%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO456^6 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 08:47:50 AM UTC 2026
% Result : Theorem 0.22s 0.29s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 11
% Syntax : Number of formulae : 111 ( 63 unt; 0 typ; 2 def)
% Number of atoms : 744 ( 136 equ; 0 cnn)
% Maximal formula atoms : 10 ( 6 avg)
% Number of connectives : 1163 ( 193 ~; 149 |; 0 &; 723 @)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 69 ( 69 >; 0 *; 0 +; 0 <<)
% Number of symbols : 59 ( 55 usr; 7 con; 0-4 aty)
% ( 86 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 239 ( 0 sgn 47 !; 0 ?; 239 :)
% 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,
rel_s5: $i > $i > $o ).
thf(func_def_33,type,
mbox_s5: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
mdia_s5: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
p: $i > $o ).
thf(func_def_36,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_37,type,
vIMP: $o > $o > $o ).
thf(func_def_38,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_42,type,
vAND: $o > $o > $o ).
thf(func_def_43,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
vOR: $o > $o > $o ).
thf(func_def_47,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_48,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_49,type,
vNOT: $o > $o ).
thf(func_def_50,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_52,type,
sK1: $i > $i ).
thf(func_def_54,type,
sK3: $i > $i ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f19,axiom,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X2: $i,X1: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',msymmetric) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( mbox_s5
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s5 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',mbox_s5) ).
thf(f33,axiom,
( mdia_s5
= ( ^ [X0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',mdia_s5) ).
thf(f36,axiom,
msymmetric @ rel_s5,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',a3) ).
thf(f37,conjecture,
mvalid @ ( mimplies @ ( mdia_s5 @ ( mbox_s5 @ ( mdia_s5 @ ( mbox_s5 @ p ) ) ) ) @ ( mdia_s5 @ ( mbox_s5 @ p ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
thf(f38,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mdia_s5 @ ( mbox_s5 @ ( mdia_s5 @ ( mbox_s5 @ p ) ) ) ) @ ( mdia_s5 @ ( mbox_s5 @ p ) ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
thf(f39,plain,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X2 @ X1 )
=> ( X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f19]) ).
thf(f40,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f39]) ).
thf(f41,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f45,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f46,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f45]) ).
thf(f50,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f55,plain,
~ ( mvalid @ ( mimplies @ ( mdia_s5 @ ( mbox_s5 @ ( mdia_s5 @ ( mbox_s5 @ p ) ) ) ) @ ( mdia_s5 @ ( mbox_s5 @ p ) ) ) ),
inference(rectify,[],[f38]) ).
thf(f56,plain,
( ( mvalid @ ( mimplies @ ( mdia_s5 @ ( mbox_s5 @ ( mdia_s5 @ ( mbox_s5 @ p ) ) ) ) @ ( mdia_s5 @ ( mbox_s5 @ p ) ) ) )
!= $true ),
inference(fool_elimination,[],[f55]) ).
thf(f65,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f66,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f65]) ).
thf(f69,plain,
( mbox_s5
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s5 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f70,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f69]) ).
thf(f80,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f81,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f80]) ).
thf(f84,plain,
msymmetric @ rel_s5,
inference(rectify,[],[f36]) ).
thf(f85,plain,
( ( msymmetric @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f84]) ).
thf(f101,plain,
( ( mvalid @ ( mimplies @ ( mdia_s5 @ ( mbox_s5 @ ( mdia_s5 @ ( mbox_s5 @ p ) ) ) ) @ ( mdia_s5 @ ( mbox_s5 @ p ) ) ) )
!= $true ),
inference(flattening,[],[f56]) ).
thf(f104,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f109,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f66]) ).
thf(f110,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f111,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f70]) ).
thf(f112,plain,
( ( msymmetric @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f85]) ).
thf(f118,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f50]) ).
thf(f123,plain,
( ( mvalid @ ( mimplies @ ( mdia_s5 @ ( mbox_s5 @ ( mdia_s5 @ ( mbox_s5 @ p ) ) ) ) @ ( mdia_s5 @ ( mbox_s5 @ p ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f101]) ).
thf(f129,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f81]) ).
thf(f136,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f46]) ).
thf(f142,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,[],[f110,f136,f129]) ).
thf(f150,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f118,f129,f111,f129]) ).
thf(f153,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
@ rel_s5 ) ),
inference(definition_unfolding,[],[f112,f104]) ).
thf(f154,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [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 )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ p ) ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ p ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f123,f109,f142,f150,f111,f150,f111,f150,f111]) ).
thf(f155,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y0 @ Y1 )
=> ( rel_s5 @ Y1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f156,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y0 @ Y1 )
=> ( rel_s5 @ Y1 @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f155]) ).
thf(f157,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel_s5 @ X1 @ Y0 )
=> ( rel_s5 @ Y0 @ X1 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f156]) ).
thf(f158,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( rel_s5 @ X1 @ Y0 )
=> ( rel_s5 @ Y0 @ X1 ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f157]) ).
thf(f159,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s5 @ X1 @ X2 )
=> ( rel_s5 @ X2 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f158]) ).
thf(f160,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s5 @ X2 @ X1 )
= $true )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f159]) ).
thf(f173,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s5 @ Y3 @ Y4 )
| ( p @ Y4 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f174,plain,
( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s5 @ Y3 @ Y4 )
| ( p @ Y4 ) ) ) ) ) ) ) ) ) )
@ sK0 )
= $false ),
inference(sigma_proxy_clausification,[],[f173]) ).
thf(f175,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f174]) ).
thf(f176,plain,
( ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f175]) ).
thf(f177,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f175]) ).
thf(f178,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f177]) ).
thf(f179,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f178]) ).
thf(f180,plain,
! [X1: $i] :
( ( ~ ( rel_s5 @ sK0 @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( p @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f179]) ).
thf(f181,plain,
! [X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( ( ~ ( rel_s5 @ sK0 @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f180]) ).
thf(f182,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( p @ Y0 ) ) )
= $false )
| ( ( ~ ( rel_s5 @ sK0 @ X1 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f181]) ).
thf(f183,plain,
! [X1: $i] :
( ( ( ~ ( rel_s5 @ sK0 @ X1 ) )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( p @ Y0 ) )
@ ( sK1 @ X1 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f182]) ).
thf(f184,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( p @ Y0 ) )
@ ( sK1 @ X1 ) )
= $false )
| ( ( rel_s5 @ sK0 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f183]) ).
thf(f185,plain,
! [X1: $i] :
( ( ( ~ ( rel_s5 @ X1 @ ( sK1 @ X1 ) )
| ( p @ ( sK1 @ X1 ) ) )
= $false )
| ( ( rel_s5 @ sK0 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f184]) ).
thf(f186,plain,
! [X1: $i] :
( ( ( rel_s5 @ sK0 @ X1 )
= $false )
| ( ( p @ ( sK1 @ X1 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f185]) ).
thf(f187,plain,
! [X1: $i] :
( ( ( ~ ( rel_s5 @ X1 @ ( sK1 @ X1 ) ) )
= $false )
| ( ( rel_s5 @ sK0 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f185]) ).
thf(f188,plain,
! [X1: $i] :
( ( ( rel_s5 @ X1 @ ( sK1 @ X1 ) )
= $true )
| ( ( rel_s5 @ sK0 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f187]) ).
thf(f189,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(not_proxy_clausification,[],[f176]) ).
thf(f190,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f189]) ).
thf(f191,plain,
( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_proxy_clausification,[],[f190]) ).
thf(f192,plain,
( ( ~ ( rel_s5 @ sK0 @ sK2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f191]) ).
thf(f193,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f192]) ).
thf(f194,plain,
( ( ~ ( rel_s5 @ sK0 @ sK2 ) )
= $false ),
inference(or_proxy_clausification,[],[f192]) ).
thf(f195,plain,
( $true
= ( rel_s5 @ sK0 @ sK2 ) ),
inference(not_proxy_clausification,[],[f194]) ).
thf(f196,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) )
= $true ),
inference(not_proxy_clausification,[],[f193]) ).
thf(f197,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f196]) ).
thf(f198,plain,
! [X1: $i] :
( ( ~ ( rel_s5 @ sK2 @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f197]) ).
thf(f199,plain,
! [X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
= $true )
| ( ( ~ ( rel_s5 @ sK2 @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f198]) ).
thf(f200,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) )
= $false )
| ( ( ~ ( rel_s5 @ sK2 @ X1 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f199]) ).
thf(f201,plain,
! [X1: $i] :
( ( ( ~ ( rel_s5 @ sK2 @ X1 ) )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ ( sK3 @ X1 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f200]) ).
thf(f202,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ ( sK3 @ X1 ) )
= $false )
| ( ( rel_s5 @ sK2 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f201]) ).
thf(f203,plain,
! [X1: $i] :
( ( ( ~ ( rel_s5 @ X1 @ ( sK3 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ ( sK3 @ X1 ) @ Y0 )
| ( p @ Y0 ) ) ) )
= $false )
| ( ( rel_s5 @ sK2 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f202]) ).
thf(f204,plain,
! [X1: $i] :
( ( ( rel_s5 @ sK2 @ X1 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ ( sK3 @ X1 ) @ Y0 )
| ( p @ Y0 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f203]) ).
thf(f205,plain,
! [X1: $i] :
( ( ( rel_s5 @ sK2 @ X1 )
= $false )
| ( ( ~ ( rel_s5 @ X1 @ ( sK3 @ X1 ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f203]) ).
thf(f206,plain,
! [X1: $i] :
( ( ( rel_s5 @ X1 @ ( sK3 @ X1 ) )
= $true )
| ( ( rel_s5 @ sK2 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f205]) ).
thf(f207,plain,
! [X1: $i] :
( ( ( rel_s5 @ sK2 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ ( sK3 @ X1 ) @ Y0 )
| ( p @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f204]) ).
thf(f208,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s5 @ sK2 @ X1 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ ( sK3 @ X1 ) @ Y0 )
| ( p @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f207]) ).
thf(f209,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ ( sK3 @ X1 ) @ X2 )
| ( p @ X2 ) ) )
| ( ( rel_s5 @ sK2 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f208]) ).
thf(f210,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s5 @ ( sK3 @ X1 ) @ X2 ) )
= $true )
| ( $true
= ( p @ X2 ) )
| ( ( rel_s5 @ sK2 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f209]) ).
thf(f211,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s5 @ ( sK3 @ X1 ) @ X2 )
= $false )
| ( $true
= ( p @ X2 ) )
| ( ( rel_s5 @ sK2 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f210]) ).
thf(f225,plain,
( ( ( rel_s5 @ sK2 @ sK0 )
= $false )
| ( ( p @ ( sK1 @ ( sK3 @ sK0 ) ) )
= $false )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f186,f206]) ).
thf(f227,plain,
( ( ( rel_s5 @ sK2 @ sK0 )
= $false )
| ( ( p @ ( sK1 @ ( sK3 @ sK0 ) ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f225]) ).
thf(f229,definition,
( spl4_1
<=> ( ( rel_s5 @ sK2 @ sK0 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f231,plain,
( ( ( rel_s5 @ sK2 @ sK0 )
= $false )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f229]) ).
thf(f233,definition,
( spl4_2
<=> ( ( p @ ( sK1 @ ( sK3 @ sK0 ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f235,plain,
( ( ( p @ ( sK1 @ ( sK3 @ sK0 ) ) )
= $false )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f233]) ).
thf(f237,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f227,f233,f229]) ).
thf(f240,plain,
! [X0: $i] :
( ( ( rel_s5 @ sK0 @ ( sK3 @ X0 ) )
= $false )
| ( $true
= ( p @ ( sK1 @ ( sK3 @ X0 ) ) ) )
| ( $true = $false )
| ( ( rel_s5 @ sK2 @ X0 )
= $false ) ),
inference(constrained_superposition,[],[f188,f211]) ).
thf(f242,plain,
! [X0: $i] :
( ( ( rel_s5 @ sK0 @ ( sK3 @ X0 ) )
= $false )
| ( $true
= ( p @ ( sK1 @ ( sK3 @ X0 ) ) ) )
| ( ( rel_s5 @ sK2 @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f240]) ).
thf(f246,plain,
( ( ( p @ ( sK1 @ ( sK3 @ sK0 ) ) )
= $true )
| ( ( rel_s5 @ sK2 @ sK0 )
= $false )
| ( $true = $false )
| ( ( rel_s5 @ sK2 @ sK0 )
= $false ) ),
inference(constrained_superposition,[],[f242,f206]) ).
thf(f248,plain,
( ( $true = $false )
| ( ( p @ ( sK1 @ ( sK3 @ sK0 ) ) )
= $true )
| ( ( rel_s5 @ sK2 @ sK0 )
= $false ) ),
inference(duplicate_literal_removal,[],[f246]) ).
thf(f249,plain,
( ( ( rel_s5 @ sK2 @ sK0 )
= $false )
| ( ( p @ ( sK1 @ ( sK3 @ sK0 ) ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f248]) ).
thf(f252,plain,
( ( $true = $false )
| ( ( rel_s5 @ sK2 @ sK0 )
= $false )
| ~ spl4_2 ),
inference(forward_demodulation,[],[f249,f235]) ).
thf(f253,plain,
( ( ( rel_s5 @ sK2 @ sK0 )
= $false )
| ~ spl4_2 ),
inference(trivial_inequality_removal,[],[f252]) ).
thf(f256,plain,
( spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f253,f233,f229]) ).
thf(f299,plain,
( ( ( rel_s5 @ sK0 @ sK2 )
= $false )
| ( $true = $false )
| ~ spl4_1 ),
inference(constrained_superposition,[],[f231,f160]) ).
thf(f309,plain,
( ( ( rel_s5 @ sK0 @ sK2 )
= $false )
| ~ spl4_1 ),
inference(trivial_inequality_removal,[],[f299]) ).
thf(f313,plain,
( ( $true = $false )
| ~ spl4_1 ),
inference(forward_demodulation,[],[f309,f195]) ).
thf(f314,plain,
( $false
| ~ spl4_1 ),
inference(trivial_inequality_removal,[],[f313]) ).
thf(f315,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f314]) ).
cnf(s2,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f237]) ).
cnf(s3,plain,
( spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f256]) ).
cnf(s6,plain,
~ spl4_1,
inference(sat_conversion,[],[f315]) ).
cnf(s7,plain,
~ spl4_2,
inference(rat,[],[s3,s6]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s2,s7,s6]) ).
thf(f316,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO456^6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n008.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 16:58:09 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.10/0.25 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.29 % (3426338)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.29 % (3426343)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=155108013:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.29 % (3426349)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.29 % (3426349)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
% 0.22/0.29 % (3426343) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3426338-3426343"...
% 0.22/0.29 % (3426344)lrs+10_16_si=on:nwc=1.5:random_seed=1359436091:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.29 % (3426345)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1935519139:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.29 % (3426349)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=4198897481:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.29 % (3426343)...printing done.
% 0.22/0.29 % (3426347)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3788648784:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.29 % (3426346)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=2208623664: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)
% 0.22/0.29 % (3426348)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2432674929:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.29 % (3426343)Refutation found. Thanks to Tanya!
% 0.22/0.29 % SZS status Theorem for theBenchmark
% 0.22/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.29 % (3426343)------------------------------
% 0.22/0.29 % (3426343)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (3426343)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (3426343)CaDiCaL version: 2.1.3
% 0.22/0.29 % (3426343)Termination reason: Refutation
% 0.22/0.29 % (3426343)Time elapsed: 0.007 s
% 0.22/0.29 % (3426343)Peak memory usage: 13 MB
% 0.22/0.29 % (3426343)Instructions burned: 24 (million)
% 0.22/0.29 % (3426338)Success in time 0.032 s
% 0.22/0.29 % Vampire exiting
%------------------------------------------------------------------------------