%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : PUZ086^1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n005.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 08:21:01 AM UTC 2026
% Result : Theorem 0.19s 0.32s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 19
% Syntax : Number of formulae : 190 ( 79 unt; 0 typ; 6 def)
% Number of atoms : 1310 ( 253 equ; 0 cnn)
% Maximal formula atoms : 12 ( 6 avg)
% Number of connectives : 1590 ( 252 ~; 288 |; 0 &; 958 @)
% ( 6 <=>; 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 : 114 ( 114 >; 0 *; 0 +; 0 <<)
% Number of symbols : 70 ( 66 usr; 14 con; 0-4 aty)
% ( 86 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 349 ( 0 sgn 110 !; 0 ?; 349 :)
% 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,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_41,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_42,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
vNOT: $o > $o ).
thf(func_def_44,type,
vOR: $o > $o > $o ).
thf(func_def_45,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_48,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_49,type,
vIMP: $o > $o > $o ).
thf(func_def_50,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_51,type,
vAND: $o > $o > $o ).
thf(func_def_52,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_59,type,
sK6: $i > $i ).
thf(func_def_60,type,
sK7: $i > ( $i > $o ) > $i ).
thf(func_def_61,type,
sK8: $i > ( $i > $o ) > $i ).
thf(func_def_62,type,
sK9: $i > ( $i > $o ) > $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(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(f18,axiom,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mreflexive) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
mreflexive @ peter,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',refl_peter) ).
thf(f33,axiom,
mreflexive @ john,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',refl_john) ).
thf(f40,axiom,
mvalid @ ( mbox @ peter @ time ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_a) ).
thf(f41,axiom,
mvalid @ ( mbox @ peter @ ( mbox @ john @ place ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_b) ).
thf(f43,axiom,
mvalid @ ( mbox @ peter @ ( mbox @ john @ ( mimplies @ ( mand @ place @ time ) @ appointment ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_d) ).
thf(f44,conjecture,
mvalid @ ( mand @ ( mbox @ peter @ ( mbox @ john @ appointment ) ) @ ( mbox @ john @ ( mbox @ peter @ appointment ) ) ),
file('/export/starexec/sandbox2/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(f48,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f49,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f48]) ).
thf(f50,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f51,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f50]) ).
thf(f52,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f53,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f66,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f67,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f66]) ).
thf(f69,plain,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f70,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f69]) ).
thf(f89,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f90,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f89]) ).
thf(f97,plain,
mreflexive @ peter,
inference(rectify,[],[f32]) ).
thf(f98,plain,
( ( mreflexive @ peter )
= $true ),
inference(fool_elimination,[],[f97]) ).
thf(f99,plain,
mreflexive @ john,
inference(rectify,[],[f33]) ).
thf(f100,plain,
( ( mreflexive @ john )
= $true ),
inference(fool_elimination,[],[f99]) ).
thf(f113,plain,
mvalid @ ( mbox @ peter @ time ),
inference(rectify,[],[f40]) ).
thf(f114,plain,
( ( mvalid @ ( mbox @ peter @ time ) )
= $true ),
inference(fool_elimination,[],[f113]) ).
thf(f115,plain,
mvalid @ ( mbox @ peter @ ( mbox @ john @ place ) ),
inference(rectify,[],[f41]) ).
thf(f116,plain,
( ( mvalid @ ( mbox @ peter @ ( mbox @ john @ place ) ) )
= $true ),
inference(fool_elimination,[],[f115]) ).
thf(f119,plain,
mvalid @ ( mbox @ peter @ ( mbox @ john @ ( mimplies @ ( mand @ place @ time ) @ appointment ) ) ),
inference(rectify,[],[f43]) ).
thf(f120,plain,
( ( mvalid @ ( mbox @ peter @ ( mbox @ john @ ( mimplies @ ( mand @ place @ time ) @ appointment ) ) ) )
= $true ),
inference(fool_elimination,[],[f119]) ).
thf(f121,plain,
~ ( mvalid @ ( mand @ ( mbox @ peter @ ( mbox @ john @ appointment ) ) @ ( mbox @ john @ ( mbox @ peter @ appointment ) ) ) ),
inference(rectify,[],[f45]) ).
thf(f122,plain,
( ( mvalid @ ( mand @ ( mbox @ peter @ ( mbox @ john @ appointment ) ) @ ( mbox @ john @ ( mbox @ peter @ appointment ) ) ) )
!= $true ),
inference(fool_elimination,[],[f121]) ).
thf(f123,plain,
( ( mvalid @ ( mand @ ( mbox @ peter @ ( mbox @ john @ appointment ) ) @ ( mbox @ john @ ( mbox @ peter @ appointment ) ) ) )
!= $true ),
inference(flattening,[],[f122]) ).
thf(f126,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f49]) ).
thf(f127,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f51]) ).
thf(f128,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f52]) ).
thf(f129,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f53]) ).
thf(f139,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f67]) ).
thf(f141,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f70]) ).
thf(f151,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f155,plain,
( ( mreflexive @ peter )
= $true ),
inference(cnf_transformation,[],[f98]) ).
thf(f156,plain,
( ( mreflexive @ john )
= $true ),
inference(cnf_transformation,[],[f100]) ).
thf(f163,plain,
( ( mvalid @ ( mbox @ peter @ time ) )
= $true ),
inference(cnf_transformation,[],[f114]) ).
thf(f164,plain,
( ( mvalid @ ( mbox @ peter @ ( mbox @ john @ place ) ) )
= $true ),
inference(cnf_transformation,[],[f116]) ).
thf(f166,plain,
( ( mvalid @ ( mbox @ peter @ ( mbox @ john @ ( mimplies @ ( mand @ place @ time ) @ appointment ) ) ) )
= $true ),
inference(cnf_transformation,[],[f120]) ).
thf(f167,plain,
( ( mvalid @ ( mand @ ( mbox @ peter @ ( mbox @ john @ appointment ) ) @ ( mbox @ john @ ( mbox @ peter @ appointment ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f123]) ).
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] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f128,f126,f127,f126,f126]) ).
thf(f171,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,[],[f129,f127,f126]) ).
thf(f179,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ peter ) ),
inference(definition_unfolding,[],[f155,f141]) ).
thf(f180,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ john ) ),
inference(definition_unfolding,[],[f156,f141]) ).
thf(f187,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 ) ) )
@ peter
@ time ) ) ),
inference(definition_unfolding,[],[f163,f151,f139]) ).
thf(f188,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 ) ) )
@ peter
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ john
@ place ) ) ) ),
inference(definition_unfolding,[],[f164,f151,f139,f139]) ).
thf(f190,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 ) ) )
@ peter
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ john
@ ( ^ [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 )
@ ( ^ [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 ) ) )
@ place
@ time )
@ appointment ) ) ) ) ),
inference(definition_unfolding,[],[f166,f151,f139,f139,f171,f170]) ).
thf(f191,plain,
( $true
!= ( ^ [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] :
( ( Y2 @ Y4 )
| ( Y3 @ 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] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ peter
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ john
@ appointment ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ john
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ peter
@ appointment ) ) ) ) ),
inference(definition_unfolding,[],[f167,f151,f170,f139,f139,f139,f139]) ).
thf(f192,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( peter @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( john @ Y1 @ Y2 )
| ( appointment @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( john @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( peter @ Y1 @ Y2 )
| ( appointment @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f191]) ).
thf(f193,plain,
( $false
= ( ^ [Y0: $i] :
~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( peter @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( john @ Y1 @ Y2 )
| ( appointment @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( john @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( peter @ Y1 @ Y2 )
| ( appointment @ Y2 ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f192]) ).
thf(f194,plain,
( $false
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( peter @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( john @ Y0 @ Y1 )
| ( appointment @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( john @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( peter @ Y0 @ Y1 )
| ( appointment @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f193]) ).
thf(f195,plain,
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( peter @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( john @ Y0 @ Y1 )
| ( appointment @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( john @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( peter @ Y0 @ Y1 )
| ( appointment @ Y1 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f194]) ).
thf(f196,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( john @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( peter @ Y0 @ Y1 )
| ( appointment @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( peter @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( john @ Y0 @ Y1 )
| ( appointment @ Y1 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f195]) ).
thf(f197,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( john @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( peter @ Y0 @ Y1 )
| ( appointment @ Y1 ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( peter @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( john @ Y0 @ Y1 )
| ( appointment @ Y1 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f196]) ).
thf(f198,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( john @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( peter @ Y0 @ Y1 )
| ( appointment @ Y1 ) ) ) )
@ sK1 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( peter @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( john @ Y0 @ Y1 )
| ( appointment @ Y1 ) ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f197]) ).
thf(f199,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( john @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( peter @ Y0 @ Y1 )
| ( appointment @ Y1 ) ) ) )
@ sK1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( peter @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( john @ Y0 @ Y1 )
| ( appointment @ Y1 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f198]) ).
thf(f200,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( john @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( peter @ Y0 @ Y1 )
| ( appointment @ Y1 ) ) ) )
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( peter @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( john @ Y0 @ Y1 )
| ( appointment @ Y1 ) ) ) )
@ sK2 ) ) ),
inference(sigma_proxy_clausification,[],[f199]) ).
thf(f201,plain,
( ( $false
= ( ~ ( john @ sK0 @ sK1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( peter @ sK1 @ Y0 )
| ( appointment @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( peter @ sK0 @ sK2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( john @ sK2 @ Y0 )
| ( appointment @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f200]) ).
thf(f202,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( peter @ sK1 @ Y0 )
| ( appointment @ Y0 ) ) ) )
| ( $false
= ( ~ ( peter @ sK0 @ sK2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( john @ sK2 @ Y0 )
| ( appointment @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f201]) ).
thf(f213,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( peter @ sK1 @ Y0 )
| ( appointment @ Y0 ) )
@ sK4 ) )
| ( $false
= ( ~ ( peter @ sK0 @ sK2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( john @ sK2 @ Y0 )
| ( appointment @ Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f202]) ).
thf(f214,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( peter @ sK1 @ Y0 )
| ( appointment @ Y0 ) )
@ sK4 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( john @ sK2 @ Y0 )
| ( appointment @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f213]) ).
thf(f221,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( peter @ sK1 @ Y0 )
| ( appointment @ Y0 ) )
@ sK4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( john @ sK2 @ Y0 )
| ( appointment @ Y0 ) )
@ sK5 ) ) ),
inference(sigma_proxy_clausification,[],[f214]) ).
thf(f222,plain,
( ( $false
= ( ~ ( peter @ sK1 @ sK4 )
| ( appointment @ sK4 ) ) )
| ( $false
= ( ~ ( john @ sK2 @ sK5 )
| ( appointment @ sK5 ) ) ) ),
inference(beta-eta_normalization,[],[f221]) ).
thf(f223,plain,
( ( $false
= ( appointment @ sK4 ) )
| ( $false
= ( ~ ( john @ sK2 @ sK5 )
| ( appointment @ sK5 ) ) ) ),
inference(or_proxy_clausification,[],[f222]) ).
thf(f224,plain,
( ( $false
= ( ~ ( peter @ sK1 @ sK4 ) ) )
| ( $false
= ( ~ ( john @ sK2 @ sK5 )
| ( appointment @ sK5 ) ) ) ),
inference(or_proxy_clausification,[],[f222]) ).
thf(f225,plain,
( ( $true
= ( peter @ sK1 @ sK4 ) )
| ( $false
= ( ~ ( john @ sK2 @ sK5 )
| ( appointment @ sK5 ) ) ) ),
inference(not_proxy_clausification,[],[f224]) ).
thf(f226,plain,
( ( $true
= ( peter @ sK1 @ sK4 ) )
| ( $false
= ( appointment @ sK5 ) ) ),
inference(or_proxy_clausification,[],[f225]) ).
thf(f227,plain,
( ( $true
= ( peter @ sK1 @ sK4 ) )
| ( $false
= ( ~ ( john @ sK2 @ sK5 ) ) ) ),
inference(or_proxy_clausification,[],[f225]) ).
thf(f228,plain,
( ( $true
= ( peter @ sK1 @ sK4 ) )
| ( $true
= ( john @ sK2 @ sK5 ) ) ),
inference(not_proxy_clausification,[],[f227]) ).
thf(f229,plain,
( ( $false
= ( appointment @ sK4 ) )
| ( $false
= ( appointment @ sK5 ) ) ),
inference(or_proxy_clausification,[],[f223]) ).
thf(f230,plain,
( ( $false
= ( appointment @ sK4 ) )
| ( $false
= ( ~ ( john @ sK2 @ sK5 ) ) ) ),
inference(or_proxy_clausification,[],[f223]) ).
thf(f231,plain,
( ( $false
= ( appointment @ sK4 ) )
| ( $true
= ( john @ sK2 @ sK5 ) ) ),
inference(not_proxy_clausification,[],[f230]) ).
thf(f232,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( peter @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( john @ Y1 @ Y2 )
| ~ ~ ( ~ ( place @ Y2 )
| ~ ( time @ Y2 ) )
| ( appointment @ Y2 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f190]) ).
thf(f233,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( peter @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( john @ Y1 @ Y2 )
| ~ ~ ( ~ ( place @ Y2 )
| ~ ( time @ Y2 ) )
| ( appointment @ Y2 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f232]) ).
thf(f234,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( peter @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( john @ Y0 @ Y1 )
| ~ ~ ( ~ ( place @ Y1 )
| ~ ( time @ Y1 ) )
| ( appointment @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f233]) ).
thf(f235,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( peter @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( john @ Y0 @ Y1 )
| ~ ~ ( ~ ( place @ Y1 )
| ~ ( time @ Y1 ) )
| ( appointment @ Y1 ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f234]) ).
thf(f236,plain,
! [X2: $i,X1: $i] :
( $true
= ( ~ ( peter @ X1 @ X2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( john @ X2 @ Y0 )
| ~ ~ ( ~ ( place @ Y0 )
| ~ ( time @ Y0 ) )
| ( appointment @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f235]) ).
thf(f237,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( john @ X2 @ Y0 )
| ~ ~ ( ~ ( place @ Y0 )
| ~ ( time @ Y0 ) )
| ( appointment @ Y0 ) ) ) )
| ( $true
= ( ~ ( peter @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f236]) ).
thf(f238,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( john @ X2 @ Y0 )
| ~ ~ ( ~ ( place @ Y0 )
| ~ ( time @ Y0 ) )
| ( appointment @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( peter @ X1 @ X2 ) ) ) ),
inference(pi_proxy_clausification,[],[f237]) ).
thf(f239,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( john @ X2 @ Y0 )
| ~ ~ ( ~ ( place @ Y0 )
| ~ ( time @ Y0 ) )
| ( appointment @ Y0 ) )
@ X3 ) )
| ( $false
= ( peter @ X1 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f238]) ).
thf(f240,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( john @ X2 @ X3 )
| ~ ~ ( ~ ( place @ X3 )
| ~ ( time @ X3 ) )
| ( appointment @ X3 ) ) )
| ( $false
= ( peter @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f239]) ).
thf(f241,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ~ ( ~ ( place @ X3 )
| ~ ( time @ X3 ) )
| ( appointment @ X3 ) ) )
| ( $false
= ( peter @ X1 @ X2 ) )
| ( $true
= ( ~ ( john @ X2 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f240]) ).
thf(f242,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( appointment @ X3 ) )
| ( $false
= ( peter @ X1 @ X2 ) )
| ( $true
= ( ~ ( john @ X2 @ X3 ) ) )
| ( $true
= ( ~ ~ ( ~ ( place @ X3 )
| ~ ( time @ X3 ) ) ) ) ),
inference(or_proxy_clausification,[],[f241]) ).
thf(f243,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( appointment @ X3 ) )
| ( $false
= ( peter @ X1 @ X2 ) )
| ( $false
= ( john @ X2 @ X3 ) )
| ( $true
= ( ~ ~ ( ~ ( place @ X3 )
| ~ ( time @ X3 ) ) ) ) ),
inference(not_proxy_clausification,[],[f242]) ).
thf(f244,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( appointment @ X3 ) )
| ( $false
= ( peter @ X1 @ X2 ) )
| ( $false
= ( john @ X2 @ X3 ) )
| ( $false
= ( ~ ( ~ ( place @ X3 )
| ~ ( time @ X3 ) ) ) ) ),
inference(not_proxy_clausification,[],[f243]) ).
thf(f245,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( appointment @ X3 ) )
| ( $false
= ( peter @ X1 @ X2 ) )
| ( $false
= ( john @ X2 @ X3 ) )
| ( $true
= ( ~ ( place @ X3 )
| ~ ( time @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f244]) ).
thf(f246,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( appointment @ X3 ) )
| ( $false
= ( peter @ X1 @ X2 ) )
| ( $false
= ( john @ X2 @ X3 ) )
| ( $true
= ( ~ ( time @ X3 ) ) )
| ( $true
= ( ~ ( place @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f245]) ).
thf(f247,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( appointment @ X3 ) )
| ( $false
= ( peter @ X1 @ X2 ) )
| ( $false
= ( john @ X2 @ X3 ) )
| ( $false
= ( time @ X3 ) )
| ( $true
= ( ~ ( place @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f246]) ).
thf(f248,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( john @ X2 @ X3 ) )
| ( $false
= ( peter @ X1 @ X2 ) )
| ( $true
= ( appointment @ X3 ) )
| ( $false
= ( time @ X3 ) )
| ( $false
= ( place @ X3 ) ) ),
inference(not_proxy_clausification,[],[f247]) ).
thf(f267,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( peter @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( john @ Y1 @ Y2 )
| ( place @ Y2 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f188]) ).
thf(f268,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( peter @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( john @ Y1 @ Y2 )
| ( place @ Y2 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f267]) ).
thf(f269,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( peter @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( john @ Y0 @ Y1 )
| ( place @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f268]) ).
thf(f270,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( peter @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( john @ Y0 @ Y1 )
| ( place @ Y1 ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f269]) ).
thf(f271,plain,
! [X2: $i,X1: $i] :
( $true
= ( ~ ( peter @ X1 @ X2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( john @ X2 @ Y0 )
| ( place @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f270]) ).
thf(f272,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( john @ X2 @ Y0 )
| ( place @ Y0 ) ) ) )
| ( $true
= ( ~ ( peter @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f271]) ).
thf(f273,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( john @ X2 @ Y0 )
| ( place @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( peter @ X1 @ X2 ) ) ) ),
inference(pi_proxy_clausification,[],[f272]) ).
thf(f274,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( john @ X2 @ Y0 )
| ( place @ Y0 ) )
@ X3 ) )
| ( $false
= ( peter @ X1 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f273]) ).
thf(f275,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( john @ X2 @ X3 )
| ( place @ X3 ) ) )
| ( $false
= ( peter @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f274]) ).
thf(f276,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( place @ X3 ) )
| ( $false
= ( peter @ X1 @ X2 ) )
| ( $true
= ( ~ ( john @ X2 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f275]) ).
thf(f277,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( john @ X2 @ X3 ) )
| ( $false
= ( peter @ X1 @ X2 ) )
| ( $true
= ( place @ X3 ) ) ),
inference(not_proxy_clausification,[],[f276]) ).
thf(f278,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( peter @ Y0 @ Y1 )
| ( time @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f187]) ).
thf(f279,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( peter @ Y0 @ Y1 )
| ( time @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f278]) ).
thf(f280,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( peter @ X1 @ Y0 )
| ( time @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f279]) ).
thf(f281,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( peter @ X1 @ Y0 )
| ( time @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f280]) ).
thf(f282,plain,
! [X2: $i,X1: $i] :
( $true
= ( ~ ( peter @ X1 @ X2 )
| ( time @ X2 ) ) ),
inference(beta-eta_normalization,[],[f281]) ).
thf(f283,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( time @ X2 ) )
| ( $true
= ( ~ ( peter @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f282]) ).
thf(f284,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( peter @ X1 @ X2 ) )
| ( $true
= ( time @ X2 ) ) ),
inference(not_proxy_clausification,[],[f283]) ).
thf(f359,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( john @ Y0 @ Y0 ) ) ),
inference(beta-eta_normalization,[],[f180]) ).
thf(f360,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( john @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f359]) ).
thf(f361,plain,
! [X1: $i] :
( $true
= ( john @ X1 @ X1 ) ),
inference(beta-eta_normalization,[],[f360]) ).
thf(f362,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( peter @ Y0 @ Y0 ) ) ),
inference(beta-eta_normalization,[],[f179]) ).
thf(f363,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( peter @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f362]) ).
thf(f364,plain,
! [X1: $i] :
( $true
= ( peter @ X1 @ X1 ) ),
inference(beta-eta_normalization,[],[f363]) ).
thf(f385,definition,
( spl10_5
<=> ( $true
= ( peter @ sK1 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_5])],[avatar_definition]) ).
thf(f387,plain,
( ( $true
= ( peter @ sK1 @ sK4 ) )
| ~ spl10_5 ),
inference(avatar_component_clause,[],[f385]) ).
thf(f390,definition,
( spl10_6
<=> ( $false
= ( appointment @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_6])],[avatar_definition]) ).
thf(f392,plain,
( ( $false
= ( appointment @ sK4 ) )
| ~ spl10_6 ),
inference(avatar_component_clause,[],[f390]) ).
thf(f395,definition,
( spl10_7
<=> ( $true
= ( john @ sK2 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_7])],[avatar_definition]) ).
thf(f397,plain,
( ( $true
= ( john @ sK2 @ sK5 ) )
| ~ spl10_7 ),
inference(avatar_component_clause,[],[f395]) ).
thf(f398,plain,
( spl10_7
| spl10_5 ),
inference(avatar_split_clause,[],[f228,f385,f395]) ).
thf(f400,definition,
( spl10_8
<=> ( $false
= ( appointment @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_8])],[avatar_definition]) ).
thf(f402,plain,
( ( $false
= ( appointment @ sK5 ) )
| ~ spl10_8 ),
inference(avatar_component_clause,[],[f400]) ).
thf(f403,plain,
( spl10_8
| spl10_5 ),
inference(avatar_split_clause,[],[f226,f385,f400]) ).
thf(f404,plain,
( spl10_7
| spl10_6 ),
inference(avatar_split_clause,[],[f231,f390,f395]) ).
thf(f405,plain,
( spl10_8
| spl10_6 ),
inference(avatar_split_clause,[],[f229,f390,f400]) ).
thf(f418,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( time @ X0 ) ) ),
inference(constrained_superposition,[],[f364,f284]) ).
thf(f421,plain,
! [X0: $i] :
( $true
= ( time @ X0 ) ),
inference(trivial_inequality_removal,[],[f418]) ).
thf(f430,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( peter @ X1 @ X0 ) )
| ( $true
= ( place @ X0 ) ) ),
inference(constrained_superposition,[],[f361,f277]) ).
thf(f432,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( john @ X0 @ X1 ) )
| ( $true
= ( place @ X1 ) ) ),
inference(constrained_superposition,[],[f364,f277]) ).
thf(f433,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( john @ X0 @ X1 ) )
| ( $true
= ( place @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f432]) ).
thf(f435,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( peter @ X1 @ X0 ) )
| ( $true
= ( place @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f430]) ).
thf(f534,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( peter @ X1 @ X0 ) )
| ( $true
= ( appointment @ X0 ) )
| ( $false
= ( time @ X0 ) )
| ( $false
= ( place @ X0 ) ) ),
inference(constrained_superposition,[],[f361,f248]) ).
thf(f538,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( john @ X0 @ X1 ) )
| ( $true
= ( appointment @ X1 ) )
| ( $false
= ( time @ X1 ) )
| ( $false
= ( place @ X1 ) ) ),
inference(constrained_superposition,[],[f364,f248]) ).
thf(f541,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( john @ X0 @ X1 ) )
| ( $true
= ( appointment @ X1 ) )
| ( $false
= ( time @ X1 ) )
| ( $false
= ( place @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f538]) ).
thf(f545,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( peter @ X1 @ X0 ) )
| ( $true
= ( appointment @ X0 ) )
| ( $false
= ( time @ X0 ) )
| ( $false
= ( place @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f534]) ).
thf(f704,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( john @ X0 @ X1 ) )
| ( $true
= ( appointment @ X1 ) )
| ( $false
= ( place @ X1 ) ) ),
inference(forward_demodulation,[],[f541,f421]) ).
thf(f705,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( john @ X0 @ X1 ) )
| ( $true
= ( appointment @ X1 ) )
| ( $false
= ( place @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f704]) ).
thf(f731,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( peter @ X1 @ X0 ) )
| ( $true
= ( appointment @ X0 ) )
| ( $false
= ( place @ X0 ) ) ),
inference(forward_demodulation,[],[f545,f421]) ).
thf(f732,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( peter @ X1 @ X0 ) )
| ( $true
= ( appointment @ X0 ) )
| ( $false
= ( place @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f731]) ).
thf(f736,plain,
( ( $true = $false )
| ( $true
= ( place @ sK5 ) )
| ~ spl10_7 ),
inference(constrained_superposition,[],[f397,f433]) ).
thf(f742,plain,
( ( $true = $false )
| ( $true
= ( appointment @ sK5 ) )
| ( $false
= ( place @ sK5 ) )
| ~ spl10_7 ),
inference(constrained_superposition,[],[f705,f397]) ).
thf(f743,plain,
( ( $true
= ( appointment @ sK5 ) )
| ( $false
= ( place @ sK5 ) )
| ~ spl10_7 ),
inference(trivial_inequality_removal,[],[f742]) ).
thf(f749,plain,
( ( $true
= ( place @ sK5 ) )
| ~ spl10_7 ),
inference(trivial_inequality_removal,[],[f736]) ).
thf(f753,plain,
( ( $true = $false )
| ( $false
= ( place @ sK5 ) )
| ~ spl10_7
| ~ spl10_8 ),
inference(forward_demodulation,[],[f743,f402]) ).
thf(f756,definition,
( spl10_17
<=> ( $true
= ( place @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_17])],[avatar_definition]) ).
thf(f758,plain,
( ( $true
= ( place @ sK5 ) )
| ~ spl10_17 ),
inference(avatar_component_clause,[],[f756]) ).
thf(f767,plain,
( spl10_17
| ~ spl10_7 ),
inference(avatar_split_clause,[],[f749,f395,f756]) ).
thf(f776,definition,
( spl10_19
<=> ( $false
= ( place @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_19])],[avatar_definition]) ).
thf(f778,plain,
( ( $false
= ( place @ sK5 ) )
| ~ spl10_19 ),
inference(avatar_component_clause,[],[f776]) ).
thf(f807,plain,
( ( $true = $false )
| ( $true
= ( place @ sK4 ) )
| ~ spl10_5 ),
inference(constrained_superposition,[],[f435,f387]) ).
thf(f808,plain,
( ( $true = $false )
| ( $true
= ( appointment @ sK4 ) )
| ( $false
= ( place @ sK4 ) )
| ~ spl10_5 ),
inference(constrained_superposition,[],[f732,f387]) ).
thf(f809,plain,
( ( $true
= ( appointment @ sK4 ) )
| ( $false
= ( place @ sK4 ) )
| ~ spl10_5 ),
inference(trivial_inequality_removal,[],[f808]) ).
thf(f810,plain,
( ( $true
= ( place @ sK4 ) )
| ~ spl10_5 ),
inference(trivial_inequality_removal,[],[f807]) ).
thf(f817,plain,
( ( $true = $false )
| ( $false
= ( place @ sK4 ) )
| ~ spl10_5
| ~ spl10_6 ),
inference(forward_demodulation,[],[f809,f392]) ).
thf(f818,plain,
( ( $false
= ( place @ sK4 ) )
| ~ spl10_5
| ~ spl10_6 ),
inference(trivial_inequality_removal,[],[f817]) ).
thf(f1126,plain,
( ( $true = $false )
| ~ spl10_5
| ~ spl10_6 ),
inference(constrained_superposition,[],[f818,f810]) ).
thf(f1138,plain,
( $false
| ~ spl10_5
| ~ spl10_6 ),
inference(trivial_inequality_removal,[],[f1126]) ).
thf(f1139,plain,
( ~ spl10_5
| ~ spl10_6 ),
inference(avatar_contradiction_clause,[],[f1138]) ).
thf(f1145,plain,
( ( $false
= ( place @ sK5 ) )
| ~ spl10_7
| ~ spl10_8 ),
inference(trivial_inequality_removal,[],[f753]) ).
thf(f1148,plain,
( spl10_19
| ~ spl10_7
| ~ spl10_8 ),
inference(avatar_split_clause,[],[f1145,f400,f395,f776]) ).
thf(f1278,plain,
( ( $true = $false )
| ~ spl10_17
| ~ spl10_19 ),
inference(constrained_superposition,[],[f758,f778]) ).
thf(f1279,plain,
( $false
| ~ spl10_17
| ~ spl10_19 ),
inference(trivial_inequality_removal,[],[f1278]) ).
thf(f1280,plain,
( ~ spl10_17
| ~ spl10_19 ),
inference(avatar_contradiction_clause,[],[f1279]) ).
cnf(s6,plain,
( spl10_5
| spl10_7 ),
inference(sat_conversion,[],[f398]) ).
cnf(s7,plain,
( spl10_5
| spl10_8 ),
inference(sat_conversion,[],[f403]) ).
cnf(s8,plain,
( spl10_6
| spl10_7 ),
inference(sat_conversion,[],[f404]) ).
cnf(s9,plain,
( spl10_6
| spl10_8 ),
inference(sat_conversion,[],[f405]) ).
cnf(s29,plain,
( ~ spl10_7
| spl10_17 ),
inference(sat_conversion,[],[f767]) ).
cnf(s34,plain,
( ~ spl10_5
| ~ spl10_6 ),
inference(sat_conversion,[],[f1139]) ).
cnf(s36,plain,
( ~ spl10_7
| ~ spl10_8
| spl10_19 ),
inference(sat_conversion,[],[f1148]) ).
cnf(s43,plain,
( ~ spl10_17
| ~ spl10_19 ),
inference(sat_conversion,[],[f1280]) ).
cnf(s56,plain,
( ~ spl10_7
| ~ spl10_8 ),
inference(rat,[],[s43,s29,s36]) ).
cnf(s57,plain,
spl10_5,
inference(rat,[],[s56,s6,s7]) ).
cnf(s58,plain,
~ spl10_6,
inference(rat,[],[s34,s57]) ).
cnf(s59,plain,
spl10_8,
inference(rat,[],[s9,s58]) ).
cnf(s60,plain,
spl10_7,
inference(rat,[],[s8,s58]) ).
cnf(s61,plain,
$false,
inference(rat,[],[s56,s59,s60]) ).
thf(f1292,plain,
$false,
inference(avatar_sat_refutation,[],[s61]) ).
%------------------------------------------------------------------------------
%----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/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n005.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 13:21:46 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.32 % (1643846)Will run a generic schedule for satisfiability detection.
% 0.19/0.32 % (1643851)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2053218387_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.32 % Exception at run slice level
% 0.19/0.32 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.32 % (1643852)% WARNING: option uhcvi not known.
% 0.19/0.32 % (1643855)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=851967576:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.32 % (1643854)dis+10_1_sil=32000:sp=arity:random_seed=1773925791:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.32 % (1643852)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=693696995:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.32 % (1643853)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2822763559:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.32 % (1643856)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3900415065:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.32 % (1643855)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.32 % (1643852)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.32 % (1643852)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.32 % (1643857)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1230596362:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.32 % (1643859)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2999789443:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.19/0.32 % Exception at run slice level
% 0.19/0.32 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.32 % (1643856)Instruction limit reached!
% 0.19/0.32 % (1643856)------------------------------
% 0.19/0.32 % (1643856)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.32 % (1643856)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.32 % (1643856)CaDiCaL version: 2.1.3
% 0.19/0.32 % (1643856)Termination reason: Instruction limit
% 0.19/0.32 % (1643856)Termination phase: Saturation
% 0.19/0.32 % (1643856)Time elapsed: 0.034 s
% 0.19/0.32 % (1643856)Peak memory usage: 12 MB
% 0.19/0.32 % (1643856)Instructions burned: 131 (million)
% 0.19/0.32 % (1643867)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3554412926:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.32 % (1643869)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=1597195727:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.19/0.32 % (1643854) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1643846-1643854"...
% 0.19/0.32 % (1643869)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.32 % (1643869)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.32 % (1643854)...printing done.
% 0.19/0.32 % (1643855)Instruction limit reached!
% 0.19/0.32 % (1643855)------------------------------
% 0.19/0.32 % (1643855)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.32 % (1643855)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.32 % (1643855)CaDiCaL version: 2.1.3
% 0.19/0.32 % (1643855)Termination reason: Instruction limit
% 0.19/0.32 % (1643855)Termination phase: Saturation
% 0.19/0.32 % (1643855)Time elapsed: 0.055 s
% 0.19/0.32 % (1643855)Peak memory usage: 12 MB
% 0.19/0.32 % (1643855)Instructions burned: 118 (million)
% 0.19/0.32 % (1643854)Refutation found. Thanks to Tanya!
% 0.19/0.32 % SZS status Theorem for theBenchmark
% 0.19/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.32 % (1643854)------------------------------
% 0.19/0.32 % (1643854)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.32 % (1643854)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.32 % (1643854)CaDiCaL version: 2.1.3
% 0.19/0.32 % (1643854)Termination reason: Refutation
% 0.19/0.32 % (1643854)Time elapsed: 0.053 s
% 0.19/0.32 % (1643854)Peak memory usage: 13 MB
% 0.19/0.32 % (1643854)Instructions burned: 110 (million)
% 0.19/0.32 % (1643846)Success in time 0.096 s
% 0.19/0.32 % Vampire exiting
%------------------------------------------------------------------------------