%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU603^2 : 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 : n026.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 08:30:16 AM UTC 2026
% Result : Theorem 0.19s 0.28s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 3
% Syntax : Number of formulae : 34 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 223 ( 66 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 256 ( 35 ~; 17 |; 12 &; 177 @)
% ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 8 con; 0-4 aty)
% Number of variables : 91 ( 31 ^; 48 !; 12 ?; 91 :)
% 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,
setminus: $i > $i > $i ).
thf(func_def_7,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
vNOT: $o > $o ).
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_15,type,
sK4: $i > $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(f2,axiom,
( ( ^ [X0: $i,X1: $i] :
( dsetconstr @ X0
@ ^ [X2: $i] :
~ ( in @ X2 @ X1 ) ) )
= setminus ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminus) ).
thf(f3,conjecture,
( dsetconstrER
=> ! [X1: $i,X2: $i,X0: $i] :
( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusER) ).
thf(f4,negated_conjecture,
~ ( dsetconstrER
=> ! [X1: $i,X2: $i,X0: $i] :
( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
~ ( dsetconstrER
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
=> ~ ( in @ X1 @ X0 ) ) ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
~ ( ( dsetconstrER = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
= $true )
=> ( ( in @ X1 @ X0 )
!= $true ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
( ( ^ [X0: $i,X1: $i] :
( dsetconstr @ X0
@ ^ [X2: $i] :
~ ( in @ X2 @ X1 ) ) )
= setminus ),
inference(rectify,[],[f2]) ).
thf(f8,plain,
( setminus
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] :
~ ( in @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
( dsetconstrER
= ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X0 @ X3 ) ) )
=> ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f10,plain,
( ( dsetconstrER = $true )
<=> ! [X2: $i,X1: $i,X0: $i > $o] :
( ( ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
= $true )
=> ( ( X0 @ X2 )
= $true ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
~ ( ( dsetconstrER = $true )
=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
= $true )
=> ( ( in @ X1 @ X0 )
!= $true ) ) ),
inference(flattening,[],[f6]) ).
thf(f12,plain,
( ( dsetconstrER = $true )
& ? [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
= $true )
& ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
= $true ) ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f13,plain,
( ( dsetconstrER = $true )
<=> ! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( X0 @ X2 )
= $true )
| ( ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
!= $true ) ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f14,plain,
( ( dsetconstrER = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
= $true )
& ( $true
= ( in @ X0 @ ( setminus @ X2 @ X1 ) ) ) ) ),
inference(rectify,[],[f12]) ).
thf(f15,plain,
( ( dsetconstrER = $true )
& ( ( in @ sK0 @ sK1 )
= $true )
& ( $true
= ( in @ sK0 @ ( setminus @ sK2 @ sK1 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f14]) ).
thf(f16,plain,
( ( ( dsetconstrER = $true )
| ? [X2: $i,X0: $i > $o,X1: $i] :
( ( ( X0 @ X2 )
!= $true )
& ( ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
= $true ) ) )
& ( ! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( X0 @ X2 )
= $true )
| ( ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
!= $true ) )
| ( dsetconstrER != $true ) ) ),
inference(nnf_transformation,[],[f13]) ).
thf(f17,plain,
( ( ( dsetconstrER = $true )
| ? [X0: $i,X1: $i > $o,X2: $i] :
( ( ( X1 @ X0 )
!= $true )
& ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true ) ) )
& ( ! [X3: $i,X4: $i > $o,X5: $i] :
( ( ( X4 @ X3 )
= $true )
| ( ( in @ X3
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) )
!= $true ) )
| ( dsetconstrER != $true ) ) ),
inference(rectify,[],[f16]) ).
thf(f18,plain,
( ( ( dsetconstrER = $true )
| ( ( ( sK4 @ sK3 )
!= $true )
& ( ( in @ sK3
@ ( dsetconstr @ sK5
@ ^ [Y0: $i] : ( sK4 @ Y0 ) ) )
= $true ) ) )
& ( ! [X3: $i,X4: $i > $o,X5: $i] :
( ( ( X4 @ X3 )
= $true )
| ( ( in @ X3
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) )
!= $true ) )
| ( dsetconstrER != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5)],[f17]) ).
thf(f19,plain,
( $true
= ( in @ sK0 @ ( setminus @ sK2 @ sK1 ) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f20,plain,
( ( in @ sK0 @ sK1 )
= $true ),
inference(cnf_transformation,[],[f15]) ).
thf(f21,plain,
dsetconstrER = $true,
inference(cnf_transformation,[],[f15]) ).
thf(f22,plain,
! [X3: $i,X4: $i > $o,X5: $i] :
( ( ( X4 @ X3 )
= $true )
| ( ( in @ X3
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) )
!= $true )
| ( dsetconstrER != $true ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f25,plain,
( setminus
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] :
~ ( in @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f28,plain,
( ( in @ sK0
@ ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] :
~ ( in @ Y2 @ Y1 ) )
@ sK2
@ sK1 ) )
= $true ),
inference(definition_unfolding,[],[f19,f25]) ).
thf(f31,plain,
! [X3: $i,X4: $i > $o,X5: $i] :
( ( $true != $true )
| ( ( in @ X3
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) )
!= $true )
| ( ( X4 @ X3 )
= $true ) ),
inference(definition_unfolding,[],[f22,f21]) ).
thf(f32,plain,
( ( in @ sK0
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] :
~ ( in @ Y0 @ sK1 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f28]) ).
thf(f33,plain,
! [X3: $i,X4: $i > $o,X5: $i] :
( ( ( in @ X3
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) )
!= $true )
| ( ( X4 @ X3 )
= $true ) ),
inference(trivial_inequality_removal,[],[f31]) ).
thf(f34,plain,
! [X3: $i,X4: $i > $o,X5: $i] :
( ( ( in @ X3 @ ( dsetconstr @ X5 @ X4 ) )
!= $true )
| ( ( X4 @ X3 )
= $true ) ),
inference(beta-eta_normalization,[],[f33]) ).
thf(f35,plain,
( ( ( ^ [Y0: $i] :
~ ( in @ Y0 @ sK1 )
@ sK0 )
= $true )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f34,f32]) ).
thf(f36,plain,
( ( ^ [Y0: $i] :
~ ( in @ Y0 @ sK1 )
@ sK0 )
= $true ),
inference(trivial_inequality_removal,[],[f35]) ).
thf(f37,plain,
( ( ~ ( in @ sK0 @ sK1 ) )
= $true ),
inference(beta-eta_normalization,[],[f36]) ).
thf(f38,plain,
( ( in @ sK0 @ sK1 )
= $false ),
inference(not_proxy_clausification,[],[f37]) ).
thf(f39,plain,
$false = $true,
inference(backward_demodulation,[],[f20,f38]) ).
thf(f40,plain,
$false,
inference(trivial_inequality_removal,[],[f39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU603^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n026.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 13:59:42 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 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
% 0.19/0.28 % (640226)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.28 % (640239)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1207048290:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.19/0.28 % (640239) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-640226-640239"...
% 0.19/0.28 % (640239)...printing done.
% 0.19/0.28 % (640239)Refutation found. Thanks to Tanya!
% 0.19/0.28 % SZS status Theorem for theBenchmark
% 0.19/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.28 % (640239)------------------------------
% 0.19/0.28 % (640239)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (640239)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (640239)CaDiCaL version: 2.1.3
% 0.19/0.28 % (640239)Termination reason: Refutation
% 0.19/0.28 % (640239)Time elapsed: 0.002 s
% 0.19/0.28 % (640239)Peak memory usage: 13 MB
% 0.19/0.28 % (640239)Instructions burned: 3 (million)
% 0.19/0.28 % (640226)Success in time 0.04 s
% 0.19/0.28 % Vampire exiting
%------------------------------------------------------------------------------