%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU354+2 : 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 : n016.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 12:48:30 PM UTC 2026
% Result : Theorem 3.89s 1.52s
% Output : Refutation 3.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 47 ( 12 unt; 2 def)
% Number of atoms : 104 ( 27 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 99 ( 42 ~; 37 |; 10 &)
% ( 6 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-1 aty)
% Number of variables : 29 ( 0 sgn 22 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f102,axiom,
! [X0,X1] :
( element(X1,X0)
=> ( proper_element(X1,X0)
<=> X1 != union(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tex_2) ).
fof(f379,axiom,
! [X0] :
? [X1] :
( element(X1,powerset(X0))
& ~ proper_element(X1,powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_tex_2) ).
fof(f627,conjecture,
! [X0,X1] :
( element(X1,powerset(X0))
=> ( proper_element(X1,powerset(X0))
<=> X1 != X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_tex_2) ).
fof(f628,negated_conjecture,
~ ! [X0,X1] :
( element(X1,powerset(X0))
=> ( proper_element(X1,powerset(X0))
<=> X1 != X0 ) ),
inference(negated_conjecture,[status(cth)],[f627]) ).
fof(f668,axiom,
! [X0] : union(powerset(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_zfmisc_1) ).
fof(f860,plain,
! [X0,X1] :
( ( proper_element(X1,X0)
<=> X1 != union(X0) )
| ~ element(X1,X0) ),
inference(ennf_transformation,[],[f102]) ).
fof(f1465,plain,
? [X0,X1] :
( ( proper_element(X1,powerset(X0))
<~> X1 != X0 )
& element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f628]) ).
fof(f1723,plain,
! [X0,X1] :
( ( ( proper_element(X1,X0)
| union(X0) = X1 )
& ( X1 != union(X0)
| ~ proper_element(X1,X0) ) )
| ~ element(X1,X0) ),
inference(nnf_transformation,[],[f860]) ).
fof(f1893,plain,
! [X0] :
( element(sK212(X0),powerset(X0))
& ~ proper_element(sK212(X0),powerset(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK212]),skolemize(X1,sK212(X0))],[f379]) ).
fof(f2241,plain,
? [X0,X1] :
( ( X0 = X1
| ~ proper_element(X1,powerset(X0)) )
& ( X1 != X0
| proper_element(X1,powerset(X0)) )
& element(X1,powerset(X0)) ),
inference(nnf_transformation,[],[f1465]) ).
fof(f2242,plain,
? [X0,X1] :
( ( X0 = X1
| ~ proper_element(X1,powerset(X0)) )
& ( X1 != X0
| proper_element(X1,powerset(X0)) )
& element(X1,powerset(X0)) ),
inference(flattening,[],[f2241]) ).
fof(f2243,plain,
( ( sK498 = sK499
| ~ proper_element(sK499,powerset(sK498)) )
& ( sK498 != sK499
| proper_element(sK499,powerset(sK498)) )
& element(sK499,powerset(sK498)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK498,sK499]),skolemize(X0,sK498),skolemize(X1,sK499)],[f2242]) ).
fof(f2570,plain,
! [X0,X1] :
( proper_element(X1,X0)
| union(X0) = X1
| ~ element(X1,X0) ),
inference(cnf_transformation,[],[f1723]) ).
fof(f3203,plain,
! [X0] : ~ proper_element(sK212(X0),powerset(X0)),
inference(cnf_transformation,[],[f1893]) ).
fof(f3204,plain,
! [X0] : element(sK212(X0),powerset(X0)),
inference(cnf_transformation,[],[f1893]) ).
fof(f4042,plain,
element(sK499,powerset(sK498)),
inference(cnf_transformation,[],[f2243]) ).
fof(f4043,plain,
( sK498 != sK499
| proper_element(sK499,powerset(sK498)) ),
inference(cnf_transformation,[],[f2243]) ).
fof(f4044,plain,
( sK498 = sK499
| ~ proper_element(sK499,powerset(sK498)) ),
inference(cnf_transformation,[],[f2243]) ).
fof(f4104,plain,
! [X0] : union(powerset(X0)) = X0,
inference(cnf_transformation,[],[f668]) ).
fof(f4399,definition,
( spl504_1
<=> proper_element(sK499,powerset(sK498)) ),
introduced(definition,[new_symbols(definition,[spl504_1])],[avatar_definition]) ).
fof(f4400,plain,
( ~ proper_element(sK499,powerset(sK498))
| spl504_1 ),
inference(avatar_component_clause,[],[f4399]) ).
fof(f4401,plain,
( proper_element(sK499,powerset(sK498))
| ~ spl504_1 ),
inference(avatar_component_clause,[],[f4399]) ).
fof(f4403,definition,
( spl504_2
<=> sK498 = sK499 ),
introduced(definition,[new_symbols(definition,[spl504_2])],[avatar_definition]) ).
fof(f4404,plain,
( sK498 = sK499
| ~ spl504_2 ),
inference(avatar_component_clause,[],[f4403]) ).
fof(f4405,plain,
( sK498 != sK499
| spl504_2 ),
inference(avatar_component_clause,[],[f4403]) ).
fof(f4406,plain,
( spl504_1
| ~ spl504_2 ),
inference(avatar_split_clause,[],[f4043,f4403,f4399]) ).
fof(f4407,plain,
( ~ spl504_1
| spl504_2 ),
inference(avatar_split_clause,[],[f4044,f4403,f4399]) ).
fof(f4662,plain,
( sK499 = union(powerset(sK498))
| ~ element(sK499,powerset(sK498))
| spl504_1 ),
inference(resolution,[],[f2570,f4400]) ).
fof(f4663,plain,
! [X0] :
( union(powerset(X0)) = sK212(X0)
| ~ element(sK212(X0),powerset(X0)) ),
inference(resolution,[],[f2570,f3203]) ).
fof(f4666,plain,
! [X0] : union(powerset(X0)) = sK212(X0),
inference(forward_subsumption_resolution,[],[f4663,f3204]) ).
fof(f4667,plain,
( sK499 = union(powerset(sK498))
| spl504_1 ),
inference(forward_subsumption_resolution,[],[f4662,f4042]) ).
fof(f4669,plain,
( sK498 = sK499
| spl504_1 ),
inference(superposition,[],[f4104,f4667]) ).
fof(f4674,plain,
( $false
| spl504_1
| spl504_2 ),
inference(forward_subsumption_resolution,[],[f4669,f4405]) ).
fof(f4675,plain,
( spl504_1
| spl504_2 ),
inference(avatar_contradiction_clause,[],[f4674]) ).
fof(f4677,plain,
( proper_element(sK498,powerset(sK498))
| ~ spl504_1
| ~ spl504_2 ),
inference(forward_demodulation,[],[f4401,f4404]) ).
fof(f4684,plain,
! [X0] : sK212(X0) = X0,
inference(forward_demodulation,[],[f4666,f4104]) ).
fof(f4686,plain,
! [X0] : ~ proper_element(X0,powerset(X0)),
inference(superposition,[],[f3203,f4684]) ).
fof(f4742,plain,
( $false
| ~ spl504_1
| ~ spl504_2 ),
inference(resolution,[],[f4686,f4677]) ).
fof(f4743,plain,
( ~ spl504_1
| ~ spl504_2 ),
inference(avatar_contradiction_clause,[],[f4742]) ).
cnf(s1,plain,
( spl504_1
| ~ spl504_2 ),
inference(sat_conversion,[],[f4406]) ).
cnf(s2,plain,
( ~ spl504_1
| spl504_2 ),
inference(sat_conversion,[],[f4407]) ).
cnf(s52,plain,
( spl504_1
| spl504_2 ),
inference(sat_conversion,[],[f4675]) ).
cnf(s60,plain,
( ~ spl504_1
| ~ spl504_2 ),
inference(sat_conversion,[],[f4743]) ).
cnf(s62,plain,
spl504_1,
inference(rat,[],[s1,s52]) ).
cnf(s63,plain,
~ spl504_2,
inference(rat,[],[s60,s62]) ).
cnf(s64,plain,
$false,
inference(rat,[],[s2,s63,s62]) ).
fof(f4744,plain,
$false,
inference(avatar_sat_refutation,[],[s64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU354+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n016.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 04:58:33 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 3.89/1.52 % (3266427)Detected formulas, will run a generic FOF schedule.
% 3.89/1.52 % (3266438)dis-21_1_sil=8000:lcm=predicate:random_seed=1044900526: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)
% 3.89/1.52 % (3266436)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=290015664:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.89/1.52 % (3266433)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=3483071819:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.89/1.52 % (3266435)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=98316084:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.89/1.52 % (3266432)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=3279347940:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.89/1.52 % (3266434)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=80887805:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.89/1.52 % (3266437)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3581214182:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.89/1.52 % (3266438)Instruction limit reached!
% 3.89/1.52 % (3266438)------------------------------
% 3.89/1.52 % (3266438)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.89/1.52 % (3266438)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/1.52 % (3266438)CaDiCaL version: 2.1.3
% 3.89/1.52 % (3266438)Termination reason: Instruction limit
% 3.89/1.52 % (3266438)Termination phase: Saturation
% 3.89/1.52 % (3266438)Time elapsed: 0.038 s
% 3.89/1.52 % (3266438)Peak memory usage: 91 MB
% 3.89/1.52 % (3266438)Instructions burned: 129 (million)
% 3.89/1.52 % (3266437)First to succeed.
% 3.89/1.52 % (3266437)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3266427"
% 3.89/1.52 % (3266435)Instruction limit reached!
% 3.89/1.52 % (3266435)------------------------------
% 3.89/1.52 % (3266435)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.89/1.52 % (3266435)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/1.52 % (3266435)CaDiCaL version: 2.1.3
% 3.89/1.52 % (3266435)Termination reason: Instruction limit
% 3.89/1.52 % (3266435)Termination phase: Saturation
% 3.89/1.52 % (3266435)Time elapsed: 0.060 s
% 3.89/1.52 % (3266435)Peak memory usage: 91 MB
% 3.89/1.52 % (3266435)Instructions burned: 109 (million)
% 3.89/1.52 % (3266436)Instruction limit reached!
% 3.89/1.52 % (3266436)------------------------------
% 3.89/1.52 % (3266436)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.89/1.52 % (3266436)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/1.52 % (3266436)CaDiCaL version: 2.1.3
% 3.89/1.52 % (3266436)Termination reason: Instruction limit
% 3.89/1.52 % (3266436)Termination phase: Saturation
% 3.89/1.52 % (3266436)Time elapsed: 0.077 s
% 3.89/1.52 % (3266436)Peak memory usage: 91 MB
% 3.89/1.52 % (3266436)Instructions burned: 119 (million)
% 3.89/1.52 % (3266446)lrs+10_1_sil=8000:sp=occurrence:random_seed=2733510500:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.89/1.52 % (3266447)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2404020086:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.89/1.52 % (3266447)Refutation not found, incomplete strategy
% 3.89/1.52 % (3266447)------------------------------
% 3.89/1.52 % (3266447)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.89/1.52 % (3266447)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/1.52 % (3266447)CaDiCaL version: 2.1.3
% 3.89/1.52 % (3266447)Termination reason: Refutation not found, incomplete strategy
% 3.89/1.52 % (3266447)Time elapsed: 0.007 s
% 3.89/1.52 % (3266447)Peak memory usage: 89 MB
% 3.89/1.52 % (3266447)Instructions burned: 10 (million)
% 3.89/1.52 % (3266446)Instruction limit reached!
% 3.89/1.52 % (3266446)------------------------------
% 3.89/1.52 % (3266446)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.89/1.52 % (3266446)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/1.52 % (3266446)CaDiCaL version: 2.1.3
% 3.89/1.52 % (3266446)Termination reason: Instruction limit
% 3.89/1.52 % (3266446)Termination phase: Saturation
% 3.89/1.52 % (3266446)Time elapsed: 0.102 s
% 3.89/1.52 % (3266446)Peak memory usage: 95 MB
% 3.89/1.52 % (3266446)Instructions burned: 286 (million)
% 3.89/1.52 % (3266448)lrs+1011_1_sil=32000:sp=occurrence:random_seed=267980979:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.89/1.52 % (3266437)Refutation found. Thanks to Tanya!
% 3.89/1.52 % SZS status Theorem for theBenchmark
% 3.89/1.52 % SZS output start Proof for theBenchmark
% See solution above
% 3.89/1.52 % (3266437)------------------------------
% 3.89/1.52 % (3266437)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.89/1.52 % (3266437)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/1.52 % (3266437)CaDiCaL version: 2.1.3
% 3.89/1.52 % (3266437)Termination reason: Refutation
% 3.89/1.52 % (3266437)Time elapsed: 0.056 s
% 3.89/1.52 % (3266437)Peak memory usage: 92 MB
% 3.89/1.52 % (3266437)Instructions burned: 92 (million)
% 3.89/1.52 % (3266437)------------------------------
% 3.89/1.52 % (3266437)------------------------------
% 3.89/1.52 % (3266427)Success in time 0.483 s
% 3.89/1.52 % Vampire exiting
%------------------------------------------------------------------------------