%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET764+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 12:44:34 PM UTC 2026
% Result : Theorem 0.10s 0.45s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 37 ( 10 unt; 2 def)
% Number of atoms : 73 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 62 ( 26 ~; 22 |; 4 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 3 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 40 ( 0 sgn 36 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',subset) ).
fof(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',equal_set) ).
fof(f6,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',empty_set) ).
fof(f24,axiom,
! [X0,X1,X2] :
( member(X2,inverse_image2(X0,X1))
<=> ? [X3] :
( member(X3,X1)
& apply(X0,X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax',inverse_image2) ).
fof(f29,conjecture,
! [X0,X1,X2] :
( maps(X0,X1,X2)
=> equal_set(inverse_image2(X0,empty_set),empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIIa14) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2] :
( maps(X0,X1,X2)
=> equal_set(inverse_image2(X0,empty_set),empty_set) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f33,plain,
! [X0,X1] :
( ( subset(X0,X1)
& subset(X1,X0) )
=> equal_set(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f34,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f35,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f36,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(flattening,[],[f35]) ).
fof(f44,plain,
? [X0,X1,X2] :
( ~ equal_set(inverse_image2(X0,empty_set),empty_set)
& maps(X0,X1,X2) ),
inference(ennf_transformation,[],[f30]) ).
fof(f46,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f48,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f57,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f6]) ).
fof(f89,plain,
! [X2,X0,X1] :
( ~ member(X2,inverse_image2(X0,X1))
| member(sK7(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f96,plain,
~ equal_set(inverse_image2(sK9,empty_set),empty_set),
inference(cnf_transformation,[],[f44]) ).
fof(f101,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(consistent_polarity_flipping,[],[f46]) ).
fof(f103,plain,
! [X0,X1] :
( ~ equal_set(X0,X1)
| subset(X0,X1)
| subset(X1,X0) ),
inference(consistent_polarity_flipping,[],[f48]) ).
fof(f106,plain,
equal_set(inverse_image2(sK9,empty_set),empty_set),
inference(consistent_polarity_flipping,[],[f96]) ).
fof(f146,plain,
( subset(inverse_image2(sK9,empty_set),empty_set)
| subset(empty_set,inverse_image2(sK9,empty_set)) ),
inference(resolution,[],[f103,f106]) ).
fof(f148,definition,
( spl12_1
<=> subset(empty_set,inverse_image2(sK9,empty_set)) ),
introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition]) ).
fof(f150,plain,
( subset(empty_set,inverse_image2(sK9,empty_set))
| ~ spl12_1 ),
inference(avatar_component_clause,[],[f148]) ).
fof(f152,definition,
( spl12_2
<=> subset(inverse_image2(sK9,empty_set),empty_set) ),
introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition]) ).
fof(f154,plain,
( subset(inverse_image2(sK9,empty_set),empty_set)
| ~ spl12_2 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f155,plain,
( spl12_1
| spl12_2 ),
inference(avatar_split_clause,[],[f146,f152,f148]) ).
fof(f169,plain,
( member(sK0(inverse_image2(sK9,empty_set),empty_set),inverse_image2(sK9,empty_set))
| ~ spl12_2 ),
inference(resolution,[],[f154,f101]) ).
fof(f232,plain,
( member(sK7(sK9,empty_set,sK0(inverse_image2(sK9,empty_set),empty_set)),empty_set)
| ~ spl12_2 ),
inference(resolution,[],[f89,f169]) ).
fof(f234,plain,
( $false
| ~ spl12_2 ),
inference(forward_subsumption_resolution,[],[f232,f57]) ).
fof(f235,plain,
~ spl12_2,
inference(avatar_contradiction_clause,[],[f234]) ).
fof(f236,plain,
( member(sK0(empty_set,inverse_image2(sK9,empty_set)),empty_set)
| ~ spl12_1 ),
inference(resolution,[],[f150,f101]) ).
fof(f238,plain,
( $false
| ~ spl12_1 ),
inference(forward_subsumption_resolution,[],[f236,f57]) ).
fof(f239,plain,
~ spl12_1,
inference(avatar_contradiction_clause,[],[f238]) ).
cnf(s1,plain,
( spl12_1
| spl12_2 ),
inference(sat_conversion,[],[f155]) ).
cnf(s4,plain,
~ spl12_2,
inference(sat_conversion,[],[f235]) ).
cnf(s5,plain,
~ spl12_1,
inference(sat_conversion,[],[f239]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s4,s5]) ).
fof(f240,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET764+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 02:47:25 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.39 Running first-order model finding
% 0.10/0.39 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 % (2945059)Will run a generic schedule for satisfiability detection.
% 0.10/0.45 % (2945066)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3604749855:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.45 % (2945065)% WARNING: option uhcvi not known.
% 0.10/0.45 % (2945064)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3047645271_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.45 % (2945067)dis+10_1_sil=32000:sp=arity:random_seed=3646746792:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.45 % (2945065)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=869885452:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/0.45 % (2945069)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3915479443:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.45 % (2945070)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4191401362:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.45 % (2945068)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3943827594:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.45 % TRYING [1]
% 0.10/0.45 % TRYING [2]
% 0.10/0.45 % (2945065) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2945059-2945065"...
% 0.10/0.45 % (2945067) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2945059-2945067"...
% 0.10/0.45 % (2945065)...printing done.
% 0.10/0.45 % (2945067)...printing done.
% 0.10/0.45 % (2945065)Refutation found. Thanks to Tanya!
% 0.10/0.45 % SZS status Theorem for theBenchmark
% 0.10/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.45 % (2945065)------------------------------
% 0.10/0.45 % (2945065)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.45 % (2945065)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.45 % (2945065)CaDiCaL version: 2.1.3
% 0.10/0.45 % (2945065)Termination reason: Refutation
% 0.10/0.45 % (2945065)Time elapsed: 0.006 s
% 0.10/0.45 % (2945065)Peak memory usage: 12 MB
% 0.10/0.45 % (2945065)Instructions burned: 7 (million)
% 0.10/0.45 % (2945059)Success in time 0.048 s
% 0.10/0.45 % Vampire exiting
%------------------------------------------------------------------------------