%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL586^1 : 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 : n009.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 0.31s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 7
% Syntax : Number of formulae : 51 ( 46 unt; 0 typ; 0 def)
% Number of atoms : 265 ( 49 equ; 0 cnn)
% Maximal formula atoms : 11 ( 5 avg)
% Number of connectives : 342 ( 32 ~; 19 |; 13 &; 247 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 69 ( 69 >; 0 *; 0 +; 0 <<)
% Number of symbols : 40 ( 35 usr; 6 con; 0-4 aty)
% ( 11 !!; 9 ??; 0 @@+; 0 @@-)
% Number of variables : 116 ( 107 ^; 7 !; 2 ?; 116 :)
% 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,
a: $i > $o ).
thf(func_def_21,type,
b: $i > $o ).
thf(func_def_22,type,
r: $i > $i > $o ).
thf(func_def_23,type,
vNOT: $o > $o ).
thf(func_def_24,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_25,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_26,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_27,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_28,type,
vIMP: $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,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_32,type,
vAND: $o > $o > $o ).
thf(func_def_33,type,
vOR: $o > $o > $o ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mnot) ).
thf(f4,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ 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(f8,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) )
= mbox ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mbox) ).
thf(f9,axiom,
( mdia
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
? [X3: $i] :
( ( X0 @ X2 @ X3 )
& ( X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mdia) ).
thf(f12,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mvalid) ).
thf(f16,conjecture,
mvalid @ ( mimpl @ ( mnot @ ( mdia @ r @ a ) ) @ ( mbox @ r @ ( mimpl @ a @ b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(f17,negated_conjecture,
~ ( mvalid @ ( mimpl @ ( mnot @ ( mdia @ r @ a ) ) @ ( mbox @ r @ ( mimpl @ a @ b ) ) ) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
thf(f18,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f19,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f20,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) )
= mbox ),
inference(rectify,[],[f8]) ).
thf(f21,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f20]) ).
thf(f22,plain,
( mdia
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
? [X3: $i] :
( ( X0 @ X2 @ X3 )
& ( X1 @ X3 ) ) ) ),
inference(rectify,[],[f9]) ).
thf(f23,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f22]) ).
thf(f26,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f27,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f26]) ).
thf(f29,plain,
~ ( mvalid @ ( mimpl @ ( mnot @ ( mdia @ r @ a ) ) @ ( mbox @ r @ ( mimpl @ a @ b ) ) ) ),
inference(rectify,[],[f17]) ).
thf(f30,plain,
( ( mvalid @ ( mimpl @ ( mnot @ ( mdia @ r @ a ) ) @ ( mbox @ r @ ( mimpl @ a @ b ) ) ) )
!= $true ),
inference(fool_elimination,[],[f29]) ).
thf(f31,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f12]) ).
thf(f32,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f31]) ).
thf(f34,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f46,plain,
( ( mvalid @ ( mimpl @ ( mnot @ ( mdia @ r @ a ) ) @ ( mbox @ r @ ( mimpl @ a @ b ) ) ) )
!= $true ),
inference(flattening,[],[f30]) ).
thf(f47,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f48,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f49,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f32]) ).
thf(f51,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f55,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f59,plain,
( ( mvalid @ ( mimpl @ ( mnot @ ( mdia @ r @ a ) ) @ ( mbox @ r @ ( mimpl @ a @ b ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f46]) ).
thf(f61,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f65,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f47,f48,f55]) ).
thf(f67,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y0 @ Y2 @ Y3 ) ) )
@ r
@ a ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ r
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ a
@ b ) ) ) ) ),
inference(definition_unfolding,[],[f59,f49,f65,f55,f51,f61,f65]) ).
thf(f68,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( ( b @ Y1 )
| ~ ( a @ Y1 ) ) ) )
| ~ ~ ( ?? @ $i
@ ^ [Y1: $i] :
( ( a @ Y1 )
& ( r @ Y0 @ Y1 ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f67]) ).
thf(f69,plain,
( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( ( b @ Y1 )
| ~ ( a @ Y1 ) ) ) )
| ~ ~ ( ?? @ $i
@ ^ [Y1: $i] :
( ( a @ Y1 )
& ( r @ Y0 @ Y1 ) ) ) )
@ sK0 )
= $false ),
inference(sigma_proxy_clausification,[],[f68]) ).
thf(f70,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( b @ Y0 )
| ~ ( a @ Y0 ) ) ) )
| ~ ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( a @ Y0 )
& ( r @ sK0 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f69]) ).
thf(f71,plain,
( $false
= ( ~ ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( a @ Y0 )
& ( r @ sK0 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f70]) ).
thf(f72,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( b @ Y0 )
| ~ ( a @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f70]) ).
thf(f73,plain,
( ( ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( b @ Y0 )
| ~ ( a @ Y0 ) ) )
@ sK1 )
= $false ),
inference(sigma_proxy_clausification,[],[f72]) ).
thf(f74,plain,
( $false
= ( ( r @ sK0 @ sK1 )
=> ( ( b @ sK1 )
| ~ ( a @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f73]) ).
thf(f75,plain,
( ( ( b @ sK1 )
| ~ ( a @ sK1 ) )
= $false ),
inference(imp_proxy_clausification,[],[f74]) ).
thf(f76,plain,
( $true
= ( r @ sK0 @ sK1 ) ),
inference(imp_proxy_clausification,[],[f74]) ).
thf(f77,plain,
( $false
= ( ~ ( a @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f75]) ).
thf(f79,plain,
( $true
= ( a @ sK1 ) ),
inference(not_proxy_clausification,[],[f77]) ).
thf(f80,plain,
( $true
= ( ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( a @ Y0 )
& ( r @ sK0 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f71]) ).
thf(f81,plain,
( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( a @ Y0 )
& ( r @ sK0 @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f80]) ).
thf(f82,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( a @ Y0 )
& ( r @ sK0 @ Y0 ) )
@ X1 )
= $false ),
inference(pi_proxy_clausification,[],[f81]) ).
thf(f83,plain,
! [X1: $i] :
( ( ( a @ X1 )
& ( r @ sK0 @ X1 ) )
= $false ),
inference(beta-eta_normalization,[],[f82]) ).
thf(f84,plain,
! [X1: $i] :
( ( $false
= ( r @ sK0 @ X1 ) )
| ( $false
= ( a @ X1 ) ) ),
inference(and_proxy_clausification,[],[f83]) ).
thf(f86,plain,
( ( $true = $false )
| ( $false
= ( a @ sK1 ) ) ),
inference(constrained_superposition,[],[f84,f76]) ).
thf(f87,plain,
( $false
= ( a @ sK1 ) ),
inference(trivial_inequality_removal,[],[f86]) ).
thf(f90,plain,
$true = $false,
inference(constrained_superposition,[],[f79,f87]) ).
thf(f91,plain,
$false,
inference(trivial_inequality_removal,[],[f90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL586^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n009.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 09:00:30 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.25 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
% 0.21/0.31 % (3731539)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.31 % (3731548)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=264391724:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.31 % (3731545)lrs+10_16_si=on:nwc=1.5:random_seed=574500229:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.31 % (3731544)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3071394802:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.31 % (3731546)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2368526977:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.31 % (3731546)Refutation not found, incomplete strategy
% 0.21/0.31 % (3731546)------------------------------
% 0.21/0.31 % (3731546)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (3731546)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (3731546)CaDiCaL version: 2.1.3
% 0.21/0.31 % (3731546)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.31 % (3731546)Time elapsed: 0.002 s
% 0.21/0.31 % (3731546)Peak memory usage: 12 MB
% 0.21/0.31 % (3731546)Instructions burned: 3 (million)
% 0.21/0.31 % (3731545) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3731539-3731545"...
% 0.21/0.31 % (3731544) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3731539-3731544"...
% 0.21/0.31 % (3731546)------------------------------
% 0.21/0.31 % (3731546)------------------------------
% 0.21/0.31 % (3731545)...printing done.
% 0.21/0.31 % (3731544)...printing done.
% 0.21/0.31 % (3731545)Refutation found. Thanks to Tanya!
% 0.21/0.31 % SZS status Theorem for theBenchmark
% 0.21/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.31 % (3731545)------------------------------
% 0.21/0.31 % (3731545)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (3731545)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (3731545)CaDiCaL version: 2.1.3
% 0.21/0.31 % (3731545)Termination reason: Refutation
% 0.21/0.31 % (3731545)Time elapsed: 0.005 s
% 0.21/0.31 % (3731545)Peak memory usage: 12 MB
% 0.21/0.31 % (3731545)Instructions burned: 7 (million)
% 0.21/0.31 % (3731539)Success in time 0.053 s
% 0.21/0.31 % Vampire exiting
%------------------------------------------------------------------------------