%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU802^2 : 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 : n013.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 08:31:31 AM UTC 2026
% Result : Theorem 0.10s 0.25s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 33 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 202 ( 63 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 277 ( 24 ~; 17 |; 12 &; 211 @)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 26 usr; 8 con; 0-4 aty)
% Number of variables : 92 ( 29 ^; 51 !; 12 ?; 92 :)
% 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,
dsetconstrER: $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_14,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_15,type,
vIMP: $o > $o > $o ).
thf(func_def_16,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_17,type,
vAND: $o > $o > $o ).
thf(func_def_18,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_21,type,
sK0: $i > $o ).
thf(func_def_27,type,
vNOT: $o > $o ).
thf(f1,axiom,
( dsetconstrER
= ( ! [X1: $i > $o,X0: $i,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrER) ).
thf(f3,axiom,
( surjFuncSet
= ( ^ [X0: $i,X1: $i] :
( dsetconstr @ ( funcSet @ X0 @ X1 )
@ ^ [X2: $i] : ( surjective @ X0 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',surjFuncSet) ).
thf(f4,conjecture,
( dsetconstrER
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( surjFuncSet @ X0 @ X1 ) )
=> ( surjective @ X0 @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',surjFuncSetFuncSurj) ).
thf(f5,negated_conjecture,
~ ( dsetconstrER
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( surjFuncSet @ X0 @ X1 ) )
=> ( surjective @ X0 @ X1 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
( surjFuncSet
= ( ^ [X0: $i,X1: $i] :
( dsetconstr @ ( funcSet @ X0 @ X1 )
@ ^ [X2: $i] : ( surjective @ X0 @ X1 @ X2 ) ) ) ),
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,
( dsetconstrER
= ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X0 @ X3 ) ) )
=> ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f9,plain,
( ! [X1: $i,X2: $i,X0: $i > $o] :
( ( $true
= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
=> ( $true
= ( X0 @ X2 ) ) )
<=> ( dsetconstrER = $true ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
~ ( dsetconstrER
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( surjFuncSet @ X0 @ X1 ) )
=> ( surjective @ X0 @ X1 @ X2 ) ) ),
inference(rectify,[],[f5]) ).
thf(f11,plain,
~ ( ( dsetconstrER = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( surjFuncSet @ X0 @ X1 ) )
= $true )
=> ( ( surjective @ X0 @ X1 @ X2 )
= $true ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f14,plain,
( ( dsetconstrER = $true )
<=> ! [X0: $i > $o,X2: $i,X1: $i] :
( ( $true
= ( X0 @ X2 ) )
| ( $true
!= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ) ) ),
inference(ennf_transformation,[],[f9]) ).
thf(f15,plain,
( ( dsetconstrER = $true )
& ? [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X2 @ ( surjFuncSet @ X0 @ X1 ) )
= $true )
& ( ( surjective @ X0 @ X1 @ X2 )
!= $true ) ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f16,plain,
( ( ( dsetconstrER = $true )
| ? [X0: $i > $o,X2: $i,X1: $i] :
( ( $true
!= ( X0 @ X2 ) )
& ( $true
= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ) ) )
& ( ! [X0: $i > $o,X2: $i,X1: $i] :
( ( $true
= ( X0 @ X2 ) )
| ( $true
!= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ) )
| ( dsetconstrER != $true ) ) ),
inference(nnf_transformation,[],[f14]) ).
thf(f17,plain,
( ( ( dsetconstrER = $true )
| ? [X0: $i > $o,X1: $i,X2: $i] :
( ( ( X0 @ X1 )
!= $true )
& ( $true
= ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ) ) )
& ( ! [X3: $i > $o,X4: $i,X5: $i] :
( ( $true
= ( X3 @ X4 ) )
| ( $true
!= ( in @ X4
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) ) ) )
| ( dsetconstrER != $true ) ) ),
inference(rectify,[],[f16]) ).
thf(f18,plain,
( ( ( dsetconstrER = $true )
| ( ( $true
!= ( sK0 @ sK1 ) )
& ( $true
= ( in @ sK1
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) ) ) ) )
& ( ! [X3: $i > $o,X4: $i,X5: $i] :
( ( $true
= ( X3 @ X4 ) )
| ( $true
!= ( in @ X4
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) ) ) )
| ( dsetconstrER != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f17]) ).
thf(f19,plain,
( ( dsetconstrER = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( surjFuncSet @ X2 @ X0 ) ) )
& ( $true
!= ( surjective @ X2 @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f15]) ).
thf(f20,plain,
( ( dsetconstrER = $true )
& ( $true
= ( in @ sK4 @ ( surjFuncSet @ sK5 @ sK3 ) ) )
& ( $true
!= ( surjective @ sK5 @ sK3 @ sK4 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5)],[f19]) ).
thf(f21,plain,
! [X3: $i > $o,X4: $i,X5: $i] :
( ( $true
!= ( in @ X4
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) ) )
| ( dsetconstrER != $true )
| ( $true
= ( X3 @ X4 ) ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f25,plain,
( surjFuncSet
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( funcSet @ Y0 @ Y1 )
@ ^ [Y2: $i] : ( surjective @ Y0 @ Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f26,plain,
( $true
!= ( surjective @ sK5 @ sK3 @ sK4 ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f27,plain,
( $true
= ( in @ sK4 @ ( surjFuncSet @ sK5 @ sK3 ) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f28,plain,
dsetconstrER = $true,
inference(cnf_transformation,[],[f20]) ).
thf(f30,plain,
! [X3: $i > $o,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( dsetconstr @ X5 @ X3 ) )
!= $true )
| ( dsetconstrER != $true )
| ( $true
= ( X3 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f21]) ).
thf(f31,plain,
( surjFuncSet
= ( ^ [Y0: $i,Y1: $i] : ( dsetconstr @ ( funcSet @ Y0 @ Y1 ) @ ( surjective @ Y0 @ Y1 ) ) ) ),
inference(beta-eta_normalization,[],[f25]) ).
thf(f34,plain,
! [X3: $i > $o,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( dsetconstr @ X5 @ X3 ) )
!= $true )
| ( $true
= ( X3 @ X4 ) ) ),
inference(forward_subsumption_resolution,[],[f30,f28]) ).
thf(f35,plain,
! [X1: $i] :
( ( surjFuncSet @ X1 )
= ( ^ [Y0: $i,Y1: $i] : ( dsetconstr @ ( funcSet @ Y0 @ Y1 ) @ ( surjective @ Y0 @ Y1 ) )
@ X1 ) ),
inference(argument_congruence,[],[f31]) ).
thf(f36,plain,
! [X1: $i] :
( ( surjFuncSet @ X1 )
= ( ^ [Y0: $i] : ( dsetconstr @ ( funcSet @ X1 @ Y0 ) @ ( surjective @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f35]) ).
thf(f37,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] : ( dsetconstr @ ( funcSet @ X1 @ Y0 ) @ ( surjective @ X1 @ Y0 ) )
@ X2 )
= ( surjFuncSet @ X1 @ X2 ) ),
inference(argument_congruence,[],[f36]) ).
thf(f38,plain,
! [X2: $i,X1: $i] :
( ( dsetconstr @ ( funcSet @ X1 @ X2 ) @ ( surjective @ X1 @ X2 ) )
= ( surjFuncSet @ X1 @ X2 ) ),
inference(beta-eta_normalization,[],[f37]) ).
thf(f39,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( surjFuncSet @ X0 @ X1 ) )
!= $true )
| ( ( surjective @ X0 @ X1 @ X2 )
= $true ) ),
inference(superposition,[],[f34,f38]) ).
thf(f42,plain,
( ( $true
= ( surjective @ sK5 @ sK3 @ sK4 ) )
| ( $true != $true ) ),
inference(superposition,[],[f39,f27]) ).
thf(f43,plain,
( $true
= ( surjective @ sK5 @ sK3 @ sK4 ) ),
inference(trivial_inequality_removal,[],[f42]) ).
thf(f44,plain,
$false,
inference(forward_subsumption_resolution,[],[f43,f26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU802^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.17 % Computer : n013.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 14:31:36 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 Running higher-order theorem proving
% 0.10/0.21 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
% 0.10/0.25 % (2201340)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.10/0.25 % (2201349)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=142499276:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.10/0.25 % (2201349) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2201340-2201349"...
% 0.10/0.25 % (2201349)...printing done.
% 0.10/0.25 % (2201349)Refutation found. Thanks to Tanya!
% 0.10/0.25 % SZS status Theorem for theBenchmark
% 0.10/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.25 % (2201349)------------------------------
% 0.10/0.25 % (2201349)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.25 % (2201349)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.25 % (2201349)CaDiCaL version: 2.1.3
% 0.10/0.25 % (2201349)Termination reason: Refutation
% 0.10/0.25 % (2201349)Time elapsed: 0.002 s
% 0.10/0.25 % (2201349)Peak memory usage: 12 MB
% 0.10/0.25 % (2201349)Instructions burned: 5 (million)
% 0.10/0.25 % (2201340)Success in time 0.032 s
% 0.10/0.25 % Vampire exiting
%------------------------------------------------------------------------------