%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU500^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 08:29:49 AM UTC 2026
% Result : Theorem 0.23s 0.29s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 33 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 191 ( 65 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 201 ( 26 ~; 19 |; 12 &; 131 @)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 8 con; 0-4 aty)
% Number of variables : 77 ( 23 ^; 44 !; 10 ?; 77 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
powerset: $i > $i ).
thf(func_def_3,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_4,type,
dsetconstrER: $o ).
thf(func_def_6,type,
prop2set: $o > $i ).
thf(func_def_9,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_11,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
sK1: $o ).
thf(func_def_14,type,
sK2: $i > $o ).
thf(func_def_17,type,
vNOT: $o > $o ).
thf(f1,axiom,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) )
= dsetconstrER ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrER) ).
thf(f2,axiom,
( ( ^ [X0: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [X1: $i] : X0 ) )
= prop2set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2set) ).
thf(f3,conjecture,
( dsetconstrER
=> ! [X0: $o,X1: $i] :
( ( in @ X1 @ ( prop2set @ X0 ) )
=> X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setE) ).
thf(f4,negated_conjecture,
~ ( dsetconstrER
=> ! [X0: $o,X1: $i] :
( ( in @ X1 @ ( prop2set @ X0 ) )
=> X0 ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
~ ( dsetconstrER
=> ! [X0: $o,X1: $i] :
( ( in @ X1 @ ( prop2set @ X0 ) )
=> X0 ) ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
~ ( ( dsetconstrER = $true )
=> ! [X1: $i,X0: $o] :
( ( ( in @ X1 @ ( prop2set @ X0 ) )
= $true )
=> ( $true = X0 ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( in @ X0
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) ) )
=> ( X2 @ X0 ) )
= dsetconstrER ),
inference(rectify,[],[f1]) ).
thf(f8,plain,
( ! [X2: $i > $o,X0: $i,X1: $i] :
( ( $true
= ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
=> ( ( X2 @ X0 )
= $true ) )
<=> ( dsetconstrER = $true ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
( ( ^ [X0: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [X1: $i] : X0 ) )
= prop2set ),
inference(rectify,[],[f2]) ).
thf(f10,plain,
( prop2set
= ( ^ [Y0: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [Y1: $i] : Y0 ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ( dsetconstrER = $true )
& ? [X1: $i,X0: $o] :
( ( $true != X0 )
& ( ( in @ X1 @ ( prop2set @ X0 ) )
= $true ) ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f12,plain,
( ! [X2: $i > $o,X1: $i,X0: $i] :
( ( $true
!= ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
| ( ( X2 @ X0 )
= $true ) )
<=> ( dsetconstrER = $true ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f13,plain,
( ( dsetconstrER = $true )
& ? [X0: $i,X1: $o] :
( ( $true != X1 )
& ( $true
= ( in @ X0 @ ( prop2set @ X1 ) ) ) ) ),
inference(rectify,[],[f11]) ).
thf(f14,plain,
( ( dsetconstrER = $true )
& ( $true != sK1 )
& ( ( in @ sK0 @ ( prop2set @ sK1 ) )
= $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f13]) ).
thf(f15,plain,
( ( ! [X2: $i > $o,X1: $i,X0: $i] :
( ( $true
!= ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
| ( ( X2 @ X0 )
= $true ) )
| ( dsetconstrER != $true ) )
& ( ( dsetconstrER = $true )
| ? [X2: $i > $o,X1: $i,X0: $i] :
( ( $true
= ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
& ( ( X2 @ X0 )
!= $true ) ) ) ),
inference(nnf_transformation,[],[f12]) ).
thf(f16,plain,
( ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
!= $true )
| ( $true
= ( X0 @ X2 ) ) )
| ( dsetconstrER != $true ) )
& ( ( dsetconstrER = $true )
| ? [X3: $i > $o,X4: $i,X5: $i] :
( ( ( in @ X5
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) )
= $true )
& ( ( X3 @ X5 )
!= $true ) ) ) ),
inference(rectify,[],[f15]) ).
thf(f17,plain,
( ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
!= $true )
| ( $true
= ( X0 @ X2 ) ) )
| ( dsetconstrER != $true ) )
& ( ( dsetconstrER = $true )
| ( ( ( in @ sK4
@ ( dsetconstr @ sK3
@ ^ [Y0: $i] : ( sK2 @ Y0 ) ) )
= $true )
& ( $true
!= ( sK2 @ sK4 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X3,sK2),skolemize(X4,sK3),skolemize(X5,sK4)],[f16]) ).
thf(f18,plain,
( prop2set
= ( ^ [Y0: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [Y1: $i] : Y0 ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f19,plain,
( ( in @ sK0 @ ( prop2set @ sK1 ) )
= $true ),
inference(cnf_transformation,[],[f14]) ).
thf(f20,plain,
$true != sK1,
inference(cnf_transformation,[],[f14]) ).
thf(f21,plain,
dsetconstrER = $true,
inference(cnf_transformation,[],[f14]) ).
thf(f24,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
!= $true )
| ( $true
= ( X0 @ X2 ) )
| ( dsetconstrER != $true ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f27,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( dsetconstrER != $true )
| ( $true
= ( X0 @ X2 ) )
| ( ( in @ X2 @ ( dsetconstr @ X1 @ X0 ) )
!= $true ) ),
inference(beta-eta_normalization,[],[f24]) ).
thf(f28,plain,
( ( $false = sK1 )
| ( $true != $true ) ),
inference(fool_paramodulation,[],[f20]) ).
thf(f29,plain,
$false = sK1,
inference(trivial_inequality_removal,[],[f28]) ).
thf(f32,plain,
( ( in @ sK0 @ ( prop2set @ $false ) )
= $true ),
inference(forward_demodulation,[],[f19,f29]) ).
thf(f33,plain,
! [X1: $o] :
( ( ^ [Y0: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [Y1: $i] : Y0 )
@ X1 )
= ( prop2set @ X1 ) ),
inference(argument_congruence,[],[f18]) ).
thf(f34,plain,
! [X1: $o] :
( ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Y0: $i] : X1 )
= ( prop2set @ X1 ) ),
inference(beta-eta_normalization,[],[f33]) ).
thf(f35,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( in @ X2 @ ( dsetconstr @ X1 @ X0 ) )
!= $true )
| ( $true
= ( X0 @ X2 ) ) ),
inference(forward_subsumption_resolution,[],[f27,f21]) ).
thf(f36,plain,
! [X0: $o,X1: $i] :
( ( ( in @ X1 @ ( prop2set @ X0 ) )
!= $true )
| ( $true
= ( ^ [Y0: $i] : X0
@ X1 ) ) ),
inference(superposition,[],[f35,f34]) ).
thf(f37,plain,
! [X0: $o,X1: $i] :
( ( ( in @ X1 @ ( prop2set @ X0 ) )
!= $true )
| ( $true = X0 ) ),
inference(beta-eta_normalization,[],[f36]) ).
thf(f38,plain,
( ( $false = $true )
| ( $true != $true ) ),
inference(superposition,[],[f37,f32]) ).
thf(f39,plain,
$false,
inference(trivial_inequality_removal,[],[f38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU500^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n016.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 13:51:34 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running higher-order theorem proving
% 0.08/0.25 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.23/0.29 % (376397)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.29 % (376406)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3708556109:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.29 % (376406) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-376397-376406"...
% 0.23/0.29 % (376406)...printing done.
% 0.23/0.29 % (376406)Refutation found. Thanks to Tanya!
% 0.23/0.29 % SZS status Theorem for theBenchmark
% 0.23/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.29 % (376406)------------------------------
% 0.23/0.29 % (376406)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.29 % (376406)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (376406)CaDiCaL version: 2.1.3
% 0.23/0.30 % (376406)Termination reason: Refutation
% 0.23/0.30 % (376406)Time elapsed: 0.002 s
% 0.23/0.30 % (376406)Peak memory usage: 12 MB
% 0.23/0.30 % (376406)Instructions burned: 3 (million)
% 0.23/0.30 % (376397)Success in time 0.033 s
% 0.23/0.30 % Vampire exiting
%------------------------------------------------------------------------------