%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV214^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n009.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 09:40:34 AM UTC 2026
% Result : Theorem 1.53s 1.28s
% Output : Refutation 1.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 60 ( 4 unt; 0 typ; 6 def)
% Number of atoms : 416 ( 264 equ; 6 cnn)
% Maximal formula atoms : 11 ( 6 avg)
% Number of connectives : 584 ( 60 ~; 111 |; 52 &; 308 @)
% ( 6 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 20 usr; 17 con; 0-2 aty)
% ( 0 !!; 30 ??; 0 @@+; 0 @@-)
% Number of variables : 183 ( 94 ^; 75 !; 14 ?; 183 :)
% 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,
cP: iS > iS > iS ).
thf(func_def_4,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_13,type,
sK0: ( iS > $o ) > iS ).
thf(func_def_14,type,
sK1: ( iS > $o ) > iS ).
thf(func_def_16,type,
ph3:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
sK4: iS ).
thf(func_def_18,type,
sK5: iS ).
thf(func_def_19,type,
sK6: iS > iS ).
thf(func_def_20,type,
sK7: iS ).
thf(func_def_21,type,
sK8: iS ).
thf(func_def_22,type,
sK9: iS ).
thf(func_def_23,type,
sK10: iS ).
thf(func_def_24,type,
sK11: iS > iS ).
thf(f162,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f27,f56,f57,f101,f102,f109,f161]) ).
thf(f161,plain,
~ spl2_4,
inference(avatar_contradiction_clause,[status(thm)],[f160]) ).
thf(f160,plain,
( $false
| ~ spl2_4 ),
inference(trivial_inequality_removal,[status(thm)],[f159]) ).
thf(f159,plain,
( ( c0 != c0 )
| ~ spl2_4 ),
inference(superposition,[status(thm)],[f16,f55]) ).
thf(f55,plain,
( ( c0
= ( cP @ sK5 @ sK4 ) )
| ~ spl2_4 ),
inference(avatar_component_clause,[status(thm)],[f53]) ).
thf(f53,definition,
( spl2_4
<=> ( c0
= ( cP @ sK5 @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition]) ).
thf(f16,plain,
! [X0: iS,X1: iS] :
( c0
!= ( cP @ X1 @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ( ( ^ [Y0: iS] :
( ( c0 = Y0 )
| ( ?? @ iS
@ ^ [Y1: iS] :
( c0
= ( cP @ Y1 @ Y0 ) ) ) ) )
!= ( ^ [Y0: iS,Y1: iS] : ( Y0 = Y1 )
@ c0 ) )
| ( ( ^ [Y0: iS] :
( ( c0 = Y0 )
| ( ?? @ iS
@ ^ [Y1: iS] :
( c0
= ( cP @ Y0 @ Y1 ) ) ) ) )
!= ( ^ [Y0: iS,Y1: iS] : ( Y0 = Y1 )
@ c0 ) ) )
& ! [X0: iS,X1: iS] :
( c0
!= ( cP @ X1 @ X0 ) )
& ! [X2: iS,X3: iS,X4: iS,X5: iS] :
( ( ( cP @ X3 @ X5 )
!= ( cP @ X4 @ X2 ) )
| ( ( X3 = X4 )
& ( X2 = X5 ) ) )
& ! [X6: iS > $o] :
( ( $true
!= ( X6 @ c0 ) )
| ! [X7: iS] :
( $true
= ( X6 @ X7 ) )
| ( ( $true
= ( X6 @ ( sK0 @ X6 ) ) )
& ( $true
!= ( X6 @ ( cP @ ( sK1 @ X6 ) @ ( sK0 @ X6 ) ) ) )
& ( $true
= ( X6 @ ( sK1 @ X6 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f8,f9]) ).
thf(f9,plain,
! [X6: iS > $o] :
( ? [X8: iS,X9: iS] :
( ( $true
= ( X6 @ X8 ) )
& ( ( X6 @ ( cP @ X9 @ X8 ) )
!= $true )
& ( $true
= ( X6 @ X9 ) ) )
=> ( ( $true
= ( X6 @ ( sK0 @ X6 ) ) )
& ( $true
!= ( X6 @ ( cP @ ( sK1 @ X6 ) @ ( sK0 @ X6 ) ) ) )
& ( $true
= ( X6 @ ( sK1 @ X6 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ( ( ( ^ [Y0: iS] :
( ( c0 = Y0 )
| ( ?? @ iS
@ ^ [Y1: iS] :
( c0
= ( cP @ Y1 @ Y0 ) ) ) ) )
!= ( ^ [Y0: iS,Y1: iS] : ( Y0 = Y1 )
@ c0 ) )
| ( ( ^ [Y0: iS] :
( ( c0 = Y0 )
| ( ?? @ iS
@ ^ [Y1: iS] :
( c0
= ( cP @ Y0 @ Y1 ) ) ) ) )
!= ( ^ [Y0: iS,Y1: iS] : ( Y0 = Y1 )
@ c0 ) ) )
& ! [X0: iS,X1: iS] :
( c0
!= ( cP @ X1 @ X0 ) )
& ! [X2: iS,X3: iS,X4: iS,X5: iS] :
( ( ( cP @ X3 @ X5 )
!= ( cP @ X4 @ X2 ) )
| ( ( X3 = X4 )
& ( X2 = X5 ) ) )
& ! [X6: iS > $o] :
( ( $true
!= ( X6 @ c0 ) )
| ! [X7: iS] :
( $true
= ( X6 @ X7 ) )
| ? [X8: iS,X9: iS] :
( ( $true
= ( X6 @ X8 ) )
& ( ( X6 @ ( cP @ X9 @ X8 ) )
!= $true )
& ( $true
= ( X6 @ X9 ) ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ( ( ^ [Y0: iS] :
( ( c0 = Y0 )
| ( ?? @ iS
@ ^ [Y1: iS] :
( c0
= ( cP @ Y1 @ Y0 ) ) ) ) )
!= ( ^ [Y0: iS,Y1: iS] : ( Y0 = Y1 )
@ c0 ) )
| ( ( ^ [Y0: iS] :
( ( c0 = Y0 )
| ( ?? @ iS
@ ^ [Y1: iS] :
( c0
= ( cP @ Y0 @ Y1 ) ) ) ) )
!= ( ^ [Y0: iS,Y1: iS] : ( Y0 = Y1 )
@ c0 ) ) )
& ! [X8: iS,X9: iS] :
( c0
!= ( cP @ X9 @ X8 ) )
& ! [X4: iS,X5: iS,X6: iS,X7: iS] :
( ( ( cP @ X5 @ X7 )
!= ( cP @ X6 @ X4 ) )
| ( ( X5 = X6 )
& ( X4 = X7 ) ) )
& ! [X0: iS > $o] :
( ( $true
!= ( X0 @ c0 ) )
| ! [X3: iS] :
( $true
= ( X0 @ X3 ) )
| ? [X1: iS,X2: iS] :
( ( $true
= ( X0 @ X1 ) )
& ( ( X0 @ ( cP @ X2 @ X1 ) )
!= $true )
& ( $true
= ( X0 @ X2 ) ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ( ( ^ [Y0: iS] :
( ( c0 = Y0 )
| ( ?? @ iS
@ ^ [Y1: iS] :
( c0
= ( cP @ Y1 @ Y0 ) ) ) ) )
!= ( ^ [Y0: iS,Y1: iS] : ( Y0 = Y1 )
@ c0 ) )
| ( ( ^ [Y0: iS] :
( ( c0 = Y0 )
| ( ?? @ iS
@ ^ [Y1: iS] :
( c0
= ( cP @ Y0 @ Y1 ) ) ) ) )
!= ( ^ [Y0: iS,Y1: iS] : ( Y0 = Y1 )
@ c0 ) ) )
& ! [X8: iS,X9: iS] :
( c0
!= ( cP @ X9 @ X8 ) )
& ! [X0: iS > $o] :
( ! [X3: iS] :
( $true
= ( X0 @ X3 ) )
| ( $true
!= ( X0 @ c0 ) )
| ? [X1: iS,X2: iS] :
( ( ( X0 @ ( cP @ X2 @ X1 ) )
!= $true )
& ( $true
= ( X0 @ X1 ) )
& ( $true
= ( X0 @ X2 ) ) ) )
& ! [X4: iS,X5: iS,X6: iS,X7: iS] :
( ( ( cP @ X5 @ X7 )
!= ( cP @ X6 @ X4 ) )
| ( ( X5 = X6 )
& ( X4 = X7 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X8: iS,X9: iS] :
( c0
!= ( cP @ X9 @ X8 ) )
& ! [X0: iS > $o] :
( ( ( $true
= ( X0 @ c0 ) )
& ! [X1: iS,X2: iS] :
( ( ( $true
= ( X0 @ X1 ) )
& ( $true
= ( X0 @ X2 ) ) )
=> ( ( X0 @ ( cP @ X2 @ X1 ) )
= $true ) ) )
=> ! [X3: iS] :
( $true
= ( X0 @ X3 ) ) )
& ! [X4: iS,X5: iS,X6: iS,X7: iS] :
( ( ( cP @ X5 @ X7 )
= ( cP @ X6 @ X4 ) )
=> ( ( X5 = X6 )
& ( X4 = X7 ) ) ) )
=> ( ( ( ^ [Y0: iS] :
( ( c0 = Y0 )
| ( ?? @ iS
@ ^ [Y1: iS] :
( c0
= ( cP @ Y1 @ Y0 ) ) ) ) )
= ( ^ [Y0: iS,Y1: iS] : ( Y0 = Y1 )
@ c0 ) )
& ( ( ^ [Y0: iS] :
( ( c0 = Y0 )
| ( ?? @ iS
@ ^ [Y1: iS] :
( c0
= ( cP @ Y0 @ Y1 ) ) ) ) )
= ( ^ [Y0: iS,Y1: iS] : ( Y0 = Y1 )
@ c0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: iS > $o] :
( ( ! [X1: iS,X2: iS] :
( ( ( X0 @ X1 )
& ( X0 @ X2 ) )
=> ( X0 @ ( cP @ X2 @ X1 ) ) )
& ( X0 @ c0 ) )
=> ! [X3: iS] : ( X0 @ X3 ) )
& ! [X4: iS,X5: iS,X6: iS,X7: iS] :
( ( ( cP @ X5 @ X7 )
= ( cP @ X6 @ X4 ) )
=> ( ( X4 = X7 )
& ( X5 = X6 ) ) )
& ! [X8: iS,X9: iS] :
( c0
!= ( cP @ X9 @ X8 ) ) )
=> ( ( ( ^ [X10: iS,X11: iS] : ( X10 = X11 )
@ c0 )
= ( ^ [X12: iS] :
( ? [X13: iS] :
( c0
= ( cP @ X13 @ X12 ) )
| ( c0 = X12 ) ) ) )
& ( ( ^ [X14: iS] :
( ? [X15: iS] :
( c0
= ( cP @ X14 @ X15 ) )
| ( c0 = X14 ) ) )
= ( ^ [X16: iS,X17: iS] : ( X16 = X17 )
@ c0 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X4: iS > $o] :
( ( ! [X1: iS,X0: iS] :
( ( ( X4 @ X1 )
& ( X4 @ X0 ) )
=> ( X4 @ ( cP @ X0 @ X1 ) ) )
& ( X4 @ c0 ) )
=> ! [X0: iS] : ( X4 @ X0 ) )
& ! [X3: iS,X0: iS,X1: iS,X2: iS] :
( ( ( cP @ X0 @ X2 )
= ( cP @ X1 @ X3 ) )
=> ( ( X2 = X3 )
& ( X0 = X1 ) ) )
& ! [X1: iS,X0: iS] :
( ( cP @ X0 @ X1 )
!= c0 ) )
=> ( ( ( ^ [X0: iS,X1: iS] : ( X0 = X1 )
@ c0 )
= ( ^ [X1: iS] :
( ? [X0: iS] :
( ( cP @ X0 @ X1 )
= c0 )
| ( c0 = X1 ) ) ) )
& ( ( ^ [X0: iS] :
( ? [X1: iS] :
( ( cP @ X0 @ X1 )
= c0 )
| ( c0 = X0 ) ) )
= ( ^ [X0: iS,X1: iS] : ( X0 = X1 )
@ c0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X4: iS > $o] :
( ( ! [X1: iS,X0: iS] :
( ( ( X4 @ X1 )
& ( X4 @ X0 ) )
=> ( X4 @ ( cP @ X0 @ X1 ) ) )
& ( X4 @ c0 ) )
=> ! [X0: iS] : ( X4 @ X0 ) )
& ! [X3: iS,X0: iS,X1: iS,X2: iS] :
( ( ( cP @ X0 @ X2 )
= ( cP @ X1 @ X3 ) )
=> ( ( X2 = X3 )
& ( X0 = X1 ) ) )
& ! [X1: iS,X0: iS] :
( ( cP @ X0 @ X1 )
!= c0 ) )
=> ( ( ( ^ [X0: iS,X1: iS] : ( X0 = X1 )
@ c0 )
= ( ^ [X1: iS] :
( ? [X0: iS] :
( ( cP @ X0 @ X1 )
= c0 )
| ( c0 = X1 ) ) ) )
& ( ( ^ [X0: iS] :
( ? [X1: iS] :
( ( cP @ X0 @ X1 )
= c0 )
| ( c0 = X0 ) ) )
= ( ^ [X0: iS,X1: iS] : ( X0 = X1 )
@ c0 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.SBwQMqzwpx/DTF2THF_27383.p',cS_T_LR_LEM2_pme) ).
thf(f109,plain,
~ spl2_6,
inference(avatar_contradiction_clause,[status(thm)],[f108]) ).
thf(f108,plain,
( $false
| ~ spl2_6 ),
inference(trivial_inequality_removal,[status(thm)],[f107]) ).
thf(f107,plain,
( ( c0 != c0 )
| ~ spl2_6 ),
inference(superposition,[status(thm)],[f16,f100]) ).
thf(f100,plain,
( ( c0
= ( cP @ sK7 @ sK8 ) )
| ~ spl2_6 ),
inference(avatar_component_clause,[status(thm)],[f98]) ).
thf(f98,definition,
( spl2_6
<=> ( c0
= ( cP @ sK7 @ sK8 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_6])],[avatar_definition]) ).
thf(f102,plain,
( ~ spl2_5
| spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f82,f24,f94]) ).
thf(f94,definition,
( spl2_5
<=> ( c0 = sK7 ) ),
introduced(definition,[new_symbols(naming,[spl2_5])],[avatar_definition]) ).
thf(f24,definition,
( spl2_2
<=> ( ( ^ [Y0: iS] :
( ( c0 = Y0 )
| ( ?? @ iS
@ ^ [Y1: iS] :
( c0
= ( cP @ Y0 @ Y1 ) ) ) ) )
= ( (=) @ c0 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f82,plain,
( ( c0 != sK7 )
| spl2_2 ),
inference(equality_proxy_clausification,[status(thm)],[f81]) ).
thf(f81,plain,
( ( ( c0 = sK7 )
= $false )
| spl2_2 ),
inference(duplicate_literal_removal,[status(thm)],[f80]) ).
thf(f80,plain,
( ( ( c0 = sK7 )
= $false )
| ( ( c0 = sK7 )
= $false )
| spl2_2 ),
inference(binary_proxy_clausification,[status(thm)],[f78]) ).
thf(f78,plain,
( ( ( ( c0 = sK7 )
| ( ?? @ iS
@ ^ [Y0: iS] :
( c0
= ( cP @ sK7 @ Y0 ) ) ) )
= $false )
| ( ( c0 = sK7 )
= $false )
| spl2_2 ),
inference(binary_proxy_clausification,[status(thm)],[f76]) ).
thf(f76,plain,
( ( ( c0 = sK7 )
!= ( ( c0 = sK7 )
| ( ?? @ iS
@ ^ [Y0: iS] :
( c0
= ( cP @ sK7 @ Y0 ) ) ) ) )
| spl2_2 ),
inference(beta_eta_normalization,[status(thm)],[f75]) ).
thf(f75,plain,
( ( ( c0 = sK7 )
!= ( ^ [Y0: iS] :
( ( c0 = Y0 )
| ( ?? @ iS
@ ^ [Y1: iS] :
( c0
= ( cP @ Y0 @ Y1 ) ) ) )
@ sK7 ) )
| spl2_2 ),
inference(negative_extensionality,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ( ^ [Y0: iS] :
( ( c0 = Y0 )
| ( ?? @ iS
@ ^ [Y1: iS] :
( c0
= ( cP @ Y0 @ Y1 ) ) ) ) )
!= ( (=) @ c0 ) )
| spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f24]) ).
thf(f101,plain,
( spl2_5
| spl2_6
| spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f92,f24,f98,f94]) ).
thf(f92,plain,
( ( c0 = sK7 )
| ( c0
= ( cP @ sK7 @ sK8 ) )
| spl2_2 ),
inference(equality_proxy_clausification,[status(thm)],[f91]) ).
thf(f91,plain,
( ( c0
= ( cP @ sK7 @ sK8 ) )
| ( $true
= ( c0 = sK7 ) )
| spl2_2 ),
inference(equality_proxy_clausification,[status(thm)],[f90]) ).
thf(f90,plain,
( ( $true
= ( c0
= ( cP @ sK7 @ sK8 ) ) )
| ( $true
= ( c0 = sK7 ) )
| spl2_2 ),
inference(beta_eta_normalization,[status(thm)],[f89]) ).
thf(f89,plain,
( ( ( ^ [Y0: iS] :
( c0
= ( cP @ sK7 @ Y0 ) )
@ sK8 )
= $true )
| ( $true
= ( c0 = sK7 ) )
| spl2_2 ),
inference(sigma_clausification,[status(thm)],[f88]) ).
thf(f88,plain,
( ( $true
= ( ?? @ iS
@ ^ [Y0: iS] :
( c0
= ( cP @ sK7 @ Y0 ) ) ) )
| ( $true
= ( c0 = sK7 ) )
| spl2_2 ),
inference(duplicate_literal_removal,[status(thm)],[f87]) ).
thf(f87,plain,
( ( $true
= ( c0 = sK7 ) )
| ( $true
= ( ?? @ iS
@ ^ [Y0: iS] :
( c0
= ( cP @ sK7 @ Y0 ) ) ) )
| ( $true
= ( c0 = sK7 ) )
| spl2_2 ),
inference(binary_proxy_clausification,[status(thm)],[f77]) ).
thf(f77,plain,
( ( $true
= ( ( c0 = sK7 )
| ( ?? @ iS
@ ^ [Y0: iS] :
( c0
= ( cP @ sK7 @ Y0 ) ) ) ) )
| ( $true
= ( c0 = sK7 ) )
| spl2_2 ),
inference(binary_proxy_clausification,[status(thm)],[f76]) ).
thf(f57,plain,
( ~ spl2_3
| spl2_1 ),
inference(avatar_split_clause,[status(thm)],[f37,f20,f49]) ).
thf(f49,definition,
( spl2_3
<=> ( c0 = sK4 ) ),
introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition]) ).
thf(f20,definition,
( spl2_1
<=> ( ( (=) @ c0 )
= ( ^ [Y0: iS] :
( ( c0 = Y0 )
| ( ?? @ iS
@ ^ [Y1: iS] :
( c0
= ( cP @ Y1 @ Y0 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f37,plain,
( ( c0 != sK4 )
| spl2_1 ),
inference(equality_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
( ( ( c0 = sK4 )
= $false )
| spl2_1 ),
inference(duplicate_literal_removal,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ( c0 = sK4 )
= $false )
| ( ( c0 = sK4 )
= $false )
| spl2_1 ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
( ( $false
= ( ( c0 = sK4 )
| ( ?? @ iS
@ ^ [Y0: iS] :
( c0
= ( cP @ Y0 @ sK4 ) ) ) ) )
| ( ( c0 = sK4 )
= $false )
| spl2_1 ),
inference(binary_proxy_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
( ( ( c0 = sK4 )
!= ( ( c0 = sK4 )
| ( ?? @ iS
@ ^ [Y0: iS] :
( c0
= ( cP @ Y0 @ sK4 ) ) ) ) )
| spl2_1 ),
inference(beta_eta_normalization,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ( ^ [Y0: iS] :
( ( c0 = Y0 )
| ( ?? @ iS
@ ^ [Y1: iS] :
( c0
= ( cP @ Y1 @ Y0 ) ) ) )
@ sK4 )
!= ( c0 = sK4 ) )
| spl2_1 ),
inference(negative_extensionality,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ( (=) @ c0 )
!= ( ^ [Y0: iS] :
( ( c0 = Y0 )
| ( ?? @ iS
@ ^ [Y1: iS] :
( c0
= ( cP @ Y1 @ Y0 ) ) ) ) ) )
| spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f20]) ).
thf(f56,plain,
( spl2_3
| spl2_4
| spl2_1 ),
inference(avatar_split_clause,[status(thm)],[f47,f20,f53,f49]) ).
thf(f47,plain,
( ( c0 = sK4 )
| ( c0
= ( cP @ sK5 @ sK4 ) )
| spl2_1 ),
inference(equality_proxy_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
( ( ( c0 = sK4 )
= $true )
| ( c0
= ( cP @ sK5 @ sK4 ) )
| spl2_1 ),
inference(equality_proxy_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
( ( $true
= ( c0
= ( cP @ sK5 @ sK4 ) ) )
| ( ( c0 = sK4 )
= $true )
| spl2_1 ),
inference(beta_eta_normalization,[status(thm)],[f44]) ).
thf(f44,plain,
( ( ( c0 = sK4 )
= $true )
| ( $true
= ( ^ [Y0: iS] :
( c0
= ( cP @ Y0 @ sK4 ) )
@ sK5 ) )
| spl2_1 ),
inference(sigma_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
( ( $true
= ( ?? @ iS
@ ^ [Y0: iS] :
( c0
= ( cP @ Y0 @ sK4 ) ) ) )
| ( ( c0 = sK4 )
= $true )
| spl2_1 ),
inference(duplicate_literal_removal,[status(thm)],[f42]) ).
thf(f42,plain,
( ( ( c0 = sK4 )
= $true )
| ( ( c0 = sK4 )
= $true )
| ( $true
= ( ?? @ iS
@ ^ [Y0: iS] :
( c0
= ( cP @ Y0 @ sK4 ) ) ) )
| spl2_1 ),
inference(binary_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
( ( $true
= ( ( c0 = sK4 )
| ( ?? @ iS
@ ^ [Y0: iS] :
( c0
= ( cP @ Y0 @ sK4 ) ) ) ) )
| ( ( c0 = sK4 )
= $true )
| spl2_1 ),
inference(binary_proxy_clausification,[status(thm)],[f31]) ).
thf(f27,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f18,f24,f20]) ).
thf(f18,plain,
( ( ( ^ [Y0: iS] :
( ( c0 = Y0 )
| ( ?? @ iS
@ ^ [Y1: iS] :
( c0
= ( cP @ Y0 @ Y1 ) ) ) ) )
!= ( (=) @ c0 ) )
| ( ( (=) @ c0 )
!= ( ^ [Y0: iS] :
( ( c0 = Y0 )
| ( ?? @ iS
@ ^ [Y1: iS] :
( c0
= ( cP @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ( ^ [Y0: iS] :
( ( c0 = Y0 )
| ( ?? @ iS
@ ^ [Y1: iS] :
( c0
= ( cP @ Y0 @ Y1 ) ) ) ) )
!= ( ^ [Y0: iS,Y1: iS] : ( Y0 = Y1 )
@ c0 ) )
| ( ( ^ [Y0: iS] :
( ( c0 = Y0 )
| ( ?? @ iS
@ ^ [Y1: iS] :
( c0
= ( cP @ Y1 @ Y0 ) ) ) ) )
!= ( ^ [Y0: iS,Y1: iS] : ( Y0 = Y1 )
@ c0 ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV214^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n009.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 12:41:55 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.45 ---- Original DTF file ---
% 0.28/0.45 thf(spec,logic,$$dhol).
% 0.28/0.45 %------------------------------------------------------------------------------
% 0.28/0.45 % File : SEV214^5 : TPTP v9.2.1. Released v4.0.0.
% 0.28/0.45 % Domain : Set Theory (Sets of sets)
% 0.28/0.45 % Problem : TPS problem from S-T-THMS
% 0.28/0.45 % Version : Especial.
% 0.28/0.45 % English :
% 0.28/0.45
% 0.28/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.28/0.45 % Source : [Bro09]
% 0.28/0.45 % Names : tps_1094 [Bro09]
% 0.28/0.45
% 0.28/0.45 % Status : Theorem
% 0.28/0.45 % Rating : 0.00 v9.0.0, 0.10 v8.2.0, 0.15 v8.1.0, 0.09 v7.5.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.40 v5.3.0, 0.60 v5.2.0, 0.80 v5.1.0, 1.00 v5.0.0, 0.80 v4.1.0, 0.67 v4.0.0
% 0.28/0.45 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.28/0.45 % Number of atoms : 12 ( 12 equ; 0 cnn)
% 0.28/0.45 % Maximal formula atoms : 6 ( 12 avg)
% 0.28/0.45 % Number of connectives : 32 ( 1 ~; 2 |; 6 &; 19 @)
% 0.28/0.45 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.28/0.45 % Maximal formula depth : 13 ( 13 avg)
% 0.28/0.45 % Number of types : 2 ( 1 usr)
% 0.28/0.45 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.28/0.45 % Number of symbols : 3 ( 2 usr; 1 con; 0-2 aty)
% 0.28/0.45 % Number of variables : 18 ( 6 ^; 10 !; 2 ?; 18 :)
% 0.28/0.45 % SPC : TH0_THM_EQU_NAR
% 0.28/0.45
% 0.28/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.28/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.28/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.28/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.28/0.45 %------------------------------------------------------------------------------
% 0.28/0.45 thf(iS_type,type,
% 0.28/0.45 iS: $tType ).
% 0.28/0.45
% 0.28/0.45 thf(c0,type,
% 0.28/0.45 c0: iS ).
% 0.28/0.45
% 0.28/0.45 thf(cP,type,
% 0.28/0.45 cP: iS > iS > iS ).
% 0.28/0.45
% 0.28/0.45 thf(cS_T_LR_LEM2_pme,conjecture,
% 0.28/0.45 ( ( ! [Xx: iS,Xy: iS] :
% 0.28/0.45 ( ( cP @ Xx @ Xy )
% 0.28/0.45 != c0 )
% 0.28/0.45 & ! [Xx: iS,Xy: iS,Xu: iS,Xv: iS] :
% 0.28/0.45 ( ( ( cP @ Xx @ Xu )
% 0.28/0.45 = ( cP @ Xy @ Xv ) )
% 0.28/0.45 => ( ( Xx = Xy )
% 0.28/0.45 & ( Xu = Xv ) ) )
% 0.28/0.45 & ! [X: iS > $o] :
% 0.28/0.45 ( ( ( X @ c0 )
% 0.28/0.45 & ! [Xx: iS,Xy: iS] :
% 0.28/0.45 ( ( ( X @ Xx )
% 0.28/0.45 & ( X @ Xy ) )
% 0.28/0.45 => ( X @ ( cP @ Xx @ Xy ) ) ) )
% 0.28/0.45 => ! [Xx: iS] : ( X @ Xx ) ) )
% 0.28/0.45 => ( ( ( ^ [Xx: iS] :
% 0.28/0.45 ( ( Xx = c0 )
% 0.28/0.45 | ? [Xy: iS] :
% 0.28/0.45 ( c0
% 0.28/0.45 = ( cP @ Xx @ Xy ) ) ) )
% 0.28/0.45 = ( ^ [Xx: iS,Xy: iS] : ( Xx = Xy )
% 0.28/0.45 @ c0 ) )
% 0.28/0.45 & ( ( ^ [Xy: iS] :
% 0.28/0.45 ( ( Xy = c0 )
% 0.28/0.45 | ? [Xx: iS] :
% 0.28/0.45 ( c0
% 0.28/0.45 = ( cP @ Xx @ Xy ) ) ) )
% 0.28/0.45 = ( ^ [Xx: iS,Xy: iS] : ( Xx = Xy )
% 0.28/0.45 @ c0 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 %------------------------------------------------------------------------------
% 0.28/0.45 ------------------------
% 1.53/1.24 ---- Embedded in THF ---
% 1.53/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.53/1.24 %%% Generated on Tue Feb 24 12:41:56 EST 2026
% 1.53/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.53/1.24 %%% Logic specification used:
% 1.53/1.24 %%% thf(spec, logic, $$dhol).
% 1.53/1.24
% 1.53/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.SBwQMqzwpx/DTF2DTF27383.p
% See solution above
% 1.53/1.24 ------------------------
% 1.53/1.25 ---- Cleaned THF ---
% 1.53/1.25 thf(iS_type,type,
% 1.53/1.25 iS: $tType ).
% 1.53/1.25
% 1.53/1.25 thf(c0,type,
% 1.53/1.25 c0: iS ).
% 1.53/1.25
% 1.53/1.25 thf(cP,type,
% 1.53/1.25 cP: iS > iS > iS ).
% 1.53/1.25
% 1.53/1.25 thf(cS_T_LR_LEM2_pme,conjecture,
% 1.53/1.25 ( ( ! [Xx: iS,Xy: iS] :
% 1.53/1.25 ( ( cP @ Xx @ Xy )
% 1.53/1.25 != c0 )
% 1.53/1.25 & ! [Xx: iS,Xy: iS,Xu: iS,Xv: iS] :
% 1.53/1.25 ( ( ( cP @ Xx @ Xu )
% 1.53/1.25 = ( cP @ Xy @ Xv ) )
% 1.53/1.25 => ( ( Xx = Xy )
% 1.53/1.25 & ( Xu = Xv ) ) )
% 1.53/1.25 & ! [X: iS > $o] :
% 1.53/1.25 ( ( ( X @ c0 )
% 1.53/1.25 & ! [Xx: iS,Xy: iS] :
% 1.53/1.25 ( ( ( X @ Xx )
% 1.53/1.25 & ( X @ Xy ) )
% 1.53/1.25 => ( X @ ( cP @ Xx @ Xy ) ) ) )
% 1.53/1.25 => ! [Xx: iS] : ( X @ Xx ) ) )
% 1.53/1.25 => ( ( ( ^ [Xx: iS] :
% 1.53/1.25 ( ( Xx = c0 )
% 1.53/1.25 | ? [Xy: iS] :
% 1.53/1.25 ( c0
% 1.53/1.25 = ( cP @ Xx @ Xy ) ) ) )
% 1.53/1.25 = ( ^ [Xx: iS,Xy: iS] : ( Xx = Xy )
% 1.53/1.25 @ c0 ) )
% 1.53/1.25 & ( ( ^ [Xy: iS] :
% 1.53/1.25 ( ( Xy = c0 )
% 1.53/1.25 | ? [Xx: iS] :
% 1.53/1.25 ( c0
% 1.53/1.25 = ( cP @ Xx @ Xy ) ) ) )
% 1.53/1.25 = ( ^ [Xx: iS,Xy: iS] : ( Xx = Xy )
% 1.53/1.25 @ c0 ) ) ) ) ).
% 1.53/1.25 ------------------------
% 1.53/1.27 % (27483)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_27383 for (2999ds/27Mi)
% 1.53/1.27 % (27485)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_27383 for (2999ds/2Mi)
% 1.53/1.27 % (27485)Instruction limit reached!
% 1.53/1.27 % (27485)------------------------------
% 1.53/1.27 % (27485)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.27 % (27485)Termination reason: Unknown
% 1.53/1.27 % (27485)Termination phase: Saturation
% 1.53/1.27
% 1.53/1.27 % (27485)Memory used [KB]: 5500
% 1.53/1.27 % (27485)Time elapsed: 0.003 s
% 1.53/1.27 % (27485)Instructions burned: 3 (million)
% 1.53/1.27 % (27485)------------------------------
% 1.53/1.27 % (27485)------------------------------
% 1.53/1.27 % (27483)First to succeed.
% 1.53/1.28 % (27483)Refutation found. Thanks to Tanya!
% 1.53/1.28 % SZS status Theorem for DTF2THF_27383
% 1.53/1.28 % SZS output start Proof for DTF2THF_27383
% 1.53/1.28 thf(type_def_5, type, iS: $tType).
% 1.53/1.28 thf(func_def_0, type, iS: $tType).
% 1.53/1.28 thf(func_def_1, type, c0: iS).
% 1.53/1.28 thf(func_def_2, type, cP: iS > iS > iS).
% 1.53/1.28 thf(func_def_4, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.53/1.28 thf(func_def_13, type, sK0: (iS > $o) > iS).
% 1.53/1.28 thf(func_def_14, type, sK1: (iS > $o) > iS).
% 1.53/1.28 thf(func_def_16, type, ph3: !>[X0: $tType]:(X0)).
% 1.53/1.28 thf(func_def_17, type, sK4: iS).
% 1.53/1.28 thf(func_def_18, type, sK5: iS).
% 1.53/1.28 thf(func_def_19, type, sK6: iS > iS).
% 1.53/1.28 thf(func_def_20, type, sK7: iS).
% 1.53/1.28 thf(func_def_21, type, sK8: iS).
% 1.53/1.28 thf(func_def_22, type, sK9: iS).
% 1.53/1.28 thf(func_def_23, type, sK10: iS).
% 1.53/1.28 thf(func_def_24, type, sK11: iS > iS).
% 1.53/1.28 thf(f162,plain,(
% 1.53/1.28 $false),
% 1.53/1.28 inference(avatar_sat_refutation,[status(thm)],[f27,f56,f57,f101,f102,f109,f161])).
% 1.53/1.28 thf(f161,plain,(
% 1.53/1.28 ~spl2_4),
% 1.53/1.28 inference(avatar_contradiction_clause,[status(thm)],[f160])).
% 1.53/1.28 thf(f160,plain,(
% 1.53/1.28 $false | ~spl2_4),
% 1.53/1.28 inference(trivial_inequality_removal,[status(thm)],[f159])).
% 1.53/1.28 thf(f159,plain,(
% 1.53/1.28 (c0 != c0) | ~spl2_4),
% 1.53/1.28 inference(superposition,[status(thm)],[f16,f55])).
% 1.53/1.28 thf(f55,plain,(
% 1.53/1.28 (c0 = (cP @ sK5 @ sK4)) | ~spl2_4),
% 1.53/1.28 inference(avatar_component_clause,[status(thm)],[f53])).
% 1.53/1.28 thf(f53,definition,(
% 1.53/1.28 spl2_4 <=> (c0 = (cP @ sK5 @ sK4))),
% 1.53/1.28 introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition])).
% 1.53/1.28 thf(f16,plain,(
% 1.53/1.28 ( ! [X0 : iS,X1 : iS] : ((c0 != (cP @ X1 @ X0))) )),
% 1.53/1.28 inference(cnf_transformation,[status(thm)],[f10])).
% 1.53/1.28 thf(f10,plain,(
% 1.53/1.28 (((^[Y0 : iS]: ((c0 = Y0) | (?? @ iS @ (^[Y1 : iS]: (c0 = (cP @ Y1 @ Y0)))))) != ((^[Y0 : iS]: ((^[Y1 : iS]: (Y0 = Y1)))) @ c0)) | ((^[Y0 : iS]: ((c0 = Y0) | (?? @ iS @ (^[Y1 : iS]: (c0 = (cP @ Y0 @ Y1)))))) != ((^[Y0 : iS]: ((^[Y1 : iS]: (Y0 = Y1)))) @ c0))) & ! [X0 : iS,X1 : iS] : (c0 != (cP @ X1 @ X0)) & ! [X2 : iS,X3 : iS,X4 : iS,X5 : iS] : (((cP @ X3 @ X5) != (cP @ X4 @ X2)) | ((X3 = X4) & (X2 = X5))) & ! [X6 : iS > $o] : (($true != (X6 @ c0)) | ! [X7 : iS] : ($true = (X6 @ X7)) | (($true = (X6 @ (sK0 @ X6))) & ($true != (X6 @ (cP @ (sK1 @ X6) @ (sK0 @ X6)))) & ($true = (X6 @ (sK1 @ X6)))))),
% 1.53/1.28 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f8,f9])).
% 1.53/1.28 thf(f9,plain,(
% 1.53/1.28 ! [X6 : iS > $o] : (? [X8 : iS,X9 : iS] : (($true = (X6 @ X8)) & ((X6 @ (cP @ X9 @ X8)) != $true) & ($true = (X6 @ X9))) => (($true = (X6 @ (sK0 @ X6))) & ($true != (X6 @ (cP @ (sK1 @ X6) @ (sK0 @ X6)))) & ($true = (X6 @ (sK1 @ X6)))))),
% 1.53/1.28 introduced(definition,[],[choice_axiom])).
% 1.53/1.28 thf(f8,plain,(
% 1.53/1.28 (((^[Y0 : iS]: ((c0 = Y0) | (?? @ iS @ (^[Y1 : iS]: (c0 = (cP @ Y1 @ Y0)))))) != ((^[Y0 : iS]: ((^[Y1 : iS]: (Y0 = Y1)))) @ c0)) | ((^[Y0 : iS]: ((c0 = Y0) | (?? @ iS @ (^[Y1 : iS]: (c0 = (cP @ Y0 @ Y1)))))) != ((^[Y0 : iS]: ((^[Y1 : iS]: (Y0 = Y1)))) @ c0))) & ! [X0 : iS,X1 : iS] : (c0 != (cP @ X1 @ X0)) & ! [X2 : iS,X3 : iS,X4 : iS,X5 : iS] : (((cP @ X3 @ X5) != (cP @ X4 @ X2)) | ((X3 = X4) & (X2 = X5))) & ! [X6 : iS > $o] : (($true != (X6 @ c0)) | ! [X7 : iS] : ($true = (X6 @ X7)) | ? [X8 : iS,X9 : iS] : (($true = (X6 @ X8)) & ((X6 @ (cP @ X9 @ X8)) != $true) & ($true = (X6 @ X9))))),
% 1.53/1.28 inference(rectify,[status(thm)],[f7])).
% 1.53/1.28 thf(f7,plain,(
% 1.53/1.28 (((^[Y0 : iS]: ((c0 = Y0) | (?? @ iS @ (^[Y1 : iS]: (c0 = (cP @ Y1 @ Y0)))))) != ((^[Y0 : iS]: ((^[Y1 : iS]: (Y0 = Y1)))) @ c0)) | ((^[Y0 : iS]: ((c0 = Y0) | (?? @ iS @ (^[Y1 : iS]: (c0 = (cP @ Y0 @ Y1)))))) != ((^[Y0 : iS]: ((^[Y1 : iS]: (Y0 = Y1)))) @ c0))) & ! [X8 : iS,X9 : iS] : (c0 != (cP @ X9 @ X8)) & ! [X4 : iS,X5 : iS,X6 : iS,X7 : iS] : (((cP @ X5 @ X7) != (cP @ X6 @ X4)) | ((X5 = X6) & (X4 = X7))) & ! [X0 : iS > $o] : (($true != (X0 @ c0)) | ! [X3 : iS] : ($true = (X0 @ X3)) | ? [X1 : iS,X2 : iS] : (($true = (X0 @ X1)) & ((X0 @ (cP @ X2 @ X1)) != $true) & ($true = (X0 @ X2))))),
% 1.53/1.28 inference(flattening,[status(thm)],[f6])).
% 1.53/1.28 thf(f6,plain,(
% 1.53/1.28 (((^[Y0 : iS]: ((c0 = Y0) | (?? @ iS @ (^[Y1 : iS]: (c0 = (cP @ Y1 @ Y0)))))) != ((^[Y0 : iS]: ((^[Y1 : iS]: (Y0 = Y1)))) @ c0)) | ((^[Y0 : iS]: ((c0 = Y0) | (?? @ iS @ (^[Y1 : iS]: (c0 = (cP @ Y0 @ Y1)))))) != ((^[Y0 : iS]: ((^[Y1 : iS]: (Y0 = Y1)))) @ c0))) & (! [X8 : iS,X9 : iS] : (c0 != (cP @ X9 @ X8)) & ! [X0 : iS > $o] : (! [X3 : iS] : ($true = (X0 @ X3)) | (($true != (X0 @ c0)) | ? [X1 : iS,X2 : iS] : (((X0 @ (cP @ X2 @ X1)) != $true) & (($true = (X0 @ X1)) & ($true = (X0 @ X2)))))) & ! [X4 : iS,X5 : iS,X6 : iS,X7 : iS] : (((cP @ X5 @ X7) != (cP @ X6 @ X4)) | ((X5 = X6) & (X4 = X7))))),
% 1.53/1.28 inference(ennf_transformation,[status(thm)],[f5])).
% 1.53/1.28 thf(f5,plain,(
% 1.53/1.28 ~((! [X8 : iS,X9 : iS] : (c0 != (cP @ X9 @ X8)) & ! [X0 : iS > $o] : ((($true = (X0 @ c0)) & ! [X1 : iS,X2 : iS] : ((($true = (X0 @ X1)) & ($true = (X0 @ X2))) => ((X0 @ (cP @ X2 @ X1)) = $true))) => ! [X3 : iS] : ($true = (X0 @ X3))) & ! [X4 : iS,X5 : iS,X6 : iS,X7 : iS] : (((cP @ X5 @ X7) = (cP @ X6 @ X4)) => ((X5 = X6) & (X4 = X7)))) => (((^[Y0 : iS]: ((c0 = Y0) | (?? @ iS @ (^[Y1 : iS]: (c0 = (cP @ Y1 @ Y0)))))) = ((^[Y0 : iS]: ((^[Y1 : iS]: (Y0 = Y1)))) @ c0)) & ((^[Y0 : iS]: ((c0 = Y0) | (?? @ iS @ (^[Y1 : iS]: (c0 = (cP @ Y0 @ Y1)))))) = ((^[Y0 : iS]: ((^[Y1 : iS]: (Y0 = Y1)))) @ c0))))),
% 1.53/1.28 inference(fool_elimination,[status(thm)],[f4])).
% 1.53/1.28 thf(f4,plain,(
% 1.53/1.28 ~((! [X0 : iS > $o] : ((! [X1 : iS,X2 : iS] : (((X0 @ X1) & (X0 @ X2)) => (X0 @ (cP @ X2 @ X1))) & (X0 @ c0)) => ! [X3 : iS] : (X0 @ X3)) & ! [X4 : iS,X5 : iS,X6 : iS,X7 : iS] : (((cP @ X5 @ X7) = (cP @ X6 @ X4)) => ((X4 = X7) & (X5 = X6))) & ! [X8 : iS,X9 : iS] : (c0 != (cP @ X9 @ X8))) => ((((^[X10 : iS, X11 : iS] : ((X10 = X11))) @ c0) = (^[X12 : iS] : (? [X13 : iS] : (c0 = (cP @ X13 @ X12)) | (c0 = X12)))) & ((^[X14 : iS] : (? [X15 : iS] : (c0 = (cP @ X14 @ X15)) | (c0 = X14))) = ((^[X16 : iS, X17 : iS] : ((X16 = X17))) @ c0))))),
% 1.53/1.28 inference(rectify,[status(thm)],[f2])).
% 1.53/1.28 thf(f2,negated_conjecture,(
% 1.53/1.28 ~((! [X4 : iS > $o] : ((! [X1 : iS,X0 : iS] : (((X4 @ X1) & (X4 @ X0)) => (X4 @ (cP @ X0 @ X1))) & (X4 @ c0)) => ! [X0 : iS] : (X4 @ X0)) & ! [X3 : iS,X0 : iS,X1 : iS,X2 : iS] : (((cP @ X0 @ X2) = (cP @ X1 @ X3)) => ((X2 = X3) & (X0 = X1))) & ! [X1 : iS,X0 : iS] : ((cP @ X0 @ X1) != c0)) => ((((^[X0 : iS, X1 : iS] : ((X0 = X1))) @ c0) = (^[X1 : iS] : (? [X0 : iS] : ((cP @ X0 @ X1) = c0) | (c0 = X1)))) & ((^[X0 : iS] : (? [X1 : iS] : ((cP @ X0 @ X1) = c0) | (c0 = X0))) = ((^[X0 : iS, X1 : iS] : ((X0 = X1))) @ c0))))),
% 1.53/1.28 inference(negated_conjecture,[status(cth)],[f1])).
% 1.53/1.28 thf(f1,conjecture,(
% 1.53/1.28 (! [X4 : iS > $o] : ((! [X1 : iS,X0 : iS] : (((X4 @ X1) & (X4 @ X0)) => (X4 @ (cP @ X0 @ X1))) & (X4 @ c0)) => ! [X0 : iS] : (X4 @ X0)) & ! [X3 : iS,X0 : iS,X1 : iS,X2 : iS] : (((cP @ X0 @ X2) = (cP @ X1 @ X3)) => ((X2 = X3) & (X0 = X1))) & ! [X1 : iS,X0 : iS] : ((cP @ X0 @ X1) != c0)) => ((((^[X0 : iS, X1 : iS] : ((X0 = X1))) @ c0) = (^[X1 : iS] : (? [X0 : iS] : ((cP @ X0 @ X1) = c0) | (c0 = X1)))) & ((^[X0 : iS] : (? [X1 : iS] : ((cP @ X0 @ X1) = c0) | (c0 = X0))) = ((^[X0 : iS, X1 : iS] : ((X0 = X1))) @ c0)))),
% 1.53/1.28 file('/export/starexec/sandbox2/tmp/tmp.SBwQMqzwpx/DTF2THF_27383.p',cS_T_LR_LEM2_pme)).
% 1.53/1.28 thf(f109,plain,(
% 1.53/1.28 ~spl2_6),
% 1.53/1.28 inference(avatar_contradiction_clause,[status(thm)],[f108])).
% 1.53/1.28 thf(f108,plain,(
% 1.53/1.28 $false | ~spl2_6),
% 1.53/1.28 inference(trivial_inequality_removal,[status(thm)],[f107])).
% 1.53/1.28 thf(f107,plain,(
% 1.53/1.28 (c0 != c0) | ~spl2_6),
% 1.53/1.28 inference(superposition,[status(thm)],[f16,f100])).
% 1.53/1.28 thf(f100,plain,(
% 1.53/1.28 (c0 = (cP @ sK7 @ sK8)) | ~spl2_6),
% 1.53/1.28 inference(avatar_component_clause,[status(thm)],[f98])).
% 1.53/1.28 thf(f98,definition,(
% 1.53/1.28 spl2_6 <=> (c0 = (cP @ sK7 @ sK8))),
% 1.53/1.28 introduced(definition,[new_symbols(naming,[spl2_6])],[avatar_definition])).
% 1.53/1.28 thf(f102,plain,(
% 1.53/1.28 ~spl2_5 | spl2_2),
% 1.53/1.28 inference(avatar_split_clause,[status(thm)],[f82,f24,f94])).
% 1.53/1.28 thf(f94,definition,(
% 1.53/1.28 spl2_5 <=> (c0 = sK7)),
% 1.53/1.28 introduced(definition,[new_symbols(naming,[spl2_5])],[avatar_definition])).
% 1.53/1.28 thf(f24,definition,(
% 1.53/1.28 spl2_2 <=> ((^[Y0 : iS]: ((c0 = Y0) | (?? @ iS @ (^[Y1 : iS]: (c0 = (cP @ Y0 @ Y1)))))) = (= @ c0))),
% 1.53/1.28 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.53/1.28 thf(f82,plain,(
% 1.53/1.28 (c0 != sK7) | spl2_2),
% 1.53/1.28 inference(equality_proxy_clausification,[status(thm)],[f81])).
% 1.53/1.28 thf(f81,plain,(
% 1.53/1.28 ((c0 = sK7) = $false) | spl2_2),
% 1.53/1.28 inference(duplicate_literal_removal,[status(thm)],[f80])).
% 1.53/1.28 thf(f80,plain,(
% 1.53/1.28 ((c0 = sK7) = $false) | ((c0 = sK7) = $false) | spl2_2),
% 1.53/1.28 inference(binary_proxy_clausification,[status(thm)],[f78])).
% 1.53/1.28 thf(f78,plain,(
% 1.53/1.28 (((c0 = sK7) | (?? @ iS @ (^[Y0 : iS]: (c0 = (cP @ sK7 @ Y0))))) = $false) | ((c0 = sK7) = $false) | spl2_2),
% 1.53/1.28 inference(binary_proxy_clausification,[status(thm)],[f76])).
% 1.53/1.28 thf(f76,plain,(
% 1.53/1.28 ((c0 = sK7) != ((c0 = sK7) | (?? @ iS @ (^[Y0 : iS]: (c0 = (cP @ sK7 @ Y0)))))) | spl2_2),
% 1.53/1.28 inference(beta_eta_normalization,[status(thm)],[f75])).
% 1.53/1.28 thf(f75,plain,(
% 1.53/1.28 ((c0 = sK7) != ((^[Y0 : iS]: ((c0 = Y0) | (?? @ iS @ (^[Y1 : iS]: (c0 = (cP @ Y0 @ Y1)))))) @ sK7)) | spl2_2),
% 1.53/1.28 inference(negative_extensionality,[status(thm)],[f26])).
% 1.53/1.28 thf(f26,plain,(
% 1.53/1.28 ((^[Y0 : iS]: ((c0 = Y0) | (?? @ iS @ (^[Y1 : iS]: (c0 = (cP @ Y0 @ Y1)))))) != (= @ c0)) | spl2_2),
% 1.53/1.28 inference(avatar_component_clause,[status(thm)],[f24])).
% 1.53/1.28 thf(f101,plain,(
% 1.53/1.28 spl2_5 | spl2_6 | spl2_2),
% 1.53/1.28 inference(avatar_split_clause,[status(thm)],[f92,f24,f98,f94])).
% 1.53/1.28 thf(f92,plain,(
% 1.53/1.28 (c0 = sK7) | (c0 = (cP @ sK7 @ sK8)) | spl2_2),
% 1.53/1.28 inference(equality_proxy_clausification,[status(thm)],[f91])).
% 1.53/1.28 thf(f91,plain,(
% 1.53/1.28 (c0 = (cP @ sK7 @ sK8)) | ($true = (c0 = sK7)) | spl2_2),
% 1.53/1.28 inference(equality_proxy_clausification,[status(thm)],[f90])).
% 1.53/1.28 thf(f90,plain,(
% 1.53/1.28 ($true = (c0 = (cP @ sK7 @ sK8))) | ($true = (c0 = sK7)) | spl2_2),
% 1.53/1.28 inference(beta_eta_normalization,[status(thm)],[f89])).
% 1.53/1.28 thf(f89,plain,(
% 1.53/1.28 (((^[Y0 : iS]: (c0 = (cP @ sK7 @ Y0))) @ sK8) = $true) | ($true = (c0 = sK7)) | spl2_2),
% 1.53/1.28 inference(sigma_clausification,[status(thm)],[f88])).
% 1.53/1.28 thf(f88,plain,(
% 1.53/1.28 ($true = (?? @ iS @ (^[Y0 : iS]: (c0 = (cP @ sK7 @ Y0))))) | ($true = (c0 = sK7)) | spl2_2),
% 1.53/1.28 inference(duplicate_literal_removal,[status(thm)],[f87])).
% 1.53/1.28 thf(f87,plain,(
% 1.53/1.28 ($true = (c0 = sK7)) | ($true = (?? @ iS @ (^[Y0 : iS]: (c0 = (cP @ sK7 @ Y0))))) | ($true = (c0 = sK7)) | spl2_2),
% 1.53/1.28 inference(binary_proxy_clausification,[status(thm)],[f77])).
% 1.53/1.28 thf(f77,plain,(
% 1.53/1.28 ($true = ((c0 = sK7) | (?? @ iS @ (^[Y0 : iS]: (c0 = (cP @ sK7 @ Y0)))))) | ($true = (c0 = sK7)) | spl2_2),
% 1.53/1.28 inference(binary_proxy_clausification,[status(thm)],[f76])).
% 1.53/1.28 thf(f57,plain,(
% 1.53/1.28 ~spl2_3 | spl2_1),
% 1.53/1.28 inference(avatar_split_clause,[status(thm)],[f37,f20,f49])).
% 1.53/1.28 thf(f49,definition,(
% 1.53/1.28 spl2_3 <=> (c0 = sK4)),
% 1.53/1.28 introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition])).
% 1.53/1.28 thf(f20,definition,(
% 1.53/1.28 spl2_1 <=> ((= @ c0) = (^[Y0 : iS]: ((c0 = Y0) | (?? @ iS @ (^[Y1 : iS]: (c0 = (cP @ Y1 @ Y0)))))))),
% 1.53/1.28 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.53/1.28 thf(f37,plain,(
% 1.53/1.28 (c0 != sK4) | spl2_1),
% 1.53/1.28 inference(equality_proxy_clausification,[status(thm)],[f36])).
% 1.53/1.28 thf(f36,plain,(
% 1.53/1.28 ((c0 = sK4) = $false) | spl2_1),
% 1.53/1.28 inference(duplicate_literal_removal,[status(thm)],[f35])).
% 1.53/1.28 thf(f35,plain,(
% 1.53/1.28 ((c0 = sK4) = $false) | ((c0 = sK4) = $false) | spl2_1),
% 1.53/1.28 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 1.53/1.28 thf(f33,plain,(
% 1.53/1.28 ($false = ((c0 = sK4) | (?? @ iS @ (^[Y0 : iS]: (c0 = (cP @ Y0 @ sK4)))))) | ((c0 = sK4) = $false) | spl2_1),
% 1.53/1.28 inference(binary_proxy_clausification,[status(thm)],[f31])).
% 1.53/1.28 thf(f31,plain,(
% 1.53/1.28 ((c0 = sK4) != ((c0 = sK4) | (?? @ iS @ (^[Y0 : iS]: (c0 = (cP @ Y0 @ sK4)))))) | spl2_1),
% 1.53/1.28 inference(beta_eta_normalization,[status(thm)],[f30])).
% 1.53/1.28 thf(f30,plain,(
% 1.53/1.28 (((^[Y0 : iS]: ((c0 = Y0) | (?? @ iS @ (^[Y1 : iS]: (c0 = (cP @ Y1 @ Y0)))))) @ sK4) != (c0 = sK4)) | spl2_1),
% 1.53/1.28 inference(negative_extensionality,[status(thm)],[f22])).
% 1.53/1.28 thf(f22,plain,(
% 1.53/1.28 ((= @ c0) != (^[Y0 : iS]: ((c0 = Y0) | (?? @ iS @ (^[Y1 : iS]: (c0 = (cP @ Y1 @ Y0))))))) | spl2_1),
% 1.53/1.28 inference(avatar_component_clause,[status(thm)],[f20])).
% 1.53/1.28 thf(f56,plain,(
% 1.53/1.28 spl2_3 | spl2_4 | spl2_1),
% 1.53/1.28 inference(avatar_split_clause,[status(thm)],[f47,f20,f53,f49])).
% 1.53/1.28 thf(f47,plain,(
% 1.53/1.28 (c0 = sK4) | (c0 = (cP @ sK5 @ sK4)) | spl2_1),
% 1.53/1.28 inference(equality_proxy_clausification,[status(thm)],[f46])).
% 1.53/1.28 thf(f46,plain,(
% 1.53/1.28 ((c0 = sK4) = $true) | (c0 = (cP @ sK5 @ sK4)) | spl2_1),
% 1.53/1.28 inference(equality_proxy_clausification,[status(thm)],[f45])).
% 1.53/1.28 thf(f45,plain,(
% 1.53/1.28 ($true = (c0 = (cP @ sK5 @ sK4))) | ((c0 = sK4) = $true) | spl2_1),
% 1.53/1.28 inference(beta_eta_normalization,[status(thm)],[f44])).
% 1.53/1.28 thf(f44,plain,(
% 1.53/1.28 ((c0 = sK4) = $true) | ($true = ((^[Y0 : iS]: (c0 = (cP @ Y0 @ sK4))) @ sK5)) | spl2_1),
% 1.53/1.28 inference(sigma_clausification,[status(thm)],[f43])).
% 1.53/1.28 thf(f43,plain,(
% 1.53/1.28 ($true = (?? @ iS @ (^[Y0 : iS]: (c0 = (cP @ Y0 @ sK4))))) | ((c0 = sK4) = $true) | spl2_1),
% 1.53/1.28 inference(duplicate_literal_removal,[status(thm)],[f42])).
% 1.53/1.28 thf(f42,plain,(
% 1.53/1.28 ((c0 = sK4) = $true) | ((c0 = sK4) = $true) | ($true = (?? @ iS @ (^[Y0 : iS]: (c0 = (cP @ Y0 @ sK4))))) | spl2_1),
% 1.53/1.28 inference(binary_proxy_clausification,[status(thm)],[f32])).
% 1.53/1.28 thf(f32,plain,(
% 1.53/1.28 ($true = ((c0 = sK4) | (?? @ iS @ (^[Y0 : iS]: (c0 = (cP @ Y0 @ sK4)))))) | ((c0 = sK4) = $true) | spl2_1),
% 1.53/1.28 inference(binary_proxy_clausification,[status(thm)],[f31])).
% 1.53/1.28 thf(f27,plain,(
% 1.53/1.28 ~spl2_1 | ~spl2_2),
% 1.53/1.28 inference(avatar_split_clause,[status(thm)],[f18,f24,f20])).
% 1.53/1.28 thf(f18,plain,(
% 1.53/1.28 ((^[Y0 : iS]: ((c0 = Y0) | (?? @ iS @ (^[Y1 : iS]: (c0 = (cP @ Y0 @ Y1)))))) != (= @ c0)) | ((= @ c0) != (^[Y0 : iS]: ((c0 = Y0) | (?? @ iS @ (^[Y1 : iS]: (c0 = (cP @ Y1 @ Y0)))))))),
% 1.53/1.28 inference(beta_eta_normalization,[status(thm)],[f17])).
% 1.53/1.28 thf(f17,plain,(
% 1.53/1.28 ((^[Y0 : iS]: ((c0 = Y0) | (?? @ iS @ (^[Y1 : iS]: (c0 = (cP @ Y0 @ Y1)))))) != ((^[Y0 : iS]: ((^[Y1 : iS]: (Y0 = Y1)))) @ c0)) | ((^[Y0 : iS]: ((c0 = Y0) | (?? @ iS @ (^[Y1 : iS]: (c0 = (cP @ Y1 @ Y0)))))) != ((^[Y0 : iS]: ((^[Y1 : iS]: (Y0 = Y1)))) @ c0))),
% 1.53/1.28 inference(cnf_transformation,[status(thm)],[f10])).
% 1.53/1.28 % SZS output end Proof for DTF2THF_27383
% 1.53/1.28 % (27483)------------------------------
% 1.53/1.28 % (27483)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.28 % (27483)Termination reason: Refutation
% 1.53/1.28
% 1.53/1.28 % (27483)Memory used [KB]: 5628
% 1.53/1.28 % (27483)Time elapsed: 0.006 s
% 1.53/1.28 % (27483)Instructions burned: 9 (million)
% 1.53/1.28 % (27483)------------------------------
% 1.53/1.28 % (27483)------------------------------
% 1.53/1.28 % (27480)Success in time 0.005 s
%------------------------------------------------------------------------------