%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM011-1 : 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 : n001.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 12:17:48 PM UTC 2026
% Result : Unsatisfiable 0.08s 0.47s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of formulae : 41 ( 16 unt; 2 def)
% Number of atoms : 73 ( 7 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 67 ( 35 ~; 30 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ~ member(X0,X1)
| little_set(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',a2) ).
fof(f6,axiom,
! [X2,X0,X1] :
( member(X0,non_ordered_pair(X1,X2))
| ~ little_set(X0)
| X0 != X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',non_ordered_pair2) ).
fof(f9,axiom,
! [X0] : singleton_set(X0) = non_ordered_pair(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',singleton_set) ).
fof(f35,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',intersection2) ).
fof(f37,axiom,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',complement1) ).
fof(f38,axiom,
! [X0,X1] :
( member(X0,complement(X1))
| ~ little_set(X0)
| member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',complement2) ).
fof(f39,axiom,
! [X0,X1] : union(X0,X1) = complement(intersection(complement(X0),complement(X1))),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',union) ).
fof(f69,axiom,
! [X0] : successor(X0) = union(X0,singleton_set(X0)),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',successor) ).
fof(f70,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',empty_set) ).
fof(f247,axiom,
member(f75,natural_numbers),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_natural_number) ).
fof(f248,negated_conjecture,
empty_set = successor(f75),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_zero_is_first) ).
fof(f249,plain,
! [X0] : successor(X0) = complement(intersection(complement(X0),complement(non_ordered_pair(X0,X0)))),
inference(definition_unfolding,[],[f69,f39,f9]) ).
fof(f317,plain,
empty_set = complement(intersection(complement(f75),complement(non_ordered_pair(f75,f75)))),
inference(definition_unfolding,[],[f248,f249]) ).
fof(f318,plain,
! [X2,X1] :
( member(X1,non_ordered_pair(X1,X2))
| ~ little_set(X1) ),
inference(equality_resolution,[],[f6]) ).
fof(f337,plain,
! [X0,X1] :
( little_set(X0)
| member(X0,X1) ),
inference(consistent_polarity_flipping,[],[f1]) ).
fof(f341,plain,
! [X2,X1] :
( ~ member(X1,non_ordered_pair(X1,X2))
| ~ little_set(X1) ),
inference(consistent_polarity_flipping,[],[f318]) ).
fof(f361,plain,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2) ),
inference(consistent_polarity_flipping,[],[f35]) ).
fof(f363,plain,
! [X0,X1] :
( member(X0,complement(X1))
| member(X0,X1) ),
inference(consistent_polarity_flipping,[],[f37]) ).
fof(f364,plain,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ little_set(X0)
| ~ member(X0,X1) ),
inference(consistent_polarity_flipping,[],[f38]) ).
fof(f388,plain,
! [X0] : member(X0,empty_set),
inference(consistent_polarity_flipping,[],[f70]) ).
fof(f528,plain,
~ member(f75,natural_numbers),
inference(consistent_polarity_flipping,[],[f247]) ).
fof(f706,plain,
! [X0] :
( ~ member(X0,intersection(complement(f75),complement(non_ordered_pair(f75,f75))))
| ~ little_set(X0)
| ~ member(X0,empty_set) ),
inference(superposition,[],[f364,f317]) ).
fof(f707,plain,
! [X0] :
( ~ member(X0,complement(non_ordered_pair(f75,f75)))
| ~ member(X0,empty_set)
| ~ little_set(X0) ),
inference(resolution,[],[f706,f361]) ).
fof(f810,plain,
! [X0] :
( member(X0,non_ordered_pair(f75,f75))
| ~ little_set(X0)
| ~ member(X0,empty_set) ),
inference(resolution,[],[f707,f363]) ).
fof(f850,plain,
( ~ little_set(f75)
| ~ member(f75,empty_set)
| ~ little_set(f75) ),
inference(resolution,[],[f810,f341]) ).
fof(f856,plain,
( ~ little_set(f75)
| ~ member(f75,empty_set) ),
inference(duplicate_literal_removal,[],[f850]) ).
fof(f871,definition,
( spl0_35
<=> member(f75,empty_set) ),
introduced(definition,[new_symbols(definition,[spl0_35])],[avatar_definition]) ).
fof(f873,plain,
( ~ member(f75,empty_set)
| spl0_35 ),
inference(avatar_component_clause,[],[f871]) ).
fof(f875,definition,
( spl0_36
<=> little_set(f75) ),
introduced(definition,[new_symbols(definition,[spl0_36])],[avatar_definition]) ).
fof(f877,plain,
( ~ little_set(f75)
| spl0_36 ),
inference(avatar_component_clause,[],[f875]) ).
fof(f879,plain,
( ~ spl0_35
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f856,f875,f871]) ).
fof(f882,plain,
( ! [X0] : member(f75,X0)
| spl0_36 ),
inference(resolution,[],[f877,f337]) ).
fof(f884,plain,
( $false
| spl0_35 ),
inference(resolution,[],[f873,f388]) ).
fof(f887,plain,
spl0_35,
inference(avatar_contradiction_clause,[],[f884]) ).
fof(f890,plain,
( $false
| spl0_36 ),
inference(resolution,[],[f882,f528]) ).
fof(f899,plain,
spl0_36,
inference(avatar_contradiction_clause,[],[f890]) ).
cnf(s23,plain,
( ~ spl0_35
| ~ spl0_36 ),
inference(sat_conversion,[],[f879]) ).
cnf(s24,plain,
spl0_35,
inference(sat_conversion,[],[f887]) ).
cnf(s25,plain,
spl0_36,
inference(sat_conversion,[],[f899]) ).
cnf(s26,plain,
$false,
inference(rat,[],[s23,s25,s24]) ).
fof(f900,plain,
$false,
inference(avatar_sat_refutation,[],[s26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM011-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.36 % Computer : n001.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 27 18:45:01 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.40 Running first-order model finding
% 0.08/0.40 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
% 0.08/0.47 % (3884706)Will run a generic schedule for satisfiability detection.
% 0.08/0.47 % (3884717)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3999005052:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.08/0.47 % (3884714)dis+10_1_sil=32000:sp=arity:random_seed=4287522714:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.47 % (3884712)% WARNING: option uhcvi not known.
% 0.08/0.47 % (3884717) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3884706-3884717"...
% 0.08/0.47 % (3884717)...printing done.
% 0.08/0.47 % (3884711)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=486697744_2999 on theBenchmark for (2999ds/0Mi)
% 0.08/0.47 % (3884716)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2779971151:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.08/0.47 % (3884713)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2120652172:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.47 % (3884715)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2831721954:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.08/0.47 % (3884712)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=44328945:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.47 % (3884717)Refutation found. Thanks to Tanya!
% 0.08/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.08/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.47 % (3884717)------------------------------
% 0.08/0.47 % (3884717)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.47 % (3884717)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.47 % (3884717)CaDiCaL version: 2.1.3
% 0.08/0.47 % (3884717)Termination reason: Refutation
% 0.08/0.47 % (3884717)Time elapsed: 0.010 s
% 0.08/0.47 % (3884717)Peak memory usage: 13 MB
% 0.08/0.47 % (3884717)Instructions burned: 24 (million)
% 0.08/0.47 % (3884706)Success in time 0.058 s
% 0.08/0.47 % Vampire exiting
%------------------------------------------------------------------------------