%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET098-7 : 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 : n017.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 12:40:06 PM UTC 2026
% Result : Unsatisfiable 3.69s 1.43s
% Output : Refutation 3.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 27 ( 13 unt; 1 def)
% Number of atoms : 46 ( 16 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 36 ( 17 ~; 18 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 13 ( 0 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( member(not_subclass_element(X0,X1),X0)
| subclass(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_subclass_members1) ).
fof(f22,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection2) ).
fof(f113,axiom,
! [X0] : ~ member(X0,null_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_null_class) ).
fof(f115,axiom,
! [X0] :
( ~ subclass(X0,null_class)
| X0 = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_of_null_class_is_subclass) ).
fof(f116,plain,
! [X0] :
( ~ subclass(X0,null_class)
| null_class = X0 ),
inference(reorient_equations,[],[f115]) ).
fof(f156,axiom,
! [X0] :
( member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X0,null_class))),X0),null_class),intersection(complement(singleton(not_subclass_element(X0,null_class))),X0))
| singleton(not_subclass_element(X0,null_class)) = X0
| X0 = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',number_of_elements_in_class) ).
fof(f157,plain,
! [X0] :
( member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X0,null_class))),X0),null_class),intersection(complement(singleton(not_subclass_element(X0,null_class))),X0))
| singleton(not_subclass_element(X0,null_class)) = X0
| null_class = X0 ),
inference(reorient_equations,[],[f156]) ).
fof(f158,negated_conjecture,
~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_1_to_number_of_elements_in_class_1) ).
fof(f159,negated_conjecture,
singleton(not_subclass_element(x,null_class)) != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_1_to_number_of_elements_in_class_2) ).
fof(f160,plain,
x != singleton(not_subclass_element(x,null_class)),
inference(reorient_equations,[],[f159]) ).
fof(f161,negated_conjecture,
x != null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_1_to_number_of_elements_in_class_3) ).
fof(f162,plain,
null_class != x,
inference(reorient_equations,[],[f161]) ).
fof(f182,plain,
! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,X1),X2),X1)
| subclass(intersection(X0,X1),X2) ),
inference(resolution,[],[f22,f2]) ).
fof(f421,definition,
( spl0_8
<=> subclass(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f423,plain,
( subclass(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f421]) ).
fof(f499,plain,
subclass(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),
inference(resolution,[],[f182,f158]) ).
fof(f511,plain,
spl0_8,
inference(avatar_split_clause,[],[f499,f421]) ).
fof(f513,plain,
( null_class = intersection(complement(singleton(not_subclass_element(x,null_class))),x)
| ~ spl0_8 ),
inference(resolution,[],[f423,f116]) ).
fof(f535,plain,
( member(not_subclass_element(null_class,null_class),null_class)
| x = singleton(not_subclass_element(x,null_class))
| null_class = x
| ~ spl0_8 ),
inference(superposition,[],[f157,f513]) ).
fof(f544,plain,
( x = singleton(not_subclass_element(x,null_class))
| null_class = x
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f535,f113]) ).
fof(f547,plain,
( null_class = x
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f544,f160]) ).
fof(f548,plain,
( $false
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f547,f162]) ).
fof(f549,plain,
~ spl0_8,
inference(avatar_contradiction_clause,[],[f548]) ).
cnf(s9,plain,
spl0_8,
inference(sat_conversion,[],[f511]) ).
cnf(s11,plain,
~ spl0_8,
inference(sat_conversion,[],[f549]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s9,s11]) ).
fof(f550,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET098-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n017.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 00:36:05 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 3.69/1.43 % (3112492)Input is clausal, will run a generic CNF schedule.
% 3.69/1.43 % (3112497)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=1713421767:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.69/1.43 % (3112499)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3914554838:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.69/1.43 % (3112500)lrs+10_1_sil=8000:sp=occurrence:random_seed=2555382855:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.69/1.43 % (3112503)dis-21_1_sil=8000:lcm=predicate:random_seed=3820544737: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)
% 3.69/1.43 % (3112501)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3337989451:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.69/1.43 % (3112498)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1697034799:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.69/1.43 % (3112502)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2124996852:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.69/1.43 % (3112500)First to succeed.
% 3.69/1.43 % (3112500)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3112492"
% 3.69/1.43 % (3112501)Also succeeded, but the first one will report.
% 3.69/1.43 % (3112503)Instruction limit reached!
% 3.69/1.43 % (3112503)------------------------------
% 3.69/1.43 % (3112503)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.43 % (3112503)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.43 % (3112503)CaDiCaL version: 2.1.3
% 3.69/1.43 % (3112503)Termination reason: Instruction limit
% 3.69/1.43 % (3112503)Termination phase: Saturation
% 3.69/1.43 % (3112503)Time elapsed: 0.076 s
% 3.69/1.43 % (3112503)Peak memory usage: 89 MB
% 3.69/1.43 % (3112503)Instructions burned: 117 (million)
% 3.69/1.43 % (3112502)Also succeeded, but the first one will report.
% 3.69/1.43 % (3112511)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=878612060:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.69/1.43 % (3112511)Refutation not found, incomplete strategy
% 3.69/1.43 % (3112511)------------------------------
% 3.69/1.43 % (3112511)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.43 % (3112511)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.43 % (3112511)CaDiCaL version: 2.1.3
% 3.69/1.43 % (3112511)Termination reason: Refutation not found, incomplete strategy
% 3.69/1.43 % (3112511)Time elapsed: 0.004 s
% 3.69/1.43 % (3112511)Peak memory usage: 88 MB
% 3.69/1.43 % (3112511)Instructions burned: 4 (million)
% 3.69/1.43 % (3112500)Refutation found. Thanks to Tanya!
% 3.69/1.43 % SZS status Unsatisfiable for theBenchmark
% 3.69/1.43 % SZS output start Proof for theBenchmark
% See solution above
% 3.69/1.43 % (3112500)------------------------------
% 3.69/1.43 % (3112500)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.43 % (3112500)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.43 % (3112500)CaDiCaL version: 2.1.3
% 3.69/1.43 % (3112500)Termination reason: Refutation
% 3.69/1.43 % (3112500)Time elapsed: 0.012 s
% 3.69/1.43 % (3112500)Peak memory usage: 89 MB
% 3.69/1.43 % (3112500)Instructions burned: 13 (million)
% 3.69/1.43 % (3112500)------------------------------
% 3.69/1.43 % (3112500)------------------------------
% 3.69/1.43 % (3112492)Success in time 0.454 s
% 3.69/1.43 % Vampire exiting
%------------------------------------------------------------------------------