%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU809^2 : 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 : 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 : Wed Sep 30 08:33:30 AM UTC 2026
% Result : Theorem 0.10s 0.26s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 2
% Syntax : Number of formulae : 21 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 135 ( 25 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 132 ( 7 ~; 2 |; 4 &; 101 @)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 11 usr; 6 con; 0-4 aty)
% ( 3 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 14 ( 4 ^; 9 !; 1 ?; 14 :)
% 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,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_6,type,
vIMP: $o > $o > $o ).
thf(func_def_7,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_8,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/sandbox2/benchmark/theBenchmark.p',omegaSAx) ).
thf(f2,conjecture,
( omegaSAx
=> ! [X0: $i] :
( ( in @ X0 @ omega )
=> ( in @ ( setadjoin @ X0 @ X0 ) @ omega ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaSclos) ).
thf(f3,negated_conjecture,
~ ( omegaSAx
=> ! [X0: $i] :
( ( in @ X0 @ omega )
=> ( in @ ( setadjoin @ X0 @ X0 ) @ omega ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
( omegaSAx
= ( ! [X0: $i] :
( ( in @ X0 @ omega )
=> ( in @ ( setadjoin @ X0 @ X0 ) @ omega ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f5,plain,
( omegaSAx
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ omega )
=> ( in @ ( setadjoin @ Y0 @ Y0 ) @ omega ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
~ ( omegaSAx
=> ! [X0: $i] :
( ( in @ X0 @ omega )
=> ( in @ ( setadjoin @ X0 @ X0 ) @ omega ) ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ( ( omegaSAx = $true )
=> ! [X0: $i] :
( ( ( in @ X0 @ omega )
= $true )
=> ( ( in @ ( setadjoin @ X0 @ X0 ) @ omega )
= $true ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( ? [X0: $i] :
( ( ( in @ ( setadjoin @ X0 @ X0 ) @ omega )
!= $true )
& ( ( in @ X0 @ omega )
= $true ) )
& ( omegaSAx = $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f9,plain,
( ( $true
!= ( in @ ( setadjoin @ sK0 @ sK0 ) @ omega ) )
& ( $true
= ( in @ sK0 @ omega ) )
& ( omegaSAx = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f8]) ).
thf(f10,plain,
( omegaSAx
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ omega )
=> ( in @ ( setadjoin @ Y0 @ Y0 ) @ omega ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f11,plain,
omegaSAx = $true,
inference(cnf_transformation,[],[f9]) ).
thf(f12,plain,
( $true
= ( in @ sK0 @ omega ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f13,plain,
( $true
!= ( in @ ( setadjoin @ sK0 @ sK0 ) @ omega ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f16,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ omega )
=> ( in @ ( setadjoin @ Y0 @ Y0 ) @ omega ) ) )
= $true ),
inference(definition_unfolding,[],[f10,f11]) ).
thf(f17,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ omega )
=> ( in @ ( setadjoin @ Y0 @ Y0 ) @ omega ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f16]) ).
thf(f18,plain,
! [X1: $i] :
( $true
= ( ( in @ X1 @ omega )
=> ( in @ ( setadjoin @ X1 @ X1 ) @ omega ) ) ),
inference(beta-eta_normalization,[],[f17]) ).
thf(f19,plain,
! [X1: $i] :
( ( $true
= ( in @ ( setadjoin @ X1 @ X1 ) @ omega ) )
| ( $false
= ( in @ X1 @ omega ) ) ),
inference(imp_proxy_clausification,[],[f18]) ).
thf(f20,plain,
( ( $true != $true )
| ( ( in @ sK0 @ omega )
= $false ) ),
inference(constrained_superposition,[],[f13,f19]) ).
thf(f21,plain,
( ( in @ sK0 @ omega )
= $false ),
inference(trivial_inequality_removal,[],[f20]) ).
thf(f23,plain,
$true = $false,
inference(constrained_superposition,[],[f12,f21]) ).
thf(f24,plain,
$false,
inference(trivial_inequality_removal,[],[f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU809^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.17 % Computer : n007.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Sep 29 14:31:11 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.19 Running first-order model finding
% 0.10/0.19 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
% 0.10/0.26 % (3446186)Will run a generic schedule for satisfiability detection.
% 0.10/0.26 % (3446191)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4211202897_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.26 % Exception at run slice level
% 0.10/0.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.10/0.26 % (3446192)% WARNING: option uhcvi not known.
% 0.10/0.26 % (3446199)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3330040027:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.10/0.26 % Exception at run slice level
% 0.10/0.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.10/0.26 % (3446192)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3019048309:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/0.26 % (3446192)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.10/0.26 % (3446192)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.10/0.26 % (3446194)dis+10_1_sil=32000:sp=arity:random_seed=2548506222:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.26 % (3446192) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3446186-3446192"...
% 0.10/0.26 % (3446201)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=203319686:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.26 % (3446192)...printing done.
% 0.10/0.26 % (3446201) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3446186-3446201"...
% 0.10/0.26 % (3446194) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3446186-3446194"...
% 0.10/0.26 % (3446192)Refutation found. Thanks to Tanya!
% 0.10/0.26 % SZS status Theorem for theBenchmark
% 0.10/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.26 % (3446192)------------------------------
% 0.10/0.26 % (3446192)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.26 % (3446192)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.26 % (3446192)CaDiCaL version: 2.1.3
% 0.10/0.26 % (3446192)Termination reason: Refutation
% 0.10/0.26 % (3446192)Time elapsed: 0.006 s
% 0.10/0.26 % (3446192)Peak memory usage: 12 MB
% 0.10/0.26 % (3446192)Instructions burned: 2 (million)
% 0.10/0.26 % (3446186)Success in time 0.055 s
% 0.10/0.26 % Vampire exiting
%------------------------------------------------------------------------------