%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU623^2 : 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 : n003.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 08:32:43 AM UTC 2026
% Result : Theorem 0.07s 0.25s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 4
% Syntax : Number of formulae : 52 ( 38 unt; 0 typ; 0 def)
% Number of atoms : 357 ( 77 equ; 0 cnn)
% Maximal formula atoms : 7 ( 6 avg)
% Number of connectives : 464 ( 8 ~; 9 |; 15 &; 349 @)
% ( 0 <=>; 52 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 21 usr; 11 con; 0-4 aty)
% ( 31 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 104 ( 38 ^; 60 !; 6 ?; 104 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
powerset: $i > $i ).
thf(func_def_4,type,
subset: $i > $i > $o ).
thf(func_def_5,type,
subsetE: $o ).
thf(func_def_7,type,
powersetsubset: $o ).
thf(func_def_8,type,
binunion: $i > $i > $i ).
thf(func_def_9,type,
binunionLsub: $o ).
thf(func_def_10,type,
singletoninpowerset: $o ).
thf(func_def_11,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_12,type,
vIMP: $o > $o > $o ).
thf(func_def_13,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_22,type,
vNOT: $o > $o ).
thf(f1,axiom,
( subsetE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( subset @ X0 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE) ).
thf(f3,axiom,
( binunionLsub
= ( ! [X0: $i,X1: $i] : ( subset @ X0 @ ( binunion @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionLsub) ).
thf(f4,axiom,
( singletoninpowerset
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ X0 )
=> ( in @ ( setadjoin @ X1 @ emptyset ) @ ( powerset @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletoninpowerset) ).
thf(f5,conjecture,
( subsetE
=> ( powersetsubset
=> ( binunionLsub
=> ( singletoninpowerset
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X0 @ X1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletoninpowunion) ).
thf(f6,negated_conjecture,
~ ( subsetE
=> ( powersetsubset
=> ( binunionLsub
=> ( singletoninpowerset
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X0 @ X1 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f7,plain,
( subsetE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( subset @ X0 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f8,plain,
( subsetE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ Y1 )
=> ( ( in @ Y0 @ Y2 )
=> ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f11,plain,
( binunionLsub
= ( ! [X0: $i,X1: $i] : ( subset @ X0 @ ( binunion @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f12,plain,
( binunionLsub
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( subset @ Y1 @ ( binunion @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
( singletoninpowerset
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ X0 )
=> ( in @ ( setadjoin @ X1 @ emptyset ) @ ( powerset @ X0 ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f14,plain,
( singletoninpowerset
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ Y1 )
=> ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( powerset @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
~ ( subsetE
=> ( powersetsubset
=> ( binunionLsub
=> ( singletoninpowerset
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X0 @ X1 ) ) ) ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f16,plain,
~ ( ( subsetE = $true )
=> ( ( powersetsubset = $true )
=> ( ( binunionLsub = $true )
=> ( ( singletoninpowerset = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X0 @ X1 ) ) )
= $true ) ) ) ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X0 @ X1 ) ) )
!= $true )
& ( ( in @ X2 @ X0 )
= $true ) )
& ( singletoninpowerset = $true )
& ( binunionLsub = $true )
& ( powersetsubset = $true )
& ( subsetE = $true ) ),
inference(ennf_transformation,[],[f16]) ).
thf(f18,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X0 @ X1 ) ) )
!= $true )
& ( ( in @ X2 @ X0 )
= $true ) )
& ( singletoninpowerset = $true )
& ( binunionLsub = $true )
& ( powersetsubset = $true )
& ( subsetE = $true ) ),
inference(flattening,[],[f17]) ).
thf(f19,plain,
( ( $true
!= ( in @ ( setadjoin @ sK2 @ emptyset ) @ ( powerset @ ( binunion @ sK0 @ sK1 ) ) ) )
& ( $true
= ( in @ sK2 @ sK0 ) )
& ( singletoninpowerset = $true )
& ( binunionLsub = $true )
& ( powersetsubset = $true )
& ( subsetE = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f18]) ).
thf(f20,plain,
( subsetE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ Y1 )
=> ( ( in @ Y0 @ Y2 )
=> ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f22,plain,
( binunionLsub
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( subset @ Y1 @ ( binunion @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f23,plain,
( singletoninpowerset
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ Y1 )
=> ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( powerset @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f24,plain,
subsetE = $true,
inference(cnf_transformation,[],[f19]) ).
thf(f26,plain,
binunionLsub = $true,
inference(cnf_transformation,[],[f19]) ).
thf(f27,plain,
singletoninpowerset = $true,
inference(cnf_transformation,[],[f19]) ).
thf(f28,plain,
( $true
= ( in @ sK2 @ sK0 ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f29,plain,
( $true
!= ( in @ ( setadjoin @ sK2 @ emptyset ) @ ( powerset @ ( binunion @ sK0 @ sK1 ) ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f32,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ Y1 )
=> ( ( in @ Y0 @ Y2 )
=> ( in @ Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f20,f24]) ).
thf(f34,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( subset @ Y1 @ ( binunion @ Y1 @ Y0 ) ) ) )
= $true ),
inference(definition_unfolding,[],[f22,f26]) ).
thf(f35,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ Y1 )
=> ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( powerset @ Y1 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f23,f27]) ).
thf(f36,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ Y1 )
=> ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( powerset @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f35]) ).
thf(f37,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( in @ ( setadjoin @ X1 @ emptyset ) @ ( powerset @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f36]) ).
thf(f38,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( in @ ( setadjoin @ X1 @ emptyset ) @ ( powerset @ Y0 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f37]) ).
thf(f39,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( in @ X1 @ X2 )
=> ( in @ ( setadjoin @ X1 @ emptyset ) @ ( powerset @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f38]) ).
thf(f40,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ ( setadjoin @ X1 @ emptyset ) @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f39]) ).
thf(f41,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( subset @ Y1 @ ( binunion @ Y1 @ Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f34]) ).
thf(f42,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( subset @ Y0 @ ( binunion @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f41]) ).
thf(f43,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] : ( subset @ Y0 @ ( binunion @ Y0 @ X1 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f42]) ).
thf(f44,plain,
! [X2: $i,X1: $i] :
( $true
= ( subset @ X2 @ ( binunion @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f43]) ).
thf(f50,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ Y1 )
=> ( ( in @ Y0 @ Y2 )
=> ( in @ Y0 @ Y1 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f32]) ).
thf(f51,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( in @ X1 @ Y1 )
=> ( in @ X1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f50]) ).
thf(f52,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( in @ X1 @ Y1 )
=> ( in @ X1 @ Y0 ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f51]) ).
thf(f53,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ Y0 @ X2 )
=> ( ( in @ X1 @ Y0 )
=> ( in @ X1 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f52]) ).
thf(f54,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( subset @ Y0 @ X2 )
=> ( ( in @ X1 @ Y0 )
=> ( in @ X1 @ X2 ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f53]) ).
thf(f55,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( subset @ X3 @ X2 )
=> ( ( in @ X1 @ X3 )
=> ( in @ X1 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f54]) ).
thf(f56,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( subset @ X3 @ X2 ) )
| ( $true
= ( ( in @ X1 @ X3 )
=> ( in @ X1 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f55]) ).
thf(f57,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( subset @ X3 @ X2 ) )
| ( $false
= ( in @ X1 @ X3 ) )
| ( $true
= ( in @ X1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f56]) ).
thf(f65,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( subset @ sK0 @ X0 ) )
| ( $true
= ( in @ sK2 @ X0 ) ) ),
inference(constrained_superposition,[],[f28,f57]) ).
thf(f70,plain,
! [X0: $i] :
( ( $true
= ( in @ sK2 @ X0 ) )
| ( $false
= ( subset @ sK0 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f65]) ).
thf(f83,plain,
( ( $true != $true )
| ( $false
= ( in @ sK2 @ ( binunion @ sK0 @ sK1 ) ) ) ),
inference(constrained_superposition,[],[f29,f40]) ).
thf(f86,plain,
( $false
= ( in @ sK2 @ ( binunion @ sK0 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f83]) ).
thf(f90,plain,
( ( $true = $false )
| ( $false
= ( subset @ sK0 @ ( binunion @ sK0 @ sK1 ) ) ) ),
inference(constrained_superposition,[],[f70,f86]) ).
thf(f93,plain,
( $false
= ( subset @ sK0 @ ( binunion @ sK0 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f90]) ).
thf(f96,plain,
$true = $false,
inference(forward_demodulation,[],[f93,f44]) ).
thf(f97,plain,
$false,
inference(trivial_inequality_removal,[],[f96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU623^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.18 % Computer : n003.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 14:00:59 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.21 Running first-order model finding
% 0.07/0.21 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
% 0.07/0.25 % (2551282)Will run a generic schedule for satisfiability detection.
% 0.07/0.25 % (2551292)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2719334735:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.07/0.25 % (2551292) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2551282-2551292"...
% 0.07/0.25 % (2551288)% WARNING: option uhcvi not known.
% 0.07/0.25 % (2551292)...printing done.
% 0.07/0.25 % (2551292)Refutation found. Thanks to Tanya!
% 0.07/0.25 % SZS status Theorem for theBenchmark
% 0.07/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.25 % (2551292)------------------------------
% 0.07/0.25 % (2551292)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.26 % (2551292)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.26 % (2551292)CaDiCaL version: 2.1.3
% 0.07/0.26 % (2551292)Termination reason: Refutation
% 0.07/0.26 % (2551292)Time elapsed: 0.003 s
% 0.07/0.26 % (2551292)Peak memory usage: 12 MB
% 0.07/0.26 % (2551292)Instructions burned: 9 (million)
% 0.07/0.26 % (2551282)Success in time 0.032 s
% 0.07/0.26 % Vampire exiting
%------------------------------------------------------------------------------