%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU311+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n015.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 12:52:49 PM UTC 2026
% Result : Theorem 0.23s 0.46s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 5
% Syntax : Number of formulae : 55 ( 12 unt; 0 def)
% Number of atoms : 216 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 253 ( 92 ~; 94 |; 47 &)
% ( 9 <=>; 9 =>; 0 <=; 2 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 89 ( 69 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1] :
( ( topological_space(X0)
& top_str(X0)
& element(X1,powerset(powerset(the_carrier(X0)))) )
=> ? [X2] :
( element(X2,powerset(powerset(the_carrier(X0))))
& ! [X3] :
( element(X3,powerset(the_carrier(X0)))
=> ( in(X3,X2)
<=> in(set_difference(cast_as_carrier_subset(X0),X3),X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s3_subset_1__e2_37_1_1__pre_topc) ).
fof(f2,negated_conjecture,
~ ! [X0,X1] :
( ( topological_space(X0)
& top_str(X0)
& element(X1,powerset(powerset(the_carrier(X0)))) )
=> ? [X2] :
( element(X2,powerset(powerset(the_carrier(X0))))
& ! [X3] :
( element(X3,powerset(the_carrier(X0)))
=> ( in(X3,X2)
<=> in(set_difference(cast_as_carrier_subset(X0),X3),X1) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f36,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f37,axiom,
! [X0,X1] :
( ( topological_space(X0)
& top_str(X0)
& element(X1,powerset(powerset(the_carrier(X0)))) )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( in(X3,powerset(the_carrier(X0)))
& in(set_difference(cast_as_carrier_subset(X0),X3),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e2_37_1_1__pre_topc__1) ).
fof(f38,axiom,
! [X0,X1] :
( ( ~ empty(X0)
=> ( element(X1,X0)
<=> in(X1,X0) ) )
& ( empty(X0)
=> ( element(X1,X0)
<=> empty(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
fof(f42,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
=> in(X2,X1) )
=> element(X0,powerset(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l71_subset_1) ).
fof(f65,plain,
? [X0,X1] :
( ! [X2] :
( ~ element(X2,powerset(powerset(the_carrier(X0))))
| ? [X3] :
( ( in(X3,X2)
<~> in(set_difference(cast_as_carrier_subset(X0),X3),X1) )
& element(X3,powerset(the_carrier(X0))) ) )
& topological_space(X0)
& top_str(X0)
& element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(ennf_transformation,[],[f2]) ).
fof(f66,plain,
? [X0,X1] :
( ! [X2] :
( ~ element(X2,powerset(powerset(the_carrier(X0))))
| ? [X3] :
( ( in(X3,X2)
<~> in(set_difference(cast_as_carrier_subset(X0),X3),X1) )
& element(X3,powerset(the_carrier(X0))) ) )
& topological_space(X0)
& top_str(X0)
& element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(flattening,[],[f65]) ).
fof(f88,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( in(X3,powerset(the_carrier(X0)))
& in(set_difference(cast_as_carrier_subset(X0),X3),X1) ) )
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(ennf_transformation,[],[f37]) ).
fof(f89,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( in(X3,powerset(the_carrier(X0)))
& in(set_difference(cast_as_carrier_subset(X0),X3),X1) ) )
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(flattening,[],[f88]) ).
fof(f90,plain,
! [X0,X1] :
( ( ( element(X1,X0)
<=> in(X1,X0) )
| empty(X0) )
& ( ( element(X1,X0)
<=> empty(X1) )
| ~ empty(X0) ) ),
inference(ennf_transformation,[],[f38]) ).
fof(f91,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) ),
inference(ennf_transformation,[],[f42]) ).
fof(f95,plain,
? [X0,X1] :
( ! [X2] :
( ~ element(X2,powerset(powerset(the_carrier(X0))))
| ? [X3] :
( ( ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| ~ in(X3,X2) )
& ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| in(X3,X2) )
& element(X3,powerset(the_carrier(X0))) ) )
& topological_space(X0)
& top_str(X0)
& element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(nnf_transformation,[],[f66]) ).
fof(f96,plain,
? [X0,X1] :
( ! [X2] :
( ~ element(X2,powerset(powerset(the_carrier(X0))))
| ? [X3] :
( ( ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| ~ in(X3,X2) )
& ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| in(X3,X2) )
& element(X3,powerset(the_carrier(X0))) ) )
& topological_space(X0)
& top_str(X0)
& element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(flattening,[],[f95]) ).
fof(f97,plain,
( ! [X2] :
( ~ element(X2,powerset(powerset(the_carrier(sK0))))
| ( ( ~ in(set_difference(cast_as_carrier_subset(sK0),sK2(X2)),sK1)
| ~ in(sK2(X2),X2) )
& ( in(set_difference(cast_as_carrier_subset(sK0),sK2(X2)),sK1)
| in(sK2(X2),X2) )
& element(sK2(X2),powerset(the_carrier(sK0))) ) )
& topological_space(sK0)
& top_str(sK0)
& element(sK1,powerset(powerset(the_carrier(sK0)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X3,sK2(X2))],[f96]) ).
fof(f102,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( in(X3,X2)
| ~ in(X3,powerset(the_carrier(X0)))
| ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1) )
& ( ( in(X3,powerset(the_carrier(X0)))
& in(set_difference(cast_as_carrier_subset(X0),X3),X1) )
| ~ in(X3,X2) ) )
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(nnf_transformation,[],[f89]) ).
fof(f103,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( in(X3,X2)
| ~ in(X3,powerset(the_carrier(X0)))
| ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1) )
& ( ( in(X3,powerset(the_carrier(X0)))
& in(set_difference(cast_as_carrier_subset(X0),X3),X1) )
| ~ in(X3,X2) ) )
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(flattening,[],[f102]) ).
fof(f104,plain,
! [X0,X1] :
( ! [X3] :
( ( in(X3,sK7(X0,X1))
| ~ in(X3,powerset(the_carrier(X0)))
| ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1) )
& ( ( in(X3,powerset(the_carrier(X0)))
& in(set_difference(cast_as_carrier_subset(X0),X3),X1) )
| ~ in(X3,sK7(X0,X1)) ) )
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X2,sK7(X0,X1))],[f103]) ).
fof(f105,plain,
! [X0,X1] :
( ( ( ( element(X1,X0)
| ~ in(X1,X0) )
& ( in(X1,X0)
| ~ element(X1,X0) ) )
| empty(X0) )
& ( ( ( element(X1,X0)
| ~ empty(X1) )
& ( empty(X1)
| ~ element(X1,X0) ) )
| ~ empty(X0) ) ),
inference(nnf_transformation,[],[f90]) ).
fof(f107,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ( ~ in(sK9(X0,X1),X1)
& in(sK9(X0,X1),X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X2,sK9(X0,X1))],[f91]) ).
fof(f110,plain,
element(sK1,powerset(powerset(the_carrier(sK0)))),
inference(cnf_transformation,[],[f97]) ).
fof(f111,plain,
top_str(sK0),
inference(cnf_transformation,[],[f97]) ).
fof(f112,plain,
topological_space(sK0),
inference(cnf_transformation,[],[f97]) ).
fof(f113,plain,
! [X2] :
( ~ element(X2,powerset(powerset(the_carrier(sK0))))
| element(sK2(X2),powerset(the_carrier(sK0))) ),
inference(cnf_transformation,[],[f97]) ).
fof(f114,plain,
! [X2] :
( ~ element(X2,powerset(powerset(the_carrier(sK0))))
| in(set_difference(cast_as_carrier_subset(sK0),sK2(X2)),sK1)
| in(sK2(X2),X2) ),
inference(cnf_transformation,[],[f97]) ).
fof(f115,plain,
! [X2] :
( ~ in(set_difference(cast_as_carrier_subset(sK0),sK2(X2)),sK1)
| ~ element(X2,powerset(powerset(the_carrier(sK0))))
| ~ in(sK2(X2),X2) ),
inference(cnf_transformation,[],[f97]) ).
fof(f169,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f36]) ).
fof(f170,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ in(X3,sK7(X0,X1))
| ~ topological_space(X0)
| ~ top_str(X0)
| in(set_difference(cast_as_carrier_subset(X0),X3),X1) ),
inference(cnf_transformation,[],[f104]) ).
fof(f171,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ in(X3,sK7(X0,X1))
| ~ topological_space(X0)
| ~ top_str(X0)
| in(X3,powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f104]) ).
fof(f172,plain,
! [X3,X0,X1] :
( ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| ~ in(X3,powerset(the_carrier(X0)))
| in(X3,sK7(X0,X1))
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f104]) ).
fof(f175,plain,
! [X0,X1] :
( ~ element(X1,X0)
| in(X1,X0)
| empty(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f179,plain,
! [X0,X1] :
( in(sK9(X0,X1),X0)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f107]) ).
fof(f180,plain,
! [X0,X1] :
( ~ in(sK9(X0,X1),X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f107]) ).
fof(f683,plain,
! [X0] :
( ~ in(X0,sK7(sK0,sK1))
| ~ topological_space(sK0)
| ~ top_str(sK0)
| in(X0,powerset(the_carrier(sK0))) ),
inference(resolution,[],[f171,f110]) ).
fof(f689,plain,
! [X0] :
( ~ in(X0,sK7(sK0,sK1))
| ~ top_str(sK0)
| in(X0,powerset(the_carrier(sK0))) ),
inference(forward_subsumption_resolution,[],[f683,f112]) ).
fof(f690,plain,
! [X0] :
( ~ in(X0,sK7(sK0,sK1))
| in(X0,powerset(the_carrier(sK0))) ),
inference(forward_subsumption_resolution,[],[f689,f111]) ).
fof(f694,plain,
! [X0] :
( ~ in(X0,sK7(sK0,sK1))
| ~ topological_space(sK0)
| ~ top_str(sK0)
| in(set_difference(cast_as_carrier_subset(sK0),X0),sK1) ),
inference(resolution,[],[f170,f110]) ).
fof(f701,plain,
! [X0] :
( ~ in(X0,sK7(sK0,sK1))
| ~ top_str(sK0)
| in(set_difference(cast_as_carrier_subset(sK0),X0),sK1) ),
inference(forward_subsumption_resolution,[],[f694,f112]) ).
fof(f702,plain,
! [X0] :
( in(set_difference(cast_as_carrier_subset(sK0),X0),sK1)
| ~ in(X0,sK7(sK0,sK1)) ),
inference(forward_subsumption_resolution,[],[f701,f111]) ).
fof(f717,plain,
! [X0] :
( in(sK9(sK7(sK0,sK1),X0),powerset(the_carrier(sK0)))
| element(sK7(sK0,sK1),powerset(X0)) ),
inference(resolution,[],[f690,f179]) ).
fof(f865,plain,
( element(sK7(sK0,sK1),powerset(powerset(the_carrier(sK0))))
| element(sK7(sK0,sK1),powerset(powerset(the_carrier(sK0)))) ),
inference(resolution,[],[f717,f180]) ).
fof(f869,plain,
element(sK7(sK0,sK1),powerset(powerset(the_carrier(sK0)))),
inference(duplicate_literal_removal,[],[f865]) ).
fof(f870,plain,
( in(set_difference(cast_as_carrier_subset(sK0),sK2(sK7(sK0,sK1))),sK1)
| in(sK2(sK7(sK0,sK1)),sK7(sK0,sK1)) ),
inference(resolution,[],[f869,f114]) ).
fof(f871,plain,
element(sK2(sK7(sK0,sK1)),powerset(the_carrier(sK0))),
inference(resolution,[],[f869,f113]) ).
fof(f894,plain,
in(set_difference(cast_as_carrier_subset(sK0),sK2(sK7(sK0,sK1))),sK1),
inference(forward_subsumption_resolution,[],[f870,f702]) ).
fof(f912,plain,
( in(sK2(sK7(sK0,sK1)),powerset(the_carrier(sK0)))
| empty(powerset(the_carrier(sK0))) ),
inference(resolution,[],[f871,f175]) ).
fof(f914,plain,
in(sK2(sK7(sK0,sK1)),powerset(the_carrier(sK0))),
inference(forward_subsumption_resolution,[],[f912,f169]) ).
fof(f922,plain,
( ~ element(sK7(sK0,sK1),powerset(powerset(the_carrier(sK0))))
| ~ in(sK2(sK7(sK0,sK1)),sK7(sK0,sK1)) ),
inference(resolution,[],[f894,f115]) ).
fof(f926,plain,
( ~ in(sK2(sK7(sK0,sK1)),powerset(the_carrier(sK0)))
| in(sK2(sK7(sK0,sK1)),sK7(sK0,sK1))
| ~ topological_space(sK0)
| ~ top_str(sK0)
| ~ element(sK1,powerset(powerset(the_carrier(sK0)))) ),
inference(resolution,[],[f894,f172]) ).
fof(f927,plain,
( in(sK2(sK7(sK0,sK1)),sK7(sK0,sK1))
| ~ topological_space(sK0)
| ~ top_str(sK0)
| ~ element(sK1,powerset(powerset(the_carrier(sK0)))) ),
inference(forward_subsumption_resolution,[],[f926,f914]) ).
fof(f928,plain,
~ in(sK2(sK7(sK0,sK1)),sK7(sK0,sK1)),
inference(forward_subsumption_resolution,[],[f922,f869]) ).
fof(f929,plain,
( in(sK2(sK7(sK0,sK1)),sK7(sK0,sK1))
| ~ top_str(sK0)
| ~ element(sK1,powerset(powerset(the_carrier(sK0)))) ),
inference(forward_subsumption_resolution,[],[f927,f112]) ).
fof(f930,plain,
( in(sK2(sK7(sK0,sK1)),sK7(sK0,sK1))
| ~ element(sK1,powerset(powerset(the_carrier(sK0)))) ),
inference(forward_subsumption_resolution,[],[f929,f111]) ).
fof(f931,plain,
in(sK2(sK7(sK0,sK1)),sK7(sK0,sK1)),
inference(forward_subsumption_resolution,[],[f930,f110]) ).
fof(f933,plain,
$false,
inference(forward_subsumption_resolution,[],[f931,f928]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU311+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n015.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 04:41:47 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.23/0.46 % (2261481)Will run a generic schedule for satisfiability detection.
% 0.23/0.46 % (2261490)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2042183827:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.23/0.46 % (2261487)% WARNING: option uhcvi not known.
% 0.23/0.46 % (2261486)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=954111266_2999 on theBenchmark for (2999ds/0Mi)
% 0.23/0.46 % (2261487)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2510957043:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.23/0.46 % (2261488)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2261669012:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.23/0.46 % (2261489)dis+10_1_sil=32000:sp=arity:random_seed=2688817287:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.23/0.46 % (2261492)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1760046832:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.23/0.46 % (2261491)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2159379438:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.23/0.46 % TRYING [1]
% 0.23/0.46 % TRYING [2]
% 0.23/0.46 % TRYING [3]
% 0.23/0.46 % TRYING [4]
% 0.23/0.46 % (2261489) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2261481-2261489"...
% 0.23/0.46 % (2261489)...printing done.
% 0.23/0.46 % (2261489)Refutation found. Thanks to Tanya!
% 0.23/0.46 % SZS status Theorem for theBenchmark
% 0.23/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.47 % (2261489)------------------------------
% 0.23/0.47 % (2261489)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.47 % (2261489)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.47 % (2261489)CaDiCaL version: 2.1.3
% 0.23/0.47 % (2261489)Termination reason: Refutation
% 0.23/0.47 % (2261489)Time elapsed: 0.014 s
% 0.23/0.47 % (2261489)Peak memory usage: 12 MB
% 0.23/0.47 % (2261489)Instructions burned: 20 (million)
% 0.23/0.47 % (2261481)Success in time 0.049 s
% 0.23/0.47 % Vampire exiting
%------------------------------------------------------------------------------