%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n026.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 0.16s 0.26s
% Output : Refutation 0.16s
% 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 : 365 ( 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 : 82 ( 78 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 > mu > $i ).
thf(func_def_65,type,
sK3: $i > mu > $i ).
thf(func_def_66,type,
sK4: $i > 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,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/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/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,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] : ( X0 @ X2 @ X1 ) ) ),
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(f57,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f58,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f57]) ).
thf(f59,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f60,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f59]) ).
thf(f62,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f66,plain,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f10]) ).
thf(f67,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f66]) ).
thf(f70,plain,
( mexists_ind
= ( ^ [X0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X1: mu] : ( mnot @ ( X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f12]) ).
thf(f71,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f70]) ).
thf(f75,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f76,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f75]) ).
thf(f98,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f99,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f98]) ).
thf(f106,plain,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] : ( mimplies @ ( maths_teacher @ X0 ) @ ( mbox @ r4 @ ( good_in_maths @ X0 ) ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f107,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] : ( mimplies @ ( maths_teacher @ Y0 ) @ ( mbox @ r4 @ ( good_in_maths @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f106]) ).
thf(f140,plain,
mvalid @ ( maths_teacher @ john ),
inference(rectify,[],[f49]) ).
thf(f141,plain,
( ( mvalid @ ( maths_teacher @ john ) )
= $true ),
inference(fool_elimination,[],[f140]) ).
thf(f148,plain,
~ ( mvalid
@ ( mexists_ind
@ ^ [X0: mu] : ( mbox @ r4 @ ( good_in_maths @ X0 ) ) ) ),
inference(rectify,[],[f54]) ).
thf(f149,plain,
( $true
!= ( mvalid
@ ( mexists_ind
@ ^ [Y0: mu] : ( mbox @ r4 @ ( good_in_maths @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f148]) ).
thf(f150,plain,
( $true
!= ( mvalid
@ ( mexists_ind
@ ^ [Y0: mu] : ( mbox @ r4 @ ( good_in_maths @ Y0 ) ) ) ) ),
inference(flattening,[],[f149]) ).
thf(f153,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f58]) ).
thf(f154,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f60]) ).
thf(f156,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f62]) ).
thf(f160,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f67]) ).
thf(f162,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f71]) ).
thf(f166,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f76]) ).
thf(f178,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f99]) ).
thf(f182,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] : ( mimplies @ ( maths_teacher @ Y0 ) @ ( mbox @ r4 @ ( good_in_maths @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f107]) ).
thf(f199,plain,
( ( mvalid @ ( maths_teacher @ john ) )
= $true ),
inference(cnf_transformation,[],[f141]) ).
thf(f203,plain,
( $true
!= ( mvalid
@ ( mexists_ind
@ ^ [Y0: mu] : ( mbox @ r4 @ ( good_in_maths @ Y0 ) ) ) ) ),
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,[],[f156,f154,f153]) ).
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,[],[f162,f153,f160,f153]) ).
thf(f215,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,[],[f182,f178,f160,f207,f166]) ).
thf(f232,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( maths_teacher @ john ) ) ),
inference(definition_unfolding,[],[f199,f178]) ).
thf(f236,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,[],[f203,f178,f211,f166]) ).
thf(f237,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
~ ( !! @ mu
@ ^ [Y1: mu] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( r4 @ Y0 @ Y2 )
| ( good_in_maths @ Y1 @ Y2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f236]) ).
thf(f238,plain,
( $false
= ( ^ [Y0: $i] :
~ ( !! @ mu
@ ^ [Y1: mu] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( r4 @ Y0 @ Y2 )
| ( good_in_maths @ Y1 @ Y2 ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f237]) ).
thf(f239,plain,
( $false
= ( ~ ( !! @ mu
@ ^ [Y0: mu] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( r4 @ sK0 @ Y1 )
| ( good_in_maths @ Y0 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f238]) ).
thf(f240,plain,
( $true
= ( !! @ mu
@ ^ [Y0: mu] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( r4 @ sK0 @ Y1 )
| ( good_in_maths @ Y0 @ Y1 ) ) ) ) ),
inference(not_proxy_clausification,[],[f239]) ).
thf(f241,plain,
! [X1: mu] :
( $true
= ( ^ [Y0: mu] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( r4 @ sK0 @ Y1 )
| ( good_in_maths @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f240]) ).
thf(f242,plain,
! [X1: mu] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( r4 @ sK0 @ Y0 )
| ( good_in_maths @ X1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f241]) ).
thf(f243,plain,
! [X1: mu] :
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( r4 @ sK0 @ Y0 )
| ( good_in_maths @ X1 @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f242]) ).
thf(f244,plain,
! [X1: mu] :
( $false
= ( ^ [Y0: $i] :
( ~ ( r4 @ sK0 @ Y0 )
| ( good_in_maths @ X1 @ Y0 ) )
@ ( sK1 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f243]) ).
thf(f245,plain,
! [X1: mu] :
( $false
= ( ~ ( r4 @ sK0 @ ( sK1 @ X1 ) )
| ( good_in_maths @ X1 @ ( sK1 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f244]) ).
thf(f246,plain,
! [X1: mu] :
( $false
= ( good_in_maths @ X1 @ ( sK1 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f245]) ).
thf(f247,plain,
! [X1: mu] :
( $false
= ( ~ ( r4 @ sK0 @ ( sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f245]) ).
thf(f248,plain,
! [X1: mu] :
( $true
= ( r4 @ sK0 @ ( sK1 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f247]) ).
thf(f270,plain,
( $true
= ( !! @ $i @ ( maths_teacher @ john ) ) ),
inference(beta-eta_normalization,[],[f232]) ).
thf(f271,plain,
! [X1: $i] :
( $true
= ( maths_teacher @ john @ X1 ) ),
inference(pi_proxy_clausification,[],[f270]) ).
thf(f570,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,[],[f215]) ).
thf(f571,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,[],[f570]) ).
thf(f572,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,[],[f571]) ).
thf(f573,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,[],[f572]) ).
thf(f574,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,[],[f573]) ).
thf(f575,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,[],[f574]) ).
thf(f576,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,[],[f575]) ).
thf(f577,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,[],[f576]) ).
thf(f578,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,[],[f577]) ).
thf(f579,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,[],[f578]) ).
thf(f580,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,[],[f579]) ).
thf(f601,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $true
= ( good_in_maths @ john @ X1 ) )
| ( $false
= ( r4 @ X0 @ X1 ) ) ),
inference(constrained_superposition,[],[f271,f580]) ).
thf(f602,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( good_in_maths @ john @ X1 ) )
| ( $false
= ( r4 @ X0 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f601]) ).
thf(f610,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( r4 @ X0 @ ( sK1 @ john ) ) ) ),
inference(constrained_superposition,[],[f246,f602]) ).
thf(f611,plain,
! [X0: $i] :
( $false
= ( r4 @ X0 @ ( sK1 @ john ) ) ),
inference(trivial_inequality_removal,[],[f610]) ).
thf(f616,plain,
$true = $false,
inference(constrained_superposition,[],[f248,f611]) ).
thf(f617,plain,
$false,
inference(trivial_inequality_removal,[],[f616]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : AGT028^2 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.17 % Computer : n026.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 17:32:21 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.20 Running first-order model finding
% 0.07/0.20 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.26 % (915971)Will run a generic schedule for satisfiability detection.
% 0.16/0.26 % (915980)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1700656957:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.26 % (915980)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.16/0.26 % (915977)% WARNING: option uhcvi not known.
% 0.16/0.26 % (915976)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=408417931_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.26 % (915977)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=763516450:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.26 % (915981)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1950364393:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.26 % (915978)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2091024332:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.26 % (915979)dis+10_1_sil=32000:sp=arity:random_seed=415310441:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.26 % (915982)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2506259164:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.26 % (915977)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.16/0.26 % (915980) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-915971-915980"...
% 0.16/0.26 % (915980)...printing done.
% 0.16/0.26 % (915980)Refutation found. Thanks to Tanya!
% 0.16/0.26 % SZS status Theorem for theBenchmark
% 0.16/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.26 % (915980)------------------------------
% 0.16/0.26 % (915980)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.26 % (915980)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.26 % (915980)CaDiCaL version: 2.1.3
% 0.16/0.26 % (915980)Termination reason: Refutation
% 0.16/0.26 % (915980)Time elapsed: 0.013 s
% 0.16/0.26 % (915980)Peak memory usage: 12 MB
% 0.16/0.26 % (915980)Instructions burned: 51 (million)
% 0.16/0.26 % (915971)Success in time 0.049 s
% 0.16/0.26 % Vampire exiting
%------------------------------------------------------------------------------