%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM049-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n020.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 12:17:53 PM UTC 2026
% Result : Unsatisfiable 0.19s 0.52s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of formulae : 27 ( 16 unt; 0 def)
% Number of atoms : 40 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 29 ( 16 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 11 ( 3 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-2 aty)
% Number of variables : 27 ( 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',subclass_members) ).
fof(f2,axiom,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).
fof(f3,axiom,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members2) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
fof(f21,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection1) ).
fof(f24,axiom,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).
fof(f25,axiom,
! [X0,X1] :
( member(X0,complement(X1))
| ~ member(X0,universal_class)
| member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement2) ).
fof(f26,axiom,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',union) ).
fof(f39,axiom,
! [X0] : domain_of(flip(cross_product(X0,universal_class))) = inverse(X0),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',inverse) ).
fof(f122,axiom,
! [X0] : union(X0,inverse(X0)) = symmetrization_of(X0),
file('/export/starexec/sandbox/benchmark/Axioms/NUM004-0.ax',symmetrization) ).
fof(f126,axiom,
! [X0,X1] :
( ~ subclass(cross_product(X0,X0),union(identity_relation,symmetrization_of(X1)))
| connected(X1,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM004-0.ax',connected2) ).
fof(f176,negated_conjecture,
subclass(cross_product(y,y),identity_relation),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_connect_class_property4_1) ).
fof(f177,negated_conjecture,
~ connected(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_connect_class_property4_2) ).
fof(f191,plain,
! [X0] : symmetrization_of(X0) = complement(intersection(complement(X0),complement(domain_of(flip(cross_product(X0,universal_class)))))),
inference(definition_unfolding,[],[f122,f26,f39]) ).
fof(f247,plain,
! [X0,X1] :
( connected(X1,X0)
| ~ subclass(cross_product(X0,X0),complement(intersection(complement(identity_relation),complement(complement(intersection(complement(X1),complement(domain_of(flip(cross_product(X1,universal_class)))))))))) ),
inference(definition_unfolding,[],[f126,f26,f191]) ).
fof(f312,plain,
! [X0,X1] :
( ~ member(X0,X1)
| member(X0,universal_class) ),
inference(resolution,[],[f1,f4]) ).
fof(f316,plain,
! [X0] :
( ~ member(X0,cross_product(y,y))
| member(X0,identity_relation) ),
inference(resolution,[],[f1,f176]) ).
fof(f750,plain,
~ subclass(cross_product(y,y),complement(intersection(complement(identity_relation),complement(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))))))),
inference(resolution,[],[f247,f177]) ).
fof(f964,plain,
~ member(not_subclass_element(cross_product(y,y),complement(intersection(complement(identity_relation),complement(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))))))),complement(intersection(complement(identity_relation),complement(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))))))),
inference(resolution,[],[f750,f3]) ).
fof(f965,plain,
member(not_subclass_element(cross_product(y,y),complement(intersection(complement(identity_relation),complement(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))))))),cross_product(y,y)),
inference(resolution,[],[f750,f2]) ).
fof(f1008,plain,
member(not_subclass_element(cross_product(y,y),complement(intersection(complement(identity_relation),complement(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))))))),identity_relation),
inference(resolution,[],[f965,f316]) ).
fof(f1010,plain,
member(not_subclass_element(cross_product(y,y),complement(intersection(complement(identity_relation),complement(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))))))),universal_class),
inference(resolution,[],[f965,f312]) ).
fof(f1354,plain,
( ~ member(not_subclass_element(cross_product(y,y),complement(intersection(complement(identity_relation),complement(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))))))),universal_class)
| member(not_subclass_element(cross_product(y,y),complement(intersection(complement(identity_relation),complement(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))))))),intersection(complement(identity_relation),complement(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class))))))))) ),
inference(resolution,[],[f964,f25]) ).
fof(f1355,plain,
member(not_subclass_element(cross_product(y,y),complement(intersection(complement(identity_relation),complement(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))))))),intersection(complement(identity_relation),complement(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class))))))))),
inference(forward_subsumption_resolution,[],[f1354,f1010]) ).
fof(f1393,plain,
member(not_subclass_element(cross_product(y,y),complement(intersection(complement(identity_relation),complement(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))))))),complement(identity_relation)),
inference(resolution,[],[f1355,f21]) ).
fof(f1936,plain,
~ member(not_subclass_element(cross_product(y,y),complement(intersection(complement(identity_relation),complement(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))))))),identity_relation),
inference(resolution,[],[f1393,f24]) ).
fof(f1938,plain,
$false,
inference(forward_subsumption_resolution,[],[f1936,f1008]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM049-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n020.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 : Sun Sep 27 18:46:04 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.43 Running first-order model finding
% 0.12/0.43 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.52 % (3678063)Will run a generic schedule for satisfiability detection.
% 0.19/0.52 % (3678072)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3704613534:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.52 % (3678069)% WARNING: option uhcvi not known.
% 0.19/0.52 % (3678068)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=311572181_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.52 % (3678069)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=693161921:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.52 % (3678071)dis+10_1_sil=32000:sp=arity:random_seed=220107220:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.52 % (3678070)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1455054585:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.52 % (3678073)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=886173296:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.52 % (3678074)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=963859032:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.52 % (3678072) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3678063-3678072"...
% 0.19/0.52 % (3678072)...printing done.
% 0.19/0.52 % (3678072)Refutation found. Thanks to Tanya!
% 0.19/0.52 % SZS status Unsatisfiable for theBenchmark
% 0.19/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.52 % (3678072)------------------------------
% 0.19/0.52 % (3678072)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.52 % (3678072)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.52 % (3678072)CaDiCaL version: 2.1.3
% 0.19/0.52 % (3678072)Termination reason: Refutation
% 0.19/0.52 % (3678072)Time elapsed: 0.036 s
% 0.19/0.52 % (3678072)Peak memory usage: 13 MB
% 0.19/0.52 % (3678072)Instructions burned: 110 (million)
% 0.19/0.52 % (3678063)Success in time 0.082 s
% 0.19/0.52 % Vampire exiting
%------------------------------------------------------------------------------