%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM156-1 : 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 : n006.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 12:18:01 PM UTC 2026
% Result : Unsatisfiable 0.16s 0.52s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 16
% Syntax : Number of formulae : 29 ( 21 unt; 0 def)
% Number of atoms : 39 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 12 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 6 con; 0-3 aty)
% Number of variables : 30 ( 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ member(X2,X0)
| ~ subclass(X0,X1)
| 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(f10,axiom,
! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair3) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',singleton_set) ).
fof(f21,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection1) ).
fof(f24,axiom,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement1) ).
fof(f25,axiom,
! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,complement(X1))
| member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement2) ).
fof(f26,axiom,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',union) ).
fof(f28,axiom,
! [X2,X0,X1] : intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',restriction1) ).
fof(f39,axiom,
! [X0] : domain_of(flip(cross_product(X0,universal_class))) = inverse(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',inverse) ).
fof(f40,axiom,
! [X0] : domain_of(inverse(X0)) = range_of(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',range_of) ).
fof(f43,axiom,
! [X0,X1] : range_of(restrict(X0,X1,universal_class)) = image(X0,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',image) ).
fof(f48,axiom,
! [X0] :
( ~ inductive(X0)
| member(null_class,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',inductive1) ).
fof(f51,axiom,
inductive(omega),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',omega_is_inductive1) ).
fof(f154,axiom,
union(singleton(null_class),image(successor_relation,ordinal_numbers)) = kind_1_ordinals,
file('/export/starexec/sandbox2/benchmark/Axioms/NUM004-0.ax',kind_1_ordinals) ).
fof(f176,negated_conjecture,
~ member(null_class,kind_1_ordinals),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_null_class_is_kind_1_1) ).
fof(f178,plain,
! [X0] : range_of(X0) = domain_of(domain_of(flip(cross_product(X0,universal_class)))),
inference(definition_unfolding,[],[f40,f39]) ).
fof(f181,plain,
! [X0,X1] : image(X0,X1) = domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,universal_class)),universal_class)))),
inference(definition_unfolding,[],[f43,f178,f28]) ).
fof(f259,plain,
kind_1_ordinals = complement(intersection(complement(unordered_pair(null_class,null_class)),complement(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(ordinal_numbers,universal_class)),universal_class))))))),
inference(definition_unfolding,[],[f154,f26,f12,f181]) ).
fof(f267,plain,
member(null_class,omega),
inference(resolution,[],[f48,f51]) ).
fof(f389,plain,
! [X0] :
( ~ subclass(omega,X0)
| member(null_class,X0) ),
inference(resolution,[],[f1,f267]) ).
fof(f890,plain,
~ member(null_class,complement(intersection(complement(unordered_pair(null_class,null_class)),complement(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(ordinal_numbers,universal_class)),universal_class)))))))),
inference(superposition,[],[f176,f259]) ).
fof(f896,plain,
member(null_class,universal_class),
inference(resolution,[],[f389,f4]) ).
fof(f900,plain,
! [X0] : member(null_class,unordered_pair(X0,null_class)),
inference(resolution,[],[f896,f10]) ).
fof(f901,plain,
! [X0] :
( member(null_class,complement(X0))
| member(null_class,X0) ),
inference(resolution,[],[f896,f25]) ).
fof(f1012,plain,
member(null_class,intersection(complement(unordered_pair(null_class,null_class)),complement(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(ordinal_numbers,universal_class)),universal_class))))))),
inference(resolution,[],[f890,f901]) ).
fof(f1016,plain,
member(null_class,complement(unordered_pair(null_class,null_class))),
inference(resolution,[],[f1012,f21]) ).
fof(f1049,plain,
~ member(null_class,unordered_pair(null_class,null_class)),
inference(resolution,[],[f1016,f24]) ).
fof(f1058,plain,
$false,
inference(forward_subsumption_resolution,[],[f1049,f900]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM156-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 % Computer : n006.cluster.edu
% 0.11/0.40 % Model : x86_64 x86_64
% 0.11/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.40 % Memory : 8046.5625MB
% 0.11/0.40 % OS : Linux 6.8.0-71-generic
% 0.11/0.40 % CPULimit : 300
% 0.11/0.40 % WCLimit : 300
% 0.11/0.40 % DateTime : Sun Sep 27 19:02:11 UTC 2026
% 0.11/0.41 % CPUTime :
% 0.11/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.44 Running first-order model finding
% 0.11/0.44 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
% 0.16/0.52 % (3257696)Will run a generic schedule for satisfiability detection.
% 0.16/0.52 % (3257707)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3524022036:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.52 % (3257702)% WARNING: option uhcvi not known.
% 0.16/0.52 % (3257701)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3558280760_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.52 % (3257702)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2021042441:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.52 % (3257703)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3088332634:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.52 % (3257706)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=378954077:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.52 % (3257704)dis+10_1_sil=32000:sp=arity:random_seed=762765897:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.52 % (3257705)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3581603937:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.52 % (3257706) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3257696-3257706"...
% 0.16/0.52 % (3257706)...printing done.
% 0.16/0.52 % (3257706)Refutation found. Thanks to Tanya!
% 0.16/0.52 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.52 % (3257706)------------------------------
% 0.16/0.52 % (3257706)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.52 % (3257706)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.52 % (3257706)CaDiCaL version: 2.1.3
% 0.16/0.52 % (3257706)Termination reason: Refutation
% 0.16/0.52 % (3257706)Time elapsed: 0.032 s
% 0.16/0.52 % (3257706)Peak memory usage: 12 MB
% 0.16/0.52 % (3257706)Instructions burned: 48 (million)
% 0.16/0.52 % (3257696)Success in time 0.071 s
% 0.16/0.52 % Vampire exiting
%------------------------------------------------------------------------------