%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : AGT033^2 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 07:44:38 AM UTC 2026
% Result : Theorem 0.22s 0.31s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 11
% Syntax : Number of formulae : 92 ( 74 unt; 0 typ; 0 def)
% Number of atoms : 453 ( 99 equ; 0 cnn)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 817 ( 119 ~; 53 |; 0 &; 591 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 118 ( 118 >; 0 *; 0 +; 0 <<)
% Number of symbols : 66 ( 62 usr; 9 con; 0-4 aty)
% ( 54 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 297 ( 223 ^; 74 !; 0 ?; 297 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
meq_ind: mu > mu > $i > $o ).
thf(func_def_1,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mtrue: $i > $o ).
thf(func_def_15,type,
mfalse: $i > $o ).
thf(func_def_16,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_29,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_30,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_31,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_32,type,
a1: $i > $i > $o ).
thf(func_def_33,type,
a2: $i > $i > $o ).
thf(func_def_34,type,
a3: $i > $i > $o ).
thf(func_def_35,type,
jan: mu ).
thf(func_def_36,type,
piotr: mu ).
thf(func_def_37,type,
cola: mu ).
thf(func_def_38,type,
pepsi: mu ).
thf(func_def_39,type,
beer: mu ).
thf(func_def_40,type,
likes: mu > mu > $i > $o ).
thf(func_def_41,type,
very_much_likes: mu > mu > $i > $o ).
thf(func_def_42,type,
possibly_likes: mu > mu > $i > $o ).
thf(func_def_43,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_44,type,
vIMP: $o > $o > $o ).
thf(func_def_45,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_46,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_48,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_51,type,
vAND: $o > $o > $o ).
thf(func_def_52,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_53,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_54,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_55,type,
vNOT: $o > $o ).
thf(func_def_56,type,
vOR: $o > $o > $o ).
thf(func_def_57,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_58,type,
sK0: $i > $i ).
thf(func_def_60,type,
sK2: mu > $i > mu > $i ).
thf(func_def_61,type,
sK3: $i > $i ).
thf(func_def_62,type,
sK4: mu > $i > mu > $i ).
thf(func_def_63,type,
sK5: mu > $i > mu > $i ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f10,axiom,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mforall_ind) ).
thf(f12,axiom,
( mexists_ind
= ( ^ [X0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X1: mu] : ( mnot @ ( X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mexists_ind) ).
thf(f16,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ~ ( X0 @ X2 @ X3 )
| ( X1 @ X3 ) ) )
= mbox ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mbox) ).
thf(f17,axiom,
( mdia
= ( ^ [X0: $i > $i > $o,X1: $i > $o] : ( mnot @ ( mbox @ X0 @ ( mnot @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mdia) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f43,axiom,
mvalid @ ( mdia @ a1 @ ( likes @ piotr @ beer ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_a3_3) ).
thf(f47,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] : ( mimplies @ ( mdia @ a1 @ ( likes @ X0 @ X1 ) ) @ ( possibly_likes @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_user_communication_3) ).
thf(f50,conjecture,
( mvalid
@ ( mexists_ind
@ ^ [X0: mu] :
( mexists_ind
@ ^ [X1: mu] : ( possibly_likes @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(f51,negated_conjecture,
~ ( mvalid
@ ( mexists_ind
@ ^ [X0: mu] :
( mexists_ind
@ ^ [X1: mu] : ( possibly_likes @ X0 @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f50]) ).
thf(f76,plain,
mvalid @ ( mdia @ a1 @ ( likes @ piotr @ beer ) ),
inference(rectify,[],[f43]) ).
thf(f77,plain,
( ( mvalid @ ( mdia @ a1 @ ( likes @ piotr @ beer ) ) )
= $true ),
inference(fool_elimination,[],[f76]) ).
thf(f81,plain,
~ ( mvalid
@ ( mexists_ind
@ ^ [X0: mu] :
( mexists_ind
@ ^ [X1: mu] : ( possibly_likes @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f51]) ).
thf(f82,plain,
( $true
!= ( mvalid
@ ( mexists_ind
@ ^ [Y0: mu] :
( mexists_ind
@ ^ [Y1: mu] : ( possibly_likes @ Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f81]) ).
thf(f84,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o] : ( mnot @ ( mbox @ Y0 @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f17]) ).
thf(f107,plain,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] : ( mimplies @ ( mdia @ a1 @ ( likes @ X0 @ X1 ) ) @ ( possibly_likes @ X0 @ X1 ) ) ) ) ),
inference(rectify,[],[f47]) ).
thf(f108,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mimplies @ ( mdia @ a1 @ ( likes @ Y0 @ Y1 ) ) @ ( possibly_likes @ Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f107]) ).
thf(f109,plain,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f10]) ).
thf(f110,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f109]) ).
thf(f111,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f112,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f113,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f112]) ).
thf(f114,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f115,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f114]) ).
thf(f125,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f126,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f125]) ).
thf(f127,plain,
( mexists_ind
= ( ^ [X0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X1: mu] : ( mnot @ ( X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f12]) ).
thf(f128,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f127]) ).
thf(f134,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ~ ( X0 @ X2 @ X3 )
| ( X1 @ X3 ) ) )
= mbox ),
inference(rectify,[],[f16]) ).
thf(f135,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f134]) ).
thf(f141,plain,
( $true
!= ( mvalid
@ ( mexists_ind
@ ^ [Y0: mu] :
( mexists_ind
@ ^ [Y1: mu] : ( possibly_likes @ Y0 @ Y1 ) ) ) ) ),
inference(flattening,[],[f82]) ).
thf(f143,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f126]) ).
thf(f144,plain,
( ( mvalid @ ( mdia @ a1 @ ( likes @ piotr @ beer ) ) )
= $true ),
inference(cnf_transformation,[],[f77]) ).
thf(f147,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f110]) ).
thf(f148,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f111]) ).
thf(f152,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o] : ( mnot @ ( mbox @ Y0 @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f84]) ).
thf(f158,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mimplies @ ( mdia @ a1 @ ( likes @ Y0 @ Y1 ) ) @ ( possibly_likes @ Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f108]) ).
thf(f160,plain,
( $true
!= ( mvalid
@ ( mexists_ind
@ ^ [Y0: mu] :
( mexists_ind
@ ^ [Y1: mu] : ( possibly_likes @ Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f141]) ).
thf(f166,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f135]) ).
thf(f177,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f115]) ).
thf(f178,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f113]) ).
thf(f191,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f128]) ).
thf(f195,plain,
( mimplies
= ( ^ [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,[],[f148,f177,f178]) ).
thf(f199,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: mu > $i > $o,Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( Y0 @ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[],[f191,f178,f147,f178]) ).
thf(f202,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ Y0
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f152,f178,f166,f178]) ).
thf(f204,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ Y0
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) )
@ a1
@ ( likes @ piotr @ beer ) ) ) ),
inference(definition_unfolding,[],[f144,f143,f202]) ).
thf(f210,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: mu] :
( ^ [Y1: mu > $i > $o,Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $i > $o,Y5: $i > $o,Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 )
| ~ ( Y4 @ Y6 @ Y7 ) ) )
@ Y2
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ a1
@ ( likes @ Y0 @ Y1 ) )
@ ( possibly_likes @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f158,f143,f147,f147,f195,f202]) ).
thf(f212,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: mu > $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: mu > $i > $o,Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( Y0 @ Y1 ) ) ) )
@ ^ [Y0: mu] :
( ^ [Y1: mu > $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: mu > $i > $o,Y3: $i] :
( !! @ mu
@ ^ [Y4: mu] : ( Y2 @ Y4 @ Y3 ) )
@ ^ [Y2: mu] :
( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ ( Y1 @ Y2 ) ) ) )
@ ^ [Y1: mu] : ( possibly_likes @ Y0 @ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f160,f143,f199,f199]) ).
thf(f229,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( likes @ piotr @ beer @ Y1 )
| ~ ( a1 @ Y0 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f204]) ).
thf(f230,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( likes @ piotr @ beer @ Y1 )
| ~ ( a1 @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f229]) ).
thf(f231,plain,
! [X1: $i] :
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( likes @ piotr @ beer @ Y0 )
| ~ ( a1 @ X1 @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f230]) ).
thf(f232,plain,
! [X1: $i] :
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( likes @ piotr @ beer @ Y0 )
| ~ ( a1 @ X1 @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f231]) ).
thf(f233,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ~ ( likes @ piotr @ beer @ Y0 )
| ~ ( a1 @ X1 @ Y0 ) )
@ ( sK0 @ X1 ) )
= $false ),
inference(sigma_proxy_clausification,[],[f232]) ).
thf(f234,plain,
! [X1: $i] :
( ( ~ ( likes @ piotr @ beer @ ( sK0 @ X1 ) )
| ~ ( a1 @ X1 @ ( sK0 @ X1 ) ) )
= $false ),
inference(beta-eta_normalization,[],[f233]) ).
thf(f235,plain,
! [X1: $i] :
( $false
= ( ~ ( a1 @ X1 @ ( sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f234]) ).
thf(f236,plain,
! [X1: $i] :
( ( ~ ( likes @ piotr @ beer @ ( sK0 @ X1 ) ) )
= $false ),
inference(or_proxy_clausification,[],[f234]) ).
thf(f237,plain,
! [X1: $i] :
( ( likes @ piotr @ beer @ ( sK0 @ X1 ) )
= $true ),
inference(not_proxy_clausification,[],[f236]) ).
thf(f238,plain,
! [X1: $i] :
( $true
= ( a1 @ X1 @ ( sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f235]) ).
thf(f261,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( !! @ mu
@ ^ [Y2: mu] :
( ~ ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( likes @ Y1 @ Y2 @ Y3 )
| ~ ( a1 @ Y0 @ Y3 ) ) )
| ( possibly_likes @ Y1 @ Y2 @ Y0 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f210]) ).
thf(f262,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( !! @ mu
@ ^ [Y2: mu] :
( ~ ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( likes @ Y1 @ Y2 @ Y3 )
| ~ ( a1 @ Y0 @ Y3 ) ) )
| ( possibly_likes @ Y1 @ Y2 @ Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f261]) ).
thf(f263,plain,
! [X1: $i] :
( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( !! @ mu
@ ^ [Y1: mu] :
( ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( likes @ Y0 @ Y1 @ Y2 )
| ~ ( a1 @ X1 @ Y2 ) ) )
| ( possibly_likes @ Y0 @ Y1 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f262]) ).
thf(f264,plain,
! [X2: mu,X1: $i] :
( $true
= ( ^ [Y0: mu] :
( !! @ mu
@ ^ [Y1: mu] :
( ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( likes @ Y0 @ Y1 @ Y2 )
| ~ ( a1 @ X1 @ Y2 ) ) )
| ( possibly_likes @ Y0 @ Y1 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f263]) ).
thf(f265,plain,
! [X2: mu,X1: $i] :
( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( likes @ X2 @ Y0 @ Y1 )
| ~ ( a1 @ X1 @ Y1 ) ) )
| ( possibly_likes @ X2 @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f264]) ).
thf(f266,plain,
! [X2: mu,X3: mu,X1: $i] :
( $true
= ( ^ [Y0: mu] :
( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( likes @ X2 @ Y0 @ Y1 )
| ~ ( a1 @ X1 @ Y1 ) ) )
| ( possibly_likes @ X2 @ Y0 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f265]) ).
thf(f267,plain,
! [X2: mu,X3: mu,X1: $i] :
( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( likes @ X2 @ X3 @ Y0 )
| ~ ( a1 @ X1 @ Y0 ) ) )
| ( possibly_likes @ X2 @ X3 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f266]) ).
thf(f268,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( likes @ X2 @ X3 @ Y0 )
| ~ ( a1 @ X1 @ Y0 ) ) ) ) )
| ( ( possibly_likes @ X2 @ X3 @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f267]) ).
thf(f269,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( possibly_likes @ X2 @ X3 @ X1 )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( likes @ X2 @ X3 @ Y0 )
| ~ ( a1 @ X1 @ Y0 ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f268]) ).
thf(f270,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( likes @ X2 @ X3 @ Y0 )
| ~ ( a1 @ X1 @ Y0 ) ) ) )
| ( ( possibly_likes @ X2 @ X3 @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f269]) ).
thf(f271,plain,
! [X2: mu,X3: mu,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( likes @ X2 @ X3 @ Y0 )
| ~ ( a1 @ X1 @ Y0 ) )
@ X4 ) )
| ( ( possibly_likes @ X2 @ X3 @ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f270]) ).
thf(f272,plain,
! [X2: mu,X3: mu,X1: $i,X4: $i] :
( ( $true
= ( ~ ( likes @ X2 @ X3 @ X4 )
| ~ ( a1 @ X1 @ X4 ) ) )
| ( ( possibly_likes @ X2 @ X3 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f271]) ).
thf(f273,plain,
! [X2: mu,X3: mu,X1: $i,X4: $i] :
( ( $true
= ( ~ ( a1 @ X1 @ X4 ) ) )
| ( ( possibly_likes @ X2 @ X3 @ X1 )
= $true )
| ( ( ~ ( likes @ X2 @ X3 @ X4 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f272]) ).
thf(f274,plain,
! [X2: mu,X3: mu,X1: $i,X4: $i] :
( ( ( ~ ( likes @ X2 @ X3 @ X4 ) )
= $true )
| ( ( possibly_likes @ X2 @ X3 @ X1 )
= $true )
| ( $false
= ( a1 @ X1 @ X4 ) ) ),
inference(not_proxy_clausification,[],[f273]) ).
thf(f275,plain,
! [X2: mu,X3: mu,X1: $i,X4: $i] :
( ( ( possibly_likes @ X2 @ X3 @ X1 )
= $true )
| ( ( likes @ X2 @ X3 @ X4 )
= $false )
| ( $false
= ( a1 @ X1 @ X4 ) ) ),
inference(not_proxy_clausification,[],[f274]) ).
thf(f276,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
~ ( !! @ mu
@ ^ [Y1: mu] :
~ ~ ( !! @ mu
@ ^ [Y2: mu] :
~ ( possibly_likes @ Y1 @ Y2 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f212]) ).
thf(f277,plain,
( $false
= ( ^ [Y0: $i] :
~ ( !! @ mu
@ ^ [Y1: mu] :
~ ~ ( !! @ mu
@ ^ [Y2: mu] :
~ ( possibly_likes @ Y1 @ Y2 @ Y0 ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f276]) ).
thf(f278,plain,
( $false
= ( ~ ( !! @ mu
@ ^ [Y0: mu] :
~ ~ ( !! @ mu
@ ^ [Y1: mu] :
~ ( possibly_likes @ Y0 @ Y1 @ sK1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f277]) ).
thf(f279,plain,
( $true
= ( !! @ mu
@ ^ [Y0: mu] :
~ ~ ( !! @ mu
@ ^ [Y1: mu] :
~ ( possibly_likes @ Y0 @ Y1 @ sK1 ) ) ) ),
inference(not_proxy_clausification,[],[f278]) ).
thf(f280,plain,
! [X1: mu] :
( $true
= ( ^ [Y0: mu] :
~ ~ ( !! @ mu
@ ^ [Y1: mu] :
~ ( possibly_likes @ Y0 @ Y1 @ sK1 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f279]) ).
thf(f281,plain,
! [X1: mu] :
( ( ~ ~ ( !! @ mu
@ ^ [Y0: mu] :
~ ( possibly_likes @ X1 @ Y0 @ sK1 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f280]) ).
thf(f282,plain,
! [X1: mu] :
( ( ~ ( !! @ mu
@ ^ [Y0: mu] :
~ ( possibly_likes @ X1 @ Y0 @ sK1 ) ) )
= $false ),
inference(not_proxy_clausification,[],[f281]) ).
thf(f283,plain,
! [X1: mu] :
( $true
= ( !! @ mu
@ ^ [Y0: mu] :
~ ( possibly_likes @ X1 @ Y0 @ sK1 ) ) ),
inference(not_proxy_clausification,[],[f282]) ).
thf(f284,plain,
! [X2: mu,X1: mu] :
( ( ^ [Y0: mu] :
~ ( possibly_likes @ X1 @ Y0 @ sK1 )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f283]) ).
thf(f285,plain,
! [X2: mu,X1: mu] :
( $true
= ( ~ ( possibly_likes @ X1 @ X2 @ sK1 ) ) ),
inference(beta-eta_normalization,[],[f284]) ).
thf(f286,plain,
! [X2: mu,X1: mu] :
( $false
= ( possibly_likes @ X1 @ X2 @ sK1 ) ),
inference(not_proxy_clausification,[],[f285]) ).
thf(f460,plain,
! [X2: $i,X0: mu,X1: mu] :
( ( ( likes @ X0 @ X1 @ X2 )
= $false )
| ( ( a1 @ sK1 @ X2 )
= $false )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f286,f275]) ).
thf(f461,plain,
! [X2: $i,X0: mu,X1: mu] :
( ( ( likes @ X0 @ X1 @ X2 )
= $false )
| ( ( a1 @ sK1 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f460]) ).
thf(f469,plain,
! [X0: $i] :
( ( $true = $false )
| ( ( a1 @ sK1 @ ( sK0 @ X0 ) )
= $false ) ),
inference(constrained_superposition,[],[f461,f237]) ).
thf(f472,plain,
! [X0: $i] :
( ( a1 @ sK1 @ ( sK0 @ X0 ) )
= $false ),
inference(trivial_inequality_removal,[],[f469]) ).
thf(f476,plain,
$true = $false,
inference(constrained_superposition,[],[f238,f472]) ).
thf(f477,plain,
$false,
inference(trivial_inequality_removal,[],[f476]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : AGT033^2 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n006.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 17:29:55 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 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
% 0.22/0.31 % (1055709)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.31 % (1055718)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=113557744:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.31 % (1055720)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.31 % (1055720)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.22/0.31 % (1055714)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2004770885:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.31 % (1055715)lrs+10_16_si=on:nwc=1.5:random_seed=4264135081:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.31 % (1055716)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=993591336:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.31 % (1055718)Instruction limit reached!
% 0.22/0.31 % (1055718)------------------------------
% 0.22/0.31 % (1055718)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (1055718)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (1055718)CaDiCaL version: 2.1.3
% 0.22/0.31 % (1055718)Termination reason: Instruction limit
% 0.22/0.31 % (1055718)Termination phase: Saturation
% 0.22/0.31 % (1055718)Time elapsed: 0.007 s
% 0.22/0.31 % (1055718)Peak memory usage: 11 MB
% 0.22/0.31 % (1055718)Instructions burned: 25 (million)
% 0.22/0.31 % (1055717)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=2081228085:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.22/0.31 % (1055719)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3370077043:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.31 % (1055720)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=4198709528:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.31 % (1055716)Instruction limit reached!
% 0.22/0.31 % (1055716)------------------------------
% 0.22/0.31 % (1055716)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (1055716)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (1055716)CaDiCaL version: 2.1.3
% 0.22/0.31 % (1055716)Termination reason: Instruction limit
% 0.22/0.31 % (1055716)Termination phase: Property scanning
% 0.22/0.31 % (1055716)Time elapsed: 0.002 s
% 0.22/0.31 % (1055716)Peak memory usage: 10 MB
% 0.22/0.31 % (1055716)Instructions burned: 4 (million)
% 0.22/0.31 % (1055715)Instruction limit reached!
% 0.22/0.31 % (1055715)------------------------------
% 0.22/0.31 % (1055715)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (1055715)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (1055715)CaDiCaL version: 2.1.3
% 0.22/0.31 % (1055715)Termination reason: Instruction limit
% 0.22/0.31 % (1055715)Termination phase: Saturation
% 0.22/0.31 % (1055715)Time elapsed: 0.008 s
% 0.22/0.31 % (1055715)Peak memory usage: 11 MB
% 0.22/0.31 % (1055715)Instructions burned: 19 (million)
% 0.22/0.31 % (1055728)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=31338418:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.31 % (1055728)Instruction limit reached!
% 0.22/0.31 % (1055728)------------------------------
% 0.22/0.31 % (1055728)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (1055728)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (1055728)CaDiCaL version: 2.1.3
% 0.22/0.31 % (1055728)Termination reason: Instruction limit
% 0.22/0.31 % (1055728)Termination phase: Property scanning
% 0.22/0.31 % (1055728)Time elapsed: 0.001 s
% 0.22/0.31 % (1055728)Peak memory usage: 10 MB
% 0.22/0.31 % (1055728)Instructions burned: 4 (million)
% 0.22/0.31 % (1055714) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1055709-1055714"...
% 0.22/0.31 % (1055729)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2911612646:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.22/0.31 % (1055714)...printing done.
% 0.22/0.31 % (1055732)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=489389285:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.22/0.31 % (1055714)Refutation found. Thanks to Tanya!
% 0.22/0.31 % SZS status Theorem for theBenchmark
% 0.22/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.31 % (1055714)------------------------------
% 0.22/0.31 % (1055714)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (1055714)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (1055714)CaDiCaL version: 2.1.3
% 0.22/0.31 % (1055714)Termination reason: Refutation
% 0.22/0.31 % (1055714)Time elapsed: 0.021 s
% 0.22/0.31 % (1055714)Peak memory usage: 12 MB
% 0.22/0.31 % (1055714)Instructions burned: 44 (million)
% 0.22/0.31 % (1055709)Success in time 0.067 s
% 0.22/0.31 % Vampire exiting
%------------------------------------------------------------------------------