%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU628^2 : 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 : n003.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 08:30:24 AM UTC 2026
% Result : Theorem 0.20s 0.30s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 36 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 457 ( 106 equ; 0 cnn)
% Maximal formula atoms : 8 ( 12 avg)
% Number of connectives : 628 ( 48 ~; 36 |; 27 &; 488 @)
% ( 4 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 15 con; 0-2 aty)
% Number of variables : 90 ( 0 ^; 70 !; 20 ?; 90 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
powerset: $i > $i ).
thf(func_def_4,type,
subset: $i > $i > $o ).
thf(func_def_5,type,
powersetI1: $o ).
thf(func_def_7,type,
binunion: $i > $i > $i ).
thf(func_def_8,type,
ubforcartprodlem1: $o ).
thf(f1,axiom,
( powersetI1
= ( ! [X1: $i,X0: $i] :
( ( subset @ X1 @ X0 )
=> ( in @ X1 @ ( powerset @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI1) ).
thf(f2,axiom,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X0 @ X1 ) ) ) ) )
= ubforcartprodlem1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem1) ).
thf(f3,conjecture,
( powersetI1
=> ( ubforcartprodlem1
=> ! [X1: $i,X2: $i,X0: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X0 @ X1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem2) ).
thf(f4,negated_conjecture,
~ ( powersetI1
=> ( ubforcartprodlem1
=> ! [X1: $i,X2: $i,X0: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X0 @ X1 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
( powersetI1
= ( ! [X0: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( in @ X0 @ ( powerset @ X1 ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f6,plain,
( ( powersetI1 = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
=> ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
= ubforcartprodlem1 ),
inference(rectify,[],[f2]) ).
thf(f8,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
=> ( ( subset @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) )
= $true ) ) )
<=> ( ubforcartprodlem1 = $true ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
~ ( powersetI1
=> ( ubforcartprodlem1
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X2 @ X0 ) ) ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f10,plain,
~ ( ( powersetI1 = $true )
=> ( ( ubforcartprodlem1 = $true )
=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ X2 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( in @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X2 @ X0 ) ) ) )
= $true ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ( ubforcartprodlem1 = $true )
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
!= $true )
| ! [X3: $i] :
( ( ( subset @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) )
= $true )
| ( ( in @ X3 @ X2 )
!= $true ) ) ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f12,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X2 @ X0 ) ) ) )
!= $true ) ) )
& ( ubforcartprodlem1 = $true )
& ( powersetI1 = $true ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f13,plain,
( ( powersetI1 = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X2 @ X0 ) ) ) )
!= $true ) ) )
& ( ubforcartprodlem1 = $true ) ),
inference(flattening,[],[f12]) ).
thf(f14,plain,
( ! [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
| ( ( subset @ X0 @ X1 )
!= $true ) )
<=> ( powersetI1 = $true ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f15,plain,
( ( powersetI1 = $true )
& ( ( in @ sK1 @ sK2 )
= $true )
& ( ( in @ sK3 @ sK0 )
= $true )
& ( ( in @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ sK2 @ sK0 ) ) ) )
!= $true )
& ( ubforcartprodlem1 = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f13]) ).
thf(f16,plain,
( ( ! [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
| ( ( subset @ X0 @ X1 )
!= $true ) )
| ( powersetI1 != $true ) )
& ( ( powersetI1 = $true )
| ? [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
& ( ( subset @ X0 @ X1 )
= $true ) ) ) ),
inference(nnf_transformation,[],[f14]) ).
thf(f17,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
| ( ( subset @ X1 @ X0 )
!= $true ) )
| ( powersetI1 != $true ) )
& ( ( powersetI1 = $true )
| ? [X2: $i,X3: $i] :
( ( ( in @ X3 @ ( powerset @ X2 ) )
!= $true )
& ( ( subset @ X3 @ X2 )
= $true ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f18,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
| ( ( subset @ X1 @ X0 )
!= $true ) )
| ( powersetI1 != $true ) )
& ( ( powersetI1 = $true )
| ( ( ( in @ sK5 @ ( powerset @ sK4 ) )
!= $true )
& ( ( subset @ sK5 @ sK4 )
= $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X2,sK4),skolemize(X3,sK5)],[f17]) ).
thf(f19,plain,
( ( ( ubforcartprodlem1 = $true )
| ? [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
= $true )
& ? [X3: $i] :
( ( ( subset @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) )
!= $true )
& ( ( in @ X3 @ X2 )
= $true ) ) ) )
& ( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
!= $true )
| ! [X3: $i] :
( ( ( subset @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) )
= $true )
| ( ( in @ X3 @ X2 )
!= $true ) ) )
| ( ubforcartprodlem1 != $true ) ) ),
inference(nnf_transformation,[],[f11]) ).
thf(f20,plain,
( ( ( ubforcartprodlem1 = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
= $true )
& ? [X3: $i] :
( ( ( subset @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X2 @ X0 ) ) )
!= $true )
& ( ( in @ X3 @ X0 )
= $true ) ) ) )
& ( ! [X4: $i,X5: $i,X6: $i] :
( ( ( in @ X5 @ X6 )
!= $true )
| ! [X7: $i] :
( ( ( subset @ ( setadjoin @ ( setadjoin @ X5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X5 @ ( setadjoin @ X7 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X6 @ X4 ) ) )
= $true )
| ( ( in @ X7 @ X4 )
!= $true ) ) )
| ( ubforcartprodlem1 != $true ) ) ),
inference(rectify,[],[f19]) ).
thf(f21,plain,
( ( ( ubforcartprodlem1 = $true )
| ( ( ( in @ sK7 @ sK8 )
= $true )
& ( ( subset @ ( setadjoin @ ( setadjoin @ sK7 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK7 @ ( setadjoin @ sK9 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ sK8 @ sK6 ) ) )
!= $true )
& ( ( in @ sK9 @ sK6 )
= $true ) ) )
& ( ! [X4: $i,X5: $i,X6: $i] :
( ( ( in @ X5 @ X6 )
!= $true )
| ! [X7: $i] :
( ( ( subset @ ( setadjoin @ ( setadjoin @ X5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X5 @ ( setadjoin @ X7 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X6 @ X4 ) ) )
= $true )
| ( ( in @ X7 @ X4 )
!= $true ) ) )
| ( ubforcartprodlem1 != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9]),skolemize(X0,sK6),skolemize(X1,sK7),skolemize(X2,sK8),skolemize(X3,sK9)],[f20]) ).
thf(f22,plain,
ubforcartprodlem1 = $true,
inference(cnf_transformation,[],[f15]) ).
thf(f23,plain,
( ( in @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ sK2 @ sK0 ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f15]) ).
thf(f24,plain,
( ( in @ sK3 @ sK0 )
= $true ),
inference(cnf_transformation,[],[f15]) ).
thf(f25,plain,
( ( in @ sK1 @ sK2 )
= $true ),
inference(cnf_transformation,[],[f15]) ).
thf(f26,plain,
powersetI1 = $true,
inference(cnf_transformation,[],[f15]) ).
thf(f29,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
| ( powersetI1 != $true ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f30,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X6 )
!= $true )
| ( ubforcartprodlem1 != $true )
| ( ( subset @ ( setadjoin @ ( setadjoin @ X5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X5 @ ( setadjoin @ X7 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X6 @ X4 ) ) )
= $true )
| ( ( in @ X7 @ X4 )
!= $true ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f37,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
| ( ( subset @ X1 @ X0 )
!= $true ) ),
inference(forward_subsumption_resolution,[],[f29,f26]) ).
thf(f38,plain,
( ( ( subset @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ sK2 @ sK0 ) ) )
!= $true )
| ( $true != $true ) ),
inference(superposition,[],[f23,f37]) ).
thf(f39,plain,
( ( subset @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ sK2 @ sK0 ) ) )
!= $true ),
inference(trivial_inequality_removal,[],[f38]) ).
thf(f40,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( subset @ ( setadjoin @ ( setadjoin @ X5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X5 @ ( setadjoin @ X7 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X6 @ X4 ) ) )
= $true )
| ( ( in @ X7 @ X4 )
!= $true )
| ( ( in @ X5 @ X6 )
!= $true ) ),
inference(forward_subsumption_resolution,[],[f30,f22]) ).
thf(f41,plain,
( ( ( in @ sK1 @ sK2 )
!= $true )
| ( ( in @ sK3 @ sK0 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[],[f39,f40]) ).
thf(f42,plain,
( ( ( in @ sK3 @ sK0 )
!= $true )
| ( ( in @ sK1 @ sK2 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f41]) ).
thf(f43,plain,
( ( in @ sK1 @ sK2 )
!= $true ),
inference(forward_subsumption_resolution,[],[f42,f24]) ).
thf(f44,plain,
$false,
inference(forward_subsumption_resolution,[],[f43,f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU628^2 : 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 : n003.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 14:01:14 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 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
% 0.20/0.30 % (2551823)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.30 % (2551832)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3318289687:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.30 % (2551832) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2551823-2551832"...
% 0.20/0.30 % (2551832)...printing done.
% 0.20/0.30 % (2551832)Refutation found. Thanks to Tanya!
% 0.20/0.30 % SZS status Theorem for theBenchmark
% 0.20/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.30 % (2551832)------------------------------
% 0.20/0.30 % (2551832)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (2551832)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (2551832)CaDiCaL version: 2.1.3
% 0.20/0.30 % (2551832)Termination reason: Refutation
% 0.20/0.30 % (2551832)Time elapsed: 0.002 s
% 0.20/0.30 % (2551832)Peak memory usage: 12 MB
% 0.20/0.30 % (2551832)Instructions burned: 7 (million)
% 0.20/0.30 % (2551823)Success in time 0.04 s
% 0.20/0.30 % Vampire exiting
%------------------------------------------------------------------------------