%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU319+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 12:52:51 PM UTC 2026
% Result : Theorem 0.10s 0.42s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 8 unt; 2 def)
% Number of atoms : 119 ( 5 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 123 ( 48 ~; 47 |; 12 &)
% ( 6 <=>; 9 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 29 ( 0 sgn 23 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( closed_subset(X1,X0)
<=> open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_pre_topc) ).
fof(f7,axiom,
! [X0] :
( top_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
fof(f17,axiom,
! [X0] :
( one_sorted_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset_complement(the_carrier(X0),X1) = subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_pre_topc) ).
fof(f18,conjecture,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( closed_subset(X1,X0)
<=> open_subset(subset_complement(the_carrier(X0),X1),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_tops_1) ).
fof(f19,negated_conjecture,
~ ! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( closed_subset(X1,X0)
<=> open_subset(subset_complement(the_carrier(X0),X1),X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f23,plain,
! [X0] :
( ! [X1] :
( ( closed_subset(X1,X0)
<=> open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f28,plain,
! [X0] :
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f32,plain,
! [X0] :
( ! [X1] :
( subset_complement(the_carrier(X0),X1) = subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1)
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f33,plain,
? [X0] :
( ? [X1] :
( ( closed_subset(X1,X0)
<~> open_subset(subset_complement(the_carrier(X0),X1),X0) )
& element(X1,powerset(the_carrier(X0))) )
& top_str(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f35,plain,
! [X0] :
( ! [X1] :
( ( ( closed_subset(X1,X0)
| ~ open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0) )
& ( open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0)
| ~ closed_subset(X1,X0) ) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(nnf_transformation,[],[f23]) ).
fof(f39,plain,
? [X0] :
( ? [X1] :
( ( ~ open_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ closed_subset(X1,X0) )
& ( open_subset(subset_complement(the_carrier(X0),X1),X0)
| closed_subset(X1,X0) )
& element(X1,powerset(the_carrier(X0))) )
& top_str(X0) ),
inference(nnf_transformation,[],[f33]) ).
fof(f40,plain,
? [X0] :
( ? [X1] :
( ( ~ open_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ closed_subset(X1,X0) )
& ( open_subset(subset_complement(the_carrier(X0),X1),X0)
| closed_subset(X1,X0) )
& element(X1,powerset(the_carrier(X0))) )
& top_str(X0) ),
inference(flattening,[],[f39]) ).
fof(f41,plain,
( ( ~ open_subset(subset_complement(the_carrier(sK3),sK4),sK3)
| ~ closed_subset(sK4,sK3) )
& ( open_subset(subset_complement(the_carrier(sK3),sK4),sK3)
| closed_subset(sK4,sK3) )
& element(sK4,powerset(the_carrier(sK3)))
& top_str(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f40]) ).
fof(f42,plain,
! [X0,X1] :
( open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0)
| ~ closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f43,plain,
! [X0,X1] :
( ~ open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0)
| closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f47,plain,
! [X0] :
( ~ top_str(X0)
| one_sorted_str(X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f54,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1) = subset_complement(the_carrier(X0),X1)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f55,plain,
top_str(sK3),
inference(cnf_transformation,[],[f41]) ).
fof(f56,plain,
element(sK4,powerset(the_carrier(sK3))),
inference(cnf_transformation,[],[f41]) ).
fof(f57,plain,
( open_subset(subset_complement(the_carrier(sK3),sK4),sK3)
| closed_subset(sK4,sK3) ),
inference(cnf_transformation,[],[f41]) ).
fof(f58,plain,
( ~ open_subset(subset_complement(the_carrier(sK3),sK4),sK3)
| ~ closed_subset(sK4,sK3) ),
inference(cnf_transformation,[],[f41]) ).
fof(f61,definition,
( spl5_1
<=> closed_subset(sK4,sK3) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f65,definition,
( spl5_2
<=> open_subset(subset_complement(the_carrier(sK3),sK4),sK3) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f68,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f57,f65,f61]) ).
fof(f69,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f58,f65,f61]) ).
fof(f70,plain,
one_sorted_str(sK3),
inference(resolution,[],[f47,f55]) ).
fof(f106,plain,
( subset_complement(the_carrier(sK3),sK4) = subset_difference(the_carrier(sK3),cast_as_carrier_subset(sK3),sK4)
| ~ one_sorted_str(sK3) ),
inference(resolution,[],[f54,f56]) ).
fof(f108,plain,
subset_complement(the_carrier(sK3),sK4) = subset_difference(the_carrier(sK3),cast_as_carrier_subset(sK3),sK4),
inference(forward_subsumption_resolution,[],[f106,f70]) ).
fof(f110,plain,
( ~ open_subset(subset_complement(the_carrier(sK3),sK4),sK3)
| closed_subset(sK4,sK3)
| ~ element(sK4,powerset(the_carrier(sK3)))
| ~ top_str(sK3) ),
inference(superposition,[],[f43,f108]) ).
fof(f111,plain,
( open_subset(subset_complement(the_carrier(sK3),sK4),sK3)
| ~ closed_subset(sK4,sK3)
| ~ element(sK4,powerset(the_carrier(sK3)))
| ~ top_str(sK3) ),
inference(superposition,[],[f42,f108]) ).
fof(f118,plain,
( open_subset(subset_complement(the_carrier(sK3),sK4),sK3)
| ~ closed_subset(sK4,sK3)
| ~ top_str(sK3) ),
inference(forward_subsumption_resolution,[],[f111,f56]) ).
fof(f119,plain,
( ~ open_subset(subset_complement(the_carrier(sK3),sK4),sK3)
| closed_subset(sK4,sK3)
| ~ top_str(sK3) ),
inference(forward_subsumption_resolution,[],[f110,f56]) ).
fof(f120,plain,
( open_subset(subset_complement(the_carrier(sK3),sK4),sK3)
| ~ closed_subset(sK4,sK3) ),
inference(forward_subsumption_resolution,[],[f118,f55]) ).
fof(f121,plain,
( ~ open_subset(subset_complement(the_carrier(sK3),sK4),sK3)
| closed_subset(sK4,sK3) ),
inference(forward_subsumption_resolution,[],[f119,f55]) ).
fof(f122,plain,
( ~ spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f120,f65,f61]) ).
fof(f123,plain,
( spl5_1
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f121,f65,f61]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f68]) ).
cnf(s2,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(sat_conversion,[],[f69]) ).
cnf(s4,plain,
( ~ spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f122]) ).
cnf(s5,plain,
( spl5_1
| ~ spl5_2 ),
inference(sat_conversion,[],[f123]) ).
cnf(s6,plain,
spl5_1,
inference(rat,[],[s1,s5]) ).
cnf(s7,plain,
spl5_2,
inference(rat,[],[s4,s6]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s2,s7,s6]) ).
fof(f124,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU319+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 04:40:07 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.39 Running first-order model finding
% 0.10/0.39 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
% 0.10/0.42 % (806309)Will run a generic schedule for satisfiability detection.
% 0.10/0.42 % (806317)dis+10_1_sil=32000:sp=arity:random_seed=1599369050:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.42 % (806317) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-806309-806317"...
% 0.10/0.42 % (806315)% WARNING: option uhcvi not known.
% 0.10/0.42 % (806317)...printing done.
% 0.10/0.42 % (806317)Refutation found. Thanks to Tanya!
% 0.10/0.42 % SZS status Theorem for theBenchmark
% 0.10/0.42 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.42 % (806317)------------------------------
% 0.10/0.42 % (806317)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.42 % (806317)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.42 % (806317)CaDiCaL version: 2.1.3
% 0.10/0.42 % (806317)Termination reason: Refutation
% 0.10/0.42 % (806317)Time elapsed: 0.002 s
% 0.10/0.42 % (806317)Peak memory usage: 12 MB
% 0.10/0.42 % (806317)Instructions burned: 4 (million)
% 0.10/0.42 % (806309)Success in time 0.026 s
% 0.10/0.42 % Vampire exiting
%------------------------------------------------------------------------------