%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU738^2 : 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 : n004.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 08:31:03 AM UTC 2026
% Result : Theorem 0.21s 0.27s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 2
% Syntax : Number of formulae : 26 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 277 ( 77 equ; 0 cnn)
% Maximal formula atoms : 6 ( 10 avg)
% Number of connectives : 326 ( 36 ~; 16 |; 26 &; 218 @)
% ( 2 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 70 ( 0 ^; 52 !; 18 ?; 70 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_2,type,
binunion: $i > $i > $i ).
thf(func_def_3,type,
binunionIL: $o ).
thf(func_def_14,type,
vNOT: $o > $o ).
thf(f1,axiom,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
=> ( in @ X2 @ ( binunion @ X0 @ X1 ) ) )
= binunionIL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionIL) ).
thf(f2,conjecture,
( binunionIL
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ~ ( in @ X3 @ ( binunion @ X1 @ X2 ) )
=> ~ ( in @ X3 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionTILcontra) ).
thf(f3,negated_conjecture,
~ ( binunionIL
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ~ ( in @ X3 @ ( binunion @ X1 @ X2 ) )
=> ~ ( in @ X3 @ X1 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
=> ( in @ X2 @ ( binunion @ X0 @ X1 ) ) )
= binunionIL ),
inference(rectify,[],[f1]) ).
thf(f5,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
= $true ) )
<=> ( binunionIL = $true ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
~ ( binunionIL
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ~ ( in @ X3 @ ( binunion @ X0 @ X2 ) )
=> ~ ( in @ X3 @ X0 ) ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ( ( binunionIL = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( ( in @ X3 @ ( binunion @ X0 @ X2 ) )
!= $true )
=> ( ( in @ X3 @ X0 )
!= $true ) ) ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
~ ( ( binunionIL = $true )
=> ! [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( ( in @ X3 @ ( binunion @ X0 @ X2 ) )
!= $true )
=> ( ( in @ X3 @ X0 )
!= $true ) ) ) ) ) ),
inference(flattening,[],[f7]) ).
thf(f9,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
= $true ) )
<=> ( binunionIL = $true ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f10,plain,
( ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ ( binunion @ X0 @ X2 ) )
!= $true )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
& ( binunionIL = $true ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f11,plain,
( ( binunionIL = $true )
& ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
& ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ ( binunion @ X0 @ X2 ) )
!= $true ) ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) ) ),
inference(flattening,[],[f10]) ).
thf(f12,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
= $true ) )
| ( binunionIL != $true ) )
& ( ( binunionIL = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
!= $true ) ) ) ),
inference(nnf_transformation,[],[f9]) ).
thf(f13,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
= $true ) )
| ( binunionIL != $true ) )
& ( ( binunionIL = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X3 )
= $true )
& ( $true
!= ( in @ X5 @ ( binunion @ X3 @ X4 ) ) ) ) ) ),
inference(rectify,[],[f12]) ).
thf(f14,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
= $true ) )
| ( binunionIL != $true ) )
& ( ( binunionIL = $true )
| ( ( ( in @ sK2 @ sK0 )
= $true )
& ( ( in @ sK2 @ ( binunion @ sK0 @ sK1 ) )
!= $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X3,sK0),skolemize(X4,sK1),skolemize(X5,sK2)],[f13]) ).
thf(f15,plain,
( ( binunionIL = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
!= $true ) ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ) ),
inference(rectify,[],[f11]) ).
thf(f16,plain,
( ( binunionIL = $true )
& ( $true
= ( in @ sK5 @ ( powerset @ sK3 ) ) )
& ( ( in @ sK6 @ sK4 )
= $true )
& ( ( in @ sK6 @ sK3 )
= $true )
& ( ( in @ sK6 @ ( binunion @ sK4 @ sK5 ) )
!= $true )
& ( ( in @ sK4 @ ( powerset @ sK3 ) )
= $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5),skolemize(X3,sK6)],[f15]) ).
thf(f19,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
= $true )
| ( binunionIL != $true ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f21,plain,
( ( in @ sK6 @ ( binunion @ sK4 @ sK5 ) )
!= $true ),
inference(cnf_transformation,[],[f16]) ).
thf(f23,plain,
( ( in @ sK6 @ sK4 )
= $true ),
inference(cnf_transformation,[],[f16]) ).
thf(f25,plain,
binunionIL = $true,
inference(cnf_transformation,[],[f16]) ).
thf(f28,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) ),
inference(definition_unfolding,[],[f19,f25]) ).
thf(f31,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f28]) ).
thf(f33,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( in @ sK6 @ ( binunion @ sK4 @ X0 ) )
= $true ) ),
inference(constrained_superposition,[],[f31,f23]) ).
thf(f37,plain,
! [X0: $i] :
( ( in @ sK6 @ ( binunion @ sK4 @ X0 ) )
= $true ),
inference(trivial_inequality_removal,[],[f33]) ).
thf(f41,plain,
$true != $true,
inference(constrained_superposition,[],[f21,f37]) ).
thf(f43,plain,
$false,
inference(trivial_inequality_removal,[],[f41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU738^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n004.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 14:18:52 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.23 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
% 0.21/0.27 % (1354912)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.27 % (1354923)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3308267263:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.27 % (1354923) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1354912-1354923"...
% 0.21/0.27 % (1354923)...printing done.
% 0.21/0.27 % (1354923)Refutation found. Thanks to Tanya!
% 0.21/0.27 % SZS status Theorem for theBenchmark
% 0.21/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.27 % (1354923)------------------------------
% 0.21/0.27 % (1354923)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (1354923)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (1354923)CaDiCaL version: 2.1.3
% 0.21/0.27 % (1354923)Termination reason: Refutation
% 0.21/0.27 % (1354923)Time elapsed: 0.002 s
% 0.21/0.27 % (1354923)Peak memory usage: 12 MB
% 0.21/0.27 % (1354923)Instructions burned: 4 (million)
% 0.21/0.27 % (1354912)Success in time 0.032 s
% 0.21/0.27 % Vampire exiting
%------------------------------------------------------------------------------