%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU692^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:36:27 AM UTC 2026
% Result : Theorem 1.59s 1.33s
% Output : Refutation 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 9
% Syntax : Number of formulae : 58 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 825 ( 245 equ; 0 cnn)
% Maximal formula atoms : 12 ( 14 avg)
% Number of connectives : 1135 ( 111 ~; 92 |; 67 &; 815 @)
% ( 5 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 15 con; 0-4 aty)
% Number of variables : 177 ( 0 ^; 131 !; 46 ?; 177 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
func: $i > $i > $i > $o ).
thf(func_def_2,type,
funcSet: $i > $i > $i ).
thf(func_def_3,type,
ap: $i > $i > $i > $i > $i ).
thf(func_def_17,type,
sK8: $i > $i > $i > $i > $i ).
thf(f82,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f81,f60]) ).
thf(f60,plain,
( ( func @ sK1 @ sK2 @ sK3 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f58]) ).
thf(f58,plain,
( ( ( func @ sK1 @ sK2 @ sK3 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f57,f32]) ).
thf(f32,plain,
( ( in @ sK3 @ ( funcSet @ sK1 @ sK2 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ( funcext = $true )
& ( ( in @ sK0 @ ( funcSet @ sK1 @ sK2 ) )
= $true )
& ( sK0 != sK3 )
& ! [X4: $i] :
( ( ( ap @ sK1 @ sK2 @ sK0 @ X4 )
= ( ap @ sK1 @ sK2 @ sK3 @ X4 ) )
| ( ( in @ X4 @ sK1 )
!= $true ) )
& ( ( in @ sK3 @ ( funcSet @ sK1 @ sK2 ) )
= $true )
& ( infuncsetfunc = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f17,f19,f18]) ).
thf(f18,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( funcSet @ X1 @ X2 ) )
= $true )
& ? [X3: $i] :
( ( X0 != X3 )
& ! [X4: $i] :
( ( ( ap @ X1 @ X2 @ X3 @ X4 )
= ( ap @ X1 @ X2 @ X0 @ X4 ) )
| ( ( in @ X4 @ X1 )
!= $true ) )
& ( ( in @ X3 @ ( funcSet @ X1 @ X2 ) )
= $true ) ) )
=> ( ( ( in @ sK0 @ ( funcSet @ sK1 @ sK2 ) )
= $true )
& ? [X3: $i] :
( ( sK0 != X3 )
& ! [X4: $i] :
( ( ( ap @ sK1 @ sK2 @ sK0 @ X4 )
= ( ap @ sK1 @ sK2 @ X3 @ X4 ) )
| ( ( in @ X4 @ sK1 )
!= $true ) )
& ( ( in @ X3 @ ( funcSet @ sK1 @ sK2 ) )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f19,plain,
( ? [X3: $i] :
( ( sK0 != X3 )
& ! [X4: $i] :
( ( ( ap @ sK1 @ sK2 @ sK0 @ X4 )
= ( ap @ sK1 @ sK2 @ X3 @ X4 ) )
| ( ( in @ X4 @ sK1 )
!= $true ) )
& ( ( in @ X3 @ ( funcSet @ sK1 @ sK2 ) )
= $true ) )
=> ( ( sK0 != sK3 )
& ! [X4: $i] :
( ( ( ap @ sK1 @ sK2 @ sK0 @ X4 )
= ( ap @ sK1 @ sK2 @ sK3 @ X4 ) )
| ( ( in @ X4 @ sK1 )
!= $true ) )
& ( ( in @ sK3 @ ( funcSet @ sK1 @ sK2 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
( ( funcext = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( funcSet @ X1 @ X2 ) )
= $true )
& ? [X3: $i] :
( ( X0 != X3 )
& ! [X4: $i] :
( ( ( ap @ X1 @ X2 @ X3 @ X4 )
= ( ap @ X1 @ X2 @ X0 @ X4 ) )
| ( ( in @ X4 @ X1 )
!= $true ) )
& ( ( in @ X3 @ ( funcSet @ X1 @ X2 ) )
= $true ) ) )
& ( infuncsetfunc = $true ) ),
inference(rectify,[status(thm)],[f15]) ).
thf(f15,plain,
( ( funcext = $true )
& ? [X1: $i,X0: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( funcSet @ X0 @ X2 ) ) )
& ? [X3: $i] :
( ( X1 != X3 )
& ! [X4: $i] :
( ( ( ap @ X0 @ X2 @ X1 @ X4 )
= ( ap @ X0 @ X2 @ X3 @ X4 ) )
| ( ( in @ X4 @ X0 )
!= $true ) )
& ( ( in @ X3 @ ( funcSet @ X0 @ X2 ) )
= $true ) ) )
& ( infuncsetfunc = $true ) ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
( ? [X1: $i,X0: $i,X2: $i] :
( ? [X3: $i] :
( ( X1 != X3 )
& ! [X4: $i] :
( ( ( ap @ X0 @ X2 @ X1 @ X4 )
= ( ap @ X0 @ X2 @ X3 @ X4 ) )
| ( ( in @ X4 @ X0 )
!= $true ) )
& ( ( in @ X3 @ ( funcSet @ X0 @ X2 ) )
= $true ) )
& ( $true
= ( in @ X1 @ ( funcSet @ X0 @ X2 ) ) ) )
& ( funcext = $true )
& ( infuncsetfunc = $true ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( ( infuncsetfunc = $true )
=> ( ( funcext = $true )
=> ! [X1: $i,X0: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( funcSet @ X0 @ X2 ) ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ ( funcSet @ X0 @ X2 ) )
= $true )
=> ( ! [X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
=> ( ( ap @ X0 @ X2 @ X1 @ X4 )
= ( ap @ X0 @ X2 @ X3 @ X4 ) ) )
=> ( X1 = X3 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( infuncsetfunc
=> ( funcext
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ ( funcSet @ X0 @ X2 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( funcSet @ X0 @ X2 ) )
=> ( ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( ap @ X0 @ X2 @ X1 @ X4 )
= ( ap @ X0 @ X2 @ X3 @ X4 ) ) )
=> ( X1 = X3 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( infuncsetfunc
=> ( funcext
=> ! [X0: $i,X2: $i,X1: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( funcSet @ X0 @ X1 ) )
=> ( ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( ap @ X0 @ X1 @ X2 @ X4 )
= ( ap @ X0 @ X1 @ X3 @ X4 ) ) )
=> ( X2 = X3 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( infuncsetfunc
=> ( funcext
=> ! [X0: $i,X2: $i,X1: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( funcSet @ X0 @ X1 ) )
=> ( ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( ap @ X0 @ X1 @ X2 @ X4 )
= ( ap @ X0 @ X1 @ X3 @ X4 ) ) )
=> ( X2 = X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.W6JbVk1m11/DTF2THF_18697.p',funcext2) ).
thf(f57,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X4 @ ( funcSet @ X5 @ X3 ) ) )
| ( ( func @ X5 @ X3 @ X4 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f54]) ).
thf(f54,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( func @ X5 @ X3 @ X4 )
= $true )
| ( $true != $true )
| ( $true
!= ( in @ X4 @ ( funcSet @ X5 @ X3 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f43,f31]) ).
thf(f31,plain,
infuncsetfunc = $true,
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f43,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X4 @ ( funcSet @ X5 @ X3 ) ) )
| ( ( func @ X5 @ X3 @ X4 )
= $true )
| ( infuncsetfunc != $true ) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ( infuncsetfunc = $true )
| ( ( $true
= ( in @ sK10 @ ( funcSet @ sK11 @ sK9 ) ) )
& ( $true
!= ( func @ sK11 @ sK9 @ sK10 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X4 @ ( funcSet @ X5 @ X3 ) ) )
| ( ( func @ X5 @ X3 @ X4 )
= $true ) )
| ( infuncsetfunc != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f28,f29]) ).
thf(f29,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( funcSet @ X2 @ X0 ) )
= $true )
& ( ( func @ X2 @ X0 @ X1 )
!= $true ) )
=> ( ( $true
= ( in @ sK10 @ ( funcSet @ sK11 @ sK9 ) ) )
& ( $true
!= ( func @ sK11 @ sK9 @ sK10 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f28,plain,
( ( ( infuncsetfunc = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( funcSet @ X2 @ X0 ) )
= $true )
& ( ( func @ X2 @ X0 @ X1 )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X4 @ ( funcSet @ X5 @ X3 ) ) )
| ( ( func @ X5 @ X3 @ X4 )
= $true ) )
| ( infuncsetfunc != $true ) ) ),
inference(rectify,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ( infuncsetfunc = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( funcSet @ X2 @ X0 ) )
= $true )
& ( ( func @ X2 @ X0 @ X1 )
!= $true ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( funcSet @ X2 @ X0 ) )
!= $true )
| ( ( func @ X2 @ X0 @ X1 )
= $true ) )
| ( infuncsetfunc != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( infuncsetfunc = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( funcSet @ X2 @ X0 ) )
!= $true )
| ( ( func @ X2 @ X0 @ X1 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( funcSet @ X2 @ X0 ) )
= $true )
=> ( ( func @ X2 @ X0 @ X1 )
= $true ) )
<=> ( infuncsetfunc = $true ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( funcSet @ X2 @ X0 ) )
=> ( func @ X2 @ X0 @ X1 ) )
= infuncsetfunc ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ( func @ X0 @ X1 @ X2 ) )
= infuncsetfunc ),
file('/export/starexec/sandbox2/tmp/tmp.W6JbVk1m11/DTF2THF_18697.p',infuncsetfunc) ).
thf(f81,plain,
( ( func @ sK1 @ sK2 @ sK3 )
!= $true ),
inference(subsumption_resolution,[status(thm)],[f80,f34]) ).
thf(f34,plain,
sK0 != sK3,
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f80,plain,
( ( sK0 = sK3 )
| ( ( func @ sK1 @ sK2 @ sK3 )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f79,f61]) ).
thf(f61,plain,
( ( func @ sK1 @ sK2 @ sK0 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f59]) ).
thf(f59,plain,
( ( $true != $true )
| ( ( func @ sK1 @ sK2 @ sK0 )
= $true ) ),
inference(superposition,[status(thm)],[f57,f35]) ).
thf(f35,plain,
( ( in @ sK0 @ ( funcSet @ sK1 @ sK2 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f79,plain,
( ( ( func @ sK1 @ sK2 @ sK0 )
!= $true )
| ( sK0 = sK3 )
| ( ( func @ sK1 @ sK2 @ sK3 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f78]) ).
thf(f78,plain,
( ( ( func @ sK1 @ sK2 @ sK3 )
!= $true )
| ( sK0 = sK3 )
| ( ( func @ sK1 @ sK2 @ sK0 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f73,f55]) ).
thf(f55,plain,
! [X8: $i,X6: $i,X7: $i,X5: $i] :
( ( ( in @ ( sK8 @ X8 @ X7 @ X6 @ X5 ) @ X6 )
= $true )
| ( X5 = X8 )
| ( ( func @ X6 @ X7 @ X8 )
!= $true )
| ( ( func @ X6 @ X7 @ X5 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f50]) ).
thf(f50,plain,
! [X8: $i,X6: $i,X7: $i,X5: $i] :
( ( $true != $true )
| ( X5 = X8 )
| ( ( func @ X6 @ X7 @ X5 )
!= $true )
| ( ( func @ X6 @ X7 @ X8 )
!= $true )
| ( ( in @ ( sK8 @ X8 @ X7 @ X6 @ X5 ) @ X6 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f38,f36]) ).
thf(f36,plain,
funcext = $true,
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f38,plain,
! [X8: $i,X6: $i,X7: $i,X5: $i] :
( ( ( func @ X6 @ X7 @ X5 )
!= $true )
| ( ( in @ ( sK8 @ X8 @ X7 @ X6 @ X5 ) @ X6 )
= $true )
| ( ( func @ X6 @ X7 @ X8 )
!= $true )
| ( X5 = X8 )
| ( funcext != $true ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ( funcext = $true )
| ( ( ( func @ sK5 @ sK6 @ sK4 )
= $true )
& ! [X4: $i] :
( ( ( in @ X4 @ sK5 )
!= $true )
| ( ( ap @ sK5 @ sK6 @ sK7 @ X4 )
= ( ap @ sK5 @ sK6 @ sK4 @ X4 ) ) )
& ( ( func @ sK5 @ sK6 @ sK7 )
= $true )
& ( sK7 != sK4 ) ) )
& ( ! [X5: $i,X6: $i,X7: $i] :
( ( ( func @ X6 @ X7 @ X5 )
!= $true )
| ! [X8: $i] :
( ( ( ( in @ ( sK8 @ X8 @ X7 @ X6 @ X5 ) @ X6 )
= $true )
& ( ( ap @ X6 @ X7 @ X8 @ ( sK8 @ X8 @ X7 @ X6 @ X5 ) )
!= ( ap @ X6 @ X7 @ X5 @ ( sK8 @ X8 @ X7 @ X6 @ X5 ) ) ) )
| ( ( func @ X6 @ X7 @ X8 )
!= $true )
| ( X5 = X8 ) ) )
| ( funcext != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8])],[f22,f25,f24,f23]) ).
thf(f23,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X1 @ X2 @ X0 )
= $true )
& ? [X3: $i] :
( ! [X4: $i] :
( ( ( in @ X4 @ X1 )
!= $true )
| ( ( ap @ X1 @ X2 @ X3 @ X4 )
= ( ap @ X1 @ X2 @ X0 @ X4 ) ) )
& ( ( func @ X1 @ X2 @ X3 )
= $true )
& ( X0 != X3 ) ) )
=> ( ( ( func @ sK5 @ sK6 @ sK4 )
= $true )
& ? [X3: $i] :
( ! [X4: $i] :
( ( ( in @ X4 @ sK5 )
!= $true )
| ( ( ap @ sK5 @ sK6 @ sK4 @ X4 )
= ( ap @ sK5 @ sK6 @ X3 @ X4 ) ) )
& ( ( func @ sK5 @ sK6 @ X3 )
= $true )
& ( sK4 != X3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f24,plain,
( ? [X3: $i] :
( ! [X4: $i] :
( ( ( in @ X4 @ sK5 )
!= $true )
| ( ( ap @ sK5 @ sK6 @ sK4 @ X4 )
= ( ap @ sK5 @ sK6 @ X3 @ X4 ) ) )
& ( ( func @ sK5 @ sK6 @ X3 )
= $true )
& ( sK4 != X3 ) )
=> ( ! [X4: $i] :
( ( ( in @ X4 @ sK5 )
!= $true )
| ( ( ap @ sK5 @ sK6 @ sK7 @ X4 )
= ( ap @ sK5 @ sK6 @ sK4 @ X4 ) ) )
& ( ( func @ sK5 @ sK6 @ sK7 )
= $true )
& ( sK7 != sK4 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f25,plain,
! [X5: $i,X6: $i,X7: $i,X8: $i] :
( ? [X9: $i] :
( ( ( in @ X9 @ X6 )
= $true )
& ( ( ap @ X6 @ X7 @ X5 @ X9 )
!= ( ap @ X6 @ X7 @ X8 @ X9 ) ) )
=> ( ( ( in @ ( sK8 @ X8 @ X7 @ X6 @ X5 ) @ X6 )
= $true )
& ( ( ap @ X6 @ X7 @ X8 @ ( sK8 @ X8 @ X7 @ X6 @ X5 ) )
!= ( ap @ X6 @ X7 @ X5 @ ( sK8 @ X8 @ X7 @ X6 @ X5 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f22,plain,
( ( ( funcext = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X1 @ X2 @ X0 )
= $true )
& ? [X3: $i] :
( ! [X4: $i] :
( ( ( in @ X4 @ X1 )
!= $true )
| ( ( ap @ X1 @ X2 @ X3 @ X4 )
= ( ap @ X1 @ X2 @ X0 @ X4 ) ) )
& ( ( func @ X1 @ X2 @ X3 )
= $true )
& ( X0 != X3 ) ) ) )
& ( ! [X5: $i,X6: $i,X7: $i] :
( ( ( func @ X6 @ X7 @ X5 )
!= $true )
| ! [X8: $i] :
( ? [X9: $i] :
( ( ( in @ X9 @ X6 )
= $true )
& ( ( ap @ X6 @ X7 @ X5 @ X9 )
!= ( ap @ X6 @ X7 @ X8 @ X9 ) ) )
| ( ( func @ X6 @ X7 @ X8 )
!= $true )
| ( X5 = X8 ) ) )
| ( funcext != $true ) ) ),
inference(rectify,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ( funcext = $true )
| ? [X1: $i,X2: $i,X0: $i] :
( ( ( func @ X2 @ X0 @ X1 )
= $true )
& ? [X3: $i] :
( ! [X4: $i] :
( ( ( in @ X4 @ X2 )
!= $true )
| ( ( ap @ X2 @ X0 @ X3 @ X4 )
= ( ap @ X2 @ X0 @ X1 @ X4 ) ) )
& ( ( func @ X2 @ X0 @ X3 )
= $true )
& ( X1 != X3 ) ) ) )
& ( ! [X1: $i,X2: $i,X0: $i] :
( ( ( func @ X2 @ X0 @ X1 )
!= $true )
| ! [X3: $i] :
( ? [X4: $i] :
( ( ( in @ X4 @ X2 )
= $true )
& ( ( ap @ X2 @ X0 @ X3 @ X4 )
!= ( ap @ X2 @ X0 @ X1 @ X4 ) ) )
| ( ( func @ X2 @ X0 @ X3 )
!= $true )
| ( X1 = X3 ) ) )
| ( funcext != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( funcext = $true )
<=> ! [X1: $i,X2: $i,X0: $i] :
( ( ( func @ X2 @ X0 @ X1 )
!= $true )
| ! [X3: $i] :
( ? [X4: $i] :
( ( ( in @ X4 @ X2 )
= $true )
& ( ( ap @ X2 @ X0 @ X3 @ X4 )
!= ( ap @ X2 @ X0 @ X1 @ X4 ) ) )
| ( ( func @ X2 @ X0 @ X3 )
!= $true )
| ( X1 = X3 ) ) ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ( funcext = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( X1 = X3 )
| ? [X4: $i] :
( ( ( in @ X4 @ X2 )
= $true )
& ( ( ap @ X2 @ X0 @ X3 @ X4 )
!= ( ap @ X2 @ X0 @ X1 @ X4 ) ) )
| ( ( func @ X2 @ X0 @ X3 )
!= $true ) )
| ( ( func @ X2 @ X0 @ X1 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( funcext = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X2 @ X0 @ X1 )
= $true )
=> ! [X3: $i] :
( ( ( func @ X2 @ X0 @ X3 )
= $true )
=> ( ! [X4: $i] :
( ( ( in @ X4 @ X2 )
= $true )
=> ( ( ap @ X2 @ X0 @ X3 @ X4 )
= ( ap @ X2 @ X0 @ X1 @ X4 ) ) )
=> ( X1 = X3 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X2 @ X0 @ X1 )
=> ! [X3: $i] :
( ( func @ X2 @ X0 @ X3 )
=> ( ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( ap @ X2 @ X0 @ X3 @ X4 )
= ( ap @ X2 @ X0 @ X1 @ X4 ) ) )
=> ( X1 = X3 ) ) ) )
= funcext ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X1: $i,X2: $i,X0: $i] :
( ( ( func @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( func @ X0 @ X1 @ X3 )
=> ( ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( ap @ X0 @ X1 @ X2 @ X4 )
= ( ap @ X0 @ X1 @ X3 @ X4 ) ) )
=> ( X2 = X3 ) ) ) )
= funcext ),
file('/export/starexec/sandbox2/tmp/tmp.W6JbVk1m11/DTF2THF_18697.p',funcext) ).
thf(f73,plain,
( ( in @ ( sK8 @ sK3 @ sK2 @ sK1 @ sK0 ) @ sK1 )
!= $true ),
inference(subsumption_resolution,[status(thm)],[f72,f34]) ).
thf(f72,plain,
( ( ( in @ ( sK8 @ sK3 @ sK2 @ sK1 @ sK0 ) @ sK1 )
!= $true )
| ( sK0 = sK3 ) ),
inference(subsumption_resolution,[status(thm)],[f71,f61]) ).
thf(f71,plain,
( ( ( func @ sK1 @ sK2 @ sK0 )
!= $true )
| ( ( in @ ( sK8 @ sK3 @ sK2 @ sK1 @ sK0 ) @ sK1 )
!= $true )
| ( sK0 = sK3 ) ),
inference(equality_resolution,[status(thm)],[f68]) ).
thf(f68,plain,
! [X0: $i] :
( ( ( ap @ sK1 @ sK2 @ X0 @ ( sK8 @ sK3 @ sK2 @ sK1 @ X0 ) )
!= ( ap @ sK1 @ sK2 @ sK0 @ ( sK8 @ sK3 @ sK2 @ sK1 @ X0 ) ) )
| ( ( in @ ( sK8 @ sK3 @ sK2 @ sK1 @ X0 ) @ sK1 )
!= $true )
| ( ( func @ sK1 @ sK2 @ X0 )
!= $true )
| ( sK3 = X0 ) ),
inference(subsumption_resolution,[status(thm)],[f64,f60]) ).
thf(f64,plain,
! [X0: $i] :
( ( ( func @ sK1 @ sK2 @ X0 )
!= $true )
| ( ( in @ ( sK8 @ sK3 @ sK2 @ sK1 @ X0 ) @ sK1 )
!= $true )
| ( ( ap @ sK1 @ sK2 @ X0 @ ( sK8 @ sK3 @ sK2 @ sK1 @ X0 ) )
!= ( ap @ sK1 @ sK2 @ sK0 @ ( sK8 @ sK3 @ sK2 @ sK1 @ X0 ) ) )
| ( ( func @ sK1 @ sK2 @ sK3 )
!= $true )
| ( sK3 = X0 ) ),
inference(superposition,[status(thm)],[f56,f33]) ).
thf(f33,plain,
! [X4: $i] :
( ( ( ap @ sK1 @ sK2 @ sK0 @ X4 )
= ( ap @ sK1 @ sK2 @ sK3 @ X4 ) )
| ( ( in @ X4 @ sK1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f56,plain,
! [X8: $i,X6: $i,X7: $i,X5: $i] :
( ( ( ap @ X6 @ X7 @ X8 @ ( sK8 @ X8 @ X7 @ X6 @ X5 ) )
!= ( ap @ X6 @ X7 @ X5 @ ( sK8 @ X8 @ X7 @ X6 @ X5 ) ) )
| ( ( func @ X6 @ X7 @ X5 )
!= $true )
| ( X5 = X8 )
| ( ( func @ X6 @ X7 @ X8 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f51]) ).
thf(f51,plain,
! [X8: $i,X6: $i,X7: $i,X5: $i] :
( ( ( ap @ X6 @ X7 @ X8 @ ( sK8 @ X8 @ X7 @ X6 @ X5 ) )
!= ( ap @ X6 @ X7 @ X5 @ ( sK8 @ X8 @ X7 @ X6 @ X5 ) ) )
| ( ( func @ X6 @ X7 @ X8 )
!= $true )
| ( X5 = X8 )
| ( ( func @ X6 @ X7 @ X5 )
!= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f37,f36]) ).
thf(f37,plain,
! [X8: $i,X6: $i,X7: $i,X5: $i] :
( ( ( func @ X6 @ X7 @ X5 )
!= $true )
| ( ( ap @ X6 @ X7 @ X8 @ ( sK8 @ X8 @ X7 @ X6 @ X5 ) )
!= ( ap @ X6 @ X7 @ X5 @ ( sK8 @ X8 @ X7 @ X6 @ X5 ) ) )
| ( ( func @ X6 @ X7 @ X8 )
!= $true )
| ( X5 = X8 )
| ( funcext != $true ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU692^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.09 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n022.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 12:31:06 EST 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.38 ---- Original DTF file ---
% 0.18/0.38 thf(spec,logic,$$dhol).
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 % File : SEU692^2 : TPTP v9.2.1. Released v3.7.0.
% 0.18/0.38 % Domain : Set Theory
% 0.18/0.38 % Problem : Functions - Extensionality and Beta Reduction
% 0.18/0.38 % Version : Especial > Reduced > Especial.
% 0.18/0.38 % English : (! A:i.! B:i.! f:i.in f (funcSet A B) -> (! g:i.in g
% 0.18/0.38 % (funcSet A B) -> (! x:i.in x A -> ap A B f x = ap A B g x) ->
% 0.18/0.38 % f = g))
% 0.18/0.38
% 0.18/0.38 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.18/0.38 % Source : [Bro08]
% 0.18/0.38 % Names : ZFC194l [Bro08]
% 0.18/0.38
% 0.18/0.38 % Status : Theorem
% 0.18/0.38 % Rating : 0.00 v8.2.0, 0.15 v8.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v3.7.0
% 0.18/0.38 % Syntax : Number of formulae : 9 ( 2 unt; 6 typ; 2 def)
% 0.18/0.38 % Number of atoms : 18 ( 6 equ; 0 cnn)
% 0.18/0.38 % Maximal formula atoms : 7 ( 6 avg)
% 0.18/0.38 % Number of connectives : 52 ( 0 ~; 0 |; 0 &; 41 @)
% 0.18/0.38 % ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% 0.18/0.38 % Maximal formula depth : 14 ( 5 avg)
% 0.18/0.38 % Number of types : 2 ( 0 usr)
% 0.18/0.38 % Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% 0.18/0.38 % Number of symbols : 7 ( 6 usr; 2 con; 0-4 aty)
% 0.18/0.38 % Number of variables : 13 ( 0 ^; 13 !; 0 ?; 13 :)
% 0.18/0.38 % SPC : TH0_THM_EQU_NAR
% 0.18/0.38
% 0.18/0.38 % Comments : http://mathgate.info/detsetitem.php?id=246
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 thf(in_type,type,
% 0.18/0.38 in: $i > $i > $o ).
% 0.18/0.38
% 0.18/0.38 thf(func_type,type,
% 0.18/0.38 func: $i > $i > $i > $o ).
% 0.18/0.38
% 0.18/0.38 thf(funcSet_type,type,
% 0.18/0.38 funcSet: $i > $i > $i ).
% 0.18/0.38
% 0.18/0.38 thf(ap_type,type,
% 0.18/0.38 ap: $i > $i > $i > $i > $i ).
% 0.18/0.38
% 0.18/0.38 thf(infuncsetfunc_type,type,
% 0.18/0.38 infuncsetfunc: $o ).
% 0.18/0.38
% 0.18/0.38 thf(infuncsetfunc,definition,
% 0.18/0.38 ( infuncsetfunc
% 0.18/0.38 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.18/0.38 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.18/0.38 => ( func @ A @ B @ Xf ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(funcext_type,type,
% 0.18/0.38 funcext: $o ).
% 0.18/0.38
% 0.18/0.38 thf(funcext,definition,
% 0.18/0.38 ( funcext
% 0.18/0.38 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.18/0.38 ( ( func @ A @ B @ Xf )
% 0.18/0.38 => ! [Xg: $i] :
% 0.18/0.38 ( ( func @ A @ B @ Xg )
% 0.18/0.38 => ( ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ A )
% 0.18/0.38 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.18/0.38 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.18/0.38 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(funcext2,conjecture,
% 0.18/0.38 ( infuncsetfunc
% 0.18/0.38 => ( funcext
% 0.18/0.38 => ! [A: $i,B: $i,Xf: $i] :
% 0.18/0.38 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.18/0.38 => ! [Xg: $i] :
% 0.18/0.38 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 0.18/0.38 => ( ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ A )
% 0.18/0.38 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.18/0.38 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.18/0.38 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 ------------------------
% 1.40/1.29 ---- Embedded in THF ---
% 1.40/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.40/1.29 %%% Generated on Tue Feb 24 12:31:07 EST 2026
% 1.40/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.40/1.29 %%% Logic specification used:
% 1.40/1.29 %%% thf(spec, logic, $$dhol).
% 1.40/1.29
% 1.40/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.W6JbVk1m11/DTF2DTF18697.p
% See solution above
% 1.40/1.29 ------------------------
% 1.59/1.30 ---- Cleaned THF ---
% 1.59/1.30 thf(in_type,type,
% 1.59/1.30 in: $i > $i > $o ).
% 1.59/1.30
% 1.59/1.30 thf(func_type,type,
% 1.59/1.30 func: $i > $i > $i > $o ).
% 1.59/1.30
% 1.59/1.30 thf(funcSet_type,type,
% 1.59/1.30 funcSet: $i > $i > $i ).
% 1.59/1.30
% 1.59/1.30 thf(ap_type,type,
% 1.59/1.30 ap: $i > $i > $i > $i > $i ).
% 1.59/1.30
% 1.59/1.30 thf(infuncsetfunc_type,type,
% 1.59/1.30 infuncsetfunc: $o ).
% 1.59/1.30
% 1.59/1.30 thf(infuncsetfunc,definition,
% 1.59/1.30 ( infuncsetfunc
% 1.59/1.30 = ( ! [A: $i,B: $i,Xf: $i] :
% 1.59/1.30 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 1.59/1.30 => ( func @ A @ B @ Xf ) ) ) ) ).
% 1.59/1.30
% 1.59/1.30 thf(funcext_type,type,
% 1.59/1.30 funcext: $o ).
% 1.59/1.30
% 1.59/1.30 thf(funcext,definition,
% 1.59/1.30 ( funcext
% 1.59/1.30 = ( ! [A: $i,B: $i,Xf: $i] :
% 1.59/1.30 ( ( func @ A @ B @ Xf )
% 1.59/1.30 => ! [Xg: $i] :
% 1.59/1.30 ( ( func @ A @ B @ Xg )
% 1.59/1.30 => ( ! [Xx: $i] :
% 1.59/1.30 ( ( in @ Xx @ A )
% 1.59/1.30 => ( ( ap @ A @ B @ Xf @ Xx )
% 1.59/1.30 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 1.59/1.30 => ( Xf = Xg ) ) ) ) ) ) ).
% 1.59/1.30
% 1.59/1.30 thf(funcext2,conjecture,
% 1.59/1.30 ( infuncsetfunc
% 1.59/1.30 => ( funcext
% 1.59/1.30 => ! [A: $i,B: $i,Xf: $i] :
% 1.59/1.30 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 1.59/1.30 => ! [Xg: $i] :
% 1.59/1.30 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 1.59/1.30 => ( ! [Xx: $i] :
% 1.59/1.30 ( ( in @ Xx @ A )
% 1.59/1.30 => ( ( ap @ A @ B @ Xf @ Xx )
% 1.59/1.30 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 1.59/1.30 => ( Xf = Xg ) ) ) ) ) ) ).
% 1.59/1.30 ------------------------
% 1.59/1.32 % (18799)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_18697 for (2999ds/2Mi)
% 1.59/1.32 % (18800)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_18697 for (2999ds/275Mi)
% 1.59/1.32 % (18801)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_18697 for (2999ds/18Mi)
% 1.59/1.32 % (18797)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_18697 for (2999ds/27Mi)
% 1.59/1.32 % (18798)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_18697 for (2999ds/2Mi)
% 1.59/1.32 % (18795)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_18697 for (2999ds/183Mi)
% 1.59/1.32 % (18796)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_18697 for (2999ds/4Mi)
% 1.59/1.32 % (18798)Instruction limit reached!
% 1.59/1.32 % (18798)------------------------------
% 1.59/1.32 % (18798)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.32 % (18798)Termination reason: Unknown
% 1.59/1.32 % (18799)Instruction limit reached!
% 1.59/1.32 % (18799)------------------------------
% 1.59/1.32 % (18799)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.32 % (18798)Termination phase: Property scanning
% 1.59/1.32
% 1.59/1.32 % (18798)Memory used [KB]: 1023
% 1.59/1.32 % (18798)Time elapsed: 0.003 s
% 1.59/1.32 % (18798)Instructions burned: 3 (million)
% 1.59/1.32 % (18798)------------------------------
% 1.59/1.32 % (18798)------------------------------
% 1.59/1.32 % (18799)Termination reason: Unknown
% 1.59/1.32 % (18799)Termination phase: Function definition elimination
% 1.59/1.32
% 1.59/1.32 % (18799)Memory used [KB]: 1023
% 1.59/1.32 % (18799)Time elapsed: 0.003 s
% 1.59/1.32 % (18799)Instructions burned: 3 (million)
% 1.59/1.32 % (18799)------------------------------
% 1.59/1.32 % (18799)------------------------------
% 1.59/1.32 % (18796)Instruction limit reached!
% 1.59/1.32 % (18796)------------------------------
% 1.59/1.32 % (18796)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.32 % (18796)Termination reason: Unknown
% 1.59/1.32 % (18796)Termination phase: Saturation
% 1.59/1.32
% 1.59/1.32 % (18796)Memory used [KB]: 5500
% 1.59/1.32 % (18796)Time elapsed: 0.004 s
% 1.59/1.32 % (18796)Instructions burned: 4 (million)
% 1.59/1.32 % (18796)------------------------------
% 1.59/1.32 % (18796)------------------------------
% 1.59/1.33 % (18800)First to succeed.
% 1.59/1.33 % (18801)Also succeeded, but the first one will report.
% 1.59/1.33 % (18795)Also succeeded, but the first one will report.
% 1.59/1.33 % (18800)Refutation found. Thanks to Tanya!
% 1.59/1.33 % SZS status Theorem for DTF2THF_18697
% 1.59/1.33 % SZS output start Proof for DTF2THF_18697
% 1.59/1.33 thf(func_def_0, type, in: $i > $i > $o).
% 1.59/1.33 thf(func_def_1, type, func: $i > $i > $i > $o).
% 1.59/1.33 thf(func_def_2, type, funcSet: $i > $i > $i).
% 1.59/1.33 thf(func_def_3, type, ap: $i > $i > $i > $i > $i).
% 1.59/1.33 thf(func_def_17, type, sK8: $i > $i > $i > $i > $i).
% 1.59/1.33 thf(f82,plain,(
% 1.59/1.33 $false),
% 1.59/1.33 inference(subsumption_resolution,[status(thm)],[f81,f60])).
% 1.59/1.33 thf(f60,plain,(
% 1.59/1.33 ((func @ sK1 @ sK2 @ sK3) = $true)),
% 1.59/1.33 inference(trivial_inequality_removal,[status(thm)],[f58])).
% 1.59/1.33 thf(f58,plain,(
% 1.59/1.33 ((func @ sK1 @ sK2 @ sK3) = $true) | ($true != $true)),
% 1.59/1.33 inference(superposition,[status(thm)],[f57,f32])).
% 1.59/1.33 thf(f32,plain,(
% 1.59/1.33 ((in @ sK3 @ (funcSet @ sK1 @ sK2)) = $true)),
% 1.59/1.33 inference(cnf_transformation,[status(thm)],[f20])).
% 1.59/1.33 thf(f20,plain,(
% 1.59/1.33 (funcext = $true) & (((in @ sK0 @ (funcSet @ sK1 @ sK2)) = $true) & ((sK0 != sK3) & ! [X4 : $i] : (((ap @ sK1 @ sK2 @ sK0 @ X4) = (ap @ sK1 @ sK2 @ sK3 @ X4)) | ((in @ X4 @ sK1) != $true)) & ((in @ sK3 @ (funcSet @ sK1 @ sK2)) = $true))) & (infuncsetfunc = $true)),
% 1.59/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f17,f19,f18])).
% 1.59/1.33 thf(f18,plain,(
% 1.59/1.33 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ (funcSet @ X1 @ X2)) = $true) & ? [X3 : $i] : ((X0 != X3) & ! [X4 : $i] : (((ap @ X1 @ X2 @ X3 @ X4) = (ap @ X1 @ X2 @ X0 @ X4)) | ((in @ X4 @ X1) != $true)) & ((in @ X3 @ (funcSet @ X1 @ X2)) = $true))) => (((in @ sK0 @ (funcSet @ sK1 @ sK2)) = $true) & ? [X3 : $i] : ((sK0 != X3) & ! [X4 : $i] : (((ap @ sK1 @ sK2 @ sK0 @ X4) = (ap @ sK1 @ sK2 @ X3 @ X4)) | ((in @ X4 @ sK1) != $true)) & ((in @ X3 @ (funcSet @ sK1 @ sK2)) = $true)))),
% 1.59/1.33 introduced(definition,[],[choice_axiom])).
% 1.59/1.33 thf(f19,plain,(
% 1.59/1.33 ? [X3 : $i] : ((sK0 != X3) & ! [X4 : $i] : (((ap @ sK1 @ sK2 @ sK0 @ X4) = (ap @ sK1 @ sK2 @ X3 @ X4)) | ((in @ X4 @ sK1) != $true)) & ((in @ X3 @ (funcSet @ sK1 @ sK2)) = $true)) => ((sK0 != sK3) & ! [X4 : $i] : (((ap @ sK1 @ sK2 @ sK0 @ X4) = (ap @ sK1 @ sK2 @ sK3 @ X4)) | ((in @ X4 @ sK1) != $true)) & ((in @ sK3 @ (funcSet @ sK1 @ sK2)) = $true))),
% 1.59/1.33 introduced(definition,[],[choice_axiom])).
% 1.59/1.33 thf(f17,plain,(
% 1.59/1.33 (funcext = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ (funcSet @ X1 @ X2)) = $true) & ? [X3 : $i] : ((X0 != X3) & ! [X4 : $i] : (((ap @ X1 @ X2 @ X3 @ X4) = (ap @ X1 @ X2 @ X0 @ X4)) | ((in @ X4 @ X1) != $true)) & ((in @ X3 @ (funcSet @ X1 @ X2)) = $true))) & (infuncsetfunc = $true)),
% 1.59/1.33 inference(rectify,[status(thm)],[f15])).
% 1.59/1.33 thf(f15,plain,(
% 1.59/1.33 (funcext = $true) & ? [X1 : $i,X0 : $i,X2 : $i] : (($true = (in @ X1 @ (funcSet @ X0 @ X2))) & ? [X3 : $i] : ((X1 != X3) & ! [X4 : $i] : (((ap @ X0 @ X2 @ X1 @ X4) = (ap @ X0 @ X2 @ X3 @ X4)) | ((in @ X4 @ X0) != $true)) & ((in @ X3 @ (funcSet @ X0 @ X2)) = $true))) & (infuncsetfunc = $true)),
% 1.59/1.33 inference(flattening,[status(thm)],[f14])).
% 1.59/1.33 thf(f14,plain,(
% 1.59/1.33 (? [X1 : $i,X0 : $i,X2 : $i] : (? [X3 : $i] : (((X1 != X3) & ! [X4 : $i] : (((ap @ X0 @ X2 @ X1 @ X4) = (ap @ X0 @ X2 @ X3 @ X4)) | ((in @ X4 @ X0) != $true))) & ((in @ X3 @ (funcSet @ X0 @ X2)) = $true)) & ($true = (in @ X1 @ (funcSet @ X0 @ X2)))) & (funcext = $true)) & (infuncsetfunc = $true)),
% 1.59/1.33 inference(ennf_transformation,[status(thm)],[f7])).
% 1.59/1.33 thf(f7,plain,(
% 1.59/1.33 ~((infuncsetfunc = $true) => ((funcext = $true) => ! [X1 : $i,X0 : $i,X2 : $i] : (($true = (in @ X1 @ (funcSet @ X0 @ X2))) => ! [X3 : $i] : (((in @ X3 @ (funcSet @ X0 @ X2)) = $true) => (! [X4 : $i] : (((in @ X4 @ X0) = $true) => ((ap @ X0 @ X2 @ X1 @ X4) = (ap @ X0 @ X2 @ X3 @ X4))) => (X1 = X3))))))),
% 1.59/1.33 inference(fool_elimination,[status(thm)],[f6])).
% 1.59/1.33 thf(f6,plain,(
% 1.59/1.33 ~(infuncsetfunc => (funcext => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (funcSet @ X0 @ X2)) => ! [X3 : $i] : ((in @ X3 @ (funcSet @ X0 @ X2)) => (! [X4 : $i] : ((in @ X4 @ X0) => ((ap @ X0 @ X2 @ X1 @ X4) = (ap @ X0 @ X2 @ X3 @ X4))) => (X1 = X3))))))),
% 1.59/1.33 inference(rectify,[status(thm)],[f4])).
% 1.59/1.33 thf(f4,negated_conjecture,(
% 1.59/1.33 ~(infuncsetfunc => (funcext => ! [X0 : $i,X2 : $i,X1 : $i] : ((in @ X2 @ (funcSet @ X0 @ X1)) => ! [X3 : $i] : ((in @ X3 @ (funcSet @ X0 @ X1)) => (! [X4 : $i] : ((in @ X4 @ X0) => ((ap @ X0 @ X1 @ X2 @ X4) = (ap @ X0 @ X1 @ X3 @ X4))) => (X2 = X3))))))),
% 1.59/1.33 inference(negated_conjecture,[status(cth)],[f3])).
% 1.59/1.33 thf(f3,conjecture,(
% 1.59/1.33 infuncsetfunc => (funcext => ! [X0 : $i,X2 : $i,X1 : $i] : ((in @ X2 @ (funcSet @ X0 @ X1)) => ! [X3 : $i] : ((in @ X3 @ (funcSet @ X0 @ X1)) => (! [X4 : $i] : ((in @ X4 @ X0) => ((ap @ X0 @ X1 @ X2 @ X4) = (ap @ X0 @ X1 @ X3 @ X4))) => (X2 = X3)))))),
% 1.59/1.33 file('/export/starexec/sandbox2/tmp/tmp.W6JbVk1m11/DTF2THF_18697.p',funcext2)).
% 1.59/1.33 thf(f57,plain,(
% 1.59/1.33 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X4 @ (funcSet @ X5 @ X3))) | ((func @ X5 @ X3 @ X4) = $true)) )),
% 1.59/1.33 inference(trivial_inequality_removal,[status(thm)],[f54])).
% 1.59/1.33 thf(f54,plain,(
% 1.59/1.33 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((func @ X5 @ X3 @ X4) = $true) | ($true != $true) | ($true != (in @ X4 @ (funcSet @ X5 @ X3)))) )),
% 1.59/1.33 inference(definition_unfolding,[status(thm)],[f43,f31])).
% 1.59/1.33 thf(f31,plain,(
% 1.59/1.33 (infuncsetfunc = $true)),
% 1.59/1.33 inference(cnf_transformation,[status(thm)],[f20])).
% 1.59/1.33 thf(f43,plain,(
% 1.59/1.33 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X4 @ (funcSet @ X5 @ X3))) | ((func @ X5 @ X3 @ X4) = $true) | (infuncsetfunc != $true)) )),
% 1.59/1.33 inference(cnf_transformation,[status(thm)],[f30])).
% 1.59/1.33 thf(f30,plain,(
% 1.59/1.33 ((infuncsetfunc = $true) | (($true = (in @ sK10 @ (funcSet @ sK11 @ sK9))) & ($true != (func @ sK11 @ sK9 @ sK10)))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X4 @ (funcSet @ X5 @ X3))) | ((func @ X5 @ X3 @ X4) = $true)) | (infuncsetfunc != $true))),
% 1.59/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f28,f29])).
% 1.59/1.33 thf(f29,plain,(
% 1.59/1.33 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (funcSet @ X2 @ X0)) = $true) & ((func @ X2 @ X0 @ X1) != $true)) => (($true = (in @ sK10 @ (funcSet @ sK11 @ sK9))) & ($true != (func @ sK11 @ sK9 @ sK10)))),
% 1.59/1.33 introduced(definition,[],[choice_axiom])).
% 1.59/1.33 thf(f28,plain,(
% 1.59/1.33 ((infuncsetfunc = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (funcSet @ X2 @ X0)) = $true) & ((func @ X2 @ X0 @ X1) != $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X4 @ (funcSet @ X5 @ X3))) | ((func @ X5 @ X3 @ X4) = $true)) | (infuncsetfunc != $true))),
% 1.59/1.33 inference(rectify,[status(thm)],[f27])).
% 1.59/1.33 thf(f27,plain,(
% 1.59/1.33 ((infuncsetfunc = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (funcSet @ X2 @ X0)) = $true) & ((func @ X2 @ X0 @ X1) != $true))) & (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (funcSet @ X2 @ X0)) != $true) | ((func @ X2 @ X0 @ X1) = $true)) | (infuncsetfunc != $true))),
% 1.59/1.33 inference(nnf_transformation,[status(thm)],[f16])).
% 1.59/1.33 thf(f16,plain,(
% 1.59/1.33 (infuncsetfunc = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (funcSet @ X2 @ X0)) != $true) | ((func @ X2 @ X0 @ X1) = $true))),
% 1.59/1.33 inference(ennf_transformation,[status(thm)],[f9])).
% 1.59/1.33 thf(f9,plain,(
% 1.59/1.33 ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (funcSet @ X2 @ X0)) = $true) => ((func @ X2 @ X0 @ X1) = $true)) <=> (infuncsetfunc = $true)),
% 1.59/1.33 inference(fool_elimination,[status(thm)],[f8])).
% 1.59/1.33 thf(f8,plain,(
% 1.59/1.33 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (funcSet @ X2 @ X0)) => (func @ X2 @ X0 @ X1)) = infuncsetfunc)),
% 1.59/1.33 inference(rectify,[status(thm)],[f1])).
% 1.59/1.33 thf(f1,axiom,(
% 1.59/1.33 (! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ (funcSet @ X0 @ X1)) => (func @ X0 @ X1 @ X2)) = infuncsetfunc)),
% 1.59/1.33 file('/export/starexec/sandbox2/tmp/tmp.W6JbVk1m11/DTF2THF_18697.p',infuncsetfunc)).
% 1.59/1.33 thf(f81,plain,(
% 1.59/1.33 ((func @ sK1 @ sK2 @ sK3) != $true)),
% 1.59/1.33 inference(subsumption_resolution,[status(thm)],[f80,f34])).
% 1.59/1.33 thf(f34,plain,(
% 1.59/1.33 (sK0 != sK3)),
% 1.59/1.33 inference(cnf_transformation,[status(thm)],[f20])).
% 1.59/1.33 thf(f80,plain,(
% 1.59/1.33 (sK0 = sK3) | ((func @ sK1 @ sK2 @ sK3) != $true)),
% 1.59/1.33 inference(subsumption_resolution,[status(thm)],[f79,f61])).
% 1.59/1.33 thf(f61,plain,(
% 1.59/1.33 ((func @ sK1 @ sK2 @ sK0) = $true)),
% 1.59/1.33 inference(trivial_inequality_removal,[status(thm)],[f59])).
% 1.59/1.33 thf(f59,plain,(
% 1.59/1.33 ($true != $true) | ((func @ sK1 @ sK2 @ sK0) = $true)),
% 1.59/1.33 inference(superposition,[status(thm)],[f57,f35])).
% 1.59/1.33 thf(f35,plain,(
% 1.59/1.33 ((in @ sK0 @ (funcSet @ sK1 @ sK2)) = $true)),
% 1.59/1.33 inference(cnf_transformation,[status(thm)],[f20])).
% 1.59/1.33 thf(f79,plain,(
% 1.59/1.33 ((func @ sK1 @ sK2 @ sK0) != $true) | (sK0 = sK3) | ((func @ sK1 @ sK2 @ sK3) != $true)),
% 1.59/1.33 inference(trivial_inequality_removal,[status(thm)],[f78])).
% 1.59/1.33 thf(f78,plain,(
% 1.59/1.33 ((func @ sK1 @ sK2 @ sK3) != $true) | (sK0 = sK3) | ((func @ sK1 @ sK2 @ sK0) != $true) | ($true != $true)),
% 1.59/1.33 inference(superposition,[status(thm)],[f73,f55])).
% 1.59/1.33 thf(f55,plain,(
% 1.59/1.33 ( ! [X8 : $i,X6 : $i,X7 : $i,X5 : $i] : (((in @ (sK8 @ X8 @ X7 @ X6 @ X5) @ X6) = $true) | (X5 = X8) | ((func @ X6 @ X7 @ X8) != $true) | ((func @ X6 @ X7 @ X5) != $true)) )),
% 1.59/1.33 inference(trivial_inequality_removal,[status(thm)],[f50])).
% 1.59/1.33 thf(f50,plain,(
% 1.59/1.33 ( ! [X8 : $i,X6 : $i,X7 : $i,X5 : $i] : (($true != $true) | (X5 = X8) | ((func @ X6 @ X7 @ X5) != $true) | ((func @ X6 @ X7 @ X8) != $true) | ((in @ (sK8 @ X8 @ X7 @ X6 @ X5) @ X6) = $true)) )),
% 1.59/1.33 inference(definition_unfolding,[status(thm)],[f38,f36])).
% 1.59/1.33 thf(f36,plain,(
% 1.59/1.33 (funcext = $true)),
% 1.59/1.33 inference(cnf_transformation,[status(thm)],[f20])).
% 1.59/1.33 thf(f38,plain,(
% 1.59/1.33 ( ! [X8 : $i,X6 : $i,X7 : $i,X5 : $i] : (((func @ X6 @ X7 @ X5) != $true) | ((in @ (sK8 @ X8 @ X7 @ X6 @ X5) @ X6) = $true) | ((func @ X6 @ X7 @ X8) != $true) | (X5 = X8) | (funcext != $true)) )),
% 1.59/1.33 inference(cnf_transformation,[status(thm)],[f26])).
% 1.59/1.33 thf(f26,plain,(
% 1.59/1.33 ((funcext = $true) | (((func @ sK5 @ sK6 @ sK4) = $true) & (! [X4 : $i] : (((in @ X4 @ sK5) != $true) | ((ap @ sK5 @ sK6 @ sK7 @ X4) = (ap @ sK5 @ sK6 @ sK4 @ X4))) & ((func @ sK5 @ sK6 @ sK7) = $true) & (sK7 != sK4)))) & (! [X5 : $i,X6 : $i,X7 : $i] : (((func @ X6 @ X7 @ X5) != $true) | ! [X8 : $i] : ((((in @ (sK8 @ X8 @ X7 @ X6 @ X5) @ X6) = $true) & ((ap @ X6 @ X7 @ X8 @ (sK8 @ X8 @ X7 @ X6 @ X5)) != (ap @ X6 @ X7 @ X5 @ (sK8 @ X8 @ X7 @ X6 @ X5)))) | ((func @ X6 @ X7 @ X8) != $true) | (X5 = X8))) | (funcext != $true))),
% 1.59/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8])],[f22,f25,f24,f23])).
% 1.59/1.33 thf(f23,plain,(
% 1.59/1.33 ? [X0 : $i,X1 : $i,X2 : $i] : (((func @ X1 @ X2 @ X0) = $true) & ? [X3 : $i] : (! [X4 : $i] : (((in @ X4 @ X1) != $true) | ((ap @ X1 @ X2 @ X3 @ X4) = (ap @ X1 @ X2 @ X0 @ X4))) & ((func @ X1 @ X2 @ X3) = $true) & (X0 != X3))) => (((func @ sK5 @ sK6 @ sK4) = $true) & ? [X3 : $i] : (! [X4 : $i] : (((in @ X4 @ sK5) != $true) | ((ap @ sK5 @ sK6 @ sK4 @ X4) = (ap @ sK5 @ sK6 @ X3 @ X4))) & ((func @ sK5 @ sK6 @ X3) = $true) & (sK4 != X3)))),
% 1.59/1.33 introduced(definition,[],[choice_axiom])).
% 1.59/1.33 thf(f24,plain,(
% 1.59/1.33 ? [X3 : $i] : (! [X4 : $i] : (((in @ X4 @ sK5) != $true) | ((ap @ sK5 @ sK6 @ sK4 @ X4) = (ap @ sK5 @ sK6 @ X3 @ X4))) & ((func @ sK5 @ sK6 @ X3) = $true) & (sK4 != X3)) => (! [X4 : $i] : (((in @ X4 @ sK5) != $true) | ((ap @ sK5 @ sK6 @ sK7 @ X4) = (ap @ sK5 @ sK6 @ sK4 @ X4))) & ((func @ sK5 @ sK6 @ sK7) = $true) & (sK7 != sK4))),
% 1.59/1.33 introduced(definition,[],[choice_axiom])).
% 1.59/1.33 thf(f25,plain,(
% 1.59/1.33 ! [X5 : $i,X6 : $i,X7 : $i,X8 : $i] : (? [X9 : $i] : (((in @ X9 @ X6) = $true) & ((ap @ X6 @ X7 @ X5 @ X9) != (ap @ X6 @ X7 @ X8 @ X9))) => (((in @ (sK8 @ X8 @ X7 @ X6 @ X5) @ X6) = $true) & ((ap @ X6 @ X7 @ X8 @ (sK8 @ X8 @ X7 @ X6 @ X5)) != (ap @ X6 @ X7 @ X5 @ (sK8 @ X8 @ X7 @ X6 @ X5)))))),
% 1.59/1.33 introduced(definition,[],[choice_axiom])).
% 1.59/1.33 thf(f22,plain,(
% 1.59/1.33 ((funcext = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((func @ X1 @ X2 @ X0) = $true) & ? [X3 : $i] : (! [X4 : $i] : (((in @ X4 @ X1) != $true) | ((ap @ X1 @ X2 @ X3 @ X4) = (ap @ X1 @ X2 @ X0 @ X4))) & ((func @ X1 @ X2 @ X3) = $true) & (X0 != X3)))) & (! [X5 : $i,X6 : $i,X7 : $i] : (((func @ X6 @ X7 @ X5) != $true) | ! [X8 : $i] : (? [X9 : $i] : (((in @ X9 @ X6) = $true) & ((ap @ X6 @ X7 @ X5 @ X9) != (ap @ X6 @ X7 @ X8 @ X9))) | ((func @ X6 @ X7 @ X8) != $true) | (X5 = X8))) | (funcext != $true))),
% 1.59/1.33 inference(rectify,[status(thm)],[f21])).
% 1.59/1.33 thf(f21,plain,(
% 1.59/1.33 ((funcext = $true) | ? [X1 : $i,X2 : $i,X0 : $i] : (((func @ X2 @ X0 @ X1) = $true) & ? [X3 : $i] : (! [X4 : $i] : (((in @ X4 @ X2) != $true) | ((ap @ X2 @ X0 @ X3 @ X4) = (ap @ X2 @ X0 @ X1 @ X4))) & ((func @ X2 @ X0 @ X3) = $true) & (X1 != X3)))) & (! [X1 : $i,X2 : $i,X0 : $i] : (((func @ X2 @ X0 @ X1) != $true) | ! [X3 : $i] : (? [X4 : $i] : (((in @ X4 @ X2) = $true) & ((ap @ X2 @ X0 @ X3 @ X4) != (ap @ X2 @ X0 @ X1 @ X4))) | ((func @ X2 @ X0 @ X3) != $true) | (X1 = X3))) | (funcext != $true))),
% 1.59/1.33 inference(nnf_transformation,[status(thm)],[f13])).
% 1.59/1.33 thf(f13,plain,(
% 1.59/1.33 (funcext = $true) <=> ! [X1 : $i,X2 : $i,X0 : $i] : (((func @ X2 @ X0 @ X1) != $true) | ! [X3 : $i] : (? [X4 : $i] : (((in @ X4 @ X2) = $true) & ((ap @ X2 @ X0 @ X3 @ X4) != (ap @ X2 @ X0 @ X1 @ X4))) | ((func @ X2 @ X0 @ X3) != $true) | (X1 = X3)))),
% 1.59/1.33 inference(flattening,[status(thm)],[f12])).
% 1.59/1.33 thf(f12,plain,(
% 1.59/1.33 (funcext = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $i] : (((X1 = X3) | ? [X4 : $i] : (((in @ X4 @ X2) = $true) & ((ap @ X2 @ X0 @ X3 @ X4) != (ap @ X2 @ X0 @ X1 @ X4)))) | ((func @ X2 @ X0 @ X3) != $true)) | ((func @ X2 @ X0 @ X1) != $true))),
% 1.59/1.33 inference(ennf_transformation,[status(thm)],[f11])).
% 1.59/1.33 thf(f11,plain,(
% 1.59/1.33 (funcext = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((func @ X2 @ X0 @ X1) = $true) => ! [X3 : $i] : (((func @ X2 @ X0 @ X3) = $true) => (! [X4 : $i] : (((in @ X4 @ X2) = $true) => ((ap @ X2 @ X0 @ X3 @ X4) = (ap @ X2 @ X0 @ X1 @ X4))) => (X1 = X3))))),
% 1.59/1.33 inference(fool_elimination,[status(thm)],[f10])).
% 1.59/1.33 thf(f10,plain,(
% 1.59/1.33 (! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X2 @ X0 @ X1) => ! [X3 : $i] : ((func @ X2 @ X0 @ X3) => (! [X4 : $i] : ((in @ X4 @ X2) => ((ap @ X2 @ X0 @ X3 @ X4) = (ap @ X2 @ X0 @ X1 @ X4))) => (X1 = X3)))) = funcext)),
% 1.59/1.33 inference(rectify,[status(thm)],[f2])).
% 1.59/1.33 thf(f2,axiom,(
% 1.59/1.33 (! [X1 : $i,X2 : $i,X0 : $i] : ((func @ X0 @ X1 @ X2) => ! [X3 : $i] : ((func @ X0 @ X1 @ X3) => (! [X4 : $i] : ((in @ X4 @ X0) => ((ap @ X0 @ X1 @ X2 @ X4) = (ap @ X0 @ X1 @ X3 @ X4))) => (X2 = X3)))) = funcext)),
% 1.59/1.33 file('/export/starexec/sandbox2/tmp/tmp.W6JbVk1m11/DTF2THF_18697.p',funcext)).
% 1.59/1.33 thf(f73,plain,(
% 1.59/1.33 ((in @ (sK8 @ sK3 @ sK2 @ sK1 @ sK0) @ sK1) != $true)),
% 1.59/1.33 inference(subsumption_resolution,[status(thm)],[f72,f34])).
% 1.59/1.33 thf(f72,plain,(
% 1.59/1.33 ((in @ (sK8 @ sK3 @ sK2 @ sK1 @ sK0) @ sK1) != $true) | (sK0 = sK3)),
% 1.59/1.33 inference(subsumption_resolution,[status(thm)],[f71,f61])).
% 1.59/1.33 thf(f71,plain,(
% 1.59/1.33 ((func @ sK1 @ sK2 @ sK0) != $true) | ((in @ (sK8 @ sK3 @ sK2 @ sK1 @ sK0) @ sK1) != $true) | (sK0 = sK3)),
% 1.59/1.33 inference(equality_resolution,[status(thm)],[f68])).
% 1.59/1.33 thf(f68,plain,(
% 1.59/1.33 ( ! [X0 : $i] : (((ap @ sK1 @ sK2 @ X0 @ (sK8 @ sK3 @ sK2 @ sK1 @ X0)) != (ap @ sK1 @ sK2 @ sK0 @ (sK8 @ sK3 @ sK2 @ sK1 @ X0))) | ((in @ (sK8 @ sK3 @ sK2 @ sK1 @ X0) @ sK1) != $true) | ((func @ sK1 @ sK2 @ X0) != $true) | (sK3 = X0)) )),
% 1.59/1.33 inference(subsumption_resolution,[status(thm)],[f64,f60])).
% 1.59/1.33 thf(f64,plain,(
% 1.59/1.33 ( ! [X0 : $i] : (((func @ sK1 @ sK2 @ X0) != $true) | ((in @ (sK8 @ sK3 @ sK2 @ sK1 @ X0) @ sK1) != $true) | ((ap @ sK1 @ sK2 @ X0 @ (sK8 @ sK3 @ sK2 @ sK1 @ X0)) != (ap @ sK1 @ sK2 @ sK0 @ (sK8 @ sK3 @ sK2 @ sK1 @ X0))) | ((func @ sK1 @ sK2 @ sK3) != $true) | (sK3 = X0)) )),
% 1.59/1.33 inference(superposition,[status(thm)],[f56,f33])).
% 1.59/1.33 thf(f33,plain,(
% 1.59/1.33 ( ! [X4 : $i] : (((ap @ sK1 @ sK2 @ sK0 @ X4) = (ap @ sK1 @ sK2 @ sK3 @ X4)) | ((in @ X4 @ sK1) != $true)) )),
% 1.59/1.33 inference(cnf_transformation,[status(thm)],[f20])).
% 1.59/1.33 thf(f56,plain,(
% 1.59/1.33 ( ! [X8 : $i,X6 : $i,X7 : $i,X5 : $i] : (((ap @ X6 @ X7 @ X8 @ (sK8 @ X8 @ X7 @ X6 @ X5)) != (ap @ X6 @ X7 @ X5 @ (sK8 @ X8 @ X7 @ X6 @ X5))) | ((func @ X6 @ X7 @ X5) != $true) | (X5 = X8) | ((func @ X6 @ X7 @ X8) != $true)) )),
% 1.59/1.33 inference(trivial_inequality_removal,[status(thm)],[f51])).
% 1.59/1.33 thf(f51,plain,(
% 1.59/1.33 ( ! [X8 : $i,X6 : $i,X7 : $i,X5 : $i] : (((ap @ X6 @ X7 @ X8 @ (sK8 @ X8 @ X7 @ X6 @ X5)) != (ap @ X6 @ X7 @ X5 @ (sK8 @ X8 @ X7 @ X6 @ X5))) | ((func @ X6 @ X7 @ X8) != $true) | (X5 = X8) | ((func @ X6 @ X7 @ X5) != $true) | ($true != $true)) )),
% 1.59/1.33 inference(definition_unfolding,[status(thm)],[f37,f36])).
% 1.59/1.33 thf(f37,plain,(
% 1.59/1.33 ( ! [X8 : $i,X6 : $i,X7 : $i,X5 : $i] : (((func @ X6 @ X7 @ X5) != $true) | ((ap @ X6 @ X7 @ X8 @ (sK8 @ X8 @ X7 @ X6 @ X5)) != (ap @ X6 @ X7 @ X5 @ (sK8 @ X8 @ X7 @ X6 @ X5))) | ((func @ X6 @ X7 @ X8) != $true) | (X5 = X8) | (funcext != $true)) )),
% 1.59/1.33 inference(cnf_transformation,[status(thm)],[f26])).
% 1.59/1.33 % SZS output end Proof for DTF2THF_18697
% 1.59/1.33 % (18800)------------------------------
% 1.59/1.33 % (18800)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.33 % (18800)Termination reason: Refutation
% 1.59/1.33
% 1.59/1.33 % (18800)Memory used [KB]: 5628
% 1.59/1.33 % (18800)Time elapsed: 0.010 s
% 1.59/1.33 % (18800)Instructions burned: 12 (million)
% 1.59/1.33 % (18800)------------------------------
% 1.59/1.33 % (18800)------------------------------
% 1.59/1.33 % (18794)Success in time 0.025 s
%------------------------------------------------------------------------------