%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL591^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 08:14:24 AM UTC 2026
% Result : Theorem 0.21s 0.30s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 126 ( 29 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 138 ( 9 ~; 0 |; 3 &; 100 @)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 39 ( 39 >; 0 *; 0 +; 0 <<)
% Number of symbols : 38 ( 34 usr; 5 con; 0-4 aty)
% ( 12 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 51 ( 34 ^; 13 !; 4 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_6,type,
individuals: $tType ).
thf(func_def_1,type,
prop_a: $i > $o ).
thf(func_def_2,type,
prop_b: $i > $o ).
thf(func_def_3,type,
prop_c: $i > $o ).
thf(func_def_4,type,
mfalse: $i > $o ).
thf(func_def_5,type,
mtrue: $i > $o ).
thf(func_def_6,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mimpl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_11,type,
miff: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_12,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_13,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_14,type,
mall: ( individuals > $i > $o ) > $i > $o ).
thf(func_def_15,type,
mexists: ( individuals > $i > $o ) > $i > $o ).
thf(func_def_16,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_17,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_18,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_19,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_20,type,
vNOT: $o > $o ).
thf(func_def_21,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_23,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_24,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_27,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_28,type,
vAND: $o > $o > $o ).
thf(func_def_29,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_30,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_31,type,
vIMP: $o > $o > $o ).
thf(func_def_32,type,
vOR: $o > $o > $o ).
thf(func_def_33,type,
sK0: $i > $o ).
thf(func_def_34,type,
sK1: $i > $i > $o ).
thf(f8,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) )
= mbox ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mbox) ).
thf(f12,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mvalid) ).
thf(f16,conjecture,
! [X0: $i > $i > $o,X1: $i > $o] :
( ( mvalid @ X1 )
=> ( mvalid @ ( mbox @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(f17,negated_conjecture,
~ ! [X0: $i > $i > $o,X1: $i > $o] :
( ( mvalid @ X1 )
=> ( mvalid @ ( mbox @ X0 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
thf(f33,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) )
= mbox ),
inference(rectify,[],[f8]) ).
thf(f34,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f40,plain,
~ ! [X0: $i > $i > $o,X1: $i > $o] :
( ( mvalid @ X1 )
=> ( mvalid @ ( mbox @ X0 @ X1 ) ) ),
inference(rectify,[],[f17]) ).
thf(f41,plain,
~ ! [X1: $i > $o,X0: $i > $i > $o] :
( ( ( mvalid @ X1 )
= $true )
=> ( ( mvalid @ ( mbox @ X0 @ X1 ) )
= $true ) ),
inference(fool_elimination,[],[f40]) ).
thf(f44,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f12]) ).
thf(f45,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f44]) ).
thf(f46,plain,
? [X1: $i > $o,X0: $i > $i > $o] :
( ( ( mvalid @ X1 )
= $true )
& ( ( mvalid @ ( mbox @ X0 @ X1 ) )
!= $true ) ),
inference(ennf_transformation,[],[f41]) ).
thf(f47,plain,
? [X0: $i > $o,X1: $i > $i > $o] :
( ( $true
= ( mvalid @ X0 ) )
& ( $true
!= ( mvalid @ ( mbox @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f46]) ).
thf(f48,plain,
( ( ( mvalid @ sK0 )
= $true )
& ( $true
!= ( mvalid @ ( mbox @ sK1 @ sK0 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f47]) ).
thf(f51,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f55,plain,
( $true
!= ( mvalid @ ( mbox @ sK1 @ sK0 ) ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f56,plain,
( ( mvalid @ sK0 )
= $true ),
inference(cnf_transformation,[],[f48]) ).
thf(f59,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f70,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ sK0 ) ),
inference(definition_unfolding,[],[f56,f51]) ).
thf(f71,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ sK1
@ sK0 ) )
!= $true ),
inference(definition_unfolding,[],[f55,f51,f59]) ).
thf(f72,plain,
( ( !! @ $i @ sK0 )
= $true ),
inference(beta-eta_normalization,[],[f70]) ).
thf(f73,plain,
! [X1: $i] :
( ( sK0 @ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f72]) ).
thf(f74,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y0 @ Y1 )
=> ( sK0 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f71]) ).
thf(f75,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y0 @ Y1 )
=> ( sK0 @ Y1 ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f74]) ).
thf(f76,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ sK2 @ Y0 )
=> ( sK0 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f75]) ).
thf(f77,plain,
( $false
= ( ^ [Y0: $i] :
( ( sK1 @ sK2 @ Y0 )
=> ( sK0 @ Y0 ) )
@ sK3 ) ),
inference(sigma_proxy_clausification,[],[f76]) ).
thf(f78,plain,
( $false
= ( ( sK1 @ sK2 @ sK3 )
=> ( sK0 @ sK3 ) ) ),
inference(beta-eta_normalization,[],[f77]) ).
thf(f79,plain,
( $false
= ( sK0 @ sK3 ) ),
inference(imp_proxy_clausification,[],[f78]) ).
thf(f81,plain,
$false = $true,
inference(forward_demodulation,[],[f79,f73]) ).
thf(f82,plain,
$false,
inference(trivial_inequality_removal,[],[f81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL591^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n026.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 09:07:42 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.24 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
% 0.21/0.30 % (323125)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.30 % (323130)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3863080877:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.30 % (323130) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-323125-323130"...
% 0.21/0.30 % (323130)...printing done.
% 0.21/0.30 % (323130)Refutation found. Thanks to Tanya!
% 0.21/0.30 % SZS status Theorem for theBenchmark
% 0.21/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.30 % (323130)------------------------------
% 0.21/0.30 % (323130)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (323130)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (323130)CaDiCaL version: 2.1.3
% 0.21/0.30 % (323130)Termination reason: Refutation
% 0.21/0.30 % (323130)Time elapsed: 0.002 s
% 0.21/0.30 % (323130)Peak memory usage: 12 MB
% 0.21/0.30 % (323130)Instructions burned: 4 (million)
% 0.21/0.30 % (323125)Success in time 0.047 s
% 0.21/0.30 % Vampire exiting
%------------------------------------------------------------------------------