%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU651^2 : 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 : n010.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 09:35:57 AM UTC 2026
% Result : Theorem 1.32s 1.16s
% Output : Refutation 1.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 8
% Syntax : Number of formulae : 58 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 619 ( 168 equ; 0 cnn)
% Maximal formula atoms : 6 ( 10 avg)
% Number of connectives : 823 ( 57 ~; 40 |; 43 &; 648 @)
% ( 5 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 16 con; 0-2 aty)
% Number of variables : 108 ( 0 ^; 74 !; 34 ?; 108 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(f78,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f77,f52]) ).
thf(f52,plain,
sK4 != sK5,
inference(definition_unfolding,[status(thm)],[f37,f39]) ).
thf(f39,plain,
sK2 = sK5,
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
( ( secondinupair = $true )
& ( uniqinunit = $true )
& ( setukpairinjR12 = $true )
& ( sK2 = sK5 )
& ( ( setadjoin @ ( setadjoin @ sK5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK5 @ ( setadjoin @ sK2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ sK4 @ emptyset ) ) @ emptyset ) ) )
& ( sK2 != sK4 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f23,f24]) ).
thf(f24,plain,
( ? [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X3 )
& ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) )
& ( X0 != X2 ) )
=> ( ( sK2 = sK5 )
& ( ( setadjoin @ ( setadjoin @ sK5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK5 @ ( setadjoin @ sK2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ sK4 @ emptyset ) ) @ emptyset ) ) )
& ( sK2 != sK4 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f23,plain,
( ( secondinupair = $true )
& ( uniqinunit = $true )
& ( setukpairinjR12 = $true )
& ? [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X3 )
& ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) )
& ( X0 != X2 ) ) ),
inference(rectify,[status(thm)],[f16]) ).
thf(f16,plain,
( ( secondinupair = $true )
& ( uniqinunit = $true )
& ( setukpairinjR12 = $true )
& ? [X3: $i,X2: $i,X0: $i,X1: $i] :
( ( X1 = X3 )
& ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
& ( X0 != X3 ) ) ),
inference(flattening,[status(thm)],[f15]) ).
thf(f15,plain,
( ? [X3: $i,X1: $i,X2: $i,X0: $i] :
( ( X0 != X3 )
& ( X1 = X3 )
& ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) )
& ( setukpairinjR12 = $true )
& ( secondinupair = $true )
& ( uniqinunit = $true ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( ( uniqinunit = $true )
=> ( ( secondinupair = $true )
=> ( ( setukpairinjR12 = $true )
=> ! [X3: $i,X1: $i,X2: $i,X0: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X1 = X3 )
=> ( X0 = X3 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( uniqinunit
=> ( secondinupair
=> ( setukpairinjR12
=> ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X1 = X3 )
=> ( X0 = X3 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( uniqinunit
=> ( secondinupair
=> ( setukpairinjR12
=> ! [X1: $i,X2: $i,X0: $i,X3: $i] :
( ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X2 = X3 )
=> ( X1 = X3 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( uniqinunit
=> ( secondinupair
=> ( setukpairinjR12
=> ! [X1: $i,X2: $i,X0: $i,X3: $i] :
( ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X2 = X3 )
=> ( X1 = X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4996kHAqqq/DTF2THF_3262.p',setukpairinjR1) ).
thf(f37,plain,
sK2 != sK4,
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f77,plain,
sK4 = sK5,
inference(trivial_inequality_removal,[status(thm)],[f76]) ).
thf(f76,plain,
( ( sK4 = sK5 )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f61,f75]) ).
thf(f75,plain,
( ( in @ sK4 @ ( setadjoin @ sK5 @ emptyset ) )
= $true ),
inference(superposition,[status(thm)],[f60,f71]) ).
thf(f71,plain,
( ( setadjoin @ sK5 @ emptyset )
= ( setadjoin @ sK3 @ ( setadjoin @ sK4 @ emptyset ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f70]) ).
thf(f70,plain,
( ( ( setadjoin @ sK5 @ emptyset )
= ( setadjoin @ sK3 @ ( setadjoin @ sK4 @ emptyset ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f61,f66]) ).
thf(f66,plain,
( $true
= ( in @ ( setadjoin @ sK3 @ ( setadjoin @ sK4 @ emptyset ) ) @ ( setadjoin @ ( setadjoin @ sK5 @ emptyset ) @ emptyset ) ) ),
inference(superposition,[status(thm)],[f60,f62]) ).
thf(f62,plain,
( ( setadjoin @ ( setadjoin @ sK5 @ emptyset ) @ emptyset )
= ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ sK4 @ emptyset ) ) @ emptyset ) ) ),
inference(forward_demodulation,[status(thm)],[f51,f59]) ).
thf(f59,plain,
! [X3: $i] :
( ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ emptyset ) ),
inference(trivial_inequality_removal,[status(thm)],[f58]) ).
thf(f58,plain,
! [X3: $i] :
( ( $true != $true )
| ( ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ emptyset ) ) ),
inference(equality_resolution,[status(thm)],[f50]) ).
thf(f50,plain,
! [X2: $i,X3: $i] :
( ( X2 != X3 )
| ( ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ emptyset ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f34,f40]) ).
thf(f40,plain,
setukpairinjR12 = $true,
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f34,plain,
! [X2: $i,X3: $i] :
( ( X2 != X3 )
| ( ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ emptyset ) )
| ( setukpairinjR12 != $true ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ( setukpairinjR12 = $true )
| ( ( sK0 = sK1 )
& ( ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ emptyset ) ) ) )
& ( ! [X2: $i,X3: $i] :
( ( X2 != X3 )
| ( ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ emptyset ) ) )
| ( setukpairinjR12 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f20,f21]) ).
thf(f21,plain,
( ? [X0: $i,X1: $i] :
( ( X0 = X1 )
& ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset )
!= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ( sK0 = sK1 )
& ( ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ emptyset ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f20,plain,
( ( ( setukpairinjR12 = $true )
| ? [X0: $i,X1: $i] :
( ( X0 = X1 )
& ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset )
!= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) ) )
& ( ! [X2: $i,X3: $i] :
( ( X2 != X3 )
| ( ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ emptyset ) ) )
| ( setukpairinjR12 != $true ) ) ),
inference(rectify,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ( setukpairinjR12 = $true )
| ? [X0: $i,X1: $i] :
( ( X0 = X1 )
& ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset )
!= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) ) )
& ( ! [X0: $i,X1: $i] :
( ( X0 != X1 )
| ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) )
| ( setukpairinjR12 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ( setukpairinjR12 = $true )
<=> ! [X0: $i,X1: $i] :
( ( X0 != X1 )
| ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( setukpairinjR12 = $true )
<=> ! [X1: $i,X0: $i] :
( ( X0 = X1 )
=> ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $i,X1: $i] :
( ( ( X0 = X1 )
=> ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) )
= setukpairinjR12 ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X1: $i,X0: $i] :
( ( ( X0 = X1 )
=> ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ emptyset ) ) )
= setukpairinjR12 ),
file('/export/starexec/sandbox/tmp/tmp.4996kHAqqq/DTF2THF_3262.p',setukpairinjR12) ).
thf(f51,plain,
( ( setadjoin @ ( setadjoin @ sK5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK5 @ ( setadjoin @ sK5 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ sK4 @ emptyset ) ) @ emptyset ) ) ),
inference(definition_unfolding,[status(thm)],[f38,f39]) ).
thf(f38,plain,
( ( setadjoin @ ( setadjoin @ sK5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK5 @ ( setadjoin @ sK2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ sK4 @ emptyset ) ) @ emptyset ) ) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f60,plain,
! [X2: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f57]) ).
thf(f57,plain,
! [X2: $i,X3: $i] :
( ( ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f46,f42]) ).
thf(f42,plain,
secondinupair = $true,
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f46,plain,
! [X2: $i,X3: $i] :
( ( ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
= $true )
| ( secondinupair != $true ) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ( secondinupair = $true )
| ( ( in @ sK9 @ ( setadjoin @ sK8 @ ( setadjoin @ sK9 @ emptyset ) ) )
!= $true ) )
& ( ! [X2: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
= $true )
| ( secondinupair != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f31,f32]) ).
thf(f32,plain,
( ? [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
!= $true )
=> ( ( in @ sK9 @ ( setadjoin @ sK8 @ ( setadjoin @ sK9 @ emptyset ) ) )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f31,plain,
( ( ( secondinupair = $true )
| ? [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
!= $true ) )
& ( ! [X2: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
= $true )
| ( secondinupair != $true ) ) ),
inference(rectify,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ( secondinupair = $true )
| ? [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
!= $true ) )
& ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= $true )
| ( secondinupair != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( secondinupair = $true )
<=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= secondinupair ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= secondinupair ),
file('/export/starexec/sandbox/tmp/tmp.4996kHAqqq/DTF2THF_3262.p',secondinupair) ).
thf(f61,plain,
! [X2: $i,X3: $i] :
( ( ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) )
!= $true )
| ( X2 = X3 ) ),
inference(trivial_inequality_removal,[status(thm)],[f55]) ).
thf(f55,plain,
! [X2: $i,X3: $i] :
( ( $true != $true )
| ( ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) )
!= $true )
| ( X2 = X3 ) ),
inference(definition_unfolding,[status(thm)],[f43,f41]) ).
thf(f41,plain,
uniqinunit = $true,
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f43,plain,
! [X2: $i,X3: $i] :
( ( ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) )
!= $true )
| ( X2 = X3 )
| ( uniqinunit != $true ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ( uniqinunit = $true )
| ( ( ( in @ sK7 @ ( setadjoin @ sK6 @ emptyset ) )
= $true )
& ( sK7 != sK6 ) ) )
& ( ! [X2: $i,X3: $i] :
( ( ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) )
!= $true )
| ( X2 = X3 ) )
| ( uniqinunit != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f27,f28]) ).
thf(f28,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
= $true )
& ( X0 != X1 ) )
=> ( ( ( in @ sK7 @ ( setadjoin @ sK6 @ emptyset ) )
= $true )
& ( sK7 != sK6 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f27,plain,
( ( ( uniqinunit = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
= $true )
& ( X0 != X1 ) ) )
& ( ! [X2: $i,X3: $i] :
( ( ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) )
!= $true )
| ( X2 = X3 ) )
| ( uniqinunit != $true ) ) ),
inference(rectify,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ( uniqinunit = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
= $true )
& ( X0 != X1 ) ) )
& ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
!= $true )
| ( X0 = X1 ) )
| ( uniqinunit != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( uniqinunit = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
!= $true )
| ( X0 = X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( uniqinunit = $true )
<=> ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
= $true )
=> ( X0 = X1 ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
=> ( X0 = X1 ) )
= uniqinunit ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X0 = X1 ) )
= uniqinunit ),
file('/export/starexec/sandbox/tmp/tmp.4996kHAqqq/DTF2THF_3262.p',uniqinunit) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU651^2 : 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
% 0.12/0.30 % Computer : n010.cluster.edu
% 0.12/0.30 % Model : x86_64 x86_64
% 0.12/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.30 % Memory : 8042.1875MB
% 0.12/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.30 % CPULimit : 300
% 0.12/0.30 % WCLimit : 300
% 0.12/0.30 % DateTime : Tue Feb 24 12:29:03 EST 2026
% 0.12/0.30 % CPUTime :
% 0.12/0.30 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/0.38 ---- Original DTF file ---
% 0.14/0.38 thf(spec,logic,$$dhol).
% 0.14/0.38 %------------------------------------------------------------------------------
% 0.14/0.38 % File : SEU651^2 : TPTP v9.2.1. Released v3.7.0.
% 0.14/0.38 % Domain : Set Theory
% 0.14/0.38 % Problem : Ordered Pairs - Properties of Pairs
% 0.14/0.38 % Version : Especial > Reduced > Especial.
% 0.14/0.38 % English : (! x:i.! y:i.! z:i.! u:i.setadjoin (setadjoin x emptyset)
% 0.14/0.38 % (setadjoin (setadjoin x (setadjoin y emptyset)) emptyset) =
% 0.14/0.38 % setadjoin (setadjoin z emptyset) (setadjoin (setadjoin z
% 0.14/0.38 % (setadjoin u emptyset)) emptyset) -> z = u -> y = u)
% 0.14/0.38
% 0.14/0.38 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.14/0.38 % Source : [Bro08]
% 0.14/0.38 % Names : ZFC153l [Bro08]
% 0.14/0.38
% 0.14/0.38 % Status : Theorem
% 0.14/0.38 % Rating : 0.00 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.60 v5.1.0, 0.80 v5.0.0, 0.60 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0, 0.33 v3.7.0
% 0.14/0.38 % Syntax : Number of formulae : 10 ( 3 unt; 6 typ; 3 def)
% 0.14/0.38 % Number of atoms : 17 ( 9 equ; 0 cnn)
% 0.14/0.38 % Maximal formula atoms : 6 ( 4 avg)
% 0.14/0.38 % Number of connectives : 51 ( 0 ~; 0 |; 0 &; 44 @)
% 0.14/0.38 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.14/0.38 % Maximal formula depth : 10 ( 3 avg)
% 0.14/0.38 % Number of types : 2 ( 0 usr)
% 0.14/0.38 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.14/0.38 % Number of symbols : 7 ( 6 usr; 4 con; 0-2 aty)
% 0.14/0.38 % Number of variables : 10 ( 0 ^; 10 !; 0 ?; 10 :)
% 0.14/0.38 % SPC : TH0_THM_EQU_NAR
% 0.14/0.38
% 0.14/0.38 % Comments : http://mathgate.info/detsetitem.php?id=207
% 0.14/0.38 %------------------------------------------------------------------------------
% 0.14/0.38 thf(in_type,type,
% 0.14/0.38 in: $i > $i > $o ).
% 0.14/0.38
% 0.14/0.38 thf(emptyset_type,type,
% 0.14/0.38 emptyset: $i ).
% 0.14/0.38
% 0.14/0.38 thf(setadjoin_type,type,
% 0.14/0.38 setadjoin: $i > $i > $i ).
% 0.14/0.38
% 0.14/0.38 thf(uniqinunit_type,type,
% 0.14/0.38 uniqinunit: $o ).
% 0.14/0.38
% 0.14/0.38 thf(uniqinunit,definition,
% 0.14/0.38 ( uniqinunit
% 0.14/0.38 = ( ! [Xx: $i,Xy: $i] :
% 0.14/0.38 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.14/0.38 => ( Xx = Xy ) ) ) ) ).
% 0.14/0.38
% 0.14/0.38 thf(secondinupair_type,type,
% 0.14/0.38 secondinupair: $o ).
% 0.14/0.38
% 0.14/0.38 thf(secondinupair,definition,
% 0.14/0.38 ( secondinupair
% 0.14/0.38 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.14/0.38
% 0.14/0.38 thf(setukpairinjR12_type,type,
% 0.14/0.38 setukpairinjR12: $o ).
% 0.14/0.38
% 0.14/0.38 thf(setukpairinjR12,definition,
% 0.14/0.38 ( setukpairinjR12
% 0.14/0.38 = ( ! [Xx: $i,Xy: $i] :
% 0.14/0.38 ( ( Xx = Xy )
% 0.14/0.38 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.14/0.38 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 0.14/0.38
% 0.14/0.38 thf(setukpairinjR1,conjecture,
% 0.14/0.38 ( uniqinunit
% 0.14/0.38 => ( secondinupair
% 0.14/0.38 => ( setukpairinjR12
% 0.14/0.38 => ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.14/0.38 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.14/0.38 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.14/0.38 => ( ( Xz = Xu )
% 0.14/0.38 => ( Xy = Xu ) ) ) ) ) ) ).
% 0.14/0.38
% 0.14/0.38 %------------------------------------------------------------------------------
% 0.14/0.38 ------------------------
% 1.32/1.14 ---- Embedded in THF ---
% 1.32/1.14 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.32/1.14 %%% Generated on Tue Feb 24 12:29:03 EST 2026
% 1.32/1.14 %%% using '$$dhol' embedding, version 1.3.0.
% 1.32/1.14 %%% Logic specification used:
% 1.32/1.14 %%% thf(spec, logic, $$dhol).
% 1.32/1.14
% 1.32/1.14 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.4996kHAqqq/DTF2DTF3262.p
% See solution above
% 1.32/1.14 ------------------------
% 1.32/1.14 ---- Cleaned THF ---
% 1.32/1.14 thf(in_type,type,
% 1.32/1.14 in: $i > $i > $o ).
% 1.32/1.14
% 1.32/1.14 thf(emptyset_type,type,
% 1.32/1.14 emptyset: $i ).
% 1.32/1.14
% 1.32/1.14 thf(setadjoin_type,type,
% 1.32/1.14 setadjoin: $i > $i > $i ).
% 1.32/1.14
% 1.32/1.14 thf(uniqinunit_type,type,
% 1.32/1.14 uniqinunit: $o ).
% 1.32/1.14
% 1.32/1.14 thf(uniqinunit,definition,
% 1.32/1.14 ( uniqinunit
% 1.32/1.14 = ( ! [Xx: $i,Xy: $i] :
% 1.32/1.14 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 1.32/1.14 => ( Xx = Xy ) ) ) ) ).
% 1.32/1.14
% 1.32/1.14 thf(secondinupair_type,type,
% 1.32/1.14 secondinupair: $o ).
% 1.32/1.14
% 1.32/1.14 thf(secondinupair,definition,
% 1.32/1.14 ( secondinupair
% 1.32/1.14 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 1.32/1.14
% 1.32/1.14 thf(setukpairinjR12_type,type,
% 1.32/1.14 setukpairinjR12: $o ).
% 1.32/1.14
% 1.32/1.14 thf(setukpairinjR12,definition,
% 1.32/1.14 ( setukpairinjR12
% 1.32/1.14 = ( ! [Xx: $i,Xy: $i] :
% 1.32/1.14 ( ( Xx = Xy )
% 1.32/1.14 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 1.32/1.14 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 1.32/1.14
% 1.32/1.14 thf(setukpairinjR1,conjecture,
% 1.32/1.14 ( uniqinunit
% 1.32/1.14 => ( secondinupair
% 1.32/1.14 => ( setukpairinjR12
% 1.32/1.14 => ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 1.32/1.14 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 1.32/1.14 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 1.32/1.14 => ( ( Xz = Xu )
% 1.32/1.14 => ( Xy = Xu ) ) ) ) ) ) ).
% 1.32/1.14 ------------------------
% 1.32/1.16 % (3376)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3262 for (3000ds/2Mi)
% 1.32/1.16 % (3375)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_3262 for (3000ds/27Mi)
% 1.32/1.16 % (3374)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_3262 for (3000ds/4Mi)
% 1.32/1.16 % (3373)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3262 for (3000ds/183Mi)
% 1.32/1.16 % (3378)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_3262 for (3000ds/275Mi)
% 1.32/1.16 % (3377)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_3262 for (3000ds/2Mi)
% 1.32/1.16 % (3379)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3262 for (3000ds/18Mi)
% 1.32/1.16 % (3376)Instruction limit reached!
% 1.32/1.16 % (3376)------------------------------
% 1.32/1.16 % (3376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.32/1.16 % (3376)Termination reason: Unknown
% 1.32/1.16 % (3376)Termination phase: Function definition elimination
% 1.32/1.16
% 1.32/1.16 % (3376)Memory used [KB]: 1023
% 1.32/1.16 % (3376)Time elapsed: 0.002 s
% 1.32/1.16 % (3376)Instructions burned: 3 (million)
% 1.32/1.16 % (3376)------------------------------
% 1.32/1.16 % (3376)------------------------------
% 1.32/1.16 % (3377)Instruction limit reached!
% 1.32/1.16 % (3377)------------------------------
% 1.32/1.16 % (3377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.32/1.16 % (3377)Termination reason: Unknown
% 1.32/1.16 % (3377)Termination phase: Function definition elimination
% 1.32/1.16
% 1.32/1.16 % (3377)Memory used [KB]: 895
% 1.32/1.16 % (3377)Time elapsed: 0.002 s
% 1.32/1.16 % (3377)Instructions burned: 3 (million)
% 1.32/1.16 % (3377)------------------------------
% 1.32/1.16 % (3377)------------------------------
% 1.32/1.16 % (3374)Instruction limit reached!
% 1.32/1.16 % (3374)------------------------------
% 1.32/1.16 % (3374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.32/1.16 % (3374)Termination reason: Unknown
% 1.32/1.16 % (3374)Termination phase: Saturation
% 1.32/1.16
% 1.32/1.16 % (3374)Memory used [KB]: 5500
% 1.32/1.16 % (3374)Time elapsed: 0.003 s
% 1.32/1.16 % (3374)Instructions burned: 5 (million)
% 1.32/1.16 % (3374)------------------------------
% 1.32/1.16 % (3374)------------------------------
% 1.32/1.16 % (3378)First to succeed.
% 1.32/1.16 % (3379)Also succeeded, but the first one will report.
% 1.32/1.16 % (3378)Refutation found. Thanks to Tanya!
% 1.32/1.16 % SZS status Theorem for DTF2THF_3262
% 1.32/1.16 % SZS output start Proof for DTF2THF_3262
% 1.32/1.16 thf(func_def_0, type, in: $i > $i > $o).
% 1.32/1.16 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 1.32/1.16 thf(f78,plain,(
% 1.32/1.16 $false),
% 1.32/1.16 inference(subsumption_resolution,[status(thm)],[f77,f52])).
% 1.32/1.16 thf(f52,plain,(
% 1.32/1.16 (sK4 != sK5)),
% 1.32/1.16 inference(definition_unfolding,[status(thm)],[f37,f39])).
% 1.32/1.16 thf(f39,plain,(
% 1.32/1.16 (sK2 = sK5)),
% 1.32/1.16 inference(cnf_transformation,[status(thm)],[f25])).
% 1.32/1.16 thf(f25,plain,(
% 1.32/1.16 (secondinupair = $true) & (uniqinunit = $true) & (setukpairinjR12 = $true) & ((sK2 = sK5) & ((setadjoin @ (setadjoin @ sK5 @ emptyset) @ (setadjoin @ (setadjoin @ sK5 @ (setadjoin @ sK2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ sK4 @ emptyset)) @ emptyset))) & (sK2 != sK4))),
% 1.32/1.16 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f23,f24])).
% 1.32/1.16 thf(f24,plain,(
% 1.32/1.16 ? [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((X0 = X3) & ((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X0 @ emptyset)) @ emptyset))) & (X0 != X2)) => ((sK2 = sK5) & ((setadjoin @ (setadjoin @ sK5 @ emptyset) @ (setadjoin @ (setadjoin @ sK5 @ (setadjoin @ sK2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ sK4 @ emptyset)) @ emptyset))) & (sK2 != sK4))),
% 1.32/1.16 introduced(definition,[],[choice_axiom])).
% 1.32/1.16 thf(f23,plain,(
% 1.32/1.16 (secondinupair = $true) & (uniqinunit = $true) & (setukpairinjR12 = $true) & ? [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((X0 = X3) & ((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X0 @ emptyset)) @ emptyset))) & (X0 != X2))),
% 1.32/1.16 inference(rectify,[status(thm)],[f16])).
% 1.32/1.16 thf(f16,plain,(
% 1.32/1.16 (secondinupair = $true) & (uniqinunit = $true) & (setukpairinjR12 = $true) & ? [X3 : $i,X2 : $i,X0 : $i,X1 : $i] : ((X1 = X3) & ((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X3 @ emptyset)) @ emptyset))) & (X0 != X3))),
% 1.32/1.16 inference(flattening,[status(thm)],[f15])).
% 1.32/1.16 thf(f15,plain,(
% 1.32/1.16 ((? [X3 : $i,X1 : $i,X2 : $i,X0 : $i] : (((X0 != X3) & (X1 = X3)) & ((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))) & (setukpairinjR12 = $true)) & (secondinupair = $true)) & (uniqinunit = $true)),
% 1.32/1.16 inference(ennf_transformation,[status(thm)],[f8])).
% 1.32/1.16 thf(f8,plain,(
% 1.32/1.16 ~((uniqinunit = $true) => ((secondinupair = $true) => ((setukpairinjR12 = $true) => ! [X3 : $i,X1 : $i,X2 : $i,X0 : $i] : (((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X3 @ emptyset)) @ emptyset))) => ((X1 = X3) => (X0 = X3))))))),
% 1.32/1.16 inference(fool_elimination,[status(thm)],[f7])).
% 1.32/1.16 thf(f7,plain,(
% 1.32/1.16 ~(uniqinunit => (secondinupair => (setukpairinjR12 => ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X3 @ emptyset)) @ emptyset))) => ((X1 = X3) => (X0 = X3))))))),
% 1.32/1.16 inference(rectify,[status(thm)],[f5])).
% 1.32/1.16 thf(f5,negated_conjecture,(
% 1.32/1.16 ~(uniqinunit => (secondinupair => (setukpairinjR12 => ! [X1 : $i,X2 : $i,X0 : $i,X3 : $i] : (((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))) => ((X2 = X3) => (X1 = X3))))))),
% 1.32/1.16 inference(negated_conjecture,[status(cth)],[f4])).
% 1.32/1.16 thf(f4,conjecture,(
% 1.32/1.16 uniqinunit => (secondinupair => (setukpairinjR12 => ! [X1 : $i,X2 : $i,X0 : $i,X3 : $i] : (((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))) => ((X2 = X3) => (X1 = X3)))))),
% 1.32/1.16 file('/export/starexec/sandbox/tmp/tmp.4996kHAqqq/DTF2THF_3262.p',setukpairinjR1)).
% 1.32/1.16 thf(f37,plain,(
% 1.32/1.16 (sK2 != sK4)),
% 1.32/1.16 inference(cnf_transformation,[status(thm)],[f25])).
% 1.32/1.16 thf(f77,plain,(
% 1.32/1.16 (sK4 = sK5)),
% 1.32/1.16 inference(trivial_inequality_removal,[status(thm)],[f76])).
% 1.32/1.16 thf(f76,plain,(
% 1.32/1.16 (sK4 = sK5) | ($true != $true)),
% 1.32/1.16 inference(superposition,[status(thm)],[f61,f75])).
% 1.32/1.16 thf(f75,plain,(
% 1.32/1.16 ((in @ sK4 @ (setadjoin @ sK5 @ emptyset)) = $true)),
% 1.32/1.16 inference(superposition,[status(thm)],[f60,f71])).
% 1.32/1.16 thf(f71,plain,(
% 1.32/1.16 ((setadjoin @ sK5 @ emptyset) = (setadjoin @ sK3 @ (setadjoin @ sK4 @ emptyset)))),
% 1.32/1.16 inference(trivial_inequality_removal,[status(thm)],[f70])).
% 1.32/1.16 thf(f70,plain,(
% 1.32/1.16 ((setadjoin @ sK5 @ emptyset) = (setadjoin @ sK3 @ (setadjoin @ sK4 @ emptyset))) | ($true != $true)),
% 1.32/1.16 inference(superposition,[status(thm)],[f61,f66])).
% 1.32/1.16 thf(f66,plain,(
% 1.32/1.16 ($true = (in @ (setadjoin @ sK3 @ (setadjoin @ sK4 @ emptyset)) @ (setadjoin @ (setadjoin @ sK5 @ emptyset) @ emptyset)))),
% 1.32/1.16 inference(superposition,[status(thm)],[f60,f62])).
% 1.32/1.16 thf(f62,plain,(
% 1.32/1.16 ((setadjoin @ (setadjoin @ sK5 @ emptyset) @ emptyset) = (setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ sK4 @ emptyset)) @ emptyset)))),
% 1.32/1.16 inference(forward_demodulation,[status(thm)],[f51,f59])).
% 1.32/1.16 thf(f59,plain,(
% 1.32/1.16 ( ! [X3 : $i] : (((setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X3 @ emptyset) @ emptyset))) )),
% 1.32/1.16 inference(trivial_inequality_removal,[status(thm)],[f58])).
% 1.32/1.16 thf(f58,plain,(
% 1.32/1.16 ( ! [X3 : $i] : (($true != $true) | ((setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X3 @ emptyset) @ emptyset))) )),
% 1.32/1.16 inference(equality_resolution,[status(thm)],[f50])).
% 1.32/1.16 thf(f50,plain,(
% 1.32/1.16 ( ! [X2 : $i,X3 : $i] : ((X2 != X3) | ((setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X3 @ emptyset) @ emptyset)) | ($true != $true)) )),
% 1.32/1.16 inference(definition_unfolding,[status(thm)],[f34,f40])).
% 1.32/1.16 thf(f40,plain,(
% 1.32/1.16 (setukpairinjR12 = $true)),
% 1.32/1.16 inference(cnf_transformation,[status(thm)],[f25])).
% 1.32/1.16 thf(f34,plain,(
% 1.32/1.16 ( ! [X2 : $i,X3 : $i] : ((X2 != X3) | ((setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X3 @ emptyset) @ emptyset)) | (setukpairinjR12 != $true)) )),
% 1.32/1.16 inference(cnf_transformation,[status(thm)],[f22])).
% 1.32/1.16 thf(f22,plain,(
% 1.32/1.16 ((setukpairinjR12 = $true) | ((sK0 = sK1) & ((setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)) != (setadjoin @ (setadjoin @ sK1 @ emptyset) @ emptyset)))) & (! [X2 : $i,X3 : $i] : ((X2 != X3) | ((setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X3 @ emptyset) @ emptyset))) | (setukpairinjR12 != $true))),
% 1.32/1.16 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f20,f21])).
% 1.32/1.16 thf(f21,plain,(
% 1.32/1.16 ? [X0 : $i,X1 : $i] : ((X0 = X1) & ((setadjoin @ (setadjoin @ X1 @ emptyset) @ emptyset) != (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset)))) => ((sK0 = sK1) & ((setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)) != (setadjoin @ (setadjoin @ sK1 @ emptyset) @ emptyset)))),
% 1.32/1.16 introduced(definition,[],[choice_axiom])).
% 1.32/1.16 thf(f20,plain,(
% 1.32/1.16 ((setukpairinjR12 = $true) | ? [X0 : $i,X1 : $i] : ((X0 = X1) & ((setadjoin @ (setadjoin @ X1 @ emptyset) @ emptyset) != (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset))))) & (! [X2 : $i,X3 : $i] : ((X2 != X3) | ((setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X3 @ emptyset) @ emptyset))) | (setukpairinjR12 != $true))),
% 1.32/1.16 inference(rectify,[status(thm)],[f19])).
% 1.32/1.16 thf(f19,plain,(
% 1.32/1.16 ((setukpairinjR12 = $true) | ? [X0 : $i,X1 : $i] : ((X0 = X1) & ((setadjoin @ (setadjoin @ X1 @ emptyset) @ emptyset) != (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset))))) & (! [X0 : $i,X1 : $i] : ((X0 != X1) | ((setadjoin @ (setadjoin @ X1 @ emptyset) @ emptyset) = (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset)))) | (setukpairinjR12 != $true))),
% 1.32/1.16 inference(nnf_transformation,[status(thm)],[f18])).
% 1.32/1.16 thf(f18,plain,(
% 1.32/1.16 (setukpairinjR12 = $true) <=> ! [X0 : $i,X1 : $i] : ((X0 != X1) | ((setadjoin @ (setadjoin @ X1 @ emptyset) @ emptyset) = (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset))))),
% 1.32/1.16 inference(ennf_transformation,[status(thm)],[f10])).
% 1.32/1.16 thf(f10,plain,(
% 1.32/1.16 (setukpairinjR12 = $true) <=> ! [X1 : $i,X0 : $i] : ((X0 = X1) => ((setadjoin @ (setadjoin @ X1 @ emptyset) @ emptyset) = (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset))))),
% 1.32/1.16 inference(fool_elimination,[status(thm)],[f9])).
% 1.32/1.16 thf(f9,plain,(
% 1.32/1.16 (! [X0 : $i,X1 : $i] : ((X0 = X1) => ((setadjoin @ (setadjoin @ X1 @ emptyset) @ emptyset) = (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset)))) = setukpairinjR12)),
% 1.32/1.16 inference(rectify,[status(thm)],[f3])).
% 1.32/1.16 thf(f3,axiom,(
% 1.32/1.16 (! [X1 : $i,X0 : $i] : ((X0 = X1) => ((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X0 @ emptyset) @ emptyset))) = setukpairinjR12)),
% 1.32/1.16 file('/export/starexec/sandbox/tmp/tmp.4996kHAqqq/DTF2THF_3262.p',setukpairinjR12)).
% 1.32/1.16 thf(f51,plain,(
% 1.32/1.16 ((setadjoin @ (setadjoin @ sK5 @ emptyset) @ (setadjoin @ (setadjoin @ sK5 @ (setadjoin @ sK5 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ sK4 @ emptyset)) @ emptyset)))),
% 1.32/1.16 inference(definition_unfolding,[status(thm)],[f38,f39])).
% 1.32/1.16 thf(f38,plain,(
% 1.32/1.16 ((setadjoin @ (setadjoin @ sK5 @ emptyset) @ (setadjoin @ (setadjoin @ sK5 @ (setadjoin @ sK2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ sK4 @ emptyset)) @ emptyset)))),
% 1.32/1.16 inference(cnf_transformation,[status(thm)],[f25])).
% 1.32/1.16 thf(f60,plain,(
% 1.32/1.16 ( ! [X2 : $i,X3 : $i] : (((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))) = $true)) )),
% 1.32/1.16 inference(trivial_inequality_removal,[status(thm)],[f57])).
% 1.32/1.16 thf(f57,plain,(
% 1.32/1.16 ( ! [X2 : $i,X3 : $i] : (((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))) = $true) | ($true != $true)) )),
% 1.32/1.16 inference(definition_unfolding,[status(thm)],[f46,f42])).
% 1.32/1.16 thf(f42,plain,(
% 1.32/1.16 (secondinupair = $true)),
% 1.32/1.16 inference(cnf_transformation,[status(thm)],[f25])).
% 1.32/1.16 thf(f46,plain,(
% 1.32/1.16 ( ! [X2 : $i,X3 : $i] : (((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))) = $true) | (secondinupair != $true)) )),
% 1.32/1.16 inference(cnf_transformation,[status(thm)],[f33])).
% 1.32/1.16 thf(f33,plain,(
% 1.32/1.16 ((secondinupair = $true) | ((in @ sK9 @ (setadjoin @ sK8 @ (setadjoin @ sK9 @ emptyset))) != $true)) & (! [X2 : $i,X3 : $i] : ((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))) = $true) | (secondinupair != $true))),
% 1.32/1.16 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f31,f32])).
% 1.32/1.16 thf(f32,plain,(
% 1.32/1.16 ? [X0 : $i,X1 : $i] : ((in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) != $true) => ((in @ sK9 @ (setadjoin @ sK8 @ (setadjoin @ sK9 @ emptyset))) != $true)),
% 1.32/1.16 introduced(definition,[],[choice_axiom])).
% 1.32/1.16 thf(f31,plain,(
% 1.32/1.16 ((secondinupair = $true) | ? [X0 : $i,X1 : $i] : ((in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) != $true)) & (! [X2 : $i,X3 : $i] : ((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))) = $true) | (secondinupair != $true))),
% 1.32/1.16 inference(rectify,[status(thm)],[f30])).
% 1.32/1.16 thf(f30,plain,(
% 1.32/1.16 ((secondinupair = $true) | ? [X0 : $i,X1 : $i] : ((in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) != $true)) & (! [X0 : $i,X1 : $i] : ((in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = $true) | (secondinupair != $true))),
% 1.32/1.16 inference(nnf_transformation,[status(thm)],[f12])).
% 1.32/1.16 thf(f12,plain,(
% 1.32/1.16 (secondinupair = $true) <=> ! [X0 : $i,X1 : $i] : ((in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = $true)),
% 1.32/1.16 inference(fool_elimination,[status(thm)],[f11])).
% 1.32/1.16 thf(f11,plain,(
% 1.32/1.16 (! [X0 : $i,X1 : $i] : (in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = secondinupair)),
% 1.32/1.16 inference(rectify,[status(thm)],[f2])).
% 1.32/1.16 thf(f2,axiom,(
% 1.32/1.16 (! [X0 : $i,X1 : $i] : (in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = secondinupair)),
% 1.32/1.16 file('/export/starexec/sandbox/tmp/tmp.4996kHAqqq/DTF2THF_3262.p',secondinupair)).
% 1.32/1.16 thf(f61,plain,(
% 1.32/1.16 ( ! [X2 : $i,X3 : $i] : (((in @ X3 @ (setadjoin @ X2 @ emptyset)) != $true) | (X2 = X3)) )),
% 1.32/1.16 inference(trivial_inequality_removal,[status(thm)],[f55])).
% 1.32/1.16 thf(f55,plain,(
% 1.32/1.16 ( ! [X2 : $i,X3 : $i] : (($true != $true) | ((in @ X3 @ (setadjoin @ X2 @ emptyset)) != $true) | (X2 = X3)) )),
% 1.32/1.16 inference(definition_unfolding,[status(thm)],[f43,f41])).
% 1.32/1.16 thf(f41,plain,(
% 1.32/1.16 (uniqinunit = $true)),
% 1.32/1.16 inference(cnf_transformation,[status(thm)],[f25])).
% 1.32/1.16 thf(f43,plain,(
% 1.32/1.16 ( ! [X2 : $i,X3 : $i] : (((in @ X3 @ (setadjoin @ X2 @ emptyset)) != $true) | (X2 = X3) | (uniqinunit != $true)) )),
% 1.32/1.16 inference(cnf_transformation,[status(thm)],[f29])).
% 1.32/1.16 thf(f29,plain,(
% 1.32/1.16 ((uniqinunit = $true) | (((in @ sK7 @ (setadjoin @ sK6 @ emptyset)) = $true) & (sK7 != sK6))) & (! [X2 : $i,X3 : $i] : (((in @ X3 @ (setadjoin @ X2 @ emptyset)) != $true) | (X2 = X3)) | (uniqinunit != $true))),
% 1.32/1.16 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f27,f28])).
% 1.32/1.16 thf(f28,plain,(
% 1.32/1.16 ? [X0 : $i,X1 : $i] : (((in @ X1 @ (setadjoin @ X0 @ emptyset)) = $true) & (X0 != X1)) => (((in @ sK7 @ (setadjoin @ sK6 @ emptyset)) = $true) & (sK7 != sK6))),
% 1.32/1.16 introduced(definition,[],[choice_axiom])).
% 1.32/1.16 thf(f27,plain,(
% 1.32/1.16 ((uniqinunit = $true) | ? [X0 : $i,X1 : $i] : (((in @ X1 @ (setadjoin @ X0 @ emptyset)) = $true) & (X0 != X1))) & (! [X2 : $i,X3 : $i] : (((in @ X3 @ (setadjoin @ X2 @ emptyset)) != $true) | (X2 = X3)) | (uniqinunit != $true))),
% 1.32/1.16 inference(rectify,[status(thm)],[f26])).
% 1.32/1.16 thf(f26,plain,(
% 1.32/1.16 ((uniqinunit = $true) | ? [X0 : $i,X1 : $i] : (((in @ X1 @ (setadjoin @ X0 @ emptyset)) = $true) & (X0 != X1))) & (! [X0 : $i,X1 : $i] : (((in @ X1 @ (setadjoin @ X0 @ emptyset)) != $true) | (X0 = X1)) | (uniqinunit != $true))),
% 1.32/1.16 inference(nnf_transformation,[status(thm)],[f17])).
% 1.32/1.16 thf(f17,plain,(
% 1.32/1.16 (uniqinunit = $true) <=> ! [X0 : $i,X1 : $i] : (((in @ X1 @ (setadjoin @ X0 @ emptyset)) != $true) | (X0 = X1))),
% 1.32/1.16 inference(ennf_transformation,[status(thm)],[f14])).
% 1.32/1.16 thf(f14,plain,(
% 1.32/1.16 (uniqinunit = $true) <=> ! [X1 : $i,X0 : $i] : (((in @ X1 @ (setadjoin @ X0 @ emptyset)) = $true) => (X0 = X1))),
% 1.32/1.16 inference(fool_elimination,[status(thm)],[f13])).
% 1.32/1.16 thf(f13,plain,(
% 1.32/1.16 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (setadjoin @ X0 @ emptyset)) => (X0 = X1)) = uniqinunit)),
% 1.32/1.16 inference(rectify,[status(thm)],[f1])).
% 1.32/1.16 thf(f1,axiom,(
% 1.32/1.16 (! [X1 : $i,X0 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (X0 = X1)) = uniqinunit)),
% 1.32/1.16 file('/export/starexec/sandbox/tmp/tmp.4996kHAqqq/DTF2THF_3262.p',uniqinunit)).
% 1.32/1.16 % SZS output end Proof for DTF2THF_3262
% 1.32/1.16 % (3378)------------------------------
% 1.32/1.16 % (3378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.32/1.16 % (3378)Termination reason: Refutation
% 1.32/1.16
% 1.32/1.16 % (3378)Memory used [KB]: 5500
% 1.32/1.16 % (3378)Time elapsed: 0.005 s
% 1.32/1.16 % (3378)Instructions burned: 8 (million)
% 1.32/1.16 % (3378)------------------------------
% 1.32/1.16 % (3378)------------------------------
% 1.32/1.16 % (3371)Success in time 0.013 s
%------------------------------------------------------------------------------