TSTP Solution File: SEV123^5 by Vampire---4.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SEV123^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 16:01:54 EDT 2024
% Result : Theorem 0.19s 0.43s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 6
% Syntax : Number of formulae : 68 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 984 ( 347 equ; 0 cnn)
% Maximal formula atoms : 22 ( 14 avg)
% Number of connectives : 1713 ( 159 ~; 209 |; 96 &;1098 @)
% ( 0 <=>; 84 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 9 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 378 ( 378 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 13 usr; 5 con; 0-5 aty)
% ( 67 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 444 ( 168 ^ 218 !; 58 ?; 444 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_11,type,
sK0: ( a > a > $o ) > $o ).
thf(func_def_12,type,
sK1: a ).
thf(func_def_13,type,
sK2: a ).
thf(func_def_14,type,
sK3: ( a > a > $o ) > $o ).
thf(func_def_15,type,
sK4: ( a > a > $o ) > a ).
thf(func_def_16,type,
sK5: ( a > a > $o ) > a ).
thf(func_def_17,type,
sK6: ( a > a > $o ) > a > a > $o ).
thf(func_def_18,type,
sK7: ( a > a > $o ) > a > a > $o ).
thf(func_def_19,type,
sK8: a > a > $o ).
thf(func_def_21,type,
ph10:
!>[X0: $tType] : X0 ).
thf(func_def_24,type,
sK11: ( a > a > $o ) > ( a > a > $o ) > a ).
thf(func_def_25,type,
sK12: ( a > a > $o ) > ( a > a > $o ) > a ).
thf(func_def_26,type,
sK13: a > ( a > a > $o ) > a > a > a > $o ).
thf(f543,plain,
$false,
inference(subsumption_resolution,[],[f542,f16]) ).
thf(f16,plain,
( $true
= ( sK0 @ sK8 ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f14,plain,
( ! [X4: a > a > $o] :
( ( ( ( X4 @ ( sK4 @ X4 ) @ ( sK5 @ X4 ) )
!= $true )
& ( $true
= ( sK6 @ X4 @ ( sK4 @ X4 ) @ ( sK5 @ X4 ) ) )
& ( ( sK3 @ ( sK7 @ X4 ) )
= $true )
& ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK7 @ X4 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
= ( sK6 @ X4 ) ) )
| ( $true
!= ( sK0 @ X4 ) )
| ( $true
= ( X4 @ sK2 @ sK1 ) ) )
& ( ( sK8 @ sK2 @ sK1 )
!= $true )
& ( $true
= ( sK0 @ sK8 ) )
& ! [X10: a,X11: a] :
( ( $true
= ( sK8 @ X10 @ X11 ) )
| ! [X12: a > a > $o] :
( ( $true
!= ( X12 @ X10 @ X11 ) )
| ( $true
!= ( sK3 @ X12 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8])],[f8,f13,f12,f11,f10,f9]) ).
thf(f9,plain,
( ? [X0: ( a > a > $o ) > $o,X1: a,X2: a,X3: ( a > a > $o ) > $o] :
( ! [X4: a > a > $o] :
( ? [X5: a,X6: a] :
( ( ( X4 @ X5 @ X6 )
!= $true )
& ? [X7: a > a > $o] :
( ( ( X7 @ X5 @ X6 )
= $true )
& ? [X8: a > a > $o] :
( ( ( X3 @ X8 )
= $true )
& ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( X0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X8 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
= X7 ) ) ) )
| ( ( X0 @ X4 )
!= $true )
| ( $true
= ( X4 @ X2 @ X1 ) ) )
& ? [X9: a > a > $o] :
( ( ( X9 @ X2 @ X1 )
!= $true )
& ( $true
= ( X0 @ X9 ) )
& ! [X10: a,X11: a] :
( ( ( X9 @ X10 @ X11 )
= $true )
| ! [X12: a > a > $o] :
( ( $true
!= ( X12 @ X10 @ X11 ) )
| ( ( X3 @ X12 )
!= $true ) ) ) ) )
=> ( ! [X4: a > a > $o] :
( ? [X6: a,X5: a] :
( ( ( X4 @ X5 @ X6 )
!= $true )
& ? [X7: a > a > $o] :
( ( ( X7 @ X5 @ X6 )
= $true )
& ? [X8: a > a > $o] :
( ( ( sK3 @ X8 )
= $true )
& ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X8 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
= X7 ) ) ) )
| ( $true
!= ( sK0 @ X4 ) )
| ( $true
= ( X4 @ sK2 @ sK1 ) ) )
& ? [X9: a > a > $o] :
( ( $true
!= ( X9 @ sK2 @ sK1 ) )
& ( $true
= ( sK0 @ X9 ) )
& ! [X11: a,X10: a] :
( ( ( X9 @ X10 @ X11 )
= $true )
| ! [X12: a > a > $o] :
( ( $true
!= ( X12 @ X10 @ X11 ) )
| ( $true
!= ( sK3 @ X12 ) ) ) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f10,plain,
! [X4: a > a > $o] :
( ? [X6: a,X5: a] :
( ( ( X4 @ X5 @ X6 )
!= $true )
& ? [X7: a > a > $o] :
( ( ( X7 @ X5 @ X6 )
= $true )
& ? [X8: a > a > $o] :
( ( ( sK3 @ X8 )
= $true )
& ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X8 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
= X7 ) ) ) )
=> ( ( ( X4 @ ( sK4 @ X4 ) @ ( sK5 @ X4 ) )
!= $true )
& ? [X7: a > a > $o] :
( ( $true
= ( X7 @ ( sK4 @ X4 ) @ ( sK5 @ X4 ) ) )
& ? [X8: a > a > $o] :
( ( ( sK3 @ X8 )
= $true )
& ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X8 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
= X7 ) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f11,plain,
! [X4: a > a > $o] :
( ? [X7: a > a > $o] :
( ( $true
= ( X7 @ ( sK4 @ X4 ) @ ( sK5 @ X4 ) ) )
& ? [X8: a > a > $o] :
( ( ( sK3 @ X8 )
= $true )
& ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X8 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
= X7 ) ) )
=> ( ( $true
= ( sK6 @ X4 @ ( sK4 @ X4 ) @ ( sK5 @ X4 ) ) )
& ? [X8: a > a > $o] :
( ( ( sK3 @ X8 )
= $true )
& ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X8 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
= ( sK6 @ X4 ) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f12,plain,
! [X4: a > a > $o] :
( ? [X8: a > a > $o] :
( ( ( sK3 @ X8 )
= $true )
& ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X8 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
= ( sK6 @ X4 ) ) )
=> ( ( ( sK3 @ ( sK7 @ X4 ) )
= $true )
& ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK7 @ X4 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
= ( sK6 @ X4 ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f13,plain,
( ? [X9: a > a > $o] :
( ( $true
!= ( X9 @ sK2 @ sK1 ) )
& ( $true
= ( sK0 @ X9 ) )
& ! [X11: a,X10: a] :
( ( ( X9 @ X10 @ X11 )
= $true )
| ! [X12: a > a > $o] :
( ( $true
!= ( X12 @ X10 @ X11 ) )
| ( $true
!= ( sK3 @ X12 ) ) ) ) )
=> ( ( ( sK8 @ sK2 @ sK1 )
!= $true )
& ( $true
= ( sK0 @ sK8 ) )
& ! [X11: a,X10: a] :
( ( $true
= ( sK8 @ X10 @ X11 ) )
| ! [X12: a > a > $o] :
( ( $true
!= ( X12 @ X10 @ X11 ) )
| ( $true
!= ( sK3 @ X12 ) ) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f8,plain,
? [X0: ( a > a > $o ) > $o,X1: a,X2: a,X3: ( a > a > $o ) > $o] :
( ! [X4: a > a > $o] :
( ? [X5: a,X6: a] :
( ( ( X4 @ X5 @ X6 )
!= $true )
& ? [X7: a > a > $o] :
( ( ( X7 @ X5 @ X6 )
= $true )
& ? [X8: a > a > $o] :
( ( ( X3 @ X8 )
= $true )
& ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( X0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X8 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
= X7 ) ) ) )
| ( ( X0 @ X4 )
!= $true )
| ( $true
= ( X4 @ X2 @ X1 ) ) )
& ? [X9: a > a > $o] :
( ( ( X9 @ X2 @ X1 )
!= $true )
& ( $true
= ( X0 @ X9 ) )
& ! [X10: a,X11: a] :
( ( ( X9 @ X10 @ X11 )
= $true )
| ! [X12: a > a > $o] :
( ( $true
!= ( X12 @ X10 @ X11 ) )
| ( ( X3 @ X12 )
!= $true ) ) ) ) ),
inference(flattening,[],[f7]) ).
thf(f7,plain,
? [X0: ( a > a > $o ) > $o,X1: a,X2: a,X3: ( a > a > $o ) > $o] :
( ? [X9: a > a > $o] :
( ( ( X9 @ X2 @ X1 )
!= $true )
& ( $true
= ( X0 @ X9 ) )
& ! [X10: a,X11: a] :
( ( ( X9 @ X10 @ X11 )
= $true )
| ! [X12: a > a > $o] :
( ( $true
!= ( X12 @ X10 @ X11 ) )
| ( ( X3 @ X12 )
!= $true ) ) ) )
& ! [X4: a > a > $o] :
( ( $true
= ( X4 @ X2 @ X1 ) )
| ? [X5: a,X6: a] :
( ( ( X4 @ X5 @ X6 )
!= $true )
& ? [X7: a > a > $o] :
( ( ( X7 @ X5 @ X6 )
= $true )
& ? [X8: a > a > $o] :
( ( ( X3 @ X8 )
= $true )
& ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( X0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X8 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
= X7 ) ) ) )
| ( ( X0 @ X4 )
!= $true ) ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f6,plain,
~ ! [X0: ( a > a > $o ) > $o,X1: a,X2: a,X3: ( a > a > $o ) > $o] :
( ! [X4: a > a > $o] :
( ( ! [X5: a,X6: a] :
( ? [X7: a > a > $o] :
( ( ( X7 @ X5 @ X6 )
= $true )
& ? [X8: a > a > $o] :
( ( ( X3 @ X8 )
= $true )
& ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( X0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X8 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
= X7 ) ) )
=> ( ( X4 @ X5 @ X6 )
= $true ) )
& ( ( X0 @ X4 )
= $true ) )
=> ( $true
= ( X4 @ X2 @ X1 ) ) )
=> ! [X9: a > a > $o] :
( ( ( $true
= ( X0 @ X9 ) )
& ! [X10: a,X11: a] :
( ? [X12: a > a > $o] :
( ( $true
= ( X12 @ X10 @ X11 ) )
& ( ( X3 @ X12 )
= $true ) )
=> ( ( X9 @ X10 @ X11 )
= $true ) ) )
=> ( ( X9 @ X2 @ X1 )
= $true ) ) ),
inference(rectify,[],[f5]) ).
thf(f5,plain,
~ ! [X0: ( a > a > $o ) > $o,X1: a,X2: a,X3: ( a > a > $o ) > $o] :
( ! [X4: a > a > $o] :
( ( ! [X5: a,X6: a] :
( ? [X7: a > a > $o] :
( ( ( X7 @ X5 @ X6 )
= $true )
& ? [X8: a > a > $o] :
( ( ( X3 @ X8 )
= $true )
& ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( X0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X8 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
= X7 ) ) )
=> ( ( X4 @ X5 @ X6 )
= $true ) )
& ( ( X0 @ X4 )
= $true ) )
=> ( $true
= ( X4 @ X2 @ X1 ) ) )
=> ! [X14: a > a > $o] :
( ( ( $true
= ( X0 @ X14 ) )
& ! [X15: a,X16: a] :
( ? [X17: a > a > $o] :
( ( $true
= ( X3 @ X17 ) )
& ( $true
= ( X17 @ X15 @ X16 ) ) )
=> ( $true
= ( X14 @ X15 @ X16 ) ) ) )
=> ( $true
= ( X14 @ X2 @ X1 ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f4,plain,
~ ! [X0: ( a > a > $o ) > $o,X1: a,X2: a,X3: ( a > a > $o ) > $o] :
( ! [X4: a > a > $o] :
( ( ! [X5: a,X6: a] :
( ? [X7: a > a > $o] :
( ? [X8: a > a > $o] :
( ( X3 @ X8 )
& ( X7
= ( ^ [X9: a,X10: a] :
! [X11: a > a > $o] :
( ( ! [X12: a,X13: a] :
( ( X8 @ X12 @ X13 )
=> ( X11 @ X12 @ X13 ) )
& ( X0 @ X11 ) )
=> ( X11 @ X9 @ X10 ) ) ) ) )
& ( X7 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
& ( X0 @ X4 ) )
=> ( X4 @ X2 @ X1 ) )
=> ! [X14: a > a > $o] :
( ( ( X0 @ X14 )
& ! [X15: a,X16: a] :
( ? [X17: a > a > $o] :
( ( X3 @ X17 )
& ( X17 @ X15 @ X16 ) )
=> ( X14 @ X15 @ X16 ) ) )
=> ( X14 @ X2 @ X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: ( a > a > $o ) > $o,X3: a,X2: a,X1: ( a > a > $o ) > $o] :
( ! [X4: a > a > $o] :
( ( ! [X5: a,X6: a] :
( ? [X7: a > a > $o] :
( ? [X8: a > a > $o] :
( ( X1 @ X8 )
& ( X7
= ( ^ [X9: a,X10: a] :
! [X11: a > a > $o] :
( ( ! [X12: a,X13: a] :
( ( X8 @ X12 @ X13 )
=> ( X11 @ X12 @ X13 ) )
& ( X0 @ X11 ) )
=> ( X11 @ X9 @ X10 ) ) ) ) )
& ( X7 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
& ( X0 @ X4 ) )
=> ( X4 @ X2 @ X3 ) )
=> ! [X4: a > a > $o] :
( ( ( X0 @ X4 )
& ! [X5: a,X6: a] :
( ? [X7: a > a > $o] :
( ( X1 @ X7 )
& ( X7 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
! [X0: ( a > a > $o ) > $o,X3: a,X2: a,X1: ( a > a > $o ) > $o] :
( ! [X4: a > a > $o] :
( ( ! [X5: a,X6: a] :
( ? [X7: a > a > $o] :
( ? [X8: a > a > $o] :
( ( X1 @ X8 )
& ( X7
= ( ^ [X9: a,X10: a] :
! [X11: a > a > $o] :
( ( ! [X12: a,X13: a] :
( ( X8 @ X12 @ X13 )
=> ( X11 @ X12 @ X13 ) )
& ( X0 @ X11 ) )
=> ( X11 @ X9 @ X10 ) ) ) ) )
& ( X7 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
& ( X0 @ X4 ) )
=> ( X4 @ X2 @ X3 ) )
=> ! [X4: a > a > $o] :
( ( ( X0 @ X4 )
& ! [X5: a,X6: a] :
( ? [X7: a > a > $o] :
( ( X1 @ X7 )
& ( X7 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM254_B_pme) ).
thf(f542,plain,
( $true
!= ( sK0 @ sK8 ) ),
inference(subsumption_resolution,[],[f541,f17]) ).
thf(f17,plain,
( ( sK8 @ sK2 @ sK1 )
!= $true ),
inference(cnf_transformation,[],[f14]) ).
thf(f541,plain,
( ( ( sK8 @ sK2 @ sK1 )
= $true )
| ( $true
!= ( sK0 @ sK8 ) ) ),
inference(trivial_inequality_removal,[],[f540]) ).
thf(f540,plain,
( ( ( sK8 @ sK2 @ sK1 )
= $true )
| ( $true
!= ( sK0 @ sK8 ) )
| ( $true = $false ) ),
inference(duplicate_literal_removal,[],[f531]) ).
thf(f531,plain,
( ( $true = $false )
| ( $true
!= ( sK0 @ sK8 ) )
| ( ( sK8 @ sK2 @ sK1 )
= $true )
| ( $true
!= ( sK0 @ sK8 ) )
| ( ( sK8 @ sK2 @ sK1 )
= $true ) ),
inference(superposition,[],[f530,f146]) ).
thf(f146,plain,
! [X10: a > a > $o] :
( ( ( X10 @ ( sK4 @ X10 ) @ ( sK5 @ X10 ) )
= $false )
| ( $true
!= ( sK0 @ X10 ) )
| ( ( X10 @ sK2 @ sK1 )
= $true ) ),
inference(not_proxy_clausification,[],[f145]) ).
thf(f145,plain,
! [X10: a > a > $o] :
( ( $true
!= ( sK0 @ X10 ) )
| ( ( X10 @ sK2 @ sK1 )
= $true )
| ( $true
= ( ~ ( X10 @ ( sK4 @ X10 ) @ ( sK5 @ X10 ) ) ) ) ),
inference(not_proxy_clausification,[],[f144]) ).
thf(f144,plain,
! [X10: a > a > $o] :
( ( $false
= ( ~ ( X10 @ sK2 @ sK1 ) ) )
| ( $true
= ( ~ ( X10 @ ( sK4 @ X10 ) @ ( sK5 @ X10 ) ) ) )
| ( $true
!= ( sK0 @ X10 ) ) ),
inference(beta_eta_normalization,[],[f143]) ).
thf(f143,plain,
! [X10: a > a > $o] :
( ( $true
= ( ~ ( X10 @ ( sK4 @ X10 ) @ ( sK5 @ X10 ) ) ) )
| ( $false
= ( ~ ( X10 @ sK2 @ sK1 ) ) )
| ( $true
!= ( sK0
@ ^ [Y0: a,Y1: a] : ( X10 @ Y0 @ Y1 ) ) ) ),
inference(boolean_simplification,[],[f142]) ).
thf(f142,plain,
! [X10: a > a > $o] :
( ( $false
= ( ~ ( X10 @ sK2 @ sK1 ) ) )
| ( $true
= ( ~ ( X10 @ ( sK4 @ X10 ) @ ( sK5 @ X10 ) ) ) )
| ( ( sK0
@ ^ [Y0: a,Y1: a] :
~ ~ ( X10 @ Y0 @ Y1 ) )
!= $true ) ),
inference(beta_eta_normalization,[],[f141]) ).
thf(f141,plain,
! [X10: a > a > $o] :
( ( $false
= ( ~ ( X10 @ sK2 @ sK1 ) ) )
| ( ( ~ ( X10
@ ( sK4
@ ^ [Y0: a,Y1: a] : ( X10 @ Y0 @ Y1 ) )
@ ( sK5
@ ^ [Y0: a,Y1: a] : ( X10 @ Y0 @ Y1 ) ) ) )
= $true )
| ( ( sK0
@ ^ [Y0: a,Y1: a] :
~ ~ ( X10 @ Y0 @ Y1 ) )
!= $true ) ),
inference(boolean_simplification,[],[f140]) ).
thf(f140,plain,
! [X10: a > a > $o] :
( ( ( ~ ( X10
@ ( sK4
@ ^ [Y0: a,Y1: a] :
~ ~ ( X10 @ Y0 @ Y1 ) )
@ ( sK5
@ ^ [Y0: a,Y1: a] :
~ ~ ( X10 @ Y0 @ Y1 ) ) ) )
= $true )
| ( ( sK0
@ ^ [Y0: a,Y1: a] :
~ ~ ( X10 @ Y0 @ Y1 ) )
!= $true )
| ( $false
= ( ~ ( X10 @ sK2 @ sK1 ) ) ) ),
inference(beta_eta_normalization,[],[f131]) ).
thf(f131,plain,
! [X10: a > a > $o] :
( ( $true
= ( ^ [Y0: a,Y1: a] :
~ ( X10 @ Y0 @ Y1 )
@ ( sK4
@ ^ [Y0: a,Y1: a] :
~ ( ^ [Y2: a,Y3: a] :
~ ( X10 @ Y2 @ Y3 )
@ Y0
@ Y1 ) )
@ ( sK5
@ ^ [Y0: a,Y1: a] :
~ ( ^ [Y2: a,Y3: a] :
~ ( X10 @ Y2 @ Y3 )
@ Y0
@ Y1 ) ) ) )
| ( ( sK0
@ ^ [Y0: a,Y1: a] :
~ ( ^ [Y2: a,Y3: a] :
~ ( X10 @ Y2 @ Y3 )
@ Y0
@ Y1 ) )
!= $true )
| ( $false
= ( ^ [Y0: a,Y1: a] :
~ ( X10 @ Y0 @ Y1 )
@ sK2
@ sK1 ) ) ),
inference(primitive_instantiation,[],[f81]) ).
thf(f81,plain,
! [X7: a > a > $o] :
( ( $true
= ( X7
@ ( sK4
@ ^ [Y0: a,Y1: a] :
~ ( X7 @ Y0 @ Y1 ) )
@ ( sK5
@ ^ [Y0: a,Y1: a] :
~ ( X7 @ Y0 @ Y1 ) ) ) )
| ( ( X7 @ sK2 @ sK1 )
= $false )
| ( $true
!= ( sK0
@ ^ [Y0: a,Y1: a] :
~ ( X7 @ Y0 @ Y1 ) ) ) ),
inference(not_proxy_clausification,[],[f80]) ).
thf(f80,plain,
! [X7: a > a > $o] :
( ( ( X7 @ sK2 @ sK1 )
= $false )
| ( ( ~ ( X7
@ ( sK4
@ ^ [Y0: a,Y1: a] :
~ ( X7 @ Y0 @ Y1 ) )
@ ( sK5
@ ^ [Y0: a,Y1: a] :
~ ( X7 @ Y0 @ Y1 ) ) ) )
!= $true )
| ( $true
!= ( sK0
@ ^ [Y0: a,Y1: a] :
~ ( X7 @ Y0 @ Y1 ) ) ) ),
inference(not_proxy_clausification,[],[f79]) ).
thf(f79,plain,
! [X7: a > a > $o] :
( ( $true
!= ( sK0
@ ^ [Y0: a,Y1: a] :
~ ( X7 @ Y0 @ Y1 ) ) )
| ( $true
= ( ~ ( X7 @ sK2 @ sK1 ) ) )
| ( ( ~ ( X7
@ ( sK4
@ ^ [Y0: a,Y1: a] :
~ ( X7 @ Y0 @ Y1 ) )
@ ( sK5
@ ^ [Y0: a,Y1: a] :
~ ( X7 @ Y0 @ Y1 ) ) ) )
!= $true ) ),
inference(beta_eta_normalization,[],[f68]) ).
thf(f68,plain,
! [X7: a > a > $o] :
( ( $true
= ( ^ [Y0: a,Y1: a] :
~ ( X7 @ Y0 @ Y1 )
@ sK2
@ sK1 ) )
| ( ( ^ [Y0: a,Y1: a] :
~ ( X7 @ Y0 @ Y1 )
@ ( sK4
@ ^ [Y0: a,Y1: a] :
~ ( X7 @ Y0 @ Y1 ) )
@ ( sK5
@ ^ [Y0: a,Y1: a] :
~ ( X7 @ Y0 @ Y1 ) ) )
!= $true )
| ( $true
!= ( sK0
@ ^ [Y0: a,Y1: a] :
~ ( X7 @ Y0 @ Y1 ) ) ) ),
inference(primitive_instantiation,[],[f21]) ).
thf(f21,plain,
! [X4: a > a > $o] :
( ( ( X4 @ ( sK4 @ X4 ) @ ( sK5 @ X4 ) )
!= $true )
| ( $true
!= ( sK0 @ X4 ) )
| ( $true
= ( X4 @ sK2 @ sK1 ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f530,plain,
! [X0: a > a > $o] :
( ( $true
= ( sK8 @ ( sK4 @ X0 ) @ ( sK5 @ X0 ) ) )
| ( $true
!= ( sK0 @ X0 ) )
| ( $true
= ( X0 @ sK2 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f529]) ).
thf(f529,plain,
! [X0: a > a > $o] :
( ( $true
= ( X0 @ sK2 @ sK1 ) )
| ( $true = $false )
| ( $true
!= ( sK0 @ X0 ) )
| ( $true
= ( sK8 @ ( sK4 @ X0 ) @ ( sK5 @ X0 ) ) ) ),
inference(duplicate_literal_removal,[],[f504]) ).
thf(f504,plain,
! [X0: a > a > $o] :
( ( $true
= ( sK8 @ ( sK4 @ X0 ) @ ( sK5 @ X0 ) ) )
| ( $true
= ( X0 @ sK2 @ sK1 ) )
| ( $true = $false )
| ( $true
= ( X0 @ sK2 @ sK1 ) )
| ( $true
!= ( sK0 @ X0 ) )
| ( $true
!= ( sK0 @ X0 ) ) ),
inference(superposition,[],[f497,f20]) ).
thf(f20,plain,
! [X4: a > a > $o] :
( ( $true
= ( sK6 @ X4 @ ( sK4 @ X4 ) @ ( sK5 @ X4 ) ) )
| ( $true
= ( X4 @ sK2 @ sK1 ) )
| ( $true
!= ( sK0 @ X4 ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f497,plain,
! [X2: a,X0: a > a > $o,X1: a] :
( ( ( sK6 @ X0 @ X1 @ X2 )
= $false )
| ( $true
= ( X0 @ sK2 @ sK1 ) )
| ( $true
= ( sK8 @ X1 @ X2 ) )
| ( $true
!= ( sK0 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f496]) ).
thf(f496,plain,
! [X2: a,X0: a > a > $o,X1: a] :
( ( $true
= ( X0 @ sK2 @ sK1 ) )
| ( $false != $false )
| ( ( sK6 @ X0 @ X1 @ X2 )
= $false )
| ( $true
!= ( sK0 @ X0 ) )
| ( $true
= ( sK8 @ X1 @ X2 ) ) ),
inference(duplicate_literal_removal,[],[f486]) ).
thf(f486,plain,
! [X2: a,X0: a > a > $o,X1: a] :
( ( ( sK6 @ X0 @ X1 @ X2 )
= $false )
| ( $true
!= ( sK0 @ X0 ) )
| ( $true
= ( X0 @ sK2 @ sK1 ) )
| ( $true
= ( sK8 @ X1 @ X2 ) )
| ( $false != $false )
| ( $true
= ( sK8 @ X1 @ X2 ) ) ),
inference(equality_factoring,[],[f329]) ).
thf(f329,plain,
! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( ( sK6 @ X0 @ X3 @ X4 )
= $false )
| ( $true
= ( X0 @ sK2 @ sK1 ) )
| ( $true
= ( sK8 @ X1 @ X2 ) )
| ( $true
= ( sK8 @ X3 @ X4 ) )
| ( $true
!= ( sK0 @ X0 ) )
| ( ( sK6 @ X0 @ X1 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f328]) ).
thf(f328,plain,
! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( ( sK6 @ X0 @ X1 @ X2 )
= $false )
| ( $true
= ( sK8 @ X3 @ X4 ) )
| ( $true = $false )
| ( ( sK6 @ X0 @ X3 @ X4 )
= $false )
| ( $true
= ( sK8 @ X1 @ X2 ) )
| ( $true
= ( X0 @ sK2 @ sK1 ) )
| ( $true
!= ( sK0 @ X0 ) ) ),
inference(forward_demodulation,[],[f327,f16]) ).
thf(f327,plain,
! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( ( sK6 @ X0 @ X3 @ X4 )
= $false )
| ( $true
= ( X0 @ sK2 @ sK1 ) )
| ( ( sK6 @ X0 @ X1 @ X2 )
= $false )
| ( $true
= ( sK8 @ X1 @ X2 ) )
| ( ( sK0 @ sK8 )
= $false )
| ( $true
!= ( sK0 @ X0 ) )
| ( $true
= ( sK8 @ X3 @ X4 ) ) ),
inference(subsumption_resolution,[],[f322,f19]) ).
thf(f19,plain,
! [X4: a > a > $o] :
( ( ( sK3 @ ( sK7 @ X4 ) )
= $true )
| ( $true
!= ( sK0 @ X4 ) )
| ( $true
= ( X4 @ sK2 @ sK1 ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f322,plain,
! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( $true
= ( X0 @ sK2 @ sK1 ) )
| ( $true
= ( sK8 @ X3 @ X4 ) )
| ( ( sK6 @ X0 @ X3 @ X4 )
= $false )
| ( $true
!= ( sK0 @ X0 ) )
| ( $true
= ( sK8 @ X1 @ X2 ) )
| ( ( sK6 @ X0 @ X1 @ X2 )
= $false )
| ( ( sK0 @ sK8 )
= $false )
| ( $true
!= ( sK3 @ ( sK7 @ X0 ) ) ) ),
inference(trivial_inequality_removal,[],[f321]) ).
thf(f321,plain,
! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( $true
= ( sK8 @ X3 @ X4 ) )
| ( $true
= ( sK8 @ X1 @ X2 ) )
| ( ( sK6 @ X0 @ X3 @ X4 )
= $false )
| ( ( sK0 @ sK8 )
= $false )
| ( $true
!= ( sK0 @ X0 ) )
| ( ( sK6 @ X0 @ X1 @ X2 )
= $false )
| ( $true
!= ( sK3 @ ( sK7 @ X0 ) ) )
| ( $true
= ( X0 @ sK2 @ sK1 ) )
| ( $true != $true ) ),
inference(duplicate_literal_removal,[],[f309]) ).
thf(f309,plain,
! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( $true
!= ( sK3 @ ( sK7 @ X0 ) ) )
| ( $true
= ( sK8 @ X3 @ X4 ) )
| ( $true
= ( X0 @ sK2 @ sK1 ) )
| ( $true
!= ( sK0 @ X0 ) )
| ( $true
= ( X0 @ sK2 @ sK1 ) )
| ( ( sK0 @ sK8 )
= $false )
| ( $true
= ( sK8 @ X1 @ X2 ) )
| ( ( sK6 @ X0 @ X1 @ X2 )
= $false )
| ( ( sK6 @ X0 @ X3 @ X4 )
= $false )
| ( $true
!= ( sK0 @ X0 ) )
| ( $true != $true ) ),
inference(superposition,[],[f269,f164]) ).
thf(f164,plain,
! [X6: a,X7: a > a > $o,X4: a > a > $o,X5: a] :
( ( ( sK7 @ X4 @ ( sK12 @ X7 @ X4 ) @ ( sK11 @ X7 @ X4 ) )
= $true )
| ( $true
!= ( sK0 @ X4 ) )
| ( ( sK6 @ X4 @ X5 @ X6 )
= $false )
| ( ( X7 @ X5 @ X6 )
= $true )
| ( ( sK0 @ X7 )
= $false )
| ( $true
= ( X4 @ sK2 @ sK1 ) ) ),
inference(binary_proxy_clausification,[],[f162]) ).
thf(f162,plain,
! [X6: a,X7: a > a > $o,X4: a > a > $o,X5: a] :
( ( ( ( sK7 @ X4 @ ( sK12 @ X7 @ X4 ) @ ( sK11 @ X7 @ X4 ) )
=> ( X7 @ ( sK12 @ X7 @ X4 ) @ ( sK11 @ X7 @ X4 ) ) )
= $false )
| ( ( sK6 @ X4 @ X5 @ X6 )
= $false )
| ( ( sK0 @ X7 )
= $false )
| ( $true
= ( X4 @ sK2 @ sK1 ) )
| ( ( X7 @ X5 @ X6 )
= $true )
| ( $true
!= ( sK0 @ X4 ) ) ),
inference(beta_eta_normalization,[],[f161]) ).
thf(f161,plain,
! [X6: a,X7: a > a > $o,X4: a > a > $o,X5: a] :
( ( ( sK6 @ X4 @ X5 @ X6 )
= $false )
| ( ( ^ [Y0: a] :
( ( sK7 @ X4 @ Y0 @ ( sK11 @ X7 @ X4 ) )
=> ( X7 @ Y0 @ ( sK11 @ X7 @ X4 ) ) )
@ ( sK12 @ X7 @ X4 ) )
= $false )
| ( ( sK0 @ X7 )
= $false )
| ( ( X7 @ X5 @ X6 )
= $true )
| ( $true
!= ( sK0 @ X4 ) )
| ( $true
= ( X4 @ sK2 @ sK1 ) ) ),
inference(sigma_clausification,[],[f160]) ).
thf(f160,plain,
! [X6: a,X7: a > a > $o,X4: a > a > $o,X5: a] :
( ( ( sK6 @ X4 @ X5 @ X6 )
= $false )
| ( ( X7 @ X5 @ X6 )
= $true )
| ( $true
= ( X4 @ sK2 @ sK1 ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( sK7 @ X4 @ Y0 @ ( sK11 @ X7 @ X4 ) )
=> ( X7 @ Y0 @ ( sK11 @ X7 @ X4 ) ) ) )
= $false )
| ( ( sK0 @ X7 )
= $false )
| ( $true
!= ( sK0 @ X4 ) ) ),
inference(beta_eta_normalization,[],[f159]) ).
thf(f159,plain,
! [X6: a,X7: a > a > $o,X4: a > a > $o,X5: a] :
( ( $true
= ( X4 @ sK2 @ sK1 ) )
| ( ( X7 @ X5 @ X6 )
= $true )
| ( $true
!= ( sK0 @ X4 ) )
| ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK7 @ X4 @ Y1 @ Y0 )
=> ( X7 @ Y1 @ Y0 ) ) )
@ ( sK11 @ X7 @ X4 ) )
= $false )
| ( ( sK0 @ X7 )
= $false )
| ( ( sK6 @ X4 @ X5 @ X6 )
= $false ) ),
inference(sigma_clausification,[],[f158]) ).
thf(f158,plain,
! [X6: a,X7: a > a > $o,X4: a > a > $o,X5: a] :
( ( ( X7 @ X5 @ X6 )
= $true )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK7 @ X4 @ Y1 @ Y0 )
=> ( X7 @ Y1 @ Y0 ) ) ) )
= $false )
| ( $true
= ( X4 @ sK2 @ sK1 ) )
| ( ( sK6 @ X4 @ X5 @ X6 )
= $false )
| ( $true
!= ( sK0 @ X4 ) )
| ( ( sK0 @ X7 )
= $false ) ),
inference(binary_proxy_clausification,[],[f157]) ).
thf(f157,plain,
! [X6: a,X7: a > a > $o,X4: a > a > $o,X5: a] :
( ( $true
= ( X4 @ sK2 @ sK1 ) )
| ( ( sK6 @ X4 @ X5 @ X6 )
= $false )
| ( $true
!= ( sK0 @ X4 ) )
| ( ( X7 @ X5 @ X6 )
= $true )
| ( ( ( sK0 @ X7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK7 @ X4 @ Y1 @ Y0 )
=> ( X7 @ Y1 @ Y0 ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f156]) ).
thf(f156,plain,
! [X6: a,X7: a > a > $o,X4: a > a > $o,X5: a] :
( ( $true
!= ( sK0 @ X4 ) )
| ( ( sK6 @ X4 @ X5 @ X6 )
= $false )
| ( $true
= ( X4 @ sK2 @ sK1 ) )
| ( $true
= ( ( ( sK0 @ X7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK7 @ X4 @ Y1 @ Y0 )
=> ( X7 @ Y1 @ Y0 ) ) ) ) )
=> ( X7 @ X5 @ X6 ) ) ) ),
inference(beta_eta_normalization,[],[f155]) ).
thf(f155,plain,
! [X6: a,X7: a > a > $o,X4: a > a > $o,X5: a] :
( ( ( ^ [Y0: a > a > $o] :
( ( ( sK0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK7 @ X4 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ X5 @ X6 ) )
@ X7 )
= $true )
| ( ( sK6 @ X4 @ X5 @ X6 )
= $false )
| ( $true
!= ( sK0 @ X4 ) )
| ( $true
= ( X4 @ sK2 @ sK1 ) ) ),
inference(pi_clausification,[],[f154]) ).
thf(f154,plain,
! [X6: a,X4: a > a > $o,X5: a] :
( ( $true
= ( X4 @ sK2 @ sK1 ) )
| ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK7 @ X4 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ X5 @ X6 ) ) ) )
| ( $true
!= ( sK0 @ X4 ) )
| ( ( sK6 @ X4 @ X5 @ X6 )
= $false ) ),
inference(binary_proxy_clausification,[],[f152]) ).
thf(f152,plain,
! [X6: a,X4: a > a > $o,X5: a] :
( ( $true
!= ( sK0 @ X4 ) )
| ( $true
= ( X4 @ sK2 @ sK1 ) )
| ( ( sK6 @ X4 @ X5 @ X6 )
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK7 @ X4 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ X5 @ X6 ) ) ) ) ),
inference(beta_eta_normalization,[],[f151]) ).
thf(f151,plain,
! [X6: a,X4: a > a > $o,X5: a] :
( ( $true
= ( X4 @ sK2 @ sK1 ) )
| ( ( sK6 @ X4 @ X5 @ X6 )
= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK7 @ X4 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ X5 @ Y0 ) ) )
@ X6 ) )
| ( $true
!= ( sK0 @ X4 ) ) ),
inference(argument_congruence,[],[f105]) ).
thf(f105,plain,
! [X4: a > a > $o,X5: a] :
( ( ( sK6 @ X4 @ X5 )
= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK7 @ X4 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ X5 @ Y0 ) ) ) ) )
| ( $true
!= ( sK0 @ X4 ) )
| ( $true
= ( X4 @ sK2 @ sK1 ) ) ),
inference(beta_eta_normalization,[],[f104]) ).
thf(f104,plain,
! [X4: a > a > $o,X5: a] :
( ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK7 @ X4 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X5 )
= ( sK6 @ X4 @ X5 ) )
| ( $true
!= ( sK0 @ X4 ) )
| ( $true
= ( X4 @ sK2 @ sK1 ) ) ),
inference(argument_congruence,[],[f18]) ).
thf(f18,plain,
! [X4: a > a > $o] :
( ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK7 @ X4 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
= ( sK6 @ X4 ) )
| ( $true
!= ( sK0 @ X4 ) )
| ( $true
= ( X4 @ sK2 @ sK1 ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f269,plain,
! [X2: a,X3: a > a > $o,X0: a > a > $o,X1: a] :
( ( $true
!= ( X3 @ ( sK12 @ sK8 @ X0 ) @ ( sK11 @ sK8 @ X0 ) ) )
| ( ( sK3 @ X3 )
!= $true )
| ( ( sK6 @ X0 @ X1 @ X2 )
= $false )
| ( $true
= ( sK8 @ X1 @ X2 ) )
| ( $true
!= ( sK0 @ X0 ) )
| ( $true
= ( X0 @ sK2 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f268]) ).
thf(f268,plain,
! [X2: a,X3: a > a > $o,X0: a > a > $o,X1: a] :
( ( ( sK3 @ X3 )
!= $true )
| ( $true
= ( X0 @ sK2 @ sK1 ) )
| ( $true
!= ( X3 @ ( sK12 @ sK8 @ X0 ) @ ( sK11 @ sK8 @ X0 ) ) )
| ( $true
= ( sK8 @ X1 @ X2 ) )
| ( $true = $false )
| ( $true
!= ( sK0 @ X0 ) )
| ( ( sK6 @ X0 @ X1 @ X2 )
= $false ) ),
inference(forward_demodulation,[],[f254,f16]) ).
thf(f254,plain,
! [X2: a,X3: a > a > $o,X0: a > a > $o,X1: a] :
( ( ( sK3 @ X3 )
!= $true )
| ( ( sK6 @ X0 @ X1 @ X2 )
= $false )
| ( ( sK0 @ sK8 )
= $false )
| ( $true
= ( sK8 @ X1 @ X2 ) )
| ( $true
= ( X0 @ sK2 @ sK1 ) )
| ( $true
!= ( sK0 @ X0 ) )
| ( $true
!= ( X3 @ ( sK12 @ sK8 @ X0 ) @ ( sK11 @ sK8 @ X0 ) ) ) ),
inference(trivial_inequality_removal,[],[f236]) ).
thf(f236,plain,
! [X2: a,X3: a > a > $o,X0: a > a > $o,X1: a] :
( ( ( sK6 @ X0 @ X1 @ X2 )
= $false )
| ( $true
!= ( sK0 @ X0 ) )
| ( $true
!= ( X3 @ ( sK12 @ sK8 @ X0 ) @ ( sK11 @ sK8 @ X0 ) ) )
| ( $true
= ( sK8 @ X1 @ X2 ) )
| ( $true
= ( X0 @ sK2 @ sK1 ) )
| ( ( sK0 @ sK8 )
= $false )
| ( ( sK3 @ X3 )
!= $true )
| ( $true = $false ) ),
inference(superposition,[],[f163,f15]) ).
thf(f15,plain,
! [X10: a,X11: a,X12: a > a > $o] :
( ( $true
= ( sK8 @ X10 @ X11 ) )
| ( $true
!= ( X12 @ X10 @ X11 ) )
| ( $true
!= ( sK3 @ X12 ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f163,plain,
! [X6: a,X7: a > a > $o,X4: a > a > $o,X5: a] :
( ( ( X7 @ ( sK12 @ X7 @ X4 ) @ ( sK11 @ X7 @ X4 ) )
= $false )
| ( $true
= ( X4 @ sK2 @ sK1 ) )
| ( ( X7 @ X5 @ X6 )
= $true )
| ( ( sK0 @ X7 )
= $false )
| ( $true
!= ( sK0 @ X4 ) )
| ( ( sK6 @ X4 @ X5 @ X6 )
= $false ) ),
inference(binary_proxy_clausification,[],[f162]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEV123^5 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.11 % Command : run_vampire %s %d THM
% 0.10/0.31 % Computer : n028.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Fri Jun 21 19:31:53 EDT 2024
% 0.16/0.31 % CPUTime :
% 0.16/0.33 This is a TH0_THM_EQU_NAR problem
% 0.16/0.33 Running higher-order theorem proving
% 0.16/0.33 Running /export/starexec/sandbox/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox/benchmark/theBenchmark.p -m 16384 -t 300
% 0.19/0.35 % (12013)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.19/0.35 % (12014)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.19/0.35 % (12016)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.35 % (12015)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.35 % (12017)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.19/0.35 % (12018)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.19/0.36 % (12012)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.19/0.36 % (12015)Instruction limit reached!
% 0.19/0.36 % (12015)------------------------------
% 0.19/0.36 % (12015)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.36 % (12016)Instruction limit reached!
% 0.19/0.36 % (12016)------------------------------
% 0.19/0.36 % (12016)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.36 % (12015)Termination reason: Unknown
% 0.19/0.36 % (12015)Termination phase: Preprocessing 3
% 0.19/0.36
% 0.19/0.36 % (12015)Memory used [KB]: 1023
% 0.19/0.36 % (12015)Time elapsed: 0.003 s
% 0.19/0.36 % (12015)Instructions burned: 2 (million)
% 0.19/0.36 % (12015)------------------------------
% 0.19/0.36 % (12015)------------------------------
% 0.19/0.36 % (12016)Termination reason: Unknown
% 0.19/0.36 % (12016)Termination phase: Saturation
% 0.19/0.36
% 0.19/0.36 % (12016)Memory used [KB]: 1023
% 0.19/0.36 % (12016)Time elapsed: 0.004 s
% 0.19/0.36 % (12016)Instructions burned: 3 (million)
% 0.19/0.36 % (12016)------------------------------
% 0.19/0.36 % (12016)------------------------------
% 0.19/0.36 % (12013)Instruction limit reached!
% 0.19/0.36 % (12013)------------------------------
% 0.19/0.36 % (12013)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.36 % (12013)Termination reason: Unknown
% 0.19/0.36 % (12013)Termination phase: Saturation
% 0.19/0.36
% 0.19/0.36 % (12013)Memory used [KB]: 5500
% 0.19/0.36 % (12013)Time elapsed: 0.005 s
% 0.19/0.36 % (12013)Instructions burned: 4 (million)
% 0.19/0.36 % (12013)------------------------------
% 0.19/0.36 % (12013)------------------------------
% 0.19/0.37 % (12018)Instruction limit reached!
% 0.19/0.37 % (12018)------------------------------
% 0.19/0.37 % (12018)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.37 % (12018)Termination reason: Unknown
% 0.19/0.37 % (12018)Termination phase: Saturation
% 0.19/0.37
% 0.19/0.37 % (12018)Memory used [KB]: 5628
% 0.19/0.37 % (12018)Time elapsed: 0.015 s
% 0.19/0.37 % (12018)Instructions burned: 18 (million)
% 0.19/0.37 % (12018)------------------------------
% 0.19/0.37 % (12018)------------------------------
% 0.19/0.37 % (12019)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.37 % (12020)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.19/0.37 % (12014)Instruction limit reached!
% 0.19/0.37 % (12014)------------------------------
% 0.19/0.37 % (12014)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.37 % (12014)Termination reason: Unknown
% 0.19/0.37 % (12014)Termination phase: Saturation
% 0.19/0.37
% 0.19/0.37 % (12014)Memory used [KB]: 5756
% 0.19/0.37 % (12014)Time elapsed: 0.021 s
% 0.19/0.37 % (12014)Instructions burned: 27 (million)
% 0.19/0.37 % (12014)------------------------------
% 0.19/0.37 % (12014)------------------------------
% 0.19/0.37 % (12019)Instruction limit reached!
% 0.19/0.37 % (12019)------------------------------
% 0.19/0.37 % (12019)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.37 % (12019)Termination reason: Unknown
% 0.19/0.37 % (12019)Termination phase: Saturation
% 0.19/0.37
% 0.19/0.37 % (12019)Memory used [KB]: 1023
% 0.19/0.37 % (12019)Time elapsed: 0.004 s
% 0.19/0.37 % (12019)Instructions burned: 3 (million)
% 0.19/0.37 % (12019)------------------------------
% 0.19/0.37 % (12019)------------------------------
% 0.19/0.37 % (12021)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.19/0.38 % (12022)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.38 % (12022)Instruction limit reached!
% 0.19/0.38 % (12022)------------------------------
% 0.19/0.38 % (12022)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.38 % (12022)Termination reason: Unknown
% 0.19/0.38 % (12022)Termination phase: Saturation
% 0.19/0.38
% 0.19/0.38 % (12022)Memory used [KB]: 1023
% 0.19/0.38 % (12022)Time elapsed: 0.004 s
% 0.19/0.38 % (12022)Instructions burned: 3 (million)
% 0.19/0.38 % (12022)------------------------------
% 0.19/0.38 % (12022)------------------------------
% 0.19/0.39 % (12021)Instruction limit reached!
% 0.19/0.39 % (12021)------------------------------
% 0.19/0.39 % (12021)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.39 % (12021)Termination reason: Unknown
% 0.19/0.39 % (12021)Termination phase: Saturation
% 0.19/0.39
% 0.19/0.39 % (12021)Memory used [KB]: 5756
% 0.19/0.39 % (12021)Time elapsed: 0.014 s
% 0.19/0.39 % (12021)Instructions burned: 16 (million)
% 0.19/0.39 % (12021)------------------------------
% 0.19/0.39 % (12021)------------------------------
% 0.19/0.39 % (12023)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi)
% 0.19/0.39 % (12024)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.39 % (12020)Instruction limit reached!
% 0.19/0.39 % (12020)------------------------------
% 0.19/0.39 % (12020)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.39 % (12020)Termination reason: Unknown
% 0.19/0.39 % (12020)Termination phase: Saturation
% 0.19/0.39
% 0.19/0.39 % (12020)Memory used [KB]: 6140
% 0.19/0.39 % (12020)Time elapsed: 0.023 s
% 0.19/0.39 % (12020)Instructions burned: 38 (million)
% 0.19/0.39 % (12020)------------------------------
% 0.19/0.39 % (12020)------------------------------
% 0.19/0.40 % (12024)Instruction limit reached!
% 0.19/0.40 % (12024)------------------------------
% 0.19/0.40 % (12024)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.40 % (12024)Termination reason: Unknown
% 0.19/0.40 % (12024)Termination phase: Saturation
% 0.19/0.40
% 0.19/0.40 % (12024)Memory used [KB]: 1151
% 0.19/0.40 % (12024)Time elapsed: 0.007 s
% 0.19/0.40 % (12024)Instructions burned: 8 (million)
% 0.19/0.40 % (12024)------------------------------
% 0.19/0.40 % (12024)------------------------------
% 0.19/0.40 % (12025)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.19/0.40 % (12026)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.40 % (12026)Instruction limit reached!
% 0.19/0.40 % (12026)------------------------------
% 0.19/0.40 % (12026)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.40 % (12026)Termination reason: Unknown
% 0.19/0.40 % (12026)Termination phase: Property scanning
% 0.19/0.40
% 0.19/0.40 % (12026)Memory used [KB]: 1023
% 0.19/0.40 % (12026)Time elapsed: 0.005 s
% 0.19/0.40 % (12026)Instructions burned: 4 (million)
% 0.19/0.40 % (12026)------------------------------
% 0.19/0.40 % (12026)------------------------------
% 0.19/0.41 % (12027)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.41 % (12027)Instruction limit reached!
% 0.19/0.41 % (12027)------------------------------
% 0.19/0.41 % (12027)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.41 % (12027)Termination reason: Unknown
% 0.19/0.41 % (12027)Termination phase: Property scanning
% 0.19/0.41
% 0.19/0.41 % (12027)Memory used [KB]: 1023
% 0.19/0.41 % (12027)Time elapsed: 0.004 s
% 0.19/0.41 % (12027)Instructions burned: 3 (million)
% 0.19/0.41 % (12027)------------------------------
% 0.19/0.41 % (12027)------------------------------
% 0.19/0.41 % (12025)Instruction limit reached!
% 0.19/0.41 % (12025)------------------------------
% 0.19/0.41 % (12025)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.41 % (12025)Termination reason: Unknown
% 0.19/0.41 % (12025)Termination phase: Saturation
% 0.19/0.41
% 0.19/0.41 % (12025)Memory used [KB]: 5628
% 0.19/0.41 % (12025)Time elapsed: 0.013 s
% 0.19/0.41 % (12028)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.41 % (12025)Instructions burned: 16 (million)
% 0.19/0.41 % (12025)------------------------------
% 0.19/0.41 % (12025)------------------------------
% 0.19/0.42 % (12028)Instruction limit reached!
% 0.19/0.42 % (12028)------------------------------
% 0.19/0.42 % (12028)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.42 % (12028)Termination reason: Unknown
% 0.19/0.42 % (12028)Termination phase: Saturation
% 0.19/0.42
% 0.19/0.42 % (12028)Memory used [KB]: 5500
% 0.19/0.42 % (12028)Time elapsed: 0.008 s
% 0.19/0.42 % (12028)Instructions burned: 8 (million)
% 0.19/0.42 % (12028)------------------------------
% 0.19/0.42 % (12028)------------------------------
% 0.19/0.42 % (12029)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.42 % (12029)Instruction limit reached!
% 0.19/0.42 % (12029)------------------------------
% 0.19/0.42 % (12029)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.42 % (12029)Termination reason: Unknown
% 0.19/0.42 % (12029)Termination phase: Saturation
% 0.19/0.42
% 0.19/0.42 % (12029)Memory used [KB]: 5500
% 0.19/0.42 % (12029)Time elapsed: 0.004 s
% 0.19/0.42 % (12029)Instructions burned: 3 (million)
% 0.19/0.42 % (12029)------------------------------
% 0.19/0.42 % (12029)------------------------------
% 0.19/0.42 % (12017)First to succeed.
% 0.19/0.43 % (12031)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.19/0.43 % (12030)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.19/0.43 % (12017)Refutation found. Thanks to Tanya!
% 0.19/0.43 % SZS status Theorem for theBenchmark
% 0.19/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.43 % (12017)------------------------------
% 0.19/0.43 % (12017)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.43 % (12017)Termination reason: Refutation
% 0.19/0.43
% 0.19/0.43 % (12017)Memory used [KB]: 6012
% 0.19/0.43 % (12017)Time elapsed: 0.076 s
% 0.19/0.43 % (12017)Instructions burned: 108 (million)
% 0.19/0.43 % (12017)------------------------------
% 0.19/0.43 % (12017)------------------------------
% 0.19/0.43 % (12011)Success in time 0.094 s
%------------------------------------------------------------------------------