%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU718^2 : 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 : n017.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 08:30:56 AM UTC 2026
% Result : Theorem 0.21s 0.27s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 40 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 464 ( 131 equ; 0 cnn)
% Maximal formula atoms : 8 ( 11 avg)
% Number of connectives : 450 ( 51 ~; 44 |; 36 &; 277 @)
% ( 5 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 13 con; 0-2 aty)
% Number of variables : 89 ( 0 ^; 71 !; 18 ?; 89 :)
% 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,
subset: $i > $i > $o ).
thf(func_def_3,type,
subsetE: $o ).
thf(func_def_5,type,
powersetE1: $o ).
thf(func_def_17,type,
vNOT: $o > $o ).
thf(f1,axiom,
( subsetE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( subset @ X0 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE) ).
thf(f2,axiom,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ( subset @ X1 @ X0 ) )
= powersetE1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE1) ).
thf(f3,conjecture,
( subsetE
=> ( powersetE1
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X1 @ ( powerset @ X2 ) )
=> ( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetTE1) ).
thf(f4,negated_conjecture,
~ ( subsetE
=> ( powersetE1
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X1 @ ( powerset @ X2 ) )
=> ( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ( subset @ X1 @ X0 ) )
= powersetE1 ),
inference(rectify,[],[f2]) ).
thf(f6,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ( ( subset @ X1 @ X0 )
= $true ) )
<=> ( powersetE1 = $true ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
( subsetE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( subset @ X0 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f8,plain,
( ( subsetE = $true )
<=> ! [X1: $i,X2: $i,X0: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
=> ( ( ( in @ X2 @ X0 )
= $true )
=> ( ( in @ X2 @ X1 )
= $true ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
~ ( subsetE
=> ( powersetE1
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X1 @ ( powerset @ X2 ) )
=> ( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) ) ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f10,plain,
~ ( ( subsetE = $true )
=> ( ( powersetE1 = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( ( in @ X1 @ ( powerset @ X2 ) )
= $true )
=> ( ( ( in @ X3 @ X1 )
= $true )
=> ( ( in @ X3 @ X2 )
= $true ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ( subsetE = $true )
<=> ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( ( subset @ X0 @ X1 )
!= $true ) ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f12,plain,
( ( subsetE = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
= $true ) ) ),
inference(flattening,[],[f11]) ).
thf(f13,plain,
( ( powersetE1 = $true )
<=> ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( subset @ X1 @ X0 )
= $true ) ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f14,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
& ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X1 @ ( powerset @ X2 ) )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( powersetE1 = $true )
& ( subsetE = $true ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f15,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X1 @ ( powerset @ X2 ) )
= $true )
& ( ( in @ X3 @ X2 )
!= $true ) ) ) )
& ( subsetE = $true )
& ( powersetE1 = $true ) ),
inference(flattening,[],[f14]) ).
thf(f16,plain,
( ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $true )
& ( ( in @ sK2 @ ( powerset @ sK0 ) )
= $true )
& ( ( in @ sK3 @ sK1 )
= $true )
& ( ( in @ sK3 @ sK0 )
= $true )
& ( ( in @ sK1 @ ( powerset @ sK2 ) )
= $true )
& ( ( in @ sK3 @ sK2 )
!= $true )
& ( subsetE = $true )
& ( powersetE1 = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f15]) ).
thf(f17,plain,
( ( ( subsetE = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
!= $true ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
= $true ) )
| ( subsetE != $true ) ) ),
inference(nnf_transformation,[],[f12]) ).
thf(f18,plain,
( ( ( subsetE = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X3 @ X4 )
!= $true )
| ( ( in @ X5 @ X3 )
!= $true )
| ( ( in @ X5 @ X4 )
= $true ) )
| ( subsetE != $true ) ) ),
inference(rectify,[],[f17]) ).
thf(f19,plain,
( ( ( subsetE = $true )
| ( ( ( subset @ sK4 @ sK5 )
= $true )
& ( ( in @ sK6 @ sK4 )
= $true )
& ( ( in @ sK6 @ sK5 )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X3 @ X4 )
!= $true )
| ( ( in @ X5 @ X3 )
!= $true )
| ( ( in @ X5 @ X4 )
= $true ) )
| ( subsetE != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6)],[f18]) ).
thf(f20,plain,
( ( ( powersetE1 = $true )
| ? [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ( ( subset @ X1 @ X0 )
!= $true ) ) )
& ( ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( subset @ X1 @ X0 )
= $true ) )
| ( powersetE1 != $true ) ) ),
inference(nnf_transformation,[],[f13]) ).
thf(f21,plain,
( ( ( powersetE1 = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
& ( ( subset @ X0 @ X1 )
!= $true ) ) )
& ( ! [X2: $i,X3: $i] :
( ( $true
!= ( in @ X2 @ ( powerset @ X3 ) ) )
| ( ( subset @ X2 @ X3 )
= $true ) )
| ( powersetE1 != $true ) ) ),
inference(rectify,[],[f20]) ).
thf(f22,plain,
( ( ( powersetE1 = $true )
| ( ( $true
= ( in @ sK7 @ ( powerset @ sK8 ) ) )
& ( ( subset @ sK7 @ sK8 )
!= $true ) ) )
& ( ! [X2: $i,X3: $i] :
( ( $true
!= ( in @ X2 @ ( powerset @ X3 ) ) )
| ( ( subset @ X2 @ X3 )
= $true ) )
| ( powersetE1 != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X0,sK7),skolemize(X1,sK8)],[f21]) ).
thf(f23,plain,
powersetE1 = $true,
inference(cnf_transformation,[],[f16]) ).
thf(f24,plain,
subsetE = $true,
inference(cnf_transformation,[],[f16]) ).
thf(f25,plain,
( ( in @ sK3 @ sK2 )
!= $true ),
inference(cnf_transformation,[],[f16]) ).
thf(f26,plain,
( ( in @ sK1 @ ( powerset @ sK2 ) )
= $true ),
inference(cnf_transformation,[],[f16]) ).
thf(f28,plain,
( ( in @ sK3 @ sK1 )
= $true ),
inference(cnf_transformation,[],[f16]) ).
thf(f31,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X3 @ X4 )
!= $true )
| ( ( in @ X5 @ X3 )
!= $true )
| ( ( in @ X5 @ X4 )
= $true )
| ( subsetE != $true ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f35,plain,
! [X2: $i,X3: $i] :
( ( $true
!= ( in @ X2 @ ( powerset @ X3 ) ) )
| ( ( subset @ X2 @ X3 )
= $true )
| ( powersetE1 != $true ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f43,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X4 )
= $true )
| ( ( in @ X5 @ X3 )
!= $true )
| ( $true != $true )
| ( ( subset @ X3 @ X4 )
!= $true ) ),
inference(definition_unfolding,[],[f31,f24]) ).
thf(f46,plain,
! [X2: $i,X3: $i] :
( ( ( subset @ X2 @ X3 )
= $true )
| ( $true
!= ( in @ X2 @ ( powerset @ X3 ) ) )
| ( $true != $true ) ),
inference(definition_unfolding,[],[f35,f23]) ).
thf(f47,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X3 @ X4 )
!= $true )
| ( ( in @ X5 @ X4 )
= $true )
| ( ( in @ X5 @ X3 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f43]) ).
thf(f48,plain,
! [X2: $i,X3: $i] :
( ( $true
!= ( in @ X2 @ ( powerset @ X3 ) ) )
| ( ( subset @ X2 @ X3 )
= $true ) ),
inference(trivial_inequality_removal,[],[f46]) ).
thf(f49,plain,
( ( ( subset @ sK1 @ sK2 )
= $true )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f48,f26]) ).
thf(f54,plain,
( ( subset @ sK1 @ sK2 )
= $true ),
inference(trivial_inequality_removal,[],[f49]) ).
thf(f57,plain,
! [X0: $i] :
( ( ( in @ X0 @ sK2 )
= $true )
| ( $true != $true )
| ( ( in @ X0 @ sK1 )
!= $true ) ),
inference(constrained_superposition,[],[f47,f54]) ).
thf(f60,plain,
! [X0: $i] :
( ( ( in @ X0 @ sK1 )
!= $true )
| ( ( in @ X0 @ sK2 )
= $true ) ),
inference(trivial_inequality_removal,[],[f57]) ).
thf(f63,plain,
( ( ( in @ sK3 @ sK2 )
= $true )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f60,f28]) ).
thf(f64,plain,
( ( in @ sK3 @ sK2 )
= $true ),
inference(trivial_inequality_removal,[],[f63]) ).
thf(f65,plain,
$false,
inference(forward_subsumption_resolution,[],[f64,f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU718^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n017.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 14:10:22 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 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
% 0.21/0.27 % (397582)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.27 % (397587)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3343129090:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.27 % (397587) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-397582-397587"...
% 0.21/0.27 % (397587)...printing done.
% 0.21/0.27 % (397587)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 % (397587)------------------------------
% 0.21/0.27 % (397587)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (397587)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (397587)CaDiCaL version: 2.1.3
% 0.21/0.27 % (397587)Termination reason: Refutation
% 0.21/0.27 % (397587)Time elapsed: 0.002 s
% 0.21/0.27 % (397587)Peak memory usage: 12 MB
% 0.21/0.27 % (397587)Instructions burned: 5 (million)
% 0.21/0.27 % (397582)Success in time 0.029 s
% 0.21/0.27 % Vampire exiting
%------------------------------------------------------------------------------