%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV096^5 : 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 : n023.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 09:40:16 AM UTC 2026
% Result : Theorem 1.46s 1.27s
% Output : Refutation 1.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 358 ( 105 equ; 0 cnn)
% Maximal formula atoms : 14 ( 19 avg)
% Number of connectives : 481 ( 52 ~; 39 |; 63 &; 299 @)
% ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 8 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 144 ( 0 ^; 120 !; 24 ?; 144 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_7,type,
b: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
b: $tType ).
thf(func_def_2,type,
z: a ).
thf(func_def_3,type,
cR: a > a > $o ).
thf(func_def_4,type,
f: a > b > $o ).
thf(func_def_5,type,
cS: b > b > $o ).
thf(func_def_9,type,
sK0: a > b ).
thf(func_def_10,type,
sK1: b ).
thf(func_def_11,type,
sK2: a > a ).
thf(f23,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f22,f15]) ).
thf(f15,plain,
! [X10: a] :
( $true
!= ( f @ X10 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ! [X0: b,X1: a,X2: b] :
( ( $true
= ( cS @ X2 @ X0 ) )
| ( ( f @ X1 @ X0 )
!= $true )
| ( ( f @ X1 @ X2 )
!= $true ) )
& ! [X3: a] :
( ( cR @ X3 @ X3 )
= $true )
& ! [X4: a] :
( ( f @ X4 @ ( sK0 @ X4 ) )
= $true )
& ! [X6: a,X7: a,X8: b] :
( ( ( cR @ X7 @ X6 )
= $true )
| ( ( f @ X7 @ X8 )
!= $true )
| ( ( f @ X6 @ X8 )
!= $true ) )
& ! [X10: a] :
( ( ( ( f @ ( sK2 @ X10 ) @ sK1 )
= $true )
| ( ( cR @ X10 @ z )
!= $true ) )
& ( $true
!= ( f @ X10 @ sK1 ) ) )
& ! [X12: a,X13: a,X14: a] :
( ( $true
!= ( cR @ X13 @ X12 ) )
| ( $true
!= ( cR @ X14 @ X12 ) )
| ( ( cR @ X14 @ X13 )
= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f9,f12,f11,f10]) ).
thf(f10,plain,
! [X4: a] :
( ? [X5: b] :
( ( f @ X4 @ X5 )
= $true )
=> ( ( f @ X4 @ ( sK0 @ X4 ) )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X9: b] :
! [X10: a] :
? [X11: a] :
( ( ( ( f @ X11 @ X9 )
= $true )
| ( ( cR @ X10 @ z )
!= $true ) )
& ( $true
!= ( f @ X10 @ X9 ) ) )
=> ! [X10: a] :
? [X11: a] :
( ( ( ( f @ X11 @ sK1 )
= $true )
| ( ( cR @ X10 @ z )
!= $true ) )
& ( $true
!= ( f @ X10 @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
! [X10: a] :
( ? [X11: a] :
( ( ( ( f @ X11 @ sK1 )
= $true )
| ( ( cR @ X10 @ z )
!= $true ) )
& ( $true
!= ( f @ X10 @ sK1 ) ) )
=> ( ( ( ( f @ ( sK2 @ X10 ) @ sK1 )
= $true )
| ( ( cR @ X10 @ z )
!= $true ) )
& ( $true
!= ( f @ X10 @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ! [X0: b,X1: a,X2: b] :
( ( $true
= ( cS @ X2 @ X0 ) )
| ( ( f @ X1 @ X0 )
!= $true )
| ( ( f @ X1 @ X2 )
!= $true ) )
& ! [X3: a] :
( ( cR @ X3 @ X3 )
= $true )
& ! [X4: a] :
? [X5: b] :
( ( f @ X4 @ X5 )
= $true )
& ! [X6: a,X7: a,X8: b] :
( ( ( cR @ X7 @ X6 )
= $true )
| ( ( f @ X7 @ X8 )
!= $true )
| ( ( f @ X6 @ X8 )
!= $true ) )
& ? [X9: b] :
! [X10: a] :
? [X11: a] :
( ( ( ( f @ X11 @ X9 )
= $true )
| ( ( cR @ X10 @ z )
!= $true ) )
& ( $true
!= ( f @ X10 @ X9 ) ) )
& ! [X12: a,X13: a,X14: a] :
( ( $true
!= ( cR @ X13 @ X12 ) )
| ( $true
!= ( cR @ X14 @ X12 ) )
| ( ( cR @ X14 @ X13 )
= $true ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
( ! [X9: b,X10: a,X11: b] :
( ( $true
= ( cS @ X11 @ X9 ) )
| ( $true
!= ( f @ X10 @ X9 ) )
| ( ( f @ X10 @ X11 )
!= $true ) )
& ! [X0: a] :
( ( cR @ X0 @ X0 )
= $true )
& ! [X4: a] :
? [X5: b] :
( ( f @ X4 @ X5 )
= $true )
& ! [X8: a,X6: a,X7: b] :
( ( ( cR @ X6 @ X8 )
= $true )
| ( $true
!= ( f @ X6 @ X7 ) )
| ( ( f @ X8 @ X7 )
!= $true ) )
& ? [X12: b] :
! [X13: a] :
? [X14: a] :
( ( ( ( f @ X14 @ X12 )
= $true )
| ( ( cR @ X13 @ z )
!= $true ) )
& ( ( f @ X13 @ X12 )
!= $true ) )
& ! [X2: a,X3: a,X1: a] :
( ( $true
!= ( cR @ X3 @ X2 ) )
| ( $true
!= ( cR @ X1 @ X2 ) )
| ( ( cR @ X1 @ X3 )
= $true ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
( ? [X12: b] :
! [X13: a] :
? [X14: a] :
( ( ( ( f @ X14 @ X12 )
= $true )
| ( ( cR @ X13 @ z )
!= $true ) )
& ( ( f @ X13 @ X12 )
!= $true ) )
& ! [X6: a,X8: a,X7: b] :
( ( ( cR @ X6 @ X8 )
= $true )
| ( $true
!= ( f @ X6 @ X7 ) )
| ( ( f @ X8 @ X7 )
!= $true ) )
& ! [X4: a] :
? [X5: b] :
( ( f @ X4 @ X5 )
= $true )
& ! [X10: a,X11: b,X9: b] :
( ( $true
= ( cS @ X11 @ X9 ) )
| ( ( f @ X10 @ X11 )
!= $true )
| ( $true
!= ( f @ X10 @ X9 ) ) )
& ! [X2: a,X3: a,X1: a] :
( ( ( cR @ X1 @ X3 )
= $true )
| ( $true
!= ( cR @ X1 @ X2 ) )
| ( $true
!= ( cR @ X3 @ X2 ) ) )
& ! [X0: a] :
( ( cR @ X0 @ X0 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ( ! [X2: a,X3: a,X1: a] :
( ( ( $true
= ( cR @ X1 @ X2 ) )
& ( $true
= ( cR @ X3 @ X2 ) ) )
=> ( ( cR @ X1 @ X3 )
= $true ) )
& ! [X0: a] :
( ( cR @ X0 @ X0 )
= $true ) )
=> ( ( ! [X6: a,X8: a,X7: b] :
( ( ( $true
= ( f @ X6 @ X7 ) )
& ( ( f @ X8 @ X7 )
= $true ) )
=> ( ( cR @ X6 @ X8 )
= $true ) )
& ! [X4: a] :
? [X5: b] :
( ( f @ X4 @ X5 )
= $true )
& ! [X10: a,X11: b,X9: b] :
( ( ( ( f @ X10 @ X11 )
= $true )
& ( $true
= ( f @ X10 @ X9 ) ) )
=> ( $true
= ( cS @ X11 @ X9 ) ) ) )
=> ! [X12: b] :
? [X13: a] :
! [X14: a] :
( ( ( ( f @ X14 @ X12 )
!= $true )
& ( ( cR @ X13 @ z )
= $true ) )
| ( ( f @ X13 @ X12 )
= $true ) ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X2: a,X3: a,X1: a] :
( ( ( $true
= ( cR @ X1 @ X2 ) )
& ( $true
= ( cR @ X3 @ X2 ) ) )
=> ( ( cR @ X1 @ X3 )
= $true ) )
& ! [X0: a] :
( ( cR @ X0 @ X0 )
= $true ) )
=> ( ( ! [X6: a,X8: a,X7: b] :
( ( ( $true
= ( f @ X6 @ X7 ) )
& ( ( f @ X8 @ X7 )
= $true ) )
=> ( ( cR @ X6 @ X8 )
= $true ) )
& ! [X4: a] :
? [X5: b] :
( ( f @ X4 @ X5 )
= $true )
& ! [X10: a,X11: b,X9: b] :
( ( ( ( f @ X10 @ X11 )
= $true )
& ( $true
= ( f @ X10 @ X9 ) ) )
=> ( $true
= ( cS @ X11 @ X9 ) ) ) )
=> ! [X12: b] :
? [X13: a] :
! [X14: a] :
( ( ( f @ X13 @ X12 )
= $true )
| ( ( ( f @ X14 @ X12 )
!= $true )
& ( ( cR @ X13 @ z )
= $true ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: a] : ( cR @ X0 @ X0 )
& ! [X1: a,X2: a,X3: a] :
( ( ( cR @ X3 @ X2 )
& ( cR @ X1 @ X2 ) )
=> ( cR @ X1 @ X3 ) ) )
=> ( ( ! [X4: a] :
? [X5: b] : ( f @ X4 @ X5 )
& ! [X6: a,X7: b,X8: a] :
( ( ( f @ X8 @ X7 )
& ( f @ X6 @ X7 ) )
=> ( cR @ X6 @ X8 ) )
& ! [X9: b,X10: a,X11: b] :
( ( ( f @ X10 @ X9 )
& ( f @ X10 @ X11 ) )
=> ( cS @ X11 @ X9 ) ) )
=> ! [X12: b] :
? [X13: a] :
! [X14: a] :
( ( f @ X13 @ X12 )
| ( ~ ( f @ X14 @ X12 )
& ( cR @ X13 @ z ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X3: a] : ( cR @ X3 @ X3 )
& ! [X0: a,X1: a,X2: a] :
( ( ( cR @ X2 @ X1 )
& ( cR @ X0 @ X1 ) )
=> ( cR @ X0 @ X2 ) ) )
=> ( ( ! [X3: a] :
? [X4: b] : ( f @ X3 @ X4 )
& ! [X7: a,X4: b,X8: a] :
( ( ( f @ X8 @ X4 )
& ( f @ X7 @ X4 ) )
=> ( cR @ X7 @ X8 ) )
& ! [X6: b,X3: a,X5: b] :
( ( ( f @ X3 @ X6 )
& ( f @ X3 @ X5 ) )
=> ( cS @ X5 @ X6 ) ) )
=> ! [X4: b] :
? [X3: a] :
! [X2: a] :
( ( f @ X3 @ X4 )
| ( ~ ( f @ X2 @ X4 )
& ( cR @ X3 @ z ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X3: a] : ( cR @ X3 @ X3 )
& ! [X0: a,X1: a,X2: a] :
( ( ( cR @ X2 @ X1 )
& ( cR @ X0 @ X1 ) )
=> ( cR @ X0 @ X2 ) ) )
=> ( ( ! [X3: a] :
? [X4: b] : ( f @ X3 @ X4 )
& ! [X7: a,X4: b,X8: a] :
( ( ( f @ X8 @ X4 )
& ( f @ X7 @ X4 ) )
=> ( cR @ X7 @ X8 ) )
& ! [X6: b,X3: a,X5: b] :
( ( ( f @ X3 @ X6 )
& ( f @ X3 @ X5 ) )
=> ( cS @ X5 @ X6 ) ) )
=> ! [X4: b] :
? [X3: a] :
! [X2: a] :
( ( f @ X3 @ X4 )
| ( ~ ( f @ X2 @ X4 )
& ( cR @ X3 @ z ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.sfyibSciBY/DTF2THF_2434.p',cTHM552E_pme) ).
thf(f22,plain,
( $true
= ( f @ ( sK2 @ z ) @ sK1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f21]) ).
thf(f21,plain,
( ( $true != $true )
| ( $true
= ( f @ ( sK2 @ z ) @ sK1 ) ) ),
inference(superposition,[status(thm)],[f16,f19]) ).
thf(f19,plain,
! [X3: a] :
( ( cR @ X3 @ X3 )
= $true ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f16,plain,
! [X10: a] :
( ( ( cR @ X10 @ z )
!= $true )
| ( ( f @ ( sK2 @ X10 ) @ sK1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV096^5 : 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
% 0.16/0.33 % Computer : n023.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 12:40:49 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.28/0.45 ---- Original DTF file ---
% 0.28/0.46 thf(spec,logic,$$dhol).
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 % File : SEV096^5 : TPTP v9.2.1. Released v4.0.0.
% 0.28/0.46 % Domain : Set Theory (Relations)
% 0.28/0.46 % Problem : TPS problem from RELN-THMS
% 0.28/0.46 % Version : Especial.
% 0.28/0.46 % English :
% 0.28/0.46
% 0.28/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.28/0.46 % Source : [Bro09]
% 0.28/0.46 % Names : tps_1072 [Bro09]
% 0.28/0.46
% 0.28/0.46 % Status : Theorem
% 0.28/0.46 % Rating : 0.08 v9.1.0, 0.12 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.08 v7.4.0, 0.11 v7.3.0, 0.10 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.0.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.28/0.46 % Syntax : Number of formulae : 7 ( 0 unt; 6 typ; 0 def)
% 0.28/0.46 % Number of atoms : 14 ( 0 equ; 0 cnn)
% 0.28/0.46 % Maximal formula atoms : 14 ( 14 avg)
% 0.28/0.46 % Number of connectives : 42 ( 1 ~; 1 |; 7 &; 28 @)
% 0.28/0.46 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.28/0.46 % Maximal formula depth : 12 ( 12 avg)
% 0.28/0.46 % Number of types : 3 ( 2 usr)
% 0.28/0.46 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.28/0.46 % Number of symbols : 4 ( 4 usr; 1 con; 0-2 aty)
% 0.28/0.46 % Number of variables : 15 ( 0 ^; 13 !; 2 ?; 15 :)
% 0.28/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.28/0.46
% 0.28/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.28/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.28/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.28/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 thf(a_type,type,
% 0.28/0.46 a: $tType ).
% 0.28/0.46
% 0.28/0.46 thf(b_type,type,
% 0.28/0.46 b: $tType ).
% 0.28/0.46
% 0.28/0.46 thf(z,type,
% 0.28/0.46 z: a ).
% 0.28/0.46
% 0.28/0.46 thf(cR,type,
% 0.28/0.46 cR: a > a > $o ).
% 0.28/0.46
% 0.28/0.46 thf(f,type,
% 0.28/0.46 f: a > b > $o ).
% 0.28/0.46
% 0.28/0.46 thf(cS,type,
% 0.28/0.46 cS: b > b > $o ).
% 0.28/0.46
% 0.28/0.46 thf(cTHM552E_pme,conjecture,
% 0.28/0.46 ( ( ! [Xu: a,Xv: a,Xw: a] :
% 0.28/0.46 ( ( ( cR @ Xu @ Xv )
% 0.28/0.46 & ( cR @ Xw @ Xv ) )
% 0.28/0.46 => ( cR @ Xu @ Xw ) )
% 0.28/0.46 & ! [Xx: a] : ( cR @ Xx @ Xx ) )
% 0.28/0.46 => ( ( ! [Xx: a] :
% 0.28/0.46 ? [Xy: b] : ( f @ Xx @ Xy )
% 0.28/0.46 & ! [Xx: a,Xy1: b,Xy2: b] :
% 0.28/0.46 ( ( ( f @ Xx @ Xy1 )
% 0.28/0.46 & ( f @ Xx @ Xy2 ) )
% 0.28/0.46 => ( cS @ Xy1 @ Xy2 ) )
% 0.28/0.46 & ! [Xx1: a,Xx2: a,Xy: b] :
% 0.28/0.46 ( ( ( f @ Xx1 @ Xy )
% 0.28/0.46 & ( f @ Xx2 @ Xy ) )
% 0.28/0.46 => ( cR @ Xx1 @ Xx2 ) ) )
% 0.28/0.46 => ! [Xy: b] :
% 0.28/0.46 ? [Xx: a] :
% 0.28/0.46 ! [Xw: a] :
% 0.28/0.46 ( ( f @ Xx @ Xy )
% 0.28/0.46 | ( ~ ( f @ Xw @ Xy )
% 0.28/0.46 & ( cR @ Xx @ z ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 ------------------------
% 1.46/1.24 ---- Embedded in THF ---
% 1.46/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.25 %%% Generated on Tue Feb 24 12:40:50 EST 2026
% 1.46/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.25 %%% Logic specification used:
% 1.46/1.25 %%% thf(spec, logic, $$dhol).
% 1.46/1.25
% 1.46/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.sfyibSciBY/DTF2DTF2434.p
% See solution above
% 1.46/1.25 ------------------------
% 1.46/1.26 ---- Cleaned THF ---
% 1.46/1.26 thf(a_type,type,
% 1.46/1.26 a: $tType ).
% 1.46/1.26
% 1.46/1.26 thf(b_type,type,
% 1.46/1.26 b: $tType ).
% 1.46/1.26
% 1.46/1.26 thf(z,type,
% 1.46/1.26 z: a ).
% 1.46/1.26
% 1.46/1.26 thf(cR,type,
% 1.46/1.26 cR: a > a > $o ).
% 1.46/1.26
% 1.46/1.26 thf(f,type,
% 1.46/1.26 f: a > b > $o ).
% 1.46/1.26
% 1.46/1.26 thf(cS,type,
% 1.46/1.26 cS: b > b > $o ).
% 1.46/1.26
% 1.46/1.26 thf(cTHM552E_pme,conjecture,
% 1.46/1.26 ( ( ! [Xu: a,Xv: a,Xw: a] :
% 1.46/1.26 ( ( ( cR @ Xu @ Xv )
% 1.46/1.26 & ( cR @ Xw @ Xv ) )
% 1.46/1.26 => ( cR @ Xu @ Xw ) )
% 1.46/1.26 & ! [Xx: a] : ( cR @ Xx @ Xx ) )
% 1.46/1.26 => ( ( ! [Xx: a] :
% 1.46/1.26 ? [Xy: b] : ( f @ Xx @ Xy )
% 1.46/1.26 & ! [Xx: a,Xy1: b,Xy2: b] :
% 1.46/1.26 ( ( ( f @ Xx @ Xy1 )
% 1.46/1.26 & ( f @ Xx @ Xy2 ) )
% 1.46/1.26 => ( cS @ Xy1 @ Xy2 ) )
% 1.46/1.26 & ! [Xx1: a,Xx2: a,Xy: b] :
% 1.46/1.26 ( ( ( f @ Xx1 @ Xy )
% 1.46/1.26 & ( f @ Xx2 @ Xy ) )
% 1.46/1.26 => ( cR @ Xx1 @ Xx2 ) ) )
% 1.46/1.26 => ! [Xy: b] :
% 1.46/1.26 ? [Xx: a] :
% 1.46/1.26 ! [Xw: a] :
% 1.46/1.26 ( ( f @ Xx @ Xy )
% 1.46/1.26 | ( ~ ( f @ Xw @ Xy )
% 1.46/1.26 & ( cR @ Xx @ z ) ) ) ) ) ).
% 1.46/1.26 ------------------------
% 1.46/1.27 % (2713)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_2434 for (2999ds/18Mi)
% 1.46/1.27 % (2711)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_2434 for (2999ds/2Mi)
% 1.46/1.27 % (2713)First to succeed.
% 1.46/1.27 % (2711)Instruction limit reached!
% 1.46/1.27 % (2711)------------------------------
% 1.46/1.27 % (2711)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.27 % (2711)Termination reason: Unknown
% 1.46/1.27 % (2711)Termination phase: Saturation
% 1.46/1.27
% 1.46/1.27 % (2711)Memory used [KB]: 5500
% 1.46/1.27 % (2711)Time elapsed: 0.002 s
% 1.46/1.27 % (2711)Instructions burned: 3 (million)
% 1.46/1.27 % (2711)------------------------------
% 1.46/1.27 % (2711)------------------------------
% 1.46/1.27 % (2713)Refutation found. Thanks to Tanya!
% 1.46/1.27 % SZS status Theorem for DTF2THF_2434
% 1.46/1.27 % SZS output start Proof for DTF2THF_2434
% 1.46/1.27 thf(type_def_5, type, a: $tType).
% 1.46/1.27 thf(type_def_7, type, b: $tType).
% 1.46/1.27 thf(func_def_0, type, a: $tType).
% 1.46/1.27 thf(func_def_1, type, b: $tType).
% 1.46/1.27 thf(func_def_2, type, z: a).
% 1.46/1.27 thf(func_def_3, type, cR: a > a > $o).
% 1.46/1.27 thf(func_def_4, type, f: a > b > $o).
% 1.46/1.27 thf(func_def_5, type, cS: b > b > $o).
% 1.46/1.27 thf(func_def_9, type, sK0: a > b).
% 1.46/1.27 thf(func_def_10, type, sK1: b).
% 1.46/1.27 thf(func_def_11, type, sK2: a > a).
% 1.46/1.27 thf(f23,plain,(
% 1.46/1.27 $false),
% 1.46/1.27 inference(subsumption_resolution,[status(thm)],[f22,f15])).
% 1.46/1.27 thf(f15,plain,(
% 1.46/1.27 ( ! [X10 : a] : (($true != (f @ X10 @ sK1))) )),
% 1.46/1.27 inference(cnf_transformation,[status(thm)],[f13])).
% 1.46/1.27 thf(f13,plain,(
% 1.46/1.27 ! [X0 : b,X1 : a,X2 : b] : (($true = (cS @ X2 @ X0)) | ((f @ X1 @ X0) != $true) | ((f @ X1 @ X2) != $true)) & ! [X3 : a] : ((cR @ X3 @ X3) = $true) & ! [X4 : a] : ((f @ X4 @ (sK0 @ X4)) = $true) & ! [X6 : a,X7 : a,X8 : b] : (((cR @ X7 @ X6) = $true) | ((f @ X7 @ X8) != $true) | ((f @ X6 @ X8) != $true)) & ! [X10 : a] : ((((f @ (sK2 @ X10) @ sK1) = $true) | ((cR @ X10 @ z) != $true)) & ($true != (f @ X10 @ sK1))) & ! [X12 : a,X13 : a,X14 : a] : (($true != (cR @ X13 @ X12)) | ($true != (cR @ X14 @ X12)) | ((cR @ X14 @ X13) = $true))),
% 1.46/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f9,f12,f11,f10])).
% 1.46/1.27 thf(f10,plain,(
% 1.46/1.27 ! [X4 : a] : (? [X5 : b] : ((f @ X4 @ X5) = $true) => ((f @ X4 @ (sK0 @ X4)) = $true))),
% 1.46/1.27 introduced(definition,[],[choice_axiom])).
% 1.46/1.27 thf(f11,plain,(
% 1.46/1.27 ? [X9 : b] : ! [X10 : a] : ? [X11 : a] : ((((f @ X11 @ X9) = $true) | ((cR @ X10 @ z) != $true)) & ($true != (f @ X10 @ X9))) => ! [X10 : a] : ? [X11 : a] : ((((f @ X11 @ sK1) = $true) | ((cR @ X10 @ z) != $true)) & ($true != (f @ X10 @ sK1)))),
% 1.46/1.27 introduced(definition,[],[choice_axiom])).
% 1.46/1.27 thf(f12,plain,(
% 1.46/1.27 ! [X10 : a] : (? [X11 : a] : ((((f @ X11 @ sK1) = $true) | ((cR @ X10 @ z) != $true)) & ($true != (f @ X10 @ sK1))) => ((((f @ (sK2 @ X10) @ sK1) = $true) | ((cR @ X10 @ z) != $true)) & ($true != (f @ X10 @ sK1))))),
% 1.46/1.27 introduced(definition,[],[choice_axiom])).
% 1.46/1.27 thf(f9,plain,(
% 1.46/1.27 ! [X0 : b,X1 : a,X2 : b] : (($true = (cS @ X2 @ X0)) | ((f @ X1 @ X0) != $true) | ((f @ X1 @ X2) != $true)) & ! [X3 : a] : ((cR @ X3 @ X3) = $true) & ! [X4 : a] : ? [X5 : b] : ((f @ X4 @ X5) = $true) & ! [X6 : a,X7 : a,X8 : b] : (((cR @ X7 @ X6) = $true) | ((f @ X7 @ X8) != $true) | ((f @ X6 @ X8) != $true)) & ? [X9 : b] : ! [X10 : a] : ? [X11 : a] : ((((f @ X11 @ X9) = $true) | ((cR @ X10 @ z) != $true)) & ($true != (f @ X10 @ X9))) & ! [X12 : a,X13 : a,X14 : a] : (($true != (cR @ X13 @ X12)) | ($true != (cR @ X14 @ X12)) | ((cR @ X14 @ X13) = $true))),
% 1.46/1.27 inference(rectify,[status(thm)],[f8])).
% 1.46/1.27 thf(f8,plain,(
% 1.46/1.27 ! [X9 : b,X10 : a,X11 : b] : (($true = (cS @ X11 @ X9)) | ($true != (f @ X10 @ X9)) | ((f @ X10 @ X11) != $true)) & ! [X0 : a] : ((cR @ X0 @ X0) = $true) & ! [X4 : a] : ? [X5 : b] : ((f @ X4 @ X5) = $true) & ! [X8 : a,X6 : a,X7 : b] : (((cR @ X6 @ X8) = $true) | ($true != (f @ X6 @ X7)) | ((f @ X8 @ X7) != $true)) & ? [X12 : b] : ! [X13 : a] : ? [X14 : a] : ((((f @ X14 @ X12) = $true) | ((cR @ X13 @ z) != $true)) & ((f @ X13 @ X12) != $true)) & ! [X2 : a,X3 : a,X1 : a] : (($true != (cR @ X3 @ X2)) | ($true != (cR @ X1 @ X2)) | ((cR @ X1 @ X3) = $true))),
% 1.46/1.27 inference(flattening,[status(thm)],[f7])).
% 1.46/1.27 thf(f7,plain,(
% 1.46/1.27 (? [X12 : b] : ! [X13 : a] : ? [X14 : a] : ((((f @ X14 @ X12) = $true) | ((cR @ X13 @ z) != $true)) & ((f @ X13 @ X12) != $true)) & (! [X6 : a,X8 : a,X7 : b] : (((cR @ X6 @ X8) = $true) | (($true != (f @ X6 @ X7)) | ((f @ X8 @ X7) != $true))) & ! [X4 : a] : ? [X5 : b] : ((f @ X4 @ X5) = $true) & ! [X10 : a,X11 : b,X9 : b] : (($true = (cS @ X11 @ X9)) | (((f @ X10 @ X11) != $true) | ($true != (f @ X10 @ X9)))))) & (! [X2 : a,X3 : a,X1 : a] : (((cR @ X1 @ X3) = $true) | (($true != (cR @ X1 @ X2)) | ($true != (cR @ X3 @ X2)))) & ! [X0 : a] : ((cR @ X0 @ X0) = $true))),
% 1.46/1.27 inference(ennf_transformation,[status(thm)],[f6])).
% 1.46/1.27 thf(f6,plain,(
% 1.46/1.27 ~((! [X2 : a,X3 : a,X1 : a] : ((($true = (cR @ X1 @ X2)) & ($true = (cR @ X3 @ X2))) => ((cR @ X1 @ X3) = $true)) & ! [X0 : a] : ((cR @ X0 @ X0) = $true)) => ((! [X6 : a,X8 : a,X7 : b] : ((($true = (f @ X6 @ X7)) & ((f @ X8 @ X7) = $true)) => ((cR @ X6 @ X8) = $true)) & ! [X4 : a] : ? [X5 : b] : ((f @ X4 @ X5) = $true) & ! [X10 : a,X11 : b,X9 : b] : ((((f @ X10 @ X11) = $true) & ($true = (f @ X10 @ X9))) => ($true = (cS @ X11 @ X9)))) => ! [X12 : b] : ? [X13 : a] : ! [X14 : a] : ((((f @ X14 @ X12) != $true) & ((cR @ X13 @ z) = $true)) | ((f @ X13 @ X12) = $true))))),
% 1.46/1.27 inference(flattening,[status(thm)],[f5])).
% 1.46/1.27 thf(f5,plain,(
% 1.46/1.27 ~((! [X2 : a,X3 : a,X1 : a] : ((($true = (cR @ X1 @ X2)) & ($true = (cR @ X3 @ X2))) => ((cR @ X1 @ X3) = $true)) & ! [X0 : a] : ((cR @ X0 @ X0) = $true)) => ((! [X6 : a,X8 : a,X7 : b] : ((($true = (f @ X6 @ X7)) & ((f @ X8 @ X7) = $true)) => ((cR @ X6 @ X8) = $true)) & ! [X4 : a] : ? [X5 : b] : ((f @ X4 @ X5) = $true) & ! [X10 : a,X11 : b,X9 : b] : ((((f @ X10 @ X11) = $true) & ($true = (f @ X10 @ X9))) => ($true = (cS @ X11 @ X9)))) => ! [X12 : b] : ? [X13 : a] : ! [X14 : a] : (((f @ X13 @ X12) = $true) | (~((f @ X14 @ X12) = $true) & ((cR @ X13 @ z) = $true)))))),
% 1.46/1.27 inference(fool_elimination,[status(thm)],[f4])).
% 1.46/1.27 thf(f4,plain,(
% 1.46/1.27 ~((! [X0 : a] : (cR @ X0 @ X0) & ! [X1 : a,X2 : a,X3 : a] : (((cR @ X3 @ X2) & (cR @ X1 @ X2)) => (cR @ X1 @ X3))) => ((! [X4 : a] : ? [X5 : b] : (f @ X4 @ X5) & ! [X6 : a,X7 : b,X8 : a] : (((f @ X8 @ X7) & (f @ X6 @ X7)) => (cR @ X6 @ X8)) & ! [X9 : b,X10 : a,X11 : b] : (((f @ X10 @ X9) & (f @ X10 @ X11)) => (cS @ X11 @ X9))) => ! [X12 : b] : ? [X13 : a] : ! [X14 : a] : ((f @ X13 @ X12) | (~(f @ X14 @ X12) & (cR @ X13 @ z)))))),
% 1.46/1.27 inference(rectify,[status(thm)],[f2])).
% 1.46/1.27 thf(f2,negated_conjecture,(
% 1.46/1.27 ~((! [X3 : a] : (cR @ X3 @ X3) & ! [X0 : a,X1 : a,X2 : a] : (((cR @ X2 @ X1) & (cR @ X0 @ X1)) => (cR @ X0 @ X2))) => ((! [X3 : a] : ? [X4 : b] : (f @ X3 @ X4) & ! [X7 : a,X4 : b,X8 : a] : (((f @ X8 @ X4) & (f @ X7 @ X4)) => (cR @ X7 @ X8)) & ! [X6 : b,X3 : a,X5 : b] : (((f @ X3 @ X6) & (f @ X3 @ X5)) => (cS @ X5 @ X6))) => ! [X4 : b] : ? [X3 : a] : ! [X2 : a] : ((f @ X3 @ X4) | (~(f @ X2 @ X4) & (cR @ X3 @ z)))))),
% 1.46/1.27 inference(negated_conjecture,[status(cth)],[f1])).
% 1.46/1.27 thf(f1,conjecture,(
% 1.46/1.27 (! [X3 : a] : (cR @ X3 @ X3) & ! [X0 : a,X1 : a,X2 : a] : (((cR @ X2 @ X1) & (cR @ X0 @ X1)) => (cR @ X0 @ X2))) => ((! [X3 : a] : ? [X4 : b] : (f @ X3 @ X4) & ! [X7 : a,X4 : b,X8 : a] : (((f @ X8 @ X4) & (f @ X7 @ X4)) => (cR @ X7 @ X8)) & ! [X6 : b,X3 : a,X5 : b] : (((f @ X3 @ X6) & (f @ X3 @ X5)) => (cS @ X5 @ X6))) => ! [X4 : b] : ? [X3 : a] : ! [X2 : a] : ((f @ X3 @ X4) | (~(f @ X2 @ X4) & (cR @ X3 @ z))))),
% 1.46/1.27 file('/export/starexec/sandbox2/tmp/tmp.sfyibSciBY/DTF2THF_2434.p',cTHM552E_pme)).
% 1.46/1.27 thf(f22,plain,(
% 1.46/1.27 ($true = (f @ (sK2 @ z) @ sK1))),
% 1.46/1.27 inference(trivial_inequality_removal,[status(thm)],[f21])).
% 1.46/1.27 thf(f21,plain,(
% 1.46/1.27 ($true != $true) | ($true = (f @ (sK2 @ z) @ sK1))),
% 1.46/1.27 inference(superposition,[status(thm)],[f16,f19])).
% 1.46/1.27 thf(f19,plain,(
% 1.46/1.27 ( ! [X3 : a] : (((cR @ X3 @ X3) = $true)) )),
% 1.46/1.27 inference(cnf_transformation,[status(thm)],[f13])).
% 1.46/1.27 thf(f16,plain,(
% 1.46/1.27 ( ! [X10 : a] : (((cR @ X10 @ z) != $true) | ((f @ (sK2 @ X10) @ sK1) = $true)) )),
% 1.46/1.27 inference(cnf_transformation,[status(thm)],[f13])).
% 1.46/1.27 % SZS output end Proof for DTF2THF_2434
% 1.46/1.27 % (2713)------------------------------
% 1.46/1.27 % (2713)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.27 % (2713)Termination reason: Refutation
% 1.46/1.27
% 1.46/1.27 % (2713)Memory used [KB]: 5500
% 1.46/1.27 % (2713)Time elapsed: 0.003 s
% 1.46/1.27 % (2713)Instructions burned: 2 (million)
% 1.46/1.27 % (2713)------------------------------
% 1.46/1.27 % (2713)------------------------------
% 1.46/1.27 % (2706)Success in time 0.013 s
%------------------------------------------------------------------------------