%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL867^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n015.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 08:15:12 AM UTC 2026
% Result : Theorem 0.95s 0.44s
% Output : Refutation 0.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 18
% Syntax : Number of formulae : 256 ( 28 unt; 0 typ; 14 def)
% Number of atoms : 2318 ( 374 equ; 0 cnn)
% Maximal formula atoms : 8 ( 9 avg)
% Number of connectives : 2459 ( 278 ~; 493 |; 107 &;1335 @)
% ( 18 <=>; 102 =>; 0 <=; 1 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 62 ( 62 >; 0 *; 0 +; 0 <<)
% Number of symbols : 74 ( 70 usr; 27 con; 0-4 aty)
% ( 125 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 296 ( 0 sgn 115 !; 3 ?; 296 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
meq_ind: mu > mu > $i > $o ).
thf(func_def_1,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mtrue: $i > $o ).
thf(func_def_15,type,
mfalse: $i > $o ).
thf(func_def_16,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_29,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_30,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_31,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_32,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_35,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_36,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
vNOT: $o > $o ).
thf(func_def_38,type,
vOR: $o > $o > $o ).
thf(func_def_39,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_42,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
vIMP: $o > $o > $o ).
thf(func_def_44,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_45,type,
vAND: $o > $o > $o ).
thf(func_def_46,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
sK0: $i > $i > $o ).
thf(f19,axiom,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',msymmetric) ).
thf(f21,axiom,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mtransitive) ).
thf(f22,axiom,
( meuclidean
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X1 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',meuclidean) ).
thf(f32,conjecture,
! [X0: $i > $i > $o] :
( ( ( meuclidean @ X0 )
& ( msymmetric @ X0 ) )
<=> ( ( msymmetric @ X0 )
& ( mtransitive @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(f33,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( ( ( meuclidean @ X0 )
& ( msymmetric @ X0 ) )
<=> ( ( msymmetric @ X0 )
& ( mtransitive @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
thf(f59,plain,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f19]) ).
thf(f60,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f59]) ).
thf(f63,plain,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
inference(rectify,[],[f21]) ).
thf(f64,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f63]) ).
thf(f65,plain,
( meuclidean
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X1 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f22]) ).
thf(f66,plain,
( meuclidean
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f65]) ).
thf(f85,plain,
~ ! [X0: $i > $i > $o] :
( ( ( meuclidean @ X0 )
& ( msymmetric @ X0 ) )
<=> ( ( msymmetric @ X0 )
& ( mtransitive @ X0 ) ) ),
inference(rectify,[],[f33]) ).
thf(f86,plain,
~ ! [X0: $i > $i > $o] :
( ( ( ( meuclidean @ X0 )
= $true )
& ( ( msymmetric @ X0 )
= $true ) )
<=> ( ( ( msymmetric @ X0 )
= $true )
& ( ( mtransitive @ X0 )
= $true ) ) ),
inference(fool_elimination,[],[f85]) ).
thf(f87,plain,
? [X0: $i > $i > $o] :
( ( ( ( meuclidean @ X0 )
= $true )
& ( ( msymmetric @ X0 )
= $true ) )
<~> ( ( ( msymmetric @ X0 )
= $true )
& ( ( mtransitive @ X0 )
= $true ) ) ),
inference(ennf_transformation,[],[f86]) ).
thf(f88,plain,
? [X0: $i > $i > $o] :
( ( ( ( msymmetric @ X0 )
!= $true )
| ( ( mtransitive @ X0 )
!= $true )
| ( ( meuclidean @ X0 )
!= $true )
| ( ( msymmetric @ X0 )
!= $true ) )
& ( ( ( ( msymmetric @ X0 )
= $true )
& ( ( mtransitive @ X0 )
= $true ) )
| ( ( ( meuclidean @ X0 )
= $true )
& ( ( msymmetric @ X0 )
= $true ) ) ) ),
inference(nnf_transformation,[],[f87]) ).
thf(f89,plain,
? [X0: $i > $i > $o] :
( ( ( ( msymmetric @ X0 )
!= $true )
| ( ( mtransitive @ X0 )
!= $true )
| ( ( meuclidean @ X0 )
!= $true )
| ( ( msymmetric @ X0 )
!= $true ) )
& ( ( ( ( msymmetric @ X0 )
= $true )
& ( ( mtransitive @ X0 )
= $true ) )
| ( ( ( meuclidean @ X0 )
= $true )
& ( ( msymmetric @ X0 )
= $true ) ) ) ),
inference(flattening,[],[f88]) ).
thf(f90,plain,
( ( ( $true
!= ( msymmetric @ sK0 ) )
| ( $true
!= ( mtransitive @ sK0 ) )
| ( $true
!= ( meuclidean @ sK0 ) )
| ( $true
!= ( msymmetric @ sK0 ) ) )
& ( ( ( $true
= ( msymmetric @ sK0 ) )
& ( $true
= ( mtransitive @ sK0 ) ) )
| ( ( $true
= ( meuclidean @ sK0 ) )
& ( $true
= ( msymmetric @ sK0 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f89]) ).
thf(f109,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f60]) ).
thf(f111,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f64]) ).
thf(f112,plain,
( meuclidean
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f66]) ).
thf(f123,plain,
( ( $true
= ( mtransitive @ sK0 ) )
| ( $true
= ( meuclidean @ sK0 ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f124,plain,
( ( $true
= ( msymmetric @ sK0 ) )
| ( $true
= ( msymmetric @ sK0 ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f126,plain,
( ( $true
!= ( msymmetric @ sK0 ) )
| ( $true
!= ( mtransitive @ sK0 ) )
| ( $true
!= ( meuclidean @ sK0 ) )
| ( $true
!= ( msymmetric @ sK0 ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f138,plain,
( ( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
@ sK0 ) )
| ( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
@ sK0 ) )
| ( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
@ sK0 ) )
| ( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
@ sK0 ) ) ),
inference(definition_unfolding,[],[f126,f109,f111,f112,f109]) ).
thf(f140,plain,
( ( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
@ sK0 ) )
| ( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
@ sK0 ) ) ),
inference(definition_unfolding,[],[f124,f109,f109]) ).
thf(f141,plain,
( ( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
@ sK0 ) )
| ( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
@ sK0 ) ) ),
inference(definition_unfolding,[],[f123,f111,f112]) ).
thf(f155,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y2 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f141]) ).
thf(f156,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y2 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f155]) ).
thf(f157,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y2 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f156]) ).
thf(f158,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ X1 ) )
=> ( sK0 @ Y1 @ X1 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ X2 ) )
=> ( sK0 @ Y0 @ X2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f157]) ).
thf(f159,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ X1 ) )
=> ( sK0 @ Y1 @ X1 ) ) )
@ X3 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ X2 ) )
=> ( sK0 @ Y0 @ X2 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f158]) ).
thf(f160,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ X1 ) )
=> ( sK0 @ Y1 @ X1 ) ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ X2 ) )
=> ( sK0 @ Y0 @ X2 ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f159]) ).
thf(f161,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X3 )
& ( sK0 @ X3 @ X1 ) )
=> ( sK0 @ Y0 @ X1 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X4 )
& ( sK0 @ Y0 @ X2 ) )
=> ( sK0 @ X4 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f160]) ).
thf(f162,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X3 )
& ( sK0 @ X3 @ X1 ) )
=> ( sK0 @ Y0 @ X1 ) )
@ X5 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X4 )
& ( sK0 @ Y0 @ X2 ) )
=> ( sK0 @ X4 @ X2 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f161]) ).
thf(f163,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X3 )
& ( sK0 @ X3 @ X1 ) )
=> ( sK0 @ Y0 @ X1 ) )
@ X5 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X4 )
& ( sK0 @ Y0 @ X2 ) )
=> ( sK0 @ X4 @ X2 ) )
@ X6 ) ) ),
inference(pi_proxy_clausification,[],[f162]) ).
thf(f164,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $true
= ( ( ( sK0 @ X5 @ X3 )
& ( sK0 @ X3 @ X1 ) )
=> ( sK0 @ X5 @ X1 ) ) )
| ( $true
= ( ( ( sK0 @ X6 @ X4 )
& ( sK0 @ X6 @ X2 ) )
=> ( sK0 @ X4 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f163]) ).
thf(f165,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $false
= ( ( sK0 @ X5 @ X3 )
& ( sK0 @ X3 @ X1 ) ) )
| ( $true
= ( ( ( sK0 @ X6 @ X4 )
& ( sK0 @ X6 @ X2 ) )
=> ( sK0 @ X4 @ X2 ) ) )
| ( $true
= ( sK0 @ X5 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f164]) ).
thf(f166,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $true
= ( ( ( sK0 @ X6 @ X4 )
& ( sK0 @ X6 @ X2 ) )
=> ( sK0 @ X4 @ X2 ) ) )
| ( $true
= ( sK0 @ X5 @ X1 ) )
| ( $false
= ( sK0 @ X5 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f165]) ).
thf(f167,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $false
= ( ( sK0 @ X6 @ X4 )
& ( sK0 @ X6 @ X2 ) ) )
| ( $true
= ( sK0 @ X5 @ X1 ) )
| ( $false
= ( sK0 @ X5 @ X3 ) )
| ( $true
= ( sK0 @ X4 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f166]) ).
thf(f168,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $false
= ( sK0 @ X6 @ X2 ) )
| ( $true
= ( sK0 @ X5 @ X1 ) )
| ( $false
= ( sK0 @ X5 @ X3 ) )
| ( $true
= ( sK0 @ X4 @ X2 ) )
| ( $false
= ( sK0 @ X6 @ X4 ) ) ),
inference(and_proxy_clausification,[],[f167]) ).
thf(f169,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
@ sK0 ) ),
inference(duplicate_literal_removal,[],[f140]) ).
thf(f170,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f169]) ).
thf(f171,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f170]) ).
thf(f172,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 @ X1 )
=> ( sK0 @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f171]) ).
thf(f173,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ X1 )
=> ( sK0 @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f172]) ).
thf(f174,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( sK0 @ X2 @ X1 )
=> ( sK0 @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f173]) ).
thf(f175,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ X2 @ X1 ) )
| ( $true
= ( sK0 @ X1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f174]) ).
thf(f188,plain,
( ( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
@ sK0 ) )
| ( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
@ sK0 ) )
| ( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
@ sK0 ) ) ),
inference(duplicate_literal_removal,[],[f138]) ).
thf(f189,plain,
( ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) ) ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) ) ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y2 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f188]) ).
thf(f190,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ sK1 ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) ) ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y2 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f189]) ).
thf(f191,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) )
@ sK2 ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y2 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f190]) ).
thf(f192,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y2 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) )
@ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f191]) ).
thf(f193,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK1 )
=> ( sK0 @ sK1 @ Y0 ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ sK2 ) )
=> ( sK0 @ Y1 @ sK2 ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ sK3 ) )
=> ( sK0 @ Y0 @ sK3 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f192]) ).
thf(f194,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK1 )
=> ( sK0 @ sK1 @ Y0 ) )
@ sK4 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ sK2 ) )
=> ( sK0 @ Y1 @ sK2 ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ sK3 ) )
=> ( sK0 @ Y0 @ sK3 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f193]) ).
thf(f195,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK1 )
=> ( sK0 @ sK1 @ Y0 ) )
@ sK4 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ sK2 ) )
=> ( sK0 @ Y1 @ sK2 ) ) )
@ sK5 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ sK3 ) )
=> ( sK0 @ Y0 @ sK3 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f194]) ).
thf(f196,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK1 )
=> ( sK0 @ sK1 @ Y0 ) )
@ sK4 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ sK2 ) )
=> ( sK0 @ Y1 @ sK2 ) ) )
@ sK5 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ sK3 ) )
=> ( sK0 @ Y0 @ sK3 ) ) )
@ sK6 ) ) ),
inference(sigma_proxy_clausification,[],[f195]) ).
thf(f197,plain,
( ( $false
= ( ( sK0 @ sK4 @ sK1 )
=> ( sK0 @ sK1 @ sK4 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK5 )
& ( sK0 @ sK5 @ sK2 ) )
=> ( sK0 @ Y0 @ sK2 ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK6 )
& ( sK0 @ Y0 @ sK3 ) )
=> ( sK0 @ sK6 @ sK3 ) ) ) ) ),
inference(beta-eta_normalization,[],[f196]) ).
thf(f198,plain,
( ( $false
= ( sK0 @ sK1 @ sK4 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK5 )
& ( sK0 @ sK5 @ sK2 ) )
=> ( sK0 @ Y0 @ sK2 ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK6 )
& ( sK0 @ Y0 @ sK3 ) )
=> ( sK0 @ sK6 @ sK3 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f197]) ).
thf(f199,plain,
( ( $true
= ( sK0 @ sK4 @ sK1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK5 )
& ( sK0 @ sK5 @ sK2 ) )
=> ( sK0 @ Y0 @ sK2 ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK6 )
& ( sK0 @ Y0 @ sK3 ) )
=> ( sK0 @ sK6 @ sK3 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f197]) ).
thf(f200,plain,
( ( $true
= ( sK0 @ sK4 @ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK5 )
& ( sK0 @ sK5 @ sK2 ) )
=> ( sK0 @ Y0 @ sK2 ) )
@ sK7 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK6 )
& ( sK0 @ Y0 @ sK3 ) )
=> ( sK0 @ sK6 @ sK3 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f199]) ).
thf(f201,plain,
( ( $true
= ( sK0 @ sK4 @ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK5 )
& ( sK0 @ sK5 @ sK2 ) )
=> ( sK0 @ Y0 @ sK2 ) )
@ sK7 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK6 )
& ( sK0 @ Y0 @ sK3 ) )
=> ( sK0 @ sK6 @ sK3 ) )
@ sK8 ) ) ),
inference(sigma_proxy_clausification,[],[f200]) ).
thf(f202,plain,
( ( $true
= ( sK0 @ sK4 @ sK1 ) )
| ( $false
= ( ( ( sK0 @ sK7 @ sK5 )
& ( sK0 @ sK5 @ sK2 ) )
=> ( sK0 @ sK7 @ sK2 ) ) )
| ( $false
= ( ( ( sK0 @ sK8 @ sK6 )
& ( sK0 @ sK8 @ sK3 ) )
=> ( sK0 @ sK6 @ sK3 ) ) ) ),
inference(beta-eta_normalization,[],[f201]) ).
thf(f203,plain,
( ( $true
= ( sK0 @ sK4 @ sK1 ) )
| ( $false
= ( sK0 @ sK7 @ sK2 ) )
| ( $false
= ( ( ( sK0 @ sK8 @ sK6 )
& ( sK0 @ sK8 @ sK3 ) )
=> ( sK0 @ sK6 @ sK3 ) ) ) ),
inference(imp_proxy_clausification,[],[f202]) ).
thf(f204,plain,
( ( $true
= ( sK0 @ sK4 @ sK1 ) )
| ( $true
= ( ( sK0 @ sK7 @ sK5 )
& ( sK0 @ sK5 @ sK2 ) ) )
| ( $false
= ( ( ( sK0 @ sK8 @ sK6 )
& ( sK0 @ sK8 @ sK3 ) )
=> ( sK0 @ sK6 @ sK3 ) ) ) ),
inference(imp_proxy_clausification,[],[f202]) ).
thf(f205,plain,
( ( $true
= ( sK0 @ sK4 @ sK1 ) )
| ( $true
= ( sK0 @ sK5 @ sK2 ) )
| ( $false
= ( ( ( sK0 @ sK8 @ sK6 )
& ( sK0 @ sK8 @ sK3 ) )
=> ( sK0 @ sK6 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f204]) ).
thf(f206,plain,
( ( $true
= ( sK0 @ sK4 @ sK1 ) )
| ( $true
= ( sK0 @ sK7 @ sK5 ) )
| ( $false
= ( ( ( sK0 @ sK8 @ sK6 )
& ( sK0 @ sK8 @ sK3 ) )
=> ( sK0 @ sK6 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f204]) ).
thf(f207,plain,
( ( $true
= ( sK0 @ sK4 @ sK1 ) )
| ( $true
= ( sK0 @ sK7 @ sK5 ) )
| ( $false
= ( sK0 @ sK6 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f206]) ).
thf(f208,plain,
( ( $true
= ( sK0 @ sK4 @ sK1 ) )
| ( $true
= ( sK0 @ sK7 @ sK5 ) )
| ( $true
= ( ( sK0 @ sK8 @ sK6 )
& ( sK0 @ sK8 @ sK3 ) ) ) ),
inference(imp_proxy_clausification,[],[f206]) ).
thf(f209,plain,
( ( $true
= ( sK0 @ sK4 @ sK1 ) )
| ( $true
= ( sK0 @ sK7 @ sK5 ) )
| ( $true
= ( sK0 @ sK8 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f208]) ).
thf(f210,plain,
( ( $true
= ( sK0 @ sK4 @ sK1 ) )
| ( $true
= ( sK0 @ sK7 @ sK5 ) )
| ( $true
= ( sK0 @ sK8 @ sK6 ) ) ),
inference(and_proxy_clausification,[],[f208]) ).
thf(f211,plain,
( ( $true
= ( sK0 @ sK4 @ sK1 ) )
| ( $true
= ( sK0 @ sK5 @ sK2 ) )
| ( $false
= ( sK0 @ sK6 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f205]) ).
thf(f212,plain,
( ( $true
= ( sK0 @ sK4 @ sK1 ) )
| ( $true
= ( sK0 @ sK5 @ sK2 ) )
| ( $true
= ( ( sK0 @ sK8 @ sK6 )
& ( sK0 @ sK8 @ sK3 ) ) ) ),
inference(imp_proxy_clausification,[],[f205]) ).
thf(f213,plain,
( ( $true
= ( sK0 @ sK4 @ sK1 ) )
| ( $true
= ( sK0 @ sK5 @ sK2 ) )
| ( $true
= ( sK0 @ sK8 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f212]) ).
thf(f214,plain,
( ( $true
= ( sK0 @ sK4 @ sK1 ) )
| ( $true
= ( sK0 @ sK5 @ sK2 ) )
| ( $true
= ( sK0 @ sK8 @ sK6 ) ) ),
inference(and_proxy_clausification,[],[f212]) ).
thf(f215,plain,
( ( $true
= ( sK0 @ sK4 @ sK1 ) )
| ( $false
= ( sK0 @ sK7 @ sK2 ) )
| ( $false
= ( sK0 @ sK6 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f203]) ).
thf(f216,plain,
( ( $true
= ( sK0 @ sK4 @ sK1 ) )
| ( $false
= ( sK0 @ sK7 @ sK2 ) )
| ( $true
= ( ( sK0 @ sK8 @ sK6 )
& ( sK0 @ sK8 @ sK3 ) ) ) ),
inference(imp_proxy_clausification,[],[f203]) ).
thf(f217,plain,
( ( $true
= ( sK0 @ sK4 @ sK1 ) )
| ( $false
= ( sK0 @ sK7 @ sK2 ) )
| ( $true
= ( sK0 @ sK8 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f216]) ).
thf(f218,plain,
( ( $true
= ( sK0 @ sK4 @ sK1 ) )
| ( $false
= ( sK0 @ sK7 @ sK2 ) )
| ( $true
= ( sK0 @ sK8 @ sK6 ) ) ),
inference(and_proxy_clausification,[],[f216]) ).
thf(f219,plain,
( ( $false
= ( sK0 @ sK1 @ sK4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK5 )
& ( sK0 @ sK5 @ sK2 ) )
=> ( sK0 @ Y0 @ sK2 ) )
@ sK9 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK6 )
& ( sK0 @ Y0 @ sK3 ) )
=> ( sK0 @ sK6 @ sK3 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f198]) ).
thf(f220,plain,
( ( $false
= ( sK0 @ sK1 @ sK4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK5 )
& ( sK0 @ sK5 @ sK2 ) )
=> ( sK0 @ Y0 @ sK2 ) )
@ sK9 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK6 )
& ( sK0 @ Y0 @ sK3 ) )
=> ( sK0 @ sK6 @ sK3 ) )
@ sK10 ) ) ),
inference(sigma_proxy_clausification,[],[f219]) ).
thf(f221,plain,
( ( $false
= ( sK0 @ sK1 @ sK4 ) )
| ( $false
= ( ( ( sK0 @ sK9 @ sK5 )
& ( sK0 @ sK5 @ sK2 ) )
=> ( sK0 @ sK9 @ sK2 ) ) )
| ( $false
= ( ( ( sK0 @ sK10 @ sK6 )
& ( sK0 @ sK10 @ sK3 ) )
=> ( sK0 @ sK6 @ sK3 ) ) ) ),
inference(beta-eta_normalization,[],[f220]) ).
thf(f222,plain,
( ( $false
= ( sK0 @ sK1 @ sK4 ) )
| ( $false
= ( sK0 @ sK9 @ sK2 ) )
| ( $false
= ( ( ( sK0 @ sK10 @ sK6 )
& ( sK0 @ sK10 @ sK3 ) )
=> ( sK0 @ sK6 @ sK3 ) ) ) ),
inference(imp_proxy_clausification,[],[f221]) ).
thf(f223,plain,
( ( $false
= ( sK0 @ sK1 @ sK4 ) )
| ( $true
= ( ( sK0 @ sK9 @ sK5 )
& ( sK0 @ sK5 @ sK2 ) ) )
| ( $false
= ( ( ( sK0 @ sK10 @ sK6 )
& ( sK0 @ sK10 @ sK3 ) )
=> ( sK0 @ sK6 @ sK3 ) ) ) ),
inference(imp_proxy_clausification,[],[f221]) ).
thf(f224,plain,
( ( $false
= ( sK0 @ sK1 @ sK4 ) )
| ( $true
= ( sK0 @ sK5 @ sK2 ) )
| ( $false
= ( ( ( sK0 @ sK10 @ sK6 )
& ( sK0 @ sK10 @ sK3 ) )
=> ( sK0 @ sK6 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f223]) ).
thf(f225,plain,
( ( $false
= ( sK0 @ sK1 @ sK4 ) )
| ( $true
= ( sK0 @ sK9 @ sK5 ) )
| ( $false
= ( ( ( sK0 @ sK10 @ sK6 )
& ( sK0 @ sK10 @ sK3 ) )
=> ( sK0 @ sK6 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f223]) ).
thf(f226,plain,
( ( $false
= ( sK0 @ sK1 @ sK4 ) )
| ( $true
= ( sK0 @ sK9 @ sK5 ) )
| ( $false
= ( sK0 @ sK6 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f225]) ).
thf(f227,plain,
( ( $false
= ( sK0 @ sK1 @ sK4 ) )
| ( $true
= ( sK0 @ sK9 @ sK5 ) )
| ( $true
= ( ( sK0 @ sK10 @ sK6 )
& ( sK0 @ sK10 @ sK3 ) ) ) ),
inference(imp_proxy_clausification,[],[f225]) ).
thf(f228,plain,
( ( $false
= ( sK0 @ sK1 @ sK4 ) )
| ( $true
= ( sK0 @ sK9 @ sK5 ) )
| ( $true
= ( sK0 @ sK10 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f227]) ).
thf(f229,plain,
( ( $false
= ( sK0 @ sK1 @ sK4 ) )
| ( $true
= ( sK0 @ sK9 @ sK5 ) )
| ( $true
= ( sK0 @ sK10 @ sK6 ) ) ),
inference(and_proxy_clausification,[],[f227]) ).
thf(f230,plain,
( ( $false
= ( sK0 @ sK1 @ sK4 ) )
| ( $true
= ( sK0 @ sK5 @ sK2 ) )
| ( $false
= ( sK0 @ sK6 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f224]) ).
thf(f231,plain,
( ( $false
= ( sK0 @ sK1 @ sK4 ) )
| ( $true
= ( sK0 @ sK5 @ sK2 ) )
| ( $true
= ( ( sK0 @ sK10 @ sK6 )
& ( sK0 @ sK10 @ sK3 ) ) ) ),
inference(imp_proxy_clausification,[],[f224]) ).
thf(f232,plain,
( ( $false
= ( sK0 @ sK1 @ sK4 ) )
| ( $true
= ( sK0 @ sK5 @ sK2 ) )
| ( $true
= ( sK0 @ sK10 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f231]) ).
thf(f233,plain,
( ( $false
= ( sK0 @ sK1 @ sK4 ) )
| ( $true
= ( sK0 @ sK5 @ sK2 ) )
| ( $true
= ( sK0 @ sK10 @ sK6 ) ) ),
inference(and_proxy_clausification,[],[f231]) ).
thf(f234,plain,
( ( $false
= ( sK0 @ sK1 @ sK4 ) )
| ( $false
= ( sK0 @ sK9 @ sK2 ) )
| ( $false
= ( sK0 @ sK6 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f222]) ).
thf(f235,plain,
( ( $false
= ( sK0 @ sK1 @ sK4 ) )
| ( $false
= ( sK0 @ sK9 @ sK2 ) )
| ( $true
= ( ( sK0 @ sK10 @ sK6 )
& ( sK0 @ sK10 @ sK3 ) ) ) ),
inference(imp_proxy_clausification,[],[f222]) ).
thf(f236,plain,
( ( $false
= ( sK0 @ sK1 @ sK4 ) )
| ( $false
= ( sK0 @ sK9 @ sK2 ) )
| ( $true
= ( sK0 @ sK10 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f235]) ).
thf(f237,plain,
( ( $false
= ( sK0 @ sK1 @ sK4 ) )
| ( $false
= ( sK0 @ sK9 @ sK2 ) )
| ( $true
= ( sK0 @ sK10 @ sK6 ) ) ),
inference(and_proxy_clausification,[],[f235]) ).
thf(f242,definition,
( spl11_2
<=> ! [X5: $i,X1: $i,X3: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $false
= ( sK0 @ X5 @ X3 ) )
| ( $true
= ( sK0 @ X5 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl11_2])],[avatar_definition]) ).
thf(f243,plain,
( ! [X3: $i,X1: $i,X5: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $false
= ( sK0 @ X5 @ X3 ) )
| ( $true
= ( sK0 @ X5 @ X1 ) ) )
| ~ spl11_2 ),
inference(avatar_component_clause,[],[f242]) ).
thf(f246,definition,
( spl11_3
<=> ! [X6: $i,X2: $i,X4: $i] :
( ( $false
= ( sK0 @ X6 @ X2 ) )
| ( $false
= ( sK0 @ X6 @ X4 ) )
| ( $true
= ( sK0 @ X4 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl11_3])],[avatar_definition]) ).
thf(f247,plain,
( ! [X2: $i,X6: $i,X4: $i] :
( ( $false
= ( sK0 @ X6 @ X2 ) )
| ( $false
= ( sK0 @ X6 @ X4 ) )
| ( $true
= ( sK0 @ X4 @ X2 ) ) )
| ~ spl11_3 ),
inference(avatar_component_clause,[],[f246]) ).
thf(f248,plain,
( spl11_3
| spl11_2 ),
inference(avatar_split_clause,[],[f168,f242,f246]) ).
thf(f251,definition,
( spl11_4
<=> ( $true
= ( sK0 @ sK8 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_4])],[avatar_definition]) ).
thf(f253,plain,
( ( $true
= ( sK0 @ sK8 @ sK6 ) )
| ~ spl11_4 ),
inference(avatar_component_clause,[],[f251]) ).
thf(f255,definition,
( spl11_5
<=> ( $true
= ( sK0 @ sK7 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_5])],[avatar_definition]) ).
thf(f257,plain,
( ( $true
= ( sK0 @ sK7 @ sK5 ) )
| ~ spl11_5 ),
inference(avatar_component_clause,[],[f255]) ).
thf(f259,definition,
( spl11_6
<=> ( $true
= ( sK0 @ sK4 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_6])],[avatar_definition]) ).
thf(f261,plain,
( ( $true
= ( sK0 @ sK4 @ sK1 ) )
| ~ spl11_6 ),
inference(avatar_component_clause,[],[f259]) ).
thf(f262,plain,
( spl11_4
| spl11_5
| spl11_6 ),
inference(avatar_split_clause,[],[f210,f259,f255,f251]) ).
thf(f264,definition,
( spl11_7
<=> ( $true
= ( sK0 @ sK8 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_7])],[avatar_definition]) ).
thf(f266,plain,
( ( $true
= ( sK0 @ sK8 @ sK3 ) )
| ~ spl11_7 ),
inference(avatar_component_clause,[],[f264]) ).
thf(f267,plain,
( spl11_7
| spl11_5
| spl11_6 ),
inference(avatar_split_clause,[],[f209,f259,f255,f264]) ).
thf(f269,definition,
( spl11_8
<=> ( $false
= ( sK0 @ sK6 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_8])],[avatar_definition]) ).
thf(f271,plain,
( ( $false
= ( sK0 @ sK6 @ sK3 ) )
| ~ spl11_8 ),
inference(avatar_component_clause,[],[f269]) ).
thf(f272,plain,
( spl11_8
| spl11_5
| spl11_6 ),
inference(avatar_split_clause,[],[f207,f259,f255,f269]) ).
thf(f274,definition,
( spl11_9
<=> ( $true
= ( sK0 @ sK5 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_9])],[avatar_definition]) ).
thf(f276,plain,
( ( $true
= ( sK0 @ sK5 @ sK2 ) )
| ~ spl11_9 ),
inference(avatar_component_clause,[],[f274]) ).
thf(f277,plain,
( spl11_4
| spl11_9
| spl11_6 ),
inference(avatar_split_clause,[],[f214,f259,f274,f251]) ).
thf(f278,plain,
( spl11_7
| spl11_9
| spl11_6 ),
inference(avatar_split_clause,[],[f213,f259,f274,f264]) ).
thf(f279,plain,
( spl11_8
| spl11_9
| spl11_6 ),
inference(avatar_split_clause,[],[f211,f259,f274,f269]) ).
thf(f281,definition,
( spl11_10
<=> ( $false
= ( sK0 @ sK7 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_10])],[avatar_definition]) ).
thf(f283,plain,
( ( $false
= ( sK0 @ sK7 @ sK2 ) )
| ~ spl11_10 ),
inference(avatar_component_clause,[],[f281]) ).
thf(f284,plain,
( spl11_4
| spl11_10
| spl11_6 ),
inference(avatar_split_clause,[],[f218,f259,f281,f251]) ).
thf(f285,plain,
( spl11_7
| spl11_10
| spl11_6 ),
inference(avatar_split_clause,[],[f217,f259,f281,f264]) ).
thf(f286,plain,
( spl11_8
| spl11_10
| spl11_6 ),
inference(avatar_split_clause,[],[f215,f259,f281,f269]) ).
thf(f288,definition,
( spl11_11
<=> ( $true
= ( sK0 @ sK10 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_11])],[avatar_definition]) ).
thf(f290,plain,
( ( $true
= ( sK0 @ sK10 @ sK6 ) )
| ~ spl11_11 ),
inference(avatar_component_clause,[],[f288]) ).
thf(f292,definition,
( spl11_12
<=> ( $true
= ( sK0 @ sK9 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_12])],[avatar_definition]) ).
thf(f294,plain,
( ( $true
= ( sK0 @ sK9 @ sK5 ) )
| ~ spl11_12 ),
inference(avatar_component_clause,[],[f292]) ).
thf(f296,definition,
( spl11_13
<=> ( $false
= ( sK0 @ sK1 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_13])],[avatar_definition]) ).
thf(f298,plain,
( ( $false
= ( sK0 @ sK1 @ sK4 ) )
| ~ spl11_13 ),
inference(avatar_component_clause,[],[f296]) ).
thf(f299,plain,
( spl11_11
| spl11_12
| spl11_13 ),
inference(avatar_split_clause,[],[f229,f296,f292,f288]) ).
thf(f301,definition,
( spl11_14
<=> ( $true
= ( sK0 @ sK10 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_14])],[avatar_definition]) ).
thf(f303,plain,
( ( $true
= ( sK0 @ sK10 @ sK3 ) )
| ~ spl11_14 ),
inference(avatar_component_clause,[],[f301]) ).
thf(f304,plain,
( spl11_14
| spl11_12
| spl11_13 ),
inference(avatar_split_clause,[],[f228,f296,f292,f301]) ).
thf(f305,plain,
( spl11_8
| spl11_12
| spl11_13 ),
inference(avatar_split_clause,[],[f226,f296,f292,f269]) ).
thf(f306,plain,
( spl11_11
| spl11_9
| spl11_13 ),
inference(avatar_split_clause,[],[f233,f296,f274,f288]) ).
thf(f307,plain,
( spl11_14
| spl11_9
| spl11_13 ),
inference(avatar_split_clause,[],[f232,f296,f274,f301]) ).
thf(f308,plain,
( spl11_8
| spl11_9
| spl11_13 ),
inference(avatar_split_clause,[],[f230,f296,f274,f269]) ).
thf(f310,definition,
( spl11_15
<=> ( $false
= ( sK0 @ sK9 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_15])],[avatar_definition]) ).
thf(f312,plain,
( ( $false
= ( sK0 @ sK9 @ sK2 ) )
| ~ spl11_15 ),
inference(avatar_component_clause,[],[f310]) ).
thf(f313,plain,
( spl11_11
| spl11_15
| spl11_13 ),
inference(avatar_split_clause,[],[f237,f296,f310,f288]) ).
thf(f314,plain,
( spl11_14
| spl11_15
| spl11_13 ),
inference(avatar_split_clause,[],[f236,f296,f310,f301]) ).
thf(f315,plain,
( spl11_8
| spl11_15
| spl11_13 ),
inference(avatar_split_clause,[],[f234,f296,f310,f269]) ).
thf(f316,plain,
( ( $true = $false )
| ( $true
= ( sK0 @ sK1 @ sK4 ) )
| ~ spl11_6 ),
inference(constrained_superposition,[],[f175,f261]) ).
thf(f329,plain,
( ( $true
= ( sK0 @ sK1 @ sK4 ) )
| ~ spl11_6 ),
inference(trivial_inequality_removal,[],[f316]) ).
thf(f333,plain,
( ( $true = $false )
| ~ spl11_6
| ~ spl11_13 ),
inference(forward_demodulation,[],[f329,f298]) ).
thf(f334,plain,
( $false
| ~ spl11_6
| ~ spl11_13 ),
inference(trivial_inequality_removal,[],[f333]) ).
thf(f335,plain,
( ~ spl11_6
| ~ spl11_13 ),
inference(avatar_contradiction_clause,[],[f334]) ).
thf(f341,plain,
( ( $true = $false )
| ( $true
= ( sK0 @ sK6 @ sK10 ) )
| ~ spl11_11 ),
inference(constrained_superposition,[],[f175,f290]) ).
thf(f342,plain,
( ( $true
= ( sK0 @ sK6 @ sK10 ) )
| ~ spl11_11 ),
inference(trivial_inequality_removal,[],[f341]) ).
thf(f408,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ X0 @ sK3 ) )
| ( $false
= ( sK0 @ sK6 @ X0 ) ) )
| ~ spl11_2
| ~ spl11_8 ),
inference(constrained_superposition,[],[f271,f243]) ).
thf(f417,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK3 ) )
| ( $false
= ( sK0 @ sK6 @ X0 ) ) )
| ~ spl11_2
| ~ spl11_8 ),
inference(trivial_inequality_removal,[],[f408]) ).
thf(f485,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK6 @ sK10 ) )
| ~ spl11_2
| ~ spl11_8
| ~ spl11_14 ),
inference(constrained_superposition,[],[f303,f417]) ).
thf(f492,plain,
( ( $false
= ( sK0 @ sK6 @ sK10 ) )
| ~ spl11_2
| ~ spl11_8
| ~ spl11_14 ),
inference(trivial_inequality_removal,[],[f485]) ).
thf(f505,plain,
( ( $true = $false )
| ~ spl11_2
| ~ spl11_8
| ~ spl11_11
| ~ spl11_14 ),
inference(constrained_superposition,[],[f492,f342]) ).
thf(f515,plain,
( $false
| ~ spl11_2
| ~ spl11_8
| ~ spl11_11
| ~ spl11_14 ),
inference(trivial_inequality_removal,[],[f505]) ).
thf(f516,plain,
( ~ spl11_2
| ~ spl11_8
| ~ spl11_11
| ~ spl11_14 ),
inference(avatar_contradiction_clause,[],[f515]) ).
thf(f522,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ X0 @ sK2 ) )
| ( $false
= ( sK0 @ sK9 @ X0 ) ) )
| ~ spl11_2
| ~ spl11_15 ),
inference(constrained_superposition,[],[f243,f312]) ).
thf(f525,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK2 ) )
| ( $false
= ( sK0 @ sK9 @ X0 ) ) )
| ~ spl11_2
| ~ spl11_15 ),
inference(trivial_inequality_removal,[],[f522]) ).
thf(f631,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK5 @ sK2 ) )
| ~ spl11_2
| ~ spl11_12
| ~ spl11_15 ),
inference(constrained_superposition,[],[f294,f525]) ).
thf(f632,plain,
( ( $false
= ( sK0 @ sK5 @ sK2 ) )
| ~ spl11_2
| ~ spl11_12
| ~ spl11_15 ),
inference(trivial_inequality_removal,[],[f631]) ).
thf(f648,plain,
( ( $true = $false )
| ~ spl11_2
| ~ spl11_9
| ~ spl11_12
| ~ spl11_15 ),
inference(constrained_superposition,[],[f632,f276]) ).
thf(f658,plain,
( $false
| ~ spl11_2
| ~ spl11_9
| ~ spl11_12
| ~ spl11_15 ),
inference(trivial_inequality_removal,[],[f648]) ).
thf(f659,plain,
( ~ spl11_2
| ~ spl11_9
| ~ spl11_12
| ~ spl11_15 ),
inference(avatar_contradiction_clause,[],[f658]) ).
thf(f667,plain,
( ( $true = $false )
| ( $true
= ( sK0 @ sK6 @ sK8 ) )
| ~ spl11_4 ),
inference(constrained_superposition,[],[f175,f253]) ).
thf(f668,plain,
( ( $true
= ( sK0 @ sK6 @ sK8 ) )
| ~ spl11_4 ),
inference(trivial_inequality_removal,[],[f667]) ).
thf(f690,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK6 @ sK8 ) )
| ~ spl11_2
| ~ spl11_7
| ~ spl11_8 ),
inference(constrained_superposition,[],[f417,f266]) ).
thf(f691,plain,
( ( $false
= ( sK0 @ sK6 @ sK8 ) )
| ~ spl11_2
| ~ spl11_7
| ~ spl11_8 ),
inference(trivial_inequality_removal,[],[f690]) ).
thf(f915,plain,
( ( $true = $false )
| ~ spl11_2
| ~ spl11_4
| ~ spl11_7
| ~ spl11_8 ),
inference(constrained_superposition,[],[f691,f668]) ).
thf(f927,plain,
( $false
| ~ spl11_2
| ~ spl11_4
| ~ spl11_7
| ~ spl11_8 ),
inference(trivial_inequality_removal,[],[f915]) ).
thf(f928,plain,
( ~ spl11_2
| ~ spl11_4
| ~ spl11_7
| ~ spl11_8 ),
inference(avatar_contradiction_clause,[],[f927]) ).
thf(f965,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ X1 @ X0 ) )
| ( $false
= ( sK0 @ X0 @ X2 ) )
| ( $true
= ( sK0 @ X1 @ X2 ) ) )
| ~ spl11_3 ),
inference(constrained_superposition,[],[f175,f247]) ).
thf(f982,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ X0 @ sK3 ) )
| ( $false
= ( sK0 @ X0 @ sK6 ) ) )
| ~ spl11_3
| ~ spl11_8 ),
inference(constrained_superposition,[],[f271,f247]) ).
thf(f996,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK6 ) )
| ( $false
= ( sK0 @ X0 @ sK3 ) ) )
| ~ spl11_3
| ~ spl11_8 ),
inference(trivial_inequality_removal,[],[f982]) ).
thf(f1010,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X1 @ X0 ) )
| ( $false
= ( sK0 @ X0 @ X2 ) )
| ( $true
= ( sK0 @ X1 @ X2 ) ) )
| ~ spl11_3 ),
inference(trivial_inequality_removal,[],[f965]) ).
thf(f1185,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK8 @ sK3 ) )
| ~ spl11_3
| ~ spl11_4
| ~ spl11_8 ),
inference(constrained_superposition,[],[f253,f996]) ).
thf(f1186,plain,
( ( $false
= ( sK0 @ sK8 @ sK3 ) )
| ~ spl11_3
| ~ spl11_4
| ~ spl11_8 ),
inference(trivial_inequality_removal,[],[f1185]) ).
thf(f1201,plain,
( ( $true = $false )
| ~ spl11_3
| ~ spl11_4
| ~ spl11_7
| ~ spl11_8 ),
inference(constrained_superposition,[],[f1186,f266]) ).
thf(f1211,plain,
( $false
| ~ spl11_3
| ~ spl11_4
| ~ spl11_7
| ~ spl11_8 ),
inference(trivial_inequality_removal,[],[f1201]) ).
thf(f1212,plain,
( ~ spl11_3
| ~ spl11_4
| ~ spl11_7
| ~ spl11_8 ),
inference(avatar_contradiction_clause,[],[f1211]) ).
thf(f1219,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ X0 @ sK2 ) )
| ( $false
= ( sK0 @ X0 @ sK7 ) ) )
| ~ spl11_3
| ~ spl11_10 ),
inference(constrained_superposition,[],[f247,f283]) ).
thf(f1220,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK7 ) )
| ( $false
= ( sK0 @ X0 @ sK2 ) ) )
| ~ spl11_3
| ~ spl11_10 ),
inference(trivial_inequality_removal,[],[f1219]) ).
thf(f1242,plain,
( ( $true = $false )
| ( $true
= ( sK0 @ sK5 @ sK7 ) )
| ~ spl11_5 ),
inference(constrained_superposition,[],[f175,f257]) ).
thf(f1251,plain,
( ( $true
= ( sK0 @ sK5 @ sK7 ) )
| ~ spl11_5 ),
inference(trivial_inequality_removal,[],[f1242]) ).
thf(f1621,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK5 @ sK2 ) )
| ~ spl11_3
| ~ spl11_5
| ~ spl11_10 ),
inference(constrained_superposition,[],[f1251,f1220]) ).
thf(f1624,plain,
( ( $false
= ( sK0 @ sK5 @ sK2 ) )
| ~ spl11_3
| ~ spl11_5
| ~ spl11_10 ),
inference(trivial_inequality_removal,[],[f1621]) ).
thf(f1641,plain,
( ( $true = $false )
| ~ spl11_3
| ~ spl11_5
| ~ spl11_9
| ~ spl11_10 ),
inference(constrained_superposition,[],[f1624,f276]) ).
thf(f1653,plain,
( $false
| ~ spl11_3
| ~ spl11_5
| ~ spl11_9
| ~ spl11_10 ),
inference(trivial_inequality_removal,[],[f1641]) ).
thf(f1654,plain,
( ~ spl11_3
| ~ spl11_5
| ~ spl11_9
| ~ spl11_10 ),
inference(avatar_contradiction_clause,[],[f1653]) ).
thf(f1891,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ X0 @ sK2 ) )
| ( $false
= ( sK0 @ sK7 @ X0 ) ) )
| ~ spl11_2
| ~ spl11_10 ),
inference(constrained_superposition,[],[f283,f243]) ).
thf(f1909,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK2 ) )
| ( $false
= ( sK0 @ sK7 @ X0 ) ) )
| ~ spl11_2
| ~ spl11_10 ),
inference(trivial_inequality_removal,[],[f1891]) ).
thf(f2002,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK5 @ sK2 ) )
| ~ spl11_2
| ~ spl11_5
| ~ spl11_10 ),
inference(constrained_superposition,[],[f257,f1909]) ).
thf(f2003,plain,
( ( $false
= ( sK0 @ sK5 @ sK2 ) )
| ~ spl11_2
| ~ spl11_5
| ~ spl11_10 ),
inference(trivial_inequality_removal,[],[f2002]) ).
thf(f2022,plain,
( ( $true = $false )
| ~ spl11_2
| ~ spl11_5
| ~ spl11_9
| ~ spl11_10 ),
inference(constrained_superposition,[],[f2003,f276]) ).
thf(f2032,plain,
( $false
| ~ spl11_2
| ~ spl11_5
| ~ spl11_9
| ~ spl11_10 ),
inference(trivial_inequality_removal,[],[f2022]) ).
thf(f2033,plain,
( ~ spl11_2
| ~ spl11_5
| ~ spl11_9
| ~ spl11_10 ),
inference(avatar_contradiction_clause,[],[f2032]) ).
thf(f2953,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK10 @ sK3 ) )
| ~ spl11_3
| ~ spl11_8
| ~ spl11_11 ),
inference(constrained_superposition,[],[f290,f996]) ).
thf(f2954,plain,
( ( $false
= ( sK0 @ sK10 @ sK3 ) )
| ~ spl11_3
| ~ spl11_8
| ~ spl11_11 ),
inference(trivial_inequality_removal,[],[f2953]) ).
thf(f2972,plain,
( ( $true = $false )
| ~ spl11_3
| ~ spl11_8
| ~ spl11_11
| ~ spl11_14 ),
inference(constrained_superposition,[],[f2954,f303]) ).
thf(f2984,plain,
( $false
| ~ spl11_3
| ~ spl11_8
| ~ spl11_11
| ~ spl11_14 ),
inference(trivial_inequality_removal,[],[f2972]) ).
thf(f2985,plain,
( ~ spl11_3
| ~ spl11_8
| ~ spl11_11
| ~ spl11_14 ),
inference(avatar_contradiction_clause,[],[f2984]) ).
thf(f2995,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ sK9 @ X0 ) )
| ( $false
= ( sK0 @ X0 @ sK2 ) ) )
| ~ spl11_3
| ~ spl11_15 ),
inference(constrained_superposition,[],[f1010,f312]) ).
thf(f2996,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ sK9 @ X0 ) )
| ( $false
= ( sK0 @ X0 @ sK2 ) ) )
| ~ spl11_3
| ~ spl11_15 ),
inference(trivial_inequality_removal,[],[f2995]) ).
thf(f3610,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK9 @ sK5 ) )
| ~ spl11_3
| ~ spl11_9
| ~ spl11_15 ),
inference(constrained_superposition,[],[f276,f2996]) ).
thf(f3617,plain,
( ( $false
= ( sK0 @ sK9 @ sK5 ) )
| ~ spl11_3
| ~ spl11_9
| ~ spl11_15 ),
inference(trivial_inequality_removal,[],[f3610]) ).
thf(f3661,plain,
( ( $true = $false )
| ~ spl11_3
| ~ spl11_9
| ~ spl11_12
| ~ spl11_15 ),
inference(constrained_superposition,[],[f3617,f294]) ).
thf(f3675,plain,
( $false
| ~ spl11_3
| ~ spl11_9
| ~ spl11_12
| ~ spl11_15 ),
inference(trivial_inequality_removal,[],[f3661]) ).
thf(f3676,plain,
( ~ spl11_3
| ~ spl11_9
| ~ spl11_12
| ~ spl11_15 ),
inference(avatar_contradiction_clause,[],[f3675]) ).
cnf(s2,plain,
( spl11_2
| spl11_3 ),
inference(sat_conversion,[],[f248]) ).
cnf(s4,plain,
( spl11_4
| spl11_5
| spl11_6 ),
inference(sat_conversion,[],[f262]) ).
cnf(s5,plain,
( spl11_5
| spl11_6
| spl11_7 ),
inference(sat_conversion,[],[f267]) ).
cnf(s6,plain,
( spl11_5
| spl11_6
| spl11_8 ),
inference(sat_conversion,[],[f272]) ).
cnf(s7,plain,
( spl11_4
| spl11_6
| spl11_9 ),
inference(sat_conversion,[],[f277]) ).
cnf(s8,plain,
( spl11_6
| spl11_7
| spl11_9 ),
inference(sat_conversion,[],[f278]) ).
cnf(s9,plain,
( spl11_6
| spl11_8
| spl11_9 ),
inference(sat_conversion,[],[f279]) ).
cnf(s10,plain,
( spl11_4
| spl11_6
| spl11_10 ),
inference(sat_conversion,[],[f284]) ).
cnf(s11,plain,
( spl11_6
| spl11_7
| spl11_10 ),
inference(sat_conversion,[],[f285]) ).
cnf(s12,plain,
( spl11_6
| spl11_8
| spl11_10 ),
inference(sat_conversion,[],[f286]) ).
cnf(s13,plain,
( spl11_11
| spl11_12
| spl11_13 ),
inference(sat_conversion,[],[f299]) ).
cnf(s14,plain,
( spl11_12
| spl11_13
| spl11_14 ),
inference(sat_conversion,[],[f304]) ).
cnf(s15,plain,
( spl11_8
| spl11_12
| spl11_13 ),
inference(sat_conversion,[],[f305]) ).
cnf(s16,plain,
( spl11_9
| spl11_11
| spl11_13 ),
inference(sat_conversion,[],[f306]) ).
cnf(s17,plain,
( spl11_9
| spl11_13
| spl11_14 ),
inference(sat_conversion,[],[f307]) ).
cnf(s18,plain,
( spl11_8
| spl11_9
| spl11_13 ),
inference(sat_conversion,[],[f308]) ).
cnf(s19,plain,
( spl11_11
| spl11_13
| spl11_15 ),
inference(sat_conversion,[],[f313]) ).
cnf(s20,plain,
( spl11_13
| spl11_14
| spl11_15 ),
inference(sat_conversion,[],[f314]) ).
cnf(s21,plain,
( spl11_8
| spl11_13
| spl11_15 ),
inference(sat_conversion,[],[f315]) ).
cnf(s23,plain,
( ~ spl11_6
| ~ spl11_13 ),
inference(sat_conversion,[],[f335]) ).
cnf(s25,plain,
( ~ spl11_2
| ~ spl11_8
| ~ spl11_11
| ~ spl11_14 ),
inference(sat_conversion,[],[f516]) ).
cnf(s27,plain,
( ~ spl11_2
| ~ spl11_9
| ~ spl11_12
| ~ spl11_15 ),
inference(sat_conversion,[],[f659]) ).
cnf(s29,plain,
( ~ spl11_2
| ~ spl11_4
| ~ spl11_7
| ~ spl11_8 ),
inference(sat_conversion,[],[f928]) ).
cnf(s31,plain,
( ~ spl11_3
| ~ spl11_4
| ~ spl11_7
| ~ spl11_8 ),
inference(sat_conversion,[],[f1212]) ).
cnf(s33,plain,
( ~ spl11_3
| ~ spl11_5
| ~ spl11_9
| ~ spl11_10 ),
inference(sat_conversion,[],[f1654]) ).
cnf(s35,plain,
( ~ spl11_2
| ~ spl11_5
| ~ spl11_9
| ~ spl11_10 ),
inference(sat_conversion,[],[f2033]) ).
cnf(s37,plain,
( ~ spl11_3
| ~ spl11_8
| ~ spl11_11
| ~ spl11_14 ),
inference(sat_conversion,[],[f2985]) ).
cnf(s39,plain,
( ~ spl11_3
| ~ spl11_9
| ~ spl11_12
| ~ spl11_15 ),
inference(sat_conversion,[],[f3676]) ).
cnf(s40,plain,
( spl11_8
| spl11_13
| ~ spl11_3 ),
inference(rat,[],[s39,s21,s15,s18]) ).
cnf(s41,plain,
( spl11_15
| spl11_13
| ~ spl11_3 ),
inference(rat,[],[s37,s19,s20,s40]) ).
cnf(s42,plain,
( spl11_12
| spl11_13
| ~ spl11_3 ),
inference(rat,[],[s37,s13,s14,s40]) ).
cnf(s43,plain,
( spl11_13
| ~ spl11_3 ),
inference(rat,[],[s37,s16,s17,s39,s42,s41,s40]) ).
cnf(s48,plain,
( spl11_15
| ~ spl11_8
| spl11_13 ),
inference(rat,[],[s25,s19,s20,s2,s43]) ).
cnf(s49,plain,
( spl11_12
| ~ spl11_8
| spl11_13 ),
inference(rat,[],[s25,s13,s14,s2,s43]) ).
cnf(s50,plain,
( ~ spl11_8
| spl11_13 ),
inference(rat,[],[s25,s16,s17,s27,s49,s48,s2,s43]) ).
cnf(s51,plain,
spl11_13,
inference(rat,[],[s27,s21,s15,s18,s50,s2,s43]) ).
cnf(s52,plain,
~ spl11_6,
inference(rat,[],[s23,s51]) ).
cnf(s53,plain,
( ~ spl11_10
| ~ spl11_5
| ~ spl11_9 ),
inference(rat,[],[s2,s33,s35]) ).
cnf(s54,plain,
spl11_4,
inference(rat,[],[s53,s4,s10,s7,s52]) ).
cnf(s55,plain,
( ~ spl11_7
| ~ spl11_8 ),
inference(rat,[],[s2,s31,s29,s54]) ).
cnf(s56,plain,
spl11_5,
inference(rat,[],[s55,s5,s6,s52]) ).
cnf(s57,plain,
spl11_7,
inference(rat,[],[s53,s8,s11,s56,s52]) ).
cnf(s58,plain,
~ spl11_8,
inference(rat,[],[s55,s57]) ).
cnf(s59,plain,
spl11_9,
inference(rat,[],[s9,s52,s58]) ).
cnf(s60,plain,
spl11_10,
inference(rat,[],[s12,s52,s58]) ).
cnf(s61,plain,
$false,
inference(rat,[],[s53,s56,s59,s60]) ).
thf(f3681,plain,
$false,
inference(avatar_sat_refutation,[],[s61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL867^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n015.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 10:19:33 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.95/0.44 % (3345434)Will run a generic schedule for satisfiability detection.
% 0.95/0.44 % (3345439)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3596765934_2999 on theBenchmark for (2999ds/0Mi)
% 0.95/0.44 % Exception at run slice level
% 0.95/0.44 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.95/0.44 % (3345440)% WARNING: option uhcvi not known.
% 0.95/0.44 % (3345441)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1879339198:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.95/0.44 % (3345443)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1599106415:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.95/0.44 % (3345440)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1569102460:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.95/0.44 % (3345442)dis+10_1_sil=32000:sp=arity:random_seed=3278895023:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.95/0.44 % (3345445)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3770299360:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.95/0.44 % (3345443)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.95/0.44 % (3345440)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.95/0.44 % (3345440)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.95/0.44 % (3345447)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=103802895:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.95/0.44 % Exception at run slice level
% 0.95/0.44 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.95/0.44 % (3345444)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=820202778:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.95/0.44 % (3345454)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=863829905:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.95/0.44 % (3345442)Instruction limit reached!
% 0.95/0.44 % (3345442)------------------------------
% 0.95/0.44 % (3345442)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.44 % (3345442)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.44 % (3345442)CaDiCaL version: 2.1.3
% 0.95/0.44 % (3345442)Termination reason: Instruction limit
% 0.95/0.44 % (3345442)Termination phase: Saturation
% 0.95/0.44 % (3345442)Time elapsed: 0.046 s
% 0.95/0.44 % (3345442)Peak memory usage: 12 MB
% 0.95/0.44 % (3345442)Instructions burned: 104 (million)
% 0.95/0.44 % (3345443)Instruction limit reached!
% 0.95/0.44 % (3345443)------------------------------
% 0.95/0.44 % (3345443)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.44 % (3345443)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.44 % (3345443)CaDiCaL version: 2.1.3
% 0.95/0.44 % (3345443)Termination reason: Instruction limit
% 0.95/0.44 % (3345443)Termination phase: Saturation
% 0.95/0.44 % (3345443)Time elapsed: 0.051 s
% 0.95/0.44 % (3345443)Peak memory usage: 12 MB
% 0.95/0.44 % (3345443)Instructions burned: 116 (million)
% 0.95/0.44 % (3345454)Instruction limit reached!
% 0.95/0.44 % (3345454)------------------------------
% 0.95/0.44 % (3345454)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.44 % (3345454)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.44 % (3345454)CaDiCaL version: 2.1.3
% 0.95/0.44 % (3345454)Termination reason: Instruction limit
% 0.95/0.44 % (3345454)Termination phase: Saturation
% 0.95/0.44 % (3345454)Time elapsed: 0.031 s
% 0.95/0.44 % (3345454)Peak memory usage: 12 MB
% 0.95/0.44 % (3345454)Instructions burned: 132 (million)
% 0.95/0.44 % (3345459)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=4106890561:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 0.95/0.44 % (3345457)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=1736595317:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.95/0.44 % (3345457)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.95/0.44 % (3345458)ott-21_1_sil=16000:fs=off:random_seed=788300840:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 0.95/0.44 % (3345457)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.95/0.44 % (3345445)Instruction limit reached!
% 0.95/0.44 % (3345445)------------------------------
% 0.95/0.44 % (3345445)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.44 % (3345445)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.44 % (3345445)CaDiCaL version: 2.1.3
% 0.95/0.44 % (3345445)Termination reason: Instruction limit
% 0.95/0.44 % (3345445)Termination phase: Saturation
% 0.95/0.44 % (3345445)Time elapsed: 0.076 s
% 0.95/0.44 % (3345445)Peak memory usage: 13 MB
% 0.95/0.44 % (3345445)Instructions burned: 160 (million)
% 0.95/0.44 % (3345463)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1852486179:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 0.95/0.44 % Exception at run slice level
% 0.95/0.44 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.95/0.44 % (3345444)Instruction limit reached!
% 0.95/0.44 % (3345444)------------------------------
% 0.95/0.44 % (3345444)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.44 % (3345444)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.44 % (3345444)CaDiCaL version: 2.1.3
% 0.95/0.44 % (3345444)Termination reason: Instruction limit
% 0.95/0.44 % (3345444)Termination phase: Saturation
% 0.95/0.44 % (3345444)Time elapsed: 0.104 s
% 0.95/0.44 % (3345444)Peak memory usage: 12 MB
% 0.95/0.44 % (3345444)Instructions burned: 132 (million)
% 0.95/0.44 % (3345465)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=238235557:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 0.95/0.44 % (3345466)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=98352812:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 0.95/0.44 % Exception at run slice level
% 0.95/0.44 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.95/0.44 % (3345457) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3345434-3345457"...
% 0.95/0.44 % (3345458)Instruction limit reached!
% 0.95/0.44 % (3345458)------------------------------
% 0.95/0.44 % (3345458)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.44 % (3345458)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.44 % (3345458)CaDiCaL version: 2.1.3
% 0.95/0.44 % (3345458)Termination reason: Instruction limit
% 0.95/0.44 % (3345458)Termination phase: Saturation
% 0.95/0.44 % (3345458)Time elapsed: 0.087 s
% 0.95/0.44 % (3345458)Peak memory usage: 12 MB
% 0.95/0.44 % (3345458)Instructions burned: 181 (million)
% 0.95/0.44 % (3345457)...printing done.
% 0.95/0.44 % (3345457)Refutation found. Thanks to Tanya!
% 0.95/0.44 % SZS status Theorem for theBenchmark
% 0.95/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.95/0.44 % (3345457)------------------------------
% 0.95/0.44 % (3345457)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.44 % (3345457)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.44 % (3345457)CaDiCaL version: 2.1.3
% 0.95/0.44 % (3345457)Termination reason: Refutation
% 0.95/0.44 % (3345457)Time elapsed: 0.094 s
% 0.95/0.44 % (3345457)Peak memory usage: 13 MB
% 0.95/0.44 % (3345457)Instructions burned: 176 (million)
% 0.95/0.44 % (3345434)Success in time 0.211 s
% 0.95/0.44 % Vampire exiting
%------------------------------------------------------------------------------