%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU118+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 12:47:17 PM UTC 2026
% Result : Theorem 3.78s 1.49s
% Output : Refutation 3.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 47 ( 11 unt; 2 def)
% Number of atoms : 159 ( 11 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 182 ( 70 ~; 68 |; 29 &)
% ( 7 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 59 ( 0 sgn 52 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
( finite(X0)
=> ! [X1] :
( element(X1,powerset(X0))
=> finite(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
fof(f7,axiom,
! [X0,X1] :
( preboolean(X1)
=> ( X1 = finite_subsets(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ( subset(X2,X0)
& finite(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_finsub_1) ).
fof(f8,axiom,
! [X0] : preboolean(finite_subsets(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_finsub_1) ).
fof(f25,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f27,conjecture,
! [X0,X1] :
( element(X1,powerset(X0))
=> ( finite(X0)
=> element(X1,finite_subsets(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_finsub_1) ).
fof(f28,negated_conjecture,
~ ! [X0,X1] :
( element(X1,powerset(X0))
=> ( finite(X0)
=> element(X1,finite_subsets(X0)) ) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f29,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f47,plain,
! [X0] :
( ! [X1] :
( finite(X1)
| ~ element(X1,powerset(X0)) )
| ~ finite(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f51,plain,
! [X0,X1] :
( ( X1 = finite_subsets(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ( subset(X2,X0)
& finite(X2) ) ) )
| ~ preboolean(X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f57,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f25]) ).
fof(f60,plain,
? [X0,X1] :
( ~ element(X1,finite_subsets(X0))
& finite(X0)
& element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f28]) ).
fof(f61,plain,
? [X0,X1] :
( ~ element(X1,finite_subsets(X0))
& finite(X0)
& element(X1,powerset(X0)) ),
inference(flattening,[],[f60]) ).
fof(f68,plain,
! [X0,X1] :
( ( ( X1 = finite_subsets(X0)
| ? [X2] :
( ( ~ subset(X2,X0)
| ~ finite(X2)
| ~ in(X2,X1) )
& ( ( subset(X2,X0)
& finite(X2) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ~ subset(X2,X0)
| ~ finite(X2) )
& ( ( subset(X2,X0)
& finite(X2) )
| ~ in(X2,X1) ) )
| finite_subsets(X0) != X1 ) )
| ~ preboolean(X1) ),
inference(nnf_transformation,[],[f51]) ).
fof(f69,plain,
! [X0,X1] :
( ( ( X1 = finite_subsets(X0)
| ? [X2] :
( ( ~ subset(X2,X0)
| ~ finite(X2)
| ~ in(X2,X1) )
& ( ( subset(X2,X0)
& finite(X2) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ~ subset(X2,X0)
| ~ finite(X2) )
& ( ( subset(X2,X0)
& finite(X2) )
| ~ in(X2,X1) ) )
| finite_subsets(X0) != X1 ) )
| ~ preboolean(X1) ),
inference(flattening,[],[f68]) ).
fof(f70,plain,
! [X0,X1] :
( ( ( X1 = finite_subsets(X0)
| ? [X2] :
( ( ~ subset(X2,X0)
| ~ finite(X2)
| ~ in(X2,X1) )
& ( ( subset(X2,X0)
& finite(X2) )
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ subset(X3,X0)
| ~ finite(X3) )
& ( ( subset(X3,X0)
& finite(X3) )
| ~ in(X3,X1) ) )
| finite_subsets(X0) != X1 ) )
| ~ preboolean(X1) ),
inference(rectify,[],[f69]) ).
fof(f71,plain,
! [X0,X1] :
( ( ( X1 = finite_subsets(X0)
| ( ( ~ subset(sK0(X0,X1),X0)
| ~ finite(sK0(X0,X1))
| ~ in(sK0(X0,X1),X1) )
& ( ( subset(sK0(X0,X1),X0)
& finite(sK0(X0,X1)) )
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ subset(X3,X0)
| ~ finite(X3) )
& ( ( subset(X3,X0)
& finite(X3) )
| ~ in(X3,X1) ) )
| finite_subsets(X0) != X1 ) )
| ~ preboolean(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f70]) ).
fof(f82,plain,
( ~ element(sK12,finite_subsets(sK11))
& finite(sK11)
& element(sK12,powerset(sK11)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12]),skolemize(X0,sK11),skolemize(X1,sK12)],[f61]) ).
fof(f83,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f29]) ).
fof(f88,plain,
! [X0,X1] :
( finite(X1)
| ~ element(X1,powerset(X0))
| ~ finite(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f93,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ subset(X3,X0)
| ~ finite(X3)
| finite_subsets(X0) != X1
| ~ preboolean(X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f97,plain,
! [X0] : preboolean(finite_subsets(X0)),
inference(cnf_transformation,[],[f8]) ).
fof(f132,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f134,plain,
element(sK12,powerset(sK11)),
inference(cnf_transformation,[],[f82]) ).
fof(f135,plain,
finite(sK11),
inference(cnf_transformation,[],[f82]) ).
fof(f136,plain,
~ element(sK12,finite_subsets(sK11)),
inference(cnf_transformation,[],[f82]) ).
fof(f137,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f83]) ).
fof(f144,plain,
! [X3,X0] :
( in(X3,finite_subsets(X0))
| ~ subset(X3,X0)
| ~ finite(X3)
| ~ preboolean(finite_subsets(X0)) ),
inference(equality_resolution,[],[f93]) ).
fof(f172,plain,
! [X3,X0] :
( ~ subset(X3,X0)
| in(X3,finite_subsets(X0))
| ~ finite(X3) ),
inference(forward_subsumption_resolution,[],[f144,f97]) ).
fof(f182,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| ~ finite(X0)
| in(X0,finite_subsets(X1)) ),
inference(resolution,[],[f172,f137]) ).
fof(f203,plain,
( ~ finite(sK12)
| in(sK12,finite_subsets(sK11)) ),
inference(resolution,[],[f182,f134]) ).
fof(f205,definition,
( spl13_1
<=> in(sK12,finite_subsets(sK11)) ),
introduced(definition,[new_symbols(definition,[spl13_1])],[avatar_definition]) ).
fof(f207,plain,
( in(sK12,finite_subsets(sK11))
| ~ spl13_1 ),
inference(avatar_component_clause,[],[f205]) ).
fof(f209,definition,
( spl13_2
<=> finite(sK12) ),
introduced(definition,[new_symbols(definition,[spl13_2])],[avatar_definition]) ).
fof(f211,plain,
( ~ finite(sK12)
| spl13_2 ),
inference(avatar_component_clause,[],[f209]) ).
fof(f212,plain,
( spl13_1
| ~ spl13_2 ),
inference(avatar_split_clause,[],[f203,f209,f205]) ).
fof(f222,plain,
( ! [X0] :
( ~ element(sK12,powerset(X0))
| ~ finite(X0) )
| spl13_2 ),
inference(resolution,[],[f211,f88]) ).
fof(f267,plain,
( ~ finite(sK11)
| spl13_2 ),
inference(resolution,[],[f222,f134]) ).
fof(f270,plain,
( $false
| spl13_2 ),
inference(forward_subsumption_resolution,[],[f267,f135]) ).
fof(f271,plain,
spl13_2,
inference(avatar_contradiction_clause,[],[f270]) ).
fof(f283,plain,
( element(sK12,finite_subsets(sK11))
| ~ spl13_1 ),
inference(resolution,[],[f207,f132]) ).
fof(f284,plain,
( $false
| ~ spl13_1 ),
inference(forward_subsumption_resolution,[],[f283,f136]) ).
fof(f285,plain,
~ spl13_1,
inference(avatar_contradiction_clause,[],[f284]) ).
cnf(s1,plain,
( spl13_1
| ~ spl13_2 ),
inference(sat_conversion,[],[f212]) ).
cnf(s2,plain,
spl13_2,
inference(sat_conversion,[],[f271]) ).
cnf(s4,plain,
~ spl13_1,
inference(sat_conversion,[],[f285]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s2,s4]) ).
fof(f286,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU118+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n005.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 03:35:47 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.39 Running first-order theorem proving
% 0.10/0.39 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
% 3.78/1.49 % (412083)Detected formulas, will run a generic FOF schedule.
% 3.78/1.49 % (412088)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=3951849739:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.78/1.49 % (412089)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=1829688196:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.78/1.49 % (412091)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4210205376:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.78/1.49 % (412092)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3004294969:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.78/1.49 % (412090)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=877117961:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.78/1.49 % (412091)Refutation not found, incomplete strategy
% 3.78/1.49 % (412091)------------------------------
% 3.78/1.49 % (412091)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.78/1.49 % (412091)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/1.49 % (412091)CaDiCaL version: 2.1.3
% 3.78/1.49 % (412091)Termination reason: Refutation not found, incomplete strategy
% 3.78/1.49 % (412091)Time elapsed: 0.001 s
% 3.78/1.49 % (412091)Peak memory usage: 87 MB
% 3.78/1.49 % (412092)Refutation not found, incomplete strategy
% 3.78/1.49 % (412092)------------------------------
% 3.78/1.49 % (412092)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.78/1.49 % (412092)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/1.49 % (412092)CaDiCaL version: 2.1.3
% 3.78/1.49 % (412092)Termination reason: Refutation not found, incomplete strategy
% 3.78/1.49 % (412092)Time elapsed: 0.002 s
% 3.78/1.49 % (412092)Peak memory usage: 87 MB
% 3.78/1.49 % (412092)Instructions burned: 1 (million)
% 3.78/1.49 % (412094)dis-21_1_sil=8000:lcm=predicate:random_seed=144041053: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)
% 3.78/1.49 % (412093)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2530350523:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.78/1.49 % (412093)First to succeed.
% 3.78/1.49 % (412093)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-412083"
% 3.78/1.49 % (412094)Instruction limit reached!
% 3.78/1.49 % (412094)------------------------------
% 3.78/1.49 % (412094)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.78/1.49 % (412094)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/1.49 % (412094)CaDiCaL version: 2.1.3
% 3.78/1.49 % (412094)Termination reason: Instruction limit
% 3.78/1.49 % (412094)Termination phase: Saturation
% 3.78/1.49 % (412094)Time elapsed: 0.074 s
% 3.78/1.49 % (412094)Peak memory usage: 90 MB
% 3.78/1.49 % (412094)Instructions burned: 130 (million)
% 3.78/1.49 % (412092)------------------------------
% 3.78/1.49 % (412092)------------------------------
% 3.78/1.49 % (412091)------------------------------
% 3.78/1.49 % (412091)------------------------------
% 3.78/1.49 % (412102)lrs+10_1_sil=8000:sp=occurrence:random_seed=1472814456:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.78/1.49 % (412102)Also succeeded, but the first one will report.
% 3.78/1.49 % (412093)Refutation found. Thanks to Tanya!
% 3.78/1.49 % SZS status Theorem for theBenchmark
% 3.78/1.49 % SZS output start Proof for theBenchmark
% See solution above
% 3.78/1.50 % (412093)------------------------------
% 3.78/1.50 % (412093)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.78/1.50 % (412093)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/1.50 % (412093)CaDiCaL version: 2.1.3
% 3.78/1.50 % (412093)Termination reason: Refutation
% 3.78/1.50 % (412093)Time elapsed: 0.008 s
% 3.78/1.50 % (412093)Peak memory usage: 89 MB
% 3.78/1.50 % (412093)Instructions burned: 8 (million)
% 3.78/1.50 % (412093)------------------------------
% 3.78/1.50 % (412093)------------------------------
% 3.78/1.50 % (412083)Success in time 0.454 s
% 3.78/1.50 % Vampire exiting
%------------------------------------------------------------------------------