%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:21:00 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% 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_35,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_36,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_38,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_39,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
vNOT: $o > $o ).
thf(func_def_41,type,
vOR: $o > $o > $o ).
thf(func_def_42,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_45,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_46,type,
vIMP: $o > $o > $o ).
thf(func_def_47,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_48,type,
vAND: $o > $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] :
( ( 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(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,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
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(f42,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f43,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f42]) ).
thf(f44,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f45,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f44]) ).
thf(f47,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f53,plain,
( mforall_prop
= ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f11]) ).
thf(f54,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f53]) ).
thf(f60,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f61,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f60]) ).
thf(f69,plain,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
inference(rectify,[],[f21]) ).
thf(f70,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f69]) ).
thf(f83,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f84,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f83]) ).
thf(f101,plain,
mtransitive @ ( wife @ peter ),
inference(rectify,[],[f37]) ).
thf(f102,plain,
( ( mtransitive @ ( wife @ peter ) )
= $true ),
inference(fool_elimination,[],[f101]) ).
thf(f103,plain,
~ ( mvalid
@ ( mforall_prop
@ ^ [X0: $i > $o] : ( mimplies @ ( mbox @ ( wife @ peter ) @ X0 ) @ ( mbox @ ( wife @ peter ) @ ( mbox @ ( wife @ peter ) @ X0 ) ) ) ) ),
inference(rectify,[],[f39]) ).
thf(f104,plain,
( $true
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ ( wife @ peter ) @ Y0 ) @ ( mbox @ ( wife @ peter ) @ ( mbox @ ( wife @ peter ) @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f103]) ).
thf(f105,plain,
( $true
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ ( wife @ peter ) @ Y0 ) @ ( mbox @ ( wife @ peter ) @ ( mbox @ ( wife @ peter ) @ Y0 ) ) ) ) ) ),
inference(flattening,[],[f104]) ).
thf(f108,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f109,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f111,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f47]) ).
thf(f116,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f54]) ).
thf(f121,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f61]) ).
thf(f126,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f70]) ).
thf(f133,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f84]) ).
thf(f142,plain,
( ( mtransitive @ ( wife @ peter ) )
= $true ),
inference(cnf_transformation,[],[f102]) ).
thf(f143,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(f147,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,[],[f111,f109,f108]) ).
thf(f160,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
@ ( wife @ peter ) ) ),
inference(definition_unfolding,[],[f142,f126]) ).
thf(f161,plain,
( $true
!= ( ^ [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] :
( ( Y3 @ Y5 )
| ( Y4 @ 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 ) ) ) ) ) ),
inference(definition_unfolding,[],[f143,f133,f116,f147,f121,f121,f121]) ).
thf(f162,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( wife @ peter @ Y0 @ Y2 )
| ( Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( wife @ peter @ Y0 @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( wife @ peter @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f161]) ).
thf(f163,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( wife @ peter @ Y0 @ Y2 )
| ( Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( wife @ peter @ Y0 @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( wife @ peter @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( wife @ peter @ sK0 @ Y1 )
| ( Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( wife @ peter @ sK0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( wife @ peter @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f163]) ).
thf(f165,plain,
( $false
= ( ^ [Y0: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( wife @ peter @ sK0 @ Y1 )
| ( Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( wife @ peter @ sK0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( wife @ peter @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f164]) ).
thf(f166,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( wife @ peter @ sK0 @ Y0 )
| ( sK1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( wife @ peter @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( wife @ peter @ Y0 @ Y1 )
| ( sK1 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f165]) ).
thf(f167,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( wife @ peter @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( wife @ peter @ Y0 @ Y1 )
| ( sK1 @ Y1 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f166]) ).
thf(f168,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( wife @ peter @ sK0 @ Y0 )
| ( sK1 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f166]) ).
thf(f169,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( wife @ peter @ sK0 @ Y0 )
| ( sK1 @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f168]) ).
thf(f170,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( wife @ peter @ sK0 @ Y0 )
| ( sK1 @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f169]) ).
thf(f171,plain,
! [X1: $i] :
( $true
= ( ~ ( wife @ peter @ sK0 @ X1 )
| ( sK1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f170]) ).
thf(f172,plain,
! [X1: $i] :
( ( $true
= ( sK1 @ X1 ) )
| ( $true
= ( ~ ( wife @ peter @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f171]) ).
thf(f173,plain,
! [X1: $i] :
( ( $false
= ( wife @ peter @ sK0 @ X1 ) )
| ( $true
= ( sK1 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f172]) ).
thf(f174,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ( wife @ peter @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( wife @ peter @ Y0 @ Y1 )
| ( sK1 @ Y1 ) ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f167]) ).
thf(f175,plain,
( $false
= ( ~ ( wife @ peter @ sK0 @ sK2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( wife @ peter @ sK2 @ Y0 )
| ( sK1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f174]) ).
thf(f176,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( wife @ peter @ sK2 @ Y0 )
| ( sK1 @ Y0 ) ) ) ),
inference(or_proxy_clausification,[],[f175]) ).
thf(f177,plain,
( $false
= ( ~ ( wife @ peter @ sK0 @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f175]) ).
thf(f178,plain,
( $true
= ( wife @ peter @ sK0 @ sK2 ) ),
inference(not_proxy_clausification,[],[f177]) ).
thf(f179,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ( wife @ peter @ sK2 @ Y0 )
| ( sK1 @ Y0 ) )
@ sK3 ) ),
inference(sigma_proxy_clausification,[],[f176]) ).
thf(f180,plain,
( $false
= ( ~ ( wife @ peter @ sK2 @ sK3 )
| ( sK1 @ sK3 ) ) ),
inference(beta-eta_normalization,[],[f179]) ).
thf(f181,plain,
( $false
= ( sK1 @ sK3 ) ),
inference(or_proxy_clausification,[],[f180]) ).
thf(f182,plain,
( $false
= ( ~ ( wife @ peter @ sK2 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f180]) ).
thf(f183,plain,
( $true
= ( wife @ peter @ sK2 @ sK3 ) ),
inference(not_proxy_clausification,[],[f182]) ).
thf(f184,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( wife @ peter @ Y2 @ Y1 )
& ( wife @ peter @ Y1 @ Y0 ) )
=> ( wife @ peter @ Y2 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f160]) ).
thf(f185,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( wife @ peter @ Y2 @ Y1 )
& ( wife @ peter @ Y1 @ Y0 ) )
=> ( wife @ peter @ Y2 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f184]) ).
thf(f186,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( wife @ peter @ Y1 @ Y0 )
& ( wife @ peter @ Y0 @ X1 ) )
=> ( wife @ peter @ Y1 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f185]) ).
thf(f187,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( wife @ peter @ Y1 @ Y0 )
& ( wife @ peter @ Y0 @ X1 ) )
=> ( wife @ peter @ Y1 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f186]) ).
thf(f188,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( wife @ peter @ Y0 @ X2 )
& ( wife @ peter @ X2 @ X1 ) )
=> ( wife @ peter @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f187]) ).
thf(f189,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( wife @ peter @ Y0 @ X2 )
& ( wife @ peter @ X2 @ X1 ) )
=> ( wife @ peter @ Y0 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f188]) ).
thf(f190,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( wife @ peter @ X3 @ X2 )
& ( wife @ peter @ X2 @ X1 ) )
=> ( wife @ peter @ X3 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f189]) ).
thf(f191,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( wife @ peter @ X3 @ X2 )
& ( wife @ peter @ X2 @ X1 ) ) )
| ( $true
= ( wife @ peter @ X3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f190]) ).
thf(f192,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( wife @ peter @ X2 @ X1 ) )
| ( $true
= ( wife @ peter @ X3 @ X1 ) )
| ( $false
= ( wife @ peter @ X3 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f191]) ).
thf(f296,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( wife @ peter @ X0 @ sK3 ) )
| ( $false
= ( wife @ peter @ X0 @ sK2 ) ) ),
inference(constrained_superposition,[],[f183,f192]) ).
thf(f303,plain,
! [X0: $i] :
( ( $true
= ( wife @ peter @ X0 @ sK3 ) )
| ( $false
= ( wife @ peter @ X0 @ sK2 ) ) ),
inference(trivial_inequality_removal,[],[f296]) ).
thf(f390,plain,
( ( $true = $false )
| ( $false
= ( wife @ peter @ sK0 @ sK2 ) )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(constrained_superposition,[],[f303,f173]) ).
thf(f401,plain,
( ( $false
= ( wife @ peter @ sK0 @ sK2 ) )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(trivial_inequality_removal,[],[f390]) ).
thf(f404,plain,
( ( $true = $false )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(forward_demodulation,[],[f401,f178]) ).
thf(f405,plain,
( $true
= ( sK1 @ sK3 ) ),
inference(trivial_inequality_removal,[],[f404]) ).
thf(f406,plain,
$true = $false,
inference(forward_demodulation,[],[f405,f181]) ).
thf(f407,plain,
$false,
inference(trivial_inequality_removal,[],[f406]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ085^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n010.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 13:22:18 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 0.20/0.28 % (2834447)Will run a generic schedule for satisfiability detection.
% 0.20/0.28 % (2834456)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2673070771:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.28 % (2834456)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.28 % (2834453)% WARNING: option uhcvi not known.
% 0.20/0.28 % (2834453)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3655106197:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.28 % (2834452)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=429159038_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.28 % (2834454)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3921138909:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.28 % (2834455)dis+10_1_sil=32000:sp=arity:random_seed=3696024218:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.28 % (2834456) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2834447-2834456"...
% 0.20/0.28 % (2834453)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.28 % (2834456)...printing done.
% 0.20/0.28 % (2834457)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=719961522:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.28 % (2834456)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (2834456)------------------------------
% 0.20/0.28 % (2834456)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (2834456)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (2834456)CaDiCaL version: 2.1.3
% 0.20/0.28 % (2834456)Termination reason: Refutation
% 0.20/0.28 % (2834456)Time elapsed: 0.009 s
% 0.20/0.28 % (2834456)Peak memory usage: 12 MB
% 0.20/0.28 % (2834456)Instructions burned: 30 (million)
% 0.20/0.28 % (2834447)Success in time 0.043 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------