%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n020.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 07:44:41 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% 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,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_46,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_47,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_48,type,
vNOT: $o > $o ).
thf(func_def_49,type,
vOR: $o > $o > $o ).
thf(func_def_50,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_53,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_54,type,
vIMP: $o > $o > $o ).
thf(func_def_55,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_56,type,
vAND: $o > $o > $o ).
thf(func_def_57,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_59,type,
sK1: mu > $i > mu > $i ).
thf(func_def_60,type,
sK2: mu > mu > $i > $i ).
thf(func_def_61,type,
sK3: mu > mu > $i > $i ).
thf(func_def_62,type,
sK4: $i > $i ).
thf(func_def_63,type,
sK5: $i > $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,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
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,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) ),
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(f42,axiom,
mvalid @ ( mdia @ a3 @ ( likes @ piotr @ pepsi ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_a3_2) ).
thf(f49,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] : ( mimplies @ ( mdia @ a3 @ ( likes @ X0 @ X1 ) ) @ ( possibly_likes @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_user_communication_5) ).
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(f54,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f55,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f54]) ).
thf(f56,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f57,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f56]) ).
thf(f59,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f63,plain,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f10]) ).
thf(f64,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f63]) ).
thf(f67,plain,
( mexists_ind
= ( ^ [X0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X1: mu] : ( mnot @ ( X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f12]) ).
thf(f68,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f67]) ).
thf(f72,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f73,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f72]) ).
thf(f74,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o] : ( mnot @ ( mbox @ Y0 @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f17]) ).
thf(f95,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f96,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f95]) ).
thf(f123,plain,
mvalid @ ( mdia @ a3 @ ( likes @ piotr @ pepsi ) ),
inference(rectify,[],[f42]) ).
thf(f124,plain,
( ( mvalid @ ( mdia @ a3 @ ( likes @ piotr @ pepsi ) ) )
= $true ),
inference(fool_elimination,[],[f123]) ).
thf(f137,plain,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] : ( mimplies @ ( mdia @ a3 @ ( likes @ X0 @ X1 ) ) @ ( possibly_likes @ X0 @ X1 ) ) ) ) ),
inference(rectify,[],[f49]) ).
thf(f138,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mimplies @ ( mdia @ a3 @ ( likes @ Y0 @ Y1 ) ) @ ( possibly_likes @ Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f137]) ).
thf(f139,plain,
~ ( mvalid
@ ( mexists_ind
@ ^ [X0: mu] :
( mexists_ind
@ ^ [X1: mu] : ( possibly_likes @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f51]) ).
thf(f140,plain,
( $true
!= ( mvalid
@ ( mexists_ind
@ ^ [Y0: mu] :
( mexists_ind
@ ^ [Y1: mu] : ( possibly_likes @ Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f139]) ).
thf(f141,plain,
( $true
!= ( mvalid
@ ( mexists_ind
@ ^ [Y0: mu] :
( mexists_ind
@ ^ [Y1: mu] : ( possibly_likes @ Y0 @ Y1 ) ) ) ) ),
inference(flattening,[],[f140]) ).
thf(f144,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f55]) ).
thf(f145,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f57]) ).
thf(f147,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f59]) ).
thf(f151,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f64]) ).
thf(f153,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f68]) ).
thf(f157,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f73]) ).
thf(f158,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o] : ( mnot @ ( mbox @ Y0 @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f74]) ).
thf(f169,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f96]) ).
thf(f183,plain,
( ( mvalid @ ( mdia @ a3 @ ( likes @ piotr @ pepsi ) ) )
= $true ),
inference(cnf_transformation,[],[f124]) ).
thf(f190,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mimplies @ ( mdia @ a3 @ ( likes @ Y0 @ Y1 ) ) @ ( possibly_likes @ Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f138]) ).
thf(f191,plain,
( $true
!= ( mvalid
@ ( mexists_ind
@ ^ [Y0: mu] :
( mexists_ind
@ ^ [Y1: mu] : ( possibly_likes @ Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f141]) ).
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,[],[f147,f145,f144]) ).
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,[],[f153,f144,f151,f144]) ).
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] :
( ~ ( Y2 @ Y4 @ Y5 )
| ( Y3 @ Y5 ) ) )
@ Y0
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f158,f144,f157,f144]) ).
thf(f213,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] :
( ~ ( Y2 @ Y4 @ Y5 )
| ( Y3 @ Y5 ) ) )
@ Y0
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) )
@ a3
@ ( likes @ piotr @ pepsi ) ) ) ),
inference(definition_unfolding,[],[f183,f169,f202]) ).
thf(f220,plain,
( $true
= ( ^ [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] :
( ~ ( Y4 @ Y6 @ Y7 )
| ( Y5 @ Y7 ) ) )
@ Y2
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ a3
@ ( likes @ Y0 @ Y1 ) )
@ ( possibly_likes @ Y0 @ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[],[f190,f169,f151,f151,f195,f202]) ).
thf(f221,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,[],[f191,f169,f199,f199]) ).
thf(f222,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
~ ( !! @ mu
@ ^ [Y1: mu] :
~ ~ ( !! @ mu
@ ^ [Y2: mu] :
~ ( possibly_likes @ Y1 @ Y2 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f221]) ).
thf(f223,plain,
( $false
= ( ^ [Y0: $i] :
~ ( !! @ mu
@ ^ [Y1: mu] :
~ ~ ( !! @ mu
@ ^ [Y2: mu] :
~ ( possibly_likes @ Y1 @ Y2 @ Y0 ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f222]) ).
thf(f224,plain,
( $false
= ( ~ ( !! @ mu
@ ^ [Y0: mu] :
~ ~ ( !! @ mu
@ ^ [Y1: mu] :
~ ( possibly_likes @ Y0 @ Y1 @ sK0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f223]) ).
thf(f225,plain,
( $true
= ( !! @ mu
@ ^ [Y0: mu] :
~ ~ ( !! @ mu
@ ^ [Y1: mu] :
~ ( possibly_likes @ Y0 @ Y1 @ sK0 ) ) ) ),
inference(not_proxy_clausification,[],[f224]) ).
thf(f226,plain,
! [X1: mu] :
( $true
= ( ^ [Y0: mu] :
~ ~ ( !! @ mu
@ ^ [Y1: mu] :
~ ( possibly_likes @ Y0 @ Y1 @ sK0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f225]) ).
thf(f227,plain,
! [X1: mu] :
( $true
= ( ~ ~ ( !! @ mu
@ ^ [Y0: mu] :
~ ( possibly_likes @ X1 @ Y0 @ sK0 ) ) ) ),
inference(beta-eta_normalization,[],[f226]) ).
thf(f228,plain,
! [X1: mu] :
( $false
= ( ~ ( !! @ mu
@ ^ [Y0: mu] :
~ ( possibly_likes @ X1 @ Y0 @ sK0 ) ) ) ),
inference(not_proxy_clausification,[],[f227]) ).
thf(f229,plain,
! [X1: mu] :
( $true
= ( !! @ mu
@ ^ [Y0: mu] :
~ ( possibly_likes @ X1 @ Y0 @ sK0 ) ) ),
inference(not_proxy_clausification,[],[f228]) ).
thf(f230,plain,
! [X2: mu,X1: mu] :
( $true
= ( ^ [Y0: mu] :
~ ( possibly_likes @ X1 @ Y0 @ sK0 )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f229]) ).
thf(f231,plain,
! [X2: mu,X1: mu] :
( $true
= ( ~ ( possibly_likes @ X1 @ X2 @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f230]) ).
thf(f232,plain,
! [X2: mu,X1: mu] :
( $false
= ( possibly_likes @ X1 @ X2 @ sK0 ) ),
inference(not_proxy_clausification,[],[f231]) ).
thf(f233,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( !! @ mu
@ ^ [Y2: mu] :
( ~ ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( a3 @ Y0 @ Y3 )
| ~ ( likes @ Y1 @ Y2 @ Y3 ) ) )
| ( possibly_likes @ Y1 @ Y2 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f220]) ).
thf(f234,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( !! @ mu
@ ^ [Y2: mu] :
( ~ ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( a3 @ Y0 @ Y3 )
| ~ ( likes @ Y1 @ Y2 @ Y3 ) ) )
| ( possibly_likes @ Y1 @ Y2 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f233]) ).
thf(f235,plain,
! [X1: $i] :
( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( !! @ mu
@ ^ [Y1: mu] :
( ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( a3 @ X1 @ Y2 )
| ~ ( likes @ Y0 @ Y1 @ Y2 ) ) )
| ( possibly_likes @ Y0 @ Y1 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f234]) ).
thf(f236,plain,
! [X2: mu,X1: $i] :
( $true
= ( ^ [Y0: mu] :
( !! @ mu
@ ^ [Y1: mu] :
( ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( a3 @ X1 @ Y2 )
| ~ ( likes @ Y0 @ Y1 @ Y2 ) ) )
| ( possibly_likes @ Y0 @ Y1 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f235]) ).
thf(f237,plain,
! [X2: mu,X1: $i] :
( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a3 @ X1 @ Y1 )
| ~ ( likes @ X2 @ Y0 @ Y1 ) ) )
| ( possibly_likes @ X2 @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f236]) ).
thf(f238,plain,
! [X2: mu,X3: mu,X1: $i] :
( $true
= ( ^ [Y0: mu] :
( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a3 @ X1 @ Y1 )
| ~ ( likes @ X2 @ Y0 @ Y1 ) ) )
| ( possibly_likes @ X2 @ Y0 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f237]) ).
thf(f239,plain,
! [X2: mu,X3: mu,X1: $i] :
( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a3 @ X1 @ Y0 )
| ~ ( likes @ X2 @ X3 @ Y0 ) ) )
| ( possibly_likes @ X2 @ X3 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f238]) ).
thf(f240,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( possibly_likes @ X2 @ X3 @ X1 ) )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a3 @ X1 @ Y0 )
| ~ ( likes @ X2 @ X3 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f239]) ).
thf(f241,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( possibly_likes @ X2 @ X3 @ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a3 @ X1 @ Y0 )
| ~ ( likes @ X2 @ X3 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f240]) ).
thf(f242,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( possibly_likes @ X2 @ X3 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a3 @ X1 @ Y0 )
| ~ ( likes @ X2 @ X3 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f241]) ).
thf(f243,plain,
! [X2: mu,X3: mu,X1: $i,X4: $i] :
( ( $true
= ( possibly_likes @ X2 @ X3 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( a3 @ X1 @ Y0 )
| ~ ( likes @ X2 @ X3 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f242]) ).
thf(f244,plain,
! [X2: mu,X3: mu,X1: $i,X4: $i] :
( ( $true
= ( possibly_likes @ X2 @ X3 @ X1 ) )
| ( $true
= ( ~ ( a3 @ X1 @ X4 )
| ~ ( likes @ X2 @ X3 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f243]) ).
thf(f245,plain,
! [X2: mu,X3: mu,X1: $i,X4: $i] :
( ( $true
= ( possibly_likes @ X2 @ X3 @ X1 ) )
| ( $true
= ( ~ ( likes @ X2 @ X3 @ X4 ) ) )
| ( $true
= ( ~ ( a3 @ X1 @ X4 ) ) ) ),
inference(or_proxy_clausification,[],[f244]) ).
thf(f246,plain,
! [X2: mu,X3: mu,X1: $i,X4: $i] :
( ( $true
= ( possibly_likes @ X2 @ X3 @ X1 ) )
| ( $false
= ( likes @ X2 @ X3 @ X4 ) )
| ( $true
= ( ~ ( a3 @ X1 @ X4 ) ) ) ),
inference(not_proxy_clausification,[],[f245]) ).
thf(f247,plain,
! [X2: mu,X3: mu,X1: $i,X4: $i] :
( ( $true
= ( possibly_likes @ X2 @ X3 @ X1 ) )
| ( $false
= ( likes @ X2 @ X3 @ X4 ) )
| ( $false
= ( a3 @ X1 @ X4 ) ) ),
inference(not_proxy_clausification,[],[f246]) ).
thf(f350,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a3 @ Y0 @ Y1 )
| ~ ( likes @ piotr @ pepsi @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f213]) ).
thf(f351,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a3 @ Y0 @ Y1 )
| ~ ( likes @ piotr @ pepsi @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f350]) ).
thf(f352,plain,
! [X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a3 @ X1 @ Y0 )
| ~ ( likes @ piotr @ pepsi @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f351]) ).
thf(f353,plain,
! [X1: $i] :
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a3 @ X1 @ Y0 )
| ~ ( likes @ piotr @ pepsi @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f352]) ).
thf(f354,plain,
! [X1: $i] :
( $false
= ( ^ [Y0: $i] :
( ~ ( a3 @ X1 @ Y0 )
| ~ ( likes @ piotr @ pepsi @ Y0 ) )
@ ( sK5 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f353]) ).
thf(f355,plain,
! [X1: $i] :
( $false
= ( ~ ( a3 @ X1 @ ( sK5 @ X1 ) )
| ~ ( likes @ piotr @ pepsi @ ( sK5 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f354]) ).
thf(f356,plain,
! [X1: $i] :
( $false
= ( ~ ( likes @ piotr @ pepsi @ ( sK5 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f355]) ).
thf(f357,plain,
! [X1: $i] :
( $false
= ( ~ ( a3 @ X1 @ ( sK5 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f355]) ).
thf(f358,plain,
! [X1: $i] :
( $true
= ( a3 @ X1 @ ( sK5 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f357]) ).
thf(f359,plain,
! [X1: $i] :
( $true
= ( likes @ piotr @ pepsi @ ( sK5 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f356]) ).
thf(f602,plain,
! [X2: $i,X0: mu,X1: mu] :
( ( $true = $false )
| ( $false
= ( likes @ X0 @ X1 @ X2 ) )
| ( $false
= ( a3 @ sK0 @ X2 ) ) ),
inference(constrained_superposition,[],[f232,f247]) ).
thf(f633,plain,
! [X2: $i,X0: mu,X1: mu] :
( ( $false
= ( likes @ X0 @ X1 @ X2 ) )
| ( $false
= ( a3 @ sK0 @ X2 ) ) ),
inference(trivial_inequality_removal,[],[f602]) ).
thf(f679,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( a3 @ sK0 @ ( sK5 @ X0 ) ) ) ),
inference(constrained_superposition,[],[f359,f633]) ).
thf(f680,plain,
! [X0: $i] :
( $false
= ( a3 @ sK0 @ ( sK5 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f679]) ).
thf(f730,plain,
$true = $false,
inference(constrained_superposition,[],[f358,f680]) ).
thf(f731,plain,
$false,
inference(trivial_inequality_removal,[],[f730]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : AGT033^2 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n020.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 17:31:04 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.28 % (1357770)Will run a generic schedule for satisfiability detection.
% 0.20/0.28 % (1357777)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3796085917:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.28 % (1357776)% WARNING: option uhcvi not known.
% 0.20/0.28 % (1357775)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=250792107_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.28 % (1357776)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1780584965:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.28 % (1357778)dis+10_1_sil=32000:sp=arity:random_seed=2193980023:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.28 % (1357779)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1071561755:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.28 % (1357776)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.28 % (1357779)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.28 % Exception at run slice level
% 0.20/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.28 % (1357776)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.28 % (1357777) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1357770-1357777"...
% 0.20/0.28 % (1357780)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3791648564:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.28 % (1357777)...printing done.
% 0.20/0.28 % (1357781)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=346950149:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.28 % (1357777)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.29 % (1357777)------------------------------
% 0.20/0.29 % (1357777)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (1357777)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (1357777)CaDiCaL version: 2.1.3
% 0.20/0.29 % (1357777)Termination reason: Refutation
% 0.20/0.29 % (1357777)Time elapsed: 0.017 s
% 0.20/0.29 % (1357777)Peak memory usage: 12 MB
% 0.20/0.29 % (1357777)Instructions burned: 59 (million)
% 0.20/0.29 % (1357770)Success in time 0.052 s
% 0.20/0.29 % Vampire exiting
%------------------------------------------------------------------------------