%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET064-6 : 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 : 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 12:39:53 PM UTC 2026
% Result : Unsatisfiable 4.27s 1.59s
% Output : Refutation 4.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 41 ( 12 unt; 1 def)
% Number of atoms : 77 ( 22 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 67 ( 31 ~; 35 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_members) ).
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(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(f22,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection2) ).
fof(f24,axiom,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement1) ).
fof(f67,axiom,
! [X0] :
( X0 = null_class
| member(regular(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity1) ).
fof(f68,plain,
! [X0] :
( member(regular(X0),X0)
| null_class = X0 ),
inference(reorient_equations,[],[f67]) ).
fof(f101,negated_conjecture,
z != null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_null_class_is_unique_1) ).
fof(f102,plain,
null_class != z,
inference(reorient_equations,[],[f101]) ).
fof(f103,negated_conjecture,
~ member(not_subclass_element(z,null_class),z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_null_class_is_unique_2) ).
fof(f109,plain,
! [X0] :
( ~ member(regular(complement(X0)),X0)
| complement(X0) = null_class ),
inference(resolution,[],[f68,f24]) ).
fof(f113,plain,
! [X0,X1] :
( member(regular(intersection(X0,X1)),X0)
| intersection(X0,X1) = null_class ),
inference(resolution,[],[f21,f68]) ).
fof(f117,plain,
! [X0,X1] :
( member(regular(intersection(X0,X1)),X1)
| intersection(X0,X1) = null_class ),
inference(resolution,[],[f22,f68]) ).
fof(f158,plain,
! [X0,X1] :
( ~ subclass(X0,X1)
| X0 = X1
| member(not_subclass_element(X1,X0),X1) ),
inference(resolution,[],[f7,f2]) ).
fof(f471,plain,
! [X0,X1] :
( ~ subclass(X1,X0)
| ~ member(regular(complement(X0)),X1)
| complement(X0) = null_class ),
inference(resolution,[],[f109,f1]) ).
fof(f592,definition,
( spl0_37
<=> null_class = complement(universal_class) ),
introduced(definition,[new_symbols(definition,[spl0_37])],[avatar_definition]) ).
fof(f593,plain,
( null_class != complement(universal_class)
| spl0_37 ),
inference(avatar_component_clause,[],[f592]) ).
fof(f594,plain,
( null_class = complement(universal_class)
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f592]) ).
fof(f650,plain,
! [X0,X1] :
( ~ member(regular(intersection(complement(X0),X1)),X0)
| null_class = intersection(complement(X0),X1) ),
inference(resolution,[],[f113,f24]) ).
fof(f770,plain,
! [X0,X1] :
( member(not_subclass_element(X1,X0),X1)
| X0 = X1
| member(not_subclass_element(X0,X1),X0) ),
inference(resolution,[],[f158,f2]) ).
fof(f2203,plain,
! [X0] :
( ~ member(regular(complement(universal_class)),X0)
| null_class = complement(universal_class) ),
inference(resolution,[],[f471,f4]) ).
fof(f2269,plain,
( ! [X0] : ~ member(regular(complement(universal_class)),X0)
| spl0_37 ),
inference(forward_subsumption_resolution,[],[f2203,f593]) ).
fof(f2407,plain,
( null_class = complement(universal_class)
| spl0_37 ),
inference(resolution,[],[f2269,f68]) ).
fof(f2421,plain,
( $false
| spl0_37 ),
inference(forward_subsumption_resolution,[],[f2407,f593]) ).
fof(f2422,plain,
spl0_37,
inference(avatar_contradiction_clause,[],[f2421]) ).
fof(f2433,plain,
( ! [X0] :
( ~ member(X0,null_class)
| ~ member(X0,universal_class) )
| ~ spl0_37 ),
inference(superposition,[],[f24,f594]) ).
fof(f2891,plain,
! [X0] :
( null_class = intersection(complement(X0),X0)
| null_class = intersection(complement(X0),X0) ),
inference(resolution,[],[f650,f117]) ).
fof(f2912,plain,
! [X0] : null_class = intersection(complement(X0),X0),
inference(duplicate_literal_removal,[],[f2891]) ).
fof(f2917,plain,
( null_class = intersection(null_class,universal_class)
| ~ spl0_37 ),
inference(superposition,[],[f2912,f594]) ).
fof(f2942,plain,
( ! [X0] :
( ~ member(X0,null_class)
| member(X0,universal_class) )
| ~ spl0_37 ),
inference(superposition,[],[f22,f2917]) ).
fof(f2952,plain,
( ! [X0] : ~ member(X0,null_class)
| ~ spl0_37 ),
inference(forward_subsumption_resolution,[],[f2942,f2433]) ).
fof(f3231,plain,
( null_class = z
| member(not_subclass_element(null_class,z),null_class) ),
inference(resolution,[],[f770,f103]) ).
fof(f3259,plain,
member(not_subclass_element(null_class,z),null_class),
inference(forward_subsumption_resolution,[],[f3231,f102]) ).
fof(f3268,plain,
( $false
| ~ spl0_37 ),
inference(forward_subsumption_resolution,[],[f3259,f2952]) ).
fof(f3269,plain,
~ spl0_37,
inference(avatar_contradiction_clause,[],[f3268]) ).
cnf(s124,plain,
spl0_37,
inference(sat_conversion,[],[f2422]) ).
cnf(s145,plain,
~ spl0_37,
inference(sat_conversion,[],[f3269]) ).
cnf(s149,plain,
$false,
inference(rat,[],[s124,s145]) ).
fof(f3284,plain,
$false,
inference(avatar_sat_refutation,[],[s149]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET064-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n003.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 00:29:41 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 4.27/1.59 % (1077070)Input is clausal, will run a generic CNF schedule.
% 4.27/1.59 % (1077075)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=2846556699:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.27/1.59 % (1077076)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4205072351:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.27/1.59 % (1077079)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3913605621:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.27/1.59 % (1077081)dis-21_1_sil=8000:lcm=predicate:random_seed=1608906620: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)
% 4.27/1.59 % (1077078)lrs+10_1_sil=8000:sp=occurrence:random_seed=2341396745:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.27/1.59 % (1077077)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2177873870:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.27/1.59 % (1077080)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=898241775:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.27/1.59 % (1077081)Instruction limit reached!
% 4.27/1.59 % (1077081)------------------------------
% 4.27/1.59 % (1077081)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.27/1.59 % (1077081)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.27/1.59 % (1077081)CaDiCaL version: 2.1.3
% 4.27/1.59 % (1077081)Termination reason: Instruction limit
% 4.27/1.59 % (1077081)Termination phase: Saturation
% 4.27/1.59 % (1077081)Time elapsed: 0.067 s
% 4.27/1.59 % (1077081)Peak memory usage: 89 MB
% 4.27/1.59 % (1077081)Instructions burned: 119 (million)
% 4.27/1.59 % (1077079)Instruction limit reached!
% 4.27/1.59 % (1077079)------------------------------
% 4.27/1.59 % (1077079)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.27/1.59 % (1077079)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.27/1.59 % (1077079)CaDiCaL version: 2.1.3
% 4.27/1.59 % (1077079)Termination reason: Instruction limit
% 4.27/1.59 % (1077079)Termination phase: Saturation
% 4.27/1.59 % (1077079)Time elapsed: 0.070 s
% 4.27/1.59 % (1077079)Peak memory usage: 89 MB
% 4.27/1.59 % (1077079)Instructions burned: 114 (million)
% 4.27/1.59 % (1077078)Instruction limit reached!
% 4.27/1.59 % (1077078)------------------------------
% 4.27/1.59 % (1077078)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.27/1.59 % (1077078)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.27/1.59 % (1077078)CaDiCaL version: 2.1.3
% 4.27/1.59 % (1077078)Termination reason: Instruction limit
% 4.27/1.59 % (1077078)Termination phase: Saturation
% 4.27/1.59 % (1077078)Time elapsed: 0.074 s
% 4.27/1.59 % (1077078)Peak memory usage: 89 MB
% 4.27/1.59 % (1077078)Instructions burned: 109 (million)
% 4.27/1.59 % (1077080)First to succeed.
% 4.27/1.59 % (1077080)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1077070"
% 4.27/1.59 % (1077090)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1143604448: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)
% 4.27/1.59 % (1077089)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=1737137625:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 4.27/1.59 % (1077089)Refutation not found, incomplete strategy
% 4.27/1.59 % (1077089)------------------------------
% 4.27/1.59 % (1077089)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.27/1.59 % (1077089)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.27/1.59 % (1077089)CaDiCaL version: 2.1.3
% 4.27/1.59 % (1077089)Termination reason: Refutation not found, incomplete strategy
% 4.27/1.59 % (1077089)Time elapsed: 0.003 s
% 4.27/1.59 % (1077089)Peak memory usage: 88 MB
% 4.27/1.59 % (1077089)Instructions burned: 3 (million)
% 4.27/1.59 % (1077090)Also succeeded, but the first one will report.
% 4.27/1.59 % (1077091)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3948793608:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 4.27/1.59 % (1077075)Also succeeded, but the first one will report.
% 4.27/1.59 % (1077080)Refutation found. Thanks to Tanya!
% 4.27/1.59 % SZS status Unsatisfiable for theBenchmark
% 4.27/1.59 % SZS output start Proof for theBenchmark
% See solution above
% 4.27/1.59 % (1077080)------------------------------
% 4.27/1.59 % (1077080)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.27/1.59 % (1077080)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.27/1.59 % (1077080)CaDiCaL version: 2.1.3
% 4.27/1.59 % (1077080)Termination reason: Refutation
% 4.27/1.59 % (1077080)Time elapsed: 0.094 s
% 4.27/1.59 % (1077080)Peak memory usage: 91 MB
% 4.27/1.59 % (1077080)Instructions burned: 123 (million)
% 4.27/1.59 % (1077080)------------------------------
% 4.27/1.59 % (1077080)------------------------------
% 4.27/1.59 % (1077070)Success in time 0.534 s
% 4.27/1.59 % Vampire exiting
%------------------------------------------------------------------------------