%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET014-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n017.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 12:42:35 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.45s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 16
% Syntax : Number of formulae : 52 ( 18 unt; 5 def)
% Number of atoms : 96 ( 1 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 86 ( 42 ~; 39 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( little_set(X0)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
fof(f7,axiom,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection3) ).
fof(f8,axiom,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).
fof(f9,axiom,
! [X0,X1] :
( ~ little_set(X0)
| member(X0,complement(X1))
| member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement2) ).
fof(f10,axiom,
! [X0,X1] : union(X0,X1) = complement(intersection(complement(X0),complement(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).
fof(f13,axiom,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset1) ).
fof(f14,axiom,
! [X0,X1] :
( subset(X0,X1)
| member(f17(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset2) ).
fof(f15,axiom,
! [X0,X1] :
( subset(X0,X1)
| ~ member(f17(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset3) ).
fof(f16,axiom,
subset(as,cs),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_subset_of_c) ).
fof(f17,axiom,
subset(bs,cs),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_subset_of_c) ).
fof(f18,negated_conjecture,
~ subset(union(as,bs),cs),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_union_b_subset_of_c) ).
fof(f19,plain,
~ subset(complement(intersection(complement(as),complement(bs))),cs),
inference(definition_unfolding,[],[f18,f10]) ).
fof(f22,plain,
member(f17(complement(intersection(complement(as),complement(bs))),cs),complement(intersection(complement(as),complement(bs)))),
inference(resolution,[],[f14,f19]) ).
fof(f23,plain,
~ member(f17(complement(intersection(complement(as),complement(bs))),cs),intersection(complement(as),complement(bs))),
inference(resolution,[],[f22,f8]) ).
fof(f25,plain,
~ member(f17(complement(intersection(complement(as),complement(bs))),cs),cs),
inference(resolution,[],[f15,f19]) ).
fof(f26,plain,
! [X2,X0,X1] :
( member(X0,complement(X1))
| ~ member(X0,X2)
| member(X0,X1) ),
inference(resolution,[],[f9,f1]) ).
fof(f28,plain,
! [X0] :
( ~ member(X0,as)
| member(X0,cs) ),
inference(resolution,[],[f13,f16]) ).
fof(f29,plain,
! [X0] :
( ~ member(X0,bs)
| member(X0,cs) ),
inference(resolution,[],[f13,f17]) ).
fof(f35,plain,
( ~ member(f17(complement(intersection(complement(as),complement(bs))),cs),complement(as))
| ~ member(f17(complement(intersection(complement(as),complement(bs))),cs),complement(bs)) ),
inference(resolution,[],[f7,f23]) ).
fof(f37,definition,
( spl0_1
<=> member(f17(complement(intersection(complement(as),complement(bs))),cs),complement(bs)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f39,plain,
( ~ member(f17(complement(intersection(complement(as),complement(bs))),cs),complement(bs))
| spl0_1 ),
inference(avatar_component_clause,[],[f37]) ).
fof(f41,definition,
( spl0_2
<=> member(f17(complement(intersection(complement(as),complement(bs))),cs),complement(as)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f43,plain,
( ~ member(f17(complement(intersection(complement(as),complement(bs))),cs),complement(as))
| spl0_2 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f44,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f35,f41,f37]) ).
fof(f128,plain,
( ! [X0] :
( ~ member(f17(complement(intersection(complement(as),complement(bs))),cs),X0)
| member(f17(complement(intersection(complement(as),complement(bs))),cs),bs) )
| spl0_1 ),
inference(resolution,[],[f26,f39]) ).
fof(f151,definition,
( spl0_9
<=> member(f17(complement(intersection(complement(as),complement(bs))),cs),bs) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f153,plain,
( member(f17(complement(intersection(complement(as),complement(bs))),cs),bs)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f155,definition,
( spl0_10
<=> ! [X0] : ~ member(f17(complement(intersection(complement(as),complement(bs))),cs),X0) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f156,plain,
( ! [X0] : ~ member(f17(complement(intersection(complement(as),complement(bs))),cs),X0)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f157,plain,
( spl0_9
| spl0_10
| spl0_1 ),
inference(avatar_split_clause,[],[f128,f37,f155,f151]) ).
fof(f248,plain,
( ! [X0] :
( ~ member(f17(complement(intersection(complement(as),complement(bs))),cs),X0)
| member(f17(complement(intersection(complement(as),complement(bs))),cs),as) )
| spl0_2 ),
inference(resolution,[],[f43,f26]) ).
fof(f252,definition,
( spl0_11
<=> member(f17(complement(intersection(complement(as),complement(bs))),cs),as) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f254,plain,
( member(f17(complement(intersection(complement(as),complement(bs))),cs),as)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f252]) ).
fof(f255,plain,
( spl0_11
| spl0_10
| spl0_2 ),
inference(avatar_split_clause,[],[f248,f41,f155,f252]) ).
fof(f279,plain,
( member(f17(complement(intersection(complement(as),complement(bs))),cs),cs)
| ~ spl0_9 ),
inference(resolution,[],[f153,f29]) ).
fof(f282,plain,
( $false
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f279,f25]) ).
fof(f283,plain,
~ spl0_9,
inference(avatar_contradiction_clause,[],[f282]) ).
fof(f338,plain,
( $false
| ~ spl0_10 ),
inference(resolution,[],[f156,f22]) ).
fof(f347,plain,
~ spl0_10,
inference(avatar_contradiction_clause,[],[f338]) ).
fof(f377,plain,
( member(f17(complement(intersection(complement(as),complement(bs))),cs),cs)
| ~ spl0_11 ),
inference(resolution,[],[f254,f28]) ).
fof(f380,plain,
( $false
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f377,f25]) ).
fof(f381,plain,
~ spl0_11,
inference(avatar_contradiction_clause,[],[f380]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f44]) ).
cnf(s8,plain,
( spl0_1
| spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f157]) ).
cnf(s10,plain,
( spl0_2
| spl0_10
| spl0_11 ),
inference(sat_conversion,[],[f255]) ).
cnf(s11,plain,
~ spl0_9,
inference(sat_conversion,[],[f283]) ).
cnf(s13,plain,
~ spl0_10,
inference(sat_conversion,[],[f347]) ).
cnf(s14,plain,
~ spl0_11,
inference(sat_conversion,[],[f381]) ).
cnf(s15,plain,
spl0_2,
inference(rat,[],[s10,s14,s13]) ).
cnf(s16,plain,
spl0_1,
inference(rat,[],[s8,s13,s11]) ).
cnf(s17,plain,
$false,
inference(rat,[],[s1,s15,s16]) ).
fof(f382,plain,
$false,
inference(avatar_sat_refutation,[],[s17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET014-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n017.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 : Sun Sep 27 23:59:05 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 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 % (3093828)Will run a generic schedule for satisfiability detection.
% 0.10/0.45 % (3093837)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1348549652:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.45 % (3093834)% WARNING: option uhcvi not known.
% 0.10/0.45 % (3093837) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3093828-3093837"...
% 0.10/0.45 % (3093833)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1545333504_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.45 % (3093834)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3220968233:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/0.45 % (3093835)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3247034716:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.45 % (3093836)dis+10_1_sil=32000:sp=arity:random_seed=296868089:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.45 % (3093837)...printing done.
% 0.10/0.45 % (3093838)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2948882529:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.45 % (3093839)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2516367936:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.45 % TRYING [1]
% 0.10/0.45 % (3093837)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 % (3093837)------------------------------
% 0.10/0.45 % (3093837)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.45 % (3093837)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.45 % (3093837)CaDiCaL version: 2.1.3
% 0.10/0.45 % (3093837)Termination reason: Refutation
% 0.10/0.45 % (3093837)Time elapsed: 0.007 s
% 0.10/0.45 % (3093837)Peak memory usage: 12 MB
% 0.10/0.45 % (3093837)Instructions burned: 18 (million)
% 0.10/0.45 % (3093828)Success in time 0.034 s
% 0.10/0.45 % Vampire exiting
%------------------------------------------------------------------------------