%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : AGT034^2 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 07:44:41 AM UTC 2026
% Result : Theorem 5.73s 1.06s
% Output : Refutation 5.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 66
% Number of leaves : 20
% Syntax : Number of formulae : 258 ( 125 unt; 0 typ; 3 def)
% Number of atoms : 2011 ( 473 equ; 0 cnn)
% Maximal formula atoms : 16 ( 7 avg)
% Number of connectives : 3679 ( 370 ~; 471 |; 0 &;2681 @)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 174 ( 174 >; 0 *; 0 +; 0 <<)
% Number of symbols : 69 ( 65 usr; 12 con; 0-4 aty)
% ( 154 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 788 ( 0 sgn 368 !; 0 ?; 788 :)
% 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/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(f5,axiom,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mand) ).
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(f32,axiom,
mvalid @ ( mbox @ a1 @ ( likes @ jan @ cola ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a1_1) ).
thf(f36,axiom,
mvalid @ ( mbox @ a2 @ ( likes @ jan @ pepsi ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a2_1) ).
thf(f39,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] : ( mbox @ a2 @ ( mimplies @ ( likes @ X0 @ pepsi ) @ ( likes @ X0 @ cola ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a2_4) ).
thf(f41,axiom,
mvalid @ ( mbox @ a3 @ ( likes @ jan @ cola ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a3_1) ).
thf(f42,axiom,
mvalid @ ( mdia @ a3 @ ( likes @ piotr @ pepsi ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a3_2) ).
thf(f44,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] : ( mbox @ a3 @ ( mimplies @ ( mand @ ( likes @ X0 @ X1 ) @ ( mand @ ( mbox @ a1 @ ( likes @ X0 @ X1 ) ) @ ( mbox @ a2 @ ( likes @ X0 @ X1 ) ) ) ) @ ( very_much_likes @ X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a3_4) ).
thf(f45,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] : ( mimplies @ ( mbox @ a3 @ ( very_much_likes @ X0 @ X1 ) ) @ ( very_much_likes @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_user_communication_1) ).
thf(f46,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] : ( mimplies @ ( mdia @ a3 @ ( very_much_likes @ X0 @ X1 ) ) @ ( likes @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_user_communication_2) ).
thf(f50,conjecture,
mvalid @ ( very_much_likes @ jan @ cola ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(f51,negated_conjecture,
~ ( mvalid @ ( very_much_likes @ jan @ cola ) ),
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(f58,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
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(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(f103,plain,
mvalid @ ( mbox @ a1 @ ( likes @ jan @ cola ) ),
inference(rectify,[],[f32]) ).
thf(f104,plain,
( ( mvalid @ ( mbox @ a1 @ ( likes @ jan @ cola ) ) )
= $true ),
inference(fool_elimination,[],[f103]) ).
thf(f111,plain,
mvalid @ ( mbox @ a2 @ ( likes @ jan @ pepsi ) ),
inference(rectify,[],[f36]) ).
thf(f112,plain,
( ( mvalid @ ( mbox @ a2 @ ( likes @ jan @ pepsi ) ) )
= $true ),
inference(fool_elimination,[],[f111]) ).
thf(f117,plain,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] : ( mbox @ a2 @ ( mimplies @ ( likes @ X0 @ pepsi ) @ ( likes @ X0 @ cola ) ) ) ) ),
inference(rectify,[],[f39]) ).
thf(f118,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] : ( mbox @ a2 @ ( mimplies @ ( likes @ Y0 @ pepsi ) @ ( likes @ Y0 @ cola ) ) ) ) ) ),
inference(fool_elimination,[],[f117]) ).
thf(f121,plain,
mvalid @ ( mbox @ a3 @ ( likes @ jan @ cola ) ),
inference(rectify,[],[f41]) ).
thf(f122,plain,
( ( mvalid @ ( mbox @ a3 @ ( likes @ jan @ cola ) ) )
= $true ),
inference(fool_elimination,[],[f121]) ).
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(f127,plain,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] : ( mbox @ a3 @ ( mimplies @ ( mand @ ( likes @ X0 @ X1 ) @ ( mand @ ( mbox @ a1 @ ( likes @ X0 @ X1 ) ) @ ( mbox @ a2 @ ( likes @ X0 @ X1 ) ) ) ) @ ( very_much_likes @ X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f44]) ).
thf(f128,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mbox @ a3 @ ( mimplies @ ( mand @ ( likes @ Y0 @ Y1 ) @ ( mand @ ( mbox @ a1 @ ( likes @ Y0 @ Y1 ) ) @ ( mbox @ a2 @ ( likes @ Y0 @ Y1 ) ) ) ) @ ( very_much_likes @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f127]) ).
thf(f129,plain,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] : ( mimplies @ ( mbox @ a3 @ ( very_much_likes @ X0 @ X1 ) ) @ ( very_much_likes @ X0 @ X1 ) ) ) ) ),
inference(rectify,[],[f45]) ).
thf(f130,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mimplies @ ( mbox @ a3 @ ( very_much_likes @ Y0 @ Y1 ) ) @ ( very_much_likes @ Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f129]) ).
thf(f131,plain,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] : ( mimplies @ ( mdia @ a3 @ ( very_much_likes @ X0 @ X1 ) ) @ ( likes @ X0 @ X1 ) ) ) ) ),
inference(rectify,[],[f46]) ).
thf(f132,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mimplies @ ( mdia @ a3 @ ( very_much_likes @ Y0 @ Y1 ) ) @ ( likes @ Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f131]) ).
thf(f139,plain,
~ ( mvalid @ ( very_much_likes @ jan @ cola ) ),
inference(rectify,[],[f51]) ).
thf(f140,plain,
( ( mvalid @ ( very_much_likes @ jan @ cola ) )
!= $true ),
inference(fool_elimination,[],[f139]) ).
thf(f141,plain,
( ( mvalid @ ( very_much_likes @ jan @ cola ) )
!= $true ),
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(f146,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f58]) ).
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(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(f173,plain,
( ( mvalid @ ( mbox @ a1 @ ( likes @ jan @ cola ) ) )
= $true ),
inference(cnf_transformation,[],[f104]) ).
thf(f177,plain,
( ( mvalid @ ( mbox @ a2 @ ( likes @ jan @ pepsi ) ) )
= $true ),
inference(cnf_transformation,[],[f112]) ).
thf(f180,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] : ( mbox @ a2 @ ( mimplies @ ( likes @ Y0 @ pepsi ) @ ( likes @ Y0 @ cola ) ) ) ) ) ),
inference(cnf_transformation,[],[f118]) ).
thf(f182,plain,
( ( mvalid @ ( mbox @ a3 @ ( likes @ jan @ cola ) ) )
= $true ),
inference(cnf_transformation,[],[f122]) ).
thf(f183,plain,
( ( mvalid @ ( mdia @ a3 @ ( likes @ piotr @ pepsi ) ) )
= $true ),
inference(cnf_transformation,[],[f124]) ).
thf(f185,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mbox @ a3 @ ( mimplies @ ( mand @ ( likes @ Y0 @ Y1 ) @ ( mand @ ( mbox @ a1 @ ( likes @ Y0 @ Y1 ) ) @ ( mbox @ a2 @ ( likes @ Y0 @ Y1 ) ) ) ) @ ( very_much_likes @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f128]) ).
thf(f186,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mimplies @ ( mbox @ a3 @ ( very_much_likes @ Y0 @ Y1 ) ) @ ( very_much_likes @ Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f130]) ).
thf(f187,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mimplies @ ( mdia @ a3 @ ( very_much_likes @ Y0 @ Y1 ) ) @ ( likes @ Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f132]) ).
thf(f191,plain,
( ( mvalid @ ( very_much_likes @ jan @ cola ) )
!= $true ),
inference(cnf_transformation,[],[f141]) ).
thf(f194,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f146,f144,f145,f144,f144]) ).
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(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(f203,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 ) ) )
@ a1
@ ( likes @ jan @ cola ) ) ) ),
inference(definition_unfolding,[],[f173,f169,f157]) ).
thf(f207,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,[],[f177,f169,f157]) ).
thf(f210,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: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ a2
@ ( ^ [Y1: $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y3 @ Y5 )
| ( Y4 @ Y5 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y1 )
@ Y2 )
@ ( likes @ Y0 @ pepsi )
@ ( likes @ Y0 @ cola ) ) ) ) ) ),
inference(definition_unfolding,[],[f180,f169,f151,f157,f195]) ).
thf(f212,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 ) ) )
@ a3
@ ( likes @ jan @ cola ) ) ) ),
inference(definition_unfolding,[],[f182,f169,f157]) ).
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(f215,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 > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y4 @ Y5 )
| ( Y3 @ Y5 ) ) )
@ a3
@ ( ^ [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 > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( likes @ Y0 @ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y4 @ Y5 )
| ( Y3 @ Y5 ) ) )
@ a1
@ ( likes @ Y0 @ Y1 ) )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y4 @ Y5 )
| ( Y3 @ Y5 ) ) )
@ a2
@ ( likes @ Y0 @ Y1 ) ) ) )
@ ( very_much_likes @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f185,f169,f151,f151,f157,f195,f194,f194,f157,f157]) ).
thf(f216,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] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y4 @ Y5 )
| ( Y3 @ Y5 ) ) )
@ a3
@ ( very_much_likes @ Y0 @ Y1 ) )
@ ( very_much_likes @ Y0 @ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[],[f186,f169,f151,f151,f195,f157]) ).
thf(f217,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
@ ( very_much_likes @ Y0 @ Y1 ) )
@ ( likes @ Y0 @ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[],[f187,f169,f151,f151,f195,f202]) ).
thf(f221,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( very_much_likes @ jan @ cola ) ) ),
inference(definition_unfolding,[],[f191,f169]) ).
thf(f222,plain,
( $true
!= ( !! @ $i @ ( very_much_likes @ jan @ cola ) ) ),
inference(beta-eta_normalization,[],[f221]) ).
thf(f223,plain,
( $false
= ( very_much_likes @ jan @ cola @ sK0 ) ),
inference(sigma_proxy_clausification,[],[f222]) ).
thf(f269,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( !! @ mu
@ ^ [Y2: mu] :
( ~ ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( a3 @ Y0 @ Y3 )
| ~ ( very_much_likes @ Y1 @ Y2 @ Y3 ) ) )
| ( likes @ Y1 @ Y2 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f217]) ).
thf(f270,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( !! @ mu
@ ^ [Y2: mu] :
( ~ ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( a3 @ Y0 @ Y3 )
| ~ ( very_much_likes @ Y1 @ Y2 @ Y3 ) ) )
| ( likes @ Y1 @ Y2 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f269]) ).
thf(f271,plain,
! [X1: $i] :
( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( !! @ mu
@ ^ [Y1: mu] :
( ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( a3 @ X1 @ Y2 )
| ~ ( very_much_likes @ Y0 @ Y1 @ Y2 ) ) )
| ( likes @ Y0 @ Y1 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f270]) ).
thf(f272,plain,
! [X2: mu,X1: $i] :
( $true
= ( ^ [Y0: mu] :
( !! @ mu
@ ^ [Y1: mu] :
( ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( a3 @ X1 @ Y2 )
| ~ ( very_much_likes @ Y0 @ Y1 @ Y2 ) ) )
| ( likes @ Y0 @ Y1 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f271]) ).
thf(f273,plain,
! [X2: mu,X1: $i] :
( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a3 @ X1 @ Y1 )
| ~ ( very_much_likes @ X2 @ Y0 @ Y1 ) ) )
| ( likes @ X2 @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f272]) ).
thf(f274,plain,
! [X2: mu,X3: mu,X1: $i] :
( $true
= ( ^ [Y0: mu] :
( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a3 @ X1 @ Y1 )
| ~ ( very_much_likes @ X2 @ Y0 @ Y1 ) ) )
| ( likes @ X2 @ Y0 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f273]) ).
thf(f275,plain,
! [X2: mu,X3: mu,X1: $i] :
( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a3 @ X1 @ Y0 )
| ~ ( very_much_likes @ X2 @ X3 @ Y0 ) ) )
| ( likes @ X2 @ X3 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f274]) ).
thf(f276,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( likes @ X2 @ X3 @ X1 ) )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a3 @ X1 @ Y0 )
| ~ ( very_much_likes @ X2 @ X3 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f275]) ).
thf(f277,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( likes @ X2 @ X3 @ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a3 @ X1 @ Y0 )
| ~ ( very_much_likes @ X2 @ X3 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f276]) ).
thf(f278,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( likes @ X2 @ X3 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a3 @ X1 @ Y0 )
| ~ ( very_much_likes @ X2 @ X3 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f277]) ).
thf(f279,plain,
! [X2: mu,X3: mu,X1: $i,X4: $i] :
( ( $true
= ( likes @ X2 @ X3 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( a3 @ X1 @ Y0 )
| ~ ( very_much_likes @ X2 @ X3 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f278]) ).
thf(f280,plain,
! [X2: mu,X3: mu,X1: $i,X4: $i] :
( ( $true
= ( likes @ X2 @ X3 @ X1 ) )
| ( $true
= ( ~ ( a3 @ X1 @ X4 )
| ~ ( very_much_likes @ X2 @ X3 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f279]) ).
thf(f281,plain,
! [X2: mu,X3: mu,X1: $i,X4: $i] :
( ( $true
= ( likes @ X2 @ X3 @ X1 ) )
| ( $true
= ( ~ ( very_much_likes @ X2 @ X3 @ X4 ) ) )
| ( $true
= ( ~ ( a3 @ X1 @ X4 ) ) ) ),
inference(or_proxy_clausification,[],[f280]) ).
thf(f282,plain,
! [X2: mu,X3: mu,X1: $i,X4: $i] :
( ( $true
= ( likes @ X2 @ X3 @ X1 ) )
| ( $false
= ( very_much_likes @ X2 @ X3 @ X4 ) )
| ( $true
= ( ~ ( a3 @ X1 @ X4 ) ) ) ),
inference(not_proxy_clausification,[],[f281]) ).
thf(f283,plain,
! [X2: mu,X3: mu,X1: $i,X4: $i] :
( ( $true
= ( likes @ X2 @ X3 @ X1 ) )
| ( $false
= ( very_much_likes @ X2 @ X3 @ X4 ) )
| ( $false
= ( a3 @ X1 @ X4 ) ) ),
inference(not_proxy_clausification,[],[f282]) ).
thf(f284,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( !! @ mu
@ ^ [Y2: mu] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( a3 @ Y0 @ Y3 )
| ( very_much_likes @ Y1 @ Y2 @ Y3 ) ) )
| ( very_much_likes @ Y1 @ Y2 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f216]) ).
thf(f285,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( !! @ mu
@ ^ [Y2: mu] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( a3 @ Y0 @ Y3 )
| ( very_much_likes @ Y1 @ Y2 @ Y3 ) ) )
| ( very_much_likes @ Y1 @ Y2 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f284]) ).
thf(f286,plain,
! [X1: $i] :
( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( !! @ mu
@ ^ [Y1: mu] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( a3 @ X1 @ Y2 )
| ( very_much_likes @ Y0 @ Y1 @ Y2 ) ) )
| ( very_much_likes @ Y0 @ Y1 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f285]) ).
thf(f287,plain,
! [X2: mu,X1: $i] :
( $true
= ( ^ [Y0: mu] :
( !! @ mu
@ ^ [Y1: mu] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( a3 @ X1 @ Y2 )
| ( very_much_likes @ Y0 @ Y1 @ Y2 ) ) )
| ( very_much_likes @ Y0 @ Y1 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f286]) ).
thf(f288,plain,
! [X2: mu,X1: $i] :
( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a3 @ X1 @ Y1 )
| ( very_much_likes @ X2 @ Y0 @ Y1 ) ) )
| ( very_much_likes @ X2 @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f287]) ).
thf(f289,plain,
! [X2: mu,X3: mu,X1: $i] :
( $true
= ( ^ [Y0: mu] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a3 @ X1 @ Y1 )
| ( very_much_likes @ X2 @ Y0 @ Y1 ) ) )
| ( very_much_likes @ X2 @ Y0 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f288]) ).
thf(f290,plain,
! [X2: mu,X3: mu,X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a3 @ X1 @ Y0 )
| ( very_much_likes @ X2 @ X3 @ Y0 ) ) )
| ( very_much_likes @ X2 @ X3 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f289]) ).
thf(f291,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( very_much_likes @ X2 @ X3 @ X1 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a3 @ X1 @ Y0 )
| ( very_much_likes @ X2 @ X3 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f290]) ).
thf(f292,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( very_much_likes @ X2 @ X3 @ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a3 @ X1 @ Y0 )
| ( very_much_likes @ X2 @ X3 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f291]) ).
thf(f293,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( very_much_likes @ X2 @ X3 @ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( a3 @ X1 @ Y0 )
| ( very_much_likes @ X2 @ X3 @ Y0 ) )
@ ( sK1 @ X3 @ X1 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f292]) ).
thf(f294,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( very_much_likes @ X2 @ X3 @ X1 ) )
| ( $false
= ( ~ ( a3 @ X1 @ ( sK1 @ X3 @ X1 @ X2 ) )
| ( very_much_likes @ X2 @ X3 @ ( sK1 @ X3 @ X1 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f293]) ).
thf(f295,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $false
= ( very_much_likes @ X2 @ X3 @ ( sK1 @ X3 @ X1 @ X2 ) ) )
| ( $true
= ( very_much_likes @ X2 @ X3 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f294]) ).
thf(f296,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( very_much_likes @ X2 @ X3 @ X1 ) )
| ( $false
= ( ~ ( a3 @ X1 @ ( sK1 @ X3 @ X1 @ X2 ) ) ) ) ),
inference(or_proxy_clausification,[],[f294]) ).
thf(f297,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( a3 @ X1 @ ( sK1 @ X3 @ X1 @ X2 ) ) )
| ( $true
= ( very_much_likes @ X2 @ X3 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f296]) ).
thf(f298,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( !! @ mu
@ ^ [Y2: mu] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( a3 @ Y0 @ Y3 )
| ~ ~ ( ~ ( likes @ Y1 @ Y2 @ Y3 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( a1 @ Y3 @ Y4 )
| ( likes @ Y1 @ Y2 @ Y4 ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( a2 @ Y3 @ Y4 )
| ( likes @ Y1 @ Y2 @ Y4 ) ) ) ) )
| ( very_much_likes @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f215]) ).
thf(f299,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( !! @ mu
@ ^ [Y2: mu] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( a3 @ Y0 @ Y3 )
| ~ ~ ( ~ ( likes @ Y1 @ Y2 @ Y3 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( a1 @ Y3 @ Y4 )
| ( likes @ Y1 @ Y2 @ Y4 ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( a2 @ Y3 @ Y4 )
| ( likes @ Y1 @ Y2 @ Y4 ) ) ) ) )
| ( very_much_likes @ Y1 @ Y2 @ Y3 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f298]) ).
thf(f300,plain,
! [X1: $i] :
( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( !! @ mu
@ ^ [Y1: mu] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( a3 @ X1 @ Y2 )
| ~ ~ ( ~ ( likes @ Y0 @ Y1 @ Y2 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( a1 @ Y2 @ Y3 )
| ( likes @ Y0 @ Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( a2 @ Y2 @ Y3 )
| ( likes @ Y0 @ Y1 @ Y3 ) ) ) ) )
| ( very_much_likes @ Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f299]) ).
thf(f301,plain,
! [X2: mu,X1: $i] :
( $true
= ( ^ [Y0: mu] :
( !! @ mu
@ ^ [Y1: mu] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( a3 @ X1 @ Y2 )
| ~ ~ ( ~ ( likes @ Y0 @ Y1 @ Y2 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( a1 @ Y2 @ Y3 )
| ( likes @ Y0 @ Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( a2 @ Y2 @ Y3 )
| ( likes @ Y0 @ Y1 @ Y3 ) ) ) ) )
| ( very_much_likes @ Y0 @ Y1 @ Y2 ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f300]) ).
thf(f302,plain,
! [X2: mu,X1: $i] :
( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a3 @ X1 @ Y1 )
| ~ ~ ( ~ ( likes @ X2 @ Y0 @ Y1 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( a1 @ Y1 @ Y2 )
| ( likes @ X2 @ Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( a2 @ Y1 @ Y2 )
| ( likes @ X2 @ Y0 @ Y2 ) ) ) ) )
| ( very_much_likes @ X2 @ Y0 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f301]) ).
thf(f303,plain,
! [X2: mu,X3: mu,X1: $i] :
( $true
= ( ^ [Y0: mu] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a3 @ X1 @ Y1 )
| ~ ~ ( ~ ( likes @ X2 @ Y0 @ Y1 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( a1 @ Y1 @ Y2 )
| ( likes @ X2 @ Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( a2 @ Y1 @ Y2 )
| ( likes @ X2 @ Y0 @ Y2 ) ) ) ) )
| ( very_much_likes @ X2 @ Y0 @ Y1 ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f302]) ).
thf(f304,plain,
! [X2: mu,X3: mu,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a3 @ X1 @ Y0 )
| ~ ~ ( ~ ( likes @ X2 @ X3 @ Y0 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a1 @ Y0 @ Y1 )
| ( likes @ X2 @ X3 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a2 @ Y0 @ Y1 )
| ( likes @ X2 @ X3 @ Y1 ) ) ) ) )
| ( very_much_likes @ X2 @ X3 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f303]) ).
thf(f305,plain,
! [X2: mu,X3: mu,X1: $i,X4: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( a3 @ X1 @ Y0 )
| ~ ~ ( ~ ( likes @ X2 @ X3 @ Y0 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a1 @ Y0 @ Y1 )
| ( likes @ X2 @ X3 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a2 @ Y0 @ Y1 )
| ( likes @ X2 @ X3 @ Y1 ) ) ) ) )
| ( very_much_likes @ X2 @ X3 @ Y0 ) )
@ X4 ) ),
inference(pi_proxy_clausification,[],[f304]) ).
thf(f306,plain,
! [X2: mu,X3: mu,X1: $i,X4: $i] :
( $true
= ( ~ ( a3 @ X1 @ X4 )
| ~ ~ ( ~ ( likes @ X2 @ X3 @ X4 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a1 @ X4 @ Y0 )
| ( likes @ X2 @ X3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a2 @ X4 @ Y0 )
| ( likes @ X2 @ X3 @ Y0 ) ) ) ) )
| ( very_much_likes @ X2 @ X3 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f305]) ).
thf(f307,plain,
! [X2: mu,X3: mu,X1: $i,X4: $i] :
( ( $true
= ( ~ ~ ( ~ ( likes @ X2 @ X3 @ X4 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a1 @ X4 @ Y0 )
| ( likes @ X2 @ X3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a2 @ X4 @ Y0 )
| ( likes @ X2 @ X3 @ Y0 ) ) ) ) )
| ( very_much_likes @ X2 @ X3 @ X4 ) ) )
| ( $true
= ( ~ ( a3 @ X1 @ X4 ) ) ) ),
inference(or_proxy_clausification,[],[f306]) ).
thf(f308,plain,
! [X2: mu,X3: mu,X1: $i,X4: $i] :
( ( $true
= ( very_much_likes @ X2 @ X3 @ X4 ) )
| ( $true
= ( ~ ( a3 @ X1 @ X4 ) ) )
| ( $true
= ( ~ ~ ( ~ ( likes @ X2 @ X3 @ X4 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a1 @ X4 @ Y0 )
| ( likes @ X2 @ X3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a2 @ X4 @ Y0 )
| ( likes @ X2 @ X3 @ Y0 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f307]) ).
thf(f309,plain,
! [X2: mu,X3: mu,X1: $i,X4: $i] :
( ( $true
= ( very_much_likes @ X2 @ X3 @ X4 ) )
| ( $false
= ( a3 @ X1 @ X4 ) )
| ( $true
= ( ~ ~ ( ~ ( likes @ X2 @ X3 @ X4 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a1 @ X4 @ Y0 )
| ( likes @ X2 @ X3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a2 @ X4 @ Y0 )
| ( likes @ X2 @ X3 @ Y0 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f308]) ).
thf(f310,plain,
! [X2: mu,X3: mu,X1: $i,X4: $i] :
( ( $true
= ( very_much_likes @ X2 @ X3 @ X4 ) )
| ( $false
= ( a3 @ X1 @ X4 ) )
| ( $false
= ( ~ ( ~ ( likes @ X2 @ X3 @ X4 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a1 @ X4 @ Y0 )
| ( likes @ X2 @ X3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a2 @ X4 @ Y0 )
| ( likes @ X2 @ X3 @ Y0 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f309]) ).
thf(f311,plain,
! [X2: mu,X3: mu,X1: $i,X4: $i] :
( ( $true
= ( very_much_likes @ X2 @ X3 @ X4 ) )
| ( $false
= ( a3 @ X1 @ X4 ) )
| ( $true
= ( ~ ( likes @ X2 @ X3 @ X4 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a1 @ X4 @ Y0 )
| ( likes @ X2 @ X3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a2 @ X4 @ Y0 )
| ( likes @ X2 @ X3 @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f310]) ).
thf(f312,plain,
! [X2: mu,X3: mu,X1: $i,X4: $i] :
( ( $true
= ( very_much_likes @ X2 @ X3 @ X4 ) )
| ( $false
= ( a3 @ X1 @ X4 ) )
| ( $true
= ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a1 @ X4 @ Y0 )
| ( likes @ X2 @ X3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a2 @ X4 @ Y0 )
| ( likes @ X2 @ X3 @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( likes @ X2 @ X3 @ X4 ) ) ) ),
inference(or_proxy_clausification,[],[f311]) ).
thf(f313,plain,
! [X2: mu,X3: mu,X1: $i,X4: $i] :
( ( $true
= ( very_much_likes @ X2 @ X3 @ X4 ) )
| ( $false
= ( a3 @ X1 @ X4 ) )
| ( $false
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a1 @ X4 @ Y0 )
| ( likes @ X2 @ X3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a2 @ X4 @ Y0 )
| ( likes @ X2 @ X3 @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( likes @ X2 @ X3 @ X4 ) ) ) ),
inference(not_proxy_clausification,[],[f312]) ).
thf(f314,plain,
! [X2: mu,X3: mu,X1: $i,X4: $i] :
( ( $true
= ( very_much_likes @ X2 @ X3 @ X4 ) )
| ( $false
= ( a3 @ X1 @ X4 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a1 @ X4 @ Y0 )
| ( likes @ X2 @ X3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a2 @ X4 @ Y0 )
| ( likes @ X2 @ X3 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( likes @ X2 @ X3 @ X4 ) ) ) ),
inference(not_proxy_clausification,[],[f313]) ).
thf(f315,plain,
! [X2: mu,X3: mu,X1: $i,X4: $i] :
( ( $true
= ( very_much_likes @ X2 @ X3 @ X4 ) )
| ( $false
= ( a3 @ X1 @ X4 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a2 @ X4 @ Y0 )
| ( likes @ X2 @ X3 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( likes @ X2 @ X3 @ X4 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a1 @ X4 @ Y0 )
| ( likes @ X2 @ X3 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f314]) ).
thf(f316,plain,
! [X2: mu,X3: mu,X1: $i,X4: $i] :
( ( $true
= ( very_much_likes @ X2 @ X3 @ X4 ) )
| ( $false
= ( a3 @ X1 @ X4 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a2 @ X4 @ Y0 )
| ( likes @ X2 @ X3 @ Y0 ) ) ) )
| ( $true
= ( ~ ( likes @ X2 @ X3 @ X4 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a1 @ X4 @ Y0 )
| ( likes @ X2 @ X3 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f315]) ).
thf(f317,plain,
! [X2: mu,X3: mu,X1: $i,X4: $i] :
( ( $true
= ( very_much_likes @ X2 @ X3 @ X4 ) )
| ( $false
= ( a3 @ X1 @ X4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( a2 @ X4 @ Y0 )
| ( likes @ X2 @ X3 @ Y0 ) )
@ ( sK2 @ X3 @ X2 @ X4 ) ) )
| ( $true
= ( ~ ( likes @ X2 @ X3 @ X4 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a1 @ X4 @ Y0 )
| ( likes @ X2 @ X3 @ Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f316]) ).
thf(f318,plain,
! [X2: mu,X3: mu,X1: $i,X4: $i] :
( ( $true
= ( very_much_likes @ X2 @ X3 @ X4 ) )
| ( $false
= ( a3 @ X1 @ X4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( a2 @ X4 @ Y0 )
| ( likes @ X2 @ X3 @ Y0 ) )
@ ( sK2 @ X3 @ X2 @ X4 ) ) )
| ( $false
= ( likes @ X2 @ X3 @ X4 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a1 @ X4 @ Y0 )
| ( likes @ X2 @ X3 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f317]) ).
thf(f319,plain,
! [X2: mu,X3: mu,X1: $i,X4: $i] :
( ( $true
= ( very_much_likes @ X2 @ X3 @ X4 ) )
| ( $false
= ( a3 @ X1 @ X4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( a2 @ X4 @ Y0 )
| ( likes @ X2 @ X3 @ Y0 ) )
@ ( sK2 @ X3 @ X2 @ X4 ) ) )
| ( $false
= ( likes @ X2 @ X3 @ X4 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a1 @ X4 @ Y0 )
| ( likes @ X2 @ X3 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f318]) ).
thf(f320,plain,
! [X2: mu,X3: mu,X1: $i,X4: $i] :
( ( $true
= ( very_much_likes @ X2 @ X3 @ X4 ) )
| ( $false
= ( a3 @ X1 @ X4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( a2 @ X4 @ Y0 )
| ( likes @ X2 @ X3 @ Y0 ) )
@ ( sK2 @ X3 @ X2 @ X4 ) ) )
| ( $false
= ( likes @ X2 @ X3 @ X4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( a1 @ X4 @ Y0 )
| ( likes @ X2 @ X3 @ Y0 ) )
@ ( sK3 @ X3 @ X2 @ X4 ) ) ) ),
inference(sigma_proxy_clausification,[],[f319]) ).
thf(f321,plain,
! [X2: mu,X3: mu,X1: $i,X4: $i] :
( ( $true
= ( very_much_likes @ X2 @ X3 @ X4 ) )
| ( $false
= ( a3 @ X1 @ X4 ) )
| ( $false
= ( ~ ( a2 @ X4 @ ( sK2 @ X3 @ X2 @ X4 ) )
| ( likes @ X2 @ X3 @ ( sK2 @ X3 @ X2 @ X4 ) ) ) )
| ( $false
= ( likes @ X2 @ X3 @ X4 ) )
| ( $false
= ( ~ ( a1 @ X4 @ ( sK3 @ X3 @ X2 @ X4 ) )
| ( likes @ X2 @ X3 @ ( sK3 @ X3 @ X2 @ X4 ) ) ) ) ),
inference(beta-eta_normalization,[],[f320]) ).
thf(f322,plain,
! [X2: mu,X3: mu,X1: $i,X4: $i] :
( ( $true
= ( very_much_likes @ X2 @ X3 @ X4 ) )
| ( $false
= ( a3 @ X1 @ X4 ) )
| ( $false
= ( likes @ X2 @ X3 @ ( sK2 @ X3 @ X2 @ X4 ) ) )
| ( $false
= ( likes @ X2 @ X3 @ X4 ) )
| ( $false
= ( ~ ( a1 @ X4 @ ( sK3 @ X3 @ X2 @ X4 ) )
| ( likes @ X2 @ X3 @ ( sK3 @ X3 @ X2 @ X4 ) ) ) ) ),
inference(or_proxy_clausification,[],[f321]) ).
thf(f323,plain,
! [X2: mu,X3: mu,X1: $i,X4: $i] :
( ( $true
= ( very_much_likes @ X2 @ X3 @ X4 ) )
| ( $false
= ( a3 @ X1 @ X4 ) )
| ( $false
= ( ~ ( a2 @ X4 @ ( sK2 @ X3 @ X2 @ X4 ) ) ) )
| ( $false
= ( likes @ X2 @ X3 @ X4 ) )
| ( $false
= ( ~ ( a1 @ X4 @ ( sK3 @ X3 @ X2 @ X4 ) )
| ( likes @ X2 @ X3 @ ( sK3 @ X3 @ X2 @ X4 ) ) ) ) ),
inference(or_proxy_clausification,[],[f321]) ).
thf(f324,plain,
! [X2: mu,X3: mu,X1: $i,X4: $i] :
( ( $true
= ( very_much_likes @ X2 @ X3 @ X4 ) )
| ( $false
= ( a3 @ X1 @ X4 ) )
| ( $true
= ( a2 @ X4 @ ( sK2 @ X3 @ X2 @ X4 ) ) )
| ( $false
= ( likes @ X2 @ X3 @ X4 ) )
| ( $false
= ( ~ ( a1 @ X4 @ ( sK3 @ X3 @ X2 @ X4 ) )
| ( likes @ X2 @ X3 @ ( sK3 @ X3 @ X2 @ X4 ) ) ) ) ),
inference(not_proxy_clausification,[],[f323]) ).
thf(f325,plain,
! [X2: mu,X3: mu,X1: $i,X4: $i] :
( ( $false
= ( likes @ X2 @ X3 @ ( sK3 @ X3 @ X2 @ X4 ) ) )
| ( $true
= ( a2 @ X4 @ ( sK2 @ X3 @ X2 @ X4 ) ) )
| ( $false
= ( a3 @ X1 @ X4 ) )
| ( $false
= ( likes @ X2 @ X3 @ X4 ) )
| ( $true
= ( very_much_likes @ X2 @ X3 @ X4 ) ) ),
inference(or_proxy_clausification,[],[f324]) ).
thf(f326,plain,
! [X2: mu,X3: mu,X1: $i,X4: $i] :
( ( $true
= ( very_much_likes @ X2 @ X3 @ X4 ) )
| ( $false
= ( a3 @ X1 @ X4 ) )
| ( $true
= ( a2 @ X4 @ ( sK2 @ X3 @ X2 @ X4 ) ) )
| ( $false
= ( likes @ X2 @ X3 @ X4 ) )
| ( $false
= ( ~ ( a1 @ X4 @ ( sK3 @ X3 @ X2 @ X4 ) ) ) ) ),
inference(or_proxy_clausification,[],[f324]) ).
thf(f327,plain,
! [X2: mu,X3: mu,X1: $i,X4: $i] :
( ( $true
= ( a2 @ X4 @ ( sK2 @ X3 @ X2 @ X4 ) ) )
| ( $false
= ( a3 @ X1 @ X4 ) )
| ( $true
= ( very_much_likes @ X2 @ X3 @ X4 ) )
| ( $false
= ( likes @ X2 @ X3 @ X4 ) )
| ( $true
= ( a1 @ X4 @ ( sK3 @ X3 @ X2 @ X4 ) ) ) ),
inference(not_proxy_clausification,[],[f326]) ).
thf(f328,plain,
! [X2: mu,X3: mu,X1: $i,X4: $i] :
( ( $false
= ( likes @ X2 @ X3 @ ( sK3 @ X3 @ X2 @ X4 ) ) )
| ( $false
= ( a3 @ X1 @ X4 ) )
| ( $false
= ( likes @ X2 @ X3 @ ( sK2 @ X3 @ X2 @ X4 ) ) )
| ( $false
= ( likes @ X2 @ X3 @ X4 ) )
| ( $true
= ( very_much_likes @ X2 @ X3 @ X4 ) ) ),
inference(or_proxy_clausification,[],[f322]) ).
thf(f329,plain,
! [X2: mu,X3: mu,X1: $i,X4: $i] :
( ( $true
= ( very_much_likes @ X2 @ X3 @ X4 ) )
| ( $false
= ( a3 @ X1 @ X4 ) )
| ( $false
= ( likes @ X2 @ X3 @ ( sK2 @ X3 @ X2 @ X4 ) ) )
| ( $false
= ( likes @ X2 @ X3 @ X4 ) )
| ( $false
= ( ~ ( a1 @ X4 @ ( sK3 @ X3 @ X2 @ X4 ) ) ) ) ),
inference(or_proxy_clausification,[],[f322]) ).
thf(f330,plain,
! [X2: mu,X3: mu,X1: $i,X4: $i] :
( ( $false
= ( likes @ X2 @ X3 @ ( sK2 @ X3 @ X2 @ X4 ) ) )
| ( $true
= ( a1 @ X4 @ ( sK3 @ X3 @ X2 @ X4 ) ) )
| ( $false
= ( a3 @ X1 @ X4 ) )
| ( $false
= ( likes @ X2 @ X3 @ X4 ) )
| ( $true
= ( very_much_likes @ X2 @ X3 @ X4 ) ) ),
inference(not_proxy_clausification,[],[f329]) ).
thf(f341,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a3 @ Y0 @ Y1 )
| ~ ( likes @ piotr @ pepsi @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f213]) ).
thf(f342,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a3 @ Y0 @ Y1 )
| ~ ( likes @ piotr @ pepsi @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f341]) ).
thf(f343,plain,
! [X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a3 @ X1 @ Y0 )
| ~ ( likes @ piotr @ pepsi @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f342]) ).
thf(f344,plain,
! [X1: $i] :
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a3 @ X1 @ Y0 )
| ~ ( likes @ piotr @ pepsi @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f343]) ).
thf(f345,plain,
! [X1: $i] :
( $false
= ( ^ [Y0: $i] :
( ~ ( a3 @ X1 @ Y0 )
| ~ ( likes @ piotr @ pepsi @ Y0 ) )
@ ( sK5 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f344]) ).
thf(f346,plain,
! [X1: $i] :
( $false
= ( ~ ( a3 @ X1 @ ( sK5 @ X1 ) )
| ~ ( likes @ piotr @ pepsi @ ( sK5 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f345]) ).
thf(f348,plain,
! [X1: $i] :
( $false
= ( ~ ( a3 @ X1 @ ( sK5 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f346]) ).
thf(f349,plain,
! [X1: $i] :
( $true
= ( a3 @ X1 @ ( sK5 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f348]) ).
thf(f351,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a3 @ Y0 @ Y1 )
| ( likes @ jan @ cola @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f212]) ).
thf(f352,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a3 @ Y0 @ Y1 )
| ( likes @ jan @ cola @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f351]) ).
thf(f353,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a3 @ X1 @ Y0 )
| ( likes @ jan @ cola @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f352]) ).
thf(f354,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( a3 @ X1 @ Y0 )
| ( likes @ jan @ cola @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f353]) ).
thf(f355,plain,
! [X2: $i,X1: $i] :
( $true
= ( ~ ( a3 @ X1 @ X2 )
| ( likes @ jan @ cola @ X2 ) ) ),
inference(beta-eta_normalization,[],[f354]) ).
thf(f356,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( likes @ jan @ cola @ X2 ) )
| ( $true
= ( ~ ( a3 @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f355]) ).
thf(f357,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( likes @ jan @ cola @ X2 ) )
| ( $false
= ( a3 @ X1 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f356]) ).
thf(f369,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( a2 @ Y0 @ Y2 )
| ~ ( likes @ Y1 @ pepsi @ Y2 )
| ( likes @ Y1 @ cola @ Y2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f210]) ).
thf(f370,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( a2 @ Y0 @ Y2 )
| ~ ( likes @ Y1 @ pepsi @ Y2 )
| ( likes @ Y1 @ cola @ Y2 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f369]) ).
thf(f371,plain,
! [X1: $i] :
( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a2 @ X1 @ Y1 )
| ~ ( likes @ Y0 @ pepsi @ Y1 )
| ( likes @ Y0 @ cola @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f370]) ).
thf(f372,plain,
! [X2: mu,X1: $i] :
( $true
= ( ^ [Y0: mu] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a2 @ X1 @ Y1 )
| ~ ( likes @ Y0 @ pepsi @ Y1 )
| ( likes @ Y0 @ cola @ Y1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f371]) ).
thf(f373,plain,
! [X2: mu,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a2 @ X1 @ Y0 )
| ~ ( likes @ X2 @ pepsi @ Y0 )
| ( likes @ X2 @ cola @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f372]) ).
thf(f374,plain,
! [X2: mu,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( a2 @ X1 @ Y0 )
| ~ ( likes @ X2 @ pepsi @ Y0 )
| ( likes @ X2 @ cola @ Y0 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f373]) ).
thf(f375,plain,
! [X2: mu,X3: $i,X1: $i] :
( $true
= ( ~ ( a2 @ X1 @ X3 )
| ~ ( likes @ X2 @ pepsi @ X3 )
| ( likes @ X2 @ cola @ X3 ) ) ),
inference(beta-eta_normalization,[],[f374]) ).
thf(f376,plain,
! [X2: mu,X3: $i,X1: $i] :
( ( $true
= ( ~ ( likes @ X2 @ pepsi @ X3 )
| ( likes @ X2 @ cola @ X3 ) ) )
| ( $true
= ( ~ ( a2 @ X1 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f375]) ).
thf(f377,plain,
! [X2: mu,X3: $i,X1: $i] :
( ( $true
= ( likes @ X2 @ cola @ X3 ) )
| ( $true
= ( ~ ( a2 @ X1 @ X3 ) ) )
| ( $true
= ( ~ ( likes @ X2 @ pepsi @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f376]) ).
thf(f378,plain,
! [X2: mu,X3: $i,X1: $i] :
( ( $true
= ( likes @ X2 @ cola @ X3 ) )
| ( $false
= ( a2 @ X1 @ X3 ) )
| ( $true
= ( ~ ( likes @ X2 @ pepsi @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f377]) ).
thf(f379,plain,
! [X2: mu,X3: $i,X1: $i] :
( ( $false
= ( likes @ X2 @ pepsi @ X3 ) )
| ( $false
= ( a2 @ X1 @ X3 ) )
| ( $true
= ( likes @ X2 @ cola @ X3 ) ) ),
inference(not_proxy_clausification,[],[f378]) ).
thf(f394,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a2 @ Y0 @ Y1 )
| ( likes @ jan @ pepsi @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f207]) ).
thf(f395,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a2 @ Y0 @ Y1 )
| ( likes @ jan @ pepsi @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f394]) ).
thf(f396,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a2 @ X1 @ Y0 )
| ( likes @ jan @ pepsi @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f395]) ).
thf(f397,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( a2 @ X1 @ Y0 )
| ( likes @ jan @ pepsi @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f396]) ).
thf(f398,plain,
! [X2: $i,X1: $i] :
( $true
= ( ~ ( a2 @ X1 @ X2 )
| ( likes @ jan @ pepsi @ X2 ) ) ),
inference(beta-eta_normalization,[],[f397]) ).
thf(f399,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( likes @ jan @ pepsi @ X2 ) )
| ( $true
= ( ~ ( a2 @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f398]) ).
thf(f400,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( likes @ jan @ pepsi @ X2 ) )
| ( $false
= ( a2 @ X1 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f399]) ).
thf(f442,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a1 @ Y0 @ Y1 )
| ( likes @ jan @ cola @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f203]) ).
thf(f443,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a1 @ Y0 @ Y1 )
| ( likes @ jan @ cola @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f442]) ).
thf(f444,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a1 @ X1 @ Y0 )
| ( likes @ jan @ cola @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f443]) ).
thf(f445,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( a1 @ X1 @ Y0 )
| ( likes @ jan @ cola @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f444]) ).
thf(f446,plain,
! [X2: $i,X1: $i] :
( $true
= ( ~ ( a1 @ X1 @ X2 )
| ( likes @ jan @ cola @ X2 ) ) ),
inference(beta-eta_normalization,[],[f445]) ).
thf(f447,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( likes @ jan @ cola @ X2 ) )
| ( $true
= ( ~ ( a1 @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f446]) ).
thf(f448,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( likes @ jan @ cola @ X2 ) )
| ( $false
= ( a1 @ X1 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f447]) ).
thf(f488,definition,
( spl6_3
<=> ! [X2: $i] :
( $true
= ( likes @ jan @ cola @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
thf(f489,plain,
( ! [X2: $i] :
( $true
= ( likes @ jan @ cola @ X2 ) )
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f488]) ).
thf(f495,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( likes @ jan @ cola @ ( sK5 @ X0 ) ) ) ),
inference(constrained_superposition,[],[f349,f357]) ).
thf(f496,plain,
! [X0: $i] :
( $true
= ( likes @ jan @ cola @ ( sK5 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f495]) ).
thf(f722,plain,
! [X2: mu,X0: $i,X1: mu] :
( ( $true = $false )
| ( $true
= ( likes @ X1 @ X2 @ X0 ) )
| ( $false
= ( very_much_likes @ X1 @ X2 @ ( sK5 @ X0 ) ) ) ),
inference(constrained_superposition,[],[f349,f283]) ).
thf(f727,plain,
! [X2: mu,X0: $i,X1: mu] :
( ( $false
= ( very_much_likes @ X1 @ X2 @ ( sK5 @ X0 ) ) )
| ( $true
= ( likes @ X1 @ X2 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f722]) ).
thf(f1309,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( a2 @ X1 @ X0 ) )
| ( $false
= ( a2 @ X2 @ X0 ) )
| ( $true
= ( likes @ jan @ cola @ X0 ) ) ),
inference(constrained_superposition,[],[f400,f379]) ).
thf(f1322,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( a2 @ X1 @ X0 ) )
| ( $false
= ( a2 @ X2 @ X0 ) )
| ( $true
= ( likes @ jan @ cola @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1309]) ).
thf(f1462,plain,
( ! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( a3 @ X1 @ X0 ) )
| ( $false
= ( likes @ jan @ cola @ ( sK2 @ cola @ jan @ X0 ) ) )
| ( $false
= ( likes @ jan @ cola @ X0 ) )
| ( $true
= ( very_much_likes @ jan @ cola @ X0 ) ) )
| ~ spl6_3 ),
inference(constrained_superposition,[],[f489,f328]) ).
thf(f1497,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( a3 @ X1 @ X0 ) )
| ( $false
= ( likes @ jan @ cola @ ( sK2 @ cola @ jan @ X0 ) ) )
| ( $false
= ( likes @ jan @ cola @ X0 ) )
| ( $true
= ( very_much_likes @ jan @ cola @ X0 ) ) )
| ~ spl6_3 ),
inference(trivial_inequality_removal,[],[f1462]) ).
thf(f1550,plain,
( ! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( a3 @ X1 @ X0 ) )
| ( $false
= ( likes @ jan @ cola @ X0 ) )
| ( $true
= ( very_much_likes @ jan @ cola @ X0 ) ) )
| ~ spl6_3 ),
inference(forward_demodulation,[],[f1497,f489]) ).
thf(f1551,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( a3 @ X1 @ X0 ) )
| ( $false
= ( likes @ jan @ cola @ X0 ) )
| ( $true
= ( very_much_likes @ jan @ cola @ X0 ) ) )
| ~ spl6_3 ),
inference(trivial_inequality_removal,[],[f1550]) ).
thf(f1612,plain,
( ! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( a3 @ X1 @ X0 ) )
| ( $true
= ( very_much_likes @ jan @ cola @ X0 ) ) )
| ~ spl6_3 ),
inference(forward_demodulation,[],[f1551,f489]) ).
thf(f1613,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( a3 @ X1 @ X0 ) )
| ( $true
= ( very_much_likes @ jan @ cola @ X0 ) ) )
| ~ spl6_3 ),
inference(trivial_inequality_removal,[],[f1612]) ).
thf(f1651,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( a3 @ X1 @ X0 ) )
| ( $true
= ( very_much_likes @ jan @ cola @ X0 ) ) )
| ~ spl6_3 ),
inference(global_subsumption,[],[f1613]) ).
thf(f1893,definition,
( spl6_34
<=> ! [X0: $i] :
( $true
= ( very_much_likes @ jan @ cola @ X0 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_34])],[avatar_definition]) ).
thf(f1894,plain,
( ! [X0: $i] :
( $true
= ( very_much_likes @ jan @ cola @ X0 ) )
| ~ spl6_34 ),
inference(avatar_component_clause,[],[f1893]) ).
thf(f1906,plain,
( ! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $true
= ( very_much_likes @ jan @ cola @ X0 ) )
| ( $false
= ( a3 @ X1 @ ( sK1 @ cola @ X0 @ jan ) ) ) )
| ~ spl6_3 ),
inference(constrained_superposition,[],[f295,f1651]) ).
thf(f1909,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( a3 @ X1 @ ( sK1 @ cola @ X0 @ jan ) ) )
| ( $true
= ( very_much_likes @ jan @ cola @ X0 ) ) )
| ~ spl6_3 ),
inference(trivial_inequality_removal,[],[f1906]) ).
thf(f1926,plain,
( ( $true = $false )
| ~ spl6_34 ),
inference(constrained_superposition,[],[f1894,f223]) ).
thf(f1936,plain,
( $false
| ~ spl6_34 ),
inference(trivial_inequality_removal,[],[f1926]) ).
thf(f1937,plain,
~ spl6_34,
inference(avatar_contradiction_clause,[],[f1936]) ).
thf(f2004,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( very_much_likes @ jan @ cola @ X0 ) )
| ( $true
= ( very_much_likes @ jan @ cola @ X0 ) ) )
| ~ spl6_3 ),
inference(constrained_superposition,[],[f297,f1909]) ).
thf(f2005,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( very_much_likes @ jan @ cola @ X0 ) ) )
| ~ spl6_3 ),
inference(duplicate_literal_removal,[],[f2004]) ).
thf(f2006,plain,
( ! [X0: $i] :
( $true
= ( very_much_likes @ jan @ cola @ X0 ) )
| ~ spl6_3 ),
inference(trivial_inequality_removal,[],[f2005]) ).
thf(f2010,plain,
( spl6_34
| ~ spl6_3 ),
inference(avatar_split_clause,[],[f2006,f488,f1893]) ).
thf(f5792,definition,
( spl6_70
<=> ! [X0: $i] :
( $true
= ( very_much_likes @ jan @ cola @ ( sK5 @ X0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl6_70])],[avatar_definition]) ).
thf(f5793,plain,
( ! [X0: $i] :
( $true
= ( very_much_likes @ jan @ cola @ ( sK5 @ X0 ) ) )
| ~ spl6_70 ),
inference(avatar_component_clause,[],[f5792]) ).
thf(f5822,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( likes @ jan @ cola @ X0 ) ) )
| ~ spl6_70 ),
inference(constrained_superposition,[],[f727,f5793]) ).
thf(f5823,plain,
( ! [X0: $i] :
( $true
= ( likes @ jan @ cola @ X0 ) )
| ~ spl6_70 ),
inference(trivial_inequality_removal,[],[f5822]) ).
thf(f5829,plain,
( spl6_3
| ~ spl6_70 ),
inference(avatar_split_clause,[],[f5823,f5792,f488]) ).
thf(f8500,plain,
! [X0: $i,X1: $i] :
( ( $false != $false )
| ( $false
= ( a2 @ X0 @ X1 ) )
| ( $true
= ( likes @ jan @ cola @ X1 ) ) ),
inference(equality_factoring,[],[f1322]) ).
thf(f8501,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( a2 @ X0 @ X1 ) )
| ( $true
= ( likes @ jan @ cola @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f8500]) ).
thf(f8565,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $true
= ( a1 @ X0 @ ( sK3 @ cola @ jan @ X0 ) ) )
| ( $false
= ( a3 @ X1 @ X0 ) )
| ( $false
= ( likes @ jan @ cola @ X0 ) )
| ( $true
= ( very_much_likes @ jan @ cola @ X0 ) )
| ( $false
= ( a2 @ X2 @ ( sK2 @ cola @ jan @ X0 ) ) ) ),
inference(constrained_superposition,[],[f330,f8501]) ).
thf(f8570,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( a1 @ X0 @ ( sK3 @ cola @ jan @ X0 ) ) )
| ( $false
= ( a2 @ X2 @ ( sK2 @ cola @ jan @ X0 ) ) )
| ( $false
= ( a3 @ X1 @ X0 ) )
| ( $true
= ( very_much_likes @ jan @ cola @ X0 ) )
| ( $false
= ( likes @ jan @ cola @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f8565]) ).
thf(f18523,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( a3 @ X1 @ X0 ) )
| ( $true
= ( very_much_likes @ jan @ cola @ X0 ) )
| ( $false
= ( likes @ jan @ cola @ X0 ) )
| ( $true
= ( a1 @ X0 @ ( sK3 @ cola @ jan @ X0 ) ) )
| ( $true
= ( a1 @ X0 @ ( sK3 @ cola @ jan @ X0 ) ) )
| ( $false
= ( a3 @ X2 @ X0 ) )
| ( $true
= ( very_much_likes @ jan @ cola @ X0 ) )
| ( $false
= ( likes @ jan @ cola @ X0 ) ) ),
inference(constrained_superposition,[],[f327,f8570]) ).
thf(f18527,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( a3 @ X1 @ X0 ) )
| ( $true
= ( very_much_likes @ jan @ cola @ X0 ) )
| ( $false
= ( likes @ jan @ cola @ X0 ) )
| ( $true
= ( a1 @ X0 @ ( sK3 @ cola @ jan @ X0 ) ) )
| ( $false
= ( a3 @ X2 @ X0 ) ) ),
inference(duplicate_literal_removal,[],[f18523]) ).
thf(f18528,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( a3 @ X1 @ X0 ) )
| ( $true
= ( very_much_likes @ jan @ cola @ X0 ) )
| ( $false
= ( likes @ jan @ cola @ X0 ) )
| ( $true
= ( a1 @ X0 @ ( sK3 @ cola @ jan @ X0 ) ) )
| ( $false
= ( a3 @ X2 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f18527]) ).
thf(f18577,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( a1 @ X0 @ ( sK3 @ cola @ jan @ X0 ) ) )
| ( $false
= ( a3 @ X2 @ X0 ) )
| ( $false
= ( a3 @ X1 @ X0 ) )
| ( $true
= ( very_much_likes @ jan @ cola @ X0 ) )
| ( $false
= ( likes @ jan @ cola @ X0 ) ) ),
inference(global_subsumption,[],[f18528]) ).
thf(f18941,plain,
! [X0: $i,X1: $i] :
( ( $false != $false )
| ( $true
= ( a1 @ X1 @ ( sK3 @ cola @ jan @ X1 ) ) )
| ( $false
= ( a3 @ X0 @ X1 ) )
| ( $true
= ( very_much_likes @ jan @ cola @ X1 ) )
| ( $false
= ( likes @ jan @ cola @ X1 ) ) ),
inference(equality_factoring,[],[f18577]) ).
thf(f18942,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( a1 @ X1 @ ( sK3 @ cola @ jan @ X1 ) ) )
| ( $false
= ( a3 @ X0 @ X1 ) )
| ( $true
= ( very_much_likes @ jan @ cola @ X1 ) )
| ( $false
= ( likes @ jan @ cola @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f18941]) ).
thf(f19865,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $true
= ( likes @ jan @ cola @ ( sK3 @ cola @ jan @ X0 ) ) )
| ( $false
= ( a3 @ X1 @ X0 ) )
| ( $true
= ( very_much_likes @ jan @ cola @ X0 ) )
| ( $false
= ( likes @ jan @ cola @ X0 ) ) ),
inference(constrained_superposition,[],[f448,f18942]) ).
thf(f19888,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( likes @ jan @ cola @ ( sK3 @ cola @ jan @ X0 ) ) )
| ( $false
= ( a3 @ X1 @ X0 ) )
| ( $true
= ( very_much_likes @ jan @ cola @ X0 ) )
| ( $false
= ( likes @ jan @ cola @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f19865]) ).
thf(f21171,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( likes @ jan @ cola @ ( sK3 @ cola @ jan @ ( sK5 @ X0 ) ) ) )
| ( $true
= ( very_much_likes @ jan @ cola @ ( sK5 @ X0 ) ) )
| ( $false
= ( likes @ jan @ cola @ ( sK5 @ X0 ) ) ) ),
inference(constrained_superposition,[],[f349,f19888]) ).
thf(f21174,plain,
! [X0: $i] :
( ( $true
= ( likes @ jan @ cola @ ( sK3 @ cola @ jan @ ( sK5 @ X0 ) ) ) )
| ( $true
= ( very_much_likes @ jan @ cola @ ( sK5 @ X0 ) ) )
| ( $false
= ( likes @ jan @ cola @ ( sK5 @ X0 ) ) ) ),
inference(trivial_inequality_removal,[],[f21171]) ).
thf(f21196,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( likes @ jan @ cola @ ( sK3 @ cola @ jan @ ( sK5 @ X0 ) ) ) )
| ( $true
= ( very_much_likes @ jan @ cola @ ( sK5 @ X0 ) ) ) ),
inference(forward_demodulation,[],[f21174,f496]) ).
thf(f21197,plain,
! [X0: $i] :
( ( $true
= ( likes @ jan @ cola @ ( sK3 @ cola @ jan @ ( sK5 @ X0 ) ) ) )
| ( $true
= ( very_much_likes @ jan @ cola @ ( sK5 @ X0 ) ) ) ),
inference(trivial_inequality_removal,[],[f21196]) ).
thf(f21315,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $true
= ( a2 @ ( sK5 @ X0 ) @ ( sK2 @ cola @ jan @ ( sK5 @ X0 ) ) ) )
| ( $false
= ( a3 @ X1 @ ( sK5 @ X0 ) ) )
| ( $false
= ( likes @ jan @ cola @ ( sK5 @ X0 ) ) )
| ( $true
= ( very_much_likes @ jan @ cola @ ( sK5 @ X0 ) ) )
| ( $true
= ( very_much_likes @ jan @ cola @ ( sK5 @ X0 ) ) ) ),
inference(constrained_superposition,[],[f325,f21197]) ).
thf(f21316,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( a3 @ X1 @ ( sK5 @ X0 ) ) )
| ( $false
= ( likes @ jan @ cola @ ( sK2 @ cola @ jan @ ( sK5 @ X0 ) ) ) )
| ( $false
= ( likes @ jan @ cola @ ( sK5 @ X0 ) ) )
| ( $true
= ( very_much_likes @ jan @ cola @ ( sK5 @ X0 ) ) )
| ( $true
= ( very_much_likes @ jan @ cola @ ( sK5 @ X0 ) ) ) ),
inference(constrained_superposition,[],[f328,f21197]) ).
thf(f21317,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( a3 @ X1 @ ( sK5 @ X0 ) ) )
| ( $false
= ( likes @ jan @ cola @ ( sK2 @ cola @ jan @ ( sK5 @ X0 ) ) ) )
| ( $false
= ( likes @ jan @ cola @ ( sK5 @ X0 ) ) )
| ( $true
= ( very_much_likes @ jan @ cola @ ( sK5 @ X0 ) ) ) ),
inference(duplicate_literal_removal,[],[f21316]) ).
thf(f21318,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( a3 @ X1 @ ( sK5 @ X0 ) ) )
| ( $false
= ( likes @ jan @ cola @ ( sK2 @ cola @ jan @ ( sK5 @ X0 ) ) ) )
| ( $false
= ( likes @ jan @ cola @ ( sK5 @ X0 ) ) )
| ( $true
= ( very_much_likes @ jan @ cola @ ( sK5 @ X0 ) ) ) ),
inference(trivial_inequality_removal,[],[f21317]) ).
thf(f21319,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $true
= ( a2 @ ( sK5 @ X0 ) @ ( sK2 @ cola @ jan @ ( sK5 @ X0 ) ) ) )
| ( $false
= ( a3 @ X1 @ ( sK5 @ X0 ) ) )
| ( $false
= ( likes @ jan @ cola @ ( sK5 @ X0 ) ) )
| ( $true
= ( very_much_likes @ jan @ cola @ ( sK5 @ X0 ) ) ) ),
inference(duplicate_literal_removal,[],[f21315]) ).
thf(f21320,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( a2 @ ( sK5 @ X0 ) @ ( sK2 @ cola @ jan @ ( sK5 @ X0 ) ) ) )
| ( $false
= ( a3 @ X1 @ ( sK5 @ X0 ) ) )
| ( $false
= ( likes @ jan @ cola @ ( sK5 @ X0 ) ) )
| ( $true
= ( very_much_likes @ jan @ cola @ ( sK5 @ X0 ) ) ) ),
inference(trivial_inequality_removal,[],[f21319]) ).
thf(f21335,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $true
= ( a2 @ ( sK5 @ X0 ) @ ( sK2 @ cola @ jan @ ( sK5 @ X0 ) ) ) )
| ( $false
= ( a3 @ X1 @ ( sK5 @ X0 ) ) )
| ( $true
= ( very_much_likes @ jan @ cola @ ( sK5 @ X0 ) ) ) ),
inference(forward_demodulation,[],[f21320,f496]) ).
thf(f21336,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( a2 @ ( sK5 @ X0 ) @ ( sK2 @ cola @ jan @ ( sK5 @ X0 ) ) ) )
| ( $false
= ( a3 @ X1 @ ( sK5 @ X0 ) ) )
| ( $true
= ( very_much_likes @ jan @ cola @ ( sK5 @ X0 ) ) ) ),
inference(trivial_inequality_removal,[],[f21335]) ).
thf(f21372,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( a3 @ X1 @ ( sK5 @ X0 ) ) )
| ( $false
= ( likes @ jan @ cola @ ( sK2 @ cola @ jan @ ( sK5 @ X0 ) ) ) )
| ( $true
= ( very_much_likes @ jan @ cola @ ( sK5 @ X0 ) ) ) ),
inference(forward_demodulation,[],[f21318,f496]) ).
thf(f21373,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( likes @ jan @ cola @ ( sK2 @ cola @ jan @ ( sK5 @ X0 ) ) ) )
| ( $false
= ( a3 @ X1 @ ( sK5 @ X0 ) ) )
| ( $true
= ( very_much_likes @ jan @ cola @ ( sK5 @ X0 ) ) ) ),
inference(trivial_inequality_removal,[],[f21372]) ).
thf(f21451,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( likes @ jan @ cola @ ( sK2 @ cola @ jan @ ( sK5 @ X0 ) ) ) )
| ( $true
= ( very_much_likes @ jan @ cola @ ( sK5 @ X0 ) ) ) ),
inference(constrained_superposition,[],[f349,f21373]) ).
thf(f21452,plain,
! [X0: $i] :
( ( $false
= ( likes @ jan @ cola @ ( sK2 @ cola @ jan @ ( sK5 @ X0 ) ) ) )
| ( $true
= ( very_much_likes @ jan @ cola @ ( sK5 @ X0 ) ) ) ),
inference(trivial_inequality_removal,[],[f21451]) ).
thf(f21481,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( a2 @ X1 @ ( sK2 @ cola @ jan @ ( sK5 @ X0 ) ) ) )
| ( $true
= ( very_much_likes @ jan @ cola @ ( sK5 @ X0 ) ) ) ),
inference(constrained_superposition,[],[f8501,f21452]) ).
thf(f21496,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( a2 @ X1 @ ( sK2 @ cola @ jan @ ( sK5 @ X0 ) ) ) )
| ( $true
= ( very_much_likes @ jan @ cola @ ( sK5 @ X0 ) ) ) ),
inference(trivial_inequality_removal,[],[f21481]) ).
thf(f21514,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( a3 @ X1 @ ( sK5 @ X0 ) ) )
| ( $true
= ( very_much_likes @ jan @ cola @ ( sK5 @ X0 ) ) )
| ( $true
= ( very_much_likes @ jan @ cola @ ( sK5 @ X0 ) ) ) ),
inference(constrained_superposition,[],[f21336,f21496]) ).
thf(f21515,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( a3 @ X1 @ ( sK5 @ X0 ) ) )
| ( $true
= ( very_much_likes @ jan @ cola @ ( sK5 @ X0 ) ) ) ),
inference(duplicate_literal_removal,[],[f21514]) ).
thf(f21516,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( a3 @ X1 @ ( sK5 @ X0 ) ) )
| ( $true
= ( very_much_likes @ jan @ cola @ ( sK5 @ X0 ) ) ) ),
inference(trivial_inequality_removal,[],[f21515]) ).
thf(f21551,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( very_much_likes @ jan @ cola @ ( sK5 @ X0 ) ) ) ),
inference(constrained_superposition,[],[f349,f21516]) ).
thf(f21562,plain,
! [X0: $i] :
( $true
= ( very_much_likes @ jan @ cola @ ( sK5 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f21551]) ).
thf(f21570,plain,
spl6_70,
inference(avatar_split_clause,[],[f21562,f5792]) ).
cnf(s533,plain,
~ spl6_34,
inference(sat_conversion,[],[f1937]) ).
cnf(s561,plain,
( ~ spl6_3
| spl6_34 ),
inference(sat_conversion,[],[f2010]) ).
cnf(s1852,plain,
( spl6_3
| ~ spl6_70 ),
inference(sat_conversion,[],[f5829]) ).
cnf(s6347,plain,
spl6_70,
inference(sat_conversion,[],[f21570]) ).
cnf(s6348,plain,
spl6_3,
inference(rat,[],[s1852,s6347]) ).
cnf(s6349,plain,
spl6_34,
inference(rat,[],[s561,s6348]) ).
cnf(s6350,plain,
$false,
inference(rat,[],[s533,s6349]) ).
thf(f21571,plain,
$false,
inference(avatar_sat_refutation,[],[s6350]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : AGT034^2 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n009.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 17:30:46 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 4.25/0.95 % (110392)Will run a generic schedule for satisfiability detection.
% 4.25/0.95 % (110399)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1705848744:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 4.25/0.95 % (110398)% WARNING: option uhcvi not known.
% 4.25/0.95 % (110397)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=488027623_2999 on theBenchmark for (2999ds/0Mi)
% 4.25/0.95 % (110398)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3082513841:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 4.25/0.95 % (110401)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1446511210:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 4.25/0.95 % (110400)dis+10_1_sil=32000:sp=arity:random_seed=1549270541:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 4.25/0.95 % (110402)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3334952583:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 4.25/0.95 % (110403)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=71684342:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 4.25/0.95 % (110398)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.25/0.95 % (110401)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.25/0.95 % Exception at run slice level
% 4.25/0.95 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.25/0.95 % (110398)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 4.25/0.95 % (110411)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=4000124345:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 4.25/0.95 % Exception at run slice level
% 4.25/0.95 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.25/0.95 % (110400)Instruction limit reached!
% 4.25/0.95 % (110400)------------------------------
% 4.25/0.95 % (110400)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.25/0.95 % (110400)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/0.95 % (110400)CaDiCaL version: 2.1.3
% 4.25/0.95 % (110400)Termination reason: Instruction limit
% 4.25/0.95 % (110400)Termination phase: Saturation
% 4.25/0.95 % (110400)Time elapsed: 0.049 s
% 4.25/0.95 % (110400)Peak memory usage: 12 MB
% 4.25/0.95 % (110400)Instructions burned: 103 (million)
% 4.25/0.95 % (110413)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3050711718:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 4.25/0.95 % (110401)Instruction limit reached!
% 4.25/0.95 % (110401)------------------------------
% 4.25/0.95 % (110401)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.25/0.95 % (110401)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/0.95 % (110401)CaDiCaL version: 2.1.3
% 4.25/0.95 % (110401)Termination reason: Instruction limit
% 4.25/0.95 % (110401)Termination phase: Saturation
% 4.25/0.95 % (110401)Time elapsed: 0.056 s
% 4.25/0.95 % (110401)Peak memory usage: 12 MB
% 4.25/0.95 % (110401)Instructions burned: 117 (million)
% 4.25/0.95 % (110402)Instruction limit reached!
% 4.25/0.95 % (110402)------------------------------
% 4.25/0.95 % (110402)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.25/0.95 % (110402)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/0.95 % (110402)CaDiCaL version: 2.1.3
% 4.25/0.95 % (110402)Termination reason: Instruction limit
% 4.25/0.95 % (110402)Termination phase: Saturation
% 4.25/0.95 % (110402)Time elapsed: 0.062 s
% 4.25/0.95 % (110402)Peak memory usage: 12 MB
% 4.25/0.95 % (110402)Instructions burned: 131 (million)
% 4.25/0.95 % (110414)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=1428293087:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 4.25/0.95 % (110414)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.25/0.95 % (110416)ott-21_1_sil=16000:fs=off:random_seed=2753699870:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 4.25/0.95 % (110414)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 4.25/0.95 % (110403)Instruction limit reached!
% 4.25/0.95 % (110403)------------------------------
% 5.73/1.06 % (110403)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.73/1.06 % (110403)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.73/1.06 % (110403)CaDiCaL version: 2.1.3
% 5.73/1.06 % (110403)Termination reason: Instruction limit
% 5.73/1.06 % (110403)Termination phase: Saturation
% 5.73/1.06 % (110403)Time elapsed: 0.079 s
% 5.73/1.06 % (110403)Peak memory usage: 12 MB
% 5.73/1.06 % (110403)Instructions burned: 160 (million)
% 5.73/1.06 % (110417)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=4282337592:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 5.73/1.06 % (110425)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=4158524552:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 5.73/1.06 % Exception at run slice level
% 5.73/1.06 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.73/1.06 % (110413)Instruction limit reached!
% 5.73/1.06 % (110413)------------------------------
% 5.73/1.06 % (110413)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.73/1.06 % (110413)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.73/1.06 % (110413)CaDiCaL version: 2.1.3
% 5.73/1.06 % (110413)Termination reason: Instruction limit
% 5.73/1.06 % (110413)Termination phase: Saturation
% 5.73/1.06 % (110413)Time elapsed: 0.070 s
% 5.73/1.06 % (110413)Peak memory usage: 12 MB
% 5.73/1.06 % (110413)Instructions burned: 132 (million)
% 5.73/1.06 % (110436)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1044701754:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 5.73/1.06 % (110450)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3124729784:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 5.73/1.06 % Exception at run slice level
% 5.73/1.06 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.73/1.06 % (110416)Instruction limit reached!
% 5.73/1.06 % (110416)------------------------------
% 5.73/1.06 % (110416)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.73/1.06 % (110416)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.73/1.06 % (110416)CaDiCaL version: 2.1.3
% 5.73/1.06 % (110416)Termination reason: Instruction limit
% 5.73/1.06 % (110416)Termination phase: Saturation
% 5.73/1.06 % (110416)Time elapsed: 0.083 s
% 5.73/1.06 % (110416)Peak memory usage: 12 MB
% 5.73/1.06 % (110416)Instructions burned: 181 (million)
% 5.73/1.06 % (110468)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=1828916779:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 5.73/1.06 % (110468)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.73/1.06 % (110471)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=2081086748:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 5.73/1.06 % (110471)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.73/1.06 % (110417)Instruction limit reached!
% 5.73/1.06 % (110417)------------------------------
% 5.73/1.06 % (110417)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.73/1.06 % (110417)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.73/1.06 % (110417)CaDiCaL version: 2.1.3
% 5.73/1.06 % (110417)Termination reason: Instruction limit
% 5.73/1.06 % (110417)Termination phase: Saturation
% 5.73/1.06 % (110417)Time elapsed: 0.259 s
% 5.73/1.06 % (110417)Peak memory usage: 13 MB
% 5.73/1.06 % (110417)Instructions burned: 477 (million)
% 5.73/1.06 % (110478)fmb+10_1_sil=64000:random_seed=428387733:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 5.73/1.06 % (110478)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 5.73/1.06 % Exception at run slice level
% 5.73/1.06 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.73/1.06 % (110480)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=1460465294:i=9515:nm=5_2996 on theBenchmark for (2996ds/9515Mi)
% 5.73/1.06 % (110414)Instruction limit reached!
% 5.73/1.06 % (110414)------------------------------
% 5.73/1.06 % (110414)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.73/1.06 % (110414)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.73/1.06 % (110414)CaDiCaL version: 2.1.3
% 5.73/1.06 % (110414)Termination reason: Instruction limit
% 5.73/1.06 % (110414)Termination phase: Saturation
% 5.73/1.06 % (110414)Time elapsed: 0.319 s
% 5.73/1.06 % (110414)Peak memory usage: 13 MB
% 5.73/1.06 % (110414)Instructions burned: 685 (million)
% 5.73/1.06 % Exception at run slice level
% 5.73/1.06 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.73/1.06 % (110482)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=2283185155:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 5.73/1.06 % (110483)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=2795149240:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 5.73/1.06 % Exception at run slice level
% 5.73/1.06 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.73/1.06 % (110483)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.73/1.06 % (110486)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=1144915949:i=1472:ins=7:fdi=8:gsp=on_2995 on theBenchmark for (2995ds/1472Mi)
% 5.73/1.06 % (110486)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 5.73/1.06 % (110486)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.73/1.06 % (110468)Instruction limit reached!
% 5.73/1.06 % (110468)------------------------------
% 5.73/1.06 % (110468)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.73/1.06 % (110468)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.73/1.06 % (110468)CaDiCaL version: 2.1.3
% 5.73/1.06 % (110468)Termination reason: Instruction limit
% 5.73/1.06 % (110468)Termination phase: Saturation
% 5.73/1.06 % (110468)Time elapsed: 0.335 s
% 5.73/1.06 % (110468)Peak memory usage: 14 MB
% 5.73/1.06 % (110468)Instructions burned: 692 (million)
% 5.73/1.06 % (110488)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=3795726675:i=6324_2994 on theBenchmark for (2994ds/6324Mi)
% 5.73/1.06 % Exception at run slice level
% 5.73/1.06 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.73/1.06 % (110490)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=1152328103:fmbsr=2.30978:i=2174_2994 on theBenchmark for (2994ds/2174Mi)
% 5.73/1.06 % Exception at run slice level
% 5.73/1.06 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.73/1.06 % (110492)ott-2_1_sil=16000:newcnf=on:random_seed=4045056831:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2994 on theBenchmark for (2994ds/869Mi)
% 5.73/1.06 % (110492)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.73/1.06 % (110471)Instruction limit reached!
% 5.73/1.06 % (110471)------------------------------
% 5.73/1.06 % (110471)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.73/1.06 % (110471)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.73/1.06 % (110471)CaDiCaL version: 2.1.3
% 5.73/1.06 % (110471)Termination reason: Instruction limit
% 5.73/1.06 % (110471)Termination phase: Saturation
% 5.73/1.06 % (110471)Time elapsed: 0.436 s
% 5.73/1.06 % (110471)Peak memory usage: 14 MB
% 5.73/1.06 % (110471)Instructions burned: 879 (million)
% 5.73/1.06 % (110494)ott+10_1_sil=32000:tgt=ground:random_seed=180516473:i=5114:av=off_2993 on theBenchmark for (2993ds/5114Mi)
% 5.73/1.06 % (110436)Instruction limit reached!
% 5.73/1.06 % (110436)------------------------------
% 5.73/1.06 % (110436)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.73/1.06 % (110436)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.73/1.06 % (110436)CaDiCaL version: 2.1.3
% 5.73/1.06 % (110436)Termination reason: Instruction limit
% 5.73/1.06 % (110436)Termination phase: Saturation
% 5.73/1.06 % (110436)Time elapsed: 0.525 s
% 5.73/1.06 % (110436)Peak memory usage: 13 MB
% 5.73/1.06 % (110436)Instructions burned: 1180 (million)
% 5.73/1.06 % (110496)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=212723550:i=54282_2993 on theBenchmark for (2993ds/54282Mi)
% 5.73/1.06 % Exception at run slice level
% 5.73/1.06 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.73/1.06 % (110498)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=2097871455:i=3512:aac=none_2993 on theBenchmark for (2993ds/3512Mi)
% 5.73/1.06 % (110498)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.73/1.06 % (110399) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-110392-110399"...
% 5.73/1.06 % (110399)...printing done.
% 5.73/1.06 % (110399)Refutation found. Thanks to Tanya!
% 5.73/1.06 % SZS status Theorem for theBenchmark
% 5.73/1.06 % SZS output start Proof for theBenchmark
% See solution above
% 5.73/1.06 % (110399)------------------------------
% 5.73/1.06 % (110399)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.73/1.06 % (110399)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.73/1.06 % (110399)CaDiCaL version: 2.1.3
% 5.73/1.06 % (110399)Termination reason: Refutation
% 5.73/1.06 % (110399)Time elapsed: 0.811 s
% 5.73/1.06 % (110399)Peak memory usage: 19 MB
% 5.73/1.06 % (110399)Instructions burned: 2936 (million)
% 5.73/1.06 % (110392)Success in time 0.83 s
% 5.73/1.06 % Vampire exiting
%------------------------------------------------------------------------------