%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PUZ086^1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 08:20:51 AM UTC 2026
% Result : Theorem 0.25s 0.35s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 18
% Syntax : Number of formulae : 161 ( 81 unt; 0 typ; 5 def)
% Number of atoms : 1168 ( 228 equ; 0 cnn)
% Maximal formula atoms : 12 ( 7 avg)
% Number of connectives : 1657 ( 246 ~; 269 |; 0 &;1035 @)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 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; 13 con; 0-4 aty)
% ( 103 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 442 ( 0 sgn 116 !; 0 ?; 442 :)
% 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,
peter: $i > $i > $o ).
thf(func_def_33,type,
john: $i > $i > $o ).
thf(func_def_34,type,
wife: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_35,type,
time: $i > $o ).
thf(func_def_36,type,
place: $i > $o ).
thf(func_def_37,type,
appointment: $i > $o ).
thf(func_def_38,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_39,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_44,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_45,type,
vNOT: $o > $o ).
thf(func_def_46,type,
vIMP: $o > $o > $o ).
thf(func_def_47,type,
vAND: $o > $o > $o ).
thf(func_def_48,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_49,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_50,type,
vOR: $o > $o > $o ).
thf(func_def_51,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_52,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_53,type,
sF0: $o ).
thf(func_def_54,type,
sK1: $i > ( $i > $o ) > $i ).
thf(func_def_55,type,
sK2: $i > $i ).
thf(func_def_63,type,
sK10: $i > ( $i > $o ) > $i ).
thf(func_def_64,type,
sK11: $i > ( $i > $o ) > $i ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/LCL013^0.ax',mand) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f16,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ~ ( X0 @ X2 @ X3 )
| ( X1 @ X3 ) ) )
= mbox ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mbox) ).
thf(f18,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) )
= mreflexive ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mreflexive) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
mreflexive @ peter,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',refl_peter) ).
thf(f33,axiom,
mreflexive @ john,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',refl_john) ).
thf(f40,axiom,
mvalid @ ( mbox @ peter @ time ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_a) ).
thf(f41,axiom,
mvalid @ ( mbox @ peter @ ( mbox @ john @ place ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_b) ).
thf(f43,axiom,
mvalid @ ( mbox @ peter @ ( mbox @ john @ ( mimplies @ ( mand @ place @ time ) @ appointment ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_d) ).
thf(f44,conjecture,
mvalid @ ( mand @ ( mbox @ peter @ ( mbox @ john @ appointment ) ) @ ( mbox @ john @ ( mbox @ peter @ appointment ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(f45,negated_conjecture,
~ ( mvalid @ ( mand @ ( mbox @ peter @ ( mbox @ john @ appointment ) ) @ ( mbox @ john @ ( mbox @ peter @ appointment ) ) ) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
thf(f46,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f47,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f46]) ).
thf(f50,plain,
mvalid @ ( mbox @ peter @ ( mbox @ john @ place ) ),
inference(rectify,[],[f41]) ).
thf(f51,plain,
( ( mvalid @ ( mbox @ peter @ ( mbox @ john @ place ) ) )
= $true ),
inference(fool_elimination,[],[f50]) ).
thf(f53,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f68,plain,
~ ( mvalid @ ( mand @ ( mbox @ peter @ ( mbox @ john @ appointment ) ) @ ( mbox @ john @ ( mbox @ peter @ appointment ) ) ) ),
inference(rectify,[],[f45]) ).
thf(f69,plain,
( ( mvalid @ ( mand @ ( mbox @ peter @ ( mbox @ john @ appointment ) ) @ ( mbox @ john @ ( mbox @ peter @ appointment ) ) ) )
!= $true ),
inference(fool_elimination,[],[f68]) ).
thf(f70,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f71,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f70]) ).
thf(f73,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) )
= mreflexive ),
inference(rectify,[],[f18]) ).
thf(f74,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f73]) ).
thf(f86,plain,
mreflexive @ john,
inference(rectify,[],[f33]) ).
thf(f87,plain,
( ( mreflexive @ john )
= $true ),
inference(fool_elimination,[],[f86]) ).
thf(f88,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f89,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f88]) ).
thf(f103,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f108,plain,
mvalid @ ( mbox @ peter @ ( mbox @ john @ ( mimplies @ ( mand @ place @ time ) @ appointment ) ) ),
inference(rectify,[],[f43]) ).
thf(f109,plain,
( ( mvalid @ ( mbox @ peter @ ( mbox @ john @ ( mimplies @ ( mand @ place @ time ) @ appointment ) ) ) )
= $true ),
inference(fool_elimination,[],[f108]) ).
thf(f110,plain,
mreflexive @ peter,
inference(rectify,[],[f32]) ).
thf(f111,plain,
( ( mreflexive @ peter )
= $true ),
inference(fool_elimination,[],[f110]) ).
thf(f112,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ~ ( X0 @ X2 @ X3 )
| ( X1 @ X3 ) ) )
= mbox ),
inference(rectify,[],[f16]) ).
thf(f113,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f112]) ).
thf(f114,plain,
mvalid @ ( mbox @ peter @ time ),
inference(rectify,[],[f40]) ).
thf(f115,plain,
( ( mvalid @ ( mbox @ peter @ time ) )
= $true ),
inference(fool_elimination,[],[f114]) ).
thf(f123,plain,
( ( mvalid @ ( mand @ ( mbox @ peter @ ( mbox @ john @ appointment ) ) @ ( mbox @ john @ ( mbox @ peter @ appointment ) ) ) )
!= $true ),
inference(flattening,[],[f69]) ).
thf(f126,plain,
( ( mvalid @ ( mbox @ peter @ ( mbox @ john @ ( mimplies @ ( mand @ place @ time ) @ appointment ) ) ) )
= $true ),
inference(cnf_transformation,[],[f109]) ).
thf(f127,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f47]) ).
thf(f128,plain,
( ( mreflexive @ peter )
= $true ),
inference(cnf_transformation,[],[f111]) ).
thf(f135,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f113]) ).
thf(f138,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f53]) ).
thf(f142,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f74]) ).
thf(f146,plain,
( ( mvalid @ ( mbox @ peter @ ( mbox @ john @ place ) ) )
= $true ),
inference(cnf_transformation,[],[f51]) ).
thf(f152,plain,
( ( mvalid @ ( mand @ ( mbox @ peter @ ( mbox @ john @ appointment ) ) @ ( mbox @ john @ ( mbox @ peter @ appointment ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f123]) ).
thf(f156,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f89]) ).
thf(f158,plain,
( ( mreflexive @ john )
= $true ),
inference(cnf_transformation,[],[f87]) ).
thf(f159,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f71]) ).
thf(f160,plain,
( ( mvalid @ ( mbox @ peter @ time ) )
= $true ),
inference(cnf_transformation,[],[f115]) ).
thf(f167,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f103]) ).
thf(f170,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f167,f156,f159,f156,f156]) ).
thf(f171,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f138,f159,f156]) ).
thf(f179,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) )
@ peter
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) )
@ john
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) )
@ place
@ time )
@ appointment ) ) ) ) ),
inference(definition_unfolding,[],[f126,f127,f135,f135,f171,f170]) ).
thf(f180,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ peter )
= $true ),
inference(definition_unfolding,[],[f128,f142]) ).
thf(f186,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) )
@ peter
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) )
@ john
@ place ) ) )
= $true ),
inference(definition_unfolding,[],[f146,f127,f135,f135]) ).
thf(f188,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) )
@ peter
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) )
@ john
@ appointment ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) )
@ john
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) )
@ peter
@ appointment ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f152,f127,f170,f135,f135,f135,f135]) ).
thf(f190,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ john ) ),
inference(definition_unfolding,[],[f158,f142]) ).
thf(f191,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) )
@ peter
@ time ) )
= $true ),
inference(definition_unfolding,[],[f160,f127,f135]) ).
thf(f192,definition,
( sF0
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) )
@ peter
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) )
@ john
@ appointment ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) )
@ john
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) )
@ peter
@ appointment ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f193,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) )
@ peter
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) )
@ john
@ appointment ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) )
@ john
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) )
@ peter
@ appointment ) ) ) )
= sF0 ),
inference(reorient_equations,[],[f192]) ).
thf(f194,plain,
$true != sF0,
inference(definition_folding,[],[f188,f193]) ).
thf(f195,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( time @ Y1 )
| ~ ( peter @ Y0 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f191]) ).
thf(f196,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( time @ Y1 )
| ~ ( peter @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f195]) ).
thf(f197,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( time @ Y0 )
| ~ ( peter @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f196]) ).
thf(f198,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( time @ Y0 )
| ~ ( peter @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f197]) ).
thf(f199,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( time @ X2 )
| ~ ( peter @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f198]) ).
thf(f200,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( peter @ X1 @ X2 ) ) )
| ( $true
= ( time @ X2 ) ) ),
inference(or_proxy_clausification,[],[f199]) ).
thf(f201,plain,
! [X2: $i,X1: $i] :
( ( ( peter @ X1 @ X2 )
= $false )
| ( $true
= ( time @ X2 ) ) ),
inference(not_proxy_clausification,[],[f200]) ).
thf(f202,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( place @ Y2 )
| ~ ( john @ Y1 @ Y2 ) ) )
| ~ ( peter @ Y0 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f186]) ).
thf(f203,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( place @ Y2 )
| ~ ( john @ Y1 @ Y2 ) ) )
| ~ ( peter @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f202]) ).
thf(f204,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( place @ Y1 )
| ~ ( john @ Y0 @ Y1 ) ) )
| ~ ( peter @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f203]) ).
thf(f205,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( place @ Y1 )
| ~ ( john @ Y0 @ Y1 ) ) )
| ~ ( peter @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f204]) ).
thf(f206,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( place @ Y0 )
| ~ ( john @ X2 @ Y0 ) ) )
| ~ ( peter @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f205]) ).
thf(f207,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( place @ Y0 )
| ~ ( john @ X2 @ Y0 ) ) ) )
| ( $true
= ( ~ ( peter @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f206]) ).
thf(f208,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( peter @ X1 @ X2 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( place @ Y0 )
| ~ ( john @ X2 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f207]) ).
thf(f209,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( place @ Y0 )
| ~ ( john @ X2 @ Y0 ) )
@ X3 ) )
| ( ( peter @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f208]) ).
thf(f210,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( place @ X3 )
| ~ ( john @ X2 @ X3 ) ) )
| ( ( peter @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f209]) ).
thf(f211,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( peter @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( john @ X2 @ X3 ) ) )
| ( ( place @ X3 )
= $true ) ),
inference(or_proxy_clausification,[],[f210]) ).
thf(f212,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( john @ X2 @ X3 )
= $false )
| ( ( place @ X3 )
= $true )
| ( ( peter @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f211]) ).
thf(f213,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( appointment @ Y2 )
| ~ ~ ( ~ ( time @ Y2 )
| ~ ( place @ Y2 ) )
| ~ ( john @ Y1 @ Y2 ) ) )
| ~ ( peter @ Y0 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f179]) ).
thf(f214,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( appointment @ Y2 )
| ~ ~ ( ~ ( time @ Y2 )
| ~ ( place @ Y2 ) )
| ~ ( john @ Y1 @ Y2 ) ) )
| ~ ( peter @ Y0 @ Y1 ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f213]) ).
thf(f215,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( appointment @ Y1 )
| ~ ~ ( ~ ( time @ Y1 )
| ~ ( place @ Y1 ) )
| ~ ( john @ Y0 @ Y1 ) ) )
| ~ ( peter @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f214]) ).
thf(f216,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( appointment @ Y1 )
| ~ ~ ( ~ ( time @ Y1 )
| ~ ( place @ Y1 ) )
| ~ ( john @ Y0 @ Y1 ) ) )
| ~ ( peter @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f215]) ).
thf(f217,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( appointment @ Y0 )
| ~ ~ ( ~ ( time @ Y0 )
| ~ ( place @ Y0 ) )
| ~ ( john @ X2 @ Y0 ) ) )
| ~ ( peter @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f216]) ).
thf(f218,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( appointment @ Y0 )
| ~ ~ ( ~ ( time @ Y0 )
| ~ ( place @ Y0 ) )
| ~ ( john @ X2 @ Y0 ) ) ) )
| ( $true
= ( ~ ( peter @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f217]) ).
thf(f219,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( appointment @ Y0 )
| ~ ~ ( ~ ( time @ Y0 )
| ~ ( place @ Y0 ) )
| ~ ( john @ X2 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( peter @ X1 @ X2 ) ) ) ),
inference(pi_proxy_clausification,[],[f218]) ).
thf(f220,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( appointment @ Y0 )
| ~ ~ ( ~ ( time @ Y0 )
| ~ ( place @ Y0 ) )
| ~ ( john @ X2 @ Y0 ) )
@ X3 ) )
| ( ( peter @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f219]) ).
thf(f221,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( appointment @ X3 )
| ~ ~ ( ~ ( time @ X3 )
| ~ ( place @ X3 ) )
| ~ ( john @ X2 @ X3 ) ) )
| ( ( peter @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f220]) ).
thf(f222,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( appointment @ X3 )
| ~ ~ ( ~ ( time @ X3 )
| ~ ( place @ X3 ) ) ) )
| ( $true
= ( ~ ( john @ X2 @ X3 ) ) )
| ( ( peter @ X1 @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f221]) ).
thf(f223,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( john @ X2 @ X3 ) ) )
| ( ( ~ ~ ( ~ ( time @ X3 )
| ~ ( place @ X3 ) ) )
= $true )
| ( ( peter @ X1 @ X2 )
= $false )
| ( $true
= ( appointment @ X3 ) ) ),
inference(or_proxy_clausification,[],[f222]) ).
thf(f224,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ~ ~ ( ~ ( time @ X3 )
| ~ ( place @ X3 ) ) )
= $true )
| ( $true
= ( appointment @ X3 ) )
| ( ( peter @ X1 @ X2 )
= $false )
| ( ( john @ X2 @ X3 )
= $false ) ),
inference(not_proxy_clausification,[],[f223]) ).
thf(f225,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( appointment @ X3 ) )
| ( ( john @ X2 @ X3 )
= $false )
| ( ( peter @ X1 @ X2 )
= $false )
| ( ( ~ ( ~ ( time @ X3 )
| ~ ( place @ X3 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f224]) ).
thf(f226,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( appointment @ X3 ) )
| ( ( john @ X2 @ X3 )
= $false )
| ( ( peter @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( time @ X3 )
| ~ ( place @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f225]) ).
thf(f227,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( john @ X2 @ X3 )
= $false )
| ( $true
= ( ~ ( time @ X3 ) ) )
| ( $true
= ( ~ ( place @ X3 ) ) )
| ( $true
= ( appointment @ X3 ) )
| ( ( peter @ X1 @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f226]) ).
thf(f228,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( appointment @ X3 ) )
| ( ( peter @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( place @ X3 ) ) )
| ( ( john @ X2 @ X3 )
= $false )
| ( ( time @ X3 )
= $false ) ),
inference(not_proxy_clausification,[],[f227]) ).
thf(f229,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( appointment @ X3 ) )
| ( ( place @ X3 )
= $false )
| ( ( john @ X2 @ X3 )
= $false )
| ( ( time @ X3 )
= $false )
| ( ( peter @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f228]) ).
thf(f230,plain,
( ( !! @ $i
@ ^ [Y0: $i] : ( peter @ Y0 @ Y0 ) )
= $true ),
inference(beta-eta_normalization,[],[f180]) ).
thf(f231,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( peter @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f230]) ).
thf(f232,plain,
! [X1: $i] :
( $true
= ( peter @ X1 @ X1 ) ),
inference(beta-eta_normalization,[],[f231]) ).
thf(f293,plain,
( ( $true = sF0 )
| ( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) )
@ peter
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) )
@ john
@ appointment ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) )
@ john
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) )
@ peter
@ appointment ) ) ) )
= $false ) ),
inference(iff_proxy_clausification,[],[f193]) ).
thf(f294,plain,
( ( $true = sF0 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( appointment @ Y2 )
| ~ ( peter @ Y1 @ Y2 ) ) )
| ~ ( john @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( appointment @ Y2 )
| ~ ( john @ Y1 @ Y2 ) ) )
| ~ ( peter @ Y0 @ Y1 ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f293]) ).
thf(f295,plain,
( ( $true = sF0 )
| ( ( ^ [Y0: $i] :
~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( appointment @ Y2 )
| ~ ( peter @ Y1 @ Y2 ) ) )
| ~ ( john @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( appointment @ Y2 )
| ~ ( john @ Y1 @ Y2 ) ) )
| ~ ( peter @ Y0 @ Y1 ) ) ) )
@ sK3 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f294]) ).
thf(f296,plain,
( ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( appointment @ Y1 )
| ~ ( peter @ Y0 @ Y1 ) ) )
| ~ ( john @ sK3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( appointment @ Y1 )
| ~ ( john @ Y0 @ Y1 ) ) )
| ~ ( peter @ sK3 @ Y0 ) ) ) ) )
= $false )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f295]) ).
thf(f297,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( appointment @ Y1 )
| ~ ( peter @ Y0 @ Y1 ) ) )
| ~ ( john @ sK3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( appointment @ Y1 )
| ~ ( john @ Y0 @ Y1 ) ) )
| ~ ( peter @ sK3 @ Y0 ) ) ) ) )
| ( $true = sF0 ) ),
inference(not_proxy_clausification,[],[f296]) ).
thf(f298,plain,
( ( $true = sF0 )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( appointment @ Y1 )
| ~ ( john @ Y0 @ Y1 ) ) )
| ~ ( peter @ sK3 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( appointment @ Y1 )
| ~ ( peter @ Y0 @ Y1 ) ) )
| ~ ( john @ sK3 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f297]) ).
thf(f299,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( appointment @ Y1 )
| ~ ( peter @ Y0 @ Y1 ) ) )
| ~ ( john @ sK3 @ Y0 ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( appointment @ Y1 )
| ~ ( john @ Y0 @ Y1 ) ) )
| ~ ( peter @ sK3 @ Y0 ) ) )
= $false )
| ( $true = sF0 ) ),
inference(not_proxy_clausification,[],[f298]) ).
thf(f300,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( appointment @ Y1 )
| ~ ( peter @ Y0 @ Y1 ) ) )
| ~ ( john @ sK3 @ Y0 ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( appointment @ Y1 )
| ~ ( john @ Y0 @ Y1 ) ) )
| ~ ( peter @ sK3 @ Y0 ) ) )
= $false )
| ( $true = sF0 ) ),
inference(not_proxy_clausification,[],[f299]) ).
thf(f301,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( appointment @ Y1 )
| ~ ( peter @ Y0 @ Y1 ) ) )
| ~ ( john @ sK3 @ Y0 ) )
@ sK4 ) )
| ( $true = sF0 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( appointment @ Y1 )
| ~ ( john @ Y0 @ Y1 ) ) )
| ~ ( peter @ sK3 @ Y0 ) ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f300]) ).
thf(f302,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( appointment @ Y1 )
| ~ ( peter @ Y0 @ Y1 ) ) )
| ~ ( john @ sK3 @ Y0 ) )
@ sK4 ) )
| ( $true = sF0 )
| ( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( appointment @ Y1 )
| ~ ( john @ Y0 @ Y1 ) ) )
| ~ ( peter @ sK3 @ Y0 ) )
@ sK5 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f301]) ).
thf(f303,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( appointment @ Y0 )
| ~ ( peter @ sK4 @ Y0 ) ) )
| ~ ( john @ sK3 @ sK4 ) )
= $false )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( appointment @ Y0 )
| ~ ( john @ sK5 @ Y0 ) ) )
| ~ ( peter @ sK3 @ sK5 ) ) )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f302]) ).
thf(f305,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( appointment @ Y0 )
| ~ ( john @ sK5 @ Y0 ) ) )
| ~ ( peter @ sK3 @ sK5 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( appointment @ Y0 )
| ~ ( peter @ sK4 @ Y0 ) ) )
= $false )
| ( $true = sF0 ) ),
inference(or_proxy_clausification,[],[f303]) ).
thf(f307,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( appointment @ Y0 )
| ~ ( peter @ sK4 @ Y0 ) ) )
= $false )
| ( $true = sF0 )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( appointment @ Y0 )
| ~ ( john @ sK5 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f305]) ).
thf(f308,plain,
( ( $true = sF0 )
| ( ( ^ [Y0: $i] :
( ( appointment @ Y0 )
| ~ ( peter @ sK4 @ Y0 ) )
@ sK6 )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( appointment @ Y0 )
| ~ ( john @ sK5 @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f307]) ).
thf(f309,plain,
( ( $true = sF0 )
| ( ( ^ [Y0: $i] :
( ( appointment @ Y0 )
| ~ ( peter @ sK4 @ Y0 ) )
@ sK6 )
= $false )
| ( ( ^ [Y0: $i] :
( ( appointment @ Y0 )
| ~ ( john @ sK5 @ Y0 ) )
@ sK7 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f308]) ).
thf(f310,plain,
( ( $true = sF0 )
| ( $false
= ( ( appointment @ sK7 )
| ~ ( john @ sK5 @ sK7 ) ) )
| ( ( ( appointment @ sK6 )
| ~ ( peter @ sK4 @ sK6 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f309]) ).
thf(f312,plain,
( ( ( appointment @ sK7 )
= $false )
| ( ( ( appointment @ sK6 )
| ~ ( peter @ sK4 @ sK6 ) )
= $false )
| ( $true = sF0 ) ),
inference(or_proxy_clausification,[],[f310]) ).
thf(f314,plain,
( ( $true = sF0 )
| ( ( appointment @ sK6 )
= $false )
| ( ( appointment @ sK7 )
= $false ) ),
inference(or_proxy_clausification,[],[f312]) ).
thf(f394,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( john @ Y0 @ Y0 ) ) ),
inference(beta-eta_normalization,[],[f190]) ).
thf(f395,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( john @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f394]) ).
thf(f396,plain,
! [X1: $i] :
( $true
= ( john @ X1 @ X1 ) ),
inference(beta-eta_normalization,[],[f395]) ).
thf(f398,definition,
( spl12_1
<=> ( $true = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition]) ).
thf(f402,definition,
( spl12_2
<=> ( ( appointment @ sK6 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition]) ).
thf(f404,plain,
( ( ( appointment @ sK6 )
= $false )
| ~ spl12_2 ),
inference(avatar_component_clause,[],[f402]) ).
thf(f406,definition,
( spl12_3
<=> ( ( appointment @ sK7 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl12_3])],[avatar_definition]) ).
thf(f408,plain,
( ( ( appointment @ sK7 )
= $false )
| ~ spl12_3 ),
inference(avatar_component_clause,[],[f406]) ).
thf(f409,plain,
( spl12_1
| spl12_2
| spl12_3 ),
inference(avatar_split_clause,[],[f314,f406,f402,f398]) ).
thf(f459,definition,
( spl12_14
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( $true
= ( appointment @ X3 ) )
| ( ( peter @ X1 @ X2 )
= $false )
| ( ( john @ X2 @ X3 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl12_14])],[avatar_definition]) ).
thf(f460,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ( john @ X2 @ X3 )
= $false )
| ( $true
= ( appointment @ X3 ) )
| ( ( peter @ X1 @ X2 )
= $false ) )
| ~ spl12_14 ),
inference(avatar_component_clause,[],[f459]) ).
thf(f462,plain,
~ spl12_1,
inference(avatar_split_clause,[],[f194,f398]) ).
thf(f475,plain,
! [X0: $i] :
( ( $true
= ( time @ X0 ) )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f201,f232]) ).
thf(f480,plain,
! [X0: $i] :
( $true
= ( time @ X0 ) ),
inference(trivial_inequality_removal,[],[f475]) ).
thf(f489,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( peter @ X1 @ X0 ) )
| ( $true = $false )
| ( $true
= ( place @ X0 ) ) ),
inference(constrained_superposition,[],[f212,f396]) ).
thf(f495,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( peter @ X1 @ X0 ) )
| ( $true
= ( place @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f489]) ).
thf(f561,plain,
! [X0: $i] :
( ( $true
= ( place @ X0 ) )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f232,f495]) ).
thf(f568,plain,
! [X0: $i] :
( $true
= ( place @ X0 ) ),
inference(trivial_inequality_removal,[],[f561]) ).
thf(f597,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( time @ X3 )
= $false )
| ( $true
= ( appointment @ X3 ) )
| ( ( john @ X2 @ X3 )
= $false )
| ( $true = $false )
| ( ( peter @ X1 @ X2 )
= $false ) ),
inference(forward_demodulation,[],[f229,f568]) ).
thf(f598,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( time @ X3 )
= $false )
| ( ( peter @ X1 @ X2 )
= $false )
| ( ( john @ X2 @ X3 )
= $false )
| ( $true
= ( appointment @ X3 ) ) ),
inference(trivial_inequality_removal,[],[f597]) ).
thf(f599,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( john @ X2 @ X3 )
= $false )
| ( $true = $false )
| ( ( peter @ X1 @ X2 )
= $false )
| ( $true
= ( appointment @ X3 ) ) ),
inference(forward_demodulation,[],[f598,f480]) ).
thf(f600,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( appointment @ X3 ) )
| ( ( john @ X2 @ X3 )
= $false )
| ( ( peter @ X1 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f599]) ).
thf(f601,plain,
spl12_14,
inference(avatar_split_clause,[],[f600,f459]) ).
thf(f606,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( appointment @ X0 ) )
| ( $true = $false )
| ( $false
= ( peter @ X1 @ X0 ) ) )
| ~ spl12_14 ),
inference(constrained_superposition,[],[f396,f460]) ).
thf(f615,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( peter @ X1 @ X0 ) )
| ( $true
= ( appointment @ X0 ) ) )
| ~ spl12_14 ),
inference(trivial_inequality_removal,[],[f606]) ).
thf(f695,plain,
( ! [X0: $i] :
( ( $true
= ( appointment @ X0 ) )
| ( $true = $false ) )
| ~ spl12_14 ),
inference(constrained_superposition,[],[f232,f615]) ).
thf(f703,plain,
( ! [X0: $i] :
( $true
= ( appointment @ X0 ) )
| ~ spl12_14 ),
inference(trivial_inequality_removal,[],[f695]) ).
thf(f714,plain,
( ( $true = $false )
| ~ spl12_2
| ~ spl12_14 ),
inference(constrained_superposition,[],[f703,f404]) ).
thf(f720,plain,
( $false
| ~ spl12_2
| ~ spl12_14 ),
inference(trivial_inequality_removal,[],[f714]) ).
thf(f721,plain,
( ~ spl12_2
| ~ spl12_14 ),
inference(avatar_contradiction_clause,[],[f720]) ).
thf(f728,plain,
( ( $true = $false )
| ~ spl12_3
| ~ spl12_14 ),
inference(forward_demodulation,[],[f408,f703]) ).
thf(f729,plain,
( $false
| ~ spl12_3
| ~ spl12_14 ),
inference(trivial_inequality_removal,[],[f728]) ).
thf(f730,plain,
( ~ spl12_3
| ~ spl12_14 ),
inference(avatar_contradiction_clause,[],[f729]) ).
cnf(s1,plain,
( spl12_1
| spl12_2
| spl12_3 ),
inference(sat_conversion,[],[f409]) ).
cnf(s12,plain,
~ spl12_1,
inference(sat_conversion,[],[f462]) ).
cnf(s21,plain,
spl12_14,
inference(sat_conversion,[],[f601]) ).
cnf(s33,plain,
( ~ spl12_2
| ~ spl12_14 ),
inference(sat_conversion,[],[f721]) ).
cnf(s36,plain,
( ~ spl12_3
| ~ spl12_14 ),
inference(sat_conversion,[],[f730]) ).
cnf(s38,plain,
~ spl12_3,
inference(rat,[],[s36,s21]) ).
cnf(s40,plain,
~ spl12_2,
inference(rat,[],[s33,s21]) ).
cnf(s57,plain,
$false,
inference(rat,[],[s1,s38,s40,s12]) ).
thf(f731,plain,
$false,
inference(avatar_sat_refutation,[],[s57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ086^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.22 % Computer : n014.cluster.edu
% 0.12/0.22 % Model : x86_64 x86_64
% 0.12/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.22 % Memory : 8046.5625MB
% 0.12/0.22 % OS : Linux 6.8.0-71-generic
% 0.12/0.22 % CPULimit : 300
% 0.12/0.22 % WCLimit : 300
% 0.12/0.22 % DateTime : Tue Sep 29 13:21:45 UTC 2026
% 0.12/0.23 % CPUTime :
% 0.12/0.23 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.26 Running higher-order theorem proving
% 0.12/0.28 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.25/0.35 % (2637373)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.25/0.35 % (2637393)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1961615208:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.25/0.35 % (2637395)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.25/0.35 % (2637395)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.25/0.35 % (2637389)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3396170885:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.25/0.35 % (2637390)lrs+10_16_si=on:nwc=1.5:random_seed=2842319537:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.25/0.35 % (2637393)Instruction limit reached!
% 0.25/0.35 % (2637393)------------------------------
% 0.25/0.35 % (2637393)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.35 % (2637393)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.35 % (2637393)CaDiCaL version: 2.1.3
% 0.25/0.35 % (2637393)Termination reason: Instruction limit
% 0.25/0.35 % (2637393)Termination phase: Saturation
% 0.25/0.35 % (2637393)Time elapsed: 0.007 s
% 0.25/0.35 % (2637393)Peak memory usage: 11 MB
% 0.25/0.35 % (2637391)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3693043446:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.25/0.35 % (2637393)Instructions burned: 25 (million)
% 0.25/0.35 % (2637392)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=4277284069:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.25/0.35 % (2637395)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=1473096881:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.25/0.35 % (2637394)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=728939125:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.25/0.35 % (2637391)Instruction limit reached!
% 0.25/0.35 % (2637391)------------------------------
% 0.25/0.35 % (2637391)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.35 % (2637391)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.35 % (2637391)CaDiCaL version: 2.1.3
% 0.25/0.35 % (2637391)Termination reason: Instruction limit
% 0.25/0.35 % (2637391)Termination phase: Property scanning
% 0.25/0.35 % (2637391)Time elapsed: 0.002 s
% 0.25/0.35 % (2637391)Peak memory usage: 10 MB
% 0.25/0.35 % (2637391)Instructions burned: 4 (million)
% 0.25/0.35 % (2637390)Instruction limit reached!
% 0.25/0.35 % (2637390)------------------------------
% 0.25/0.35 % (2637390)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.35 % (2637390)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.35 % (2637390)CaDiCaL version: 2.1.3
% 0.25/0.35 % (2637390)Termination reason: Instruction limit
% 0.25/0.35 % (2637390)Termination phase: Saturation
% 0.25/0.35 % (2637390)Time elapsed: 0.008 s
% 0.25/0.35 % (2637390)Peak memory usage: 11 MB
% 0.25/0.35 % (2637390)Instructions burned: 18 (million)
% 0.25/0.35 % (2637407)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=593996355:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.25/0.35 % (2637407)Instruction limit reached!
% 0.25/0.35 % (2637407)------------------------------
% 0.25/0.35 % (2637407)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.35 % (2637407)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.35 % (2637407)CaDiCaL version: 2.1.3
% 0.25/0.35 % (2637407)Termination reason: Instruction limit
% 0.25/0.35 % (2637407)Termination phase: Property scanning
% 0.25/0.35 % (2637407)Time elapsed: 0.001 s
% 0.25/0.35 % (2637407)Peak memory usage: 10 MB
% 0.25/0.35 % (2637407)Instructions burned: 6 (million)
% 0.25/0.35 % (2637395) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2637373-2637395"...
% 0.25/0.35 % (2637409)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=166344244:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.25/0.35 % (2637409)Instruction limit reached!
% 0.25/0.35 % (2637409)------------------------------
% 0.25/0.35 % (2637409)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.35 % (2637409)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.35 % (2637409)CaDiCaL version: 2.1.3
% 0.25/0.35 % (2637409)Termination reason: Instruction limit
% 0.25/0.35 % (2637409)Termination phase: Property scanning
% 0.25/0.35 % (2637409)Time elapsed: 0.003 s
% 0.25/0.35 % (2637409)Peak memory usage: 10 MB
% 0.25/0.35 % (2637409)Instructions burned: 5 (million)
% 0.25/0.35 % (2637395)...printing done.
% 0.25/0.35 % (2637415)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2257321384:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.25/0.35 % (2637394) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2637373-2637394"...
% 0.25/0.35 % (2637395)Refutation found. Thanks to Tanya!
% 0.25/0.35 % SZS status Theorem for theBenchmark
% 0.25/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/0.35 % (2637395)------------------------------
% 0.25/0.35 % (2637395)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.35 % (2637395)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.35 % (2637395)CaDiCaL version: 2.1.3
% 0.25/0.35 % (2637395)Termination reason: Refutation
% 0.25/0.35 % (2637395)Time elapsed: 0.023 s
% 0.25/0.35 % (2637395)Peak memory usage: 13 MB
% 0.25/0.35 % (2637395)Instructions burned: 44 (million)
% 0.25/0.35 % (2637373)Success in time 0.061 s
% 0.25/0.35 % Vampire exiting
%------------------------------------------------------------------------------