%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : AGT039^1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n004.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 07:44:42 AM UTC 2026
% Result : Theorem 0.21s 0.37s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 12
% Syntax : Number of formulae : 90 ( 67 unt; 0 typ; 0 def)
% Number of atoms : 417 ( 98 equ; 0 cnn)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 683 ( 74 ~; 55 |; 0 &; 506 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 97 ( 97 >; 0 *; 0 +; 0 <<)
% Number of symbols : 72 ( 67 usr; 10 con; 0-4 aty)
% ( 42 !!; 6 ??; 0 @@+; 0 @@-)
% Number of variables : 234 ( 164 ^; 68 !; 2 ?; 234 :)
% 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,
subrel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(func_def_44,type,
cond4s: ( $i > $i > $o ) > ( $i > $i > $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,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_48,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_49,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_50,type,
vNOT: $o > $o ).
thf(func_def_51,type,
vOR: $o > $o > $o ).
thf(func_def_52,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_55,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_56,type,
vIMP: $o > $o > $o ).
thf(func_def_57,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_58,type,
vAND: $o > $o > $o ).
thf(func_def_59,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_61,type,
sK1: $i > $i ).
thf(func_def_62,type,
sK2: $i > $i ).
thf(func_def_63,type,
sK3: $i > $i ).
thf(func_def_64,type,
sK4: mu > $i > mu > $i ).
thf(func_def_65,type,
sK5: mu > mu > $i > $i ).
thf(func_def_66,type,
sK6: mu > mu > $i > $i ).
thf(func_def_67,type,
sK7: $i > $i ).
thf(func_def_68,type,
sK8: $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(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(f20,axiom,
( mserial
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] :
? [X2: $i] : ( X0 @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mserial) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f36,axiom,
mvalid @ ( mbox @ a2 @ ( likes @ jan @ pepsi ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_a2_1) ).
thf(f48,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] : ( mimplies @ ( mdia @ a2 @ ( likes @ X0 @ X1 ) ) @ ( possibly_likes @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_user_communication_4) ).
thf(f54,axiom,
mserial @ a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axioms_D_a2) ).
thf(f73,conjecture,
mvalid @ ( possibly_likes @ jan @ pepsi ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(f74,negated_conjecture,
~ ( mvalid @ ( possibly_likes @ jan @ pepsi ) ),
inference(negated_conjecture,[status(cth)],[f73]) ).
thf(f77,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f78,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f77]) ).
thf(f79,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f80,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f79]) ).
thf(f82,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f86,plain,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f10]) ).
thf(f87,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f86]) ).
thf(f95,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f96,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f95]) ).
thf(f97,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o] : ( mnot @ ( mbox @ Y0 @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f17]) ).
thf(f102,plain,
( mserial
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] :
? [X2: $i] : ( X0 @ X1 @ X2 ) ) ),
inference(rectify,[],[f20]) ).
thf(f103,plain,
( mserial
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f102]) ).
thf(f118,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f119,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f118]) ).
thf(f134,plain,
mvalid @ ( mbox @ a2 @ ( likes @ jan @ pepsi ) ),
inference(rectify,[],[f36]) ).
thf(f135,plain,
( ( mvalid @ ( mbox @ a2 @ ( likes @ jan @ pepsi ) ) )
= $true ),
inference(fool_elimination,[],[f134]) ).
thf(f158,plain,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] : ( mimplies @ ( mdia @ a2 @ ( likes @ X0 @ X1 ) ) @ ( possibly_likes @ X0 @ X1 ) ) ) ) ),
inference(rectify,[],[f48]) ).
thf(f159,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mimplies @ ( mdia @ a2 @ ( likes @ Y0 @ Y1 ) ) @ ( possibly_likes @ Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f158]) ).
thf(f170,plain,
mserial @ a2,
inference(rectify,[],[f54]) ).
thf(f171,plain,
( ( mserial @ a2 )
= $true ),
inference(fool_elimination,[],[f170]) ).
thf(f208,plain,
~ ( mvalid @ ( possibly_likes @ jan @ pepsi ) ),
inference(rectify,[],[f74]) ).
thf(f209,plain,
( ( mvalid @ ( possibly_likes @ jan @ pepsi ) )
!= $true ),
inference(fool_elimination,[],[f208]) ).
thf(f210,plain,
( ( mvalid @ ( possibly_likes @ jan @ pepsi ) )
!= $true ),
inference(flattening,[],[f209]) ).
thf(f213,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f78]) ).
thf(f214,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f80]) ).
thf(f216,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f82]) ).
thf(f220,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f87]) ).
thf(f226,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f96]) ).
thf(f227,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o] : ( mnot @ ( mbox @ Y0 @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f97]) ).
thf(f230,plain,
( mserial
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f103]) ).
thf(f238,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f119]) ).
thf(f246,plain,
( ( mvalid @ ( mbox @ a2 @ ( likes @ jan @ pepsi ) ) )
= $true ),
inference(cnf_transformation,[],[f135]) ).
thf(f258,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mimplies @ ( mdia @ a2 @ ( likes @ Y0 @ Y1 ) ) @ ( possibly_likes @ Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f159]) ).
thf(f264,plain,
( ( mserial @ a2 )
= $true ),
inference(cnf_transformation,[],[f171]) ).
thf(f283,plain,
( ( mvalid @ ( possibly_likes @ jan @ pepsi ) )
!= $true ),
inference(cnf_transformation,[],[f210]) ).
thf(f287,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,[],[f216,f214,f213]) ).
thf(f294,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,[],[f227,f213,f226,f213]) ).
thf(f299,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ a2
@ ( likes @ jan @ pepsi ) ) ) ),
inference(definition_unfolding,[],[f246,f238,f226]) ).
thf(f311,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 ) ) )
@ a2
@ ( likes @ Y0 @ Y1 ) )
@ ( possibly_likes @ Y0 @ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[],[f258,f238,f220,f220,f287,f294]) ).
thf(f317,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) )
@ a2 ) ),
inference(definition_unfolding,[],[f264,f230]) ).
thf(f334,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( possibly_likes @ jan @ pepsi ) ) ),
inference(definition_unfolding,[],[f283,f238]) ).
thf(f335,plain,
( $true
!= ( !! @ $i @ ( possibly_likes @ jan @ pepsi ) ) ),
inference(beta-eta_normalization,[],[f334]) ).
thf(f336,plain,
( $false
= ( possibly_likes @ jan @ pepsi @ sK0 ) ),
inference(sigma_proxy_clausification,[],[f335]) ).
thf(f467,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( ?? @ $i @ ( a2 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f317]) ).
thf(f468,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( ?? @ $i @ ( a2 @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f467]) ).
thf(f469,plain,
! [X1: $i] :
( $true
= ( ?? @ $i @ ( a2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f468]) ).
thf(f470,plain,
! [X1: $i] :
( $true
= ( a2 @ X1 @ ( sK2 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f469]) ).
thf(f508,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( !! @ mu
@ ^ [Y2: mu] :
( ~ ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( a2 @ Y0 @ Y3 )
| ~ ( likes @ Y1 @ Y2 @ Y3 ) ) )
| ( possibly_likes @ Y1 @ Y2 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f311]) ).
thf(f509,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( !! @ mu
@ ^ [Y2: mu] :
( ~ ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( a2 @ Y0 @ Y3 )
| ~ ( likes @ Y1 @ Y2 @ Y3 ) ) )
| ( possibly_likes @ Y1 @ Y2 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f508]) ).
thf(f510,plain,
! [X1: $i] :
( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( !! @ mu
@ ^ [Y1: mu] :
( ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( a2 @ X1 @ Y2 )
| ~ ( likes @ Y0 @ Y1 @ Y2 ) ) )
| ( possibly_likes @ Y0 @ Y1 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f509]) ).
thf(f511,plain,
! [X2: mu,X1: $i] :
( $true
= ( ^ [Y0: mu] :
( !! @ mu
@ ^ [Y1: mu] :
( ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( a2 @ X1 @ Y2 )
| ~ ( likes @ Y0 @ Y1 @ Y2 ) ) )
| ( possibly_likes @ Y0 @ Y1 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f510]) ).
thf(f512,plain,
! [X2: mu,X1: $i] :
( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a2 @ X1 @ Y1 )
| ~ ( likes @ X2 @ Y0 @ Y1 ) ) )
| ( possibly_likes @ X2 @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f511]) ).
thf(f513,plain,
! [X2: mu,X3: mu,X1: $i] :
( $true
= ( ^ [Y0: mu] :
( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a2 @ X1 @ Y1 )
| ~ ( likes @ X2 @ Y0 @ Y1 ) ) )
| ( possibly_likes @ X2 @ Y0 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f512]) ).
thf(f514,plain,
! [X2: mu,X3: mu,X1: $i] :
( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a2 @ X1 @ Y0 )
| ~ ( likes @ X2 @ X3 @ Y0 ) ) )
| ( possibly_likes @ X2 @ X3 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f513]) ).
thf(f515,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( possibly_likes @ X2 @ X3 @ X1 ) )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a2 @ X1 @ Y0 )
| ~ ( likes @ X2 @ X3 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f514]) ).
thf(f516,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( possibly_likes @ X2 @ X3 @ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a2 @ X1 @ Y0 )
| ~ ( likes @ X2 @ X3 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f515]) ).
thf(f517,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( possibly_likes @ X2 @ X3 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a2 @ X1 @ Y0 )
| ~ ( likes @ X2 @ X3 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f516]) ).
thf(f518,plain,
! [X2: mu,X3: mu,X1: $i,X4: $i] :
( ( $true
= ( possibly_likes @ X2 @ X3 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( a2 @ X1 @ Y0 )
| ~ ( likes @ X2 @ X3 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f517]) ).
thf(f519,plain,
! [X2: mu,X3: mu,X1: $i,X4: $i] :
( ( $true
= ( possibly_likes @ X2 @ X3 @ X1 ) )
| ( $true
= ( ~ ( a2 @ X1 @ X4 )
| ~ ( likes @ X2 @ X3 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f518]) ).
thf(f520,plain,
! [X2: mu,X3: mu,X1: $i,X4: $i] :
( ( $true
= ( possibly_likes @ X2 @ X3 @ X1 ) )
| ( $true
= ( ~ ( likes @ X2 @ X3 @ X4 ) ) )
| ( $true
= ( ~ ( a2 @ X1 @ X4 ) ) ) ),
inference(or_proxy_clausification,[],[f519]) ).
thf(f521,plain,
! [X2: mu,X3: mu,X1: $i,X4: $i] :
( ( $true
= ( possibly_likes @ X2 @ X3 @ X1 ) )
| ( $false
= ( likes @ X2 @ X3 @ X4 ) )
| ( $true
= ( ~ ( a2 @ X1 @ X4 ) ) ) ),
inference(not_proxy_clausification,[],[f520]) ).
thf(f522,plain,
! [X2: mu,X3: mu,X1: $i,X4: $i] :
( ( $true
= ( possibly_likes @ X2 @ X3 @ X1 ) )
| ( $false
= ( likes @ X2 @ X3 @ X4 ) )
| ( $false
= ( a2 @ X1 @ X4 ) ) ),
inference(not_proxy_clausification,[],[f521]) ).
thf(f663,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a2 @ Y0 @ Y1 )
| ( likes @ jan @ pepsi @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f299]) ).
thf(f664,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a2 @ Y0 @ Y1 )
| ( likes @ jan @ pepsi @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f663]) ).
thf(f665,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a2 @ X1 @ Y0 )
| ( likes @ jan @ pepsi @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f664]) ).
thf(f666,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( a2 @ X1 @ Y0 )
| ( likes @ jan @ pepsi @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f665]) ).
thf(f667,plain,
! [X2: $i,X1: $i] :
( $true
= ( ~ ( a2 @ X1 @ X2 )
| ( likes @ jan @ pepsi @ X2 ) ) ),
inference(beta-eta_normalization,[],[f666]) ).
thf(f668,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( likes @ jan @ pepsi @ X2 ) )
| ( $true
= ( ~ ( a2 @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f667]) ).
thf(f669,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( likes @ jan @ pepsi @ X2 ) )
| ( $false
= ( a2 @ X1 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f668]) ).
thf(f816,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( likes @ jan @ pepsi @ ( sK2 @ X0 ) ) ) ),
inference(constrained_superposition,[],[f470,f669]) ).
thf(f817,plain,
! [X0: $i] :
( $true
= ( likes @ jan @ pepsi @ ( sK2 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f816]) ).
thf(f1699,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( likes @ jan @ pepsi @ X0 ) )
| ( $false
= ( a2 @ sK0 @ X0 ) ) ),
inference(constrained_superposition,[],[f336,f522]) ).
thf(f1734,plain,
! [X0: $i] :
( ( $false
= ( likes @ jan @ pepsi @ X0 ) )
| ( $false
= ( a2 @ sK0 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1699]) ).
thf(f2357,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( a2 @ sK0 @ ( sK2 @ X0 ) ) ) ),
inference(constrained_superposition,[],[f1734,f817]) ).
thf(f2368,plain,
! [X0: $i] :
( $false
= ( a2 @ sK0 @ ( sK2 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f2357]) ).
thf(f2387,plain,
$true = $false,
inference(constrained_superposition,[],[f470,f2368]) ).
thf(f2388,plain,
$false,
inference(trivial_inequality_removal,[],[f2387]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : AGT039^1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n004.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
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 17:30:52 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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
% 0.21/0.36 % (1607061)Will run a generic schedule for satisfiability detection.
% 0.21/0.36 % (1607068)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2374867194:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.36 % (1607067)% WARNING: option uhcvi not known.
% 0.21/0.36 % (1607066)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1457669487_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.36 % (1607067)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2557811634:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.36 % (1607070)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1231297707:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.36 % (1607071)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2325453902:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.36 % (1607072)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1781089638:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.21/0.36 % (1607067)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.36 % (1607070)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.36 % Exception at run slice level
% 0.21/0.36 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.36 % (1607067)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.21/0.36 % (1607069)dis+10_1_sil=32000:sp=arity:random_seed=1716339744:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.36 % (1607079)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3697244102:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.21/0.36 % Exception at run slice level
% 0.21/0.36 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.36 % (1607082)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=4133859842:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.36 % (1607070)Instruction limit reached!
% 0.21/0.36 % (1607070)------------------------------
% 0.21/0.36 % (1607070)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (1607070)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (1607070)CaDiCaL version: 2.1.3
% 0.21/0.36 % (1607070)Termination reason: Instruction limit
% 0.21/0.36 % (1607070)Termination phase: Saturation
% 0.21/0.36 % (1607070)Time elapsed: 0.054 s
% 0.21/0.36 % (1607070)Peak memory usage: 12 MB
% 0.21/0.36 % (1607070)Instructions burned: 120 (million)
% 0.21/0.36 % (1607071)Instruction limit reached!
% 0.21/0.36 % (1607071)------------------------------
% 0.21/0.36 % (1607071)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (1607071)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (1607071)CaDiCaL version: 2.1.3
% 0.21/0.36 % (1607071)Termination reason: Instruction limit
% 0.21/0.36 % (1607071)Termination phase: Saturation
% 0.21/0.36 % (1607071)Time elapsed: 0.060 s
% 0.21/0.36 % (1607071)Peak memory usage: 12 MB
% 0.21/0.36 % (1607071)Instructions burned: 132 (million)
% 0.21/0.36 % (1607084)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=1873476661:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.21/0.37 % (1607069)Instruction limit reached!
% 0.21/0.37 % (1607069)------------------------------
% 0.21/0.37 % (1607069)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.37 % (1607069)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.37 % (1607069)CaDiCaL version: 2.1.3
% 0.21/0.37 % (1607069)Termination reason: Instruction limit
% 0.21/0.37 % (1607069)Termination phase: Saturation
% 0.21/0.37 % (1607069)Time elapsed: 0.063 s
% 0.21/0.37 % (1607069)Peak memory usage: 12 MB
% 0.21/0.37 % (1607069)Instructions burned: 103 (million)
% 0.21/0.37 % (1607084)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.37 % (1607067) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1607061-1607067"...
% 0.21/0.37 % (1607072)Instruction limit reached!
% 0.21/0.37 % (1607072)------------------------------
% 0.21/0.37 % (1607072)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.37 % (1607072)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.37 % (1607072)CaDiCaL version: 2.1.3
% 0.21/0.37 % (1607072)Termination reason: Instruction limit
% 0.21/0.37 % (1607072)Termination phase: Saturation
% 0.21/0.37 % (1607072)Time elapsed: 0.079 s
% 0.21/0.37 % (1607072)Peak memory usage: 12 MB
% 0.21/0.37 % (1607072)Instructions burned: 167 (million)
% 0.21/0.37 % (1607067)...printing done.
% 0.21/0.37 % (1607084)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.21/0.37 % (1607085)ott-21_1_sil=16000:fs=off:random_seed=3412479866:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 0.21/0.37 % (1607067)Refutation found. Thanks to Tanya!
% 0.21/0.37 % SZS status Theorem for theBenchmark
% 0.21/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.37 % (1607067)------------------------------
% 0.21/0.37 % (1607067)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.37 % (1607067)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.37 % (1607067)CaDiCaL version: 2.1.3
% 0.21/0.37 % (1607067)Termination reason: Refutation
% 0.21/0.37 % (1607067)Time elapsed: 0.082 s
% 0.21/0.37 % (1607067)Peak memory usage: 13 MB
% 0.21/0.37 % (1607067)Instructions burned: 178 (million)
% 0.21/0.37 % (1607061)Success in time 0.126 s
% 0.21/0.37 % Vampire exiting
%------------------------------------------------------------------------------