%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : PUZ107^5 : TPTP v9.2.1. Bugfixed v6.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n021.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 09:28:29 AM UTC 2026
% Result : Theorem 1.72s 1.47s
% Output : Refutation 1.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 6
% Syntax : Number of formulae : 77 ( 43 unt; 0 typ; 1 def)
% Number of atoms : 905 ( 354 equ; 0 cnn)
% Maximal formula atoms : 6 ( 11 avg)
% Number of connectives : 1371 ( 102 ~; 64 |; 204 &; 781 @)
% ( 1 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 196 ( 196 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 11 usr; 8 con; 0-4 aty)
% ( 110 !!; 73 ??; 0 @@+; 0 @@-)
% Number of variables : 340 ( 252 ^; 78 !; 10 ?; 340 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
cCKB_FIN: ( $i > $i > $o ) > $o ).
thf(func_def_2,type,
cCKB_INF: ( $i > $i > $o ) > $o ).
thf(func_def_3,type,
cCKB_INJ: ( $i > $i > $i > $i > $o ) > $o ).
thf(func_def_4,type,
cCKB_XPL: ( $i > $i > $i > $i > $o ) > ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_26,type,
sK3: $i > $i > $i > $i > $o ).
thf(func_def_27,type,
sK4: $i > $i > $i ).
thf(func_def_28,type,
sK5: $i > $i > $i ).
thf(f101,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f98,f100]) ).
thf(f100,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f99]) ).
thf(f99,plain,
( $false
| ~ spl0_1 ),
inference(equality_resolution,[status(thm)],[f97]) ).
thf(f97,plain,
( ! [X0: $i] : ( c1 != X0 )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f96]) ).
thf(f96,definition,
( spl0_1
<=> ! [X0: $i] : ( c1 != X0 ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f98,plain,
( spl0_1
| spl0_1 ),
inference(avatar_split_clause,[status(thm)],[f94,f96,f96]) ).
thf(f94,plain,
! [X0: $i,X1: $i] :
( ( c1 != X1 )
| ( c1 != X0 ) ),
inference(subsumption_resolution,[status(thm)],[f93,f68]) ).
thf(f68,plain,
c1 = sK2,
inference(equality_proxy_clausification,[status(thm)],[f67]) ).
thf(f67,plain,
( $true
= ( c1 = sK2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
( $true
= ( ( c1 = sK2 )
& ( c1 = sK1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( c1 = Y1 )
& ( c1 = Y0 ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( c1 = Y3 )
& ( c1 = Y2 )
& ( sK3 @ Y1 @ Y0 @ Y3 @ Y2 )
& ~ ( ( sK2 = Y3 )
& ( sK1 = Y2 ) ) ) ) ) ) ) )
& ( c1 = sK2 )
& ( c1 = sK1 ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( c1 = Y1 )
& ( c1 = Y0 ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( c1 = Y3 )
& ( c1 = Y2 )
& ( sK3 @ Y1 @ Y0 @ Y3 @ Y2 )
& ~ ( ( sK2 = Y3 )
& ( sK1 = Y2 ) ) ) ) ) ) ) )
& ( c1 = sK2 )
& ( c1 = sK1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( sK3 @ Y0 @ Y3 @ Y5 @ Y1 )
& ( sK3 @ Y2 @ Y4 @ Y5 @ Y1 ) )
=> ( ( Y4 = Y3 )
& ( Y2 = Y0 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ^ [Y0: $i > $i > $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( c1 = Y2 )
& ( c1 = Y1 ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( c1 = Y4 )
& ( c1 = Y3 )
& ( Y0 @ Y2 @ Y1 @ Y4 @ Y3 )
& ~ ( ( sK2 = Y4 )
& ( sK1 = Y3 ) ) ) ) ) ) ) )
& ( c1 = sK2 )
& ( c1 = sK1 )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y0 @ Y1 @ Y4 @ Y6 @ Y2 )
& ( Y0 @ Y3 @ Y5 @ Y6 @ Y2 ) )
=> ( ( Y5 = Y4 )
& ( Y3 = Y1 ) ) ) ) ) ) ) ) ) )
@ sK3 )
= $true ),
inference(sigma_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
( ( ?? @ ( $i > $i > $i > $i > $o )
@ ^ [Y0: $i > $i > $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( c1 = Y2 )
& ( c1 = Y1 ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( c1 = Y4 )
& ( c1 = Y3 )
& ( Y0 @ Y2 @ Y1 @ Y4 @ Y3 )
& ~ ( ( sK2 = Y4 )
& ( sK1 = Y3 ) ) ) ) ) ) ) )
& ( c1 = sK2 )
& ( c1 = sK1 )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y0 @ Y1 @ Y4 @ Y6 @ Y2 )
& ( Y0 @ Y3 @ Y5 @ Y6 @ Y2 ) )
=> ( ( Y5 = Y4 )
& ( Y3 = Y1 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f31]) ).
thf(f31,plain,
( ( ^ [Y0: $i] :
( ?? @ ( $i > $i > $i > $i > $o )
@ ^ [Y1: $i > $i > $i > $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( c1 = Y3 )
& ( c1 = Y2 ) )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] :
( ( c1 = Y5 )
& ( c1 = Y4 )
& ( Y1 @ Y3 @ Y2 @ Y5 @ Y4 )
& ~ ( ( Y0 = Y5 )
& ( sK1 = Y4 ) ) ) ) ) ) ) )
& ( c1 = Y0 )
& ( c1 = sK1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( Y1 @ Y2 @ Y5 @ Y7 @ Y3 )
& ( Y1 @ Y4 @ Y6 @ Y7 @ Y3 ) )
=> ( ( Y6 = Y5 )
& ( Y4 = Y2 ) ) ) ) ) ) ) ) ) ) )
@ sK2 )
= $true ),
inference(sigma_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ?? @ ( $i > $i > $i > $i > $o )
@ ^ [Y1: $i > $i > $i > $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( c1 = Y3 )
& ( c1 = Y2 ) )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] :
( ( c1 = Y5 )
& ( c1 = Y4 )
& ( Y1 @ Y3 @ Y2 @ Y5 @ Y4 )
& ~ ( ( Y0 = Y5 )
& ( sK1 = Y4 ) ) ) ) ) ) ) )
& ( c1 = Y0 )
& ( c1 = sK1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( Y1 @ Y2 @ Y5 @ Y7 @ Y3 )
& ( Y1 @ Y4 @ Y6 @ Y7 @ Y3 ) )
=> ( ( Y6 = Y5 )
& ( Y4 = Y2 ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f29]) ).
thf(f29,plain,
( $true
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ ( $i > $i > $i > $i > $o )
@ ^ [Y2: $i > $i > $i > $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( c1 = Y4 )
& ( c1 = Y3 ) )
=> ( ?? @ $i
@ ^ [Y5: $i] :
( ?? @ $i
@ ^ [Y6: $i] :
( ( c1 = Y6 )
& ( c1 = Y5 )
& ( Y2 @ Y4 @ Y3 @ Y6 @ Y5 )
& ~ ( ( Y1 = Y6 )
& ( Y0 = Y5 ) ) ) ) ) ) ) )
& ( c1 = Y1 )
& ( c1 = Y0 )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( ( Y2 @ Y3 @ Y6 @ Y8 @ Y4 )
& ( Y2 @ Y5 @ Y7 @ Y8 @ Y4 ) )
=> ( ( Y7 = Y6 )
& ( Y5 = Y3 ) ) ) ) ) ) ) ) ) ) ) )
@ sK1 ) ),
inference(sigma_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ ( $i > $i > $i > $i > $o )
@ ^ [Y2: $i > $i > $i > $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( c1 = Y4 )
& ( c1 = Y3 ) )
=> ( ?? @ $i
@ ^ [Y5: $i] :
( ?? @ $i
@ ^ [Y6: $i] :
( ( c1 = Y6 )
& ( c1 = Y5 )
& ( Y2 @ Y4 @ Y3 @ Y6 @ Y5 )
& ~ ( ( Y1 = Y6 )
& ( Y0 = Y5 ) ) ) ) ) ) ) )
& ( c1 = Y1 )
& ( c1 = Y0 )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( ( Y2 @ Y3 @ Y6 @ Y8 @ Y4 )
& ( Y2 @ Y5 @ Y7 @ Y8 @ Y4 ) )
=> ( ( Y7 = Y6 )
& ( Y5 = Y3 ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(not_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ ( $i > $i > $i > $i > $o )
@ ^ [Y2: $i > $i > $i > $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( c1 = Y4 )
& ( c1 = Y3 ) )
=> ( ?? @ $i
@ ^ [Y5: $i] :
( ?? @ $i
@ ^ [Y6: $i] :
( ( c1 = Y6 )
& ( c1 = Y5 )
& ( Y2 @ Y4 @ Y3 @ Y6 @ Y5 )
& ~ ( ( Y1 = Y6 )
& ( Y0 = Y5 ) ) ) ) ) ) ) )
& ( c1 = Y1 )
& ( c1 = Y0 )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( ( Y2 @ Y3 @ Y6 @ Y8 @ Y4 )
& ( Y2 @ Y5 @ Y7 @ Y8 @ Y4 ) )
=> ( ( Y7 = Y6 )
& ( Y5 = Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ^ [Y0: $i > $i > $o] :
~ ( ^ [Y1: $i > $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ?? @ ( $i > $i > $i > $i > $o )
@ ^ [Y4: $i > $i > $i > $i > $o] :
( ( ^ [Y5: $i > $i > $i > $i > $o,Y6: $i > $i > $o,Y7: $i,Y8: $i] :
( ( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y6 @ Y10 @ Y9 )
=> ( ?? @ $i
@ ^ [Y11: $i] :
( ?? @ $i
@ ^ [Y12: $i] :
( ( Y6 @ Y12 @ Y11 )
& ( Y5 @ Y10 @ Y9 @ Y12 @ Y11 )
& ~ ( ( Y7 = Y12 )
& ( Y8 = Y11 ) ) ) ) ) ) ) )
& ( Y6 @ Y7 @ Y8 ) )
@ Y4
@ Y1
@ Y3
@ Y2 )
& ( ^ [Y5: $i > $i > $i > $i > $o] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( !! @ $i
@ ^ [Y11: $i] :
( ( ( Y5 @ Y6 @ Y9 @ Y11 @ Y7 )
& ( Y5 @ Y8 @ Y10 @ Y11 @ Y7 ) )
=> ( ( Y10 = Y9 )
& ( Y8 = Y6 ) ) ) ) ) ) ) ) )
@ Y4 ) ) ) ) )
@ Y0 )
@ ^ [Y0: $i,Y1: $i] :
( ( c1 = Y0 )
& ( c1 = Y1 ) ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f19,f25]) ).
thf(f25,plain,
( cCKB_FIN
= ( ^ [Y0: $i > $i > $o] :
~ ( ^ [Y1: $i > $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ?? @ ( $i > $i > $i > $i > $o )
@ ^ [Y4: $i > $i > $i > $i > $o] :
( ( ^ [Y5: $i > $i > $i > $i > $o,Y6: $i > $i > $o,Y7: $i,Y8: $i] :
( ( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y6 @ Y10 @ Y9 )
=> ( ?? @ $i
@ ^ [Y11: $i] :
( ?? @ $i
@ ^ [Y12: $i] :
( ( Y6 @ Y12 @ Y11 )
& ( Y5 @ Y10 @ Y9 @ Y12 @ Y11 )
& ~ ( ( Y7 = Y12 )
& ( Y8 = Y11 ) ) ) ) ) ) ) )
& ( Y6 @ Y7 @ Y8 ) )
@ Y4
@ Y1
@ Y3
@ Y2 )
& ( ^ [Y5: $i > $i > $i > $i > $o] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( !! @ $i
@ ^ [Y11: $i] :
( ( ( Y5 @ Y6 @ Y9 @ Y11 @ Y7 )
& ( Y5 @ Y8 @ Y10 @ Y11 @ Y7 ) )
=> ( ( Y10 = Y9 )
& ( Y8 = Y6 ) ) ) ) ) ) ) ) )
@ Y4 ) ) ) ) )
@ Y0 ) ) ),
inference(definition_unfolding,[status(thm)],[f22,f24]) ).
thf(f24,plain,
( cCKB_INF
= ( ^ [Y0: $i > $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ ( $i > $i > $i > $i > $o )
@ ^ [Y3: $i > $i > $i > $i > $o] :
( ( ^ [Y4: $i > $i > $i > $i > $o,Y5: $i > $i > $o,Y6: $i,Y7: $i] :
( ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y5 @ Y9 @ Y8 )
=> ( ?? @ $i
@ ^ [Y10: $i] :
( ?? @ $i
@ ^ [Y11: $i] :
( ( Y5 @ Y11 @ Y10 )
& ( Y4 @ Y9 @ Y8 @ Y11 @ Y10 )
& ~ ( ( Y6 = Y11 )
& ( Y7 = Y10 ) ) ) ) ) ) ) )
& ( Y5 @ Y6 @ Y7 ) )
@ Y3
@ Y0
@ Y2
@ Y1 )
& ( ^ [Y4: $i > $i > $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( ( Y4 @ Y5 @ Y8 @ Y10 @ Y6 )
& ( Y4 @ Y7 @ Y9 @ Y10 @ Y6 ) )
=> ( ( Y9 = Y8 )
& ( Y7 = Y5 ) ) ) ) ) ) ) ) )
@ Y3 ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f20,f21,f23]) ).
thf(f23,plain,
( cCKB_INJ
= ( ^ [Y0: $i > $i > $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y0 @ Y1 @ Y4 @ Y6 @ Y2 )
& ( Y0 @ Y3 @ Y5 @ Y6 @ Y2 ) )
=> ( ( Y5 = Y4 )
& ( Y3 = Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( cCKB_INJ
= ( ^ [Y0: $i > $i > $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y0 @ Y1 @ Y4 @ Y6 @ Y2 )
& ( Y0 @ Y3 @ Y5 @ Y6 @ Y2 ) )
=> ( ( Y5 = Y4 )
& ( Y3 = Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
( cCKB_INJ
= ( ^ [X0: $i > $i > $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( ( X0 @ X4 @ X2 @ X1 @ X5 )
& ( X0 @ X6 @ X3 @ X1 @ X5 ) )
=> ( ( X4 = X6 )
& ( X2 = X3 ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( cCKB_INJ
= ( ^ [X0: $i > $i > $i > $i > $o] :
! [X5: $i,X2: $i,X4: $i,X1: $i,X6: $i,X3: $i] :
( ( ( X0 @ X1 @ X2 @ X5 @ X6 )
& ( X0 @ X3 @ X4 @ X5 @ X6 ) )
=> ( ( X1 = X3 )
& ( X2 = X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.gaSco8raog/DTF2THF_16387.p',cCKB_INJ_def) ).
thf(f21,plain,
( cCKB_XPL
= ( ^ [Y0: $i > $i > $i > $i > $o,Y1: $i > $i > $o,Y2: $i,Y3: $i] :
( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y1 @ Y5 @ Y4 )
=> ( ?? @ $i
@ ^ [Y6: $i] :
( ?? @ $i
@ ^ [Y7: $i] :
( ( Y1 @ Y7 @ Y6 )
& ( Y0 @ Y5 @ Y4 @ Y7 @ Y6 )
& ~ ( ( Y2 = Y7 )
& ( Y3 = Y6 ) ) ) ) ) ) ) )
& ( Y1 @ Y2 @ Y3 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( cCKB_XPL
= ( ^ [Y0: $i > $i > $i > $i > $o,Y1: $i > $i > $o,Y2: $i,Y3: $i] :
( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y1 @ Y5 @ Y4 )
=> ( ?? @ $i
@ ^ [Y6: $i] :
( ?? @ $i
@ ^ [Y7: $i] :
( ( Y1 @ Y7 @ Y6 )
& ( Y0 @ Y5 @ Y4 @ Y7 @ Y6 )
& ~ ( ( Y2 = Y7 )
& ( Y3 = Y6 ) ) ) ) ) ) ) )
& ( Y1 @ Y2 @ Y3 ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ^ [X0: $i > $i > $i > $i > $o,X1: $i > $i > $o,X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
& ! [X4: $i,X5: $i] :
( ( X1 @ X4 @ X5 )
=> ? [X6: $i,X7: $i] :
( ~ ( ( X3 = X7 )
& ( X2 = X6 ) )
& ( X0 @ X4 @ X5 @ X6 @ X7 )
& ( X1 @ X6 @ X7 ) ) ) ) )
= cCKB_XPL ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( ( ^ [X0: $i > $i > $i > $i > $o,X7: $i > $i > $o,X8: $i,X9: $i] :
( ( X7 @ X8 @ X9 )
& ! [X10: $i,X11: $i] :
( ( X7 @ X10 @ X11 )
=> ? [X5: $i,X6: $i] :
( ~ ( ( X6 = X9 )
& ( X5 = X8 ) )
& ( X0 @ X10 @ X11 @ X5 @ X6 )
& ( X7 @ X5 @ X6 ) ) ) ) )
= cCKB_XPL ),
file('/export/starexec/sandbox/tmp/tmp.gaSco8raog/DTF2THF_16387.p',cCKB_XPL_def) ).
thf(f20,plain,
( cCKB_INF
= ( ^ [Y0: $i > $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ ( $i > $i > $i > $i > $o )
@ ^ [Y3: $i > $i > $i > $i > $o] :
( ( cCKB_XPL @ Y3 @ Y0 @ Y2 @ Y1 )
& ( cCKB_INJ @ Y3 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( cCKB_INF
= ( ^ [Y0: $i > $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ ( $i > $i > $i > $i > $o )
@ ^ [Y3: $i > $i > $i > $i > $o] :
( ( cCKB_XPL @ Y3 @ Y0 @ Y2 @ Y1 )
& ( cCKB_INJ @ Y3 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [X0: $i > $i > $o] :
? [X1: $i > $i > $i > $i > $o,X2: $i,X3: $i] :
( ( cCKB_INJ @ X1 )
& ( cCKB_XPL @ X1 @ X0 @ X2 @ X3 ) ) )
= cCKB_INF ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( ( ^ [X7: $i > $i > $o] :
? [X0: $i > $i > $i > $i > $o,X8: $i,X9: $i] :
( ( cCKB_INJ @ X0 )
& ( cCKB_XPL @ X0 @ X7 @ X8 @ X9 ) ) )
= cCKB_INF ),
file('/export/starexec/sandbox/tmp/tmp.gaSco8raog/DTF2THF_16387.p',cCKB_INF_def) ).
thf(f22,plain,
( cCKB_FIN
= ( ^ [Y0: $i > $i > $o] :
~ ( cCKB_INF @ Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( cCKB_FIN
= ( ^ [Y0: $i > $i > $o] :
~ ( cCKB_INF @ Y0 ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
( cCKB_FIN
= ( ^ [X0: $i > $i > $o] :
~ ( cCKB_INF @ X0 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( cCKB_FIN
= ( ^ [X7: $i > $i > $o] :
~ ( cCKB_INF @ X7 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.gaSco8raog/DTF2THF_16387.p',cCKB_FIN_def) ).
thf(f19,plain,
( ( cCKB_FIN
@ ^ [Y0: $i,Y1: $i] :
( ( c1 = Y0 )
& ( c1 = Y1 ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ( cCKB_FIN
@ ^ [Y0: $i,Y1: $i] :
( ( c1 = Y0 )
& ( c1 = Y1 ) ) )
!= $true ),
inference(flattening,[status(thm)],[f13]) ).
thf(f13,plain,
( ( cCKB_FIN
@ ^ [Y0: $i,Y1: $i] :
( ( c1 = Y0 )
& ( c1 = Y1 ) ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
~ ( cCKB_FIN
@ ^ [X0: $i,X1: $i] :
( ( c1 = X1 )
& ( c1 = X0 ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( cCKB_FIN
@ ^ [X5: $i,X6: $i] :
( ( c1 = X6 )
& ( c1 = X5 ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
( cCKB_FIN
@ ^ [X5: $i,X6: $i] :
( ( c1 = X6 )
& ( c1 = X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.gaSco8raog/DTF2THF_16387.p',cL3000) ).
thf(f93,plain,
! [X0: $i,X1: $i] :
( ( c1 != sK2 )
| ( c1 != X0 )
| ( c1 != X1 ) ),
inference(duplicate_literal_removal,[status(thm)],[f92]) ).
thf(f92,plain,
! [X0: $i,X1: $i] :
( ( c1 != X0 )
| ( c1 != X1 )
| ( c1 != X1 )
| ( c1 != sK2 )
| ( c1 != X0 ) ),
inference(superposition,[status(thm)],[f91,f57]) ).
thf(f57,plain,
! [X2: $i,X1: $i] :
( ( c1
= ( sK5 @ X1 @ X2 ) )
| ( c1 != X2 )
| ( c1 != X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
! [X2: $i,X1: $i] :
( ( ( c1
= ( sK5 @ X1 @ X2 ) )
= $true )
| ( c1 != X2 )
| ( c1 != X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( c1 = X2 ) )
| ( ( c1
= ( sK5 @ X1 @ X2 ) )
= $true )
| ( c1 != X1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
! [X2: $i,X1: $i] :
( ( ( ( c1
= ( sK5 @ X1 @ X2 ) )
& ( c1
= ( sK4 @ X1 @ X2 ) ) )
= $true )
| ( c1 != X1 )
| ( $false
= ( c1 = X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
! [X2: $i,X1: $i] :
( ( c1 != X1 )
| ( $true
= ( ( c1
= ( sK5 @ X1 @ X2 ) )
& ( c1
= ( sK4 @ X1 @ X2 ) )
& ( sK3 @ X2 @ X1 @ ( sK5 @ X1 @ X2 ) @ ( sK4 @ X1 @ X2 ) ) ) )
| ( $false
= ( c1 = X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f49]) ).
thf(f49,plain,
! [X2: $i,X1: $i] :
( ( c1 != X1 )
| ( ( ( c1
= ( sK5 @ X1 @ X2 ) )
& ( c1
= ( sK4 @ X1 @ X2 ) )
& ( sK3 @ X2 @ X1 @ ( sK5 @ X1 @ X2 ) @ ( sK4 @ X1 @ X2 ) )
& ~ ( ( sK2
= ( sK5 @ X1 @ X2 ) )
& ( sK1
= ( sK4 @ X1 @ X2 ) ) ) )
= $true )
| ( $false
= ( c1 = X2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f48]) ).
thf(f48,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( c1 = Y0 )
& ( c1
= ( sK4 @ X1 @ X2 ) )
& ( sK3 @ X2 @ X1 @ Y0 @ ( sK4 @ X1 @ X2 ) )
& ~ ( ( sK2 = Y0 )
& ( sK1
= ( sK4 @ X1 @ X2 ) ) ) )
@ ( sK5 @ X1 @ X2 ) )
= $true )
| ( c1 != X1 )
| ( $false
= ( c1 = X2 ) ) ),
inference(sigma_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( c1 = Y0 )
& ( c1
= ( sK4 @ X1 @ X2 ) )
& ( sK3 @ X2 @ X1 @ Y0 @ ( sK4 @ X1 @ X2 ) )
& ~ ( ( sK2 = Y0 )
& ( sK1
= ( sK4 @ X1 @ X2 ) ) ) ) ) )
| ( $false
= ( c1 = X2 ) )
| ( c1 != X1 ) ),
inference(beta_eta_normalization,[status(thm)],[f46]) ).
thf(f46,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( c1 = X2 ) )
| ( c1 != X1 )
| ( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( c1 = Y1 )
& ( c1 = Y0 )
& ( sK3 @ X2 @ X1 @ Y1 @ Y0 )
& ~ ( ( sK2 = Y1 )
& ( sK1 = Y0 ) ) ) )
@ ( sK4 @ X1 @ X2 ) )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
! [X2: $i,X1: $i] :
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( c1 = Y1 )
& ( c1 = Y0 )
& ( sK3 @ X2 @ X1 @ Y1 @ Y0 )
& ~ ( ( sK2 = Y1 )
& ( sK1 = Y0 ) ) ) ) )
= $true )
| ( $false
= ( c1 = X2 ) )
| ( c1 != X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( c1 = X1 ) )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( c1 = Y1 )
& ( c1 = Y0 )
& ( sK3 @ X2 @ X1 @ Y1 @ Y0 )
& ~ ( ( sK2 = Y1 )
& ( sK1 = Y0 ) ) ) ) )
= $true )
| ( $false
= ( c1 = X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( c1 = X2 )
& ( c1 = X1 ) ) )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( c1 = Y1 )
& ( c1 = Y0 )
& ( sK3 @ X2 @ X1 @ Y1 @ Y0 )
& ~ ( ( sK2 = Y1 )
& ( sK1 = Y0 ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
! [X2: $i,X1: $i] :
( ( ( ( c1 = X2 )
& ( c1 = X1 ) )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( c1 = Y1 )
& ( c1 = Y0 )
& ( sK3 @ X2 @ X1 @ Y1 @ Y0 )
& ~ ( ( sK2 = Y1 )
& ( sK1 = Y0 ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f41]) ).
thf(f41,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( ( c1 = Y0 )
& ( c1 = X1 ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( c1 = Y2 )
& ( c1 = Y1 )
& ( sK3 @ Y0 @ X1 @ Y2 @ Y1 )
& ~ ( ( sK2 = Y2 )
& ( sK1 = Y1 ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( c1 = Y0 )
& ( c1 = X1 ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( c1 = Y2 )
& ( c1 = Y1 )
& ( sK3 @ Y0 @ X1 @ Y2 @ Y1 )
& ~ ( ( sK2 = Y2 )
& ( sK1 = Y1 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f39]) ).
thf(f39,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( c1 = Y1 )
& ( c1 = Y0 ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( c1 = Y3 )
& ( c1 = Y2 )
& ( sK3 @ Y1 @ Y0 @ Y3 @ Y2 )
& ~ ( ( sK2 = Y3 )
& ( sK1 = Y2 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( c1 = Y1 )
& ( c1 = Y0 ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( c1 = Y3 )
& ( c1 = Y2 )
& ( sK3 @ Y1 @ Y0 @ Y3 @ Y2 )
& ~ ( ( sK2 = Y3 )
& ( sK1 = Y2 ) ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
thf(f91,plain,
! [X0: $i,X1: $i] :
( ( ( sK5 @ X0 @ X1 )
!= sK2 )
| ( c1 != X1 )
| ( c1 != X0 ) ),
inference(subsumption_resolution,[status(thm)],[f90,f69]) ).
thf(f69,plain,
c1 = sK1,
inference(equality_proxy_clausification,[status(thm)],[f66]) ).
thf(f66,plain,
( ( c1 = sK1 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f37]) ).
thf(f90,plain,
! [X0: $i,X1: $i] :
( ( c1 != sK1 )
| ( c1 != X0 )
| ( ( sK5 @ X0 @ X1 )
!= sK2 )
| ( c1 != X1 ) ),
inference(duplicate_literal_removal,[status(thm)],[f89]) ).
thf(f89,plain,
! [X0: $i,X1: $i] :
( ( c1 != X1 )
| ( c1 != X0 )
| ( c1 != X0 )
| ( ( sK5 @ X0 @ X1 )
!= sK2 )
| ( c1 != sK1 )
| ( c1 != X1 ) ),
inference(superposition,[status(thm)],[f65,f59]) ).
thf(f59,plain,
! [X2: $i,X1: $i] :
( ( c1
= ( sK4 @ X1 @ X2 ) )
| ( c1 != X2 )
| ( c1 != X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f58]) ).
thf(f58,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( c1 = X2 ) )
| ( c1 != X1 )
| ( c1
= ( sK4 @ X1 @ X2 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
! [X2: $i,X1: $i] :
( ( c1 != X1 )
| ( ( c1
= ( sK4 @ X1 @ X2 ) )
= $true )
| ( $false
= ( c1 = X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f53]) ).
thf(f65,plain,
! [X2: $i,X1: $i] :
( ( sK1
!= ( sK4 @ X1 @ X2 ) )
| ( c1 != X1 )
| ( c1 != X2 )
| ( ( sK5 @ X1 @ X2 )
!= sK2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f64]) ).
thf(f64,plain,
! [X2: $i,X1: $i] :
( ( c1 != X1 )
| ( ( sK5 @ X1 @ X2 )
!= sK2 )
| ( c1 != X2 )
| ( $false
= ( sK1
= ( sK4 @ X1 @ X2 ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f63]) ).
thf(f63,plain,
! [X2: $i,X1: $i] :
( ( ( sK2
= ( sK5 @ X1 @ X2 ) )
= $false )
| ( $false
= ( sK1
= ( sK4 @ X1 @ X2 ) ) )
| ( c1 != X2 )
| ( c1 != X1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f62]) ).
thf(f62,plain,
! [X2: $i,X1: $i] :
( ( c1 != X2 )
| ( $false
= ( ( sK2
= ( sK5 @ X1 @ X2 ) )
& ( sK1
= ( sK4 @ X1 @ X2 ) ) ) )
| ( c1 != X1 ) ),
inference(not_proxy_clausification,[status(thm)],[f61]) ).
thf(f61,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( ( sK2
= ( sK5 @ X1 @ X2 ) )
& ( sK1
= ( sK4 @ X1 @ X2 ) ) ) )
= $true )
| ( c1 != X1 )
| ( c1 != X2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f50]) ).
thf(f50,plain,
! [X2: $i,X1: $i] :
( ( c1 != X1 )
| ( $false
= ( c1 = X2 ) )
| ( ( ~ ( ( sK2
= ( sK5 @ X1 @ X2 ) )
& ( sK1
= ( sK4 @ X1 @ X2 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : PUZ107^5 : TPTP v9.2.1. Bugfixed v6.2.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.33 % Computer : n021.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue Feb 24 11:33:08 EST 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.47 ---- Original DTF file ---
% 0.19/0.47 thf(spec,logic,$$dhol).
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 % File : PUZ107^5 : TPTP v9.2.1. Bugfixed v6.2.0.
% 0.19/0.47 % Domain : Puzzles
% 0.19/0.47 % Problem : TPS problem from CHECKERBOARD-THMS
% 0.19/0.47 % Version : Especial.
% 0.19/0.47 % English :
% 0.19/0.47
% 0.19/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.47 % Source : [Bro09]
% 0.19/0.47 % Names : tps_0672 [Bro09]
% 0.19/0.47
% 0.19/0.47 % Status : Theorem
% 0.19/0.47 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.31 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0
% 0.19/0.47 % Syntax : Number of formulae : 10 ( 4 unt; 5 typ; 4 def)
% 0.19/0.47 % Number of atoms : 18 ( 10 equ; 0 cnn)
% 0.19/0.47 % Maximal formula atoms : 3 ( 3 avg)
% 0.19/0.47 % Number of connectives : 37 ( 2 ~; 0 |; 8 &; 25 @)
% 0.19/0.47 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.19/0.47 % Maximal formula depth : 5 ( 2 avg)
% 0.19/0.47 % Number of types : 2 ( 0 usr)
% 0.19/0.47 % Number of type conns : 39 ( 39 >; 0 *; 0 +; 0 <<)
% 0.19/0.47 % Number of symbols : 6 ( 5 usr; 1 con; 0-4 aty)
% 0.19/0.47 % Number of variables : 22 ( 9 ^; 8 !; 5 ?; 22 :)
% 0.19/0.47 % SPC : TH0_THM_EQU_NAR
% 0.19/0.47
% 0.19/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.47 % Bugfixes : v5.2.0 - Added missing type declarations.
% 0.19/0.47 % : v6.2.0 - Reordered definitions.
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 thf(c1_type,type,
% 0.19/0.47 c1: $i ).
% 0.19/0.47
% 0.19/0.47 thf(cCKB_FIN_type,type,
% 0.19/0.47 cCKB_FIN: ( $i > $i > $o ) > $o ).
% 0.19/0.47
% 0.19/0.47 thf(cCKB_INF_type,type,
% 0.19/0.47 cCKB_INF: ( $i > $i > $o ) > $o ).
% 0.19/0.47
% 0.19/0.47 thf(cCKB_INJ_type,type,
% 0.19/0.47 cCKB_INJ: ( $i > $i > $i > $i > $o ) > $o ).
% 0.19/0.47
% 0.19/0.47 thf(cCKB_XPL_type,type,
% 0.19/0.47 cCKB_XPL: ( $i > $i > $i > $i > $o ) > ( $i > $i > $o ) > $i > $i > $o ).
% 0.19/0.47
% 0.19/0.47 thf(cCKB_INJ_def,definition,
% 0.19/0.47 ( cCKB_INJ
% 0.19/0.47 = ( ^ [Xh: $i > $i > $i > $i > $o] :
% 0.19/0.47 ! [Xx1: $i,Xy1: $i,Xx2: $i,Xy2: $i,Xu: $i,Xv: $i] :
% 0.19/0.47 ( ( ( Xh @ Xx1 @ Xy1 @ Xu @ Xv )
% 0.19/0.47 & ( Xh @ Xx2 @ Xy2 @ Xu @ Xv ) )
% 0.19/0.47 => ( ( Xx1 = Xx2 )
% 0.19/0.47 & ( Xy1 = Xy2 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(cCKB_XPL_def,definition,
% 0.19/0.47 ( cCKB_XPL
% 0.19/0.47 = ( ^ [Xh: $i > $i > $i > $i > $o,Xk: $i > $i > $o,Xm: $i,Xn: $i] :
% 0.19/0.47 ( ( Xk @ Xm @ Xn )
% 0.19/0.47 & ! [Xx: $i,Xy: $i] :
% 0.19/0.47 ( ( Xk @ Xx @ Xy )
% 0.19/0.47 => ? [Xu: $i,Xv: $i] :
% 0.19/0.47 ( ( Xh @ Xx @ Xy @ Xu @ Xv )
% 0.19/0.47 & ( Xk @ Xu @ Xv )
% 0.19/0.47 & ~ ( ( Xu = Xm )
% 0.19/0.47 & ( Xv = Xn ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(cCKB_INF_def,definition,
% 0.19/0.47 ( cCKB_INF
% 0.19/0.47 = ( ^ [Xk: $i > $i > $o] :
% 0.19/0.47 ? [Xh: $i > $i > $i > $i > $o,Xm: $i,Xn: $i] :
% 0.19/0.47 ( ( cCKB_INJ @ Xh )
% 0.19/0.47 & ( cCKB_XPL @ Xh @ Xk @ Xm @ Xn ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(cCKB_FIN_def,definition,
% 0.19/0.47 ( cCKB_FIN
% 0.19/0.47 = ( ^ [Xk: $i > $i > $o] :
% 0.19/0.47 ~ ( cCKB_INF @ Xk ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(cL3000,conjecture,
% 0.19/0.47 ( cCKB_FIN
% 0.19/0.47 @ ^ [Xu: $i,Xv: $i] :
% 0.19/0.47 ( ( Xu = c1 )
% 0.19/0.47 & ( Xv = c1 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 ------------------------
% 1.72/1.42 ---- Embedded in THF ---
% 1.72/1.42 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.72/1.42 %%% Generated on Tue Feb 24 11:33:09 EST 2026
% 1.72/1.42 %%% using '$$dhol' embedding, version 1.3.0.
% 1.72/1.42 %%% Logic specification used:
% 1.72/1.42 %%% thf(spec, logic, $$dhol).
% 1.72/1.42
% 1.72/1.42 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.gaSco8raog/DTF2DTF16387.p
% See solution above
% 1.72/1.42 ------------------------
% 1.72/1.43 ---- Cleaned THF ---
% 1.72/1.43 thf(c1_type,type,
% 1.72/1.43 c1: $i ).
% 1.72/1.43
% 1.72/1.43 thf(cCKB_FIN_type,type,
% 1.72/1.43 cCKB_FIN: ( $i > $i > $o ) > $o ).
% 1.72/1.43
% 1.72/1.43 thf(cCKB_INF_type,type,
% 1.72/1.43 cCKB_INF: ( $i > $i > $o ) > $o ).
% 1.72/1.43
% 1.72/1.43 thf(cCKB_INJ_type,type,
% 1.72/1.43 cCKB_INJ: ( $i > $i > $i > $i > $o ) > $o ).
% 1.72/1.43
% 1.72/1.43 thf(cCKB_XPL_type,type,
% 1.72/1.43 cCKB_XPL: ( $i > $i > $i > $i > $o ) > ( $i > $i > $o ) > $i > $i > $o ).
% 1.72/1.43
% 1.72/1.43 thf(cCKB_INJ_def,definition,
% 1.72/1.43 ( cCKB_INJ
% 1.72/1.43 = ( ^ [Xh: $i > $i > $i > $i > $o] :
% 1.72/1.43 ! [Xx1: $i,Xy1: $i,Xx2: $i,Xy2: $i,Xu: $i,Xv: $i] :
% 1.72/1.43 ( ( ( Xh @ Xx1 @ Xy1 @ Xu @ Xv )
% 1.72/1.43 & ( Xh @ Xx2 @ Xy2 @ Xu @ Xv ) )
% 1.72/1.43 => ( ( Xx1 = Xx2 )
% 1.72/1.43 & ( Xy1 = Xy2 ) ) ) ) ) ).
% 1.72/1.43
% 1.72/1.43 thf(cCKB_XPL_def,definition,
% 1.72/1.43 ( cCKB_XPL
% 1.72/1.43 = ( ^ [Xh: $i > $i > $i > $i > $o,Xk: $i > $i > $o,Xm: $i,Xn: $i] :
% 1.72/1.43 ( ( Xk @ Xm @ Xn )
% 1.72/1.43 & ! [Xx: $i,Xy: $i] :
% 1.72/1.43 ( ( Xk @ Xx @ Xy )
% 1.72/1.43 => ? [Xu: $i,Xv: $i] :
% 1.72/1.43 ( ( Xh @ Xx @ Xy @ Xu @ Xv )
% 1.72/1.43 & ( Xk @ Xu @ Xv )
% 1.72/1.43 & ~ ( ( Xu = Xm )
% 1.72/1.43 & ( Xv = Xn ) ) ) ) ) ) ) ).
% 1.72/1.43
% 1.72/1.43 thf(cCKB_INF_def,definition,
% 1.72/1.43 ( cCKB_INF
% 1.72/1.43 = ( ^ [Xk: $i > $i > $o] :
% 1.72/1.43 ? [Xh: $i > $i > $i > $i > $o,Xm: $i,Xn: $i] :
% 1.72/1.43 ( ( cCKB_INJ @ Xh )
% 1.72/1.43 & ( cCKB_XPL @ Xh @ Xk @ Xm @ Xn ) ) ) ) ).
% 1.72/1.43
% 1.72/1.43 thf(cCKB_FIN_def,definition,
% 1.72/1.43 ( cCKB_FIN
% 1.72/1.43 = ( ^ [Xk: $i > $i > $o] :
% 1.72/1.43 ~ ( cCKB_INF @ Xk ) ) ) ).
% 1.72/1.43
% 1.72/1.43 thf(cL3000,conjecture,
% 1.72/1.43 ( cCKB_FIN
% 1.72/1.43 @ ^ [Xu: $i,Xv: $i] :
% 1.72/1.43 ( ( Xu = c1 )
% 1.72/1.43 & ( Xv = c1 ) ) ) ).
% 1.72/1.43 ------------------------
% 1.72/1.45 % (16485)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_16387 for (2999ds/4Mi)
% 1.72/1.45 % (16484)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_16387 for (2999ds/183Mi)
% 1.72/1.45 % (16486)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_16387 for (2999ds/27Mi)
% 1.72/1.45 % (16489)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_16387 for (2999ds/275Mi)
% 1.72/1.45 % (16490)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_16387 for (2999ds/18Mi)
% 1.72/1.45 % (16487)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_16387 for (2999ds/2Mi)
% 1.72/1.45 % (16488)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_16387 for (2999ds/2Mi)
% 1.72/1.45 % (16487)Instruction limit reached!
% 1.72/1.45 % (16487)------------------------------
% 1.72/1.45 % (16487)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.45 % (16487)Termination reason: Unknown
% 1.72/1.45 % (16487)Termination phase: Property scanning
% 1.72/1.45
% 1.72/1.45 % (16487)Memory used [KB]: 1023
% 1.72/1.45 % (16487)Time elapsed: 0.003 s
% 1.72/1.45 % (16487)Instructions burned: 2 (million)
% 1.72/1.45 % (16487)------------------------------
% 1.72/1.45 % (16487)------------------------------
% 1.72/1.45 % (16488)Instruction limit reached!
% 1.72/1.45 % (16488)------------------------------
% 1.72/1.45 % (16488)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.45 % (16488)Termination reason: Unknown
% 1.72/1.45 % (16488)Termination phase: shuffling
% 1.72/1.45
% 1.72/1.45 % (16488)Memory used [KB]: 1023
% 1.72/1.45 % (16488)Time elapsed: 0.003 s
% 1.72/1.45 % (16488)Instructions burned: 2 (million)
% 1.72/1.45 % (16488)------------------------------
% 1.72/1.45 % (16488)------------------------------
% 1.72/1.46 % (16485)Instruction limit reached!
% 1.72/1.46 % (16485)------------------------------
% 1.72/1.46 % (16485)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.46 % (16485)Termination reason: Unknown
% 1.72/1.46 % (16485)Termination phase: Saturation
% 1.72/1.46
% 1.72/1.46 % (16485)Memory used [KB]: 1023
% 1.72/1.46 % (16485)Time elapsed: 0.004 s
% 1.72/1.46 % (16485)Instructions burned: 4 (million)
% 1.72/1.46 % (16485)------------------------------
% 1.72/1.46 % (16485)------------------------------
% 1.72/1.46 % (16489)Refutation not found, incomplete strategy
% 1.72/1.46 % (16489)------------------------------
% 1.72/1.46 % (16489)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.46 % (16489)Termination reason: Refutation not found, incomplete strategy
% 1.72/1.46
% 1.72/1.46
% 1.72/1.46 % (16489)Memory used [KB]: 5500
% 1.72/1.46 % (16489)Time elapsed: 0.005 s
% 1.72/1.46 % (16489)Instructions burned: 4 (million)
% 1.72/1.46 % (16489)------------------------------
% 1.72/1.46 % (16489)------------------------------
% 1.72/1.46 % (16484)First to succeed.
% 1.72/1.46 % (16486)Also succeeded, but the first one will report.
% 1.72/1.47 % (16484)Refutation found. Thanks to Tanya!
% 1.72/1.47 % SZS status Theorem for DTF2THF_16387
% 1.72/1.47 % SZS output start Proof for DTF2THF_16387
% 1.72/1.47 thf(func_def_1, type, cCKB_FIN: ($i > $i > $o) > $o).
% 1.72/1.47 thf(func_def_2, type, cCKB_INF: ($i > $i > $o) > $o).
% 1.72/1.47 thf(func_def_3, type, cCKB_INJ: ($i > $i > $i > $i > $o) > $o).
% 1.72/1.47 thf(func_def_4, type, cCKB_XPL: ($i > $i > $i > $i > $o) > ($i > $i > $o) > $i > $i > $o).
% 1.72/1.47 thf(func_def_26, type, sK3: $i > $i > $i > $i > $o).
% 1.72/1.47 thf(func_def_27, type, sK4: $i > $i > $i).
% 1.72/1.47 thf(func_def_28, type, sK5: $i > $i > $i).
% 1.72/1.47 thf(f101,plain,(
% 1.72/1.47 $false),
% 1.72/1.47 inference(avatar_sat_refutation,[status(thm)],[f98,f100])).
% 1.72/1.47 thf(f100,plain,(
% 1.72/1.47 ~spl0_1),
% 1.72/1.47 inference(avatar_contradiction_clause,[status(thm)],[f99])).
% 1.72/1.47 thf(f99,plain,(
% 1.72/1.47 $false | ~spl0_1),
% 1.72/1.47 inference(equality_resolution,[status(thm)],[f97])).
% 1.72/1.47 thf(f97,plain,(
% 1.72/1.47 ( ! [X0 : $i] : ((c1 != X0)) ) | ~spl0_1),
% 1.72/1.47 inference(avatar_component_clause,[status(thm)],[f96])).
% 1.72/1.47 thf(f96,definition,(
% 1.72/1.47 spl0_1 <=> ! [X0 : $i] : (c1 != X0)),
% 1.72/1.47 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.72/1.47 thf(f98,plain,(
% 1.72/1.47 spl0_1 | spl0_1),
% 1.72/1.47 inference(avatar_split_clause,[status(thm)],[f94,f96,f96])).
% 1.72/1.47 thf(f94,plain,(
% 1.72/1.47 ( ! [X0 : $i,X1 : $i] : ((c1 != X1) | (c1 != X0)) )),
% 1.72/1.47 inference(subsumption_resolution,[status(thm)],[f93,f68])).
% 1.72/1.47 thf(f68,plain,(
% 1.72/1.47 (c1 = sK2)),
% 1.72/1.47 inference(equality_proxy_clausification,[status(thm)],[f67])).
% 1.72/1.47 thf(f67,plain,(
% 1.72/1.47 ($true = (c1 = sK2))),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f37])).
% 1.72/1.47 thf(f37,plain,(
% 1.72/1.47 ($true = ((c1 = sK2) & (c1 = sK1)))),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 1.72/1.47 thf(f36,plain,(
% 1.72/1.47 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((c1 = Y1) & (c1 = Y0)) => (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((((c1 = Y3) & (c1 = Y2)) & (sK3 @ Y1 @ Y0 @ Y3 @ Y2)) & (~ ((sK2 = Y3) & (sK1 = Y2))))))))))))) & ((c1 = sK2) & (c1 = sK1))) = $true)),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f34])).
% 1.72/1.47 thf(f34,plain,(
% 1.72/1.47 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((c1 = Y1) & (c1 = Y0)) => (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((((c1 = Y3) & (c1 = Y2)) & (sK3 @ Y1 @ Y0 @ Y3 @ Y2)) & (~ ((sK2 = Y3) & (sK1 = Y2))))))))))))) & ((c1 = sK2) & (c1 = sK1))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((sK3 @ Y0 @ Y3 @ Y5 @ Y1) & (sK3 @ Y2 @ Y4 @ Y5 @ Y1)) => ((Y4 = Y3) & (Y2 = Y0)))))))))))))))) = $true)),
% 1.72/1.47 inference(beta_eta_normalization,[status(thm)],[f33])).
% 1.72/1.47 thf(f33,plain,(
% 1.72/1.47 (((^[Y0 : $i > $i > $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((c1 = Y2) & (c1 = Y1)) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((c1 = Y4) & (c1 = Y3)) & (Y0 @ Y2 @ Y1 @ Y4 @ Y3)) & (~ ((sK2 = Y4) & (sK1 = Y3))))))))))))) & ((c1 = sK2) & (c1 = sK1))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y0 @ Y1 @ Y4 @ Y6 @ Y2) & (Y0 @ Y3 @ Y5 @ Y6 @ Y2)) => ((Y5 = Y4) & (Y3 = Y1))))))))))))))))) @ sK3) = $true)),
% 1.72/1.47 inference(sigma_clausification,[status(thm)],[f32])).
% 1.72/1.47 thf(f32,plain,(
% 1.72/1.47 ((?? @ ($i > $i > $i > $i > $o) @ (^[Y0 : $i > $i > $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((c1 = Y2) & (c1 = Y1)) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((c1 = Y4) & (c1 = Y3)) & (Y0 @ Y2 @ Y1 @ Y4 @ Y3)) & (~ ((sK2 = Y4) & (sK1 = Y3))))))))))))) & ((c1 = sK2) & (c1 = sK1))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y0 @ Y1 @ Y4 @ Y6 @ Y2) & (Y0 @ Y3 @ Y5 @ Y6 @ Y2)) => ((Y5 = Y4) & (Y3 = Y1)))))))))))))))))) = $true)),
% 1.72/1.47 inference(beta_eta_normalization,[status(thm)],[f31])).
% 1.72/1.47 thf(f31,plain,(
% 1.72/1.47 (((^[Y0 : $i]: (?? @ ($i > $i > $i > $i > $o) @ (^[Y1 : $i > $i > $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((c1 = Y3) & (c1 = Y2)) => (?? @ $i @ (^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: ((((c1 = Y5) & (c1 = Y4)) & (Y1 @ Y3 @ Y2 @ Y5 @ Y4)) & (~ ((Y0 = Y5) & (sK1 = Y4))))))))))))) & ((c1 = Y0) & (c1 = sK1))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y1 @ Y2 @ Y5 @ Y7 @ Y3) & (Y1 @ Y4 @ Y6 @ Y7 @ Y3)) => ((Y6 = Y5) & (Y4 = Y2))))))))))))))))))) @ sK2) = $true)),
% 1.72/1.47 inference(sigma_clausification,[status(thm)],[f30])).
% 1.72/1.47 thf(f30,plain,(
% 1.72/1.47 ((?? @ $i @ (^[Y0 : $i]: (?? @ ($i > $i > $i > $i > $o) @ (^[Y1 : $i > $i > $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((c1 = Y3) & (c1 = Y2)) => (?? @ $i @ (^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: ((((c1 = Y5) & (c1 = Y4)) & (Y1 @ Y3 @ Y2 @ Y5 @ Y4)) & (~ ((Y0 = Y5) & (sK1 = Y4))))))))))))) & ((c1 = Y0) & (c1 = sK1))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y1 @ Y2 @ Y5 @ Y7 @ Y3) & (Y1 @ Y4 @ Y6 @ Y7 @ Y3)) => ((Y6 = Y5) & (Y4 = Y2)))))))))))))))))))) = $true)),
% 1.72/1.47 inference(beta_eta_normalization,[status(thm)],[f29])).
% 1.72/1.47 thf(f29,plain,(
% 1.72/1.47 ($true = ((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ ($i > $i > $i > $i > $o) @ (^[Y2 : $i > $i > $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((c1 = Y4) & (c1 = Y3)) => (?? @ $i @ (^[Y5 : $i]: (?? @ $i @ (^[Y6 : $i]: ((((c1 = Y6) & (c1 = Y5)) & (Y2 @ Y4 @ Y3 @ Y6 @ Y5)) & (~ ((Y1 = Y6) & (Y0 = Y5))))))))))))) & ((c1 = Y1) & (c1 = Y0))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y2 @ Y3 @ Y6 @ Y8 @ Y4) & (Y2 @ Y5 @ Y7 @ Y8 @ Y4)) => ((Y7 = Y6) & (Y5 = Y3))))))))))))))))))))) @ sK1))),
% 1.72/1.47 inference(sigma_clausification,[status(thm)],[f28])).
% 1.72/1.47 thf(f28,plain,(
% 1.72/1.47 ((?? @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ ($i > $i > $i > $i > $o) @ (^[Y2 : $i > $i > $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((c1 = Y4) & (c1 = Y3)) => (?? @ $i @ (^[Y5 : $i]: (?? @ $i @ (^[Y6 : $i]: ((((c1 = Y6) & (c1 = Y5)) & (Y2 @ Y4 @ Y3 @ Y6 @ Y5)) & (~ ((Y1 = Y6) & (Y0 = Y5))))))))))))) & ((c1 = Y1) & (c1 = Y0))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y2 @ Y3 @ Y6 @ Y8 @ Y4) & (Y2 @ Y5 @ Y7 @ Y8 @ Y4)) => ((Y7 = Y6) & (Y5 = Y3)))))))))))))))))))))) = $true)),
% 1.72/1.47 inference(not_proxy_clausification,[status(thm)],[f27])).
% 1.72/1.47 thf(f27,plain,(
% 1.72/1.47 ((~ (?? @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ ($i > $i > $i > $i > $o) @ (^[Y2 : $i > $i > $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((c1 = Y4) & (c1 = Y3)) => (?? @ $i @ (^[Y5 : $i]: (?? @ $i @ (^[Y6 : $i]: ((((c1 = Y6) & (c1 = Y5)) & (Y2 @ Y4 @ Y3 @ Y6 @ Y5)) & (~ ((Y1 = Y6) & (Y0 = Y5))))))))))))) & ((c1 = Y1) & (c1 = Y0))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y2 @ Y3 @ Y6 @ Y8 @ Y4) & (Y2 @ Y5 @ Y7 @ Y8 @ Y4)) => ((Y7 = Y6) & (Y5 = Y3))))))))))))))))))))))) != $true)),
% 1.72/1.47 inference(beta_eta_normalization,[status(thm)],[f26])).
% 1.72/1.47 thf(f26,plain,(
% 1.72/1.47 (((^[Y0 : $i > $i > $o]: (~ ((^[Y1 : $i > $i > $o]: (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (?? @ ($i > $i > $i > $i > $o) @ (^[Y4 : $i > $i > $i > $i > $o]: (((^[Y5 : $i > $i > $i > $i > $o]: ((^[Y6 : $i > $i > $o]: ((^[Y7 : $i]: ((^[Y8 : $i]: ((!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: ((Y6 @ Y10 @ Y9) => (?? @ $i @ (^[Y11 : $i]: (?? @ $i @ (^[Y12 : $i]: (((Y6 @ Y12 @ Y11) & (Y5 @ Y10 @ Y9 @ Y12 @ Y11)) & (~ ((Y7 = Y12) & (Y8 = Y11))))))))))))) & (Y6 @ Y7 @ Y8))))))))) @ Y4 @ Y1 @ Y3 @ Y2) & ((^[Y5 : $i > $i > $i > $i > $o]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (!! @ $i @ (^[Y11 : $i]: (((Y5 @ Y6 @ Y9 @ Y11 @ Y7) & (Y5 @ Y8 @ Y10 @ Y11 @ Y7)) => ((Y10 = Y9) & (Y8 = Y6)))))))))))))))) @ Y4))))))))) @ Y0))) @ (^[Y0 : $i]: ((^[Y1 : $i]: ((c1 = Y0) & (c1 = Y1)))))) != $true)),
% 1.72/1.47 inference(definition_unfolding,[status(thm)],[f19,f25])).
% 1.72/1.47 thf(f25,plain,(
% 1.72/1.47 (cCKB_FIN = (^[Y0 : $i > $i > $o]: (~ ((^[Y1 : $i > $i > $o]: (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (?? @ ($i > $i > $i > $i > $o) @ (^[Y4 : $i > $i > $i > $i > $o]: (((^[Y5 : $i > $i > $i > $i > $o]: ((^[Y6 : $i > $i > $o]: ((^[Y7 : $i]: ((^[Y8 : $i]: ((!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: ((Y6 @ Y10 @ Y9) => (?? @ $i @ (^[Y11 : $i]: (?? @ $i @ (^[Y12 : $i]: (((Y6 @ Y12 @ Y11) & (Y5 @ Y10 @ Y9 @ Y12 @ Y11)) & (~ ((Y7 = Y12) & (Y8 = Y11))))))))))))) & (Y6 @ Y7 @ Y8))))))))) @ Y4 @ Y1 @ Y3 @ Y2) & ((^[Y5 : $i > $i > $i > $i > $o]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (!! @ $i @ (^[Y11 : $i]: (((Y5 @ Y6 @ Y9 @ Y11 @ Y7) & (Y5 @ Y8 @ Y10 @ Y11 @ Y7)) => ((Y10 = Y9) & (Y8 = Y6)))))))))))))))) @ Y4))))))))) @ Y0))))),
% 1.72/1.47 inference(definition_unfolding,[status(thm)],[f22,f24])).
% 1.72/1.47 thf(f24,plain,(
% 1.72/1.47 (cCKB_INF = (^[Y0 : $i > $i > $o]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (?? @ ($i > $i > $i > $i > $o) @ (^[Y3 : $i > $i > $i > $i > $o]: (((^[Y4 : $i > $i > $i > $i > $o]: ((^[Y5 : $i > $i > $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: ((!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y5 @ Y9 @ Y8) => (?? @ $i @ (^[Y10 : $i]: (?? @ $i @ (^[Y11 : $i]: (((Y5 @ Y11 @ Y10) & (Y4 @ Y9 @ Y8 @ Y11 @ Y10)) & (~ ((Y6 = Y11) & (Y7 = Y10))))))))))))) & (Y5 @ Y6 @ Y7))))))))) @ Y3 @ Y0 @ Y2 @ Y1) & ((^[Y4 : $i > $i > $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y4 @ Y5 @ Y8 @ Y10 @ Y6) & (Y4 @ Y7 @ Y9 @ Y10 @ Y6)) => ((Y9 = Y8) & (Y7 = Y5)))))))))))))))) @ Y3))))))))))),
% 1.72/1.47 inference(definition_unfolding,[status(thm)],[f20,f21,f23])).
% 1.72/1.47 thf(f23,plain,(
% 1.72/1.47 (cCKB_INJ = (^[Y0 : $i > $i > $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y0 @ Y1 @ Y4 @ Y6 @ Y2) & (Y0 @ Y3 @ Y5 @ Y6 @ Y2)) => ((Y5 = Y4) & (Y3 = Y1)))))))))))))))))),
% 1.72/1.47 inference(cnf_transformation,[status(thm)],[f17])).
% 1.72/1.47 thf(f17,plain,(
% 1.72/1.47 (cCKB_INJ = (^[Y0 : $i > $i > $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y0 @ Y1 @ Y4 @ Y6 @ Y2) & (Y0 @ Y3 @ Y5 @ Y6 @ Y2)) => ((Y5 = Y4) & (Y3 = Y1)))))))))))))))))),
% 1.72/1.47 inference(fool_elimination,[status(thm)],[f16])).
% 1.72/1.47 thf(f16,plain,(
% 1.72/1.47 (cCKB_INJ = (^[X0 : $i > $i > $i > $i > $o] : (! [X1 : $i,X2 : $i,X3 : $i,X4 : $i,X5 : $i,X6 : $i] : (((X0 @ X4 @ X2 @ X1 @ X5) & (X0 @ X6 @ X3 @ X1 @ X5)) => ((X4 = X6) & (X2 = X3))))))),
% 1.72/1.47 inference(rectify,[status(thm)],[f1])).
% 1.72/1.47 thf(f1,axiom,(
% 1.72/1.47 (cCKB_INJ = (^[X0 : $i > $i > $i > $i > $o] : (! [X5 : $i,X2 : $i,X4 : $i,X1 : $i,X6 : $i,X3 : $i] : (((X0 @ X1 @ X2 @ X5 @ X6) & (X0 @ X3 @ X4 @ X5 @ X6)) => ((X1 = X3) & (X2 = X4))))))),
% 1.72/1.47 file('/export/starexec/sandbox/tmp/tmp.gaSco8raog/DTF2THF_16387.p',cCKB_INJ_def)).
% 1.72/1.47 thf(f21,plain,(
% 1.72/1.47 (cCKB_XPL = (^[Y0 : $i > $i > $i > $i > $o]: ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y1 @ Y5 @ Y4) => (?? @ $i @ (^[Y6 : $i]: (?? @ $i @ (^[Y7 : $i]: (((Y1 @ Y7 @ Y6) & (Y0 @ Y5 @ Y4 @ Y7 @ Y6)) & (~ ((Y2 = Y7) & (Y3 = Y6))))))))))))) & (Y1 @ Y2 @ Y3))))))))))),
% 1.72/1.47 inference(cnf_transformation,[status(thm)],[f9])).
% 1.72/1.47 thf(f9,plain,(
% 1.72/1.47 (cCKB_XPL = (^[Y0 : $i > $i > $i > $i > $o]: ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y1 @ Y5 @ Y4) => (?? @ $i @ (^[Y6 : $i]: (?? @ $i @ (^[Y7 : $i]: (((Y1 @ Y7 @ Y6) & (Y0 @ Y5 @ Y4 @ Y7 @ Y6)) & (~ ((Y2 = Y7) & (Y3 = Y6))))))))))))) & (Y1 @ Y2 @ Y3))))))))))),
% 1.72/1.47 inference(fool_elimination,[status(thm)],[f8])).
% 1.72/1.47 thf(f8,plain,(
% 1.72/1.47 ((^[X0 : $i > $i > $i > $i > $o, X1 : $i > $i > $o, X2 : $i, X3 : $i] : ((X1 @ X2 @ X3) & ! [X4 : $i,X5 : $i] : ((X1 @ X4 @ X5) => ? [X6 : $i,X7 : $i] : (~((X3 = X7) & (X2 = X6)) & (X0 @ X4 @ X5 @ X6 @ X7) & (X1 @ X6 @ X7))))) = cCKB_XPL)),
% 1.72/1.47 inference(rectify,[status(thm)],[f2])).
% 1.72/1.47 thf(f2,axiom,(
% 1.72/1.47 ((^[X0 : $i > $i > $i > $i > $o, X7 : $i > $i > $o, X8 : $i, X9 : $i] : ((X7 @ X8 @ X9) & ! [X10 : $i,X11 : $i] : ((X7 @ X10 @ X11) => ? [X5 : $i,X6 : $i] : (~((X6 = X9) & (X5 = X8)) & (X0 @ X10 @ X11 @ X5 @ X6) & (X7 @ X5 @ X6))))) = cCKB_XPL)),
% 1.72/1.47 file('/export/starexec/sandbox/tmp/tmp.gaSco8raog/DTF2THF_16387.p',cCKB_XPL_def)).
% 1.72/1.47 thf(f20,plain,(
% 1.72/1.47 (cCKB_INF = (^[Y0 : $i > $i > $o]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (?? @ ($i > $i > $i > $i > $o) @ (^[Y3 : $i > $i > $i > $i > $o]: ((cCKB_XPL @ Y3 @ Y0 @ Y2 @ Y1) & (cCKB_INJ @ Y3))))))))))),
% 1.72/1.47 inference(cnf_transformation,[status(thm)],[f11])).
% 1.72/1.47 thf(f11,plain,(
% 1.72/1.47 (cCKB_INF = (^[Y0 : $i > $i > $o]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (?? @ ($i > $i > $i > $i > $o) @ (^[Y3 : $i > $i > $i > $i > $o]: ((cCKB_XPL @ Y3 @ Y0 @ Y2 @ Y1) & (cCKB_INJ @ Y3))))))))))),
% 1.72/1.47 inference(fool_elimination,[status(thm)],[f10])).
% 1.72/1.47 thf(f10,plain,(
% 1.72/1.47 ((^[X0 : $i > $i > $o] : (? [X1 : $i > $i > $i > $i > $o,X2 : $i,X3 : $i] : ((cCKB_INJ @ X1) & (cCKB_XPL @ X1 @ X0 @ X2 @ X3)))) = cCKB_INF)),
% 1.72/1.47 inference(rectify,[status(thm)],[f3])).
% 1.72/1.47 thf(f3,axiom,(
% 1.72/1.47 ((^[X7 : $i > $i > $o] : (? [X0 : $i > $i > $i > $i > $o,X8 : $i,X9 : $i] : ((cCKB_INJ @ X0) & (cCKB_XPL @ X0 @ X7 @ X8 @ X9)))) = cCKB_INF)),
% 1.72/1.47 file('/export/starexec/sandbox/tmp/tmp.gaSco8raog/DTF2THF_16387.p',cCKB_INF_def)).
% 1.72/1.47 thf(f22,plain,(
% 1.72/1.47 (cCKB_FIN = (^[Y0 : $i > $i > $o]: (~ (cCKB_INF @ Y0))))),
% 1.72/1.47 inference(cnf_transformation,[status(thm)],[f15])).
% 1.72/1.47 thf(f15,plain,(
% 1.72/1.47 (cCKB_FIN = (^[Y0 : $i > $i > $o]: (~ (cCKB_INF @ Y0))))),
% 1.72/1.47 inference(fool_elimination,[status(thm)],[f14])).
% 1.72/1.47 thf(f14,plain,(
% 1.72/1.47 (cCKB_FIN = (^[X0 : $i > $i > $o] : (~(cCKB_INF @ X0))))),
% 1.72/1.47 inference(rectify,[status(thm)],[f4])).
% 1.72/1.47 thf(f4,axiom,(
% 1.72/1.47 (cCKB_FIN = (^[X7 : $i > $i > $o] : (~(cCKB_INF @ X7))))),
% 1.72/1.47 file('/export/starexec/sandbox/tmp/tmp.gaSco8raog/DTF2THF_16387.p',cCKB_FIN_def)).
% 1.72/1.47 thf(f19,plain,(
% 1.72/1.47 ((cCKB_FIN @ (^[Y0 : $i]: ((^[Y1 : $i]: ((c1 = Y0) & (c1 = Y1)))))) != $true)),
% 1.72/1.47 inference(cnf_transformation,[status(thm)],[f18])).
% 1.72/1.47 thf(f18,plain,(
% 1.72/1.47 ((cCKB_FIN @ (^[Y0 : $i]: ((^[Y1 : $i]: ((c1 = Y0) & (c1 = Y1)))))) != $true)),
% 1.72/1.47 inference(flattening,[status(thm)],[f13])).
% 1.72/1.47 thf(f13,plain,(
% 1.72/1.47 ~((cCKB_FIN @ (^[Y0 : $i]: ((^[Y1 : $i]: ((c1 = Y0) & (c1 = Y1)))))) = $true)),
% 1.72/1.47 inference(fool_elimination,[status(thm)],[f12])).
% 1.72/1.47 thf(f12,plain,(
% 1.72/1.47 ~(cCKB_FIN @ (^[X0 : $i, X1 : $i] : ((c1 = X1) & (c1 = X0))))),
% 1.72/1.47 inference(rectify,[status(thm)],[f6])).
% 1.72/1.47 thf(f6,negated_conjecture,(
% 1.72/1.47 ~(cCKB_FIN @ (^[X5 : $i, X6 : $i] : ((c1 = X6) & (c1 = X5))))),
% 1.72/1.47 inference(negated_conjecture,[status(cth)],[f5])).
% 1.72/1.47 thf(f5,conjecture,(
% 1.72/1.47 (cCKB_FIN @ (^[X5 : $i, X6 : $i] : ((c1 = X6) & (c1 = X5))))),
% 1.72/1.47 file('/export/starexec/sandbox/tmp/tmp.gaSco8raog/DTF2THF_16387.p',cL3000)).
% 1.72/1.47 thf(f93,plain,(
% 1.72/1.47 ( ! [X0 : $i,X1 : $i] : ((c1 != sK2) | (c1 != X0) | (c1 != X1)) )),
% 1.72/1.47 inference(duplicate_literal_removal,[status(thm)],[f92])).
% 1.72/1.47 thf(f92,plain,(
% 1.72/1.47 ( ! [X0 : $i,X1 : $i] : ((c1 != X0) | (c1 != X1) | (c1 != X1) | (c1 != sK2) | (c1 != X0)) )),
% 1.72/1.47 inference(superposition,[status(thm)],[f91,f57])).
% 1.72/1.47 thf(f57,plain,(
% 1.72/1.47 ( ! [X2 : $i,X1 : $i] : ((c1 = (sK5 @ X1 @ X2)) | (c1 != X2) | (c1 != X1)) )),
% 1.72/1.47 inference(equality_proxy_clausification,[status(thm)],[f56])).
% 1.72/1.47 thf(f56,plain,(
% 1.72/1.47 ( ! [X2 : $i,X1 : $i] : (((c1 = (sK5 @ X1 @ X2)) = $true) | (c1 != X2) | (c1 != X1)) )),
% 1.72/1.47 inference(equality_proxy_clausification,[status(thm)],[f55])).
% 1.72/1.47 thf(f55,plain,(
% 1.72/1.47 ( ! [X2 : $i,X1 : $i] : (($false = (c1 = X2)) | ((c1 = (sK5 @ X1 @ X2)) = $true) | (c1 != X1)) )),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f53])).
% 1.72/1.47 thf(f53,plain,(
% 1.72/1.47 ( ! [X2 : $i,X1 : $i] : ((((c1 = (sK5 @ X1 @ X2)) & (c1 = (sK4 @ X1 @ X2))) = $true) | (c1 != X1) | ($false = (c1 = X2))) )),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f51])).
% 1.72/1.47 thf(f51,plain,(
% 1.72/1.47 ( ! [X2 : $i,X1 : $i] : ((c1 != X1) | ($true = (((c1 = (sK5 @ X1 @ X2)) & (c1 = (sK4 @ X1 @ X2))) & (sK3 @ X2 @ X1 @ (sK5 @ X1 @ X2) @ (sK4 @ X1 @ X2)))) | ($false = (c1 = X2))) )),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f49])).
% 1.72/1.47 thf(f49,plain,(
% 1.72/1.47 ( ! [X2 : $i,X1 : $i] : ((c1 != X1) | (((((c1 = (sK5 @ X1 @ X2)) & (c1 = (sK4 @ X1 @ X2))) & (sK3 @ X2 @ X1 @ (sK5 @ X1 @ X2) @ (sK4 @ X1 @ X2))) & (~ ((sK2 = (sK5 @ X1 @ X2)) & (sK1 = (sK4 @ X1 @ X2))))) = $true) | ($false = (c1 = X2))) )),
% 1.72/1.47 inference(beta_eta_normalization,[status(thm)],[f48])).
% 1.72/1.47 thf(f48,plain,(
% 1.72/1.47 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((((c1 = Y0) & (c1 = (sK4 @ X1 @ X2))) & (sK3 @ X2 @ X1 @ Y0 @ (sK4 @ X1 @ X2))) & (~ ((sK2 = Y0) & (sK1 = (sK4 @ X1 @ X2)))))) @ (sK5 @ X1 @ X2)) = $true) | (c1 != X1) | ($false = (c1 = X2))) )),
% 1.72/1.47 inference(sigma_clausification,[status(thm)],[f47])).
% 1.72/1.47 thf(f47,plain,(
% 1.72/1.47 ( ! [X2 : $i,X1 : $i] : (($true = (?? @ $i @ (^[Y0 : $i]: ((((c1 = Y0) & (c1 = (sK4 @ X1 @ X2))) & (sK3 @ X2 @ X1 @ Y0 @ (sK4 @ X1 @ X2))) & (~ ((sK2 = Y0) & (sK1 = (sK4 @ X1 @ X2)))))))) | ($false = (c1 = X2)) | (c1 != X1)) )),
% 1.72/1.47 inference(beta_eta_normalization,[status(thm)],[f46])).
% 1.72/1.47 thf(f46,plain,(
% 1.72/1.47 ( ! [X2 : $i,X1 : $i] : (($false = (c1 = X2)) | (c1 != X1) | (((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((c1 = Y1) & (c1 = Y0)) & (sK3 @ X2 @ X1 @ Y1 @ Y0)) & (~ ((sK2 = Y1) & (sK1 = Y0))))))) @ (sK4 @ X1 @ X2)) = $true)) )),
% 1.72/1.47 inference(sigma_clausification,[status(thm)],[f45])).
% 1.72/1.47 thf(f45,plain,(
% 1.72/1.47 ( ! [X2 : $i,X1 : $i] : (((?? @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((c1 = Y1) & (c1 = Y0)) & (sK3 @ X2 @ X1 @ Y1 @ Y0)) & (~ ((sK2 = Y1) & (sK1 = Y0)))))))) = $true) | ($false = (c1 = X2)) | (c1 != X1)) )),
% 1.72/1.47 inference(equality_proxy_clausification,[status(thm)],[f44])).
% 1.72/1.47 thf(f44,plain,(
% 1.72/1.47 ( ! [X2 : $i,X1 : $i] : (($false = (c1 = X1)) | ((?? @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((c1 = Y1) & (c1 = Y0)) & (sK3 @ X2 @ X1 @ Y1 @ Y0)) & (~ ((sK2 = Y1) & (sK1 = Y0)))))))) = $true) | ($false = (c1 = X2))) )),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f43])).
% 1.72/1.47 thf(f43,plain,(
% 1.72/1.47 ( ! [X2 : $i,X1 : $i] : (($false = ((c1 = X2) & (c1 = X1))) | ((?? @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((c1 = Y1) & (c1 = Y0)) & (sK3 @ X2 @ X1 @ Y1 @ Y0)) & (~ ((sK2 = Y1) & (sK1 = Y0)))))))) = $true)) )),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f42])).
% 1.72/1.47 thf(f42,plain,(
% 1.72/1.47 ( ! [X2 : $i,X1 : $i] : (((((c1 = X2) & (c1 = X1)) => (?? @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((c1 = Y1) & (c1 = Y0)) & (sK3 @ X2 @ X1 @ Y1 @ Y0)) & (~ ((sK2 = Y1) & (sK1 = Y0))))))))) = $true)) )),
% 1.72/1.47 inference(beta_eta_normalization,[status(thm)],[f41])).
% 1.72/1.47 thf(f41,plain,(
% 1.72/1.47 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (((c1 = Y0) & (c1 = X1)) => (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((((c1 = Y2) & (c1 = Y1)) & (sK3 @ Y0 @ X1 @ Y2 @ Y1)) & (~ ((sK2 = Y2) & (sK1 = Y1)))))))))) @ X2) = $true)) )),
% 1.72/1.47 inference(pi_clausification,[status(thm)],[f40])).
% 1.72/1.47 thf(f40,plain,(
% 1.72/1.47 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (((c1 = Y0) & (c1 = X1)) => (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((((c1 = Y2) & (c1 = Y1)) & (sK3 @ Y0 @ X1 @ Y2 @ Y1)) & (~ ((sK2 = Y2) & (sK1 = Y1))))))))))))) )),
% 1.72/1.47 inference(beta_eta_normalization,[status(thm)],[f39])).
% 1.72/1.47 thf(f39,plain,(
% 1.72/1.47 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((c1 = Y1) & (c1 = Y0)) => (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((((c1 = Y3) & (c1 = Y2)) & (sK3 @ Y1 @ Y0 @ Y3 @ Y2)) & (~ ((sK2 = Y3) & (sK1 = Y2)))))))))))) @ X1))) )),
% 1.72/1.47 inference(pi_clausification,[status(thm)],[f38])).
% 1.72/1.47 thf(f38,plain,(
% 1.72/1.47 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((c1 = Y1) & (c1 = Y0)) => (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((((c1 = Y3) & (c1 = Y2)) & (sK3 @ Y1 @ Y0 @ Y3 @ Y2)) & (~ ((sK2 = Y3) & (sK1 = Y2))))))))))))) = $true)),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 1.72/1.47 thf(f91,plain,(
% 1.72/1.47 ( ! [X0 : $i,X1 : $i] : (((sK5 @ X0 @ X1) != sK2) | (c1 != X1) | (c1 != X0)) )),
% 1.72/1.47 inference(subsumption_resolution,[status(thm)],[f90,f69])).
% 1.72/1.47 thf(f69,plain,(
% 1.72/1.47 (c1 = sK1)),
% 1.72/1.47 inference(equality_proxy_clausification,[status(thm)],[f66])).
% 1.72/1.47 thf(f66,plain,(
% 1.72/1.47 ((c1 = sK1) = $true)),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f37])).
% 1.72/1.47 thf(f90,plain,(
% 1.72/1.47 ( ! [X0 : $i,X1 : $i] : ((c1 != sK1) | (c1 != X0) | ((sK5 @ X0 @ X1) != sK2) | (c1 != X1)) )),
% 1.72/1.47 inference(duplicate_literal_removal,[status(thm)],[f89])).
% 1.72/1.47 thf(f89,plain,(
% 1.72/1.47 ( ! [X0 : $i,X1 : $i] : ((c1 != X1) | (c1 != X0) | (c1 != X0) | ((sK5 @ X0 @ X1) != sK2) | (c1 != sK1) | (c1 != X1)) )),
% 1.72/1.47 inference(superposition,[status(thm)],[f65,f59])).
% 1.72/1.47 thf(f59,plain,(
% 1.72/1.47 ( ! [X2 : $i,X1 : $i] : ((c1 = (sK4 @ X1 @ X2)) | (c1 != X2) | (c1 != X1)) )),
% 1.72/1.47 inference(equality_proxy_clausification,[status(thm)],[f58])).
% 1.72/1.47 thf(f58,plain,(
% 1.72/1.47 ( ! [X2 : $i,X1 : $i] : (($false = (c1 = X2)) | (c1 != X1) | (c1 = (sK4 @ X1 @ X2))) )),
% 1.72/1.47 inference(equality_proxy_clausification,[status(thm)],[f54])).
% 1.72/1.47 thf(f54,plain,(
% 1.72/1.47 ( ! [X2 : $i,X1 : $i] : ((c1 != X1) | ((c1 = (sK4 @ X1 @ X2)) = $true) | ($false = (c1 = X2))) )),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f53])).
% 1.72/1.47 thf(f65,plain,(
% 1.72/1.47 ( ! [X2 : $i,X1 : $i] : ((sK1 != (sK4 @ X1 @ X2)) | (c1 != X1) | (c1 != X2) | ((sK5 @ X1 @ X2) != sK2)) )),
% 1.72/1.47 inference(equality_proxy_clausification,[status(thm)],[f64])).
% 1.72/1.47 thf(f64,plain,(
% 1.72/1.47 ( ! [X2 : $i,X1 : $i] : ((c1 != X1) | ((sK5 @ X1 @ X2) != sK2) | (c1 != X2) | ($false = (sK1 = (sK4 @ X1 @ X2)))) )),
% 1.72/1.47 inference(equality_proxy_clausification,[status(thm)],[f63])).
% 1.72/1.47 thf(f63,plain,(
% 1.72/1.47 ( ! [X2 : $i,X1 : $i] : (((sK2 = (sK5 @ X1 @ X2)) = $false) | ($false = (sK1 = (sK4 @ X1 @ X2))) | (c1 != X2) | (c1 != X1)) )),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f62])).
% 1.72/1.47 thf(f62,plain,(
% 1.72/1.47 ( ! [X2 : $i,X1 : $i] : ((c1 != X2) | ($false = ((sK2 = (sK5 @ X1 @ X2)) & (sK1 = (sK4 @ X1 @ X2)))) | (c1 != X1)) )),
% 1.72/1.47 inference(not_proxy_clausification,[status(thm)],[f61])).
% 1.72/1.47 thf(f61,plain,(
% 1.72/1.47 ( ! [X2 : $i,X1 : $i] : (((~ ((sK2 = (sK5 @ X1 @ X2)) & (sK1 = (sK4 @ X1 @ X2)))) = $true) | (c1 != X1) | (c1 != X2)) )),
% 1.72/1.47 inference(equality_proxy_clausification,[status(thm)],[f50])).
% 1.72/1.47 thf(f50,plain,(
% 1.72/1.47 ( ! [X2 : $i,X1 : $i] : ((c1 != X1) | ($false = (c1 = X2)) | ((~ ((sK2 = (sK5 @ X1 @ X2)) & (sK1 = (sK4 @ X1 @ X2)))) = $true)) )),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f49])).
% 1.72/1.47 % SZS output end Proof for DTF2THF_16387
% 1.72/1.47 % (16484)------------------------------
% 1.72/1.47 % (16484)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.47 % (16484)Termination reason: Refutation
% 1.72/1.47
% 1.72/1.47 % (16484)Memory used [KB]: 5628
% 1.72/1.47 % (16484)Time elapsed: 0.012 s
% 1.72/1.47 % (16484)Instructions burned: 12 (million)
% 1.72/1.47 % (16484)------------------------------
% 1.72/1.47 % (16484)------------------------------
% 1.72/1.47 % (16483)Success in time 0.025 s
%------------------------------------------------------------------------------