%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU801^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 08:31:30 AM UTC 2026
% Result : Theorem 0.23s 0.32s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of formulae : 36 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 211 ( 49 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 384 ( 7 ~; 2 |; 13 &; 311 @)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 23 usr; 8 con; 0-4 aty)
% ( 20 !!; 5 ??; 0 @@+; 0 @@-)
% Number of variables : 114 ( 71 ^; 35 !; 8 ?; 114 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_2,type,
dsetconstrEL: $o ).
thf(func_def_4,type,
funcSet: $i > $i > $i ).
thf(func_def_5,type,
ap: $i > $i > $i > $i > $i ).
thf(func_def_6,type,
surjective: $i > $i > $i > $o ).
thf(func_def_7,type,
surjFuncSet: $i > $i > $i ).
thf(func_def_8,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_12,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_13,type,
vIMP: $o > $o > $o ).
thf(func_def_14,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_15,type,
vAND: $o > $o > $o ).
thf(func_def_16,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_24,type,
vNOT: $o > $o ).
thf(f1,axiom,
( dsetconstrEL
= ( ! [X2: $i,X1: $i > $o,X0: $i] :
( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(f2,axiom,
( surjective
= ( ^ [X0: $i,X1: $i,X2: $i] :
! [X3: $i] :
( ( in @ X3 @ X1 )
=> ? [X4: $i] :
( ( ( ap @ X0 @ X1 @ X2 @ X4 )
= X3 )
& ( in @ X4 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',surjective) ).
thf(f3,axiom,
( ( ^ [X0: $i,X1: $i] :
( dsetconstr @ ( funcSet @ X0 @ X1 )
@ ^ [X2: $i] : ( surjective @ X0 @ X1 @ X2 ) ) )
= surjFuncSet ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',surjFuncSet) ).
thf(f4,conjecture,
( dsetconstrEL
=> ! [X2: $i,X0: $i,X1: $i] :
( ( in @ X2 @ ( surjFuncSet @ X0 @ X1 ) )
=> ( in @ X2 @ ( funcSet @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',surjFuncSetFuncIn) ).
thf(f5,negated_conjecture,
~ ( dsetconstrEL
=> ! [X2: $i,X0: $i,X1: $i] :
( ( in @ X2 @ ( surjFuncSet @ X0 @ X1 ) )
=> ( in @ X2 @ ( funcSet @ X0 @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
( ( ^ [X0: $i,X1: $i] :
( dsetconstr @ ( funcSet @ X0 @ X1 )
@ ^ [X2: $i] : ( surjective @ X0 @ X1 @ X2 ) ) )
= surjFuncSet ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
( surjFuncSet
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( funcSet @ Y0 @ Y1 )
@ ^ [Y2: $i] : ( surjective @ Y0 @ Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( surjective
= ( ^ [X0: $i,X1: $i,X2: $i] :
! [X3: $i] :
( ( in @ X3 @ X1 )
=> ? [X4: $i] :
( ( ( ap @ X0 @ X1 @ X2 @ X4 )
= X3 )
& ( in @ X4 @ X0 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f9,plain,
( surjective
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
& ( ( ap @ Y0 @ Y1 @ Y2 @ Y4 )
= Y3 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
( dsetconstrEL
= ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X0 @ X2 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f11,plain,
( dsetconstrEL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( in @ Y2 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
~ ( dsetconstrEL
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ ( surjFuncSet @ X1 @ X2 ) )
=> ( in @ X0 @ ( funcSet @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f13,plain,
~ ( ( dsetconstrEL = $true )
=> ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X0 @ ( surjFuncSet @ X1 @ X2 ) )
= $true )
=> ( ( in @ X0 @ ( funcSet @ X1 @ X2 ) )
= $true ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
( ? [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X0 @ ( funcSet @ X1 @ X2 ) )
!= $true )
& ( ( in @ X0 @ ( surjFuncSet @ X1 @ X2 ) )
= $true ) )
& ( dsetconstrEL = $true ) ),
inference(ennf_transformation,[],[f13]) ).
thf(f15,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( funcSet @ X0 @ X2 ) ) )
& ( $true
= ( in @ X1 @ ( surjFuncSet @ X0 @ X2 ) ) ) )
& ( dsetconstrEL = $true ) ),
inference(rectify,[],[f14]) ).
thf(f16,plain,
( ( $true
!= ( in @ sK1 @ ( funcSet @ sK0 @ sK2 ) ) )
& ( $true
= ( in @ sK1 @ ( surjFuncSet @ sK0 @ sK2 ) ) )
& ( dsetconstrEL = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f15]) ).
thf(f17,plain,
dsetconstrEL = $true,
inference(cnf_transformation,[],[f16]) ).
thf(f18,plain,
( $true
= ( in @ sK1 @ ( surjFuncSet @ sK0 @ sK2 ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f19,plain,
( $true
!= ( in @ sK1 @ ( funcSet @ sK0 @ sK2 ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f20,plain,
( surjFuncSet
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( funcSet @ Y0 @ Y1 )
@ ^ [Y2: $i] : ( surjective @ Y0 @ Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f21,plain,
( surjective
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
& ( ( ap @ Y0 @ Y1 @ Y2 @ Y4 )
= Y3 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f22,plain,
( dsetconstrEL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( in @ Y2 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f25,plain,
( surjFuncSet
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( funcSet @ Y0 @ Y1 )
@ ^ [Y2: $i] :
( ^ [Y3: $i,Y4: $i,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y4 )
=> ( ?? @ $i
@ ^ [Y7: $i] :
( ( in @ Y7 @ Y3 )
& ( ( ap @ Y3 @ Y4 @ Y5 @ Y7 )
= Y6 ) ) ) ) )
@ Y0
@ Y1
@ Y2 ) ) ) ),
inference(definition_unfolding,[],[f20,f21]) ).
thf(f26,plain,
( ( in @ sK1
@ ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( funcSet @ Y0 @ Y1 )
@ ^ [Y2: $i] :
( ^ [Y3: $i,Y4: $i,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y4 )
=> ( ?? @ $i
@ ^ [Y7: $i] :
( ( in @ Y7 @ Y3 )
& ( ( ap @ Y3 @ Y4 @ Y5 @ Y7 )
= Y6 ) ) ) ) )
@ Y0
@ Y1
@ Y2 ) )
@ sK0
@ sK2 ) )
= $true ),
inference(definition_unfolding,[],[f18,f25]) ).
thf(f27,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( in @ Y2 @ Y0 ) ) ) ) ) ),
inference(definition_unfolding,[],[f22,f17]) ).
thf(f28,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( in @ Y2 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f27]) ).
thf(f29,plain,
! [X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( dsetconstr @ X1 @ Y0 ) )
=> ( in @ Y1 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f28]) ).
thf(f30,plain,
! [X2: $i > $o,X1: $i] :
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( dsetconstr @ X1 @ Y0 ) )
=> ( in @ Y1 @ X1 ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f29]) ).
thf(f31,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X1 @ X2 ) )
=> ( in @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f30]) ).
thf(f32,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X1 @ X2 ) )
=> ( in @ Y0 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f31]) ).
thf(f33,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
=> ( in @ X3 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f32]) ).
thf(f34,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false
= ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) )
| ( ( in @ X3 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f33]) ).
thf(f35,plain,
( ( in @ sK1
@ ( dsetconstr @ ( funcSet @ sK0 @ sK2 )
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK0 )
& ( ( ap @ sK0 @ sK2 @ Y0 @ Y2 )
= Y1 ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f26]) ).
thf(f36,plain,
( ( $true
= ( in @ sK1 @ ( funcSet @ sK0 @ sK2 ) ) )
| ( $false = $true ) ),
inference(constrained_superposition,[],[f35,f34]) ).
thf(f38,plain,
( $true
= ( in @ sK1 @ ( funcSet @ sK0 @ sK2 ) ) ),
inference(trivial_inequality_removal,[],[f36]) ).
thf(f40,plain,
$false,
inference(forward_subsumption_resolution,[],[f38,f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU801^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 % Computer : n009.cluster.edu
% 0.08/0.21 % Model : x86_64 x86_64
% 0.08/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.21 % Memory : 8046.5625MB
% 0.08/0.21 % OS : Linux 6.8.0-71-generic
% 0.08/0.21 % CPULimit : 300
% 0.08/0.21 % WCLimit : 300
% 0.08/0.21 % DateTime : Tue Sep 29 14:32:15 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.25 Running higher-order theorem proving
% 0.23/0.27 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.23/0.32 % (4083370)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.32 % (4083377)lrs+10_16_si=on:nwc=1.5:random_seed=2941324265:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.32 % (4083376)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3801036706:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.32 % (4083376) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4083370-4083376"...
% 0.23/0.32 % (4083377) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4083370-4083377"...
% 0.23/0.32 % (4083376)...printing done.
% 0.23/0.32 % (4083377)...printing done.
% 0.23/0.32 % (4083377)Refutation found. Thanks to Tanya!
% 0.23/0.32 % SZS status Theorem for theBenchmark
% 0.23/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.32 % (4083377)------------------------------
% 0.23/0.32 % (4083377)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.32 % (4083377)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.32 % (4083377)CaDiCaL version: 2.1.3
% 0.23/0.32 % (4083377)Termination reason: Refutation
% 0.23/0.32 % (4083377)Time elapsed: 0.004 s
% 0.23/0.32 % (4083377)Peak memory usage: 12 MB
% 0.23/0.32 % (4083377)Instructions burned: 5 (million)
% 0.23/0.32 % (4083370)Success in time 0.037 s
% 0.23/0.32 % Vampire exiting
%------------------------------------------------------------------------------