%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : AGT028^2 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 07:44:36 AM UTC 2026
% Result : Theorem 0.08s 0.17s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 10
% Syntax : Number of formulae : 77 ( 61 unt; 0 typ; 0 def)
% Number of atoms : 368 ( 81 equ; 0 cnn)
% Maximal formula atoms : 7 ( 4 avg)
% Number of connectives : 541 ( 58 ~; 47 |; 0 &; 398 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 83 ( 83 >; 0 *; 0 +; 0 <<)
% Number of symbols : 82 ( 78 usr; 8 con; 0-4 aty)
% ( 38 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 197 ( 154 ^; 43 !; 0 ?; 197 :)
% 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,
r1: $i > $i > $o ).
thf(func_def_33,type,
r2: $i > $i > $o ).
thf(func_def_34,type,
r3: $i > $i > $o ).
thf(func_def_35,type,
r4: $i > $i > $o ).
thf(func_def_36,type,
r5: $i > $i > $o ).
thf(func_def_37,type,
john: mu ).
thf(func_def_38,type,
tom: mu ).
thf(func_def_39,type,
peter: mu ).
thf(func_def_40,type,
mike: mu ).
thf(func_def_41,type,
good_in_maths: mu > $i > $o ).
thf(func_def_42,type,
maths_teacher: mu > $i > $o ).
thf(func_def_43,type,
mathematician: mu > $i > $o ).
thf(func_def_44,type,
maths_student: mu > $i > $o ).
thf(func_def_45,type,
good_in_physics: mu > $i > $o ).
thf(func_def_46,type,
physics_student: mu > $i > $o ).
thf(func_def_47,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_48,type,
vNOT: $o > $o ).
thf(func_def_49,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_50,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_51,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_54,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_55,type,
vOR: $o > $o > $o ).
thf(func_def_56,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_57,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_58,type,
vIMP: $o > $o > $o ).
thf(func_def_59,type,
vAND: $o > $o > $o ).
thf(func_def_60,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_61,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_62,type,
sK0: $i > mu > $i ).
thf(func_def_63,type,
sK1: $i > mu > $i ).
thf(func_def_64,type,
sK2: $i > mu > $i ).
thf(func_def_66,type,
sK4: mu > $i ).
thf(func_def_67,type,
sK5: $i > mu > $i ).
thf(func_def_68,type,
sK6: $i > mu > $i ).
thf(func_def_69,type,
sK7: $i > mu > $i ).
thf(func_def_70,type,
sK8: $i > mu > $i ).
thf(func_def_71,type,
sK9: $i > mu > $i ).
thf(func_def_72,type,
sK10: $i > mu > $i ).
thf(func_def_73,type,
sK11: $i > mu > $i ).
thf(func_def_74,type,
sK12: $i > mu > $i ).
thf(func_def_75,type,
sK13: $i > mu > $i ).
thf(func_def_76,type,
sK14: $i > mu > $i ).
thf(func_def_77,type,
sK15: $i > mu > $i ).
thf(func_def_78,type,
sK16: $i > mu > $i ).
thf(func_def_79,type,
sK17: $i > mu > $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] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mor) ).
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(f10,axiom,
( ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] : ( X0 @ X2 @ X1 ) )
= mforall_ind ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/LCL013^0.ax',mbox) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] : ( mimplies @ ( maths_teacher @ X0 ) @ ( mbox @ r4 @ ( good_in_maths @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_r1) ).
thf(f49,axiom,
mvalid @ ( maths_teacher @ john ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_a6) ).
thf(f53,conjecture,
( mvalid
@ ( mexists_ind
@ ^ [X0: mu] : ( mbox @ r4 @ ( good_in_maths @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(f54,negated_conjecture,
~ ( mvalid
@ ( mexists_ind
@ ^ [X0: mu] : ( mbox @ r4 @ ( good_in_maths @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
thf(f62,plain,
mvalid @ ( maths_teacher @ john ),
inference(rectify,[],[f49]) ).
thf(f63,plain,
( ( mvalid @ ( maths_teacher @ john ) )
= $true ),
inference(fool_elimination,[],[f62]) ).
thf(f64,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f65,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f64]) ).
thf(f70,plain,
~ ( mvalid
@ ( mexists_ind
@ ^ [X0: mu] : ( mbox @ r4 @ ( good_in_maths @ X0 ) ) ) ),
inference(rectify,[],[f54]) ).
thf(f71,plain,
( ( mvalid
@ ( mexists_ind
@ ^ [Y0: mu] : ( mbox @ r4 @ ( good_in_maths @ Y0 ) ) ) )
!= $true ),
inference(fool_elimination,[],[f70]) ).
thf(f74,plain,
( ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] : ( X0 @ X2 @ X1 ) )
= mforall_ind ),
inference(rectify,[],[f10]) ).
thf(f75,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f74]) ).
thf(f80,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f81,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f80]) ).
thf(f96,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f97,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f96]) ).
thf(f107,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f110,plain,
( mexists_ind
= ( ^ [X0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X1: mu] : ( mnot @ ( X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f12]) ).
thf(f111,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f110]) ).
thf(f121,plain,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] : ( mimplies @ ( maths_teacher @ X0 ) @ ( mbox @ r4 @ ( good_in_maths @ X0 ) ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f122,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] : ( mimplies @ ( maths_teacher @ Y0 ) @ ( mbox @ r4 @ ( good_in_maths @ Y0 ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f121]) ).
thf(f143,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f144,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f143]) ).
thf(f150,plain,
( ( mvalid
@ ( mexists_ind
@ ^ [Y0: mu] : ( mbox @ r4 @ ( good_in_maths @ Y0 ) ) ) )
!= $true ),
inference(flattening,[],[f71]) ).
thf(f154,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f107]) ).
thf(f161,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f97]) ).
thf(f168,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f144]) ).
thf(f170,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f65]) ).
thf(f174,plain,
( ( mvalid @ ( maths_teacher @ john ) )
= $true ),
inference(cnf_transformation,[],[f63]) ).
thf(f186,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] : ( mimplies @ ( maths_teacher @ Y0 ) @ ( mbox @ r4 @ ( good_in_maths @ Y0 ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f122]) ).
thf(f189,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f111]) ).
thf(f190,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f81]) ).
thf(f198,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f75]) ).
thf(f201,plain,
( ( mvalid
@ ( mexists_ind
@ ^ [Y0: mu] : ( mbox @ r4 @ ( good_in_maths @ Y0 ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f150]) ).
thf(f207,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,[],[f154,f161,f190]) ).
thf(f211,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,[],[f189,f190,f198,f190]) ).
thf(f223,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( maths_teacher @ john ) )
= $true ),
inference(definition_unfolding,[],[f174,f168]) ).
thf(f231,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: mu] :
( ^ [Y1: $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y3 @ Y5 )
| ( Y4 @ Y5 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y1 )
@ Y2 )
@ ( maths_teacher @ Y0 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ r4
@ ( good_in_maths @ Y0 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f186,f168,f198,f207,f170]) ).
thf(f235,plain,
( ( ^ [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: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ r4
@ ( good_in_maths @ Y0 ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f201,f168,f211,f170]) ).
thf(f237,plain,
( ( !! @ $i @ ( maths_teacher @ john ) )
= $true ),
inference(beta-eta_normalization,[],[f223]) ).
thf(f238,plain,
! [X1: $i] :
( ( maths_teacher @ john @ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f237]) ).
thf(f294,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
~ ( !! @ mu
@ ^ [Y1: mu] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( r4 @ Y0 @ Y2 )
| ( good_in_maths @ Y1 @ Y2 ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f235]) ).
thf(f295,plain,
( $false
= ( ^ [Y0: $i] :
~ ( !! @ mu
@ ^ [Y1: mu] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( r4 @ Y0 @ Y2 )
| ( good_in_maths @ Y1 @ Y2 ) ) ) )
@ sK3 ) ),
inference(sigma_proxy_clausification,[],[f294]) ).
thf(f296,plain,
( $false
= ( ~ ( !! @ mu
@ ^ [Y0: mu] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( r4 @ sK3 @ Y1 )
| ( good_in_maths @ Y0 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f295]) ).
thf(f297,plain,
( ( !! @ mu
@ ^ [Y0: mu] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( r4 @ sK3 @ Y1 )
| ( good_in_maths @ Y0 @ Y1 ) ) ) )
= $true ),
inference(not_proxy_clausification,[],[f296]) ).
thf(f298,plain,
! [X1: mu] :
( $true
= ( ^ [Y0: mu] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( r4 @ sK3 @ Y1 )
| ( good_in_maths @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f297]) ).
thf(f299,plain,
! [X1: mu] :
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( r4 @ sK3 @ Y0 )
| ( good_in_maths @ X1 @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f298]) ).
thf(f300,plain,
! [X1: mu] :
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( r4 @ sK3 @ Y0 )
| ( good_in_maths @ X1 @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f299]) ).
thf(f301,plain,
! [X1: mu] :
( ( ^ [Y0: $i] :
( ~ ( r4 @ sK3 @ Y0 )
| ( good_in_maths @ X1 @ Y0 ) )
@ ( sK4 @ X1 ) )
= $false ),
inference(sigma_proxy_clausification,[],[f300]) ).
thf(f302,plain,
! [X1: mu] :
( $false
= ( ~ ( r4 @ sK3 @ ( sK4 @ X1 ) )
| ( good_in_maths @ X1 @ ( sK4 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f301]) ).
thf(f303,plain,
! [X1: mu] :
( $false
= ( good_in_maths @ X1 @ ( sK4 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f302]) ).
thf(f304,plain,
! [X1: mu] :
( $false
= ( ~ ( r4 @ sK3 @ ( sK4 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f302]) ).
thf(f305,plain,
! [X1: mu] :
( ( r4 @ sK3 @ ( sK4 @ X1 ) )
= $true ),
inference(not_proxy_clausification,[],[f304]) ).
thf(f536,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ~ ( maths_teacher @ Y1 @ Y0 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( r4 @ Y0 @ Y2 )
| ( good_in_maths @ Y1 @ Y2 ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f231]) ).
thf(f537,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ~ ( maths_teacher @ Y1 @ Y0 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( r4 @ Y0 @ Y2 )
| ( good_in_maths @ Y1 @ Y2 ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f536]) ).
thf(f538,plain,
! [X1: $i] :
( ( !! @ mu
@ ^ [Y0: mu] :
( ~ ( maths_teacher @ Y0 @ X1 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( r4 @ X1 @ Y1 )
| ( good_in_maths @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f537]) ).
thf(f539,plain,
! [X2: mu,X1: $i] :
( ( ^ [Y0: mu] :
( ~ ( maths_teacher @ Y0 @ X1 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( r4 @ X1 @ Y1 )
| ( good_in_maths @ Y0 @ Y1 ) ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f538]) ).
thf(f540,plain,
! [X2: mu,X1: $i] :
( ( ~ ( maths_teacher @ X2 @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( r4 @ X1 @ Y0 )
| ( good_in_maths @ X2 @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f539]) ).
thf(f541,plain,
! [X2: mu,X1: $i] :
( ( ( ~ ( maths_teacher @ X2 @ X1 ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( r4 @ X1 @ Y0 )
| ( good_in_maths @ X2 @ Y0 ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f540]) ).
thf(f542,plain,
! [X2: mu,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( r4 @ X1 @ Y0 )
| ( good_in_maths @ X2 @ Y0 ) ) )
= $true )
| ( $false
= ( maths_teacher @ X2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f541]) ).
thf(f543,plain,
! [X2: mu,X3: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( r4 @ X1 @ Y0 )
| ( good_in_maths @ X2 @ Y0 ) )
@ X3 )
= $true )
| ( $false
= ( maths_teacher @ X2 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f542]) ).
thf(f544,plain,
! [X2: mu,X3: $i,X1: $i] :
( ( $false
= ( maths_teacher @ X2 @ X1 ) )
| ( $true
= ( ~ ( r4 @ X1 @ X3 )
| ( good_in_maths @ X2 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f543]) ).
thf(f545,plain,
! [X2: mu,X3: $i,X1: $i] :
( ( ( good_in_maths @ X2 @ X3 )
= $true )
| ( ( ~ ( r4 @ X1 @ X3 ) )
= $true )
| ( $false
= ( maths_teacher @ X2 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f544]) ).
thf(f546,plain,
! [X2: mu,X3: $i,X1: $i] :
( ( ( r4 @ X1 @ X3 )
= $false )
| ( $false
= ( maths_teacher @ X2 @ X1 ) )
| ( ( good_in_maths @ X2 @ X3 )
= $true ) ),
inference(not_proxy_clausification,[],[f545]) ).
thf(f586,plain,
! [X0: mu,X1: $i] :
( ( $false = $true )
| ( $false
= ( r4 @ X1 @ ( sK4 @ X0 ) ) )
| ( $false
= ( maths_teacher @ X0 @ X1 ) ) ),
inference(constrained_superposition,[],[f303,f546]) ).
thf(f588,plain,
! [X0: mu,X1: $i] :
( ( $false
= ( r4 @ X1 @ ( sK4 @ X0 ) ) )
| ( $false
= ( maths_teacher @ X0 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f586]) ).
thf(f592,plain,
! [X0: mu] :
( ( ( maths_teacher @ X0 @ sK3 )
= $false )
| ( $false = $true ) ),
inference(constrained_superposition,[],[f305,f588]) ).
thf(f593,plain,
! [X0: mu] :
( ( maths_teacher @ X0 @ sK3 )
= $false ),
inference(trivial_inequality_removal,[],[f592]) ).
thf(f596,plain,
$false = $true,
inference(constrained_superposition,[],[f238,f593]) ).
thf(f597,plain,
$false,
inference(trivial_inequality_removal,[],[f596]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : AGT028^2 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Sep 29 17:29:12 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.12 Running higher-order theorem proving
% 0.08/0.13 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
% 0.08/0.17 % (423588)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.08/0.17 % (423608)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.08/0.17 % (423608)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
% 0.08/0.17 % (423604)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2795561940:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.08/0.17 % (423601)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1941859399:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.08/0.17 % (423606)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2114182109:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.08/0.17 % (423603)lrs+10_16_si=on:nwc=1.5:random_seed=449656154:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.08/0.17 % (423605)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=4081869096: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)
% 0.08/0.17 % (423608)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=2903180328:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.08/0.17 % (423607)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2035717069:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.08/0.17 % (423604)Instruction limit reached!
% 0.08/0.17 % (423604)------------------------------
% 0.08/0.17 % (423604)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.17 % (423604)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.17 % (423604)CaDiCaL version: 2.1.3
% 0.08/0.17 % (423604)Termination reason: Instruction limit
% 0.08/0.17 % (423604)Termination phase: shuffling
% 0.08/0.17 % (423604)Time elapsed: 0.001 s
% 0.08/0.17 % (423604)Peak memory usage: 9 MB
% 0.08/0.17 % (423604)Instructions burned: 4 (million)
% 0.08/0.17 % (423603)Instruction limit reached!
% 0.08/0.17 % (423603)------------------------------
% 0.08/0.17 % (423603)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.17 % (423603)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.17 % (423603)CaDiCaL version: 2.1.3
% 0.08/0.17 % (423603)Termination reason: Instruction limit
% 0.08/0.17 % (423603)Termination phase: Saturation
% 0.08/0.17 % (423603)Time elapsed: 0.004 s
% 0.08/0.17 % (423603)Peak memory usage: 11 MB
% 0.08/0.17 % (423603)Instructions burned: 19 (million)
% 0.08/0.17 % (423606)Instruction limit reached!
% 0.08/0.17 % (423606)------------------------------
% 0.08/0.17 % (423606)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.17 % (423606)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.17 % (423606)CaDiCaL version: 2.1.3
% 0.08/0.17 % (423606)Termination reason: Instruction limit
% 0.08/0.17 % (423606)Termination phase: Saturation
% 0.08/0.17 % (423606)Time elapsed: 0.007 s
% 0.08/0.17 % (423606)Peak memory usage: 11 MB
% 0.08/0.17 % (423606)Instructions burned: 25 (million)
% 0.08/0.17 % (423623)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1486344007:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.08/0.17 % (423601) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-423588-423601"...
% 0.08/0.17 % (423608) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-423588-423608"...
% 0.08/0.17 % (423623)Instruction limit reached!
% 0.08/0.17 % (423623)------------------------------
% 0.08/0.17 % (423623)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.17 % (423623)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.17 % (423623)CaDiCaL version: 2.1.3
% 0.08/0.17 % (423623)Termination reason: Instruction limit
% 0.08/0.17 % (423623)Termination phase: shuffling
% 0.08/0.17 % (423623)Time elapsed: 0.001 s
% 0.08/0.17 % (423623)Peak memory usage: 9 MB
% 0.08/0.17 % (423623)Instructions burned: 4 (million)
% 0.08/0.17 % (423601)...printing done.
% 0.08/0.17 % (423607) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-423588-423607"...
% 0.08/0.17 % (423608)...printing done.
% 0.08/0.17 % (423601)Refutation found. Thanks to Tanya!
% 0.08/0.17 % SZS status Theorem for theBenchmark
% 0.08/0.17 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.18 % (423601)------------------------------
% 0.08/0.18 % (423601)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.18 % (423601)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.18 % (423601)CaDiCaL version: 2.1.3
% 0.08/0.18 % (423601)Termination reason: Refutation
% 0.08/0.18 % (423601)Time elapsed: 0.013 s
% 0.08/0.18 % (423601)Peak memory usage: 12 MB
% 0.08/0.18 % (423601)Instructions burned: 51 (million)
% 0.08/0.18 % (423588)Success in time 0.035 s
% 0.08/0.18 % Vampire exiting
%------------------------------------------------------------------------------