%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV095^5 : 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 : n011.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 08:37:38 AM UTC 2026
% Result : Theorem 1.81s 0.61s
% Output : Refutation 1.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 6
% Syntax : Number of formulae : 110 ( 16 unt; 0 typ; 5 def)
% Number of atoms : 1239 ( 329 equ; 0 cnn)
% Maximal formula atoms : 4 ( 11 avg)
% Number of connectives : 3306 ( 62 ~; 303 |; 49 &;2294 @)
% ( 5 <=>; 153 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 1070 (1070 >; 0 *; 0 +; 0 <<)
% Number of symbols : 56 ( 51 usr; 11 con; 0-4 aty)
% ( 432 !!; 8 ??; 0 @@+; 0 @@-)
% Number of variables : 888 ( 150 sgn 113 !; 6 ?; 888 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
vNOT: $o > $o ).
thf(func_def_2,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
vAND: $o > $o > $o ).
thf(func_def_4,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_5,type,
vOR: $o > $o > $o ).
thf(func_def_6,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_11,type,
vIMP: $o > $o > $o ).
thf(func_def_12,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
sK0: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_17,type,
sK1: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_18,type,
sK2: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_19,type,
sK3: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i ).
thf(func_def_20,type,
sK4: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_21,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_23,type,
sK6: $i > $o ).
thf(func_def_25,type,
sK8: $i > $o ).
thf(func_def_26,type,
sK9: $i > $o ).
thf(func_def_28,type,
sK11: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_29,type,
sK12: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i ).
thf(func_def_30,type,
sK13: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_31,type,
sK14: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i ).
thf(func_def_32,type,
sK15: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i ).
thf(func_def_33,type,
sK16: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i ).
thf(func_def_34,type,
sK17: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i ).
thf(func_def_35,type,
sK18: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i ).
thf(func_def_36,type,
sK19: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i ).
thf(func_def_37,type,
sK20: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i ).
thf(func_def_38,type,
sK21: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i ).
thf(func_def_39,type,
sK22: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i ).
thf(func_def_40,type,
sK23: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_41,type,
sK24: $i > $o ).
thf(func_def_42,type,
sK25: $i > $o ).
thf(func_def_43,type,
sK26: $i > $o ).
thf(func_def_44,type,
sK27: $i > $o ).
thf(func_def_46,type,
sK29: $i > $o ).
thf(func_def_49,type,
sK32: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_50,type,
sK33: $i > $o ).
thf(func_def_51,type,
sK34: $i > $o ).
thf(f1,conjecture,
? [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X0: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ! [X7: $i > $o,X5: $i > $o,X6: $i > $o] :
( ( ! [X4: $i] :
( ( X1 @ X7 @ X5 @ X4 )
| ( X0 @ X7 @ X5 @ X4 ) )
& ! [X4: $i] :
( ( X0 @ X6 @ X7 @ X4 )
| ( X1 @ X6 @ X7 @ X4 ) ) )
=> ! [X4: $i] :
( ( X1 @ X6 @ X5 @ X4 )
| ( X0 @ X6 @ X5 @ X4 ) ) )
& ! [X2: $i > $o,X3: $i > $o] :
( ! [X4: $i] :
( ( X1 @ X2 @ X3 @ X4 )
| ( X0 @ X2 @ X3 @ X4 ) )
=> ! [X5: $i] :
( ( X2 @ X5 )
=> ( X3 @ X5 ) ) )
& ! [X4: $i,X6: $i > $o] :
( ( X1 @ X6 @ X6 @ X4 )
| ( X0 @ X6 @ X6 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM122C_pme) ).
thf(f2,negated_conjecture,
~ ? [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X0: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ! [X7: $i > $o,X5: $i > $o,X6: $i > $o] :
( ( ! [X4: $i] :
( ( X1 @ X7 @ X5 @ X4 )
| ( X0 @ X7 @ X5 @ X4 ) )
& ! [X4: $i] :
( ( X0 @ X6 @ X7 @ X4 )
| ( X1 @ X6 @ X7 @ X4 ) ) )
=> ! [X4: $i] :
( ( X1 @ X6 @ X5 @ X4 )
| ( X0 @ X6 @ X5 @ X4 ) ) )
& ! [X2: $i > $o,X3: $i > $o] :
( ! [X4: $i] :
( ( X1 @ X2 @ X3 @ X4 )
| ( X0 @ X2 @ X3 @ X4 ) )
=> ! [X5: $i] :
( ( X2 @ X5 )
=> ( X3 @ X5 ) ) )
& ! [X4: $i,X6: $i > $o] :
( ( X1 @ X6 @ X6 @ X4 )
| ( X0 @ X6 @ X6 @ X4 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ! [X2: $i > $o,X3: $i > $o,X4: $i > $o] :
( ( ! [X5: $i] :
( ( X0 @ X2 @ X3 @ X5 )
| ( X1 @ X2 @ X3 @ X5 ) )
& ! [X6: $i] :
( ( X1 @ X4 @ X2 @ X6 )
| ( X0 @ X4 @ X2 @ X6 ) ) )
=> ! [X7: $i] :
( ( X0 @ X4 @ X3 @ X7 )
| ( X1 @ X4 @ X3 @ X7 ) ) )
& ! [X8: $i > $o,X9: $i > $o] :
( ! [X10: $i] :
( ( X0 @ X8 @ X9 @ X10 )
| ( X1 @ X8 @ X9 @ X10 ) )
=> ! [X11: $i] :
( ( X8 @ X11 )
=> ( X9 @ X11 ) ) )
& ! [X12: $i,X13: $i > $o] :
( ( X0 @ X13 @ X13 @ X12 )
| ( X1 @ X13 @ X13 @ X12 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
( $true
= ( ~ ( ?? @ ( ( $i > $o ) > ( $i > $o ) > $i > $o )
@ ^ [Y0: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ?? @ ( ( $i > $o ) > ( $i > $o ) > $i > $o )
@ ^ [Y1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y2 @ Y3 ) ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y3 @ Y2 @ Y4 )
| ( Y1 @ Y3 @ Y2 @ Y4 ) ) )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) ) ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y4: $i > $o] :
( ( ( !! @ $i
@ ^ [Y5: $i] :
( ( Y1 @ Y2 @ Y4 @ Y5 )
| ( Y0 @ Y2 @ Y4 @ Y5 ) ) )
& ( !! @ $i
@ ^ [Y5: $i] :
( ( Y0 @ Y4 @ Y3 @ Y5 )
| ( Y1 @ Y4 @ Y3 @ Y5 ) ) ) )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( Y0 @ Y2 @ Y3 @ Y5 )
| ( Y1 @ Y2 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( $true
= ( ~ ( ?? @ ( ( $i > $o ) > ( $i > $o ) > $i > $o )
@ ^ [Y0: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ?? @ ( ( $i > $o ) > ( $i > $o ) > $i > $o )
@ ^ [Y1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y2 @ Y3 ) ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y3 @ Y2 @ Y4 )
| ( Y1 @ Y3 @ Y2 @ Y4 ) ) )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) ) ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y4: $i > $o] :
( ( ( !! @ $i
@ ^ [Y5: $i] :
( ( Y1 @ Y2 @ Y4 @ Y5 )
| ( Y0 @ Y2 @ Y4 @ Y5 ) ) )
& ( !! @ $i
@ ^ [Y5: $i] :
( ( Y0 @ Y4 @ Y3 @ Y5 )
| ( Y1 @ Y4 @ Y3 @ Y5 ) ) ) )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( Y0 @ Y2 @ Y3 @ Y5 )
| ( Y1 @ Y2 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f4]) ).
thf(f8,plain,
( ( ?? @ ( ( $i > $o ) > ( $i > $o ) > $i > $o )
@ ^ [Y0: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ?? @ ( ( $i > $o ) > ( $i > $o ) > $i > $o )
@ ^ [Y1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y2 @ Y3 ) ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y3 @ Y2 @ Y4 )
| ( Y1 @ Y3 @ Y2 @ Y4 ) ) )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) ) ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y4: $i > $o] :
( ( ( !! @ $i
@ ^ [Y5: $i] :
( ( Y1 @ Y2 @ Y4 @ Y5 )
| ( Y0 @ Y2 @ Y4 @ Y5 ) ) )
& ( !! @ $i
@ ^ [Y5: $i] :
( ( Y0 @ Y4 @ Y3 @ Y5 )
| ( Y1 @ Y4 @ Y3 @ Y5 ) ) ) )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( Y0 @ Y2 @ Y3 @ Y5 )
| ( Y1 @ Y2 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f5]) ).
thf(f9,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( $false
= ( ^ [Y0: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ?? @ ( ( $i > $o ) > ( $i > $o ) > $i > $o )
@ ^ [Y1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y2 @ Y3 ) ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y3 @ Y2 @ Y4 )
| ( Y1 @ Y3 @ Y2 @ Y4 ) ) )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) ) ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y4: $i > $o] :
( ( ( !! @ $i
@ ^ [Y5: $i] :
( ( Y1 @ Y2 @ Y4 @ Y5 )
| ( Y0 @ Y2 @ Y4 @ Y5 ) ) )
& ( !! @ $i
@ ^ [Y5: $i] :
( ( Y0 @ Y4 @ Y3 @ Y5 )
| ( Y1 @ Y4 @ Y3 @ Y5 ) ) ) )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( Y0 @ Y2 @ Y3 @ Y5 )
| ( Y1 @ Y2 @ Y3 @ Y5 ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f8]) ).
thf(f11,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ?? @ ( ( $i > $o ) > ( $i > $o ) > $i > $o )
@ ^ [Y0: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( X1 @ Y1 @ Y1 @ Y2 )
| ( Y0 @ Y1 @ Y1 @ Y2 ) ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( X1 @ Y2 @ Y1 @ Y3 )
| ( Y0 @ Y2 @ Y1 @ Y3 ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y1 @ Y3 @ Y4 )
| ( X1 @ Y1 @ Y3 @ Y4 ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( ( X1 @ Y3 @ Y2 @ Y4 )
| ( Y0 @ Y3 @ Y2 @ Y4 ) ) ) )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( X1 @ Y1 @ Y2 @ Y4 )
| ( Y0 @ Y1 @ Y2 @ Y4 ) ) ) ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f9]) ).
thf(f13,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ^ [Y0: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( X1 @ Y1 @ Y1 @ Y2 )
| ( Y0 @ Y1 @ Y1 @ Y2 ) ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( X1 @ Y2 @ Y1 @ Y3 )
| ( Y0 @ Y2 @ Y1 @ Y3 ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y1 @ Y3 @ Y4 )
| ( X1 @ Y1 @ Y3 @ Y4 ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( ( X1 @ Y3 @ Y2 @ Y4 )
| ( Y0 @ Y3 @ Y2 @ Y4 ) ) ) )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( X1 @ Y1 @ Y2 @ Y4 )
| ( Y0 @ Y1 @ Y2 @ Y4 ) ) ) ) ) ) ) )
@ X2 )
= $false ),
inference(pi_proxy_clausification,[],[f11]) ).
thf(f14,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( $false
= ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y0 @ Y0 @ Y1 )
| ( X2 @ Y0 @ Y0 @ Y1 ) ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( X1 @ Y1 @ Y0 @ Y2 )
| ( X2 @ Y1 @ Y0 @ Y2 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ( X2 @ Y0 @ Y2 @ Y3 )
| ( X1 @ Y0 @ Y2 @ Y3 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( X1 @ Y2 @ Y1 @ Y3 )
| ( X2 @ Y2 @ Y1 @ Y3 ) ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( X1 @ Y0 @ Y1 @ Y3 )
| ( X2 @ Y0 @ Y1 @ Y3 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f13]) ).
thf(f15,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ( X2 @ Y0 @ Y2 @ Y3 )
| ( X1 @ Y0 @ Y2 @ Y3 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( X1 @ Y2 @ Y1 @ Y3 )
| ( X2 @ Y2 @ Y1 @ Y3 ) ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( X1 @ Y0 @ Y1 @ Y3 )
| ( X2 @ Y0 @ Y1 @ Y3 ) ) ) ) ) ) ) )
| ( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y0 @ Y0 @ Y1 )
| ( X2 @ Y0 @ Y0 @ Y1 ) ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( X1 @ Y1 @ Y0 @ Y2 )
| ( X2 @ Y1 @ Y0 @ Y2 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f14]) ).
thf(f16,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( $false
= ( ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ( X2 @ Y0 @ Y2 @ Y3 )
| ( X1 @ Y0 @ Y2 @ Y3 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( X1 @ Y2 @ Y1 @ Y3 )
| ( X2 @ Y2 @ Y1 @ Y3 ) ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( X1 @ Y0 @ Y1 @ Y3 )
| ( X2 @ Y0 @ Y1 @ Y3 ) ) ) ) ) )
@ ( sK0 @ X1 @ X2 ) ) )
| ( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y0 @ Y0 @ Y1 )
| ( X2 @ Y0 @ Y0 @ Y1 ) ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( X1 @ Y1 @ Y0 @ Y2 )
| ( X2 @ Y1 @ Y0 @ Y2 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f15]) ).
thf(f17,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( ( X2 @ ( sK0 @ X1 @ X2 ) @ Y1 @ Y2 )
| ( X1 @ ( sK0 @ X1 @ X2 ) @ Y1 @ Y2 ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( X1 @ Y1 @ Y0 @ Y2 )
| ( X2 @ Y1 @ Y0 @ Y2 ) ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( X1 @ ( sK0 @ X1 @ X2 ) @ Y0 @ Y2 )
| ( X2 @ ( sK0 @ X1 @ X2 ) @ Y0 @ Y2 ) ) ) ) ) ) )
| ( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y0 @ Y0 @ Y1 )
| ( X2 @ Y0 @ Y0 @ Y1 ) ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( X1 @ Y1 @ Y0 @ Y2 )
| ( X2 @ Y1 @ Y0 @ Y2 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f16]) ).
thf(f18,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y0 @ Y0 @ Y1 )
| ( X2 @ Y0 @ Y0 @ Y1 ) ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( X1 @ Y1 @ Y0 @ Y2 )
| ( X2 @ Y1 @ Y0 @ Y2 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) ) )
= $false )
| ( $false
= ( ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( ( X2 @ ( sK0 @ X1 @ X2 ) @ Y1 @ Y2 )
| ( X1 @ ( sK0 @ X1 @ X2 ) @ Y1 @ Y2 ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( X1 @ Y1 @ Y0 @ Y2 )
| ( X2 @ Y1 @ Y0 @ Y2 ) ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( X1 @ ( sK0 @ X1 @ X2 ) @ Y0 @ Y2 )
| ( X2 @ ( sK0 @ X1 @ X2 ) @ Y0 @ Y2 ) ) ) ) )
@ ( sK1 @ X1 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f17]) ).
thf(f19,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ ( sK0 @ X1 @ X2 ) @ Y0 @ Y1 )
| ( X1 @ ( sK0 @ X1 @ X2 ) @ Y0 @ Y1 ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y0 @ ( sK1 @ X1 @ X2 ) @ Y1 )
| ( X2 @ Y0 @ ( sK1 @ X1 @ X2 ) @ Y1 ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ ( sK0 @ X1 @ X2 ) @ ( sK1 @ X1 @ X2 ) @ Y1 )
| ( X2 @ ( sK0 @ X1 @ X2 ) @ ( sK1 @ X1 @ X2 ) @ Y1 ) ) ) ) )
= $false )
| ( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y0 @ Y0 @ Y1 )
| ( X2 @ Y0 @ Y0 @ Y1 ) ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( X1 @ Y1 @ Y0 @ Y2 )
| ( X2 @ Y1 @ Y0 @ Y2 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f18]) ).
thf(f20,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y0 @ Y0 @ Y1 )
| ( X2 @ Y0 @ Y0 @ Y1 ) ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( X1 @ Y1 @ Y0 @ Y2 )
| ( X2 @ Y1 @ Y0 @ Y2 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) ) )
= $false )
| ( $false
= ( ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ ( sK0 @ X1 @ X2 ) @ Y0 @ Y1 )
| ( X1 @ ( sK0 @ X1 @ X2 ) @ Y0 @ Y1 ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y0 @ ( sK1 @ X1 @ X2 ) @ Y1 )
| ( X2 @ Y0 @ ( sK1 @ X1 @ X2 ) @ Y1 ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ ( sK0 @ X1 @ X2 ) @ ( sK1 @ X1 @ X2 ) @ Y1 )
| ( X2 @ ( sK0 @ X1 @ X2 ) @ ( sK1 @ X1 @ X2 ) @ Y1 ) ) ) )
@ ( sK2 @ X1 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f19]) ).
thf(f21,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ ( sK0 @ X1 @ X2 ) @ ( sK2 @ X1 @ X2 ) @ Y0 )
| ( X1 @ ( sK0 @ X1 @ X2 ) @ ( sK2 @ X1 @ X2 ) @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ ( sK2 @ X1 @ X2 ) @ ( sK1 @ X1 @ X2 ) @ Y0 )
| ( X2 @ ( sK2 @ X1 @ X2 ) @ ( sK1 @ X1 @ X2 ) @ Y0 ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ ( sK0 @ X1 @ X2 ) @ ( sK1 @ X1 @ X2 ) @ Y0 )
| ( X2 @ ( sK0 @ X1 @ X2 ) @ ( sK1 @ X1 @ X2 ) @ Y0 ) ) ) )
= $false )
| ( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y0 @ Y0 @ Y1 )
| ( X2 @ Y0 @ Y0 @ Y1 ) ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( X1 @ Y1 @ Y0 @ Y2 )
| ( X2 @ Y1 @ Y0 @ Y2 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f20]) ).
thf(f22,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y0 @ Y0 @ Y1 )
| ( X2 @ Y0 @ Y0 @ Y1 ) ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( X1 @ Y1 @ Y0 @ Y2 )
| ( X2 @ Y1 @ Y0 @ Y2 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ ( sK0 @ X1 @ X2 ) @ ( sK1 @ X1 @ X2 ) @ Y0 )
| ( X2 @ ( sK0 @ X1 @ X2 ) @ ( sK1 @ X1 @ X2 ) @ Y0 ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f21]) ).
thf(f23,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ ( sK0 @ X1 @ X2 ) @ ( sK2 @ X1 @ X2 ) @ Y0 )
| ( X1 @ ( sK0 @ X1 @ X2 ) @ ( sK2 @ X1 @ X2 ) @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ ( sK2 @ X1 @ X2 ) @ ( sK1 @ X1 @ X2 ) @ Y0 )
| ( X2 @ ( sK2 @ X1 @ X2 ) @ ( sK1 @ X1 @ X2 ) @ Y0 ) ) ) ) )
| ( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y0 @ Y0 @ Y1 )
| ( X2 @ Y0 @ Y0 @ Y1 ) ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( X1 @ Y1 @ Y0 @ Y2 )
| ( X2 @ Y1 @ Y0 @ Y2 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f21]) ).
thf(f24,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ ( sK0 @ X1 @ X2 ) @ ( sK1 @ X1 @ X2 ) @ Y0 )
| ( X2 @ ( sK0 @ X1 @ X2 ) @ ( sK1 @ X1 @ X2 ) @ Y0 ) ) )
= $false )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y0 @ Y0 @ Y1 )
| ( X2 @ Y0 @ Y0 @ Y1 ) ) ) ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( X1 @ Y1 @ Y0 @ Y2 )
| ( X2 @ Y1 @ Y0 @ Y2 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f22]) ).
thf(f25,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ( ^ [Y0: $i] :
( ( X1 @ ( sK0 @ X1 @ X2 ) @ ( sK1 @ X1 @ X2 ) @ Y0 )
| ( X2 @ ( sK0 @ X1 @ X2 ) @ ( sK1 @ X1 @ X2 ) @ Y0 ) )
@ ( sK3 @ X1 @ X2 ) )
= $false )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( X1 @ Y1 @ Y0 @ Y2 )
| ( X2 @ Y1 @ Y0 @ Y2 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y0 @ Y0 @ Y1 )
| ( X2 @ Y0 @ Y0 @ Y1 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f24]) ).
thf(f26,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ( ( X1 @ ( sK0 @ X1 @ X2 ) @ ( sK1 @ X1 @ X2 ) @ ( sK3 @ X1 @ X2 ) )
| ( X2 @ ( sK0 @ X1 @ X2 ) @ ( sK1 @ X1 @ X2 ) @ ( sK3 @ X1 @ X2 ) ) )
= $false )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( X1 @ Y1 @ Y0 @ Y2 )
| ( X2 @ Y1 @ Y0 @ Y2 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y0 @ Y0 @ Y1 )
| ( X2 @ Y0 @ Y0 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f25]) ).
thf(f27,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( X1 @ Y1 @ Y0 @ Y2 )
| ( X2 @ Y1 @ Y0 @ Y2 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) ) )
| ( $false
= ( X2 @ ( sK0 @ X1 @ X2 ) @ ( sK1 @ X1 @ X2 ) @ ( sK3 @ X1 @ X2 ) ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y0 @ Y0 @ Y1 )
| ( X2 @ Y0 @ Y0 @ Y1 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f26]) ).
thf(f29,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y0 @ Y0 @ Y1 )
| ( X2 @ Y0 @ Y0 @ Y1 ) ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( X1 @ Y1 @ Y0 @ Y2 )
| ( X2 @ Y1 @ Y0 @ Y2 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ ( sK2 @ X1 @ X2 ) @ ( sK1 @ X1 @ X2 ) @ Y0 )
| ( X2 @ ( sK2 @ X1 @ X2 ) @ ( sK1 @ X1 @ X2 ) @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f23]) ).
thf(f30,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y0 @ Y0 @ Y1 )
| ( X2 @ Y0 @ Y0 @ Y1 ) ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( X1 @ Y1 @ Y0 @ Y2 )
| ( X2 @ Y1 @ Y0 @ Y2 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ ( sK0 @ X1 @ X2 ) @ ( sK2 @ X1 @ X2 ) @ Y0 )
| ( X1 @ ( sK0 @ X1 @ X2 ) @ ( sK2 @ X1 @ X2 ) @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f23]) ).
thf(f32,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 )
@ ( sK0 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) )
@ ( sK1 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) )
@ ( sK3 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) ) )
= $false )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( X1 @ Y1 @ Y0 @ Y2 )
| ( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] : ( Y3 = Y4 )
@ Y1
@ Y0
@ Y2 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y0 @ Y0 @ Y1 )
| ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] : ( Y2 = Y3 )
@ Y0
@ Y0
@ Y1 ) ) ) ) ) ),
inference(primitive_instantiation,[],[f27]) ).
thf(f57,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y0 @ Y0 @ Y1 )
| ( Y0 = Y0 ) ) ) )
= $false )
| ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( X1 @ Y1 @ Y0 @ Y2 )
| ( Y1 = Y0 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) )
= $false )
| ( $false
= ( ( sK0 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) )
= ( sK1 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f32]) ).
thf(f58,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( X1 @ Y1 @ Y0 @ Y2 )
| ( Y1 = Y0 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) )
= $false )
| ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y0 @ Y0 @ Y1 )
| $true ) ) )
= $false )
| ( $false
= ( ( sK0 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) )
= ( sK1 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) ) ) ) ),
inference(boolean_simplification,[],[f57]) ).
thf(f59,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : $true ) )
= $false )
| ( $false
= ( ( sK0 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) )
= ( sK1 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) ) ) )
| ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( X1 @ Y1 @ Y0 @ Y2 )
| ( Y1 = Y0 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) )
= $false ) ),
inference(boolean_simplification,[],[f58]) ).
thf(f67,definition,
( spl5_2
<=> ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : $true ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
thf(f68,plain,
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : $true ) )
!= $false )
| spl5_2 ),
inference(avatar_component_clause,[],[f67]) ).
thf(f69,plain,
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : $true ) )
= $false )
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f67]) ).
thf(f72,definition,
( spl5_3
<=> ! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( $false
= ( ( sK0 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) )
= ( sK1 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) ) ) )
| ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( X1 @ Y1 @ Y0 @ Y2 )
| ( Y1 = Y0 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
thf(f73,plain,
( ! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( $false
= ( ( sK0 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) )
= ( sK1 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) ) ) )
| ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( X1 @ Y1 @ Y0 @ Y2 )
| ( Y1 = Y0 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) )
= $false ) )
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f72]) ).
thf(f74,plain,
( spl5_3
| spl5_2 ),
inference(avatar_split_clause,[],[f59,f67,f72]) ).
thf(f75,plain,
( ( $false
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : $true )
@ sK6 ) )
| ~ spl5_2 ),
inference(sigma_proxy_clausification,[],[f69]) ).
thf(f76,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] : $true )
= $false )
| ~ spl5_2 ),
inference(beta-eta_normalization,[],[f75]) ).
thf(f77,plain,
( ( $false
= ( ^ [Y0: $i] : $true
@ sK7 ) )
| ~ spl5_2 ),
inference(sigma_proxy_clausification,[],[f76]) ).
thf(f78,plain,
( ( $true = $false )
| ~ spl5_2 ),
inference(beta-eta_normalization,[],[f77]) ).
thf(f79,plain,
( $false
| ~ spl5_2 ),
inference(trivial_inequality_removal,[],[f78]) ).
thf(f80,plain,
~ spl5_2,
inference(avatar_contradiction_clause,[],[f79]) ).
thf(f170,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ ( sK2 @ X1 @ X2 ) @ ( sK1 @ X1 @ X2 ) @ Y0 )
| ( X2 @ ( sK2 @ X1 @ X2 ) @ ( sK1 @ X1 @ X2 ) @ Y0 ) ) ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y0 @ Y0 @ Y1 )
| ( X2 @ Y0 @ Y0 @ Y1 ) ) ) ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( X1 @ Y1 @ Y0 @ Y2 )
| ( X2 @ Y1 @ Y0 @ Y2 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f29]) ).
thf(f173,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X3: $i,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( $true
= ( ^ [Y0: $i] :
( ( X1 @ ( sK2 @ X1 @ X2 ) @ ( sK1 @ X1 @ X2 ) @ Y0 )
| ( X2 @ ( sK2 @ X1 @ X2 ) @ ( sK1 @ X1 @ X2 ) @ Y0 ) )
@ X3 ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y0 @ Y0 @ Y1 )
| ( X2 @ Y0 @ Y0 @ Y1 ) ) ) ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( X1 @ Y1 @ Y0 @ Y2 )
| ( X2 @ Y1 @ Y0 @ Y2 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f170]) ).
thf(f174,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X3: $i,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( $true
= ( ( X1 @ ( sK2 @ X1 @ X2 ) @ ( sK1 @ X1 @ X2 ) @ X3 )
| ( X2 @ ( sK2 @ X1 @ X2 ) @ ( sK1 @ X1 @ X2 ) @ X3 ) ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( X1 @ Y1 @ Y0 @ Y2 )
| ( X2 @ Y1 @ Y0 @ Y2 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y0 @ Y0 @ Y1 )
| ( X2 @ Y0 @ Y0 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f173]) ).
thf(f181,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X3: $i,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( X1 @ Y1 @ Y0 @ Y2 )
| ( X2 @ Y1 @ Y0 @ Y2 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) ) )
| ( $true
= ( X2 @ ( sK2 @ X1 @ X2 ) @ ( sK1 @ X1 @ X2 ) @ X3 ) )
| ( $true
= ( X1 @ ( sK2 @ X1 @ X2 ) @ ( sK1 @ X1 @ X2 ) @ X3 ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y0 @ Y0 @ Y1 )
| ( X2 @ Y0 @ Y0 @ Y1 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f174]) ).
thf(f199,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: $i] :
( ( $true
= ( X0 @ ( sK2 @ X0 @ X0 ) @ ( sK1 @ X0 @ X0 ) @ X1 ) )
| ( $true != $true )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X0 @ Y0 @ Y0 @ Y1 )
| ( X0 @ Y0 @ Y0 @ Y1 ) ) ) ) )
| ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( X0 @ Y1 @ Y0 @ Y2 )
| ( X0 @ Y1 @ Y0 @ Y2 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) )
= $false ) ),
inference(equality_factoring,[],[f181]) ).
thf(f205,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: $i] :
( ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X0 @ Y0 @ Y0 @ Y1 )
| ( X0 @ Y0 @ Y0 @ Y1 ) ) ) ) )
| ( $true
= ( X0 @ ( sK2 @ X0 @ X0 ) @ ( sK1 @ X0 @ X0 ) @ X1 ) )
| ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( X0 @ Y1 @ Y0 @ Y2 )
| ( X0 @ Y1 @ Y0 @ Y2 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f199]) ).
thf(f206,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: $i] :
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( X0 @ Y1 @ Y0 @ Y2 )
| ( X0 @ Y1 @ Y0 @ Y2 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( X0 @ Y0 @ Y0 @ Y1 ) ) ) )
| ( $true
= ( X0 @ ( sK2 @ X0 @ X0 ) @ ( sK1 @ X0 @ X0 ) @ X1 ) ) ),
inference(boolean_simplification,[],[f205]) ).
thf(f207,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: $i] :
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : ( !! @ $i @ ( X0 @ Y0 @ Y0 ) ) )
= $false )
| ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( X0 @ Y1 @ Y0 @ Y2 )
| ( X0 @ Y1 @ Y0 @ Y2 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) )
= $false )
| ( $true
= ( X0 @ ( sK2 @ X0 @ X0 ) @ ( sK1 @ X0 @ X0 ) @ X1 ) ) ),
inference(beta-eta_normalization,[],[f206]) ).
thf(f208,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: $i] :
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] : ( X0 @ Y1 @ Y0 @ Y2 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) )
= $false )
| ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : ( !! @ $i @ ( X0 @ Y0 @ Y0 ) ) )
= $false )
| ( $true
= ( X0 @ ( sK2 @ X0 @ X0 ) @ ( sK1 @ X0 @ X0 ) @ X1 ) ) ),
inference(boolean_simplification,[],[f207]) ).
thf(f209,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: $i] :
( ( $true
= ( X0 @ ( sK2 @ X0 @ X0 ) @ ( sK1 @ X0 @ X0 ) @ X1 ) )
| ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : ( !! @ $i @ ( X0 @ Y0 @ Y0 ) ) )
= $false )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i @ ( X0 @ Y1 @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f208]) ).
thf(f262,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ ( sK0 @ X1 @ X2 ) @ ( sK2 @ X1 @ X2 ) @ Y0 )
| ( X1 @ ( sK0 @ X1 @ X2 ) @ ( sK2 @ X1 @ X2 ) @ Y0 ) ) ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( X1 @ Y1 @ Y0 @ Y2 )
| ( X2 @ Y1 @ Y0 @ Y2 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y0 @ Y0 @ Y1 )
| ( X2 @ Y0 @ Y0 @ Y1 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f30]) ).
thf(f264,plain,
! [X1: $i] :
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ( ^ [Y1: $i > $o,Y2: $i > $o,Y3: $i] : ( Y1 = Y2 )
@ Y0
@ Y0 ) ) )
= $false )
| ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 )
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) )
@ ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) )
@ X1 ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] : ( Y2 = Y3 )
@ Y1
@ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(primitive_instantiation,[],[f209]) ).
thf(f280,plain,
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 = Y0 ) ) )
= $false )
| ( $true
= ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) )
= ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) ) ) )
| ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] : ( Y1 = Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f264]) ).
thf(f281,plain,
( ( $true
= ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) )
= ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) ) ) )
| ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] : ( Y1 = Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) )
= $false )
| ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : $true ) )
= $false ) ),
inference(boolean_simplification,[],[f280]) ).
thf(f289,plain,
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] : ( Y1 = Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) )
= $false )
| ( $true
= ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) )
= ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) ) ) )
| spl5_2 ),
inference(forward_subsumption_resolution,[],[f281,f68]) ).
thf(f309,definition,
( spl5_8
<=> ( $true
= ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) )
= ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_8])],[avatar_definition]) ).
thf(f311,plain,
( ( $true
= ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) )
= ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) ) ) )
| ~ spl5_8 ),
inference(avatar_component_clause,[],[f309]) ).
thf(f313,definition,
( spl5_9
<=> ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] : ( Y1 = Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl5_9])],[avatar_definition]) ).
thf(f314,plain,
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] : ( Y1 = Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) )
!= $false )
| spl5_9 ),
inference(avatar_component_clause,[],[f313]) ).
thf(f315,plain,
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] : ( Y1 = Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) )
= $false )
| ~ spl5_9 ),
inference(avatar_component_clause,[],[f313]) ).
thf(f316,plain,
( spl5_8
| spl5_9
| spl5_2 ),
inference(avatar_split_clause,[],[f289,f67,f313,f309]) ).
thf(f343,plain,
( ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) ) )
| ~ spl5_8 ),
inference(equality_proxy_clausification,[],[f311]) ).
thf(f414,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X3: $i,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ( ^ [Y0: $i] :
( ( X2 @ ( sK0 @ X1 @ X2 ) @ ( sK2 @ X1 @ X2 ) @ Y0 )
| ( X1 @ ( sK0 @ X1 @ X2 ) @ ( sK2 @ X1 @ X2 ) @ Y0 ) )
@ X3 )
= $true )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y0 @ Y0 @ Y1 )
| ( X2 @ Y0 @ Y0 @ Y1 ) ) ) ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( X1 @ Y1 @ Y0 @ Y2 )
| ( X2 @ Y1 @ Y0 @ Y2 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f262]) ).
thf(f415,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X3: $i,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( $true
= ( ( X2 @ ( sK0 @ X1 @ X2 ) @ ( sK2 @ X1 @ X2 ) @ X3 )
| ( X1 @ ( sK0 @ X1 @ X2 ) @ ( sK2 @ X1 @ X2 ) @ X3 ) ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y0 @ Y0 @ Y1 )
| ( X2 @ Y0 @ Y0 @ Y1 ) ) ) ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( X1 @ Y1 @ Y0 @ Y2 )
| ( X2 @ Y1 @ Y0 @ Y2 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f414]) ).
thf(f419,plain,
( ! [X0: $i] :
( ( $true
= ( ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 )
@ ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) )
@ ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) )
@ X0 )
| ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 )
@ ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) )
@ ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) )
@ X0 ) ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] : ( Y3 = Y4 )
@ Y1
@ Y0
@ Y2 )
| ( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] : ( Y3 = Y4 )
@ Y1
@ Y0
@ Y2 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) ) )
| ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] : ( Y2 = Y3 )
@ Y0
@ Y0
@ Y1 )
| ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] : ( Y2 = Y3 )
@ Y0
@ Y0
@ Y1 ) ) ) )
= $false ) )
| ~ spl5_8 ),
inference(superposition,[],[f415,f343]) ).
thf(f420,plain,
( ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 = Y0 )
| ( Y0 = Y0 ) ) ) ) )
| ( $true
= ( ( ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) )
= ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) ) )
| ( ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) )
= ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) ) ) ) )
| ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 = Y0 )
| ( Y1 = Y0 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) )
= $false )
| ~ spl5_8 ),
inference(beta-eta_normalization,[],[f419]) ).
thf(f421,plain,
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 = Y0 ) ) )
= $false )
| ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 = Y0 )
| ( Y1 = Y0 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) )
= $false )
| ( $true
= ( ( ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) )
= ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) ) )
| ( ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) )
= ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) ) ) ) )
| ~ spl5_8 ),
inference(boolean_simplification,[],[f420]) ).
thf(f422,plain,
( ( $true
= ( ( ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) )
= ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) ) )
| ( ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) )
= ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) ) ) ) )
| ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : $true ) )
= $false )
| ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 = Y0 )
| ( Y1 = Y0 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) )
= $false )
| ~ spl5_8 ),
inference(boolean_simplification,[],[f421]) ).
thf(f423,plain,
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 = Y0 )
| ( Y1 = Y0 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) )
= $false )
| ( $true
= ( ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) )
= ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) ) ) )
| ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : $true ) )
= $false )
| ~ spl5_8 ),
inference(boolean_simplification,[],[f422]) ).
thf(f424,plain,
( ( $true
= ( ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) )
= ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) ) ) )
| ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : $true ) )
= $false )
| ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] : ( Y1 = Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) )
= $false )
| ~ spl5_8 ),
inference(boolean_simplification,[],[f423]) ).
thf(f425,plain,
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] : ( Y1 = Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) )
= $false )
| ( $true
= ( ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) )
= ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) ) ) )
| spl5_2
| ~ spl5_8 ),
inference(forward_subsumption_resolution,[],[f424,f68]) ).
thf(f427,definition,
( spl5_14
<=> ( $true
= ( ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) )
= ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_14])],[avatar_definition]) ).
thf(f429,plain,
( ( $true
= ( ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) )
= ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y0 = Y1 ) ) ) )
| ~ spl5_14 ),
inference(avatar_component_clause,[],[f427]) ).
thf(f430,plain,
( spl5_9
| spl5_14
| spl5_2
| ~ spl5_8 ),
inference(avatar_split_clause,[],[f425,f309,f67,f427,f313]) ).
thf(f431,plain,
( ( ( ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] : ( Y1 = Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) )
@ sK33 )
= $false )
| ~ spl5_9 ),
inference(sigma_proxy_clausification,[],[f315]) ).
thf(f432,plain,
( ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] : ( Y0 = sK33 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK33 @ Y1 ) ) ) ) ) )
| ~ spl5_9 ),
inference(beta-eta_normalization,[],[f431]) ).
thf(f433,plain,
( ( $false
= ( ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] : ( Y0 = sK33 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK33 @ Y1 ) ) ) )
@ sK34 ) )
| ~ spl5_9 ),
inference(sigma_proxy_clausification,[],[f432]) ).
thf(f434,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] : ( sK34 = sK33 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( sK34 @ Y0 )
=> ( sK33 @ Y0 ) ) ) ) )
| ~ spl5_9 ),
inference(beta-eta_normalization,[],[f433]) ).
thf(f435,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK34 @ Y0 )
=> ( sK33 @ Y0 ) ) )
= $false )
| ~ spl5_9 ),
inference(imp_proxy_clausification,[],[f434]) ).
thf(f436,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( sK34 = sK33 ) ) )
| ~ spl5_9 ),
inference(imp_proxy_clausification,[],[f434]) ).
thf(f437,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] : ( sK34 = sK33 )
@ X1 )
= $true )
| ~ spl5_9 ),
inference(pi_proxy_clausification,[],[f436]) ).
thf(f438,plain,
( ( $true
= ( sK34 = sK33 ) )
| ~ spl5_9 ),
inference(beta-eta_normalization,[],[f437]) ).
thf(f439,plain,
( ( sK33 = sK34 )
| ~ spl5_9 ),
inference(equality_proxy_clausification,[],[f438]) ).
thf(f440,plain,
( ! [X1: $i] :
( ( sK33 @ X1 )
= ( sK34 @ X1 ) )
| ~ spl5_9 ),
inference(argument_congruence,[],[f439]) ).
thf(f447,plain,
( ( ( ^ [Y0: $i] :
( ( sK34 @ Y0 )
=> ( sK33 @ Y0 ) )
@ sK35 )
= $false )
| ~ spl5_9 ),
inference(sigma_proxy_clausification,[],[f435]) ).
thf(f448,plain,
( ( $false
= ( ( sK34 @ sK35 )
=> ( sK33 @ sK35 ) ) )
| ~ spl5_9 ),
inference(beta-eta_normalization,[],[f447]) ).
thf(f449,plain,
( ( $false
= ( ( sK33 @ sK35 )
=> ( sK33 @ sK35 ) ) )
| ~ spl5_9 ),
inference(forward_demodulation,[],[f448,f440]) ).
thf(f450,plain,
( ( $true = $false )
| ~ spl5_9 ),
inference(boolean_simplification,[],[f449]) ).
thf(f451,plain,
( $false
| ~ spl5_9 ),
inference(trivial_inequality_removal,[],[f450]) ).
thf(f452,plain,
~ spl5_9,
inference(avatar_contradiction_clause,[],[f451]) ).
thf(f459,plain,
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] : ( Y3 = Y4 )
@ Y1
@ Y0
@ Y2 )
| ( Y1 = Y0 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) )
= $false )
| ( $true = $false )
| ~ spl5_3
| ~ spl5_14 ),
inference(superposition,[],[f429,f73]) ).
thf(f464,plain,
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] : ( Y3 = Y4 )
@ Y1
@ Y0
@ Y2 )
| ( Y1 = Y0 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) )
= $false )
| ~ spl5_3
| ~ spl5_14 ),
inference(trivial_inequality_removal,[],[f459]) ).
thf(f465,plain,
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 = Y0 )
| ( Y1 = Y0 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) )
= $false )
| ~ spl5_3
| ~ spl5_14 ),
inference(beta-eta_normalization,[],[f464]) ).
thf(f466,plain,
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] : ( Y1 = Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) )
= $false )
| ~ spl5_3
| ~ spl5_14 ),
inference(boolean_simplification,[],[f465]) ).
thf(f469,plain,
( $false
| ~ spl5_3
| spl5_9
| ~ spl5_14 ),
inference(forward_subsumption_resolution,[],[f466,f314]) ).
thf(f470,plain,
( ~ spl5_3
| spl5_9
| ~ spl5_14 ),
inference(avatar_contradiction_clause,[],[f469]) ).
cnf(s2,plain,
( spl5_2
| spl5_3 ),
inference(sat_conversion,[],[f74]) ).
cnf(s3,plain,
~ spl5_2,
inference(sat_conversion,[],[f80]) ).
cnf(s6,plain,
( spl5_2
| spl5_8
| spl5_9 ),
inference(sat_conversion,[],[f316]) ).
cnf(s10,plain,
( spl5_2
| ~ spl5_8
| spl5_9
| spl5_14 ),
inference(sat_conversion,[],[f430]) ).
cnf(s11,plain,
~ spl5_9,
inference(sat_conversion,[],[f452]) ).
cnf(s13,plain,
( ~ spl5_3
| spl5_9
| ~ spl5_14 ),
inference(sat_conversion,[],[f470]) ).
cnf(s14,plain,
( spl5_2
| ~ spl5_8
| spl5_14 ),
inference(rat,[],[s10,s11]) ).
cnf(s15,plain,
( spl5_2
| spl5_8 ),
inference(rat,[],[s6,s11]) ).
cnf(s17,plain,
spl5_8,
inference(rat,[],[s15,s3]) ).
cnf(s18,plain,
spl5_14,
inference(rat,[],[s14,s3,s17]) ).
cnf(s19,plain,
~ spl5_3,
inference(rat,[],[s13,s11,s18]) ).
cnf(s20,plain,
$false,
inference(rat,[],[s2,s19,s3]) ).
thf(f471,plain,
$false,
inference(avatar_sat_refutation,[],[s20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV095^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n011.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 15:10:01 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.23 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
% 0.21/0.36 % (198924)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.36 % (198932)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=19133197:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.36 % (198933)lrs+10_16_si=on:nwc=1.5:random_seed=3245913056:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.36 % (198938)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.36 % (198938)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.21/0.36 % (198934)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3135246296:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.36 % (198935)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=4047530427:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.21/0.36 % (198934)Instruction limit reached!
% 0.21/0.36 % (198934)------------------------------
% 0.21/0.36 % (198934)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (198934)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (198934)CaDiCaL version: 2.1.3
% 0.21/0.36 % (198934)Termination reason: Instruction limit
% 0.21/0.36 % (198934)Termination phase: Saturation
% 0.21/0.36 % (198934)Time elapsed: 0.002 s
% 0.21/0.36 % (198934)Peak memory usage: 11 MB
% 0.21/0.36 % (198934)Instructions burned: 4 (million)
% 0.21/0.36 % (198936)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1513465990:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.36 % (198938)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=3219038376:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.36 % (198937)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=928773946:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.36 % (198933)Instruction limit reached!
% 0.21/0.36 % (198933)------------------------------
% 0.21/0.36 % (198933)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (198933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (198933)CaDiCaL version: 2.1.3
% 0.21/0.36 % (198933)Termination reason: Instruction limit
% 0.21/0.36 % (198933)Termination phase: Saturation
% 0.21/0.36 % (198933)Time elapsed: 0.009 s
% 0.21/0.36 % (198933)Peak memory usage: 12 MB
% 0.21/0.36 % (198933)Instructions burned: 19 (million)
% 0.21/0.36 % (198956)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2349108901:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.36 % (198956)Instruction limit reached!
% 0.21/0.36 % (198956)------------------------------
% 0.21/0.36 % (198956)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (198956)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (198956)CaDiCaL version: 2.1.3
% 0.21/0.36 % (198956)Termination reason: Instruction limit
% 0.21/0.36 % (198956)Termination phase: Saturation
% 0.21/0.36 % (198956)Time elapsed: 0.001 s
% 0.21/0.36 % (198956)Peak memory usage: 12 MB
% 0.21/0.36 % (198956)Instructions burned: 4 (million)
% 0.21/0.36 % (198936)Instruction limit reached!
% 0.21/0.36 % (198936)------------------------------
% 0.21/0.36 % (198936)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (198936)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (198936)CaDiCaL version: 2.1.3
% 0.21/0.36 % (198936)Termination reason: Instruction limit
% 0.21/0.36 % (198936)Termination phase: Saturation
% 0.21/0.36 % (198936)Time elapsed: 0.020 s
% 0.21/0.36 % (198936)Peak memory usage: 12 MB
% 0.21/0.36 % (198936)Instructions burned: 24 (million)
% 0.21/0.36 % (198960)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=882868877:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.21/0.36 % (198960)Instruction limit reached!
% 0.93/0.40 % (198960)------------------------------
% 0.93/0.40 % (198960)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.93/0.40 % (198960)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.93/0.40 % (198960)CaDiCaL version: 2.1.3
% 0.93/0.40 % (198960)Termination reason: Instruction limit
% 0.93/0.40 % (198960)Termination phase: Saturation
% 0.93/0.40 % (198960)Time elapsed: 0.003 s
% 0.93/0.40 % (198960)Peak memory usage: 11 MB
% 0.93/0.40 % (198960)Instructions burned: 5 (million)
% 0.93/0.40 % (198963)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.93/0.40 % (198964)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=508841150:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.93/0.40 % (198963)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=571259839:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.93/0.40 % (198964)Instruction limit reached!
% 0.93/0.40 % (198964)------------------------------
% 0.93/0.40 % (198964)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.93/0.40 % (198964)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.93/0.40 % (198964)CaDiCaL version: 2.1.3
% 0.93/0.40 % (198964)Termination reason: Instruction limit
% 0.93/0.40 % (198964)Termination phase: Saturation
% 0.93/0.40 % (198964)Time elapsed: 0.004 s
% 0.93/0.40 % (198964)Peak memory usage: 12 MB
% 0.93/0.40 % (198964)Instructions burned: 15 (million)
% 0.93/0.40 % (198963)Instruction limit reached!
% 0.93/0.40 % (198963)------------------------------
% 0.93/0.40 % (198963)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.93/0.40 % (198963)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.93/0.40 % (198963)CaDiCaL version: 2.1.3
% 0.93/0.40 % (198963)Termination reason: Instruction limit
% 0.93/0.40 % (198963)Termination phase: Saturation
% 0.93/0.40 % (198963)Time elapsed: 0.005 s
% 0.93/0.40 % (198963)Peak memory usage: 12 MB
% 0.93/0.40 % (198963)Instructions burned: 8 (million)
% 0.93/0.40 % (198932)Instruction limit reached!
% 0.93/0.40 % (198932)------------------------------
% 0.93/0.40 % (198932)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.93/0.40 % (198932)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.93/0.40 % (198932)CaDiCaL version: 2.1.3
% 0.93/0.40 % (198932)Termination reason: Instruction limit
% 0.93/0.40 % (198932)Termination phase: Saturation
% 0.93/0.40 % (198932)Time elapsed: 0.042 s
% 0.93/0.40 % (198932)Peak memory usage: 13 MB
% 0.93/0.40 % (198932)Instructions burned: 87 (million)
% 0.93/0.40 % (198937)Instruction limit reached!
% 0.93/0.40 % (198937)------------------------------
% 0.93/0.40 % (198937)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.93/0.40 % (198937)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.93/0.40 % (198937)CaDiCaL version: 2.1.3
% 0.93/0.40 % (198937)Termination reason: Instruction limit
% 0.93/0.40 % (198937)Termination phase: Saturation
% 0.93/0.40 % (198937)Time elapsed: 0.036 s
% 0.93/0.40 % (198937)Peak memory usage: 14 MB
% 0.93/0.40 % (198937)Instructions burned: 75 (million)
% 0.93/0.40 % (198966)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
% 0.93/0.40 % (198966)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.93/0.40 % (198969)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=999291875:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.93/0.40 % (198966)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1588405795:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.93/0.40 % (198971)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.93/0.40 % (198970)lrs+10_1_si=on:cs=on:random_seed=824347210:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.93/0.43 % (198971)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=1658660853:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.93/0.43 % (198970)Instruction limit reached!
% 0.93/0.43 % (198970)------------------------------
% 0.93/0.43 % (198970)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.93/0.43 % (198970)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.93/0.43 % (198970)CaDiCaL version: 2.1.3
% 0.93/0.43 % (198970)Termination reason: Instruction limit
% 0.93/0.43 % (198970)Termination phase: Saturation
% 0.93/0.43 % (198970)Time elapsed: 0.005 s
% 0.93/0.43 % (198970)Peak memory usage: 12 MB
% 0.93/0.43 % (198970)Instructions burned: 8 (million)
% 0.93/0.43 % (198971)Instruction limit reached!
% 0.93/0.43 % (198971)------------------------------
% 0.93/0.43 % (198971)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.93/0.43 % (198971)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.93/0.43 % (198971)CaDiCaL version: 2.1.3
% 0.93/0.43 % (198971)Termination reason: Instruction limit
% 0.93/0.43 % (198971)Termination phase: Saturation
% 0.93/0.43 % (198971)Time elapsed: 0.003 s
% 0.93/0.43 % (198971)Peak memory usage: 11 MB
% 0.93/0.43 % (198971)Instructions burned: 2 (million)
% 0.93/0.43 % (198966)Instruction limit reached!
% 0.93/0.43 % (198966)------------------------------
% 0.93/0.43 % (198966)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.93/0.43 % (198966)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.93/0.43 % (198966)CaDiCaL version: 2.1.3
% 0.93/0.43 % (198966)Termination reason: Instruction limit
% 0.93/0.43 % (198966)Termination phase: Saturation
% 0.93/0.43 % (198966)Time elapsed: 0.014 s
% 0.93/0.43 % (198966)Peak memory usage: 12 MB
% 0.93/0.43 % (198966)Instructions burned: 29 (million)
% 0.93/0.43 % (198973)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3637156543:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.93/0.43 % (198969)Instruction limit reached!
% 0.93/0.43 % (198969)------------------------------
% 0.93/0.43 % (198969)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.93/0.43 % (198969)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.93/0.43 % (198969)CaDiCaL version: 2.1.3
% 0.93/0.43 % (198969)Termination reason: Instruction limit
% 0.93/0.43 % (198969)Termination phase: Saturation
% 0.93/0.43 % (198969)Time elapsed: 0.026 s
% 0.93/0.43 % (198969)Peak memory usage: 13 MB
% 0.93/0.43 % (198969)Instructions burned: 92 (million)
% 0.93/0.43 % (198988)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=4094374578:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.93/0.43 % (198995)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2293106149:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.93/0.43 % (198938)Instruction limit reached!
% 0.93/0.43 % (198938)------------------------------
% 0.93/0.43 % (198938)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.93/0.43 % (198938)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.93/0.43 % (198938)CaDiCaL version: 2.1.3
% 0.93/0.43 % (198938)Termination reason: Instruction limit
% 0.93/0.43 % (198938)Termination phase: Saturation
% 0.93/0.43 % (198938)Time elapsed: 0.085 s
% 0.93/0.43 % (198938)Peak memory usage: 13 MB
% 0.93/0.43 % (198938)Instructions burned: 158 (million)
% 0.93/0.43 % (198973)Instruction limit reached!
% 0.93/0.43 % (198973)------------------------------
% 0.93/0.43 % (198973)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.93/0.43 % (198973)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.93/0.43 % (198973)CaDiCaL version: 2.1.3
% 0.93/0.43 % (198973)Termination reason: Instruction limit
% 0.93/0.43 % (198973)Termination phase: Saturation
% 0.93/0.43 % (198973)Time elapsed: 0.020 s
% 0.93/0.43 % (198973)Peak memory usage: 12 MB
% 0.93/0.43 % (198973)Instructions burned: 38 (million)
% 0.93/0.43 % (198993)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3126861685:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.93/0.43 % (198989)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=196997853:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.93/0.46 % (198989)Refutation not found, incomplete strategy
% 0.93/0.46 % (198989)------------------------------
% 0.93/0.46 % (198989)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.93/0.46 % (198989)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.93/0.46 % (198989)CaDiCaL version: 2.1.3
% 0.93/0.46 % (198989)Termination reason: Refutation not found, incomplete strategy
% 0.93/0.46 % (198989)Time elapsed: 0.006 s
% 0.93/0.46 % (198989)Peak memory usage: 12 MB
% 0.93/0.46 % (198989)Instructions burned: 10 (million)
% 0.93/0.46 % (198989)------------------------------
% 0.93/0.46 % (198989)------------------------------
% 0.93/0.46 % (198993)Instruction limit reached!
% 0.93/0.46 % (198993)------------------------------
% 0.93/0.46 % (198993)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.93/0.46 % (198993)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.93/0.46 % (198993)CaDiCaL version: 2.1.3
% 0.93/0.46 % (198993)Termination reason: Instruction limit
% 0.93/0.46 % (198993)Termination phase: Saturation
% 0.93/0.46 % (198993)Time elapsed: 0.008 s
% 0.93/0.46 % (198993)Peak memory usage: 12 MB
% 0.93/0.46 % (198993)Instructions burned: 15 (million)
% 0.93/0.46 % (199002)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1064844014:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 0.93/0.46 % (199001)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2494899955:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.93/0.46 % (199002)Instruction limit reached!
% 0.93/0.46 % (199002)------------------------------
% 0.93/0.46 % (199002)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.93/0.46 % (199002)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.93/0.46 % (199002)CaDiCaL version: 2.1.3
% 0.93/0.46 % (199002)Termination reason: Instruction limit
% 0.93/0.46 % (199002)Termination phase: Saturation
% 0.93/0.46 % (199002)Time elapsed: 0.003 s
% 0.93/0.46 % (199002)Peak memory usage: 12 MB
% 0.93/0.46 % (199002)Instructions burned: 6 (million)
% 0.93/0.46 % (199004)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1917578268:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 0.93/0.46 % (199005)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=3390465712:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 0.93/0.46 % (199001)Instruction limit reached!
% 0.93/0.46 % (199001)------------------------------
% 0.93/0.46 % (199001)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.93/0.46 % (199001)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.93/0.46 % (199001)CaDiCaL version: 2.1.3
% 0.93/0.46 % (199001)Termination reason: Instruction limit
% 0.93/0.46 % (199001)Termination phase: Saturation
% 0.93/0.46 % (199001)Time elapsed: 0.009 s
% 0.93/0.46 % (199001)Peak memory usage: 12 MB
% 0.93/0.46 % (199001)Instructions burned: 15 (million)
% 0.93/0.46 % (198988)Refutation not found, incomplete strategy
% 0.93/0.46 % (198988)------------------------------
% 0.93/0.46 % (198988)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.93/0.46 % (199004)Instruction limit reached!
% 0.93/0.46 % (199004)------------------------------
% 0.93/0.46 % (199004)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.93/0.46 % (198988)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.93/0.46 % (199004)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.93/0.46 % (198988)CaDiCaL version: 2.1.3
% 0.93/0.46 % (199004)CaDiCaL version: 2.1.3
% 0.93/0.46 % (198988)Termination reason: Refutation not found, incomplete strategy
% 0.93/0.46 % (198988)Time elapsed: 0.046 s
% 0.93/0.46 % (199004)Termination reason: Instruction limit
% 0.93/0.46 % (199004)Termination phase: Saturation
% 0.93/0.46 % (199004)Time elapsed: 0.014 s
% 0.93/0.46 % (198988)Peak memory usage: 13 MB
% 0.93/0.46 % (199004)Peak memory usage: 12 MB
% 0.93/0.46 % (198988)Instructions burned: 90 (million)
% 0.93/0.46 % (199004)Instructions burned: 26 (million)
% 0.93/0.46 % (198935)Refutation not found, incomplete strategy
% 0.93/0.46 % (198935)------------------------------
% 0.93/0.46 % (198935)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.53 % (198935)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.53 % (198935)CaDiCaL version: 2.1.3
% 1.81/0.53 % (198935)Termination reason: Refutation not found, incomplete strategy
% 1.81/0.53 % (198935)Time elapsed: 0.132 s
% 1.81/0.53 % (198935)Peak memory usage: 14 MB
% 1.81/0.53 % (198935)Instructions burned: 227 (million)
% 1.81/0.53 % (199005)Instruction limit reached!
% 1.81/0.53 % (199005)------------------------------
% 1.81/0.53 % (199005)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.53 % (199005)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.53 % (199005)CaDiCaL version: 2.1.3
% 1.81/0.53 % (199005)Termination reason: Instruction limit
% 1.81/0.53 % (199005)Termination phase: Saturation
% 1.81/0.53 % (199005)Time elapsed: 0.013 s
% 1.81/0.53 % (199005)Peak memory usage: 12 MB
% 1.81/0.53 % (199005)Instructions burned: 23 (million)
% 1.81/0.53 % (198988)------------------------------
% 1.81/0.53 % (198988)------------------------------
% 1.81/0.53 % (198935)------------------------------
% 1.81/0.53 % (198935)------------------------------
% 1.81/0.53 % (199012)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=2602991036:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.81/0.53 % (199015)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) 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
% 1.81/0.53 % (199015)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.81/0.53 % (199015)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=2404395530:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.81/0.53 % (199018)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.81/0.53 % (199015)Instruction limit reached!
% 1.81/0.53 % (199015)------------------------------
% 1.81/0.53 % (199015)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.53 % (199015)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.53 % (199015)CaDiCaL version: 2.1.3
% 1.81/0.53 % (199015)Termination reason: Instruction limit
% 1.81/0.53 % (199015)Termination phase: Saturation
% 1.81/0.53 % (199015)Time elapsed: 0.008 s
% 1.81/0.53 % (199015)Peak memory usage: 12 MB
% 1.81/0.53 % (199015)Instructions burned: 15 (million)
% 1.81/0.53 % (199018)lrs+1010_4:1_slsqr=8,1:to=kbo:cha=on:drc=off:si=on:sp=arity:lcm=predicate:uwa=off:fd=preordered:gs=on:nwc=5:s2agt=32:slsqc=1:kmz=on:updr=off:chr=on:pe=on:slsq=on:random_seed=4155611455:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.81/0.53 % (199019)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=1679251565:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.81/0.53 % (199022)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=2530119547:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.81/0.53 % (199021)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=1512268182:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.81/0.53 % (199018)Instruction limit reached!
% 1.81/0.53 % (199018)------------------------------
% 1.81/0.53 % (199018)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.53 % (199018)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.53 % (199018)CaDiCaL version: 2.1.3
% 1.81/0.53 % (199018)Termination reason: Instruction limit
% 1.81/0.53 % (199018)Termination phase: Saturation
% 1.81/0.53 % (199018)Time elapsed: 0.005 s
% 1.81/0.53 % (199018)Peak memory usage: 12 MB
% 1.81/0.53 % (199018)Instructions burned: 9 (million)
% 1.81/0.53 % (199021)Instruction limit reached!
% 1.81/0.53 % (199021)------------------------------
% 1.81/0.53 % (199021)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.53 % (199021)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.53 % (199021)CaDiCaL version: 2.1.3
% 1.81/0.53 % (199021)Termination reason: Instruction limit
% 1.81/0.60 % (199021)Termination phase: Saturation
% 1.81/0.60 % (199021)Time elapsed: 0.004 s
% 1.81/0.60 % (199021)Peak memory usage: 12 MB
% 1.81/0.60 % (199021)Instructions burned: 7 (million)
% 1.81/0.60 % (199022)Instruction limit reached!
% 1.81/0.60 % (199022)------------------------------
% 1.81/0.60 % (199022)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.60 % (199022)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.60 % (199022)CaDiCaL version: 2.1.3
% 1.81/0.60 % (199022)Termination reason: Instruction limit
% 1.81/0.60 % (199022)Termination phase: Saturation
% 1.81/0.60 % (199022)Time elapsed: 0.010 s
% 1.81/0.60 % (199022)Peak memory usage: 11 MB
% 1.81/0.60 % (199022)Instructions burned: 25 (million)
% 1.81/0.60 % (199019)Instruction limit reached!
% 1.81/0.60 % (199019)------------------------------
% 1.81/0.60 % (199019)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.60 % (199019)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.60 % (199019)CaDiCaL version: 2.1.3
% 1.81/0.60 % (199019)Termination reason: Instruction limit
% 1.81/0.60 % (199019)Termination phase: Saturation
% 1.81/0.60 % (199019)Time elapsed: 0.015 s
% 1.81/0.60 % (199019)Peak memory usage: 12 MB
% 1.81/0.60 % (199019)Instructions burned: 32 (million)
% 1.81/0.60 % (199012)Instruction limit reached!
% 1.81/0.60 % (199012)------------------------------
% 1.81/0.60 % (199012)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.60 % (199012)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.60 % (199012)CaDiCaL version: 2.1.3
% 1.81/0.60 % (199012)Termination reason: Instruction limit
% 1.81/0.60 % (199012)Termination phase: Saturation
% 1.81/0.60 % (199012)Time elapsed: 0.033 s
% 1.81/0.60 % (199012)Peak memory usage: 12 MB
% 1.81/0.60 % (199012)Instructions burned: 61 (million)
% 1.81/0.60 % (199028)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=203083124:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 1.81/0.60 % (199034)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=1815660833:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 1.81/0.60 % (199035)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=2241081179:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 1.81/0.60 % (198995)Instruction limit reached!
% 1.81/0.60 % (198995)------------------------------
% 1.81/0.60 % (198995)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.60 % (198995)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.60 % (198995)CaDiCaL version: 2.1.3
% 1.81/0.60 % (198995)Termination reason: Instruction limit
% 1.81/0.60 % (198995)Termination phase: Saturation
% 1.81/0.60 % (198995)Time elapsed: 0.089 s
% 1.81/0.60 % (198995)Peak memory usage: 14 MB
% 1.81/0.60 % (198995)Instructions burned: 331 (million)
% 1.81/0.60 % (199037)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=1650763523:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/193Mi)
% 1.81/0.60 % (199040)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.81/0.60 % (199028)Instruction limit reached!
% 1.81/0.60 % (199028)------------------------------
% 1.81/0.60 % (199028)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.60 % (199028)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.60 % (199028)CaDiCaL version: 2.1.3
% 1.81/0.60 % (199028)Termination reason: Instruction limit
% 1.81/0.60 % (199028)Termination phase: Saturation
% 1.81/0.60 % (199028)Time elapsed: 0.015 s
% 1.81/0.60 % (199028)Peak memory usage: 13 MB
% 1.81/0.60 % (199028)Instructions burned: 21 (million)
% 1.81/0.60 % (199039)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2335042381:i=42:hud=10:rtra=on_2998 on theBenchmark for (2998ds/42Mi)
% 1.81/0.60 % (199040)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3601375697:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2998 on theBenchmark for (2998ds/7Mi)
% 1.81/0.60 % (199040)Instruction limit reached!
% 1.81/0.60 % (199040)------------------------------
% 1.81/0.60 % (199040)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.60 % (199040)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.61 % (199040)CaDiCaL version: 2.1.3
% 1.81/0.61 % (199040)Termination reason: Instruction limit
% 1.81/0.61 % (199040)Termination phase: Saturation
% 1.81/0.61 % (199040)Time elapsed: 0.005 s
% 1.81/0.61 % (199040)Peak memory usage: 12 MB
% 1.81/0.61 % (199040)Instructions burned: 7 (million)
% 1.81/0.61 % (199047)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=188496812:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 1.81/0.61 % (199051)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=3859853409:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/169Mi)
% 1.81/0.61 % (199039)Instruction limit reached!
% 1.81/0.61 % (199039)------------------------------
% 1.81/0.61 % (199039)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.61 % (199039)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.61 % (199039)CaDiCaL version: 2.1.3
% 1.81/0.61 % (199039)Termination reason: Instruction limit
% 1.81/0.61 % (199039)Termination phase: Saturation
% 1.81/0.61 % (199039)Time elapsed: 0.020 s
% 1.81/0.61 % (199039)Peak memory usage: 12 MB
% 1.81/0.61 % (199039)Instructions burned: 44 (million)
% 1.81/0.61 % (199058)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 1.81/0.61 % (199058)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=2800381146:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 1.81/0.61 % (199058)Instruction limit reached!
% 1.81/0.61 % (199058)------------------------------
% 1.81/0.61 % (199058)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.61 % (199058)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.61 % (199058)CaDiCaL version: 2.1.3
% 1.81/0.61 % (199058)Termination reason: Instruction limit
% 1.81/0.61 % (199058)Termination phase: Saturation
% 1.81/0.61 % (199058)Time elapsed: 0.004 s
% 1.81/0.61 % (199058)Peak memory usage: 12 MB
% 1.81/0.61 % (199058)Instructions burned: 6 (million)
% 1.81/0.61 % (199061)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=2373319865:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2997 on theBenchmark for (2997ds/22Mi)
% 1.81/0.61 % (199061)Instruction limit reached!
% 1.81/0.61 % (199061)------------------------------
% 1.81/0.61 % (199061)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.61 % (199061)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.61 % (199061)CaDiCaL version: 2.1.3
% 1.81/0.61 % (199061)Termination reason: Instruction limit
% 1.81/0.61 % (199061)Termination phase: Saturation
% 1.81/0.61 % (199061)Time elapsed: 0.013 s
% 1.81/0.61 % (199061)Peak memory usage: 12 MB
% 1.81/0.61 % (199061)Instructions burned: 23 (million)
% 1.81/0.61 % (199035)Instruction limit reached!
% 1.81/0.61 % (199035)------------------------------
% 1.81/0.61 % (199035)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.61 % (199035)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.61 % (199035)CaDiCaL version: 2.1.3
% 1.81/0.61 % (199035)Termination reason: Instruction limit
% 1.81/0.61 % (199035)Termination phase: Saturation
% 1.81/0.61 % (199035)Time elapsed: 0.065 s
% 1.81/0.61 % (199035)Peak memory usage: 13 MB
% 1.81/0.61 % (199035)Instructions burned: 143 (million)
% 1.81/0.61 % (199067)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=1968658694:i=19:add=on:rtra=on_2997 on theBenchmark for (2997ds/19Mi)
% 1.81/0.61 % (199067)Instruction limit reached!
% 1.81/0.61 % (199067)------------------------------
% 1.81/0.61 % (199067)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.61 % (199067)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.61 % (199067)CaDiCaL version: 2.1.3
% 1.81/0.61 % (199067)Termination reason: Instruction limit
% 1.81/0.61 % (199067)Termination phase: Saturation
% 1.81/0.61 % (199067)Time elapsed: 0.010 s
% 1.81/0.61 % (199067)Peak memory usage: 12 MB
% 1.81/0.61 % (199067)Instructions burned: 19 (million)
% 1.81/0.61 % (199071)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=2657398232:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/316Mi)
% 1.81/0.61 % (199037)Instruction limit reached!
% 1.81/0.61 % (199037)------------------------------
% 1.81/0.61 % (199037)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.61 % (199037)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.61 % (199037)CaDiCaL version: 2.1.3
% 1.81/0.61 % (199037)Termination reason: Instruction limit
% 1.81/0.61 % (199037)Termination phase: Saturation
% 1.81/0.61 % (199037)Time elapsed: 0.082 s
% 1.81/0.61 % (199037)Peak memory usage: 13 MB
% 1.81/0.61 % (199037)Instructions burned: 195 (million)
% 1.81/0.61 % (199072)dis+1004_4:1_slsqr=1,2:to=lpo:plsq=on:fde=unused:e2e=on:si=on:spb=goal_then_units:acc=on:urr=on:uwa=off:fd=preordered:s2agt=16:slsqc=1:slsq=on:random_seed=3972419061:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2997 on theBenchmark for (2997ds/853Mi)
% 1.81/0.61 % (199074)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=1880630168:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2997 on theBenchmark for (2997ds/45Mi)
% 1.81/0.61 % (199080)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=981734352:i=480:rtra=on_2997 on theBenchmark for (2997ds/480Mi)
% 1.81/0.61 % (199051)Instruction limit reached!
% 1.81/0.61 % (199051)------------------------------
% 1.81/0.61 % (199051)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.61 % (199051)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.61 % (199051)CaDiCaL version: 2.1.3
% 1.81/0.61 % (199051)Termination reason: Instruction limit
% 1.81/0.61 % (199051)Termination phase: Saturation
% 1.81/0.61 % (199051)Time elapsed: 0.093 s
% 1.81/0.61 % (199051)Peak memory usage: 13 MB
% 1.81/0.61 % (199051)Instructions burned: 169 (million)
% 1.81/0.61 % (199047)Instruction limit reached!
% 1.81/0.61 % (199047)------------------------------
% 1.81/0.61 % (199047)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.61 % (199047)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.61 % (199047)CaDiCaL version: 2.1.3
% 1.81/0.61 % (199047)Termination reason: Instruction limit
% 1.81/0.61 % (199047)Termination phase: Saturation
% 1.81/0.61 % (199047)Time elapsed: 0.100 s
% 1.81/0.61 % (199047)Peak memory usage: 16 MB
% 1.81/0.61 % (199047)Instructions burned: 181 (million)
% 1.81/0.61 % (199074)Instruction limit reached!
% 1.81/0.61 % (199074)------------------------------
% 1.81/0.61 % (199074)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.61 % (199074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.61 % (199074)CaDiCaL version: 2.1.3
% 1.81/0.61 % (199074)Termination reason: Instruction limit
% 1.81/0.61 % (199074)Termination phase: Saturation
% 1.81/0.61 % (199074)Time elapsed: 0.035 s
% 1.81/0.61 % (199074)Peak memory usage: 12 MB
% 1.81/0.61 % (199074)Instructions burned: 46 (million)
% 1.81/0.61 % (199080)Refutation not found, incomplete strategy
% 1.81/0.61 % (199080)------------------------------
% 1.81/0.61 % (199080)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.61 % (199080)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.61 % (199080)CaDiCaL version: 2.1.3
% 1.81/0.61 % (199080)Termination reason: Refutation not found, incomplete strategy
% 1.81/0.61 % (199080)Time elapsed: 0.038 s
% 1.81/0.61 % (199080)Peak memory usage: 12 MB
% 1.81/0.61 % (199080)Instructions burned: 91 (million)
% 1.81/0.61 % (199080)------------------------------
% 1.81/0.61 % (199080)------------------------------
% 1.81/0.61 % (199071) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-198924-199071"...
% 1.81/0.61 % (199094)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 1.81/0.61 % (199103)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=3875717026:i=66:s2at=3:nm=2:rtra=on:rawr=on_2996 on theBenchmark for (2996ds/66Mi)
% 1.81/0.61 % (199094)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=1099098965:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/200Mi)
% 1.81/0.61 % (199093)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=2138004383:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2996 on theBenchmark for (2996ds/21Mi)
% 1.81/0.61 % (199102)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1874006546:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2996 on theBenchmark for (2996ds/13Mi)
% 1.81/0.61 % (199071)...printing done.
% 1.81/0.61 % (199071)Refutation found. Thanks to Tanya!
% 1.81/0.61 % SZS status Theorem for theBenchmark
% 1.81/0.61 % SZS output start Proof for theBenchmark
% See solution above
% 1.81/0.61 % (199071)------------------------------
% 1.81/0.61 % (199071)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.61 % (199071)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.61 % (199071)CaDiCaL version: 2.1.3
% 1.81/0.61 % (199071)Termination reason: Refutation
% 1.81/0.61 % (199071)Time elapsed: 0.078 s
% 1.81/0.61 % (199071)Peak memory usage: 14 MB
% 1.81/0.61 % (199071)Instructions burned: 115 (million)
% 1.81/0.61 % (198924)Success in time 0.371 s
% 1.81/0.61 % Vampire exiting
%------------------------------------------------------------------------------