%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV097^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n008.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 1.66s 1.46s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 346 ( 101 equ; 0 cnn)
% Maximal formula atoms : 14 ( 21 avg)
% Number of connectives : 468 ( 51 ~; 37 |; 63 &; 289 @)
% ( 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 : 11 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 143 ( 0 ^; 119 !; 24 ?; 143 :)
% 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_7,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_10,type,
sK0: a ).
thf(func_def_11,type,
sK1: b > a ).
thf(func_def_12,type,
sK2: a > b ).
thf(f30,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f29]) ).
thf(f29,plain,
$true != $true,
inference(superposition,[status(thm)],[f16,f14]) ).
thf(f14,plain,
! [X13: a] :
( $true
= ( f @ X13 @ ( sK2 @ X13 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ! [X0: a] :
( $true
= ( cR @ X0 @ X0 ) )
& ! [X1: b,X2: a,X3: b] :
( ( $true
!= ( f @ X2 @ X1 ) )
| ( $true
= ( cS @ X3 @ X1 ) )
| ( $true
!= ( f @ X2 @ X3 ) ) )
& ! [X4: a,X5: a,X6: a] :
( ( $true
= ( cR @ X4 @ X6 ) )
| ( $true
!= ( cR @ X6 @ X5 ) )
| ( $true
!= ( cR @ X4 @ X5 ) ) )
& ! [X7: b,X8: a,X9: a] :
( ( $true
!= ( f @ X9 @ X7 ) )
| ( ( f @ X8 @ X7 )
!= $true )
| ( $true
= ( cR @ X9 @ X8 ) ) )
& ! [X11: b] :
( ( $true
!= ( f @ sK0 @ X11 ) )
& ( ( $true
= ( f @ ( sK1 @ X11 ) @ X11 ) )
| ( $true
!= ( cR @ sK0 @ z ) ) ) )
& ! [X13: a] :
( $true
= ( f @ X13 @ ( sK2 @ X13 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f9,f12,f11,f10]) ).
thf(f10,plain,
( ? [X10: a] :
! [X11: b] :
? [X12: a] :
( ( $true
!= ( f @ X10 @ X11 ) )
& ( ( $true
= ( f @ X12 @ X11 ) )
| ( $true
!= ( cR @ X10 @ z ) ) ) )
=> ! [X11: b] :
? [X12: a] :
( ( $true
!= ( f @ sK0 @ X11 ) )
& ( ( $true
= ( f @ X12 @ X11 ) )
| ( $true
!= ( cR @ sK0 @ z ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
! [X11: b] :
( ? [X12: a] :
( ( $true
!= ( f @ sK0 @ X11 ) )
& ( ( $true
= ( f @ X12 @ X11 ) )
| ( $true
!= ( cR @ sK0 @ z ) ) ) )
=> ( ( $true
!= ( f @ sK0 @ X11 ) )
& ( ( $true
= ( f @ ( sK1 @ X11 ) @ X11 ) )
| ( $true
!= ( cR @ sK0 @ z ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
! [X13: a] :
( ? [X14: b] :
( $true
= ( f @ X13 @ X14 ) )
=> ( $true
= ( f @ X13 @ ( sK2 @ X13 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ! [X0: a] :
( $true
= ( cR @ X0 @ X0 ) )
& ! [X1: b,X2: a,X3: b] :
( ( $true
!= ( f @ X2 @ X1 ) )
| ( $true
= ( cS @ X3 @ X1 ) )
| ( $true
!= ( f @ X2 @ X3 ) ) )
& ! [X4: a,X5: a,X6: a] :
( ( $true
= ( cR @ X4 @ X6 ) )
| ( $true
!= ( cR @ X6 @ X5 ) )
| ( $true
!= ( cR @ X4 @ X5 ) ) )
& ! [X7: b,X8: a,X9: a] :
( ( $true
!= ( f @ X9 @ X7 ) )
| ( ( f @ X8 @ X7 )
!= $true )
| ( $true
= ( cR @ X9 @ X8 ) ) )
& ? [X10: a] :
! [X11: b] :
? [X12: a] :
( ( $true
!= ( f @ X10 @ X11 ) )
& ( ( $true
= ( f @ X12 @ X11 ) )
| ( $true
!= ( cR @ X10 @ z ) ) ) )
& ! [X13: a] :
? [X14: b] :
( $true
= ( f @ X13 @ X14 ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
( ! [X0: a] :
( $true
= ( cR @ X0 @ X0 ) )
& ! [X6: b,X4: a,X5: b] :
( ( $true
!= ( f @ X4 @ X6 ) )
| ( ( cS @ X5 @ X6 )
= $true )
| ( $true
!= ( f @ X4 @ X5 ) ) )
& ! [X1: a,X3: a,X2: a] :
( ( $true
= ( cR @ X1 @ X2 ) )
| ( $true
!= ( cR @ X2 @ X3 ) )
| ( $true
!= ( cR @ X1 @ X3 ) ) )
& ! [X9: b,X11: a,X10: a] :
( ( $true
!= ( f @ X10 @ X9 ) )
| ( $true
!= ( f @ X11 @ X9 ) )
| ( $true
= ( cR @ X10 @ X11 ) ) )
& ? [X12: a] :
! [X13: b] :
? [X14: a] :
( ( $true
!= ( f @ X12 @ X13 ) )
& ( ( $true
= ( f @ X14 @ X13 ) )
| ( $true
!= ( cR @ X12 @ z ) ) ) )
& ! [X7: a] :
? [X8: b] :
( $true
= ( f @ X7 @ X8 ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
( ? [X12: a] :
! [X13: b] :
? [X14: a] :
( ( $true
!= ( f @ X12 @ X13 ) )
& ( ( $true
= ( f @ X14 @ X13 ) )
| ( $true
!= ( cR @ X12 @ z ) ) ) )
& ! [X7: a] :
? [X8: b] :
( $true
= ( f @ X7 @ X8 ) )
& ! [X9: b,X11: a,X10: a] :
( ( $true
= ( cR @ X10 @ X11 ) )
| ( $true
!= ( f @ X11 @ X9 ) )
| ( $true
!= ( f @ X10 @ X9 ) ) )
& ! [X5: b,X4: a,X6: b] :
( ( ( cS @ X5 @ X6 )
= $true )
| ( $true
!= ( f @ X4 @ X5 ) )
| ( $true
!= ( f @ X4 @ X6 ) ) )
& ! [X0: a] :
( $true
= ( cR @ X0 @ X0 ) )
& ! [X3: a,X2: a,X1: a] :
( ( $true
= ( cR @ X1 @ X2 ) )
| ( $true
!= ( cR @ X1 @ X3 ) )
| ( $true
!= ( cR @ X2 @ X3 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ( ! [X0: a] :
( $true
= ( cR @ X0 @ X0 ) )
& ! [X3: a,X2: a,X1: a] :
( ( ( $true
= ( cR @ X1 @ X3 ) )
& ( $true
= ( cR @ X2 @ X3 ) ) )
=> ( $true
= ( cR @ X1 @ X2 ) ) ) )
=> ( ( ! [X7: a] :
? [X8: b] :
( $true
= ( f @ X7 @ X8 ) )
& ! [X9: b,X11: a,X10: a] :
( ( ( $true
= ( f @ X11 @ X9 ) )
& ( $true
= ( f @ X10 @ X9 ) ) )
=> ( $true
= ( cR @ X10 @ X11 ) ) )
& ! [X5: b,X4: a,X6: b] :
( ( ( $true
= ( f @ X4 @ X5 ) )
& ( $true
= ( f @ X4 @ X6 ) ) )
=> ( ( cS @ X5 @ X6 )
= $true ) ) )
=> ! [X12: a] :
? [X13: b] :
! [X14: a] :
( ( $true
= ( f @ X12 @ X13 ) )
| ( ( $true
!= ( f @ X14 @ X13 ) )
& ( $true
= ( cR @ X12 @ z ) ) ) ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X0: a] :
( $true
= ( cR @ X0 @ X0 ) )
& ! [X3: a,X2: a,X1: a] :
( ( ( $true
= ( cR @ X1 @ X3 ) )
& ( $true
= ( cR @ X2 @ X3 ) ) )
=> ( $true
= ( cR @ X1 @ X2 ) ) ) )
=> ( ( ! [X7: a] :
? [X8: b] :
( $true
= ( f @ X7 @ X8 ) )
& ! [X9: b,X11: a,X10: a] :
( ( ( $true
= ( f @ X11 @ X9 ) )
& ( $true
= ( f @ X10 @ X9 ) ) )
=> ( $true
= ( cR @ X10 @ X11 ) ) )
& ! [X5: b,X4: a,X6: b] :
( ( ( $true
= ( f @ X4 @ X5 ) )
& ( $true
= ( f @ X4 @ X6 ) ) )
=> ( ( cS @ X5 @ X6 )
= $true ) ) )
=> ! [X12: a] :
? [X13: b] :
! [X14: a] :
( ( ( $true
!= ( f @ X14 @ X13 ) )
& ( $true
= ( cR @ X12 @ z ) ) )
| ( $true
= ( f @ X12 @ X13 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: a] : ( cR @ X0 @ X0 )
& ! [X1: a,X2: a,X3: a] :
( ( ( cR @ X1 @ X3 )
& ( cR @ X2 @ X3 ) )
=> ( cR @ X1 @ X2 ) ) )
=> ( ( ! [X4: a,X5: b,X6: b] :
( ( ( f @ X4 @ X6 )
& ( f @ X4 @ X5 ) )
=> ( cS @ X5 @ X6 ) )
& ! [X7: a] :
? [X8: b] : ( f @ X7 @ X8 )
& ! [X9: b,X10: a,X11: a] :
( ( ( f @ X10 @ X9 )
& ( f @ X11 @ X9 ) )
=> ( cR @ X10 @ X11 ) ) )
=> ! [X12: a] :
? [X13: b] :
! [X14: a] :
( ( ~ ( f @ X14 @ X13 )
& ( cR @ X12 @ z ) )
| ( f @ X12 @ X13 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X3: a] : ( cR @ X3 @ X3 )
& ! [X0: a,X2: a,X1: a] :
( ( ( cR @ X0 @ X1 )
& ( cR @ X2 @ X1 ) )
=> ( cR @ X0 @ X2 ) ) )
=> ( ( ! [X3: a,X5: b,X6: b] :
( ( ( f @ X3 @ X6 )
& ( f @ X3 @ X5 ) )
=> ( cS @ X5 @ X6 ) )
& ! [X3: a] :
? [X4: b] : ( f @ X3 @ X4 )
& ! [X4: b,X7: a,X8: a] :
( ( ( f @ X7 @ X4 )
& ( f @ X8 @ X4 ) )
=> ( cR @ X7 @ X8 ) ) )
=> ! [X3: a] :
? [X4: b] :
! [X2: a] :
( ( ~ ( f @ X2 @ X4 )
& ( cR @ X3 @ z ) )
| ( f @ X3 @ X4 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X3: a] : ( cR @ X3 @ X3 )
& ! [X0: a,X2: a,X1: a] :
( ( ( cR @ X0 @ X1 )
& ( cR @ X2 @ X1 ) )
=> ( cR @ X0 @ X2 ) ) )
=> ( ( ! [X3: a,X5: b,X6: b] :
( ( ( f @ X3 @ X6 )
& ( f @ X3 @ X5 ) )
=> ( cS @ X5 @ X6 ) )
& ! [X3: a] :
? [X4: b] : ( f @ X3 @ X4 )
& ! [X4: b,X7: a,X8: a] :
( ( ( f @ X7 @ X4 )
& ( f @ X8 @ X4 ) )
=> ( cR @ X7 @ X8 ) ) )
=> ! [X3: a] :
? [X4: b] :
! [X2: a] :
( ( ~ ( f @ X2 @ X4 )
& ( cR @ X3 @ z ) )
| ( f @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.FluTenTuQH/DTF2THF_6289.p',cTHM552C_pme) ).
thf(f16,plain,
! [X11: b] :
( $true
!= ( f @ sK0 @ X11 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV097^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/0.34 % Computer : n008.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Feb 24 12:40:09 EST 2026
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.48 ---- Original DTF file ---
% 0.19/0.48 thf(spec,logic,$$dhol).
% 0.19/0.48 %------------------------------------------------------------------------------
% 0.19/0.48 % File : SEV097^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.48 % Domain : Set Theory (Relations)
% 0.19/0.48 % Problem : TPS problem from RELN-THMS
% 0.19/0.48 % Version : Especial.
% 0.19/0.48 % English :
% 0.19/0.48
% 0.19/0.48 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.48 % Source : [Bro09]
% 0.19/0.48 % Names : tps_1073 [Bro09]
% 0.19/0.48
% 0.19/0.48 % Status : Theorem
% 0.19/0.48 % Rating : 0.00 v6.2.0, 0.17 v6.0.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.19/0.48 % Syntax : Number of formulae : 7 ( 0 unt; 6 typ; 0 def)
% 0.19/0.48 % Number of atoms : 14 ( 0 equ; 0 cnn)
% 0.19/0.48 % Maximal formula atoms : 14 ( 14 avg)
% 0.19/0.48 % Number of connectives : 42 ( 1 ~; 1 |; 7 &; 28 @)
% 0.19/0.48 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.19/0.48 % Maximal formula depth : 12 ( 12 avg)
% 0.19/0.48 % Number of types : 3 ( 2 usr)
% 0.19/0.48 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.19/0.48 % Number of symbols : 4 ( 4 usr; 1 con; 0-2 aty)
% 0.19/0.48 % Number of variables : 15 ( 0 ^; 13 !; 2 ?; 15 :)
% 0.19/0.48 % SPC : TH0_THM_NEQ_NAR
% 0.19/0.48
% 0.19/0.48 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.48 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.48 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.48 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.48 %------------------------------------------------------------------------------
% 0.19/0.48 thf(a_type,type,
% 0.19/0.48 a: $tType ).
% 0.19/0.48
% 0.19/0.48 thf(b_type,type,
% 0.19/0.48 b: $tType ).
% 0.19/0.48
% 0.19/0.48 thf(z,type,
% 0.19/0.48 z: a ).
% 0.19/0.48
% 0.19/0.48 thf(cR,type,
% 0.19/0.48 cR: a > a > $o ).
% 0.19/0.48
% 0.19/0.48 thf(f,type,
% 0.19/0.48 f: a > b > $o ).
% 0.19/0.48
% 0.19/0.48 thf(cS,type,
% 0.19/0.48 cS: b > b > $o ).
% 0.19/0.48
% 0.19/0.48 thf(cTHM552C_pme,conjecture,
% 0.19/0.48 ( ( ! [Xu: a,Xv: a,Xw: a] :
% 0.19/0.48 ( ( ( cR @ Xu @ Xv )
% 0.19/0.48 & ( cR @ Xw @ Xv ) )
% 0.19/0.48 => ( cR @ Xu @ Xw ) )
% 0.19/0.48 & ! [Xx: a] : ( cR @ Xx @ Xx ) )
% 0.19/0.48 => ( ( ! [Xx: a] :
% 0.19/0.48 ? [Xy: b] : ( f @ Xx @ Xy )
% 0.19/0.48 & ! [Xx: a,Xy1: b,Xy2: b] :
% 0.19/0.48 ( ( ( f @ Xx @ Xy1 )
% 0.19/0.48 & ( f @ Xx @ Xy2 ) )
% 0.19/0.48 => ( cS @ Xy1 @ Xy2 ) )
% 0.19/0.48 & ! [Xx1: a,Xx2: a,Xy: b] :
% 0.19/0.48 ( ( ( f @ Xx1 @ Xy )
% 0.19/0.48 & ( f @ Xx2 @ Xy ) )
% 0.19/0.48 => ( cR @ Xx1 @ Xx2 ) ) )
% 0.19/0.48 => ! [Xx: a] :
% 0.19/0.48 ? [Xy: b] :
% 0.19/0.48 ! [Xw: a] :
% 0.19/0.48 ( ( f @ Xx @ Xy )
% 0.19/0.48 | ( ~ ( f @ Xw @ Xy )
% 0.19/0.48 & ( cR @ Xx @ z ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 %------------------------------------------------------------------------------
% 0.19/0.48 ------------------------
% 1.66/1.43 ---- Embedded in THF ---
% 1.66/1.43 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.66/1.43 %%% Generated on Tue Feb 24 12:40:10 EST 2026
% 1.66/1.43 %%% using '$$dhol' embedding, version 1.3.0.
% 1.66/1.43 %%% Logic specification used:
% 1.66/1.43 %%% thf(spec, logic, $$dhol).
% 1.66/1.43
% 1.66/1.43 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.FluTenTuQH/DTF2DTF6289.p
% See solution above
% 1.66/1.43 ------------------------
% 1.66/1.44 ---- Cleaned THF ---
% 1.66/1.44 thf(a_type,type,
% 1.66/1.44 a: $tType ).
% 1.66/1.44
% 1.66/1.44 thf(b_type,type,
% 1.66/1.44 b: $tType ).
% 1.66/1.44
% 1.66/1.44 thf(z,type,
% 1.66/1.44 z: a ).
% 1.66/1.44
% 1.66/1.44 thf(cR,type,
% 1.66/1.44 cR: a > a > $o ).
% 1.66/1.44
% 1.66/1.44 thf(f,type,
% 1.66/1.44 f: a > b > $o ).
% 1.66/1.44
% 1.66/1.44 thf(cS,type,
% 1.66/1.44 cS: b > b > $o ).
% 1.66/1.44
% 1.66/1.44 thf(cTHM552C_pme,conjecture,
% 1.66/1.44 ( ( ! [Xu: a,Xv: a,Xw: a] :
% 1.66/1.44 ( ( ( cR @ Xu @ Xv )
% 1.66/1.44 & ( cR @ Xw @ Xv ) )
% 1.66/1.44 => ( cR @ Xu @ Xw ) )
% 1.66/1.44 & ! [Xx: a] : ( cR @ Xx @ Xx ) )
% 1.66/1.44 => ( ( ! [Xx: a] :
% 1.66/1.44 ? [Xy: b] : ( f @ Xx @ Xy )
% 1.66/1.44 & ! [Xx: a,Xy1: b,Xy2: b] :
% 1.66/1.44 ( ( ( f @ Xx @ Xy1 )
% 1.66/1.44 & ( f @ Xx @ Xy2 ) )
% 1.66/1.44 => ( cS @ Xy1 @ Xy2 ) )
% 1.66/1.44 & ! [Xx1: a,Xx2: a,Xy: b] :
% 1.66/1.44 ( ( ( f @ Xx1 @ Xy )
% 1.66/1.44 & ( f @ Xx2 @ Xy ) )
% 1.66/1.44 => ( cR @ Xx1 @ Xx2 ) ) )
% 1.66/1.44 => ! [Xx: a] :
% 1.66/1.44 ? [Xy: b] :
% 1.66/1.44 ! [Xw: a] :
% 1.66/1.44 ( ( f @ Xx @ Xy )
% 1.66/1.44 | ( ~ ( f @ Xw @ Xy )
% 1.66/1.44 & ( cR @ Xx @ z ) ) ) ) ) ).
% 1.66/1.44 ------------------------
% 1.66/1.46 % (6388)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_6289 for (2999ds/4Mi)
% 1.66/1.46 % (6387)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_6289 for (2999ds/183Mi)
% 1.66/1.46 % (6389)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_6289 for (2999ds/27Mi)
% 1.66/1.46 % (6390)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_6289 for (2999ds/2Mi)
% 1.66/1.46 % (6391)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_6289 for (2999ds/2Mi)
% 1.66/1.46 % (6392)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_6289 for (2999ds/275Mi)
% 1.66/1.46 % (6393)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_6289 for (2999ds/18Mi)
% 1.66/1.46 % (6390)Instruction limit reached!
% 1.66/1.46 % (6390)------------------------------
% 1.66/1.46 % (6390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.46 % (6390)Termination reason: Unknown
% 1.66/1.46 % (6391)Instruction limit reached!
% 1.66/1.46 % (6391)------------------------------
% 1.66/1.46 % (6391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.46 % (6390)Termination phase: Saturation
% 1.66/1.46
% 1.66/1.46 % (6390)Memory used [KB]: 5500
% 1.66/1.46 % (6390)Time elapsed: 0.003 s
% 1.66/1.46 % (6390)Instructions burned: 3 (million)
% 1.66/1.46 % (6390)------------------------------
% 1.66/1.46 % (6390)------------------------------
% 1.66/1.46 % (6391)Termination reason: Unknown
% 1.66/1.46 % (6391)Termination phase: Saturation
% 1.66/1.46
% 1.66/1.46 % (6391)Memory used [KB]: 5500
% 1.66/1.46 % (6391)Time elapsed: 0.003 s
% 1.66/1.46 % (6391)Instructions burned: 3 (million)
% 1.66/1.46 % (6391)------------------------------
% 1.66/1.46 % (6391)------------------------------
% 1.66/1.46 % (6389)First to succeed.
% 1.66/1.46 % (6388)Instruction limit reached!
% 1.66/1.46 % (6388)------------------------------
% 1.66/1.46 % (6388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.46 % (6388)Termination reason: Unknown
% 1.66/1.46 % (6388)Termination phase: Saturation
% 1.66/1.46
% 1.66/1.46 % (6388)Memory used [KB]: 5500
% 1.66/1.46 % (6388)Time elapsed: 0.004 s
% 1.66/1.46 % (6388)Instructions burned: 4 (million)
% 1.66/1.46 % (6388)------------------------------
% 1.66/1.46 % (6388)------------------------------
% 1.66/1.46 % (6392)Also succeeded, but the first one will report.
% 1.66/1.46 % (6387)Also succeeded, but the first one will report.
% 1.66/1.46 % (6389)Refutation found. Thanks to Tanya!
% 1.66/1.46 % SZS status Theorem for DTF2THF_6289
% 1.66/1.46 % SZS output start Proof for DTF2THF_6289
% 1.66/1.46 thf(type_def_5, type, a: $tType).
% 1.66/1.46 thf(type_def_7, type, b: $tType).
% 1.66/1.46 thf(func_def_0, type, a: $tType).
% 1.66/1.46 thf(func_def_1, type, b: $tType).
% 1.66/1.46 thf(func_def_2, type, z: a).
% 1.66/1.46 thf(func_def_3, type, cR: a > a > $o).
% 1.66/1.46 thf(func_def_4, type, f: a > b > $o).
% 1.66/1.46 thf(func_def_5, type, cS: b > b > $o).
% 1.66/1.46 thf(func_def_7, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.66/1.46 thf(func_def_10, type, sK0: a).
% 1.66/1.46 thf(func_def_11, type, sK1: b > a).
% 1.66/1.46 thf(func_def_12, type, sK2: a > b).
% 1.66/1.46 thf(f30,plain,(
% 1.66/1.46 $false),
% 1.66/1.46 inference(trivial_inequality_removal,[status(thm)],[f29])).
% 1.66/1.46 thf(f29,plain,(
% 1.66/1.46 ($true != $true)),
% 1.66/1.46 inference(superposition,[status(thm)],[f16,f14])).
% 1.66/1.46 thf(f14,plain,(
% 1.66/1.46 ( ! [X13 : a] : (($true = (f @ X13 @ (sK2 @ X13)))) )),
% 1.66/1.46 inference(cnf_transformation,[status(thm)],[f13])).
% 1.66/1.46 thf(f13,plain,(
% 1.66/1.46 ! [X0 : a] : ($true = (cR @ X0 @ X0)) & ! [X1 : b,X2 : a,X3 : b] : (($true != (f @ X2 @ X1)) | ($true = (cS @ X3 @ X1)) | ($true != (f @ X2 @ X3))) & ! [X4 : a,X5 : a,X6 : a] : (($true = (cR @ X4 @ X6)) | ($true != (cR @ X6 @ X5)) | ($true != (cR @ X4 @ X5))) & ! [X7 : b,X8 : a,X9 : a] : (($true != (f @ X9 @ X7)) | ((f @ X8 @ X7) != $true) | ($true = (cR @ X9 @ X8))) & ! [X11 : b] : (($true != (f @ sK0 @ X11)) & (($true = (f @ (sK1 @ X11) @ X11)) | ($true != (cR @ sK0 @ z)))) & ! [X13 : a] : ($true = (f @ X13 @ (sK2 @ X13)))),
% 1.66/1.46 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f9,f12,f11,f10])).
% 1.66/1.46 thf(f10,plain,(
% 1.66/1.46 ? [X10 : a] : ! [X11 : b] : ? [X12 : a] : (($true != (f @ X10 @ X11)) & (($true = (f @ X12 @ X11)) | ($true != (cR @ X10 @ z)))) => ! [X11 : b] : ? [X12 : a] : (($true != (f @ sK0 @ X11)) & (($true = (f @ X12 @ X11)) | ($true != (cR @ sK0 @ z))))),
% 1.66/1.46 introduced(definition,[],[choice_axiom])).
% 1.66/1.46 thf(f11,plain,(
% 1.66/1.46 ! [X11 : b] : (? [X12 : a] : (($true != (f @ sK0 @ X11)) & (($true = (f @ X12 @ X11)) | ($true != (cR @ sK0 @ z)))) => (($true != (f @ sK0 @ X11)) & (($true = (f @ (sK1 @ X11) @ X11)) | ($true != (cR @ sK0 @ z)))))),
% 1.66/1.46 introduced(definition,[],[choice_axiom])).
% 1.66/1.46 thf(f12,plain,(
% 1.66/1.46 ! [X13 : a] : (? [X14 : b] : ($true = (f @ X13 @ X14)) => ($true = (f @ X13 @ (sK2 @ X13))))),
% 1.66/1.46 introduced(definition,[],[choice_axiom])).
% 1.66/1.46 thf(f9,plain,(
% 1.66/1.46 ! [X0 : a] : ($true = (cR @ X0 @ X0)) & ! [X1 : b,X2 : a,X3 : b] : (($true != (f @ X2 @ X1)) | ($true = (cS @ X3 @ X1)) | ($true != (f @ X2 @ X3))) & ! [X4 : a,X5 : a,X6 : a] : (($true = (cR @ X4 @ X6)) | ($true != (cR @ X6 @ X5)) | ($true != (cR @ X4 @ X5))) & ! [X7 : b,X8 : a,X9 : a] : (($true != (f @ X9 @ X7)) | ((f @ X8 @ X7) != $true) | ($true = (cR @ X9 @ X8))) & ? [X10 : a] : ! [X11 : b] : ? [X12 : a] : (($true != (f @ X10 @ X11)) & (($true = (f @ X12 @ X11)) | ($true != (cR @ X10 @ z)))) & ! [X13 : a] : ? [X14 : b] : ($true = (f @ X13 @ X14))),
% 1.66/1.46 inference(rectify,[status(thm)],[f8])).
% 1.66/1.46 thf(f8,plain,(
% 1.66/1.46 ! [X0 : a] : ($true = (cR @ X0 @ X0)) & ! [X6 : b,X4 : a,X5 : b] : (($true != (f @ X4 @ X6)) | ((cS @ X5 @ X6) = $true) | ($true != (f @ X4 @ X5))) & ! [X1 : a,X3 : a,X2 : a] : (($true = (cR @ X1 @ X2)) | ($true != (cR @ X2 @ X3)) | ($true != (cR @ X1 @ X3))) & ! [X9 : b,X11 : a,X10 : a] : (($true != (f @ X10 @ X9)) | ($true != (f @ X11 @ X9)) | ($true = (cR @ X10 @ X11))) & ? [X12 : a] : ! [X13 : b] : ? [X14 : a] : (($true != (f @ X12 @ X13)) & (($true = (f @ X14 @ X13)) | ($true != (cR @ X12 @ z)))) & ! [X7 : a] : ? [X8 : b] : ($true = (f @ X7 @ X8))),
% 1.66/1.46 inference(flattening,[status(thm)],[f7])).
% 1.66/1.46 thf(f7,plain,(
% 1.66/1.46 (? [X12 : a] : ! [X13 : b] : ? [X14 : a] : (($true != (f @ X12 @ X13)) & (($true = (f @ X14 @ X13)) | ($true != (cR @ X12 @ z)))) & (! [X7 : a] : ? [X8 : b] : ($true = (f @ X7 @ X8)) & ! [X9 : b,X11 : a,X10 : a] : (($true = (cR @ X10 @ X11)) | (($true != (f @ X11 @ X9)) | ($true != (f @ X10 @ X9)))) & ! [X5 : b,X4 : a,X6 : b] : (((cS @ X5 @ X6) = $true) | (($true != (f @ X4 @ X5)) | ($true != (f @ X4 @ X6)))))) & (! [X0 : a] : ($true = (cR @ X0 @ X0)) & ! [X3 : a,X2 : a,X1 : a] : (($true = (cR @ X1 @ X2)) | (($true != (cR @ X1 @ X3)) | ($true != (cR @ X2 @ X3)))))),
% 1.66/1.46 inference(ennf_transformation,[status(thm)],[f6])).
% 1.66/1.46 thf(f6,plain,(
% 1.66/1.46 ~((! [X0 : a] : ($true = (cR @ X0 @ X0)) & ! [X3 : a,X2 : a,X1 : a] : ((($true = (cR @ X1 @ X3)) & ($true = (cR @ X2 @ X3))) => ($true = (cR @ X1 @ X2)))) => ((! [X7 : a] : ? [X8 : b] : ($true = (f @ X7 @ X8)) & ! [X9 : b,X11 : a,X10 : a] : ((($true = (f @ X11 @ X9)) & ($true = (f @ X10 @ X9))) => ($true = (cR @ X10 @ X11))) & ! [X5 : b,X4 : a,X6 : b] : ((($true = (f @ X4 @ X5)) & ($true = (f @ X4 @ X6))) => ((cS @ X5 @ X6) = $true))) => ! [X12 : a] : ? [X13 : b] : ! [X14 : a] : (($true = (f @ X12 @ X13)) | (($true != (f @ X14 @ X13)) & ($true = (cR @ X12 @ z))))))),
% 1.66/1.46 inference(flattening,[status(thm)],[f5])).
% 1.66/1.46 thf(f5,plain,(
% 1.66/1.46 ~((! [X0 : a] : ($true = (cR @ X0 @ X0)) & ! [X3 : a,X2 : a,X1 : a] : ((($true = (cR @ X1 @ X3)) & ($true = (cR @ X2 @ X3))) => ($true = (cR @ X1 @ X2)))) => ((! [X7 : a] : ? [X8 : b] : ($true = (f @ X7 @ X8)) & ! [X9 : b,X11 : a,X10 : a] : ((($true = (f @ X11 @ X9)) & ($true = (f @ X10 @ X9))) => ($true = (cR @ X10 @ X11))) & ! [X5 : b,X4 : a,X6 : b] : ((($true = (f @ X4 @ X5)) & ($true = (f @ X4 @ X6))) => ((cS @ X5 @ X6) = $true))) => ! [X12 : a] : ? [X13 : b] : ! [X14 : a] : ((~($true = (f @ X14 @ X13)) & ($true = (cR @ X12 @ z))) | ($true = (f @ X12 @ X13)))))),
% 1.66/1.46 inference(fool_elimination,[status(thm)],[f4])).
% 1.66/1.46 thf(f4,plain,(
% 1.66/1.46 ~((! [X0 : a] : (cR @ X0 @ X0) & ! [X1 : a,X2 : a,X3 : a] : (((cR @ X1 @ X3) & (cR @ X2 @ X3)) => (cR @ X1 @ X2))) => ((! [X4 : a,X5 : b,X6 : b] : (((f @ X4 @ X6) & (f @ X4 @ X5)) => (cS @ X5 @ X6)) & ! [X7 : a] : ? [X8 : b] : (f @ X7 @ X8) & ! [X9 : b,X10 : a,X11 : a] : (((f @ X10 @ X9) & (f @ X11 @ X9)) => (cR @ X10 @ X11))) => ! [X12 : a] : ? [X13 : b] : ! [X14 : a] : ((~(f @ X14 @ X13) & (cR @ X12 @ z)) | (f @ X12 @ X13))))),
% 1.66/1.46 inference(rectify,[status(thm)],[f2])).
% 1.66/1.46 thf(f2,negated_conjecture,(
% 1.66/1.46 ~((! [X3 : a] : (cR @ X3 @ X3) & ! [X0 : a,X2 : a,X1 : a] : (((cR @ X0 @ X1) & (cR @ X2 @ X1)) => (cR @ X0 @ X2))) => ((! [X3 : a,X5 : b,X6 : b] : (((f @ X3 @ X6) & (f @ X3 @ X5)) => (cS @ X5 @ X6)) & ! [X3 : a] : ? [X4 : b] : (f @ X3 @ X4) & ! [X4 : b,X7 : a,X8 : a] : (((f @ X7 @ X4) & (f @ X8 @ X4)) => (cR @ X7 @ X8))) => ! [X3 : a] : ? [X4 : b] : ! [X2 : a] : ((~(f @ X2 @ X4) & (cR @ X3 @ z)) | (f @ X3 @ X4))))),
% 1.66/1.46 inference(negated_conjecture,[status(cth)],[f1])).
% 1.66/1.46 thf(f1,conjecture,(
% 1.66/1.46 (! [X3 : a] : (cR @ X3 @ X3) & ! [X0 : a,X2 : a,X1 : a] : (((cR @ X0 @ X1) & (cR @ X2 @ X1)) => (cR @ X0 @ X2))) => ((! [X3 : a,X5 : b,X6 : b] : (((f @ X3 @ X6) & (f @ X3 @ X5)) => (cS @ X5 @ X6)) & ! [X3 : a] : ? [X4 : b] : (f @ X3 @ X4) & ! [X4 : b,X7 : a,X8 : a] : (((f @ X7 @ X4) & (f @ X8 @ X4)) => (cR @ X7 @ X8))) => ! [X3 : a] : ? [X4 : b] : ! [X2 : a] : ((~(f @ X2 @ X4) & (cR @ X3 @ z)) | (f @ X3 @ X4)))),
% 1.66/1.46 file('/export/starexec/sandbox/tmp/tmp.FluTenTuQH/DTF2THF_6289.p',cTHM552C_pme)).
% 1.66/1.46 thf(f16,plain,(
% 1.66/1.46 ( ! [X11 : b] : (($true != (f @ sK0 @ X11))) )),
% 1.66/1.46 inference(cnf_transformation,[status(thm)],[f13])).
% 1.66/1.46 % SZS output end Proof for DTF2THF_6289
% 1.66/1.46 % (6389)------------------------------
% 1.66/1.46 % (6389)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.46 % (6389)Termination reason: Refutation
% 1.66/1.46
% 1.66/1.46 % (6389)Memory used [KB]: 5500
% 1.66/1.46 % (6389)Time elapsed: 0.005 s
% 1.66/1.46 % (6389)Instructions burned: 2 (million)
% 1.66/1.46 % (6389)------------------------------
% 1.66/1.46 % (6389)------------------------------
% 1.66/1.46 % (6386)Success in time 0.019 s
%------------------------------------------------------------------------------