%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET099-7 : 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 : n013.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 2.64s 1.32s
% Output : Refutation 2.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of formulae : 45 ( 19 unt; 3 def)
% Number of atoms : 77 ( 23 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 65 ( 33 ~; 30 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 19 ( 0 sgn 19 !; 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(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f9,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair2) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set) ).
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(f117,axiom,
! [X0] :
( X0 = null_class
| member(not_subclass_element(X0,null_class),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',null_class_is_unique) ).
fof(f118,plain,
! [X0] :
( member(not_subclass_element(X0,null_class),X0)
| null_class = X0 ),
inference(reorient_equations,[],[f117]) ).
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/sandbox2/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,
not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class) = not_subclass_element(x,null_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_2_to_number_of_elements_in_class_1) ).
fof(f159,plain,
not_subclass_element(x,null_class) = not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),
inference(reorient_equations,[],[f158]) ).
fof(f160,negated_conjecture,
singleton(not_subclass_element(x,null_class)) != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_2_to_number_of_elements_in_class_2) ).
fof(f161,plain,
x != singleton(not_subclass_element(x,null_class)),
inference(reorient_equations,[],[f160]) ).
fof(f162,negated_conjecture,
x != null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_2_to_number_of_elements_in_class_3) ).
fof(f163,plain,
null_class != x,
inference(reorient_equations,[],[f162]) ).
fof(f165,plain,
not_subclass_element(x,null_class) = not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class),
inference(definition_unfolding,[],[f159,f12]) ).
fof(f166,plain,
x != unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)),
inference(definition_unfolding,[],[f161,f12]) ).
fof(f167,plain,
! [X0] :
( member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(X0,null_class),not_subclass_element(X0,null_class))),X0),null_class),intersection(complement(unordered_pair(not_subclass_element(X0,null_class),not_subclass_element(X0,null_class))),X0))
| unordered_pair(not_subclass_element(X0,null_class),not_subclass_element(X0,null_class)) = X0
| null_class = X0 ),
inference(definition_unfolding,[],[f157,f12,f12,f12]) ).
fof(f194,definition,
~ sP0(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f195,plain,
sP0(x),
inference(inequality_splitting,[],[f166,f194]) ).
fof(f214,definition,
( spl1_2
<=> member(not_subclass_element(x,null_class),intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x)) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f215,plain,
( member(not_subclass_element(x,null_class),intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x))
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f214]) ).
fof(f227,plain,
( member(not_subclass_element(x,null_class),complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))))
| ~ spl1_2 ),
inference(resolution,[],[f21,f215]) ).
fof(f230,plain,
( ~ member(not_subclass_element(x,null_class),unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)))
| ~ spl1_2 ),
inference(resolution,[],[f227,f24]) ).
fof(f241,plain,
( ~ member(not_subclass_element(x,null_class),universal_class)
| ~ spl1_2 ),
inference(resolution,[],[f230,f9]) ).
fof(f303,plain,
( ! [X0] :
( ~ member(not_subclass_element(x,null_class),X0)
| ~ subclass(X0,universal_class) )
| ~ spl1_2 ),
inference(resolution,[],[f1,f241]) ).
fof(f304,plain,
( ! [X0] : ~ member(not_subclass_element(x,null_class),X0)
| ~ spl1_2 ),
inference(forward_subsumption_resolution,[],[f303,f4]) ).
fof(f305,plain,
( null_class = x
| ~ spl1_2 ),
inference(resolution,[],[f304,f118]) ).
fof(f319,plain,
( $false
| ~ spl1_2 ),
inference(forward_subsumption_resolution,[],[f305,f163]) ).
fof(f320,plain,
~ spl1_2,
inference(avatar_contradiction_clause,[],[f319]) ).
fof(f1122,plain,
( member(not_subclass_element(x,null_class),intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x))
| x = unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))
| null_class = x ),
inference(superposition,[],[f167,f165]) ).
fof(f1136,plain,
( member(not_subclass_element(x,null_class),intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x))
| x = unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)) ),
inference(forward_subsumption_resolution,[],[f1122,f163]) ).
fof(f1146,definition,
( spl1_24
<=> x = unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)) ),
introduced(definition,[new_symbols(definition,[spl1_24])],[avatar_definition]) ).
fof(f1147,plain,
( x = unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))
| ~ spl1_24 ),
inference(avatar_component_clause,[],[f1146]) ).
fof(f1148,plain,
( spl1_24
| spl1_2 ),
inference(avatar_split_clause,[],[f1136,f214,f1146]) ).
fof(f1160,plain,
( ~ sP0(x)
| ~ spl1_24 ),
inference(superposition,[],[f194,f1147]) ).
fof(f1221,plain,
( $false
| ~ spl1_24 ),
inference(forward_subsumption_resolution,[],[f1160,f195]) ).
fof(f1222,plain,
~ spl1_24,
inference(avatar_contradiction_clause,[],[f1221]) ).
cnf(s6,plain,
~ spl1_2,
inference(sat_conversion,[],[f320]) ).
cnf(s33,plain,
( spl1_2
| spl1_24 ),
inference(sat_conversion,[],[f1148]) ).
cnf(s35,plain,
~ spl1_24,
inference(sat_conversion,[],[f1222]) ).
cnf(s38,plain,
spl1_2,
inference(rat,[],[s33,s35]) ).
cnf(s40,plain,
$false,
inference(rat,[],[s6,s38]) ).
fof(f1224,plain,
$false,
inference(avatar_sat_refutation,[],[s40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET099-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n013.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 00:41:37 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.39 Running first-order theorem proving
% 0.10/0.39 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
% 2.64/1.32 % (706466)Input is clausal, will run a generic CNF schedule.
% 2.64/1.32 % (706475)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3522452041:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.64/1.32 % (706475)First to succeed.
% 2.64/1.32 % (706475)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-706466"
% 2.64/1.32 % (706476)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1796350901:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.64/1.32 % (706474)lrs+10_1_sil=8000:sp=occurrence:random_seed=2368519944:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.64/1.32 % (706473)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2797249525:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.64/1.32 % (706471)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=951661924:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.64/1.32 % (706472)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=611533837:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.64/1.32 % (706477)dis-21_1_sil=8000:lcm=predicate:random_seed=1437424157: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)
% 2.64/1.32 % (706474)Also succeeded, but the first one will report.
% 2.64/1.32 % (706476)Also succeeded, but the first one will report.
% 2.64/1.32 % (706477)Instruction limit reached!
% 2.64/1.32 % (706477)------------------------------
% 2.64/1.32 % (706477)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.64/1.32 % (706477)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.64/1.32 % (706477)CaDiCaL version: 2.1.3
% 2.64/1.32 % (706477)Termination reason: Instruction limit
% 2.64/1.32 % (706477)Termination phase: Saturation
% 2.64/1.32 % (706477)Time elapsed: 0.074 s
% 2.64/1.32 % (706477)Peak memory usage: 89 MB
% 2.64/1.32 % (706477)Instructions burned: 117 (million)
% 2.64/1.32 % (706475)Refutation found. Thanks to Tanya!
% 2.64/1.32 % SZS status Unsatisfiable for theBenchmark
% 2.64/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 2.64/1.32 % (706475)------------------------------
% 2.64/1.32 % (706475)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.64/1.32 % (706475)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.64/1.32 % (706475)CaDiCaL version: 2.1.3
% 2.64/1.32 % (706475)Termination reason: Refutation
% 2.64/1.32 % (706475)Time elapsed: 0.017 s
% 2.64/1.32 % (706475)Peak memory usage: 90 MB
% 2.64/1.32 % (706475)Instructions burned: 45 (million)
% 2.64/1.32 % (706475)------------------------------
% 2.64/1.32 % (706475)------------------------------
% 2.64/1.32 % (706466)Success in time 0.29 s
% 2.64/1.32 % Vampire exiting
%------------------------------------------------------------------------------