%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV311^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 08:38:14 AM UTC 2026
% Result : Theorem 0.21s 0.34s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 1
% Syntax : Number of formulae : 50 ( 32 unt; 0 typ; 0 def)
% Number of atoms : 375 ( 61 equ; 0 cnn)
% Maximal formula atoms : 5 ( 7 avg)
% Number of connectives : 903 ( 20 ~; 15 |; 0 &; 593 @)
% ( 0 <=>; 160 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 127 ( 127 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 13 usr; 4 con; 0-4 aty)
% ( 115 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 199 ( 149 ^; 50 !; 0 ?; 199 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cF: ( a > $o ) > a > $o ).
thf(func_def_2,type,
vNOT: $o > $o ).
thf(func_def_3,type,
vIMP: $o > $o > $o ).
thf(func_def_4,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_5,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_11,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_12,type,
sK0: a ).
thf(func_def_13,type,
sK1: a > $o ).
thf(func_def_14,type,
sK2: ( a > $o ) > a ).
thf(f1,conjecture,
( ! [X0: a > $o,X1: a > $o] :
( ! [X2: a] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) )
=> ! [X2: a] :
( ( cF @ X0 @ X2 )
=> ( cF @ X1 @ X2 ) ) )
=> ! [X2: a] :
( ( cF
@ ^ [X3: a] :
! [X4: a > $o] :
( ! [X5: a] :
( ( cF @ X4 @ X5 )
=> ( X4 @ X5 ) )
=> ( X4 @ X3 ) )
@ X2 )
=> ! [X4: a > $o] :
( ! [X3: a] :
( ( cF @ X4 @ X3 )
=> ( X4 @ X3 ) )
=> ( X4 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM521_pme) ).
thf(f2,negated_conjecture,
~ ( ! [X0: a > $o,X1: a > $o] :
( ! [X2: a] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) )
=> ! [X2: a] :
( ( cF @ X0 @ X2 )
=> ( cF @ X1 @ X2 ) ) )
=> ! [X2: a] :
( ( cF
@ ^ [X3: a] :
! [X4: a > $o] :
( ! [X5: a] :
( ( cF @ X4 @ X5 )
=> ( X4 @ X5 ) )
=> ( X4 @ X3 ) )
@ X2 )
=> ! [X4: a > $o] :
( ! [X3: a] :
( ( cF @ X4 @ X3 )
=> ( X4 @ X3 ) )
=> ( X4 @ X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ! [X0: a > $o,X1: a > $o] :
( ! [X2: a] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) )
=> ! [X3: a] :
( ( cF @ X0 @ X3 )
=> ( cF @ X1 @ X3 ) ) )
=> ! [X4: a] :
( ( cF
@ ^ [X5: a] :
! [X6: a > $o] :
( ! [X7: a] :
( ( cF @ X6 @ X7 )
=> ( X6 @ X7 ) )
=> ( X6 @ X5 ) )
@ X4 )
=> ! [X8: a > $o] :
( ! [X9: a] :
( ( cF @ X8 @ X9 )
=> ( X8 @ X9 ) )
=> ( X8 @ X4 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
( ( ~ ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( cF @ Y1 @ Y2 )
=> ( cF @ Y0 @ Y2 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y0: a] :
( ( cF
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( cF @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( cF @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( ~ ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( cF @ Y1 @ Y2 )
=> ( cF @ Y0 @ Y2 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y0: a] :
( ( cF
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( cF @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( cF @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f4]) ).
thf(f8,plain,
( $false
= ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( cF @ Y1 @ Y2 )
=> ( cF @ Y0 @ Y2 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y0: a] :
( ( cF
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( cF @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( cF @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f5]) ).
thf(f9,plain,
( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( cF
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( cF @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( cF @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f8]) ).
thf(f10,plain,
( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( cF @ Y1 @ Y2 )
=> ( cF @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f8]) ).
thf(f13,plain,
! [X1: a > $o] :
( ( ^ [Y0: a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( cF @ Y1 @ Y2 )
=> ( cF @ Y0 @ Y2 ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f10]) ).
thf(f14,plain,
! [X1: a > $o] :
( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( X1 @ Y1 ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( cF @ Y0 @ Y1 )
=> ( cF @ X1 @ Y1 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f13]) ).
thf(f15,plain,
! [X2: a > $o,X1: a > $o] :
( ( ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( X1 @ Y1 ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( cF @ Y0 @ Y1 )
=> ( cF @ X1 @ Y1 ) ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f14]) ).
thf(f16,plain,
! [X2: a > $o,X1: a > $o] :
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( X2 @ Y0 )
=> ( X1 @ Y0 ) ) )
=> ( !! @ a
@ ^ [Y0: a] :
( ( cF @ X2 @ Y0 )
=> ( cF @ X1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f15]) ).
thf(f17,plain,
! [X2: a > $o,X1: a > $o] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( cF @ X2 @ Y0 )
=> ( cF @ X1 @ Y0 ) ) ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( X2 @ Y0 )
=> ( X1 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f16]) ).
thf(f18,plain,
( $false
= ( ^ [Y0: a] :
( ( cF
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( cF @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( cF @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f9]) ).
thf(f19,plain,
( $false
= ( ( cF
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( cF @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) )
@ sK0 )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( ( cF @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0 @ sK0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f18]) ).
thf(f20,plain,
( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( ( cF @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0 @ sK0 ) ) ) ),
inference(imp_proxy_clausification,[],[f19]) ).
thf(f21,plain,
( ( cF
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( cF @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) )
@ sK0 )
= $true ),
inference(imp_proxy_clausification,[],[f19]) ).
thf(f22,plain,
( ( ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( ( cF @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0 @ sK0 ) )
@ sK1 )
= $false ),
inference(sigma_proxy_clausification,[],[f20]) ).
thf(f23,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( cF @ sK1 @ Y0 )
=> ( sK1 @ Y0 ) ) )
=> ( sK1 @ sK0 ) )
= $false ),
inference(beta-eta_normalization,[],[f22]) ).
thf(f24,plain,
( $false
= ( sK1 @ sK0 ) ),
inference(imp_proxy_clausification,[],[f23]) ).
thf(f25,plain,
( ( !! @ a
@ ^ [Y0: a] :
( ( cF @ sK1 @ Y0 )
=> ( sK1 @ Y0 ) ) )
= $true ),
inference(imp_proxy_clausification,[],[f23]) ).
thf(f30,plain,
! [X1: a] :
( ( ^ [Y0: a] :
( ( cF @ sK1 @ Y0 )
=> ( sK1 @ Y0 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f25]) ).
thf(f31,plain,
! [X1: a] :
( ( ( cF @ sK1 @ X1 )
=> ( sK1 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f30]) ).
thf(f33,plain,
( ( ( cF @ sK1 @ sK0 )
=> $false )
= $true ),
inference(constrained_superposition,[],[f31,f24]) ).
thf(f34,plain,
( $true
= ( ~ ( cF @ sK1 @ sK0 ) ) ),
inference(boolean_simplification,[],[f33]) ).
thf(f35,plain,
( $false
= ( cF @ sK1 @ sK0 ) ),
inference(not_proxy_clausification,[],[f34]) ).
thf(f46,plain,
! [X2: a > $o,X3: a,X1: a > $o] :
( ( ( ^ [Y0: a] :
( ( cF @ X2 @ Y0 )
=> ( cF @ X1 @ Y0 ) )
@ X3 )
= $true )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( X2 @ Y0 )
=> ( X1 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f17]) ).
thf(f47,plain,
! [X2: a > $o,X3: a,X1: a > $o] :
( ( $true
= ( ( cF @ X2 @ X3 )
=> ( cF @ X1 @ X3 ) ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( X2 @ Y0 )
=> ( X1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f46]) ).
thf(f50,plain,
! [X0: a > $o] :
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( X0 @ Y0 )
=> ( sK1 @ Y0 ) ) ) )
| ( $true
= ( ( cF @ X0 @ sK0 )
=> $false ) ) ),
inference(constrained_superposition,[],[f47,f35]) ).
thf(f55,plain,
! [X0: a > $o] :
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( X0 @ Y0 )
=> ( sK1 @ Y0 ) ) ) )
| ( $true
= ( ~ ( cF @ X0 @ sK0 ) ) ) ),
inference(boolean_simplification,[],[f50]) ).
thf(f63,plain,
! [X0: a > $o] :
( ( $false
= ( ^ [Y0: a] :
( ( X0 @ Y0 )
=> ( sK1 @ Y0 ) )
@ ( sK2 @ X0 ) ) )
| ( $true
= ( ~ ( cF @ X0 @ sK0 ) ) ) ),
inference(sigma_proxy_clausification,[],[f55]) ).
thf(f64,plain,
! [X0: a > $o] :
( ( $false
= ( ( X0 @ ( sK2 @ X0 ) )
=> ( sK1 @ ( sK2 @ X0 ) ) ) )
| ( $true
= ( ~ ( cF @ X0 @ sK0 ) ) ) ),
inference(beta-eta_normalization,[],[f63]) ).
thf(f65,plain,
! [X0: a > $o] :
( ( $true
= ( ~ ( cF @ X0 @ sK0 ) ) )
| ( ( sK1 @ ( sK2 @ X0 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f64]) ).
thf(f83,plain,
( ( ( ~ $true ) = $true )
| ( $false
= ( sK1
@ ( sK2
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( cF @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) ) ),
inference(constrained_superposition,[],[f65,f21]) ).
thf(f86,plain,
( ( $false = $true )
| ( $false
= ( sK1
@ ( sK2
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( cF @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) ) ),
inference(boolean_simplification,[],[f83]) ).
thf(f87,plain,
( $false
= ( sK1
@ ( sK2
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( cF @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) ),
inference(trivial_inequality_removal,[],[f86]) ).
thf(f91,plain,
( ( $false
= ( ( ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( cF @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) )
@ ( sK2
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( cF @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
=> $false ) )
| ( $true
= ( ~ ( cF
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( cF @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) )
@ sK0 ) ) ) ),
inference(constrained_superposition,[],[f64,f87]) ).
thf(f93,plain,
( ( $true
= ( ~ ( cF
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( cF @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) )
@ sK0 ) ) )
| ( $false
= ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( ( cF @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0
@ ( sK2
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( cF @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) )
=> $false ) ) ),
inference(beta-eta_normalization,[],[f91]) ).
thf(f94,plain,
( ( $true
= ( ~ ( cF
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( cF @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) )
@ sK0 ) ) )
| ( $false
= ( ~ ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( ( cF @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0
@ ( sK2
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( cF @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[],[f93]) ).
thf(f96,plain,
( ( ( ~ $true ) = $true )
| ( $false
= ( ~ ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( ( cF @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0
@ ( sK2
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( cF @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[],[f94,f21]) ).
thf(f97,plain,
( ( $false
= ( ~ ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( ( cF @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0
@ ( sK2
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( cF @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) ) ) )
| ( $false = $true ) ),
inference(boolean_simplification,[],[f96]) ).
thf(f98,plain,
( $false
= ( ~ ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( ( cF @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0
@ ( sK2
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( cF @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(trivial_inequality_removal,[],[f97]) ).
thf(f110,plain,
( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( ( cF @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0
@ ( sK2
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( cF @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f98]) ).
thf(f111,plain,
! [X1: a > $o] :
( $true
= ( ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( ( cF @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0
@ ( sK2
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( cF @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f110]) ).
thf(f112,plain,
! [X1: a > $o] :
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( cF @ X1 @ Y0 )
=> ( X1 @ Y0 ) ) )
=> ( X1
@ ( sK2
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( cF @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f111]) ).
thf(f114,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( cF @ sK1 @ Y0 )
=> ( sK1 @ Y0 ) ) )
=> $false )
= $true ),
inference(constrained_superposition,[],[f112,f87]) ).
thf(f118,plain,
( ( ~ ( !! @ a
@ ^ [Y0: a] :
( ( cF @ sK1 @ Y0 )
=> ( sK1 @ Y0 ) ) ) )
= $true ),
inference(boolean_simplification,[],[f114]) ).
thf(f122,plain,
( ( ~ $true ) = $true ),
inference(forward_demodulation,[],[f118,f25]) ).
thf(f123,plain,
$false = $true,
inference(boolean_simplification,[],[f122]) ).
thf(f124,plain,
$false,
inference(trivial_inequality_removal,[],[f123]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV311^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n009.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 15:33:45 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.25 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.34 % (4141924)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.34 % (4141934)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1240475473:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.34 % (4141935)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.34 % (4141935)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.21/0.34 % (4141929)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1367920720:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.34 % (4141930)lrs+10_16_si=on:nwc=1.5:random_seed=2580826614:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.34 % (4141931)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3719399305:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.34 % (4141935)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=329472670:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.34 % (4141933)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3864028517:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.34 % (4141932)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=2095644153:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.21/0.34 % (4141931)Refutation not found, incomplete strategy
% 0.21/0.34 % (4141931)------------------------------
% 0.21/0.34 % (4141931)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.34 % (4141931)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.34 % (4141931)CaDiCaL version: 2.1.3
% 0.21/0.34 % (4141931)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.34 % (4141931)Time elapsed: 0.002 s
% 0.21/0.34 % (4141931)Peak memory usage: 12 MB
% 0.21/0.34 % (4141931)Instructions burned: 3 (million)
% 0.21/0.34 % (4141931)------------------------------
% 0.21/0.34 % (4141931)------------------------------
% 0.21/0.34 % (4141930)Instruction limit reached!
% 0.21/0.34 % (4141930)------------------------------
% 0.21/0.34 % (4141930)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.34 % (4141930)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.34 % (4141930)CaDiCaL version: 2.1.3
% 0.21/0.34 % (4141930)Termination reason: Instruction limit
% 0.21/0.34 % (4141930)Termination phase: Saturation
% 0.21/0.34 % (4141930)Time elapsed: 0.012 s
% 0.21/0.34 % (4141930)Peak memory usage: 12 MB
% 0.21/0.34 % (4141930)Instructions burned: 19 (million)
% 0.21/0.34 % (4141934)Instruction limit reached!
% 0.21/0.34 % (4141934)------------------------------
% 0.21/0.34 % (4141934)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.34 % (4141934)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.34 % (4141934)CaDiCaL version: 2.1.3
% 0.21/0.34 % (4141934)Termination reason: Instruction limit
% 0.21/0.34 % (4141934)Termination phase: Saturation
% 0.21/0.34 % (4141934)Time elapsed: 0.021 s
% 0.21/0.34 % (4141934)Peak memory usage: 12 MB
% 0.21/0.34 % (4141934)Instructions burned: 77 (million)
% 0.21/0.34 % (4141933)Instruction limit reached!
% 0.21/0.34 % (4141933)------------------------------
% 0.21/0.34 % (4141933)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.34 % (4141933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.34 % (4141933)CaDiCaL version: 2.1.3
% 0.21/0.34 % (4141933)Termination reason: Instruction limit
% 0.21/0.34 % (4141933)Termination phase: Saturation
% 0.21/0.34 % (4141933)Time elapsed: 0.014 s
% 0.21/0.34 % (4141933)Peak memory usage: 12 MB
% 0.21/0.34 % (4141933)Instructions burned: 25 (million)
% 0.21/0.34 % (4141945)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.34 % (4141943)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3265341714:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.34 % (4141945)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=4289943393:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.21/0.34 % (4141943)Instruction limit reached!
% 0.21/0.34 % (4141943)------------------------------
% 0.21/0.34 % (4141943)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.34 % (4141943)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.34 % (4141943)CaDiCaL version: 2.1.3
% 0.21/0.34 % (4141943)Termination reason: Instruction limit
% 0.21/0.34 % (4141943)Termination phase: Saturation
% 0.21/0.34 % (4141943)Time elapsed: 0.002 s
% 0.21/0.34 % (4141943)Peak memory usage: 12 MB
% 0.21/0.34 % (4141943)Instructions burned: 2 (million)
% 0.21/0.34 % (4141945)Instruction limit reached!
% 0.21/0.34 % (4141945)------------------------------
% 0.21/0.34 % (4141945)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.34 % (4141945)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.34 % (4141945)CaDiCaL version: 2.1.3
% 0.21/0.34 % (4141945)Termination reason: Instruction limit
% 0.21/0.34 % (4141945)Termination phase: Saturation
% 0.21/0.34 % (4141945)Time elapsed: 0.003 s
% 0.21/0.34 % (4141945)Peak memory usage: 12 MB
% 0.21/0.34 % (4141945)Instructions burned: 11 (million)
% 0.21/0.34 % (4141944)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=4106113748:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.21/0.34 % (4141946)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1266381406:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.21/0.34 % (4141944)Instruction limit reached!
% 0.21/0.34 % (4141944)------------------------------
% 0.21/0.34 % (4141944)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.34 % (4141944)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.34 % (4141944)CaDiCaL version: 2.1.3
% 0.21/0.34 % (4141944)Termination reason: Instruction limit
% 0.21/0.34 % (4141944)Termination phase: Saturation
% 0.21/0.34 % (4141944)Time elapsed: 0.004 s
% 0.21/0.34 % (4141944)Peak memory usage: 12 MB
% 0.21/0.34 % (4141944)Instructions burned: 6 (million)
% 0.21/0.34 % (4141950)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=2482391612:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.21/0.34 % (4141949)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.21/0.34 % (4141949)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.34 % (4141946)Instruction limit reached!
% 0.21/0.34 % (4141946)------------------------------
% 0.21/0.34 % (4141946)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.34 % (4141946)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.34 % (4141946)CaDiCaL version: 2.1.3
% 0.21/0.34 % (4141946)Termination reason: Instruction limit
% 0.21/0.34 % (4141946)Termination phase: Saturation
% 0.21/0.34 % (4141946)Time elapsed: 0.009 s
% 0.21/0.34 % (4141946)Peak memory usage: 12 MB
% 0.21/0.34 % (4141946)Instructions burned: 14 (million)
% 0.21/0.34 % (4141950) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4141924-4141950"...
% 0.21/0.34 % (4141950)...printing done.
% 0.21/0.34 % (4141950)Refutation found. Thanks to Tanya!
% 0.21/0.34 % SZS status Theorem for theBenchmark
% 0.21/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.34 % (4141950)------------------------------
% 0.21/0.34 % (4141950)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.34 % (4141950)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.34 % (4141950)CaDiCaL version: 2.1.3
% 0.21/0.34 % (4141950)Termination reason: Refutation
% 0.21/0.34 % (4141950)Time elapsed: 0.006 s
% 0.21/0.34 % (4141950)Peak memory usage: 12 MB
% 0.21/0.34 % (4141950)Instructions burned: 18 (million)
% 0.21/0.34 % (4141924)Success in time 0.082 s
% 0.21/0.34 % Vampire exiting
%------------------------------------------------------------------------------