%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU688^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n002.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 09:36:25 AM UTC 2026
% Result : Theorem 1.74s 1.43s
% Output : Refutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 50 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 776 ( 218 equ; 0 cnn)
% Maximal formula atoms : 12 ( 15 avg)
% Number of connectives : 917 ( 93 ~; 67 |; 77 &; 629 @)
% ( 5 <=>; 46 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 27 usr; 17 con; 0-4 aty)
% Number of variables : 159 ( 0 ^; 108 !; 51 ?; 159 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_4,type,
subset: $i > $i > $o ).
thf(func_def_5,type,
kpair: $i > $i > $i ).
thf(func_def_6,type,
cartprod: $i > $i > $i ).
thf(func_def_7,type,
singleton: $i > $o ).
thf(func_def_9,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_10,type,
breln: $i > $i > $i > $o ).
thf(func_def_11,type,
func: $i > $i > $i > $o ).
thf(func_def_12,type,
funcSet: $i > $i > $i ).
thf(func_def_13,type,
ap: $i > $i > $i > $i > $i ).
thf(f79,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f78,f53]) ).
thf(f53,plain,
( $true
= ( in @ sK12 @ sK8 ) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
thf(f42,plain,
( ( funcGraphProp2 = $true )
& ( ( in @ sK9 @ ( funcSet @ sK10 @ sK8 ) )
= $true )
& ( $true
= ( in @ sK11 @ sK10 ) )
& ( ( ap @ sK10 @ sK8 @ sK9 @ sK11 )
!= sK12 )
& ( $true
= ( in @ ( kpair @ sK11 @ sK12 ) @ sK9 ) )
& ( $true
= ( in @ sK12 @ sK8 ) )
& ( infuncsetfunc = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11,sK12])],[f28,f41,f40,f39]) ).
thf(f39,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( funcSet @ X2 @ X0 ) ) )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ X2 ) )
& ? [X4: $i] :
( ( ( ap @ X2 @ X0 @ X1 @ X3 )
!= X4 )
& ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
= $true )
& ( $true
= ( in @ X4 @ X0 ) ) ) ) )
=> ( ( ( in @ sK9 @ ( funcSet @ sK10 @ sK8 ) )
= $true )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ sK10 ) )
& ? [X4: $i] :
( ( ( ap @ sK10 @ sK8 @ sK9 @ X3 )
!= X4 )
& ( ( in @ ( kpair @ X3 @ X4 ) @ sK9 )
= $true )
& ( ( in @ X4 @ sK8 )
= $true ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f40,plain,
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ sK10 ) )
& ? [X4: $i] :
( ( ( ap @ sK10 @ sK8 @ sK9 @ X3 )
!= X4 )
& ( ( in @ ( kpair @ X3 @ X4 ) @ sK9 )
= $true )
& ( ( in @ X4 @ sK8 )
= $true ) ) )
=> ( ( $true
= ( in @ sK11 @ sK10 ) )
& ? [X4: $i] :
( ( ( ap @ sK10 @ sK8 @ sK9 @ sK11 )
!= X4 )
& ( $true
= ( in @ ( kpair @ sK11 @ X4 ) @ sK9 ) )
& ( ( in @ X4 @ sK8 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f41,plain,
( ? [X4: $i] :
( ( ( ap @ sK10 @ sK8 @ sK9 @ sK11 )
!= X4 )
& ( $true
= ( in @ ( kpair @ sK11 @ X4 ) @ sK9 ) )
& ( ( in @ X4 @ sK8 )
= $true ) )
=> ( ( ( ap @ sK10 @ sK8 @ sK9 @ sK11 )
!= sK12 )
& ( $true
= ( in @ ( kpair @ sK11 @ sK12 ) @ sK9 ) )
& ( $true
= ( in @ sK12 @ sK8 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f28,plain,
( ( funcGraphProp2 = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( funcSet @ X2 @ X0 ) ) )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ X2 ) )
& ? [X4: $i] :
( ( ( ap @ X2 @ X0 @ X1 @ X3 )
!= X4 )
& ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
= $true )
& ( $true
= ( in @ X4 @ X0 ) ) ) ) )
& ( infuncsetfunc = $true ) ),
inference(flattening,[status(thm)],[f27]) ).
thf(f27,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( ap @ X2 @ X0 @ X1 @ X3 )
!= X4 )
& ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
= $true )
& ( $true
= ( in @ X4 @ X0 ) ) )
& ( $true
= ( in @ X3 @ X2 ) ) )
& ( $true
= ( in @ X1 @ ( funcSet @ X2 @ X0 ) ) ) )
& ( funcGraphProp2 = $true )
& ( infuncsetfunc = $true ) ),
inference(ennf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
~ ( ( infuncsetfunc = $true )
=> ( ( funcGraphProp2 = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( funcSet @ X2 @ X0 ) ) )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X2 ) )
=> ! [X4: $i] :
( ( $true
= ( in @ X4 @ X0 ) )
=> ( ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
= $true )
=> ( ( ap @ X2 @ X0 @ X1 @ X3 )
= X4 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
~ ( infuncsetfunc
=> ( funcGraphProp2
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ ( funcSet @ X2 @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
=> ( ( ap @ X2 @ X0 @ X1 @ X3 )
= X4 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,negated_conjecture,
~ ( infuncsetfunc
=> ( funcGraphProp2
=> ! [X3: $i,X7: $i,X0: $i] :
( ( in @ X7 @ ( funcSet @ X0 @ X3 ) )
=> ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ! [X6: $i] :
( ( in @ X6 @ X3 )
=> ( ( in @ ( kpair @ X1 @ X6 ) @ X7 )
=> ( ( ap @ X0 @ X3 @ X7 @ X1 )
= X6 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f7,conjecture,
( infuncsetfunc
=> ( funcGraphProp2
=> ! [X3: $i,X7: $i,X0: $i] :
( ( in @ X7 @ ( funcSet @ X0 @ X3 ) )
=> ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ! [X6: $i] :
( ( in @ X6 @ X3 )
=> ( ( in @ ( kpair @ X1 @ X6 ) @ X7 )
=> ( ( ap @ X0 @ X3 @ X7 @ X1 )
= X6 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qKKwlDXAuP/DTF2THF_6218.p',funcGraphProp4) ).
thf(f78,plain,
( $true
!= ( in @ sK12 @ sK8 ) ),
inference(trivial_inequality_removal,[status(thm)],[f77]) ).
thf(f77,plain,
( ( $true
!= ( in @ sK12 @ sK8 ) )
| ( sK12 != sK12 )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f76,f54]) ).
thf(f54,plain,
( $true
= ( in @ ( kpair @ sK11 @ sK12 ) @ sK9 ) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
thf(f76,plain,
! [X0: $i] :
( ( $true
!= ( in @ ( kpair @ sK11 @ X0 ) @ sK9 ) )
| ( $true
!= ( in @ X0 @ sK8 ) )
| ( sK12 != X0 ) ),
inference(subsumption_resolution,[status(thm)],[f75,f71]) ).
thf(f71,plain,
( $true
= ( func @ sK10 @ sK8 @ sK9 ) ),
inference(trivial_inequality_removal,[status(thm)],[f70]) ).
thf(f70,plain,
( ( $true
= ( func @ sK10 @ sK8 @ sK9 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f69,f57]) ).
thf(f57,plain,
( ( in @ sK9 @ ( funcSet @ sK10 @ sK8 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f42]) ).
thf(f69,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X2 @ ( funcSet @ X0 @ X1 ) ) )
| ( ( func @ X0 @ X1 @ X2 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f65]) ).
thf(f65,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( func @ X0 @ X1 @ X2 )
= $true )
| ( $true
!= ( in @ X2 @ ( funcSet @ X0 @ X1 ) ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f51,f52]) ).
thf(f52,plain,
infuncsetfunc = $true,
inference(cnf_transformation,[status(thm)],[f42]) ).
thf(f51,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( func @ X0 @ X1 @ X2 )
= $true )
| ( $true
!= ( in @ X2 @ ( funcSet @ X0 @ X1 ) ) )
| ( infuncsetfunc != $true ) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f38,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X0 @ X1 @ X2 )
= $true )
| ( $true
!= ( in @ X2 @ ( funcSet @ X0 @ X1 ) ) ) )
| ( infuncsetfunc != $true ) )
& ( ( infuncsetfunc = $true )
| ( ( $true
!= ( func @ sK5 @ sK6 @ sK7 ) )
& ( $true
= ( in @ sK7 @ ( funcSet @ sK5 @ sK6 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f36,f37]) ).
thf(f37,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( ( func @ X3 @ X4 @ X5 )
!= $true )
& ( $true
= ( in @ X5 @ ( funcSet @ X3 @ X4 ) ) ) )
=> ( ( $true
!= ( func @ sK5 @ sK6 @ sK7 ) )
& ( $true
= ( in @ sK7 @ ( funcSet @ sK5 @ sK6 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f36,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X0 @ X1 @ X2 )
= $true )
| ( $true
!= ( in @ X2 @ ( funcSet @ X0 @ X1 ) ) ) )
| ( infuncsetfunc != $true ) )
& ( ( infuncsetfunc = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( func @ X3 @ X4 @ X5 )
!= $true )
& ( $true
= ( in @ X5 @ ( funcSet @ X3 @ X4 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X0 @ X1 @ X2 )
= $true )
| ( $true
!= ( in @ X2 @ ( funcSet @ X0 @ X1 ) ) ) )
| ( infuncsetfunc != $true ) )
& ( ( infuncsetfunc = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X0 @ X1 @ X2 )
!= $true )
& ( $true
= ( in @ X2 @ ( funcSet @ X0 @ X1 ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X0 @ X1 @ X2 )
= $true )
| ( $true
!= ( in @ X2 @ ( funcSet @ X0 @ X1 ) ) ) )
<=> ( infuncsetfunc = $true ) ),
inference(ennf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( infuncsetfunc = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X2 @ ( funcSet @ X0 @ X1 ) ) )
=> ( ( func @ X0 @ X1 @ X2 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ( func @ X0 @ X1 @ X2 ) )
= infuncsetfunc ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X0: $i,X3: $i,X7: $i] :
( ( ( in @ X7 @ ( funcSet @ X0 @ X3 ) )
=> ( func @ X0 @ X3 @ X7 ) )
= infuncsetfunc ),
file('/export/starexec/sandbox/tmp/tmp.qKKwlDXAuP/DTF2THF_6218.p',infuncsetfunc) ).
thf(f75,plain,
! [X0: $i] :
( ( $true
!= ( in @ ( kpair @ sK11 @ X0 ) @ sK9 ) )
| ( $true
!= ( in @ X0 @ sK8 ) )
| ( $true
!= ( func @ sK10 @ sK8 @ sK9 ) )
| ( sK12 != X0 ) ),
inference(subsumption_resolution,[status(thm)],[f73,f56]) ).
thf(f56,plain,
( $true
= ( in @ sK11 @ sK10 ) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
thf(f73,plain,
! [X0: $i] :
( ( $true
!= ( in @ X0 @ sK8 ) )
| ( $true
!= ( in @ ( kpair @ sK11 @ X0 ) @ sK9 ) )
| ( $true
!= ( in @ sK11 @ sK10 ) )
| ( $true
!= ( func @ sK10 @ sK8 @ sK9 ) )
| ( sK12 != X0 ) ),
inference(superposition,[status(thm)],[f55,f68]) ).
thf(f68,plain,
! [X8: $i,X6: $i,X9: $i,X7: $i,X5: $i] :
( ( ( ap @ X6 @ X7 @ X5 @ X8 )
= X9 )
| ( ( in @ X9 @ X7 )
!= $true )
| ( ( in @ ( kpair @ X8 @ X9 ) @ X5 )
!= $true )
| ( $true
!= ( in @ X8 @ X6 ) )
| ( $true
!= ( func @ X6 @ X7 @ X5 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f64]) ).
thf(f64,plain,
! [X8: $i,X6: $i,X9: $i,X7: $i,X5: $i] :
( ( ( in @ X9 @ X7 )
!= $true )
| ( ( in @ ( kpair @ X8 @ X9 ) @ X5 )
!= $true )
| ( $true != $true )
| ( $true
!= ( in @ X8 @ X6 ) )
| ( $true
!= ( func @ X6 @ X7 @ X5 ) )
| ( ( ap @ X6 @ X7 @ X5 @ X8 )
= X9 ) ),
inference(definition_unfolding,[status(thm)],[f43,f58]) ).
thf(f58,plain,
funcGraphProp2 = $true,
inference(cnf_transformation,[status(thm)],[f42]) ).
thf(f43,plain,
! [X8: $i,X6: $i,X9: $i,X7: $i,X5: $i] :
( ( ( in @ ( kpair @ X8 @ X9 ) @ X5 )
!= $true )
| ( ( ap @ X6 @ X7 @ X5 @ X8 )
= X9 )
| ( ( in @ X9 @ X7 )
!= $true )
| ( $true
!= ( in @ X8 @ X6 ) )
| ( $true
!= ( func @ X6 @ X7 @ X5 ) )
| ( funcGraphProp2 != $true ) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
thf(f34,plain,
( ( ( funcGraphProp2 = $true )
| ( ( $true
= ( in @ ( kpair @ sK3 @ sK4 ) @ sK0 ) )
& ( ( ap @ sK1 @ sK2 @ sK0 @ sK3 )
!= sK4 )
& ( ( in @ sK4 @ sK2 )
= $true )
& ( $true
= ( in @ sK3 @ sK1 ) )
& ( $true
= ( func @ sK1 @ sK2 @ sK0 ) ) ) )
& ( ! [X5: $i,X6: $i,X7: $i] :
( ! [X8: $i] :
( ! [X9: $i] :
( ( ( in @ ( kpair @ X8 @ X9 ) @ X5 )
!= $true )
| ( ( ap @ X6 @ X7 @ X5 @ X8 )
= X9 )
| ( ( in @ X9 @ X7 )
!= $true ) )
| ( $true
!= ( in @ X8 @ X6 ) ) )
| ( $true
!= ( func @ X6 @ X7 @ X5 ) ) )
| ( funcGraphProp2 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f30,f33,f32,f31]) ).
thf(f31,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ X0 ) )
& ( ( ap @ X1 @ X2 @ X0 @ X3 )
!= X4 )
& ( $true
= ( in @ X4 @ X2 ) ) )
& ( $true
= ( in @ X3 @ X1 ) ) )
& ( ( func @ X1 @ X2 @ X0 )
= $true ) )
=> ( ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ sK0 )
= $true )
& ( ( ap @ sK1 @ sK2 @ sK0 @ X3 )
!= X4 )
& ( $true
= ( in @ X4 @ sK2 ) ) )
& ( $true
= ( in @ X3 @ sK1 ) ) )
& ( $true
= ( func @ sK1 @ sK2 @ sK0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f32,plain,
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ sK0 )
= $true )
& ( ( ap @ sK1 @ sK2 @ sK0 @ X3 )
!= X4 )
& ( $true
= ( in @ X4 @ sK2 ) ) )
& ( $true
= ( in @ X3 @ sK1 ) ) )
=> ( ? [X4: $i] :
( ( $true
= ( in @ ( kpair @ sK3 @ X4 ) @ sK0 ) )
& ( ( ap @ sK1 @ sK2 @ sK0 @ sK3 )
!= X4 )
& ( $true
= ( in @ X4 @ sK2 ) ) )
& ( $true
= ( in @ sK3 @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f33,plain,
( ? [X4: $i] :
( ( $true
= ( in @ ( kpair @ sK3 @ X4 ) @ sK0 ) )
& ( ( ap @ sK1 @ sK2 @ sK0 @ sK3 )
!= X4 )
& ( $true
= ( in @ X4 @ sK2 ) ) )
=> ( ( $true
= ( in @ ( kpair @ sK3 @ sK4 ) @ sK0 ) )
& ( ( ap @ sK1 @ sK2 @ sK0 @ sK3 )
!= sK4 )
& ( ( in @ sK4 @ sK2 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f30,plain,
( ( ( funcGraphProp2 = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ X0 ) )
& ( ( ap @ X1 @ X2 @ X0 @ X3 )
!= X4 )
& ( $true
= ( in @ X4 @ X2 ) ) )
& ( $true
= ( in @ X3 @ X1 ) ) )
& ( ( func @ X1 @ X2 @ X0 )
= $true ) ) )
& ( ! [X5: $i,X6: $i,X7: $i] :
( ! [X8: $i] :
( ! [X9: $i] :
( ( ( in @ ( kpair @ X8 @ X9 ) @ X5 )
!= $true )
| ( ( ap @ X6 @ X7 @ X5 @ X8 )
= X9 )
| ( ( in @ X9 @ X7 )
!= $true ) )
| ( $true
!= ( in @ X8 @ X6 ) ) )
| ( $true
!= ( func @ X6 @ X7 @ X5 ) ) )
| ( funcGraphProp2 != $true ) ) ),
inference(rectify,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ( funcGraphProp2 = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ X0 ) )
& ( ( ap @ X1 @ X2 @ X0 @ X3 )
!= X4 )
& ( $true
= ( in @ X4 @ X2 ) ) )
& ( $true
= ( in @ X3 @ X1 ) ) )
& ( ( func @ X1 @ X2 @ X0 )
= $true ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( $true
!= ( in @ ( kpair @ X3 @ X4 ) @ X0 ) )
| ( ( ap @ X1 @ X2 @ X0 @ X3 )
= X4 )
| ( $true
!= ( in @ X4 @ X2 ) ) )
| ( $true
!= ( in @ X3 @ X1 ) ) )
| ( ( func @ X1 @ X2 @ X0 )
!= $true ) )
| ( funcGraphProp2 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
( ( funcGraphProp2 = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( $true
!= ( in @ ( kpair @ X3 @ X4 ) @ X0 ) )
| ( ( ap @ X1 @ X2 @ X0 @ X3 )
= X4 )
| ( $true
!= ( in @ X4 @ X2 ) ) )
| ( $true
!= ( in @ X3 @ X1 ) ) )
| ( ( func @ X1 @ X2 @ X0 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f24]) ).
thf(f24,plain,
( ( funcGraphProp2 = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( ( ap @ X1 @ X2 @ X0 @ X3 )
= X4 )
| ( $true
!= ( in @ ( kpair @ X3 @ X4 ) @ X0 ) )
| ( $true
!= ( in @ X4 @ X2 ) ) )
| ( $true
!= ( in @ X3 @ X1 ) ) )
| ( ( func @ X1 @ X2 @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( funcGraphProp2 = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X1 @ X2 @ X0 )
= $true )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
=> ! [X4: $i] :
( ( $true
= ( in @ X4 @ X2 ) )
=> ( ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ X0 ) )
=> ( ( ap @ X1 @ X2 @ X0 @ X3 )
= X4 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X1 @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X0 )
=> ( ( ap @ X1 @ X2 @ X0 @ X3 )
= X4 ) ) ) ) )
= funcGraphProp2 ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
! [X7: $i,X0: $i,X3: $i] :
( ( ( func @ X0 @ X3 @ X7 )
=> ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ! [X6: $i] :
( ( in @ X6 @ X3 )
=> ( ( in @ ( kpair @ X1 @ X6 ) @ X7 )
=> ( ( ap @ X0 @ X3 @ X7 @ X1 )
= X6 ) ) ) ) )
= funcGraphProp2 ),
file('/export/starexec/sandbox/tmp/tmp.qKKwlDXAuP/DTF2THF_6218.p',funcGraphProp2) ).
thf(f55,plain,
( ( ap @ sK10 @ sK8 @ sK9 @ sK11 )
!= sK12 ),
inference(cnf_transformation,[status(thm)],[f42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU688^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/0.31 % Computer : n002.cluster.edu
% 0.13/0.31 % Model : x86_64 x86_64
% 0.13/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.31 % Memory : 8042.1875MB
% 0.13/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.31 % CPULimit : 300
% 0.13/0.31 % WCLimit : 300
% 0.13/0.31 % DateTime : Tue Feb 24 12:31:18 EST 2026
% 0.13/0.31 % CPUTime :
% 0.13/0.31 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.43 ---- Original DTF file ---
% 0.19/0.43 thf(spec,logic,$$dhol).
% 0.19/0.43 %------------------------------------------------------------------------------
% 0.19/0.43 % File : SEU688^2 : TPTP v9.2.1. Released v3.7.0.
% 0.19/0.43 % Domain : Set Theory
% 0.19/0.43 % Problem : Functions - Extensionality and Beta Reduction
% 0.19/0.43 % Version : Especial > Reduced > Especial.
% 0.19/0.43 % English : (! A:i.! B:i.! f:i.in f (funcSet A B) -> (! x:i.in x A ->
% 0.19/0.43 % (! y:i.in y B -> in (kpair x y) f -> ap A B f x = y)))
% 0.19/0.43
% 0.19/0.43 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.19/0.43 % Source : [Bro08]
% 0.19/0.43 % Names : ZFC190l [Bro08]
% 0.19/0.43
% 0.19/0.43 % Status : Theorem
% 0.19/0.43 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0, 0.27 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v6.0.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.3.0, 0.60 v5.2.0, 0.40 v4.1.0, 0.33 v4.0.0, 0.67 v3.7.0
% 0.19/0.43 % Syntax : Number of formulae : 22 ( 6 unt; 15 typ; 6 def)
% 0.19/0.43 % Number of atoms : 34 ( 9 equ; 0 cnn)
% 0.19/0.43 % Maximal formula atoms : 7 ( 4 avg)
% 0.19/0.43 % Number of connectives : 75 ( 0 ~; 0 |; 2 &; 61 @)
% 0.19/0.43 % ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% 0.19/0.43 % Maximal formula depth : 16 ( 3 avg)
% 0.19/0.43 % Number of types : 2 ( 0 usr)
% 0.19/0.43 % Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% 0.19/0.43 % Number of symbols : 16 ( 15 usr; 3 con; 0-4 aty)
% 0.19/0.43 % Number of variables : 26 ( 11 ^; 14 !; 1 ?; 26 :)
% 0.19/0.43 % SPC : TH0_THM_EQU_NAR
% 0.19/0.43
% 0.19/0.43 % Comments : http://mathgate.info/detsetitem.php?id=413
% 0.19/0.43 %------------------------------------------------------------------------------
% 0.19/0.43 thf(in_type,type,
% 0.19/0.43 in: $i > $i > $o ).
% 0.19/0.43
% 0.19/0.43 thf(emptyset_type,type,
% 0.19/0.43 emptyset: $i ).
% 0.19/0.43
% 0.19/0.43 thf(setadjoin_type,type,
% 0.19/0.43 setadjoin: $i > $i > $i ).
% 0.19/0.43
% 0.19/0.43 thf(dsetconstr_type,type,
% 0.19/0.43 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.19/0.43
% 0.19/0.43 thf(subset_type,type,
% 0.19/0.43 subset: $i > $i > $o ).
% 0.19/0.43
% 0.19/0.43 thf(kpair_type,type,
% 0.19/0.43 kpair: $i > $i > $i ).
% 0.19/0.43
% 0.19/0.43 thf(cartprod_type,type,
% 0.19/0.43 cartprod: $i > $i > $i ).
% 0.19/0.43
% 0.19/0.43 thf(singleton_type,type,
% 0.19/0.43 singleton: $i > $o ).
% 0.19/0.43
% 0.19/0.43 thf(singleton,definition,
% 0.19/0.43 ( singleton
% 0.19/0.43 = ( ^ [A: $i] :
% 0.19/0.43 ? [Xx: $i] :
% 0.19/0.43 ( ( in @ Xx @ A )
% 0.19/0.43 & ( A
% 0.19/0.43 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.19/0.43
% 0.19/0.43 thf(ex1_type,type,
% 0.19/0.43 ex1: $i > ( $i > $o ) > $o ).
% 0.19/0.43
% 0.19/0.43 thf(ex1,definition,
% 0.19/0.43 ( ex1
% 0.19/0.43 = ( ^ [A: $i,Xphi: $i > $o] :
% 0.19/0.43 ( singleton
% 0.19/0.43 @ ( dsetconstr @ A
% 0.19/0.43 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.43
% 0.19/0.43 thf(breln_type,type,
% 0.19/0.43 breln: $i > $i > $i > $o ).
% 0.19/0.43
% 0.19/0.43 thf(breln,definition,
% 0.19/0.43 ( breln
% 0.19/0.43 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.19/0.43
% 0.19/0.43 thf(func_type,type,
% 0.19/0.43 func: $i > $i > $i > $o ).
% 0.19/0.43
% 0.19/0.43 thf(func,definition,
% 0.19/0.43 ( func
% 0.19/0.43 = ( ^ [A: $i,B: $i,R: $i] :
% 0.19/0.43 ( ( breln @ A @ B @ R )
% 0.19/0.43 & ! [Xx: $i] :
% 0.19/0.43 ( ( in @ Xx @ A )
% 0.19/0.43 => ( ex1 @ B
% 0.19/0.43 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ).
% 0.19/0.43
% 0.19/0.43 thf(funcSet_type,type,
% 0.19/0.43 funcSet: $i > $i > $i ).
% 0.19/0.43
% 0.19/0.43 thf(ap_type,type,
% 0.19/0.43 ap: $i > $i > $i > $i > $i ).
% 0.19/0.43
% 0.19/0.43 thf(infuncsetfunc_type,type,
% 0.19/0.43 infuncsetfunc: $o ).
% 0.19/0.43
% 0.19/0.43 thf(infuncsetfunc,definition,
% 0.19/0.43 ( infuncsetfunc
% 0.19/0.43 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.19/0.43 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.19/0.43 => ( func @ A @ B @ Xf ) ) ) ) ).
% 0.19/0.43
% 0.19/0.43 thf(funcGraphProp2_type,type,
% 0.19/0.43 funcGraphProp2: $o ).
% 0.19/0.43
% 0.19/0.43 thf(funcGraphProp2,definition,
% 0.19/0.43 ( funcGraphProp2
% 0.19/0.43 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.19/0.43 ( ( func @ A @ B @ Xf )
% 0.19/0.43 => ! [Xx: $i] :
% 0.19/0.43 ( ( in @ Xx @ A )
% 0.19/0.43 => ! [Xy: $i] :
% 0.19/0.43 ( ( in @ Xy @ B )
% 0.19/0.43 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.19/0.43 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.19/0.43 = Xy ) ) ) ) ) ) ) ).
% 0.19/0.43
% 0.19/0.43 thf(funcGraphProp4,conjecture,
% 0.19/0.43 ( infuncsetfunc
% 0.19/0.43 => ( funcGraphProp2
% 0.19/0.43 => ! [A: $i,B: $i,Xf: $i] :
% 0.19/0.43 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.19/0.43 => ! [Xx: $i] :
% 0.19/0.43 ( ( in @ Xx @ A )
% 0.19/0.43 => ! [Xy: $i] :
% 0.19/0.43 ( ( in @ Xy @ B )
% 0.19/0.43 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.19/0.43 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.19/0.43 = Xy ) ) ) ) ) ) ) ).
% 0.19/0.43
% 0.19/0.43 %------------------------------------------------------------------------------
% 0.19/0.43 ------------------------
% 1.54/1.39 ---- Embedded in THF ---
% 1.54/1.39 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.54/1.39 %%% Generated on Tue Feb 24 12:31:19 EST 2026
% 1.54/1.39 %%% using '$$dhol' embedding, version 1.3.0.
% 1.54/1.39 %%% Logic specification used:
% 1.54/1.39 %%% thf(spec, logic, $$dhol).
% 1.54/1.39
% 1.54/1.39 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.qKKwlDXAuP/DTF2DTF6218.p
% See solution above
% 1.54/1.39 ------------------------
% 1.74/1.40 ---- Cleaned THF ---
% 1.74/1.40 thf(in_type,type,
% 1.74/1.40 in: $i > $i > $o ).
% 1.74/1.40
% 1.74/1.40 thf(emptyset_type,type,
% 1.74/1.40 emptyset: $i ).
% 1.74/1.40
% 1.74/1.40 thf(setadjoin_type,type,
% 1.74/1.40 setadjoin: $i > $i > $i ).
% 1.74/1.40
% 1.74/1.40 thf(dsetconstr_type,type,
% 1.74/1.40 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.74/1.40
% 1.74/1.40 thf(subset_type,type,
% 1.74/1.40 subset: $i > $i > $o ).
% 1.74/1.40
% 1.74/1.40 thf(kpair_type,type,
% 1.74/1.40 kpair: $i > $i > $i ).
% 1.74/1.40
% 1.74/1.40 thf(cartprod_type,type,
% 1.74/1.40 cartprod: $i > $i > $i ).
% 1.74/1.40
% 1.74/1.40 thf(singleton_type,type,
% 1.74/1.40 singleton: $i > $o ).
% 1.74/1.40
% 1.74/1.40 thf(singleton,definition,
% 1.74/1.40 ( singleton
% 1.74/1.40 = ( ^ [A: $i] :
% 1.74/1.40 ? [Xx: $i] :
% 1.74/1.40 ( ( in @ Xx @ A )
% 1.74/1.40 & ( A
% 1.74/1.40 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 1.74/1.40
% 1.74/1.40 thf(ex1_type,type,
% 1.74/1.40 ex1: $i > ( $i > $o ) > $o ).
% 1.74/1.40
% 1.74/1.40 thf(ex1,definition,
% 1.74/1.40 ( ex1
% 1.74/1.40 = ( ^ [A: $i,Xphi: $i > $o] :
% 1.74/1.40 ( singleton
% 1.74/1.40 @ ( dsetconstr @ A
% 1.74/1.40 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 1.74/1.40
% 1.74/1.40 thf(breln_type,type,
% 1.74/1.40 breln: $i > $i > $i > $o ).
% 1.74/1.40
% 1.74/1.40 thf(breln,definition,
% 1.74/1.40 ( breln
% 1.74/1.40 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 1.74/1.40
% 1.74/1.40 thf(func_type,type,
% 1.74/1.40 func: $i > $i > $i > $o ).
% 1.74/1.40
% 1.74/1.40 thf(func,definition,
% 1.74/1.40 ( func
% 1.74/1.40 = ( ^ [A: $i,B: $i,R: $i] :
% 1.74/1.40 ( ( breln @ A @ B @ R )
% 1.74/1.40 & ! [Xx: $i] :
% 1.74/1.40 ( ( in @ Xx @ A )
% 1.74/1.40 => ( ex1 @ B
% 1.74/1.40 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ).
% 1.74/1.40
% 1.74/1.40 thf(funcSet_type,type,
% 1.74/1.40 funcSet: $i > $i > $i ).
% 1.74/1.40
% 1.74/1.40 thf(ap_type,type,
% 1.74/1.40 ap: $i > $i > $i > $i > $i ).
% 1.74/1.40
% 1.74/1.40 thf(infuncsetfunc_type,type,
% 1.74/1.40 infuncsetfunc: $o ).
% 1.74/1.40
% 1.74/1.40 thf(infuncsetfunc,definition,
% 1.74/1.40 ( infuncsetfunc
% 1.74/1.40 = ( ! [A: $i,B: $i,Xf: $i] :
% 1.74/1.40 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 1.74/1.40 => ( func @ A @ B @ Xf ) ) ) ) ).
% 1.74/1.40
% 1.74/1.40 thf(funcGraphProp2_type,type,
% 1.74/1.40 funcGraphProp2: $o ).
% 1.74/1.40
% 1.74/1.40 thf(funcGraphProp2,definition,
% 1.74/1.40 ( funcGraphProp2
% 1.74/1.40 = ( ! [A: $i,B: $i,Xf: $i] :
% 1.74/1.40 ( ( func @ A @ B @ Xf )
% 1.74/1.40 => ! [Xx: $i] :
% 1.74/1.40 ( ( in @ Xx @ A )
% 1.74/1.40 => ! [Xy: $i] :
% 1.74/1.40 ( ( in @ Xy @ B )
% 1.74/1.40 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 1.74/1.40 => ( ( ap @ A @ B @ Xf @ Xx )
% 1.74/1.40 = Xy ) ) ) ) ) ) ) ).
% 1.74/1.40
% 1.74/1.40 thf(funcGraphProp4,conjecture,
% 1.74/1.40 ( infuncsetfunc
% 1.74/1.40 => ( funcGraphProp2
% 1.74/1.40 => ! [A: $i,B: $i,Xf: $i] :
% 1.74/1.40 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 1.74/1.40 => ! [Xx: $i] :
% 1.74/1.40 ( ( in @ Xx @ A )
% 1.74/1.40 => ! [Xy: $i] :
% 1.74/1.40 ( ( in @ Xy @ B )
% 1.74/1.40 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 1.74/1.40 => ( ( ap @ A @ B @ Xf @ Xx )
% 1.74/1.40 = Xy ) ) ) ) ) ) ) ).
% 1.74/1.40 ------------------------
% 1.74/1.42 % (6336)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_6218 for (2999ds/183Mi)
% 1.74/1.42 % (6337)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_6218 for (2999ds/4Mi)
% 1.74/1.42 % (6338)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_6218 for (2999ds/27Mi)
% 1.74/1.42 % (6340)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_6218 for (2999ds/2Mi)
% 1.74/1.42 % (6339)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_6218 for (2999ds/2Mi)
% 1.74/1.42 % (6341)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_6218 for (2999ds/275Mi)
% 1.74/1.42 % (6342)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_6218 for (2999ds/18Mi)
% 1.74/1.42 % (6339)Instruction limit reached!
% 1.74/1.42 % (6339)------------------------------
% 1.74/1.42 % (6339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.42 % (6339)Termination reason: Unknown
% 1.74/1.42 % (6340)Instruction limit reached!
% 1.74/1.42 % (6340)------------------------------
% 1.74/1.42 % (6340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.42 % (6339)Termination phase: Preprocessing 3
% 1.74/1.42
% 1.74/1.42 % (6339)Memory used [KB]: 1023
% 1.74/1.42 % (6339)Time elapsed: 0.003 s
% 1.74/1.42 % (6339)Instructions burned: 3 (million)
% 1.74/1.42 % (6339)------------------------------
% 1.74/1.42 % (6339)------------------------------
% 1.74/1.42 % (6340)Termination reason: Unknown
% 1.74/1.42 % (6340)Termination phase: Property scanning
% 1.74/1.42
% 1.74/1.42 % (6340)Memory used [KB]: 1023
% 1.74/1.42 % (6340)Time elapsed: 0.003 s
% 1.74/1.42 % (6340)Instructions burned: 3 (million)
% 1.74/1.42 % (6340)------------------------------
% 1.74/1.42 % (6340)------------------------------
% 1.74/1.42 % (6337)Instruction limit reached!
% 1.74/1.42 % (6337)------------------------------
% 1.74/1.42 % (6337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.42 % (6337)Termination reason: Unknown
% 1.74/1.42 % (6337)Termination phase: Saturation
% 1.74/1.42
% 1.74/1.42 % (6337)Memory used [KB]: 1023
% 1.74/1.42 % (6337)Time elapsed: 0.004 s
% 1.74/1.42 % (6337)Instructions burned: 5 (million)
% 1.74/1.42 % (6337)------------------------------
% 1.74/1.42 % (6337)------------------------------
% 1.74/1.42 % (6341)First to succeed.
% 1.74/1.43 % (6341)Refutation found. Thanks to Tanya!
% 1.74/1.43 % SZS status Theorem for DTF2THF_6218
% 1.74/1.43 % SZS output start Proof for DTF2THF_6218
% 1.74/1.43 thf(func_def_0, type, in: $i > $i > $o).
% 1.74/1.43 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 1.74/1.43 thf(func_def_3, type, dsetconstr: $i > ($i > $o) > $i).
% 1.74/1.43 thf(func_def_4, type, subset: $i > $i > $o).
% 1.74/1.43 thf(func_def_5, type, kpair: $i > $i > $i).
% 1.74/1.43 thf(func_def_6, type, cartprod: $i > $i > $i).
% 1.74/1.43 thf(func_def_7, type, singleton: $i > $o).
% 1.74/1.43 thf(func_def_9, type, ex1: $i > ($i > $o) > $o).
% 1.74/1.43 thf(func_def_10, type, breln: $i > $i > $i > $o).
% 1.74/1.43 thf(func_def_11, type, func: $i > $i > $i > $o).
% 1.74/1.43 thf(func_def_12, type, funcSet: $i > $i > $i).
% 1.74/1.43 thf(func_def_13, type, ap: $i > $i > $i > $i > $i).
% 1.74/1.43 thf(f79,plain,(
% 1.74/1.43 $false),
% 1.74/1.43 inference(subsumption_resolution,[status(thm)],[f78,f53])).
% 1.74/1.43 thf(f53,plain,(
% 1.74/1.43 ($true = (in @ sK12 @ sK8))),
% 1.74/1.43 inference(cnf_transformation,[status(thm)],[f42])).
% 1.74/1.43 thf(f42,plain,(
% 1.74/1.43 (funcGraphProp2 = $true) & (((in @ sK9 @ (funcSet @ sK10 @ sK8)) = $true) & (($true = (in @ sK11 @ sK10)) & (((ap @ sK10 @ sK8 @ sK9 @ sK11) != sK12) & ($true = (in @ (kpair @ sK11 @ sK12) @ sK9)) & ($true = (in @ sK12 @ sK8))))) & (infuncsetfunc = $true)),
% 1.74/1.43 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11,sK12])],[f28,f41,f40,f39])).
% 1.74/1.43 thf(f39,plain,(
% 1.74/1.43 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ (funcSet @ X2 @ X0))) & ? [X3 : $i] : (($true = (in @ X3 @ X2)) & ? [X4 : $i] : (((ap @ X2 @ X0 @ X1 @ X3) != X4) & ((in @ (kpair @ X3 @ X4) @ X1) = $true) & ($true = (in @ X4 @ X0))))) => (((in @ sK9 @ (funcSet @ sK10 @ sK8)) = $true) & ? [X3 : $i] : (($true = (in @ X3 @ sK10)) & ? [X4 : $i] : (((ap @ sK10 @ sK8 @ sK9 @ X3) != X4) & ((in @ (kpair @ X3 @ X4) @ sK9) = $true) & ((in @ X4 @ sK8) = $true))))),
% 1.74/1.43 introduced(definition,[],[choice_axiom])).
% 1.74/1.43 thf(f40,plain,(
% 1.74/1.43 ? [X3 : $i] : (($true = (in @ X3 @ sK10)) & ? [X4 : $i] : (((ap @ sK10 @ sK8 @ sK9 @ X3) != X4) & ((in @ (kpair @ X3 @ X4) @ sK9) = $true) & ((in @ X4 @ sK8) = $true))) => (($true = (in @ sK11 @ sK10)) & ? [X4 : $i] : (((ap @ sK10 @ sK8 @ sK9 @ sK11) != X4) & ($true = (in @ (kpair @ sK11 @ X4) @ sK9)) & ((in @ X4 @ sK8) = $true)))),
% 1.74/1.43 introduced(definition,[],[choice_axiom])).
% 1.74/1.43 thf(f41,plain,(
% 1.74/1.43 ? [X4 : $i] : (((ap @ sK10 @ sK8 @ sK9 @ sK11) != X4) & ($true = (in @ (kpair @ sK11 @ X4) @ sK9)) & ((in @ X4 @ sK8) = $true)) => (((ap @ sK10 @ sK8 @ sK9 @ sK11) != sK12) & ($true = (in @ (kpair @ sK11 @ sK12) @ sK9)) & ($true = (in @ sK12 @ sK8)))),
% 1.74/1.43 introduced(definition,[],[choice_axiom])).
% 1.74/1.43 thf(f28,plain,(
% 1.74/1.43 (funcGraphProp2 = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ (funcSet @ X2 @ X0))) & ? [X3 : $i] : (($true = (in @ X3 @ X2)) & ? [X4 : $i] : (((ap @ X2 @ X0 @ X1 @ X3) != X4) & ((in @ (kpair @ X3 @ X4) @ X1) = $true) & ($true = (in @ X4 @ X0))))) & (infuncsetfunc = $true)),
% 1.74/1.43 inference(flattening,[status(thm)],[f27])).
% 1.74/1.43 thf(f27,plain,(
% 1.74/1.43 (? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : ((((ap @ X2 @ X0 @ X1 @ X3) != X4) & ((in @ (kpair @ X3 @ X4) @ X1) = $true)) & ($true = (in @ X4 @ X0))) & ($true = (in @ X3 @ X2))) & ($true = (in @ X1 @ (funcSet @ X2 @ X0)))) & (funcGraphProp2 = $true)) & (infuncsetfunc = $true)),
% 1.74/1.43 inference(ennf_transformation,[status(thm)],[f17])).
% 1.74/1.43 thf(f17,plain,(
% 1.74/1.43 ~((infuncsetfunc = $true) => ((funcGraphProp2 = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ (funcSet @ X2 @ X0))) => ! [X3 : $i] : (($true = (in @ X3 @ X2)) => ! [X4 : $i] : (($true = (in @ X4 @ X0)) => (((in @ (kpair @ X3 @ X4) @ X1) = $true) => ((ap @ X2 @ X0 @ X1 @ X3) = X4)))))))),
% 1.74/1.43 inference(fool_elimination,[status(thm)],[f16])).
% 1.74/1.43 thf(f16,plain,(
% 1.74/1.43 ~(infuncsetfunc => (funcGraphProp2 => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (funcSet @ X2 @ X0)) => ! [X3 : $i] : ((in @ X3 @ X2) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ X1) => ((ap @ X2 @ X0 @ X1 @ X3) = X4)))))))),
% 1.74/1.43 inference(rectify,[status(thm)],[f8])).
% 1.74/1.43 thf(f8,negated_conjecture,(
% 1.74/1.43 ~(infuncsetfunc => (funcGraphProp2 => ! [X3 : $i,X7 : $i,X0 : $i] : ((in @ X7 @ (funcSet @ X0 @ X3)) => ! [X1 : $i] : ((in @ X1 @ X0) => ! [X6 : $i] : ((in @ X6 @ X3) => ((in @ (kpair @ X1 @ X6) @ X7) => ((ap @ X0 @ X3 @ X7 @ X1) = X6)))))))),
% 1.74/1.43 inference(negated_conjecture,[status(cth)],[f7])).
% 1.74/1.43 thf(f7,conjecture,(
% 1.74/1.43 infuncsetfunc => (funcGraphProp2 => ! [X3 : $i,X7 : $i,X0 : $i] : ((in @ X7 @ (funcSet @ X0 @ X3)) => ! [X1 : $i] : ((in @ X1 @ X0) => ! [X6 : $i] : ((in @ X6 @ X3) => ((in @ (kpair @ X1 @ X6) @ X7) => ((ap @ X0 @ X3 @ X7 @ X1) = X6))))))),
% 1.74/1.43 file('/export/starexec/sandbox/tmp/tmp.qKKwlDXAuP/DTF2THF_6218.p',funcGraphProp4)).
% 1.74/1.43 thf(f78,plain,(
% 1.74/1.43 ($true != (in @ sK12 @ sK8))),
% 1.74/1.43 inference(trivial_inequality_removal,[status(thm)],[f77])).
% 1.74/1.43 thf(f77,plain,(
% 1.74/1.43 ($true != (in @ sK12 @ sK8)) | (sK12 != sK12) | ($true != $true)),
% 1.74/1.43 inference(superposition,[status(thm)],[f76,f54])).
% 1.74/1.43 thf(f54,plain,(
% 1.74/1.43 ($true = (in @ (kpair @ sK11 @ sK12) @ sK9))),
% 1.74/1.43 inference(cnf_transformation,[status(thm)],[f42])).
% 1.74/1.43 thf(f76,plain,(
% 1.74/1.43 ( ! [X0 : $i] : (($true != (in @ (kpair @ sK11 @ X0) @ sK9)) | ($true != (in @ X0 @ sK8)) | (sK12 != X0)) )),
% 1.74/1.43 inference(subsumption_resolution,[status(thm)],[f75,f71])).
% 1.74/1.43 thf(f71,plain,(
% 1.74/1.43 ($true = (func @ sK10 @ sK8 @ sK9))),
% 1.74/1.43 inference(trivial_inequality_removal,[status(thm)],[f70])).
% 1.74/1.43 thf(f70,plain,(
% 1.74/1.43 ($true = (func @ sK10 @ sK8 @ sK9)) | ($true != $true)),
% 1.74/1.43 inference(superposition,[status(thm)],[f69,f57])).
% 1.74/1.43 thf(f57,plain,(
% 1.74/1.43 ((in @ sK9 @ (funcSet @ sK10 @ sK8)) = $true)),
% 1.74/1.43 inference(cnf_transformation,[status(thm)],[f42])).
% 1.74/1.43 thf(f69,plain,(
% 1.74/1.43 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X2 @ (funcSet @ X0 @ X1))) | ((func @ X0 @ X1 @ X2) = $true)) )),
% 1.74/1.43 inference(trivial_inequality_removal,[status(thm)],[f65])).
% 1.74/1.43 thf(f65,plain,(
% 1.74/1.43 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((func @ X0 @ X1 @ X2) = $true) | ($true != (in @ X2 @ (funcSet @ X0 @ X1))) | ($true != $true)) )),
% 1.74/1.43 inference(definition_unfolding,[status(thm)],[f51,f52])).
% 1.74/1.43 thf(f52,plain,(
% 1.74/1.43 (infuncsetfunc = $true)),
% 1.74/1.43 inference(cnf_transformation,[status(thm)],[f42])).
% 1.74/1.43 thf(f51,plain,(
% 1.74/1.43 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((func @ X0 @ X1 @ X2) = $true) | ($true != (in @ X2 @ (funcSet @ X0 @ X1))) | (infuncsetfunc != $true)) )),
% 1.74/1.43 inference(cnf_transformation,[status(thm)],[f38])).
% 1.74/1.43 thf(f38,plain,(
% 1.74/1.43 (! [X0 : $i,X1 : $i,X2 : $i] : (((func @ X0 @ X1 @ X2) = $true) | ($true != (in @ X2 @ (funcSet @ X0 @ X1)))) | (infuncsetfunc != $true)) & ((infuncsetfunc = $true) | (($true != (func @ sK5 @ sK6 @ sK7)) & ($true = (in @ sK7 @ (funcSet @ sK5 @ sK6)))))),
% 1.74/1.43 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f36,f37])).
% 1.74/1.43 thf(f37,plain,(
% 1.74/1.43 ? [X3 : $i,X4 : $i,X5 : $i] : (((func @ X3 @ X4 @ X5) != $true) & ($true = (in @ X5 @ (funcSet @ X3 @ X4)))) => (($true != (func @ sK5 @ sK6 @ sK7)) & ($true = (in @ sK7 @ (funcSet @ sK5 @ sK6))))),
% 1.74/1.43 introduced(definition,[],[choice_axiom])).
% 1.74/1.43 thf(f36,plain,(
% 1.74/1.43 (! [X0 : $i,X1 : $i,X2 : $i] : (((func @ X0 @ X1 @ X2) = $true) | ($true != (in @ X2 @ (funcSet @ X0 @ X1)))) | (infuncsetfunc != $true)) & ((infuncsetfunc = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (((func @ X3 @ X4 @ X5) != $true) & ($true = (in @ X5 @ (funcSet @ X3 @ X4)))))),
% 1.74/1.43 inference(rectify,[status(thm)],[f35])).
% 1.74/1.43 thf(f35,plain,(
% 1.74/1.43 (! [X0 : $i,X1 : $i,X2 : $i] : (((func @ X0 @ X1 @ X2) = $true) | ($true != (in @ X2 @ (funcSet @ X0 @ X1)))) | (infuncsetfunc != $true)) & ((infuncsetfunc = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((func @ X0 @ X1 @ X2) != $true) & ($true = (in @ X2 @ (funcSet @ X0 @ X1)))))),
% 1.74/1.43 inference(nnf_transformation,[status(thm)],[f26])).
% 1.74/1.43 thf(f26,plain,(
% 1.74/1.43 ! [X0 : $i,X1 : $i,X2 : $i] : (((func @ X0 @ X1 @ X2) = $true) | ($true != (in @ X2 @ (funcSet @ X0 @ X1)))) <=> (infuncsetfunc = $true)),
% 1.74/1.43 inference(ennf_transformation,[status(thm)],[f15])).
% 1.74/1.43 thf(f15,plain,(
% 1.74/1.43 (infuncsetfunc = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X2 @ (funcSet @ X0 @ X1))) => ((func @ X0 @ X1 @ X2) = $true))),
% 1.74/1.43 inference(fool_elimination,[status(thm)],[f14])).
% 1.74/1.43 thf(f14,plain,(
% 1.74/1.43 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (funcSet @ X0 @ X1)) => (func @ X0 @ X1 @ X2)) = infuncsetfunc)),
% 1.74/1.43 inference(rectify,[status(thm)],[f5])).
% 1.74/1.43 thf(f5,axiom,(
% 1.74/1.43 (! [X0 : $i,X3 : $i,X7 : $i] : ((in @ X7 @ (funcSet @ X0 @ X3)) => (func @ X0 @ X3 @ X7)) = infuncsetfunc)),
% 1.74/1.43 file('/export/starexec/sandbox/tmp/tmp.qKKwlDXAuP/DTF2THF_6218.p',infuncsetfunc)).
% 1.74/1.43 thf(f75,plain,(
% 1.74/1.43 ( ! [X0 : $i] : (($true != (in @ (kpair @ sK11 @ X0) @ sK9)) | ($true != (in @ X0 @ sK8)) | ($true != (func @ sK10 @ sK8 @ sK9)) | (sK12 != X0)) )),
% 1.74/1.43 inference(subsumption_resolution,[status(thm)],[f73,f56])).
% 1.74/1.43 thf(f56,plain,(
% 1.74/1.43 ($true = (in @ sK11 @ sK10))),
% 1.74/1.43 inference(cnf_transformation,[status(thm)],[f42])).
% 1.74/1.43 thf(f73,plain,(
% 1.74/1.43 ( ! [X0 : $i] : (($true != (in @ X0 @ sK8)) | ($true != (in @ (kpair @ sK11 @ X0) @ sK9)) | ($true != (in @ sK11 @ sK10)) | ($true != (func @ sK10 @ sK8 @ sK9)) | (sK12 != X0)) )),
% 1.74/1.43 inference(superposition,[status(thm)],[f55,f68])).
% 1.74/1.43 thf(f68,plain,(
% 1.74/1.43 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i,X5 : $i] : (((ap @ X6 @ X7 @ X5 @ X8) = X9) | ((in @ X9 @ X7) != $true) | ((in @ (kpair @ X8 @ X9) @ X5) != $true) | ($true != (in @ X8 @ X6)) | ($true != (func @ X6 @ X7 @ X5))) )),
% 1.74/1.43 inference(trivial_inequality_removal,[status(thm)],[f64])).
% 1.74/1.43 thf(f64,plain,(
% 1.74/1.43 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i,X5 : $i] : (((in @ X9 @ X7) != $true) | ((in @ (kpair @ X8 @ X9) @ X5) != $true) | ($true != $true) | ($true != (in @ X8 @ X6)) | ($true != (func @ X6 @ X7 @ X5)) | ((ap @ X6 @ X7 @ X5 @ X8) = X9)) )),
% 1.74/1.43 inference(definition_unfolding,[status(thm)],[f43,f58])).
% 1.74/1.43 thf(f58,plain,(
% 1.74/1.43 (funcGraphProp2 = $true)),
% 1.74/1.43 inference(cnf_transformation,[status(thm)],[f42])).
% 1.74/1.43 thf(f43,plain,(
% 1.74/1.43 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i,X5 : $i] : (((in @ (kpair @ X8 @ X9) @ X5) != $true) | ((ap @ X6 @ X7 @ X5 @ X8) = X9) | ((in @ X9 @ X7) != $true) | ($true != (in @ X8 @ X6)) | ($true != (func @ X6 @ X7 @ X5)) | (funcGraphProp2 != $true)) )),
% 1.74/1.43 inference(cnf_transformation,[status(thm)],[f34])).
% 1.74/1.43 thf(f34,plain,(
% 1.74/1.43 ((funcGraphProp2 = $true) | (((($true = (in @ (kpair @ sK3 @ sK4) @ sK0)) & ((ap @ sK1 @ sK2 @ sK0 @ sK3) != sK4) & ((in @ sK4 @ sK2) = $true)) & ($true = (in @ sK3 @ sK1))) & ($true = (func @ sK1 @ sK2 @ sK0)))) & (! [X5 : $i,X6 : $i,X7 : $i] : (! [X8 : $i] : (! [X9 : $i] : (((in @ (kpair @ X8 @ X9) @ X5) != $true) | ((ap @ X6 @ X7 @ X5 @ X8) = X9) | ((in @ X9 @ X7) != $true)) | ($true != (in @ X8 @ X6))) | ($true != (func @ X6 @ X7 @ X5))) | (funcGraphProp2 != $true))),
% 1.74/1.43 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f30,f33,f32,f31])).
% 1.74/1.43 thf(f31,plain,(
% 1.74/1.43 ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (($true = (in @ (kpair @ X3 @ X4) @ X0)) & ((ap @ X1 @ X2 @ X0 @ X3) != X4) & ($true = (in @ X4 @ X2))) & ($true = (in @ X3 @ X1))) & ((func @ X1 @ X2 @ X0) = $true)) => (? [X3 : $i] : (? [X4 : $i] : (((in @ (kpair @ X3 @ X4) @ sK0) = $true) & ((ap @ sK1 @ sK2 @ sK0 @ X3) != X4) & ($true = (in @ X4 @ sK2))) & ($true = (in @ X3 @ sK1))) & ($true = (func @ sK1 @ sK2 @ sK0)))),
% 1.74/1.43 introduced(definition,[],[choice_axiom])).
% 1.74/1.43 thf(f32,plain,(
% 1.74/1.43 ? [X3 : $i] : (? [X4 : $i] : (((in @ (kpair @ X3 @ X4) @ sK0) = $true) & ((ap @ sK1 @ sK2 @ sK0 @ X3) != X4) & ($true = (in @ X4 @ sK2))) & ($true = (in @ X3 @ sK1))) => (? [X4 : $i] : (($true = (in @ (kpair @ sK3 @ X4) @ sK0)) & ((ap @ sK1 @ sK2 @ sK0 @ sK3) != X4) & ($true = (in @ X4 @ sK2))) & ($true = (in @ sK3 @ sK1)))),
% 1.74/1.43 introduced(definition,[],[choice_axiom])).
% 1.74/1.43 thf(f33,plain,(
% 1.74/1.43 ? [X4 : $i] : (($true = (in @ (kpair @ sK3 @ X4) @ sK0)) & ((ap @ sK1 @ sK2 @ sK0 @ sK3) != X4) & ($true = (in @ X4 @ sK2))) => (($true = (in @ (kpair @ sK3 @ sK4) @ sK0)) & ((ap @ sK1 @ sK2 @ sK0 @ sK3) != sK4) & ((in @ sK4 @ sK2) = $true))),
% 1.74/1.43 introduced(definition,[],[choice_axiom])).
% 1.74/1.43 thf(f30,plain,(
% 1.74/1.43 ((funcGraphProp2 = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (($true = (in @ (kpair @ X3 @ X4) @ X0)) & ((ap @ X1 @ X2 @ X0 @ X3) != X4) & ($true = (in @ X4 @ X2))) & ($true = (in @ X3 @ X1))) & ((func @ X1 @ X2 @ X0) = $true))) & (! [X5 : $i,X6 : $i,X7 : $i] : (! [X8 : $i] : (! [X9 : $i] : (((in @ (kpair @ X8 @ X9) @ X5) != $true) | ((ap @ X6 @ X7 @ X5 @ X8) = X9) | ((in @ X9 @ X7) != $true)) | ($true != (in @ X8 @ X6))) | ($true != (func @ X6 @ X7 @ X5))) | (funcGraphProp2 != $true))),
% 1.74/1.43 inference(rectify,[status(thm)],[f29])).
% 1.74/1.43 thf(f29,plain,(
% 1.74/1.43 ((funcGraphProp2 = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (($true = (in @ (kpair @ X3 @ X4) @ X0)) & ((ap @ X1 @ X2 @ X0 @ X3) != X4) & ($true = (in @ X4 @ X2))) & ($true = (in @ X3 @ X1))) & ((func @ X1 @ X2 @ X0) = $true))) & (! [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $i] : (! [X4 : $i] : (($true != (in @ (kpair @ X3 @ X4) @ X0)) | ((ap @ X1 @ X2 @ X0 @ X3) = X4) | ($true != (in @ X4 @ X2))) | ($true != (in @ X3 @ X1))) | ((func @ X1 @ X2 @ X0) != $true)) | (funcGraphProp2 != $true))),
% 1.74/1.43 inference(nnf_transformation,[status(thm)],[f25])).
% 1.74/1.43 thf(f25,plain,(
% 1.74/1.43 (funcGraphProp2 = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $i] : (! [X4 : $i] : (($true != (in @ (kpair @ X3 @ X4) @ X0)) | ((ap @ X1 @ X2 @ X0 @ X3) = X4) | ($true != (in @ X4 @ X2))) | ($true != (in @ X3 @ X1))) | ((func @ X1 @ X2 @ X0) != $true))),
% 1.74/1.43 inference(flattening,[status(thm)],[f24])).
% 1.74/1.43 thf(f24,plain,(
% 1.74/1.43 (funcGraphProp2 = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $i] : (! [X4 : $i] : ((((ap @ X1 @ X2 @ X0 @ X3) = X4) | ($true != (in @ (kpair @ X3 @ X4) @ X0))) | ($true != (in @ X4 @ X2))) | ($true != (in @ X3 @ X1))) | ((func @ X1 @ X2 @ X0) != $true))),
% 1.74/1.43 inference(ennf_transformation,[status(thm)],[f11])).
% 1.74/1.43 thf(f11,plain,(
% 1.74/1.43 (funcGraphProp2 = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((func @ X1 @ X2 @ X0) = $true) => ! [X3 : $i] : (($true = (in @ X3 @ X1)) => ! [X4 : $i] : (($true = (in @ X4 @ X2)) => (($true = (in @ (kpair @ X3 @ X4) @ X0)) => ((ap @ X1 @ X2 @ X0 @ X3) = X4)))))),
% 1.74/1.43 inference(fool_elimination,[status(thm)],[f10])).
% 1.74/1.43 thf(f10,plain,(
% 1.74/1.43 (! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X1 @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => ! [X4 : $i] : ((in @ X4 @ X2) => ((in @ (kpair @ X3 @ X4) @ X0) => ((ap @ X1 @ X2 @ X0 @ X3) = X4))))) = funcGraphProp2)),
% 1.74/1.43 inference(rectify,[status(thm)],[f6])).
% 1.74/1.43 thf(f6,axiom,(
% 1.74/1.43 (! [X7 : $i,X0 : $i,X3 : $i] : ((func @ X0 @ X3 @ X7) => ! [X1 : $i] : ((in @ X1 @ X0) => ! [X6 : $i] : ((in @ X6 @ X3) => ((in @ (kpair @ X1 @ X6) @ X7) => ((ap @ X0 @ X3 @ X7 @ X1) = X6))))) = funcGraphProp2)),
% 1.74/1.43 file('/export/starexec/sandbox/tmp/tmp.qKKwlDXAuP/DTF2THF_6218.p',funcGraphProp2)).
% 1.74/1.43 thf(f55,plain,(
% 1.74/1.43 ((ap @ sK10 @ sK8 @ sK9 @ sK11) != sK12)),
% 1.74/1.43 inference(cnf_transformation,[status(thm)],[f42])).
% 1.74/1.43 % SZS output end Proof for DTF2THF_6218
% 1.74/1.43 % (6341)------------------------------
% 1.74/1.43 % (6341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.43 % (6341)Termination reason: Refutation
% 1.74/1.43
% 1.74/1.43 % (6341)Memory used [KB]: 5500
% 1.74/1.43 % (6341)Time elapsed: 0.008 s
% 1.74/1.43 % (6341)Instructions burned: 8 (million)
% 1.74/1.43 % (6341)------------------------------
% 1.74/1.43 % (6341)------------------------------
% 1.74/1.43 % (6335)Success in time 0.023 s
%------------------------------------------------------------------------------