%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL879^1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 08:14:39 AM UTC 2026
% Result : Theorem 0.20s 0.35s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 11
% Syntax : Number of formulae : 139 ( 38 unt; 0 typ; 4 def)
% Number of atoms : 1021 ( 148 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 1972 ( 278 ~; 293 |; 34 &;1118 @)
% ( 7 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 197 ( 197 >; 0 *; 0 +; 0 <<)
% Number of symbols : 66 ( 62 usr; 13 con; 0-4 aty)
% ( 207 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 372 ( 0 sgn 64 !; 0 ?; 372 :)
% 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,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_35,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_36,type,
vIMP: $o > $o > $o ).
thf(func_def_37,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_39,type,
vAND: $o > $o > $o ).
thf(func_def_40,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_42,type,
vNOT: $o > $o ).
thf(func_def_45,type,
vOR: $o > $o > $o ).
thf(func_def_46,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
vIFF: $o > $o > $o ).
thf(func_def_48,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_49,type,
db6:
!>[X0: $tType] : X0 ).
thf(func_def_50,type,
sK0: $i > $i > $o ).
thf(func_def_51,type,
sK1: $i > $i > $o ).
thf(func_def_56,type,
sK6: ( $i > $o ) > $i ).
thf(func_def_58,type,
sK8: $i > $o ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f6,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimplies ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f11,axiom,
( ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) )
= mforall_prop ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mforall_prop) ).
thf(f16,axiom,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ~ ( X0 @ X2 @ X3 )
| ( X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mbox) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,conjecture,
! [X0: $i > $i > $o,X1: $i > $i > $o] :
( ! [X4: $i,X5: $i,X3: $i] :
( ( ( X1 @ X3 @ X4 )
& ( X0 @ X4 @ X5 ) )
=> ( X0 @ X3 @ X5 ) )
<=> ( mvalid
@ ( mforall_prop
@ ^ [X2: $i > $o] : ( mimplies @ ( mbox @ X0 @ X2 ) @ ( mbox @ X1 @ ( mbox @ X0 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(f33,negated_conjecture,
~ ! [X0: $i > $i > $o,X1: $i > $i > $o] :
( ! [X4: $i,X5: $i,X3: $i] :
( ( ( X1 @ X3 @ X4 )
& ( X0 @ X4 @ X5 ) )
=> ( X0 @ X3 @ X5 ) )
<=> ( mvalid
@ ( mforall_prop
@ ^ [X2: $i > $o] : ( mimplies @ ( mbox @ X0 @ X2 ) @ ( mbox @ X1 @ ( mbox @ X0 @ X2 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
thf(f41,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f42,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f41]) ).
thf(f50,plain,
( ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) )
= mforall_prop ),
inference(rectify,[],[f11]) ).
thf(f51,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f50]) ).
thf(f56,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f59,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f60,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f59]) ).
thf(f63,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f64,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f63]) ).
thf(f65,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ~ ( X0 @ X2 @ X3 )
| ( X1 @ X3 ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f66,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f65]) ).
thf(f83,plain,
~ ! [X0: $i > $i > $o,X1: $i > $i > $o] :
( ! [X2: $i,X3: $i,X4: $i] :
( ( ( X1 @ X4 @ X2 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X4 @ X3 ) )
<=> ( mvalid
@ ( mforall_prop
@ ^ [X5: $i > $o] : ( mimplies @ ( mbox @ X0 @ X5 ) @ ( mbox @ X1 @ ( mbox @ X0 @ X5 ) ) ) ) ) ),
inference(rectify,[],[f33]) ).
thf(f84,plain,
( $true
= ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y0 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
= ( mvalid
@ ( mforall_prop
@ ^ [Y2: $i > $o] : ( mimplies @ ( mbox @ Y1 @ Y2 ) @ ( mbox @ Y0 @ ( mbox @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f83]) ).
thf(f88,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f66]) ).
thf(f94,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f56]) ).
thf(f106,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f107,plain,
( $true
= ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y0 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
= ( mvalid
@ ( mforall_prop
@ ^ [Y2: $i > $o] : ( mimplies @ ( mbox @ Y1 @ Y2 ) @ ( mbox @ Y0 @ ( mbox @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f84]) ).
thf(f109,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f60]) ).
thf(f113,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f51]) ).
thf(f118,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f64]) ).
thf(f123,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f94,f118,f106]) ).
thf(f131,plain,
( $true
= ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y0 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
= ( ^ [Y2: $i > $o] :
( !! @ $i
@ ^ [Y3: $i] : ( Y2 @ Y3 ) )
@ ( ^ [Y2: ( $i > $o ) > $i > $o,Y3: $i] :
( !! @ ( $i > $o )
@ ^ [Y4: $i > $o] : ( Y2 @ Y4 @ Y3 ) )
@ ^ [Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o] :
( ^ [Y5: $i > $o,Y6: $i > $o,Y7: $i] :
( ( Y6 @ Y7 )
| ( Y5 @ Y7 ) )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y3 )
@ Y4 )
@ ( ^ [Y3: $i > $i > $o,Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 ) ) )
@ Y1
@ Y2 )
@ ( ^ [Y3: $i > $i > $o,Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 ) ) )
@ Y0
@ ( ^ [Y3: $i > $i > $o,Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 ) ) )
@ Y1
@ Y2 ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f107,f109,f113,f123,f88,f88,f88]) ).
thf(f132,plain,
( $true
= ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y0 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
= ( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y1 @ Y4 @ Y5 ) ) )
| ~ ( Y0 @ Y2 @ Y4 ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
| ~ ( Y1 @ Y2 @ Y4 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f131]) ).
thf(f133,plain,
( $false
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y0 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
= ( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y1 @ Y4 @ Y5 ) ) )
| ~ ( Y0 @ Y2 @ Y4 ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
| ~ ( Y1 @ Y2 @ Y4 ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f132]) ).
thf(f134,plain,
( $false
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y0 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
= ( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y1 @ Y4 @ Y5 ) ) )
| ~ ( Y0 @ Y2 @ Y4 ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
| ~ ( Y1 @ Y2 @ Y4 ) ) ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f133]) ).
thf(f137,plain,
( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( sK0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
= ( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( Y0 @ Y3 @ Y4 ) ) )
| ~ ( sK0 @ Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f134]) ).
thf(f138,plain,
( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( sK0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
= ( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( Y0 @ Y3 @ Y4 ) ) )
| ~ ( sK0 @ Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) )
@ sK1 )
= $false ),
inference(sigma_proxy_clausification,[],[f137]) ).
thf(f139,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK1 @ Y2 @ Y1 )
& ( sK0 @ Y0 @ Y2 ) )
=> ( sK1 @ Y0 @ Y1 ) ) ) ) )
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( sK1 @ Y2 @ Y3 ) ) )
| ~ ( sK0 @ Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( sK1 @ Y0 @ Y2 ) ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f138]) ).
thf(f140,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( sK1 @ Y2 @ Y3 ) ) )
| ~ ( sK0 @ Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( sK1 @ Y0 @ Y2 ) ) ) ) ) )
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK1 @ Y2 @ Y1 )
& ( sK0 @ Y0 @ Y2 ) )
=> ( sK1 @ Y0 @ Y1 ) ) ) ) ) ),
inference(iff_proxy_clausification,[],[f139]) ).
thf(f141,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( sK1 @ Y2 @ Y3 ) ) )
| ~ ( sK0 @ Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( sK1 @ Y0 @ Y2 ) ) ) ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK1 @ Y2 @ Y1 )
& ( sK0 @ Y0 @ Y2 ) )
=> ( sK1 @ Y0 @ Y1 ) ) ) ) )
= $true ) ),
inference(xor_proxy_clausification,[],[f140]) ).
thf(f142,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK1 @ Y2 @ Y1 )
& ( sK0 @ Y0 @ Y2 ) )
=> ( sK1 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( sK1 @ Y2 @ Y3 ) ) )
| ~ ( sK0 @ Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( sK1 @ Y0 @ Y2 ) ) ) ) ) )
= $false ) ),
inference(xor_proxy_clausification,[],[f140]) ).
thf(f144,definition,
( spl2_1
<=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( sK1 @ Y2 @ Y3 ) ) )
| ~ ( sK0 @ Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( sK1 @ Y0 @ Y2 ) ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f146,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( sK1 @ Y2 @ Y3 ) ) )
| ~ ( sK0 @ Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( sK1 @ Y0 @ Y2 ) ) ) ) ) )
= $false )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f144]) ).
thf(f148,definition,
( spl2_2
<=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK1 @ Y2 @ Y1 )
& ( sK0 @ Y0 @ Y2 ) )
=> ( sK1 @ Y0 @ Y1 ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f149,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK1 @ Y2 @ Y1 )
& ( sK0 @ Y0 @ Y2 ) )
=> ( sK1 @ Y0 @ Y1 ) ) ) ) )
!= $false )
| spl2_2 ),
inference(avatar_component_clause,[],[f148]) ).
thf(f150,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK1 @ Y2 @ Y1 )
& ( sK0 @ Y0 @ Y2 ) )
=> ( sK1 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f148]) ).
thf(f151,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f142,f148,f144]) ).
thf(f153,definition,
( spl2_3
<=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( sK1 @ Y2 @ Y3 ) ) )
| ~ ( sK0 @ Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( sK1 @ Y0 @ Y2 ) ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
thf(f155,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( sK1 @ Y2 @ Y3 ) ) )
| ~ ( sK0 @ Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( sK1 @ Y0 @ Y2 ) ) ) ) ) )
= $true )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f153]) ).
thf(f157,definition,
( spl2_4
<=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK1 @ Y2 @ Y1 )
& ( sK0 @ Y0 @ Y2 ) )
=> ( sK1 @ Y0 @ Y1 ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
thf(f159,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK1 @ Y2 @ Y1 )
& ( sK0 @ Y0 @ Y2 ) )
=> ( sK1 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f157]) ).
thf(f160,plain,
( spl2_3
| spl2_4 ),
inference(avatar_split_clause,[],[f141,f157,f153]) ).
thf(f161,plain,
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK1 @ Y2 @ Y1 )
& ( sK0 @ Y0 @ Y2 ) )
=> ( sK1 @ Y0 @ Y1 ) ) ) )
@ sK3 )
= $false )
| ~ spl2_2 ),
inference(sigma_proxy_clausification,[],[f150]) ).
thf(f162,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK1 @ Y1 @ Y0 )
& ( sK0 @ sK3 @ Y1 ) )
=> ( sK1 @ sK3 @ Y0 ) ) ) ) )
| ~ spl2_2 ),
inference(beta-eta_normalization,[],[f161]) ).
thf(f163,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK1 @ Y1 @ Y0 )
& ( sK0 @ sK3 @ Y1 ) )
=> ( sK1 @ sK3 @ Y0 ) ) )
@ sK4 ) )
| ~ spl2_2 ),
inference(sigma_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK1 @ Y0 @ sK4 )
& ( sK0 @ sK3 @ Y0 ) )
=> ( sK1 @ sK3 @ sK4 ) ) )
= $false )
| ~ spl2_2 ),
inference(beta-eta_normalization,[],[f163]) ).
thf(f165,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK1 @ Y0 @ sK4 )
& ( sK0 @ sK3 @ Y0 ) )
=> ( sK1 @ sK3 @ sK4 ) )
@ sK5 ) )
| ~ spl2_2 ),
inference(sigma_proxy_clausification,[],[f164]) ).
thf(f166,plain,
( ( ( ( ( sK1 @ sK5 @ sK4 )
& ( sK0 @ sK3 @ sK5 ) )
=> ( sK1 @ sK3 @ sK4 ) )
= $false )
| ~ spl2_2 ),
inference(beta-eta_normalization,[],[f165]) ).
thf(f167,plain,
( ( ( sK1 @ sK3 @ sK4 )
= $false )
| ~ spl2_2 ),
inference(imp_proxy_clausification,[],[f166]) ).
thf(f168,plain,
( ( $true
= ( ( sK1 @ sK5 @ sK4 )
& ( sK0 @ sK3 @ sK5 ) ) )
| ~ spl2_2 ),
inference(imp_proxy_clausification,[],[f166]) ).
thf(f173,plain,
( ( $true
= ( sK0 @ sK3 @ sK5 ) )
| ~ spl2_2 ),
inference(and_proxy_clausification,[],[f168]) ).
thf(f174,plain,
( ( ( sK1 @ sK5 @ sK4 )
= $true )
| ~ spl2_2 ),
inference(and_proxy_clausification,[],[f168]) ).
thf(f189,plain,
( ! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( sK1 @ Y2 @ Y3 ) ) )
| ~ ( sK0 @ Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( sK1 @ Y0 @ Y2 ) ) ) ) )
@ X1 ) )
| ~ spl2_3 ),
inference(pi_proxy_clausification,[],[f155]) ).
thf(f190,plain,
( ! [X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( sK1 @ Y1 @ Y2 ) ) )
| ~ ( sK0 @ X1 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ( sK1 @ X1 @ Y1 ) ) ) ) ) )
| ~ spl2_3 ),
inference(beta-eta_normalization,[],[f189]) ).
thf(f191,plain,
( ! [X2: $i > $o,X1: $i] :
( ( ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( sK1 @ Y1 @ Y2 ) ) )
| ~ ( sK0 @ X1 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ( sK1 @ X1 @ Y1 ) ) ) )
@ X2 )
= $true )
| ~ spl2_3 ),
inference(pi_proxy_clausification,[],[f190]) ).
thf(f192,plain,
( ! [X2: $i > $o,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y1 )
| ~ ( sK1 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ X1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK1 @ X1 @ Y0 ) ) ) )
= $true )
| ~ spl2_3 ),
inference(beta-eta_normalization,[],[f191]) ).
thf(f193,plain,
( ! [X2: $i > $o,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y1 )
| ~ ( sK1 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ X1 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK1 @ X1 @ Y0 ) ) ) ) ) )
| ~ spl2_3 ),
inference(or_proxy_clausification,[],[f192]) ).
thf(f194,plain,
( ! [X2: $i > $o,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y1 )
| ~ ( sK1 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ X1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK1 @ X1 @ Y0 ) ) ) ) ) )
| ~ spl2_3 ),
inference(pi_proxy_clausification,[],[f193]) ).
thf(f195,plain,
( ! [X2: $i > $o,X3: $i,X1: $i] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK1 @ X3 @ Y0 ) ) )
| ~ ( sK0 @ X1 @ X3 ) )
= $true )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK1 @ X1 @ Y0 ) ) ) ) ) )
| ~ spl2_3 ),
inference(beta-eta_normalization,[],[f194]) ).
thf(f197,plain,
( ! [X0: $i > $o] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X0 @ Y0 )
| ~ ( sK1 @ sK5 @ Y0 ) ) )
| ~ $true ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X0 @ Y0 )
| ~ ( sK1 @ sK3 @ Y0 ) ) ) ) ) )
| ~ spl2_2
| ~ spl2_3 ),
inference(constrained_superposition,[],[f195,f173]) ).
thf(f198,plain,
( ! [X0: $i > $o] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X0 @ Y0 )
| ~ ( sK1 @ sK5 @ Y0 ) ) )
| $false ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X0 @ Y0 )
| ~ ( sK1 @ sK3 @ Y0 ) ) ) ) ) )
| ~ spl2_2
| ~ spl2_3 ),
inference(boolean_simplification,[],[f197]) ).
thf(f199,plain,
( ! [X0: $i > $o] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X0 @ Y0 )
| ~ ( sK1 @ sK3 @ Y0 ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X0 @ Y0 )
| ~ ( sK1 @ sK5 @ Y0 ) ) )
= $true ) )
| ~ spl2_2
| ~ spl2_3 ),
inference(boolean_simplification,[],[f198]) ).
thf(f200,plain,
( ! [X0: $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X0 @ Y0 )
| ~ ( sK1 @ sK3 @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X0 @ Y0 )
| ~ ( sK1 @ sK5 @ Y0 ) ) )
= $true ) )
| ~ spl2_2
| ~ spl2_3 ),
inference(not_proxy_clausification,[],[f199]) ).
thf(f201,plain,
( ! [X0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X0 @ Y0 )
| ~ ( sK1 @ sK5 @ Y0 ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( ( X0 @ Y0 )
| ~ ( sK1 @ sK3 @ Y0 ) )
@ ( sK6 @ X0 ) )
= $false ) )
| ~ spl2_2
| ~ spl2_3 ),
inference(sigma_proxy_clausification,[],[f200]) ).
thf(f202,plain,
( ! [X0: $i > $o] :
( ( $false
= ( ( X0 @ ( sK6 @ X0 ) )
| ~ ( sK1 @ sK3 @ ( sK6 @ X0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X0 @ Y0 )
| ~ ( sK1 @ sK5 @ Y0 ) ) )
= $true ) )
| ~ spl2_2
| ~ spl2_3 ),
inference(beta-eta_normalization,[],[f201]) ).
thf(f204,plain,
( ! [X0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X0 @ Y0 )
| ~ ( sK1 @ sK5 @ Y0 ) ) )
= $true )
| ( $false
= ( X0 @ ( sK6 @ X0 ) ) ) )
| ~ spl2_2
| ~ spl2_3 ),
inference(or_proxy_clausification,[],[f202]) ).
thf(f205,plain,
( ! [X0: $i > $o,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( X0 @ Y0 )
| ~ ( sK1 @ sK5 @ Y0 ) )
@ X1 )
= $true )
| ( $false
= ( X0 @ ( sK6 @ X0 ) ) ) )
| ~ spl2_2
| ~ spl2_3 ),
inference(pi_proxy_clausification,[],[f204]) ).
thf(f206,plain,
( ! [X0: $i > $o,X1: $i] :
( ( $true
= ( ( X0 @ X1 )
| ~ ( sK1 @ sK5 @ X1 ) ) )
| ( $false
= ( X0 @ ( sK6 @ X0 ) ) ) )
| ~ spl2_2
| ~ spl2_3 ),
inference(beta-eta_normalization,[],[f205]) ).
thf(f209,plain,
( ( $true
= ( $false
| ~ ( sK1 @ sK5 @ sK4 ) ) )
| ( $false
= ( sK1 @ sK3 @ ( sK6 @ ( sK1 @ sK3 ) ) ) )
| ~ spl2_2
| ~ spl2_3 ),
inference(constrained_superposition,[],[f206,f167]) ).
thf(f213,plain,
( ( ( ~ ( sK1 @ sK5 @ sK4 ) )
= $true )
| ( $false
= ( sK1 @ sK3 @ ( sK6 @ ( sK1 @ sK3 ) ) ) )
| ~ spl2_2
| ~ spl2_3 ),
inference(boolean_simplification,[],[f209]) ).
thf(f217,plain,
( ( $false
= ( sK1 @ sK3 @ ( sK6 @ ( sK1 @ sK3 ) ) ) )
| ( ( ~ $true ) = $true )
| ~ spl2_2
| ~ spl2_3 ),
inference(forward_demodulation,[],[f213,f174]) ).
thf(f218,plain,
( ( $true = $false )
| ( $false
= ( sK1 @ sK3 @ ( sK6 @ ( sK1 @ sK3 ) ) ) )
| ~ spl2_2
| ~ spl2_3 ),
inference(boolean_simplification,[],[f217]) ).
thf(f219,plain,
( ( $false
= ( sK1 @ sK3 @ ( sK6 @ ( sK1 @ sK3 ) ) ) )
| ~ spl2_2
| ~ spl2_3 ),
inference(trivial_inequality_removal,[],[f218]) ).
thf(f221,plain,
( ( $false
= ( $false
| ~ $false ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ sK3 @ Y0 )
| ~ ( sK1 @ sK5 @ Y0 ) ) ) )
| ~ spl2_2
| ~ spl2_3 ),
inference(constrained_superposition,[],[f202,f219]) ).
thf(f222,plain,
( ( $true = $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ sK3 @ Y0 )
| ~ ( sK1 @ sK5 @ Y0 ) ) ) )
| ~ spl2_2
| ~ spl2_3 ),
inference(boolean_simplification,[],[f221]) ).
thf(f223,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ sK3 @ Y0 )
| ~ ( sK1 @ sK5 @ Y0 ) ) ) )
| ~ spl2_2
| ~ spl2_3 ),
inference(trivial_inequality_removal,[],[f222]) ).
thf(f226,plain,
( ! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( sK1 @ sK3 @ Y0 )
| ~ ( sK1 @ sK5 @ Y0 ) )
@ X1 ) )
| ~ spl2_2
| ~ spl2_3 ),
inference(pi_proxy_clausification,[],[f223]) ).
thf(f227,plain,
( ! [X1: $i] :
( ( ( sK1 @ sK3 @ X1 )
| ~ ( sK1 @ sK5 @ X1 ) )
= $true )
| ~ spl2_2
| ~ spl2_3 ),
inference(beta-eta_normalization,[],[f226]) ).
thf(f230,plain,
( ( $true
= ( $false
| ~ ( sK1 @ sK5 @ sK4 ) ) )
| ~ spl2_2
| ~ spl2_3 ),
inference(constrained_superposition,[],[f227,f167]) ).
thf(f235,plain,
( ( ( ~ ( sK1 @ sK5 @ sK4 ) )
= $true )
| ~ spl2_2
| ~ spl2_3 ),
inference(boolean_simplification,[],[f230]) ).
thf(f239,plain,
( ( ( ~ $true ) = $true )
| ~ spl2_2
| ~ spl2_3 ),
inference(forward_demodulation,[],[f235,f174]) ).
thf(f240,plain,
( ( $true = $false )
| ~ spl2_2
| ~ spl2_3 ),
inference(boolean_simplification,[],[f239]) ).
thf(f241,plain,
( $false
| ~ spl2_2
| ~ spl2_3 ),
inference(trivial_inequality_removal,[],[f240]) ).
thf(f242,plain,
( ~ spl2_2
| ~ spl2_3 ),
inference(avatar_contradiction_clause,[],[f241]) ).
thf(f243,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK1 @ Y2 @ Y1 )
& ( sK0 @ Y0 @ Y2 ) )
=> ( sK1 @ Y0 @ Y1 ) ) ) )
@ X1 )
= $true )
| spl2_2 ),
inference(pi_proxy_clausification,[],[f149]) ).
thf(f244,plain,
( ! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK1 @ Y1 @ Y0 )
& ( sK0 @ X1 @ Y1 ) )
=> ( sK1 @ X1 @ Y0 ) ) ) )
= $true )
| spl2_2 ),
inference(beta-eta_normalization,[],[f243]) ).
thf(f245,plain,
( ! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK1 @ Y1 @ Y0 )
& ( sK0 @ X1 @ Y1 ) )
=> ( sK1 @ X1 @ Y0 ) ) )
@ X2 )
= $true )
| spl2_2 ),
inference(pi_proxy_clausification,[],[f244]) ).
thf(f246,plain,
( ! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK1 @ Y0 @ X2 )
& ( sK0 @ X1 @ Y0 ) )
=> ( sK1 @ X1 @ X2 ) ) ) )
| spl2_2 ),
inference(beta-eta_normalization,[],[f245]) ).
thf(f247,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( ( sK1 @ Y0 @ X2 )
& ( sK0 @ X1 @ Y0 ) )
=> ( sK1 @ X1 @ X2 ) )
@ X3 )
= $true )
| spl2_2 ),
inference(pi_proxy_clausification,[],[f246]) ).
thf(f250,plain,
( ( ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( sK1 @ Y2 @ Y3 ) ) )
| ~ ( sK0 @ Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( sK1 @ Y0 @ Y2 ) ) ) ) )
@ sK7 )
= $false )
| ~ spl2_1 ),
inference(sigma_proxy_clausification,[],[f146]) ).
thf(f251,plain,
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( sK1 @ Y1 @ Y2 ) ) )
| ~ ( sK0 @ sK7 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ( sK1 @ sK7 @ Y1 ) ) ) ) )
= $false )
| ~ spl2_1 ),
inference(beta-eta_normalization,[],[f250]) ).
thf(f275,plain,
( ( $true = $false )
| ~ spl2_2
| ~ spl2_4 ),
inference(forward_demodulation,[],[f159,f150]) ).
thf(f276,plain,
( $false
| ~ spl2_2
| ~ spl2_4 ),
inference(trivial_inequality_removal,[],[f275]) ).
thf(f277,plain,
( ~ spl2_2
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[],[f276]) ).
thf(f290,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( sK1 @ X3 @ X2 )
& ( sK0 @ X1 @ X3 ) )
=> ( sK1 @ X1 @ X2 ) ) )
| spl2_2 ),
inference(beta-eta_normalization,[],[f247]) ).
thf(f304,plain,
( ( $false
= ( ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( sK1 @ Y1 @ Y2 ) ) )
| ~ ( sK0 @ sK7 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ( sK1 @ sK7 @ Y1 ) ) ) )
@ sK8 ) )
| ~ spl2_1 ),
inference(sigma_proxy_clausification,[],[f251]) ).
thf(f305,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK8 @ Y1 )
| ~ ( sK1 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ sK7 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK8 @ Y0 )
| ~ ( sK1 @ sK7 @ Y0 ) ) ) ) )
| ~ spl2_1 ),
inference(beta-eta_normalization,[],[f304]) ).
thf(f306,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK8 @ Y0 )
| ~ ( sK1 @ sK7 @ Y0 ) ) ) )
= $false )
| ~ spl2_1 ),
inference(or_proxy_clausification,[],[f305]) ).
thf(f307,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK8 @ Y1 )
| ~ ( sK1 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ sK7 @ Y0 ) ) ) )
| ~ spl2_1 ),
inference(or_proxy_clausification,[],[f305]) ).
thf(f308,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK8 @ Y0 )
| ~ ( sK1 @ sK7 @ Y0 ) ) ) )
| ~ spl2_1 ),
inference(not_proxy_clausification,[],[f306]) ).
thf(f309,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] :
( ( sK8 @ Y0 )
| ~ ( sK1 @ sK7 @ Y0 ) )
@ X1 )
= $true )
| ~ spl2_1 ),
inference(pi_proxy_clausification,[],[f308]) ).
thf(f310,plain,
( ! [X1: $i] :
( $true
= ( ( sK8 @ X1 )
| ~ ( sK1 @ sK7 @ X1 ) ) )
| ~ spl2_1 ),
inference(beta-eta_normalization,[],[f309]) ).
thf(f312,plain,
( ( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK8 @ Y1 )
| ~ ( sK1 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ sK7 @ Y0 ) )
@ sK9 )
= $false )
| ~ spl2_1 ),
inference(sigma_proxy_clausification,[],[f307]) ).
thf(f313,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK8 @ Y0 )
| ~ ( sK1 @ sK9 @ Y0 ) ) )
| ~ ( sK0 @ sK7 @ sK9 ) )
= $false )
| ~ spl2_1 ),
inference(beta-eta_normalization,[],[f312]) ).
thf(f314,plain,
( ( ( ~ ( sK0 @ sK7 @ sK9 ) )
= $false )
| ~ spl2_1 ),
inference(or_proxy_clausification,[],[f313]) ).
thf(f315,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK8 @ Y0 )
| ~ ( sK1 @ sK9 @ Y0 ) ) )
= $false )
| ~ spl2_1 ),
inference(or_proxy_clausification,[],[f313]) ).
thf(f316,plain,
( ( $true
= ( sK0 @ sK7 @ sK9 ) )
| ~ spl2_1 ),
inference(not_proxy_clausification,[],[f314]) ).
thf(f322,plain,
( ! [X0: $i] :
( $true
= ( ( ( sK1 @ sK9 @ X0 )
& $true )
=> ( sK1 @ sK7 @ X0 ) ) )
| ~ spl2_1
| spl2_2 ),
inference(constrained_superposition,[],[f290,f316]) ).
thf(f325,plain,
( ! [X0: $i] :
( $true
= ( ( sK1 @ sK9 @ X0 )
=> ( sK1 @ sK7 @ X0 ) ) )
| ~ spl2_1
| spl2_2 ),
inference(boolean_simplification,[],[f322]) ).
thf(f329,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( sK8 @ Y0 )
| ~ ( sK1 @ sK9 @ Y0 ) )
@ sK10 ) )
| ~ spl2_1 ),
inference(sigma_proxy_clausification,[],[f315]) ).
thf(f330,plain,
( ( ( ( sK8 @ sK10 )
| ~ ( sK1 @ sK9 @ sK10 ) )
= $false )
| ~ spl2_1 ),
inference(beta-eta_normalization,[],[f329]) ).
thf(f331,plain,
( ( ( ~ ( sK1 @ sK9 @ sK10 ) )
= $false )
| ~ spl2_1 ),
inference(or_proxy_clausification,[],[f330]) ).
thf(f332,plain,
( ( $false
= ( sK8 @ sK10 ) )
| ~ spl2_1 ),
inference(or_proxy_clausification,[],[f330]) ).
thf(f337,plain,
( ( $true
= ( sK1 @ sK9 @ sK10 ) )
| ~ spl2_1 ),
inference(not_proxy_clausification,[],[f331]) ).
thf(f342,plain,
( ( ( $true
=> ( sK1 @ sK7 @ sK10 ) )
= $true )
| ~ spl2_1
| spl2_2 ),
inference(constrained_superposition,[],[f325,f337]) ).
thf(f349,plain,
( ( ( sK1 @ sK7 @ sK10 )
= $true )
| ~ spl2_1
| spl2_2 ),
inference(boolean_simplification,[],[f342]) ).
thf(f354,plain,
( ( $true
= ( ( sK8 @ sK10 )
| ~ $true ) )
| ~ spl2_1
| spl2_2 ),
inference(constrained_superposition,[],[f310,f349]) ).
thf(f362,plain,
( ( $true
= ( ( sK8 @ sK10 )
| $false ) )
| ~ spl2_1
| spl2_2 ),
inference(boolean_simplification,[],[f354]) ).
thf(f363,plain,
( ( $true
= ( sK8 @ sK10 ) )
| ~ spl2_1
| spl2_2 ),
inference(boolean_simplification,[],[f362]) ).
thf(f364,plain,
( ( $true = $false )
| ~ spl2_1
| spl2_2 ),
inference(forward_demodulation,[],[f363,f332]) ).
thf(f365,plain,
( $false
| ~ spl2_1
| spl2_2 ),
inference(trivial_inequality_removal,[],[f364]) ).
thf(f366,plain,
( ~ spl2_1
| spl2_2 ),
inference(avatar_contradiction_clause,[],[f365]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f151]) ).
cnf(s2,plain,
( spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f160]) ).
cnf(s4,plain,
( ~ spl2_2
| ~ spl2_3 ),
inference(sat_conversion,[],[f242]) ).
cnf(s6,plain,
( ~ spl2_2
| ~ spl2_4 ),
inference(sat_conversion,[],[f277]) ).
cnf(s7,plain,
( ~ spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f366]) ).
cnf(s8,plain,
~ spl2_2,
inference(rat,[],[s2,s4,s6]) ).
cnf(s9,plain,
~ spl2_1,
inference(rat,[],[s7,s8]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s1,s8,s9]) ).
thf(f367,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL879^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n026.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 10:27:42 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.35 % (409273)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.35 % (409279)lrs+10_16_si=on:nwc=1.5:random_seed=1584912755:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.35 % (409279)Instruction limit reached!
% 0.20/0.35 % (409279)------------------------------
% 0.20/0.35 % (409279)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (409279)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (409279)CaDiCaL version: 2.1.3
% 0.20/0.35 % (409279)Termination reason: Instruction limit
% 0.20/0.35 % (409279)Termination phase: Saturation
% 0.20/0.35 % (409279)Time elapsed: 0.005 s
% 0.20/0.35 % (409279)Peak memory usage: 12 MB
% 0.20/0.35 % (409279)Instructions burned: 18 (million)
% 0.20/0.35 % (409278)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=906490132:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.35 % (409286)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3223536980:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.35 % (409286)Instruction limit reached!
% 0.20/0.35 % (409286)------------------------------
% 0.20/0.35 % (409286)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (409286)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (409286)CaDiCaL version: 2.1.3
% 0.20/0.35 % (409286)Termination reason: Instruction limit
% 0.20/0.35 % (409286)Termination phase: Property scanning
% 0.20/0.35 % (409286)Time elapsed: 0.001 s
% 0.20/0.35 % (409286)Peak memory usage: 10 MB
% 0.20/0.35 % (409286)Instructions burned: 4 (million)
% 0.20/0.35 % (409280)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3759620009:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.35 % (409280)Instruction limit reached!
% 0.20/0.35 % (409280)------------------------------
% 0.20/0.35 % (409280)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (409280)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (409280)CaDiCaL version: 2.1.3
% 0.20/0.35 % (409280)Termination reason: Instruction limit
% 0.20/0.35 % (409280)Termination phase: Property scanning
% 0.20/0.35 % (409280)Time elapsed: 0.003 s
% 0.20/0.35 % (409280)Peak memory usage: 10 MB
% 0.20/0.35 % (409280)Instructions burned: 3 (million)
% 0.20/0.35 % (409289)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=696713028:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.20/0.35 % (409289)Instruction limit reached!
% 0.20/0.35 % (409289)------------------------------
% 0.20/0.35 % (409289)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (409289)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (409289)CaDiCaL version: 2.1.3
% 0.20/0.35 % (409289)Termination reason: Instruction limit
% 0.20/0.35 % (409289)Termination phase: Property scanning
% 0.20/0.35 % (409289)Time elapsed: 0.002 s
% 0.20/0.35 % (409289)Peak memory usage: 10 MB
% 0.20/0.35 % (409289)Instructions burned: 9 (million)
% 0.20/0.35 % (409283)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2646829552:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.35 % (409282)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1476336755:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.35 % (409284)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.35 % (409284)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.20/0.35 % (409281)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=1091102312:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.20/0.35 % (409284)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=2983868762:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.35 % (409278)Instruction limit reached!
% 0.20/0.35 % (409278)------------------------------
% 0.20/0.35 % (409278)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (409278)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (409278)CaDiCaL version: 2.1.3
% 0.20/0.35 % (409278)Termination reason: Instruction limit
% 0.20/0.35 % (409278)Termination phase: Saturation
% 0.20/0.35 % (409278)Time elapsed: 0.043 s
% 0.20/0.35 % (409278)Peak memory usage: 12 MB
% 0.20/0.35 % (409278)Instructions burned: 88 (million)
% 0.20/0.35 % (409282)Instruction limit reached!
% 0.20/0.35 % (409282)------------------------------
% 0.20/0.35 % (409282)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (409282)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (409282)CaDiCaL version: 2.1.3
% 0.20/0.35 % (409282)Termination reason: Instruction limit
% 0.20/0.35 % (409282)Termination phase: Saturation
% 0.20/0.35 % (409282)Time elapsed: 0.013 s
% 0.20/0.35 % (409282)Peak memory usage: 12 MB
% 0.20/0.35 % (409282)Instructions burned: 24 (million)
% 0.20/0.35 % (409291)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.35 % (409291)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3180534518:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.20/0.35 % (409299)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=3410460382:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.20/0.35 % (409298)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.20/0.35 % (409298)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.35 % (409291)Instruction limit reached!
% 0.20/0.35 % (409291)------------------------------
% 0.20/0.35 % (409291)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (409291)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (409291)CaDiCaL version: 2.1.3
% 0.20/0.35 % (409291)Termination reason: Instruction limit
% 0.20/0.35 % (409291)Termination phase: Saturation
% 0.20/0.35 % (409291)Time elapsed: 0.011 s
% 0.20/0.35 % (409291)Peak memory usage: 10 MB
% 0.20/0.35 % (409291)Instructions burned: 7 (million)
% 0.20/0.35 % (409298)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3257234138:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.20/0.35 % (409299) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-409273-409299"...
% 0.20/0.35 % (409283)Instruction limit reached!
% 0.20/0.35 % (409283)------------------------------
% 0.20/0.35 % (409283)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (409283)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (409283)CaDiCaL version: 2.1.3
% 0.20/0.35 % (409283)Termination reason: Instruction limit
% 0.20/0.35 % (409283)Termination phase: Saturation
% 0.20/0.35 % (409283)Time elapsed: 0.038 s
% 0.20/0.35 % (409283)Peak memory usage: 13 MB
% 0.20/0.35 % (409293)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3259261661:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.20/0.35 % (409283)Instructions burned: 76 (million)
% 0.20/0.35 % (409299)...printing done.
% 0.20/0.35 % (409299)Refutation found. Thanks to Tanya!
% 0.20/0.35 % SZS status Theorem for theBenchmark
% 0.20/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.35 % (409299)------------------------------
% 0.20/0.35 % (409299)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (409299)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (409299)CaDiCaL version: 2.1.3
% 0.20/0.35 % (409299)Termination reason: Refutation
% 0.20/0.35 % (409299)Time elapsed: 0.013 s
% 0.20/0.35 % (409299)Peak memory usage: 13 MB
% 0.20/0.35 % (409299)Instructions burned: 43 (million)
% 0.20/0.35 % (409273)Success in time 0.107 s
% 0.20/0.35 % Vampire exiting
%------------------------------------------------------------------------------