%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU728^2 : 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 : n011.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 08:30:59 AM UTC 2026
% Result : Theorem 0.24s 0.31s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 42 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 461 ( 130 equ; 0 cnn)
% Maximal formula atoms : 8 ( 10 avg)
% Number of connectives : 500 ( 58 ~; 44 |; 30 &; 329 @)
% ( 7 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 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 : 101 ( 0 ^; 83 !; 18 ?; 101 :)
% 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,
setminus: $i > $i > $i ).
thf(func_def_3,type,
setminusI: $o ).
thf(func_def_5,type,
setminusER: $o ).
thf(func_def_17,type,
vNOT: $o > $o ).
thf(f1,axiom,
! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) )
= setminusI ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusI) ).
thf(f2,axiom,
! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) )
= setminusER ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusER) ).
thf(f3,conjecture,
( setminusI
=> ( setminusER
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) )
=> ( in @ X2 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',doubleComplementE1) ).
thf(f4,negated_conjecture,
~ ( setminusI
=> ( setminusER
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) )
=> ( in @ X2 @ X1 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
~ ( setminusI
=> ( setminusER
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) )
=> ( in @ X2 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
~ ( ( setminusI = $true )
=> ( ( setminusER = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( ( ( in @ X2 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) )
= $true )
=> ( ( in @ X2 @ X1 )
= $true ) ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
=> ~ ( in @ X1 @ X2 ) )
= setminusER ),
inference(rectify,[],[f2]) ).
thf(f8,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
= $true )
=> ( $true
!= ( in @ X1 @ X2 ) ) )
<=> ( setminusER = $true ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
=> ( ~ ( in @ X0 @ X1 )
=> ( in @ X0 @ ( setminus @ X2 @ X1 ) ) ) )
= setminusI ),
inference(rectify,[],[f1]) ).
thf(f10,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
= $true )
=> ( ( ( in @ X0 @ X1 )
!= $true )
=> ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
= $true ) ) )
<=> ( setminusI = $true ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
= $true )
=> ( $true
!= ( in @ X1 @ X2 ) ) )
<=> ( setminusER = $true ) ),
inference(flattening,[],[f8]) ).
thf(f12,plain,
( ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X0 @ X2 )
= $true )
=> ( ( ( in @ X0 @ X1 )
!= $true )
=> ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
= $true ) ) )
<=> ( setminusI = $true ) ),
inference(flattening,[],[f10]) ).
thf(f13,plain,
( ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
= $true )
| ( ( in @ X0 @ X1 )
= $true )
| ( ( in @ X0 @ X2 )
!= $true ) )
<=> ( setminusI = $true ) ),
inference(ennf_transformation,[],[f12]) ).
thf(f14,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
= $true )
| ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
= $true )
| ( ( in @ X0 @ X2 )
!= $true ) )
<=> ( setminusI = $true ) ),
inference(flattening,[],[f13]) ).
thf(f15,plain,
( ( setminusER = $true )
<=> ! [X2: $i,X1: $i,X0: $i] :
( ( $true
!= ( in @ X1 @ X2 ) )
| ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
!= $true ) ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f16,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) )
= $true )
& ( ( in @ X2 @ X0 )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( setminusER = $true )
& ( setminusI = $true ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f17,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) )
= $true ) ) )
& ( setminusER = $true )
& ( setminusI = $true ) ),
inference(flattening,[],[f16]) ).
thf(f18,plain,
( ( ( setminusER = $true )
| ? [X2: $i,X1: $i,X0: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
& ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
= $true ) ) )
& ( ! [X2: $i,X1: $i,X0: $i] :
( ( $true
!= ( in @ X1 @ X2 ) )
| ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
!= $true ) )
| ( setminusER != $true ) ) ),
inference(nnf_transformation,[],[f15]) ).
thf(f19,plain,
( ( ( setminusER = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
= $true )
& ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X3 )
!= $true )
| ( ( in @ X4 @ ( setminus @ X5 @ X3 ) )
!= $true ) )
| ( setminusER != $true ) ) ),
inference(rectify,[],[f18]) ).
thf(f20,plain,
( ( ( setminusER = $true )
| ( ( ( in @ sK1 @ sK0 )
= $true )
& ( ( in @ sK1 @ ( setminus @ sK2 @ sK0 ) )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X3 )
!= $true )
| ( ( in @ X4 @ ( setminus @ X5 @ X3 ) )
!= $true ) )
| ( setminusER != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f19]) ).
thf(f21,plain,
( ( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
= $true )
| ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
= $true )
| ( ( in @ X0 @ X2 )
!= $true ) )
| ( setminusI != $true ) )
& ( ( setminusI = $true )
| ? [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
!= $true )
& ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
!= $true )
& ( ( in @ X0 @ X2 )
= $true ) ) ) ),
inference(nnf_transformation,[],[f14]) ).
thf(f22,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
| ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
= $true )
| ( ( in @ X1 @ X0 )
!= $true ) )
| ( setminusI != $true ) )
& ( ( setminusI = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X5 )
!= $true )
& ( $true
!= ( in @ X4 @ ( setminus @ X3 @ X5 ) ) )
& ( ( in @ X4 @ X3 )
= $true ) ) ) ),
inference(rectify,[],[f21]) ).
thf(f23,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
| ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
= $true )
| ( ( in @ X1 @ X0 )
!= $true ) )
| ( setminusI != $true ) )
& ( ( setminusI = $true )
| ( ( ( in @ sK4 @ sK5 )
!= $true )
& ( ( in @ sK4 @ ( setminus @ sK3 @ sK5 ) )
!= $true )
& ( ( in @ sK4 @ sK3 )
= $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5)],[f22]) ).
thf(f24,plain,
( ( ( in @ sK7 @ ( powerset @ sK6 ) )
= $true )
& ( ( in @ sK8 @ sK7 )
!= $true )
& ( $true
= ( in @ sK8 @ sK6 ) )
& ( $true
= ( in @ sK8 @ ( setminus @ sK6 @ ( setminus @ sK6 @ sK7 ) ) ) )
& ( setminusER = $true )
& ( setminusI = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8]),skolemize(X0,sK6),skolemize(X1,sK7),skolemize(X2,sK8)],[f17]) ).
thf(f25,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X3 )
!= $true )
| ( ( in @ X4 @ ( setminus @ X5 @ X3 ) )
!= $true )
| ( setminusER != $true ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f31,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
| ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
= $true )
| ( ( in @ X1 @ X0 )
!= $true )
| ( setminusI != $true ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f32,plain,
setminusI = $true,
inference(cnf_transformation,[],[f24]) ).
thf(f33,plain,
setminusER = $true,
inference(cnf_transformation,[],[f24]) ).
thf(f34,plain,
( $true
= ( in @ sK8 @ ( setminus @ sK6 @ ( setminus @ sK6 @ sK7 ) ) ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f35,plain,
( $true
= ( in @ sK8 @ sK6 ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f36,plain,
( ( in @ sK8 @ sK7 )
!= $true ),
inference(cnf_transformation,[],[f24]) ).
thf(f42,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true != $true )
| ( ( in @ X4 @ ( setminus @ X5 @ X3 ) )
!= $true )
| ( ( in @ X4 @ X3 )
!= $true ) ),
inference(definition_unfolding,[],[f25,f33]) ).
thf(f43,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
= ( in @ X1 @ X2 ) )
| ( ( in @ X1 @ X0 )
!= $true )
| ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
= $true ) ),
inference(definition_unfolding,[],[f31,f32]) ).
thf(f47,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
= $true )
| ( $true
= ( in @ X1 @ X2 ) ) ),
inference(trivial_inequality_removal,[],[f43]) ).
thf(f48,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( setminus @ X5 @ X3 ) )
!= $true )
| ( ( in @ X4 @ X3 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f42]) ).
thf(f49,plain,
( ( ( in @ sK8 @ ( setminus @ sK6 @ sK7 ) )
!= $true )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f48,f34]) ).
thf(f50,plain,
( ( in @ sK8 @ ( setminus @ sK6 @ sK7 ) )
!= $true ),
inference(trivial_inequality_removal,[],[f49]) ).
thf(f51,plain,
! [X0: $i] :
( ( ( in @ sK8 @ X0 )
= $true )
| ( ( in @ sK8 @ ( setminus @ sK6 @ X0 ) )
= $true )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f47,f35]) ).
thf(f55,plain,
! [X0: $i] :
( ( ( in @ sK8 @ ( setminus @ sK6 @ X0 ) )
= $true )
| ( ( in @ sK8 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[],[f51]) ).
thf(f57,plain,
( ( ( in @ sK8 @ sK7 )
= $true )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f50,f55]) ).
thf(f61,plain,
( ( in @ sK8 @ sK7 )
= $true ),
inference(trivial_inequality_removal,[],[f57]) ).
thf(f62,plain,
$false,
inference(forward_subsumption_resolution,[],[f61,f36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU728^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n011.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 14:17:16 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.25 Running higher-order theorem proving
% 0.10/0.26 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
% 0.24/0.31 % (156044)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.31 % (156051)lrs+10_16_si=on:nwc=1.5:random_seed=1136994469:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.24/0.31 % (156050)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3486770006:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.24/0.31 % (156052)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2017612753:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.24/0.31 % (156051) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-156044-156051"...
% 0.24/0.31 % (156052)Refutation not found, incomplete strategy
% 0.24/0.31 % (156052)------------------------------
% 0.24/0.31 % (156052)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.31 % (156052)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.31 % (156052)CaDiCaL version: 2.1.3
% 0.24/0.31 % (156052)Termination reason: Refutation not found, incomplete strategy
% 0.24/0.31 % (156052)Time elapsed: 0.002 s
% 0.24/0.31 % (156052)Peak memory usage: 12 MB
% 0.24/0.31 % (156052)Instructions burned: 2 (million)
% 0.24/0.31 % (156050) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-156044-156050"...
% 0.24/0.31 % (156052)------------------------------
% 0.24/0.31 % (156052)------------------------------
% 0.24/0.31 % (156051)...printing done.
% 0.24/0.31 % (156050)...printing done.
% 0.24/0.31 % (156050)Refutation found. Thanks to Tanya!
% 0.24/0.31 % SZS status Theorem for theBenchmark
% 0.24/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.31 % (156050)------------------------------
% 0.24/0.31 % (156050)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.31 % (156050)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.31 % (156050)CaDiCaL version: 2.1.3
% 0.24/0.31 % (156050)Termination reason: Refutation
% 0.24/0.31 % (156050)Time elapsed: 0.004 s
% 0.24/0.31 % (156050)Peak memory usage: 12 MB
% 0.24/0.31 % (156050)Instructions burned: 6 (million)
% 0.24/0.31 % (156044)Success in time 0.043 s
% 0.24/0.31 % Vampire exiting
%------------------------------------------------------------------------------