%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV289^5 : TPTP v9.3.1. Bugfixed v6.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 08:38:11 AM UTC 2026
% Result : Theorem 0.22s 0.31s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 4
% Syntax : Number of formulae : 43 ( 40 unt; 0 typ; 0 def)
% Number of atoms : 286 ( 77 equ; 0 cnn)
% Maximal formula atoms : 3 ( 6 avg)
% Number of connectives : 783 ( 67 ~; 0 |; 99 &; 455 @)
% ( 0 <=>; 62 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 329 ( 329 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 18 usr; 4 con; 0-4 aty)
% ( 43 !!; 57 ??; 0 @@+; 0 @@-)
% Number of variables : 217 ( 202 ^; 11 !; 4 ?; 217 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cNAT: ( ( $i > $o ) > $o ) > $o ).
thf(func_def_1,type,
cSUCC: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).
thf(func_def_2,type,
cZERO: ( $i > $o ) > $o ).
thf(func_def_4,type,
vNOT: $o > $o ).
thf(func_def_5,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_6,type,
vIMP: $o > $o > $o ).
thf(func_def_7,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_11,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_12,type,
vAND: $o > $o > $o ).
thf(func_def_13,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_16,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
sK0: ( $i > $o ) > $o ).
thf(func_def_18,type,
sK1: ( ( $i > $o ) > $o ) > $o ).
thf(func_def_19,type,
db4:
!>[X0: $tType] : X0 ).
thf(f1,axiom,
( cZERO
= ( ^ [X0: $i > $o] :
~ ? [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cZERO_def) ).
thf(f2,axiom,
( cSUCC
= ( ^ [X0: ( $i > $o ) > $o,X1: $i > $o] :
? [X2: $i] :
( ( X1 @ X2 )
& ( X0
@ ^ [X3: $i] :
( ( X3 != X2 )
& ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cSUCC_def) ).
thf(f3,axiom,
( cNAT
= ( ^ [X0: ( $i > $o ) > $o] :
! [X1: ( ( $i > $o ) > $o ) > $o] :
( ( ! [X2: ( $i > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( cSUCC @ X2 ) ) )
& ( X1 @ cZERO ) )
=> ( X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cNAT_def) ).
thf(f4,conjecture,
! [X0: ( $i > $o ) > $o] :
( ( cNAT @ X0 )
=> ( cNAT @ ( cSUCC @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTTTP6101) ).
thf(f5,negated_conjecture,
~ ! [X0: ( $i > $o ) > $o] :
( ( cNAT @ X0 )
=> ( cNAT @ ( cSUCC @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
~ ! [X0: ( $i > $o ) > $o] :
( ( cNAT @ X0 )
=> ( cNAT @ ( cSUCC @ X0 ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
( $true
= ( ~ ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( cNAT @ Y0 )
=> ( cNAT @ ( cSUCC @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( cSUCC
= ( ^ [X0: ( $i > $o ) > $o,X1: $i > $o] :
? [X2: $i] :
( ( X1 @ X2 )
& ( X0
@ ^ [X3: $i] :
( ( X3 != X2 )
& ( X1 @ X3 ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f9,plain,
( cSUCC
= ( ^ [Y0: ( $i > $o ) > $o,Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y2 != Y3 ) ) )
& ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
( cZERO
= ( ^ [X0: $i > $o] :
~ ? [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f1]) ).
thf(f11,plain,
( cZERO
= ( ^ [Y0: $i > $o] :
~ ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
( cNAT
= ( ^ [X0: ( $i > $o ) > $o] :
! [X1: ( ( $i > $o ) > $o ) > $o] :
( ( ! [X2: ( $i > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( cSUCC @ X2 ) ) )
& ( X1 @ cZERO ) )
=> ( X1 @ X0 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f13,plain,
( cNAT
= ( ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( Y1 @ cZERO )
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cSUCC @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
( cZERO
= ( ^ [Y0: $i > $o] :
~ ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f15,plain,
( cSUCC
= ( ^ [Y0: ( $i > $o ) > $o,Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y2 != Y3 ) ) )
& ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f16,plain,
( cNAT
= ( ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( Y1 @ cZERO )
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cSUCC @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f17,plain,
( $true
= ( ~ ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( cNAT @ Y0 )
=> ( cNAT @ ( cSUCC @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f20,plain,
( cNAT
= ( ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( Y1
@ ^ [Y2: $i > $o] :
~ ( ?? @ $i
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) )
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1
@ ( ^ [Y3: ( $i > $o ) > $o,Y4: $i > $o] :
( ?? @ $i
@ ^ [Y5: $i] :
( ( Y3
@ ^ [Y6: $i] :
( ( Y4 @ Y6 )
& ( Y5 != Y6 ) ) )
& ( Y4 @ Y5 ) ) )
@ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f16,f14,f15]) ).
thf(f21,plain,
( $true
= ( ~ ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( ^ [Y1: ( $i > $o ) > $o] :
( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y2: ( ( $i > $o ) > $o ) > $o] :
( ( ( Y2
@ ^ [Y3: $i > $o] :
~ ( ?? @ $i
@ ^ [Y4: $i] : ( Y3 @ Y4 ) ) )
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y3: ( $i > $o ) > $o] :
( ( Y2 @ Y3 )
=> ( Y2
@ ( ^ [Y4: ( $i > $o ) > $o,Y5: $i > $o] :
( ?? @ $i
@ ^ [Y6: $i] :
( ( Y4
@ ^ [Y7: $i] :
( ( Y5 @ Y7 )
& ( Y6 != Y7 ) ) )
& ( Y5 @ Y6 ) ) )
@ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( ^ [Y1: ( $i > $o ) > $o] :
( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y2: ( ( $i > $o ) > $o ) > $o] :
( ( ( Y2
@ ^ [Y3: $i > $o] :
~ ( ?? @ $i
@ ^ [Y4: $i] : ( Y3 @ Y4 ) ) )
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y3: ( $i > $o ) > $o] :
( ( Y2 @ Y3 )
=> ( Y2
@ ( ^ [Y4: ( $i > $o ) > $o,Y5: $i > $o] :
( ?? @ $i
@ ^ [Y6: $i] :
( ( Y4
@ ^ [Y7: $i] :
( ( Y5 @ Y7 )
& ( Y6 != Y7 ) ) )
& ( Y5 @ Y6 ) ) )
@ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
@ ( ^ [Y1: ( $i > $o ) > $o,Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y1
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 != Y4 ) ) )
& ( Y2 @ Y3 ) ) )
@ Y0 ) ) ) ) ) ),
inference(definition_unfolding,[],[f17,f20,f20,f15]) ).
thf(f22,plain,
( $true
= ( ~ ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( Y1
@ ^ [Y2: $i > $o] :
~ ( ?? @ $i @ Y2 ) )
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1
@ ^ [Y3: $i > $o] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( Y2
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
& ( Y4 != Y5 ) ) )
& ( Y3 @ Y4 ) ) ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
=> ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( Y1
@ ^ [Y2: $i > $o] :
~ ( ?? @ $i @ Y2 ) )
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1
@ ^ [Y3: $i > $o] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( Y2
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
& ( Y4 != Y5 ) ) )
& ( Y3 @ Y4 ) ) ) ) ) ) )
=> ( Y1
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y0
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 != Y4 ) ) )
& ( Y2 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f21]) ).
thf(f23,plain,
( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( Y1
@ ^ [Y2: $i > $o] :
~ ( ?? @ $i @ Y2 ) )
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1
@ ^ [Y3: $i > $o] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( Y2
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
& ( Y4 != Y5 ) ) )
& ( Y3 @ Y4 ) ) ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
=> ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( Y1
@ ^ [Y2: $i > $o] :
~ ( ?? @ $i @ Y2 ) )
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1
@ ^ [Y3: $i > $o] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( Y2
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
& ( Y4 != Y5 ) ) )
& ( Y3 @ Y4 ) ) ) ) ) ) )
=> ( Y1
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y0
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 != Y4 ) ) )
& ( Y2 @ Y3 ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f22]) ).
thf(f24,plain,
( ( ^ [Y0: ( $i > $o ) > $o] :
( ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( Y1
@ ^ [Y2: $i > $o] :
~ ( ?? @ $i @ Y2 ) )
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1
@ ^ [Y3: $i > $o] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( Y2
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
& ( Y4 != Y5 ) ) )
& ( Y3 @ Y4 ) ) ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
=> ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( Y1
@ ^ [Y2: $i > $o] :
~ ( ?? @ $i @ Y2 ) )
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1
@ ^ [Y3: $i > $o] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( Y2
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
& ( Y4 != Y5 ) ) )
& ( Y3 @ Y4 ) ) ) ) ) ) )
=> ( Y1
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y0
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 != Y4 ) ) )
& ( Y2 @ Y3 ) ) ) ) ) ) )
@ sK0 )
= $false ),
inference(sigma_proxy_clausification,[],[f23]) ).
thf(f27,plain,
( ( ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
( ( ( Y0
@ ^ [Y1: $i > $o] :
~ ( ?? @ $i @ Y1 ) )
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( Y0 @ Y1 )
=> ( Y0
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y1
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 != Y4 ) ) )
& ( Y2 @ Y3 ) ) ) ) ) ) )
=> ( Y0 @ sK0 ) ) )
=> ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
( ( ( Y0
@ ^ [Y1: $i > $o] :
~ ( ?? @ $i @ Y1 ) )
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( Y0 @ Y1 )
=> ( Y0
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y1
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 != Y4 ) ) )
& ( Y2 @ Y3 ) ) ) ) ) ) )
=> ( Y0
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( sK0
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y2 != Y3 ) ) )
& ( Y1 @ Y2 ) ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f24]) ).
thf(f28,plain,
( ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
( ( ( Y0
@ ^ [Y1: $i > $o] :
~ ( ?? @ $i @ Y1 ) )
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( Y0 @ Y1 )
=> ( Y0
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y1
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 != Y4 ) ) )
& ( Y2 @ Y3 ) ) ) ) ) ) )
=> ( Y0
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( sK0
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y2 != Y3 ) ) )
& ( Y1 @ Y2 ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f27]) ).
thf(f29,plain,
( $true
= ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
( ( ( Y0
@ ^ [Y1: $i > $o] :
~ ( ?? @ $i @ Y1 ) )
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( Y0 @ Y1 )
=> ( Y0
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y1
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 != Y4 ) ) )
& ( Y2 @ Y3 ) ) ) ) ) ) )
=> ( Y0 @ sK0 ) ) ) ),
inference(imp_proxy_clausification,[],[f27]) ).
thf(f30,plain,
! [X1: ( ( $i > $o ) > $o ) > $o] :
( $true
= ( ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
( ( ( Y0
@ ^ [Y1: $i > $o] :
~ ( ?? @ $i @ Y1 ) )
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( Y0 @ Y1 )
=> ( Y0
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y1
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 != Y4 ) ) )
& ( Y2 @ Y3 ) ) ) ) ) ) )
=> ( Y0 @ sK0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f29]) ).
thf(f31,plain,
! [X1: ( ( $i > $o ) > $o ) > $o] :
( $true
= ( ( ( X1
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 ) )
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( X1 @ Y0 )
=> ( X1
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y2 != Y3 ) ) )
& ( Y1 @ Y2 ) ) ) ) ) ) )
=> ( X1 @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f30]) ).
thf(f33,plain,
( ( ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
( ( ( Y0
@ ^ [Y1: $i > $o] :
~ ( ?? @ $i @ Y1 ) )
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( Y0 @ Y1 )
=> ( Y0
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y1
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 != Y4 ) ) )
& ( Y2 @ Y3 ) ) ) ) ) ) )
=> ( Y0
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( sK0
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y2 != Y3 ) ) )
& ( Y1 @ Y2 ) ) ) ) )
@ sK1 )
= $false ),
inference(sigma_proxy_clausification,[],[f28]) ).
thf(f34,plain,
( ( ( ( sK1
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 ) )
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( sK1 @ Y0 )
=> ( sK1
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y2 != Y3 ) ) )
& ( Y1 @ Y2 ) ) ) ) ) ) )
=> ( sK1
@ ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 != Y2 ) ) )
& ( Y0 @ Y1 ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f33]) ).
thf(f35,plain,
( ( sK1
@ ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 != Y2 ) ) )
& ( Y0 @ Y1 ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f34]) ).
thf(f36,plain,
( $true
= ( ( sK1
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 ) )
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( sK1 @ Y0 )
=> ( sK1
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y2 != Y3 ) ) )
& ( Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f34]) ).
thf(f37,plain,
( $true
= ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( sK1 @ Y0 )
=> ( sK1
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y2 != Y3 ) ) )
& ( Y1 @ Y2 ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f36]) ).
thf(f38,plain,
( $true
= ( sK1
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 ) ) ),
inference(and_proxy_clausification,[],[f36]) ).
thf(f39,plain,
( $true
= ( ( $true
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( sK1 @ Y0 )
=> ( sK1
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y2 != Y3 ) ) )
& ( Y1 @ Y2 ) ) ) ) ) ) )
=> ( sK1 @ sK0 ) ) ),
inference(constrained_superposition,[],[f31,f38]) ).
thf(f40,plain,
( $true
= ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( sK1 @ Y0 )
=> ( sK1
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y2 != Y3 ) ) )
& ( Y1 @ Y2 ) ) ) ) ) )
=> ( sK1 @ sK0 ) ) ),
inference(boolean_simplification,[],[f39]) ).
thf(f41,plain,
( $true
= ( $true
=> ( sK1 @ sK0 ) ) ),
inference(forward_demodulation,[],[f40,f37]) ).
thf(f42,plain,
( ( sK1 @ sK0 )
= $true ),
inference(boolean_simplification,[],[f41]) ).
thf(f45,plain,
! [X1: ( $i > $o ) > $o] :
( $true
= ( ^ [Y0: ( $i > $o ) > $o] :
( ( sK1 @ Y0 )
=> ( sK1
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y2 != Y3 ) ) )
& ( Y1 @ Y2 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f37]) ).
thf(f46,plain,
! [X1: ( $i > $o ) > $o] :
( $true
= ( ( sK1 @ X1 )
=> ( sK1
@ ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( X1
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 != Y2 ) ) )
& ( Y0 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f45]) ).
thf(f50,plain,
( ( $true
=> ( sK1
@ ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 != Y2 ) ) )
& ( Y0 @ Y1 ) ) ) ) )
= $true ),
inference(constrained_superposition,[],[f46,f42]) ).
thf(f53,plain,
( ( sK1
@ ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 != Y2 ) ) )
& ( Y0 @ Y1 ) ) ) )
= $true ),
inference(boolean_simplification,[],[f50]) ).
thf(f56,plain,
$true = $false,
inference(forward_demodulation,[],[f53,f35]) ).
thf(f57,plain,
$false,
inference(trivial_inequality_removal,[],[f56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV289^5 : TPTP v9.3.1. Bugfixed v6.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n019.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 15:31:33 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.31 % (924327)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.31 % (924332)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=298808522:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.31 % (924332)Refutation not found, incomplete strategy
% 0.22/0.31 % (924332)------------------------------
% 0.22/0.31 % (924332)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (924332)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (924332)CaDiCaL version: 2.1.3
% 0.22/0.31 % (924332)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.31 % (924332)Time elapsed: 0.003 s
% 0.22/0.31 % (924332)Peak memory usage: 12 MB
% 0.22/0.31 % (924332)Instructions burned: 9 (million)
% 0.22/0.31 % (924332)------------------------------
% 0.22/0.31 % (924332)------------------------------
% 0.22/0.31 % (924338)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.31 % (924338)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.22/0.31 % (924333)lrs+10_16_si=on:nwc=1.5:random_seed=3120672953:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.31 % (924334)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3375868999:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.31 % (924335)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=3097839635:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.22/0.31 % (924337)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3369017686:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.31 % (924336)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3092615565:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.31 % (924338)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=340235864:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.31 % (924334)Refutation not found, incomplete strategy
% 0.22/0.31 % (924334)------------------------------
% 0.22/0.31 % (924334)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (924334)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (924334)CaDiCaL version: 2.1.3
% 0.22/0.31 % (924334)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.31 % (924334)Time elapsed: 0.002 s
% 0.22/0.31 % (924334)Peak memory usage: 12 MB
% 0.22/0.31 % (924334)Instructions burned: 2 (million)
% 0.22/0.31 % (924334)------------------------------
% 0.22/0.31 % (924334)------------------------------
% 0.22/0.31 % (924340)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=908902311:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.31 % (924338)Refutation not found, incomplete strategy
% 0.22/0.31 % (924338)------------------------------
% 0.22/0.31 % (924338)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (924338)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (924338)CaDiCaL version: 2.1.3
% 0.22/0.31 % (924338)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.31 % (924338)Time elapsed: 0.005 s
% 0.22/0.31 % (924338)Peak memory usage: 12 MB
% 0.22/0.31 % (924338)Instructions burned: 7 (million)
% 0.22/0.31 % (924338)------------------------------
% 0.22/0.31 % (924338)------------------------------
% 0.22/0.31 % (924340)Instruction limit reached!
% 0.22/0.31 % (924340)------------------------------
% 0.22/0.31 % (924340)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (924340)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (924340)CaDiCaL version: 2.1.3
% 0.22/0.31 % (924340)Termination reason: Instruction limit
% 0.22/0.31 % (924340)Termination phase: Saturation
% 0.22/0.31 % (924340)Time elapsed: 0.001 s
% 0.22/0.31 % (924340)Peak memory usage: 12 MB
% 0.22/0.31 % (924340)Instructions burned: 3 (million)
% 0.22/0.31 % (924333)Instruction limit reached!
% 0.22/0.31 % (924333)------------------------------
% 0.22/0.31 % (924333)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (924333)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (924333)CaDiCaL version: 2.1.3
% 0.22/0.31 % (924333)Termination reason: Instruction limit
% 0.22/0.31 % (924333)Termination phase: Saturation
% 0.22/0.31 % (924333)Time elapsed: 0.010 s
% 0.22/0.31 % (924333)Peak memory usage: 12 MB
% 0.22/0.31 % (924333)Instructions burned: 18 (million)
% 0.22/0.31 % (924336)Instruction limit reached!
% 0.22/0.31 % (924336)------------------------------
% 0.22/0.31 % (924336)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (924336)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (924336)CaDiCaL version: 2.1.3
% 0.22/0.31 % (924336)Termination reason: Instruction limit
% 0.22/0.31 % (924336)Termination phase: Saturation
% 0.22/0.31 % (924336)Time elapsed: 0.014 s
% 0.22/0.31 % (924336)Peak memory usage: 12 MB
% 0.22/0.31 % (924336)Instructions burned: 24 (million)
% 0.22/0.31 % (924349)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.22/0.31 % (924347)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3104574531:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.22/0.31 % (924349)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=645923667:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.22/0.31 % (924350)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=500773033:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.22/0.31 % (924351)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.22/0.31 % (924351)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.22/0.31 % (924347)Instruction limit reached!
% 0.22/0.31 % (924347)------------------------------
% 0.22/0.31 % (924347)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (924347)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (924347)CaDiCaL version: 2.1.3
% 0.22/0.31 % (924347)Termination reason: Instruction limit
% 0.22/0.31 % (924347)Termination phase: Saturation
% 0.22/0.31 % (924347)Time elapsed: 0.004 s
% 0.22/0.31 % (924347)Peak memory usage: 12 MB
% 0.22/0.31 % (924347)Instructions burned: 6 (million)
% 0.22/0.31 % (924351)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1787778575:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.22/0.31 % (924349)Instruction limit reached!
% 0.22/0.31 % (924349)------------------------------
% 0.22/0.31 % (924349)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (924349)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (924349)CaDiCaL version: 2.1.3
% 0.22/0.31 % (924349)Termination reason: Instruction limit
% 0.22/0.31 % (924349)Termination phase: Saturation
% 0.22/0.31 % (924349)Time elapsed: 0.004 s
% 0.22/0.31 % (924349)Peak memory usage: 12 MB
% 0.22/0.31 % (924349)Instructions burned: 7 (million)
% 0.22/0.31 % (924350)Instruction limit reached!
% 0.22/0.31 % (924350)------------------------------
% 0.22/0.31 % (924350)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (924350)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (924350)CaDiCaL version: 2.1.3
% 0.22/0.31 % (924350)Termination reason: Instruction limit
% 0.22/0.31 % (924350)Termination phase: Saturation
% 0.22/0.31 % (924350)Time elapsed: 0.007 s
% 0.22/0.31 % (924350)Peak memory usage: 12 MB
% 0.22/0.31 % (924350)Instructions burned: 12 (million)
% 0.22/0.31 % (924352)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=4290338418:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.22/0.31 % (924352) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-924327-924352"...
% 0.22/0.31 % (924337)Instruction limit reached!
% 0.22/0.31 % (924337)------------------------------
% 0.22/0.31 % (924337)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (924337)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (924337)CaDiCaL version: 2.1.3
% 0.22/0.31 % (924337)Termination reason: Instruction limit
% 0.22/0.31 % (924337)Termination phase: Saturation
% 0.22/0.31 % (924337)Time elapsed: 0.039 s
% 0.22/0.31 % (924337)Peak memory usage: 12 MB
% 0.22/0.31 % (924337)Instructions burned: 76 (million)
% 0.22/0.31 % (924352)...printing done.
% 0.22/0.31 % (924352)Refutation found. Thanks to Tanya!
% 0.22/0.31 % SZS status Theorem for theBenchmark
% 0.22/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.31 % (924352)------------------------------
% 0.22/0.31 % (924352)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (924352)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (924352)CaDiCaL version: 2.1.3
% 0.22/0.31 % (924352)Termination reason: Refutation
% 0.22/0.31 % (924352)Time elapsed: 0.008 s
% 0.22/0.31 % (924352)Peak memory usage: 12 MB
% 0.22/0.31 % (924352)Instructions burned: 15 (million)
% 0.22/0.31 % (924327)Success in time 0.064 s
% 0.22/0.31 % Vampire exiting
%------------------------------------------------------------------------------