%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU147+3 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 12:47:25 PM UTC 2026
% Result : Theorem 3.60s 1.48s
% Output : Refutation 3.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 12 unt; 0 def)
% Number of atoms : 122 ( 52 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 138 ( 52 ~; 63 |; 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 : 54 ( 50 !; 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(f7,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f8,conjecture,
powerset(empty_set) = singleton(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_zfmisc_1) ).
fof(f9,negated_conjecture,
powerset(empty_set) != singleton(empty_set),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f11,axiom,
! [X0] :
( subset(X0,empty_set)
=> X0 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
fof(f12,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f7]) ).
fof(f13,plain,
powerset(empty_set) != singleton(empty_set),
inference(flattening,[],[f9]) ).
fof(f16,plain,
! [X0] :
( X0 = empty_set
| ~ subset(X0,empty_set) ),
inference(ennf_transformation,[],[f11]) ).
fof(f17,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(f18,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,[],[f17]) ).
fof(f19,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))],[f18]) ).
fof(f20,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(f21,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,[],[f20]) ).
fof(f22,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))],[f21]) ).
fof(f28,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f19]) ).
fof(f29,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f19]) ).
fof(f34,plain,
! [X0,X1] :
( subset(sK1(X0,X1),X0)
| powerset(X0) = X1
| in(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f35,plain,
! [X0,X1] :
( ~ subset(sK1(X0,X1),X0)
| powerset(X0) = X1
| ~ in(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f39,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f12]) ).
fof(f40,plain,
powerset(empty_set) != singleton(empty_set),
inference(cnf_transformation,[],[f13]) ).
fof(f43,plain,
! [X0] :
( ~ subset(X0,empty_set)
| empty_set = X0 ),
inference(cnf_transformation,[],[f16]) ).
fof(f44,plain,
! [X3,X1] :
( in(X3,X1)
| singleton(X3) != X1 ),
inference(equality_resolution,[],[f29]) ).
fof(f45,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f44]) ).
fof(f46,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f28]) ).
fof(f69,plain,
! [X0] :
( empty_set = sK1(empty_set,X0)
| in(sK1(empty_set,X0),X0)
| powerset(empty_set) = X0 ),
inference(resolution,[],[f34,f43]) ).
fof(f76,plain,
! [X0] :
( ~ subset(empty_set,empty_set)
| powerset(empty_set) = X0
| ~ in(empty_set,X0)
| in(sK1(empty_set,X0),X0)
| powerset(empty_set) = X0 ),
inference(superposition,[],[f35,f69]) ).
fof(f79,plain,
! [X0] :
( ~ subset(empty_set,empty_set)
| powerset(empty_set) = X0
| ~ in(empty_set,X0)
| in(sK1(empty_set,X0),X0) ),
inference(duplicate_literal_removal,[],[f76]) ).
fof(f80,plain,
! [X0] :
( ~ in(empty_set,X0)
| powerset(empty_set) = X0
| in(sK1(empty_set,X0),X0) ),
inference(forward_subsumption_resolution,[],[f79,f39]) ).
fof(f81,plain,
( powerset(empty_set) = singleton(empty_set)
| in(sK1(empty_set,singleton(empty_set)),singleton(empty_set)) ),
inference(resolution,[],[f80,f45]) ).
fof(f83,plain,
in(sK1(empty_set,singleton(empty_set)),singleton(empty_set)),
inference(forward_subsumption_resolution,[],[f81,f40]) ).
fof(f89,plain,
empty_set = sK1(empty_set,singleton(empty_set)),
inference(resolution,[],[f83,f46]) ).
fof(f105,plain,
( ~ subset(empty_set,empty_set)
| powerset(empty_set) = singleton(empty_set)
| ~ in(empty_set,singleton(empty_set)) ),
inference(superposition,[],[f35,f89]) ).
fof(f107,plain,
( powerset(empty_set) = singleton(empty_set)
| ~ in(empty_set,singleton(empty_set)) ),
inference(forward_subsumption_resolution,[],[f105,f39]) ).
fof(f108,plain,
~ in(empty_set,singleton(empty_set)),
inference(forward_subsumption_resolution,[],[f107,f40]) ).
fof(f109,plain,
$false,
inference(forward_subsumption_resolution,[],[f108,f45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU147+3 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n016.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 03:49:33 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 3.60/1.48 % (3238703)Detected formulas, will run a generic FOF schedule.
% 3.60/1.48 % (3238710)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=3629370490:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.60/1.48 % (3238714)dis-21_1_sil=8000:lcm=predicate:random_seed=1134906500: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)
% 3.60/1.48 % (3238713)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4122170616:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.60/1.48 % (3238711)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2448589605:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.60/1.48 % (3238712)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4086439006:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.60/1.48 % (3238708)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=3965851916:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.60/1.48 % (3238709)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=3645289776:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.60/1.48 % (3238711)Refutation not found, incomplete strategy
% 3.60/1.48 % (3238711)------------------------------
% 3.60/1.48 % (3238711)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.60/1.48 % (3238711)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.60/1.48 % (3238711)CaDiCaL version: 2.1.3
% 3.60/1.48 % (3238711)Termination reason: Refutation not found, incomplete strategy
% 3.60/1.48 % (3238711)Time elapsed: 0.001 s
% 3.60/1.48 % (3238711)Peak memory usage: 88 MB
% 3.60/1.48 % (3238713)First to succeed.
% 3.60/1.48 % (3238712)Also succeeded, but the first one will report.
% 3.60/1.48 % (3238713)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3238703"
% 3.60/1.48 % (3238714)Instruction limit reached!
% 3.60/1.48 % (3238714)------------------------------
% 3.60/1.48 % (3238714)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.60/1.48 % (3238714)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.60/1.48 % (3238714)CaDiCaL version: 2.1.3
% 3.60/1.48 % (3238714)Termination reason: Instruction limit
% 3.60/1.48 % (3238714)Termination phase: Saturation
% 3.60/1.48 % (3238714)Time elapsed: 0.064 s
% 3.60/1.48 % (3238714)Peak memory usage: 88 MB
% 3.60/1.48 % (3238714)Instructions burned: 130 (million)
% 3.60/1.48 % (3238711)------------------------------
% 3.60/1.48 % (3238711)------------------------------
% 3.60/1.48 % (3238722)lrs+10_1_sil=8000:sp=occurrence:random_seed=798991275:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.60/1.48 % (3238722)Also succeeded, but the first one will report.
% 3.60/1.48 % (3238713)Refutation found. Thanks to Tanya!
% 3.60/1.48 % SZS status Theorem for theBenchmark
% 3.60/1.48 % SZS output start Proof for theBenchmark
% See solution above
% 3.60/1.49 % (3238713)------------------------------
% 3.60/1.49 % (3238713)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.60/1.49 % (3238713)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.60/1.49 % (3238713)CaDiCaL version: 2.1.3
% 3.60/1.49 % (3238713)Termination reason: Refutation
% 3.60/1.49 % (3238713)Time elapsed: 0.005 s
% 3.60/1.49 % (3238713)Peak memory usage: 89 MB
% 3.60/1.49 % (3238713)Instructions burned: 4 (million)
% 3.60/1.49 % (3238713)------------------------------
% 3.60/1.49 % (3238713)------------------------------
% 3.60/1.49 % (3238703)Success in time 0.43 s
% 3.60/1.49 % Vampire exiting
%------------------------------------------------------------------------------