%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n001.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 12:48:19 PM UTC 2026
% Result : Theorem 2.82s 1.38s
% Output : Refutation 2.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 36 ( 5 unt; 0 def)
% Number of atoms : 124 ( 3 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 154 ( 66 ~; 62 |; 12 &)
% ( 4 <=>; 9 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 41 ( 35 !; 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(f21,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(f22,plain,
! [X0] :
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f7]) ).
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(f25,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(f30,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,[],[f21]) ).
fof(f31,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,[],[f30]) ).
fof(f32,plain,
( ( ~ open_subset(subset_complement(the_carrier(sK0),sK1),sK0)
| ~ closed_subset(sK1,sK0) )
& ( open_subset(subset_complement(the_carrier(sK0),sK1),sK0)
| closed_subset(sK1,sK0) )
& element(sK1,powerset(the_carrier(sK0)))
& top_str(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f31]) ).
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(f37,plain,
top_str(sK0),
inference(cnf_transformation,[],[f32]) ).
fof(f38,plain,
element(sK1,powerset(the_carrier(sK0))),
inference(cnf_transformation,[],[f32]) ).
fof(f39,plain,
( open_subset(subset_complement(the_carrier(sK0),sK1),sK0)
| closed_subset(sK1,sK0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f40,plain,
( ~ open_subset(subset_complement(the_carrier(sK0),sK1),sK0)
| ~ closed_subset(sK1,sK0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f42,plain,
! [X0] :
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f44,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(f45,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(f48,plain,
! [X0,X1] :
( subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1) = subset_complement(the_carrier(X0),X1)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f56,plain,
! [X0,X1] :
( ~ open_subset(subset_complement(the_carrier(X0),X1),X0)
| closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ one_sorted_str(X0) ),
inference(superposition,[],[f45,f48]) ).
fof(f57,plain,
! [X0,X1] :
( open_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ one_sorted_str(X0) ),
inference(superposition,[],[f44,f48]) ).
fof(f60,plain,
! [X0,X1] :
( open_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ one_sorted_str(X0) ),
inference(duplicate_literal_removal,[],[f57]) ).
fof(f61,plain,
! [X0,X1] :
( ~ open_subset(subset_complement(the_carrier(X0),X1),X0)
| closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ one_sorted_str(X0) ),
inference(duplicate_literal_removal,[],[f56]) ).
fof(f62,plain,
! [X0,X1] :
( open_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(forward_subsumption_resolution,[],[f60,f42]) ).
fof(f63,plain,
! [X0,X1] :
( ~ open_subset(subset_complement(the_carrier(X0),X1),X0)
| closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(forward_subsumption_resolution,[],[f61,f42]) ).
fof(f64,plain,
( ~ closed_subset(sK1,sK0)
| ~ element(sK1,powerset(the_carrier(sK0)))
| ~ top_str(sK0)
| ~ closed_subset(sK1,sK0) ),
inference(resolution,[],[f62,f40]) ).
fof(f66,plain,
( ~ closed_subset(sK1,sK0)
| ~ element(sK1,powerset(the_carrier(sK0)))
| ~ top_str(sK0) ),
inference(duplicate_literal_removal,[],[f64]) ).
fof(f68,plain,
( ~ closed_subset(sK1,sK0)
| ~ top_str(sK0) ),
inference(forward_subsumption_resolution,[],[f66,f38]) ).
fof(f69,plain,
~ closed_subset(sK1,sK0),
inference(forward_subsumption_resolution,[],[f68,f37]) ).
fof(f70,plain,
( closed_subset(sK1,sK0)
| ~ element(sK1,powerset(the_carrier(sK0)))
| ~ top_str(sK0)
| closed_subset(sK1,sK0) ),
inference(resolution,[],[f63,f39]) ).
fof(f74,plain,
( closed_subset(sK1,sK0)
| ~ element(sK1,powerset(the_carrier(sK0)))
| ~ top_str(sK0) ),
inference(duplicate_literal_removal,[],[f70]) ).
fof(f76,plain,
( closed_subset(sK1,sK0)
| ~ top_str(sK0) ),
inference(forward_subsumption_resolution,[],[f74,f38]) ).
fof(f77,plain,
closed_subset(sK1,sK0),
inference(forward_subsumption_resolution,[],[f76,f37]) ).
fof(f78,plain,
$false,
inference(forward_subsumption_resolution,[],[f77,f69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % 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 THM
% 0.12/0.38 % Computer : n001.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 04:46:02 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.82/1.38 % (23043)Detected formulas, will run a generic FOF schedule.
% 2.82/1.38 % (23052)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1929482479:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.82/1.38 % (23052)First to succeed.
% 2.82/1.38 % (23052)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-23043"
% 2.82/1.38 % (23053)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2834931612:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.82/1.38 % (23049)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1635068078:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.82/1.38 % (23048)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=3809350944:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.82/1.38 % (23054)dis-21_1_sil=8000:lcm=predicate:random_seed=3395519186:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.82/1.38 % (23051)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2744258742:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.82/1.38 % (23050)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=795588834:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.82/1.38 % (23051)Refutation not found, incomplete strategy
% 2.82/1.38 % (23051)------------------------------
% 2.82/1.38 % (23051)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.82/1.38 % (23051)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/1.38 % (23051)CaDiCaL version: 2.1.3
% 2.82/1.38 % (23051)Termination reason: Refutation not found, incomplete strategy
% 2.82/1.38 % (23051)Time elapsed: 0.001 s
% 2.82/1.38 % (23051)Peak memory usage: 87 MB
% 2.82/1.38 % (23054)Refutation not found, incomplete strategy
% 2.82/1.38 % (23054)------------------------------
% 2.82/1.38 % (23054)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.82/1.38 % (23054)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/1.38 % (23054)CaDiCaL version: 2.1.3
% 2.82/1.38 % (23054)Termination reason: Refutation not found, incomplete strategy
% 2.82/1.38 % (23054)Time elapsed: 0.002 s
% 2.82/1.38 % (23054)Peak memory usage: 88 MB
% 2.82/1.38 % (23054)Instructions burned: 1 (million)
% 2.82/1.38 % (23053)Also succeeded, but the first one will report.
% 2.82/1.38 % (23052)Refutation found. Thanks to Tanya!
% 2.82/1.38 % SZS status Theorem for theBenchmark
% 2.82/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 2.82/1.39 % (23052)------------------------------
% 2.82/1.39 % (23052)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.82/1.39 % (23052)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/1.39 % (23052)CaDiCaL version: 2.1.3
% 2.82/1.39 % (23052)Termination reason: Refutation
% 2.82/1.39 % (23052)Time elapsed: 0.002 s
% 2.82/1.39 % (23052)Peak memory usage: 88 MB
% 2.82/1.39 % (23052)Instructions burned: 2 (million)
% 2.82/1.39 % (23052)------------------------------
% 2.82/1.39 % (23052)------------------------------
% 2.82/1.39 % (23043)Success in time 0.317 s
% 2.82/1.39 % Vampire exiting
%------------------------------------------------------------------------------