%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU169+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 : 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 12:47:33 PM UTC 2026
% Result : Theorem 2.84s 1.39s
% Output : Refutation 2.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 9 unt; 0 def)
% Number of atoms : 115 ( 8 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 129 ( 45 ~; 45 |; 24 &)
% ( 8 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 59 ( 52 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0,X1] :
( X1 = powerset(X0)
<=> ! [X2] :
( in(X2,X1)
<=> subset(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(f10,axiom,
! [X0,X1] :
( ( ~ empty(X0)
=> ( element(X1,X0)
<=> in(X1,X0) ) )
& ( empty(X0)
=> ( element(X1,X0)
<=> empty(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_subset_1) ).
fof(f14,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f33,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f47,conjecture,
! [X0,X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( in(X2,X1)
=> in(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_subset_1) ).
fof(f48,negated_conjecture,
~ ! [X0,X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( in(X2,X1)
=> in(X2,X0) ) ),
inference(negated_conjecture,[status(cth)],[f47]) ).
fof(f121,plain,
? [X0,X1] :
( ? [X2] :
( ~ in(X2,X0)
& in(X2,X1) )
& element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f48]) ).
fof(f155,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f159,plain,
! [X0,X1] :
( ( ( element(X1,X0)
<=> in(X1,X0) )
| empty(X0) )
& ( ( element(X1,X0)
<=> empty(X1) )
| ~ empty(X0) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f167,plain,
( ~ in(sK2,sK0)
& in(sK2,sK1)
& element(sK1,powerset(sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f121]) ).
fof(f193,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f155]) ).
fof(f194,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f193]) ).
fof(f195,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK9(X0,X1),X1)
& in(sK9(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X2,sK9(X0,X1))],[f194]) ).
fof(f209,plain,
! [X0,X1] :
( ( ( ( element(X1,X0)
| ~ in(X1,X0) )
& ( in(X1,X0)
| ~ element(X1,X0) ) )
| empty(X0) )
& ( ( ( element(X1,X0)
| ~ empty(X1) )
& ( empty(X1)
| ~ element(X1,X0) ) )
| ~ empty(X0) ) ),
inference(nnf_transformation,[],[f159]) ).
fof(f210,plain,
! [X0,X1] :
( ( X1 = powerset(X0)
| ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ~ subset(X2,X0) )
& ( subset(X2,X0)
| ~ in(X2,X1) ) )
| powerset(X0) != X1 ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f211,plain,
! [X0,X1] :
( ( X1 = powerset(X0)
| ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ subset(X3,X0) )
& ( subset(X3,X0)
| ~ in(X3,X1) ) )
| powerset(X0) != X1 ) ),
inference(rectify,[],[f210]) ).
fof(f212,plain,
! [X0,X1] :
( ( X1 = powerset(X0)
| ( ( ~ subset(sK14(X0,X1),X0)
| ~ in(sK14(X0,X1),X1) )
& ( subset(sK14(X0,X1),X0)
| in(sK14(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ subset(X3,X0) )
& ( subset(X3,X0)
| ~ in(X3,X1) ) )
| powerset(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X2,sK14(X0,X1))],[f211]) ).
fof(f236,plain,
element(sK1,powerset(sK0)),
inference(cnf_transformation,[],[f167]) ).
fof(f237,plain,
in(sK2,sK1),
inference(cnf_transformation,[],[f167]) ).
fof(f238,plain,
~ in(sK2,sK0),
inference(cnf_transformation,[],[f167]) ).
fof(f312,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f195]) ).
fof(f345,plain,
! [X0,X1] :
( ~ element(X1,X0)
| in(X1,X0)
| empty(X0) ),
inference(cnf_transformation,[],[f209]) ).
fof(f347,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f33]) ).
fof(f348,plain,
! [X3,X0,X1] :
( subset(X3,X0)
| ~ in(X3,X1)
| powerset(X0) != X1 ),
inference(cnf_transformation,[],[f212]) ).
fof(f476,plain,
! [X3,X0] :
( ~ in(X3,powerset(X0))
| subset(X3,X0) ),
inference(equality_resolution,[],[f348]) ).
fof(f499,plain,
( in(sK1,powerset(sK0))
| empty(powerset(sK0)) ),
inference(resolution,[],[f236,f345]) ).
fof(f500,plain,
in(sK1,powerset(sK0)),
inference(forward_subsumption_resolution,[],[f499,f347]) ).
fof(f501,plain,
subset(sK1,sK0),
inference(resolution,[],[f500,f476]) ).
fof(f506,plain,
! [X0] :
( ~ in(X0,sK1)
| in(X0,sK0) ),
inference(resolution,[],[f501,f312]) ).
fof(f528,plain,
in(sK2,sK0),
inference(resolution,[],[f506,f237]) ).
fof(f550,plain,
$false,
inference(forward_subsumption_resolution,[],[f528,f238]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU169+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 % Computer : n013.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Mon Sep 28 03:51:37 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.44 Running first-order theorem proving
% 0.12/0.44 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
% 2.84/1.39 % (785061)Detected formulas, will run a generic FOF schedule.
% 2.84/1.39 % (785068)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=2836654529:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.84/1.39 % (785071)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3858796002:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.84/1.39 % (785070)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1238575146:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.84/1.39 % (785066)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=3127522285:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.84/1.39 % (785069)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3488103967:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.84/1.39 % (785067)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=1356758086:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.84/1.39 % (785069)First to succeed.
% 2.84/1.39 % (785069)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-785061"
% 2.84/1.39 % (785072)dis-21_1_sil=8000:lcm=predicate:random_seed=1567900334: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)
% 2.84/1.39 % (785071)Also succeeded, but the first one will report.
% 2.84/1.39 % (785070)Instruction limit reached!
% 2.84/1.39 % (785070)------------------------------
% 2.84/1.39 % (785070)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.84/1.39 % (785070)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.84/1.39 % (785070)CaDiCaL version: 2.1.3
% 2.84/1.39 % (785070)Termination reason: Instruction limit
% 2.84/1.39 % (785070)Termination phase: Saturation
% 2.84/1.39 % (785070)Time elapsed: 0.078 s
% 2.84/1.39 % (785070)Peak memory usage: 89 MB
% 2.84/1.39 % (785070)Instructions burned: 119 (million)
% 2.84/1.39 % (785072)Instruction limit reached!
% 2.84/1.39 % (785072)------------------------------
% 2.84/1.39 % (785072)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.84/1.39 % (785072)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.84/1.39 % (785072)CaDiCaL version: 2.1.3
% 2.84/1.39 % (785072)Termination reason: Instruction limit
% 2.84/1.39 % (785072)Termination phase: Saturation
% 2.84/1.39 % (785072)Time elapsed: 0.079 s
% 2.84/1.39 % (785072)Peak memory usage: 90 MB
% 2.84/1.39 % (785072)Instructions burned: 130 (million)
% 2.84/1.39 % (785080)lrs+10_1_sil=8000:sp=occurrence:random_seed=1355323513:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.84/1.39 % (785080)Also succeeded, but the first one will report.
% 2.84/1.39 % (785081)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3074350144:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.84/1.39 % (785081)Also succeeded, but the first one will report.
% 2.84/1.39 % (785069)Refutation found. Thanks to Tanya!
% 2.84/1.39 % SZS status Theorem for theBenchmark
% 2.84/1.39 % SZS output start Proof for theBenchmark
% See solution above
% 2.84/1.39 % (785069)------------------------------
% 2.84/1.39 % (785069)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.84/1.39 % (785069)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.84/1.39 % (785069)CaDiCaL version: 2.1.3
% 2.84/1.39 % (785069)Termination reason: Refutation
% 2.84/1.39 % (785069)Time elapsed: 0.010 s
% 2.84/1.39 % (785069)Peak memory usage: 89 MB
% 2.84/1.39 % (785069)Instructions burned: 14 (million)
% 2.84/1.39 % (785069)------------------------------
% 2.84/1.39 % (785069)------------------------------
% 2.84/1.39 % (785061)Success in time 0.424 s
% 2.84/1.39 % Vampire exiting
%------------------------------------------------------------------------------