%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU147+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n007.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 12:52:05 PM UTC 2026
% Result : Theorem 0.09s 0.45s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 11 unt; 0 def)
% Number of atoms : 115 ( 55 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 129 ( 48 ~; 58 |; 18 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 53 ( 49 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f3,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] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f11,conjecture,
powerset(empty_set) = singleton(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_zfmisc_1) ).
fof(f12,negated_conjecture,
powerset(empty_set) != singleton(empty_set),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f14,axiom,
! [X0] :
( subset(X0,empty_set)
=> X0 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
fof(f15,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f10]) ).
fof(f16,plain,
powerset(empty_set) != singleton(empty_set),
inference(flattening,[],[f12]) ).
fof(f19,plain,
! [X0] :
( X0 = empty_set
| ~ subset(X0,empty_set) ),
inference(ennf_transformation,[],[f14]) ).
fof(f20,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X2 = X0
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X2 = X0
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f21,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X2 = X0
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ( ( sK0(X0,X1) != X0
| ~ in(sK0(X0,X1),X1) )
& ( sK0(X0,X1) = X0
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f21]) ).
fof(f23,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,[],[f3]) ).
fof(f24,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,[],[f23]) ).
fof(f25,plain,
! [X0,X1] :
( ( X1 = powerset(X0)
| ( ( ~ subset(sK1(X0,X1),X0)
| ~ in(sK1(X0,X1),X1) )
& ( subset(sK1(X0,X1),X0)
| in(sK1(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,[sK1]),skolemize(X2,sK1(X0,X1))],[f24]) ).
fof(f31,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f22]) ).
fof(f32,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f22]) ).
fof(f37,plain,
! [X0,X1] :
( subset(sK1(X0,X1),X0)
| in(sK1(X0,X1),X1)
| powerset(X0) = X1 ),
inference(cnf_transformation,[],[f25]) ).
fof(f38,plain,
! [X0,X1] :
( ~ subset(sK1(X0,X1),X0)
| powerset(X0) = X1
| ~ in(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f42,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f15]) ).
fof(f43,plain,
powerset(empty_set) != singleton(empty_set),
inference(cnf_transformation,[],[f16]) ).
fof(f46,plain,
! [X0] :
( ~ subset(X0,empty_set)
| empty_set = X0 ),
inference(cnf_transformation,[],[f19]) ).
fof(f47,plain,
! [X3,X1] :
( in(X3,X1)
| singleton(X3) != X1 ),
inference(equality_resolution,[],[f32]) ).
fof(f48,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f47]) ).
fof(f49,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f31]) ).
fof(f74,plain,
! [X0] :
( in(sK1(empty_set,X0),X0)
| powerset(empty_set) = X0
| empty_set = sK1(empty_set,X0) ),
inference(resolution,[],[f37,f46]) ).
fof(f81,plain,
! [X0] :
( sK1(empty_set,singleton(X0)) = X0
| empty_set = sK1(empty_set,singleton(X0))
| singleton(X0) = powerset(empty_set) ),
inference(resolution,[],[f74,f49]) ).
fof(f163,plain,
! [X0] :
( empty_set != X0
| empty_set = sK1(empty_set,singleton(X0))
| singleton(X0) = powerset(empty_set) ),
inference(equality_factoring,[],[f81]) ).
fof(f178,plain,
( empty_set = sK1(empty_set,singleton(empty_set))
| powerset(empty_set) = singleton(empty_set) ),
inference(equality_resolution,[],[f163]) ).
fof(f179,plain,
empty_set = sK1(empty_set,singleton(empty_set)),
inference(forward_subsumption_resolution,[],[f178,f43]) ).
fof(f185,plain,
( ~ subset(empty_set,empty_set)
| powerset(empty_set) = singleton(empty_set)
| ~ in(empty_set,singleton(empty_set)) ),
inference(superposition,[],[f38,f179]) ).
fof(f188,plain,
( powerset(empty_set) = singleton(empty_set)
| ~ in(empty_set,singleton(empty_set)) ),
inference(forward_subsumption_resolution,[],[f185,f42]) ).
fof(f189,plain,
~ in(empty_set,singleton(empty_set)),
inference(forward_subsumption_resolution,[],[f188,f43]) ).
fof(f190,plain,
$false,
inference(forward_subsumption_resolution,[],[f189,f48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU147+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 28 03:42:11 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.39 Running first-order model finding
% 0.09/0.39 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
% 0.09/0.45 % (2006725)Will run a generic schedule for satisfiability detection.
% 0.09/0.45 % (2006732)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=604481968:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.45 % (2006730)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4141317809_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.45 % (2006736)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3654861992:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.45 % (2006733)dis+10_1_sil=32000:sp=arity:random_seed=50487062:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.45 % (2006731)% WARNING: option uhcvi not known.
% 0.09/0.45 % (2006734)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3419355621:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.45 % (2006735)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=427711223:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.45 % TRYING [1]
% 0.09/0.45 % TRYING [2]
% 0.09/0.45 % TRYING [3]
% 0.09/0.45 % TRYING [4]
% 0.09/0.45 % (2006731)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=936980625:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.45 % TRYING [5]
% 0.09/0.45 % (2006736) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2006725-2006736"...
% 0.09/0.45 % (2006733) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2006725-2006733"...
% 0.09/0.45 % (2006733)...printing done.
% 0.09/0.45 % (2006736)...printing done.
% 0.09/0.45 % (2006734) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2006725-2006734"...
% 0.09/0.45 % (2006731) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2006725-2006731"...
% 0.09/0.45 % (2006733)Refutation found. Thanks to Tanya!
% 0.09/0.45 % SZS status Theorem for theBenchmark
% 0.09/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.45 % (2006733)------------------------------
% 0.09/0.45 % (2006733)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.45 % (2006733)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.45 % (2006733)CaDiCaL version: 2.1.3
% 0.09/0.45 % (2006733)Termination reason: Refutation
% 0.09/0.45 % (2006733)Time elapsed: 0.007 s
% 0.09/0.45 % (2006733)Peak memory usage: 11 MB
% 0.09/0.45 % (2006733)Instructions burned: 9 (million)
% 0.09/0.45 % (2006725)Success in time 0.044 s
% 0.09/0.45 % Vampire exiting
%------------------------------------------------------------------------------