%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM139-1 : 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 : n002.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 12:11:48 PM UTC 2026
% Result : Unsatisfiable 2.70s 1.35s
% Output : Refutation 2.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 17 ( 15 unt; 0 def)
% Number of atoms : 19 ( 8 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 5 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 11 ( 3 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 4 con; 0-3 aty)
% Number of variables : 17 ( 17 !; 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(f22,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection2) ).
fof(f29,axiom,
! [X2,X0,X1] : intersection(cross_product(X0,X1),X2) = restrict(X2,X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restriction2) ).
fof(f39,axiom,
! [X0] : domain_of(flip(cross_product(X0,universal_class))) = inverse(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
fof(f40,axiom,
! [X0] : domain_of(inverse(X0)) = range_of(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',range_of) ).
fof(f43,axiom,
! [X0,X1] : range_of(restrict(X0,X1,universal_class)) = image(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image) ).
fof(f56,axiom,
! [X0] : complement(image(element_relation,complement(X0))) = power_class(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_class_definition) ).
fof(f176,negated_conjecture,
~ member(not_subclass_element(intersection(power_class(x),z),x),z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_complete_induction3_1) ).
fof(f177,negated_conjecture,
~ subclass(intersection(power_class(x),z),x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_complete_induction3_2) ).
fof(f179,plain,
! [X0] : range_of(X0) = domain_of(domain_of(flip(cross_product(X0,universal_class)))),
inference(definition_unfolding,[],[f40,f39]) ).
fof(f180,plain,
! [X0,X1] : image(X0,X1) = domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class)))),
inference(definition_unfolding,[],[f43,f179,f29]) ).
fof(f190,plain,
! [X0] : power_class(X0) = complement(domain_of(domain_of(flip(cross_product(intersection(cross_product(complement(X0),universal_class),element_relation),universal_class))))),
inference(definition_unfolding,[],[f56,f180]) ).
fof(f192,plain,
~ member(not_subclass_element(intersection(complement(domain_of(domain_of(flip(cross_product(intersection(cross_product(complement(x),universal_class),element_relation),universal_class))))),z),x),z),
inference(definition_unfolding,[],[f176,f190]) ).
fof(f193,plain,
~ subclass(intersection(complement(domain_of(domain_of(flip(cross_product(intersection(cross_product(complement(x),universal_class),element_relation),universal_class))))),z),x),
inference(definition_unfolding,[],[f177,f190]) ).
fof(f284,plain,
member(not_subclass_element(intersection(complement(domain_of(domain_of(flip(cross_product(intersection(cross_product(complement(x),universal_class),element_relation),universal_class))))),z),x),intersection(complement(domain_of(domain_of(flip(cross_product(intersection(cross_product(complement(x),universal_class),element_relation),universal_class))))),z)),
inference(resolution,[],[f2,f193]) ).
fof(f287,plain,
member(not_subclass_element(intersection(complement(domain_of(domain_of(flip(cross_product(intersection(cross_product(complement(x),universal_class),element_relation),universal_class))))),z),x),z),
inference(resolution,[],[f22,f284]) ).
fof(f288,plain,
$false,
inference(resolution,[],[f287,f192]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM139-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n002.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 19:01:52 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 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
% 2.70/1.35 % (3818023)Input is clausal, will run a generic CNF schedule.
% 2.70/1.35 % (3818034)dis-21_1_sil=8000:lcm=predicate:random_seed=3617832701: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)
% 2.70/1.35 % (3818034)First to succeed.
% 2.70/1.35 % (3818034)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3818023"
% 2.70/1.35 % (3818031)lrs+10_1_sil=8000:sp=occurrence:random_seed=3215149370:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.70/1.35 % (3818028)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=4112897064:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.70/1.35 % (3818032)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2263232233:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.70/1.35 % (3818029)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1613417299:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.70/1.35 % (3818030)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=621660758:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.70/1.35 % (3818033)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2662046658:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.70/1.35 % (3818033)Also succeeded, but the first one will report.
% 2.70/1.35 % (3818031)Also succeeded, but the first one will report.
% 2.70/1.35 % (3818032)Also succeeded, but the first one will report.
% 2.70/1.35 % (3818034)Refutation found. Thanks to Tanya!
% 2.70/1.35 % SZS status Unsatisfiable for theBenchmark
% 2.70/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 2.70/1.35 % (3818034)------------------------------
% 2.70/1.35 % (3818034)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.70/1.35 % (3818034)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/1.35 % (3818034)CaDiCaL version: 2.1.3
% 2.70/1.35 % (3818034)Termination reason: Refutation
% 2.70/1.35 % (3818034)Time elapsed: 0.003 s
% 2.70/1.35 % (3818034)Peak memory usage: 88 MB
% 2.70/1.35 % (3818034)Instructions burned: 8 (million)
% 2.70/1.35 % (3818034)------------------------------
% 2.70/1.35 % (3818034)------------------------------
% 2.70/1.35 % (3818023)Success in time 0.301 s
% 2.70/1.35 % Vampire exiting
%------------------------------------------------------------------------------