%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL608^1 : 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 : 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 08:14:26 AM UTC 2026
% Result : Theorem 0.21s 0.27s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 42 ( 32 unt; 0 typ; 0 def)
% Number of atoms : 176 ( 49 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 169 ( 19 ~; 12 |; 10 &; 116 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 47 ( 47 >; 0 *; 0 +; 0 <<)
% Number of symbols : 37 ( 33 usr; 4 con; 0-4 aty)
% ( 8 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 75 ( 54 ^; 17 !; 4 ?; 75 :)
% 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,
vAND: $o > $o > $o ).
thf(func_def_25,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_26,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_29,type,
vOR: $o > $o > $o ).
thf(func_def_30,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_31,type,
vIMP: $o > $o > $o ).
thf(func_def_32,type,
db3:
!>[X0: $tType] : X0 ).
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/sandbox/benchmark/Axioms/LCL008^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mor) ).
thf(f6,axiom,
( mimpl
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mimpl) ).
thf(f12,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mvalid) ).
thf(f16,conjecture,
! [X1: $i > $o,X0: $i > $o] :
( ( ( mvalid @ ( mimpl @ X0 @ X1 ) )
& ( mvalid @ X0 ) )
=> ( mvalid @ X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(f17,negated_conjecture,
~ ! [X1: $i > $o,X0: $i > $o] :
( ( ( mvalid @ ( mimpl @ X0 @ X1 ) )
& ( mvalid @ X0 ) )
=> ( mvalid @ X1 ) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
thf(f18,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f19,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f22,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f25,plain,
~ ! [X0: $i > $o,X1: $i > $o] :
( ( ( mvalid @ ( mimpl @ X1 @ X0 ) )
& ( mvalid @ X1 ) )
=> ( mvalid @ X0 ) ),
inference(rectify,[],[f17]) ).
thf(f26,plain,
~ ! [X0: $i > $o,X1: $i > $o] :
( ( ( $true
= ( mvalid @ ( mimpl @ X1 @ X0 ) ) )
& ( ( mvalid @ X1 )
= $true ) )
=> ( ( mvalid @ X0 )
= $true ) ),
inference(fool_elimination,[],[f25]) ).
thf(f29,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f30,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f29]) ).
thf(f36,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f12]) ).
thf(f37,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f36]) ).
thf(f46,plain,
? [X0: $i > $o,X1: $i > $o] :
( ( ( mvalid @ X0 )
!= $true )
& ( $true
= ( mvalid @ ( mimpl @ X1 @ X0 ) ) )
& ( ( mvalid @ X1 )
= $true ) ),
inference(ennf_transformation,[],[f26]) ).
thf(f47,plain,
? [X0: $i > $o,X1: $i > $o] :
( ( ( mvalid @ X1 )
= $true )
& ( ( mvalid @ X0 )
!= $true )
& ( $true
= ( mvalid @ ( mimpl @ X1 @ X0 ) ) ) ),
inference(flattening,[],[f46]) ).
thf(f48,plain,
( ( $true
= ( mvalid @ sK1 ) )
& ( $true
!= ( mvalid @ sK0 ) )
& ( $true
= ( mvalid @ ( mimpl @ sK1 @ sK0 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f47]) ).
thf(f50,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f56,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f58,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f63,plain,
( $true
= ( mvalid @ ( mimpl @ sK1 @ sK0 ) ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f64,plain,
( $true
!= ( mvalid @ sK0 ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f65,plain,
( $true
= ( mvalid @ sK1 ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f66,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f69,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,[],[f50,f66,f58]) ).
thf(f71,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ sK1 )
= $true ),
inference(definition_unfolding,[],[f65,f56]) ).
thf(f72,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ sK0 )
!= $true ),
inference(definition_unfolding,[],[f64,f56]) ).
thf(f73,plain,
( $true
= ( ^ [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 ) ) ),
inference(definition_unfolding,[],[f63,f56,f69]) ).
thf(f74,plain,
( $true
= ( !! @ $i @ sK1 ) ),
inference(beta-eta_normalization,[],[f71]) ).
thf(f75,plain,
! [X1: $i] :
( $true
= ( sK1 @ X1 ) ),
inference(pi_proxy_clausification,[],[f74]) ).
thf(f76,plain,
( ( !! @ $i @ sK0 )
!= $true ),
inference(beta-eta_normalization,[],[f72]) ).
thf(f77,plain,
( $false
= ( sK0 @ sK2 ) ),
inference(sigma_proxy_clausification,[],[f76]) ).
thf(f78,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK1 @ Y0 )
| ( sK0 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f73]) ).
thf(f79,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( sK1 @ Y0 )
| ( sK0 @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f78]) ).
thf(f80,plain,
! [X1: $i] :
( $true
= ( ~ ( sK1 @ X1 )
| ( sK0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f79]) ).
thf(f81,plain,
! [X1: $i] :
( ( $true
= ( ~ ( sK1 @ X1 ) ) )
| ( $true
= ( sK0 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f80]) ).
thf(f82,plain,
! [X1: $i] :
( ( $false
= ( sK1 @ X1 ) )
| ( $true
= ( sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f81]) ).
thf(f83,plain,
! [X1: $i] :
( ( $true = $false )
| ( $true
= ( sK0 @ X1 ) ) ),
inference(forward_demodulation,[],[f82,f75]) ).
thf(f84,plain,
! [X1: $i] :
( $true
= ( sK0 @ X1 ) ),
inference(trivial_inequality_removal,[],[f83]) ).
thf(f86,plain,
$true = $false,
inference(constrained_superposition,[],[f77,f84]) ).
thf(f87,plain,
$false,
inference(trivial_inequality_removal,[],[f86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL608^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n007.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 09:16:56 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.23 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
% 0.21/0.27 % (3109347)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.27 % (3109352)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2759828017:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.27 % (3109352) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3109347-3109352"...
% 0.21/0.27 % (3109352)...printing done.
% 0.21/0.27 % (3109352)Refutation found. Thanks to Tanya!
% 0.21/0.27 % SZS status Theorem for theBenchmark
% 0.21/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.27 % (3109352)------------------------------
% 0.21/0.27 % (3109352)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (3109352)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (3109352)CaDiCaL version: 2.1.3
% 0.21/0.27 % (3109352)Termination reason: Refutation
% 0.21/0.27 % (3109352)Time elapsed: 0.002 s
% 0.21/0.27 % (3109352)Peak memory usage: 12 MB
% 0.21/0.27 % (3109352)Instructions burned: 5 (million)
% 0.21/0.27 % (3109347)Success in time 0.026 s
% 0.21/0.27 % Vampire exiting
%------------------------------------------------------------------------------