%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU394+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 : n007.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 12:53:07 PM UTC 2026
% Result : Theorem 0.18s 0.50s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 49 ( 14 unt; 0 def)
% Number of atoms : 181 ( 20 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 231 ( 99 ~; 86 |; 36 &)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 51 ( 47 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f59,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ~ empty(cast_as_carrier_subset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_pre_topc) ).
fof(f68,axiom,
( empty(empty_set)
& relation(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f113,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ! [X1] :
( ( ~ empty(X1)
& filtered_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0))))) )
=> set_difference(X1,singleton(empty_set)) = filter_of_net_str(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_yellow19) ).
fof(f114,conjecture,
! [X0] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ! [X1] :
( ( ~ empty(X1)
& filtered_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0))))) )
=> X1 = filter_of_net_str(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_yellow19) ).
fof(f115,negated_conjecture,
~ ! [X0] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ! [X1] :
( ( ~ empty(X1)
& filtered_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0))))) )
=> X1 = filter_of_net_str(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1)) ) ),
inference(negated_conjecture,[status(cth)],[f114]) ).
fof(f119,axiom,
! [X0] :
( ~ empty(X0)
=> ! [X1] :
( ( ~ empty(X1)
& filtered_subset(X1,boole_POSet(X0))
& upper_relstr_subset(X1,boole_POSet(X0))
& proper_element(X1,powerset(the_carrier(boole_POSet(X0))))
& element(X1,powerset(the_carrier(boole_POSet(X0)))) )
=> ! [X2] :
~ ( in(X2,X1)
& empty(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_yellow19) ).
fof(f125,axiom,
! [X0,X1] :
( set_difference(X0,singleton(X1)) = X0
<=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_zfmisc_1) ).
fof(f127,axiom,
! [X0,X1] :
~ ( in(X0,X1)
& empty(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f226,plain,
! [X0] :
( ~ empty(cast_as_carrier_subset(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f59]) ).
fof(f227,plain,
! [X0] :
( ~ empty(cast_as_carrier_subset(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(flattening,[],[f226]) ).
fof(f280,plain,
! [X0] :
( ! [X1] :
( set_difference(X1,singleton(empty_set)) = filter_of_net_str(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1))
| empty(X1)
| ~ filtered_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
| ~ upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
| ~ element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0))))) )
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f113]) ).
fof(f281,plain,
! [X0] :
( ! [X1] :
( set_difference(X1,singleton(empty_set)) = filter_of_net_str(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1))
| empty(X1)
| ~ filtered_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
| ~ upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
| ~ element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0))))) )
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(flattening,[],[f280]) ).
fof(f282,plain,
? [X0] :
( ? [X1] :
( filter_of_net_str(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1)) != X1
& ~ empty(X1)
& filtered_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0))))) )
& ~ empty_carrier(X0)
& one_sorted_str(X0) ),
inference(ennf_transformation,[],[f115]) ).
fof(f283,plain,
? [X0] :
( ? [X1] :
( filter_of_net_str(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1)) != X1
& ~ empty(X1)
& filtered_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0))))) )
& ~ empty_carrier(X0)
& one_sorted_str(X0) ),
inference(flattening,[],[f282]) ).
fof(f288,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ~ in(X2,X1)
| ~ empty(X2) )
| empty(X1)
| ~ filtered_subset(X1,boole_POSet(X0))
| ~ upper_relstr_subset(X1,boole_POSet(X0))
| ~ proper_element(X1,powerset(the_carrier(boole_POSet(X0))))
| ~ element(X1,powerset(the_carrier(boole_POSet(X0)))) )
| empty(X0) ),
inference(ennf_transformation,[],[f119]) ).
fof(f289,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ~ in(X2,X1)
| ~ empty(X2) )
| empty(X1)
| ~ filtered_subset(X1,boole_POSet(X0))
| ~ upper_relstr_subset(X1,boole_POSet(X0))
| ~ proper_element(X1,powerset(the_carrier(boole_POSet(X0))))
| ~ element(X1,powerset(the_carrier(boole_POSet(X0)))) )
| empty(X0) ),
inference(flattening,[],[f288]) ).
fof(f295,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(ennf_transformation,[],[f127]) ).
fof(f381,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ empty(cast_as_carrier_subset(X0)) ),
inference(cnf_transformation,[],[f227]) ).
fof(f408,plain,
empty(empty_set),
inference(cnf_transformation,[],[f68]) ).
fof(f603,plain,
! [X0,X1] :
( ~ upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
| empty_carrier(X0)
| ~ element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
| ~ one_sorted_str(X0)
| ~ filtered_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
| empty(X1)
| set_difference(X1,singleton(empty_set)) = filter_of_net_str(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1)) ),
inference(cnf_transformation,[],[f281]) ).
fof(f604,plain,
element(sK38,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK37))))),
inference(cnf_transformation,[],[f283]) ).
fof(f605,plain,
proper_element(sK38,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK37))))),
inference(cnf_transformation,[],[f283]) ).
fof(f606,plain,
upper_relstr_subset(sK38,boole_POSet(cast_as_carrier_subset(sK37))),
inference(cnf_transformation,[],[f283]) ).
fof(f607,plain,
filtered_subset(sK38,boole_POSet(cast_as_carrier_subset(sK37))),
inference(cnf_transformation,[],[f283]) ).
fof(f608,plain,
~ empty(sK38),
inference(cnf_transformation,[],[f283]) ).
fof(f609,plain,
sK38 != filter_of_net_str(sK37,net_of_bool_filter(sK37,cast_as_carrier_subset(sK37),sK38)),
inference(cnf_transformation,[],[f283]) ).
fof(f610,plain,
one_sorted_str(sK37),
inference(cnf_transformation,[],[f283]) ).
fof(f611,plain,
~ empty_carrier(sK37),
inference(cnf_transformation,[],[f283]) ).
fof(f616,plain,
! [X2,X0,X1] :
( empty(X0)
| ~ element(X1,powerset(the_carrier(boole_POSet(X0))))
| ~ proper_element(X1,powerset(the_carrier(boole_POSet(X0))))
| ~ upper_relstr_subset(X1,boole_POSet(X0))
| ~ filtered_subset(X1,boole_POSet(X0))
| empty(X1)
| ~ empty(X2)
| ~ in(X2,X1) ),
inference(cnf_transformation,[],[f289]) ).
fof(f622,plain,
! [X0,X1] :
( in(X1,X0)
| set_difference(X0,singleton(X1)) = X0 ),
inference(cnf_transformation,[],[f125]) ).
fof(f625,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f295]) ).
fof(f628,plain,
! [X2,X0,X1] :
( ~ proper_element(X1,powerset(the_carrier(boole_POSet(X0))))
| ~ element(X1,powerset(the_carrier(boole_POSet(X0))))
| empty(X0)
| ~ upper_relstr_subset(X1,boole_POSet(X0))
| ~ filtered_subset(X1,boole_POSet(X0))
| ~ empty(X2)
| ~ in(X2,X1) ),
inference(forward_subsumption_resolution,[],[f616,f625]) ).
fof(f712,plain,
( empty_carrier(sK37)
| ~ empty(cast_as_carrier_subset(sK37)) ),
inference(resolution,[],[f381,f610]) ).
fof(f713,plain,
~ empty(cast_as_carrier_subset(sK37)),
inference(forward_subsumption_resolution,[],[f712,f611]) ).
fof(f1558,plain,
! [X0] :
( ~ element(sK38,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK37)))))
| empty(cast_as_carrier_subset(sK37))
| ~ upper_relstr_subset(sK38,boole_POSet(cast_as_carrier_subset(sK37)))
| ~ filtered_subset(sK38,boole_POSet(cast_as_carrier_subset(sK37)))
| ~ empty(X0)
| ~ in(X0,sK38) ),
inference(resolution,[],[f628,f605]) ).
fof(f1561,plain,
! [X0] :
( empty(cast_as_carrier_subset(sK37))
| ~ upper_relstr_subset(sK38,boole_POSet(cast_as_carrier_subset(sK37)))
| ~ filtered_subset(sK38,boole_POSet(cast_as_carrier_subset(sK37)))
| ~ empty(X0)
| ~ in(X0,sK38) ),
inference(forward_subsumption_resolution,[],[f1558,f604]) ).
fof(f1563,plain,
! [X0] :
( ~ upper_relstr_subset(sK38,boole_POSet(cast_as_carrier_subset(sK37)))
| ~ filtered_subset(sK38,boole_POSet(cast_as_carrier_subset(sK37)))
| ~ empty(X0)
| ~ in(X0,sK38) ),
inference(forward_subsumption_resolution,[],[f1561,f713]) ).
fof(f1565,plain,
! [X0] :
( ~ filtered_subset(sK38,boole_POSet(cast_as_carrier_subset(sK37)))
| ~ empty(X0)
| ~ in(X0,sK38) ),
inference(forward_subsumption_resolution,[],[f1563,f606]) ).
fof(f1567,plain,
! [X0] :
( ~ in(X0,sK38)
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[],[f1565,f607]) ).
fof(f1574,plain,
! [X0] :
( ~ empty(X0)
| sK38 = set_difference(sK38,singleton(X0)) ),
inference(resolution,[],[f1567,f622]) ).
fof(f1670,plain,
sK38 = set_difference(sK38,singleton(empty_set)),
inference(resolution,[],[f1574,f408]) ).
fof(f1778,plain,
( empty_carrier(sK37)
| ~ element(sK38,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK37)))))
| ~ one_sorted_str(sK37)
| ~ filtered_subset(sK38,boole_POSet(cast_as_carrier_subset(sK37)))
| empty(sK38)
| filter_of_net_str(sK37,net_of_bool_filter(sK37,cast_as_carrier_subset(sK37),sK38)) = set_difference(sK38,singleton(empty_set)) ),
inference(resolution,[],[f603,f606]) ).
fof(f1780,plain,
( ~ element(sK38,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK37)))))
| ~ one_sorted_str(sK37)
| ~ filtered_subset(sK38,boole_POSet(cast_as_carrier_subset(sK37)))
| empty(sK38)
| filter_of_net_str(sK37,net_of_bool_filter(sK37,cast_as_carrier_subset(sK37),sK38)) = set_difference(sK38,singleton(empty_set)) ),
inference(forward_subsumption_resolution,[],[f1778,f611]) ).
fof(f1786,plain,
( ~ one_sorted_str(sK37)
| ~ filtered_subset(sK38,boole_POSet(cast_as_carrier_subset(sK37)))
| empty(sK38)
| filter_of_net_str(sK37,net_of_bool_filter(sK37,cast_as_carrier_subset(sK37),sK38)) = set_difference(sK38,singleton(empty_set)) ),
inference(forward_subsumption_resolution,[],[f1780,f604]) ).
fof(f1792,plain,
( ~ filtered_subset(sK38,boole_POSet(cast_as_carrier_subset(sK37)))
| empty(sK38)
| filter_of_net_str(sK37,net_of_bool_filter(sK37,cast_as_carrier_subset(sK37),sK38)) = set_difference(sK38,singleton(empty_set)) ),
inference(forward_subsumption_resolution,[],[f1786,f610]) ).
fof(f1796,plain,
( empty(sK38)
| filter_of_net_str(sK37,net_of_bool_filter(sK37,cast_as_carrier_subset(sK37),sK38)) = set_difference(sK38,singleton(empty_set)) ),
inference(forward_subsumption_resolution,[],[f1792,f607]) ).
fof(f1800,plain,
filter_of_net_str(sK37,net_of_bool_filter(sK37,cast_as_carrier_subset(sK37),sK38)) = set_difference(sK38,singleton(empty_set)),
inference(forward_subsumption_resolution,[],[f1796,f608]) ).
fof(f1802,plain,
sK38 = filter_of_net_str(sK37,net_of_bool_filter(sK37,cast_as_carrier_subset(sK37),sK38)),
inference(forward_demodulation,[],[f1800,f1670]) ).
fof(f1804,plain,
$false,
inference(forward_subsumption_resolution,[],[f1802,f609]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU394+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 % Computer : n007.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 05:03:25 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 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
% 0.18/0.50 % (2036204)Will run a generic schedule for satisfiability detection.
% 0.18/0.50 % (2036214)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3171974210:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.50 % (2036210)% WARNING: option uhcvi not known.
% 0.18/0.50 % (2036209)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1110716653_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.50 % (2036210)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2221054318:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.50 % (2036211)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1781888761:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.50 % (2036212)dis+10_1_sil=32000:sp=arity:random_seed=2262893204:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.50 % (2036213)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=899019393:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.50 % (2036215)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2619968667:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.50 % TRYING [1]
% 0.18/0.50 % TRYING [2]
% 0.18/0.50 % TRYING [3]
% 0.18/0.50 % (2036213) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2036204-2036213"...
% 0.18/0.50 % (2036213)...printing done.
% 0.18/0.50 % (2036214)Instruction limit reached!
% 0.18/0.50 % (2036214)------------------------------
% 0.18/0.50 % (2036214)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.50 % (2036214)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.50 % (2036214)CaDiCaL version: 2.1.3
% 0.18/0.50 % (2036214)Termination reason: Instruction limit
% 0.18/0.50 % (2036214)Termination phase: Saturation
% 0.18/0.50 % (2036214)Time elapsed: 0.044 s
% 0.18/0.50 % (2036214)Peak memory usage: 14 MB
% 0.18/0.50 % (2036214)Instructions burned: 131 (million)
% 0.18/0.50 % (2036213)Refutation found. Thanks to Tanya!
% 0.18/0.50 % SZS status Theorem for theBenchmark
% 0.18/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.51 % (2036213)------------------------------
% 0.18/0.51 % (2036213)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.51 % (2036213)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.51 % (2036213)CaDiCaL version: 2.1.3
% 0.18/0.51 % (2036213)Termination reason: Refutation
% 0.18/0.51 % (2036213)Time elapsed: 0.035 s
% 0.18/0.51 % (2036213)Peak memory usage: 13 MB
% 0.18/0.51 % (2036213)Instructions burned: 59 (million)
% 0.18/0.51 % (2036204)Success in time 0.074 s
% 0.18/0.51 % Vampire exiting
%------------------------------------------------------------------------------