%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV011^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 08:37:27 AM UTC 2026
% Result : Theorem 0.35s 0.52s
% Output : Refutation 0.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 7
% Syntax : Number of formulae : 109 ( 40 unt; 0 typ; 6 def)
% Number of atoms : 698 ( 154 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 1414 ( 95 ~; 90 |; 88 &; 856 @)
% ( 12 <=>; 111 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 76 ( 76 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 27 usr; 14 con; 0-4 aty)
% ( 154 !!; 8 ??; 0 @@+; 0 @@-)
% Number of variables : 251 ( 0 sgn 72 !; 3 ?; 251 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
vNOT: $o > $o ).
thf(func_def_2,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
vIMP: $o > $o > $o ).
thf(func_def_4,type,
vAND: $o > $o > $o ).
thf(func_def_5,type,
db3:
!>[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,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_10,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_11,type,
vIFF: $o > $o > $o ).
thf(func_def_12,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_14,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
sK0: a > a > $o ).
thf(func_def_18,type,
sK1: a ).
thf(func_def_20,type,
sK3: a ).
thf(func_def_21,type,
sK4: a ).
thf(func_def_22,type,
sK5: a > $o ).
thf(func_def_23,type,
sK6: a ).
thf(f1,conjecture,
! [X0: a > a > $o] :
( ( ! [X1: a] : ( X0 @ X1 @ X1 )
& ! [X1: a,X2: a] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) )
& ! [X1: a,X3: a,X2: a] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) )
=> ! [X1: a] :
? [X4: a > $o] :
( ( X4 @ X1 )
& ! [X5: a] :
( ( X4 @ X5 )
=> ! [X2: a] :
( ( X0 @ X5 @ X2 )
<=> ( X4 @ X2 ) ) )
& ! [X6: a > $o] :
( ( ( X6 @ X1 )
& ! [X5: a] :
( ( X6 @ X5 )
=> ! [X2: a] :
( ( X6 @ X2 )
<=> ( X0 @ X5 @ X2 ) ) ) )
=> ( X6 = X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM260_B_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > a > $o] :
( ( ! [X1: a] : ( X0 @ X1 @ X1 )
& ! [X1: a,X2: a] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) )
& ! [X1: a,X3: a,X2: a] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) )
=> ! [X1: a] :
? [X4: a > $o] :
( ( X4 @ X1 )
& ! [X5: a] :
( ( X4 @ X5 )
=> ! [X2: a] :
( ( X0 @ X5 @ X2 )
<=> ( X4 @ X2 ) ) )
& ! [X6: a > $o] :
( ( ( X6 @ X1 )
& ! [X5: a] :
( ( X6 @ X5 )
=> ! [X2: a] :
( ( X6 @ X2 )
<=> ( X0 @ X5 @ X2 ) ) ) )
=> ( X6 = X4 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > a > $o] :
( ( ! [X1: a] : ( X0 @ X1 @ X1 )
& ! [X2: a,X3: a] :
( ( X0 @ X2 @ X3 )
=> ( X0 @ X3 @ X2 ) )
& ! [X4: a,X5: a,X6: a] :
( ( ( X0 @ X6 @ X5 )
& ( X0 @ X4 @ X6 ) )
=> ( X0 @ X4 @ X5 ) ) )
=> ! [X7: a] :
? [X8: a > $o] :
( ( X8 @ X7 )
& ! [X9: a] :
( ( X8 @ X9 )
=> ! [X10: a] :
( ( X0 @ X9 @ X10 )
<=> ( X8 @ X10 ) ) )
& ! [X11: a > $o] :
( ( ( X11 @ X7 )
& ! [X12: a] :
( ( X11 @ X12 )
=> ! [X13: a] :
( ( X11 @ X13 )
<=> ( X0 @ X12 @ X13 ) ) ) )
=> ( X8 = X11 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
( $true
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] : ( Y0 @ Y1 @ Y1 ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( !! @ a
@ ^ [Y5: a] :
( ( Y3 @ Y5 )
= ( Y0 @ Y4 @ Y5 ) ) ) ) )
& ( Y3 @ Y1 ) )
=> ( Y2 = Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y3 @ Y4 )
= ( Y2 @ Y4 ) ) ) ) )
& ( Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( $true
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] : ( Y0 @ Y1 @ Y1 ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( !! @ a
@ ^ [Y5: a] :
( ( Y3 @ Y5 )
= ( Y0 @ Y4 @ Y5 ) ) ) ) )
& ( Y3 @ Y1 ) )
=> ( Y2 = Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y3 @ Y4 )
= ( Y2 @ Y4 ) ) ) ) )
& ( Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f4]) ).
thf(f8,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] : ( Y0 @ Y1 @ Y1 ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( !! @ a
@ ^ [Y5: a] :
( ( Y3 @ Y5 )
= ( Y0 @ Y4 @ Y5 ) ) ) ) )
& ( Y3 @ Y1 ) )
=> ( Y2 = Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y3 @ Y4 )
= ( Y2 @ Y4 ) ) ) ) )
& ( Y2 @ Y1 ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f5]) ).
thf(f9,plain,
( $false
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] : ( Y0 @ Y1 @ Y1 ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( !! @ a
@ ^ [Y5: a] :
( ( Y3 @ Y5 )
= ( Y0 @ Y4 @ Y5 ) ) ) ) )
& ( Y3 @ Y1 ) )
=> ( Y2 = Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y3 @ Y4 )
= ( Y2 @ Y4 ) ) ) ) )
& ( Y2 @ Y1 ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f8]) ).
thf(f12,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] : ( sK0 @ Y0 @ Y0 ) ) )
=> ( !! @ a
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 )
= ( sK0 @ Y3 @ Y4 ) ) ) ) )
& ( Y2 @ Y0 ) )
=> ( Y1 = Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( !! @ a
@ ^ [Y3: a] :
( ( sK0 @ Y2 @ Y3 )
= ( Y1 @ Y3 ) ) ) ) )
& ( Y1 @ Y0 ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f9]) ).
thf(f13,plain,
( ( !! @ a
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 )
= ( sK0 @ Y3 @ Y4 ) ) ) ) )
& ( Y2 @ Y0 ) )
=> ( Y1 = Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( !! @ a
@ ^ [Y3: a] :
( ( sK0 @ Y2 @ Y3 )
= ( Y1 @ Y3 ) ) ) ) )
& ( Y1 @ Y0 ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f12]) ).
thf(f14,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] : ( sK0 @ Y0 @ Y0 ) ) )
= $true ),
inference(imp_proxy_clausification,[],[f12]) ).
thf(f15,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] : ( sK0 @ Y0 @ Y0 ) ) ),
inference(and_proxy_clausification,[],[f14]) ).
thf(f16,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(and_proxy_clausification,[],[f14]) ).
thf(f17,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] : ( sK0 @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f15]) ).
thf(f18,plain,
! [X1: a] :
( ( sK0 @ X1 @ X1 )
= $true ),
inference(beta-eta_normalization,[],[f17]) ).
thf(f19,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) ) )
= $true ),
inference(and_proxy_clausification,[],[f16]) ).
thf(f20,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) ) )
= $true ),
inference(and_proxy_clausification,[],[f16]) ).
thf(f21,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f19]) ).
thf(f22,plain,
! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ Y0 @ X1 )
=> ( sK0 @ X1 @ Y0 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f21]) ).
thf(f23,plain,
! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( sK0 @ Y0 @ X1 )
=> ( sK0 @ X1 @ Y0 ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f22]) ).
thf(f24,plain,
! [X2: a,X1: a] :
( $true
= ( ( sK0 @ X2 @ X1 )
=> ( sK0 @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f23]) ).
thf(f25,plain,
! [X2: a,X1: a] :
( ( $true
= ( sK0 @ X1 @ X2 ) )
| ( $false
= ( sK0 @ X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f24]) ).
thf(f30,plain,
! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f20]) ).
thf(f31,plain,
! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK0 @ Y1 @ X1 )
& ( sK0 @ X1 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f30]) ).
thf(f32,plain,
! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK0 @ Y1 @ X1 )
& ( sK0 @ X1 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f31]) ).
thf(f33,plain,
! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK0 @ Y0 @ X1 )
& ( sK0 @ X1 @ X2 ) )
=> ( sK0 @ Y0 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f32]) ).
thf(f34,plain,
! [X2: a,X3: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK0 @ Y0 @ X1 )
& ( sK0 @ X1 @ X2 ) )
=> ( sK0 @ Y0 @ X2 ) )
@ X3 )
= $true ),
inference(pi_proxy_clausification,[],[f33]) ).
thf(f35,plain,
! [X2: a,X3: a,X1: a] :
( $true
= ( ( ( sK0 @ X3 @ X1 )
& ( sK0 @ X1 @ X2 ) )
=> ( sK0 @ X3 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f34]) ).
thf(f45,plain,
( ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 )
= ( sK0 @ Y3 @ Y4 ) ) ) ) )
& ( Y2 @ Y0 ) )
=> ( Y1 = Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( !! @ a
@ ^ [Y3: a] :
( ( sK0 @ Y2 @ Y3 )
= ( Y1 @ Y3 ) ) ) ) )
& ( Y1 @ Y0 ) ) )
@ sK1 )
= $false ),
inference(sigma_proxy_clausification,[],[f13]) ).
thf(f46,plain,
( $false
= ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 )
= ( sK0 @ Y2 @ Y3 ) ) ) ) )
& ( Y1 @ sK1 ) )
=> ( Y0 = Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( sK0 @ Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) ) )
& ( Y0 @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f45]) ).
thf(f47,plain,
! [X1: a > $o] :
( $false
= ( ^ [Y0: a > $o] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 )
= ( sK0 @ Y2 @ Y3 ) ) ) ) )
& ( Y1 @ sK1 ) )
=> ( Y0 = Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( sK0 @ Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) ) )
& ( Y0 @ sK1 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f46]) ).
thf(f48,plain,
! [X1: a > $o] :
( $false
= ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
= ( sK0 @ Y1 @ Y2 ) ) ) ) )
& ( Y0 @ sK1 ) )
=> ( X1 = Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK0 @ Y0 @ Y1 )
= ( X1 @ Y1 ) ) ) ) )
& ( X1 @ sK1 ) ) ),
inference(beta-eta_normalization,[],[f47]) ).
thf(f50,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
= ( sK0 @ Y1 @ Y2 ) ) ) ) )
& ( Y0 @ sK1 ) )
=> ( ( sK0 @ sK1 )
= Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ sK1 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK0 @ Y0 @ Y1 )
= ( sK0 @ sK1 @ Y1 ) ) ) ) )
& $true )
= $false ),
inference(constrained_superposition,[],[f48,f18]) ).
thf(f51,plain,
( $false
= ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
= ( sK0 @ Y1 @ Y2 ) ) ) ) )
& ( Y0 @ sK1 ) )
=> ( ( sK0 @ sK1 )
= Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ sK1 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK0 @ Y0 @ Y1 )
= ( sK0 @ sK1 @ Y1 ) ) ) ) ) ) ),
inference(boolean_simplification,[],[f50]) ).
thf(f52,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ sK1 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK0 @ Y0 @ Y1 )
= ( sK0 @ sK1 @ Y1 ) ) ) ) )
= $false )
| ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
= ( sK0 @ Y1 @ Y2 ) ) ) ) )
& ( Y0 @ sK1 ) )
=> ( ( sK0 @ sK1 )
= Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f51]) ).
thf(f54,definition,
( spl2_1
<=> ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
= ( sK0 @ Y1 @ Y2 ) ) ) ) )
& ( Y0 @ sK1 ) )
=> ( ( sK0 @ sK1 )
= Y0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f56,plain,
( ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
= ( sK0 @ Y1 @ Y2 ) ) ) ) )
& ( Y0 @ sK1 ) )
=> ( ( sK0 @ sK1 )
= Y0 ) ) ) )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f54]) ).
thf(f58,definition,
( spl2_2
<=> ( ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ sK1 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK0 @ Y0 @ Y1 )
= ( sK0 @ sK1 @ Y1 ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f60,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ sK1 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK0 @ Y0 @ Y1 )
= ( sK0 @ sK1 @ Y1 ) ) ) ) )
= $false )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f58]) ).
thf(f61,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f52,f58,f54]) ).
thf(f62,plain,
( ( ( ^ [Y0: a] :
( ( sK0 @ sK1 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK0 @ Y0 @ Y1 )
= ( sK0 @ sK1 @ Y1 ) ) ) )
@ sK3 )
= $false )
| ~ spl2_2 ),
inference(sigma_proxy_clausification,[],[f60]) ).
thf(f63,plain,
( ( $false
= ( ( sK0 @ sK1 @ sK3 )
=> ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ sK3 @ Y0 )
= ( sK0 @ sK1 @ Y0 ) ) ) ) )
| ~ spl2_2 ),
inference(beta-eta_normalization,[],[f62]) ).
thf(f64,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ sK3 @ Y0 )
= ( sK0 @ sK1 @ Y0 ) ) ) )
| ~ spl2_2 ),
inference(imp_proxy_clausification,[],[f63]) ).
thf(f65,plain,
( ( $true
= ( sK0 @ sK1 @ sK3 ) )
| ~ spl2_2 ),
inference(imp_proxy_clausification,[],[f63]) ).
thf(f67,plain,
( ! [X0: a] :
( $true
= ( ( $true
& ( sK0 @ sK3 @ X0 ) )
=> ( sK0 @ sK1 @ X0 ) ) )
| ~ spl2_2 ),
inference(constrained_superposition,[],[f35,f65]) ).
thf(f74,plain,
( ! [X0: a] :
( $true
= ( ( sK0 @ sK3 @ X0 )
=> ( sK0 @ sK1 @ X0 ) ) )
| ~ spl2_2 ),
inference(boolean_simplification,[],[f67]) ).
thf(f126,plain,
( ( ( ^ [Y0: a] :
( ( sK0 @ sK3 @ Y0 )
= ( sK0 @ sK1 @ Y0 ) )
@ sK4 )
= $false )
| ~ spl2_2 ),
inference(sigma_proxy_clausification,[],[f64]) ).
thf(f127,plain,
( ( $false
= ( ( sK0 @ sK3 @ sK4 )
= ( sK0 @ sK1 @ sK4 ) ) )
| ~ spl2_2 ),
inference(beta-eta_normalization,[],[f126]) ).
thf(f128,plain,
( ( ( sK0 @ sK1 @ sK4 )
!= ( sK0 @ sK3 @ sK4 ) )
| ~ spl2_2 ),
inference(iff_proxy_clausification,[],[f127]) ).
thf(f129,plain,
( ( ( sK0 @ sK1 @ sK4 )
= $true )
| ( $true
= ( sK0 @ sK3 @ sK4 ) )
| ~ spl2_2 ),
inference(xor_proxy_clausification,[],[f128]) ).
thf(f130,plain,
( ( ( sK0 @ sK1 @ sK4 )
= $false )
| ( $false
= ( sK0 @ sK3 @ sK4 ) )
| ~ spl2_2 ),
inference(xor_proxy_clausification,[],[f128]) ).
thf(f132,definition,
( spl2_3
<=> ( ( sK0 @ sK1 @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
thf(f133,plain,
( ( ( sK0 @ sK1 @ sK4 )
!= $true )
| spl2_3 ),
inference(avatar_component_clause,[],[f132]) ).
thf(f134,plain,
( ( ( sK0 @ sK1 @ sK4 )
= $true )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f132]) ).
thf(f136,definition,
( spl2_4
<=> ( $true
= ( sK0 @ sK3 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
thf(f138,plain,
( ( $true
= ( sK0 @ sK3 @ sK4 ) )
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f136]) ).
thf(f139,plain,
( spl2_3
| spl2_4
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f129,f58,f136,f132]) ).
thf(f141,definition,
( spl2_5
<=> ( ( sK0 @ sK1 @ sK4 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
thf(f143,plain,
( ( ( sK0 @ sK1 @ sK4 )
= $false )
| ~ spl2_5 ),
inference(avatar_component_clause,[],[f141]) ).
thf(f145,definition,
( spl2_6
<=> ( $false
= ( sK0 @ sK3 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition]) ).
thf(f147,plain,
( ( $false
= ( sK0 @ sK3 @ sK4 ) )
| ~ spl2_6 ),
inference(avatar_component_clause,[],[f145]) ).
thf(f148,plain,
( spl2_5
| spl2_6
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f130,f58,f145,f141]) ).
thf(f149,plain,
( ( $false = $true )
| ~ spl2_3
| ~ spl2_5 ),
inference(forward_demodulation,[],[f134,f143]) ).
thf(f150,plain,
( $false
| ~ spl2_3
| ~ spl2_5 ),
inference(trivial_inequality_removal,[],[f149]) ).
thf(f151,plain,
( ~ spl2_3
| ~ spl2_5 ),
inference(avatar_contradiction_clause,[],[f150]) ).
thf(f155,plain,
( ( $true
= ( $true
=> ( sK0 @ sK1 @ sK4 ) ) )
| ~ spl2_2
| ~ spl2_4 ),
inference(constrained_superposition,[],[f74,f138]) ).
thf(f166,plain,
( ( ( sK0 @ sK1 @ sK4 )
= $true )
| ~ spl2_2
| ~ spl2_4 ),
inference(boolean_simplification,[],[f155]) ).
thf(f172,plain,
( $false
| ~ spl2_2
| spl2_3
| ~ spl2_4 ),
inference(forward_subsumption_resolution,[],[f166,f133]) ).
thf(f173,plain,
( ~ spl2_2
| spl2_3
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[],[f172]) ).
thf(f265,plain,
( ! [X0: a] :
( $true
= ( ( ( sK0 @ X0 @ sK1 )
& $true )
=> ( sK0 @ X0 @ sK4 ) ) )
| ~ spl2_3 ),
inference(constrained_superposition,[],[f35,f134]) ).
thf(f269,plain,
( ! [X0: a] :
( ( ( sK0 @ X0 @ sK1 )
=> ( sK0 @ X0 @ sK4 ) )
= $true )
| ~ spl2_3 ),
inference(boolean_simplification,[],[f265]) ).
thf(f287,plain,
( ( $true
= ( ( sK0 @ sK3 @ sK1 )
=> $false ) )
| ~ spl2_3
| ~ spl2_6 ),
inference(constrained_superposition,[],[f269,f147]) ).
thf(f300,plain,
( ( ( ~ ( sK0 @ sK3 @ sK1 ) )
= $true )
| ~ spl2_3
| ~ spl2_6 ),
inference(boolean_simplification,[],[f287]) ).
thf(f302,plain,
( ( $true = ( ~ $true ) )
| ( $false
= ( sK0 @ sK1 @ sK3 ) )
| ~ spl2_3
| ~ spl2_6 ),
inference(constrained_superposition,[],[f300,f25]) ).
thf(f303,plain,
( ( $false = $true )
| ( $false
= ( sK0 @ sK1 @ sK3 ) )
| ~ spl2_3
| ~ spl2_6 ),
inference(boolean_simplification,[],[f302]) ).
thf(f304,plain,
( ( $false
= ( sK0 @ sK1 @ sK3 ) )
| ~ spl2_3
| ~ spl2_6 ),
inference(trivial_inequality_removal,[],[f303]) ).
thf(f758,plain,
( ( $false
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
= ( sK0 @ Y1 @ Y2 ) ) ) ) )
& ( Y0 @ sK1 ) )
=> ( ( sK0 @ sK1 )
= Y0 ) )
@ sK5 ) )
| ~ spl2_1 ),
inference(sigma_proxy_clausification,[],[f56]) ).
thf(f759,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK5 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y1 )
= ( sK0 @ Y0 @ Y1 ) ) ) ) )
& ( sK5 @ sK1 ) )
=> ( ( sK0 @ sK1 )
= sK5 ) ) )
| ~ spl2_1 ),
inference(beta-eta_normalization,[],[f758]) ).
thf(f760,plain,
( ( ( ( sK0 @ sK1 )
= sK5 )
= $false )
| ~ spl2_1 ),
inference(imp_proxy_clausification,[],[f759]) ).
thf(f761,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( sK5 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y1 )
= ( sK0 @ Y0 @ Y1 ) ) ) ) )
& ( sK5 @ sK1 ) ) )
| ~ spl2_1 ),
inference(imp_proxy_clausification,[],[f759]) ).
thf(f762,plain,
( ( sK5
!= ( sK0 @ sK1 ) )
| ~ spl2_1 ),
inference(equality_proxy_clausification,[],[f760]) ).
thf(f767,plain,
( ( ( sK0 @ sK1 @ sK6 )
!= ( sK5 @ sK6 ) )
| ~ spl2_1 ),
inference(negative_extensionality,[],[f762]) ).
thf(f798,plain,
( ( $true
= ( sK5 @ sK1 ) )
| ~ spl2_1 ),
inference(and_proxy_clausification,[],[f761]) ).
thf(f799,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK5 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y1 )
= ( sK0 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ~ spl2_1 ),
inference(and_proxy_clausification,[],[f761]) ).
thf(f1111,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK5 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y1 )
= ( sK0 @ Y0 @ Y1 ) ) ) )
@ X1 ) )
| ~ spl2_1 ),
inference(pi_proxy_clausification,[],[f799]) ).
thf(f1112,plain,
( ! [X1: a] :
( $true
= ( ( sK5 @ X1 )
=> ( !! @ a
@ ^ [Y0: a] :
( ( sK5 @ Y0 )
= ( sK0 @ X1 @ Y0 ) ) ) ) )
| ~ spl2_1 ),
inference(beta-eta_normalization,[],[f1111]) ).
thf(f1114,plain,
( ( $true
= ( $true
=> ( !! @ a
@ ^ [Y0: a] :
( ( sK5 @ Y0 )
= ( sK0 @ sK1 @ Y0 ) ) ) ) )
| ~ spl2_1 ),
inference(constrained_superposition,[],[f1112,f798]) ).
thf(f1116,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK5 @ Y0 )
= ( sK0 @ sK1 @ Y0 ) ) )
= $true )
| ~ spl2_1 ),
inference(boolean_simplification,[],[f1114]) ).
thf(f1118,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( ( sK5 @ Y0 )
= ( sK0 @ sK1 @ Y0 ) )
@ X1 )
= $true )
| ~ spl2_1 ),
inference(pi_proxy_clausification,[],[f1116]) ).
thf(f1119,plain,
( ! [X1: a] :
( ( ( sK5 @ X1 )
= ( sK0 @ sK1 @ X1 ) )
= $true )
| ~ spl2_1 ),
inference(beta-eta_normalization,[],[f1118]) ).
thf(f1120,plain,
( ! [X1: a] :
( ( sK0 @ sK1 @ X1 )
= ( sK5 @ X1 ) )
| ~ spl2_1 ),
inference(iff_proxy_clausification,[],[f1119]) ).
thf(f1142,plain,
( ( ( sK5 @ sK6 )
!= ( sK5 @ sK6 ) )
| ~ spl2_1 ),
inference(constrained_superposition,[],[f767,f1120]) ).
thf(f1173,plain,
( $false
| ~ spl2_1 ),
inference(trivial_inequality_removal,[],[f1142]) ).
thf(f1174,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[],[f1173]) ).
thf(f1317,plain,
( ( $false = $true )
| ~ spl2_2
| ~ spl2_3
| ~ spl2_6 ),
inference(forward_demodulation,[],[f65,f304]) ).
thf(f1318,plain,
( $false
| ~ spl2_2
| ~ spl2_3
| ~ spl2_6 ),
inference(trivial_inequality_removal,[],[f1317]) ).
thf(f1319,plain,
( ~ spl2_2
| ~ spl2_3
| ~ spl2_6 ),
inference(avatar_contradiction_clause,[],[f1318]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f61]) ).
cnf(s2,plain,
( ~ spl2_2
| spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f139]) ).
cnf(s3,plain,
( ~ spl2_2
| spl2_5
| spl2_6 ),
inference(sat_conversion,[],[f148]) ).
cnf(s4,plain,
( ~ spl2_3
| ~ spl2_5 ),
inference(sat_conversion,[],[f151]) ).
cnf(s6,plain,
( ~ spl2_2
| spl2_3
| ~ spl2_4 ),
inference(sat_conversion,[],[f173]) ).
cnf(s16,plain,
~ spl2_1,
inference(sat_conversion,[],[f1174]) ).
cnf(s30,plain,
( ~ spl2_2
| ~ spl2_3
| ~ spl2_6 ),
inference(sat_conversion,[],[f1319]) ).
cnf(s31,plain,
spl2_2,
inference(rat,[],[s1,s16]) ).
cnf(s32,plain,
spl2_3,
inference(rat,[],[s2,s6,s31]) ).
cnf(s33,plain,
~ spl2_6,
inference(rat,[],[s30,s31,s32]) ).
cnf(s34,plain,
~ spl2_5,
inference(rat,[],[s4,s32]) ).
cnf(s35,plain,
$false,
inference(rat,[],[s3,s31,s33,s34]) ).
thf(f1321,plain,
$false,
inference(avatar_sat_refutation,[],[s35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEV011^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.29 % Computer : n016.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8046.5625MB
% 0.11/0.29 % OS : Linux 6.8.0-71-generic
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Sep 29 15:04:49 UTC 2026
% 0.11/0.30 % CPUTime :
% 0.11/0.30 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.27/0.35 Running higher-order theorem proving
% 0.27/0.37 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
% 0.35/0.52 % (457293)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.35/0.52 % (457303)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1522383134:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.35/0.52 % (457300)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4267562750:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.35/0.52 % (457299)lrs+10_16_si=on:nwc=1.5:random_seed=4243711933:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.35/0.52 % (457298)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3052583305:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.35/0.52 % (457301)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=3043557589: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)
% 0.35/0.52 % (457300)Instruction limit reached!
% 0.35/0.52 % (457300)------------------------------
% 0.35/0.52 % (457300)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.52 % (457300)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.52 % (457300)CaDiCaL version: 2.1.3
% 0.35/0.52 % (457300)Termination reason: Instruction limit
% 0.35/0.52 % (457300)Termination phase: Saturation
% 0.35/0.52 % (457300)Time elapsed: 0.004 s
% 0.35/0.52 % (457300)Peak memory usage: 12 MB
% 0.35/0.52 % (457300)Instructions burned: 3 (million)
% 0.35/0.52 % (457304)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.35/0.52 % (457304)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
% 0.35/0.52 % (457299)Instruction limit reached!
% 0.35/0.52 % (457299)------------------------------
% 0.35/0.52 % (457299)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.52 % (457299)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.52 % (457299)CaDiCaL version: 2.1.3
% 0.35/0.52 % (457299)Termination reason: Instruction limit
% 0.35/0.52 % (457299)Termination phase: Saturation
% 0.35/0.52 % (457299)Time elapsed: 0.018 s
% 0.35/0.52 % (457299)Peak memory usage: 12 MB
% 0.35/0.52 % (457299)Instructions burned: 18 (million)
% 0.35/0.52 % (457302)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=449060543:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.35/0.52 % (457304)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=923339660:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.35/0.52 % (457303)Instruction limit reached!
% 0.35/0.52 % (457303)------------------------------
% 0.35/0.52 % (457303)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.52 % (457303)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.52 % (457303)CaDiCaL version: 2.1.3
% 0.35/0.52 % (457303)Termination reason: Instruction limit
% 0.35/0.52 % (457303)Termination phase: Saturation
% 0.35/0.52 % (457303)Time elapsed: 0.036 s
% 0.35/0.52 % (457303)Peak memory usage: 13 MB
% 0.35/0.52 % (457303)Instructions burned: 76 (million)
% 0.35/0.52 % (457314)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.35/0.52 % (457310)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1814867854:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.35/0.52 % (457314)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3451211797:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.35/0.52 % (457310)Instruction limit reached!
% 0.35/0.52 % (457310)------------------------------
% 0.35/0.52 % (457310)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.52 % (457310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.52 % (457310)CaDiCaL version: 2.1.3
% 0.35/0.52 % (457310)Termination reason: Instruction limit
% 0.35/0.52 % (457310)Termination phase: Saturation
% 0.35/0.52 % (457310)Time elapsed: 0.003 s
% 0.35/0.52 % (457310)Peak memory usage: 12 MB
% 0.35/0.52 % (457310)Instructions burned: 2 (million)
% 0.35/0.52 % (457302)Instruction limit reached!
% 0.35/0.52 % (457302)------------------------------
% 0.35/0.52 % (457302)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.52 % (457302)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.52 % (457302)CaDiCaL version: 2.1.3
% 0.35/0.52 % (457302)Termination reason: Instruction limit
% 0.35/0.52 % (457302)Termination phase: Saturation
% 0.35/0.52 % (457302)Time elapsed: 0.023 s
% 0.35/0.52 % (457302)Peak memory usage: 12 MB
% 0.35/0.52 % (457302)Instructions burned: 24 (million)
% 0.35/0.52 % (457314)Instruction limit reached!
% 0.35/0.52 % (457314)------------------------------
% 0.35/0.52 % (457314)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.52 % (457314)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.52 % (457314)CaDiCaL version: 2.1.3
% 0.35/0.52 % (457314)Termination reason: Instruction limit
% 0.35/0.52 % (457314)Termination phase: Saturation
% 0.35/0.52 % (457314)Time elapsed: 0.004 s
% 0.35/0.52 % (457314)Peak memory usage: 12 MB
% 0.35/0.52 % (457314)Instructions burned: 9 (million)
% 0.35/0.52 % (457313)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2769641308:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.35/0.52 % (457313)Instruction limit reached!
% 0.35/0.52 % (457313)------------------------------
% 0.35/0.52 % (457313)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.52 % (457313)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.52 % (457313)CaDiCaL version: 2.1.3
% 0.35/0.52 % (457313)Termination reason: Instruction limit
% 0.35/0.52 % (457313)Termination phase: Saturation
% 0.35/0.52 % (457313)Time elapsed: 0.006 s
% 0.35/0.52 % (457313)Peak memory usage: 12 MB
% 0.35/0.52 % (457313)Instructions burned: 6 (million)
% 0.35/0.52 % (457319)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=1548743408:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.35/0.52 % (457318)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
% 0.35/0.52 % (457318)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.35/0.52 % (457317)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2558442035:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.35/0.52 % (457318)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=907947403:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.35/0.52 % (457298)Instruction limit reached!
% 0.35/0.52 % (457298)------------------------------
% 0.35/0.52 % (457298)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.52 % (457298)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.52 % (457298)CaDiCaL version: 2.1.3
% 0.35/0.52 % (457298)Termination reason: Instruction limit
% 0.35/0.52 % (457298)Termination phase: Saturation
% 0.35/0.52 % (457298)Time elapsed: 0.079 s
% 0.35/0.52 % (457298)Peak memory usage: 13 MB
% 0.35/0.52 % (457298)Instructions burned: 87 (million)
% 0.35/0.52 % (457317)Instruction limit reached!
% 0.35/0.52 % (457317)------------------------------
% 0.35/0.52 % (457317)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.52 % (457317)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.52 % (457317)CaDiCaL version: 2.1.3
% 0.35/0.52 % (457317)Termination reason: Instruction limit
% 0.35/0.52 % (457317)Termination phase: Saturation
% 0.35/0.52 % (457317)Time elapsed: 0.013 s
% 0.35/0.52 % (457317)Peak memory usage: 12 MB
% 0.35/0.52 % (457317)Instructions burned: 12 (million)
% 0.35/0.52 % (457321)lrs+10_1_si=on:cs=on:random_seed=1580987228:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.35/0.52 % (457319) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-457293-457319"...
% 0.35/0.52 % (457321)Instruction limit reached!
% 0.35/0.52 % (457321)------------------------------
% 0.35/0.52 % (457321)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.52 % (457321)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.52 % (457321)CaDiCaL version: 2.1.3
% 0.35/0.52 % (457321)Termination reason: Instruction limit
% 0.35/0.52 % (457321)Termination phase: Saturation
% 0.35/0.52 % (457321)Time elapsed: 0.009 s
% 0.35/0.52 % (457321)Peak memory usage: 12 MB
% 0.35/0.52 % (457321)Instructions burned: 8 (million)
% 0.35/0.52 % (457319)...printing done.
% 0.35/0.52 % (457318)Instruction limit reached!
% 0.35/0.52 % (457318)------------------------------
% 0.35/0.52 % (457318)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.52 % (457318)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.52 % (457318)CaDiCaL version: 2.1.3
% 0.35/0.52 % (457318)Termination reason: Instruction limit
% 0.35/0.52 % (457318)Termination phase: Saturation
% 0.35/0.52 % (457318)Time elapsed: 0.025 s
% 0.35/0.52 % (457318)Peak memory usage: 12 MB
% 0.35/0.52 % (457318)Instructions burned: 28 (million)
% 0.35/0.52 % (457319)Refutation found. Thanks to Tanya!
% 0.35/0.52 % SZS status Theorem for theBenchmark
% 0.35/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.35/0.52 % (457319)------------------------------
% 0.35/0.52 % (457319)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.52 % (457319)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.52 % (457319)CaDiCaL version: 2.1.3
% 0.35/0.52 % (457319)Termination reason: Refutation
% 0.35/0.52 % (457319)Time elapsed: 0.036 s
% 0.35/0.52 % (457319)Peak memory usage: 13 MB
% 0.35/0.52 % (457319)Instructions burned: 71 (million)
% 0.35/0.52 % (457293)Success in time 0.142 s
% 0.35/0.52 % Vampire exiting
%------------------------------------------------------------------------------