%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU173+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 12:47:34 PM UTC 2026
% Result : Theorem 3.49s 1.46s
% Output : Refutation 3.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 45 ( 10 unt; 2 def)
% Number of atoms : 141 ( 8 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 152 ( 56 ~; 57 |; 22 &)
% ( 10 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 66 ( 0 sgn 60 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( X1 = powerset(X0)
<=> ! [X2] :
( in(X2,X1)
<=> subset(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(f3,axiom,
! [X0,X1] :
( ( ~ empty(X0)
=> ( element(X1,X0)
<=> in(X1,X0) ) )
& ( empty(X0)
=> ( element(X1,X0)
<=> empty(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
fof(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f9,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f11,conjecture,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
=> in(X2,X1) )
=> element(X0,powerset(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l71_subset_1) ).
fof(f12,negated_conjecture,
~ ! [X0,X1] :
( ! [X2] :
( in(X2,X0)
=> in(X2,X1) )
=> element(X0,powerset(X1)) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f23,plain,
! [X0,X1] :
( ( ( element(X1,X0)
<=> in(X1,X0) )
| empty(X0) )
& ( ( element(X1,X0)
<=> empty(X1) )
| ~ empty(X0) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f24,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f25,plain,
? [X0,X1] :
( ~ element(X0,powerset(X1))
& ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f30,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,[],[f2]) ).
fof(f31,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,[],[f30]) ).
fof(f32,plain,
! [X0,X1] :
( ( X1 = powerset(X0)
| ( ( ~ subset(sK0(X0,X1),X0)
| ~ in(sK0(X0,X1),X1) )
& ( subset(sK0(X0,X1),X0)
| in(sK0(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,[sK0]),skolemize(X2,sK0(X0,X1))],[f31]) ).
fof(f33,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,[],[f23]) ).
fof(f34,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,[],[f24]) ).
fof(f35,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,[],[f34]) ).
fof(f36,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK1(X0,X1),X1)
& in(sK1(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f35]) ).
fof(f38,plain,
( ~ element(sK3,powerset(sK4))
& ! [X2] :
( in(X2,sK4)
| ~ in(X2,sK3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f25]) ).
fof(f45,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ subset(X3,X0)
| powerset(X0) != X1 ),
inference(cnf_transformation,[],[f32]) ).
fof(f51,plain,
! [X0,X1] :
( element(X1,X0)
| ~ in(X1,X0)
| empty(X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f53,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f36]) ).
fof(f54,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f56,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f9]) ).
fof(f58,plain,
! [X2] :
( in(X2,sK4)
| ~ in(X2,sK3) ),
inference(cnf_transformation,[],[f38]) ).
fof(f59,plain,
~ element(sK3,powerset(sK4)),
inference(cnf_transformation,[],[f38]) ).
fof(f70,plain,
! [X3,X0] :
( ~ subset(X3,X0)
| in(X3,powerset(X0)) ),
inference(equality_resolution,[],[f45]) ).
fof(f106,plain,
( ~ in(sK3,powerset(sK4))
| empty(powerset(sK4)) ),
inference(resolution,[],[f51,f59]) ).
fof(f111,definition,
( spl10_3
<=> empty(powerset(sK4)) ),
introduced(definition,[new_symbols(definition,[spl10_3])],[avatar_definition]) ).
fof(f112,plain,
( empty(powerset(sK4))
| ~ spl10_3 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f114,definition,
( spl10_4
<=> in(sK3,powerset(sK4)) ),
introduced(definition,[new_symbols(definition,[spl10_4])],[avatar_definition]) ).
fof(f115,plain,
( ~ in(sK3,powerset(sK4))
| spl10_4 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f116,plain,
( spl10_3
| ~ spl10_4 ),
inference(avatar_split_clause,[],[f106,f114,f111]) ).
fof(f128,plain,
! [X0,X1] :
( in(sK1(X0,X1),X0)
| in(X0,powerset(X1)) ),
inference(resolution,[],[f53,f70]) ).
fof(f129,plain,
! [X0,X1] :
( ~ in(sK1(X0,X1),X1)
| in(X0,powerset(X1)) ),
inference(resolution,[],[f54,f70]) ).
fof(f142,plain,
! [X0] :
( ~ in(sK1(X0,sK4),sK3)
| in(X0,powerset(sK4)) ),
inference(resolution,[],[f129,f58]) ).
fof(f144,plain,
( in(sK3,powerset(sK4))
| in(sK3,powerset(sK4)) ),
inference(resolution,[],[f142,f128]) ).
fof(f145,plain,
in(sK3,powerset(sK4)),
inference(duplicate_literal_removal,[],[f144]) ).
fof(f149,plain,
( $false
| spl10_4 ),
inference(resolution,[],[f145,f115]) ).
fof(f151,plain,
spl10_4,
inference(avatar_contradiction_clause,[],[f149]) ).
fof(f152,plain,
( $false
| ~ spl10_3 ),
inference(resolution,[],[f112,f56]) ).
fof(f153,plain,
~ spl10_3,
inference(avatar_contradiction_clause,[],[f152]) ).
cnf(s2,plain,
( spl10_3
| ~ spl10_4 ),
inference(sat_conversion,[],[f116]) ).
cnf(s4,plain,
spl10_4,
inference(sat_conversion,[],[f151]) ).
cnf(s5,plain,
~ spl10_3,
inference(sat_conversion,[],[f153]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s2,s4,s5]) ).
fof(f154,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU173+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/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 03:58:48 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.49/1.46 % (2903)Detected formulas, will run a generic FOF schedule.
% 3.49/1.46 % (2956)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=2474281108:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.49/1.46 % (2958)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2219359448:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.49/1.46 % (2958)Refutation not found, incomplete strategy
% 3.49/1.46 % (2958)------------------------------
% 3.49/1.46 % (2958)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.46 % (2958)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.46 % (2958)CaDiCaL version: 2.1.3
% 3.49/1.46 % (2958)Termination reason: Refutation not found, incomplete strategy
% 3.49/1.46 % (2958)Time elapsed: 0.001 s
% 3.49/1.46 % (2958)Peak memory usage: 88 MB
% 3.49/1.46 % (2957)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=1050389045:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.49/1.46 % (2955)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=4248069994:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.49/1.46 % (2959)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=576451510:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.49/1.46 % (2961)dis-21_1_sil=8000:lcm=predicate:random_seed=844345192: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)
% 3.49/1.46 % (2960)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4199532120:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.49/1.46 % (2959)Refutation not found, incomplete strategy
% 3.49/1.46 % (2959)------------------------------
% 3.49/1.46 % (2959)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.46 % (2959)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.46 % (2959)CaDiCaL version: 2.1.3
% 3.49/1.46 % (2959)Termination reason: Refutation not found, incomplete strategy
% 3.49/1.46 % (2959)Time elapsed: 0.002 s
% 3.49/1.46 % (2959)Peak memory usage: 87 MB
% 3.49/1.46 % (2959)Instructions burned: 1 (million)
% 3.49/1.46 % (2961)First to succeed.
% 3.49/1.46 % (2961)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2903"
% 3.49/1.46 % (2960)Also succeeded, but the first one will report.
% 3.49/1.46 % (2958)------------------------------
% 3.49/1.46 % (2958)------------------------------
% 3.49/1.46 % (2959)------------------------------
% 3.49/1.46 % (2959)------------------------------
% 3.49/1.46 % (2961)Refutation found. Thanks to Tanya!
% 3.49/1.46 % SZS status Theorem for theBenchmark
% 3.49/1.46 % SZS output start Proof for theBenchmark
% See solution above
% 3.49/1.46 % (2961)------------------------------
% 3.49/1.46 % (2961)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.46 % (2961)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.46 % (2961)CaDiCaL version: 2.1.3
% 3.49/1.46 % (2961)Termination reason: Refutation
% 3.49/1.46 % (2961)Time elapsed: 0.004 s
% 3.49/1.46 % (2961)Peak memory usage: 89 MB
% 3.49/1.46 % (2961)Instructions burned: 3 (million)
% 3.49/1.46 % (2961)------------------------------
% 3.49/1.46 % (2961)------------------------------
% 3.49/1.46 % (2903)Success in time 0.405 s
% 3.49/1.46 % Vampire exiting
%------------------------------------------------------------------------------