%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU808^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 : Wed Sep 30 08:31:34 AM UTC 2026
% Result : Theorem 0.19s 0.26s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 226 ( 54 equ; 0 cnn)
% Maximal formula atoms : 6 ( 8 avg)
% Number of connectives : 199 ( 24 ~; 16 |; 10 &; 136 @)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 6 con; 0-4 aty)
% Number of variables : 21 ( 4 ^; 14 !; 3 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
omegaSAx: $o ).
thf(func_def_5,type,
omegaS: $i > $i ).
thf(func_def_8,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_12,type,
vNOT: $o > $o ).
thf(f1,axiom,
( omegaSAx
= ( ! [X0: $i] :
( ( in @ X0 @ omega )
=> ( in @ ( setadjoin @ X0 @ X0 ) @ omega ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaSAx) ).
thf(f2,axiom,
( omegaS
= ( ^ [X0: $i] : ( setadjoin @ X0 @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaS) ).
thf(f3,conjecture,
( omegaSAx
=> ! [X0: $i] :
( ( in @ X0 @ omega )
=> ( in @ ( omegaS @ X0 ) @ omega ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaSp) ).
thf(f4,negated_conjecture,
~ ( omegaSAx
=> ! [X0: $i] :
( ( in @ X0 @ omega )
=> ( in @ ( omegaS @ X0 ) @ omega ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
( omegaSAx
= ( ! [X0: $i] :
( ( in @ X0 @ omega )
=> ( in @ ( setadjoin @ X0 @ X0 ) @ omega ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f6,plain,
( ( omegaSAx = $true )
<=> ! [X0: $i] :
( ( ( in @ X0 @ omega )
= $true )
=> ( ( in @ ( setadjoin @ X0 @ X0 ) @ omega )
= $true ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
~ ( omegaSAx
=> ! [X0: $i] :
( ( in @ X0 @ omega )
=> ( in @ ( omegaS @ X0 ) @ omega ) ) ),
inference(rectify,[],[f4]) ).
thf(f8,plain,
~ ( ( omegaSAx = $true )
=> ! [X0: $i] :
( ( ( in @ X0 @ omega )
= $true )
=> ( ( in @ ( omegaS @ X0 ) @ omega )
= $true ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
( omegaS
= ( ^ [Y0: $i] : ( setadjoin @ Y0 @ Y0 ) ) ),
inference(fool_elimination,[],[f2]) ).
thf(f10,plain,
( ( omegaSAx = $true )
<=> ! [X0: $i] :
( ( ( in @ ( setadjoin @ X0 @ X0 ) @ omega )
= $true )
| ( ( in @ X0 @ omega )
!= $true ) ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f11,plain,
( ( omegaSAx = $true )
& ? [X0: $i] :
( ( ( in @ X0 @ omega )
= $true )
& ( ( in @ ( omegaS @ X0 ) @ omega )
!= $true ) ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f12,plain,
( ( omegaSAx = $true )
& ( $true
= ( in @ sK0 @ omega ) )
& ( $true
!= ( in @ ( omegaS @ sK0 ) @ omega ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f11]) ).
thf(f13,plain,
( ( ( omegaSAx = $true )
| ? [X0: $i] :
( ( ( in @ ( setadjoin @ X0 @ X0 ) @ omega )
!= $true )
& ( ( in @ X0 @ omega )
= $true ) ) )
& ( ! [X0: $i] :
( ( ( in @ ( setadjoin @ X0 @ X0 ) @ omega )
= $true )
| ( ( in @ X0 @ omega )
!= $true ) )
| ( omegaSAx != $true ) ) ),
inference(nnf_transformation,[],[f10]) ).
thf(f14,plain,
( ( ( omegaSAx = $true )
| ? [X0: $i] :
( ( ( in @ ( setadjoin @ X0 @ X0 ) @ omega )
!= $true )
& ( ( in @ X0 @ omega )
= $true ) ) )
& ( ! [X1: $i] :
( ( $true
= ( in @ ( setadjoin @ X1 @ X1 ) @ omega ) )
| ( ( in @ X1 @ omega )
!= $true ) )
| ( omegaSAx != $true ) ) ),
inference(rectify,[],[f13]) ).
thf(f15,plain,
( ( ( omegaSAx = $true )
| ( ( $true
!= ( in @ ( setadjoin @ sK1 @ sK1 ) @ omega ) )
& ( ( in @ sK1 @ omega )
= $true ) ) )
& ( ! [X1: $i] :
( ( $true
= ( in @ ( setadjoin @ X1 @ X1 ) @ omega ) )
| ( ( in @ X1 @ omega )
!= $true ) )
| ( omegaSAx != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f14]) ).
thf(f16,plain,
( $true
!= ( in @ ( omegaS @ sK0 ) @ omega ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f17,plain,
( $true
= ( in @ sK0 @ omega ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f18,plain,
omegaSAx = $true,
inference(cnf_transformation,[],[f12]) ).
thf(f19,plain,
! [X1: $i] :
( ( $true
= ( in @ ( setadjoin @ X1 @ X1 ) @ omega ) )
| ( ( in @ X1 @ omega )
!= $true )
| ( omegaSAx != $true ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f22,plain,
( omegaS
= ( ^ [Y0: $i] : ( setadjoin @ Y0 @ Y0 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f25,plain,
( $true
!= ( in
@ ( ^ [Y0: $i] : ( setadjoin @ Y0 @ Y0 )
@ sK0 )
@ omega ) ),
inference(definition_unfolding,[],[f16,f22]) ).
thf(f28,plain,
! [X1: $i] :
( ( ( in @ X1 @ omega )
!= $true )
| ( $true != $true )
| ( $true
= ( in @ ( setadjoin @ X1 @ X1 ) @ omega ) ) ),
inference(definition_unfolding,[],[f19,f18]) ).
thf(f29,plain,
( $true
!= ( in @ ( setadjoin @ sK0 @ sK0 ) @ omega ) ),
inference(beta-eta_normalization,[],[f25]) ).
thf(f30,plain,
! [X1: $i] :
( ( ( in @ X1 @ omega )
!= $true )
| ( $true
= ( in @ ( setadjoin @ X1 @ X1 ) @ omega ) ) ),
inference(trivial_inequality_removal,[],[f28]) ).
thf(f31,plain,
( ( $true
= ( in @ ( setadjoin @ sK0 @ sK0 ) @ omega ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f30,f17]) ).
thf(f32,plain,
( $true
= ( in @ ( setadjoin @ sK0 @ sK0 ) @ omega ) ),
inference(trivial_inequality_removal,[],[f31]) ).
thf(f33,plain,
$false,
inference(forward_subsumption_resolution,[],[f32,f29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU808^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n004.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 14:33:07 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 Running higher-order theorem proving
% 0.08/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.26 % (1366868)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.26 % (1366873)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4059925494:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.19/0.26 % (1366873) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1366868-1366873"...
% 0.19/0.26 % (1366873)...printing done.
% 0.19/0.26 % (1366875)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1704283994:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.19/0.26 % (1366874)lrs+10_16_si=on:nwc=1.5:random_seed=677997028:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.19/0.26 % (1366877)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4183815301:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.19/0.26 % (1366876)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=2624061738:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.19/0.26 % (1366873)Refutation found. Thanks to Tanya!
% 0.19/0.26 % SZS status Theorem for theBenchmark
% 0.19/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.26 % (1366873)------------------------------
% 0.19/0.26 % (1366873)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.26 % (1366873)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.26 % (1366873)CaDiCaL version: 2.1.3
% 0.19/0.26 % (1366873)Termination reason: Refutation
% 0.19/0.26 % (1366873)Time elapsed: 0.006 s
% 0.19/0.26 % (1366873)Peak memory usage: 12 MB
% 0.19/0.26 % (1366873)Instructions burned: 2 (million)
% 0.19/0.26 % (1366868)Success in time 0.038 s
% 0.19/0.26 % Vampire exiting
%------------------------------------------------------------------------------