%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET012-1 : 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 : n004.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 12:42:33 PM UTC 2026
% Result : Unsatisfiable 0.16s 0.47s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 35 ( 7 unt; 2 def)
% Number of atoms : 65 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 66 ( 36 ~; 28 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f5,axiom,
! [X0,X1] :
( member(X0,X1)
| member(X0,complement(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',member_of_set_or_complement) ).
fof(f6,axiom,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',not_member_of_set_and_complement) ).
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,negated_conjecture,
~ equal_sets(complement(complement(a)),a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_involution) ).
fof(f25,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ~ member(member_of_1_not_of_2(X0,X1),X0) ),
inference(consistent_polarity_flipping,[],[f3]) ).
fof(f26,plain,
! [X0,X1] :
( member(member_of_1_not_of_2(X0,X1),X1)
| ~ subset(X0,X1) ),
inference(consistent_polarity_flipping,[],[f4]) ).
fof(f27,plain,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
inference(consistent_polarity_flipping,[],[f5]) ).
fof(f28,plain,
! [X0,X1] :
( member(X0,complement(X1))
| member(X0,X1) ),
inference(consistent_polarity_flipping,[],[f6]) ).
fof(f37,plain,
! [X0,X1] :
( ~ equal_sets(X1,X0)
| subset(X1,X0)
| subset(X0,X1) ),
inference(consistent_polarity_flipping,[],[f15]) ).
fof(f41,plain,
equal_sets(complement(complement(a)),a),
inference(consistent_polarity_flipping,[],[f22]) ).
fof(f46,plain,
! [X0,X1] :
( ~ subset(X0,complement(X1))
| ~ member(member_of_1_not_of_2(X0,complement(X1)),X1) ),
inference(resolution,[],[f26,f27]) ).
fof(f51,plain,
( subset(complement(complement(a)),a)
| subset(a,complement(complement(a))) ),
inference(resolution,[],[f37,f41]) ).
fof(f56,definition,
( spl0_1
<=> subset(a,complement(complement(a))) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f58,plain,
( subset(a,complement(complement(a)))
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f60,definition,
( spl0_2
<=> subset(complement(complement(a)),a) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f62,plain,
( subset(complement(complement(a)),a)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f63,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f51,f60,f56]) ).
fof(f65,plain,
( ~ member(member_of_1_not_of_2(complement(complement(a)),a),complement(complement(a)))
| ~ spl0_2 ),
inference(resolution,[],[f62,f25]) ).
fof(f66,plain,
( member(member_of_1_not_of_2(complement(complement(a)),a),complement(a))
| ~ spl0_2 ),
inference(resolution,[],[f65,f28]) ).
fof(f67,plain,
( ~ member(member_of_1_not_of_2(complement(complement(a)),a),a)
| ~ spl0_2 ),
inference(resolution,[],[f66,f27]) ).
fof(f68,plain,
( ~ subset(complement(complement(a)),a)
| ~ spl0_2 ),
inference(resolution,[],[f67,f26]) ).
fof(f70,plain,
( ~ spl0_2
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f68,f60,f60]) ).
fof(f71,plain,
( ~ member(member_of_1_not_of_2(a,complement(complement(a))),a)
| ~ spl0_1 ),
inference(resolution,[],[f58,f25]) ).
fof(f77,plain,
( ~ member(member_of_1_not_of_2(a,complement(complement(a))),complement(a))
| ~ spl0_1 ),
inference(resolution,[],[f46,f58]) ).
fof(f78,plain,
( member(member_of_1_not_of_2(a,complement(complement(a))),a)
| ~ spl0_1 ),
inference(resolution,[],[f77,f28]) ).
fof(f79,plain,
( $false
| ~ spl0_1 ),
inference(resolution,[],[f78,f71]) ).
fof(f80,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f79]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f63]) ).
cnf(s2,plain,
( ~ spl0_2
| ~ spl0_2 ),
inference(sat_conversion,[],[f70]) ).
cnf(s3,plain,
~ spl0_2,
inference(rat,[],[s2]) ).
cnf(s4,plain,
~ spl0_1,
inference(sat_conversion,[],[f80]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s3,s4]) ).
fof(f81,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET012-1 : 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 : n004.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 00:03:07 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 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
% 0.16/0.47 % (4020683)Will run a generic schedule for satisfiability detection.
% 0.16/0.47 % (4020688)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1579018342_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.47 % TRYING [1]
% 0.16/0.47 % TRYING [2]
% 0.16/0.47 % TRYING [3]
% 0.16/0.47 % TRYING [4]
% 0.16/0.47 % (4020689)% WARNING: option uhcvi not known.
% 0.16/0.47 % TRYING [5]
% 0.16/0.47 % TRYING [6]
% 0.16/0.47 % (4020689)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3420135690:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.47 % (4020690)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2340421157:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.47 % (4020691)dis+10_1_sil=32000:sp=arity:random_seed=2298957012:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.47 % (4020693)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2587043005:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.47 % (4020692)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2836866925:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.47 % (4020694)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2860667751:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.47 % (4020694) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4020683-4020694"...
% 0.16/0.47 % (4020694)...printing done.
% 0.16/0.47 % TRYING [7]
% 0.16/0.47 % (4020694)Refutation found. Thanks to Tanya!
% 0.16/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.47 % (4020694)------------------------------
% 0.16/0.47 % (4020694)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.47 % (4020694)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.47 % (4020694)CaDiCaL version: 2.1.3
% 0.16/0.47 % (4020694)Termination reason: Refutation
% 0.16/0.47 % (4020694)Time elapsed: 0.002 s
% 0.16/0.47 % (4020694)Peak memory usage: 12 MB
% 0.16/0.47 % (4020694)Instructions burned: 2 (million)
% 0.16/0.47 % (4020683)Success in time 0.043 s
% 0.16/0.47 % Vampire exiting
%------------------------------------------------------------------------------