%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET131-6 : 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 : n019.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 12:40:14 PM UTC 2026
% Result : Unsatisfiable 3.39s 1.37s
% Output : Refutation 3.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 38 ( 13 unt; 3 def)
% Number of atoms : 67 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 63 ( 34 ~; 26 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 11 ( 3 avg)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 19 ( 0 sgn 19 !; 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(f22,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection2) ).
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_triple2_1) ).
fof(f103,negated_conjecture,
~ member(u,set_builder(x,set_builder(u,set_builder(z,null_class)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_member_of_triple2_2) ).
fof(f109,plain,
! [X0,X1] : set_builder(X0,X1) = complement(intersection(complement(unordered_pair(X0,X0)),complement(X1))),
inference(definition_unfolding,[],[f101,f26,f12]) ).
fof(f113,plain,
~ member(u,complement(intersection(complement(unordered_pair(x,x)),complement(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class)))))))))),
inference(definition_unfolding,[],[f103,f109,f109,f109]) ).
fof(f182,plain,
( ~ member(u,universal_class)
| member(u,intersection(complement(unordered_pair(x,x)),complement(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class))))))))) ),
inference(resolution,[],[f25,f113]) ).
fof(f185,definition,
( spl1_1
<=> member(u,intersection(complement(unordered_pair(x,x)),complement(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class))))))))) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f186,plain,
( member(u,intersection(complement(unordered_pair(x,x)),complement(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class)))))))))
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f185]) ).
fof(f188,definition,
( spl1_2
<=> member(u,universal_class) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f189,plain,
( ~ member(u,universal_class)
| spl1_2 ),
inference(avatar_component_clause,[],[f188]) ).
fof(f190,plain,
( spl1_1
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f182,f188,f185]) ).
fof(f191,plain,
( $false
| spl1_2 ),
inference(resolution,[],[f189,f102]) ).
fof(f193,plain,
spl1_2,
inference(avatar_contradiction_clause,[],[f191]) ).
fof(f194,plain,
( member(u,complement(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class))))))))
| ~ spl1_1 ),
inference(resolution,[],[f186,f22]) ).
fof(f197,plain,
( ~ member(u,complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class)))))))
| ~ spl1_1 ),
inference(resolution,[],[f194,f24]) ).
fof(f198,plain,
( ~ member(u,universal_class)
| member(u,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class))))))
| ~ spl1_1 ),
inference(resolution,[],[f197,f25]) ).
fof(f200,definition,
( spl1_3
<=> member(u,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class)))))) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f201,plain,
( member(u,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class))))))
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f200]) ).
fof(f202,plain,
( spl1_3
| ~ spl1_2
| ~ spl1_1 ),
inference(avatar_split_clause,[],[f198,f185,f188,f200]) ).
fof(f204,plain,
( member(u,complement(unordered_pair(u,u)))
| ~ spl1_3 ),
inference(resolution,[],[f201,f21]) ).
fof(f205,plain,
( ~ member(u,unordered_pair(u,u))
| ~ spl1_3 ),
inference(resolution,[],[f204,f24]) ).
fof(f207,plain,
( ~ member(u,universal_class)
| ~ spl1_3 ),
inference(resolution,[],[f205,f10]) ).
fof(f208,plain,
( ~ spl1_2
| ~ spl1_3 ),
inference(avatar_split_clause,[],[f207,f200,f188]) ).
cnf(s1,plain,
( spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f190]) ).
cnf(s2,plain,
spl1_2,
inference(sat_conversion,[],[f193]) ).
cnf(s3,plain,
( ~ spl1_1
| ~ spl1_2
| spl1_3 ),
inference(sat_conversion,[],[f202]) ).
cnf(s4,plain,
( ~ spl1_2
| ~ spl1_3 ),
inference(sat_conversion,[],[f208]) ).
cnf(s6,plain,
~ spl1_3,
inference(rat,[],[s4,s2]) ).
cnf(s7,plain,
~ spl1_1,
inference(rat,[],[s3,s6,s2]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s2,s7]) ).
fof(f209,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET131-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n019.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 00:51:49 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 3.39/1.37 % (3560922)Input is clausal, will run a generic CNF schedule.
% 3.39/1.37 % (3560928)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1418777929:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.39/1.37 % (3560930)lrs+10_1_sil=8000:sp=occurrence:random_seed=4018621645:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.39/1.37 % (3560930)Refutation not found, incomplete strategy
% 3.39/1.37 % (3560930)------------------------------
% 3.39/1.37 % (3560930)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.39/1.37 % (3560930)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.39/1.37 % (3560930)CaDiCaL version: 2.1.3
% 3.39/1.37 % (3560930)Termination reason: Refutation not found, incomplete strategy
% 3.39/1.37 % (3560930)Time elapsed: 0.003 s
% 3.39/1.37 % (3560930)Peak memory usage: 88 MB
% 3.39/1.37 % (3560930)Instructions burned: 3 (million)
% 3.39/1.37 % (3560927)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=4134366360:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.39/1.37 % (3560929)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1294290550:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.39/1.37 % (3560932)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2279551634:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.39/1.37 % (3560933)dis-21_1_sil=8000:lcm=predicate:random_seed=190547385: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)
% 3.39/1.37 % (3560931)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2562059756:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.39/1.37 % (3560933)First to succeed.
% 3.39/1.37 % (3560933)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3560922"
% 3.39/1.37 % (3560931)Instruction limit reached!
% 3.39/1.37 % (3560931)------------------------------
% 3.39/1.37 % (3560931)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.39/1.37 % (3560931)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.39/1.37 % (3560931)CaDiCaL version: 2.1.3
% 3.39/1.37 % (3560931)Termination reason: Instruction limit
% 3.39/1.37 % (3560931)Termination phase: Saturation
% 3.39/1.37 % (3560931)Time elapsed: 0.072 s
% 3.39/1.37 % (3560931)Peak memory usage: 89 MB
% 3.39/1.37 % (3560931)Instructions burned: 115 (million)
% 3.39/1.37 % (3560932)Instruction limit reached!
% 3.39/1.37 % (3560932)------------------------------
% 3.39/1.37 % (3560932)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.39/1.37 % (3560932)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.39/1.37 % (3560932)CaDiCaL version: 2.1.3
% 3.39/1.37 % (3560932)Termination reason: Instruction limit
% 3.39/1.37 % (3560932)Termination phase: Saturation
% 3.39/1.37 % (3560932)Time elapsed: 0.135 s
% 3.39/1.37 % (3560932)Peak memory usage: 90 MB
% 3.39/1.37 % (3560932)Instructions burned: 180 (million)
% 3.39/1.37 % (3560941)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=1364147730:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.39/1.37 % (3560941)Refutation not found, incomplete strategy
% 3.39/1.37 % (3560941)------------------------------
% 3.39/1.37 % (3560941)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.39/1.37 % (3560941)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.39/1.37 % (3560941)CaDiCaL version: 2.1.3
% 3.39/1.37 % (3560941)Termination reason: Refutation not found, incomplete strategy
% 3.39/1.37 % (3560941)Time elapsed: 0.003 s
% 3.39/1.37 % (3560941)Peak memory usage: 88 MB
% 3.39/1.37 % (3560941)Instructions burned: 3 (million)
% 3.39/1.37 % (3560930)------------------------------
% 3.39/1.37 % (3560930)------------------------------
% 3.39/1.37 % (3560933)Refutation found. Thanks to Tanya!
% 3.39/1.37 % SZS status Unsatisfiable for theBenchmark
% 3.39/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 3.39/1.37 % (3560933)------------------------------
% 3.39/1.37 % (3560933)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.39/1.37 % (3560933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.39/1.37 % (3560933)CaDiCaL version: 2.1.3
% 3.39/1.37 % (3560933)Termination reason: Refutation
% 3.39/1.37 % (3560933)Time elapsed: 0.005 s
% 3.39/1.37 % (3560933)Peak memory usage: 89 MB
% 3.39/1.37 % (3560933)Instructions burned: 7 (million)
% 3.39/1.37 % (3560933)------------------------------
% 3.39/1.37 % (3560933)------------------------------
% 3.39/1.37 % (3560922)Success in time 0.417 s
% 3.39/1.37 % Vampire exiting
%------------------------------------------------------------------------------