%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU545^2 : 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 : n016.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 08:30:00 AM UTC 2026
% Result : Theorem 0.19s 0.34s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 2
% Syntax : Number of formulae : 34 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 220 ( 87 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 227 ( 27 ~; 25 |; 20 &; 113 @)
% ( 0 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 19 usr; 6 con; 0-4 aty)
% ( 7 !!; 4 ??; 0 @@+; 0 @@-)
% Number of variables : 78 ( 28 ^; 38 !; 12 ?; 78 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
exu: ( $i > $o ) > $o ).
thf(func_def_2,type,
exuI1: $o ).
thf(func_def_5,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_7,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_8,type,
vIMP: $o > $o > $o ).
thf(func_def_9,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_10,type,
vAND: $o > $o > $o ).
thf(func_def_11,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_14,type,
sK0: $i > $o ).
thf(func_def_16,type,
vNOT: $o > $o ).
thf(func_def_17,type,
sK2: $i > $i ).
thf(func_def_18,type,
sK3: ( $i > $o ) > $i ).
thf(func_def_19,type,
sK4: ( $i > $o ) > $i > $i ).
thf(func_def_20,type,
sK5: ( $i > $o ) > $i > $i ).
thf(f1,axiom,
( exu
= ( ^ [X0: $i > $o] :
? [X1: $i] :
( ( X0 @ X1 )
& ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 = X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu) ).
thf(f3,conjecture,
( exuI1
=> ! [X0: $i > $o] :
( ? [X1: $i] : ( X0 @ X1 )
=> ( ! [X1: $i,X2: $i] :
( ( X0 @ X1 )
=> ( ( X0 @ X2 )
=> ( X1 = X2 ) ) )
=> ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI3) ).
thf(f4,negated_conjecture,
~ ( exuI1
=> ! [X0: $i > $o] :
( ? [X1: $i] : ( X0 @ X1 )
=> ( ! [X1: $i,X2: $i] :
( ( X0 @ X1 )
=> ( ( X0 @ X2 )
=> ( X1 = X2 ) ) )
=> ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
~ ( exuI1
=> ! [X0: $i > $o] :
( ? [X1: $i] : ( X0 @ X1 )
=> ( ! [X2: $i,X3: $i] :
( ( X0 @ X2 )
=> ( ( X0 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X4: $i] : ( X0 @ X4 ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
~ ( ( exuI1 = $true )
=> ! [X0: $i > $o] :
( ? [X1: $i] :
( ( X0 @ X1 )
= $true )
=> ( ! [X2: $i,X3: $i] :
( ( ( X0 @ X2 )
= $true )
=> ( ( ( X0 @ X3 )
= $true )
=> ( X2 = X3 ) ) )
=> ( $true
= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f9,plain,
( exu
= ( ^ [X0: $i > $o] :
? [X1: $i] :
( ( X0 @ X1 )
& ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 = X2 ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f10,plain,
( exu
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) )
& ( Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ? [X0: $i > $o] :
( ( $true
!= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
& ! [X2: $i,X3: $i] :
( ( X2 = X3 )
| ( ( X0 @ X3 )
!= $true )
| ( ( X0 @ X2 )
!= $true ) )
& ? [X1: $i] :
( ( X0 @ X1 )
= $true ) )
& ( exuI1 = $true ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f12,plain,
( ? [X0: $i > $o] :
( ( $true
!= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
& ! [X3: $i,X2: $i] :
( ( ( X0 @ X3 )
!= $true )
| ( X2 = X3 )
| ( ( X0 @ X2 )
!= $true ) )
& ? [X1: $i] :
( ( X0 @ X1 )
= $true ) )
& ( exuI1 = $true ) ),
inference(flattening,[],[f11]) ).
thf(f13,plain,
( ? [X0: $i > $o] :
( ( $true
!= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
& ! [X1: $i,X2: $i] :
( ( ( X0 @ X1 )
!= $true )
| ( X1 = X2 )
| ( ( X0 @ X2 )
!= $true ) )
& ? [X3: $i] :
( ( X0 @ X3 )
= $true ) )
& ( exuI1 = $true ) ),
inference(rectify,[],[f12]) ).
thf(f14,plain,
( ( $true
!= ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) )
& ! [X1: $i,X2: $i] :
( ( $true
!= ( sK0 @ X1 ) )
| ( X1 = X2 )
| ( ( sK0 @ X2 )
!= $true ) )
& ( ( sK0 @ sK1 )
= $true )
& ( exuI1 = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X3,sK1)],[f13]) ).
thf(f15,plain,
( exu
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) )
& ( Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f17,plain,
( ( sK0 @ sK1 )
= $true ),
inference(cnf_transformation,[],[f14]) ).
thf(f18,plain,
! [X2: $i,X1: $i] :
( ( $true
!= ( sK0 @ X1 ) )
| ( ( sK0 @ X2 )
!= $true )
| ( X1 = X2 ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f19,plain,
( $true
!= ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f23,plain,
( ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) )
& ( Y0 @ Y1 ) ) )
@ ^ [Y0: $i] : ( sK0 @ Y0 ) )
!= $true ),
inference(definition_unfolding,[],[f19,f15]) ).
thf(f25,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) )
& ( sK0 @ Y0 ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f23]) ).
thf(f26,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) )
& ( sK0 @ Y0 ) )
@ X1 )
= $false ),
inference(pi_proxy_clausification,[],[f25]) ).
thf(f27,plain,
! [X1: $i] :
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( X1 = Y0 ) ) )
& ( sK0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f26]) ).
thf(f28,plain,
! [X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( X1 = Y0 ) ) ) )
| ( $false
= ( sK0 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f27]) ).
thf(f29,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( X1 = Y0 ) )
@ ( sK2 @ X1 ) ) )
| ( $false
= ( sK0 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f28]) ).
thf(f30,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ X1 ) )
| ( $false
= ( ( sK0 @ ( sK2 @ X1 ) )
=> ( X1
= ( sK2 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f29]) ).
thf(f31,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ X1 ) )
| ( $false
= ( X1
= ( sK2 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f30]) ).
thf(f32,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ ( sK2 @ X1 ) ) )
| ( $false
= ( sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f30]) ).
thf(f33,plain,
! [X1: $i] :
( ( ( sK2 @ X1 )
!= X1 )
| ( $false
= ( sK0 @ X1 ) ) ),
inference(equality_proxy_clausification,[],[f31]) ).
thf(f56,plain,
! [X0: $i] :
( ( sK1 = X0 )
| ( $true != $true )
| ( $true
!= ( sK0 @ X0 ) ) ),
inference(constrained_superposition,[],[f18,f17]) ).
thf(f57,plain,
! [X0: $i] :
( ( $true
!= ( sK0 @ X0 ) )
| ( sK1 = X0 ) ),
inference(trivial_inequality_removal,[],[f56]) ).
thf(f58,plain,
! [X0: $i] :
( ( ( sK0 @ X0 )
= $false )
| ( $true != $true )
| ( ( sK2 @ X0 )
= sK1 ) ),
inference(constrained_superposition,[],[f57,f32]) ).
thf(f60,plain,
! [X0: $i] :
( ( ( sK2 @ X0 )
= sK1 )
| ( ( sK0 @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f58]) ).
thf(f63,plain,
! [X0: $i] :
( ( ( sK0 @ X0 )
= $false )
| ( sK1 != X0 )
| ( ( sK0 @ X0 )
= $false ) ),
inference(constrained_superposition,[],[f33,f60]) ).
thf(f64,plain,
! [X0: $i] :
( ( sK1 != X0 )
| ( ( sK0 @ X0 )
= $false ) ),
inference(duplicate_literal_removal,[],[f63]) ).
thf(f66,plain,
( ( sK0 @ sK1 )
= $false ),
inference(equality_resolution,[],[f64]) ).
thf(f68,plain,
$true = $false,
inference(constrained_superposition,[],[f17,f66]) ).
thf(f70,plain,
$false,
inference(trivial_inequality_removal,[],[f68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU545^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.26 % Computer : n016.cluster.edu
% 0.09/0.26 % Model : x86_64 x86_64
% 0.09/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.26 % Memory : 8046.5625MB
% 0.09/0.26 % OS : Linux 6.8.0-71-generic
% 0.09/0.26 % CPULimit : 300
% 0.09/0.26 % WCLimit : 300
% 0.09/0.26 % DateTime : Tue Sep 29 13:54:35 UTC 2026
% 0.09/0.26 % CPUTime :
% 0.09/0.26 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.29 Running higher-order theorem proving
% 0.19/0.30 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
% 0.19/0.34 % (386497)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.34 % (386503)lrs+10_16_si=on:nwc=1.5:random_seed=278324318:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.19/0.34 % (386503) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-386497-386503"...
% 0.19/0.34 % (386503)...printing done.
% 0.19/0.34 % (386503)Refutation found. Thanks to Tanya!
% 0.19/0.34 % SZS status Theorem for theBenchmark
% 0.19/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.34 % (386503)------------------------------
% 0.19/0.34 % (386503)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.34 % (386503)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.34 % (386503)CaDiCaL version: 2.1.3
% 0.19/0.34 % (386503)Termination reason: Refutation
% 0.19/0.34 % (386503)Time elapsed: 0.002 s
% 0.19/0.34 % (386503)Peak memory usage: 12 MB
% 0.19/0.34 % (386503)Instructions burned: 5 (million)
% 0.19/0.34 % (386497)Success in time 0.028 s
% 0.19/0.34 % Vampire exiting
%------------------------------------------------------------------------------