%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : PHI043^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 08:20:21 AM UTC 2026
% Result : Theorem 1.77s 0.52s
% Output : Refutation 1.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 16
% Syntax : Number of formulae : 128 ( 80 unt; 0 typ; 2 def)
% Number of atoms : 852 ( 221 equ; 0 cnn)
% Maximal formula atoms : 10 ( 6 avg)
% Number of connectives : 1590 ( 81 ~; 95 |; 14 &;1306 @)
% ( 4 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 328 ( 328 >; 0 *; 0 +; 0 <<)
% Number of symbols : 57 ( 52 usr; 7 con; 0-4 aty)
% ( 50 !!; 22 ??; 0 @@+; 0 @@-)
% Number of variables : 605 ( 119 sgn 121 !; 4 ?; 605 :)
% 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,
mtrue: $i > $o ).
thf(func_def_2,type,
mfalse: $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mforall_indset: ( ( mu > $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_15,type,
mexists_indset: ( ( mu > $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_16,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_17,type,
mbox_generic: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mdia_generic: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_19,type,
rel: $i > $i > $o ).
thf(func_def_20,type,
mbox: ( $i > $o ) > $i > $o ).
thf(func_def_21,type,
mdia: ( $i > $o ) > $i > $o ).
thf(func_def_22,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_23,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_24,type,
p: ( mu > $i > $o ) > $i > $o ).
thf(func_def_25,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_26,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_27,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_28,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_31,type,
vNOT: $o > $o ).
thf(func_def_32,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
vOR: $o > $o > $o ).
thf(func_def_34,type,
vAND: $o > $o > $o ).
thf(func_def_35,type,
vIMP: $o > $o > $o ).
thf(func_def_36,type,
vIFF: $o > $o > $o ).
thf(func_def_37,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_38,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_39,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
sK1: mu > $i > $o ).
thf(func_def_43,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
sK2: ( mu > $i > $o ) > $i > ( mu > $i > $o ) > $i ).
thf(func_def_45,type,
sK3: ( mu > $i > $o ) > $i > ( mu > $i > $o ) > mu ).
thf(func_def_47,type,
sK5: ( mu > $i > $o ) > ( mu > $i > mu > $i > $o ) > $i > mu ).
thf(func_def_48,type,
sK6: $i > ( mu > $i > mu > $i > $o ) > ( mu > $i > $o ) > mu ).
thf(func_def_49,type,
sK7: ( mu > $i > $o ) > ( mu > $i > mu > $i > $o ) > $i > mu ).
thf(func_def_50,type,
sK8: $i > ( mu > $i > mu > $i > $o ) > ( mu > $i > $o ) > mu ).
thf(func_def_51,type,
sK9: ( mu > $i > $o ) > ( mu > $i > mu > $i > $o ) > $i > $i ).
thf(func_def_52,type,
sK10: ( mu > $i > $o ) > ( mu > $i > mu > $i > $o ) > $i > $i ).
thf(f4,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',mnot) ).
thf(f7,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',mimplies) ).
thf(f9,axiom,
( mequiv
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
<=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',mequiv) ).
thf(f11,axiom,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',mforall_ind) ).
thf(f12,axiom,
( mforall_indset
= ( ^ [X0: ( mu > $i > $o ) > $i > $o,X1: $i] :
! [X2: mu > $i > $o] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',mforall_indset) ).
thf(f14,axiom,
( mexists_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
? [X2: mu] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',mexists_ind) ).
thf(f17,axiom,
( mbox_generic
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',mbox_generic) ).
thf(f18,axiom,
( mdia_generic
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
? [X3: $i] :
( ( X1 @ X3 )
& ( X0 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',mdia_generic) ).
thf(f19,axiom,
( mbox
= ( mbox_generic @ rel ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',mbox) ).
thf(f20,axiom,
( mdia
= ( mdia_generic @ rel ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',mdia) ).
thf(f21,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',mvalid) ).
thf(f23,axiom,
( mvalid
@ ( mnot
@ ( p
@ ^ [X0: mu,X1: $i] : ( X0 != X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax16) ).
thf(f24,axiom,
( mvalid
@ ( mforall_indset
@ ^ [X0: mu > $i > $o] :
( mforall_indset
@ ^ [X1: mu > $i > $o] :
( mimplies
@ ( mbox
@ ( mforall_ind
@ ^ [X2: mu] : ( mequiv @ ( X0 @ X2 ) @ ( X1 @ X2 ) ) ) )
@ ( mequiv @ ( p @ X0 ) @ ( p @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
thf(f25,conjecture,
( mvalid
@ ( mforall_indset
@ ^ [X0: mu > $i > $o] :
( mimplies @ ( p @ X0 )
@ ( mdia
@ ( mexists_ind
@ ^ [X1: mu] : ( X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',possible_instantiation_of_the_positive) ).
thf(f26,negated_conjecture,
~ ( mvalid
@ ( mforall_indset
@ ^ [X0: mu > $i > $o] :
( mimplies @ ( p @ X0 )
@ ( mdia
@ ( mexists_ind
@ ^ [X1: mu] : ( X0 @ X1 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f25]) ).
thf(f30,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f4]) ).
thf(f31,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f30]) ).
thf(f36,plain,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f37,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f36]) ).
thf(f40,plain,
( mequiv
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
<=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f9]) ).
thf(f41,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f40]) ).
thf(f44,plain,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f11]) ).
thf(f45,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f44]) ).
thf(f46,plain,
( mforall_indset
= ( ^ [X0: ( mu > $i > $o ) > $i > $o,X1: $i] :
! [X2: mu > $i > $o] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f12]) ).
thf(f47,plain,
( mforall_indset
= ( ^ [Y0: ( mu > $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f46]) ).
thf(f50,plain,
( mexists_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
? [X2: mu] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f14]) ).
thf(f51,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( ?? @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f50]) ).
thf(f56,plain,
( mbox_generic
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f17]) ).
thf(f57,plain,
( mbox_generic
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f56]) ).
thf(f58,plain,
( mdia_generic
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
? [X3: $i] :
( ( X1 @ X3 )
& ( X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f18]) ).
thf(f59,plain,
( mdia_generic
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f58]) ).
thf(f60,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f21]) ).
thf(f61,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f60]) ).
thf(f64,plain,
( mvalid
@ ( mnot
@ ( p
@ ^ [X0: mu,X1: $i] : ( X0 != X0 ) ) ) ),
inference(rectify,[],[f23]) ).
thf(f65,plain,
( $true
= ( mvalid
@ ( mnot
@ ( p
@ ^ [Y0: mu,Y1: $i] : ( Y0 != Y0 ) ) ) ) ),
inference(fool_elimination,[],[f64]) ).
thf(f66,plain,
( mvalid
@ ( mforall_indset
@ ^ [X0: mu > $i > $o] :
( mforall_indset
@ ^ [X1: mu > $i > $o] :
( mimplies
@ ( mbox
@ ( mforall_ind
@ ^ [X2: mu] : ( mequiv @ ( X0 @ X2 ) @ ( X1 @ X2 ) ) ) )
@ ( mequiv @ ( p @ X0 ) @ ( p @ X1 ) ) ) ) ) ),
inference(rectify,[],[f24]) ).
thf(f67,plain,
( $true
= ( mvalid
@ ( mforall_indset
@ ^ [Y0: mu > $i > $o] :
( mforall_indset
@ ^ [Y1: mu > $i > $o] :
( mimplies
@ ( mbox
@ ( mforall_ind
@ ^ [Y2: mu] : ( mequiv @ ( Y0 @ Y2 ) @ ( Y1 @ Y2 ) ) ) )
@ ( mequiv @ ( p @ Y0 ) @ ( p @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f66]) ).
thf(f68,plain,
~ ( mvalid
@ ( mforall_indset
@ ^ [X0: mu > $i > $o] :
( mimplies @ ( p @ X0 )
@ ( mdia
@ ( mexists_ind
@ ^ [X1: mu] : ( X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f26]) ).
thf(f69,plain,
( $true
!= ( mvalid
@ ( mforall_indset
@ ^ [Y0: mu > $i > $o] :
( mimplies @ ( p @ Y0 )
@ ( mdia
@ ( mexists_ind
@ ^ [Y1: mu] : ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f68]) ).
thf(f70,plain,
( $true
!= ( mvalid
@ ( mforall_indset
@ ^ [Y0: mu > $i > $o] :
( mimplies @ ( p @ Y0 )
@ ( mdia
@ ( mexists_ind
@ ^ [Y1: mu] : ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(flattening,[],[f69]) ).
thf(f74,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f77,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f79,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f81,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f82,plain,
( mforall_indset
= ( ^ [Y0: ( mu > $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f47]) ).
thf(f84,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( ?? @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f51]) ).
thf(f87,plain,
( mbox_generic
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f57]) ).
thf(f88,plain,
( mdia_generic
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f59]) ).
thf(f89,plain,
( mbox
= ( mbox_generic @ rel ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f90,plain,
( mdia
= ( mdia_generic @ rel ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f91,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f61]) ).
thf(f93,plain,
( $true
= ( mvalid
@ ( mnot
@ ( p
@ ^ [Y0: mu,Y1: $i] : ( Y0 != Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f65]) ).
thf(f94,plain,
( $true
= ( mvalid
@ ( mforall_indset
@ ^ [Y0: mu > $i > $o] :
( mforall_indset
@ ^ [Y1: mu > $i > $o] :
( mimplies
@ ( mbox
@ ( mforall_ind
@ ^ [Y2: mu] : ( mequiv @ ( Y0 @ Y2 ) @ ( Y1 @ Y2 ) ) ) )
@ ( mequiv @ ( p @ Y0 ) @ ( p @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f67]) ).
thf(f95,plain,
( $true
!= ( mvalid
@ ( mforall_indset
@ ^ [Y0: mu > $i > $o] :
( mimplies @ ( p @ Y0 )
@ ( mdia
@ ( mexists_ind
@ ^ [Y1: mu] : ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f70]) ).
thf(f98,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ rel ) ),
inference(definition_unfolding,[],[f89,f87]) ).
thf(f99,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) )
@ rel ) ),
inference(definition_unfolding,[],[f90,f88]) ).
thf(f100,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ ( p
@ ^ [Y0: mu,Y1: $i] : ( Y0 != Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f93,f91,f74]) ).
thf(f101,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( mu > $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: mu > $i > $o] :
( ^ [Y1: ( mu > $i > $o ) > $i > $o,Y2: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: mu > $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
=> ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y4 @ Y5 )
| ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: mu > $i > $o,Y3: $i] :
( !! @ mu
@ ^ [Y4: mu] : ( Y2 @ Y4 @ Y3 ) )
@ ^ [Y2: mu] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y3 @ Y5 )
= ( Y4 @ Y5 ) )
@ ( Y0 @ Y2 )
@ ( Y1 @ Y2 ) ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
= ( Y3 @ Y4 ) )
@ ( p @ Y0 )
@ ( p @ Y1 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f94,f91,f82,f82,f77,f98,f81,f79,f79]) ).
thf(f102,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( mu > $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: mu > $i > $o] :
( ^ [Y1: $i > $o,Y2: $i > $o,Y3: $i] :
( ( Y1 @ Y3 )
=> ( Y2 @ Y3 ) )
@ ( p @ Y0 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
& ( Y2 @ Y4 ) ) )
@ rel
@ ( ^ [Y1: mu > $i > $o,Y2: $i] :
( ?? @ mu
@ ^ [Y3: mu] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: mu] : ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f95,f91,f82,f77,f99,f84]) ).
thf(f103,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( p @ Y1 @ Y0 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( rel @ Y0 @ Y2 )
& ( ?? @ mu
@ ^ [Y3: mu] : ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f102]) ).
thf(f104,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( p @ Y1 @ Y0 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( rel @ Y0 @ Y2 )
& ( ?? @ mu
@ ^ [Y3: mu] : ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f103]) ).
thf(f105,plain,
( $false
= ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( p @ Y0 @ sK0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( rel @ sK0 @ Y1 )
& ( ?? @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f104]) ).
thf(f106,plain,
( $false
= ( ^ [Y0: mu > $i > $o] :
( ( p @ Y0 @ sK0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( rel @ sK0 @ Y1 )
& ( ?? @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f105]) ).
thf(f107,plain,
( $false
= ( ( p @ sK1 @ sK0 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( rel @ sK0 @ Y0 )
& ( ?? @ mu
@ ^ [Y1: mu] : ( sK1 @ Y1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f106]) ).
thf(f108,plain,
( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( rel @ sK0 @ Y0 )
& ( ?? @ mu
@ ^ [Y1: mu] : ( sK1 @ Y1 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f107]) ).
thf(f109,plain,
( $true
= ( p @ sK1 @ sK0 ) ),
inference(imp_proxy_clausification,[],[f107]) ).
thf(f110,plain,
! [X1: $i] :
( $false
= ( ^ [Y0: $i] :
( ( rel @ sK0 @ Y0 )
& ( ?? @ mu
@ ^ [Y1: mu] : ( sK1 @ Y1 @ Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f108]) ).
thf(f111,plain,
! [X1: $i] :
( $false
= ( ( rel @ sK0 @ X1 )
& ( ?? @ mu
@ ^ [Y0: mu] : ( sK1 @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f110]) ).
thf(f112,plain,
! [X1: $i] :
( ( $false
= ( ?? @ mu
@ ^ [Y0: mu] : ( sK1 @ Y0 @ X1 ) ) )
| ( $false
= ( rel @ sK0 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f111]) ).
thf(f113,plain,
! [X2: mu,X1: $i] :
( ( $false
= ( ^ [Y0: mu] : ( sK1 @ Y0 @ X1 )
@ X2 ) )
| ( $false
= ( rel @ sK0 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f112]) ).
thf(f114,plain,
! [X2: mu,X1: $i] :
( ( $false
= ( sK1 @ X2 @ X1 ) )
| ( $false
= ( rel @ sK0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f113]) ).
thf(f115,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel @ Y0 @ Y3 )
| ( !! @ mu
@ ^ [Y4: mu] :
( ( Y1 @ Y4 @ Y3 )
= ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( ( p @ Y1 @ Y0 )
= ( p @ Y2 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f101]) ).
thf(f116,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel @ Y0 @ Y3 )
| ( !! @ mu
@ ^ [Y4: mu] :
( ( Y1 @ Y4 @ Y3 )
= ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( ( p @ Y1 @ Y0 )
= ( p @ Y2 @ Y0 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f115]) ).
thf(f117,plain,
! [X1: $i] :
( $true
= ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel @ X1 @ Y2 )
| ( !! @ mu
@ ^ [Y3: mu] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( ( p @ Y0 @ X1 )
= ( p @ Y1 @ X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f116]) ).
thf(f118,plain,
! [X2: mu > $i > $o,X1: $i] :
( $true
= ( ^ [Y0: mu > $i > $o] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel @ X1 @ Y2 )
| ( !! @ mu
@ ^ [Y3: mu] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( ( p @ Y0 @ X1 )
= ( p @ Y1 @ X1 ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f117]) ).
thf(f119,plain,
! [X2: mu > $i > $o,X1: $i] :
( $true
= ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel @ X1 @ Y1 )
| ( !! @ mu
@ ^ [Y2: mu] :
( ( X2 @ Y2 @ Y1 )
= ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( ( p @ X2 @ X1 )
= ( p @ Y0 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f118]) ).
thf(f120,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( $true
= ( ^ [Y0: mu > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel @ X1 @ Y1 )
| ( !! @ mu
@ ^ [Y2: mu] :
( ( X2 @ Y2 @ Y1 )
= ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( ( p @ X2 @ X1 )
= ( p @ Y0 @ X1 ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f119]) ).
thf(f121,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel @ X1 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( X2 @ Y1 @ Y0 )
= ( X3 @ Y1 @ Y0 ) ) ) ) )
=> ( ( p @ X2 @ X1 )
= ( p @ X3 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f120]) ).
thf(f122,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel @ X1 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( X2 @ Y1 @ Y0 )
= ( X3 @ Y1 @ Y0 ) ) ) ) ) )
| ( $true
= ( ( p @ X2 @ X1 )
= ( p @ X3 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f121]) ).
thf(f123,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel @ X1 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( X2 @ Y1 @ Y0 )
= ( X3 @ Y1 @ Y0 ) ) ) )
@ ( sK2 @ X3 @ X1 @ X2 ) ) )
| ( $true
= ( ( p @ X2 @ X1 )
= ( p @ X3 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f122]) ).
thf(f124,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( $false
= ( ~ ( rel @ X1 @ ( sK2 @ X3 @ X1 @ X2 ) )
| ( !! @ mu
@ ^ [Y0: mu] :
( ( X2 @ Y0 @ ( sK2 @ X3 @ X1 @ X2 ) )
= ( X3 @ Y0 @ ( sK2 @ X3 @ X1 @ X2 ) ) ) ) ) )
| ( $true
= ( ( p @ X2 @ X1 )
= ( p @ X3 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f123]) ).
thf(f125,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( $false
= ( !! @ mu
@ ^ [Y0: mu] :
( ( X2 @ Y0 @ ( sK2 @ X3 @ X1 @ X2 ) )
= ( X3 @ Y0 @ ( sK2 @ X3 @ X1 @ X2 ) ) ) ) )
| ( $true
= ( ( p @ X2 @ X1 )
= ( p @ X3 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f124]) ).
thf(f126,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( $false
= ( ~ ( rel @ X1 @ ( sK2 @ X3 @ X1 @ X2 ) ) ) )
| ( $true
= ( ( p @ X2 @ X1 )
= ( p @ X3 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f124]) ).
thf(f127,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( $true
= ( rel @ X1 @ ( sK2 @ X3 @ X1 @ X2 ) ) )
| ( $true
= ( ( p @ X2 @ X1 )
= ( p @ X3 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f126]) ).
thf(f128,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( $true
= ( rel @ X1 @ ( sK2 @ X3 @ X1 @ X2 ) ) )
| ( ( p @ X2 @ X1 )
= ( p @ X3 @ X1 ) ) ),
inference(iff_proxy_clausification,[],[f127]) ).
thf(f129,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( $true
= ( rel @ X1 @ ( sK2 @ X3 @ X1 @ X2 ) ) )
| ( $true
= ( p @ X2 @ X1 ) )
| ( $false
= ( p @ X3 @ X1 ) ) ),
inference(iff_proxy_clausification,[],[f128]) ).
thf(f131,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( $false
= ( ^ [Y0: mu] :
( ( X2 @ Y0 @ ( sK2 @ X3 @ X1 @ X2 ) )
= ( X3 @ Y0 @ ( sK2 @ X3 @ X1 @ X2 ) ) )
@ ( sK3 @ X3 @ X1 @ X2 ) ) )
| ( $true
= ( ( p @ X2 @ X1 )
= ( p @ X3 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f125]) ).
thf(f132,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( $false
= ( ( X2 @ ( sK3 @ X3 @ X1 @ X2 ) @ ( sK2 @ X3 @ X1 @ X2 ) )
= ( X3 @ ( sK3 @ X3 @ X1 @ X2 ) @ ( sK2 @ X3 @ X1 @ X2 ) ) ) )
| ( $true
= ( ( p @ X2 @ X1 )
= ( p @ X3 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f131]) ).
thf(f133,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( ( X2 @ ( sK3 @ X3 @ X1 @ X2 ) @ ( sK2 @ X3 @ X1 @ X2 ) )
!= ( X3 @ ( sK3 @ X3 @ X1 @ X2 ) @ ( sK2 @ X3 @ X1 @ X2 ) ) )
| ( $true
= ( ( p @ X2 @ X1 )
= ( p @ X3 @ X1 ) ) ) ),
inference(iff_proxy_clausification,[],[f132]) ).
thf(f134,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( $true
= ( X2 @ ( sK3 @ X3 @ X1 @ X2 ) @ ( sK2 @ X3 @ X1 @ X2 ) ) )
| ( $true
= ( ( p @ X2 @ X1 )
= ( p @ X3 @ X1 ) ) )
| ( $true
= ( X3 @ ( sK3 @ X3 @ X1 @ X2 ) @ ( sK2 @ X3 @ X1 @ X2 ) ) ) ),
inference(xor_proxy_clausification,[],[f133]) ).
thf(f139,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( $true
= ( X2 @ ( sK3 @ X3 @ X1 @ X2 ) @ ( sK2 @ X3 @ X1 @ X2 ) ) )
| ( ( p @ X2 @ X1 )
= ( p @ X3 @ X1 ) )
| ( $true
= ( X3 @ ( sK3 @ X3 @ X1 @ X2 ) @ ( sK2 @ X3 @ X1 @ X2 ) ) ) ),
inference(iff_proxy_clausification,[],[f134]) ).
thf(f140,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( $true
= ( X3 @ ( sK3 @ X3 @ X1 @ X2 ) @ ( sK2 @ X3 @ X1 @ X2 ) ) )
| ( $true
= ( X2 @ ( sK3 @ X3 @ X1 @ X2 ) @ ( sK2 @ X3 @ X1 @ X2 ) ) )
| ( $true
= ( p @ X2 @ X1 ) )
| ( $false
= ( p @ X3 @ X1 ) ) ),
inference(iff_proxy_clausification,[],[f139]) ).
thf(f142,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
~ ( p
@ ^ [Y1: mu,Y2: $i] : ( Y1 != Y1 )
@ Y0 ) ) ),
inference(beta-eta_normalization,[],[f100]) ).
thf(f143,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
~ ( p
@ ^ [Y1: mu,Y2: $i] : ( Y1 != Y1 )
@ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f142]) ).
thf(f144,plain,
! [X1: $i] :
( $true
= ( ~ ( p
@ ^ [Y0: mu,Y1: $i] : ( Y0 != Y0 )
@ X1 ) ) ),
inference(beta-eta_normalization,[],[f143]) ).
thf(f145,plain,
! [X1: $i] :
( $false
= ( p
@ ^ [Y0: mu,Y1: $i] : ( Y0 != Y0 )
@ X1 ) ),
inference(not_proxy_clausification,[],[f144]) ).
thf(f146,plain,
! [X1: $i] :
( $false
= ( p
@ ^ [Y0: mu,Y1: $i] : ~ $true
@ X1 ) ),
inference(boolean_simplification,[],[f145]) ).
thf(f147,plain,
! [X1: $i] :
( $false
= ( p
@ ^ [Y0: mu,Y1: $i] : $false
@ X1 ) ),
inference(boolean_simplification,[],[f146]) ).
thf(f477,plain,
! [X2: mu > $i > mu,X3: mu > $i > $i,X0: mu,X1: $i,X4: $i,X5: mu > $i > $o] :
( ( $true = $false )
| ( $false
= ( rel @ sK0 @ X1 ) )
| ( $true
= ( X5
@ ( sK3
@ ^ [Y0: mu,Y1: $i] : ( sK1 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) )
@ X4
@ X5 )
@ ( sK2
@ ^ [Y0: mu,Y1: $i] : ( sK1 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) )
@ X4
@ X5 ) ) )
| ( $true
= ( p @ X5 @ X4 ) )
| ( $false
= ( p
@ ^ [Y0: mu,Y1: $i] : ( sK1 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) )
@ X4 ) )
| ( ( X2
@ ( sK3
@ ^ [Y0: mu,Y1: $i] : ( sK1 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) )
@ X4
@ X5 )
@ ( sK2
@ ^ [Y0: mu,Y1: $i] : ( sK1 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) )
@ X4
@ X5 ) )
!= X0 )
| ( ( X3
@ ( sK3
@ ^ [Y0: mu,Y1: $i] : ( sK1 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) )
@ X4
@ X5 )
@ ( sK2
@ ^ [Y0: mu,Y1: $i] : ( sK1 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) )
@ X4
@ X5 ) )
!= X1 ) ),
inference(constrained_superposition,[],[f114,f140]) ).
thf(f561,plain,
! [X2: mu > $i > mu,X3: mu > $i > $i,X0: mu,X1: $i,X4: $i,X5: mu > $i > $o] :
( ( $true
= ( X5
@ ( sK3
@ ^ [Y0: mu,Y1: $i] : ( sK1 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) )
@ X4
@ X5 )
@ ( sK2
@ ^ [Y0: mu,Y1: $i] : ( sK1 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) )
@ X4
@ X5 ) ) )
| ( $false
= ( rel @ sK0 @ X1 ) )
| ( $true
= ( p @ X5 @ X4 ) )
| ( $false
= ( p
@ ^ [Y0: mu,Y1: $i] : ( sK1 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) )
@ X4 ) )
| ( ( X2
@ ( sK3
@ ^ [Y0: mu,Y1: $i] : ( sK1 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) )
@ X4
@ X5 )
@ ( sK2
@ ^ [Y0: mu,Y1: $i] : ( sK1 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) )
@ X4
@ X5 ) )
!= X0 )
| ( ( X3
@ ( sK3
@ ^ [Y0: mu,Y1: $i] : ( sK1 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) )
@ X4
@ X5 )
@ ( sK2
@ ^ [Y0: mu,Y1: $i] : ( sK1 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) )
@ X4
@ X5 ) )
!= X1 ) ),
inference(trivial_inequality_removal,[],[f477]) ).
thf(f915,plain,
! [X2: mu > $i > mu,X3: mu > $i > $i,X0: mu,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: mu,Y1: $i] : $false
@ ( sK3
@ ^ [Y0: mu,Y1: $i] : ( sK1 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) )
@ X4
@ ^ [Y0: mu,Y1: $i] : $false )
@ ( sK2
@ ^ [Y0: mu,Y1: $i] : ( sK1 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) )
@ X4
@ ^ [Y0: mu,Y1: $i] : $false ) ) )
| ( $false
= ( rel @ sK0 @ X1 ) )
| ( $true
= ( p
@ ^ [Y0: mu,Y1: $i] : $false
@ X4 ) )
| ( $false
= ( p
@ ^ [Y0: mu,Y1: $i] : ( sK1 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) )
@ X4 ) )
| ( ( X2
@ ( sK3
@ ^ [Y0: mu,Y1: $i] : ( sK1 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) )
@ X4
@ ^ [Y0: mu,Y1: $i] : $false )
@ ( sK2
@ ^ [Y0: mu,Y1: $i] : ( sK1 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) )
@ X4
@ ^ [Y0: mu,Y1: $i] : $false ) )
!= X0 )
| ( ( X3
@ ( sK3
@ ^ [Y0: mu,Y1: $i] : ( sK1 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) )
@ X4
@ ^ [Y0: mu,Y1: $i] : $false )
@ ( sK2
@ ^ [Y0: mu,Y1: $i] : ( sK1 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) )
@ X4
@ ^ [Y0: mu,Y1: $i] : $false ) )
!= X1 ) ),
inference(primitive_instantiation,[],[f561]) ).
thf(f1043,plain,
! [X2: mu > $i > mu,X3: mu > $i > $i,X0: mu,X1: $i,X4: $i] :
( ( $true = $false )
| ( $false
= ( rel @ sK0 @ X1 ) )
| ( $true
= ( p
@ ^ [Y0: mu,Y1: $i] : $false
@ X4 ) )
| ( $false
= ( p
@ ^ [Y0: mu,Y1: $i] : ( sK1 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) )
@ X4 ) )
| ( ( X2
@ ( sK3
@ ^ [Y0: mu,Y1: $i] : ( sK1 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) )
@ X4
@ ^ [Y0: mu,Y1: $i] : $false )
@ ( sK2
@ ^ [Y0: mu,Y1: $i] : ( sK1 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) )
@ X4
@ ^ [Y0: mu,Y1: $i] : $false ) )
!= X0 )
| ( ( X3
@ ( sK3
@ ^ [Y0: mu,Y1: $i] : ( sK1 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) )
@ X4
@ ^ [Y0: mu,Y1: $i] : $false )
@ ( sK2
@ ^ [Y0: mu,Y1: $i] : ( sK1 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) )
@ X4
@ ^ [Y0: mu,Y1: $i] : $false ) )
!= X1 ) ),
inference(beta-eta_normalization,[],[f915]) ).
thf(f1044,plain,
! [X2: mu > $i > mu,X3: mu > $i > $i,X0: mu,X1: $i,X4: $i] :
( ( $false
= ( rel @ sK0 @ X1 ) )
| ( $true
= ( p
@ ^ [Y0: mu,Y1: $i] : $false
@ X4 ) )
| ( $false
= ( p
@ ^ [Y0: mu,Y1: $i] : ( sK1 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) )
@ X4 ) )
| ( ( X2
@ ( sK3
@ ^ [Y0: mu,Y1: $i] : ( sK1 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) )
@ X4
@ ^ [Y0: mu,Y1: $i] : $false )
@ ( sK2
@ ^ [Y0: mu,Y1: $i] : ( sK1 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) )
@ X4
@ ^ [Y0: mu,Y1: $i] : $false ) )
!= X0 )
| ( ( X3
@ ( sK3
@ ^ [Y0: mu,Y1: $i] : ( sK1 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) )
@ X4
@ ^ [Y0: mu,Y1: $i] : $false )
@ ( sK2
@ ^ [Y0: mu,Y1: $i] : ( sK1 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) )
@ X4
@ ^ [Y0: mu,Y1: $i] : $false ) )
!= X1 ) ),
inference(trivial_inequality_removal,[],[f1043]) ).
thf(f1048,plain,
! [X2: mu > $i > mu,X3: mu > $i > $i,X0: mu,X1: $i,X4: $i] :
( ( $true = $false )
| ( $false
= ( rel @ sK0 @ X1 ) )
| ( $false
= ( p
@ ^ [Y0: mu,Y1: $i] : ( sK1 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) )
@ X4 ) )
| ( ( X2
@ ( sK3
@ ^ [Y0: mu,Y1: $i] : ( sK1 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) )
@ X4
@ ^ [Y0: mu,Y1: $i] : $false )
@ ( sK2
@ ^ [Y0: mu,Y1: $i] : ( sK1 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) )
@ X4
@ ^ [Y0: mu,Y1: $i] : $false ) )
!= X0 )
| ( ( X3
@ ( sK3
@ ^ [Y0: mu,Y1: $i] : ( sK1 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) )
@ X4
@ ^ [Y0: mu,Y1: $i] : $false )
@ ( sK2
@ ^ [Y0: mu,Y1: $i] : ( sK1 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) )
@ X4
@ ^ [Y0: mu,Y1: $i] : $false ) )
!= X1 ) ),
inference(forward_demodulation,[],[f1044,f147]) ).
thf(f1049,plain,
! [X2: mu > $i > mu,X3: mu > $i > $i,X0: mu,X1: $i,X4: $i] :
( ( $false
= ( rel @ sK0 @ X1 ) )
| ( $false
= ( p
@ ^ [Y0: mu,Y1: $i] : ( sK1 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) )
@ X4 ) )
| ( ( X2
@ ( sK3
@ ^ [Y0: mu,Y1: $i] : ( sK1 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) )
@ X4
@ ^ [Y0: mu,Y1: $i] : $false )
@ ( sK2
@ ^ [Y0: mu,Y1: $i] : ( sK1 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) )
@ X4
@ ^ [Y0: mu,Y1: $i] : $false ) )
!= X0 )
| ( ( X3
@ ( sK3
@ ^ [Y0: mu,Y1: $i] : ( sK1 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) )
@ X4
@ ^ [Y0: mu,Y1: $i] : $false )
@ ( sK2
@ ^ [Y0: mu,Y1: $i] : ( sK1 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) )
@ X4
@ ^ [Y0: mu,Y1: $i] : $false ) )
!= X1 ) ),
inference(trivial_inequality_removal,[],[f1048]) ).
thf(f1367,plain,
! [X0: $i,X1: mu] :
( ( $true = $false )
| ( $false
= ( rel @ sK0 @ X0 ) )
| ( ( ^ [Y0: mu,Y1: $i] : Y0
@ ( sK3
@ ^ [Y0: mu,Y1: $i] :
( sK1
@ ( ^ [Y2: mu,Y3: $i] : Y2
@ Y0
@ Y1 )
@ ( ^ [Y2: mu,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ sK0
@ ^ [Y0: mu,Y1: $i] : $false )
@ ( sK2
@ ^ [Y0: mu,Y1: $i] :
( sK1
@ ( ^ [Y2: mu,Y3: $i] : Y2
@ Y0
@ Y1 )
@ ( ^ [Y2: mu,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ sK0
@ ^ [Y0: mu,Y1: $i] : $false ) )
!= X1 )
| ( ( ^ [Y0: mu,Y1: $i] : Y1
@ ( sK3
@ ^ [Y0: mu,Y1: $i] :
( sK1
@ ( ^ [Y2: mu,Y3: $i] : Y2
@ Y0
@ Y1 )
@ ( ^ [Y2: mu,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ sK0
@ ^ [Y0: mu,Y1: $i] : $false )
@ ( sK2
@ ^ [Y0: mu,Y1: $i] :
( sK1
@ ( ^ [Y2: mu,Y3: $i] : Y2
@ Y0
@ Y1 )
@ ( ^ [Y2: mu,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ sK0
@ ^ [Y0: mu,Y1: $i] : $false ) )
!= X0 ) ),
inference(constrained_superposition,[],[f1049,f109]) ).
thf(f1449,plain,
! [X0: $i,X1: mu] :
( ( $false
= ( rel @ sK0 @ X0 ) )
| ( ( ^ [Y0: mu,Y1: $i] : Y0
@ ( sK3
@ ^ [Y0: mu,Y1: $i] :
( sK1
@ ( ^ [Y2: mu,Y3: $i] : Y2
@ Y0
@ Y1 )
@ ( ^ [Y2: mu,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ sK0
@ ^ [Y0: mu,Y1: $i] : $false )
@ ( sK2
@ ^ [Y0: mu,Y1: $i] :
( sK1
@ ( ^ [Y2: mu,Y3: $i] : Y2
@ Y0
@ Y1 )
@ ( ^ [Y2: mu,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ sK0
@ ^ [Y0: mu,Y1: $i] : $false ) )
!= X1 )
| ( ( ^ [Y0: mu,Y1: $i] : Y1
@ ( sK3
@ ^ [Y0: mu,Y1: $i] :
( sK1
@ ( ^ [Y2: mu,Y3: $i] : Y2
@ Y0
@ Y1 )
@ ( ^ [Y2: mu,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ sK0
@ ^ [Y0: mu,Y1: $i] : $false )
@ ( sK2
@ ^ [Y0: mu,Y1: $i] :
( sK1
@ ( ^ [Y2: mu,Y3: $i] : Y2
@ Y0
@ Y1 )
@ ( ^ [Y2: mu,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ sK0
@ ^ [Y0: mu,Y1: $i] : $false ) )
!= X0 ) ),
inference(trivial_inequality_removal,[],[f1367]) ).
thf(f1450,plain,
! [X0: $i,X1: mu] :
( ( $false
= ( rel @ sK0 @ X0 ) )
| ( ( sK3 @ sK1 @ sK0
@ ^ [Y0: mu,Y1: $i] : $false )
!= X1 )
| ( ( sK2 @ sK1 @ sK0
@ ^ [Y0: mu,Y1: $i] : $false )
!= X0 ) ),
inference(beta-eta_normalization,[],[f1449]) ).
thf(f1471,definition,
( spl4_6
<=> ! [X1: mu] :
( ( sK3 @ sK1 @ sK0
@ ^ [Y0: mu,Y1: $i] : $false )
!= X1 ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f1472,plain,
( ! [X1: mu] :
( ( sK3 @ sK1 @ sK0
@ ^ [Y0: mu,Y1: $i] : $false )
!= X1 )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f1471]) ).
thf(f1474,definition,
( spl4_7
<=> ! [X0: $i] :
( ( $false
= ( rel @ sK0 @ X0 ) )
| ( ( sK2 @ sK1 @ sK0
@ ^ [Y0: mu,Y1: $i] : $false )
!= X0 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition]) ).
thf(f1475,plain,
( ! [X0: $i] :
( ( ( sK2 @ sK1 @ sK0
@ ^ [Y0: mu,Y1: $i] : $false )
!= X0 )
| ( $false
= ( rel @ sK0 @ X0 ) ) )
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f1474]) ).
thf(f1477,plain,
( spl4_6
| spl4_7 ),
inference(avatar_split_clause,[],[f1450,f1474,f1471]) ).
thf(f1839,plain,
( $false
| ~ spl4_6 ),
inference(equality_resolution,[],[f1472]) ).
thf(f1840,plain,
~ spl4_6,
inference(avatar_contradiction_clause,[],[f1839]) ).
thf(f1841,plain,
( ( $false
= ( rel @ sK0
@ ( sK2 @ sK1 @ sK0
@ ^ [Y0: mu,Y1: $i] : $false ) ) )
| ~ spl4_7 ),
inference(equality_resolution,[],[f1475]) ).
thf(f1866,plain,
( ( $true = $false )
| ( $true
= ( p
@ ^ [Y0: mu,Y1: $i] : $false
@ sK0 ) )
| ( $false
= ( p @ sK1 @ sK0 ) )
| ~ spl4_7 ),
inference(constrained_superposition,[],[f129,f1841]) ).
thf(f1867,plain,
( ( $true
= ( p
@ ^ [Y0: mu,Y1: $i] : $false
@ sK0 ) )
| ( $false
= ( p @ sK1 @ sK0 ) )
| ~ spl4_7 ),
inference(trivial_inequality_removal,[],[f1866]) ).
thf(f1912,plain,
( ( $true = $false )
| ( $false
= ( p @ sK1 @ sK0 ) )
| ~ spl4_7 ),
inference(forward_demodulation,[],[f1867,f147]) ).
thf(f1913,plain,
( ( $false
= ( p @ sK1 @ sK0 ) )
| ~ spl4_7 ),
inference(trivial_inequality_removal,[],[f1912]) ).
thf(f2075,plain,
( ( $true = $false )
| ~ spl4_7 ),
inference(constrained_superposition,[],[f1913,f109]) ).
thf(f2141,plain,
( $false
| ~ spl4_7 ),
inference(trivial_inequality_removal,[],[f2075]) ).
thf(f2142,plain,
~ spl4_7,
inference(avatar_contradiction_clause,[],[f2141]) ).
cnf(s14,plain,
( spl4_6
| spl4_7 ),
inference(sat_conversion,[],[f1477]) ).
cnf(s17,plain,
~ spl4_6,
inference(sat_conversion,[],[f1840]) ).
cnf(s21,plain,
~ spl4_7,
inference(sat_conversion,[],[f2142]) ).
cnf(s22,plain,
$false,
inference(rat,[],[s14,s21,s17]) ).
thf(f2143,plain,
$false,
inference(avatar_sat_refutation,[],[s22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PHI043^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n007.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 13:18:11 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 Running first-order model finding
% 0.09/0.21 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
% 1.77/0.52 % (3341090)Will run a generic schedule for satisfiability detection.
% 1.77/0.52 % (3341095)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4101566957_2999 on theBenchmark for (2999ds/0Mi)
% 1.77/0.52 % Exception at run slice level
% 1.77/0.52 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.77/0.52 % (3341096)% WARNING: option uhcvi not known.
% 1.77/0.52 % (3341096)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3607870918:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.77/0.52 % (3341097)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3045681583:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.77/0.52 % (3341098)dis+10_1_sil=32000:sp=arity:random_seed=579452349:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.77/0.52 % (3341099)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4062116824:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.77/0.52 % (3341101)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2993500756:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.77/0.52 % (3341100)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2265903406:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.77/0.52 % (3341096)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.77/0.52 % (3341099)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.77/0.52 % (3341096)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.77/0.52 % (3341103)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1830147954:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.77/0.52 % Exception at run slice level
% 1.77/0.52 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.77/0.52 % (3341111)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1731682111:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.77/0.52 % (3341098)Instruction limit reached!
% 1.77/0.52 % (3341098)------------------------------
% 1.77/0.52 % (3341098)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.52 % (3341098)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.52 % (3341098)CaDiCaL version: 2.1.3
% 1.77/0.52 % (3341098)Termination reason: Instruction limit
% 1.77/0.52 % (3341098)Termination phase: Saturation
% 1.77/0.52 % (3341098)Time elapsed: 0.048 s
% 1.77/0.52 % (3341098)Peak memory usage: 12 MB
% 1.77/0.52 % (3341098)Instructions burned: 105 (million)
% 1.77/0.52 % (3341111)Instruction limit reached!
% 1.77/0.52 % (3341111)------------------------------
% 1.77/0.52 % (3341111)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.52 % (3341111)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.52 % (3341111)CaDiCaL version: 2.1.3
% 1.77/0.52 % (3341111)Termination reason: Instruction limit
% 1.77/0.52 % (3341111)Termination phase: Saturation
% 1.77/0.52 % (3341111)Time elapsed: 0.033 s
% 1.77/0.52 % (3341111)Peak memory usage: 13 MB
% 1.77/0.52 % (3341111)Instructions burned: 134 (million)
% 1.77/0.52 % (3341099)Instruction limit reached!
% 1.77/0.52 % (3341099)------------------------------
% 1.77/0.52 % (3341099)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.52 % (3341099)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.52 % (3341099)CaDiCaL version: 2.1.3
% 1.77/0.52 % (3341099)Termination reason: Instruction limit
% 1.77/0.52 % (3341099)Termination phase: Saturation
% 1.77/0.52 % (3341099)Time elapsed: 0.054 s
% 1.77/0.52 % (3341099)Peak memory usage: 12 MB
% 1.77/0.52 % (3341099)Instructions burned: 118 (million)
% 1.77/0.52 % (3341100)Instruction limit reached!
% 1.77/0.52 % (3341100)------------------------------
% 1.77/0.52 % (3341100)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.52 % (3341100)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.52 % (3341100)CaDiCaL version: 2.1.3
% 1.77/0.52 % (3341100)Termination reason: Instruction limit
% 1.77/0.52 % (3341100)Termination phase: Saturation
% 1.77/0.52 % (3341100)Time elapsed: 0.059 s
% 1.77/0.52 % (3341100)Peak memory usage: 12 MB
% 1.77/0.52 % (3341100)Instructions burned: 131 (million)
% 1.77/0.52 % (3341114)ott-21_1_sil=16000:fs=off:random_seed=523073839:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 1.77/0.52 % (3341113)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=4118600559:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 1.77/0.52 % (3341113)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.77/0.52 % (3341113)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.77/0.52 % (3341115)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=199550059:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 1.77/0.52 % (3341101)Instruction limit reached!
% 1.77/0.52 % (3341101)------------------------------
% 1.77/0.52 % (3341101)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.52 % (3341101)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.52 % (3341101)CaDiCaL version: 2.1.3
% 1.77/0.52 % (3341101)Termination reason: Instruction limit
% 1.77/0.52 % (3341101)Termination phase: Saturation
% 1.77/0.52 % (3341101)Time elapsed: 0.074 s
% 1.77/0.52 % (3341101)Peak memory usage: 13 MB
% 1.77/0.52 % (3341101)Instructions burned: 161 (million)
% 1.77/0.52 % (3341117)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2712970264:fmbsr=1.3:i=865:ins=25_2999 on theBenchmark for (2999ds/865Mi)
% 1.77/0.52 % Exception at run slice level
% 1.77/0.52 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.77/0.52 % (3341120)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3039208991:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 1.77/0.52 % (3341122)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1816099361:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 1.77/0.52 % (3341114)Instruction limit reached!
% 1.77/0.52 % (3341114)------------------------------
% 1.77/0.52 % (3341114)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.52 % (3341114)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.52 % (3341114)CaDiCaL version: 2.1.3
% 1.77/0.52 % (3341114)Termination reason: Instruction limit
% 1.77/0.52 % (3341114)Termination phase: Saturation
% 1.77/0.52 % (3341114)Time elapsed: 0.041 s
% 1.77/0.52 % (3341114)Peak memory usage: 13 MB
% 1.77/0.52 % (3341114)Instructions burned: 182 (million)
% 1.77/0.52 % Exception at run slice level
% 1.77/0.52 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.77/0.52 % (3341126)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=248219828:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 1.77/0.52 % (3341126)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.77/0.52 % (3341128)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=1604834426:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 1.77/0.52 % (3341128)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.77/0.52 % (3341096) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3341090-3341096"...
% 1.77/0.52 % (3341096)...printing done.
% 1.77/0.52 % (3341096)Refutation found. Thanks to Tanya!
% 1.77/0.52 % SZS status Theorem for theBenchmark
% 1.77/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 1.77/0.52 % (3341096)------------------------------
% 1.77/0.52 % (3341096)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.52 % (3341096)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.52 % (3341096)CaDiCaL version: 2.1.3
% 1.77/0.52 % (3341096)Termination reason: Refutation
% 1.77/0.52 % (3341096)Time elapsed: 0.257 s
% 1.77/0.52 % (3341096)Peak memory usage: 14 MB
% 1.77/0.52 % (3341096)Instructions burned: 586 (million)
% 1.77/0.52 % (3341090)Success in time 0.3 s
% 1.77/0.52 % Vampire exiting
%------------------------------------------------------------------------------