%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM832^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:24:52 AM UTC 2026
% Result : Theorem 9.42s 2.51s
% Output : Refutation 9.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 6
% Syntax : Number of formulae : 95 ( 42 unt; 0 typ; 4 def)
% Number of atoms : 841 ( 85 equ; 0 cnn)
% Maximal formula atoms : 11 ( 8 avg)
% Number of connectives : 1812 ( 64 ~; 55 |; 55 &;1273 @)
% ( 4 <=>; 123 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 18 usr; 14 con; 0-3 aty)
% ( 172 !!; 66 ??; 0 @@+; 0 @@-)
% Number of variables : 265 ( 187 ^; 75 !; 3 ?; 265 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
cR: $i > $i > $i > $o ).
thf(func_def_2,type,
cS: $i > $i ).
thf(func_def_18,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
sK4: ( $i > $o ) > $i ).
thf(func_def_22,type,
sK5: $i > $i ).
thf(func_def_24,type,
sK7: $i > $i ).
thf(func_def_26,type,
sK9: $i > $i ).
thf(func_def_31,type,
sK14: ( $i > $o ) > $i ).
thf(f2338,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f597,f623,f1276,f2284,f2336]) ).
thf(f2336,plain,
( ~ spl0_4
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f2335]) ).
thf(f2335,plain,
( $false
| ~ spl0_4
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f2304]) ).
thf(f2304,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_6 ),
inference(backward_demodulation,[status(thm)],[f705,f2289]) ).
thf(f2289,plain,
( ! [X1: $i] :
( ( cR @ ( cS @ sK8 ) @ c0 @ X1 )
= $false )
| ~ spl0_6 ),
inference(pi_clausification,[status(thm)],[f1275]) ).
thf(f1275,plain,
( ( $false
= ( ?? @ $i @ ( cR @ ( cS @ sK8 ) @ c0 ) ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f1273]) ).
thf(f1273,definition,
( spl0_6
<=> ( $false
= ( ?? @ $i @ ( cR @ ( cS @ sK8 ) @ c0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f705,plain,
( ( $true
= ( cR @ ( cS @ sK8 ) @ c0 @ ( sK9 @ ( cS @ c0 ) ) ) )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f700]) ).
thf(f700,plain,
( ( $true
= ( $true
=> ( cR @ ( cS @ sK8 ) @ c0 @ ( sK9 @ ( cS @ c0 ) ) ) ) )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f70,f680]) ).
thf(f680,plain,
( ! [X1: $i] :
( $true
= ( cR @ sK8 @ X1 @ ( sK9 @ X1 ) ) )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f676]) ).
thf(f676,plain,
( ! [X1: $i] :
( $true
= ( ?? @ $i @ ( cR @ sK8 @ X1 ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f674]) ).
thf(f674,plain,
( ! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( ?? @ $i @ ( cR @ sK8 @ Y0 ) )
@ X1 ) )
| ~ spl0_4 ),
inference(pi_clausification,[status(thm)],[f655]) ).
thf(f655,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( ?? @ $i @ ( cR @ sK8 @ Y0 ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f629]) ).
thf(f629,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] : ( ?? @ $i @ ( cR @ sK8 @ Y0 ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] : ( ?? @ $i @ ( cR @ ( cS @ sK8 ) @ Y0 ) ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f627]) ).
thf(f627,plain,
( ( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] : ( ?? @ $i @ ( cR @ Y0 @ Y1 ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] : ( ?? @ $i @ ( cR @ ( cS @ Y0 ) @ Y1 ) ) ) )
@ sK8 )
= $false )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f596]) ).
thf(f596,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] : ( ?? @ $i @ ( cR @ Y0 @ Y1 ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] : ( ?? @ $i @ ( cR @ ( cS @ Y0 ) @ Y1 ) ) ) ) )
= $false )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f594]) ).
thf(f594,definition,
( spl0_4
<=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] : ( ?? @ $i @ ( cR @ Y0 @ Y1 ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] : ( ?? @ $i @ ( cR @ ( cS @ Y0 ) @ Y1 ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f70,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( cR @ X2 @ ( cS @ c0 ) @ X1 )
=> ( cR @ ( cS @ X2 ) @ c0 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f66]) ).
thf(f66,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( cR @ Y0 @ ( cS @ c0 ) @ X1 )
=> ( cR @ ( cS @ Y0 ) @ c0 @ X1 ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f63]) ).
thf(f63,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( cR @ Y0 @ ( cS @ c0 ) @ X1 )
=> ( cR @ ( cS @ Y0 ) @ c0 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f60]) ).
thf(f60,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cR @ Y1 @ ( cS @ c0 ) @ Y0 )
=> ( cR @ ( cS @ Y1 ) @ c0 @ Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cR @ Y1 @ ( cS @ c0 ) @ Y0 )
=> ( cR @ ( cS @ Y1 ) @ c0 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cR @ Y1 @ ( cS @ c0 ) @ Y0 )
=> ( cR @ ( cS @ Y1 ) @ c0 @ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( cR @ ( cS @ Y3 ) @ Y2 @ Y0 )
=> ( ( cR @ Y3 @ Y0 @ Y1 )
=> ( cR @ ( cS @ Y3 ) @ ( cS @ Y2 ) @ Y1 ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f35]) ).
thf(f35,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cR @ Y1 @ ( cS @ c0 ) @ Y0 )
=> ( cR @ ( cS @ Y1 ) @ c0 @ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( cR @ ( cS @ Y3 ) @ Y2 @ Y0 )
=> ( ( cR @ Y3 @ Y0 @ Y1 )
=> ( cR @ ( cS @ Y3 ) @ ( cS @ Y2 ) @ Y1 ) ) ) ) ) ) )
& $true ) ),
inference(backward_demodulation,[status(thm)],[f32,f33]) ).
thf(f33,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( cR @ c0 @ Y0 @ ( cS @ Y0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cR @ Y1 @ ( cS @ c0 ) @ Y0 )
=> ( cR @ ( cS @ Y1 ) @ c0 @ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( cR @ ( cS @ Y3 ) @ Y2 @ Y0 )
=> ( ( cR @ Y3 @ Y0 @ Y1 )
=> ( cR @ ( cS @ Y3 ) @ ( cS @ Y2 ) @ Y1 ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] : ( cR @ c0 @ Y0 @ ( cS @ Y0 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f29]) ).
thf(f29,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cR @ Y1 @ ( cS @ c0 ) @ Y0 )
=> ( cR @ ( cS @ Y1 ) @ c0 @ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( cR @ ( cS @ Y3 ) @ Y2 @ Y0 )
=> ( ( cR @ Y3 @ Y0 @ Y1 )
=> ( cR @ ( cS @ Y3 ) @ ( cS @ Y2 ) @ Y1 ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] : ( cR @ c0 @ Y0 @ ( cS @ Y0 ) ) )
& $true ) ),
inference(backward_demodulation,[status(thm)],[f16,f22]) ).
thf(f22,plain,
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( Y0 @ c0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ Y1 ) ) ) ) )
=> ( !! @ $i @ Y0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cR @ Y1 @ ( cS @ c0 ) @ Y0 )
=> ( cR @ ( cS @ Y1 ) @ c0 @ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( cR @ ( cS @ Y3 ) @ Y2 @ Y0 )
=> ( ( cR @ Y3 @ Y0 @ Y1 )
=> ( cR @ ( cS @ Y3 ) @ ( cS @ Y2 ) @ Y1 ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] : ( cR @ c0 @ Y0 @ ( cS @ Y0 ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( Y0 @ c0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ Y1 ) ) ) ) )
=> ( !! @ $i @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( $false
= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cR @ Y1 @ ( cS @ c0 ) @ Y0 )
=> ( cR @ ( cS @ Y1 ) @ c0 @ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( cR @ ( cS @ Y3 ) @ Y2 @ Y0 )
=> ( ( cR @ Y3 @ Y0 @ Y1 )
=> ( cR @ ( cS @ Y3 ) @ ( cS @ Y2 ) @ Y1 ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] : ( cR @ c0 @ Y0 @ ( cS @ Y0 ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( Y0 @ c0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ Y1 ) ) ) ) )
=> ( !! @ $i @ Y0 ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( ?? @ $i @ ( cR @ Y0 @ Y1 ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f12]) ).
thf(f12,plain,
( $true
= ( ~ ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cR @ Y1 @ ( cS @ c0 ) @ Y0 )
=> ( cR @ ( cS @ Y1 ) @ c0 @ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( cR @ ( cS @ Y3 ) @ Y2 @ Y0 )
=> ( ( cR @ Y3 @ Y0 @ Y1 )
=> ( cR @ ( cS @ Y3 ) @ ( cS @ Y2 ) @ Y1 ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] : ( cR @ c0 @ Y0 @ ( cS @ Y0 ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( Y0 @ c0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ Y1 ) ) ) ) )
=> ( !! @ $i @ Y0 ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( ?? @ $i @ ( cR @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f11]) ).
thf(f11,plain,
( $true
= ( ~ ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cR @ Y1 @ ( cS @ c0 ) @ Y0 )
=> ( cR @ ( cS @ Y1 ) @ c0 @ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( cR @ ( cS @ Y3 ) @ Y2 @ Y0 )
=> ( ( cR @ Y3 @ Y0 @ Y1 )
=> ( cR @ ( cS @ Y3 ) @ ( cS @ Y2 ) @ Y1 ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] : ( cR @ c0 @ Y0 @ ( cS @ Y0 ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( Y0 @ c0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ Y1 ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( cR @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f9,f10]) ).
thf(f10,plain,
( cIND
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( Y0 @ c0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ Y1 ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( cIND
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( Y0 @ c0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ Y1 ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
( cIND
= ( ! [X0: $i > $o] :
( ( ! [X1: $i] :
( ( X0 @ X1 )
=> ( X0 @ ( cS @ X1 ) ) )
& ( X0 @ c0 ) )
=> ! [X2: $i] : ( X0 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( cIND
= ( ! [X0: $i > $o] :
( ( ! [X1: $i] :
( ( X0 @ X1 )
=> ( X0 @ ( cS @ X1 ) ) )
& ( X0 @ c0 ) )
=> ! [X1: $i] : ( X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.5Muac0Woob/DTF2THF_13589.p',cIND_def) ).
thf(f9,plain,
( $true
= ( ~ ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cR @ Y1 @ ( cS @ c0 ) @ Y0 )
=> ( cR @ ( cS @ Y1 ) @ c0 @ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( cR @ ( cS @ Y3 ) @ Y2 @ Y0 )
=> ( ( cR @ Y3 @ Y0 @ Y1 )
=> ( cR @ ( cS @ Y3 ) @ ( cS @ Y2 ) @ Y1 ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] : ( cR @ c0 @ Y0 @ ( cS @ Y0 ) ) )
& cIND )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( cR @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( $true
= ( ~ ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cR @ Y1 @ ( cS @ c0 ) @ Y0 )
=> ( cR @ ( cS @ Y1 ) @ c0 @ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( cR @ ( cS @ Y3 ) @ Y2 @ Y0 )
=> ( ( cR @ Y3 @ Y0 @ Y1 )
=> ( cR @ ( cS @ Y3 ) @ ( cS @ Y2 ) @ Y1 ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] : ( cR @ c0 @ Y0 @ ( cS @ Y0 ) ) )
& cIND )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( cR @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( ( cIND
& ! [X0: $i] : ( cR @ c0 @ X0 @ ( cS @ X0 ) )
& ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cR @ ( cS @ X1 ) @ X2 @ X4 )
=> ( ( cR @ X1 @ X4 @ X3 )
=> ( cR @ ( cS @ X1 ) @ ( cS @ X2 ) @ X3 ) ) )
& ! [X5: $i,X6: $i] :
( ( cR @ X5 @ ( cS @ c0 ) @ X6 )
=> ( cR @ ( cS @ X5 ) @ c0 @ X6 ) ) )
=> ! [X7: $i,X8: $i] :
? [X9: $i] : ( cR @ X8 @ X7 @ X9 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ( ( cIND
& ! [X2: $i] : ( cR @ c0 @ X2 @ ( cS @ X2 ) )
& ! [X3: $i,X2: $i,X4: $i,X5: $i] :
( ( cR @ ( cS @ X3 ) @ X2 @ X5 )
=> ( ( cR @ X3 @ X5 @ X4 )
=> ( cR @ ( cS @ X3 ) @ ( cS @ X2 ) @ X4 ) ) )
& ! [X3: $i,X4: $i] :
( ( cR @ X3 @ ( cS @ c0 ) @ X4 )
=> ( cR @ ( cS @ X3 ) @ c0 @ X4 ) ) )
=> ! [X6: $i,X1: $i] :
? [X7: $i] : ( cR @ X1 @ X6 @ X7 ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( ( cIND
& ! [X2: $i] : ( cR @ c0 @ X2 @ ( cS @ X2 ) )
& ! [X3: $i,X2: $i,X4: $i,X5: $i] :
( ( cR @ ( cS @ X3 ) @ X2 @ X5 )
=> ( ( cR @ X3 @ X5 @ X4 )
=> ( cR @ ( cS @ X3 ) @ ( cS @ X2 ) @ X4 ) ) )
& ! [X3: $i,X4: $i] :
( ( cR @ X3 @ ( cS @ c0 ) @ X4 )
=> ( cR @ ( cS @ X3 ) @ c0 @ X4 ) ) )
=> ! [X6: $i,X1: $i] :
? [X7: $i] : ( cR @ X1 @ X6 @ X7 ) ),
file('/export/starexec/sandbox/tmp/tmp.5Muac0Woob/DTF2THF_13589.p',cTHM604) ).
thf(f2284,plain,
( ~ spl0_4
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f2283]) ).
thf(f2283,plain,
( $false
| ~ spl0_4
| ~ spl0_5 ),
inference(trivial_inequality_removal,[status(thm)],[f2282]) ).
thf(f2282,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_5 ),
inference(boolean_simplification,[status(thm)],[f2281]) ).
thf(f2281,plain,
( ( $true = ( ~ $true ) )
| ~ spl0_4
| ~ spl0_5 ),
inference(superposition,[status(thm)],[f2274,f2224]) ).
thf(f2224,plain,
( ( $true
= ( cR @ ( cS @ sK8 ) @ sK12 @ sK13 ) )
| ~ spl0_5 ),
inference(sigma_clausification,[status(thm)],[f1342]) ).
thf(f1342,plain,
( ( $true
= ( ?? @ $i @ ( cR @ ( cS @ sK8 ) @ sK12 ) ) )
| ~ spl0_5 ),
inference(binary_proxy_clausification,[status(thm)],[f1281]) ).
thf(f1281,plain,
( ( ( ( ?? @ $i @ ( cR @ ( cS @ sK8 ) @ sK12 ) )
=> ( ?? @ $i @ ( cR @ ( cS @ sK8 ) @ ( cS @ sK12 ) ) ) )
= $false )
| ~ spl0_5 ),
inference(beta_eta_normalization,[status(thm)],[f1279]) ).
thf(f1279,plain,
( ( ( ^ [Y0: $i] :
( ( ?? @ $i @ ( cR @ ( cS @ sK8 ) @ Y0 ) )
=> ( ?? @ $i @ ( cR @ ( cS @ sK8 ) @ ( cS @ Y0 ) ) ) )
@ sK12 )
= $false )
| ~ spl0_5 ),
inference(sigma_clausification,[status(thm)],[f1271]) ).
thf(f1271,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i @ ( cR @ ( cS @ sK8 ) @ Y0 ) )
=> ( ?? @ $i @ ( cR @ ( cS @ sK8 ) @ ( cS @ Y0 ) ) ) ) ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f1269]) ).
thf(f1269,definition,
( spl0_5
<=> ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i @ ( cR @ ( cS @ sK8 ) @ Y0 ) )
=> ( ?? @ $i @ ( cR @ ( cS @ sK8 ) @ ( cS @ Y0 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f2274,plain,
( ! [X0: $i] :
( $true
= ( ~ ( cR @ ( cS @ sK8 ) @ sK12 @ X0 ) ) )
| ~ spl0_4
| ~ spl0_5 ),
inference(boolean_simplification,[status(thm)],[f2251]) ).
thf(f2251,plain,
( ! [X0: $i] :
( $true
= ( ( cR @ ( cS @ sK8 ) @ sK12 @ X0 )
=> $false ) )
| ~ spl0_4
| ~ spl0_5 ),
inference(superposition,[status(thm)],[f704,f2242]) ).
thf(f2242,plain,
( ! [X1: $i] :
( ( cR @ ( cS @ sK8 ) @ ( cS @ sK12 ) @ X1 )
= $false )
| ~ spl0_5 ),
inference(pi_clausification,[status(thm)],[f2225]) ).
thf(f2225,plain,
( ( $false
= ( ?? @ $i @ ( cR @ ( cS @ sK8 ) @ ( cS @ sK12 ) ) ) )
| ~ spl0_5 ),
inference(boolean_simplification,[status(thm)],[f2223]) ).
thf(f2223,plain,
( ( ( $true
=> ( ?? @ $i @ ( cR @ ( cS @ sK8 ) @ ( cS @ sK12 ) ) ) )
= $false )
| ~ spl0_5 ),
inference(backward_demodulation,[status(thm)],[f1281,f1342]) ).
thf(f704,plain,
( ! [X0: $i,X1: $i] :
( $true
= ( ( cR @ ( cS @ sK8 ) @ X1 @ X0 )
=> ( cR @ ( cS @ sK8 ) @ ( cS @ X1 ) @ ( sK9 @ X0 ) ) ) )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f702]) ).
thf(f702,plain,
( ! [X0: $i,X1: $i] :
( $true
= ( ( cR @ ( cS @ sK8 ) @ X1 @ X0 )
=> ( $true
=> ( cR @ ( cS @ sK8 ) @ ( cS @ X1 ) @ ( sK9 @ X0 ) ) ) ) )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f118,f680]) ).
thf(f118,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( $true
= ( ( cR @ ( cS @ X4 ) @ X3 @ X1 )
=> ( ( cR @ X4 @ X1 @ X2 )
=> ( cR @ ( cS @ X4 ) @ ( cS @ X3 ) @ X2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f116]) ).
thf(f116,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( $true
= ( ^ [Y0: $i] :
( ( cR @ ( cS @ Y0 ) @ X3 @ X1 )
=> ( ( cR @ Y0 @ X1 @ X2 )
=> ( cR @ ( cS @ Y0 ) @ ( cS @ X3 ) @ X2 ) ) )
@ X4 ) ),
inference(pi_clausification,[status(thm)],[f98]) ).
thf(f98,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( cR @ ( cS @ Y0 ) @ X3 @ X1 )
=> ( ( cR @ Y0 @ X1 @ X2 )
=> ( cR @ ( cS @ Y0 ) @ ( cS @ X3 ) @ X2 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f96]) ).
thf(f96,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cR @ ( cS @ Y1 ) @ Y0 @ X1 )
=> ( ( cR @ Y1 @ X1 @ X2 )
=> ( cR @ ( cS @ Y1 ) @ ( cS @ Y0 ) @ X2 ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f93]) ).
thf(f93,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cR @ ( cS @ Y1 ) @ Y0 @ X1 )
=> ( ( cR @ Y1 @ X1 @ X2 )
=> ( cR @ ( cS @ Y1 ) @ ( cS @ Y0 ) @ X2 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f89]) ).
thf(f89,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( cR @ ( cS @ Y2 ) @ Y1 @ X1 )
=> ( ( cR @ Y2 @ X1 @ Y0 )
=> ( cR @ ( cS @ Y2 ) @ ( cS @ Y1 ) @ Y0 ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f86]) ).
thf(f86,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( cR @ ( cS @ Y2 ) @ Y1 @ X1 )
=> ( ( cR @ Y2 @ X1 @ Y0 )
=> ( cR @ ( cS @ Y2 ) @ ( cS @ Y1 ) @ Y0 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f84]) ).
thf(f84,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( cR @ ( cS @ Y3 ) @ Y2 @ Y0 )
=> ( ( cR @ Y3 @ Y0 @ Y1 )
=> ( cR @ ( cS @ Y3 ) @ ( cS @ Y2 ) @ Y1 ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f62]) ).
thf(f62,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( cR @ ( cS @ Y3 ) @ Y2 @ Y0 )
=> ( ( cR @ Y3 @ Y0 @ Y1 )
=> ( cR @ ( cS @ Y3 ) @ ( cS @ Y2 ) @ Y1 ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f59]) ).
thf(f59,plain,
( $true
= ( $true
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( cR @ ( cS @ Y3 ) @ Y2 @ Y0 )
=> ( ( cR @ Y3 @ Y0 @ Y1 )
=> ( cR @ ( cS @ Y3 ) @ ( cS @ Y2 ) @ Y1 ) ) ) ) ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f38,f55]) ).
thf(f1276,plain,
( spl0_5
| spl0_6
| ~ spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f726,f594,f1273,f1269]) ).
thf(f726,plain,
( ( $false
= ( ?? @ $i @ ( cR @ ( cS @ sK8 ) @ c0 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i @ ( cR @ ( cS @ sK8 ) @ Y0 ) )
=> ( ?? @ $i @ ( cR @ ( cS @ sK8 ) @ ( cS @ Y0 ) ) ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f699]) ).
thf(f699,plain,
( ( $false
= ( ( ?? @ $i @ ( cR @ ( cS @ sK8 ) @ c0 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i @ ( cR @ ( cS @ sK8 ) @ Y0 ) )
=> ( ?? @ $i @ ( cR @ ( cS @ sK8 ) @ ( cS @ Y0 ) ) ) ) ) ) )
| ~ spl0_4 ),
inference(not_proxy_clausification,[status(thm)],[f685]) ).
thf(f685,plain,
( ( $true
= ( ~ ( ( ?? @ $i @ ( cR @ ( cS @ sK8 ) @ c0 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i @ ( cR @ ( cS @ sK8 ) @ Y0 ) )
=> ( ?? @ $i @ ( cR @ ( cS @ sK8 ) @ ( cS @ Y0 ) ) ) ) ) ) ) )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f684]) ).
thf(f684,plain,
( ( $true
= ( ( ( ?? @ $i @ ( cR @ ( cS @ sK8 ) @ c0 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i @ ( cR @ ( cS @ sK8 ) @ Y0 ) )
=> ( ?? @ $i @ ( cR @ ( cS @ sK8 ) @ ( cS @ Y0 ) ) ) ) ) )
=> $false ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f682]) ).
thf(f682,plain,
( ( $true
= ( ( ( ^ [Y0: $i] : ( ?? @ $i @ ( cR @ ( cS @ sK8 ) @ Y0 ) )
@ c0 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( ^ [Y1: $i] : ( ?? @ $i @ ( cR @ ( cS @ sK8 ) @ Y1 ) )
@ Y0 )
=> ( ^ [Y1: $i] : ( ?? @ $i @ ( cR @ ( cS @ sK8 ) @ Y1 ) )
@ ( cS @ Y0 ) ) ) ) )
=> $false ) )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f31,f677]) ).
thf(f677,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] : ( ?? @ $i @ ( cR @ ( cS @ sK8 ) @ Y0 ) ) )
= $false )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f673]) ).
thf(f673,plain,
( ( ( $true
=> ( !! @ $i
@ ^ [Y0: $i] : ( ?? @ $i @ ( cR @ ( cS @ sK8 ) @ Y0 ) ) ) )
= $false )
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f629,f655]) ).
thf(f31,plain,
! [X1: $i > $o] :
( $true
= ( ( ( X1 @ c0 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( cS @ Y0 ) ) ) ) )
=> ( !! @ $i @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f30]) ).
thf(f30,plain,
! [X1: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( ( ( Y0 @ c0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ Y1 ) ) ) ) )
=> ( !! @ $i @ Y0 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f22]) ).
thf(f623,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[status(thm)],[f622]) ).
thf(f622,plain,
( $false
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f608]) ).
thf(f608,plain,
( ( $true = $false )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f605,f37]) ).
thf(f37,plain,
! [X1: $i] :
( $true
= ( cR @ c0 @ X1 @ ( cS @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f36]) ).
thf(f36,plain,
! [X1: $i] :
( ( ^ [Y0: $i] : ( cR @ c0 @ Y0 @ ( cS @ Y0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f33]) ).
thf(f605,plain,
( ! [X1: $i] :
( $false
= ( cR @ c0 @ sK6 @ X1 ) )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f602]) ).
thf(f602,plain,
( ( ( ?? @ $i @ ( cR @ c0 @ sK6 ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f599]) ).
thf(f599,plain,
( ( $false
= ( ^ [Y0: $i] : ( ?? @ $i @ ( cR @ c0 @ Y0 ) )
@ sK6 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f592]) ).
thf(f592,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] : ( ?? @ $i @ ( cR @ c0 @ Y0 ) ) )
= $false )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f590]) ).
thf(f590,definition,
( spl0_3
<=> ( ( !! @ $i
@ ^ [Y0: $i] : ( ?? @ $i @ ( cR @ c0 @ Y0 ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f597,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f82,f594,f590]) ).
thf(f82,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] : ( ?? @ $i @ ( cR @ Y0 @ Y1 ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] : ( ?? @ $i @ ( cR @ ( cS @ Y0 ) @ Y1 ) ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] : ( ?? @ $i @ ( cR @ c0 @ Y0 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] : ( ?? @ $i @ ( cR @ c0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] : ( ?? @ $i @ ( cR @ Y0 @ Y1 ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] : ( ?? @ $i @ ( cR @ ( cS @ Y0 ) @ Y1 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] : ( ?? @ $i @ ( cR @ c0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] : ( ?? @ $i @ ( cR @ Y0 @ Y1 ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] : ( ?? @ $i @ ( cR @ ( cS @ Y0 ) @ Y1 ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f46]) ).
thf(f46,plain,
( $true
= ( ( ( !! @ $i
@ ^ [Y0: $i] : ( ?? @ $i @ ( cR @ c0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] : ( ?? @ $i @ ( cR @ Y0 @ Y1 ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] : ( ?? @ $i @ ( cR @ ( cS @ Y0 ) @ Y1 ) ) ) ) ) )
=> $false ) ),
inference(beta_eta_normalization,[status(thm)],[f42]) ).
thf(f42,plain,
( $true
= ( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( ?? @ $i @ ( cR @ Y0 @ Y1 ) ) )
@ c0 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] : ( ?? @ $i @ ( cR @ Y1 @ Y2 ) ) )
@ Y0 )
=> ( ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] : ( ?? @ $i @ ( cR @ Y1 @ Y2 ) ) )
@ ( cS @ Y0 ) ) ) ) )
=> $false ) ),
inference(superposition,[status(thm)],[f31,f15]) ).
thf(f15,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( ?? @ $i @ ( cR @ Y0 @ Y1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM832^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% 0.10/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/0.33 % Computer : n004.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Feb 24 11:14:56 EST 2026
% 0.13/0.33 % CPUTime :
% 0.13/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.43 ---- Original DTF file ---
% 0.15/0.44 thf(spec,logic,$$dhol).
% 0.15/0.44 %------------------------------------------------------------------------------
% 0.15/0.44 % File : NUM832^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% 0.15/0.44 % Domain : Number Theory (Induction on naturals)
% 0.15/0.44 % Problem : TPS problem from PETER-THMS
% 0.15/0.44 % Version : Especial.
% 0.15/0.44 % English :
% 0.15/0.44
% 0.15/0.44 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.15/0.44 % Source : [Bro09]
% 0.15/0.44 % Names : tps_0998 [Bro09]
% 0.15/0.44
% 0.15/0.44 % Status : Theorem
% 0.15/0.44 % Rating : 0.78 v9.1.0, 0.75 v9.0.0, 0.90 v8.2.0, 0.92 v8.1.0, 0.91 v7.5.0, 1.00 v5.2.0
% 0.15/0.44 % Syntax : Number of formulae : 6 ( 1 unt; 4 typ; 1 def)
% 0.15/0.44 % Number of atoms : 10 ( 1 equ; 0 cnn)
% 0.15/0.44 % Maximal formula atoms : 8 ( 5 avg)
% 0.15/0.44 % Number of connectives : 42 ( 0 ~; 0 |; 4 &; 32 @)
% 0.15/0.44 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 0.15/0.44 % Maximal formula depth : 15 ( 8 avg)
% 0.15/0.44 % Number of types : 2 ( 0 usr)
% 0.15/0.44 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.15/0.44 % Number of symbols : 5 ( 4 usr; 2 con; 0-3 aty)
% 0.15/0.44 % Number of variables : 13 ( 0 ^; 12 !; 1 ?; 13 :)
% 0.15/0.44 % SPC : TH0_THM_EQU_NAR
% 0.15/0.44
% 0.15/0.44 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.15/0.44 % project in the Department of Mathematical Sciences at Carnegie
% 0.15/0.44 % Mellon University. Distributed under the Creative Commons copyleft
% 0.15/0.44 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.15/0.44 % :
% 0.15/0.44 % Bugfixes : v5.2.0 - Added missing type declarations.
% 0.15/0.44 %------------------------------------------------------------------------------
% 0.15/0.44 thf(c0_type,type,
% 0.15/0.44 c0: $i ).
% 0.15/0.44
% 0.15/0.44 thf(cR_type,type,
% 0.15/0.44 cR: $i > $i > $i > $o ).
% 0.15/0.44
% 0.15/0.44 thf(cS_type,type,
% 0.15/0.44 cS: $i > $i ).
% 0.15/0.44
% 0.15/0.44 thf(cIND_type,type,
% 0.15/0.44 cIND: $o ).
% 0.15/0.44
% 0.15/0.44 thf(cIND_def,definition,
% 0.15/0.44 ( cIND
% 0.15/0.44 = ( ! [Xp: $i > $o] :
% 0.15/0.44 ( ( ( Xp @ c0 )
% 0.15/0.44 & ! [Xx: $i] :
% 0.15/0.44 ( ( Xp @ Xx )
% 0.15/0.44 => ( Xp @ ( cS @ Xx ) ) ) )
% 0.15/0.44 => ! [Xx: $i] : ( Xp @ Xx ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 thf(cTHM604,conjecture,
% 0.15/0.44 ( ( cIND
% 0.15/0.44 & ! [Xn: $i] : ( cR @ c0 @ Xn @ ( cS @ Xn ) )
% 0.15/0.44 & ! [Xm: $i,Xk: $i] :
% 0.15/0.44 ( ( cR @ Xm @ ( cS @ c0 ) @ Xk )
% 0.15/0.44 => ( cR @ ( cS @ Xm ) @ c0 @ Xk ) )
% 0.15/0.44 & ! [Xm: $i,Xn: $i,Xk: $i,Xl: $i] :
% 0.15/0.44 ( ( cR @ ( cS @ Xm ) @ Xn @ Xl )
% 0.15/0.44 => ( ( cR @ Xm @ Xl @ Xk )
% 0.15/0.44 => ( cR @ ( cS @ Xm ) @ ( cS @ Xn ) @ Xk ) ) ) )
% 0.15/0.44 => ! [Xx: $i,Xy: $i] :
% 0.15/0.44 ? [Xz: $i] : ( cR @ Xx @ Xy @ Xz ) ) ).
% 0.15/0.44
% 0.15/0.44 %------------------------------------------------------------------------------
% 0.15/0.44 ------------------------
% 1.21/1.17 ---- Embedded in THF ---
% 1.21/1.17 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.21/1.17 %%% Generated on Tue Feb 24 11:14:57 EST 2026
% 1.21/1.17 %%% using '$$dhol' embedding, version 1.3.0.
% 1.21/1.17 %%% Logic specification used:
% 1.21/1.17 %%% thf(spec, logic, $$dhol).
% 1.21/1.17
% 1.21/1.17 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.5Muac0Woob/DTF2DTF13589.p
% See solution above
% 1.21/1.17 ------------------------
% 1.21/1.18 ---- Cleaned THF ---
% 1.21/1.18 thf(c0_type,type,
% 1.21/1.18 c0: $i ).
% 1.21/1.18
% 1.21/1.18 thf(cR_type,type,
% 1.21/1.18 cR: $i > $i > $i > $o ).
% 1.21/1.18
% 1.21/1.18 thf(cS_type,type,
% 1.21/1.18 cS: $i > $i ).
% 1.21/1.18
% 1.21/1.18 thf(cIND_type,type,
% 1.21/1.18 cIND: $o ).
% 1.21/1.18
% 1.21/1.18 thf(cIND_def,definition,
% 1.21/1.18 ( cIND
% 1.21/1.18 = ( ! [Xp: $i > $o] :
% 1.21/1.18 ( ( ( Xp @ c0 )
% 1.21/1.18 & ! [Xx: $i] :
% 1.21/1.18 ( ( Xp @ Xx )
% 1.21/1.18 => ( Xp @ ( cS @ Xx ) ) ) )
% 1.21/1.18 => ! [Xx: $i] : ( Xp @ Xx ) ) ) ) ).
% 1.21/1.18
% 1.21/1.18 thf(cTHM604,conjecture,
% 1.21/1.18 ( ( cIND
% 1.21/1.18 & ! [Xn: $i] : ( cR @ c0 @ Xn @ ( cS @ Xn ) )
% 1.21/1.18 & ! [Xm: $i,Xk: $i] :
% 1.21/1.18 ( ( cR @ Xm @ ( cS @ c0 ) @ Xk )
% 1.21/1.18 => ( cR @ ( cS @ Xm ) @ c0 @ Xk ) )
% 1.21/1.18 & ! [Xm: $i,Xn: $i,Xk: $i,Xl: $i] :
% 1.21/1.18 ( ( cR @ ( cS @ Xm ) @ Xn @ Xl )
% 1.21/1.18 => ( ( cR @ Xm @ Xl @ Xk )
% 1.21/1.18 => ( cR @ ( cS @ Xm ) @ ( cS @ Xn ) @ Xk ) ) ) )
% 1.21/1.18 => ! [Xx: $i,Xy: $i] :
% 1.21/1.18 ? [Xz: $i] : ( cR @ Xx @ Xy @ Xz ) ) ).
% 1.21/1.18 ------------------------
% 1.21/1.19 % (13692)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_13589 for (2999ds/183Mi)
% 1.34/1.20 % (13695)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_13589 for (2999ds/2Mi)
% 1.34/1.20 % (13696)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_13589 for (2999ds/2Mi)
% 1.34/1.20 % (13697)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_13589 for (2999ds/275Mi)
% 1.34/1.20 % (13694)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_13589 for (2999ds/27Mi)
% 1.34/1.20 % (13698)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_13589 for (2999ds/18Mi)
% 1.34/1.20 % (13693)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_13589 for (2999ds/4Mi)
% 1.34/1.20 % (13695)Instruction limit reached!
% 1.34/1.20 % (13695)------------------------------
% 1.34/1.20 % (13695)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.20 % (13695)Termination reason: Unknown
% 1.34/1.20 % (13695)Termination phase: Saturation
% 1.34/1.20
% 1.34/1.20 % (13696)Instruction limit reached!
% 1.34/1.20 % (13696)------------------------------
% 1.34/1.20 % (13696)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.20 % (13696)Termination reason: Unknown
% 1.34/1.20 % (13696)Termination phase: Saturation
% 1.34/1.20
% 1.34/1.20 % (13696)Memory used [KB]: 1023
% 1.34/1.20 % (13696)Time elapsed: 0.003 s
% 1.34/1.20 % (13696)Instructions burned: 3 (million)
% 1.34/1.20 % (13696)------------------------------
% 1.34/1.20 % (13696)------------------------------
% 1.34/1.20 % (13695)Memory used [KB]: 5500
% 1.34/1.20 % (13695)Time elapsed: 0.003 s
% 1.34/1.20 % (13695)Instructions burned: 3 (million)
% 1.34/1.20 % (13695)------------------------------
% 1.34/1.20 % (13695)------------------------------
% 1.34/1.20 % (13693)Instruction limit reached!
% 1.34/1.20 % (13693)------------------------------
% 1.34/1.20 % (13693)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.20 % (13693)Termination reason: Unknown
% 1.34/1.20 % (13693)Termination phase: Saturation
% 1.34/1.20
% 1.34/1.20 % (13693)Memory used [KB]: 5500
% 1.34/1.20 % (13693)Time elapsed: 0.004 s
% 1.34/1.20 % (13693)Instructions burned: 5 (million)
% 1.34/1.20 % (13693)------------------------------
% 1.34/1.20 % (13693)------------------------------
% 1.34/1.21 % (13698)Instruction limit reached!
% 1.34/1.21 % (13698)------------------------------
% 1.34/1.21 % (13698)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.21 % (13698)Termination reason: Unknown
% 1.34/1.21 % (13698)Termination phase: Saturation
% 1.34/1.21
% 1.34/1.21 % (13698)Memory used [KB]: 5628
% 1.34/1.21 % (13698)Time elapsed: 0.011 s
% 1.34/1.21 % (13698)Instructions burned: 18 (million)
% 1.34/1.21 % (13698)------------------------------
% 1.34/1.21 % (13698)------------------------------
% 1.34/1.22 % (13694)Instruction limit reached!
% 1.34/1.22 % (13694)------------------------------
% 1.34/1.22 % (13694)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.22 % (13694)Termination reason: Unknown
% 1.34/1.22 % (13694)Termination phase: Saturation
% 1.34/1.22
% 1.34/1.22 % (13694)Memory used [KB]: 5628
% 1.34/1.22 % (13694)Time elapsed: 0.016 s
% 1.34/1.22 % (13694)Instructions burned: 27 (million)
% 1.34/1.22 % (13694)------------------------------
% 1.34/1.22 % (13694)------------------------------
% 1.34/1.22 % (13699)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_13589 for (2999ds/3Mi)
% 1.34/1.22 % (13700)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_13589 for (2999ds/37Mi)
% 1.34/1.22 % (13699)Instruction limit reached!
% 1.34/1.22 % (13699)------------------------------
% 1.34/1.22 % (13699)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.22 % (13699)Termination reason: Unknown
% 1.34/1.22 % (13699)Termination phase: Saturation
% 1.34/1.22
% 1.34/1.22 % (13699)Memory used [KB]: 5500
% 1.34/1.22 % (13699)Time elapsed: 0.003 s
% 1.34/1.22 % (13699)Instructions burned: 3 (million)
% 1.34/1.22 % (13699)------------------------------
% 1.34/1.22 % (13699)------------------------------
% 1.34/1.22 % (13701)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_13589 for (2999ds/15Mi)
% 1.34/1.23 % (13702)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_13589 for (2999ds/3Mi)
% 1.34/1.23 % (13702)Instruction limit reached!
% 1.34/1.23 % (13702)------------------------------
% 1.34/1.23 % (13702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.23 % (13702)Termination reason: Unknown
% 1.34/1.23 % (13702)Termination phase: Saturation
% 1.34/1.23
% 1.34/1.23 % (13702)Memory used [KB]: 5500
% 1.34/1.23 % (13702)Time elapsed: 0.003 s
% 1.34/1.23 % (13702)Instructions burned: 3 (million)
% 1.34/1.23 % (13702)------------------------------
% 1.34/1.23 % (13702)------------------------------
% 1.34/1.23 % (13701)Instruction limit reached!
% 1.34/1.23 % (13701)------------------------------
% 1.34/1.23 % (13701)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.23 % (13701)Termination reason: Unknown
% 1.34/1.23 % (13701)Termination phase: Saturation
% 1.34/1.23
% 1.34/1.23 % (13701)Memory used [KB]: 5500
% 1.34/1.23 % (13701)Time elapsed: 0.006 s
% 1.34/1.23 % (13701)Instructions burned: 16 (million)
% 1.34/1.23 % (13701)------------------------------
% 1.34/1.23 % (13701)------------------------------
% 1.34/1.23 % (13703)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_13589 for (2999ds/1041Mi)
% 1.34/1.24 % (13704)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_13589 for (2999ds/7Mi)
% 1.34/1.24 % (13700)Instruction limit reached!
% 1.34/1.24 % (13700)------------------------------
% 1.34/1.24 % (13700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.24 % (13700)Termination reason: Unknown
% 1.34/1.24 % (13700)Termination phase: Saturation
% 1.34/1.24
% 1.34/1.24 % (13700)Memory used [KB]: 5884
% 1.34/1.24 % (13700)Time elapsed: 0.019 s
% 1.34/1.24 % (13700)Instructions burned: 37 (million)
% 1.34/1.24 % (13700)------------------------------
% 1.34/1.24 % (13700)------------------------------
% 1.34/1.24 % (13704)Instruction limit reached!
% 1.34/1.24 % (13704)------------------------------
% 1.34/1.24 % (13704)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.24 % (13704)Termination reason: Unknown
% 1.34/1.24 % (13704)Termination phase: Saturation
% 1.34/1.24
% 1.34/1.24 % (13704)Memory used [KB]: 1023
% 1.34/1.24 % (13704)Time elapsed: 0.005 s
% 1.34/1.24 % (13704)Instructions burned: 7 (million)
% 1.34/1.24 % (13704)------------------------------
% 1.34/1.24 % (13704)------------------------------
% 1.34/1.24 % (13706)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_13589 for (2999ds/3Mi)
% 1.34/1.24 % (13706)Instruction limit reached!
% 1.34/1.24 % (13706)------------------------------
% 1.34/1.24 % (13706)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.24 % (13706)Termination reason: Unknown
% 1.34/1.24 % (13706)Termination phase: Property scanning
% 1.34/1.24
% 1.34/1.24 % (13706)Memory used [KB]: 1023
% 1.34/1.24 % (13706)Time elapsed: 0.003 s
% 1.34/1.24 % (13706)Instructions burned: 4 (million)
% 1.34/1.24 % (13706)------------------------------
% 1.34/1.24 % (13706)------------------------------
% 1.34/1.24 % (13705)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_13589 for (2999ds/16Mi)
% 1.34/1.25 % (13707)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_13589 for (2999ds/3Mi)
% 1.34/1.25 % (13707)Instruction limit reached!
% 1.34/1.25 % (13707)------------------------------
% 1.34/1.25 % (13707)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.25 % (13707)Termination reason: Unknown
% 1.34/1.25 % (13707)Termination phase: Saturation
% 1.34/1.25
% 1.34/1.25 % (13707)Memory used [KB]: 1023
% 1.34/1.25 % (13707)Time elapsed: 0.003 s
% 1.34/1.25 % (13707)Instructions burned: 3 (million)
% 1.34/1.25 % (13707)------------------------------
% 1.34/1.25 % (13707)------------------------------
% 1.34/1.25 % (13705)Instruction limit reached!
% 1.34/1.25 % (13705)------------------------------
% 1.34/1.25 % (13705)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.25 % (13705)Termination reason: Unknown
% 1.34/1.25 % (13705)Termination phase: Saturation
% 1.34/1.25
% 1.34/1.25 % (13705)Memory used [KB]: 5756
% 1.34/1.25 % (13705)Time elapsed: 0.010 s
% 1.34/1.25 % (13705)Instructions burned: 16 (million)
% 1.34/1.25 % (13705)------------------------------
% 1.34/1.25 % (13705)------------------------------
% 1.34/1.26 % (13708)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_13589 for (2999ds/7Mi)
% 1.34/1.26 % (13709)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_13589 for (2999ds/3Mi)
% 1.34/1.26 % (13708)Refutation not found, incomplete strategy
% 1.34/1.26 % (13708)------------------------------
% 1.34/1.26 % (13708)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.26 % (13708)Termination reason: Refutation not found, incomplete strategy
% 1.34/1.26
% 1.34/1.26
% 1.34/1.26 % (13708)Memory used [KB]: 5500
% 1.34/1.26 % (13708)Time elapsed: 0.003 s
% 1.34/1.26 % (13708)Instructions burned: 3 (million)
% 1.34/1.26 % (13708)------------------------------
% 1.34/1.26 % (13708)------------------------------
% 1.34/1.26 % (13709)Instruction limit reached!
% 1.34/1.26 % (13709)------------------------------
% 1.34/1.26 % (13709)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.26 % (13709)Termination reason: Unknown
% 1.34/1.26 % (13709)Termination phase: Saturation
% 1.34/1.26
% 1.34/1.26 % (13709)Memory used [KB]: 5500
% 1.34/1.26 % (13709)Time elapsed: 0.003 s
% 1.34/1.26 % (13709)Instructions burned: 4 (million)
% 1.34/1.26 % (13709)------------------------------
% 1.34/1.26 % (13709)------------------------------
% 1.34/1.26 % (13710)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_13589 for (2999ds/4Mi)
% 1.34/1.27 % (13710)Instruction limit reached!
% 1.34/1.27 % (13710)------------------------------
% 1.34/1.27 % (13710)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.27 % (13710)Termination reason: Unknown
% 1.34/1.27 % (13710)Termination phase: Saturation
% 1.34/1.27
% 1.34/1.27 % (13710)Memory used [KB]: 5500
% 1.34/1.27 % (13710)Time elapsed: 0.004 s
% 1.34/1.27 % (13710)Instructions burned: 4 (million)
% 1.34/1.27 % (13710)------------------------------
% 1.34/1.27 % (13710)------------------------------
% 1.34/1.27 % (13711)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_13589 for (2999ds/18Mi)
% 1.34/1.27 % (13712)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_13589 for (2999ds/710Mi)
% 1.34/1.27 % (13713)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_13589 for (2999ds/6Mi)
% 1.34/1.28 % (13714)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_13589 for (2999ds/902Mi)
% 1.34/1.28 % (13711)Instruction limit reached!
% 1.34/1.28 % (13711)------------------------------
% 1.34/1.28 % (13711)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.28 % (13711)Termination reason: Unknown
% 1.34/1.28 % (13711)Termination phase: Saturation
% 1.34/1.28
% 1.34/1.28 % (13711)Memory used [KB]: 5628
% 1.34/1.28 % (13711)Time elapsed: 0.011 s
% 1.34/1.28 % (13711)Instructions burned: 19 (million)
% 1.34/1.28 % (13711)------------------------------
% 1.34/1.28 % (13711)------------------------------
% 1.34/1.28 % (13692)Instruction limit reached!
% 1.34/1.28 % (13692)------------------------------
% 1.34/1.28 % (13692)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.28 % (13692)Termination reason: Unknown
% 1.34/1.28 % (13692)Termination phase: Saturation
% 1.34/1.28
% 1.34/1.28 % (13692)Memory used [KB]: 6396
% 1.34/1.28 % (13692)Time elapsed: 0.081 s
% 1.34/1.28 % (13692)Instructions burned: 183 (million)
% 1.34/1.28 % (13692)------------------------------
% 1.34/1.28 % (13692)------------------------------
% 1.34/1.28 % (13713)Instruction limit reached!
% 1.34/1.28 % (13713)------------------------------
% 1.34/1.28 % (13713)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.28 % (13713)Termination reason: Unknown
% 1.34/1.28 % (13713)Termination phase: Saturation
% 1.34/1.28
% 1.34/1.28 % (13713)Memory used [KB]: 5500
% 1.34/1.28 % (13713)Time elapsed: 0.005 s
% 1.34/1.28 % (13713)Instructions burned: 7 (million)
% 1.34/1.28 % (13713)------------------------------
% 1.34/1.28 % (13713)------------------------------
% 1.34/1.29 % (13715)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_13589 for (2999ds/21Mi)
% 1.34/1.29 % (13716)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_13589 for (2999ds/5Mi)
% 1.34/1.29 % (13717)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_13589 for (2999ds/6Mi)
% 1.34/1.30 % (13716)Instruction limit reached!
% 1.34/1.30 % (13716)------------------------------
% 1.34/1.30 % (13716)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.30 % (13716)Termination reason: Unknown
% 1.34/1.30 % (13716)Termination phase: Saturation
% 1.34/1.30
% 1.34/1.30 % (13716)Memory used [KB]: 5500
% 1.34/1.30 % (13716)Time elapsed: 0.004 s
% 1.34/1.30 % (13716)Instructions burned: 5 (million)
% 1.34/1.30 % (13716)------------------------------
% 1.34/1.30 % (13716)------------------------------
% 1.34/1.30 % (13717)Instruction limit reached!
% 1.34/1.30 % (13717)------------------------------
% 1.34/1.30 % (13717)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.30 % (13717)Termination reason: Unknown
% 1.34/1.30 % (13717)Termination phase: Saturation
% 1.34/1.30
% 1.34/1.30 % (13717)Memory used [KB]: 5500
% 1.34/1.30 % (13717)Time elapsed: 0.004 s
% 1.34/1.30 % (13717)Instructions burned: 6 (million)
% 1.34/1.30 % (13717)------------------------------
% 1.34/1.30 % (13717)------------------------------
% 1.34/1.31 % (13715)Instruction limit reached!
% 1.34/1.31 % (13715)------------------------------
% 1.34/1.31 % (13715)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.31 % (13715)Termination reason: Unknown
% 1.34/1.31 % (13715)Termination phase: Saturation
% 1.34/1.31
% 1.34/1.31 % (13715)Memory used [KB]: 5628
% 1.34/1.31 % (13715)Time elapsed: 0.035 s
% 1.34/1.31 % (13715)Instructions burned: 22 (million)
% 1.34/1.31 % (13715)------------------------------
% 1.34/1.31 % (13715)------------------------------
% 1.34/1.31 % (13718)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_13589 for (2999ds/377Mi)
% 1.34/1.31 % (13719)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_13589 for (2999ds/779Mi)
% 1.34/1.32 % (13720)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_13589 for (2998ds/19Mi)
% 1.34/1.33 % (13720)Instruction limit reached!
% 1.34/1.33 % (13720)------------------------------
% 1.34/1.33 % (13720)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.33 % (13720)Termination reason: Unknown
% 1.34/1.33 % (13720)Termination phase: Saturation
% 1.34/1.33
% 1.34/1.33 % (13720)Memory used [KB]: 5628
% 1.34/1.33 % (13720)Time elapsed: 0.012 s
% 1.34/1.33 % (13720)Instructions burned: 20 (million)
% 1.34/1.33 % (13720)------------------------------
% 1.34/1.33 % (13720)------------------------------
% 1.34/1.34 % (13697)Instruction limit reached!
% 1.34/1.34 % (13697)------------------------------
% 1.34/1.34 % (13697)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.34 % (13697)Termination reason: Unknown
% 1.34/1.34 % (13697)Termination phase: Saturation
% 1.34/1.34
% 1.34/1.34 % (13697)Memory used [KB]: 6268
% 1.34/1.34 % (13697)Time elapsed: 0.137 s
% 1.34/1.34 % (13697)Instructions burned: 276 (million)
% 1.34/1.34 % (13697)------------------------------
% 1.34/1.34 % (13697)------------------------------
% 1.34/1.35 % (13722)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_13589 for (2998ds/17Mi)
% 1.34/1.36 % (13721)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_13589 for (2998ds/879Mi)
% 1.34/1.36 % (13722)Instruction limit reached!
% 1.34/1.36 % (13722)------------------------------
% 1.34/1.36 % (13722)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.36 % (13722)Termination reason: Unknown
% 1.34/1.36 % (13722)Termination phase: Saturation
% 1.34/1.36
% 1.34/1.36 % (13722)Memory used [KB]: 5628
% 1.34/1.36 % (13722)Time elapsed: 0.011 s
% 1.34/1.36 % (13722)Instructions burned: 17 (million)
% 1.34/1.36 % (13722)------------------------------
% 1.34/1.36 % (13722)------------------------------
% 1.34/1.38 % (13723)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_13589 for (2998ds/3Mi)
% 1.34/1.38 % (13723)Instruction limit reached!
% 1.34/1.38 % (13723)------------------------------
% 1.34/1.38 % (13723)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.38 % (13723)Termination reason: Unknown
% 1.34/1.38 % (13723)Termination phase: Saturation
% 1.34/1.38
% 1.34/1.38 % (13723)Memory used [KB]: 1023
% 1.34/1.38 % (13723)Time elapsed: 0.003 s
% 1.34/1.38 % (13723)Instructions burned: 3 (million)
% 1.34/1.38 % (13723)------------------------------
% 1.34/1.38 % (13723)------------------------------
% 1.34/1.40 % (13724)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_13589 for (2998ds/30Mi)
% 1.34/1.41 % (13724)Instruction limit reached!
% 1.34/1.41 % (13724)------------------------------
% 1.34/1.41 % (13724)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.41 % (13724)Termination reason: Unknown
% 1.34/1.41 % (13724)Termination phase: Saturation
% 1.34/1.41
% 1.34/1.41 % (13724)Memory used [KB]: 5628
% 1.34/1.41 % (13724)Time elapsed: 0.018 s
% 1.34/1.41 % (13724)Instructions burned: 30 (million)
% 1.34/1.41 % (13724)------------------------------
% 1.34/1.41 % (13724)------------------------------
% 1.34/1.43 % (13725)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_13589 for (2997ds/127Mi)
% 1.34/1.49 % (13718)Instruction limit reached!
% 1.34/1.49 % (13718)------------------------------
% 1.34/1.49 % (13718)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.49 % (13718)Termination reason: Unknown
% 1.34/1.49 % (13718)Termination phase: Saturation
% 1.34/1.49
% 1.34/1.49 % (13718)Memory used [KB]: 6268
% 1.34/1.49 % (13718)Time elapsed: 0.198 s
% 1.34/1.49 % (13718)Instructions burned: 377 (million)
% 1.34/1.49 % (13718)------------------------------
% 1.34/1.49 % (13718)------------------------------
% 1.34/1.49 % (13725)Instruction limit reached!
% 1.34/1.49 % (13725)------------------------------
% 1.34/1.49 % (13725)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.49 % (13725)Termination reason: Unknown
% 1.34/1.49 % (13725)Termination phase: Saturation
% 1.34/1.49
% 1.34/1.49 % (13725)Memory used [KB]: 5884
% 1.34/1.49 % (13725)Time elapsed: 0.065 s
% 1.34/1.49 % (13725)Instructions burned: 127 (million)
% 1.34/1.49 % (13725)------------------------------
% 1.34/1.49 % (13725)------------------------------
% 1.34/1.51 % (13727)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_13589 for (2996ds/3Mi)
% 1.34/1.51 % (13727)Instruction limit reached!
% 1.34/1.51 % (13727)------------------------------
% 1.34/1.51 % (13727)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.51 % (13727)Termination reason: Unknown
% 1.34/1.51 % (13727)Termination phase: Saturation
% 1.34/1.51
% 1.34/1.51 % (13727)Memory used [KB]: 1023
% 1.34/1.51 % (13727)Time elapsed: 0.003 s
% 1.34/1.51 % (13727)Instructions burned: 3 (million)
% 1.34/1.51 % (13727)------------------------------
% 1.34/1.51 % (13727)------------------------------
% 1.34/1.52 % (13726)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_13589 for (2997ds/100Mi)
% 1.34/1.53 % (13728)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_13589 for (2996ds/20Mi)
% 1.34/1.54 % (13728)Instruction limit reached!
% 1.34/1.54 % (13728)------------------------------
% 1.34/1.54 % (13728)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.54 % (13728)Termination reason: Unknown
% 1.34/1.54 % (13728)Termination phase: Saturation
% 1.34/1.54
% 1.34/1.54 % (13728)Memory used [KB]: 5628
% 1.34/1.54 % (13728)Time elapsed: 0.012 s
% 1.34/1.54 % (13728)Instructions burned: 20 (million)
% 1.34/1.54 % (13728)------------------------------
% 1.34/1.54 % (13728)------------------------------
% 1.34/1.55 % (13729)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_13589 for (2996ds/86Mi)
% 1.34/1.56 % (13726)Instruction limit reached!
% 1.34/1.56 % (13726)------------------------------
% 1.34/1.56 % (13726)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.56 % (13726)Termination reason: Unknown
% 1.34/1.56 % (13726)Termination phase: Saturation
% 1.34/1.56
% 1.34/1.56 % (13726)Memory used [KB]: 6012
% 1.34/1.56 % (13726)Time elapsed: 0.055 s
% 1.34/1.56 % (13726)Instructions burned: 102 (million)
% 1.34/1.56 % (13726)------------------------------
% 1.34/1.56 % (13726)------------------------------
% 1.34/1.57 % (13730)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_13589 for (2996ds/107Mi)
% 1.34/1.60 % (13729)Instruction limit reached!
% 1.34/1.60 % (13729)------------------------------
% 1.34/1.60 % (13729)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.60 % (13729)Termination reason: Unknown
% 1.34/1.60 % (13729)Termination phase: Saturation
% 1.34/1.60
% 1.34/1.60 % (13729)Memory used [KB]: 5884
% 1.34/1.60 % (13729)Time elapsed: 0.044 s
% 1.34/1.60 % (13729)Instructions burned: 87 (million)
% 1.34/1.60 % (13729)------------------------------
% 1.34/1.60 % (13729)------------------------------
% 1.34/1.61 % (13730)Instruction limit reached!
% 1.34/1.61 % (13730)------------------------------
% 1.34/1.61 % (13730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.61 % (13730)Termination reason: Unknown
% 1.34/1.61 % (13730)Termination phase: Saturation
% 1.34/1.61
% 1.34/1.61 % (13730)Memory used [KB]: 5884
% 1.34/1.61 % (13730)Time elapsed: 0.035 s
% 1.34/1.61 % (13730)Instructions burned: 107 (million)
% 1.34/1.61 % (13730)------------------------------
% 1.34/1.61 % (13730)------------------------------
% 1.34/1.61 % (13712)Instruction limit reached!
% 1.34/1.61 % (13712)------------------------------
% 1.34/1.61 % (13712)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.61 % (13712)Termination reason: Unknown
% 1.34/1.61 % (13712)Termination phase: Saturation
% 1.34/1.61
% 1.34/1.61 % (13712)Memory used [KB]: 7164
% 1.34/1.61 % (13712)Time elapsed: 0.340 s
% 1.34/1.61 % (13712)Instructions burned: 711 (million)
% 1.34/1.61 % (13712)------------------------------
% 1.34/1.61 % (13712)------------------------------
% 1.34/1.61 % (13731)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_13589 for (2995ds/39Mi)
% 1.34/1.62 % (13732)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_13589 for (2995ds/448Mi)
% 1.34/1.63 % (13731)Instruction limit reached!
% 1.34/1.63 % (13731)------------------------------
% 1.34/1.63 % (13731)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.63 % (13731)Termination reason: Unknown
% 1.34/1.63 % (13731)Termination phase: Saturation
% 1.34/1.63
% 1.34/1.63 % (13731)Memory used [KB]: 5756
% 1.34/1.63 % (13731)Time elapsed: 0.012 s
% 1.34/1.63 % (13731)Instructions burned: 39 (million)
% 1.34/1.63 % (13731)------------------------------
% 1.34/1.63 % (13731)------------------------------
% 1.34/1.63 % (13733)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_13589 for (2995ds/46Mi)
% 1.34/1.64 % (13734)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_13589 for (2995ds/98Mi)
% 1.34/1.65 % (13733)Instruction limit reached!
% 1.34/1.65 % (13733)------------------------------
% 1.34/1.65 % (13733)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.65 % (13733)Termination reason: Unknown
% 1.34/1.65 % (13733)Termination phase: Saturation
% 1.34/1.65
% 1.34/1.65 % (13733)Memory used [KB]: 5756
% 1.34/1.65 % (13733)Time elapsed: 0.025 s
% 1.34/1.65 % (13733)Instructions burned: 46 (million)
% 1.34/1.65 % (13733)------------------------------
% 1.34/1.65 % (13733)------------------------------
% 1.34/1.67 % (13734)Instruction limit reached!
% 1.34/1.67 % (13734)------------------------------
% 1.34/1.67 % (13734)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.67 % (13734)Termination reason: Unknown
% 1.34/1.67 % (13734)Termination phase: Saturation
% 1.34/1.67
% 1.34/1.67 % (13734)Memory used [KB]: 1279
% 1.34/1.67 % (13734)Time elapsed: 0.031 s
% 1.34/1.67 % (13734)Instructions burned: 101 (million)
% 1.34/1.67 % (13734)------------------------------
% 1.34/1.67 % (13734)------------------------------
% 1.34/1.67 % (13735)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_13589 for (2995ds/507Mi)
% 1.34/1.67 % (13721)Refutation not found, non-redundant clauses discarded% (13721)------------------------------
% 1.34/1.67 % (13721)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.67 % (13721)Termination reason: Refutation not found, non-redundant clauses discarded
% 1.34/1.67
% 1.34/1.67 % (13721)Memory used [KB]: 7291
% 1.34/1.67 % (13721)Time elapsed: 0.325 s
% 1.34/1.67 % (13721)Instructions burned: 798 (million)
% 1.34/1.67 % (13721)------------------------------
% 1.34/1.67 % (13721)------------------------------
% 1.34/1.67 % (13736)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_13589 for (2995ds/149Mi)
% 1.34/1.68 % (13714)Instruction limit reached!
% 1.34/1.68 % (13714)------------------------------
% 1.34/1.68 % (13714)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.68 % (13714)Termination reason: Unknown
% 1.34/1.68 % (13714)Termination phase: Saturation
% 1.34/1.68
% 1.34/1.68 % (13714)Memory used [KB]: 7291
% 1.34/1.68 % (13714)Time elapsed: 0.420 s
% 1.34/1.68 % (13714)Instructions burned: 902 (million)
% 1.34/1.68 % (13714)------------------------------
% 1.34/1.68 % (13714)------------------------------
% 1.34/1.68 % (13719)Instruction limit reached!
% 1.34/1.68 % (13719)------------------------------
% 1.34/1.68 % (13719)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.68 % (13719)Termination reason: Unknown
% 1.34/1.68 % (13719)Termination phase: Saturation
% 1.34/1.68
% 1.34/1.68 % (13719)Memory used [KB]: 7675
% 1.34/1.68 % (13719)Time elapsed: 0.394 s
% 1.34/1.68 % (13719)Instructions burned: 779 (million)
% 1.34/1.68 % (13719)------------------------------
% 1.34/1.68 % (13719)------------------------------
% 1.34/1.69 % (13737)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_13589 for (2995ds/39Mi)
% 1.34/1.70 % (13738)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_13589 for (2995ds/6Mi)
% 1.34/1.70 % (13739)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_13589 for (2995ds/1087Mi)
% 1.34/1.70 % (13738)Instruction limit reached!
% 1.34/1.70 % (13738)------------------------------
% 1.34/1.70 % (13738)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.70 % (13738)Termination reason: Unknown
% 1.34/1.70 % (13738)Termination phase: Saturation
% 1.34/1.70
% 1.34/1.70 % (13738)Memory used [KB]: 9978
% 1.34/1.70 % (13738)Time elapsed: 0.027 s
% 1.34/1.70 % (13738)Instructions burned: 6 (million)
% 1.34/1.70 % (13738)------------------------------
% 1.34/1.70 % (13738)------------------------------
% 1.34/1.71 % (13737)Instruction limit reached!
% 1.34/1.71 % (13737)------------------------------
% 1.34/1.71 % (13737)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.71 % (13737)Termination reason: Unknown
% 1.34/1.71 % (13737)Termination phase: Saturation
% 1.34/1.71
% 1.34/1.71 % (13737)Memory used [KB]: 5628
% 1.34/1.71 % (13737)Time elapsed: 0.022 s
% 1.34/1.71 % (13737)Instructions burned: 40 (million)
% 1.34/1.71 % (13737)------------------------------
% 1.34/1.71 % (13737)------------------------------
% 1.34/1.71 % (13703)Instruction limit reached!
% 1.34/1.71 % (13703)------------------------------
% 1.34/1.71 % (13703)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.71 % (13703)Termination reason: Unknown
% 1.34/1.71 % (13703)Termination phase: Saturation
% 1.34/1.71
% 1.34/1.71 % (13703)Memory used [KB]: 8059
% 1.34/1.71 % (13703)Time elapsed: 0.480 s
% 1.34/1.71 % (13703)Instructions burned: 1041 (million)
% 1.34/1.71 % (13703)------------------------------
% 1.34/1.71 % (13703)------------------------------
% 1.34/1.72 % (13740)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_13589 for (2994ds/47Mi)
% 1.34/1.72 % (13736)Instruction limit reached!
% 1.34/1.72 % (13736)------------------------------
% 1.34/1.72 % (13736)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.72 % (13736)Termination reason: Unknown
% 1.34/1.72 % (13736)Termination phase: Saturation
% 1.34/1.72
% 1.34/1.72 % (13736)Memory used [KB]: 6012
% 1.34/1.72 % (13736)Time elapsed: 0.049 s
% 1.34/1.72 % (13736)Instructions burned: 149 (million)
% 1.34/1.72 % (13736)------------------------------
% 1.34/1.72 % (13736)------------------------------
% 1.34/1.72 % (13741)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_13589 for (2994ds/44Mi)
% 1.34/1.73 % (13742)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_13589 for (2994ds/432Mi)
% 1.34/1.73 % (13743)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_13589 for (2994ds/62Mi)
% 1.34/1.74 % (13740)Instruction limit reached!
% 1.34/1.74 % (13740)------------------------------
% 1.34/1.74 % (13740)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.74 % (13740)Termination reason: Unknown
% 1.34/1.74 % (13740)Termination phase: Saturation
% 1.34/1.74
% 1.34/1.74 % (13740)Memory used [KB]: 5756
% 1.34/1.74 % (13740)Time elapsed: 0.025 s
% 1.34/1.74 % (13740)Instructions burned: 47 (million)
% 1.34/1.74 % (13740)------------------------------
% 1.34/1.74 % (13740)------------------------------
% 1.34/1.75 % (13741)Instruction limit reached!
% 1.34/1.75 % (13741)------------------------------
% 1.34/1.75 % (13741)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.75 % (13741)Termination reason: Unknown
% 1.34/1.75 % (13741)Termination phase: Saturation
% 1.34/1.75
% 1.34/1.75 % (13741)Memory used [KB]: 1279
% 1.34/1.75 % (13741)Time elapsed: 0.024 s
% 1.34/1.75 % (13741)Instructions burned: 46 (million)
% 1.34/1.75 % (13741)------------------------------
% 1.34/1.75 % (13741)------------------------------
% 1.34/1.75 % (13743)Instruction limit reached!
% 1.34/1.75 % (13743)------------------------------
% 1.34/1.75 % (13743)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.75 % (13743)Termination reason: Unknown
% 1.34/1.75 % (13743)Termination phase: Saturation
% 1.34/1.75
% 1.34/1.75 % (13743)Memory used [KB]: 5884
% 1.34/1.75 % (13743)Time elapsed: 0.020 s
% 1.34/1.75 % (13743)Instructions burned: 63 (million)
% 1.34/1.75 % (13743)------------------------------
% 1.34/1.75 % (13743)------------------------------
% 1.34/1.76 % (13744)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_13589 for (2994ds/31Mi)
% 1.34/1.76 % (13746)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_13589 for (2994ds/453Mi)
% 1.34/1.76 % (13745)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_13589 for (2994ds/96Mi)
% 1.34/1.78 % (13744)Instruction limit reached!
% 1.34/1.78 % (13744)------------------------------
% 1.34/1.78 % (13744)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.78 % (13744)Termination reason: Unknown
% 1.34/1.78 % (13744)Termination phase: Saturation
% 1.34/1.78
% 1.34/1.78 % (13744)Memory used [KB]: 5628
% 1.34/1.78 % (13744)Time elapsed: 0.018 s
% 1.34/1.78 % (13744)Instructions burned: 32 (million)
% 1.34/1.78 % (13744)------------------------------
% 1.34/1.78 % (13744)------------------------------
% 1.34/1.79 % (13747)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_13589 for (2994ds/71Mi)
% 1.34/1.81 % (13745)Instruction limit reached!
% 1.34/1.81 % (13745)------------------------------
% 1.34/1.81 % (13745)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.81 % (13745)Termination reason: Unknown
% 1.34/1.81 % (13745)Termination phase: Saturation
% 1.34/1.81
% 1.34/1.81 % (13745)Memory used [KB]: 5756
% 1.34/1.81 % (13745)Time elapsed: 0.048 s
% 1.34/1.81 % (13745)Instructions burned: 96 (million)
% 1.34/1.81 % (13745)------------------------------
% 1.34/1.81 % (13745)------------------------------
% 1.34/1.83 % (13748)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_13589 for (2993ds/83Mi)
% 1.34/1.83 % (13748)Refutation not found, incomplete strategy
% 1.34/1.83 % (13748)------------------------------
% 1.34/1.83 % (13748)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.83 % (13748)Termination reason: Refutation not found, incomplete strategy
% 1.34/1.83
% 1.34/1.83
% 1.34/1.83 % (13748)Memory used [KB]: 5500
% 1.34/1.83 % (13748)Time elapsed: 0.003 s
% 1.34/1.83 % (13748)Instructions burned: 3 (million)
% 1.34/1.83 % (13748)------------------------------
% 1.34/1.83 % (13748)------------------------------
% 1.34/1.83 % (13747)Instruction limit reached!
% 1.34/1.83 % (13747)------------------------------
% 1.34/1.83 % (13747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.83 % (13747)Termination reason: Unknown
% 1.34/1.83 % (13747)Termination phase: Saturation
% 1.34/1.83
% 1.34/1.83 % (13747)Memory used [KB]: 5756
% 1.34/1.83 % (13747)Time elapsed: 0.037 s
% 1.34/1.83 % (13747)Instructions burned: 71 (million)
% 1.34/1.83 % (13747)------------------------------
% 1.34/1.83 % (13747)------------------------------
% 1.34/1.83 % (13732)Instruction limit reached!
% 1.34/1.83 % (13732)------------------------------
% 1.34/1.83 % (13732)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.83 % (13732)Termination reason: Unknown
% 1.34/1.83 % (13732)Termination phase: Saturation
% 1.34/1.83
% 1.34/1.83 % (13732)Memory used [KB]: 6524
% 1.34/1.83 % (13732)Time elapsed: 0.214 s
% 1.34/1.83 % (13732)Instructions burned: 450 (million)
% 1.34/1.83 % (13732)------------------------------
% 1.34/1.83 % (13732)------------------------------
% 1.34/1.84 % (13749)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_13589 for (2993ds/11Mi)
% 1.34/1.84 % (13750)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_13589 for (2993ds/41Mi)
% 1.34/1.85 % (13749)Instruction limit reached!
% 1.34/1.85 % (13749)------------------------------
% 1.34/1.85 % (13749)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.85 % (13749)Termination reason: Unknown
% 1.34/1.85 % (13749)Termination phase: Saturation
% 1.34/1.85
% 1.34/1.85 % (13749)Memory used [KB]: 5500
% 1.34/1.85 % (13749)Time elapsed: 0.007 s
% 1.34/1.85 % (13749)Instructions burned: 11 (million)
% 1.34/1.85 % (13749)------------------------------
% 1.34/1.85 % (13749)------------------------------
% 1.34/1.85 % (13751)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_13589 for (2993ds/6Mi)
% 1.34/1.85 % (13751)Instruction limit reached!
% 1.34/1.85 % (13751)------------------------------
% 1.34/1.85 % (13751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.85 % (13751)Termination reason: Unknown
% 1.34/1.85 % (13751)Termination phase: Saturation
% 1.34/1.85
% 1.34/1.85 % (13751)Memory used [KB]: 5500
% 1.34/1.85 % (13751)Time elapsed: 0.026 s
% 1.34/1.85 % (13751)Instructions burned: 7 (million)
% 1.34/1.85 % (13751)------------------------------
% 1.34/1.85 % (13751)------------------------------
% 1.34/1.86 % (13750)Instruction limit reached!
% 1.34/1.86 % (13750)------------------------------
% 1.34/1.86 % (13750)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.86 % (13750)Termination reason: Unknown
% 1.34/1.86 % (13750)Termination phase: Saturation
% 1.34/1.86
% 1.34/1.86 % (13750)Memory used [KB]: 5756
% 1.34/1.86 % (13750)Time elapsed: 0.043 s
% 1.34/1.86 % (13750)Instructions burned: 41 (million)
% 1.34/1.86 % (13750)------------------------------
% 1.34/1.86 % (13750)------------------------------
% 1.34/1.86 % (13752)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_13589 for (2993ds/150Mi)
% 1.34/1.87 % (13753)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_13589 for (2993ds/343Mi)
% 1.34/1.88 % (13754)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_13589 for (2993ds/109Mi)
% 1.34/1.89 % (13746)Instruction limit reached!
% 1.34/1.89 % (13746)------------------------------
% 1.34/1.89 % (13746)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.89 % (13746)Termination reason: Unknown
% 1.34/1.89 % (13746)Termination phase: Saturation
% 1.34/1.89
% 1.34/1.89 % (13746)Memory used [KB]: 6268
% 1.34/1.89 % (13746)Time elapsed: 0.135 s
% 1.34/1.89 % (13746)Instructions burned: 456 (million)
% 1.34/1.89 % (13746)------------------------------
% 1.34/1.89 % (13746)------------------------------
% 1.34/1.90 % (13755)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_13589 for (2992ds/253Mi)
% 1.34/1.92 % (13735)Instruction limit reached!
% 1.34/1.92 % (13735)------------------------------
% 1.34/1.92 % (13735)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.92 % (13735)Termination reason: Unknown
% 1.34/1.92 % (13735)Termination phase: Saturation
% 1.34/1.92
% 1.34/1.92 % (13735)Memory used [KB]: 6524
% 1.34/1.92 % (13735)Time elapsed: 0.249 s
% 1.34/1.92 % (13735)Instructions burned: 508 (million)
% 1.34/1.92 % (13735)------------------------------
% 1.34/1.92 % (13735)------------------------------
% 1.34/1.93 % (13754)Instruction limit reached!
% 1.34/1.93 % (13754)------------------------------
% 1.34/1.93 % (13754)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.93 % (13754)Termination reason: Unknown
% 1.34/1.93 % (13754)Termination phase: Saturation
% 1.34/1.93
% 1.34/1.93 % (13754)Memory used [KB]: 6012
% 1.34/1.93 % (13754)Time elapsed: 0.078 s
% 1.34/1.93 % (13754)Instructions burned: 110 (million)
% 1.34/1.93 % (13754)------------------------------
% 1.34/1.93 % (13754)------------------------------
% 1.34/1.94 % (13742)Instruction limit reached!
% 1.34/1.94 % (13742)------------------------------
% 1.34/1.94 % (13742)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.94 % (13742)Termination reason: Unknown
% 1.34/1.94 % (13742)Termination phase: Saturation
% 1.34/1.94
% 1.34/1.94 % (13742)Memory used [KB]: 2814
% 1.34/1.94 % (13742)Time elapsed: 0.207 s
% 1.34/1.94 % (13742)Instructions burned: 433 (million)
% 1.34/1.94 % (13742)------------------------------
% 1.34/1.94 % (13742)------------------------------
% 1.34/1.94 % (13756)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_13589 for (2992ds/140Mi)
% 1.34/1.94 % (13752)Instruction limit reached!
% 1.34/1.94 % (13752)------------------------------
% 1.34/1.94 % (13752)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.94 % (13752)Termination reason: Unknown
% 1.34/1.94 % (13752)Termination phase: Saturation
% 1.34/1.94
% 1.34/1.94 % (13752)Memory used [KB]: 6140
% 1.34/1.94 % (13752)Time elapsed: 0.097 s
% 1.34/1.94 % (13752)Instructions burned: 151 (million)
% 1.34/1.94 % (13752)------------------------------
% 1.34/1.94 % (13752)------------------------------
% 1.34/1.95 % (13757)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_13589 for (2992ds/614Mi)
% 1.34/1.95 % (13758)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_13589 for (2992ds/202Mi)
% 1.34/1.96 % (13759)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_13589 for (2992ds/339Mi)
% 1.34/1.98 % (13756)Instruction limit reached!
% 1.34/1.98 % (13756)------------------------------
% 1.34/1.98 % (13756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.98 % (13756)Termination reason: Unknown
% 1.34/1.98 % (13756)Termination phase: Saturation
% 1.34/1.98
% 1.34/1.98 % (13756)Memory used [KB]: 6012
% 1.34/1.98 % (13756)Time elapsed: 0.042 s
% 1.34/1.98 % (13756)Instructions burned: 142 (million)
% 1.34/1.98 % (13756)------------------------------
% 1.34/1.98 % (13756)------------------------------
% 1.34/1.99 % (13760)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_13589 for (2992ds/283Mi)
% 1.34/2.01 % (13755)Instruction limit reached!
% 1.34/2.01 % (13755)------------------------------
% 1.34/2.01 % (13755)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/2.01 % (13755)Termination reason: Unknown
% 1.34/2.02 % (13755)Termination phase: Saturation
% 1.34/2.02
% 1.34/2.02 % (13755)Memory used [KB]: 6140
% 1.34/2.02 % (13755)Time elapsed: 0.111 s
% 1.34/2.02 % (13755)Instructions burned: 253 (million)
% 1.34/2.02 % (13755)------------------------------
% 1.34/2.02 % (13755)------------------------------
% 6.97/2.02 % (13753)Instruction limit reached!
% 6.97/2.02 % (13753)------------------------------
% 6.97/2.02 % (13753)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.97/2.02 % (13753)Termination reason: Unknown
% 6.97/2.02 % (13753)Termination phase: Saturation
% 6.97/2.02
% 6.97/2.02 % (13753)Memory used [KB]: 6396
% 6.97/2.02 % (13753)Time elapsed: 0.176 s
% 6.97/2.02 % (13753)Instructions burned: 343 (million)
% 6.97/2.02 % (13753)------------------------------
% 6.97/2.02 % (13753)------------------------------
% 6.97/2.03 % (13761)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_13589 for (2991ds/134Mi)
% 6.97/2.04 % (13762)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_13589 for (2991ds/298Mi)
% 6.97/2.05 % (13758)Instruction limit reached!
% 6.97/2.05 % (13758)------------------------------
% 6.97/2.05 % (13758)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.97/2.05 % (13758)Termination reason: Unknown
% 6.97/2.05 % (13758)Termination phase: Saturation
% 6.97/2.05
% 6.97/2.05 % (13758)Memory used [KB]: 6012
% 6.97/2.05 % (13758)Time elapsed: 0.101 s
% 6.97/2.05 % (13758)Instructions burned: 202 (million)
% 6.97/2.05 % (13758)------------------------------
% 6.97/2.05 % (13758)------------------------------
% 6.97/2.07 % (13763)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_13589 for (2991ds/192Mi)
% 6.97/2.09 % (13760)Instruction limit reached!
% 6.97/2.09 % (13760)------------------------------
% 6.97/2.09 % (13760)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.97/2.09 % (13760)Termination reason: Unknown
% 6.97/2.09 % (13760)Termination phase: Saturation
% 6.97/2.09
% 6.97/2.09 % (13760)Memory used [KB]: 7547
% 6.97/2.09 % (13760)Time elapsed: 0.105 s
% 6.97/2.09 % (13760)Instructions burned: 284 (million)
% 6.97/2.09 % (13760)------------------------------
% 6.97/2.09 % (13760)------------------------------
% 6.97/2.10 % (13764)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_13589 for (2991ds/258Mi)
% 6.97/2.10 % (13761)Instruction limit reached!
% 6.97/2.10 % (13761)------------------------------
% 6.97/2.10 % (13761)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.97/2.10 % (13761)Termination reason: Unknown
% 6.97/2.10 % (13761)Termination phase: Saturation
% 6.97/2.10
% 6.97/2.10 % (13761)Memory used [KB]: 6268
% 6.97/2.10 % (13761)Time elapsed: 0.068 s
% 6.97/2.10 % (13761)Instructions burned: 134 (million)
% 6.97/2.10 % (13761)------------------------------
% 6.97/2.10 % (13761)------------------------------
% 6.97/2.11 % (13765)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_13589 for (2990ds/90Mi)
% 7.48/2.12 % (13759)Instruction limit reached!
% 7.48/2.12 % (13759)------------------------------
% 7.48/2.12 % (13759)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.48/2.12 % (13759)Termination reason: Unknown
% 7.48/2.12 % (13759)Termination phase: Saturation
% 7.48/2.12
% 7.48/2.12 % (13759)Memory used [KB]: 6524
% 7.48/2.12 % (13759)Time elapsed: 0.166 s
% 7.48/2.12 % (13759)Instructions burned: 339 (million)
% 7.48/2.12 % (13759)------------------------------
% 7.48/2.12 % (13759)------------------------------
% 7.48/2.14 % (13766)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_13589 for (2990ds/231Mi)
% 7.48/2.16 % (13765)Instruction limit reached!
% 7.48/2.16 % (13765)------------------------------
% 7.48/2.16 % (13765)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.48/2.16 % (13765)Termination reason: Unknown
% 7.48/2.16 % (13765)Termination phase: Saturation
% 7.48/2.16
% 7.48/2.16 % (13765)Memory used [KB]: 6012
% 7.48/2.16 % (13765)Time elapsed: 0.045 s
% 7.48/2.16 % (13765)Instructions burned: 90 (million)
% 7.48/2.16 % (13765)------------------------------
% 7.48/2.16 % (13765)------------------------------
% 7.48/2.16 % (13763)Instruction limit reached!
% 7.48/2.16 % (13763)------------------------------
% 7.48/2.16 % (13763)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.48/2.16 % (13763)Termination reason: Unknown
% 7.48/2.16 % (13763)Termination phase: Saturation
% 7.48/2.16
% 7.48/2.16 % (13763)Memory used [KB]: 6140
% 7.48/2.16 % (13763)Time elapsed: 0.096 s
% 7.48/2.16 % (13763)Instructions burned: 193 (million)
% 7.48/2.16 % (13763)------------------------------
% 7.48/2.16 % (13763)------------------------------
% 7.48/2.17 % (13767)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_13589 for (2990ds/458Mi)
% 7.48/2.18 % (13764)Instruction limit reached!
% 7.48/2.18 % (13764)------------------------------
% 7.48/2.18 % (13764)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.48/2.18 % (13764)Termination reason: Unknown
% 7.48/2.18 % (13764)Termination phase: Saturation
% 7.48/2.18
% 7.48/2.18 % (13764)Memory used [KB]: 5884
% 7.48/2.18 % (13764)Time elapsed: 0.080 s
% 7.48/2.18 % (13764)Instructions burned: 261 (million)
% 7.48/2.18 % (13764)------------------------------
% 7.48/2.18 % (13764)------------------------------
% 7.48/2.18 % (13768)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_13589 for (2990ds/31Mi)
% 7.48/2.18 % (13762)Instruction limit reached!
% 7.48/2.18 % (13762)------------------------------
% 7.48/2.18 % (13762)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.48/2.18 % (13762)Termination reason: Unknown
% 7.48/2.18 % (13762)Termination phase: Saturation
% 7.48/2.18
% 7.48/2.18 % (13762)Memory used [KB]: 6012
% 7.48/2.18 % (13762)Time elapsed: 0.145 s
% 7.48/2.18 % (13762)Instructions burned: 299 (million)
% 7.48/2.18 % (13762)------------------------------
% 7.48/2.18 % (13762)------------------------------
% 7.48/2.18 % (13769)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_13589 for (2990ds/297Mi)
% 7.48/2.19 % (13768)Instruction limit reached!
% 7.48/2.19 % (13768)------------------------------
% 7.48/2.19 % (13768)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.48/2.19 % (13768)Termination reason: Unknown
% 7.48/2.19 % (13768)Termination phase: Saturation
% 7.48/2.19
% 7.48/2.19 % (13768)Memory used [KB]: 5628
% 7.48/2.19 % (13768)Time elapsed: 0.018 s
% 7.48/2.19 % (13768)Instructions burned: 32 (million)
% 7.48/2.19 % (13768)------------------------------
% 7.48/2.19 % (13768)------------------------------
% 8.09/2.21 % (13770)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_13589 for (2990ds/987Mi)
% 8.09/2.21 % (13771)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_13589 for (2990ds/182Mi)
% 8.09/2.22 % (13739)Instruction limit reached!
% 8.09/2.22 % (13739)------------------------------
% 8.09/2.22 % (13739)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.09/2.22 % (13739)Termination reason: Unknown
% 8.09/2.22 % (13739)Termination phase: Saturation
% 8.09/2.22
% 8.09/2.22 % (13739)Memory used [KB]: 7675
% 8.09/2.22 % (13739)Time elapsed: 0.526 s
% 8.09/2.23 % (13739)Instructions burned: 1088 (million)
% 8.09/2.23 % (13739)------------------------------
% 8.09/2.23 % (13739)------------------------------
% 8.09/2.24 % (13772)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_13589 for (2989ds/182Mi)
% 8.09/2.24 % (13757)Instruction limit reached!
% 8.09/2.24 % (13757)------------------------------
% 8.09/2.24 % (13757)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.09/2.24 % (13757)Termination reason: Unknown
% 8.09/2.24 % (13757)Termination phase: Saturation
% 8.09/2.24
% 8.09/2.24 % (13757)Memory used [KB]: 7164
% 8.09/2.24 % (13757)Time elapsed: 0.295 s
% 8.09/2.24 % (13757)Instructions burned: 615 (million)
% 8.09/2.24 % (13757)------------------------------
% 8.09/2.24 % (13757)------------------------------
% 8.09/2.26 % (13766)Instruction limit reached!
% 8.09/2.26 % (13766)------------------------------
% 8.09/2.26 % (13766)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.09/2.26 % (13766)Termination reason: Unknown
% 8.09/2.26 % (13766)Termination phase: Saturation
% 8.09/2.26
% 8.09/2.26 % (13766)Memory used [KB]: 6524
% 8.09/2.26 % (13766)Time elapsed: 0.121 s
% 8.09/2.26 % (13766)Instructions burned: 231 (million)
% 8.09/2.26 % (13766)------------------------------
% 8.09/2.26 % (13766)------------------------------
% 8.09/2.26 % (13773)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_13589 for (2989ds/154Mi)
% 8.09/2.27 % (13774)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_13589 for (2989ds/79Mi)
% 8.09/2.29 % (13769)Instruction limit reached!
% 8.09/2.29 % (13769)------------------------------
% 8.09/2.29 % (13769)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.09/2.29 % (13769)Termination reason: Unknown
% 8.09/2.29 % (13769)Termination phase: Saturation
% 8.09/2.29
% 8.09/2.29 % (13769)Memory used [KB]: 6524
% 8.09/2.29 % (13769)Time elapsed: 0.101 s
% 8.09/2.29 % (13769)Instructions burned: 299 (million)
% 8.09/2.29 % (13769)------------------------------
% 8.09/2.29 % (13769)------------------------------
% 8.09/2.30 % (13775)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_13589 for (2989ds/216Mi)
% 8.43/2.30 % (13771)Instruction limit reached!
% 8.43/2.30 % (13771)------------------------------
% 8.43/2.30 % (13771)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.43/2.30 % (13771)Termination reason: Unknown
% 8.43/2.30 % (13771)Termination phase: Saturation
% 8.43/2.30
% 8.43/2.30 % (13771)Memory used [KB]: 6140
% 8.43/2.30 % (13771)Time elapsed: 0.090 s
% 8.43/2.30 % (13771)Instructions burned: 183 (million)
% 8.43/2.30 % (13771)------------------------------
% 8.43/2.30 % (13771)------------------------------
% 8.43/2.31 % (13774)Instruction limit reached!
% 8.43/2.31 % (13774)------------------------------
% 8.43/2.31 % (13774)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.43/2.31 % (13774)Termination reason: Unknown
% 8.43/2.31 % (13774)Termination phase: Saturation
% 8.43/2.31
% 8.43/2.31 % (13774)Memory used [KB]: 5884
% 8.43/2.31 % (13774)Time elapsed: 0.042 s
% 8.43/2.31 % (13774)Instructions burned: 80 (million)
% 8.43/2.31 % (13774)------------------------------
% 8.43/2.31 % (13774)------------------------------
% 8.43/2.31 % (13776)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_13589 for (2988ds/114Mi)
% 8.43/2.33 % (13777)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_13589 for (2988ds/922Mi)
% 8.43/2.33 % (13772)Instruction limit reached!
% 8.43/2.33 % (13772)------------------------------
% 8.43/2.33 % (13772)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.43/2.33 % (13772)Termination reason: Unknown
% 8.43/2.33 % (13772)Termination phase: Saturation
% 8.43/2.33
% 8.43/2.33 % (13772)Memory used [KB]: 6140
% 8.43/2.33 % (13772)Time elapsed: 0.092 s
% 8.43/2.33 % (13772)Instructions burned: 182 (million)
% 8.43/2.33 % (13772)------------------------------
% 8.43/2.33 % (13772)------------------------------
% 8.43/2.34 % (13773)Instruction limit reached!
% 8.43/2.34 % (13773)------------------------------
% 8.43/2.34 % (13773)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.43/2.34 % (13773)Termination reason: Unknown
% 8.43/2.34 % (13773)Termination phase: Saturation
% 8.43/2.34
% 8.43/2.34 % (13773)Memory used [KB]: 6140
% 8.43/2.34 % (13773)Time elapsed: 0.077 s
% 8.43/2.34 % (13773)Instructions burned: 155 (million)
% 8.43/2.34 % (13773)------------------------------
% 8.43/2.34 % (13773)------------------------------
% 8.43/2.35 % (13778)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_13589 for (2988ds/182Mi)
% 8.43/2.35 % (13779)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_13589 for (2988ds/164Mi)
% 8.43/2.36 % (13775)Instruction limit reached!
% 8.43/2.36 % (13775)------------------------------
% 8.43/2.36 % (13775)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.43/2.36 % (13775)Termination reason: Unknown
% 8.43/2.36 % (13775)Termination phase: Saturation
% 8.43/2.36
% 8.43/2.36 % (13775)Memory used [KB]: 6012
% 8.43/2.36 % (13775)Time elapsed: 0.064 s
% 8.43/2.36 % (13775)Instructions burned: 216 (million)
% 8.43/2.36 % (13775)------------------------------
% 8.43/2.36 % (13775)------------------------------
% 8.43/2.37 % (13780)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_13589 for (2988ds/50Mi)
% 8.43/2.37 % (13776)Instruction limit reached!
% 8.43/2.37 % (13776)------------------------------
% 8.43/2.37 % (13776)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.43/2.37 % (13776)Termination reason: Unknown
% 8.43/2.37 % (13776)Termination phase: Saturation
% 8.43/2.37
% 8.43/2.37 % (13776)Memory used [KB]: 6140
% 8.43/2.37 % (13776)Time elapsed: 0.056 s
% 8.43/2.37 % (13776)Instructions burned: 114 (million)
% 8.43/2.37 % (13776)------------------------------
% 8.43/2.37 % (13776)------------------------------
% 8.43/2.38 % (13780)Instruction limit reached!
% 8.43/2.38 % (13780)------------------------------
% 8.43/2.38 % (13780)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.43/2.38 % (13780)Termination reason: Unknown
% 8.43/2.38 % (13780)Termination phase: Saturation
% 8.43/2.38
% 8.43/2.38 % (13780)Memory used [KB]: 10618
% 8.43/2.38 % (13780)Time elapsed: 0.017 s
% 8.43/2.38 % (13780)Instructions burned: 52 (million)
% 8.43/2.38 % (13780)------------------------------
% 8.43/2.38 % (13780)------------------------------
% 8.43/2.39 % (13781)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_13589 for (2988ds/368Mi)
% 8.43/2.39 % (13782)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_13589 for (2988ds/1021Mi)
% 8.96/2.40 % (13767)Instruction limit reached!
% 8.96/2.40 % (13767)------------------------------
% 8.96/2.40 % (13767)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.96/2.40 % (13767)Termination reason: Unknown
% 8.96/2.40 % (13767)Termination phase: Saturation
% 8.96/2.40
% 8.96/2.40 % (13767)Memory used [KB]: 7036
% 8.96/2.40 % (13767)Time elapsed: 0.225 s
% 8.96/2.40 % (13767)Instructions burned: 459 (million)
% 8.96/2.40 % (13767)------------------------------
% 8.96/2.40 % (13767)------------------------------
% 8.96/2.41 % (13783)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_13589 for (2988ds/267Mi)
% 8.96/2.43 % (13779)Instruction limit reached!
% 8.96/2.43 % (13779)------------------------------
% 8.96/2.43 % (13779)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.96/2.43 % (13779)Termination reason: Unknown
% 8.96/2.43 % (13779)Termination phase: Saturation
% 8.96/2.43
% 8.96/2.43 % (13779)Memory used [KB]: 1535
% 8.96/2.43 % (13779)Time elapsed: 0.082 s
% 8.96/2.43 % (13779)Instructions burned: 165 (million)
% 8.96/2.43 % (13779)------------------------------
% 8.96/2.43 % (13779)------------------------------
% 8.96/2.44 % (13778)Instruction limit reached!
% 8.96/2.44 % (13778)------------------------------
% 8.96/2.44 % (13778)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.96/2.44 % (13778)Termination reason: Unknown
% 8.96/2.44 % (13778)Termination phase: Saturation
% 8.96/2.44
% 8.96/2.44 % (13778)Memory used [KB]: 5756
% 8.96/2.44 % (13778)Time elapsed: 0.089 s
% 8.96/2.44 % (13778)Instructions burned: 183 (million)
% 8.96/2.44 % (13778)------------------------------
% 8.96/2.44 % (13778)------------------------------
% 8.96/2.45 % (13784)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_13589 for (2987ds/204Mi)
% 8.96/2.45 % (13785)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_13589 for (2987ds/26Mi)
% 8.96/2.46 % (13785)Instruction limit reached!
% 8.96/2.46 % (13785)------------------------------
% 8.96/2.46 % (13785)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.96/2.46 % (13785)Termination reason: Unknown
% 8.96/2.46 % (13785)Termination phase: Saturation
% 8.96/2.46
% 8.96/2.46 % (13785)Memory used [KB]: 5628
% 8.96/2.46 % (13785)Time elapsed: 0.036 s
% 8.96/2.46 % (13785)Instructions burned: 26 (million)
% 8.96/2.46 % (13785)------------------------------
% 8.96/2.46 % (13785)------------------------------
% 8.96/2.48 % (13786)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_13589 for (2987ds/53Mi)
% 9.42/2.50 % (13770)First to succeed.
% 9.42/2.51 % (13786)Instruction limit reached!
% 9.42/2.51 % (13786)------------------------------
% 9.42/2.51 % (13786)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.42/2.51 % (13786)Termination reason: Unknown
% 9.42/2.51 % (13786)Termination phase: Saturation
% 9.42/2.51
% 9.42/2.51 % (13786)Memory used [KB]: 5628
% 9.42/2.51 % (13786)Time elapsed: 0.027 s
% 9.42/2.51 % (13786)Instructions burned: 54 (million)
% 9.42/2.51 % (13786)------------------------------
% 9.42/2.51 % (13786)------------------------------
% 9.42/2.51 % (13770)Refutation found. Thanks to Tanya!
% 9.42/2.51 % SZS status Theorem for DTF2THF_13589
% 9.42/2.51 % SZS output start Proof for DTF2THF_13589
% 9.42/2.51 thf(func_def_1, type, cR: $i > $i > $i > $o).
% 9.42/2.51 thf(func_def_2, type, cS: $i > $i).
% 9.42/2.51 thf(func_def_18, type, ph1: !>[X0: $tType]:(X0)).
% 9.42/2.51 thf(func_def_21, type, sK4: ($i > $o) > $i).
% 9.42/2.51 thf(func_def_22, type, sK5: $i > $i).
% 9.42/2.51 thf(func_def_24, type, sK7: $i > $i).
% 9.42/2.51 thf(func_def_26, type, sK9: $i > $i).
% 9.42/2.51 thf(func_def_31, type, sK14: ($i > $o) > $i).
% 9.42/2.51 thf(f2338,plain,(
% 9.42/2.51 $false),
% 9.42/2.51 inference(avatar_sat_refutation,[status(thm)],[f597,f623,f1276,f2284,f2336])).
% 9.42/2.51 thf(f2336,plain,(
% 9.42/2.51 ~spl0_4 | ~spl0_6),
% 9.42/2.51 inference(avatar_contradiction_clause,[status(thm)],[f2335])).
% 9.42/2.51 thf(f2335,plain,(
% 9.42/2.51 $false | (~spl0_4 | ~spl0_6)),
% 9.42/2.51 inference(trivial_inequality_removal,[status(thm)],[f2304])).
% 9.42/2.51 thf(f2304,plain,(
% 9.42/2.51 ($true = $false) | (~spl0_4 | ~spl0_6)),
% 9.42/2.51 inference(backward_demodulation,[status(thm)],[f705,f2289])).
% 9.42/2.51 thf(f2289,plain,(
% 9.42/2.51 ( ! [X1 : $i] : (((cR @ (cS @ sK8) @ c0 @ X1) = $false)) ) | ~spl0_6),
% 9.42/2.51 inference(pi_clausification,[status(thm)],[f1275])).
% 9.42/2.51 thf(f1275,plain,(
% 9.42/2.51 ($false = (?? @ $i @ (cR @ (cS @ sK8) @ c0))) | ~spl0_6),
% 9.42/2.51 inference(avatar_component_clause,[status(thm)],[f1273])).
% 9.42/2.51 thf(f1273,definition,(
% 9.42/2.51 spl0_6 <=> ($false = (?? @ $i @ (cR @ (cS @ sK8) @ c0)))),
% 9.42/2.51 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 9.42/2.51 thf(f705,plain,(
% 9.42/2.51 ($true = (cR @ (cS @ sK8) @ c0 @ (sK9 @ (cS @ c0)))) | ~spl0_4),
% 9.42/2.51 inference(boolean_simplification,[status(thm)],[f700])).
% 9.42/2.51 thf(f700,plain,(
% 9.42/2.51 ($true = ($true => (cR @ (cS @ sK8) @ c0 @ (sK9 @ (cS @ c0))))) | ~spl0_4),
% 9.42/2.51 inference(superposition,[status(thm)],[f70,f680])).
% 9.42/2.51 thf(f680,plain,(
% 9.42/2.51 ( ! [X1 : $i] : (($true = (cR @ sK8 @ X1 @ (sK9 @ X1)))) ) | ~spl0_4),
% 9.42/2.51 inference(sigma_clausification,[status(thm)],[f676])).
% 9.42/2.51 thf(f676,plain,(
% 9.42/2.51 ( ! [X1 : $i] : (($true = (?? @ $i @ (cR @ sK8 @ X1)))) ) | ~spl0_4),
% 9.42/2.51 inference(beta_eta_normalization,[status(thm)],[f674])).
% 9.42/2.51 thf(f674,plain,(
% 9.42/2.51 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (?? @ $i @ (cR @ sK8 @ Y0))) @ X1))) ) | ~spl0_4),
% 9.42/2.51 inference(pi_clausification,[status(thm)],[f655])).
% 9.42/2.51 thf(f655,plain,(
% 9.42/2.51 ($true = (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (cR @ sK8 @ Y0))))) | ~spl0_4),
% 9.42/2.51 inference(binary_proxy_clausification,[status(thm)],[f629])).
% 9.42/2.51 thf(f629,plain,(
% 9.42/2.51 ($false = ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (cR @ sK8 @ Y0)))) => (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (cR @ (cS @ sK8) @ Y0)))))) | ~spl0_4),
% 9.42/2.51 inference(beta_eta_normalization,[status(thm)],[f627])).
% 9.42/2.51 thf(f627,plain,(
% 9.42/2.51 (((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (cR @ Y0 @ Y1)))) => (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (cR @ (cS @ Y0) @ Y1)))))) @ sK8) = $false) | ~spl0_4),
% 9.42/2.51 inference(sigma_clausification,[status(thm)],[f596])).
% 9.42/2.51 thf(f596,plain,(
% 9.42/2.51 ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (cR @ Y0 @ Y1)))) => (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (cR @ (cS @ Y0) @ Y1))))))) = $false) | ~spl0_4),
% 9.42/2.51 inference(avatar_component_clause,[status(thm)],[f594])).
% 9.42/2.51 thf(f594,definition,(
% 9.42/2.51 spl0_4 <=> ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (cR @ Y0 @ Y1)))) => (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (cR @ (cS @ Y0) @ Y1))))))) = $false)),
% 9.42/2.51 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 9.42/2.51 thf(f70,plain,(
% 9.42/2.51 ( ! [X2 : $i,X1 : $i] : (($true = ((cR @ X2 @ (cS @ c0) @ X1) => (cR @ (cS @ X2) @ c0 @ X1)))) )),
% 9.42/2.51 inference(beta_eta_normalization,[status(thm)],[f66])).
% 9.42/2.51 thf(f66,plain,(
% 9.42/2.51 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((cR @ Y0 @ (cS @ c0) @ X1) => (cR @ (cS @ Y0) @ c0 @ X1))) @ X2))) )),
% 9.42/2.51 inference(pi_clausification,[status(thm)],[f63])).
% 9.42/2.51 thf(f63,plain,(
% 9.42/2.51 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((cR @ Y0 @ (cS @ c0) @ X1) => (cR @ (cS @ Y0) @ c0 @ X1)))))) )),
% 9.42/2.51 inference(beta_eta_normalization,[status(thm)],[f60])).
% 9.42/2.51 thf(f60,plain,(
% 9.42/2.51 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cR @ Y1 @ (cS @ c0) @ Y0) => (cR @ (cS @ Y1) @ c0 @ Y0))))) @ X1))) )),
% 9.42/2.51 inference(pi_clausification,[status(thm)],[f55])).
% 9.42/2.51 thf(f55,plain,(
% 9.42/2.51 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cR @ Y1 @ (cS @ c0) @ Y0) => (cR @ (cS @ Y1) @ c0 @ Y0)))))))),
% 9.42/2.51 inference(binary_proxy_clausification,[status(thm)],[f38])).
% 9.42/2.51 thf(f38,plain,(
% 9.42/2.51 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cR @ Y1 @ (cS @ c0) @ Y0) => (cR @ (cS @ Y1) @ c0 @ Y0)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((cR @ (cS @ Y3) @ Y2 @ Y0) => ((cR @ Y3 @ Y0 @ Y1) => (cR @ (cS @ Y3) @ (cS @ Y2) @ Y1)))))))))))))),
% 9.42/2.51 inference(boolean_simplification,[status(thm)],[f35])).
% 9.42/2.51 thf(f35,plain,(
% 9.42/2.51 ($true = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cR @ Y1 @ (cS @ c0) @ Y0) => (cR @ (cS @ Y1) @ c0 @ Y0)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((cR @ (cS @ Y3) @ Y2 @ Y0) => ((cR @ Y3 @ Y0 @ Y1) => (cR @ (cS @ Y3) @ (cS @ Y2) @ Y1)))))))))))) & $true))),
% 9.42/2.51 inference(backward_demodulation,[status(thm)],[f32,f33])).
% 9.42/2.51 thf(f33,plain,(
% 9.42/2.51 ($true = (!! @ $i @ (^[Y0 : $i]: (cR @ c0 @ Y0 @ (cS @ Y0)))))),
% 9.42/2.51 inference(binary_proxy_clausification,[status(thm)],[f32])).
% 9.42/2.51 thf(f32,plain,(
% 9.42/2.51 ($true = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cR @ Y1 @ (cS @ c0) @ Y0) => (cR @ (cS @ Y1) @ c0 @ Y0)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((cR @ (cS @ Y3) @ Y2 @ Y0) => ((cR @ Y3 @ Y0 @ Y1) => (cR @ (cS @ Y3) @ (cS @ Y2) @ Y1)))))))))))) & (!! @ $i @ (^[Y0 : $i]: (cR @ c0 @ Y0 @ (cS @ Y0))))))),
% 9.42/2.51 inference(boolean_simplification,[status(thm)],[f29])).
% 9.42/2.51 thf(f29,plain,(
% 9.42/2.51 ($true = ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cR @ Y1 @ (cS @ c0) @ Y0) => (cR @ (cS @ Y1) @ c0 @ Y0)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((cR @ (cS @ Y3) @ Y2 @ Y0) => ((cR @ Y3 @ Y0 @ Y1) => (cR @ (cS @ Y3) @ (cS @ Y2) @ Y1)))))))))))) & (!! @ $i @ (^[Y0 : $i]: (cR @ c0 @ Y0 @ (cS @ Y0))))) & $true))),
% 9.42/2.51 inference(backward_demodulation,[status(thm)],[f16,f22])).
% 9.42/2.51 thf(f22,plain,(
% 9.42/2.51 ($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((Y0 @ c0) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1)))))) => (!! @ $i @ Y0)))))),
% 9.42/2.51 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 9.42/2.51 thf(f16,plain,(
% 9.42/2.51 ($true = ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cR @ Y1 @ (cS @ c0) @ Y0) => (cR @ (cS @ Y1) @ c0 @ Y0)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((cR @ (cS @ Y3) @ Y2 @ Y0) => ((cR @ Y3 @ Y0 @ Y1) => (cR @ (cS @ Y3) @ (cS @ Y2) @ Y1)))))))))))) & (!! @ $i @ (^[Y0 : $i]: (cR @ c0 @ Y0 @ (cS @ Y0))))) & (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((Y0 @ c0) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1)))))) => (!! @ $i @ Y0))))))),
% 9.42/2.51 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 9.42/2.51 thf(f13,plain,(
% 9.42/2.51 ($false = (((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cR @ Y1 @ (cS @ c0) @ Y0) => (cR @ (cS @ Y1) @ c0 @ Y0)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((cR @ (cS @ Y3) @ Y2 @ Y0) => ((cR @ Y3 @ Y0 @ Y1) => (cR @ (cS @ Y3) @ (cS @ Y2) @ Y1)))))))))))) & (!! @ $i @ (^[Y0 : $i]: (cR @ c0 @ Y0 @ (cS @ Y0))))) & (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((Y0 @ c0) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1)))))) => (!! @ $i @ Y0))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (cR @ Y0 @ Y1))))))))),
% 9.42/2.51 inference(not_proxy_clausification,[status(thm)],[f12])).
% 9.42/2.51 thf(f12,plain,(
% 9.42/2.51 ($true = (~ (((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cR @ Y1 @ (cS @ c0) @ Y0) => (cR @ (cS @ Y1) @ c0 @ Y0)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((cR @ (cS @ Y3) @ Y2 @ Y0) => ((cR @ Y3 @ Y0 @ Y1) => (cR @ (cS @ Y3) @ (cS @ Y2) @ Y1)))))))))))) & (!! @ $i @ (^[Y0 : $i]: (cR @ c0 @ Y0 @ (cS @ Y0))))) & (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((Y0 @ c0) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1)))))) => (!! @ $i @ Y0))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (cR @ Y0 @ Y1)))))))))),
% 9.42/2.51 inference(beta_eta_normalization,[status(thm)],[f11])).
% 9.42/2.51 thf(f11,plain,(
% 9.42/2.51 ($true = (~ (((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cR @ Y1 @ (cS @ c0) @ Y0) => (cR @ (cS @ Y1) @ c0 @ Y0)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((cR @ (cS @ Y3) @ Y2 @ Y0) => ((cR @ Y3 @ Y0 @ Y1) => (cR @ (cS @ Y3) @ (cS @ Y2) @ Y1)))))))))))) & (!! @ $i @ (^[Y0 : $i]: (cR @ c0 @ Y0 @ (cS @ Y0))))) & (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((Y0 @ c0) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1)))))) => (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (cR @ Y0 @ Y1 @ Y2))))))))))),
% 9.42/2.51 inference(definition_unfolding,[status(thm)],[f9,f10])).
% 9.42/2.51 thf(f10,plain,(
% 9.42/2.51 (cIND = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((Y0 @ c0) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1)))))) => (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))))),
% 9.42/2.51 inference(cnf_transformation,[status(thm)],[f6])).
% 9.42/2.51 thf(f6,plain,(
% 9.42/2.51 (cIND = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((Y0 @ c0) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1)))))) => (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))))),
% 9.42/2.51 inference(fool_elimination,[status(thm)],[f5])).
% 9.42/2.51 thf(f5,plain,(
% 9.42/2.51 (cIND = ! [X0 : $i > $o] : ((! [X1 : $i] : ((X0 @ X1) => (X0 @ (cS @ X1))) & (X0 @ c0)) => ! [X2 : $i] : (X0 @ X2)))),
% 9.42/2.51 inference(rectify,[status(thm)],[f1])).
% 9.42/2.51 thf(f1,axiom,(
% 9.42/2.51 (cIND = ! [X0 : $i > $o] : ((! [X1 : $i] : ((X0 @ X1) => (X0 @ (cS @ X1))) & (X0 @ c0)) => ! [X1 : $i] : (X0 @ X1)))),
% 9.42/2.51 file('/export/starexec/sandbox/tmp/tmp.5Muac0Woob/DTF2THF_13589.p',cIND_def)).
% 9.42/2.51 thf(f9,plain,(
% 9.42/2.51 ($true = (~ (((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cR @ Y1 @ (cS @ c0) @ Y0) => (cR @ (cS @ Y1) @ c0 @ Y0)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((cR @ (cS @ Y3) @ Y2 @ Y0) => ((cR @ Y3 @ Y0 @ Y1) => (cR @ (cS @ Y3) @ (cS @ Y2) @ Y1)))))))))))) & (!! @ $i @ (^[Y0 : $i]: (cR @ c0 @ Y0 @ (cS @ Y0))))) & cIND) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (cR @ Y0 @ Y1 @ Y2))))))))))),
% 9.42/2.51 inference(cnf_transformation,[status(thm)],[f8])).
% 9.42/2.51 thf(f8,plain,(
% 9.42/2.51 ($true = (~ (((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cR @ Y1 @ (cS @ c0) @ Y0) => (cR @ (cS @ Y1) @ c0 @ Y0)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((cR @ (cS @ Y3) @ Y2 @ Y0) => ((cR @ Y3 @ Y0 @ Y1) => (cR @ (cS @ Y3) @ (cS @ Y2) @ Y1)))))))))))) & (!! @ $i @ (^[Y0 : $i]: (cR @ c0 @ Y0 @ (cS @ Y0))))) & cIND) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (cR @ Y0 @ Y1 @ Y2))))))))))),
% 9.42/2.51 inference(fool_elimination,[status(thm)],[f7])).
% 9.42/2.51 thf(f7,plain,(
% 9.42/2.51 ~((cIND & ! [X0 : $i] : (cR @ c0 @ X0 @ (cS @ X0)) & ! [X1 : $i,X2 : $i,X3 : $i,X4 : $i] : ((cR @ (cS @ X1) @ X2 @ X4) => ((cR @ X1 @ X4 @ X3) => (cR @ (cS @ X1) @ (cS @ X2) @ X3))) & ! [X5 : $i,X6 : $i] : ((cR @ X5 @ (cS @ c0) @ X6) => (cR @ (cS @ X5) @ c0 @ X6))) => ! [X7 : $i,X8 : $i] : ? [X9 : $i] : (cR @ X8 @ X7 @ X9))),
% 9.42/2.51 inference(rectify,[status(thm)],[f3])).
% 9.42/2.51 thf(f3,negated_conjecture,(
% 9.42/2.51 ~((cIND & ! [X2 : $i] : (cR @ c0 @ X2 @ (cS @ X2)) & ! [X3 : $i,X2 : $i,X4 : $i,X5 : $i] : ((cR @ (cS @ X3) @ X2 @ X5) => ((cR @ X3 @ X5 @ X4) => (cR @ (cS @ X3) @ (cS @ X2) @ X4))) & ! [X3 : $i,X4 : $i] : ((cR @ X3 @ (cS @ c0) @ X4) => (cR @ (cS @ X3) @ c0 @ X4))) => ! [X6 : $i,X1 : $i] : ? [X7 : $i] : (cR @ X1 @ X6 @ X7))),
% 9.42/2.51 inference(negated_conjecture,[status(cth)],[f2])).
% 9.42/2.51 thf(f2,conjecture,(
% 9.42/2.51 (cIND & ! [X2 : $i] : (cR @ c0 @ X2 @ (cS @ X2)) & ! [X3 : $i,X2 : $i,X4 : $i,X5 : $i] : ((cR @ (cS @ X3) @ X2 @ X5) => ((cR @ X3 @ X5 @ X4) => (cR @ (cS @ X3) @ (cS @ X2) @ X4))) & ! [X3 : $i,X4 : $i] : ((cR @ X3 @ (cS @ c0) @ X4) => (cR @ (cS @ X3) @ c0 @ X4))) => ! [X6 : $i,X1 : $i] : ? [X7 : $i] : (cR @ X1 @ X6 @ X7)),
% 9.42/2.51 file('/export/starexec/sandbox/tmp/tmp.5Muac0Woob/DTF2THF_13589.p',cTHM604)).
% 9.42/2.51 thf(f2284,plain,(
% 9.42/2.51 ~spl0_4 | ~spl0_5),
% 9.42/2.51 inference(avatar_contradiction_clause,[status(thm)],[f2283])).
% 9.42/2.51 thf(f2283,plain,(
% 9.42/2.51 $false | (~spl0_4 | ~spl0_5)),
% 9.42/2.51 inference(trivial_inequality_removal,[status(thm)],[f2282])).
% 9.42/2.51 thf(f2282,plain,(
% 9.42/2.51 ($true = $false) | (~spl0_4 | ~spl0_5)),
% 9.42/2.51 inference(boolean_simplification,[status(thm)],[f2281])).
% 9.42/2.51 thf(f2281,plain,(
% 9.42/2.51 ($true = (~ $true)) | (~spl0_4 | ~spl0_5)),
% 9.42/2.51 inference(superposition,[status(thm)],[f2274,f2224])).
% 9.42/2.51 thf(f2224,plain,(
% 9.42/2.51 ($true = (cR @ (cS @ sK8) @ sK12 @ sK13)) | ~spl0_5),
% 9.42/2.51 inference(sigma_clausification,[status(thm)],[f1342])).
% 9.42/2.51 thf(f1342,plain,(
% 9.42/2.51 ($true = (?? @ $i @ (cR @ (cS @ sK8) @ sK12))) | ~spl0_5),
% 9.42/2.51 inference(binary_proxy_clausification,[status(thm)],[f1281])).
% 9.42/2.51 thf(f1281,plain,(
% 9.42/2.51 (((?? @ $i @ (cR @ (cS @ sK8) @ sK12)) => (?? @ $i @ (cR @ (cS @ sK8) @ (cS @ sK12)))) = $false) | ~spl0_5),
% 9.42/2.51 inference(beta_eta_normalization,[status(thm)],[f1279])).
% 9.42/2.51 thf(f1279,plain,(
% 9.42/2.51 (((^[Y0 : $i]: ((?? @ $i @ (cR @ (cS @ sK8) @ Y0)) => (?? @ $i @ (cR @ (cS @ sK8) @ (cS @ Y0))))) @ sK12) = $false) | ~spl0_5),
% 9.42/2.51 inference(sigma_clausification,[status(thm)],[f1271])).
% 9.42/2.51 thf(f1271,plain,(
% 9.42/2.51 ($false = (!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (cR @ (cS @ sK8) @ Y0)) => (?? @ $i @ (cR @ (cS @ sK8) @ (cS @ Y0))))))) | ~spl0_5),
% 9.42/2.51 inference(avatar_component_clause,[status(thm)],[f1269])).
% 9.42/2.51 thf(f1269,definition,(
% 9.42/2.51 spl0_5 <=> ($false = (!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (cR @ (cS @ sK8) @ Y0)) => (?? @ $i @ (cR @ (cS @ sK8) @ (cS @ Y0)))))))),
% 9.42/2.51 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 9.42/2.51 thf(f2274,plain,(
% 9.42/2.51 ( ! [X0 : $i] : (($true = (~ (cR @ (cS @ sK8) @ sK12 @ X0)))) ) | (~spl0_4 | ~spl0_5)),
% 9.42/2.51 inference(boolean_simplification,[status(thm)],[f2251])).
% 9.42/2.51 thf(f2251,plain,(
% 9.42/2.51 ( ! [X0 : $i] : (($true = ((cR @ (cS @ sK8) @ sK12 @ X0) => $false))) ) | (~spl0_4 | ~spl0_5)),
% 9.42/2.51 inference(superposition,[status(thm)],[f704,f2242])).
% 9.42/2.51 thf(f2242,plain,(
% 9.42/2.51 ( ! [X1 : $i] : (((cR @ (cS @ sK8) @ (cS @ sK12) @ X1) = $false)) ) | ~spl0_5),
% 9.42/2.51 inference(pi_clausification,[status(thm)],[f2225])).
% 9.42/2.51 thf(f2225,plain,(
% 9.42/2.51 ($false = (?? @ $i @ (cR @ (cS @ sK8) @ (cS @ sK12)))) | ~spl0_5),
% 9.42/2.51 inference(boolean_simplification,[status(thm)],[f2223])).
% 9.42/2.51 thf(f2223,plain,(
% 9.42/2.51 (($true => (?? @ $i @ (cR @ (cS @ sK8) @ (cS @ sK12)))) = $false) | ~spl0_5),
% 9.42/2.51 inference(backward_demodulation,[status(thm)],[f1281,f1342])).
% 9.42/2.51 thf(f704,plain,(
% 9.42/2.51 ( ! [X0 : $i,X1 : $i] : (($true = ((cR @ (cS @ sK8) @ X1 @ X0) => (cR @ (cS @ sK8) @ (cS @ X1) @ (sK9 @ X0))))) ) | ~spl0_4),
% 9.42/2.51 inference(boolean_simplification,[status(thm)],[f702])).
% 9.42/2.51 thf(f702,plain,(
% 9.42/2.51 ( ! [X0 : $i,X1 : $i] : (($true = ((cR @ (cS @ sK8) @ X1 @ X0) => ($true => (cR @ (cS @ sK8) @ (cS @ X1) @ (sK9 @ X0)))))) ) | ~spl0_4),
% 9.42/2.51 inference(superposition,[status(thm)],[f118,f680])).
% 9.42/2.51 thf(f118,plain,(
% 9.42/2.51 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((cR @ (cS @ X4) @ X3 @ X1) => ((cR @ X4 @ X1 @ X2) => (cR @ (cS @ X4) @ (cS @ X3) @ X2))))) )),
% 9.42/2.51 inference(beta_eta_normalization,[status(thm)],[f116])).
% 9.42/2.51 thf(f116,plain,(
% 9.42/2.51 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((^[Y0 : $i]: ((cR @ (cS @ Y0) @ X3 @ X1) => ((cR @ Y0 @ X1 @ X2) => (cR @ (cS @ Y0) @ (cS @ X3) @ X2)))) @ X4))) )),
% 9.42/2.51 inference(pi_clausification,[status(thm)],[f98])).
% 9.42/2.51 thf(f98,plain,(
% 9.42/2.51 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((cR @ (cS @ Y0) @ X3 @ X1) => ((cR @ Y0 @ X1 @ X2) => (cR @ (cS @ Y0) @ (cS @ X3) @ X2))))))) )),
% 9.42/2.51 inference(beta_eta_normalization,[status(thm)],[f96])).
% 9.42/2.51 thf(f96,plain,(
% 9.42/2.51 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cR @ (cS @ Y1) @ Y0 @ X1) => ((cR @ Y1 @ X1 @ X2) => (cR @ (cS @ Y1) @ (cS @ Y0) @ X2)))))) @ X3))) )),
% 9.42/2.51 inference(pi_clausification,[status(thm)],[f93])).
% 9.42/2.51 thf(f93,plain,(
% 9.42/2.51 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cR @ (cS @ Y1) @ Y0 @ X1) => ((cR @ Y1 @ X1 @ X2) => (cR @ (cS @ Y1) @ (cS @ Y0) @ X2))))))))) )),
% 9.42/2.51 inference(beta_eta_normalization,[status(thm)],[f89])).
% 9.42/2.51 thf(f89,plain,(
% 9.42/2.51 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((cR @ (cS @ Y2) @ Y1 @ X1) => ((cR @ Y2 @ X1 @ Y0) => (cR @ (cS @ Y2) @ (cS @ Y1) @ Y0)))))))) @ X2))) )),
% 9.42/2.51 inference(pi_clausification,[status(thm)],[f86])).
% 9.42/2.51 thf(f86,plain,(
% 9.42/2.51 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((cR @ (cS @ Y2) @ Y1 @ X1) => ((cR @ Y2 @ X1 @ Y0) => (cR @ (cS @ Y2) @ (cS @ Y1) @ Y0))))))))))) )),
% 9.42/2.51 inference(beta_eta_normalization,[status(thm)],[f84])).
% 9.42/2.51 thf(f84,plain,(
% 9.42/2.51 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((cR @ (cS @ Y3) @ Y2 @ Y0) => ((cR @ Y3 @ Y0 @ Y1) => (cR @ (cS @ Y3) @ (cS @ Y2) @ Y1)))))))))) @ X1))) )),
% 9.42/2.51 inference(pi_clausification,[status(thm)],[f62])).
% 9.42/2.51 thf(f62,plain,(
% 9.42/2.51 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((cR @ (cS @ Y3) @ Y2 @ Y0) => ((cR @ Y3 @ Y0 @ Y1) => (cR @ (cS @ Y3) @ (cS @ Y2) @ Y1))))))))))))),
% 9.42/2.51 inference(boolean_simplification,[status(thm)],[f59])).
% 9.42/2.51 thf(f59,plain,(
% 9.42/2.51 ($true = ($true & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((cR @ (cS @ Y3) @ Y2 @ Y0) => ((cR @ Y3 @ Y0 @ Y1) => (cR @ (cS @ Y3) @ (cS @ Y2) @ Y1)))))))))))))),
% 9.42/2.51 inference(backward_demodulation,[status(thm)],[f38,f55])).
% 9.42/2.51 thf(f1276,plain,(
% 9.42/2.51 spl0_5 | spl0_6 | ~spl0_4),
% 9.42/2.51 inference(avatar_split_clause,[status(thm)],[f726,f594,f1273,f1269])).
% 9.42/2.51 thf(f726,plain,(
% 9.42/2.51 ($false = (?? @ $i @ (cR @ (cS @ sK8) @ c0))) | ($false = (!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (cR @ (cS @ sK8) @ Y0)) => (?? @ $i @ (cR @ (cS @ sK8) @ (cS @ Y0))))))) | ~spl0_4),
% 9.42/2.51 inference(binary_proxy_clausification,[status(thm)],[f699])).
% 9.42/2.51 thf(f699,plain,(
% 9.42/2.51 ($false = ((?? @ $i @ (cR @ (cS @ sK8) @ c0)) & (!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (cR @ (cS @ sK8) @ Y0)) => (?? @ $i @ (cR @ (cS @ sK8) @ (cS @ Y0)))))))) | ~spl0_4),
% 9.42/2.51 inference(not_proxy_clausification,[status(thm)],[f685])).
% 9.42/2.51 thf(f685,plain,(
% 9.42/2.51 ($true = (~ ((?? @ $i @ (cR @ (cS @ sK8) @ c0)) & (!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (cR @ (cS @ sK8) @ Y0)) => (?? @ $i @ (cR @ (cS @ sK8) @ (cS @ Y0))))))))) | ~spl0_4),
% 9.42/2.51 inference(boolean_simplification,[status(thm)],[f684])).
% 9.42/2.51 thf(f684,plain,(
% 9.42/2.51 ($true = (((?? @ $i @ (cR @ (cS @ sK8) @ c0)) & (!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (cR @ (cS @ sK8) @ Y0)) => (?? @ $i @ (cR @ (cS @ sK8) @ (cS @ Y0))))))) => $false)) | ~spl0_4),
% 9.42/2.51 inference(beta_eta_normalization,[status(thm)],[f682])).
% 9.42/2.51 thf(f682,plain,(
% 9.42/2.51 ($true = ((((^[Y0 : $i]: (?? @ $i @ (cR @ (cS @ sK8) @ Y0))) @ c0) & (!! @ $i @ (^[Y0 : $i]: (((^[Y1 : $i]: (?? @ $i @ (cR @ (cS @ sK8) @ Y1))) @ Y0) => ((^[Y1 : $i]: (?? @ $i @ (cR @ (cS @ sK8) @ Y1))) @ (cS @ Y0)))))) => $false)) | ~spl0_4),
% 9.42/2.51 inference(superposition,[status(thm)],[f31,f677])).
% 9.42/2.51 thf(f677,plain,(
% 9.42/2.51 ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (cR @ (cS @ sK8) @ Y0)))) = $false) | ~spl0_4),
% 9.42/2.51 inference(boolean_simplification,[status(thm)],[f673])).
% 9.42/2.51 thf(f673,plain,(
% 9.42/2.51 (($true => (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (cR @ (cS @ sK8) @ Y0))))) = $false) | ~spl0_4),
% 9.42/2.51 inference(backward_demodulation,[status(thm)],[f629,f655])).
% 9.42/2.51 thf(f31,plain,(
% 9.42/2.51 ( ! [X1 : $i > $o] : (($true = (((X1 @ c0) & (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (cS @ Y0)))))) => (!! @ $i @ X1)))) )),
% 9.42/2.51 inference(beta_eta_normalization,[status(thm)],[f30])).
% 9.42/2.51 thf(f30,plain,(
% 9.42/2.51 ( ! [X1 : $i > $o] : (($true = ((^[Y0 : $i > $o]: (((Y0 @ c0) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1)))))) => (!! @ $i @ Y0))) @ X1))) )),
% 9.42/2.51 inference(pi_clausification,[status(thm)],[f22])).
% 9.42/2.51 thf(f623,plain,(
% 9.42/2.51 ~spl0_3),
% 9.42/2.51 inference(avatar_contradiction_clause,[status(thm)],[f622])).
% 9.42/2.51 thf(f622,plain,(
% 9.42/2.51 $false | ~spl0_3),
% 9.42/2.51 inference(trivial_inequality_removal,[status(thm)],[f608])).
% 9.42/2.51 thf(f608,plain,(
% 9.42/2.51 ($true = $false) | ~spl0_3),
% 9.42/2.51 inference(superposition,[status(thm)],[f605,f37])).
% 9.42/2.51 thf(f37,plain,(
% 9.42/2.51 ( ! [X1 : $i] : (($true = (cR @ c0 @ X1 @ (cS @ X1)))) )),
% 9.42/2.51 inference(beta_eta_normalization,[status(thm)],[f36])).
% 9.42/2.51 thf(f36,plain,(
% 9.42/2.51 ( ! [X1 : $i] : ((((^[Y0 : $i]: (cR @ c0 @ Y0 @ (cS @ Y0))) @ X1) = $true)) )),
% 9.42/2.51 inference(pi_clausification,[status(thm)],[f33])).
% 9.42/2.51 thf(f605,plain,(
% 9.42/2.51 ( ! [X1 : $i] : (($false = (cR @ c0 @ sK6 @ X1))) ) | ~spl0_3),
% 9.42/2.51 inference(pi_clausification,[status(thm)],[f602])).
% 9.42/2.51 thf(f602,plain,(
% 9.42/2.51 ((?? @ $i @ (cR @ c0 @ sK6)) = $false) | ~spl0_3),
% 9.42/2.51 inference(beta_eta_normalization,[status(thm)],[f599])).
% 9.42/2.51 thf(f599,plain,(
% 9.42/2.51 ($false = ((^[Y0 : $i]: (?? @ $i @ (cR @ c0 @ Y0))) @ sK6)) | ~spl0_3),
% 9.42/2.51 inference(sigma_clausification,[status(thm)],[f592])).
% 9.42/2.51 thf(f592,plain,(
% 9.42/2.51 ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (cR @ c0 @ Y0)))) = $false) | ~spl0_3),
% 9.42/2.51 inference(avatar_component_clause,[status(thm)],[f590])).
% 9.42/2.51 thf(f590,definition,(
% 9.42/2.51 spl0_3 <=> ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (cR @ c0 @ Y0)))) = $false)),
% 9.42/2.51 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 9.42/2.51 thf(f597,plain,(
% 9.42/2.51 spl0_3 | spl0_4),
% 9.42/2.51 inference(avatar_split_clause,[status(thm)],[f82,f594,f590])).
% 9.42/2.51 thf(f82,plain,(
% 9.42/2.51 ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (cR @ Y0 @ Y1)))) => (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (cR @ (cS @ Y0) @ Y1))))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (cR @ c0 @ Y0)))) = $false)),
% 9.42/2.51 inference(binary_proxy_clausification,[status(thm)],[f52])).
% 9.42/2.51 thf(f52,plain,(
% 9.42/2.51 ($false = ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (cR @ c0 @ Y0)))) & (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (cR @ Y0 @ Y1)))) => (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (cR @ (cS @ Y0) @ Y1)))))))))),
% 9.42/2.51 inference(not_proxy_clausification,[status(thm)],[f47])).
% 9.42/2.51 thf(f47,plain,(
% 9.42/2.51 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (cR @ c0 @ Y0)))) & (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (cR @ Y0 @ Y1)))) => (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (cR @ (cS @ Y0) @ Y1))))))))))),
% 9.42/2.51 inference(boolean_simplification,[status(thm)],[f46])).
% 9.42/2.51 thf(f46,plain,(
% 9.42/2.51 ($true = (((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (cR @ c0 @ Y0)))) & (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (cR @ Y0 @ Y1)))) => (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (cR @ (cS @ Y0) @ Y1)))))))) => $false))),
% 9.42/2.51 inference(beta_eta_normalization,[status(thm)],[f42])).
% 9.42/2.51 thf(f42,plain,(
% 9.42/2.51 ($true = ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (cR @ Y0 @ Y1))))) @ c0) & (!! @ $i @ (^[Y0 : $i]: (((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (?? @ $i @ (cR @ Y1 @ Y2))))) @ Y0) => ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (?? @ $i @ (cR @ Y1 @ Y2))))) @ (cS @ Y0)))))) => $false))),
% 9.42/2.51 inference(superposition,[status(thm)],[f31,f15])).
% 9.42/2.51 thf(f15,plain,(
% 9.42/2.51 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (cR @ Y0 @ Y1)))))))),
% 9.42/2.51 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 9.42/2.51 % SZS output end Proof for DTF2THF_13589
% 9.42/2.51 % (13770)------------------------------
% 9.42/2.51 % (13770)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.42/2.51 % (13770)Termination reason: Refutation
% 9.42/2.51
% 9.42/2.51 % (13770)Memory used [KB]: 7036
% 9.42/2.51 % (13770)Time elapsed: 0.323 s
% 9.42/2.51 % (13770)Instructions burned: 612 (million)
% 9.42/2.51 % (13770)------------------------------
% 9.42/2.51 % (13770)------------------------------
% 9.42/2.51 % (13691)Success in time 1.303 s
%------------------------------------------------------------------------------