%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET553-6 : 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 : n009.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 12:41:09 PM UTC 2026
% Result : Unsatisfiable 5.80s 1.97s
% Output : Refutation 5.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of formulae : 13 ( 10 unt; 0 def)
% Number of atoms : 16 ( 4 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 5 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 10 ( 3 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-2 aty)
% Number of variables : 11 ( 11 !; 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(f21,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection1) ).
fof(f39,axiom,
! [X0] : domain_of(flip(cross_product(X0,universal_class))) = inverse(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
fof(f81,axiom,
! [X0] : complement(domain_of(intersection(X0,identity_relation))) = diagonalise(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diagonalisation) ).
fof(f82,axiom,
! [X0] : intersection(domain_of(X0),diagonalise(compose(inverse(element_relation),X0))) = cantor(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cantor_class) ).
fof(f122,negated_conjecture,
~ subclass(cantor(x),domain_of(x)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cantor_class_alternate_defn_1) ).
fof(f127,plain,
! [X0] : cantor(X0) = intersection(domain_of(X0),complement(domain_of(intersection(compose(domain_of(flip(cross_product(element_relation,universal_class))),X0),identity_relation)))),
inference(definition_unfolding,[],[f82,f81,f39]) ).
fof(f135,plain,
~ subclass(intersection(domain_of(x),complement(domain_of(intersection(compose(domain_of(flip(cross_product(element_relation,universal_class))),x),identity_relation)))),domain_of(x)),
inference(definition_unfolding,[],[f122,f127]) ).
fof(f206,plain,
member(not_subclass_element(intersection(domain_of(x),complement(domain_of(intersection(compose(domain_of(flip(cross_product(element_relation,universal_class))),x),identity_relation)))),domain_of(x)),intersection(domain_of(x),complement(domain_of(intersection(compose(domain_of(flip(cross_product(element_relation,universal_class))),x),identity_relation))))),
inference(resolution,[],[f2,f135]) ).
fof(f207,plain,
~ member(not_subclass_element(intersection(domain_of(x),complement(domain_of(intersection(compose(domain_of(flip(cross_product(element_relation,universal_class))),x),identity_relation)))),domain_of(x)),domain_of(x)),
inference(resolution,[],[f3,f135]) ).
fof(f208,plain,
member(not_subclass_element(intersection(domain_of(x),complement(domain_of(intersection(compose(domain_of(flip(cross_product(element_relation,universal_class))),x),identity_relation)))),domain_of(x)),domain_of(x)),
inference(resolution,[],[f21,f206]) ).
fof(f210,plain,
$false,
inference(resolution,[],[f208,f207]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET553-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.43 % Computer : n009.cluster.edu
% 0.19/0.43 % Model : x86_64 x86_64
% 0.19/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.43 % Memory : 8046.5625MB
% 0.19/0.43 % OS : Linux 6.8.0-71-generic
% 0.19/0.43 % CPULimit : 300
% 0.19/0.43 % WCLimit : 300
% 0.19/0.43 % DateTime : Mon Sep 28 02:08:15 UTC 2026
% 0.19/0.43 % CPUTime :
% 0.19/0.43 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.49 Running first-order theorem proving
% 0.24/0.49 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
% 5.80/1.97 % (2600272)Input is clausal, will run a generic CNF schedule.
% 5.80/1.97 % (2600282)lrs+10_1_sil=8000:sp=occurrence:random_seed=2042288489:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.80/1.97 % (2600280)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=425758394:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.80/1.97 % (2600282)Refutation not found, incomplete strategy
% 5.80/1.97 % (2600282)------------------------------
% 5.80/1.97 % (2600282)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.80/1.97 % (2600282)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.80/1.97 % (2600282)CaDiCaL version: 2.1.3
% 5.80/1.97 % (2600282)Termination reason: Refutation not found, incomplete strategy
% 5.80/1.97 % (2600282)Time elapsed: 0.055 s
% 5.80/1.97 % (2600282)Peak memory usage: 90 MB
% 5.80/1.97 % (2600282)Instructions burned: 106 (million)
% 5.80/1.97 % (2600279)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=4137698035:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.80/1.97 % (2600285)dis-21_1_sil=8000:lcm=predicate:random_seed=199614809: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)
% 5.80/1.97 % (2600281)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1174072799:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.80/1.97 % (2600283)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1800744190:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.80/1.97 % (2600284)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=261114274:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.80/1.97 % (2600285)First to succeed.
% 5.80/1.97 % (2600285)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2600272"
% 5.80/1.97 % (2600283)Refutation not found, incomplete strategy
% 5.80/1.97 % (2600283)------------------------------
% 5.80/1.97 % (2600283)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.80/1.97 % (2600283)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.80/1.97 % (2600283)CaDiCaL version: 2.1.3
% 5.80/1.97 % (2600283)Termination reason: Refutation not found, incomplete strategy
% 5.80/1.97 % (2600283)Time elapsed: 0.022 s
% 5.80/1.97 % (2600283)Peak memory usage: 89 MB
% 5.80/1.97 % (2600283)Instructions burned: 17 (million)
% 5.80/1.97 % (2600284)Also succeeded, but the first one will report.
% 5.80/1.97 % (2600282)------------------------------
% 5.80/1.97 % (2600282)------------------------------
% 5.80/1.97 % (2600283)------------------------------
% 5.80/1.97 % (2600283)------------------------------
% 5.80/1.97 % (2600293)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=2309520893:i=143:sd=2:aac=none:ss=axioms:sgt=16_2995 on theBenchmark for (2995ds/143Mi)
% 5.80/1.97 % (2600285)Refutation found. Thanks to Tanya!
% 5.80/1.97 % SZS status Unsatisfiable for theBenchmark
% 5.80/1.97 % SZS output start Proof for theBenchmark
% See solution above
% 5.80/1.97 % (2600285)------------------------------
% 5.80/1.97 % (2600285)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.80/1.97 % (2600285)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.80/1.97 % (2600285)CaDiCaL version: 2.1.3
% 5.80/1.97 % (2600285)Termination reason: Refutation
% 5.80/1.97 % (2600285)Time elapsed: 0.008 s
% 5.80/1.97 % (2600285)Peak memory usage: 88 MB
% 5.80/1.97 % (2600285)Instructions burned: 7 (million)
% 5.80/1.97 % (2600285)------------------------------
% 5.80/1.97 % (2600285)------------------------------
% 5.80/1.97 % (2600272)Success in time 0.713 s
% 5.80/1.97 % Vampire exiting
%------------------------------------------------------------------------------