%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU940^5 : 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 : 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 08:31:59 AM UTC 2026
% Result : Theorem 0.20s 0.32s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 1
% Syntax : Number of formulae : 37 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 238 ( 97 equ; 27 cnn)
% Maximal formula atoms : 2 ( 6 avg)
% Number of connectives : 505 ( 4 ~; 12 |; 58 &; 338 @)
% ( 0 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 100 ( 100 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 16 usr; 6 con; 0-4 aty)
% ( 44 !!; 5 ??; 0 @@+; 0 @@-)
% Number of variables : 177 ( 153 ^; 21 !; 3 ?; 177 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,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,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_4,type,
vAND: $o > $o > $o ).
thf(func_def_5,type,
vIMP: $o > $o > $o ).
thf(func_def_6,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_10,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_14,type,
sK0: $i > $o ).
thf(func_def_15,type,
sK1: ( ( $i > $i ) > $o ) > $i > $i ).
thf(func_def_16,type,
sK2: ( ( $i > $i ) > $o ) > $i > $i ).
thf(f1,conjecture,
! [X0: $i > $o] :
? [X1: ( $i > $i ) > $o] :
( ( X1
@ ^ [X2: $i] : X2 )
& ! [X3: $i > $i,X4: $i > $i] :
( ( ( X1 @ X3 )
& ( X1 @ X4 ) )
=> ( ! [X5: $i] :
( ( X0 @ X5 )
=> ( X0 @ ( X3 @ X5 ) ) )
& ( X1
@ ^ [X2: $i] : ( X3 @ ( X4 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM112A_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: $i > $o] :
? [X1: ( $i > $i ) > $o] :
( ( X1
@ ^ [X2: $i] : X2 )
& ! [X3: $i > $i,X4: $i > $i] :
( ( ( X1 @ X3 )
& ( X1 @ X4 ) )
=> ( ! [X5: $i] :
( ( X0 @ X5 )
=> ( X0 @ ( X3 @ X5 ) ) )
& ( X1
@ ^ [X2: $i] : ( X3 @ ( X4 @ X2 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: $i > $o] :
? [X1: ( $i > $i ) > $o] :
( ( X1
@ ^ [X2: $i] : X2 )
& ! [X3: $i > $i,X4: $i > $i] :
( ( ( X1 @ X3 )
& ( X1 @ X4 ) )
=> ( ! [X5: $i] :
( ( X0 @ X5 )
=> ( X0 @ ( X3 @ X5 ) ) )
& ( X1
@ ^ [X6: $i] : ( X3 @ ( X4 @ X6 ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
( $true
= ( ~ ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ?? @ ( ( $i > $i ) > $o )
@ ^ [Y1: ( $i > $i ) > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( !! @ ( $i > $i )
@ ^ [Y3: $i > $i] :
( ( ( Y1 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( ( Y1
@ ^ [Y4: $i] : ( Y3 @ ( Y2 @ Y4 ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y4 )
=> ( Y0 @ ( Y3 @ Y4 ) ) ) ) ) ) ) )
& ( Y1
@ ^ [Y2: $i] : Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( $true
= ( ~ ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ?? @ ( ( $i > $i ) > $o )
@ ^ [Y1: ( $i > $i ) > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( !! @ ( $i > $i )
@ ^ [Y3: $i > $i] :
( ( ( Y1 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( ( Y1
@ ^ [Y4: $i] : ( Y3 @ ( Y2 @ Y4 ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y4 )
=> ( Y0 @ ( Y3 @ Y4 ) ) ) ) ) ) ) )
& ( Y1
@ ^ [Y2: $i] : Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f4]) ).
thf(f8,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ?? @ ( ( $i > $i ) > $o )
@ ^ [Y1: ( $i > $i ) > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( !! @ ( $i > $i )
@ ^ [Y3: $i > $i] :
( ( ( Y1 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( ( Y1
@ ^ [Y4: $i] : ( Y3 @ ( Y2 @ Y4 ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y4 )
=> ( Y0 @ ( Y3 @ Y4 ) ) ) ) ) ) ) )
& ( Y1
@ ^ [Y2: $i] : Y2 ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f5]) ).
thf(f9,plain,
( ( ^ [Y0: $i > $o] :
( ?? @ ( ( $i > $i ) > $o )
@ ^ [Y1: ( $i > $i ) > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( !! @ ( $i > $i )
@ ^ [Y3: $i > $i] :
( ( ( Y1 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( ( Y1
@ ^ [Y4: $i] : ( Y3 @ ( Y2 @ Y4 ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y4 )
=> ( Y0 @ ( Y3 @ Y4 ) ) ) ) ) ) ) )
& ( Y1
@ ^ [Y2: $i] : Y2 ) ) )
@ sK0 )
= $false ),
inference(sigma_proxy_clausification,[],[f8]) ).
thf(f12,plain,
( ( ?? @ ( ( $i > $i ) > $o )
@ ^ [Y0: ( $i > $i ) > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( ( ( Y0 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( ( Y0
@ ^ [Y3: $i] : ( Y2 @ ( Y1 @ Y3 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( sK0 @ Y3 )
=> ( sK0 @ ( Y2 @ Y3 ) ) ) ) ) ) ) )
& ( Y0
@ ^ [Y1: $i] : Y1 ) ) )
= $false ),
inference(beta-eta_normalization,[],[f9]) ).
thf(f13,plain,
! [X1: ( $i > $i ) > $o] :
( ( ^ [Y0: ( $i > $i ) > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( ( ( Y0 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( ( Y0
@ ^ [Y3: $i] : ( Y2 @ ( Y1 @ Y3 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( sK0 @ Y3 )
=> ( sK0 @ ( Y2 @ Y3 ) ) ) ) ) ) ) )
& ( Y0
@ ^ [Y1: $i] : Y1 ) )
@ X1 )
= $false ),
inference(pi_proxy_clausification,[],[f12]) ).
thf(f14,plain,
! [X1: ( $i > $i ) > $o] :
( ( ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( ( ( X1 @ Y0 )
& ( X1 @ Y1 ) )
=> ( ( X1
@ ^ [Y2: $i] : ( Y1 @ ( Y0 @ Y2 ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 )
=> ( sK0 @ ( Y1 @ Y2 ) ) ) ) ) ) ) )
& ( X1
@ ^ [Y0: $i] : Y0 ) )
= $false ),
inference(beta-eta_normalization,[],[f13]) ).
thf(f15,plain,
! [X1: ( $i > $i ) > $o] :
( ( ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( ( ( X1 @ Y0 )
& ( X1 @ Y1 ) )
=> ( ( X1
@ ^ [Y2: $i] : ( Y1 @ ( Y0 @ Y2 ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 )
=> ( sK0 @ ( Y1 @ Y2 ) ) ) ) ) ) ) )
= $false )
| ( ( X1
@ ^ [Y0: $i] : Y0 )
= $false ) ),
inference(and_proxy_clausification,[],[f14]) ).
thf(f16,plain,
! [X1: ( $i > $i ) > $o] :
( ( ( X1
@ ^ [Y0: $i] : Y0 )
= $false )
| ( ( ^ [Y0: $i > $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( ( ( X1 @ Y0 )
& ( X1 @ Y1 ) )
=> ( ( X1
@ ^ [Y2: $i] : ( Y1 @ ( Y0 @ Y2 ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 )
=> ( sK0 @ ( Y1 @ Y2 ) ) ) ) ) ) )
@ ( sK1 @ X1 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f15]) ).
thf(f17,plain,
! [X1: ( $i > $i ) > $o] :
( ( ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( ( ( X1 @ ( sK1 @ X1 ) )
& ( X1 @ Y0 ) )
=> ( ( X1
@ ^ [Y1: $i] : ( Y0 @ ( sK1 @ X1 @ Y1 ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( sK0 @ ( Y0 @ Y1 ) ) ) ) ) ) )
= $false )
| ( ( X1
@ ^ [Y0: $i] : Y0 )
= $false ) ),
inference(beta-eta_normalization,[],[f16]) ).
thf(f18,plain,
! [X1: ( $i > $i ) > $o] :
( ( ( ^ [Y0: $i > $i] :
( ( ( X1 @ ( sK1 @ X1 ) )
& ( X1 @ Y0 ) )
=> ( ( X1
@ ^ [Y1: $i] : ( Y0 @ ( sK1 @ X1 @ Y1 ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( sK0 @ ( Y0 @ Y1 ) ) ) ) ) )
@ ( sK2 @ X1 ) )
= $false )
| ( ( X1
@ ^ [Y0: $i] : Y0 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f17]) ).
thf(f19,plain,
! [X1: ( $i > $i ) > $o] :
( ( ( ( ( X1 @ ( sK1 @ X1 ) )
& ( X1 @ ( sK2 @ X1 ) ) )
=> ( ( X1
@ ^ [Y0: $i] : ( sK2 @ X1 @ ( sK1 @ X1 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK0 @ ( sK2 @ X1 @ Y0 ) ) ) ) ) )
= $false )
| ( ( X1
@ ^ [Y0: $i] : Y0 )
= $false ) ),
inference(beta-eta_normalization,[],[f18]) ).
thf(f21,plain,
! [X1: ( $i > $i ) > $o] :
( ( $true
= ( ( X1 @ ( sK1 @ X1 ) )
& ( X1 @ ( sK2 @ X1 ) ) ) )
| ( ( X1
@ ^ [Y0: $i] : Y0 )
= $false ) ),
inference(imp_proxy_clausification,[],[f19]) ).
thf(f22,plain,
! [X1: ( $i > $i ) > $o] :
( ( $true
= ( X1 @ ( sK2 @ X1 ) ) )
| ( ( X1
@ ^ [Y0: $i] : Y0 )
= $false ) ),
inference(and_proxy_clausification,[],[f21]) ).
thf(f27,plain,
( ( ^ [Y0: $i] : Y0 )
= ( sK2
@ ( (=)
@ ^ [Y0: $i] : Y0 ) ) ),
inference(leibniz_equality_elimination,[],[f22]) ).
thf(f42,plain,
( ( ( ( ( ^ [Y0: $i] : Y0 )
= ( sK1
@ ( (=)
@ ^ [Y0: $i] : Y0 ) ) )
& ( ( ^ [Y0: $i] : Y0 )
= ( ^ [Y0: $i] : Y0 ) ) )
= $true )
| ( ( ( ^ [Y0: $i] : Y0 )
= ( ^ [Y0: $i] : Y0 ) )
= $false ) ),
inference(constrained_superposition,[],[f21,f27]) ).
thf(f50,plain,
( ( ( ( ^ [Y0: $i] : Y0 )
= ( ^ [Y0: $i] : Y0 ) )
= $false )
| ( ( ( ( ^ [Y0: $i] : Y0 )
= ( sK1
@ ( (=)
@ ^ [Y0: $i] : Y0 ) ) )
& $true )
= $true ) ),
inference(boolean_simplification,[],[f42]) ).
thf(f51,plain,
( ( $true = $false )
| ( ( ( ( ^ [Y0: $i] : Y0 )
= ( sK1
@ ( (=)
@ ^ [Y0: $i] : Y0 ) ) )
& $true )
= $true ) ),
inference(boolean_simplification,[],[f50]) ).
thf(f52,plain,
( ( ( ( ^ [Y0: $i] : Y0 )
= ( sK1
@ ( (=)
@ ^ [Y0: $i] : Y0 ) ) )
& $true )
= $true ),
inference(trivial_inequality_removal,[],[f51]) ).
thf(f53,plain,
( ( ( ^ [Y0: $i] : Y0 )
= ( sK1
@ ( (=)
@ ^ [Y0: $i] : Y0 ) ) )
= $true ),
inference(boolean_simplification,[],[f52]) ).
thf(f57,plain,
( ( ( ( ^ [Y0: $i] : Y0 )
= ( ^ [Y0: $i] : Y0 ) )
= $false )
| ( ( ( $true
& ( ( ^ [Y0: $i] : Y0 )
= ( sK2
@ ( (=)
@ ^ [Y0: $i] : Y0 ) ) ) )
=> ( ( ( ^ [Y0: $i] : Y0 )
= ( ^ [Y0: $i] :
( sK2
@ ( (=)
@ ^ [Y1: $i] : Y1 )
@ ( sK1
@ ( (=)
@ ^ [Y1: $i] : Y1 )
@ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK0
@ ( sK2
@ ( (=)
@ ^ [Y1: $i] : Y1 )
@ Y0 ) ) ) ) ) )
= $false ) ),
inference(constrained_superposition,[],[f19,f53]) ).
thf(f58,plain,
( ( $true = $false )
| ( ( ( $true
& ( ( ^ [Y0: $i] : Y0 )
= ( sK2
@ ( (=)
@ ^ [Y0: $i] : Y0 ) ) ) )
=> ( ( ( ^ [Y0: $i] : Y0 )
= ( ^ [Y0: $i] :
( sK2
@ ( (=)
@ ^ [Y1: $i] : Y1 )
@ ( sK1
@ ( (=)
@ ^ [Y1: $i] : Y1 )
@ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK0
@ ( sK2
@ ( (=)
@ ^ [Y1: $i] : Y1 )
@ Y0 ) ) ) ) ) )
= $false ) ),
inference(boolean_simplification,[],[f57]) ).
thf(f59,plain,
( ( ( $true
& ( ( ^ [Y0: $i] : Y0 )
= ( sK2
@ ( (=)
@ ^ [Y0: $i] : Y0 ) ) ) )
=> ( ( ( ^ [Y0: $i] : Y0 )
= ( ^ [Y0: $i] :
( sK2
@ ( (=)
@ ^ [Y1: $i] : Y1 )
@ ( sK1
@ ( (=)
@ ^ [Y1: $i] : Y1 )
@ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK0
@ ( sK2
@ ( (=)
@ ^ [Y1: $i] : Y1 )
@ Y0 ) ) ) ) ) )
= $false ),
inference(trivial_inequality_removal,[],[f58]) ).
thf(f60,plain,
( ( ( ( ^ [Y0: $i] : Y0 )
= ( sK2
@ ( (=)
@ ^ [Y0: $i] : Y0 ) ) )
=> ( ( ( ^ [Y0: $i] : Y0 )
= ( ^ [Y0: $i] :
( sK2
@ ( (=)
@ ^ [Y1: $i] : Y1 )
@ ( sK1
@ ( (=)
@ ^ [Y1: $i] : Y1 )
@ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK0
@ ( sK2
@ ( (=)
@ ^ [Y1: $i] : Y1 )
@ Y0 ) ) ) ) ) )
= $false ),
inference(boolean_simplification,[],[f59]) ).
thf(f64,plain,
( ( ( ( ^ [Y0: $i] : Y0 )
= ( ^ [Y0: $i] : Y0 ) )
=> ( ( ( ^ [Y0: $i] : Y0 )
= ( ^ [Y0: $i] :
( ^ [Y1: $i] : Y1
@ ( sK1
@ ( (=)
@ ^ [Y1: $i] : Y1 )
@ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK0
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) ) ) ) )
= $false ),
inference(forward_demodulation,[],[f60,f27]) ).
thf(f65,plain,
( ( ( ( ^ [Y0: $i] : Y0 )
= ( ^ [Y0: $i] : Y0 ) )
=> ( ( ( ^ [Y0: $i] : Y0 )
= ( sK1
@ ( (=)
@ ^ [Y0: $i] : Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK0 @ Y0 ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f64]) ).
thf(f66,plain,
( ( ( ( ^ [Y0: $i] : Y0 )
= ( ^ [Y0: $i] : Y0 ) )
=> ( ( ( ^ [Y0: $i] : Y0 )
= ( sK1
@ ( (=)
@ ^ [Y0: $i] : Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] : $true ) ) )
= $false ),
inference(boolean_simplification,[],[f65]) ).
thf(f67,plain,
( ( $true
=> ( ( ( ^ [Y0: $i] : Y0 )
= ( sK1
@ ( (=)
@ ^ [Y0: $i] : Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] : $true ) ) )
= $false ),
inference(boolean_simplification,[],[f66]) ).
thf(f68,plain,
( ( ( ( ^ [Y0: $i] : Y0 )
= ( sK1
@ ( (=)
@ ^ [Y0: $i] : Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] : $true ) )
= $false ),
inference(boolean_simplification,[],[f67]) ).
thf(f71,plain,
( ( $true
& ( !! @ $i
@ ^ [Y0: $i] : $true ) )
= $false ),
inference(forward_demodulation,[],[f68,f53]) ).
thf(f72,plain,
( ( !! @ $i
@ ^ [Y0: $i] : $true )
= $false ),
inference(boolean_simplification,[],[f71]) ).
thf(f73,plain,
( ( ^ [Y0: $i] : $true
@ sK3 )
= $false ),
inference(sigma_proxy_clausification,[],[f72]) ).
thf(f74,plain,
$true = $false,
inference(beta-eta_normalization,[],[f73]) ).
thf(f75,plain,
$false,
inference(trivial_inequality_removal,[],[f74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU940^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/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 14:50:05 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 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
% 0.20/0.31 % (882388)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.31 % (882398)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=429756705:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.31 % (882399)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.31 % (882399)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
% 0.20/0.31 % (882393)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3663302570:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.31 % (882396)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=3918021184: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)
% 0.20/0.31 % (882394)lrs+10_16_si=on:nwc=1.5:random_seed=1864199470:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.31 % (882395)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4073156051:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.31 % (882397)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=889270709:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.31 % (882399)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=845141190:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.31 % (882395)Refutation not found, incomplete strategy
% 0.20/0.31 % (882395)------------------------------
% 0.20/0.31 % (882395)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (882395)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (882395)CaDiCaL version: 2.1.3
% 0.20/0.31 % (882395)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.31 % (882395)Time elapsed: 0.003 s
% 0.20/0.31 % (882395)Peak memory usage: 12 MB
% 0.20/0.31 % (882395)Instructions burned: 4 (million)
% 0.20/0.31 % (882395)------------------------------
% 0.20/0.31 % (882395)------------------------------
% 0.20/0.31 % (882393)Refutation not found, incomplete strategy
% 0.20/0.31 % (882393)------------------------------
% 0.20/0.31 % (882393)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (882393)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (882393)CaDiCaL version: 2.1.3
% 0.20/0.31 % (882393)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.31 % (882393)Time elapsed: 0.005 s
% 0.20/0.31 % (882393)Peak memory usage: 12 MB
% 0.20/0.31 % (882393)Instructions burned: 7 (million)
% 0.20/0.31 % (882393)------------------------------
% 0.20/0.31 % (882393)------------------------------
% 0.20/0.31 % (882397)Refutation not found, incomplete strategy
% 0.20/0.31 % (882397)------------------------------
% 0.20/0.31 % (882397)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (882397)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (882397)CaDiCaL version: 2.1.3
% 0.20/0.31 % (882397)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.31 % (882397)Time elapsed: 0.006 s
% 0.20/0.31 % (882397)Peak memory usage: 12 MB
% 0.20/0.31 % (882397)Instructions burned: 10 (million)
% 0.20/0.31 % (882399)Refutation not found, incomplete strategy
% 0.20/0.31 % (882399)------------------------------
% 0.20/0.31 % (882399)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (882399)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (882399)CaDiCaL version: 2.1.3
% 0.20/0.31 % (882399)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.31 % (882399)Time elapsed: 0.006 s
% 0.20/0.31 % (882399)Peak memory usage: 12 MB
% 0.20/0.31 % (882399)Instructions burned: 10 (million)
% 0.20/0.31 % (882397)------------------------------
% 0.20/0.31 % (882397)------------------------------
% 0.20/0.31 % (882396)Refutation not found, incomplete strategy
% 0.20/0.31 % (882396)------------------------------
% 0.20/0.31 % (882396)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (882396)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (882396)CaDiCaL version: 2.1.3
% 0.20/0.31 % (882396)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.31 % (882396)Time elapsed: 0.007 s
% 0.20/0.31 % (882396)Peak memory usage: 12 MB
% 0.20/0.31 % (882396)Instructions burned: 11 (million)
% 0.20/0.31 % (882399)------------------------------
% 0.20/0.31 % (882399)------------------------------
% 0.20/0.31 % (882396)------------------------------
% 0.20/0.31 % (882396)------------------------------
% 0.20/0.31 % (882394)Instruction limit reached!
% 0.20/0.31 % (882394)------------------------------
% 0.20/0.31 % (882394)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (882394)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (882394)CaDiCaL version: 2.1.3
% 0.20/0.31 % (882394)Termination reason: Instruction limit
% 0.20/0.31 % (882394)Termination phase: Saturation
% 0.20/0.31 % (882394)Time elapsed: 0.011 s
% 0.20/0.31 % (882394)Peak memory usage: 12 MB
% 0.20/0.31 % (882394)Instructions burned: 18 (million)
% 0.20/0.31 % (882398)Instruction limit reached!
% 0.20/0.31 % (882398)------------------------------
% 0.20/0.31 % (882398)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (882398)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (882398)CaDiCaL version: 2.1.3
% 0.20/0.31 % (882398)Termination reason: Instruction limit
% 0.20/0.31 % (882398)Termination phase: Saturation
% 0.20/0.31 % (882398)Time elapsed: 0.021 s
% 0.20/0.31 % (882398)Peak memory usage: 12 MB
% 0.20/0.31 % (882398)Instructions burned: 76 (million)
% 0.20/0.31 % (882409)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.31 % (882411)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
% 0.20/0.31 % (882407)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=797958050:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.32 % (882411)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.32 % (882413)lrs+10_1_si=on:cs=on:random_seed=3295129380:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.20/0.32 % (882408)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3481717571:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.20/0.32 % (882407)Instruction limit reached!
% 0.20/0.32 % (882407)------------------------------
% 0.20/0.32 % (882407)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (882407)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (882407)CaDiCaL version: 2.1.3
% 0.20/0.32 % (882407)Termination reason: Instruction limit
% 0.20/0.32 % (882407)Termination phase: Saturation
% 0.20/0.32 % (882407)Time elapsed: 0.002 s
% 0.20/0.32 % (882407)Peak memory usage: 12 MB
% 0.20/0.32 % (882407)Instructions burned: 2 (million)
% 0.20/0.32 % (882409)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1822087130:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.20/0.32 % (882411)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=4119906117:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.20/0.32 % (882410)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1008532767:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.20/0.32 % (882413)Instruction limit reached!
% 0.20/0.32 % (882413)------------------------------
% 0.20/0.32 % (882413)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (882413)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (882413)CaDiCaL version: 2.1.3
% 0.20/0.32 % (882413)Termination reason: Instruction limit
% 0.20/0.32 % (882413)Termination phase: Saturation
% 0.20/0.32 % (882413)Time elapsed: 0.003 s
% 0.20/0.32 % (882413)Peak memory usage: 12 MB
% 0.20/0.32 % (882413)Instructions burned: 10 (million)
% 0.20/0.32 % (882408)Instruction limit reached!
% 0.20/0.32 % (882408)------------------------------
% 0.20/0.32 % (882408)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (882408)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (882408)CaDiCaL version: 2.1.3
% 0.20/0.32 % (882408)Termination reason: Instruction limit
% 0.20/0.32 % (882408)Termination phase: Saturation
% 0.20/0.32 % (882408)Time elapsed: 0.004 s
% 0.20/0.32 % (882408)Peak memory usage: 12 MB
% 0.20/0.32 % (882408)Instructions burned: 6 (million)
% 0.20/0.32 % (882412)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=3644063135:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.20/0.32 % (882409)Instruction limit reached!
% 0.20/0.32 % (882409)------------------------------
% 0.20/0.32 % (882409)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (882409)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (882409)CaDiCaL version: 2.1.3
% 0.20/0.32 % (882409)Termination reason: Instruction limit
% 0.20/0.32 % (882409)Termination phase: Saturation
% 0.20/0.32 % (882409)Time elapsed: 0.004 s
% 0.20/0.32 % (882409)Peak memory usage: 12 MB
% 0.20/0.32 % (882409)Instructions burned: 7 (million)
% 0.20/0.32 % (882410)Instruction limit reached!
% 0.20/0.32 % (882410)------------------------------
% 0.20/0.32 % (882410)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (882410)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (882410)CaDiCaL version: 2.1.3
% 0.20/0.32 % (882410)Termination reason: Instruction limit
% 0.20/0.32 % (882410)Termination phase: Saturation
% 0.20/0.32 % (882410)Time elapsed: 0.007 s
% 0.20/0.32 % (882410)Peak memory usage: 12 MB
% 0.20/0.32 % (882410)Instructions burned: 13 (million)
% 0.20/0.32 % (882412) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-882388-882412"...
% 0.20/0.32 % (882421)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=4079463246:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.20/0.32 % (882412)...printing done.
% 0.20/0.32 % (882412)Refutation found. Thanks to Tanya!
% 0.20/0.32 % SZS status Theorem for theBenchmark
% 0.20/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.32 % (882412)------------------------------
% 0.20/0.32 % (882412)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (882412)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (882412)CaDiCaL version: 2.1.3
% 0.20/0.32 % (882412)Termination reason: Refutation
% 0.20/0.32 % (882412)Time elapsed: 0.007 s
% 0.20/0.32 % (882412)Peak memory usage: 12 MB
% 0.20/0.32 % (882412)Instructions burned: 11 (million)
% 0.20/0.32 % (882388)Success in time 0.074 s
% 0.20/0.32 % Vampire exiting
%------------------------------------------------------------------------------