%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU644^2 : 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 : n013.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 08:30:29 AM UTC 2026
% Result : Theorem 0.22s 0.28s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 31 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 182 ( 54 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 155 ( 8 ~; 0 |; 17 &; 111 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 19 usr; 9 con; 0-4 aty)
% ( 3 !!; 4 ??; 0 @@+; 0 @@-)
% Number of variables : 26 ( 14 ^; 8 !; 4 ?; 26 :)
% 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,
setunion: $i > $i ).
thf(func_def_4,type,
eqinunit: $o ).
thf(func_def_6,type,
setunionsingleton: $o ).
thf(func_def_7,type,
singleton: $i > $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,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_13,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_14,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_15,type,
vAND: $o > $o > $o ).
thf(func_def_19,type,
vNOT: $o > $o ).
thf(f2,axiom,
( setunionsingleton
= ( ! [X0: $i] :
( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
= X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton) ).
thf(f3,axiom,
( ( ^ [X0: $i] :
? [X1: $i] :
( ( in @ X1 @ X0 )
& ( X0
= ( setadjoin @ X1 @ emptyset ) ) ) )
= singleton ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton) ).
thf(f4,conjecture,
( eqinunit
=> ( setunionsingleton
=> ! [X0: $i] :
( ( singleton @ X0 )
=> ( in @ ( setunion @ X0 ) @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theprop) ).
thf(f5,negated_conjecture,
~ ( eqinunit
=> ( setunionsingleton
=> ! [X0: $i] :
( ( singleton @ X0 )
=> ( in @ ( setunion @ X0 ) @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f8,plain,
( ( ^ [X0: $i] :
? [X1: $i] :
( ( in @ X1 @ X0 )
& ( X0
= ( setadjoin @ X1 @ emptyset ) ) ) )
= singleton ),
inference(rectify,[],[f3]) ).
thf(f9,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
( setunionsingleton
= ( !! @ $i
@ ^ [Y0: $i] :
( ( setunion @ ( setadjoin @ Y0 @ emptyset ) )
= Y0 ) ) ),
inference(fool_elimination,[],[f2]) ).
thf(f11,plain,
~ ( eqinunit
=> ( setunionsingleton
=> ! [X0: $i] :
( ( singleton @ X0 )
=> ( in @ ( setunion @ X0 ) @ X0 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f12,plain,
~ ( ( eqinunit = $true )
=> ( ( setunionsingleton = $true )
=> ! [X0: $i] :
( ( ( singleton @ X0 )
= $true )
=> ( ( in @ ( setunion @ X0 ) @ X0 )
= $true ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
( ? [X0: $i] :
( ( ( singleton @ X0 )
= $true )
& ( ( in @ ( setunion @ X0 ) @ X0 )
!= $true ) )
& ( setunionsingleton = $true )
& ( eqinunit = $true ) ),
inference(ennf_transformation,[],[f12]) ).
thf(f14,plain,
( ? [X0: $i] :
( ( ( singleton @ X0 )
= $true )
& ( ( in @ ( setunion @ X0 ) @ X0 )
!= $true ) )
& ( eqinunit = $true )
& ( setunionsingleton = $true ) ),
inference(flattening,[],[f13]) ).
thf(f15,plain,
( ( ( singleton @ sK0 )
= $true )
& ( $true
!= ( in @ ( setunion @ sK0 ) @ sK0 ) )
& ( eqinunit = $true )
& ( setunionsingleton = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f14]) ).
thf(f16,plain,
setunionsingleton = $true,
inference(cnf_transformation,[],[f15]) ).
thf(f18,plain,
( $true
!= ( in @ ( setunion @ sK0 ) @ sK0 ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f19,plain,
( ( singleton @ sK0 )
= $true ),
inference(cnf_transformation,[],[f15]) ).
thf(f20,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f21,plain,
( setunionsingleton
= ( !! @ $i
@ ^ [Y0: $i] :
( ( setunion @ ( setadjoin @ Y0 @ emptyset ) )
= Y0 ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f25,plain,
( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) )
@ sK0 )
= $true ),
inference(definition_unfolding,[],[f19,f20]) ).
thf(f26,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( setunion @ ( setadjoin @ Y0 @ emptyset ) )
= Y0 ) )
= $true ),
inference(definition_unfolding,[],[f21,f16]) ).
thf(f28,plain,
( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= sK0 )
& ( in @ Y0 @ sK0 ) ) ) ),
inference(beta-eta_normalization,[],[f25]) ).
thf(f29,plain,
( $true
= ( ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= sK0 )
& ( in @ Y0 @ sK0 ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f28]) ).
thf(f30,plain,
( $true
= ( ( ( setadjoin @ sK1 @ emptyset )
= sK0 )
& ( in @ sK1 @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f29]) ).
thf(f31,plain,
( $true
= ( in @ sK1 @ sK0 ) ),
inference(and_proxy_clausification,[],[f30]) ).
thf(f32,plain,
( $true
= ( ( setadjoin @ sK1 @ emptyset )
= sK0 ) ),
inference(and_proxy_clausification,[],[f30]) ).
thf(f33,plain,
( sK0
= ( setadjoin @ sK1 @ emptyset ) ),
inference(equality_proxy_clausification,[],[f32]) ).
thf(f40,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( setunion @ ( setadjoin @ Y0 @ emptyset ) )
= Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f26]) ).
thf(f41,plain,
! [X1: $i] :
( $true
= ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
= X1 ) ),
inference(beta-eta_normalization,[],[f40]) ).
thf(f42,plain,
! [X1: $i] :
( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
= X1 ),
inference(equality_proxy_clausification,[],[f41]) ).
thf(f43,plain,
( ( setunion @ sK0 )
= sK1 ),
inference(constrained_superposition,[],[f42,f33]) ).
thf(f44,plain,
( $true
!= ( in @ sK1 @ sK0 ) ),
inference(constrained_superposition,[],[f18,f43]) ).
thf(f45,plain,
$false,
inference(forward_subsumption_resolution,[],[f44,f31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU644^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n013.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 14:00:51 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running higher-order theorem proving
% 0.10/0.24 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
% 0.22/0.28 % (2165870)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.28 % (2165876)lrs+10_16_si=on:nwc=1.5:random_seed=356654824:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.28 % (2165876) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2165870-2165876"...
% 0.22/0.28 % (2165876)...printing done.
% 0.22/0.28 % (2165876)Refutation found. Thanks to Tanya!
% 0.22/0.28 % SZS status Theorem for theBenchmark
% 0.22/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.28 % (2165876)------------------------------
% 0.22/0.28 % (2165876)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (2165876)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (2165876)CaDiCaL version: 2.1.3
% 0.22/0.28 % (2165876)Termination reason: Refutation
% 0.22/0.28 % (2165876)Time elapsed: 0.002 s
% 0.22/0.28 % (2165876)Peak memory usage: 12 MB
% 0.22/0.28 % (2165876)Instructions burned: 3 (million)
% 0.22/0.28 % (2165870)Success in time 0.033 s
% 0.22/0.28 % Vampire exiting
%------------------------------------------------------------------------------