%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : AGT028^1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 07:44:40 AM UTC 2026
% Result : Theorem 0.13s 0.27s
% Output : Refutation 0.13s
% 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 : 367 ( 81 equ; 0 cnn)
% Maximal formula atoms : 7 ( 4 avg)
% Number of connectives : 540 ( 59 ~; 47 |; 0 &; 397 @)
% ( 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 : 132 ( 128 usr; 8 con; 0-4 aty)
% ( 37 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 198 ( 154 ^; 44 !; 0 ?; 198 :)
% 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,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_48,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_49,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_50,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_51,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_52,type,
vNOT: $o > $o ).
thf(func_def_53,type,
vOR: $o > $o > $o ).
thf(func_def_54,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_57,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_58,type,
vIMP: $o > $o > $o ).
thf(func_def_59,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_60,type,
vAND: $o > $o > $o ).
thf(func_def_61,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_63,type,
sK1: mu > $i ).
thf(func_def_64,type,
sK2: $i > ( $i > $o ) > $i ).
thf(func_def_65,type,
sK3: $i > ( $i > $o ) > $i ).
thf(func_def_66,type,
sK4: $i > ( $i > $o ) > $i ).
thf(func_def_67,type,
sK5: $i > ( $i > $o ) > $i ).
thf(func_def_68,type,
sK6: $i > ( $i > $o ) > $i ).
thf(func_def_69,type,
sK7: $i > ( $i > $o ) > $i ).
thf(func_def_70,type,
sK8: $i > ( $i > $o ) > $i ).
thf(func_def_71,type,
sK9: $i > ( $i > $o ) > $i ).
thf(func_def_72,type,
sK10: $i > ( $i > $o ) > $i ).
thf(func_def_73,type,
sK11: $i > ( $i > $o ) > $i ).
thf(func_def_74,type,
sK12: $i > ( $i > $o ) > $i ).
thf(func_def_75,type,
sK13: $i > ( $i > $o ) > $i ).
thf(func_def_76,type,
sK14: $i > ( $i > $o ) > $i ).
thf(func_def_77,type,
sK15: $i > ( $i > $o ) > $i ).
thf(func_def_78,type,
sK16: $i > ( $i > $o ) > $i ).
thf(func_def_79,type,
sK17: $i > ( $i > $o ) > $i ).
thf(func_def_80,type,
sK18: $i > ( $i > $o ) > $i ).
thf(func_def_81,type,
sK19: $i > ( $i > $o ) > $i ).
thf(func_def_82,type,
sK20: $i > ( $i > $o ) > $i ).
thf(func_def_83,type,
sK21: $i > ( $i > $o ) > $i ).
thf(func_def_84,type,
sK22: $i > ( $i > $o ) > $i ).
thf(func_def_85,type,
sK23: $i > ( $i > $o ) > $i ).
thf(func_def_86,type,
sK24: $i > ( $i > $o ) > $i ).
thf(func_def_87,type,
sK25: $i > ( $i > $o ) > $i ).
thf(func_def_88,type,
sK26: $i > ( $i > $o ) > $i ).
thf(func_def_89,type,
sK27: $i > ( $i > $o ) > $i ).
thf(func_def_90,type,
sK28: $i > ( $i > $o ) > $i ).
thf(func_def_91,type,
sK29: $i > ( $i > $o ) > $i ).
thf(func_def_92,type,
sK30: $i > ( $i > $o ) > $i ).
thf(func_def_93,type,
sK31: $i > ( $i > $o ) > $i ).
thf(func_def_94,type,
sK32: $i > ( $i > $o ) > $i ).
thf(func_def_95,type,
sK33: $i > ( $i > $o ) > $i ).
thf(func_def_96,type,
sK34: $i > ( $i > $o ) > $i ).
thf(func_def_97,type,
sK35: $i > ( $i > $o ) > $i ).
thf(func_def_98,type,
sK36: $i > ( $i > $o ) > $i ).
thf(func_def_99,type,
sK37: $i > ( $i > $o ) > $i ).
thf(func_def_100,type,
sK38: $i > ( $i > $o ) > $i ).
thf(func_def_101,type,
sK39: $i > ( $i > $o ) > $i ).
thf(func_def_102,type,
sK40: $i > ( $i > $o ) > $i ).
thf(func_def_103,type,
sK41: $i > ( $i > $o ) > $i ).
thf(func_def_104,type,
sK42: $i > ( $i > $o ) > $i ).
thf(func_def_105,type,
sK43: $i > ( $i > $o ) > $i ).
thf(func_def_106,type,
sK44: $i > ( $i > $o ) > $i ).
thf(func_def_107,type,
sK45: $i > ( $i > $o ) > $i ).
thf(func_def_108,type,
sK46: $i > ( $i > $o ) > $i ).
thf(func_def_109,type,
sK47: $i > ( $i > $o ) > $i ).
thf(func_def_110,type,
sK48: $i > ( $i > $o ) > $i ).
thf(func_def_111,type,
sK49: $i > ( $i > $o ) > $i ).
thf(func_def_112,type,
sK50: $i > ( $i > $o ) > $i ).
thf(func_def_113,type,
sK51: $i > ( $i > $o ) > $i ).
thf(func_def_114,type,
sK52: $i > mu > $i ).
thf(func_def_115,type,
sK53: $i > mu > $i ).
thf(func_def_116,type,
sK54: $i > mu > $i ).
thf(func_def_117,type,
sK55: $i > mu > $i ).
thf(func_def_118,type,
sK56: $i > mu > $i ).
thf(func_def_119,type,
sK57: $i > mu > $i ).
thf(func_def_120,type,
sK58: $i > mu > $i ).
thf(func_def_121,type,
sK59: $i > mu > $i ).
thf(func_def_122,type,
sK60: $i > mu > $i ).
thf(func_def_123,type,
sK61: $i > mu > $i ).
thf(func_def_124,type,
sK62: $i > mu > $i ).
thf(func_def_125,type,
sK63: $i > mu > $i ).
thf(func_def_126,type,
sK64: $i > mu > $i ).
thf(func_def_127,type,
sK65: $i > mu > $i ).
thf(func_def_128,type,
sK66: $i > mu > $i ).
thf(func_def_129,type,
sK67: $i > mu > $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(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f10,axiom,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mforall_ind) ).
thf(f12,axiom,
( mexists_ind
= ( ^ [X0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X1: mu] : ( mnot @ ( X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mexists_ind) ).
thf(f16,axiom,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mbox) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',axiom_r1) ).
thf(f49,axiom,
mvalid @ ( maths_teacher @ john ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a6) ).
thf(f98,conjecture,
( mvalid
@ ( mexists_ind
@ ^ [X0: mu] : ( mbox @ r4 @ ( good_in_maths @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(f99,negated_conjecture,
~ ( mvalid
@ ( mexists_ind
@ ^ [X0: mu] : ( mbox @ r4 @ ( good_in_maths @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f98]) ).
thf(f102,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f103,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f102]) ).
thf(f104,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f105,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f104]) ).
thf(f107,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f111,plain,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f10]) ).
thf(f112,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f111]) ).
thf(f115,plain,
( mexists_ind
= ( ^ [X0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X1: mu] : ( mnot @ ( X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f12]) ).
thf(f116,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f115]) ).
thf(f120,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f121,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f120]) ).
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(f151,plain,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] : ( mimplies @ ( maths_teacher @ X0 ) @ ( mbox @ r4 @ ( good_in_maths @ X0 ) ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f152,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] : ( mimplies @ ( maths_teacher @ Y0 ) @ ( mbox @ r4 @ ( good_in_maths @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f151]) ).
thf(f185,plain,
mvalid @ ( maths_teacher @ john ),
inference(rectify,[],[f49]) ).
thf(f186,plain,
( ( mvalid @ ( maths_teacher @ john ) )
= $true ),
inference(fool_elimination,[],[f185]) ).
thf(f283,plain,
~ ( mvalid
@ ( mexists_ind
@ ^ [X0: mu] : ( mbox @ r4 @ ( good_in_maths @ X0 ) ) ) ),
inference(rectify,[],[f99]) ).
thf(f284,plain,
( $true
!= ( mvalid
@ ( mexists_ind
@ ^ [Y0: mu] : ( mbox @ r4 @ ( good_in_maths @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f283]) ).
thf(f285,plain,
( $true
!= ( mvalid
@ ( mexists_ind
@ ^ [Y0: mu] : ( mbox @ r4 @ ( good_in_maths @ Y0 ) ) ) ) ),
inference(flattening,[],[f284]) ).
thf(f288,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f103]) ).
thf(f289,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f105]) ).
thf(f291,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f107]) ).
thf(f295,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f112]) ).
thf(f297,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f116]) ).
thf(f301,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f121]) ).
thf(f313,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f144]) ).
thf(f317,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] : ( mimplies @ ( maths_teacher @ Y0 ) @ ( mbox @ r4 @ ( good_in_maths @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f152]) ).
thf(f334,plain,
( ( mvalid @ ( maths_teacher @ john ) )
= $true ),
inference(cnf_transformation,[],[f186]) ).
thf(f383,plain,
( $true
!= ( mvalid
@ ( mexists_ind
@ ^ [Y0: mu] : ( mbox @ r4 @ ( good_in_maths @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f285]) ).
thf(f387,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,[],[f291,f289,f288]) ).
thf(f391,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,[],[f297,f288,f295,f288]) ).
thf(f395,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: mu] :
( ^ [Y1: $i > $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 ) ) ) ) ) ),
inference(definition_unfolding,[],[f317,f313,f295,f387,f301]) ).
thf(f412,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( maths_teacher @ john ) ) ),
inference(definition_unfolding,[],[f334,f313]) ).
thf(f461,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: mu > $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: mu > $i > $o,Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( Y0 @ Y1 ) ) ) )
@ ^ [Y0: mu] :
( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ r4
@ ( good_in_maths @ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f383,f313,f391,f301]) ).
thf(f462,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
~ ( !! @ mu
@ ^ [Y1: mu] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( r4 @ Y0 @ Y2 )
| ( good_in_maths @ Y1 @ Y2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f461]) ).
thf(f463,plain,
( $false
= ( ^ [Y0: $i] :
~ ( !! @ mu
@ ^ [Y1: mu] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( r4 @ Y0 @ Y2 )
| ( good_in_maths @ Y1 @ Y2 ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f462]) ).
thf(f464,plain,
( $false
= ( ~ ( !! @ mu
@ ^ [Y0: mu] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( r4 @ sK0 @ Y1 )
| ( good_in_maths @ Y0 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f463]) ).
thf(f465,plain,
( $true
= ( !! @ mu
@ ^ [Y0: mu] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( r4 @ sK0 @ Y1 )
| ( good_in_maths @ Y0 @ Y1 ) ) ) ) ),
inference(not_proxy_clausification,[],[f464]) ).
thf(f466,plain,
! [X1: mu] :
( $true
= ( ^ [Y0: mu] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( r4 @ sK0 @ Y1 )
| ( good_in_maths @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f465]) ).
thf(f467,plain,
! [X1: mu] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( r4 @ sK0 @ Y0 )
| ( good_in_maths @ X1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f466]) ).
thf(f468,plain,
! [X1: mu] :
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( r4 @ sK0 @ Y0 )
| ( good_in_maths @ X1 @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f467]) ).
thf(f469,plain,
! [X1: mu] :
( $false
= ( ^ [Y0: $i] :
( ~ ( r4 @ sK0 @ Y0 )
| ( good_in_maths @ X1 @ Y0 ) )
@ ( sK1 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f468]) ).
thf(f470,plain,
! [X1: mu] :
( $false
= ( ~ ( r4 @ sK0 @ ( sK1 @ X1 ) )
| ( good_in_maths @ X1 @ ( sK1 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f469]) ).
thf(f471,plain,
! [X1: mu] :
( $false
= ( good_in_maths @ X1 @ ( sK1 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f470]) ).
thf(f472,plain,
! [X1: mu] :
( $false
= ( ~ ( r4 @ sK0 @ ( sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f470]) ).
thf(f473,plain,
! [X1: mu] :
( $true
= ( r4 @ sK0 @ ( sK1 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f472]) ).
thf(f1440,plain,
( $true
= ( !! @ $i @ ( maths_teacher @ john ) ) ),
inference(beta-eta_normalization,[],[f412]) ).
thf(f1441,plain,
! [X1: $i] :
( $true
= ( maths_teacher @ john @ X1 ) ),
inference(pi_proxy_clausification,[],[f1440]) ).
thf(f1740,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ~ ( maths_teacher @ Y1 @ Y0 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( r4 @ Y0 @ Y2 )
| ( good_in_maths @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f395]) ).
thf(f1741,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ~ ( maths_teacher @ Y1 @ Y0 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( r4 @ Y0 @ Y2 )
| ( good_in_maths @ Y1 @ Y2 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f1740]) ).
thf(f1742,plain,
! [X1: $i] :
( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ~ ( maths_teacher @ Y0 @ X1 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( r4 @ X1 @ Y1 )
| ( good_in_maths @ Y0 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1741]) ).
thf(f1743,plain,
! [X2: mu,X1: $i] :
( $true
= ( ^ [Y0: mu] :
( ~ ( maths_teacher @ Y0 @ X1 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( r4 @ X1 @ Y1 )
| ( good_in_maths @ Y0 @ Y1 ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f1742]) ).
thf(f1744,plain,
! [X2: mu,X1: $i] :
( $true
= ( ~ ( maths_teacher @ X2 @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( r4 @ X1 @ Y0 )
| ( good_in_maths @ X2 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f1743]) ).
thf(f1745,plain,
! [X2: mu,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( r4 @ X1 @ Y0 )
| ( good_in_maths @ X2 @ Y0 ) ) ) )
| ( $true
= ( ~ ( maths_teacher @ X2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f1744]) ).
thf(f1746,plain,
! [X2: mu,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( r4 @ X1 @ Y0 )
| ( good_in_maths @ X2 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( maths_teacher @ X2 @ X1 ) ) ) ),
inference(pi_proxy_clausification,[],[f1745]) ).
thf(f1747,plain,
! [X2: mu,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( r4 @ X1 @ Y0 )
| ( good_in_maths @ X2 @ Y0 ) )
@ X3 ) )
| ( $false
= ( maths_teacher @ X2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f1746]) ).
thf(f1748,plain,
! [X2: mu,X3: $i,X1: $i] :
( ( $true
= ( ~ ( r4 @ X1 @ X3 )
| ( good_in_maths @ X2 @ X3 ) ) )
| ( $false
= ( maths_teacher @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f1747]) ).
thf(f1749,plain,
! [X2: mu,X3: $i,X1: $i] :
( ( $true
= ( good_in_maths @ X2 @ X3 ) )
| ( $false
= ( maths_teacher @ X2 @ X1 ) )
| ( $true
= ( ~ ( r4 @ X1 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f1748]) ).
thf(f1750,plain,
! [X2: mu,X3: $i,X1: $i] :
( ( $true
= ( good_in_maths @ X2 @ X3 ) )
| ( $false
= ( maths_teacher @ X2 @ X1 ) )
| ( $false
= ( r4 @ X1 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f1749]) ).
thf(f1825,plain,
! [X0: mu,X1: $i] :
( ( $true = $false )
| ( $false
= ( maths_teacher @ X0 @ X1 ) )
| ( $false
= ( r4 @ X1 @ ( sK1 @ X0 ) ) ) ),
inference(constrained_superposition,[],[f471,f1750]) ).
thf(f1828,plain,
! [X0: mu,X1: $i] :
( ( $false
= ( r4 @ X1 @ ( sK1 @ X0 ) ) )
| ( $false
= ( maths_teacher @ X0 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f1825]) ).
thf(f1838,plain,
! [X0: mu] :
( ( $true = $false )
| ( $false
= ( maths_teacher @ X0 @ sK0 ) ) ),
inference(constrained_superposition,[],[f473,f1828]) ).
thf(f1839,plain,
! [X0: mu] :
( $false
= ( maths_teacher @ X0 @ sK0 ) ),
inference(trivial_inequality_removal,[],[f1838]) ).
thf(f1844,plain,
$true = $false,
inference(constrained_superposition,[],[f1441,f1839]) ).
thf(f1845,plain,
$false,
inference(trivial_inequality_removal,[],[f1844]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : AGT028^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.17 % Computer : n007.cluster.edu
% 0.13/0.17 % Model : x86_64 x86_64
% 0.13/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.17 % Memory : 8046.5625MB
% 0.13/0.17 % OS : Linux 6.8.0-71-generic
% 0.13/0.17 % CPULimit : 300
% 0.13/0.17 % WCLimit : 300
% 0.13/0.17 % DateTime : Tue Sep 29 17:27:34 UTC 2026
% 0.13/0.17 % CPUTime :
% 0.13/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.20 Running first-order model finding
% 0.13/0.20 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
% 0.13/0.27 % (3683966)Will run a generic schedule for satisfiability detection.
% 0.13/0.27 % (3683973)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1717566356:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.13/0.27 % (3683972)% WARNING: option uhcvi not known.
% 0.13/0.27 % (3683972)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2095450203:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.13/0.27 % (3683971)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=247746815_2999 on theBenchmark for (2999ds/0Mi)
% 0.13/0.27 % (3683974)dis+10_1_sil=32000:sp=arity:random_seed=1898610283:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.13/0.27 % (3683972)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.13/0.27 % (3683977)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=406487525:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.13/0.27 % (3683972)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.13/0.27 % (3683975)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2391085119:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.13/0.27 % (3683973) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3683966-3683973"...
% 0.13/0.27 % (3683976)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1523703512:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.13/0.27 % (3683973)...printing done.
% 0.13/0.27 % (3683973)Refutation found. Thanks to Tanya!
% 0.13/0.27 % SZS status Theorem for theBenchmark
% 0.13/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.27 % (3683973)------------------------------
% 0.13/0.27 % (3683973)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.13/0.27 % (3683973)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.13/0.27 % (3683973)CaDiCaL version: 2.1.3
% 0.13/0.27 % (3683973)Termination reason: Refutation
% 0.13/0.27 % (3683973)Time elapsed: 0.030 s
% 0.13/0.27 % (3683973)Peak memory usage: 13 MB
% 0.13/0.27 % (3683973)Instructions burned: 128 (million)
% 0.13/0.27 % (3683966)Success in time 0.058 s
% 0.13/0.27 % Vampire exiting
%------------------------------------------------------------------------------