%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU740^2 : 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 : n014.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 08:31:04 AM UTC 2026
% Result : Theorem 0.19s 0.27s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 38 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 424 ( 119 equ; 0 cnn)
% Maximal formula atoms : 8 ( 11 avg)
% Number of connectives : 479 ( 41 ~; 32 |; 40 &; 328 @)
% ( 4 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 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 : 109 ( 0 ^; 82 !; 27 ?; 109 :)
% 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_5,type,
binintersect: $i > $i > $i ).
thf(func_def_6,type,
binintersectEL: $o ).
thf(func_def_20,type,
vNOT: $o > $o ).
thf(f1,axiom,
! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
=> ( in @ X2 @ ( binunion @ X0 @ X1 ) ) )
= binunionIL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIL) ).
thf(f2,axiom,
! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X2 @ X0 ) )
= binintersectEL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectEL) ).
thf(f3,conjecture,
( binunionIL
=> ( binintersectEL
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ X4 @ ( binintersect @ X1 @ X2 ) )
=> ( in @ X4 @ ( binunion @ X1 @ X3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inIntersectImpInUnion) ).
thf(f4,negated_conjecture,
~ ( binunionIL
=> ( binintersectEL
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ X4 @ ( binintersect @ X1 @ X2 ) )
=> ( in @ X4 @ ( binunion @ X1 @ X3 ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
~ ( binunionIL
=> ( binintersectEL
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ ( binintersect @ X0 @ X2 ) )
=> ( in @ X4 @ ( binunion @ X0 @ X3 ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
~ ( ( binunionIL = $true )
=> ( ( binintersectEL = $true )
=> ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X1 ) )
= $true )
=> ! [X4: $i] :
( ( ( in @ X4 @ X1 )
= $true )
=> ( ( $true
= ( in @ X4 @ ( binintersect @ X0 @ X2 ) ) )
=> ( $true
= ( in @ X4 @ ( binunion @ X0 @ X3 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
=> ( in @ X1 @ ( binunion @ X0 @ X2 ) ) )
= binunionIL ),
inference(rectify,[],[f1]) ).
thf(f8,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
=> ( $true
= ( in @ X1 @ ( binunion @ X0 @ X2 ) ) ) )
<=> ( binunionIL = $true ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( binintersect @ X2 @ X1 ) )
=> ( in @ X0 @ X2 ) )
= binintersectEL ),
inference(rectify,[],[f2]) ).
thf(f10,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( binintersect @ X2 @ X1 ) )
= $true )
=> ( ( in @ X0 @ X2 )
= $true ) )
<=> ( binintersectEL = $true ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( $true
!= ( in @ X4 @ ( binunion @ X0 @ X3 ) ) )
& ( $true
= ( in @ X4 @ ( binintersect @ X0 @ X2 ) ) )
& ( ( in @ X4 @ X1 )
= $true ) )
& ( ( in @ X3 @ ( powerset @ X1 ) )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) )
& ( binintersectEL = $true )
& ( binunionIL = $true ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f12,plain,
( ( binunionIL = $true )
& ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X1 ) )
= $true )
& ? [X4: $i] :
( ( $true
= ( in @ X4 @ ( binintersect @ X0 @ X2 ) ) )
& ( ( in @ X4 @ X1 )
= $true )
& ( $true
!= ( in @ X4 @ ( binunion @ X0 @ X3 ) ) ) ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) )
& ( binintersectEL = $true ) ),
inference(flattening,[],[f11]) ).
thf(f13,plain,
( ( binunionIL = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ X0 ) )
| ( $true
= ( in @ X1 @ ( binunion @ X0 @ X2 ) ) ) ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f14,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( binintersect @ X2 @ X1 ) )
!= $true )
| ( ( in @ X0 @ X2 )
= $true ) )
<=> ( binintersectEL = $true ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f15,plain,
( ( ( binunionIL = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
& ( $true
!= ( in @ X1 @ ( binunion @ X0 @ X2 ) ) ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ X0 ) )
| ( $true
= ( in @ X1 @ ( binunion @ X0 @ X2 ) ) ) )
| ( binunionIL != $true ) ) ),
inference(nnf_transformation,[],[f13]) ).
thf(f16,plain,
( ( ( binunionIL = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
& ( $true
!= ( in @ X1 @ ( binunion @ X0 @ X2 ) ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X4 @ X3 ) )
| ( ( in @ X4 @ ( binunion @ X3 @ X5 ) )
= $true ) )
| ( binunionIL != $true ) ) ),
inference(rectify,[],[f15]) ).
thf(f17,plain,
( ( ( binunionIL = $true )
| ( ( $true
= ( in @ sK1 @ sK0 ) )
& ( ( in @ sK1 @ ( binunion @ sK0 @ sK2 ) )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X4 @ X3 ) )
| ( ( in @ X4 @ ( binunion @ X3 @ X5 ) )
= $true ) )
| ( binunionIL != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f16]) ).
thf(f18,plain,
( ( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( binintersect @ X2 @ X1 ) )
!= $true )
| ( ( in @ X0 @ X2 )
= $true ) )
| ( binintersectEL != $true ) )
& ( ( binintersectEL = $true )
| ? [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( binintersect @ X2 @ X1 ) )
= $true )
& ( ( in @ X0 @ X2 )
!= $true ) ) ) ),
inference(nnf_transformation,[],[f14]) ).
thf(f19,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( binintersect @ X0 @ X2 ) ) )
| ( $true
= ( in @ X1 @ X0 ) ) )
| ( binintersectEL != $true ) )
& ( ( binintersectEL = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( binintersect @ X3 @ X5 ) )
= $true )
& ( $true
!= ( in @ X4 @ X3 ) ) ) ) ),
inference(rectify,[],[f18]) ).
thf(f20,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( binintersect @ X0 @ X2 ) ) )
| ( $true
= ( in @ X1 @ X0 ) ) )
| ( binintersectEL != $true ) )
& ( ( binintersectEL = $true )
| ( ( $true
= ( in @ sK4 @ ( binintersect @ sK3 @ sK5 ) ) )
& ( $true
!= ( in @ sK4 @ sK3 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5)],[f19]) ).
thf(f21,plain,
( ( binunionIL = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X0 ) )
= $true )
& ? [X4: $i] :
( ( ( in @ X4 @ ( binintersect @ X1 @ X2 ) )
= $true )
& ( ( in @ X4 @ X0 )
= $true )
& ( ( in @ X4 @ ( binunion @ X1 @ X3 ) )
!= $true ) ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( binintersectEL = $true ) ),
inference(rectify,[],[f12]) ).
thf(f22,plain,
( ( binunionIL = $true )
& ( $true
= ( in @ sK9 @ ( powerset @ sK6 ) ) )
& ( $true
= ( in @ sK10 @ ( binintersect @ sK7 @ sK8 ) ) )
& ( $true
= ( in @ sK10 @ sK6 ) )
& ( $true
!= ( in @ sK10 @ ( binunion @ sK7 @ sK9 ) ) )
& ( $true
= ( in @ sK8 @ ( powerset @ sK6 ) ) )
& ( ( in @ sK7 @ ( powerset @ sK6 ) )
= $true )
& ( binintersectEL = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9,sK10]),skolemize(X0,sK6),skolemize(X1,sK7),skolemize(X2,sK8),skolemize(X3,sK9),skolemize(X4,sK10)],[f21]) ).
thf(f23,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X4 @ X3 ) )
| ( ( in @ X4 @ ( binunion @ X3 @ X5 ) )
= $true )
| ( binunionIL != $true ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f28,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( binintersect @ X0 @ X2 ) ) )
| ( $true
= ( in @ X1 @ X0 ) )
| ( binintersectEL != $true ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f29,plain,
binintersectEL = $true,
inference(cnf_transformation,[],[f22]) ).
thf(f32,plain,
( $true
!= ( in @ sK10 @ ( binunion @ sK7 @ sK9 ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f34,plain,
( $true
= ( in @ sK10 @ ( binintersect @ sK7 @ sK8 ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f36,plain,
binunionIL = $true,
inference(cnf_transformation,[],[f22]) ).
thf(f41,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true != $true )
| ( ( in @ X4 @ ( binunion @ X3 @ X5 ) )
= $true )
| ( $true
!= ( in @ X4 @ X3 ) ) ),
inference(definition_unfolding,[],[f23,f36]) ).
thf(f42,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( binintersect @ X0 @ X2 ) ) )
| ( $true != $true )
| ( $true
= ( in @ X1 @ X0 ) ) ),
inference(definition_unfolding,[],[f28,f29]) ).
thf(f45,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X4 @ X3 ) )
| ( ( in @ X4 @ ( binunion @ X3 @ X5 ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f41]) ).
thf(f46,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( binintersect @ X0 @ X2 ) ) )
| ( $true
= ( in @ X1 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f42]) ).
thf(f59,plain,
( ( $true != $true )
| ( ( in @ sK10 @ sK7 )
= $true ) ),
inference(constrained_superposition,[],[f46,f34]) ).
thf(f60,plain,
( ( in @ sK10 @ sK7 )
= $true ),
inference(trivial_inequality_removal,[],[f59]) ).
thf(f61,plain,
! [X0: $i] :
( ( $true != $true )
| ( $true
= ( in @ sK10 @ ( binunion @ sK7 @ X0 ) ) ) ),
inference(constrained_superposition,[],[f45,f60]) ).
thf(f62,plain,
! [X0: $i] :
( $true
= ( in @ sK10 @ ( binunion @ sK7 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f61]) ).
thf(f63,plain,
$true != $true,
inference(backward_demodulation,[],[f32,f62]) ).
thf(f64,plain,
$false,
inference(trivial_inequality_removal,[],[f63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU740^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n014.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 14:19:00 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.22 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
% 0.19/0.27 % (2732296)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.27 % (2732301)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3046922250:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.19/0.27 % (2732306)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1339115062:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.19/0.27 % (2732306) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2732296-2732306"...
% 0.19/0.27 % (2732301) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2732296-2732301"...
% 0.19/0.27 % (2732306)...printing done.
% 0.19/0.27 % (2732306)Refutation found. Thanks to Tanya!
% 0.19/0.27 % SZS status Theorem for theBenchmark
% 0.19/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.27 % (2732306)------------------------------
% 0.19/0.27 % (2732306)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (2732306)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (2732306)CaDiCaL version: 2.1.3
% 0.19/0.27 % (2732306)Termination reason: Refutation
% 0.19/0.27 % (2732306)Time elapsed: 0.002 s
% 0.19/0.27 % (2732306)Peak memory usage: 12 MB
% 0.19/0.27 % (2732306)Instructions burned: 7 (million)
% 0.19/0.27 % (2732296)Success in time 0.043 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------