%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET012-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 12:39:30 PM UTC 2026
% Result : Unsatisfiable 2.57s 1.32s
% Output : Refutation 2.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 29 ( 7 unt; 2 def)
% Number of atoms : 52 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 39 ( 16 ~; 21 |; 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 : 12 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] :
( subset(X0,X1)
| member(member_of_1_not_of_2(X0,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsets_axiom1) ).
fof(f4,axiom,
! [X0,X1] :
( ~ member(member_of_1_not_of_2(X0,X1),X1)
| subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsets_axiom2) ).
fof(f5,axiom,
! [X0,X1] :
( member(X0,complement(X1))
| member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_set_or_complement) ).
fof(f6,axiom,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_member_of_set_and_complement) ).
fof(f15,axiom,
! [X0,X1] :
( equal_sets(X1,X0)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsets_are_set_equal_sets) ).
fof(f22,negated_conjecture,
~ equal_sets(complement(complement(a)),a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_involution) ).
fof(f26,plain,
( ~ subset(complement(complement(a)),a)
| ~ subset(a,complement(complement(a))) ),
inference(resolution,[],[f15,f22]) ).
fof(f29,definition,
( spl0_1
<=> subset(complement(complement(a)),a) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f31,plain,
( ~ subset(complement(complement(a)),a)
| spl0_1 ),
inference(avatar_component_clause,[],[f29]) ).
fof(f33,definition,
( spl0_2
<=> subset(a,complement(complement(a))) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f35,plain,
( ~ subset(a,complement(complement(a)))
| spl0_2 ),
inference(avatar_component_clause,[],[f33]) ).
fof(f37,plain,
( ~ spl0_2
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f26,f29,f33]) ).
fof(f46,plain,
( member(member_of_1_not_of_2(complement(complement(a)),a),complement(complement(a)))
| spl0_1 ),
inference(resolution,[],[f3,f31]) ).
fof(f51,plain,
! [X0,X1] :
( subset(X0,complement(X1))
| member(member_of_1_not_of_2(X0,complement(X1)),X1) ),
inference(resolution,[],[f4,f5]) ).
fof(f58,plain,
( ~ member(member_of_1_not_of_2(complement(complement(a)),a),complement(a))
| spl0_1 ),
inference(resolution,[],[f46,f6]) ).
fof(f59,plain,
( member(member_of_1_not_of_2(complement(complement(a)),a),a)
| spl0_1 ),
inference(resolution,[],[f58,f5]) ).
fof(f60,plain,
( subset(complement(complement(a)),a)
| spl0_1 ),
inference(resolution,[],[f59,f4]) ).
fof(f61,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f60,f31]) ).
fof(f62,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f61]) ).
fof(f69,plain,
( member(member_of_1_not_of_2(a,complement(complement(a))),a)
| spl0_2 ),
inference(resolution,[],[f35,f3]) ).
fof(f107,plain,
( member(member_of_1_not_of_2(a,complement(complement(a))),complement(a))
| spl0_2 ),
inference(resolution,[],[f51,f35]) ).
fof(f108,plain,
( ~ member(member_of_1_not_of_2(a,complement(complement(a))),a)
| spl0_2 ),
inference(resolution,[],[f107,f6]) ).
fof(f109,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f108,f69]) ).
fof(f110,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f109]) ).
cnf(s2,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f37]) ).
cnf(s3,plain,
spl0_1,
inference(sat_conversion,[],[f62]) ).
cnf(s4,plain,
spl0_2,
inference(sat_conversion,[],[f110]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s2,s4,s3]) ).
fof(f111,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.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n003.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 28 00:04:57 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.57/1.32 % (1065463)Input is clausal, will run a generic CNF schedule.
% 2.57/1.32 % (1065515)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1008967448:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.57/1.32 % (1065515)First to succeed.
% 2.57/1.32 % (1065515)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1065463"
% 2.57/1.32 % (1065512)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=4034701069:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.57/1.32 % (1065511)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3507725371:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.57/1.32 % (1065514)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=746660327:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.57/1.32 % (1065510)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=339392648:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.57/1.32 % (1065513)lrs+10_1_sil=8000:sp=occurrence:random_seed=2082539283:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.57/1.32 % (1065513)Also succeeded, but the first one will report.
% 2.57/1.32 % (1065516)dis-21_1_sil=8000:lcm=predicate:random_seed=835744528:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 2.57/1.32 % (1065516)Also succeeded, but the first one will report.
% 2.57/1.32 % (1065514)Instruction limit reached!
% 2.57/1.32 % (1065514)------------------------------
% 2.57/1.32 % (1065514)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.57/1.32 % (1065514)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/1.32 % (1065514)CaDiCaL version: 2.1.3
% 2.57/1.32 % (1065514)Termination reason: Instruction limit
% 2.57/1.32 % (1065514)Termination phase: Saturation
% 2.57/1.32 % (1065514)Time elapsed: 0.059 s
% 2.57/1.32 % (1065514)Peak memory usage: 87 MB
% 2.57/1.32 % (1065514)Instructions burned: 115 (million)
% 2.57/1.32 % (1065515)Refutation found. Thanks to Tanya!
% 2.57/1.32 % SZS status Unsatisfiable for theBenchmark
% 2.57/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 2.57/1.32 % (1065515)------------------------------
% 2.57/1.32 % (1065515)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.57/1.32 % (1065515)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/1.32 % (1065515)CaDiCaL version: 2.1.3
% 2.57/1.32 % (1065515)Termination reason: Refutation
% 2.57/1.32 % (1065515)Time elapsed: 0.002 s
% 2.57/1.32 % (1065515)Peak memory usage: 89 MB
% 2.57/1.32 % (1065515)Instructions burned: 3 (million)
% 2.57/1.32 % (1065515)------------------------------
% 2.57/1.32 % (1065515)------------------------------
% 2.57/1.32 % (1065463)Success in time 0.273 s
% 2.57/1.32 % Vampire exiting
%------------------------------------------------------------------------------