%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU808^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 08:33:29 AM UTC 2026
% Result : Theorem 0.09s 0.25s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 26 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 147 ( 30 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 142 ( 9 ~; 2 |; 4 &; 109 @)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 12 usr; 6 con; 0-4 aty)
% ( 3 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 18 ( 8 ^; 9 !; 1 ?; 18 :)
% 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_6,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_7,type,
vIMP: $o > $o > $o ).
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_13,type,
vNOT: $o > $o ).
thf(f1,axiom,
( omegaSAx
= ( ! [X0: $i] :
( ( in @ X0 @ omega )
=> ( in @ ( setadjoin @ X0 @ X0 ) @ omega ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaSAx) ).
thf(f2,axiom,
( omegaS
= ( ^ [X0: $i] : ( setadjoin @ X0 @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaS) ).
thf(f3,conjecture,
( omegaSAx
=> ! [X0: $i] :
( ( in @ X0 @ omega )
=> ( in @ ( omegaS @ X0 ) @ omega ) ) ),
file('/export/starexec/sandbox2/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
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ omega )
=> ( in @ ( setadjoin @ Y0 @ Y0 ) @ omega ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
( omegaS
= ( ^ [Y0: $i] : ( setadjoin @ Y0 @ Y0 ) ) ),
inference(fool_elimination,[],[f2]) ).
thf(f8,plain,
~ ( omegaSAx
=> ! [X0: $i] :
( ( in @ X0 @ omega )
=> ( in @ ( omegaS @ X0 ) @ omega ) ) ),
inference(rectify,[],[f4]) ).
thf(f9,plain,
~ ( ( omegaSAx = $true )
=> ! [X0: $i] :
( ( ( in @ X0 @ omega )
= $true )
=> ( ( in @ ( omegaS @ X0 ) @ omega )
= $true ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
( ? [X0: $i] :
( ( ( in @ ( omegaS @ X0 ) @ omega )
!= $true )
& ( ( in @ X0 @ omega )
= $true ) )
& ( omegaSAx = $true ) ),
inference(ennf_transformation,[],[f9]) ).
thf(f11,plain,
( ( $true
!= ( in @ ( omegaS @ sK0 ) @ omega ) )
& ( $true
= ( in @ sK0 @ omega ) )
& ( omegaSAx = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f10]) ).
thf(f12,plain,
( omegaSAx
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ omega )
=> ( in @ ( setadjoin @ Y0 @ Y0 ) @ omega ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f13,plain,
( omegaS
= ( ^ [Y0: $i] : ( setadjoin @ Y0 @ Y0 ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f14,plain,
omegaSAx = $true,
inference(cnf_transformation,[],[f11]) ).
thf(f15,plain,
( $true
= ( in @ sK0 @ omega ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f16,plain,
( $true
!= ( in @ ( omegaS @ sK0 ) @ omega ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f19,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ omega )
=> ( in @ ( setadjoin @ Y0 @ Y0 ) @ omega ) ) )
= $true ),
inference(definition_unfolding,[],[f12,f14]) ).
thf(f20,plain,
( $true
!= ( in
@ ( ^ [Y0: $i] : ( setadjoin @ Y0 @ Y0 )
@ sK0 )
@ omega ) ),
inference(definition_unfolding,[],[f16,f13]) ).
thf(f21,plain,
( $true
!= ( in @ ( setadjoin @ sK0 @ sK0 ) @ omega ) ),
inference(beta-eta_normalization,[],[f20]) ).
thf(f22,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ omega )
=> ( in @ ( setadjoin @ Y0 @ Y0 ) @ omega ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f19]) ).
thf(f23,plain,
! [X1: $i] :
( $true
= ( ( in @ X1 @ omega )
=> ( in @ ( setadjoin @ X1 @ X1 ) @ omega ) ) ),
inference(beta-eta_normalization,[],[f22]) ).
thf(f24,plain,
! [X1: $i] :
( ( $true
= ( in @ ( setadjoin @ X1 @ X1 ) @ omega ) )
| ( $false
= ( in @ X1 @ omega ) ) ),
inference(imp_proxy_clausification,[],[f23]) ).
thf(f25,plain,
( ( $true != $true )
| ( ( in @ sK0 @ omega )
= $false ) ),
inference(constrained_superposition,[],[f21,f24]) ).
thf(f26,plain,
( ( in @ sK0 @ omega )
= $false ),
inference(trivial_inequality_removal,[],[f25]) ).
thf(f28,plain,
$true = $false,
inference(constrained_superposition,[],[f15,f26]) ).
thf(f29,plain,
$false,
inference(trivial_inequality_removal,[],[f28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU808^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n004.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 14:33:08 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.25 % (1367163)Will run a generic schedule for satisfiability detection.
% 0.09/0.25 % (1367171)dis+10_1_sil=32000:sp=arity:random_seed=256194668:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.09/0.25 % (1367171) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1367163-1367171"...
% 0.09/0.25 % (1367171)...printing done.
% 0.09/0.25 % (1367171)Refutation found. Thanks to Tanya!
% 0.09/0.25 % SZS status Theorem for theBenchmark
% 0.09/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.25 % (1367171)------------------------------
% 0.09/0.25 % (1367171)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.25 % (1367171)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.25 % (1367171)CaDiCaL version: 2.1.3
% 0.09/0.25 % (1367171)Termination reason: Refutation
% 0.09/0.25 % (1367171)Time elapsed: 0.001 s
% 0.09/0.25 % (1367171)Peak memory usage: 12 MB
% 0.09/0.25 % (1367171)Instructions burned: 2 (million)
% 0.09/0.25 % (1367163)Success in time 0.015 s
% 0.09/0.25 % Vampire exiting
%------------------------------------------------------------------------------