%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET138-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 12:40:15 PM UTC 2026
% Result : Unsatisfiable 3.62s 1.49s
% Output : Refutation 3.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 29 ( 12 unt; 2 def)
% Number of atoms : 47 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 40 ( 22 ~; 16 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 11 ( 3 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X1,X0))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair3) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set) ).
fof(f21,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection1) ).
fof(f24,axiom,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).
fof(f25,axiom,
! [X0,X1] :
( member(X0,complement(X1))
| ~ member(X0,universal_class)
| member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement2) ).
fof(f26,axiom,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).
fof(f101,axiom,
! [X0,X1] : union(singleton(X0),X1) = set_builder(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_of_set_builder) ).
fof(f102,negated_conjecture,
member(u,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_member_of_triple_kludge2_1) ).
fof(f105,negated_conjecture,
~ member(u,set_builder(u,set_builder(v,set_builder(w,null_class)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_member_of_triple_kludge2_4) ).
fof(f111,plain,
! [X0,X1] : set_builder(X0,X1) = complement(intersection(complement(unordered_pair(X0,X0)),complement(X1))),
inference(definition_unfolding,[],[f101,f26,f12]) ).
fof(f115,plain,
~ member(u,complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))),
inference(definition_unfolding,[],[f105,f111,f111,f111]) ).
fof(f184,plain,
( ~ member(u,universal_class)
| member(u,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))) ),
inference(resolution,[],[f25,f115]) ).
fof(f187,definition,
( spl1_1
<=> member(u,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f188,plain,
( member(u,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f187]) ).
fof(f190,definition,
( spl1_2
<=> member(u,universal_class) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f191,plain,
( ~ member(u,universal_class)
| spl1_2 ),
inference(avatar_component_clause,[],[f190]) ).
fof(f192,plain,
( spl1_1
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f184,f190,f187]) ).
fof(f193,plain,
( $false
| spl1_2 ),
inference(resolution,[],[f191,f102]) ).
fof(f195,plain,
spl1_2,
inference(avatar_contradiction_clause,[],[f193]) ).
fof(f197,plain,
( member(u,complement(unordered_pair(u,u)))
| ~ spl1_1 ),
inference(resolution,[],[f188,f21]) ).
fof(f198,plain,
( ~ member(u,unordered_pair(u,u))
| ~ spl1_1 ),
inference(resolution,[],[f197,f24]) ).
fof(f201,plain,
( ~ member(u,universal_class)
| ~ spl1_1 ),
inference(resolution,[],[f198,f10]) ).
fof(f202,plain,
( ~ spl1_2
| ~ spl1_1 ),
inference(avatar_split_clause,[],[f201,f187,f190]) ).
cnf(s1,plain,
( spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f192]) ).
cnf(s2,plain,
spl1_2,
inference(sat_conversion,[],[f195]) ).
cnf(s3,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f202]) ).
cnf(s5,plain,
~ spl1_1,
inference(rat,[],[s3,s2]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s2,s5]) ).
fof(f203,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET138-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n004.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 00:52:37 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.62/1.49 % (4040901)Input is clausal, will run a generic CNF schedule.
% 3.62/1.49 % (4040907)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=439627375:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.62/1.49 % (4040906)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=1120354800:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.62/1.49 % (4040909)lrs+10_1_sil=8000:sp=occurrence:random_seed=1572451768:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.62/1.49 % (4040912)dis-21_1_sil=8000:lcm=predicate:random_seed=3163651533: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)
% 3.62/1.49 % (4040910)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1284079916:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.62/1.49 % (4040908)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=925701492:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.62/1.49 % (4040911)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=528043101:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.62/1.49 % (4040909)Refutation not found, incomplete strategy
% 3.62/1.49 % (4040909)------------------------------
% 3.62/1.49 % (4040909)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.62/1.49 % (4040909)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/1.49 % (4040909)CaDiCaL version: 2.1.3
% 3.62/1.49 % (4040909)Termination reason: Refutation not found, incomplete strategy
% 3.62/1.49 % (4040909)Time elapsed: 0.003 s
% 3.62/1.49 % (4040909)Peak memory usage: 88 MB
% 3.62/1.49 % (4040909)Instructions burned: 3 (million)
% 3.62/1.49 % (4040912)First to succeed.
% 3.62/1.49 % (4040912)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4040901"
% 3.62/1.49 % (4040910)Instruction limit reached!
% 3.62/1.49 % (4040910)------------------------------
% 3.62/1.49 % (4040910)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.62/1.49 % (4040910)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/1.49 % (4040910)CaDiCaL version: 2.1.3
% 3.62/1.49 % (4040910)Termination reason: Instruction limit
% 3.62/1.49 % (4040910)Termination phase: Saturation
% 3.62/1.49 % (4040910)Time elapsed: 0.071 s
% 3.62/1.49 % (4040910)Peak memory usage: 89 MB
% 3.62/1.49 % (4040910)Instructions burned: 115 (million)
% 3.62/1.49 % (4040911)Instruction limit reached!
% 3.62/1.49 % (4040911)------------------------------
% 3.62/1.49 % (4040911)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.62/1.49 % (4040911)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/1.49 % (4040911)CaDiCaL version: 2.1.3
% 3.62/1.49 % (4040911)Termination reason: Instruction limit
% 3.62/1.49 % (4040911)Termination phase: Saturation
% 3.62/1.49 % (4040911)Time elapsed: 0.135 s
% 3.62/1.49 % (4040911)Peak memory usage: 90 MB
% 3.62/1.49 % (4040911)Instructions burned: 181 (million)
% 3.62/1.49 % (4040920)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=3156621610:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.62/1.49 % (4040920)Refutation not found, incomplete strategy
% 3.62/1.49 % (4040920)------------------------------
% 3.62/1.49 % (4040920)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.62/1.49 % (4040920)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/1.49 % (4040920)CaDiCaL version: 2.1.3
% 3.62/1.49 % (4040920)Termination reason: Refutation not found, incomplete strategy
% 3.62/1.49 % (4040920)Time elapsed: 0.003 s
% 3.62/1.49 % (4040920)Peak memory usage: 88 MB
% 3.62/1.49 % (4040920)Instructions burned: 3 (million)
% 3.62/1.49 % (4040909)------------------------------
% 3.62/1.49 % (4040909)------------------------------
% 3.62/1.49 % (4040912)Refutation found. Thanks to Tanya!
% 3.62/1.49 % SZS status Unsatisfiable for theBenchmark
% 3.62/1.49 % SZS output start Proof for theBenchmark
% See solution above
% 3.62/1.49 % (4040912)------------------------------
% 3.62/1.49 % (4040912)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.62/1.49 % (4040912)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/1.49 % (4040912)CaDiCaL version: 2.1.3
% 3.62/1.49 % (4040912)Termination reason: Refutation
% 3.62/1.49 % (4040912)Time elapsed: 0.005 s
% 3.62/1.49 % (4040912)Peak memory usage: 89 MB
% 3.62/1.49 % (4040912)Instructions burned: 7 (million)
% 3.62/1.49 % (4040912)------------------------------
% 3.62/1.49 % (4040912)------------------------------
% 3.62/1.49 % (4040901)Success in time 0.433 s
% 3.62/1.49 % Vampire exiting
%------------------------------------------------------------------------------