair(X0,X0),X0)
| unordered_pair(X0,X0) = null_class
| universal_class = unordered_pair(X0,X0) ),
inference(superposition,[],[f70,f282]) ).
fof(f287,plain,
! [X0] :
( universal_class = intersection(unordered_pair(X0,X0),X0)
| unordered_pair(X0,X0) = null_class
| universal_class = unordered_pair(X0,X0) ),
inference(forward_demodulation,[],[f283,f235]) ).
fof(f288,plain,
! [X0] :
( universal_class = unordered_pair(X0,X0)
| universal_class = intersection(unordered_pair(X0,X0),X0)
| universal_class = unordered_pair(X0,X0) ),
inference(forward_demodulation,[],[f287,f235]) ).
fof(f289,plain,
! [X0] :
( universal_class = intersection(unordered_pair(X0,X0),X0)
| universal_class = unordered_pair(X0,X0) ),
inference(duplicate_literal_removal,[],[f288]) ).
fof(f299,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,X1)
| universal_class = unordered_pair(X1,X1) ),
inference(superposition,[],[f22,f289]) ).
fof(f319,plain,
! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),universal_class)
| universal_class = unordered_pair(element_relation,element_relation)
| member(X0,X1) ),
inference(resolution,[],[f299,f140]) ).
fof(f320,plain,
! [X0,X1] :
( universal_class = unordered_pair(element_relation,element_relation)
| member(X0,X1) ),
inference(forward_subsumption_resolution,[],[f319,f11]) ).
fof(f325,definition,
( spl0_1
<=> ! [X0,X1] : member(X0,X1) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f326,plain,
( ! [X0,X1] : member(X0,X1)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f325]) ).
fof(f328,definition,
( spl0_2
<=> universal_class = unordered_pair(element_relation,element_relation) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f330,plain,
( universal_class = unordered_pair(element_relation,element_relation)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f328]) ).
fof(f331,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f320,f328,f325]) ).
fof(f342,plain,
( ! [X0] :
( ~ member(X0,universal_class)
| element_relation = X0
| element_relation = X0 )
| ~ spl0_2 ),
inference(superposition,[],[f8,f330]) ).
fof(f350,plain,
( ! [X0] :
( ~ member(X0,universal_class)
| element_relation = X0 )
| ~ spl0_2 ),
inference(duplicate_literal_removal,[],[f342]) ).
fof(f374,plain,
( universal_class = element_relation
| ~ spl0_2 ),
inference(resolution,[],[f350,f242]) ).
fof(f388,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),universal_class)
| member(X0,X1) )
| ~ spl0_2 ),
inference(superposition,[],[f140,f374]) ).
fof(f392,plain,
( ! [X0,X1] : member(X0,X1)
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f388,f11]) ).
fof(f394,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f392,f328,f325]) ).
fof(f403,plain,
( ! [X0,X1] : ~ member(X0,X1)
| ~ spl0_1 ),
inference(resolution,[],[f326,f24]) ).
fof(f411,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f403,f326]) ).
fof(f412,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f411]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f331]) ).
cnf(s3,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f394]) ).
cnf(s5,plain,
~ spl0_1,
inference(sat_conversion,[],[f412]) ).
cnf(s7,plain,
~ spl0_2,
inference(rat,[],[s3,s5]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s7,s5]) ).
fof(f416,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET507-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 02:01:15 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.45 % (2596966)Will run a generic schedule for satisfiability detection.
% 0.10/0.45 % (2596975)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1060150883:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.45 % (2596971)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=820935839_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.45 % (2596973)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4084397815:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.45 % (2596974)dis+10_1_sil=32000:sp=arity:random_seed=584363101:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.45 % (2596976)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3426271307:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.45 % (2596977)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2801658836:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.45 % (2596975) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2596966-2596975"...
% 0.10/0.45 % (2596975)...printing done.
% 0.10/0.45 % (2596975)Refutation found. Thanks to Tanya!
% 0.10/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.45 % (2596975)------------------------------
% 0.10/0.45 % (2596975)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.45 % (2596975)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.45 % (2596975)CaDiCaL version: 2.1.3
% 0.10/0.45 % (2596975)Termination reason: Refutation
% 0.10/0.45 % (2596975)Time elapsed: 0.008 s
% 0.10/0.45 % (2596975)Peak memory usage: 12 MB
% 0.10/0.45 % (2596975)Instructions burned: 21 (million)
% 0.10/0.45 % (2596966)Success in time 0.036 s
% 0.10/0.45 % Vampire exiting
%------------------------------------------------------------------------------