%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PUZ085^1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : 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 08:20:51 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 9
% Syntax : Number of formulae : 79 ( 65 unt; 0 typ; 0 def)
% Number of atoms : 528 ( 85 equ; 0 cnn)
% Maximal formula atoms : 12 ( 6 avg)
% Number of connectives : 741 ( 57 ~; 58 |; 13 &; 546 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 101 ( 101 >; 0 *; 0 +; 0 <<)
% Number of symbols : 56 ( 52 usr; 6 con; 0-4 aty)
% ( 55 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 187 ( 151 ^; 36 !; 0 ?; 187 :)
% 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_37,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_38,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_39,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_42,type,
vIMP: $o > $o > $o ).
thf(func_def_43,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
vAND: $o > $o > $o ).
thf(func_def_45,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_46,type,
vOR: $o > $o > $o ).
thf(func_def_47,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_48,type,
vNOT: $o > $o ).
thf(func_def_49,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_51,type,
sK1: $i > $o ).
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] :
( ( X0 @ X2 )
| ( X1 @ 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(f11,axiom,
( mforall_prop
= ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mforall_prop) ).
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(f21,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X3: $i,X1: $i,X2: $i] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X1 @ X3 ) ) )
= mtransitive ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mtransitive) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f37,axiom,
mtransitive @ ( wife @ peter ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',trans_wife_peter) ).
thf(f38,conjecture,
( mvalid
@ ( mforall_prop
@ ^ [X0: $i > $o] : ( mimplies @ ( mbox @ ( wife @ peter ) @ X0 ) @ ( mbox @ ( wife @ peter ) @ ( mbox @ ( wife @ peter ) @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(f39,negated_conjecture,
~ ( mvalid
@ ( mforall_prop
@ ^ [X0: $i > $o] : ( mimplies @ ( mbox @ ( wife @ peter ) @ X0 ) @ ( mbox @ ( wife @ peter ) @ ( mbox @ ( wife @ peter ) @ X0 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f38]) ).
thf(f43,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f44,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f43]) ).
thf(f58,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f59,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f60,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f59]) ).
thf(f61,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f62,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f61]) ).
thf(f68,plain,
mtransitive @ ( wife @ peter ),
inference(rectify,[],[f37]) ).
thf(f69,plain,
( ( mtransitive @ ( wife @ peter ) )
= $true ),
inference(fool_elimination,[],[f68]) ).
thf(f77,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X3 @ X1 ) )
=> ( X0 @ X2 @ X1 ) ) )
= mtransitive ),
inference(rectify,[],[f21]) ).
thf(f78,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f77]) ).
thf(f80,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f81,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f80]) ).
thf(f83,plain,
~ ( mvalid
@ ( mforall_prop
@ ^ [X0: $i > $o] : ( mimplies @ ( mbox @ ( wife @ peter ) @ X0 ) @ ( mbox @ ( wife @ peter ) @ ( mbox @ ( wife @ peter ) @ X0 ) ) ) ) ),
inference(rectify,[],[f39]) ).
thf(f84,plain,
( $true
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ ( wife @ peter ) @ Y0 ) @ ( mbox @ ( wife @ peter ) @ ( mbox @ ( wife @ peter ) @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f83]) ).
thf(f98,plain,
( mforall_prop
= ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f11]) ).
thf(f99,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f98]) ).
thf(f105,plain,
( $true
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ ( wife @ peter ) @ Y0 ) @ ( mbox @ ( wife @ peter ) @ ( mbox @ ( wife @ peter ) @ Y0 ) ) ) ) ) ),
inference(flattening,[],[f84]) ).
thf(f107,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f60]) ).
thf(f109,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f99]) ).
thf(f120,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f62]) ).
thf(f122,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f81]) ).
thf(f123,plain,
( $true
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ ( wife @ peter ) @ Y0 ) @ ( mbox @ ( wife @ peter ) @ ( mbox @ ( wife @ peter ) @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f105]) ).
thf(f127,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f128,plain,
( ( mtransitive @ ( wife @ peter ) )
= $true ),
inference(cnf_transformation,[],[f69]) ).
thf(f130,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f78]) ).
thf(f131,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f58]) ).
thf(f147,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f131,f107,f122]) ).
thf(f157,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y4 @ Y5 )
| ( Y3 @ Y5 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y1 )
@ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ ( wife @ peter )
@ Y0 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ ( wife @ peter )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ ( wife @ peter )
@ Y0 ) ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f123,f127,f109,f147,f120,f120,f120]) ).
thf(f158,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
@ ( wife @ peter ) )
= $true ),
inference(definition_unfolding,[],[f128,f130]) ).
thf(f168,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( wife @ peter @ Y0 @ Y2 )
& ( wife @ peter @ Y1 @ Y0 ) )
=> ( wife @ peter @ Y1 @ Y2 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f158]) ).
thf(f169,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( wife @ peter @ Y0 @ Y2 )
& ( wife @ peter @ Y1 @ Y0 ) )
=> ( wife @ peter @ Y1 @ Y2 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f168]) ).
thf(f170,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( wife @ peter @ X1 @ Y1 )
& ( wife @ peter @ Y0 @ X1 ) )
=> ( wife @ peter @ Y0 @ Y1 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f169]) ).
thf(f171,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( wife @ peter @ X1 @ Y1 )
& ( wife @ peter @ Y0 @ X1 ) )
=> ( wife @ peter @ Y0 @ Y1 ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f170]) ).
thf(f172,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( wife @ peter @ X1 @ Y0 )
& ( wife @ peter @ X2 @ X1 ) )
=> ( wife @ peter @ X2 @ Y0 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f171]) ).
thf(f173,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( wife @ peter @ X1 @ Y0 )
& ( wife @ peter @ X2 @ X1 ) )
=> ( wife @ peter @ X2 @ Y0 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f172]) ).
thf(f174,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( wife @ peter @ X1 @ X3 )
& ( wife @ peter @ X2 @ X1 ) )
=> ( wife @ peter @ X2 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f173]) ).
thf(f175,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( wife @ peter @ X1 @ X3 )
& ( wife @ peter @ X2 @ X1 ) )
= $false )
| ( $true
= ( wife @ peter @ X2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f174]) ).
thf(f176,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( wife @ peter @ X1 @ X3 )
= $false )
| ( ( wife @ peter @ X2 @ X1 )
= $false )
| ( $true
= ( wife @ peter @ X2 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f175]) ).
thf(f177,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( wife @ peter @ Y0 @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( wife @ peter @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( wife @ peter @ Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f157]) ).
thf(f178,plain,
( ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( wife @ peter @ Y0 @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( wife @ peter @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( wife @ peter @ Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ) )
@ sK0 )
= $false ),
inference(sigma_proxy_clausification,[],[f177]) ).
thf(f179,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( wife @ peter @ sK0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( wife @ peter @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( wife @ peter @ sK0 @ Y1 )
| ( Y0 @ Y1 ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f178]) ).
thf(f180,plain,
( $false
= ( ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( wife @ peter @ sK0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( wife @ peter @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( wife @ peter @ sK0 @ Y1 )
| ( Y0 @ Y1 ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f179]) ).
thf(f181,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( wife @ peter @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( wife @ peter @ Y0 @ Y1 )
| ( sK1 @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( wife @ peter @ sK0 @ Y0 )
| ( sK1 @ Y0 ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f180]) ).
thf(f182,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( wife @ peter @ sK0 @ Y0 )
| ( sK1 @ Y0 ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f181]) ).
thf(f183,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( wife @ peter @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( wife @ peter @ Y0 @ Y1 )
| ( sK1 @ Y1 ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f181]) ).
thf(f184,plain,
( ( ^ [Y0: $i] :
( ~ ( wife @ peter @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( wife @ peter @ Y0 @ Y1 )
| ( sK1 @ Y1 ) ) ) )
@ sK2 )
= $false ),
inference(sigma_proxy_clausification,[],[f183]) ).
thf(f185,plain,
( $false
= ( ~ ( wife @ peter @ sK0 @ sK2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( wife @ peter @ sK2 @ Y0 )
| ( sK1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f184]) ).
thf(f186,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( wife @ peter @ sK2 @ Y0 )
| ( sK1 @ Y0 ) ) )
= $false ),
inference(or_proxy_clausification,[],[f185]) ).
thf(f187,plain,
( ( ~ ( wife @ peter @ sK0 @ sK2 ) )
= $false ),
inference(or_proxy_clausification,[],[f185]) ).
thf(f188,plain,
( ( wife @ peter @ sK0 @ sK2 )
= $true ),
inference(not_proxy_clausification,[],[f187]) ).
thf(f189,plain,
( ( ^ [Y0: $i] :
( ~ ( wife @ peter @ sK2 @ Y0 )
| ( sK1 @ Y0 ) )
@ sK3 )
= $false ),
inference(sigma_proxy_clausification,[],[f186]) ).
thf(f190,plain,
( ( ~ ( wife @ peter @ sK2 @ sK3 )
| ( sK1 @ sK3 ) )
= $false ),
inference(beta-eta_normalization,[],[f189]) ).
thf(f191,plain,
( $false
= ( sK1 @ sK3 ) ),
inference(or_proxy_clausification,[],[f190]) ).
thf(f192,plain,
( ( ~ ( wife @ peter @ sK2 @ sK3 ) )
= $false ),
inference(or_proxy_clausification,[],[f190]) ).
thf(f193,plain,
( $true
= ( wife @ peter @ sK2 @ sK3 ) ),
inference(not_proxy_clausification,[],[f192]) ).
thf(f194,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( wife @ peter @ sK0 @ Y0 )
| ( sK1 @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f182]) ).
thf(f195,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ~ ( wife @ peter @ sK0 @ Y0 )
| ( sK1 @ Y0 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f194]) ).
thf(f196,plain,
! [X1: $i] :
( $true
= ( ~ ( wife @ peter @ sK0 @ X1 )
| ( sK1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f195]) ).
thf(f197,plain,
! [X1: $i] :
( ( ( sK1 @ X1 )
= $true )
| ( ( ~ ( wife @ peter @ sK0 @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f196]) ).
thf(f198,plain,
! [X1: $i] :
( ( ( wife @ peter @ sK0 @ X1 )
= $false )
| ( ( sK1 @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f197]) ).
thf(f584,plain,
! [X0: $i] :
( ( $true
= ( wife @ peter @ X0 @ sK3 ) )
| ( $true = $false )
| ( ( wife @ peter @ X0 @ sK2 )
= $false ) ),
inference(constrained_superposition,[],[f193,f176]) ).
thf(f592,plain,
! [X0: $i] :
( ( $true
= ( wife @ peter @ X0 @ sK3 ) )
| ( ( wife @ peter @ X0 @ sK2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f584]) ).
thf(f615,plain,
( ( ( wife @ peter @ sK0 @ sK2 )
= $false )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f198,f592]) ).
thf(f620,plain,
( ( ( wife @ peter @ sK0 @ sK2 )
= $false )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(trivial_inequality_removal,[],[f615]) ).
thf(f624,plain,
( ( $true = $false )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(forward_demodulation,[],[f620,f188]) ).
thf(f625,plain,
( $true
= ( sK1 @ sK3 ) ),
inference(trivial_inequality_removal,[],[f624]) ).
thf(f628,plain,
$true = $false,
inference(forward_demodulation,[],[f625,f191]) ).
thf(f629,plain,
$false,
inference(trivial_inequality_removal,[],[f628]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ085^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n026.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 13:24:43 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.25 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
% 0.21/0.29 % (574544)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (574554)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3604773616:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.29 % (574560)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.29 % (574560)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
% 0.21/0.29 % (574556)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4068547234:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.29 % (574559)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1995313891:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.29 % (574555)lrs+10_16_si=on:nwc=1.5:random_seed=3254932945:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.29 % (574558)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3698611275:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.29 % (574557)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=851193841: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)
% 0.21/0.29 % (574560)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=2678640623:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.29 % (574556)Instruction limit reached!
% 0.21/0.29 % (574556)------------------------------
% 0.21/0.29 % (574556)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (574556)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (574556)CaDiCaL version: 2.1.3
% 0.21/0.29 % (574556)Termination reason: Instruction limit
% 0.21/0.29 % (574556)Termination phase: Property scanning
% 0.21/0.29 % (574556)Time elapsed: 0.002 s
% 0.21/0.29 % (574556)Peak memory usage: 10 MB
% 0.21/0.29 % (574556)Instructions burned: 4 (million)
% 0.21/0.29 % (574554) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-574544-574554"...
% 0.21/0.29 % (574554)...printing done.
% 0.21/0.29 % (574554)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.29 % (574554)------------------------------
% 0.21/0.29 % (574554)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (574554)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (574554)CaDiCaL version: 2.1.3
% 0.21/0.29 % (574554)Termination reason: Refutation
% 0.21/0.29 % (574554)Time elapsed: 0.016 s
% 0.21/0.29 % (574554)Peak memory usage: 12 MB
% 0.21/0.29 % (574554)Instructions burned: 61 (million)
% 0.21/0.29 % (574544)Success in time 0.032 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------