%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL612^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 08:14:27 AM UTC 2026
% Result : Theorem 0.30s 0.38s
% Output : Refutation 0.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of formulae : 43 ( 32 unt; 0 typ; 0 def)
% Number of atoms : 186 ( 52 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 177 ( 20 ~; 12 |; 11 &; 121 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 53 ( 53 >; 0 *; 0 +; 0 <<)
% Number of symbols : 37 ( 33 usr; 4 con; 0-4 aty)
% ( 8 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 79 ( 54 ^; 21 !; 4 ?; 79 :)
% 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,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $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_25,type,
vNOT: $o > $o ).
thf(func_def_28,type,
vAND: $o > $o > $o ).
thf(func_def_29,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_30,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_31,type,
vOR: $o > $o > $o ).
thf(func_def_32,type,
vIMP: $o > $o > $o ).
thf(func_def_33,type,
sK0: $i > $o ).
thf(func_def_34,type,
sK1: $i > $o ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mnot) ).
thf(f4,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mor) ).
thf(f6,axiom,
( mimpl
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mimpl) ).
thf(f12,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mvalid) ).
thf(f16,conjecture,
! [X0: $i > $i > $o,X2: $i > $o,X1: $i > $o] :
( ( ( mvalid @ ( mimpl @ X1 @ X2 ) )
& ( mvalid @ X1 ) )
=> ( mvalid @ X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modus_ponens) ).
thf(f17,negated_conjecture,
~ ! [X0: $i > $i > $o,X2: $i > $o,X1: $i > $o] :
( ( ( mvalid @ ( mimpl @ X1 @ X2 ) )
& ( mvalid @ X1 ) )
=> ( mvalid @ X2 ) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
thf(f23,plain,
~ ! [X1: $i > $o,X2: $i > $o] :
( ( ( mvalid @ ( mimpl @ X2 @ X1 ) )
& ( mvalid @ X2 ) )
=> ( mvalid @ X1 ) ),
inference(rectify,[],[f17]) ).
thf(f24,plain,
~ ! [X1: $i > $o,X2: $i > $o] :
( ( ( ( mvalid @ ( mimpl @ X2 @ X1 ) )
= $true )
& ( ( mvalid @ X2 )
= $true ) )
=> ( ( mvalid @ X1 )
= $true ) ),
inference(fool_elimination,[],[f23]) ).
thf(f25,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f28,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f29,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f28]) ).
thf(f32,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f12]) ).
thf(f33,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f32]) ).
thf(f34,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f35,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f34]) ).
thf(f46,plain,
~ ! [X0: $i > $o,X1: $i > $o] :
( ( ( ( mvalid @ ( mimpl @ X1 @ X0 ) )
= $true )
& ( ( mvalid @ X1 )
= $true ) )
=> ( ( mvalid @ X0 )
= $true ) ),
inference(rectify,[],[f24]) ).
thf(f47,plain,
? [X0: $i > $o,X1: $i > $o] :
( ( ( mvalid @ X0 )
!= $true )
& ( ( mvalid @ ( mimpl @ X1 @ X0 ) )
= $true )
& ( ( mvalid @ X1 )
= $true ) ),
inference(ennf_transformation,[],[f46]) ).
thf(f48,plain,
? [X0: $i > $o,X1: $i > $o] :
( ( ( mvalid @ X0 )
!= $true )
& ( ( mvalid @ ( mimpl @ X1 @ X0 ) )
= $true )
& ( ( mvalid @ X1 )
= $true ) ),
inference(flattening,[],[f47]) ).
thf(f49,plain,
( ( ( mvalid @ sK0 )
!= $true )
& ( ( mvalid @ ( mimpl @ sK1 @ sK0 ) )
= $true )
& ( ( mvalid @ sK1 )
= $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f48]) ).
thf(f55,plain,
( ( mvalid @ sK1 )
= $true ),
inference(cnf_transformation,[],[f49]) ).
thf(f56,plain,
( ( mvalid @ ( mimpl @ sK1 @ sK0 ) )
= $true ),
inference(cnf_transformation,[],[f49]) ).
thf(f57,plain,
( ( mvalid @ sK0 )
!= $true ),
inference(cnf_transformation,[],[f49]) ).
thf(f60,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f62,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f63,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f66,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f70,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f63,f66,f60]) ).
thf(f72,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ sK0 )
!= $true ),
inference(definition_unfolding,[],[f57,f62]) ).
thf(f73,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ sK1
@ sK0 ) )
= $true ),
inference(definition_unfolding,[],[f56,f62,f70]) ).
thf(f74,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ sK1 )
= $true ),
inference(definition_unfolding,[],[f55,f62]) ).
thf(f75,plain,
( ( !! @ $i @ sK0 )
!= $true ),
inference(beta-eta_normalization,[],[f72]) ).
thf(f76,plain,
( ( sK0 @ sK2 )
= $false ),
inference(sigma_proxy_clausification,[],[f75]) ).
thf(f77,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK1 @ Y0 )
| ( sK0 @ Y0 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f73]) ).
thf(f78,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ~ ( sK1 @ Y0 )
| ( sK0 @ Y0 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f77]) ).
thf(f79,plain,
! [X1: $i] :
( ( ~ ( sK1 @ X1 )
| ( sK0 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f78]) ).
thf(f80,plain,
! [X1: $i] :
( ( ( ~ ( sK1 @ X1 ) )
= $true )
| ( ( sK0 @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f79]) ).
thf(f81,plain,
! [X1: $i] :
( ( ( sK0 @ X1 )
= $true )
| ( ( sK1 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f80]) ).
thf(f82,plain,
( ( !! @ $i @ sK1 )
= $true ),
inference(beta-eta_normalization,[],[f74]) ).
thf(f83,plain,
! [X1: $i] :
( ( sK1 @ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f82]) ).
thf(f84,plain,
! [X1: $i] :
( ( $false = $true )
| ( ( sK0 @ X1 )
= $true ) ),
inference(backward_demodulation,[],[f81,f83]) ).
thf(f85,plain,
! [X1: $i] :
( ( sK0 @ X1 )
= $true ),
inference(trivial_inequality_removal,[],[f84]) ).
thf(f86,plain,
$false = $true,
inference(backward_demodulation,[],[f76,f85]) ).
thf(f87,plain,
$false,
inference(trivial_inequality_removal,[],[f86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL612^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/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 09:36:04 UTC 2026
% 0.09/0.26 % CPUTime :
% 0.09/0.26 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.32 Running higher-order theorem proving
% 0.24/0.33 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.30/0.38 % (110536)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.30/0.38 % (110546)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4216268040:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.30/0.38 % (110546) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-110536-110546"...
% 0.30/0.38 % (110546)...printing done.
% 0.30/0.38 % (110546)Refutation found. Thanks to Tanya!
% 0.30/0.38 % SZS status Theorem for theBenchmark
% 0.30/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.30/0.38 % (110546)------------------------------
% 0.30/0.38 % (110546)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.38 % (110546)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.38 % (110546)CaDiCaL version: 2.1.3
% 0.30/0.38 % (110546)Termination reason: Refutation
% 0.30/0.38 % (110546)Time elapsed: 0.003 s
% 0.30/0.38 % (110546)Peak memory usage: 12 MB
% 0.30/0.38 % (110546)Instructions burned: 5 (million)
% 0.30/0.38 % (110536)Success in time 0.029 s
% 0.30/0.38 % Vampire exiting
%------------------------------------------------------------------------------