%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV200^5 : 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 : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:40:32 AM UTC 2026
% Result : Theorem 1.64s 1.40s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 277 ( 188 equ; 0 cnn)
% Maximal formula atoms : 22 ( 17 avg)
% Number of connectives : 640 ( 91 ~; 67 |; 105 &; 345 @)
% ( 0 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 15 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 37 ( 37 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-3 aty)
% Number of variables : 205 ( 0 ^; 163 !; 42 ?; 205 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
x: a ).
thf(func_def_2,type,
cZ: a ).
thf(func_def_3,type,
cP: a > a > a ).
thf(func_def_7,type,
sK0: ( a > $o ) > a ).
thf(func_def_8,type,
sK1: ( a > $o ) > a ).
thf(func_def_9,type,
sK2: a > a > a > $o ).
thf(f30,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f15,f29]) ).
thf(f29,plain,
! [X8: a] :
( $true
= ( sK2 @ cZ @ X8 @ X8 ) ),
inference(equality_resolution,[status(thm)],[f28]) ).
thf(f28,plain,
! [X8: a,X9: a] :
( ( $true
= ( sK2 @ X9 @ X8 @ X8 ) )
| ( cZ != X9 ) ),
inference(equality_resolution,[status(thm)],[f16]) ).
thf(f16,plain,
! [X8: a,X9: a,X7: a] :
( ( $true
= ( sK2 @ X9 @ X7 @ X8 ) )
| ( X7 != X8 )
| ( cZ != X9 ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ! [X0: a,X1: a] :
( ( cP @ X0 @ X1 )
!= cZ )
& ! [X2: a > $o] :
( ( ( $true
= ( X2 @ ( sK1 @ X2 ) ) )
& ( $true
!= ( X2 @ ( cP @ ( sK1 @ X2 ) @ ( sK0 @ X2 ) ) ) )
& ( $true
= ( X2 @ ( sK0 @ X2 ) ) ) )
| ( ( X2 @ cZ )
!= $true )
| ! [X5: a] :
( $true
= ( X2 @ X5 ) ) )
& ! [X7: a,X8: a,X9: a] :
( ( $true
= ( sK2 @ X9 @ X7 @ X8 ) )
| ( ! [X10: a,X11: a,X12: a,X13: a,X14: a,X15: a] :
( ( ( cP @ X11 @ X12 )
!= X7 )
| ( ( sK2 @ X15 @ X11 @ X13 )
!= $true )
| ( $true
!= ( sK2 @ X14 @ X12 @ X10 ) )
| ( ( cP @ X13 @ X10 )
!= X8 )
| ( ( cP @ X15 @ X14 )
!= X9 ) )
& ( ( cZ != X7 )
| ( X8 != X9 ) )
& ( ( X7 != X8 )
| ( cZ != X9 ) ) ) )
& ( $true
!= ( sK2 @ cZ @ x @ x ) )
& ! [X16: a,X17: a,X18: a,X19: a] :
( ( ( cP @ X17 @ X18 )
!= ( cP @ X16 @ X19 ) )
| ( ( X16 = X17 )
& ( X18 = X19 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f9,f11,f10]) ).
thf(f10,plain,
! [X2: a > $o] :
( ? [X3: a,X4: a] :
( ( $true
= ( X2 @ X4 ) )
& ( ( X2 @ ( cP @ X4 @ X3 ) )
!= $true )
& ( ( X2 @ X3 )
= $true ) )
=> ( ( $true
= ( X2 @ ( sK1 @ X2 ) ) )
& ( $true
!= ( X2 @ ( cP @ ( sK1 @ X2 ) @ ( sK0 @ X2 ) ) ) )
& ( $true
= ( X2 @ ( sK0 @ X2 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X6: a > a > a > $o] :
( ! [X7: a,X8: a,X9: a] :
( ( ( X6 @ X9 @ X7 @ X8 )
= $true )
| ( ! [X10: a,X11: a,X12: a,X13: a,X14: a,X15: a] :
( ( ( cP @ X11 @ X12 )
!= X7 )
| ( $true
!= ( X6 @ X15 @ X11 @ X13 ) )
| ( $true
!= ( X6 @ X14 @ X12 @ X10 ) )
| ( ( cP @ X13 @ X10 )
!= X8 )
| ( ( cP @ X15 @ X14 )
!= X9 ) )
& ( ( cZ != X7 )
| ( X8 != X9 ) )
& ( ( X7 != X8 )
| ( cZ != X9 ) ) ) )
& ( $true
!= ( X6 @ cZ @ x @ x ) ) )
=> ( ! [X9: a,X8: a,X7: a] :
( ( $true
= ( sK2 @ X9 @ X7 @ X8 ) )
| ( ! [X15: a,X14: a,X13: a,X12: a,X11: a,X10: a] :
( ( ( cP @ X11 @ X12 )
!= X7 )
| ( ( sK2 @ X15 @ X11 @ X13 )
!= $true )
| ( $true
!= ( sK2 @ X14 @ X12 @ X10 ) )
| ( ( cP @ X13 @ X10 )
!= X8 )
| ( ( cP @ X15 @ X14 )
!= X9 ) )
& ( ( cZ != X7 )
| ( X8 != X9 ) )
& ( ( X7 != X8 )
| ( cZ != X9 ) ) ) )
& ( $true
!= ( sK2 @ cZ @ x @ x ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ! [X0: a,X1: a] :
( ( cP @ X0 @ X1 )
!= cZ )
& ! [X2: a > $o] :
( ? [X3: a,X4: a] :
( ( $true
= ( X2 @ X4 ) )
& ( ( X2 @ ( cP @ X4 @ X3 ) )
!= $true )
& ( ( X2 @ X3 )
= $true ) )
| ( ( X2 @ cZ )
!= $true )
| ! [X5: a] :
( $true
= ( X2 @ X5 ) ) )
& ? [X6: a > a > a > $o] :
( ! [X7: a,X8: a,X9: a] :
( ( ( X6 @ X9 @ X7 @ X8 )
= $true )
| ( ! [X10: a,X11: a,X12: a,X13: a,X14: a,X15: a] :
( ( ( cP @ X11 @ X12 )
!= X7 )
| ( $true
!= ( X6 @ X15 @ X11 @ X13 ) )
| ( $true
!= ( X6 @ X14 @ X12 @ X10 ) )
| ( ( cP @ X13 @ X10 )
!= X8 )
| ( ( cP @ X15 @ X14 )
!= X9 ) )
& ( ( cZ != X7 )
| ( X8 != X9 ) )
& ( ( X7 != X8 )
| ( cZ != X9 ) ) ) )
& ( $true
!= ( X6 @ cZ @ x @ x ) ) )
& ! [X16: a,X17: a,X18: a,X19: a] :
( ( ( cP @ X17 @ X18 )
!= ( cP @ X16 @ X19 ) )
| ( ( X16 = X17 )
& ( X18 = X19 ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
( ! [X0: a,X1: a] :
( ( cP @ X0 @ X1 )
!= cZ )
& ! [X2: a > $o] :
( ? [X4: a,X3: a] :
( ( ( X2 @ X3 )
= $true )
& ( $true
!= ( X2 @ ( cP @ X3 @ X4 ) ) )
& ( $true
= ( X2 @ X4 ) ) )
| ( ( X2 @ cZ )
!= $true )
| ! [X5: a] :
( $true
= ( X2 @ X5 ) ) )
& ? [X10: a > a > a > $o] :
( ! [X12: a,X13: a,X11: a] :
( ( $true
= ( X10 @ X11 @ X12 @ X13 ) )
| ( ! [X15: a,X14: a,X18: a,X16: a,X17: a,X19: a] :
( ( ( cP @ X14 @ X18 )
!= X12 )
| ( $true
!= ( X10 @ X19 @ X14 @ X16 ) )
| ( $true
!= ( X10 @ X17 @ X18 @ X15 ) )
| ( ( cP @ X16 @ X15 )
!= X13 )
| ( ( cP @ X19 @ X17 )
!= X11 ) )
& ( ( cZ != X12 )
| ( X11 != X13 ) )
& ( ( X12 != X13 )
| ( cZ != X11 ) ) ) )
& ( $true
!= ( X10 @ cZ @ x @ x ) ) )
& ! [X8: a,X9: a,X7: a,X6: a] :
( ( ( cP @ X9 @ X7 )
!= ( cP @ X8 @ X6 ) )
| ( ( X8 = X9 )
& ( X6 = X7 ) ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
( ? [X10: a > a > a > $o] :
( ! [X12: a,X13: a,X11: a] :
( ( $true
= ( X10 @ X11 @ X12 @ X13 ) )
| ( ! [X15: a,X14: a,X18: a,X16: a,X17: a,X19: a] :
( ( ( cP @ X14 @ X18 )
!= X12 )
| ( $true
!= ( X10 @ X19 @ X14 @ X16 ) )
| ( $true
!= ( X10 @ X17 @ X18 @ X15 ) )
| ( ( cP @ X16 @ X15 )
!= X13 )
| ( ( cP @ X19 @ X17 )
!= X11 ) )
& ( ( cZ != X12 )
| ( X11 != X13 ) )
& ( ( X12 != X13 )
| ( cZ != X11 ) ) ) )
& ( $true
!= ( X10 @ cZ @ x @ x ) ) )
& ! [X2: a > $o] :
( ! [X5: a] :
( $true
= ( X2 @ X5 ) )
| ? [X3: a,X4: a] :
( ( $true
!= ( X2 @ ( cP @ X3 @ X4 ) ) )
& ( ( X2 @ X3 )
= $true )
& ( $true
= ( X2 @ X4 ) ) )
| ( ( X2 @ cZ )
!= $true ) )
& ! [X0: a,X1: a] :
( ( cP @ X0 @ X1 )
!= cZ )
& ! [X8: a,X9: a,X7: a,X6: a] :
( ( ( cP @ X9 @ X7 )
!= ( cP @ X8 @ X6 ) )
| ( ( X8 = X9 )
& ( X6 = X7 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ( ! [X2: a > $o] :
( ( ! [X3: a,X4: a] :
( ( ( ( X2 @ X3 )
= $true )
& ( $true
= ( X2 @ X4 ) ) )
=> ( $true
= ( X2 @ ( cP @ X3 @ X4 ) ) ) )
& ( ( X2 @ cZ )
= $true ) )
=> ! [X5: a] :
( $true
= ( X2 @ X5 ) ) )
& ! [X0: a,X1: a] :
( ( cP @ X0 @ X1 )
!= cZ )
& ! [X9: a,X6: a,X7: a,X8: a] :
( ( ( cP @ X9 @ X7 )
= ( cP @ X8 @ X6 ) )
=> ( ( X8 = X9 )
& ( X6 = X7 ) ) ) )
=> ! [X10: a > a > a > $o] :
( ! [X11: a,X13: a,X12: a] :
( ( ? [X16: a,X14: a,X15: a,X19: a,X17: a,X18: a] :
( ( ( cP @ X14 @ X18 )
= X12 )
& ( $true
= ( X10 @ X19 @ X14 @ X16 ) )
& ( ( cP @ X16 @ X15 )
= X13 )
& ( $true
= ( X10 @ X17 @ X18 @ X15 ) )
& ( ( cP @ X19 @ X17 )
= X11 ) )
| ( ( X11 = X13 )
& ( cZ = X12 ) )
| ( ( X12 = X13 )
& ( cZ = X11 ) ) )
=> ( $true
= ( X10 @ X11 @ X12 @ X13 ) ) )
=> ( $true
= ( X10 @ cZ @ x @ x ) ) ) ),
inference(true_and_false_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X2: a > $o] :
( ( ! [X3: a,X4: a] :
( ( ( ( X2 @ X3 )
= $true )
& ( $true
= ( X2 @ X4 ) ) )
=> ( $true
= ( X2 @ ( cP @ X3 @ X4 ) ) ) )
& ( ( X2 @ cZ )
= $true ) )
=> ! [X5: a] :
( $true
= ( X2 @ X5 ) ) )
& ! [X0: a,X1: a] :
( ( cP @ X0 @ X1 )
!= cZ )
& ! [X9: a,X6: a,X7: a,X8: a] :
( ( ( cP @ X9 @ X7 )
= ( cP @ X8 @ X6 ) )
=> ( ( X8 = X9 )
& ( X6 = X7 ) ) ) )
=> ! [X10: a > a > a > $o] :
( ( $true
& ! [X11: a,X13: a,X12: a] :
( ( ? [X16: a,X14: a,X15: a,X19: a,X17: a,X18: a] :
( ( ( cP @ X14 @ X18 )
= X12 )
& ( $true
= ( X10 @ X19 @ X14 @ X16 ) )
& ( ( cP @ X16 @ X15 )
= X13 )
& ( $true
= ( X10 @ X17 @ X18 @ X15 ) )
& ( ( cP @ X19 @ X17 )
= X11 ) )
| ( ( X11 = X13 )
& ( cZ = X12 ) )
| ( ( X12 = X13 )
& ( cZ = X11 ) ) )
=> ( $true
= ( X10 @ X11 @ X12 @ X13 ) ) ) )
=> ( $true
= ( X10 @ cZ @ x @ x ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: a,X1: a] :
( ( cP @ X0 @ X1 )
!= cZ )
& ! [X2: a > $o] :
( ( ( X2 @ cZ )
& ! [X3: a,X4: a] :
( ( ( X2 @ X3 )
& ( X2 @ X4 ) )
=> ( X2 @ ( cP @ X3 @ X4 ) ) ) )
=> ! [X5: a] : ( X2 @ X5 ) )
& ! [X6: a,X7: a,X8: a,X9: a] :
( ( ( cP @ X9 @ X7 )
= ( cP @ X8 @ X6 ) )
=> ( ( X6 = X7 )
& ( X8 = X9 ) ) ) )
=> ! [X10: a > a > a > $o] :
( ( $true
& ! [X11: a,X12: a,X13: a] :
( ( ( ( X12 = X13 )
& ( cZ = X11 ) )
| ? [X14: a,X15: a,X16: a,X17: a,X18: a,X19: a] :
( ( ( cP @ X19 @ X17 )
= X11 )
& ( ( cP @ X14 @ X18 )
= X12 )
& ( ( cP @ X16 @ X15 )
= X13 )
& ( X10 @ X19 @ X14 @ X16 )
& ( X10 @ X17 @ X18 @ X15 ) )
| ( ( cZ = X12 )
& ( X11 = X13 ) ) )
=> ( X10 @ X11 @ X12 @ X13 ) ) )
=> ( X10 @ cZ @ x @ x ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X0: a,X1: a] :
( ( cP @ X0 @ X1 )
!= cZ )
& ! [X4: a > $o] :
( ( ( X4 @ cZ )
& ! [X0: a,X1: a] :
( ( ( X4 @ X0 )
& ( X4 @ X1 ) )
=> ( X4 @ ( cP @ X0 @ X1 ) ) ) )
=> ! [X0: a] : ( X4 @ X0 ) )
& ! [X3: a,X2: a,X1: a,X0: a] :
( ( ( cP @ X0 @ X2 )
= ( cP @ X1 @ X3 ) )
=> ( ( X2 = X3 )
& ( X0 = X1 ) ) ) )
=> ! [X5: a > a > a > $o] :
( ( $true
& ! [X6: a,X7: a,X8: a] :
( ( ( ( X7 = X8 )
& ( cZ = X6 ) )
| ? [X11: a,X14: a,X13: a,X10: a,X12: a,X9: a] :
( ( ( cP @ X9 @ X10 )
= X6 )
& ( ( cP @ X11 @ X12 )
= X7 )
& ( ( cP @ X13 @ X14 )
= X8 )
& ( X5 @ X9 @ X11 @ X13 )
& ( X5 @ X10 @ X12 @ X14 ) )
| ( ( cZ = X7 )
& ( X6 = X8 ) ) )
=> ( X5 @ X6 @ X7 @ X8 ) ) )
=> ( X5 @ cZ @ x @ x ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X0: a,X1: a] :
( ( cP @ X0 @ X1 )
!= cZ )
& ! [X4: a > $o] :
( ( ( X4 @ cZ )
& ! [X0: a,X1: a] :
( ( ( X4 @ X0 )
& ( X4 @ X1 ) )
=> ( X4 @ ( cP @ X0 @ X1 ) ) ) )
=> ! [X0: a] : ( X4 @ X0 ) )
& ! [X3: a,X2: a,X1: a,X0: a] :
( ( ( cP @ X0 @ X2 )
= ( cP @ X1 @ X3 ) )
=> ( ( X2 = X3 )
& ( X0 = X1 ) ) ) )
=> ! [X5: a > a > a > $o] :
( ( $true
& ! [X6: a,X7: a,X8: a] :
( ( ( ( X7 = X8 )
& ( cZ = X6 ) )
| ? [X11: a,X14: a,X13: a,X10: a,X12: a,X9: a] :
( ( ( cP @ X9 @ X10 )
= X6 )
& ( ( cP @ X11 @ X12 )
= X7 )
& ( ( cP @ X13 @ X14 )
= X8 )
& ( X5 @ X9 @ X11 @ X13 )
& ( X5 @ X10 @ X12 @ X14 ) )
| ( ( cZ = X7 )
& ( X6 = X8 ) ) )
=> ( X5 @ X6 @ X7 @ X8 ) ) )
=> ( X5 @ cZ @ x @ x ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Crl5SmXrr7/DTF2THF_28859.p',cS_LEM1C_pme) ).
thf(f15,plain,
( $true
!= ( sK2 @ cZ @ x @ x ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV200^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.14/0.32 % Computer : n003.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue Feb 24 12:41:40 EST 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.32 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.44 ---- Original DTF file ---
% 0.18/0.44 thf(spec,logic,$$dhol).
% 0.18/0.44 %------------------------------------------------------------------------------
% 0.18/0.44 % File : SEV200^5 : TPTP v9.2.1. Released v4.0.0.
% 0.18/0.44 % Domain : Set Theory (Sets of sets)
% 0.18/0.44 % Problem : TPS problem from S-THMS
% 0.18/0.44 % Version : Especial.
% 0.18/0.44 % English :
% 0.18/0.44
% 0.18/0.44 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.18/0.44 % Source : [Bro09]
% 0.18/0.44 % Names : tps_1145 [Bro09]
% 0.18/0.44
% 0.18/0.44 % Status : Theorem
% 0.18/0.44 % Rating : 0.00 v6.2.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.18/0.44 % Syntax : Number of formulae : 5 ( 0 unt; 4 typ; 0 def)
% 0.18/0.44 % Number of atoms : 12 ( 11 equ; 0 cnn)
% 0.18/0.44 % Maximal formula atoms : 12 ( 12 avg)
% 0.18/0.44 % Number of connectives : 52 ( 1 ~; 2 |; 12 &; 31 @)
% 0.18/0.44 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 0.18/0.44 % Maximal formula depth : 24 ( 24 avg)
% 0.18/0.44 % Number of types : 2 ( 1 usr)
% 0.18/0.44 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.18/0.44 % Number of symbols : 5 ( 3 usr; 3 con; 0-2 aty)
% 0.18/0.44 % Number of variables : 20 ( 0 ^; 14 !; 6 ?; 20 :)
% 0.18/0.44 % SPC : TH0_THM_EQU_NAR
% 0.18/0.44
% 0.18/0.44 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.18/0.44 % project in the Department of Mathematical Sciences at Carnegie
% 0.18/0.44 % Mellon University. Distributed under the Creative Commons copyleft
% 0.18/0.44 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.18/0.44 %------------------------------------------------------------------------------
% 0.18/0.44 thf(a_type,type,
% 0.18/0.44 a: $tType ).
% 0.18/0.44
% 0.18/0.44 thf(x,type,
% 0.18/0.44 x: a ).
% 0.18/0.44
% 0.18/0.44 thf(cZ,type,
% 0.18/0.44 cZ: a ).
% 0.18/0.44
% 0.18/0.44 thf(cP,type,
% 0.18/0.44 cP: a > a > a ).
% 0.18/0.44
% 0.18/0.44 thf(cS_LEM1C_pme,conjecture,
% 0.18/0.44 ( ( ! [Xx0: a,Xy: a] :
% 0.18/0.44 ( ( cP @ Xx0 @ Xy )
% 0.18/0.44 != cZ )
% 0.18/0.44 & ! [Xx0: a,Xy: a,Xu: a,Xv: a] :
% 0.18/0.44 ( ( ( cP @ Xx0 @ Xu )
% 0.18/0.44 = ( cP @ Xy @ Xv ) )
% 0.18/0.44 => ( ( Xx0 = Xy )
% 0.18/0.44 & ( Xu = Xv ) ) )
% 0.18/0.44 & ! [X: a > $o] :
% 0.18/0.44 ( ( ( X @ cZ )
% 0.18/0.44 & ! [Xx0: a,Xy: a] :
% 0.18/0.44 ( ( ( X @ Xx0 )
% 0.18/0.44 & ( X @ Xy ) )
% 0.18/0.44 => ( X @ ( cP @ Xx0 @ Xy ) ) ) )
% 0.18/0.44 => ! [Xx0: a] : ( X @ Xx0 ) ) )
% 0.18/0.44 => ! [R: a > a > a > $o] :
% 0.18/0.44 ( ( $true
% 0.18/0.44 & ! [Xa: a,Xb: a,Xc: a] :
% 0.18/0.44 ( ( ( ( Xa = cZ )
% 0.18/0.44 & ( Xb = Xc ) )
% 0.18/0.44 | ( ( Xb = cZ )
% 0.18/0.44 & ( Xa = Xc ) )
% 0.18/0.44 | ? [Xx1: a,Xx2: a,Xy1: a,Xy2: a,Xz1: a,Xz2: a] :
% 0.18/0.44 ( ( Xa
% 0.18/0.44 = ( cP @ Xx1 @ Xx2 ) )
% 0.18/0.44 & ( Xb
% 0.18/0.44 = ( cP @ Xy1 @ Xy2 ) )
% 0.18/0.44 & ( Xc
% 0.18/0.44 = ( cP @ Xz1 @ Xz2 ) )
% 0.18/0.44 & ( R @ Xx1 @ Xy1 @ Xz1 )
% 0.18/0.44 & ( R @ Xx2 @ Xy2 @ Xz2 ) ) )
% 0.18/0.44 => ( R @ Xa @ Xb @ Xc ) ) )
% 0.18/0.44 => ( R @ cZ @ x @ x ) ) ) ).
% 0.18/0.44
% 0.18/0.44 %------------------------------------------------------------------------------
% 0.18/0.44 ------------------------
% 1.53/1.25 ---- Embedded in THF ---
% 1.53/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.53/1.25 %%% Generated on Tue Feb 24 12:41:41 EST 2026
% 1.53/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.53/1.25 %%% Logic specification used:
% 1.53/1.25 %%% thf(spec, logic, $$dhol).
% 1.53/1.25
% 1.53/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.Crl5SmXrr7/DTF2DTF28859.p
% See solution above
% 1.53/1.25 ------------------------
% 1.53/1.25 ---- Cleaned THF ---
% 1.53/1.26 thf(a_type,type,
% 1.53/1.26 a: $tType ).
% 1.53/1.26
% 1.53/1.26 thf(x,type,
% 1.53/1.26 x: a ).
% 1.53/1.26
% 1.53/1.26 thf(cZ,type,
% 1.53/1.26 cZ: a ).
% 1.53/1.26
% 1.53/1.26 thf(cP,type,
% 1.53/1.26 cP: a > a > a ).
% 1.53/1.26
% 1.53/1.26 thf(cS_LEM1C_pme,conjecture,
% 1.53/1.26 ( ( ! [Xx0: a,Xy: a] :
% 1.53/1.26 ( ( cP @ Xx0 @ Xy )
% 1.53/1.26 != cZ )
% 1.53/1.26 & ! [Xx0: a,Xy: a,Xu: a,Xv: a] :
% 1.53/1.26 ( ( ( cP @ Xx0 @ Xu )
% 1.53/1.26 = ( cP @ Xy @ Xv ) )
% 1.53/1.26 => ( ( Xx0 = Xy )
% 1.53/1.26 & ( Xu = Xv ) ) )
% 1.53/1.26 & ! [X: a > $o] :
% 1.53/1.26 ( ( ( X @ cZ )
% 1.53/1.26 & ! [Xx0: a,Xy: a] :
% 1.53/1.26 ( ( ( X @ Xx0 )
% 1.53/1.26 & ( X @ Xy ) )
% 1.53/1.26 => ( X @ ( cP @ Xx0 @ Xy ) ) ) )
% 1.53/1.26 => ! [Xx0: a] : ( X @ Xx0 ) ) )
% 1.53/1.26 => ! [R: a > a > a > $o] :
% 1.53/1.26 ( ( $true
% 1.53/1.26 & ! [Xa: a,Xb: a,Xc: a] :
% 1.53/1.26 ( ( ( ( Xa = cZ )
% 1.53/1.26 & ( Xb = Xc ) )
% 1.53/1.26 | ( ( Xb = cZ )
% 1.53/1.26 & ( Xa = Xc ) )
% 1.53/1.26 | ? [Xx1: a,Xx2: a,Xy1: a,Xy2: a,Xz1: a,Xz2: a] :
% 1.53/1.26 ( ( Xa
% 1.53/1.26 = ( cP @ Xx1 @ Xx2 ) )
% 1.53/1.26 & ( Xb
% 1.53/1.26 = ( cP @ Xy1 @ Xy2 ) )
% 1.53/1.26 & ( Xc
% 1.53/1.26 = ( cP @ Xz1 @ Xz2 ) )
% 1.53/1.26 & ( R @ Xx1 @ Xy1 @ Xz1 )
% 1.53/1.26 & ( R @ Xx2 @ Xy2 @ Xz2 ) ) )
% 1.53/1.26 => ( R @ Xa @ Xb @ Xc ) ) )
% 1.53/1.26 => ( R @ cZ @ x @ x ) ) ) ).
% 1.53/1.26 ------------------------
% 1.53/1.27 % (29026)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_28859 for (2999ds/4Mi)
% 1.53/1.27 % (29029)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_28859 for (2999ds/2Mi)
% 1.53/1.28 % (29026)Instruction limit reached!
% 1.53/1.28 % (29026)------------------------------
% 1.53/1.28 % (29026)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.28 % (29026)Termination reason: Unknown
% 1.53/1.28 % (29026)Termination phase: Saturation
% 1.53/1.28
% 1.53/1.28 % (29030)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_28859 for (2999ds/275Mi)
% 1.53/1.28 % (29026)Memory used [KB]: 5500
% 1.53/1.28 % (29026)Time elapsed: 0.003 s
% 1.53/1.28 % (29026)Instructions burned: 4 (million)
% 1.53/1.28 % (29026)------------------------------
% 1.53/1.28 % (29026)------------------------------
% 1.53/1.28 % (29029)Instruction limit reached!
% 1.53/1.28 % (29029)------------------------------
% 1.53/1.28 % (29029)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.28 % (29029)Termination reason: Unknown
% 1.53/1.28 % (29029)Termination phase: Property scanning
% 1.53/1.28
% 1.53/1.28 % (29029)Memory used [KB]: 1023
% 1.53/1.28 % (29029)Time elapsed: 0.002 s
% 1.53/1.28 % (29029)Instructions burned: 3 (million)
% 1.53/1.28 % (29029)------------------------------
% 1.53/1.28 % (29029)------------------------------
% 1.53/1.28 % (29030)First to succeed.
% 1.53/1.28 % (29025)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_28859 for (2999ds/183Mi)
% 1.53/1.28 % (29028)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_28859 for (2999ds/2Mi)
% 1.53/1.28 % (29027)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_28859 for (2999ds/27Mi)
% 1.53/1.28 % (29031)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_28859 for (2999ds/18Mi)
% 1.53/1.28 % (29028)Instruction limit reached!
% 1.53/1.28 % (29028)------------------------------
% 1.53/1.28 % (29028)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.28 % (29028)Termination reason: Unknown
% 1.53/1.28 % (29028)Termination phase: Preprocessing 3
% 1.53/1.28
% 1.53/1.28 % (29028)Memory used [KB]: 1023
% 1.53/1.28 % (29028)Time elapsed: 0.003 s
% 1.53/1.28 % (29028)Instructions burned: 2 (million)
% 1.53/1.28 % (29028)------------------------------
% 1.53/1.28 % (29028)------------------------------
% 1.53/1.29 % (29035)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_28859 for (2999ds/3Mi)
% 1.53/1.29 % (29036)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_28859 for (2999ds/37Mi)
% 1.53/1.29 % (29035)Instruction limit reached!
% 1.53/1.29 % (29035)------------------------------
% 1.53/1.29 % (29035)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.29 % (29035)Termination reason: Unknown
% 1.53/1.29 % (29035)Termination phase: Property scanning
% 1.53/1.29
% 1.53/1.29 % (29035)Memory used [KB]: 1023
% 1.53/1.29 % (29035)Time elapsed: 0.002 s
% 1.53/1.29 % (29035)Instructions burned: 3 (million)
% 1.53/1.29 % (29035)------------------------------
% 1.53/1.29 % (29035)------------------------------
% 1.64/1.30 % (29037)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_28859 for (2999ds/15Mi)
% 1.64/1.30 % (29038)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_28859 for (2999ds/3Mi)
% 1.64/1.31 % (29038)Instruction limit reached!
% 1.64/1.31 % (29038)------------------------------
% 1.64/1.31 % (29038)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.31 % (29038)Termination reason: Unknown
% 1.64/1.31 % (29038)Termination phase: Saturation
% 1.64/1.31
% 1.64/1.31 % (29038)Memory used [KB]: 5500
% 1.64/1.31 % (29038)Time elapsed: 0.004 s
% 1.64/1.31 % (29038)Instructions burned: 3 (million)
% 1.64/1.31 % (29038)------------------------------
% 1.64/1.31 % (29038)------------------------------
% 1.64/1.31 % (29037)Instruction limit reached!
% 1.64/1.31 % (29037)------------------------------
% 1.64/1.31 % (29037)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.31 % (29037)Termination reason: Unknown
% 1.64/1.31 % (29037)Termination phase: Saturation
% 1.64/1.31
% 1.64/1.31 % (29037)Memory used [KB]: 5628
% 1.64/1.31 % (29037)Time elapsed: 0.012 s
% 1.64/1.31 % (29037)Instructions burned: 15 (million)
% 1.64/1.31 % (29037)------------------------------
% 1.64/1.31 % (29037)------------------------------
% 1.64/1.32 % (29039)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_28859 for (2999ds/1041Mi)
% 1.64/1.33 % (29040)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_28859 for (2999ds/7Mi)
% 1.64/1.33 % (29040)Instruction limit reached!
% 1.64/1.33 % (29040)------------------------------
% 1.64/1.33 % (29040)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.33 % (29040)Termination reason: Unknown
% 1.64/1.33 % (29040)Termination phase: Saturation
% 1.64/1.33
% 1.64/1.33 % (29040)Memory used [KB]: 1023
% 1.64/1.33 % (29040)Time elapsed: 0.007 s
% 1.64/1.33 % (29040)Instructions burned: 8 (million)
% 1.64/1.33 % (29040)------------------------------
% 1.64/1.33 % (29040)------------------------------
% 1.64/1.35 % (29041)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_28859 for (2999ds/16Mi)
% 1.64/1.36 % (29041)Instruction limit reached!
% 1.64/1.36 % (29041)------------------------------
% 1.64/1.36 % (29041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.36 % (29041)Termination reason: Unknown
% 1.64/1.36 % (29041)Termination phase: Saturation
% 1.64/1.36
% 1.64/1.36 % (29041)Memory used [KB]: 5628
% 1.64/1.36 % (29041)Time elapsed: 0.012 s
% 1.64/1.36 % (29041)Instructions burned: 16 (million)
% 1.64/1.36 % (29041)------------------------------
% 1.64/1.36 % (29041)------------------------------
% 1.64/1.38 % (29042)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_28859 for (2999ds/3Mi)
% 1.64/1.38 % (29042)Instruction limit reached!
% 1.64/1.38 % (29042)------------------------------
% 1.64/1.38 % (29042)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.38 % (29042)Termination reason: Unknown
% 1.64/1.38 % (29042)Termination phase: Twee Goal Transformation
% 1.64/1.38
% 1.64/1.38 % (29042)Memory used [KB]: 1023
% 1.64/1.38 % (29042)Time elapsed: 0.004 s
% 1.64/1.38 % (29042)Instructions burned: 3 (million)
% 1.64/1.38 % (29042)------------------------------
% 1.64/1.38 % (29042)------------------------------
% 1.64/1.40 % (29031)Also succeeded, but the first one will report.
% 1.64/1.40 % (29027)Also succeeded, but the first one will report.
% 1.64/1.40 % (29030)Refutation found. Thanks to Tanya!
% 1.64/1.40 % SZS status Theorem for DTF2THF_28859
% 1.64/1.40 % SZS output start Proof for DTF2THF_28859
% 1.64/1.40 thf(type_def_5, type, a: $tType).
% 1.64/1.40 thf(func_def_0, type, a: $tType).
% 1.64/1.40 thf(func_def_1, type, x: a).
% 1.64/1.40 thf(func_def_2, type, cZ: a).
% 1.64/1.40 thf(func_def_3, type, cP: a > a > a).
% 1.64/1.40 thf(func_def_7, type, sK0: (a > $o) > a).
% 1.64/1.40 thf(func_def_8, type, sK1: (a > $o) > a).
% 1.64/1.40 thf(func_def_9, type, sK2: a > a > a > $o).
% 1.64/1.40 thf(f30,plain,(
% 1.64/1.40 $false),
% 1.64/1.40 inference(subsumption_resolution,[status(thm)],[f15,f29])).
% 1.64/1.40 thf(f29,plain,(
% 1.64/1.40 ( ! [X8 : a] : (($true = (sK2 @ cZ @ X8 @ X8))) )),
% 1.64/1.40 inference(equality_resolution,[status(thm)],[f28])).
% 1.64/1.40 thf(f28,plain,(
% 1.64/1.40 ( ! [X8 : a,X9 : a] : (($true = (sK2 @ X9 @ X8 @ X8)) | (cZ != X9)) )),
% 1.64/1.40 inference(equality_resolution,[status(thm)],[f16])).
% 1.64/1.40 thf(f16,plain,(
% 1.64/1.40 ( ! [X8 : a,X9 : a,X7 : a] : (($true = (sK2 @ X9 @ X7 @ X8)) | (X7 != X8) | (cZ != X9)) )),
% 1.64/1.40 inference(cnf_transformation,[status(thm)],[f12])).
% 1.64/1.40 thf(f12,plain,(
% 1.64/1.40 ! [X0 : a,X1 : a] : ((cP @ X0 @ X1) != cZ) & ! [X2 : a > $o] : ((($true = (X2 @ (sK1 @ X2))) & ($true != (X2 @ (cP @ (sK1 @ X2) @ (sK0 @ X2)))) & ($true = (X2 @ (sK0 @ X2)))) | ((X2 @ cZ) != $true) | ! [X5 : a] : ($true = (X2 @ X5))) & (! [X7 : a,X8 : a,X9 : a] : (($true = (sK2 @ X9 @ X7 @ X8)) | (! [X10 : a,X11 : a,X12 : a,X13 : a,X14 : a,X15 : a] : (((cP @ X11 @ X12) != X7) | ((sK2 @ X15 @ X11 @ X13) != $true) | ($true != (sK2 @ X14 @ X12 @ X10)) | ((cP @ X13 @ X10) != X8) | ((cP @ X15 @ X14) != X9)) & ((cZ != X7) | (X8 != X9)) & ((X7 != X8) | (cZ != X9)))) & ($true != (sK2 @ cZ @ x @ x))) & ! [X16 : a,X17 : a,X18 : a,X19 : a] : (((cP @ X17 @ X18) != (cP @ X16 @ X19)) | ((X16 = X17) & (X18 = X19)))),
% 1.64/1.40 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f9,f11,f10])).
% 1.64/1.40 thf(f10,plain,(
% 1.64/1.40 ! [X2 : a > $o] : (? [X3 : a,X4 : a] : (($true = (X2 @ X4)) & ((X2 @ (cP @ X4 @ X3)) != $true) & ((X2 @ X3) = $true)) => (($true = (X2 @ (sK1 @ X2))) & ($true != (X2 @ (cP @ (sK1 @ X2) @ (sK0 @ X2)))) & ($true = (X2 @ (sK0 @ X2)))))),
% 1.64/1.40 introduced(definition,[],[choice_axiom])).
% 1.64/1.40 thf(f11,plain,(
% 1.64/1.40 ? [X6 : a > a > a > $o] : (! [X7 : a,X8 : a,X9 : a] : (((X6 @ X9 @ X7 @ X8) = $true) | (! [X10 : a,X11 : a,X12 : a,X13 : a,X14 : a,X15 : a] : (((cP @ X11 @ X12) != X7) | ($true != (X6 @ X15 @ X11 @ X13)) | ($true != (X6 @ X14 @ X12 @ X10)) | ((cP @ X13 @ X10) != X8) | ((cP @ X15 @ X14) != X9)) & ((cZ != X7) | (X8 != X9)) & ((X7 != X8) | (cZ != X9)))) & ($true != (X6 @ cZ @ x @ x))) => (! [X9 : a,X8 : a,X7 : a] : (($true = (sK2 @ X9 @ X7 @ X8)) | (! [X15 : a,X14 : a,X13 : a,X12 : a,X11 : a,X10 : a] : (((cP @ X11 @ X12) != X7) | ((sK2 @ X15 @ X11 @ X13) != $true) | ($true != (sK2 @ X14 @ X12 @ X10)) | ((cP @ X13 @ X10) != X8) | ((cP @ X15 @ X14) != X9)) & ((cZ != X7) | (X8 != X9)) & ((X7 != X8) | (cZ != X9)))) & ($true != (sK2 @ cZ @ x @ x)))),
% 1.64/1.40 introduced(definition,[],[choice_axiom])).
% 1.64/1.40 thf(f9,plain,(
% 1.64/1.40 ! [X0 : a,X1 : a] : ((cP @ X0 @ X1) != cZ) & ! [X2 : a > $o] : (? [X3 : a,X4 : a] : (($true = (X2 @ X4)) & ((X2 @ (cP @ X4 @ X3)) != $true) & ((X2 @ X3) = $true)) | ((X2 @ cZ) != $true) | ! [X5 : a] : ($true = (X2 @ X5))) & ? [X6 : a > a > a > $o] : (! [X7 : a,X8 : a,X9 : a] : (((X6 @ X9 @ X7 @ X8) = $true) | (! [X10 : a,X11 : a,X12 : a,X13 : a,X14 : a,X15 : a] : (((cP @ X11 @ X12) != X7) | ($true != (X6 @ X15 @ X11 @ X13)) | ($true != (X6 @ X14 @ X12 @ X10)) | ((cP @ X13 @ X10) != X8) | ((cP @ X15 @ X14) != X9)) & ((cZ != X7) | (X8 != X9)) & ((X7 != X8) | (cZ != X9)))) & ($true != (X6 @ cZ @ x @ x))) & ! [X16 : a,X17 : a,X18 : a,X19 : a] : (((cP @ X17 @ X18) != (cP @ X16 @ X19)) | ((X16 = X17) & (X18 = X19)))),
% 1.64/1.40 inference(rectify,[status(thm)],[f8])).
% 1.64/1.40 thf(f8,plain,(
% 1.64/1.40 ! [X0 : a,X1 : a] : ((cP @ X0 @ X1) != cZ) & ! [X2 : a > $o] : (? [X4 : a,X3 : a] : (((X2 @ X3) = $true) & ($true != (X2 @ (cP @ X3 @ X4))) & ($true = (X2 @ X4))) | ((X2 @ cZ) != $true) | ! [X5 : a] : ($true = (X2 @ X5))) & ? [X10 : a > a > a > $o] : (! [X12 : a,X13 : a,X11 : a] : (($true = (X10 @ X11 @ X12 @ X13)) | (! [X15 : a,X14 : a,X18 : a,X16 : a,X17 : a,X19 : a] : (((cP @ X14 @ X18) != X12) | ($true != (X10 @ X19 @ X14 @ X16)) | ($true != (X10 @ X17 @ X18 @ X15)) | ((cP @ X16 @ X15) != X13) | ((cP @ X19 @ X17) != X11)) & ((cZ != X12) | (X11 != X13)) & ((X12 != X13) | (cZ != X11)))) & ($true != (X10 @ cZ @ x @ x))) & ! [X8 : a,X9 : a,X7 : a,X6 : a] : (((cP @ X9 @ X7) != (cP @ X8 @ X6)) | ((X8 = X9) & (X6 = X7)))),
% 1.64/1.40 inference(flattening,[status(thm)],[f7])).
% 1.64/1.40 thf(f7,plain,(
% 1.64/1.40 ? [X10 : a > a > a > $o] : (! [X12 : a,X13 : a,X11 : a] : (($true = (X10 @ X11 @ X12 @ X13)) | (! [X15 : a,X14 : a,X18 : a,X16 : a,X17 : a,X19 : a] : (((cP @ X14 @ X18) != X12) | ($true != (X10 @ X19 @ X14 @ X16)) | ($true != (X10 @ X17 @ X18 @ X15)) | ((cP @ X16 @ X15) != X13) | ((cP @ X19 @ X17) != X11)) & ((cZ != X12) | (X11 != X13)) & ((X12 != X13) | (cZ != X11)))) & ($true != (X10 @ cZ @ x @ x))) & (! [X2 : a > $o] : (! [X5 : a] : ($true = (X2 @ X5)) | (? [X3 : a,X4 : a] : (($true != (X2 @ (cP @ X3 @ X4))) & (((X2 @ X3) = $true) & ($true = (X2 @ X4)))) | ((X2 @ cZ) != $true))) & ! [X0 : a,X1 : a] : ((cP @ X0 @ X1) != cZ) & ! [X8 : a,X9 : a,X7 : a,X6 : a] : (((cP @ X9 @ X7) != (cP @ X8 @ X6)) | ((X8 = X9) & (X6 = X7))))),
% 1.64/1.40 inference(ennf_transformation,[status(thm)],[f6])).
% 1.64/1.40 thf(f6,plain,(
% 1.64/1.40 ~((! [X2 : a > $o] : ((! [X3 : a,X4 : a] : ((((X2 @ X3) = $true) & ($true = (X2 @ X4))) => ($true = (X2 @ (cP @ X3 @ X4)))) & ((X2 @ cZ) = $true)) => ! [X5 : a] : ($true = (X2 @ X5))) & ! [X0 : a,X1 : a] : ((cP @ X0 @ X1) != cZ) & ! [X9 : a,X6 : a,X7 : a,X8 : a] : (((cP @ X9 @ X7) = (cP @ X8 @ X6)) => ((X8 = X9) & (X6 = X7)))) => ! [X10 : a > a > a > $o] : (! [X11 : a,X13 : a,X12 : a] : ((? [X16 : a,X14 : a,X15 : a,X19 : a,X17 : a,X18 : a] : (((cP @ X14 @ X18) = X12) & ($true = (X10 @ X19 @ X14 @ X16)) & ((cP @ X16 @ X15) = X13) & ($true = (X10 @ X17 @ X18 @ X15)) & ((cP @ X19 @ X17) = X11)) | ((X11 = X13) & (cZ = X12)) | ((X12 = X13) & (cZ = X11))) => ($true = (X10 @ X11 @ X12 @ X13))) => ($true = (X10 @ cZ @ x @ x))))),
% 1.64/1.40 inference(true_and_false_elimination,[status(thm)],[f5])).
% 1.64/1.40 thf(f5,plain,(
% 1.64/1.40 ~((! [X2 : a > $o] : ((! [X3 : a,X4 : a] : ((((X2 @ X3) = $true) & ($true = (X2 @ X4))) => ($true = (X2 @ (cP @ X3 @ X4)))) & ((X2 @ cZ) = $true)) => ! [X5 : a] : ($true = (X2 @ X5))) & ! [X0 : a,X1 : a] : ((cP @ X0 @ X1) != cZ) & ! [X9 : a,X6 : a,X7 : a,X8 : a] : (((cP @ X9 @ X7) = (cP @ X8 @ X6)) => ((X8 = X9) & (X6 = X7)))) => ! [X10 : a > a > a > $o] : (($true & ! [X11 : a,X13 : a,X12 : a] : ((? [X16 : a,X14 : a,X15 : a,X19 : a,X17 : a,X18 : a] : (((cP @ X14 @ X18) = X12) & ($true = (X10 @ X19 @ X14 @ X16)) & ((cP @ X16 @ X15) = X13) & ($true = (X10 @ X17 @ X18 @ X15)) & ((cP @ X19 @ X17) = X11)) | ((X11 = X13) & (cZ = X12)) | ((X12 = X13) & (cZ = X11))) => ($true = (X10 @ X11 @ X12 @ X13)))) => ($true = (X10 @ cZ @ x @ x))))),
% 1.64/1.40 inference(fool_elimination,[status(thm)],[f4])).
% 1.64/1.40 thf(f4,plain,(
% 1.64/1.40 ~((! [X0 : a,X1 : a] : ((cP @ X0 @ X1) != cZ) & ! [X2 : a > $o] : (((X2 @ cZ) & ! [X3 : a,X4 : a] : (((X2 @ X3) & (X2 @ X4)) => (X2 @ (cP @ X3 @ X4)))) => ! [X5 : a] : (X2 @ X5)) & ! [X6 : a,X7 : a,X8 : a,X9 : a] : (((cP @ X9 @ X7) = (cP @ X8 @ X6)) => ((X6 = X7) & (X8 = X9)))) => ! [X10 : a > a > a > $o] : (($true & ! [X11 : a,X12 : a,X13 : a] : ((((X12 = X13) & (cZ = X11)) | ? [X14 : a,X15 : a,X16 : a,X17 : a,X18 : a,X19 : a] : (((cP @ X19 @ X17) = X11) & ((cP @ X14 @ X18) = X12) & ((cP @ X16 @ X15) = X13) & (X10 @ X19 @ X14 @ X16) & (X10 @ X17 @ X18 @ X15)) | ((cZ = X12) & (X11 = X13))) => (X10 @ X11 @ X12 @ X13))) => (X10 @ cZ @ x @ x)))),
% 1.64/1.40 inference(rectify,[status(thm)],[f2])).
% 1.64/1.40 thf(f2,negated_conjecture,(
% 1.64/1.40 ~((! [X0 : a,X1 : a] : ((cP @ X0 @ X1) != cZ) & ! [X4 : a > $o] : (((X4 @ cZ) & ! [X0 : a,X1 : a] : (((X4 @ X0) & (X4 @ X1)) => (X4 @ (cP @ X0 @ X1)))) => ! [X0 : a] : (X4 @ X0)) & ! [X3 : a,X2 : a,X1 : a,X0 : a] : (((cP @ X0 @ X2) = (cP @ X1 @ X3)) => ((X2 = X3) & (X0 = X1)))) => ! [X5 : a > a > a > $o] : (($true & ! [X6 : a,X7 : a,X8 : a] : ((((X7 = X8) & (cZ = X6)) | ? [X11 : a,X14 : a,X13 : a,X10 : a,X12 : a,X9 : a] : (((cP @ X9 @ X10) = X6) & ((cP @ X11 @ X12) = X7) & ((cP @ X13 @ X14) = X8) & (X5 @ X9 @ X11 @ X13) & (X5 @ X10 @ X12 @ X14)) | ((cZ = X7) & (X6 = X8))) => (X5 @ X6 @ X7 @ X8))) => (X5 @ cZ @ x @ x)))),
% 1.64/1.40 inference(negated_conjecture,[status(cth)],[f1])).
% 1.64/1.40 thf(f1,conjecture,(
% 1.64/1.40 (! [X0 : a,X1 : a] : ((cP @ X0 @ X1) != cZ) & ! [X4 : a > $o] : (((X4 @ cZ) & ! [X0 : a,X1 : a] : (((X4 @ X0) & (X4 @ X1)) => (X4 @ (cP @ X0 @ X1)))) => ! [X0 : a] : (X4 @ X0)) & ! [X3 : a,X2 : a,X1 : a,X0 : a] : (((cP @ X0 @ X2) = (cP @ X1 @ X3)) => ((X2 = X3) & (X0 = X1)))) => ! [X5 : a > a > a > $o] : (($true & ! [X6 : a,X7 : a,X8 : a] : ((((X7 = X8) & (cZ = X6)) | ? [X11 : a,X14 : a,X13 : a,X10 : a,X12 : a,X9 : a] : (((cP @ X9 @ X10) = X6) & ((cP @ X11 @ X12) = X7) & ((cP @ X13 @ X14) = X8) & (X5 @ X9 @ X11 @ X13) & (X5 @ X10 @ X12 @ X14)) | ((cZ = X7) & (X6 = X8))) => (X5 @ X6 @ X7 @ X8))) => (X5 @ cZ @ x @ x))),
% 1.64/1.40 file('/export/starexec/sandbox2/tmp/tmp.Crl5SmXrr7/DTF2THF_28859.p',cS_LEM1C_pme)).
% 1.64/1.40 thf(f15,plain,(
% 1.64/1.40 ($true != (sK2 @ cZ @ x @ x))),
% 1.64/1.40 inference(cnf_transformation,[status(thm)],[f12])).
% 1.64/1.40 % SZS output end Proof for DTF2THF_28859
% 1.64/1.40 % (29030)------------------------------
% 1.64/1.40 % (29030)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.40 % (29030)Termination reason: Refutation
% 1.64/1.40
% 1.64/1.40 % (29030)Memory used [KB]: 5500
% 1.64/1.40 % (29030)Time elapsed: 0.006 s
% 1.64/1.40 % (29030)Instructions burned: 3 (million)
% 1.64/1.40 % (29030)------------------------------
% 1.64/1.40 % (29030)------------------------------
% 1.64/1.40 % (29024)Success in time 0.135 s
%------------------------------------------------------------------------------