%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU961^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n029.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 09:37:51 AM UTC 2026
% Result : Theorem 1.32s 1.16s
% Output : Refutation 1.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 206 ( 113 equ; 0 cnn)
% Maximal formula atoms : 16 ( 9 avg)
% Number of connectives : 378 ( 43 ~; 25 |; 53 &; 218 @)
% ( 0 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 114 ( 114 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 157 ( 37 ^; 96 !; 24 ?; 157 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_5,type,
sK0: ( $i > $i ) > ( $i > $i ) > $i ).
thf(func_def_6,type,
sK1: $i > $i ).
thf(func_def_7,type,
sK2: $i > $i ).
thf(func_def_8,type,
sK3: ( ( $i > $i ) > $o ) > $i > $i ).
thf(func_def_9,type,
sK4: ( $i > $i ) > $o ).
thf(func_def_12,type,
ph6:
!>[X0: $tType] : X0 ).
thf(f30,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f27,f24]) ).
thf(f24,plain,
! [X0: $i > $i] :
( $true
= ( sK4 @ X0 ) ),
inference(superposition,[status(thm)],[f15,f22]) ).
thf(f22,plain,
! [X2: $i > $i,X3: $i > $i] : ( X2 = X3 ),
inference(subsumption_resolution,[status(thm)],[f20,f21]) ).
thf(f21,plain,
! [X0: $i,X1: $i] : ( X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ! [X0: $i,X1: $i] : ( X0 = X1 )
& ! [X2: $i > $i,X3: $i > $i] :
( ( X2 = X3 )
| ( ( X2 @ ( sK0 @ X3 @ X2 ) )
!= ( X3 @ ( sK0 @ X3 @ X2 ) ) ) )
& ! [X7: ( $i > $i ) > $o] :
( ( $true
!= ( X7 @ sK1 ) )
| ( $true
= ( X7
@ ^ [Y0: $i] : ( sK2 @ ( sK1 @ Y0 ) ) ) )
| ( ( ( X7 @ ( sK3 @ X7 ) )
= $true )
& ( ( X7
@ ^ [Y0: $i] : ( sK1 @ ( sK3 @ X7 @ Y0 ) ) )
!= $true ) ) )
& ( ( sK4 @ sK2 )
!= $true )
& ! [X10: $i > $i] :
( ( $true
!= ( sK4 @ X10 ) )
| ( $true
= ( sK4
@ ^ [Y0: $i] : ( sK1 @ ( X10 @ Y0 ) ) ) ) )
& ( $true
= ( sK4 @ sK1 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f9,f13,f12,f11,f10]) ).
thf(f10,plain,
! [X2: $i > $i,X3: $i > $i] :
( ? [X4: $i] :
( ( X2 @ X4 )
!= ( X3 @ X4 ) )
=> ( ( X2 @ ( sK0 @ X3 @ X2 ) )
!= ( X3 @ ( sK0 @ X3 @ X2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X5: $i > $i,X6: $i > $i] :
( ! [X7: ( $i > $i ) > $o] :
( ( ( X7 @ X5 )
!= $true )
| ( $true
= ( X7
@ ^ [Y0: $i] : ( X6 @ ( X5 @ Y0 ) ) ) )
| ? [X8: $i > $i] :
( ( ( X7 @ X8 )
= $true )
& ( $true
!= ( X7
@ ^ [Y0: $i] : ( X5 @ ( X8 @ Y0 ) ) ) ) ) )
& ? [X9: ( $i > $i ) > $o] :
( ( $true
!= ( X9 @ X6 ) )
& ! [X10: $i > $i] :
( ( $true
!= ( X9 @ X10 ) )
| ( $true
= ( X9
@ ^ [Y0: $i] : ( X5 @ ( X10 @ Y0 ) ) ) ) )
& ( $true
= ( X9 @ X5 ) ) ) )
=> ( ! [X7: ( $i > $i ) > $o] :
( ( $true
!= ( X7 @ sK1 ) )
| ( $true
= ( X7
@ ^ [Y0: $i] : ( sK2 @ ( sK1 @ Y0 ) ) ) )
| ? [X8: $i > $i] :
( ( ( X7 @ X8 )
= $true )
& ( $true
!= ( X7
@ ^ [Y0: $i] : ( sK1 @ ( X8 @ Y0 ) ) ) ) ) )
& ? [X9: ( $i > $i ) > $o] :
( ( $true
!= ( X9 @ sK2 ) )
& ! [X10: $i > $i] :
( ( $true
!= ( X9 @ X10 ) )
| ( ( X9
@ ^ [Y0: $i] : ( sK1 @ ( X10 @ Y0 ) ) )
= $true ) )
& ( $true
= ( X9 @ sK1 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
! [X7: ( $i > $i ) > $o] :
( ? [X8: $i > $i] :
( ( ( X7 @ X8 )
= $true )
& ( $true
!= ( X7
@ ^ [Y0: $i] : ( sK1 @ ( X8 @ Y0 ) ) ) ) )
=> ( ( ( X7 @ ( sK3 @ X7 ) )
= $true )
& ( ( X7
@ ^ [Y0: $i] : ( sK1 @ ( sK3 @ X7 @ Y0 ) ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ? [X9: ( $i > $i ) > $o] :
( ( $true
!= ( X9 @ sK2 ) )
& ! [X10: $i > $i] :
( ( $true
!= ( X9 @ X10 ) )
| ( ( X9
@ ^ [Y0: $i] : ( sK1 @ ( X10 @ Y0 ) ) )
= $true ) )
& ( $true
= ( X9 @ sK1 ) ) )
=> ( ( ( sK4 @ sK2 )
!= $true )
& ! [X10: $i > $i] :
( ( $true
!= ( sK4 @ X10 ) )
| ( $true
= ( sK4
@ ^ [Y0: $i] : ( sK1 @ ( X10 @ Y0 ) ) ) ) )
& ( $true
= ( sK4 @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ! [X0: $i,X1: $i] : ( X0 = X1 )
& ! [X2: $i > $i,X3: $i > $i] :
( ( X2 = X3 )
| ? [X4: $i] :
( ( X2 @ X4 )
!= ( X3 @ X4 ) ) )
& ? [X5: $i > $i,X6: $i > $i] :
( ! [X7: ( $i > $i ) > $o] :
( ( ( X7 @ X5 )
!= $true )
| ( $true
= ( X7
@ ^ [Y0: $i] : ( X6 @ ( X5 @ Y0 ) ) ) )
| ? [X8: $i > $i] :
( ( ( X7 @ X8 )
= $true )
& ( $true
!= ( X7
@ ^ [Y0: $i] : ( X5 @ ( X8 @ Y0 ) ) ) ) ) )
& ? [X9: ( $i > $i ) > $o] :
( ( $true
!= ( X9 @ X6 ) )
& ! [X10: $i > $i] :
( ( $true
!= ( X9 @ X10 ) )
| ( $true
= ( X9
@ ^ [Y0: $i] : ( X5 @ ( X10 @ Y0 ) ) ) ) )
& ( $true
= ( X9 @ X5 ) ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
( ! [X3: $i,X4: $i] : ( X3 = X4 )
& ! [X0: $i > $i,X1: $i > $i] :
( ( X0 = X1 )
| ? [X2: $i] :
( ( X1 @ X2 )
!= ( X0 @ X2 ) ) )
& ? [X5: $i > $i,X6: $i > $i] :
( ! [X7: ( $i > $i ) > $o] :
( ( ( X7 @ X5 )
!= $true )
| ( $true
= ( X7
@ ^ [Y0: $i] : ( X6 @ ( X5 @ Y0 ) ) ) )
| ? [X8: $i > $i] :
( ( ( X7 @ X8 )
= $true )
& ( $true
!= ( X7
@ ^ [Y0: $i] : ( X5 @ ( X8 @ Y0 ) ) ) ) ) )
& ? [X9: ( $i > $i ) > $o] :
( ( $true
!= ( X9 @ X6 ) )
& ! [X10: $i > $i] :
( ( $true
!= ( X9 @ X10 ) )
| ( $true
= ( X9
@ ^ [Y0: $i] : ( X5 @ ( X10 @ Y0 ) ) ) ) )
& ( $true
= ( X9 @ X5 ) ) ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
( ? [X5: $i > $i,X6: $i > $i] :
( ? [X9: ( $i > $i ) > $o] :
( ( $true
!= ( X9 @ X6 ) )
& ! [X10: $i > $i] :
( ( $true
!= ( X9 @ X10 ) )
| ( $true
= ( X9
@ ^ [Y0: $i] : ( X5 @ ( X10 @ Y0 ) ) ) ) )
& ( $true
= ( X9 @ X5 ) ) )
& ! [X7: ( $i > $i ) > $o] :
( ( $true
= ( X7
@ ^ [Y0: $i] : ( X6 @ ( X5 @ Y0 ) ) ) )
| ? [X8: $i > $i] :
( ( ( X7 @ X8 )
= $true )
& ( $true
!= ( X7
@ ^ [Y0: $i] : ( X5 @ ( X8 @ Y0 ) ) ) ) )
| ( ( X7 @ X5 )
!= $true ) ) )
& ! [X0: $i > $i,X1: $i > $i] :
( ( X0 = X1 )
| ? [X2: $i] :
( ( X1 @ X2 )
!= ( X0 @ X2 ) ) )
& ! [X3: $i,X4: $i] : ( X3 = X4 ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ( ! [X0: $i > $i,X1: $i > $i] :
( ! [X2: $i] :
( ( X1 @ X2 )
= ( X0 @ X2 ) )
=> ( X0 = X1 ) )
& ! [X3: $i,X4: $i] : ( X3 = X4 ) )
=> ! [X5: $i > $i,X6: $i > $i] :
( ! [X7: ( $i > $i ) > $o] :
( ( ! [X8: $i > $i] :
( ( ( X7 @ X8 )
= $true )
=> ( $true
= ( X7
@ ^ [Y0: $i] : ( X5 @ ( X8 @ Y0 ) ) ) ) )
& ( ( X7 @ X5 )
= $true ) )
=> ( $true
= ( X7
@ ^ [Y0: $i] : ( X6 @ ( X5 @ Y0 ) ) ) ) )
=> ! [X9: ( $i > $i ) > $o] :
( ( ! [X10: $i > $i] :
( ( $true
= ( X9 @ X10 ) )
=> ( $true
= ( X9
@ ^ [Y0: $i] : ( X5 @ ( X10 @ Y0 ) ) ) ) )
& ( $true
= ( X9 @ X5 ) ) )
=> ( $true
= ( X9 @ X6 ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X0: $i > $i,X1: $i > $i] :
( ! [X2: $i] :
( ( X1 @ X2 )
= ( X0 @ X2 ) )
=> ( X0 = X1 ) )
& ! [X3: $i,X4: $i] : ( X3 = X4 ) )
=> ! [X5: $i > $i,X6: $i > $i] :
( ! [X7: ( $i > $i ) > $o] :
( ( ! [X8: $i > $i] :
( ( ( X7 @ X8 )
= $true )
=> ( $true
= ( X7
@ ^ [Y0: $i] : ( X5 @ ( X8 @ Y0 ) ) ) ) )
& ( ( X7 @ X5 )
= $true ) )
=> ( $true
= ( X7
@ ^ [Y0: $i] : ( X6 @ ( X5 @ Y0 ) ) ) ) )
=> ! [X11: ( $i > $i ) > $o] :
( ( ( ( X11 @ X5 )
= $true )
& ! [X12: $i > $i] :
( ( $true
= ( X11 @ X12 ) )
=> ( $true
= ( X11
@ ^ [Y0: $i] : ( X5 @ ( X12 @ Y0 ) ) ) ) ) )
=> ( $true
= ( X11 @ X6 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: $i > $i,X1: $i > $i] :
( ! [X2: $i] :
( ( X1 @ X2 )
= ( X0 @ X2 ) )
=> ( X0 = X1 ) )
& ! [X3: $i,X4: $i] : ( X3 = X4 ) )
=> ! [X5: $i > $i,X6: $i > $i] :
( ! [X7: ( $i > $i ) > $o] :
( ( ( X7 @ X5 )
& ! [X8: $i > $i] :
( ( X7 @ X8 )
=> ( X7
@ ^ [X9: $i] : ( X5 @ ( X8 @ X9 ) ) ) ) )
=> ( X7
@ ^ [X10: $i] : ( X6 @ ( X5 @ X10 ) ) ) )
=> ! [X11: ( $i > $i ) > $o] :
( ( ( X11 @ X5 )
& ! [X12: $i > $i] :
( ( X11 @ X12 )
=> ( X11
@ ^ [X13: $i] : ( X5 @ ( X12 @ X13 ) ) ) ) )
=> ( X11 @ X6 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X2: $i > $i,X3: $i > $i] :
( ! [X4: $i] :
( ( X2 @ X4 )
= ( X3 @ X4 ) )
=> ( X2 = X3 ) )
& ! [X1: $i,X0: $i] : ( X0 = X1 ) )
=> ! [X5: $i > $i,X6: $i > $i] :
( ! [X7: ( $i > $i ) > $o] :
( ( ( X7 @ X5 )
& ! [X8: $i > $i] :
( ( X7 @ X8 )
=> ( X7
@ ^ [X4: $i] : ( X5 @ ( X8 @ X4 ) ) ) ) )
=> ( X7
@ ^ [X4: $i] : ( X6 @ ( X5 @ X4 ) ) ) )
=> ! [X7: ( $i > $i ) > $o] :
( ( ( X7 @ X5 )
& ! [X9: $i > $i] :
( ( X7 @ X9 )
=> ( X7
@ ^ [X4: $i] : ( X5 @ ( X9 @ X4 ) ) ) ) )
=> ( X7 @ X6 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X2: $i > $i,X3: $i > $i] :
( ! [X4: $i] :
( ( X2 @ X4 )
= ( X3 @ X4 ) )
=> ( X2 = X3 ) )
& ! [X1: $i,X0: $i] : ( X0 = X1 ) )
=> ! [X5: $i > $i,X6: $i > $i] :
( ! [X7: ( $i > $i ) > $o] :
( ( ( X7 @ X5 )
& ! [X8: $i > $i] :
( ( X7 @ X8 )
=> ( X7
@ ^ [X4: $i] : ( X5 @ ( X8 @ X4 ) ) ) ) )
=> ( X7
@ ^ [X4: $i] : ( X6 @ ( X5 @ X4 ) ) ) )
=> ! [X7: ( $i > $i ) > $o] :
( ( ( X7 @ X5 )
& ! [X9: $i > $i] :
( ( X7 @ X9 )
=> ( X7
@ ^ [X4: $i] : ( X5 @ ( X9 @ X4 ) ) ) ) )
=> ( X7 @ X6 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.vMnvB2ZRgb/DTF2THF_4059.p',cTHM196C_pme) ).
thf(f20,plain,
! [X2: $i > $i,X3: $i > $i] :
( ( ( X2 @ ( sK0 @ X3 @ X2 ) )
!= ( X3 @ ( sK0 @ X3 @ X2 ) ) )
| ( X2 = X3 ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f15,plain,
( $true
= ( sK4 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f27,plain,
! [X0: $i > $i] :
( $true
!= ( sK4 @ X0 ) ),
inference(superposition,[status(thm)],[f17,f22]) ).
thf(f17,plain,
( ( sK4 @ sK2 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU961^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.31 % Computer : n029.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Tue Feb 24 12:37:44 EST 2026
% 0.12/0.32 % CPUTime :
% 0.12/0.32 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.42 ---- Original DTF file ---
% 0.16/0.42 thf(spec,logic,$$dhol).
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 % File : SEU961^5 : TPTP v9.2.1. Released v4.0.0.
% 0.16/0.42 % Domain : Set Theory (Functions)
% 0.16/0.42 % Problem : TPS problem from FUNCTION-THMS
% 0.16/0.42 % Version : Especial.
% 0.16/0.42 % English :
% 0.16/0.42
% 0.16/0.42 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.42 % Source : [Bro09]
% 0.16/0.42 % Names : tps_1020 [Bro09]
% 0.16/0.42
% 0.16/0.42 % Status : Theorem
% 0.16/0.42 % Rating : 0.00 v9.0.0, 0.10 v8.2.0, 0.00 v6.2.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.67 v4.0.0
% 0.16/0.42 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.16/0.42 % Number of atoms : 3 ( 3 equ; 0 cnn)
% 0.16/0.42 % Maximal formula atoms : 3 ( 3 avg)
% 0.16/0.42 % Number of connectives : 26 ( 0 ~; 0 |; 3 &; 16 @)
% 0.16/0.42 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.16/0.42 % Maximal formula depth : 14 ( 14 avg)
% 0.16/0.42 % Number of types : 2 ( 0 usr)
% 0.16/0.42 % Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% 0.16/0.42 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.16/0.42 % Number of variables : 14 ( 3 ^; 11 !; 0 ?; 14 :)
% 0.16/0.42 % SPC : TH0_THM_EQU_NAR
% 0.16/0.42
% 0.16/0.42 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.16/0.42 % project in the Department of Mathematical Sciences at Carnegie
% 0.16/0.42 % Mellon University. Distributed under the Creative Commons copyleft
% 0.16/0.42 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 thf(cTHM196C_pme,conjecture,
% 0.16/0.42 ( ( ! [Xa: $i,Xb: $i] : ( Xa = Xb )
% 0.16/0.42 & ! [Xf: $i > $i,Xg: $i > $i] :
% 0.16/0.42 ( ! [Xx: $i] :
% 0.16/0.42 ( ( Xf @ Xx )
% 0.16/0.42 = ( Xg @ Xx ) )
% 0.16/0.42 => ( Xf = Xg ) ) )
% 0.16/0.42 => ! [Xj: $i > $i,Xk: $i > $i] :
% 0.16/0.42 ( ! [Xp: ( $i > $i ) > $o] :
% 0.16/0.42 ( ( ( Xp @ Xj )
% 0.16/0.42 & ! [Xj_0: $i > $i] :
% 0.16/0.42 ( ( Xp @ Xj_0 )
% 0.16/0.42 => ( Xp
% 0.16/0.42 @ ^ [Xx: $i] : ( Xj @ ( Xj_0 @ Xx ) ) ) ) )
% 0.16/0.42 => ( Xp
% 0.16/0.42 @ ^ [Xx: $i] : ( Xk @ ( Xj @ Xx ) ) ) )
% 0.16/0.42 => ! [Xp: ( $i > $i ) > $o] :
% 0.16/0.42 ( ( ( Xp @ Xj )
% 0.16/0.42 & ! [Xj_1: $i > $i] :
% 0.16/0.42 ( ( Xp @ Xj_1 )
% 0.16/0.42 => ( Xp
% 0.16/0.42 @ ^ [Xx: $i] : ( Xj @ ( Xj_1 @ Xx ) ) ) ) )
% 0.16/0.42 => ( Xp @ Xk ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 ------------------------
% 1.32/1.13 ---- Embedded in THF ---
% 1.32/1.13 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.32/1.13 %%% Generated on Tue Feb 24 12:37:45 EST 2026
% 1.32/1.13 %%% using '$$dhol' embedding, version 1.3.0.
% 1.32/1.13 %%% Logic specification used:
% 1.32/1.13 %%% thf(spec, logic, $$dhol).
% 1.32/1.13
% 1.32/1.13 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.vMnvB2ZRgb/DTF2DTF4059.p
% See solution above
% 1.32/1.14 ------------------------
% 1.32/1.14 ---- Cleaned THF ---
% 1.32/1.14 thf(cTHM196C_pme,conjecture,
% 1.32/1.14 ( ( ! [Xa: $i,Xb: $i] : ( Xa = Xb )
% 1.32/1.14 & ! [Xf: $i > $i,Xg: $i > $i] :
% 1.32/1.14 ( ! [Xx: $i] :
% 1.32/1.14 ( ( Xf @ Xx )
% 1.32/1.14 = ( Xg @ Xx ) )
% 1.32/1.14 => ( Xf = Xg ) ) )
% 1.32/1.14 => ! [Xj: $i > $i,Xk: $i > $i] :
% 1.32/1.14 ( ! [Xp: ( $i > $i ) > $o] :
% 1.32/1.14 ( ( ( Xp @ Xj )
% 1.32/1.14 & ! [Xj_0: $i > $i] :
% 1.32/1.14 ( ( Xp @ Xj_0 )
% 1.32/1.14 => ( Xp
% 1.32/1.14 @ ^ [Xx: $i] : ( Xj @ ( Xj_0 @ Xx ) ) ) ) )
% 1.32/1.14 => ( Xp
% 1.32/1.14 @ ^ [Xx: $i] : ( Xk @ ( Xj @ Xx ) ) ) )
% 1.32/1.14 => ! [Xp: ( $i > $i ) > $o] :
% 1.32/1.14 ( ( ( Xp @ Xj )
% 1.32/1.14 & ! [Xj_1: $i > $i] :
% 1.32/1.14 ( ( Xp @ Xj_1 )
% 1.32/1.14 => ( Xp
% 1.32/1.14 @ ^ [Xx: $i] : ( Xj @ ( Xj_1 @ Xx ) ) ) ) )
% 1.32/1.14 => ( Xp @ Xk ) ) ) ) ).
% 1.32/1.14 ------------------------
% 1.32/1.16 % (4158)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_4059 for (3000ds/183Mi)
% 1.32/1.16 % (4158)First to succeed.
% 1.32/1.16 % (4158)Refutation found. Thanks to Tanya!
% 1.32/1.16 % SZS status Theorem for DTF2THF_4059
% 1.32/1.16 % SZS output start Proof for DTF2THF_4059
% 1.32/1.16 thf(func_def_5, type, sK0: ($i > $i) > ($i > $i) > $i).
% 1.32/1.16 thf(func_def_6, type, sK1: $i > $i).
% 1.32/1.16 thf(func_def_7, type, sK2: $i > $i).
% 1.32/1.16 thf(func_def_8, type, sK3: (($i > $i) > $o) > $i > $i).
% 1.32/1.16 thf(func_def_9, type, sK4: ($i > $i) > $o).
% 1.32/1.16 thf(func_def_12, type, ph6: !>[X0: $tType]:(X0)).
% 1.32/1.16 thf(f30,plain,(
% 1.32/1.16 $false),
% 1.32/1.16 inference(subsumption_resolution,[status(thm)],[f27,f24])).
% 1.32/1.16 thf(f24,plain,(
% 1.32/1.16 ( ! [X0 : $i > $i] : (($true = (sK4 @ X0))) )),
% 1.32/1.16 inference(superposition,[status(thm)],[f15,f22])).
% 1.32/1.16 thf(f22,plain,(
% 1.32/1.16 ( ! [X2 : $i > $i,X3 : $i > $i] : ((X2 = X3)) )),
% 1.32/1.16 inference(subsumption_resolution,[status(thm)],[f20,f21])).
% 1.32/1.16 thf(f21,plain,(
% 1.32/1.16 ( ! [X0 : $i,X1 : $i] : ((X0 = X1)) )),
% 1.32/1.16 inference(cnf_transformation,[status(thm)],[f14])).
% 1.32/1.16 thf(f14,plain,(
% 1.32/1.16 ! [X0 : $i,X1 : $i] : (X0 = X1) & ! [X2 : $i > $i,X3 : $i > $i] : ((X2 = X3) | ((X2 @ (sK0 @ X3 @ X2)) != (X3 @ (sK0 @ X3 @ X2)))) & (! [X7 : ($i > $i) > $o] : (($true != (X7 @ sK1)) | ($true = (X7 @ (^[Y0 : $i]: (sK2 @ (sK1 @ Y0))))) | (((X7 @ (sK3 @ X7)) = $true) & ((X7 @ (^[Y0 : $i]: (sK1 @ (sK3 @ X7 @ Y0)))) != $true))) & (((sK4 @ sK2) != $true) & ! [X10 : $i > $i] : (($true != (sK4 @ X10)) | ($true = (sK4 @ (^[Y0 : $i]: (sK1 @ (X10 @ Y0)))))) & ($true = (sK4 @ sK1))))),
% 1.32/1.16 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f9,f13,f12,f11,f10])).
% 1.32/1.16 thf(f10,plain,(
% 1.32/1.16 ! [X2 : $i > $i,X3 : $i > $i] : (? [X4 : $i] : ((X2 @ X4) != (X3 @ X4)) => ((X2 @ (sK0 @ X3 @ X2)) != (X3 @ (sK0 @ X3 @ X2))))),
% 1.32/1.16 introduced(definition,[],[choice_axiom])).
% 1.32/1.16 thf(f11,plain,(
% 1.32/1.16 ? [X5 : $i > $i,X6 : $i > $i] : (! [X7 : ($i > $i) > $o] : (((X7 @ X5) != $true) | ($true = (X7 @ (^[Y0 : $i]: (X6 @ (X5 @ Y0))))) | ? [X8 : $i > $i] : (((X7 @ X8) = $true) & ($true != (X7 @ (^[Y0 : $i]: (X5 @ (X8 @ Y0))))))) & ? [X9 : ($i > $i) > $o] : (($true != (X9 @ X6)) & ! [X10 : $i > $i] : (($true != (X9 @ X10)) | ($true = (X9 @ (^[Y0 : $i]: (X5 @ (X10 @ Y0)))))) & ($true = (X9 @ X5)))) => (! [X7 : ($i > $i) > $o] : (($true != (X7 @ sK1)) | ($true = (X7 @ (^[Y0 : $i]: (sK2 @ (sK1 @ Y0))))) | ? [X8 : $i > $i] : (((X7 @ X8) = $true) & ($true != (X7 @ (^[Y0 : $i]: (sK1 @ (X8 @ Y0))))))) & ? [X9 : ($i > $i) > $o] : (($true != (X9 @ sK2)) & ! [X10 : $i > $i] : (($true != (X9 @ X10)) | ((X9 @ (^[Y0 : $i]: (sK1 @ (X10 @ Y0)))) = $true)) & ($true = (X9 @ sK1))))),
% 1.32/1.16 introduced(definition,[],[choice_axiom])).
% 1.32/1.16 thf(f12,plain,(
% 1.32/1.16 ! [X7 : ($i > $i) > $o] : (? [X8 : $i > $i] : (((X7 @ X8) = $true) & ($true != (X7 @ (^[Y0 : $i]: (sK1 @ (X8 @ Y0)))))) => (((X7 @ (sK3 @ X7)) = $true) & ((X7 @ (^[Y0 : $i]: (sK1 @ (sK3 @ X7 @ Y0)))) != $true)))),
% 1.32/1.16 introduced(definition,[],[choice_axiom])).
% 1.32/1.16 thf(f13,plain,(
% 1.32/1.16 ? [X9 : ($i > $i) > $o] : (($true != (X9 @ sK2)) & ! [X10 : $i > $i] : (($true != (X9 @ X10)) | ((X9 @ (^[Y0 : $i]: (sK1 @ (X10 @ Y0)))) = $true)) & ($true = (X9 @ sK1))) => (((sK4 @ sK2) != $true) & ! [X10 : $i > $i] : (($true != (sK4 @ X10)) | ($true = (sK4 @ (^[Y0 : $i]: (sK1 @ (X10 @ Y0)))))) & ($true = (sK4 @ sK1)))),
% 1.32/1.16 introduced(definition,[],[choice_axiom])).
% 1.32/1.16 thf(f9,plain,(
% 1.32/1.16 ! [X0 : $i,X1 : $i] : (X0 = X1) & ! [X2 : $i > $i,X3 : $i > $i] : ((X2 = X3) | ? [X4 : $i] : ((X2 @ X4) != (X3 @ X4))) & ? [X5 : $i > $i,X6 : $i > $i] : (! [X7 : ($i > $i) > $o] : (((X7 @ X5) != $true) | ($true = (X7 @ (^[Y0 : $i]: (X6 @ (X5 @ Y0))))) | ? [X8 : $i > $i] : (((X7 @ X8) = $true) & ($true != (X7 @ (^[Y0 : $i]: (X5 @ (X8 @ Y0))))))) & ? [X9 : ($i > $i) > $o] : (($true != (X9 @ X6)) & ! [X10 : $i > $i] : (($true != (X9 @ X10)) | ($true = (X9 @ (^[Y0 : $i]: (X5 @ (X10 @ Y0)))))) & ($true = (X9 @ X5))))),
% 1.32/1.16 inference(rectify,[status(thm)],[f8])).
% 1.32/1.16 thf(f8,plain,(
% 1.32/1.16 ! [X3 : $i,X4 : $i] : (X3 = X4) & ! [X0 : $i > $i,X1 : $i > $i] : ((X0 = X1) | ? [X2 : $i] : ((X1 @ X2) != (X0 @ X2))) & ? [X5 : $i > $i,X6 : $i > $i] : (! [X7 : ($i > $i) > $o] : (((X7 @ X5) != $true) | ($true = (X7 @ (^[Y0 : $i]: (X6 @ (X5 @ Y0))))) | ? [X8 : $i > $i] : (((X7 @ X8) = $true) & ($true != (X7 @ (^[Y0 : $i]: (X5 @ (X8 @ Y0))))))) & ? [X9 : ($i > $i) > $o] : (($true != (X9 @ X6)) & ! [X10 : $i > $i] : (($true != (X9 @ X10)) | ($true = (X9 @ (^[Y0 : $i]: (X5 @ (X10 @ Y0)))))) & ($true = (X9 @ X5))))),
% 1.32/1.16 inference(flattening,[status(thm)],[f7])).
% 1.32/1.16 thf(f7,plain,(
% 1.32/1.16 ? [X5 : $i > $i,X6 : $i > $i] : (? [X9 : ($i > $i) > $o] : (($true != (X9 @ X6)) & (! [X10 : $i > $i] : (($true != (X9 @ X10)) | ($true = (X9 @ (^[Y0 : $i]: (X5 @ (X10 @ Y0)))))) & ($true = (X9 @ X5)))) & ! [X7 : ($i > $i) > $o] : (($true = (X7 @ (^[Y0 : $i]: (X6 @ (X5 @ Y0))))) | (? [X8 : $i > $i] : (((X7 @ X8) = $true) & ($true != (X7 @ (^[Y0 : $i]: (X5 @ (X8 @ Y0)))))) | ((X7 @ X5) != $true)))) & (! [X0 : $i > $i,X1 : $i > $i] : ((X0 = X1) | ? [X2 : $i] : ((X1 @ X2) != (X0 @ X2))) & ! [X3 : $i,X4 : $i] : (X3 = X4))),
% 1.32/1.16 inference(ennf_transformation,[status(thm)],[f6])).
% 1.32/1.16 thf(f6,plain,(
% 1.32/1.16 ~((! [X0 : $i > $i,X1 : $i > $i] : (! [X2 : $i] : ((X1 @ X2) = (X0 @ X2)) => (X0 = X1)) & ! [X3 : $i,X4 : $i] : (X3 = X4)) => ! [X5 : $i > $i,X6 : $i > $i] : (! [X7 : ($i > $i) > $o] : ((! [X8 : $i > $i] : (((X7 @ X8) = $true) => ($true = (X7 @ (^[Y0 : $i]: (X5 @ (X8 @ Y0)))))) & ((X7 @ X5) = $true)) => ($true = (X7 @ (^[Y0 : $i]: (X6 @ (X5 @ Y0)))))) => ! [X9 : ($i > $i) > $o] : ((! [X10 : $i > $i] : (($true = (X9 @ X10)) => ($true = (X9 @ (^[Y0 : $i]: (X5 @ (X10 @ Y0)))))) & ($true = (X9 @ X5))) => ($true = (X9 @ X6)))))),
% 1.32/1.16 inference(rectify,[status(thm)],[f5])).
% 1.32/1.16 thf(f5,plain,(
% 1.32/1.16 ~((! [X0 : $i > $i,X1 : $i > $i] : (! [X2 : $i] : ((X1 @ X2) = (X0 @ X2)) => (X0 = X1)) & ! [X3 : $i,X4 : $i] : (X3 = X4)) => ! [X5 : $i > $i,X6 : $i > $i] : (! [X7 : ($i > $i) > $o] : ((! [X8 : $i > $i] : (((X7 @ X8) = $true) => ($true = (X7 @ (^[Y0 : $i]: (X5 @ (X8 @ Y0)))))) & ((X7 @ X5) = $true)) => ($true = (X7 @ (^[Y0 : $i]: (X6 @ (X5 @ Y0)))))) => ! [X11 : ($i > $i) > $o] : ((((X11 @ X5) = $true) & ! [X12 : $i > $i] : (($true = (X11 @ X12)) => ($true = (X11 @ (^[Y0 : $i]: (X5 @ (X12 @ Y0))))))) => ($true = (X11 @ X6)))))),
% 1.32/1.16 inference(fool_elimination,[status(thm)],[f4])).
% 1.32/1.16 thf(f4,plain,(
% 1.32/1.16 ~((! [X0 : $i > $i,X1 : $i > $i] : (! [X2 : $i] : ((X1 @ X2) = (X0 @ X2)) => (X0 = X1)) & ! [X3 : $i,X4 : $i] : (X3 = X4)) => ! [X5 : $i > $i,X6 : $i > $i] : (! [X7 : ($i > $i) > $o] : (((X7 @ X5) & ! [X8 : $i > $i] : ((X7 @ X8) => (X7 @ (^[X9 : $i] : (X5 @ (X8 @ X9)))))) => (X7 @ (^[X10 : $i] : (X6 @ (X5 @ X10))))) => ! [X11 : ($i > $i) > $o] : (((X11 @ X5) & ! [X12 : $i > $i] : ((X11 @ X12) => (X11 @ (^[X13 : $i] : (X5 @ (X12 @ X13)))))) => (X11 @ X6))))),
% 1.32/1.16 inference(rectify,[status(thm)],[f2])).
% 1.32/1.16 thf(f2,negated_conjecture,(
% 1.32/1.16 ~((! [X2 : $i > $i,X3 : $i > $i] : (! [X4 : $i] : ((X2 @ X4) = (X3 @ X4)) => (X2 = X3)) & ! [X1 : $i,X0 : $i] : (X0 = X1)) => ! [X5 : $i > $i,X6 : $i > $i] : (! [X7 : ($i > $i) > $o] : (((X7 @ X5) & ! [X8 : $i > $i] : ((X7 @ X8) => (X7 @ (^[X4 : $i] : (X5 @ (X8 @ X4)))))) => (X7 @ (^[X4 : $i] : (X6 @ (X5 @ X4))))) => ! [X7 : ($i > $i) > $o] : (((X7 @ X5) & ! [X9 : $i > $i] : ((X7 @ X9) => (X7 @ (^[X4 : $i] : (X5 @ (X9 @ X4)))))) => (X7 @ X6))))),
% 1.32/1.16 inference(negated_conjecture,[status(cth)],[f1])).
% 1.32/1.16 thf(f1,conjecture,(
% 1.32/1.16 (! [X2 : $i > $i,X3 : $i > $i] : (! [X4 : $i] : ((X2 @ X4) = (X3 @ X4)) => (X2 = X3)) & ! [X1 : $i,X0 : $i] : (X0 = X1)) => ! [X5 : $i > $i,X6 : $i > $i] : (! [X7 : ($i > $i) > $o] : (((X7 @ X5) & ! [X8 : $i > $i] : ((X7 @ X8) => (X7 @ (^[X4 : $i] : (X5 @ (X8 @ X4)))))) => (X7 @ (^[X4 : $i] : (X6 @ (X5 @ X4))))) => ! [X7 : ($i > $i) > $o] : (((X7 @ X5) & ! [X9 : $i > $i] : ((X7 @ X9) => (X7 @ (^[X4 : $i] : (X5 @ (X9 @ X4)))))) => (X7 @ X6)))),
% 1.32/1.16 file('/export/starexec/sandbox2/tmp/tmp.vMnvB2ZRgb/DTF2THF_4059.p',cTHM196C_pme)).
% 1.32/1.16 thf(f20,plain,(
% 1.32/1.16 ( ! [X2 : $i > $i,X3 : $i > $i] : (((X2 @ (sK0 @ X3 @ X2)) != (X3 @ (sK0 @ X3 @ X2))) | (X2 = X3)) )),
% 1.32/1.16 inference(cnf_transformation,[status(thm)],[f14])).
% 1.32/1.16 thf(f15,plain,(
% 1.32/1.16 ($true = (sK4 @ sK1))),
% 1.32/1.16 inference(cnf_transformation,[status(thm)],[f14])).
% 1.32/1.16 thf(f27,plain,(
% 1.32/1.16 ( ! [X0 : $i > $i] : (($true != (sK4 @ X0))) )),
% 1.32/1.16 inference(superposition,[status(thm)],[f17,f22])).
% 1.32/1.16 thf(f17,plain,(
% 1.32/1.16 ((sK4 @ sK2) != $true)),
% 1.32/1.16 inference(cnf_transformation,[status(thm)],[f14])).
% 1.32/1.16 % SZS output end Proof for DTF2THF_4059
% 1.32/1.16 % (4158)------------------------------
% 1.32/1.16 % (4158)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.32/1.16 % (4158)Termination reason: Refutation
% 1.32/1.16
% 1.32/1.16 % (4158)Memory used [KB]: 5500
% 1.32/1.16 % (4158)Time elapsed: 0.003 s
% 1.32/1.16 % (4158)Instructions burned: 2 (million)
% 1.32/1.16 % (4158)------------------------------
% 1.32/1.16 % (4158)------------------------------
% 1.32/1.16 % (4157)Success in time 0.012 s
%------------------------------------------------------------------------------