%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : AGT031^1 : 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 : n016.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 07:44:40 AM UTC 2026
% Result : Theorem 0.88s 0.45s
% Output : Refutation 0.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 18
% Syntax : Number of formulae : 166 ( 120 unt; 0 typ; 0 def)
% Number of atoms : 1071 ( 227 equ; 0 cnn)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 2068 ( 265 ~; 206 |; 0 &;1455 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 172 ( 172 >; 0 *; 0 +; 0 <<)
% Number of symbols : 72 ( 67 usr; 10 con; 0-4 aty)
% ( 120 !!; 6 ??; 0 @@+; 0 @@-)
% Number of variables : 526 ( 358 ^; 166 !; 2 ?; 526 :)
% 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(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(f12,axiom,
( mexists_ind
= ( ^ [X0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X1: mu] : ( mnot @ ( X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mexists_ind) ).
thf(f16,axiom,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) ),
file('/export/starexec/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(f19,axiom,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',msymmetric) ).
thf(f20,axiom,
( mserial
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] :
? [X2: $i] : ( X0 @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mserial) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f38,axiom,
mvalid @ ( mbox @ a1 @ ( likes @ piotr @ beer ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a2_3) ).
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(f50,axiom,
msymmetric @ a1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axioms_B_a1) ).
thf(f52,axiom,
msymmetric @ a3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axioms_B_a3) ).
thf(f53,axiom,
mserial @ a1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axioms_D_a1) ).
thf(f73,conjecture,
( mvalid
@ ( mexists_ind
@ ^ [X0: mu] :
( mexists_ind
@ ^ [X1: mu] : ( very_much_likes @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(f74,negated_conjecture,
~ ( mvalid
@ ( mexists_ind
@ ^ [X0: mu] :
( mexists_ind
@ ^ [X1: mu] : ( very_much_likes @ X0 @ X1 ) ) ) ),
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(f81,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
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(f90,plain,
( mexists_ind
= ( ^ [X0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X1: mu] : ( mnot @ ( X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f12]) ).
thf(f91,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f90]) ).
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(f100,plain,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f19]) ).
thf(f101,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f100]) ).
thf(f102,plain,
( mserial
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] :
? [X2: $i] : ( X0 @ X1 @ X2 ) ) ),
inference(rectify,[],[f20]) ).
thf(f103,plain,
( mserial
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f102]) ).
thf(f118,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f119,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f118]) ).
thf(f138,plain,
mvalid @ ( mbox @ a1 @ ( likes @ piotr @ beer ) ),
inference(rectify,[],[f38]) ).
thf(f139,plain,
( ( mvalid @ ( mbox @ a1 @ ( likes @ piotr @ beer ) ) )
= $true ),
inference(fool_elimination,[],[f138]) ).
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(f150,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(f151,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,[],[f150]) ).
thf(f162,plain,
msymmetric @ a1,
inference(rectify,[],[f50]) ).
thf(f163,plain,
( ( msymmetric @ a1 )
= $true ),
inference(fool_elimination,[],[f162]) ).
thf(f166,plain,
msymmetric @ a3,
inference(rectify,[],[f52]) ).
thf(f167,plain,
( ( msymmetric @ a3 )
= $true ),
inference(fool_elimination,[],[f166]) ).
thf(f168,plain,
mserial @ a1,
inference(rectify,[],[f53]) ).
thf(f169,plain,
( ( mserial @ a1 )
= $true ),
inference(fool_elimination,[],[f168]) ).
thf(f208,plain,
~ ( mvalid
@ ( mexists_ind
@ ^ [X0: mu] :
( mexists_ind
@ ^ [X1: mu] : ( very_much_likes @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f74]) ).
thf(f209,plain,
( $true
!= ( mvalid
@ ( mexists_ind
@ ^ [Y0: mu] :
( mexists_ind
@ ^ [Y1: mu] : ( very_much_likes @ Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f208]) ).
thf(f210,plain,
( $true
!= ( mvalid
@ ( mexists_ind
@ ^ [Y0: mu] :
( mexists_ind
@ ^ [Y1: mu] : ( very_much_likes @ Y0 @ Y1 ) ) ) ) ),
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(f215,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f81]) ).
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(f222,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f91]) ).
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(f229,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f101]) ).
thf(f230,plain,
( mserial
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f103]) ).
thf(f238,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f119]) ).
thf(f248,plain,
( ( mvalid @ ( mbox @ a1 @ ( likes @ piotr @ beer ) ) )
= $true ),
inference(cnf_transformation,[],[f139]) ).
thf(f252,plain,
( ( mvalid @ ( mdia @ a3 @ ( likes @ piotr @ pepsi ) ) )
= $true ),
inference(cnf_transformation,[],[f147]) ).
thf(f254,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,[],[f151]) ).
thf(f260,plain,
( ( msymmetric @ a1 )
= $true ),
inference(cnf_transformation,[],[f163]) ).
thf(f262,plain,
( ( msymmetric @ a3 )
= $true ),
inference(cnf_transformation,[],[f167]) ).
thf(f263,plain,
( ( mserial @ a1 )
= $true ),
inference(cnf_transformation,[],[f169]) ).
thf(f283,plain,
( $true
!= ( mvalid
@ ( mexists_ind
@ ^ [Y0: mu] :
( mexists_ind
@ ^ [Y1: mu] : ( very_much_likes @ Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f210]) ).
thf(f286,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,[],[f215,f213,f214,f213,f213]) ).
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(f291,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: mu > $i > $o,Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( Y0 @ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[],[f222,f213,f220,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(f301,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 @ piotr @ beer ) ) ) ),
inference(definition_unfolding,[],[f248,f238,f226]) ).
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(f307,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,[],[f254,f238,f220,f220,f226,f287,f286,f286,f226,f226]) ).
thf(f313,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
@ a1 ) ),
inference(definition_unfolding,[],[f260,f229]) ).
thf(f315,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
@ a3 ) ),
inference(definition_unfolding,[],[f262,f229]) ).
thf(f316,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) )
@ a1 ) ),
inference(definition_unfolding,[],[f263,f230]) ).
thf(f334,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: mu > $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: mu > $i > $o,Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( Y0 @ Y1 ) ) ) )
@ ^ [Y0: mu] :
( ^ [Y1: mu > $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: mu > $i > $o,Y3: $i] :
( !! @ mu
@ ^ [Y4: mu] : ( Y2 @ Y4 @ Y3 ) )
@ ^ [Y2: mu] :
( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ ( Y1 @ Y2 ) ) ) )
@ ^ [Y1: mu] : ( very_much_likes @ Y0 @ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f283,f238,f291,f291]) ).
thf(f335,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
~ ( !! @ mu
@ ^ [Y1: mu] :
~ ~ ( !! @ mu
@ ^ [Y2: mu] :
~ ( very_much_likes @ Y1 @ Y2 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f334]) ).
thf(f336,plain,
( $false
= ( ^ [Y0: $i] :
~ ( !! @ mu
@ ^ [Y1: mu] :
~ ~ ( !! @ mu
@ ^ [Y2: mu] :
~ ( very_much_likes @ Y1 @ Y2 @ Y0 ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f335]) ).
thf(f337,plain,
( $false
= ( ~ ( !! @ mu
@ ^ [Y0: mu] :
~ ~ ( !! @ mu
@ ^ [Y1: mu] :
~ ( very_much_likes @ Y0 @ Y1 @ sK0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f336]) ).
thf(f338,plain,
( $true
= ( !! @ mu
@ ^ [Y0: mu] :
~ ~ ( !! @ mu
@ ^ [Y1: mu] :
~ ( very_much_likes @ Y0 @ Y1 @ sK0 ) ) ) ),
inference(not_proxy_clausification,[],[f337]) ).
thf(f339,plain,
! [X1: mu] :
( $true
= ( ^ [Y0: mu] :
~ ~ ( !! @ mu
@ ^ [Y1: mu] :
~ ( very_much_likes @ Y0 @ Y1 @ sK0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f338]) ).
thf(f340,plain,
! [X1: mu] :
( $true
= ( ~ ~ ( !! @ mu
@ ^ [Y0: mu] :
~ ( very_much_likes @ X1 @ Y0 @ sK0 ) ) ) ),
inference(beta-eta_normalization,[],[f339]) ).
thf(f341,plain,
! [X1: mu] :
( $false
= ( ~ ( !! @ mu
@ ^ [Y0: mu] :
~ ( very_much_likes @ X1 @ Y0 @ sK0 ) ) ) ),
inference(not_proxy_clausification,[],[f340]) ).
thf(f342,plain,
! [X1: mu] :
( $true
= ( !! @ mu
@ ^ [Y0: mu] :
~ ( very_much_likes @ X1 @ Y0 @ sK0 ) ) ),
inference(not_proxy_clausification,[],[f341]) ).
thf(f343,plain,
! [X2: mu,X1: mu] :
( $true
= ( ^ [Y0: mu] :
~ ( very_much_likes @ X1 @ Y0 @ sK0 )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f342]) ).
thf(f344,plain,
! [X2: mu,X1: mu] :
( $true
= ( ~ ( very_much_likes @ X1 @ X2 @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f343]) ).
thf(f345,plain,
! [X2: mu,X1: mu] :
( $false
= ( very_much_likes @ X1 @ X2 @ sK0 ) ),
inference(not_proxy_clausification,[],[f344]) ).
thf(f480,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( ?? @ $i @ ( a1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f316]) ).
thf(f481,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( ?? @ $i @ ( a1 @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f480]) ).
thf(f482,plain,
! [X1: $i] :
( $true
= ( ?? @ $i @ ( a1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f481]) ).
thf(f483,plain,
! [X1: $i] :
( $true
= ( a1 @ X1 @ ( sK3 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f482]) ).
thf(f484,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( a3 @ Y1 @ Y0 )
=> ( a3 @ Y0 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f315]) ).
thf(f485,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( a3 @ Y1 @ Y0 )
=> ( a3 @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f484]) ).
thf(f486,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( a3 @ Y0 @ X1 )
=> ( a3 @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f485]) ).
thf(f487,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( a3 @ Y0 @ X1 )
=> ( a3 @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f486]) ).
thf(f488,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( a3 @ X2 @ X1 )
=> ( a3 @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f487]) ).
thf(f489,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( a3 @ X2 @ X1 ) )
| ( $true
= ( a3 @ X1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f488]) ).
thf(f496,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( a1 @ Y1 @ Y0 )
=> ( a1 @ Y0 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f313]) ).
thf(f497,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( a1 @ Y1 @ Y0 )
=> ( a1 @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f496]) ).
thf(f498,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( a1 @ Y0 @ X1 )
=> ( a1 @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f497]) ).
thf(f499,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( a1 @ Y0 @ X1 )
=> ( a1 @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f498]) ).
thf(f500,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( a1 @ X2 @ X1 )
=> ( a1 @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f499]) ).
thf(f501,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( a1 @ X2 @ X1 ) )
| ( $true
= ( a1 @ X1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f500]) ).
thf(f576,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,[],[f307]) ).
thf(f577,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,[],[f576]) ).
thf(f578,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,[],[f577]) ).
thf(f579,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,[],[f578]) ).
thf(f580,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,[],[f579]) ).
thf(f581,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,[],[f580]) ).
thf(f582,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,[],[f581]) ).
thf(f583,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,[],[f582]) ).
thf(f584,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,[],[f583]) ).
thf(f585,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,[],[f584]) ).
thf(f586,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,[],[f585]) ).
thf(f587,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,[],[f586]) ).
thf(f588,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,[],[f587]) ).
thf(f589,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,[],[f588]) ).
thf(f590,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,[],[f589]) ).
thf(f591,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,[],[f590]) ).
thf(f592,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,[],[f591]) ).
thf(f593,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,[],[f592]) ).
thf(f594,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,[],[f593]) ).
thf(f595,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 ) )
@ ( sK5 @ X3 @ X2 @ X4 ) ) )
| ( $true
= ( ~ ( likes @ X2 @ X3 @ X4 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a1 @ X4 @ Y0 )
| ( likes @ X2 @ X3 @ Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f594]) ).
thf(f596,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 ) )
@ ( sK5 @ X3 @ X2 @ X4 ) ) )
| ( $false
= ( likes @ X2 @ X3 @ X4 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a1 @ X4 @ Y0 )
| ( likes @ X2 @ X3 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f595]) ).
thf(f597,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 ) )
@ ( sK5 @ X3 @ X2 @ X4 ) ) )
| ( $false
= ( likes @ X2 @ X3 @ X4 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a1 @ X4 @ Y0 )
| ( likes @ X2 @ X3 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f596]) ).
thf(f598,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 ) )
@ ( sK5 @ X3 @ X2 @ X4 ) ) )
| ( $false
= ( likes @ X2 @ X3 @ X4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( a1 @ X4 @ Y0 )
| ( likes @ X2 @ X3 @ Y0 ) )
@ ( sK6 @ X3 @ X2 @ X4 ) ) ) ),
inference(sigma_proxy_clausification,[],[f597]) ).
thf(f599,plain,
! [X2: mu,X3: mu,X1: $i,X4: $i] :
( ( $true
= ( very_much_likes @ X2 @ X3 @ X4 ) )
| ( $false
= ( a3 @ X1 @ X4 ) )
| ( $false
= ( ~ ( a2 @ X4 @ ( sK5 @ X3 @ X2 @ X4 ) )
| ( likes @ X2 @ X3 @ ( sK5 @ X3 @ X2 @ X4 ) ) ) )
| ( $false
= ( likes @ X2 @ X3 @ X4 ) )
| ( $false
= ( ~ ( a1 @ X4 @ ( sK6 @ X3 @ X2 @ X4 ) )
| ( likes @ X2 @ X3 @ ( sK6 @ X3 @ X2 @ X4 ) ) ) ) ),
inference(beta-eta_normalization,[],[f598]) ).
thf(f600,plain,
! [X2: mu,X3: mu,X1: $i,X4: $i] :
( ( $true
= ( very_much_likes @ X2 @ X3 @ X4 ) )
| ( $false
= ( a3 @ X1 @ X4 ) )
| ( $false
= ( likes @ X2 @ X3 @ ( sK5 @ X3 @ X2 @ X4 ) ) )
| ( $false
= ( likes @ X2 @ X3 @ X4 ) )
| ( $false
= ( ~ ( a1 @ X4 @ ( sK6 @ X3 @ X2 @ X4 ) )
| ( likes @ X2 @ X3 @ ( sK6 @ X3 @ X2 @ X4 ) ) ) ) ),
inference(or_proxy_clausification,[],[f599]) ).
thf(f606,plain,
! [X2: mu,X3: mu,X1: $i,X4: $i] :
( ( $false
= ( likes @ X2 @ X3 @ ( sK6 @ X3 @ X2 @ X4 ) ) )
| ( $false
= ( a3 @ X1 @ X4 ) )
| ( $false
= ( likes @ X2 @ X3 @ ( sK5 @ X3 @ X2 @ X4 ) ) )
| ( $false
= ( likes @ X2 @ X3 @ X4 ) )
| ( $true
= ( very_much_likes @ X2 @ X3 @ X4 ) ) ),
inference(or_proxy_clausification,[],[f600]) ).
thf(f619,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a3 @ Y0 @ Y1 )
| ~ ( likes @ piotr @ pepsi @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f305]) ).
thf(f620,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a3 @ Y0 @ Y1 )
| ~ ( likes @ piotr @ pepsi @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f619]) ).
thf(f621,plain,
! [X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a3 @ X1 @ Y0 )
| ~ ( likes @ piotr @ pepsi @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f620]) ).
thf(f622,plain,
! [X1: $i] :
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a3 @ X1 @ Y0 )
| ~ ( likes @ piotr @ pepsi @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f621]) ).
thf(f623,plain,
! [X1: $i] :
( $false
= ( ^ [Y0: $i] :
( ~ ( a3 @ X1 @ Y0 )
| ~ ( likes @ piotr @ pepsi @ Y0 ) )
@ ( sK8 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f622]) ).
thf(f624,plain,
! [X1: $i] :
( $false
= ( ~ ( a3 @ X1 @ ( sK8 @ X1 ) )
| ~ ( likes @ piotr @ pepsi @ ( sK8 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f623]) ).
thf(f626,plain,
! [X1: $i] :
( $false
= ( ~ ( a3 @ X1 @ ( sK8 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f624]) ).
thf(f627,plain,
! [X1: $i] :
( $true
= ( a3 @ X1 @ ( sK8 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f626]) ).
thf(f658,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a1 @ Y0 @ Y1 )
| ( likes @ piotr @ beer @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f301]) ).
thf(f659,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a1 @ Y0 @ Y1 )
| ( likes @ piotr @ beer @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f658]) ).
thf(f660,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a1 @ X1 @ Y0 )
| ( likes @ piotr @ beer @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f659]) ).
thf(f661,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( a1 @ X1 @ Y0 )
| ( likes @ piotr @ beer @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f660]) ).
thf(f662,plain,
! [X2: $i,X1: $i] :
( $true
= ( ~ ( a1 @ X1 @ X2 )
| ( likes @ piotr @ beer @ X2 ) ) ),
inference(beta-eta_normalization,[],[f661]) ).
thf(f663,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( likes @ piotr @ beer @ X2 ) )
| ( $true
= ( ~ ( a1 @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f662]) ).
thf(f664,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( likes @ piotr @ beer @ X2 ) )
| ( $false
= ( a1 @ X1 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f663]) ).
thf(f878,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( a3 @ ( sK8 @ X0 ) @ X0 ) ) ),
inference(constrained_superposition,[],[f627,f489]) ).
thf(f889,plain,
! [X0: $i] :
( $true
= ( a3 @ ( sK8 @ X0 ) @ X0 ) ),
inference(trivial_inequality_removal,[],[f878]) ).
thf(f1055,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( a1 @ ( sK3 @ X0 ) @ X0 ) ) ),
inference(constrained_superposition,[],[f483,f501]) ).
thf(f1064,plain,
! [X0: $i] :
( $true
= ( a1 @ ( sK3 @ X0 ) @ X0 ) ),
inference(trivial_inequality_removal,[],[f1055]) ).
thf(f1214,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( likes @ piotr @ beer @ X0 ) ) ),
inference(constrained_superposition,[],[f1064,f664]) ).
thf(f1223,plain,
! [X0: $i] :
( $true
= ( likes @ piotr @ beer @ X0 ) ),
inference(trivial_inequality_removal,[],[f1214]) ).
thf(f2343,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( a3 @ X1 @ X0 ) )
| ( $false
= ( likes @ piotr @ beer @ ( sK5 @ beer @ piotr @ X0 ) ) )
| ( $false
= ( likes @ piotr @ beer @ X0 ) )
| ( $true
= ( very_much_likes @ piotr @ beer @ X0 ) ) ),
inference(constrained_superposition,[],[f1223,f606]) ).
thf(f2400,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( a3 @ X1 @ X0 ) )
| ( $false
= ( likes @ piotr @ beer @ ( sK5 @ beer @ piotr @ X0 ) ) )
| ( $false
= ( likes @ piotr @ beer @ X0 ) )
| ( $true
= ( very_much_likes @ piotr @ beer @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f2343]) ).
thf(f2436,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( a3 @ X1 @ X0 ) )
| ( $false
= ( likes @ piotr @ beer @ X0 ) )
| ( $true
= ( very_much_likes @ piotr @ beer @ X0 ) ) ),
inference(forward_demodulation,[],[f2400,f1223]) ).
thf(f2437,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( a3 @ X1 @ X0 ) )
| ( $false
= ( likes @ piotr @ beer @ X0 ) )
| ( $true
= ( very_much_likes @ piotr @ beer @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f2436]) ).
thf(f2448,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( a3 @ X1 @ X0 ) )
| ( $true
= ( very_much_likes @ piotr @ beer @ X0 ) ) ),
inference(forward_demodulation,[],[f2437,f1223]) ).
thf(f2449,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( a3 @ X1 @ X0 ) )
| ( $true
= ( very_much_likes @ piotr @ beer @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f2448]) ).
thf(f2532,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( a3 @ X0 @ sK0 ) ) ),
inference(constrained_superposition,[],[f345,f2449]) ).
thf(f2533,plain,
! [X0: $i] :
( $false
= ( a3 @ X0 @ sK0 ) ),
inference(trivial_inequality_removal,[],[f2532]) ).
thf(f2630,plain,
$true = $false,
inference(constrained_superposition,[],[f889,f2533]) ).
thf(f2643,plain,
$false,
inference(trivial_inequality_removal,[],[f2630]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : AGT031^1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.19 % Computer : n016.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 17:34:28 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.22 Running first-order model finding
% 0.07/0.22 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
% 0.88/0.45 % (660879)Will run a generic schedule for satisfiability detection.
% 0.88/0.45 % (660887)dis+10_1_sil=32000:sp=arity:random_seed=2729601584:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.88/0.45 % (660885)% WARNING: option uhcvi not known.
% 0.88/0.45 % (660884)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1608468887_2999 on theBenchmark for (2999ds/0Mi)
% 0.88/0.45 % (660885)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2664986330:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.88/0.45 % (660886)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1621898957:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.88/0.45 % (660890)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4223464110:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.88/0.45 % (660889)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4265411170:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.88/0.45 % (660888)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=339698572:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.88/0.45 % (660885)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.88/0.45 % (660888)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.88/0.45 % Exception at run slice level
% 0.88/0.45 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.88/0.45 % (660885)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.88/0.45 % (660887)Instruction limit reached!
% 0.88/0.45 % (660887)------------------------------
% 0.88/0.45 % (660887)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.88/0.45 % (660887)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.88/0.45 % (660887)CaDiCaL version: 2.1.3
% 0.88/0.45 % (660887)Termination reason: Instruction limit
% 0.88/0.45 % (660887)Termination phase: Saturation
% 0.88/0.45 % (660887)Time elapsed: 0.025 s
% 0.88/0.45 % (660887)Peak memory usage: 12 MB
% 0.88/0.45 % (660887)Instructions burned: 103 (million)
% 0.88/0.45 % (660898)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2425727644:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.88/0.45 % (660899)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=4112865365:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.88/0.45 % Exception at run slice level
% 0.88/0.45 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.88/0.45 % (660902)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=1480980058:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.88/0.45 % (660888)Instruction limit reached!
% 0.88/0.45 % (660888)------------------------------
% 0.88/0.45 % (660888)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.88/0.45 % (660888)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.88/0.45 % (660888)CaDiCaL version: 2.1.3
% 0.88/0.45 % (660888)Termination reason: Instruction limit
% 0.88/0.45 % (660888)Termination phase: Saturation
% 0.88/0.45 % (660888)Time elapsed: 0.054 s
% 0.88/0.45 % (660888)Peak memory usage: 12 MB
% 0.88/0.45 % (660888)Instructions burned: 118 (million)
% 0.88/0.45 % (660902)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.88/0.45 % (660899)Instruction limit reached!
% 0.88/0.45 % (660899)------------------------------
% 0.88/0.45 % (660899)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.88/0.45 % (660899)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.88/0.45 % (660899)CaDiCaL version: 2.1.3
% 0.88/0.45 % (660899)Termination reason: Instruction limit
% 0.88/0.45 % (660899)Termination phase: Saturation
% 0.88/0.45 % (660899)Time elapsed: 0.033 s
% 0.88/0.45 % (660899)Peak memory usage: 12 MB
% 0.88/0.45 % (660899)Instructions burned: 135 (million)
% 0.88/0.45 % (660889)Instruction limit reached!
% 0.88/0.45 % (660889)------------------------------
% 0.88/0.45 % (660889)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.88/0.45 % (660889)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.88/0.45 % (660889)CaDiCaL version: 2.1.3
% 0.88/0.45 % (660889)Termination reason: Instruction limit
% 0.88/0.45 % (660889)Termination phase: Saturation
% 0.88/0.45 % (660889)Time elapsed: 0.061 s
% 0.88/0.45 % (660889)Peak memory usage: 12 MB
% 0.88/0.45 % (660889)Instructions burned: 132 (million)
% 0.88/0.45 % (660902)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.88/0.45 % (660905)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1388428773:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 0.88/0.45 % (660904)ott-21_1_sil=16000:fs=off:random_seed=2198081715:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 0.88/0.45 % (660890)Instruction limit reached!
% 0.88/0.45 % (660890)------------------------------
% 0.88/0.45 % (660890)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.88/0.45 % (660890)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.88/0.45 % (660890)CaDiCaL version: 2.1.3
% 0.88/0.45 % (660890)Termination reason: Instruction limit
% 0.88/0.45 % (660890)Termination phase: Saturation
% 0.88/0.45 % (660890)Time elapsed: 0.077 s
% 0.88/0.45 % (660890)Peak memory usage: 12 MB
% 0.88/0.45 % (660890)Instructions burned: 160 (million)
% 0.88/0.45 % (660906)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3530889394:fmbsr=1.3:i=865:ins=25_2999 on theBenchmark for (2999ds/865Mi)
% 0.88/0.45 % Exception at run slice level
% 0.88/0.45 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.88/0.45 % (660909)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3160399860:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 0.88/0.45 % (660911)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1623548159:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 0.88/0.45 % Exception at run slice level
% 0.88/0.45 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.88/0.45 % (660914)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=2758233132: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)
% 0.88/0.45 % (660914)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.88/0.45 % (660904)Instruction limit reached!
% 0.88/0.45 % (660904)------------------------------
% 0.88/0.45 % (660904)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.88/0.45 % (660904)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.88/0.45 % (660904)CaDiCaL version: 2.1.3
% 0.88/0.45 % (660904)Termination reason: Instruction limit
% 0.88/0.45 % (660904)Termination phase: Saturation
% 0.88/0.45 % (660904)Time elapsed: 0.081 s
% 0.88/0.45 % (660904)Peak memory usage: 12 MB
% 0.88/0.45 % (660904)Instructions burned: 181 (million)
% 0.88/0.45 % (660902) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-660879-660902"...
% 0.88/0.45 % (660916)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3159610734:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 0.88/0.45 % (660916)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.88/0.45 % (660902)...printing done.
% 0.88/0.45 % (660902)Refutation found. Thanks to Tanya!
% 0.88/0.45 % SZS status Theorem for theBenchmark
% 0.88/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.88/0.45 % (660902)------------------------------
% 0.88/0.45 % (660902)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.88/0.45 % (660902)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.88/0.45 % (660902)CaDiCaL version: 2.1.3
% 0.88/0.45 % (660902)Termination reason: Refutation
% 0.88/0.45 % (660902)Time elapsed: 0.124 s
% 0.88/0.45 % (660902)Peak memory usage: 14 MB
% 0.88/0.45 % (660902)Instructions burned: 254 (million)
% 0.88/0.45 % (660879)Success in time 0.218 s
% 0.88/0.45 % Vampire exiting
%------------------------------------------------------------------------------