%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU113+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n011.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 12:51:57 PM UTC 2026
% Result : Theorem 0.11s 0.47s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 39 ( 10 unt; 0 def)
% Number of atoms : 152 ( 11 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 178 ( 65 ~; 71 |; 32 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 80 ( 74 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f8,axiom,
! [X0,X1] :
( preboolean(X1)
=> ( X1 = finite_subsets(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ( subset(X2,X0)
& finite(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_finsub_1) ).
fof(f9,axiom,
! [X0] : preboolean(finite_subsets(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_finsub_1) ).
fof(f11,axiom,
! [X0] :
( ~ empty(powerset(X0))
& cup_closed(powerset(X0))
& diff_closed(powerset(X0))
& preboolean(powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_finsub_1) ).
fof(f26,conjecture,
! [X0] : subset(finite_subsets(X0),powerset(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_finsub_1) ).
fof(f27,negated_conjecture,
~ ! [X0] : subset(finite_subsets(X0),powerset(X0)),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f28,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( empty(X1)
| in(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f29,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f51,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f52,plain,
! [X0,X1] :
( ( X1 = finite_subsets(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ( subset(X2,X0)
& finite(X2) ) ) )
| ~ preboolean(X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f57,plain,
? [X0] : ~ subset(finite_subsets(X0),powerset(X0)),
inference(ennf_transformation,[],[f27]) ).
fof(f58,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f28]) ).
fof(f59,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f58]) ).
fof(f66,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,[],[f51]) ).
fof(f67,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,[],[f66]) ).
fof(f68,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK0(X0,X1),X1)
& in(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f67]) ).
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(nnf_transformation,[],[f52]) ).
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) ) ) )
& ( ! [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,[],[f69]) ).
fof(f71,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,[],[f70]) ).
fof(f72,plain,
! [X0,X1] :
( ( ( X1 = finite_subsets(X0)
| ( ( ~ subset(sK1(X0,X1),X0)
| ~ finite(sK1(X0,X1))
| ~ in(sK1(X0,X1),X1) )
& ( ( subset(sK1(X0,X1),X0)
& finite(sK1(X0,X1)) )
| in(sK1(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,[sK1]),skolemize(X2,sK1(X0,X1))],[f71]) ).
fof(f83,plain,
~ subset(finite_subsets(sK12),powerset(sK12)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X0,sK12)],[f57]) ).
fof(f84,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f29]) ).
fof(f93,plain,
! [X0,X1] :
( in(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f94,plain,
! [X0,X1] :
( ~ in(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f96,plain,
! [X3,X0,X1] :
( subset(X3,X0)
| ~ in(X3,X1)
| finite_subsets(X0) != X1
| ~ preboolean(X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f101,plain,
! [X0] : preboolean(finite_subsets(X0)),
inference(cnf_transformation,[],[f9]) ).
fof(f106,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f11]) ).
fof(f136,plain,
~ subset(finite_subsets(sK12),powerset(sK12)),
inference(cnf_transformation,[],[f83]) ).
fof(f137,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f139,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f146,plain,
! [X3,X0] :
( subset(X3,X0)
| ~ in(X3,finite_subsets(X0))
| ~ preboolean(finite_subsets(X0)) ),
inference(equality_resolution,[],[f96]) ).
fof(f205,plain,
! [X0,X1] :
( in(X0,powerset(X1))
| empty(powerset(X1))
| ~ subset(X0,X1) ),
inference(resolution,[],[f137,f139]) ).
fof(f219,plain,
! [X0,X1] :
( in(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(forward_subsumption_resolution,[],[f205,f106]) ).
fof(f263,plain,
! [X3,X0] :
( ~ in(X3,finite_subsets(X0))
| subset(X3,X0) ),
inference(forward_subsumption_resolution,[],[f146,f101]) ).
fof(f265,plain,
! [X0,X1] :
( subset(sK0(finite_subsets(X0),X1),X0)
| subset(finite_subsets(X0),X1) ),
inference(resolution,[],[f263,f93]) ).
fof(f331,plain,
! [X0,X1] :
( ~ subset(sK0(X0,powerset(X1)),X1)
| subset(X0,powerset(X1)) ),
inference(resolution,[],[f219,f94]) ).
fof(f630,plain,
! [X0] :
( subset(finite_subsets(X0),powerset(X0))
| subset(finite_subsets(X0),powerset(X0)) ),
inference(resolution,[],[f331,f265]) ).
fof(f632,plain,
! [X0] : subset(finite_subsets(X0),powerset(X0)),
inference(duplicate_literal_removal,[],[f630]) ).
fof(f633,plain,
$false,
inference(resolution,[],[f632,f136]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU113+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n011.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 03:35:15 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.47 % (2990427)Will run a generic schedule for satisfiability detection.
% 0.11/0.47 % (2990436)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4033626048:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.47 % (2990433)% WARNING: option uhcvi not known.
% 0.11/0.47 % (2990435)dis+10_1_sil=32000:sp=arity:random_seed=3711814365:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.47 % (2990433)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2229940061:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.11/0.47 % (2990432)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2415758219_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.47 % (2990438)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1163208583:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.47 % (2990434)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1801558595:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.47 % TRYING [1]
% 0.11/0.47 % TRYING [2]
% 0.11/0.47 % TRYING [3]
% 0.11/0.47 % TRYING [4]
% 0.11/0.47 % (2990437)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=169720578:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.47 % TRYING [5]
% 0.11/0.47 % (2990435) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2990427-2990435"...
% 0.11/0.47 % (2990436) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2990427-2990436"...
% 0.11/0.47 % (2990435)...printing done.
% 0.11/0.47 % (2990436)...printing done.
% 0.11/0.47 % TRYING [6]
% 0.11/0.47 % (2990435)Refutation found. Thanks to Tanya!
% 0.11/0.47 % SZS status Theorem for theBenchmark
% 0.11/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.47 % (2990435)------------------------------
% 0.11/0.47 % (2990435)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.47 % (2990435)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.47 % (2990435)CaDiCaL version: 2.1.3
% 0.11/0.47 % (2990435)Termination reason: Refutation
% 0.11/0.47 % (2990435)Time elapsed: 0.015 s
% 0.11/0.47 % (2990435)Peak memory usage: 12 MB
% 0.11/0.47 % (2990435)Instructions burned: 19 (million)
% 0.11/0.47 % (2990427)Success in time 0.054 s
% 0.11/0.47 % Vampire exiting
%------------------------------------------------------------------------------