%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : AGT038^1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n010.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 0.18s 0.30s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 10
% Syntax : Number of formulae : 78 ( 60 unt; 0 typ; 0 def)
% Number of atoms : 368 ( 85 equ; 0 cnn)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 655 ( 87 ~; 53 |; 0 &; 476 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 92 ( 92 >; 0 *; 0 +; 0 <<)
% Number of symbols : 71 ( 67 usr; 9 con; 0-4 aty)
% ( 39 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 218 ( 158 ^; 60 !; 0 ?; 218 :)
% 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/sandbox2/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/sandbox2/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/LCL013^0.ax',mdia) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f42,axiom,
mvalid @ ( mdia @ a3 @ ( likes @ piotr @ pepsi ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',axiom_user_communication_5) ).
thf(f73,conjecture,
mvalid @ ( possibly_likes @ piotr @ pepsi ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(f74,negated_conjecture,
~ ( mvalid @ ( possibly_likes @ piotr @ 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(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(f146,plain,
mvalid @ ( mdia @ a3 @ ( likes @ piotr @ pepsi ) ),
inference(rectify,[],[f42]) ).
thf(f147,plain,
( ( mvalid @ ( mdia @ a3 @ ( likes @ piotr @ pepsi ) ) )
= $true ),
inference(fool_elimination,[],[f146]) ).
thf(f160,plain,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] : ( mimplies @ ( mdia @ a3 @ ( likes @ X0 @ X1 ) ) @ ( possibly_likes @ X0 @ X1 ) ) ) ) ),
inference(rectify,[],[f49]) ).
thf(f161,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mimplies @ ( mdia @ a3 @ ( likes @ Y0 @ Y1 ) ) @ ( possibly_likes @ Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f160]) ).
thf(f208,plain,
~ ( mvalid @ ( possibly_likes @ piotr @ pepsi ) ),
inference(rectify,[],[f74]) ).
thf(f209,plain,
( ( mvalid @ ( possibly_likes @ piotr @ pepsi ) )
!= $true ),
inference(fool_elimination,[],[f208]) ).
thf(f210,plain,
( ( mvalid @ ( possibly_likes @ piotr @ 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(f238,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f119]) ).
thf(f252,plain,
( ( mvalid @ ( mdia @ a3 @ ( likes @ piotr @ pepsi ) ) )
= $true ),
inference(cnf_transformation,[],[f147]) ).
thf(f259,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mimplies @ ( mdia @ a3 @ ( likes @ Y0 @ Y1 ) ) @ ( possibly_likes @ Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f161]) ).
thf(f283,plain,
( ( mvalid @ ( possibly_likes @ piotr @ 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(f305,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,[],[f252,f238,f294]) ).
thf(f312,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,[],[f259,f238,f220,f220,f287,f294]) ).
thf(f334,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( possibly_likes @ piotr @ pepsi ) ) ),
inference(definition_unfolding,[],[f283,f238]) ).
thf(f335,plain,
( $true
!= ( !! @ $i @ ( possibly_likes @ piotr @ pepsi ) ) ),
inference(beta-eta_normalization,[],[f334]) ).
thf(f336,plain,
( $false
= ( possibly_likes @ piotr @ pepsi @ sK0 ) ),
inference(sigma_proxy_clausification,[],[f335]) ).
thf(f493,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,[],[f312]) ).
thf(f494,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,[],[f493]) ).
thf(f495,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,[],[f494]) ).
thf(f496,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,[],[f495]) ).
thf(f497,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,[],[f496]) ).
thf(f498,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,[],[f497]) ).
thf(f499,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,[],[f498]) ).
thf(f500,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,[],[f499]) ).
thf(f501,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,[],[f500]) ).
thf(f502,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,[],[f501]) ).
thf(f503,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,[],[f502]) ).
thf(f504,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,[],[f503]) ).
thf(f505,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,[],[f504]) ).
thf(f506,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,[],[f505]) ).
thf(f507,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,[],[f506]) ).
thf(f610,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a3 @ Y0 @ Y1 )
| ~ ( likes @ piotr @ pepsi @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f305]) ).
thf(f611,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a3 @ Y0 @ Y1 )
| ~ ( likes @ piotr @ pepsi @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f610]) ).
thf(f612,plain,
! [X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a3 @ X1 @ Y0 )
| ~ ( likes @ piotr @ pepsi @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f611]) ).
thf(f613,plain,
! [X1: $i] :
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a3 @ X1 @ Y0 )
| ~ ( likes @ piotr @ pepsi @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f612]) ).
thf(f614,plain,
! [X1: $i] :
( $false
= ( ^ [Y0: $i] :
( ~ ( a3 @ X1 @ Y0 )
| ~ ( likes @ piotr @ pepsi @ Y0 ) )
@ ( sK8 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f613]) ).
thf(f615,plain,
! [X1: $i] :
( $false
= ( ~ ( a3 @ X1 @ ( sK8 @ X1 ) )
| ~ ( likes @ piotr @ pepsi @ ( sK8 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f614]) ).
thf(f616,plain,
! [X1: $i] :
( $false
= ( ~ ( likes @ piotr @ pepsi @ ( sK8 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f615]) ).
thf(f617,plain,
! [X1: $i] :
( $false
= ( ~ ( a3 @ X1 @ ( sK8 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f615]) ).
thf(f618,plain,
! [X1: $i] :
( $true
= ( a3 @ X1 @ ( sK8 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f617]) ).
thf(f619,plain,
! [X1: $i] :
( $true
= ( likes @ piotr @ pepsi @ ( sK8 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f616]) ).
thf(f1615,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( likes @ piotr @ pepsi @ X0 ) )
| ( $false
= ( a3 @ sK0 @ X0 ) ) ),
inference(constrained_superposition,[],[f336,f507]) ).
thf(f1658,plain,
! [X0: $i] :
( ( $false
= ( likes @ piotr @ pepsi @ X0 ) )
| ( $false
= ( a3 @ sK0 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1615]) ).
thf(f1687,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( a3 @ sK0 @ ( sK8 @ X0 ) ) ) ),
inference(constrained_superposition,[],[f619,f1658]) ).
thf(f1688,plain,
! [X0: $i] :
( $false
= ( a3 @ sK0 @ ( sK8 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1687]) ).
thf(f1787,plain,
$true = $false,
inference(constrained_superposition,[],[f618,f1688]) ).
thf(f1788,plain,
$false,
inference(trivial_inequality_removal,[],[f1787]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : AGT038^1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n010.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
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 17:31:03 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.30 % (3177332)Will run a generic schedule for satisfiability detection.
% 0.18/0.30 % (3177346)% WARNING: option uhcvi not known.
% 0.18/0.30 % (3177346)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1330167301:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.30 % (3177346)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.18/0.30 % (3177346)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.18/0.30 % (3177345)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=181875709_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.30 % (3177348)dis+10_1_sil=32000:sp=arity:random_seed=2165607655:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.30 % (3177347)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2835009280:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.30 % (3177350)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4150472373:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.30 % (3177351)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1080162534:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.30 % (3177352)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2179993428:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.30 % (3177350)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.18/0.30 % Exception at run slice level
% 0.18/0.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.18/0.30 % (3177346) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3177332-3177346"...
% 0.18/0.30 % (3177346)...printing done.
% 0.18/0.30 % (3177346)Refutation found. Thanks to Tanya!
% 0.18/0.30 % SZS status Theorem for theBenchmark
% 0.18/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.30 % (3177346)------------------------------
% 0.18/0.30 % (3177346)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.30 % (3177346)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.30 % (3177346)CaDiCaL version: 2.1.3
% 0.18/0.30 % (3177346)Termination reason: Refutation
% 0.18/0.30 % (3177346)Time elapsed: 0.032 s
% 0.18/0.30 % (3177346)Peak memory usage: 13 MB
% 0.18/0.30 % (3177346)Instructions burned: 128 (million)
% 0.18/0.30 % (3177332)Success in time 0.069 s
% 0.18/0.30 % Vampire exiting
%------------------------------------------------------------------------------