%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET013-2 : 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 : n008.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 12:42:34 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.46s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 19
% Syntax : Number of formulae : 88 ( 17 unt; 7 def)
% Number of atoms : 175 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 156 ( 69 ~; 80 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 8 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn 49 !; 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(f10,axiom,
! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',member_of_both_is_member_of_intersection) ).
fof(f11,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',member_of_intersection_is_member_of_set1) ).
fof(f12,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',member_of_intersection_is_member_of_set2) ).
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(intersection(as,bs),cs),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_of_a_and_b_is_c) ).
fof(f23,axiom,
equal_sets(intersection(bs,as),ds),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_of_b_and_a_is_d) ).
fof(f24,negated_conjecture,
~ equal_sets(cs,ds),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_equals_d) ).
fof(f26,plain,
! [X2,X0,X1] :
( ~ subset(X1,X2)
| member(X0,X1)
| ~ member(X0,X2) ),
inference(consistent_polarity_flipping,[],[f2]) ).
fof(f27,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(member_of_1_not_of_2(X0,X1),X0) ),
inference(consistent_polarity_flipping,[],[f3]) ).
fof(f28,plain,
! [X0,X1] :
( member(member_of_1_not_of_2(X0,X1),X1)
| subset(X0,X1) ),
inference(consistent_polarity_flipping,[],[f4]) ).
fof(f34,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2)
| member(X0,X1) ),
inference(consistent_polarity_flipping,[],[f10]) ).
fof(f35,plain,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X1) ),
inference(consistent_polarity_flipping,[],[f11]) ).
fof(f36,plain,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2) ),
inference(consistent_polarity_flipping,[],[f12]) ).
fof(f37,plain,
! [X0,X1] :
( equal_sets(X0,X1)
| subset(X0,X1) ),
inference(consistent_polarity_flipping,[],[f13]) ).
fof(f38,plain,
! [X0,X1] :
( equal_sets(X0,X1)
| subset(X1,X0) ),
inference(consistent_polarity_flipping,[],[f14]) ).
fof(f39,plain,
! [X0,X1] :
( ~ equal_sets(X1,X0)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(consistent_polarity_flipping,[],[f15]) ).
fof(f46,plain,
~ equal_sets(intersection(as,bs),cs),
inference(consistent_polarity_flipping,[],[f22]) ).
fof(f47,plain,
~ equal_sets(intersection(bs,as),ds),
inference(consistent_polarity_flipping,[],[f23]) ).
fof(f48,plain,
equal_sets(cs,ds),
inference(consistent_polarity_flipping,[],[f24]) ).
fof(f50,plain,
subset(intersection(as,bs),cs),
inference(resolution,[],[f37,f46]) ).
fof(f51,plain,
subset(intersection(bs,as),ds),
inference(resolution,[],[f37,f47]) ).
fof(f53,plain,
subset(cs,intersection(as,bs)),
inference(resolution,[],[f38,f46]) ).
fof(f54,plain,
subset(ds,intersection(bs,as)),
inference(resolution,[],[f38,f47]) ).
fof(f71,plain,
! [X0] :
( member(X0,intersection(as,bs))
| ~ member(X0,cs) ),
inference(resolution,[],[f26,f50]) ).
fof(f72,plain,
! [X0] :
( member(X0,intersection(bs,as))
| ~ member(X0,ds) ),
inference(resolution,[],[f26,f51]) ).
fof(f73,plain,
! [X0] :
( member(X0,cs)
| ~ member(X0,intersection(as,bs)) ),
inference(resolution,[],[f26,f53]) ).
fof(f74,plain,
! [X0] :
( member(X0,ds)
| ~ member(X0,intersection(bs,as)) ),
inference(resolution,[],[f26,f54]) ).
fof(f75,plain,
( ~ subset(cs,ds)
| ~ subset(ds,cs) ),
inference(resolution,[],[f39,f48]) ).
fof(f80,definition,
( spl0_1
<=> subset(ds,cs) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f82,plain,
( ~ subset(ds,cs)
| spl0_1 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f84,definition,
( spl0_2
<=> subset(cs,ds) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f86,plain,
( ~ subset(cs,ds)
| spl0_2 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f87,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f75,f84,f80]) ).
fof(f88,plain,
( ~ member(member_of_1_not_of_2(ds,cs),ds)
| spl0_1 ),
inference(resolution,[],[f82,f27]) ).
fof(f89,plain,
( ~ member(member_of_1_not_of_2(cs,ds),cs)
| spl0_2 ),
inference(resolution,[],[f86,f27]) ).
fof(f90,plain,
( ~ member(member_of_1_not_of_2(ds,cs),intersection(bs,as))
| spl0_1 ),
inference(resolution,[],[f88,f74]) ).
fof(f91,plain,
( ~ member(member_of_1_not_of_2(cs,ds),intersection(as,bs))
| spl0_2 ),
inference(resolution,[],[f89,f73]) ).
fof(f99,plain,
( ~ member(member_of_1_not_of_2(ds,cs),as)
| spl0_1 ),
inference(resolution,[],[f90,f36]) ).
fof(f100,plain,
( ~ member(member_of_1_not_of_2(ds,cs),bs)
| spl0_1 ),
inference(resolution,[],[f90,f35]) ).
fof(f102,plain,
( ~ member(member_of_1_not_of_2(cs,ds),bs)
| spl0_2 ),
inference(resolution,[],[f91,f36]) ).
fof(f103,plain,
( ~ member(member_of_1_not_of_2(cs,ds),as)
| spl0_2 ),
inference(resolution,[],[f91,f35]) ).
fof(f122,plain,
! [X0] :
( member(X0,bs)
| member(X0,as)
| ~ member(X0,cs) ),
inference(resolution,[],[f34,f71]) ).
fof(f125,plain,
( member(member_of_1_not_of_2(ds,cs),as)
| ~ member(member_of_1_not_of_2(ds,cs),cs)
| spl0_1 ),
inference(resolution,[],[f122,f100]) ).
fof(f128,definition,
( spl0_3
<=> member(member_of_1_not_of_2(ds,cs),cs) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f130,plain,
( ~ member(member_of_1_not_of_2(ds,cs),cs)
| spl0_3 ),
inference(avatar_component_clause,[],[f128]) ).
fof(f132,definition,
( spl0_4
<=> member(member_of_1_not_of_2(ds,cs),as) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f134,plain,
( member(member_of_1_not_of_2(ds,cs),as)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f135,plain,
( ~ spl0_3
| spl0_4
| spl0_1 ),
inference(avatar_split_clause,[],[f125,f80,f132,f128]) ).
fof(f136,plain,
( subset(ds,cs)
| spl0_3 ),
inference(resolution,[],[f130,f28]) ).
fof(f138,plain,
( spl0_1
| spl0_3 ),
inference(avatar_split_clause,[],[f136,f128,f80]) ).
fof(f151,plain,
( $false
| spl0_1
| ~ spl0_4 ),
inference(resolution,[],[f134,f99]) ).
fof(f152,plain,
( spl0_1
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f151]) ).
fof(f184,definition,
( spl0_5
<=> member(member_of_1_not_of_2(cs,ds),intersection(bs,as)) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f185,plain,
( member(member_of_1_not_of_2(cs,ds),intersection(bs,as))
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f184]) ).
fof(f186,plain,
( ~ member(member_of_1_not_of_2(cs,ds),intersection(bs,as))
| spl0_5 ),
inference(avatar_component_clause,[],[f184]) ).
fof(f195,plain,
( ~ member(member_of_1_not_of_2(cs,ds),ds)
| spl0_5 ),
inference(resolution,[],[f186,f72]) ).
fof(f199,plain,
( subset(cs,ds)
| spl0_5 ),
inference(resolution,[],[f195,f28]) ).
fof(f203,plain,
( spl0_2
| spl0_5 ),
inference(avatar_split_clause,[],[f199,f184,f84]) ).
fof(f204,plain,
( member(member_of_1_not_of_2(cs,ds),as)
| member(member_of_1_not_of_2(cs,ds),bs)
| ~ spl0_5 ),
inference(resolution,[],[f185,f34]) ).
fof(f206,definition,
( spl0_7
<=> member(member_of_1_not_of_2(cs,ds),bs) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f208,plain,
( member(member_of_1_not_of_2(cs,ds),bs)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f206]) ).
fof(f210,definition,
( spl0_8
<=> member(member_of_1_not_of_2(cs,ds),as) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f212,plain,
( member(member_of_1_not_of_2(cs,ds),as)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f210]) ).
fof(f213,plain,
( spl0_7
| spl0_8
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f204,f184,f210,f206]) ).
fof(f215,plain,
( $false
| spl0_2
| ~ spl0_8 ),
inference(resolution,[],[f212,f103]) ).
fof(f218,plain,
( spl0_2
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f215]) ).
fof(f219,plain,
( $false
| spl0_2
| ~ spl0_7 ),
inference(resolution,[],[f208,f102]) ).
fof(f222,plain,
( spl0_2
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f219]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f87]) ).
cnf(s2,plain,
( spl0_1
| ~ spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f135]) ).
cnf(s3,plain,
( spl0_1
| spl0_3 ),
inference(sat_conversion,[],[f138]) ).
cnf(s4,plain,
( spl0_1
| ~ spl0_4 ),
inference(sat_conversion,[],[f152]) ).
cnf(s8,plain,
( spl0_2
| spl0_5 ),
inference(sat_conversion,[],[f203]) ).
cnf(s9,plain,
( ~ spl0_5
| spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f213]) ).
cnf(s10,plain,
( spl0_2
| ~ spl0_8 ),
inference(sat_conversion,[],[f218]) ).
cnf(s11,plain,
( spl0_2
| ~ spl0_7 ),
inference(sat_conversion,[],[f222]) ).
cnf(s12,plain,
spl0_1,
inference(rat,[],[s2,s3,s4]) ).
cnf(s13,plain,
~ spl0_2,
inference(rat,[],[s1,s12]) ).
cnf(s14,plain,
~ spl0_7,
inference(rat,[],[s11,s13]) ).
cnf(s15,plain,
~ spl0_8,
inference(rat,[],[s10,s13]) ).
cnf(s16,plain,
spl0_5,
inference(rat,[],[s8,s13]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s9,s14,s15,s16]) ).
fof(f223,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET013-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n008.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 00:04:25 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.40 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
% 0.11/0.46 % (1745992)Will run a generic schedule for satisfiability detection.
% 0.11/0.46 % (1745999)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3397999680:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.46 % (1745997)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3015334545_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.46 % (1746003)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=155453776:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.46 % (1746000)dis+10_1_sil=32000:sp=arity:random_seed=4214865844:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.46 % (1746001)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3859804075:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.46 % (1746002)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3821938899:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.46 % TRYING [1]
% 0.11/0.46 % TRYING [2]
% 0.11/0.46 % TRYING [3]
% 0.11/0.46 % (1745998)% WARNING: option uhcvi not known.
% 0.11/0.46 % (1746003) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1745992-1746003"...
% 0.11/0.46 % TRYING [4]
% 0.11/0.46 % (1746003)...printing done.
% 0.11/0.46 % (1746003)Refutation found. Thanks to Tanya!
% 0.11/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.46 % (1746003)------------------------------
% 0.11/0.46 % (1746003)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.46 % (1746003)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.46 % (1746003)CaDiCaL version: 2.1.3
% 0.11/0.46 % (1746003)Termination reason: Refutation
% 0.11/0.46 % (1746003)Time elapsed: 0.005 s
% 0.11/0.46 % (1746003)Peak memory usage: 12 MB
% 0.11/0.46 % (1746003)Instructions burned: 6 (million)
% 0.11/0.46 % (1745992)Success in time 0.047 s
% 0.11/0.46 % Vampire exiting
%------------------------------------------------------------------------------