%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU629^2 : 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 : n010.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 0.24s 0.30s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 3
% Syntax : Number of formulae : 37 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 316 ( 54 equ; 0 cnn)
% Maximal formula atoms : 4 ( 8 avg)
% Number of connectives : 616 ( 10 ~; 9 |; 9 &; 526 @)
% ( 0 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 20 usr; 9 con; 0-4 aty)
% ( 25 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 96 ( 37 ^; 51 !; 8 ?; 96 :)
% 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,
binunion: $i > $i > $i ).
thf(func_def_5,type,
kpair: $i > $i > $i ).
thf(func_def_7,type,
ubforcartprodlem2: $o ).
thf(func_def_8,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_9,type,
vIMP: $o > $o > $o ).
thf(func_def_10,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_21,type,
vNOT: $o > $o ).
thf(f1,axiom,
( ( ^ [X0: $i,X1: $i] : ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= kpair ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpair) ).
thf(f2,axiom,
( ubforcartprodlem2
= ( ! [X2: $i,X1: $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(f3,conjecture,
( ubforcartprodlem2
=> ! [X0: $i,X2: $i,X1: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( powerset @ ( powerset @ ( binunion @ X0 @ X1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem3) ).
thf(f4,negated_conjecture,
~ ( ubforcartprodlem2
=> ! [X0: $i,X2: $i,X1: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( powerset @ ( powerset @ ( binunion @ X0 @ X1 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
( ubforcartprodlem2
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X2 @ X1 ) ) ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f6,plain,
( ubforcartprodlem2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
( kpair
= ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f8,plain,
~ ( ubforcartprodlem2
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ ( kpair @ X1 @ X3 ) @ ( powerset @ ( powerset @ ( binunion @ X0 @ X2 ) ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f9,plain,
~ ( ( ubforcartprodlem2 = $true )
=> ! [X2: $i,X1: $i,X0: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X2 ) )
=> ( $true
= ( in @ ( kpair @ X1 @ X3 ) @ ( powerset @ ( powerset @ ( binunion @ X0 @ X2 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
( ? [X2: $i,X0: $i,X1: $i] :
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ X2 ) )
& ( $true
!= ( in @ ( kpair @ X1 @ X3 ) @ ( powerset @ ( powerset @ ( binunion @ X0 @ X2 ) ) ) ) ) )
& ( $true
= ( in @ X1 @ X0 ) ) )
& ( ubforcartprodlem2 = $true ) ),
inference(ennf_transformation,[],[f9]) ).
thf(f11,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ X0 ) )
& ( ( in @ ( kpair @ X2 @ X3 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X0 ) ) ) )
!= $true ) )
& ( $true
= ( in @ X2 @ X1 ) ) )
& ( ubforcartprodlem2 = $true ) ),
inference(rectify,[],[f10]) ).
thf(f12,plain,
( ( ( in @ sK3 @ sK0 )
= $true )
& ( $true
!= ( in @ ( kpair @ sK2 @ sK3 ) @ ( powerset @ ( powerset @ ( binunion @ sK1 @ sK0 ) ) ) ) )
& ( $true
= ( in @ sK2 @ sK1 ) )
& ( ubforcartprodlem2 = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f11]) ).
thf(f13,plain,
( kpair
= ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f14,plain,
( ubforcartprodlem2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f15,plain,
ubforcartprodlem2 = $true,
inference(cnf_transformation,[],[f12]) ).
thf(f16,plain,
( $true
= ( in @ sK2 @ sK1 ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f17,plain,
( $true
!= ( in @ ( kpair @ sK2 @ sK3 ) @ ( powerset @ ( powerset @ ( binunion @ sK1 @ sK0 ) ) ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f18,plain,
( ( in @ sK3 @ sK0 )
= $true ),
inference(cnf_transformation,[],[f12]) ).
thf(f21,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f14,f15]) ).
thf(f22,plain,
( $true
!= ( in
@ ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
@ sK2
@ sK3 )
@ ( powerset @ ( powerset @ ( binunion @ sK1 @ sK0 ) ) ) ) ),
inference(definition_unfolding,[],[f17,f13]) ).
thf(f23,plain,
( $true
!= ( in @ ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ sK1 @ sK0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f22]) ).
thf(f24,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ Y0 @ Y1 ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f21]) ).
thf(f25,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f24]) ).
thf(f26,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ Y0 ) ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f25]) ).
thf(f27,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( in @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f26]) ).
thf(f28,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( in @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f27]) ).
thf(f29,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X3 @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f28]) ).
thf(f30,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) ) )
| ( ( in @ X3 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f29]) ).
thf(f31,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
@ X4 ) )
| ( ( in @ X3 @ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f30]) ).
thf(f32,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ( in @ X4 @ X2 )
=> ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
| ( ( in @ X3 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f31]) ).
thf(f33,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
| ( ( in @ X3 @ X1 )
= $false )
| ( ( in @ X4 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f32]) ).
thf(f34,plain,
( ( ( in @ sK3 @ sK0 )
= $false )
| ( $true != $true )
| ( ( in @ sK2 @ sK1 )
= $false ) ),
inference(constrained_superposition,[],[f23,f33]) ).
thf(f35,plain,
( ( ( in @ sK3 @ sK0 )
= $false )
| ( ( in @ sK2 @ sK1 )
= $false ) ),
inference(trivial_inequality_removal,[],[f34]) ).
thf(f36,plain,
( ( ( in @ sK2 @ sK1 )
= $false )
| ( $true = $false ) ),
inference(forward_demodulation,[],[f35,f18]) ).
thf(f37,plain,
( ( in @ sK2 @ sK1 )
= $false ),
inference(trivial_inequality_removal,[],[f36]) ).
thf(f39,plain,
$true = $false,
inference(constrained_superposition,[],[f16,f37]) ).
thf(f40,plain,
$false,
inference(trivial_inequality_removal,[],[f39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU629^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n010.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 13:59:48 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.09/0.25 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
% 0.24/0.30 % (2903339)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.30 % (2903345)lrs+10_16_si=on:nwc=1.5:random_seed=2959726628:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.24/0.30 % (2903344)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2427592232:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.24/0.30 % (2903345) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2903339-2903345"...
% 0.24/0.30 % (2903345)...printing done.
% 0.24/0.30 % (2903345)Refutation found. Thanks to Tanya!
% 0.24/0.30 % SZS status Theorem for theBenchmark
% 0.24/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.30 % (2903345)------------------------------
% 0.24/0.30 % (2903345)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.30 % (2903345)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.30 % (2903345)CaDiCaL version: 2.1.3
% 0.24/0.30 % (2903345)Termination reason: Refutation
% 0.24/0.30 % (2903345)Time elapsed: 0.004 s
% 0.24/0.30 % (2903345)Peak memory usage: 12 MB
% 0.24/0.30 % (2903345)Instructions burned: 6 (million)
% 0.24/0.30 % (2903339)Success in time 0.035 s
% 0.24/0.30 % Vampire exiting
%------------------------------------------------------------------------------