%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV190^5 : TPTP v9.2.1. Bugfixed v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n022.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 09:40:31 AM UTC 2026
% Result : Theorem 1.89s 1.61s
% Output : Refutation 1.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 3
% Syntax : Number of formulae : 68 ( 46 unt; 0 typ; 1 def)
% Number of atoms : 573 ( 105 equ; 0 cnn)
% Maximal formula atoms : 7 ( 8 avg)
% Number of connectives : 1849 ( 41 ~; 18 |; 140 &;1341 @)
% ( 1 <=>; 85 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 47 ( 47 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 11 usr; 10 con; 0-3 aty)
% ( 223 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 340 ( 245 ^; 95 !; 0 ?; 340 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
iS: $tType ).
thf(func_def_0,type,
iS: $tType ).
thf(func_def_1,type,
c0: iS ).
thf(func_def_2,type,
cJOIN: iS > iS > iS > $o ).
thf(func_def_3,type,
cP: iS > iS > iS ).
thf(func_def_4,type,
cS_JOIN_CLOS: iS > ( iS > iS > iS ) > ( iS > iS > iS > $o ) > $o ).
thf(func_def_23,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_24,type,
sK2: iS ).
thf(func_def_25,type,
sK3: iS ).
thf(func_def_26,type,
sK4: iS ).
thf(func_def_27,type,
sK5: iS ).
thf(func_def_28,type,
sK6: iS ).
thf(f220,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f216,f219]) ).
thf(f219,plain,
spl0_2,
inference(avatar_split_clause,[status(thm)],[f218,f42]) ).
thf(f42,definition,
( spl0_2
<=> ( ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( ( ( cJOIN @ Y0 @ Y0 @ Y0 )
& ( cJOIN @ Y1 @ Y1 @ Y1 ) )
=> ( cJOIN @ ( cP @ Y0 @ Y1 ) @ ( cP @ Y0 @ Y1 ) @ ( cP @ Y0 @ Y1 ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f218,plain,
( ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( ( ( cJOIN @ Y0 @ Y0 @ Y0 )
& ( cJOIN @ Y1 @ Y1 @ Y1 ) )
=> ( cJOIN @ ( cP @ Y0 @ Y1 ) @ ( cP @ Y0 @ Y1 ) @ ( cP @ Y0 @ Y1 ) ) ) ) )
= $false ),
inference(boolean_simplification,[status(thm)],[f217]) ).
thf(f217,plain,
( ( ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( ( ( cJOIN @ Y0 @ Y0 @ Y0 )
& ( cJOIN @ Y1 @ Y1 @ Y1 ) )
=> ( cJOIN @ ( cP @ Y0 @ Y1 ) @ ( cP @ Y0 @ Y1 ) @ ( cP @ Y0 @ Y1 ) ) ) ) )
& $true )
= $false ),
inference(forward_demodulation,[status(thm)],[f34,f93]) ).
thf(f93,plain,
! [X1: iS] :
( $true
= ( cJOIN @ X1 @ c0 @ X1 ) ),
inference(beta_eta_normalization,[status(thm)],[f91]) ).
thf(f91,plain,
! [X1: iS] :
( $true
= ( ^ [Y0: iS] : ( cJOIN @ Y0 @ c0 @ Y0 )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f78]) ).
thf(f78,plain,
( $true
= ( !! @ iS
@ ^ [Y0: iS] : ( cJOIN @ Y0 @ c0 @ Y0 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f77]) ).
thf(f77,plain,
( $true
= ( ( !! @ iS
@ ^ [Y0: iS] : ( cJOIN @ c0 @ Y0 @ Y0 ) )
& ( !! @ iS
@ ^ [Y0: iS] : ( cJOIN @ Y0 @ c0 @ Y0 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f76]) ).
thf(f76,plain,
( $true
= ( ( !! @ iS
@ ^ [Y0: iS] : ( cJOIN @ c0 @ Y0 @ Y0 ) )
& ( !! @ iS
@ ^ [Y0: iS] : ( cJOIN @ Y0 @ c0 @ Y0 ) )
& $true ) ),
inference(backward_demodulation,[status(thm)],[f73,f74]) ).
thf(f74,plain,
( ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( !! @ iS
@ ^ [Y3: iS] :
( !! @ iS
@ ^ [Y4: iS] :
( !! @ iS
@ ^ [Y5: iS] :
( ( ( cJOIN @ Y5 @ Y1 @ Y0 )
& ( cJOIN @ Y2 @ Y4 @ Y3 ) )
=> ( cJOIN @ ( cP @ Y5 @ Y2 ) @ ( cP @ Y1 @ Y4 ) @ ( cP @ Y0 @ Y3 ) ) ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f73]) ).
thf(f73,plain,
( $true
= ( ( !! @ iS
@ ^ [Y0: iS] : ( cJOIN @ c0 @ Y0 @ Y0 ) )
& ( !! @ iS
@ ^ [Y0: iS] : ( cJOIN @ Y0 @ c0 @ Y0 ) )
& ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( !! @ iS
@ ^ [Y3: iS] :
( !! @ iS
@ ^ [Y4: iS] :
( !! @ iS
@ ^ [Y5: iS] :
( ( ( cJOIN @ Y5 @ Y1 @ Y0 )
& ( cJOIN @ Y2 @ Y4 @ Y3 ) )
=> ( cJOIN @ ( cP @ Y5 @ Y2 ) @ ( cP @ Y1 @ Y4 ) @ ( cP @ Y0 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f72]) ).
thf(f72,plain,
( $true
= ( $true
& ( !! @ iS
@ ^ [Y0: iS] : ( cJOIN @ c0 @ Y0 @ Y0 ) )
& ( !! @ iS
@ ^ [Y0: iS] : ( cJOIN @ Y0 @ c0 @ Y0 ) )
& ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( !! @ iS
@ ^ [Y3: iS] :
( !! @ iS
@ ^ [Y4: iS] :
( !! @ iS
@ ^ [Y5: iS] :
( ( ( cJOIN @ Y5 @ Y1 @ Y0 )
& ( cJOIN @ Y2 @ Y4 @ Y3 ) )
=> ( cJOIN @ ( cP @ Y5 @ Y2 ) @ ( cP @ Y1 @ Y4 ) @ ( cP @ Y0 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f25,f71]) ).
thf(f71,plain,
( $true
= ( ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( !! @ iS
@ ^ [Y3: iS] :
( ( ( cP @ Y3 @ Y2 )
= ( cP @ Y1 @ Y0 ) )
=> ( ( Y3 = Y1 )
& ( Y2 = Y0 ) ) ) ) ) ) )
& ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( c0
!= ( cP @ Y1 @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( $true
= ( ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( !! @ iS
@ ^ [Y3: iS] :
( ( ( cP @ Y3 @ Y2 )
= ( cP @ Y1 @ Y0 ) )
=> ( ( Y3 = Y1 )
& ( Y2 = Y0 ) ) ) ) ) ) )
& ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( c0
!= ( cP @ Y1 @ Y0 ) ) ) )
& ( !! @ iS
@ ^ [Y0: iS] : ( cJOIN @ c0 @ Y0 @ Y0 ) )
& ( !! @ iS
@ ^ [Y0: iS] : ( cJOIN @ Y0 @ c0 @ Y0 ) )
& ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( !! @ iS
@ ^ [Y3: iS] :
( !! @ iS
@ ^ [Y4: iS] :
( !! @ iS
@ ^ [Y5: iS] :
( ( ( cJOIN @ Y5 @ Y1 @ Y0 )
& ( cJOIN @ Y2 @ Y4 @ Y3 ) )
=> ( cJOIN @ ( cP @ Y5 @ Y2 ) @ ( cP @ Y1 @ Y4 ) @ ( cP @ Y0 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( $true
= ( ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( !! @ iS
@ ^ [Y3: iS] :
( ( ( cP @ Y3 @ Y2 )
= ( cP @ Y1 @ Y0 ) )
=> ( ( Y3 = Y1 )
& ( Y2 = Y0 ) ) ) ) ) ) )
& ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( c0
!= ( cP @ Y1 @ Y0 ) ) ) )
& ( !! @ iS
@ ^ [Y0: iS] : ( cJOIN @ c0 @ Y0 @ Y0 ) )
& ( !! @ iS
@ ^ [Y0: iS] : ( cJOIN @ Y0 @ c0 @ Y0 ) )
& ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( !! @ iS
@ ^ [Y3: iS] :
( !! @ iS
@ ^ [Y4: iS] :
( !! @ iS
@ ^ [Y5: iS] :
( ( ( cJOIN @ Y5 @ Y1 @ Y0 )
& ( cJOIN @ Y2 @ Y4 @ Y3 ) )
=> ( cJOIN @ ( cP @ Y5 @ Y2 ) @ ( cP @ Y1 @ Y4 ) @ ( cP @ Y0 @ Y3 ) ) ) ) ) ) ) ) )
& ( !! @ ( iS > $o )
@ ^ [Y0: iS > $o] :
( ( ( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( ( ( Y0 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ ( cP @ Y1 @ Y2 ) ) ) ) )
& ( Y0 @ c0 ) )
=> ( !! @ iS @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ( ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( !! @ iS
@ ^ [Y3: iS] :
( ( ( cP @ Y3 @ Y2 )
= ( cP @ Y1 @ Y0 ) )
=> ( ( Y3 = Y1 )
& ( Y2 = Y0 ) ) ) ) ) ) )
& ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( c0
!= ( cP @ Y1 @ Y0 ) ) ) )
& ( !! @ iS
@ ^ [Y0: iS] : ( cJOIN @ c0 @ Y0 @ Y0 ) )
& ( !! @ iS
@ ^ [Y0: iS] : ( cJOIN @ Y0 @ c0 @ Y0 ) )
& ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( !! @ iS
@ ^ [Y3: iS] :
( !! @ iS
@ ^ [Y4: iS] :
( !! @ iS
@ ^ [Y5: iS] :
( ( ( cJOIN @ Y5 @ Y1 @ Y0 )
& ( cJOIN @ Y2 @ Y4 @ Y3 ) )
=> ( cJOIN @ ( cP @ Y5 @ Y2 ) @ ( cP @ Y1 @ Y4 ) @ ( cP @ Y0 @ Y3 ) ) ) ) ) ) ) ) )
& ( !! @ ( iS > $o )
@ ^ [Y0: iS > $o] :
( ( ( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( ( ( Y0 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ ( cP @ Y1 @ Y2 ) ) ) ) )
& ( Y0 @ c0 ) )
=> ( !! @ iS @ Y0 ) ) ) )
=> ( !! @ iS
@ ^ [Y0: iS] : ( cJOIN @ Y0 @ Y0 @ Y0 ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f12]) ).
thf(f12,plain,
( $true
= ( ~ ( ( ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( !! @ iS
@ ^ [Y3: iS] :
( ( ( cP @ Y3 @ Y2 )
= ( cP @ Y1 @ Y0 ) )
=> ( ( Y3 = Y1 )
& ( Y2 = Y0 ) ) ) ) ) ) )
& ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( c0
!= ( cP @ Y1 @ Y0 ) ) ) )
& ( !! @ iS
@ ^ [Y0: iS] : ( cJOIN @ c0 @ Y0 @ Y0 ) )
& ( !! @ iS
@ ^ [Y0: iS] : ( cJOIN @ Y0 @ c0 @ Y0 ) )
& ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( !! @ iS
@ ^ [Y3: iS] :
( !! @ iS
@ ^ [Y4: iS] :
( !! @ iS
@ ^ [Y5: iS] :
( ( ( cJOIN @ Y5 @ Y1 @ Y0 )
& ( cJOIN @ Y2 @ Y4 @ Y3 ) )
=> ( cJOIN @ ( cP @ Y5 @ Y2 ) @ ( cP @ Y1 @ Y4 ) @ ( cP @ Y0 @ Y3 ) ) ) ) ) ) ) ) )
& ( !! @ ( iS > $o )
@ ^ [Y0: iS > $o] :
( ( ( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( ( ( Y0 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ ( cP @ Y1 @ Y2 ) ) ) ) )
& ( Y0 @ c0 ) )
=> ( !! @ iS @ Y0 ) ) ) )
=> ( !! @ iS
@ ^ [Y0: iS] : ( cJOIN @ Y0 @ Y0 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f11]) ).
thf(f11,plain,
( $true
= ( ~ ( ( ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( !! @ iS
@ ^ [Y3: iS] :
( ( ( cP @ Y3 @ Y2 )
= ( cP @ Y1 @ Y0 ) )
=> ( ( Y3 = Y1 )
& ( Y2 = Y0 ) ) ) ) ) ) )
& ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( c0
!= ( cP @ Y1 @ Y0 ) ) ) )
& ( ^ [Y0: iS,Y1: iS > iS > iS,Y2: iS > iS > iS > $o] :
( ( !! @ iS
@ ^ [Y3: iS] : ( Y2 @ Y0 @ Y3 @ Y3 ) )
& ( !! @ iS
@ ^ [Y3: iS] : ( Y2 @ Y3 @ Y0 @ Y3 ) )
& ( !! @ iS
@ ^ [Y3: iS] :
( !! @ iS
@ ^ [Y4: iS] :
( !! @ iS
@ ^ [Y5: iS] :
( !! @ iS
@ ^ [Y6: iS] :
( !! @ iS
@ ^ [Y7: iS] :
( !! @ iS
@ ^ [Y8: iS] :
( ( ( Y2 @ Y8 @ Y4 @ Y3 )
& ( Y2 @ Y5 @ Y7 @ Y6 ) )
=> ( Y2 @ ( Y1 @ Y8 @ Y5 ) @ ( Y1 @ Y4 @ Y7 ) @ ( Y1 @ Y3 @ Y6 ) ) ) ) ) ) ) ) ) )
@ c0
@ cP
@ cJOIN )
& ( !! @ ( iS > $o )
@ ^ [Y0: iS > $o] :
( ( ( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( ( ( Y0 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ ( cP @ Y1 @ Y2 ) ) ) ) )
& ( Y0 @ c0 ) )
=> ( !! @ iS
@ ^ [Y1: iS] : ( Y0 @ Y1 ) ) ) ) )
=> ( !! @ iS
@ ^ [Y0: iS] : ( cJOIN @ Y0 @ Y0 @ Y0 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f10,f9]) ).
thf(f9,plain,
( cS_JOIN_CLOS
= ( ^ [Y0: iS,Y1: iS > iS > iS,Y2: iS > iS > iS > $o] :
( ( !! @ iS
@ ^ [Y3: iS] : ( Y2 @ Y0 @ Y3 @ Y3 ) )
& ( !! @ iS
@ ^ [Y3: iS] : ( Y2 @ Y3 @ Y0 @ Y3 ) )
& ( !! @ iS
@ ^ [Y3: iS] :
( !! @ iS
@ ^ [Y4: iS] :
( !! @ iS
@ ^ [Y5: iS] :
( !! @ iS
@ ^ [Y6: iS] :
( !! @ iS
@ ^ [Y7: iS] :
( !! @ iS
@ ^ [Y8: iS] :
( ( ( Y2 @ Y8 @ Y4 @ Y3 )
& ( Y2 @ Y5 @ Y7 @ Y6 ) )
=> ( Y2 @ ( Y1 @ Y8 @ Y5 ) @ ( Y1 @ Y4 @ Y7 ) @ ( Y1 @ Y3 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( cS_JOIN_CLOS
= ( ^ [Y0: iS,Y1: iS > iS > iS,Y2: iS > iS > iS > $o] :
( ( !! @ iS
@ ^ [Y3: iS] : ( Y2 @ Y0 @ Y3 @ Y3 ) )
& ( !! @ iS
@ ^ [Y3: iS] : ( Y2 @ Y3 @ Y0 @ Y3 ) )
& ( !! @ iS
@ ^ [Y3: iS] :
( !! @ iS
@ ^ [Y4: iS] :
( !! @ iS
@ ^ [Y5: iS] :
( !! @ iS
@ ^ [Y6: iS] :
( !! @ iS
@ ^ [Y7: iS] :
( !! @ iS
@ ^ [Y8: iS] :
( ( ( Y2 @ Y8 @ Y4 @ Y3 )
& ( Y2 @ Y5 @ Y7 @ Y6 ) )
=> ( Y2 @ ( Y1 @ Y8 @ Y5 ) @ ( Y1 @ Y4 @ Y7 ) @ ( Y1 @ Y3 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
( cS_JOIN_CLOS
= ( ^ [X0: iS,X1: iS > iS > iS,X2: iS > iS > iS > $o] :
( ! [X3: iS,X4: iS,X5: iS,X6: iS,X7: iS,X8: iS] :
( ( ( X2 @ X6 @ X4 @ X5 )
& ( X2 @ X3 @ X7 @ X8 ) )
=> ( X2 @ ( X1 @ X3 @ X6 ) @ ( X1 @ X7 @ X4 ) @ ( X1 @ X8 @ X5 ) ) )
& ! [X9: iS] : ( X2 @ X9 @ X0 @ X9 )
& ! [X10: iS] : ( X2 @ X0 @ X10 @ X10 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( cS_JOIN_CLOS
= ( ^ [X0: iS,X1: iS > iS > iS,X2: iS > iS > iS > $o] :
( ! [X3: iS,X7: iS,X8: iS,X6: iS,X4: iS,X5: iS] :
( ( ( X2 @ X6 @ X7 @ X8 )
& ( X2 @ X3 @ X4 @ X5 ) )
=> ( X2 @ ( X1 @ X3 @ X6 ) @ ( X1 @ X4 @ X7 ) @ ( X1 @ X5 @ X8 ) ) )
& ! [X3: iS] : ( X2 @ X3 @ X0 @ X3 )
& ! [X4: iS] : ( X2 @ X0 @ X4 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.dFLP254zJF/DTF2THF_24191.p',cS_JOIN_CLOS_def) ).
thf(f10,plain,
( $true
= ( ~ ( ( ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( !! @ iS
@ ^ [Y3: iS] :
( ( ( cP @ Y3 @ Y2 )
= ( cP @ Y1 @ Y0 ) )
=> ( ( Y3 = Y1 )
& ( Y2 = Y0 ) ) ) ) ) ) )
& ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( c0
!= ( cP @ Y1 @ Y0 ) ) ) )
& ( cS_JOIN_CLOS @ c0 @ cP @ cJOIN )
& ( !! @ ( iS > $o )
@ ^ [Y0: iS > $o] :
( ( ( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( ( ( Y0 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ ( cP @ Y1 @ Y2 ) ) ) ) )
& ( Y0 @ c0 ) )
=> ( !! @ iS
@ ^ [Y1: iS] : ( Y0 @ Y1 ) ) ) ) )
=> ( !! @ iS
@ ^ [Y0: iS] : ( cJOIN @ Y0 @ Y0 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( $true
= ( ~ ( ( ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( !! @ iS
@ ^ [Y3: iS] :
( ( ( cP @ Y3 @ Y2 )
= ( cP @ Y1 @ Y0 ) )
=> ( ( Y3 = Y1 )
& ( Y2 = Y0 ) ) ) ) ) ) )
& ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( c0
!= ( cP @ Y1 @ Y0 ) ) ) )
& ( cS_JOIN_CLOS @ c0 @ cP @ cJOIN )
& ( !! @ ( iS > $o )
@ ^ [Y0: iS > $o] :
( ( ( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( ( ( Y0 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ ( cP @ Y1 @ Y2 ) ) ) ) )
& ( Y0 @ c0 ) )
=> ( !! @ iS
@ ^ [Y1: iS] : ( Y0 @ Y1 ) ) ) ) )
=> ( !! @ iS
@ ^ [Y0: iS] : ( cJOIN @ Y0 @ Y0 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( ( ! [X0: iS > $o] :
( ( ( X0 @ c0 )
& ! [X1: iS,X2: iS] :
( ( ( X0 @ X1 )
& ( X0 @ X2 ) )
=> ( X0 @ ( cP @ X2 @ X1 ) ) ) )
=> ! [X3: iS] : ( X0 @ X3 ) )
& ( cS_JOIN_CLOS @ c0 @ cP @ cJOIN )
& ! [X4: iS,X5: iS] :
( c0
!= ( cP @ X4 @ X5 ) )
& ! [X6: iS,X7: iS,X8: iS,X9: iS] :
( ( ( cP @ X6 @ X7 )
= ( cP @ X8 @ X9 ) )
=> ( ( X7 = X9 )
& ( X6 = X8 ) ) ) )
=> ! [X10: iS] : ( cJOIN @ X10 @ X10 @ X10 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ( ( ! [X9: iS > $o] :
( ( ( X9 @ c0 )
& ! [X4: iS,X3: iS] :
( ( ( X9 @ X4 )
& ( X9 @ X3 ) )
=> ( X9 @ ( cP @ X3 @ X4 ) ) ) )
=> ! [X3: iS] : ( X9 @ X3 ) )
& ( cS_JOIN_CLOS @ c0 @ cP @ cJOIN )
& ! [X3: iS,X4: iS] :
( ( cP @ X3 @ X4 )
!= c0 )
& ! [X4: iS,X7: iS,X3: iS,X6: iS] :
( ( ( cP @ X3 @ X6 )
= ( cP @ X4 @ X7 ) )
=> ( ( X6 = X7 )
& ( X3 = X4 ) ) ) )
=> ! [X3: iS] : ( cJOIN @ X3 @ X3 @ X3 ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( ( ! [X9: iS > $o] :
( ( ( X9 @ c0 )
& ! [X4: iS,X3: iS] :
( ( ( X9 @ X4 )
& ( X9 @ X3 ) )
=> ( X9 @ ( cP @ X3 @ X4 ) ) ) )
=> ! [X3: iS] : ( X9 @ X3 ) )
& ( cS_JOIN_CLOS @ c0 @ cP @ cJOIN )
& ! [X3: iS,X4: iS] :
( ( cP @ X3 @ X4 )
!= c0 )
& ! [X4: iS,X7: iS,X3: iS,X6: iS] :
( ( ( cP @ X3 @ X6 )
= ( cP @ X4 @ X7 ) )
=> ( ( X6 = X7 )
& ( X3 = X4 ) ) ) )
=> ! [X3: iS] : ( cJOIN @ X3 @ X3 @ X3 ) ),
file('/export/starexec/sandbox/tmp/tmp.dFLP254zJF/DTF2THF_24191.p',cTHM580_pme) ).
thf(f34,plain,
( ( ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( ( ( cJOIN @ Y0 @ Y0 @ Y0 )
& ( cJOIN @ Y1 @ Y1 @ Y1 ) )
=> ( cJOIN @ ( cP @ Y0 @ Y1 ) @ ( cP @ Y0 @ Y1 ) @ ( cP @ Y0 @ Y1 ) ) ) ) )
& ( cJOIN @ c0 @ c0 @ c0 ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
( $true
= ( ~ ( ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( ( ( cJOIN @ Y0 @ Y0 @ Y0 )
& ( cJOIN @ Y1 @ Y1 @ Y1 ) )
=> ( cJOIN @ ( cP @ Y0 @ Y1 ) @ ( cP @ Y0 @ Y1 ) @ ( cP @ Y0 @ Y1 ) ) ) ) )
& ( cJOIN @ c0 @ c0 @ c0 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f32]) ).
thf(f32,plain,
( ( ( ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( ( ( cJOIN @ Y0 @ Y0 @ Y0 )
& ( cJOIN @ Y1 @ Y1 @ Y1 ) )
=> ( cJOIN @ ( cP @ Y0 @ Y1 ) @ ( cP @ Y0 @ Y1 ) @ ( cP @ Y0 @ Y1 ) ) ) ) )
& ( cJOIN @ c0 @ c0 @ c0 ) )
=> $false )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f31]) ).
thf(f31,plain,
( $true
= ( ( ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( ( ( ^ [Y2: iS] : ( cJOIN @ Y2 @ Y2 @ Y2 )
@ Y0 )
& ( ^ [Y2: iS] : ( cJOIN @ Y2 @ Y2 @ Y2 )
@ Y1 ) )
=> ( ^ [Y2: iS] : ( cJOIN @ Y2 @ Y2 @ Y2 )
@ ( cP @ Y0 @ Y1 ) ) ) ) )
& ( ^ [Y0: iS] : ( cJOIN @ Y0 @ Y0 @ Y0 )
@ c0 ) )
=> $false ) ),
inference(superposition,[status(thm)],[f29,f16]) ).
thf(f16,plain,
( ( !! @ iS
@ ^ [Y0: iS] : ( cJOIN @ Y0 @ Y0 @ Y0 ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f29,plain,
! [X1: iS > $o] :
( ( ( ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( ( ( X1 @ Y0 )
& ( X1 @ Y1 ) )
=> ( X1 @ ( cP @ Y0 @ Y1 ) ) ) ) )
& ( X1 @ c0 ) )
=> ( !! @ iS @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f28]) ).
thf(f28,plain,
! [X1: iS > $o] :
( $true
= ( ^ [Y0: iS > $o] :
( ( ( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( ( ( Y0 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ ( cP @ Y1 @ Y2 ) ) ) ) )
& ( Y0 @ c0 ) )
=> ( !! @ iS @ Y0 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
( ( !! @ ( iS > $o )
@ ^ [Y0: iS > $o] :
( ( ( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( ( ( Y0 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ ( cP @ Y1 @ Y2 ) ) ) ) )
& ( Y0 @ c0 ) )
=> ( !! @ iS @ Y0 ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f26]) ).
thf(f26,plain,
( ( $true
& ( !! @ ( iS > $o )
@ ^ [Y0: iS > $o] :
( ( ( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( ( ( Y0 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ ( cP @ Y1 @ Y2 ) ) ) ) )
& ( Y0 @ c0 ) )
=> ( !! @ iS @ Y0 ) ) ) )
= $true ),
inference(backward_demodulation,[status(thm)],[f17,f25]) ).
thf(f216,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f215]) ).
thf(f215,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f214]) ).
thf(f214,plain,
( ( $true = $false )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f213]) ).
thf(f213,plain,
( ( ( ~ $true ) = $true )
| ~ spl0_2 ),
inference(forward_demodulation,[status(thm)],[f212,f65]) ).
thf(f65,plain,
( ( $true
= ( cJOIN @ sK4 @ sK4 @ sK4 ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f63]) ).
thf(f63,plain,
( ( ( $true
& ( cJOIN @ sK4 @ sK4 @ sK4 ) )
= $true )
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f58,f62]) ).
thf(f62,plain,
( ( ( cJOIN @ sK3 @ sK3 @ sK3 )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f58]) ).
thf(f58,plain,
( ( ( ( cJOIN @ sK3 @ sK3 @ sK3 )
& ( cJOIN @ sK4 @ sK4 @ sK4 ) )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
( ( $false
= ( ( ( cJOIN @ sK3 @ sK3 @ sK3 )
& ( cJOIN @ sK4 @ sK4 @ sK4 ) )
=> ( cJOIN @ ( cP @ sK3 @ sK4 ) @ ( cP @ sK3 @ sK4 ) @ ( cP @ sK3 @ sK4 ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f52]) ).
thf(f52,plain,
( ( ( ^ [Y0: iS] :
( ( ( cJOIN @ sK3 @ sK3 @ sK3 )
& ( cJOIN @ Y0 @ Y0 @ Y0 ) )
=> ( cJOIN @ ( cP @ sK3 @ Y0 ) @ ( cP @ sK3 @ Y0 ) @ ( cP @ sK3 @ Y0 ) ) )
@ sK4 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
( ( $false
= ( !! @ iS
@ ^ [Y0: iS] :
( ( ( cJOIN @ sK3 @ sK3 @ sK3 )
& ( cJOIN @ Y0 @ Y0 @ Y0 ) )
=> ( cJOIN @ ( cP @ sK3 @ Y0 ) @ ( cP @ sK3 @ Y0 ) @ ( cP @ sK3 @ Y0 ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f47]) ).
thf(f47,plain,
( ( $false
= ( ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( ( ( cJOIN @ Y0 @ Y0 @ Y0 )
& ( cJOIN @ Y1 @ Y1 @ Y1 ) )
=> ( cJOIN @ ( cP @ Y0 @ Y1 ) @ ( cP @ Y0 @ Y1 ) @ ( cP @ Y0 @ Y1 ) ) ) )
@ sK3 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
( ( ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( ( ( cJOIN @ Y0 @ Y0 @ Y0 )
& ( cJOIN @ Y1 @ Y1 @ Y1 ) )
=> ( cJOIN @ ( cP @ Y0 @ Y1 ) @ ( cP @ Y0 @ Y1 ) @ ( cP @ Y0 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f42]) ).
thf(f212,plain,
( ( $true
= ( ~ ( cJOIN @ sK4 @ sK4 @ sK4 ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f211]) ).
thf(f211,plain,
( ( ( ~ ( $true
& ( cJOIN @ sK4 @ sK4 @ sK4 ) ) )
= $true )
| ~ spl0_2 ),
inference(forward_demodulation,[status(thm)],[f190,f62]) ).
thf(f190,plain,
( ( ( ~ ( ( cJOIN @ sK3 @ sK3 @ sK3 )
& ( cJOIN @ sK4 @ sK4 @ sK4 ) ) )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f167]) ).
thf(f167,plain,
( ( $true
= ( ( ( cJOIN @ sK3 @ sK3 @ sK3 )
& ( cJOIN @ sK4 @ sK4 @ sK4 ) )
=> $false ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f165,f60]) ).
thf(f60,plain,
( ( $false
= ( cJOIN @ ( cP @ sK3 @ sK4 ) @ ( cP @ sK3 @ sK4 ) @ ( cP @ sK3 @ sK4 ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f59]) ).
thf(f59,plain,
( ( $false
= ( $true
=> ( cJOIN @ ( cP @ sK3 @ sK4 ) @ ( cP @ sK3 @ sK4 ) @ ( cP @ sK3 @ sK4 ) ) ) )
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f56,f58]) ).
thf(f165,plain,
! [X2: iS,X3: iS,X1: iS,X6: iS,X4: iS,X5: iS] :
( $true
= ( ( ( cJOIN @ X6 @ X2 @ X1 )
& ( cJOIN @ X3 @ X5 @ X4 ) )
=> ( cJOIN @ ( cP @ X6 @ X3 ) @ ( cP @ X2 @ X5 ) @ ( cP @ X1 @ X4 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f161]) ).
thf(f161,plain,
! [X2: iS,X3: iS,X1: iS,X6: iS,X4: iS,X5: iS] :
( $true
= ( ^ [Y0: iS] :
( ( ( cJOIN @ Y0 @ X2 @ X1 )
& ( cJOIN @ X3 @ X5 @ X4 ) )
=> ( cJOIN @ ( cP @ Y0 @ X3 ) @ ( cP @ X2 @ X5 ) @ ( cP @ X1 @ X4 ) ) )
@ X6 ) ),
inference(pi_clausification,[status(thm)],[f158]) ).
thf(f158,plain,
! [X2: iS,X3: iS,X1: iS,X4: iS,X5: iS] :
( $true
= ( !! @ iS
@ ^ [Y0: iS] :
( ( ( cJOIN @ Y0 @ X2 @ X1 )
& ( cJOIN @ X3 @ X5 @ X4 ) )
=> ( cJOIN @ ( cP @ Y0 @ X3 ) @ ( cP @ X2 @ X5 ) @ ( cP @ X1 @ X4 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f156]) ).
thf(f156,plain,
! [X2: iS,X3: iS,X1: iS,X4: iS,X5: iS] :
( $true
= ( ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( ( ( cJOIN @ Y1 @ X2 @ X1 )
& ( cJOIN @ X3 @ Y0 @ X4 ) )
=> ( cJOIN @ ( cP @ Y1 @ X3 ) @ ( cP @ X2 @ Y0 ) @ ( cP @ X1 @ X4 ) ) ) )
@ X5 ) ),
inference(pi_clausification,[status(thm)],[f155]) ).
thf(f155,plain,
! [X2: iS,X3: iS,X1: iS,X4: iS] :
( $true
= ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( ( ( cJOIN @ Y1 @ X2 @ X1 )
& ( cJOIN @ X3 @ Y0 @ X4 ) )
=> ( cJOIN @ ( cP @ Y1 @ X3 ) @ ( cP @ X2 @ Y0 ) @ ( cP @ X1 @ X4 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f151]) ).
thf(f151,plain,
! [X2: iS,X3: iS,X1: iS,X4: iS] :
( $true
= ( ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( ( ( cJOIN @ Y2 @ X2 @ X1 )
& ( cJOIN @ X3 @ Y1 @ Y0 ) )
=> ( cJOIN @ ( cP @ Y2 @ X3 ) @ ( cP @ X2 @ Y1 ) @ ( cP @ X1 @ Y0 ) ) ) ) )
@ X4 ) ),
inference(pi_clausification,[status(thm)],[f150]) ).
thf(f150,plain,
! [X2: iS,X3: iS,X1: iS] :
( $true
= ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( ( ( cJOIN @ Y2 @ X2 @ X1 )
& ( cJOIN @ X3 @ Y1 @ Y0 ) )
=> ( cJOIN @ ( cP @ Y2 @ X3 ) @ ( cP @ X2 @ Y1 ) @ ( cP @ X1 @ Y0 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f146]) ).
thf(f146,plain,
! [X2: iS,X3: iS,X1: iS] :
( $true
= ( ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( !! @ iS
@ ^ [Y3: iS] :
( ( ( cJOIN @ Y3 @ X2 @ X1 )
& ( cJOIN @ Y0 @ Y2 @ Y1 ) )
=> ( cJOIN @ ( cP @ Y3 @ Y0 ) @ ( cP @ X2 @ Y2 ) @ ( cP @ X1 @ Y1 ) ) ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f143]) ).
thf(f143,plain,
! [X2: iS,X1: iS] :
( $true
= ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( !! @ iS
@ ^ [Y3: iS] :
( ( ( cJOIN @ Y3 @ X2 @ X1 )
& ( cJOIN @ Y0 @ Y2 @ Y1 ) )
=> ( cJOIN @ ( cP @ Y3 @ Y0 ) @ ( cP @ X2 @ Y2 ) @ ( cP @ X1 @ Y1 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f141]) ).
thf(f141,plain,
! [X2: iS,X1: iS] :
( $true
= ( ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( !! @ iS
@ ^ [Y3: iS] :
( !! @ iS
@ ^ [Y4: iS] :
( ( ( cJOIN @ Y4 @ Y0 @ X1 )
& ( cJOIN @ Y1 @ Y3 @ Y2 ) )
=> ( cJOIN @ ( cP @ Y4 @ Y1 ) @ ( cP @ Y0 @ Y3 ) @ ( cP @ X1 @ Y2 ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f131]) ).
thf(f131,plain,
! [X1: iS] :
( ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( !! @ iS
@ ^ [Y3: iS] :
( !! @ iS
@ ^ [Y4: iS] :
( ( ( cJOIN @ Y4 @ Y0 @ X1 )
& ( cJOIN @ Y1 @ Y3 @ Y2 ) )
=> ( cJOIN @ ( cP @ Y4 @ Y1 ) @ ( cP @ Y0 @ Y3 ) @ ( cP @ X1 @ Y2 ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f127]) ).
thf(f127,plain,
! [X1: iS] :
( $true
= ( ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( !! @ iS
@ ^ [Y3: iS] :
( !! @ iS
@ ^ [Y4: iS] :
( !! @ iS
@ ^ [Y5: iS] :
( ( ( cJOIN @ Y5 @ Y1 @ Y0 )
& ( cJOIN @ Y2 @ Y4 @ Y3 ) )
=> ( cJOIN @ ( cP @ Y5 @ Y2 ) @ ( cP @ Y1 @ Y4 ) @ ( cP @ Y0 @ Y3 ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV190^5 : TPTP v9.2.1. Bugfixed v5.3.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n022.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:41:36 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.34/0.48 ---- Original DTF file ---
% 0.34/0.48 thf(spec,logic,$$dhol).
% 0.34/0.48 %------------------------------------------------------------------------------
% 0.34/0.48 % File : SEV190^5 : TPTP v9.2.1. Bugfixed v5.3.0.
% 0.34/0.48 % Domain : Set Theory (Sets of sets)
% 0.34/0.48 % Problem : TPS problem THM580
% 0.34/0.48 % Version : Especial.
% 0.34/0.48 % English : The join (in the initial pairing algebra $) of x and x is x.
% 0.34/0.48
% 0.34/0.48 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.34/0.48 % Source : [Bro09]
% 0.34/0.48 % Names : tps_0471 [Bro09]
% 0.34/0.48 % : THM580 [TPS]
% 0.34/0.48
% 0.34/0.48 % Status : Theorem
% 0.34/0.48 % Rating : 0.44 v9.1.0, 0.38 v9.0.0, 0.50 v8.2.0, 0.69 v8.1.0, 0.64 v7.5.0, 0.57 v7.4.0, 0.67 v7.2.0, 0.62 v7.0.0, 0.57 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.57 v5.5.0, 0.83 v5.4.0, 0.60 v5.3.0
% 0.34/0.48 % Syntax : Number of formulae : 7 ( 1 unt; 5 typ; 1 def)
% 0.34/0.48 % Number of atoms : 9 ( 5 equ; 0 cnn)
% 0.34/0.48 % Maximal formula atoms : 7 ( 4 avg)
% 0.34/0.48 % Number of connectives : 55 ( 1 ~; 0 |; 9 &; 40 @)
% 0.34/0.48 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.34/0.48 % Maximal formula depth : 14 ( 8 avg)
% 0.34/0.48 % Number of types : 2 ( 1 usr)
% 0.34/0.48 % Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% 0.34/0.48 % Number of symbols : 5 ( 4 usr; 1 con; 0-3 aty)
% 0.34/0.48 % Number of variables : 22 ( 3 ^; 19 !; 0 ?; 22 :)
% 0.34/0.48 % SPC : TH0_THM_EQU_NAR
% 0.34/0.48
% 0.34/0.48 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.34/0.48 % project in the Department of Mathematical Sciences at Carnegie
% 0.34/0.48 % Mellon University. Distributed under the Creative Commons copyleft
% 0.34/0.48 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.34/0.48 % : Polymorphic definitions expanded.
% 0.34/0.48 % Bugfixes : v5.2.0 - Added missing type declarations.
% 0.34/0.48 % : v5.3.0 - Fixed tType to $tType from last bugfixes.
% 0.34/0.48 %------------------------------------------------------------------------------
% 0.34/0.48 thf(iS_type,type,
% 0.34/0.48 iS: $tType ).
% 0.34/0.48
% 0.34/0.48 thf(c0_type,type,
% 0.34/0.48 c0: iS ).
% 0.34/0.48
% 0.34/0.48 thf(cJOIN_type,type,
% 0.34/0.48 cJOIN: iS > iS > iS > $o ).
% 0.34/0.48
% 0.34/0.48 thf(cP_type,type,
% 0.34/0.48 cP: iS > iS > iS ).
% 0.34/0.48
% 0.34/0.48 thf(cS_JOIN_CLOS_type,type,
% 0.34/0.48 cS_JOIN_CLOS: iS > ( iS > iS > iS ) > ( iS > iS > iS > $o ) > $o ).
% 0.34/0.48
% 0.34/0.48 thf(cS_JOIN_CLOS_def,definition,
% 0.34/0.48 ( cS_JOIN_CLOS
% 0.34/0.48 = ( ^ [X0: iS,P: iS > iS > iS,JOIN: iS > iS > iS > $o] :
% 0.34/0.48 ( ! [Xx: iS] : ( JOIN @ Xx @ X0 @ Xx )
% 0.34/0.48 & ! [Xy: iS] : ( JOIN @ X0 @ Xy @ Xy )
% 0.34/0.48 & ! [Xx: iS,Xy: iS,Xz: iS,Xu: iS,Xv: iS,Xw: iS] :
% 0.34/0.48 ( ( ( JOIN @ Xx @ Xy @ Xz )
% 0.34/0.48 & ( JOIN @ Xu @ Xv @ Xw ) )
% 0.34/0.48 => ( JOIN @ ( P @ Xx @ Xu ) @ ( P @ Xy @ Xv ) @ ( P @ Xz @ Xw ) ) ) ) ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(cTHM580_pme,conjecture,
% 0.34/0.48 ( ( ! [Xx: iS,Xy: iS] :
% 0.34/0.48 ( ( cP @ Xx @ Xy )
% 0.34/0.48 != c0 )
% 0.34/0.48 & ! [Xx: iS,Xy: iS,Xu: iS,Xv: iS] :
% 0.34/0.48 ( ( ( cP @ Xx @ Xu )
% 0.34/0.48 = ( cP @ Xy @ Xv ) )
% 0.34/0.48 => ( ( Xx = Xy )
% 0.34/0.48 & ( Xu = Xv ) ) )
% 0.34/0.48 & ! [X: iS > $o] :
% 0.34/0.48 ( ( ( X @ c0 )
% 0.34/0.48 & ! [Xx: iS,Xy: iS] :
% 0.34/0.48 ( ( ( X @ Xx )
% 0.34/0.48 & ( X @ Xy ) )
% 0.34/0.48 => ( X @ ( cP @ Xx @ Xy ) ) ) )
% 0.34/0.48 => ! [Xx: iS] : ( X @ Xx ) )
% 0.34/0.48 & ( cS_JOIN_CLOS @ c0 @ cP @ cJOIN ) )
% 0.34/0.48 => ! [Xx: iS] : ( cJOIN @ Xx @ Xx @ Xx ) ) ).
% 0.34/0.48
% 0.34/0.48 %------------------------------------------------------------------------------
% 0.34/0.48 ------------------------
% 1.87/1.51 ---- Embedded in THF ---
% 1.87/1.51 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.87/1.51 %%% Generated on Tue Feb 24 12:41:37 EST 2026
% 1.87/1.51 %%% using '$$dhol' embedding, version 1.3.0.
% 1.87/1.51 %%% Logic specification used:
% 1.87/1.51 %%% thf(spec, logic, $$dhol).
% 1.87/1.51
% 1.87/1.51 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.dFLP254zJF/DTF2DTF24191.p
% See solution above
% 1.87/1.51 ------------------------
% 1.87/1.52 ---- Cleaned THF ---
% 1.87/1.52 thf(iS_type,type,
% 1.87/1.52 iS: $tType ).
% 1.87/1.52
% 1.87/1.52 thf(c0_type,type,
% 1.87/1.52 c0: iS ).
% 1.87/1.52
% 1.87/1.52 thf(cJOIN_type,type,
% 1.87/1.52 cJOIN: iS > iS > iS > $o ).
% 1.87/1.52
% 1.87/1.52 thf(cP_type,type,
% 1.87/1.52 cP: iS > iS > iS ).
% 1.87/1.52
% 1.87/1.52 thf(cS_JOIN_CLOS_type,type,
% 1.87/1.52 cS_JOIN_CLOS: iS > ( iS > iS > iS ) > ( iS > iS > iS > $o ) > $o ).
% 1.87/1.52
% 1.87/1.52 thf(cS_JOIN_CLOS_def,definition,
% 1.87/1.52 ( cS_JOIN_CLOS
% 1.87/1.52 = ( ^ [X0: iS,P: iS > iS > iS,JOIN: iS > iS > iS > $o] :
% 1.87/1.52 ( ! [Xx: iS] : ( JOIN @ Xx @ X0 @ Xx )
% 1.87/1.52 & ! [Xy: iS] : ( JOIN @ X0 @ Xy @ Xy )
% 1.87/1.52 & ! [Xx: iS,Xy: iS,Xz: iS,Xu: iS,Xv: iS,Xw: iS] :
% 1.87/1.52 ( ( ( JOIN @ Xx @ Xy @ Xz )
% 1.87/1.52 & ( JOIN @ Xu @ Xv @ Xw ) )
% 1.87/1.52 => ( JOIN @ ( P @ Xx @ Xu ) @ ( P @ Xy @ Xv ) @ ( P @ Xz @ Xw ) ) ) ) ) ) ).
% 1.87/1.52
% 1.87/1.52 thf(cTHM580_pme,conjecture,
% 1.87/1.52 ( ( ! [Xx: iS,Xy: iS] :
% 1.87/1.52 ( ( cP @ Xx @ Xy )
% 1.87/1.52 != c0 )
% 1.87/1.52 & ! [Xx: iS,Xy: iS,Xu: iS,Xv: iS] :
% 1.87/1.52 ( ( ( cP @ Xx @ Xu )
% 1.87/1.52 = ( cP @ Xy @ Xv ) )
% 1.87/1.52 => ( ( Xx = Xy )
% 1.87/1.52 & ( Xu = Xv ) ) )
% 1.87/1.52 & ! [X: iS > $o] :
% 1.87/1.52 ( ( ( X @ c0 )
% 1.87/1.52 & ! [Xx: iS,Xy: iS] :
% 1.87/1.52 ( ( ( X @ Xx )
% 1.87/1.52 & ( X @ Xy ) )
% 1.87/1.52 => ( X @ ( cP @ Xx @ Xy ) ) ) )
% 1.87/1.52 => ! [Xx: iS] : ( X @ Xx ) )
% 1.87/1.52 & ( cS_JOIN_CLOS @ c0 @ cP @ cJOIN ) )
% 1.87/1.52 => ! [Xx: iS] : ( cJOIN @ Xx @ Xx @ Xx ) ) ).
% 1.87/1.52 ------------------------
% 1.87/1.54 % (24314)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_24191 for (2999ds/2Mi)
% 1.87/1.54 % (24313)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_24191 for (2999ds/2Mi)
% 1.87/1.54 % (24312)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_24191 for (2999ds/27Mi)
% 1.87/1.54 % (24310)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_24191 for (2999ds/183Mi)
% 1.87/1.54 % (24316)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_24191 for (2999ds/18Mi)
% 1.87/1.54 % (24315)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_24191 for (2999ds/275Mi)
% 1.87/1.54 % (24311)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_24191 for (2999ds/4Mi)
% 1.87/1.54 % (24313)Instruction limit reached!
% 1.87/1.54 % (24313)------------------------------
% 1.87/1.54 % (24313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/1.54 % (24313)Termination reason: Unknown
% 1.87/1.54 % (24313)Termination phase: Property scanning
% 1.87/1.54
% 1.87/1.54 % (24314)Instruction limit reached!
% 1.87/1.54 % (24314)------------------------------
% 1.87/1.54 % (24314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/1.54 % (24314)Termination reason: Unknown
% 1.87/1.54 % (24314)Termination phase: Property scanning
% 1.87/1.54
% 1.87/1.54 % (24314)Memory used [KB]: 1023
% 1.87/1.54 % (24314)Time elapsed: 0.004 s
% 1.87/1.54 % (24314)Instructions burned: 3 (million)
% 1.87/1.54 % (24314)------------------------------
% 1.87/1.54 % (24314)------------------------------
% 1.87/1.54 % (24313)Memory used [KB]: 1023
% 1.87/1.54 % (24313)Time elapsed: 0.003 s
% 1.87/1.54 % (24313)Instructions burned: 3 (million)
% 1.87/1.54 % (24313)------------------------------
% 1.87/1.54 % (24313)------------------------------
% 1.87/1.55 % (24311)Instruction limit reached!
% 1.87/1.55 % (24311)------------------------------
% 1.87/1.55 % (24311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/1.55 % (24311)Termination reason: Unknown
% 1.87/1.55 % (24311)Termination phase: Saturation
% 1.87/1.55
% 1.87/1.55 % (24311)Memory used [KB]: 5500
% 1.87/1.55 % (24311)Time elapsed: 0.004 s
% 1.87/1.55 % (24311)Instructions burned: 4 (million)
% 1.87/1.55 % (24311)------------------------------
% 1.87/1.55 % (24311)------------------------------
% 1.87/1.55 % (24312)Refutation not found, incomplete strategy
% 1.87/1.55 % (24312)------------------------------
% 1.87/1.55 % (24312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/1.55 % (24312)Termination reason: Refutation not found, incomplete strategy
% 1.87/1.55
% 1.87/1.55
% 1.87/1.55 % (24312)Memory used [KB]: 5628
% 1.87/1.55 % (24312)Time elapsed: 0.008 s
% 1.87/1.55 % (24312)Instructions burned: 11 (million)
% 1.87/1.55 % (24312)------------------------------
% 1.87/1.55 % (24312)------------------------------
% 1.87/1.55 % (24316)Instruction limit reached!
% 1.87/1.55 % (24316)------------------------------
% 1.87/1.55 % (24316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/1.55 % (24316)Termination reason: Unknown
% 1.87/1.55 % (24316)Termination phase: Saturation
% 1.87/1.55
% 1.87/1.55 % (24316)Memory used [KB]: 5628
% 1.87/1.55 % (24316)Time elapsed: 0.012 s
% 1.87/1.55 % (24316)Instructions burned: 18 (million)
% 1.87/1.55 % (24316)------------------------------
% 1.87/1.55 % (24316)------------------------------
% 1.87/1.56 % (24317)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_24191 for (2999ds/3Mi)
% 1.87/1.56 % (24318)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_24191 for (2999ds/37Mi)
% 1.87/1.56 % (24319)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_24191 for (2999ds/15Mi)
% 1.87/1.56 % (24317)Instruction limit reached!
% 1.87/1.56 % (24317)------------------------------
% 1.87/1.56 % (24317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/1.56 % (24317)Termination reason: Unknown
% 1.87/1.56 % (24317)Termination phase: Saturation
% 1.87/1.56
% 1.87/1.56 % (24317)Memory used [KB]: 5500
% 1.87/1.56 % (24317)Time elapsed: 0.004 s
% 1.87/1.56 % (24317)Instructions burned: 4 (million)
% 1.87/1.56 % (24317)------------------------------
% 1.87/1.56 % (24317)------------------------------
% 1.87/1.57 % (24320)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_24191 for (2999ds/3Mi)
% 1.87/1.57 % (24320)Instruction limit reached!
% 1.87/1.57 % (24320)------------------------------
% 1.87/1.57 % (24320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/1.57 % (24320)Termination reason: Unknown
% 1.87/1.57 % (24320)Termination phase: Saturation
% 1.87/1.57
% 1.87/1.57 % (24320)Memory used [KB]: 1023
% 1.87/1.57 % (24320)Time elapsed: 0.004 s
% 1.87/1.57 % (24320)Instructions burned: 4 (million)
% 1.87/1.57 % (24320)------------------------------
% 1.87/1.57 % (24320)------------------------------
% 1.87/1.57 % (24321)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_24191 for (2999ds/1041Mi)
% 1.87/1.57 % (24319)Instruction limit reached!
% 1.87/1.57 % (24319)------------------------------
% 1.87/1.57 % (24319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/1.57 % (24319)Termination reason: Unknown
% 1.87/1.57 % (24319)Termination phase: Saturation
% 1.87/1.57
% 1.87/1.57 % (24319)Memory used [KB]: 5628
% 1.87/1.57 % (24319)Time elapsed: 0.010 s
% 1.87/1.57 % (24319)Instructions burned: 15 (million)
% 1.87/1.57 % (24319)------------------------------
% 1.87/1.57 % (24319)------------------------------
% 1.87/1.58 % (24318)Instruction limit reached!
% 1.87/1.58 % (24318)------------------------------
% 1.87/1.58 % (24318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/1.58 % (24318)Termination reason: Unknown
% 1.87/1.58 % (24318)Termination phase: Saturation
% 1.87/1.58
% 1.87/1.58 % (24318)Memory used [KB]: 5884
% 1.87/1.58 % (24318)Time elapsed: 0.020 s
% 1.87/1.58 % (24318)Instructions burned: 39 (million)
% 1.87/1.58 % (24318)------------------------------
% 1.87/1.58 % (24318)------------------------------
% 1.87/1.58 % (24322)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_24191 for (2999ds/7Mi)
% 1.87/1.58 % (24322)Instruction limit reached!
% 1.87/1.58 % (24322)------------------------------
% 1.87/1.58 % (24322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/1.58 % (24322)Termination reason: Unknown
% 1.87/1.58 % (24322)Termination phase: Saturation
% 1.87/1.58
% 1.87/1.58 % (24322)Memory used [KB]: 1023
% 1.87/1.58 % (24322)Time elapsed: 0.006 s
% 1.87/1.58 % (24322)Instructions burned: 7 (million)
% 1.87/1.58 % (24322)------------------------------
% 1.87/1.58 % (24322)------------------------------
% 1.87/1.59 % (24323)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_24191 for (2999ds/16Mi)
% 1.87/1.59 % (24324)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_24191 for (2999ds/3Mi)
% 1.87/1.59 % (24324)Instruction limit reached!
% 1.87/1.59 % (24324)------------------------------
% 1.87/1.59 % (24324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/1.59 % (24324)Termination reason: Unknown
% 1.87/1.59 % (24324)Termination phase: Twee Goal Transformation
% 1.87/1.59
% 1.87/1.59 % (24324)Memory used [KB]: 1023
% 1.87/1.59 % (24324)Time elapsed: 0.004 s
% 1.87/1.59 % (24324)Instructions burned: 4 (million)
% 1.87/1.59 % (24324)------------------------------
% 1.87/1.59 % (24324)------------------------------
% 1.87/1.59 % (24323)Instruction limit reached!
% 1.87/1.59 % (24323)------------------------------
% 1.87/1.59 % (24323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/1.59 % (24323)Termination reason: Unknown
% 1.87/1.59 % (24323)Termination phase: Saturation
% 1.87/1.59
% 1.87/1.59 % (24323)Memory used [KB]: 5756
% 1.87/1.59 % (24323)Time elapsed: 0.011 s
% 1.87/1.59 % (24323)Instructions burned: 16 (million)
% 1.87/1.59 % (24323)------------------------------
% 1.87/1.59 % (24323)------------------------------
% 1.87/1.60 % (24325)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_24191 for (2999ds/3Mi)
% 1.89/1.60 % (24325)Instruction limit reached!
% 1.89/1.60 % (24325)------------------------------
% 1.89/1.60 % (24325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.60 % (24325)Termination reason: Unknown
% 1.89/1.60 % (24325)Termination phase: Property scanning
% 1.89/1.60
% 1.89/1.60 % (24325)Memory used [KB]: 1023
% 1.89/1.60 % (24325)Time elapsed: 0.004 s
% 1.89/1.60 % (24325)Instructions burned: 4 (million)
% 1.89/1.60 % (24325)------------------------------
% 1.89/1.60 % (24325)------------------------------
% 1.89/1.60 % (24326)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_24191 for (2999ds/7Mi)
% 1.89/1.60 % (24326)Instruction limit reached!
% 1.89/1.60 % (24326)------------------------------
% 1.89/1.60 % (24326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.60 % (24326)Termination reason: Unknown
% 1.89/1.60 % (24326)Termination phase: Saturation
% 1.89/1.60
% 1.89/1.60 % (24326)Memory used [KB]: 5500
% 1.89/1.60 % (24326)Time elapsed: 0.006 s
% 1.89/1.60 % (24326)Instructions burned: 9 (million)
% 1.89/1.60 % (24326)------------------------------
% 1.89/1.60 % (24326)------------------------------
% 1.89/1.61 % (24321)First to succeed.
% 1.89/1.61 % (24327)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_24191 for (2999ds/3Mi)
% 1.89/1.61 % (24327)Instruction limit reached!
% 1.89/1.61 % (24327)------------------------------
% 1.89/1.61 % (24327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.61 % (24327)Termination reason: Unknown
% 1.89/1.61 % (24327)Termination phase: Property scanning
% 1.89/1.61
% 1.89/1.61 % (24327)Memory used [KB]: 1023
% 1.89/1.61 % (24327)Time elapsed: 0.004 s
% 1.89/1.61 % (24327)Instructions burned: 4 (million)
% 1.89/1.61 % (24327)------------------------------
% 1.89/1.61 % (24327)------------------------------
% 1.89/1.61 % (24321)Refutation found. Thanks to Tanya!
% 1.89/1.61 % SZS status Theorem for DTF2THF_24191
% 1.89/1.61 % SZS output start Proof for DTF2THF_24191
% 1.89/1.61 thf(type_def_5, type, iS: $tType).
% 1.89/1.61 thf(func_def_0, type, iS: $tType).
% 1.89/1.61 thf(func_def_1, type, c0: iS).
% 1.89/1.61 thf(func_def_2, type, cJOIN: iS > iS > iS > $o).
% 1.89/1.61 thf(func_def_3, type, cP: iS > iS > iS).
% 1.89/1.61 thf(func_def_4, type, cS_JOIN_CLOS: iS > (iS > iS > iS) > (iS > iS > iS > $o) > $o).
% 1.89/1.61 thf(func_def_23, type, ph1: !>[X0: $tType]:(X0)).
% 1.89/1.61 thf(func_def_24, type, sK2: iS).
% 1.89/1.61 thf(func_def_25, type, sK3: iS).
% 1.89/1.61 thf(func_def_26, type, sK4: iS).
% 1.89/1.61 thf(func_def_27, type, sK5: iS).
% 1.89/1.61 thf(func_def_28, type, sK6: iS).
% 1.89/1.61 thf(f220,plain,(
% 1.89/1.61 $false),
% 1.89/1.61 inference(avatar_sat_refutation,[status(thm)],[f216,f219])).
% 1.89/1.61 thf(f219,plain,(
% 1.89/1.61 spl0_2),
% 1.89/1.61 inference(avatar_split_clause,[status(thm)],[f218,f42])).
% 1.89/1.61 thf(f42,definition,(
% 1.89/1.61 spl0_2 <=> ((!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (((cJOIN @ Y0 @ Y0 @ Y0) & (cJOIN @ Y1 @ Y1 @ Y1)) => (cJOIN @ (cP @ Y0 @ Y1) @ (cP @ Y0 @ Y1) @ (cP @ Y0 @ Y1))))))) = $false)),
% 1.89/1.61 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.89/1.61 thf(f218,plain,(
% 1.89/1.61 ((!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (((cJOIN @ Y0 @ Y0 @ Y0) & (cJOIN @ Y1 @ Y1 @ Y1)) => (cJOIN @ (cP @ Y0 @ Y1) @ (cP @ Y0 @ Y1) @ (cP @ Y0 @ Y1))))))) = $false)),
% 1.89/1.61 inference(boolean_simplification,[status(thm)],[f217])).
% 1.89/1.61 thf(f217,plain,(
% 1.89/1.61 (((!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (((cJOIN @ Y0 @ Y0 @ Y0) & (cJOIN @ Y1 @ Y1 @ Y1)) => (cJOIN @ (cP @ Y0 @ Y1) @ (cP @ Y0 @ Y1) @ (cP @ Y0 @ Y1))))))) & $true) = $false)),
% 1.89/1.61 inference(forward_demodulation,[status(thm)],[f34,f93])).
% 1.89/1.61 thf(f93,plain,(
% 1.89/1.61 ( ! [X1 : iS] : (($true = (cJOIN @ X1 @ c0 @ X1))) )),
% 1.89/1.61 inference(beta_eta_normalization,[status(thm)],[f91])).
% 1.89/1.61 thf(f91,plain,(
% 1.89/1.61 ( ! [X1 : iS] : (($true = ((^[Y0 : iS]: (cJOIN @ Y0 @ c0 @ Y0)) @ X1))) )),
% 1.89/1.61 inference(pi_clausification,[status(thm)],[f78])).
% 1.89/1.61 thf(f78,plain,(
% 1.89/1.61 ($true = (!! @ iS @ (^[Y0 : iS]: (cJOIN @ Y0 @ c0 @ Y0))))),
% 1.89/1.61 inference(binary_proxy_clausification,[status(thm)],[f77])).
% 1.89/1.61 thf(f77,plain,(
% 1.89/1.61 ($true = ((!! @ iS @ (^[Y0 : iS]: (cJOIN @ c0 @ Y0 @ Y0))) & (!! @ iS @ (^[Y0 : iS]: (cJOIN @ Y0 @ c0 @ Y0)))))),
% 1.89/1.61 inference(boolean_simplification,[status(thm)],[f76])).
% 1.89/1.61 thf(f76,plain,(
% 1.89/1.61 ($true = (((!! @ iS @ (^[Y0 : iS]: (cJOIN @ c0 @ Y0 @ Y0))) & (!! @ iS @ (^[Y0 : iS]: (cJOIN @ Y0 @ c0 @ Y0)))) & $true))),
% 1.89/1.61 inference(backward_demodulation,[status(thm)],[f73,f74])).
% 1.89/1.61 thf(f74,plain,(
% 1.89/1.61 ((!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (!! @ iS @ (^[Y3 : iS]: (!! @ iS @ (^[Y4 : iS]: (!! @ iS @ (^[Y5 : iS]: (((cJOIN @ Y5 @ Y1 @ Y0) & (cJOIN @ Y2 @ Y4 @ Y3)) => (cJOIN @ (cP @ Y5 @ Y2) @ (cP @ Y1 @ Y4) @ (cP @ Y0 @ Y3))))))))))))))) = $true)),
% 1.89/1.61 inference(binary_proxy_clausification,[status(thm)],[f73])).
% 1.89/1.61 thf(f73,plain,(
% 1.89/1.61 ($true = (((!! @ iS @ (^[Y0 : iS]: (cJOIN @ c0 @ Y0 @ Y0))) & (!! @ iS @ (^[Y0 : iS]: (cJOIN @ Y0 @ c0 @ Y0)))) & (!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (!! @ iS @ (^[Y3 : iS]: (!! @ iS @ (^[Y4 : iS]: (!! @ iS @ (^[Y5 : iS]: (((cJOIN @ Y5 @ Y1 @ Y0) & (cJOIN @ Y2 @ Y4 @ Y3)) => (cJOIN @ (cP @ Y5 @ Y2) @ (cP @ Y1 @ Y4) @ (cP @ Y0 @ Y3)))))))))))))))))),
% 1.89/1.61 inference(boolean_simplification,[status(thm)],[f72])).
% 1.89/1.61 thf(f72,plain,(
% 1.89/1.61 ($true = ($true & (((!! @ iS @ (^[Y0 : iS]: (cJOIN @ c0 @ Y0 @ Y0))) & (!! @ iS @ (^[Y0 : iS]: (cJOIN @ Y0 @ c0 @ Y0)))) & (!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (!! @ iS @ (^[Y3 : iS]: (!! @ iS @ (^[Y4 : iS]: (!! @ iS @ (^[Y5 : iS]: (((cJOIN @ Y5 @ Y1 @ Y0) & (cJOIN @ Y2 @ Y4 @ Y3)) => (cJOIN @ (cP @ Y5 @ Y2) @ (cP @ Y1 @ Y4) @ (cP @ Y0 @ Y3))))))))))))))))))),
% 1.89/1.61 inference(backward_demodulation,[status(thm)],[f25,f71])).
% 1.89/1.61 thf(f71,plain,(
% 1.89/1.61 ($true = ((!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (!! @ iS @ (^[Y3 : iS]: (((cP @ Y3 @ Y2) = (cP @ Y1 @ Y0)) => ((Y3 = Y1) & (Y2 = Y0))))))))))) & (!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (~ (c0 = (cP @ Y1 @ Y0)))))))))),
% 1.89/1.61 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.89/1.61 thf(f25,plain,(
% 1.89/1.61 ($true = (((!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (!! @ iS @ (^[Y3 : iS]: (((cP @ Y3 @ Y2) = (cP @ Y1 @ Y0)) => ((Y3 = Y1) & (Y2 = Y0))))))))))) & (!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (~ (c0 = (cP @ Y1 @ Y0)))))))) & (((!! @ iS @ (^[Y0 : iS]: (cJOIN @ c0 @ Y0 @ Y0))) & (!! @ iS @ (^[Y0 : iS]: (cJOIN @ Y0 @ c0 @ Y0)))) & (!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (!! @ iS @ (^[Y3 : iS]: (!! @ iS @ (^[Y4 : iS]: (!! @ iS @ (^[Y5 : iS]: (((cJOIN @ Y5 @ Y1 @ Y0) & (cJOIN @ Y2 @ Y4 @ Y3)) => (cJOIN @ (cP @ Y5 @ Y2) @ (cP @ Y1 @ Y4) @ (cP @ Y0 @ Y3))))))))))))))))))),
% 1.89/1.61 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.89/1.61 thf(f17,plain,(
% 1.89/1.61 ($true = ((((!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (!! @ iS @ (^[Y3 : iS]: (((cP @ Y3 @ Y2) = (cP @ Y1 @ Y0)) => ((Y3 = Y1) & (Y2 = Y0))))))))))) & (!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (~ (c0 = (cP @ Y1 @ Y0)))))))) & (((!! @ iS @ (^[Y0 : iS]: (cJOIN @ c0 @ Y0 @ Y0))) & (!! @ iS @ (^[Y0 : iS]: (cJOIN @ Y0 @ c0 @ Y0)))) & (!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (!! @ iS @ (^[Y3 : iS]: (!! @ iS @ (^[Y4 : iS]: (!! @ iS @ (^[Y5 : iS]: (((cJOIN @ Y5 @ Y1 @ Y0) & (cJOIN @ Y2 @ Y4 @ Y3)) => (cJOIN @ (cP @ Y5 @ Y2) @ (cP @ Y1 @ Y4) @ (cP @ Y0 @ Y3))))))))))))))))) & (!! @ (iS > $o) @ (^[Y0 : iS > $o]: (((!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (((Y0 @ Y1) & (Y0 @ Y2)) => (Y0 @ (cP @ Y1 @ Y2))))))) & (Y0 @ c0)) => (!! @ iS @ Y0))))))),
% 1.89/1.61 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.89/1.61 thf(f13,plain,(
% 1.89/1.61 ((((((!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (!! @ iS @ (^[Y3 : iS]: (((cP @ Y3 @ Y2) = (cP @ Y1 @ Y0)) => ((Y3 = Y1) & (Y2 = Y0))))))))))) & (!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (~ (c0 = (cP @ Y1 @ Y0)))))))) & (((!! @ iS @ (^[Y0 : iS]: (cJOIN @ c0 @ Y0 @ Y0))) & (!! @ iS @ (^[Y0 : iS]: (cJOIN @ Y0 @ c0 @ Y0)))) & (!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (!! @ iS @ (^[Y3 : iS]: (!! @ iS @ (^[Y4 : iS]: (!! @ iS @ (^[Y5 : iS]: (((cJOIN @ Y5 @ Y1 @ Y0) & (cJOIN @ Y2 @ Y4 @ Y3)) => (cJOIN @ (cP @ Y5 @ Y2) @ (cP @ Y1 @ Y4) @ (cP @ Y0 @ Y3))))))))))))))))) & (!! @ (iS > $o) @ (^[Y0 : iS > $o]: (((!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (((Y0 @ Y1) & (Y0 @ Y2)) => (Y0 @ (cP @ Y1 @ Y2))))))) & (Y0 @ c0)) => (!! @ iS @ Y0))))) => (!! @ iS @ (^[Y0 : iS]: (cJOIN @ Y0 @ Y0 @ Y0)))) = $false)),
% 1.89/1.61 inference(not_proxy_clausification,[status(thm)],[f12])).
% 1.89/1.61 thf(f12,plain,(
% 1.89/1.61 ($true = (~ (((((!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (!! @ iS @ (^[Y3 : iS]: (((cP @ Y3 @ Y2) = (cP @ Y1 @ Y0)) => ((Y3 = Y1) & (Y2 = Y0))))))))))) & (!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (~ (c0 = (cP @ Y1 @ Y0)))))))) & (((!! @ iS @ (^[Y0 : iS]: (cJOIN @ c0 @ Y0 @ Y0))) & (!! @ iS @ (^[Y0 : iS]: (cJOIN @ Y0 @ c0 @ Y0)))) & (!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (!! @ iS @ (^[Y3 : iS]: (!! @ iS @ (^[Y4 : iS]: (!! @ iS @ (^[Y5 : iS]: (((cJOIN @ Y5 @ Y1 @ Y0) & (cJOIN @ Y2 @ Y4 @ Y3)) => (cJOIN @ (cP @ Y5 @ Y2) @ (cP @ Y1 @ Y4) @ (cP @ Y0 @ Y3))))))))))))))))) & (!! @ (iS > $o) @ (^[Y0 : iS > $o]: (((!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (((Y0 @ Y1) & (Y0 @ Y2)) => (Y0 @ (cP @ Y1 @ Y2))))))) & (Y0 @ c0)) => (!! @ iS @ Y0))))) => (!! @ iS @ (^[Y0 : iS]: (cJOIN @ Y0 @ Y0 @ Y0))))))),
% 1.89/1.61 inference(beta_eta_normalization,[status(thm)],[f11])).
% 1.89/1.61 thf(f11,plain,(
% 1.89/1.61 ($true = (~ (((((!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (!! @ iS @ (^[Y3 : iS]: (((cP @ Y3 @ Y2) = (cP @ Y1 @ Y0)) => ((Y3 = Y1) & (Y2 = Y0))))))))))) & (!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (~ (c0 = (cP @ Y1 @ Y0)))))))) & ((^[Y0 : iS]: ((^[Y1 : iS > iS > iS]: ((^[Y2 : iS > iS > iS > $o]: (((!! @ iS @ (^[Y3 : iS]: (Y2 @ Y0 @ Y3 @ Y3))) & (!! @ iS @ (^[Y3 : iS]: (Y2 @ Y3 @ Y0 @ Y3)))) & (!! @ iS @ (^[Y3 : iS]: (!! @ iS @ (^[Y4 : iS]: (!! @ iS @ (^[Y5 : iS]: (!! @ iS @ (^[Y6 : iS]: (!! @ iS @ (^[Y7 : iS]: (!! @ iS @ (^[Y8 : iS]: (((Y2 @ Y8 @ Y4 @ Y3) & (Y2 @ Y5 @ Y7 @ Y6)) => (Y2 @ (Y1 @ Y8 @ Y5) @ (Y1 @ Y4 @ Y7) @ (Y1 @ Y3 @ Y6))))))))))))))))))))) @ c0 @ cP @ cJOIN)) & (!! @ (iS > $o) @ (^[Y0 : iS > $o]: (((!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (((Y0 @ Y1) & (Y0 @ Y2)) => (Y0 @ (cP @ Y1 @ Y2))))))) & (Y0 @ c0)) => (!! @ iS @ (^[Y1 : iS]: (Y0 @ Y1))))))) => (!! @ iS @ (^[Y0 : iS]: (cJOIN @ Y0 @ Y0 @ Y0))))))),
% 1.89/1.61 inference(definition_unfolding,[status(thm)],[f10,f9])).
% 1.89/1.61 thf(f9,plain,(
% 1.89/1.61 (cS_JOIN_CLOS = (^[Y0 : iS]: ((^[Y1 : iS > iS > iS]: ((^[Y2 : iS > iS > iS > $o]: (((!! @ iS @ (^[Y3 : iS]: (Y2 @ Y0 @ Y3 @ Y3))) & (!! @ iS @ (^[Y3 : iS]: (Y2 @ Y3 @ Y0 @ Y3)))) & (!! @ iS @ (^[Y3 : iS]: (!! @ iS @ (^[Y4 : iS]: (!! @ iS @ (^[Y5 : iS]: (!! @ iS @ (^[Y6 : iS]: (!! @ iS @ (^[Y7 : iS]: (!! @ iS @ (^[Y8 : iS]: (((Y2 @ Y8 @ Y4 @ Y3) & (Y2 @ Y5 @ Y7 @ Y6)) => (Y2 @ (Y1 @ Y8 @ Y5) @ (Y1 @ Y4 @ Y7) @ (Y1 @ Y3 @ Y6))))))))))))))))))))))),
% 1.89/1.61 inference(cnf_transformation,[status(thm)],[f6])).
% 1.89/1.61 thf(f6,plain,(
% 1.89/1.61 (cS_JOIN_CLOS = (^[Y0 : iS]: ((^[Y1 : iS > iS > iS]: ((^[Y2 : iS > iS > iS > $o]: (((!! @ iS @ (^[Y3 : iS]: (Y2 @ Y0 @ Y3 @ Y3))) & (!! @ iS @ (^[Y3 : iS]: (Y2 @ Y3 @ Y0 @ Y3)))) & (!! @ iS @ (^[Y3 : iS]: (!! @ iS @ (^[Y4 : iS]: (!! @ iS @ (^[Y5 : iS]: (!! @ iS @ (^[Y6 : iS]: (!! @ iS @ (^[Y7 : iS]: (!! @ iS @ (^[Y8 : iS]: (((Y2 @ Y8 @ Y4 @ Y3) & (Y2 @ Y5 @ Y7 @ Y6)) => (Y2 @ (Y1 @ Y8 @ Y5) @ (Y1 @ Y4 @ Y7) @ (Y1 @ Y3 @ Y6))))))))))))))))))))))),
% 1.89/1.61 inference(fool_elimination,[status(thm)],[f5])).
% 1.89/1.61 thf(f5,plain,(
% 1.89/1.61 (cS_JOIN_CLOS = (^[X0 : iS, X1 : iS > iS > iS, X2 : iS > iS > iS > $o] : (! [X3 : iS,X4 : iS,X5 : iS,X6 : iS,X7 : iS,X8 : iS] : (((X2 @ X6 @ X4 @ X5) & (X2 @ X3 @ X7 @ X8)) => (X2 @ (X1 @ X3 @ X6) @ (X1 @ X7 @ X4) @ (X1 @ X8 @ X5))) & ! [X9 : iS] : (X2 @ X9 @ X0 @ X9) & ! [X10 : iS] : (X2 @ X0 @ X10 @ X10))))),
% 1.89/1.61 inference(rectify,[status(thm)],[f1])).
% 1.89/1.61 thf(f1,axiom,(
% 1.89/1.61 (cS_JOIN_CLOS = (^[X0 : iS, X1 : iS > iS > iS, X2 : iS > iS > iS > $o] : (! [X3 : iS,X7 : iS,X8 : iS,X6 : iS,X4 : iS,X5 : iS] : (((X2 @ X6 @ X7 @ X8) & (X2 @ X3 @ X4 @ X5)) => (X2 @ (X1 @ X3 @ X6) @ (X1 @ X4 @ X7) @ (X1 @ X5 @ X8))) & ! [X3 : iS] : (X2 @ X3 @ X0 @ X3) & ! [X4 : iS] : (X2 @ X0 @ X4 @ X4))))),
% 1.89/1.61 file('/export/starexec/sandbox/tmp/tmp.dFLP254zJF/DTF2THF_24191.p',cS_JOIN_CLOS_def)).
% 1.89/1.61 thf(f10,plain,(
% 1.89/1.61 ($true = (~ (((((!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (!! @ iS @ (^[Y3 : iS]: (((cP @ Y3 @ Y2) = (cP @ Y1 @ Y0)) => ((Y3 = Y1) & (Y2 = Y0))))))))))) & (!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (~ (c0 = (cP @ Y1 @ Y0)))))))) & (cS_JOIN_CLOS @ c0 @ cP @ cJOIN)) & (!! @ (iS > $o) @ (^[Y0 : iS > $o]: (((!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (((Y0 @ Y1) & (Y0 @ Y2)) => (Y0 @ (cP @ Y1 @ Y2))))))) & (Y0 @ c0)) => (!! @ iS @ (^[Y1 : iS]: (Y0 @ Y1))))))) => (!! @ iS @ (^[Y0 : iS]: (cJOIN @ Y0 @ Y0 @ Y0))))))),
% 1.89/1.61 inference(cnf_transformation,[status(thm)],[f8])).
% 1.89/1.61 thf(f8,plain,(
% 1.89/1.61 ($true = (~ (((((!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (!! @ iS @ (^[Y3 : iS]: (((cP @ Y3 @ Y2) = (cP @ Y1 @ Y0)) => ((Y3 = Y1) & (Y2 = Y0))))))))))) & (!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (~ (c0 = (cP @ Y1 @ Y0)))))))) & (cS_JOIN_CLOS @ c0 @ cP @ cJOIN)) & (!! @ (iS > $o) @ (^[Y0 : iS > $o]: (((!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (((Y0 @ Y1) & (Y0 @ Y2)) => (Y0 @ (cP @ Y1 @ Y2))))))) & (Y0 @ c0)) => (!! @ iS @ (^[Y1 : iS]: (Y0 @ Y1))))))) => (!! @ iS @ (^[Y0 : iS]: (cJOIN @ Y0 @ Y0 @ Y0))))))),
% 1.89/1.61 inference(fool_elimination,[status(thm)],[f7])).
% 1.89/1.61 thf(f7,plain,(
% 1.89/1.61 ~((! [X0 : iS > $o] : (((X0 @ c0) & ! [X1 : iS,X2 : iS] : (((X0 @ X1) & (X0 @ X2)) => (X0 @ (cP @ X2 @ X1)))) => ! [X3 : iS] : (X0 @ X3)) & (cS_JOIN_CLOS @ c0 @ cP @ cJOIN) & ! [X4 : iS,X5 : iS] : (c0 != (cP @ X4 @ X5)) & ! [X6 : iS,X7 : iS,X8 : iS,X9 : iS] : (((cP @ X6 @ X7) = (cP @ X8 @ X9)) => ((X7 = X9) & (X6 = X8)))) => ! [X10 : iS] : (cJOIN @ X10 @ X10 @ X10))),
% 1.89/1.61 inference(rectify,[status(thm)],[f3])).
% 1.89/1.61 thf(f3,negated_conjecture,(
% 1.89/1.61 ~((! [X9 : iS > $o] : (((X9 @ c0) & ! [X4 : iS,X3 : iS] : (((X9 @ X4) & (X9 @ X3)) => (X9 @ (cP @ X3 @ X4)))) => ! [X3 : iS] : (X9 @ X3)) & (cS_JOIN_CLOS @ c0 @ cP @ cJOIN) & ! [X3 : iS,X4 : iS] : ((cP @ X3 @ X4) != c0) & ! [X4 : iS,X7 : iS,X3 : iS,X6 : iS] : (((cP @ X3 @ X6) = (cP @ X4 @ X7)) => ((X6 = X7) & (X3 = X4)))) => ! [X3 : iS] : (cJOIN @ X3 @ X3 @ X3))),
% 1.89/1.61 inference(negated_conjecture,[status(cth)],[f2])).
% 1.89/1.61 thf(f2,conjecture,(
% 1.89/1.61 (! [X9 : iS > $o] : (((X9 @ c0) & ! [X4 : iS,X3 : iS] : (((X9 @ X4) & (X9 @ X3)) => (X9 @ (cP @ X3 @ X4)))) => ! [X3 : iS] : (X9 @ X3)) & (cS_JOIN_CLOS @ c0 @ cP @ cJOIN) & ! [X3 : iS,X4 : iS] : ((cP @ X3 @ X4) != c0) & ! [X4 : iS,X7 : iS,X3 : iS,X6 : iS] : (((cP @ X3 @ X6) = (cP @ X4 @ X7)) => ((X6 = X7) & (X3 = X4)))) => ! [X3 : iS] : (cJOIN @ X3 @ X3 @ X3)),
% 1.89/1.61 file('/export/starexec/sandbox/tmp/tmp.dFLP254zJF/DTF2THF_24191.p',cTHM580_pme)).
% 1.89/1.61 thf(f34,plain,(
% 1.89/1.61 (((!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (((cJOIN @ Y0 @ Y0 @ Y0) & (cJOIN @ Y1 @ Y1 @ Y1)) => (cJOIN @ (cP @ Y0 @ Y1) @ (cP @ Y0 @ Y1) @ (cP @ Y0 @ Y1))))))) & (cJOIN @ c0 @ c0 @ c0)) = $false)),
% 1.89/1.61 inference(not_proxy_clausification,[status(thm)],[f33])).
% 1.89/1.61 thf(f33,plain,(
% 1.89/1.61 ($true = (~ ((!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (((cJOIN @ Y0 @ Y0 @ Y0) & (cJOIN @ Y1 @ Y1 @ Y1)) => (cJOIN @ (cP @ Y0 @ Y1) @ (cP @ Y0 @ Y1) @ (cP @ Y0 @ Y1))))))) & (cJOIN @ c0 @ c0 @ c0))))),
% 1.89/1.61 inference(boolean_simplification,[status(thm)],[f32])).
% 1.89/1.61 thf(f32,plain,(
% 1.89/1.61 ((((!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (((cJOIN @ Y0 @ Y0 @ Y0) & (cJOIN @ Y1 @ Y1 @ Y1)) => (cJOIN @ (cP @ Y0 @ Y1) @ (cP @ Y0 @ Y1) @ (cP @ Y0 @ Y1))))))) & (cJOIN @ c0 @ c0 @ c0)) => $false) = $true)),
% 1.89/1.61 inference(beta_eta_normalization,[status(thm)],[f31])).
% 1.89/1.61 thf(f31,plain,(
% 1.89/1.61 ($true = (((!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: ((((^[Y2 : iS]: (cJOIN @ Y2 @ Y2 @ Y2)) @ Y0) & ((^[Y2 : iS]: (cJOIN @ Y2 @ Y2 @ Y2)) @ Y1)) => ((^[Y2 : iS]: (cJOIN @ Y2 @ Y2 @ Y2)) @ (cP @ Y0 @ Y1))))))) & ((^[Y0 : iS]: (cJOIN @ Y0 @ Y0 @ Y0)) @ c0)) => $false))),
% 1.89/1.61 inference(superposition,[status(thm)],[f29,f16])).
% 1.89/1.61 thf(f16,plain,(
% 1.89/1.61 ((!! @ iS @ (^[Y0 : iS]: (cJOIN @ Y0 @ Y0 @ Y0))) = $false)),
% 1.89/1.61 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.89/1.61 thf(f29,plain,(
% 1.89/1.61 ( ! [X1 : iS > $o] : (((((!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (((X1 @ Y0) & (X1 @ Y1)) => (X1 @ (cP @ Y0 @ Y1))))))) & (X1 @ c0)) => (!! @ iS @ X1)) = $true)) )),
% 1.89/1.61 inference(beta_eta_normalization,[status(thm)],[f28])).
% 1.89/1.61 thf(f28,plain,(
% 1.89/1.61 ( ! [X1 : iS > $o] : (($true = ((^[Y0 : iS > $o]: (((!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (((Y0 @ Y1) & (Y0 @ Y2)) => (Y0 @ (cP @ Y1 @ Y2))))))) & (Y0 @ c0)) => (!! @ iS @ Y0))) @ X1))) )),
% 1.89/1.61 inference(pi_clausification,[status(thm)],[f27])).
% 1.89/1.61 thf(f27,plain,(
% 1.89/1.61 ((!! @ (iS > $o) @ (^[Y0 : iS > $o]: (((!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (((Y0 @ Y1) & (Y0 @ Y2)) => (Y0 @ (cP @ Y1 @ Y2))))))) & (Y0 @ c0)) => (!! @ iS @ Y0)))) = $true)),
% 1.89/1.61 inference(boolean_simplification,[status(thm)],[f26])).
% 1.89/1.61 thf(f26,plain,(
% 1.89/1.61 (($true & (!! @ (iS > $o) @ (^[Y0 : iS > $o]: (((!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (((Y0 @ Y1) & (Y0 @ Y2)) => (Y0 @ (cP @ Y1 @ Y2))))))) & (Y0 @ c0)) => (!! @ iS @ Y0))))) = $true)),
% 1.89/1.61 inference(backward_demodulation,[status(thm)],[f17,f25])).
% 1.89/1.61 thf(f216,plain,(
% 1.89/1.61 ~spl0_2),
% 1.89/1.61 inference(avatar_contradiction_clause,[status(thm)],[f215])).
% 1.89/1.61 thf(f215,plain,(
% 1.89/1.61 $false | ~spl0_2),
% 1.89/1.61 inference(trivial_inequality_removal,[status(thm)],[f214])).
% 1.89/1.61 thf(f214,plain,(
% 1.89/1.61 ($true = $false) | ~spl0_2),
% 1.89/1.61 inference(boolean_simplification,[status(thm)],[f213])).
% 1.89/1.61 thf(f213,plain,(
% 1.89/1.61 ((~ $true) = $true) | ~spl0_2),
% 1.89/1.61 inference(forward_demodulation,[status(thm)],[f212,f65])).
% 1.89/1.61 thf(f65,plain,(
% 1.89/1.61 ($true = (cJOIN @ sK4 @ sK4 @ sK4)) | ~spl0_2),
% 1.89/1.61 inference(boolean_simplification,[status(thm)],[f63])).
% 1.89/1.61 thf(f63,plain,(
% 1.89/1.61 (($true & (cJOIN @ sK4 @ sK4 @ sK4)) = $true) | ~spl0_2),
% 1.89/1.61 inference(backward_demodulation,[status(thm)],[f58,f62])).
% 1.89/1.61 thf(f62,plain,(
% 1.89/1.61 ((cJOIN @ sK3 @ sK3 @ sK3) = $true) | ~spl0_2),
% 1.89/1.61 inference(binary_proxy_clausification,[status(thm)],[f58])).
% 1.89/1.61 thf(f58,plain,(
% 1.89/1.61 (((cJOIN @ sK3 @ sK3 @ sK3) & (cJOIN @ sK4 @ sK4 @ sK4)) = $true) | ~spl0_2),
% 1.89/1.61 inference(binary_proxy_clausification,[status(thm)],[f56])).
% 1.89/1.61 thf(f56,plain,(
% 1.89/1.61 ($false = (((cJOIN @ sK3 @ sK3 @ sK3) & (cJOIN @ sK4 @ sK4 @ sK4)) => (cJOIN @ (cP @ sK3 @ sK4) @ (cP @ sK3 @ sK4) @ (cP @ sK3 @ sK4)))) | ~spl0_2),
% 1.89/1.61 inference(beta_eta_normalization,[status(thm)],[f52])).
% 1.89/1.61 thf(f52,plain,(
% 1.89/1.61 (((^[Y0 : iS]: (((cJOIN @ sK3 @ sK3 @ sK3) & (cJOIN @ Y0 @ Y0 @ Y0)) => (cJOIN @ (cP @ sK3 @ Y0) @ (cP @ sK3 @ Y0) @ (cP @ sK3 @ Y0)))) @ sK4) = $false) | ~spl0_2),
% 1.89/1.61 inference(sigma_clausification,[status(thm)],[f51])).
% 1.89/1.61 thf(f51,plain,(
% 1.89/1.61 ($false = (!! @ iS @ (^[Y0 : iS]: (((cJOIN @ sK3 @ sK3 @ sK3) & (cJOIN @ Y0 @ Y0 @ Y0)) => (cJOIN @ (cP @ sK3 @ Y0) @ (cP @ sK3 @ Y0) @ (cP @ sK3 @ Y0)))))) | ~spl0_2),
% 1.89/1.61 inference(beta_eta_normalization,[status(thm)],[f47])).
% 1.89/1.61 thf(f47,plain,(
% 1.89/1.61 ($false = ((^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (((cJOIN @ Y0 @ Y0 @ Y0) & (cJOIN @ Y1 @ Y1 @ Y1)) => (cJOIN @ (cP @ Y0 @ Y1) @ (cP @ Y0 @ Y1) @ (cP @ Y0 @ Y1)))))) @ sK3)) | ~spl0_2),
% 1.89/1.61 inference(sigma_clausification,[status(thm)],[f43])).
% 1.89/1.61 thf(f43,plain,(
% 1.89/1.61 ((!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (((cJOIN @ Y0 @ Y0 @ Y0) & (cJOIN @ Y1 @ Y1 @ Y1)) => (cJOIN @ (cP @ Y0 @ Y1) @ (cP @ Y0 @ Y1) @ (cP @ Y0 @ Y1))))))) = $false) | ~spl0_2),
% 1.89/1.61 inference(avatar_component_clause,[status(thm)],[f42])).
% 1.89/1.61 thf(f212,plain,(
% 1.89/1.61 ($true = (~ (cJOIN @ sK4 @ sK4 @ sK4))) | ~spl0_2),
% 1.89/1.61 inference(boolean_simplification,[status(thm)],[f211])).
% 1.89/1.61 thf(f211,plain,(
% 1.89/1.61 ((~ ($true & (cJOIN @ sK4 @ sK4 @ sK4))) = $true) | ~spl0_2),
% 1.89/1.61 inference(forward_demodulation,[status(thm)],[f190,f62])).
% 1.89/1.61 thf(f190,plain,(
% 1.89/1.61 ((~ ((cJOIN @ sK3 @ sK3 @ sK3) & (cJOIN @ sK4 @ sK4 @ sK4))) = $true) | ~spl0_2),
% 1.89/1.61 inference(boolean_simplification,[status(thm)],[f167])).
% 1.89/1.61 thf(f167,plain,(
% 1.89/1.61 ($true = (((cJOIN @ sK3 @ sK3 @ sK3) & (cJOIN @ sK4 @ sK4 @ sK4)) => $false)) | ~spl0_2),
% 1.89/1.61 inference(superposition,[status(thm)],[f165,f60])).
% 1.89/1.61 thf(f60,plain,(
% 1.89/1.61 ($false = (cJOIN @ (cP @ sK3 @ sK4) @ (cP @ sK3 @ sK4) @ (cP @ sK3 @ sK4))) | ~spl0_2),
% 1.89/1.61 inference(boolean_simplification,[status(thm)],[f59])).
% 1.89/1.61 thf(f59,plain,(
% 1.89/1.61 ($false = ($true => (cJOIN @ (cP @ sK3 @ sK4) @ (cP @ sK3 @ sK4) @ (cP @ sK3 @ sK4)))) | ~spl0_2),
% 1.89/1.61 inference(backward_demodulation,[status(thm)],[f56,f58])).
% 1.89/1.61 thf(f165,plain,(
% 1.89/1.61 ( ! [X2 : iS,X3 : iS,X1 : iS,X6 : iS,X4 : iS,X5 : iS] : (($true = (((cJOIN @ X6 @ X2 @ X1) & (cJOIN @ X3 @ X5 @ X4)) => (cJOIN @ (cP @ X6 @ X3) @ (cP @ X2 @ X5) @ (cP @ X1 @ X4))))) )),
% 1.89/1.61 inference(beta_eta_normalization,[status(thm)],[f161])).
% 1.89/1.61 thf(f161,plain,(
% 1.89/1.61 ( ! [X2 : iS,X3 : iS,X1 : iS,X6 : iS,X4 : iS,X5 : iS] : (($true = ((^[Y0 : iS]: (((cJOIN @ Y0 @ X2 @ X1) & (cJOIN @ X3 @ X5 @ X4)) => (cJOIN @ (cP @ Y0 @ X3) @ (cP @ X2 @ X5) @ (cP @ X1 @ X4)))) @ X6))) )),
% 1.89/1.61 inference(pi_clausification,[status(thm)],[f158])).
% 1.89/1.61 thf(f158,plain,(
% 1.89/1.61 ( ! [X2 : iS,X3 : iS,X1 : iS,X4 : iS,X5 : iS] : (($true = (!! @ iS @ (^[Y0 : iS]: (((cJOIN @ Y0 @ X2 @ X1) & (cJOIN @ X3 @ X5 @ X4)) => (cJOIN @ (cP @ Y0 @ X3) @ (cP @ X2 @ X5) @ (cP @ X1 @ X4))))))) )),
% 1.89/1.61 inference(beta_eta_normalization,[status(thm)],[f156])).
% 1.89/1.61 thf(f156,plain,(
% 1.89/1.61 ( ! [X2 : iS,X3 : iS,X1 : iS,X4 : iS,X5 : iS] : (($true = ((^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (((cJOIN @ Y1 @ X2 @ X1) & (cJOIN @ X3 @ Y0 @ X4)) => (cJOIN @ (cP @ Y1 @ X3) @ (cP @ X2 @ Y0) @ (cP @ X1 @ X4)))))) @ X5))) )),
% 1.89/1.61 inference(pi_clausification,[status(thm)],[f155])).
% 1.89/1.61 thf(f155,plain,(
% 1.89/1.61 ( ! [X2 : iS,X3 : iS,X1 : iS,X4 : iS] : (($true = (!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (((cJOIN @ Y1 @ X2 @ X1) & (cJOIN @ X3 @ Y0 @ X4)) => (cJOIN @ (cP @ Y1 @ X3) @ (cP @ X2 @ Y0) @ (cP @ X1 @ X4))))))))) )),
% 1.89/1.61 inference(beta_eta_normalization,[status(thm)],[f151])).
% 1.89/1.61 thf(f151,plain,(
% 1.89/1.61 ( ! [X2 : iS,X3 : iS,X1 : iS,X4 : iS] : (($true = ((^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (((cJOIN @ Y2 @ X2 @ X1) & (cJOIN @ X3 @ Y1 @ Y0)) => (cJOIN @ (cP @ Y2 @ X3) @ (cP @ X2 @ Y1) @ (cP @ X1 @ Y0)))))))) @ X4))) )),
% 1.89/1.61 inference(pi_clausification,[status(thm)],[f150])).
% 1.89/1.61 thf(f150,plain,(
% 1.89/1.61 ( ! [X2 : iS,X3 : iS,X1 : iS] : (($true = (!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (((cJOIN @ Y2 @ X2 @ X1) & (cJOIN @ X3 @ Y1 @ Y0)) => (cJOIN @ (cP @ Y2 @ X3) @ (cP @ X2 @ Y1) @ (cP @ X1 @ Y0))))))))))) )),
% 1.89/1.61 inference(beta_eta_normalization,[status(thm)],[f146])).
% 1.89/1.61 thf(f146,plain,(
% 1.89/1.61 ( ! [X2 : iS,X3 : iS,X1 : iS] : (($true = ((^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (!! @ iS @ (^[Y3 : iS]: (((cJOIN @ Y3 @ X2 @ X1) & (cJOIN @ Y0 @ Y2 @ Y1)) => (cJOIN @ (cP @ Y3 @ Y0) @ (cP @ X2 @ Y2) @ (cP @ X1 @ Y1)))))))))) @ X3))) )),
% 1.89/1.61 inference(pi_clausification,[status(thm)],[f143])).
% 1.89/1.61 thf(f143,plain,(
% 1.89/1.61 ( ! [X2 : iS,X1 : iS] : (($true = (!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (!! @ iS @ (^[Y3 : iS]: (((cJOIN @ Y3 @ X2 @ X1) & (cJOIN @ Y0 @ Y2 @ Y1)) => (cJOIN @ (cP @ Y3 @ Y0) @ (cP @ X2 @ Y2) @ (cP @ X1 @ Y1))))))))))))) )),
% 1.89/1.61 inference(beta_eta_normalization,[status(thm)],[f141])).
% 1.89/1.61 thf(f141,plain,(
% 1.89/1.61 ( ! [X2 : iS,X1 : iS] : (($true = ((^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (!! @ iS @ (^[Y3 : iS]: (!! @ iS @ (^[Y4 : iS]: (((cJOIN @ Y4 @ Y0 @ X1) & (cJOIN @ Y1 @ Y3 @ Y2)) => (cJOIN @ (cP @ Y4 @ Y1) @ (cP @ Y0 @ Y3) @ (cP @ X1 @ Y2)))))))))))) @ X2))) )),
% 1.89/1.61 inference(pi_clausification,[status(thm)],[f131])).
% 1.89/1.61 thf(f131,plain,(
% 1.89/1.61 ( ! [X1 : iS] : (((!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (!! @ iS @ (^[Y3 : iS]: (!! @ iS @ (^[Y4 : iS]: (((cJOIN @ Y4 @ Y0 @ X1) & (cJOIN @ Y1 @ Y3 @ Y2)) => (cJOIN @ (cP @ Y4 @ Y1) @ (cP @ Y0 @ Y3) @ (cP @ X1 @ Y2))))))))))))) = $true)) )),
% 1.89/1.61 inference(beta_eta_normalization,[status(thm)],[f127])).
% 1.89/1.61 thf(f127,plain,(
% 1.89/1.61 ( ! [X1 : iS] : (($true = ((^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (!! @ iS @ (^[Y3 : iS]: (!! @ iS @ (^[Y4 : iS]: (!! @ iS @ (^[Y5 : iS]: (((cJOIN @ Y5 @ Y1 @ Y0) & (cJOIN @ Y2 @ Y4 @ Y3)) => (cJOIN @ (cP @ Y5 @ Y2) @ (cP @ Y1 @ Y4) @ (cP @ Y0 @ Y3)))))))))))))) @ X1))) )),
% 1.89/1.61 inference(pi_clausification,[status(thm)],[f74])).
% 1.89/1.61 % SZS output end Proof for DTF2THF_24191
% 1.89/1.61 % (24321)------------------------------
% 1.89/1.61 % (24321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.61 % (24321)Termination reason: Refutation
% 1.89/1.61
% 1.89/1.61 % (24321)Memory used [KB]: 6012
% 1.89/1.61 % (24321)Time elapsed: 0.042 s
% 1.89/1.61 % (24321)Instructions burned: 72 (million)
% 1.89/1.61 % (24321)------------------------------
% 1.89/1.61 % (24321)------------------------------
% 1.89/1.61 % (24309)Success in time 0.075 s
%------------------------------------------------------------------------------