%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET163-6 : 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 : 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 12:40:21 PM UTC 2026
% Result : Unsatisfiable 3.85s 1.54s
% Output : Refutation 3.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 45 ( 13 unt; 5 def)
% Number of atoms : 84 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 74 ( 35 ~; 34 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 20 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_subclass_members1) ).
fof(f3,axiom,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_subclass_members2) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f7,axiom,
! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_implies_equal) ).
fof(f21,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection1) ).
fof(f24,axiom,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement1) ).
fof(f25,axiom,
! [X0,X1] :
( member(X0,complement(X1))
| ~ member(X0,universal_class)
| member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement2) ).
fof(f26,axiom,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union) ).
fof(f122,negated_conjecture,
union(universal_class,x) != universal_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_union_with_universal_class_1) ).
fof(f123,plain,
universal_class != union(universal_class,x),
inference(reorient_equations,[],[f122]) ).
fof(f137,plain,
universal_class != complement(intersection(complement(universal_class),complement(x))),
inference(definition_unfolding,[],[f123,f26]) ).
fof(f181,definition,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
fof(f182,plain,
~ sQ0_eqProxy(universal_class,complement(intersection(complement(universal_class),complement(x)))),
inference(equality_proxy_replacement,[],[f137,f181]) ).
fof(f183,plain,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(equality_proxy_replacement,[],[f7,f181]) ).
fof(f219,plain,
( ~ subclass(complement(intersection(complement(universal_class),complement(x))),universal_class)
| ~ subclass(universal_class,complement(intersection(complement(universal_class),complement(x)))) ),
inference(resolution,[],[f183,f182]) ).
fof(f222,definition,
( spl1_1
<=> subclass(complement(intersection(complement(universal_class),complement(x))),universal_class) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f223,plain,
( ~ subclass(complement(intersection(complement(universal_class),complement(x))),universal_class)
| spl1_1 ),
inference(avatar_component_clause,[],[f222]) ).
fof(f225,definition,
( spl1_2
<=> subclass(universal_class,complement(intersection(complement(universal_class),complement(x)))) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f226,plain,
( ~ subclass(universal_class,complement(intersection(complement(universal_class),complement(x))))
| spl1_2 ),
inference(avatar_component_clause,[],[f225]) ).
fof(f228,plain,
( ~ spl1_2
| ~ spl1_1 ),
inference(avatar_split_clause,[],[f219,f222,f225]) ).
fof(f229,plain,
( $false
| spl1_1 ),
inference(resolution,[],[f223,f4]) ).
fof(f232,plain,
spl1_1,
inference(avatar_contradiction_clause,[],[f229]) ).
fof(f233,plain,
( ~ member(not_subclass_element(universal_class,complement(intersection(complement(universal_class),complement(x)))),complement(intersection(complement(universal_class),complement(x))))
| spl1_2 ),
inference(resolution,[],[f226,f3]) ).
fof(f234,plain,
( member(not_subclass_element(universal_class,complement(intersection(complement(universal_class),complement(x)))),universal_class)
| spl1_2 ),
inference(resolution,[],[f226,f2]) ).
fof(f236,plain,
( ~ member(not_subclass_element(universal_class,complement(intersection(complement(universal_class),complement(x)))),universal_class)
| member(not_subclass_element(universal_class,complement(intersection(complement(universal_class),complement(x)))),intersection(complement(universal_class),complement(x)))
| spl1_2 ),
inference(resolution,[],[f25,f233]) ).
fof(f238,definition,
( spl1_3
<=> member(not_subclass_element(universal_class,complement(intersection(complement(universal_class),complement(x)))),intersection(complement(universal_class),complement(x))) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f239,plain,
( member(not_subclass_element(universal_class,complement(intersection(complement(universal_class),complement(x)))),intersection(complement(universal_class),complement(x)))
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f238]) ).
fof(f241,definition,
( spl1_4
<=> member(not_subclass_element(universal_class,complement(intersection(complement(universal_class),complement(x)))),universal_class) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f242,plain,
( ~ member(not_subclass_element(universal_class,complement(intersection(complement(universal_class),complement(x)))),universal_class)
| spl1_4 ),
inference(avatar_component_clause,[],[f241]) ).
fof(f243,plain,
( spl1_3
| ~ spl1_4
| spl1_2 ),
inference(avatar_split_clause,[],[f236,f225,f241,f238]) ).
fof(f244,plain,
( $false
| spl1_2
| spl1_4 ),
inference(resolution,[],[f242,f234]) ).
fof(f246,plain,
( spl1_2
| spl1_4 ),
inference(avatar_contradiction_clause,[],[f244]) ).
fof(f248,plain,
( member(not_subclass_element(universal_class,complement(intersection(complement(universal_class),complement(x)))),complement(universal_class))
| ~ spl1_3 ),
inference(resolution,[],[f239,f21]) ).
fof(f250,plain,
( ~ member(not_subclass_element(universal_class,complement(intersection(complement(universal_class),complement(x)))),universal_class)
| ~ spl1_3 ),
inference(resolution,[],[f248,f24]) ).
fof(f251,plain,
( ~ spl1_4
| ~ spl1_3 ),
inference(avatar_split_clause,[],[f250,f238,f241]) ).
cnf(s2,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f228]) ).
cnf(s3,plain,
spl1_1,
inference(sat_conversion,[],[f232]) ).
cnf(s4,plain,
( spl1_2
| spl1_3
| ~ spl1_4 ),
inference(sat_conversion,[],[f243]) ).
cnf(s5,plain,
( spl1_2
| spl1_4 ),
inference(sat_conversion,[],[f246]) ).
cnf(s6,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(sat_conversion,[],[f251]) ).
cnf(s7,plain,
~ spl1_2,
inference(rat,[],[s2,s3]) ).
cnf(s8,plain,
spl1_4,
inference(rat,[],[s5,s7]) ).
cnf(s9,plain,
spl1_3,
inference(rat,[],[s4,s8,s7]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s6,s8,s9]) ).
fof(f252,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET163-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n001.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Mon Sep 28 01:03:47 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 3.85/1.54 % (4121888)Input is clausal, will run a generic CNF schedule.
% 3.85/1.54 % (4121896)lrs+10_1_sil=8000:sp=occurrence:random_seed=3816127433:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.85/1.54 % (4121896)Refutation not found, incomplete strategy
% 3.85/1.54 % (4121896)------------------------------
% 3.85/1.54 % (4121896)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.85/1.54 % (4121896)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.85/1.54 % (4121896)CaDiCaL version: 2.1.3
% 3.85/1.54 % (4121896)Termination reason: Refutation not found, incomplete strategy
% 3.85/1.54 % (4121896)Time elapsed: 0.002 s
% 3.85/1.54 % (4121896)Peak memory usage: 88 MB
% 3.85/1.54 % (4121896)Instructions burned: 4 (million)
% 3.85/1.54 % (4121895)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2954551610:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.85/1.54 % (4121893)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=3820455806:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.85/1.54 % (4121894)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=496996937:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.85/1.54 % (4121898)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=33457601:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.85/1.54 % (4121897)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1499414795:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.85/1.54 % (4121899)dis-21_1_sil=8000:lcm=predicate:random_seed=1706727282: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)
% 3.85/1.54 % (4121899)First to succeed.
% 3.85/1.54 % (4121899)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4121888"
% 3.85/1.54 % (4121897)Instruction limit reached!
% 3.85/1.54 % (4121897)------------------------------
% 3.85/1.54 % (4121897)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.85/1.54 % (4121897)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.85/1.54 % (4121897)CaDiCaL version: 2.1.3
% 3.85/1.54 % (4121897)Termination reason: Instruction limit
% 3.85/1.54 % (4121897)Termination phase: Saturation
% 3.85/1.54 % (4121897)Time elapsed: 0.069 s
% 3.85/1.54 % (4121897)Peak memory usage: 89 MB
% 3.85/1.54 % (4121897)Instructions burned: 114 (million)
% 3.85/1.54 % (4121896)------------------------------
% 3.85/1.54 % (4121896)------------------------------
% 3.85/1.54 % (4121898)Instruction limit reached!
% 3.85/1.54 % (4121898)------------------------------
% 3.85/1.54 % (4121898)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.85/1.54 % (4121898)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.85/1.54 % (4121898)CaDiCaL version: 2.1.3
% 3.85/1.54 % (4121898)Termination reason: Instruction limit
% 3.85/1.54 % (4121898)Termination phase: Saturation
% 3.85/1.54 % (4121898)Time elapsed: 0.135 s
% 3.85/1.54 % (4121898)Peak memory usage: 90 MB
% 3.85/1.54 % (4121898)Instructions burned: 181 (million)
% 3.85/1.54 % (4121908)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3549986448:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 3.85/1.54 % (4121907)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=3425609597:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.85/1.54 % (4121907)Refutation not found, incomplete strategy
% 3.85/1.54 % (4121907)------------------------------
% 3.85/1.54 % (4121907)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.85/1.54 % (4121907)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.85/1.54 % (4121907)CaDiCaL version: 2.1.3
% 3.85/1.54 % (4121907)Termination reason: Refutation not found, incomplete strategy
% 3.85/1.54 % (4121907)Time elapsed: 0.002 s
% 3.85/1.54 % (4121907)Peak memory usage: 88 MB
% 3.85/1.54 % (4121907)Instructions burned: 2 (million)
% 3.85/1.54 % (4121908)Also succeeded, but the first one will report.
% 3.85/1.54 % (4121899)Refutation found. Thanks to Tanya!
% 3.85/1.54 % SZS status Unsatisfiable for theBenchmark
% 3.85/1.54 % SZS output start Proof for theBenchmark
% See solution above
% 3.85/1.54 % (4121899)------------------------------
% 3.85/1.54 % (4121899)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.85/1.54 % (4121899)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.85/1.54 % (4121899)CaDiCaL version: 2.1.3
% 3.85/1.54 % (4121899)Termination reason: Refutation
% 3.85/1.54 % (4121899)Time elapsed: 0.006 s
% 3.85/1.54 % (4121899)Peak memory usage: 89 MB
% 3.85/1.54 % (4121899)Instructions burned: 8 (million)
% 3.85/1.54 % (4121899)------------------------------
% 3.85/1.54 % (4121899)------------------------------
% 3.85/1.54 % (4121888)Success in time 0.451 s
% 3.85/1.54 % Vampire exiting
%------------------------------------------------------------------------------