%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU623^2 : 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 : n007.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 08:30:22 AM UTC 2026
% Result : Theorem 0.22s 0.29s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 47 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 506 ( 141 equ; 0 cnn)
% Maximal formula atoms : 8 ( 10 avg)
% Number of connectives : 486 ( 56 ~; 46 |; 38 &; 311 @)
% ( 6 <=>; 29 =>; 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 : 24 ( 21 usr; 17 con; 0-2 aty)
% Number of variables : 103 ( 0 ^; 80 !; 23 ?; 103 :)
% 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,
subsetE: $o ).
thf(func_def_7,type,
powersetsubset: $o ).
thf(func_def_8,type,
binunion: $i > $i > $i ).
thf(func_def_9,type,
binunionLsub: $o ).
thf(func_def_10,type,
singletoninpowerset: $o ).
thf(f1,axiom,
! [X2: $i,X1: $i,X0: $i] :
( ( ( subset @ X0 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) )
= subsetE ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE) ).
thf(f3,axiom,
! [X0: $i,X1: $i] :
( ( subset @ X0 @ ( binunion @ X0 @ X1 ) )
= binunionLsub ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionLsub) ).
thf(f4,axiom,
( singletoninpowerset
= ( ! [X1: $i,X0: $i] :
( ( in @ X1 @ X0 )
=> ( in @ ( setadjoin @ X1 @ emptyset ) @ ( powerset @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowerset) ).
thf(f5,conjecture,
( subsetE
=> ( powersetsubset
=> ( binunionLsub
=> ( singletoninpowerset
=> ! [X2: $i,X1: $i,X0: $i] :
( ( in @ X2 @ X0 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X0 @ X1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowunion) ).
thf(f6,negated_conjecture,
~ ( subsetE
=> ( powersetsubset
=> ( binunionLsub
=> ( singletoninpowerset
=> ! [X2: $i,X1: $i,X0: $i] :
( ( in @ X2 @ X0 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X0 @ X1 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f7,plain,
~ ( subsetE
=> ( powersetsubset
=> ( binunionLsub
=> ( singletoninpowerset
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ X2 )
=> ( in @ ( setadjoin @ X0 @ emptyset ) @ ( powerset @ ( binunion @ X2 @ X1 ) ) ) ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
~ ( ( subsetE = $true )
=> ( ( powersetsubset = $true )
=> ( ( binunionLsub = $true )
=> ( ( singletoninpowerset = $true )
=> ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X0 @ X2 )
= $true )
=> ( $true
= ( in @ ( setadjoin @ X0 @ emptyset ) @ ( powerset @ ( binunion @ X2 @ X1 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X2 @ X1 )
=> ( ( in @ X0 @ X2 )
=> ( in @ X0 @ X1 ) ) )
= subsetE ),
inference(rectify,[],[f1]) ).
thf(f10,plain,
( ( subsetE = $true )
<=> ! [X2: $i,X1: $i,X0: $i] :
( ( ( subset @ X2 @ X1 )
= $true )
=> ( ( ( in @ X0 @ X2 )
= $true )
=> ( ( in @ X0 @ X1 )
= $true ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
! [X0: $i,X1: $i] :
( ( subset @ X0 @ ( binunion @ X0 @ X1 ) )
= binunionLsub ),
inference(rectify,[],[f3]) ).
thf(f12,plain,
( ! [X1: $i,X0: $i] :
( ( subset @ X0 @ ( binunion @ X0 @ X1 ) )
= $true )
<=> ( binunionLsub = $true ) ),
inference(fool_elimination,[],[f11]) ).
thf(f15,plain,
( singletoninpowerset
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ X1 )
=> ( in @ ( setadjoin @ X0 @ emptyset ) @ ( powerset @ X1 ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f16,plain,
( ! [X1: $i,X0: $i] :
( ( ( in @ X0 @ X1 )
= $true )
=> ( ( in @ ( setadjoin @ X0 @ emptyset ) @ ( powerset @ X1 ) )
= $true ) )
<=> ( singletoninpowerset = $true ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
( ( subsetE = $true )
<=> ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X0 @ X1 )
= $true )
| ( ( in @ X0 @ X2 )
!= $true )
| ( ( subset @ X2 @ X1 )
!= $true ) ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f18,plain,
( ( subsetE = $true )
<=> ! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
!= $true )
| ( ( in @ X0 @ X1 )
= $true )
| ( ( subset @ X2 @ X1 )
!= $true ) ) ),
inference(flattening,[],[f17]) ).
thf(f19,plain,
( ? [X0: $i,X2: $i,X1: $i] :
( ( $true
!= ( in @ ( setadjoin @ X0 @ emptyset ) @ ( powerset @ ( binunion @ X2 @ X1 ) ) ) )
& ( ( in @ X0 @ X2 )
= $true ) )
& ( singletoninpowerset = $true )
& ( binunionLsub = $true )
& ( powersetsubset = $true )
& ( subsetE = $true ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f20,plain,
( ( singletoninpowerset = $true )
& ( subsetE = $true )
& ( binunionLsub = $true )
& ( powersetsubset = $true )
& ? [X0: $i,X2: $i,X1: $i] :
( ( $true
!= ( in @ ( setadjoin @ X0 @ emptyset ) @ ( powerset @ ( binunion @ X2 @ X1 ) ) ) )
& ( ( in @ X0 @ X2 )
= $true ) ) ),
inference(flattening,[],[f19]) ).
thf(f21,plain,
( ( singletoninpowerset = $true )
<=> ! [X1: $i,X0: $i] :
( ( ( in @ X0 @ X1 )
!= $true )
| ( ( in @ ( setadjoin @ X0 @ emptyset ) @ ( powerset @ X1 ) )
= $true ) ) ),
inference(ennf_transformation,[],[f16]) ).
thf(f26,plain,
( ( singletoninpowerset = $true )
& ( subsetE = $true )
& ( binunionLsub = $true )
& ( powersetsubset = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ ( setadjoin @ X0 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
& ( ( in @ X0 @ X1 )
= $true ) ) ),
inference(rectify,[],[f20]) ).
thf(f27,plain,
( ( singletoninpowerset = $true )
& ( subsetE = $true )
& ( binunionLsub = $true )
& ( powersetsubset = $true )
& ( ( in @ ( setadjoin @ sK2 @ emptyset ) @ ( powerset @ ( binunion @ sK3 @ sK4 ) ) )
!= $true )
& ( ( in @ sK2 @ sK3 )
= $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f26]) ).
thf(f28,plain,
( ( ! [X1: $i,X0: $i] :
( ( subset @ X0 @ ( binunion @ X0 @ X1 ) )
= $true )
| ( binunionLsub != $true ) )
& ( ( binunionLsub = $true )
| ? [X1: $i,X0: $i] :
( ( subset @ X0 @ ( binunion @ X0 @ X1 ) )
!= $true ) ) ),
inference(nnf_transformation,[],[f12]) ).
thf(f29,plain,
( ( ! [X0: $i,X1: $i] :
( ( subset @ X1 @ ( binunion @ X1 @ X0 ) )
= $true )
| ( binunionLsub != $true ) )
& ( ( binunionLsub = $true )
| ? [X2: $i,X3: $i] :
( ( subset @ X3 @ ( binunion @ X3 @ X2 ) )
!= $true ) ) ),
inference(rectify,[],[f28]) ).
thf(f30,plain,
( ( ! [X0: $i,X1: $i] :
( ( subset @ X1 @ ( binunion @ X1 @ X0 ) )
= $true )
| ( binunionLsub != $true ) )
& ( ( binunionLsub = $true )
| ( ( subset @ sK6 @ ( binunion @ sK6 @ sK5 ) )
!= $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X2,sK5),skolemize(X3,sK6)],[f29]) ).
thf(f31,plain,
( ( ( singletoninpowerset = $true )
| ? [X1: $i,X0: $i] :
( ( ( in @ X0 @ X1 )
= $true )
& ( ( in @ ( setadjoin @ X0 @ emptyset ) @ ( powerset @ X1 ) )
!= $true ) ) )
& ( ! [X1: $i,X0: $i] :
( ( ( in @ X0 @ X1 )
!= $true )
| ( ( in @ ( setadjoin @ X0 @ emptyset ) @ ( powerset @ X1 ) )
= $true ) )
| ( singletoninpowerset != $true ) ) ),
inference(nnf_transformation,[],[f21]) ).
thf(f32,plain,
( ( ( singletoninpowerset = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
& ( ( in @ ( setadjoin @ X1 @ emptyset ) @ ( powerset @ X0 ) )
!= $true ) ) )
& ( ! [X2: $i,X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
| ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ X2 ) )
= $true ) )
| ( singletoninpowerset != $true ) ) ),
inference(rectify,[],[f31]) ).
thf(f33,plain,
( ( ( singletoninpowerset = $true )
| ( ( ( in @ sK8 @ sK7 )
= $true )
& ( ( in @ ( setadjoin @ sK8 @ emptyset ) @ ( powerset @ sK7 ) )
!= $true ) ) )
& ( ! [X2: $i,X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
| ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ X2 ) )
= $true ) )
| ( singletoninpowerset != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X0,sK7),skolemize(X1,sK8)],[f32]) ).
thf(f34,plain,
( ( ( subsetE = $true )
| ? [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
= $true )
& ( ( in @ X0 @ X1 )
!= $true )
& ( ( subset @ X2 @ X1 )
= $true ) ) )
& ( ! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
!= $true )
| ( ( in @ X0 @ X1 )
= $true )
| ( ( subset @ X2 @ X1 )
!= $true ) )
| ( subsetE != $true ) ) ),
inference(nnf_transformation,[],[f18]) ).
thf(f35,plain,
( ( ( subsetE = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
= $true )
& ( ( in @ X1 @ X0 )
!= $true )
& ( ( subset @ X2 @ X0 )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X5 )
!= $true )
| ( $true
= ( in @ X4 @ X3 ) )
| ( $true
!= ( subset @ X5 @ X3 ) ) )
| ( subsetE != $true ) ) ),
inference(rectify,[],[f34]) ).
thf(f36,plain,
( ( ( subsetE = $true )
| ( ( ( in @ sK10 @ sK11 )
= $true )
& ( $true
!= ( in @ sK10 @ sK9 ) )
& ( $true
= ( subset @ sK11 @ sK9 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X5 )
!= $true )
| ( $true
= ( in @ X4 @ X3 ) )
| ( $true
!= ( subset @ X5 @ X3 ) ) )
| ( subsetE != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11]),skolemize(X0,sK9),skolemize(X1,sK10),skolemize(X2,sK11)],[f35]) ).
thf(f40,plain,
( ( in @ sK2 @ sK3 )
= $true ),
inference(cnf_transformation,[],[f27]) ).
thf(f41,plain,
( ( in @ ( setadjoin @ sK2 @ emptyset ) @ ( powerset @ ( binunion @ sK3 @ sK4 ) ) )
!= $true ),
inference(cnf_transformation,[],[f27]) ).
thf(f43,plain,
binunionLsub = $true,
inference(cnf_transformation,[],[f27]) ).
thf(f44,plain,
subsetE = $true,
inference(cnf_transformation,[],[f27]) ).
thf(f45,plain,
singletoninpowerset = $true,
inference(cnf_transformation,[],[f27]) ).
thf(f47,plain,
! [X0: $i,X1: $i] :
( ( binunionLsub != $true )
| ( ( subset @ X1 @ ( binunion @ X1 @ X0 ) )
= $true ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f48,plain,
! [X2: $i,X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
| ( singletoninpowerset != $true )
| ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ X2 ) )
= $true ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f51,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( subsetE != $true )
| ( $true
!= ( subset @ X5 @ X3 ) )
| ( $true
= ( in @ X4 @ X3 ) )
| ( ( in @ X4 @ X5 )
!= $true ) ),
inference(cnf_transformation,[],[f36]) ).
thf(f60,plain,
! [X0: $i,X1: $i] :
( ( subset @ X1 @ ( binunion @ X1 @ X0 ) )
= $true ),
inference(forward_subsumption_resolution,[],[f47,f43]) ).
thf(f62,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X5 )
!= $true )
| ( $true
= ( in @ X4 @ X3 ) )
| ( $true
!= ( subset @ X5 @ X3 ) ) ),
inference(forward_subsumption_resolution,[],[f51,f44]) ).
thf(f63,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( subset @ sK3 @ X0 )
!= $true )
| ( ( in @ sK2 @ X0 )
= $true ) ),
inference(superposition,[],[f62,f40]) ).
thf(f64,plain,
! [X0: $i] :
( ( ( subset @ sK3 @ X0 )
!= $true )
| ( ( in @ sK2 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[],[f63]) ).
thf(f65,plain,
! [X2: $i,X3: $i] :
( ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ X2 ) )
= $true )
| ( ( in @ X3 @ X2 )
!= $true ) ),
inference(forward_subsumption_resolution,[],[f48,f45]) ).
thf(f66,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( in @ sK2 @ ( binunion @ sK3 @ X0 ) )
= $true ) ),
inference(superposition,[],[f64,f60]) ).
thf(f67,plain,
! [X0: $i] :
( ( in @ sK2 @ ( binunion @ sK3 @ X0 ) )
= $true ),
inference(trivial_inequality_removal,[],[f66]) ).
thf(f74,plain,
( ( ( in @ sK2 @ ( binunion @ sK3 @ sK4 ) )
!= $true )
| ( $true != $true ) ),
inference(superposition,[],[f41,f65]) ).
thf(f77,plain,
( ( in @ sK2 @ ( binunion @ sK3 @ sK4 ) )
!= $true ),
inference(trivial_inequality_removal,[],[f74]) ).
thf(f78,plain,
$false,
inference(forward_subsumption_resolution,[],[f77,f67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU623^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n007.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 13:57:11 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 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
% 0.22/0.29 % (3409231)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.29 % (3409240)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2681740444:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.29 % (3409240) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3409231-3409240"...
% 0.22/0.29 % (3409240)...printing done.
% 0.22/0.29 % (3409242)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.29 % (3409240)Refutation found. Thanks to Tanya!
% 0.22/0.29 % SZS status Theorem for theBenchmark
% 0.22/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.29 % (3409240)------------------------------
% 0.22/0.29 % (3409240)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (3409240)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (3409240)CaDiCaL version: 2.1.3
% 0.22/0.29 % (3409240)Termination reason: Refutation
% 0.22/0.29 % (3409240)Time elapsed: 0.002 s
% 0.22/0.29 % (3409240)Peak memory usage: 12 MB
% 0.22/0.29 % (3409240)Instructions burned: 7 (million)
% 0.22/0.29 % (3409231)Success in time 0.036 s
% 0.22/0.29 % Vampire exiting
%------------------------------------------------------------------------------