%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET015-2 : 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 : n026.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 12:42:36 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.47s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 18
% Syntax : Number of formulae : 78 ( 16 unt; 6 def)
% Number of atoms : 155 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 161 ( 84 ~; 71 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 7 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn 41 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ subset(X1,X2)
| member(X0,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',membership_in_subsets) ).
fof(f3,axiom,
! [X0,X1] :
( subset(X0,X1)
| member(member_of_1_not_of_2(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',subsets_axiom1) ).
fof(f4,axiom,
! [X0,X1] :
( ~ member(member_of_1_not_of_2(X0,X1),X1)
| subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',subsets_axiom2) ).
fof(f7,axiom,
! [X2,X0,X1] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',member_of_set1_is_member_of_union) ).
fof(f8,axiom,
! [X2,X0,X1] :
( member(X0,union(X2,X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',member_of_set2_is_member_of_union) ).
fof(f9,axiom,
! [X2,X0,X1] :
( ~ member(X0,union(X1,X2))
| member(X0,X1)
| member(X0,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',member_of_union_is_member_of_one_set) ).
fof(f13,axiom,
! [X0,X1] :
( ~ equal_sets(X0,X1)
| subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',set_equal_sets_are_subsets1) ).
fof(f14,axiom,
! [X0,X1] :
( ~ equal_sets(X0,X1)
| subset(X1,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',set_equal_sets_are_subsets2) ).
fof(f15,axiom,
! [X0,X1] :
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| equal_sets(X1,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',subsets_are_set_equal_sets) ).
fof(f22,axiom,
equal_sets(union(as,bs),cs),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_union_b_is_c) ).
fof(f23,axiom,
equal_sets(union(bs,as),ds),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_union_a_is_d) ).
fof(f24,negated_conjecture,
~ equal_sets(cs,ds),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_equals_d) ).
fof(f25,plain,
! [X2,X0,X1] :
( subset(X1,X2)
| ~ member(X0,X1)
| member(X0,X2) ),
inference(consistent_polarity_flipping,[],[f2]) ).
fof(f26,plain,
! [X0,X1] :
( member(member_of_1_not_of_2(X0,X1),X0)
| ~ subset(X0,X1) ),
inference(consistent_polarity_flipping,[],[f3]) ).
fof(f27,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ~ member(member_of_1_not_of_2(X0,X1),X1) ),
inference(consistent_polarity_flipping,[],[f4]) ).
fof(f28,plain,
! [X0,X1] :
( equal_sets(X0,X1)
| ~ subset(X0,X1) ),
inference(consistent_polarity_flipping,[],[f13]) ).
fof(f29,plain,
! [X0,X1] :
( equal_sets(X0,X1)
| ~ subset(X1,X0) ),
inference(consistent_polarity_flipping,[],[f14]) ).
fof(f30,plain,
! [X0,X1] :
( ~ equal_sets(X1,X0)
| subset(X1,X0)
| subset(X0,X1) ),
inference(consistent_polarity_flipping,[],[f15]) ).
fof(f34,plain,
~ equal_sets(union(as,bs),cs),
inference(consistent_polarity_flipping,[],[f22]) ).
fof(f35,plain,
~ equal_sets(union(bs,as),ds),
inference(consistent_polarity_flipping,[],[f23]) ).
fof(f36,plain,
equal_sets(cs,ds),
inference(consistent_polarity_flipping,[],[f24]) ).
fof(f38,plain,
~ subset(union(as,bs),cs),
inference(resolution,[],[f28,f34]) ).
fof(f39,plain,
~ subset(union(bs,as),ds),
inference(resolution,[],[f28,f35]) ).
fof(f41,plain,
~ subset(cs,union(as,bs)),
inference(resolution,[],[f29,f34]) ).
fof(f42,plain,
~ subset(ds,union(bs,as)),
inference(resolution,[],[f29,f35]) ).
fof(f60,plain,
! [X0] :
( member(X0,cs)
| ~ member(X0,union(as,bs)) ),
inference(resolution,[],[f25,f38]) ).
fof(f61,plain,
! [X0] :
( member(X0,ds)
| ~ member(X0,union(bs,as)) ),
inference(resolution,[],[f25,f39]) ).
fof(f62,plain,
! [X0] :
( member(X0,union(as,bs))
| ~ member(X0,cs) ),
inference(resolution,[],[f25,f41]) ).
fof(f63,plain,
! [X0] :
( member(X0,union(bs,as))
| ~ member(X0,ds) ),
inference(resolution,[],[f25,f42]) ).
fof(f64,plain,
( subset(cs,ds)
| subset(ds,cs) ),
inference(resolution,[],[f30,f36]) ).
fof(f69,definition,
( spl0_1
<=> subset(ds,cs) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f71,plain,
( subset(ds,cs)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f69]) ).
fof(f73,definition,
( spl0_2
<=> subset(cs,ds) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f75,plain,
( subset(cs,ds)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f76,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f64,f73,f69]) ).
fof(f78,plain,
( ~ member(member_of_1_not_of_2(cs,ds),ds)
| ~ spl0_2 ),
inference(resolution,[],[f75,f27]) ).
fof(f85,plain,
( ~ member(member_of_1_not_of_2(cs,ds),union(bs,as))
| ~ spl0_2 ),
inference(resolution,[],[f78,f61]) ).
fof(f87,plain,
( ~ member(member_of_1_not_of_2(cs,ds),as)
| ~ spl0_2 ),
inference(resolution,[],[f85,f8]) ).
fof(f88,plain,
( ~ member(member_of_1_not_of_2(cs,ds),bs)
| ~ spl0_2 ),
inference(resolution,[],[f85,f7]) ).
fof(f104,plain,
! [X0] :
( member(X0,bs)
| member(X0,as)
| ~ member(X0,cs) ),
inference(resolution,[],[f9,f62]) ).
fof(f105,plain,
! [X0] :
( member(X0,bs)
| member(X0,as)
| ~ member(X0,ds) ),
inference(resolution,[],[f9,f63]) ).
fof(f107,plain,
( member(member_of_1_not_of_2(cs,ds),as)
| ~ member(member_of_1_not_of_2(cs,ds),cs)
| ~ spl0_2 ),
inference(resolution,[],[f104,f88]) ).
fof(f109,definition,
( spl0_3
<=> member(member_of_1_not_of_2(cs,ds),cs) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f111,plain,
( ~ member(member_of_1_not_of_2(cs,ds),cs)
| spl0_3 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f113,definition,
( spl0_4
<=> member(member_of_1_not_of_2(cs,ds),as) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f115,plain,
( member(member_of_1_not_of_2(cs,ds),as)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f116,plain,
( ~ spl0_3
| spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f107,f73,f113,f109]) ).
fof(f117,plain,
( ~ subset(cs,ds)
| spl0_3 ),
inference(resolution,[],[f111,f26]) ).
fof(f120,plain,
( ~ spl0_2
| spl0_3 ),
inference(avatar_split_clause,[],[f117,f109,f73]) ).
fof(f121,plain,
( $false
| ~ spl0_2
| ~ spl0_4 ),
inference(resolution,[],[f115,f87]) ).
fof(f122,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f121]) ).
fof(f123,plain,
( ~ member(member_of_1_not_of_2(ds,cs),cs)
| ~ spl0_1 ),
inference(resolution,[],[f71,f27]) ).
fof(f127,plain,
( ~ member(member_of_1_not_of_2(ds,cs),union(as,bs))
| ~ spl0_1 ),
inference(resolution,[],[f123,f60]) ).
fof(f129,plain,
( ~ member(member_of_1_not_of_2(ds,cs),bs)
| ~ spl0_1 ),
inference(resolution,[],[f127,f8]) ).
fof(f130,plain,
( ~ member(member_of_1_not_of_2(ds,cs),as)
| ~ spl0_1 ),
inference(resolution,[],[f127,f7]) ).
fof(f132,plain,
( member(member_of_1_not_of_2(ds,cs),as)
| ~ member(member_of_1_not_of_2(ds,cs),ds)
| ~ spl0_1 ),
inference(resolution,[],[f105,f129]) ).
fof(f134,definition,
( spl0_5
<=> member(member_of_1_not_of_2(ds,cs),ds) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f136,plain,
( ~ member(member_of_1_not_of_2(ds,cs),ds)
| spl0_5 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f138,definition,
( spl0_6
<=> member(member_of_1_not_of_2(ds,cs),as) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f140,plain,
( member(member_of_1_not_of_2(ds,cs),as)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f138]) ).
fof(f141,plain,
( ~ spl0_5
| spl0_6
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f132,f69,f138,f134]) ).
fof(f142,plain,
( ~ subset(ds,cs)
| spl0_5 ),
inference(resolution,[],[f136,f26]) ).
fof(f145,plain,
( ~ spl0_1
| spl0_5 ),
inference(avatar_split_clause,[],[f142,f134,f69]) ).
fof(f146,plain,
( $false
| ~ spl0_1
| ~ spl0_6 ),
inference(resolution,[],[f140,f130]) ).
fof(f147,plain,
( ~ spl0_1
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f146]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f76]) ).
cnf(s2,plain,
( ~ spl0_2
| ~ spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f116]) ).
cnf(s3,plain,
( ~ spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f120]) ).
cnf(s4,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(sat_conversion,[],[f122]) ).
cnf(s5,plain,
( ~ spl0_1
| ~ spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f141]) ).
cnf(s6,plain,
( ~ spl0_1
| spl0_5 ),
inference(sat_conversion,[],[f145]) ).
cnf(s7,plain,
( ~ spl0_1
| ~ spl0_6 ),
inference(sat_conversion,[],[f147]) ).
cnf(s8,plain,
~ spl0_2,
inference(rat,[],[s2,s3,s4]) ).
cnf(s9,plain,
spl0_1,
inference(rat,[],[s1,s8]) ).
cnf(s10,plain,
~ spl0_6,
inference(rat,[],[s7,s9]) ).
cnf(s11,plain,
spl0_5,
inference(rat,[],[s6,s9]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s5,s10,s11,s9]) ).
fof(f148,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET015-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n026.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 00:07:11 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 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
% 0.15/0.47 % (3353890)Will run a generic schedule for satisfiability detection.
% 0.15/0.47 % (3353898)dis+10_1_sil=32000:sp=arity:random_seed=1821840854:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.47 % (3353896)% WARNING: option uhcvi not known.
% 0.15/0.47 % (3353895)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3230751892_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.47 % (3353900)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2472367815:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.47 % (3353896)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1029059618:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.47 % (3353897)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2209324053:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.47 % (3353899)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3813941994:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.47 % (3353901)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3975337047:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.47 % TRYING [1]
% 0.15/0.47 % TRYING [2]
% 0.15/0.47 % TRYING [3]
% 0.15/0.47 % (3353901) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3353890-3353901"...
% 0.15/0.47 % TRYING [4]
% 0.15/0.47 % (3353901)...printing done.
% 0.15/0.47 % (3353901)Refutation found. Thanks to Tanya!
% 0.15/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.47 % (3353901)------------------------------
% 0.15/0.47 % (3353901)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.47 % (3353901)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.47 % (3353901)CaDiCaL version: 2.1.3
% 0.15/0.47 % (3353901)Termination reason: Refutation
% 0.15/0.47 % (3353901)Time elapsed: 0.004 s
% 0.15/0.47 % (3353901)Peak memory usage: 12 MB
% 0.15/0.47 % (3353901)Instructions burned: 4 (million)
% 0.15/0.47 % (3353890)Success in time 0.045 s
% 0.15/0.47 % Vampire exiting
%------------------------------------------------------------------------------