%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU519_8 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 12:49:25 PM UTC 2026
% Result : Theorem 2.77s 1.38s
% Output : Refutation 2.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 50 ( 17 unt; 0 typ; 5 def)
% Number of atoms : 161 ( 12 equ)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 100 ( 39 ~; 30 |; 8 &)
% ( 7 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 63 ( 52 fml; 11 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 12 usr; 11 prp; 0-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 44 ( 0 sgn 41 !; 3 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
tff(f1,axiom,
( emptysetE
= ( ! [X0: $i] :
( in(X0,emptyset)
=> ! [X1: $o] : (X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).
tff(f2,axiom,
( powersetI
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( in(X2,X1)
=> in(X2,X0) )
=> in(X1,powerset(X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI) ).
tff(f3,conjecture,
( emptysetE
=> ( powersetI
=> ! [X0: $i] : in(emptyset,powerset(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinPowerset) ).
tff(f4,negated_conjecture,
~ ( emptysetE
=> ( powersetI
=> ! [X0: $i] : in(emptyset,powerset(X0)) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
tff(f5,plain,
( emptysetE
= ( ! [X0: $i] :
( in(X0,emptyset)
=> ! [X1: $o] : (X1) ) ) ),
inference(rectify,[],[f1]) ).
tff(f6,plain,
( emptysetE
<=> ! [X0: $i] :
( in(X0,emptyset)
=> ! [X1: $o] : ( $true = (X1) ) ) ),
inference(fool_elimination,[],[f5]) ).
tff(f7,plain,
( powersetI
<=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( in(X2,X1)
=> in(X2,X0) )
=> in(X1,powerset(X0)) ) ),
inference(fool_elimination,[],[f2]) ).
tff(f8,plain,
( powersetI
=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( in(X2,X1)
=> in(X2,X0) )
=> in(X1,powerset(X0)) ) ),
inference(unused_predicate_definition_removal,[],[f7]) ).
tff(f9,plain,
( emptysetE
=> ! [X0: $i] :
( in(X0,emptyset)
=> ! [X1: $o] : ( $true = (X1) ) ) ),
inference(unused_predicate_definition_removal,[],[f6]) ).
tff(f10,plain,
( ! [X0: $i] :
( ! [X1: $o] : ( $true = (X1) )
| ~ in(X0,emptyset) )
| ~ emptysetE ),
inference(ennf_transformation,[],[f9]) ).
tff(f11,plain,
( ! [X0: $i,X1: $i] :
( in(X1,powerset(X0))
| ? [X2: $i] :
( ~ in(X2,X0)
& in(X2,X1) ) )
| ~ powersetI ),
inference(ennf_transformation,[],[f8]) ).
tff(f12,plain,
( ? [X0: $i] : ~ in(emptyset,powerset(X0))
& powersetI
& emptysetE ),
inference(ennf_transformation,[],[f4]) ).
tff(f13,plain,
( ? [X0: $i] : ~ in(emptyset,powerset(X0))
& powersetI
& emptysetE ),
inference(flattening,[],[f12]) ).
tff(f14,plain,
( ! [X0: $i,X1: $i] :
( in(X1,powerset(X0))
| ( ~ in(sK0(X0,X1),X0)
& in(sK0(X0,X1),X1) ) )
| ~ powersetI ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f11]) ).
tff(f15,plain,
( ~ in(emptyset,powerset(sK1))
& powersetI
& emptysetE ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f13]) ).
tff(f16,plain,
! [X0: $i,X1: $o] :
( ( $true = (X1) )
| ~ in(X0,emptyset)
| ~ emptysetE ),
inference(cnf_transformation,[],[f10]) ).
tff(f17,plain,
! [X0: $i,X1: $i] :
( in(X1,powerset(X0))
| in(sK0(X0,X1),X1)
| ~ powersetI ),
inference(cnf_transformation,[],[f14]) ).
tff(f19,plain,
emptysetE,
inference(cnf_transformation,[],[f15]) ).
tff(f20,plain,
powersetI,
inference(cnf_transformation,[],[f15]) ).
tff(f21,plain,
~ in(emptyset,powerset(sK1)),
inference(cnf_transformation,[],[f15]) ).
tff(f22,plain,
$true != $false,
introduced(definition,[],[fool_distinctness_axiom]) ).
tff(f25,definition,
( spl2_1
<=> powersetI ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
tff(f29,definition,
( spl2_2
<=> ! [X0: $i,X1: $i] :
( in(X1,powerset(X0))
| in(sK0(X0,X1),X1) ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
tff(f30,plain,
( ! [X0: $i,X1: $i] :
( in(sK0(X0,X1),X1)
| in(X1,powerset(X0)) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f29]) ).
tff(f31,plain,
( ~ spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f17,f29,f25]) ).
tff(f37,definition,
( spl2_4
<=> emptysetE ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
tff(f41,definition,
( spl2_5
<=> ! [X0: $i] : ~ in(X0,emptyset) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
tff(f42,plain,
( ! [X0: $i] : ~ in(X0,emptyset)
| ~ spl2_5 ),
inference(avatar_component_clause,[],[f41]) ).
tff(f44,definition,
( spl2_6
<=> ! [X1: $o] : ( $true = (X1) ) ),
introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition]) ).
tff(f45,plain,
( ! [X1: $o] : ( $true = (X1) )
| ~ spl2_6 ),
inference(avatar_component_clause,[],[f44]) ).
tff(f46,plain,
( ~ spl2_4
| spl2_5
| spl2_6 ),
inference(avatar_split_clause,[],[f16,f44,f41,f37]) ).
tff(f47,plain,
spl2_4,
inference(avatar_split_clause,[],[f19,f37]) ).
tff(f48,plain,
spl2_1,
inference(avatar_split_clause,[],[f20,f25]) ).
tff(f49,plain,
( ! [X0: $i] : in(emptyset,powerset(X0))
| ~ spl2_2
| ~ spl2_5 ),
inference(resolution,[],[f30,f42]) ).
tff(f50,plain,
( $false
| ~ spl2_2
| ~ spl2_5 ),
inference(resolution,[],[f49,f21]) ).
tff(f51,plain,
( ~ spl2_2
| ~ spl2_5 ),
inference(avatar_contradiction_clause,[],[f50]) ).
tff(f52,plain,
( ! [X0: $o,X1: $o] : ( (X0) = (X1) )
| ~ spl2_6 ),
inference(superposition,[],[f45,f45]) ).
tff(f55,plain,
( ! [X0: $o] : ( $false != (X0) )
| ~ spl2_6 ),
inference(superposition,[],[f22,f52]) ).
tff(f60,plain,
( $false
| ~ spl2_6 ),
inference(forward_subsumption_resolution,[],[f55,f52]) ).
tff(f61,plain,
~ spl2_6,
inference(avatar_contradiction_clause,[],[f60]) ).
cnf(s1,plain,
( ~ spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f31]) ).
cnf(s3,plain,
( ~ spl2_4
| spl2_5
| spl2_6 ),
inference(sat_conversion,[],[f46]) ).
cnf(s4,plain,
spl2_4,
inference(sat_conversion,[],[f47]) ).
cnf(s5,plain,
spl2_1,
inference(sat_conversion,[],[f48]) ).
cnf(s6,plain,
( ~ spl2_2
| ~ spl2_5 ),
inference(sat_conversion,[],[f51]) ).
cnf(s8,plain,
~ spl2_6,
inference(sat_conversion,[],[f61]) ).
cnf(s9,plain,
spl2_5,
inference(rat,[],[s3,s8,s4]) ).
cnf(s10,plain,
~ spl2_2,
inference(rat,[],[s6,s9]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s1,s10,s5]) ).
tff(f62,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU519_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n006.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
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 05:41:40 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.42 Running first-order theorem proving
% 0.17/0.43 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
% 2.77/1.38 % (3672213)Detected formulas, will run a generic FOF schedule.
% 2.77/1.38 % (3672324)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1854921655:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.77/1.38 % (3672324)First to succeed.
% 2.77/1.38 % (3672324)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3672213"
% 2.77/1.38 % (3672321)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=1221543685:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.77/1.38 % (3672319)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=625750524:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.77/1.38 % (3672323)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=849013237:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.77/1.38 % (3672325)dis-21_1_sil=8000:lcm=predicate:random_seed=245019930: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)
% 2.77/1.38 % (3672320)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=572737539:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.77/1.38 % (3672323)Refutation not found, incomplete strategy
% 2.77/1.38 % (3672323)------------------------------
% 2.77/1.38 % (3672323)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.38 % (3672323)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.38 % (3672323)CaDiCaL version: 2.1.3
% 2.77/1.38 % (3672323)Termination reason: Refutation not found, incomplete strategy
% 2.77/1.38 % (3672323)Time elapsed: 0.001 s
% 2.77/1.38 % (3672323)Peak memory usage: 88 MB
% 2.77/1.38 % (3672325)Also succeeded, but the first one will report.
% 2.77/1.38 % (3672322)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=331843363:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.77/1.38 % (3672322)Refutation not found, incomplete strategy
% 2.77/1.38 % (3672322)------------------------------
% 2.77/1.38 % (3672322)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.38 % (3672322)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.38 % (3672322)CaDiCaL version: 2.1.3
% 2.77/1.38 % (3672322)Termination reason: Refutation not found, incomplete strategy
% 2.77/1.38 % (3672322)Time elapsed: 0.001 s
% 2.77/1.38 % (3672322)Peak memory usage: 88 MB
% 2.77/1.38 % (3672324)Refutation found. Thanks to Tanya!
% 2.77/1.38 % SZS status Theorem for theBenchmark
% 2.77/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 2.77/1.38 % (3672324)------------------------------
% 2.77/1.38 % (3672324)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.38 % (3672324)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.38 % (3672324)CaDiCaL version: 2.1.3
% 2.77/1.38 % (3672324)Termination reason: Refutation
% 2.77/1.38 % (3672324)Time elapsed: 0.002 s
% 2.77/1.38 % (3672324)Peak memory usage: 90 MB
% 2.77/1.38 % (3672324)Instructions burned: 2 (million)
% 2.77/1.38 % (3672324)------------------------------
% 2.77/1.38 % (3672324)------------------------------
% 2.77/1.38 % (3672213)Success in time 0.308 s
% 2.77/1.38 % Vampire exiting
%------------------------------------------------------------------------------