%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : CAT042^1 : TPTP v9.2.1. Released v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n005.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 08:40:56 AM UTC 2026
% Result : Theorem 1.86s 1.57s
% Output : Refutation 1.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 237 ( 70 equ; 0 cnn)
% Maximal formula atoms : 12 ( 9 avg)
% Number of connectives : 951 ( 30 ~; 15 |; 31 &; 848 @)
% ( 0 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 9 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 8 con; 0-5 aty)
% Number of variables : 86 ( 0 ^; 66 !; 20 ?; 86 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
obj: $tType ).
thf(type_def_7,type,
mor: $tType ).
thf(func_def_0,type,
isPer:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > $o ) ).
thf(func_def_2,type,
obj: $tType ).
thf(func_def_3,type,
objStar: obj > obj > $o ).
thf(func_def_4,type,
mor: $tType ).
thf(func_def_5,type,
morStar: obj > obj > mor > mor > $o ).
thf(func_def_6,type,
id: obj > mor ).
thf(func_def_7,type,
comp: obj > obj > obj > mor > mor > mor ).
thf(func_def_10,type,
sK0: obj ).
thf(func_def_11,type,
sK1: obj ).
thf(func_def_12,type,
sK2: obj ).
thf(func_def_13,type,
sK3: mor ).
thf(func_def_14,type,
sK4: mor ).
thf(func_def_15,type,
sK5: mor ).
thf(f55,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f54,f45]) ).
thf(f45,plain,
( $true
= ( morStar @ sK0 @ sK2 @ sK5 @ sK5 ) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
thf(f39,plain,
( ( $true
= ( morStar @ sK1 @ sK0 @ sK4 @ sK4 ) )
& ( $true
!= ( morStar @ sK0 @ sK2 @ ( comp @ sK0 @ sK1 @ sK2 @ sK3 @ ( comp @ sK1 @ sK0 @ sK2 @ sK4 @ sK5 ) ) @ ( comp @ sK0 @ sK0 @ sK2 @ ( comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4 ) @ sK5 ) ) )
& ( $true
= ( morStar @ sK0 @ sK2 @ sK5 @ sK5 ) )
& ( $true
= ( morStar @ sK0 @ sK0 @ ( comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4 ) @ ( id @ sK0 ) ) )
& ( $true
= ( morStar @ sK0 @ sK1 @ sK3 @ sK3 ) )
& ( $true
= ( morStar @ sK0 @ sK1 @ ( comp @ sK1 @ sK0 @ sK1 @ sK4 @ sK3 ) @ ( id @ sK1 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f31,f38,f37]) ).
thf(f37,plain,
( ? [X0: obj,X1: obj,X2: obj,X3: mor,X4: mor] :
( ( $true
= ( morStar @ X1 @ X0 @ X4 @ X4 ) )
& ? [X5: mor] :
( ( $true
!= ( morStar @ X0 @ X2 @ ( comp @ X0 @ X1 @ X2 @ X3 @ ( comp @ X1 @ X0 @ X2 @ X4 @ X5 ) ) @ ( comp @ X0 @ X0 @ X2 @ ( comp @ X0 @ X1 @ X0 @ X3 @ X4 ) @ X5 ) ) )
& ( $true
= ( morStar @ X0 @ X2 @ X5 @ X5 ) ) )
& ( $true
= ( morStar @ X0 @ X0 @ ( comp @ X0 @ X1 @ X0 @ X3 @ X4 ) @ ( id @ X0 ) ) )
& ( $true
= ( morStar @ X0 @ X1 @ X3 @ X3 ) )
& ( $true
= ( morStar @ X0 @ X1 @ ( comp @ X1 @ X0 @ X1 @ X4 @ X3 ) @ ( id @ X1 ) ) ) )
=> ( ( $true
= ( morStar @ sK1 @ sK0 @ sK4 @ sK4 ) )
& ? [X5: mor] :
( ( $true
!= ( morStar @ sK0 @ sK2 @ ( comp @ sK0 @ sK1 @ sK2 @ sK3 @ ( comp @ sK1 @ sK0 @ sK2 @ sK4 @ X5 ) ) @ ( comp @ sK0 @ sK0 @ sK2 @ ( comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4 ) @ X5 ) ) )
& ( $true
= ( morStar @ sK0 @ sK2 @ X5 @ X5 ) ) )
& ( $true
= ( morStar @ sK0 @ sK0 @ ( comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4 ) @ ( id @ sK0 ) ) )
& ( $true
= ( morStar @ sK0 @ sK1 @ sK3 @ sK3 ) )
& ( $true
= ( morStar @ sK0 @ sK1 @ ( comp @ sK1 @ sK0 @ sK1 @ sK4 @ sK3 ) @ ( id @ sK1 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f38,plain,
( ? [X5: mor] :
( ( $true
!= ( morStar @ sK0 @ sK2 @ ( comp @ sK0 @ sK1 @ sK2 @ sK3 @ ( comp @ sK1 @ sK0 @ sK2 @ sK4 @ X5 ) ) @ ( comp @ sK0 @ sK0 @ sK2 @ ( comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4 ) @ X5 ) ) )
& ( $true
= ( morStar @ sK0 @ sK2 @ X5 @ X5 ) ) )
=> ( ( $true
!= ( morStar @ sK0 @ sK2 @ ( comp @ sK0 @ sK1 @ sK2 @ sK3 @ ( comp @ sK1 @ sK0 @ sK2 @ sK4 @ sK5 ) ) @ ( comp @ sK0 @ sK0 @ sK2 @ ( comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4 ) @ sK5 ) ) )
& ( $true
= ( morStar @ sK0 @ sK2 @ sK5 @ sK5 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f31,plain,
? [X0: obj,X1: obj,X2: obj,X3: mor,X4: mor] :
( ( $true
= ( morStar @ X1 @ X0 @ X4 @ X4 ) )
& ? [X5: mor] :
( ( $true
!= ( morStar @ X0 @ X2 @ ( comp @ X0 @ X1 @ X2 @ X3 @ ( comp @ X1 @ X0 @ X2 @ X4 @ X5 ) ) @ ( comp @ X0 @ X0 @ X2 @ ( comp @ X0 @ X1 @ X0 @ X3 @ X4 ) @ X5 ) ) )
& ( $true
= ( morStar @ X0 @ X2 @ X5 @ X5 ) ) )
& ( $true
= ( morStar @ X0 @ X0 @ ( comp @ X0 @ X1 @ X0 @ X3 @ X4 ) @ ( id @ X0 ) ) )
& ( $true
= ( morStar @ X0 @ X1 @ X3 @ X3 ) )
& ( $true
= ( morStar @ X0 @ X1 @ ( comp @ X1 @ X0 @ X1 @ X4 @ X3 ) @ ( id @ X1 ) ) ) ),
inference(flattening,[status(thm)],[f30]) ).
thf(f30,plain,
? [X0: obj,X1: obj,X2: obj,X3: mor,X4: mor] :
( ? [X5: mor] :
( ( $true
!= ( morStar @ X0 @ X2 @ ( comp @ X0 @ X1 @ X2 @ X3 @ ( comp @ X1 @ X0 @ X2 @ X4 @ X5 ) ) @ ( comp @ X0 @ X0 @ X2 @ ( comp @ X0 @ X1 @ X0 @ X3 @ X4 ) @ X5 ) ) )
& ( $true
= ( morStar @ X0 @ X2 @ X5 @ X5 ) ) )
& ( $true
= ( morStar @ X0 @ X1 @ ( comp @ X1 @ X0 @ X1 @ X4 @ X3 ) @ ( id @ X1 ) ) )
& ( $true
= ( morStar @ X0 @ X0 @ ( comp @ X0 @ X1 @ X0 @ X3 @ X4 ) @ ( id @ X0 ) ) )
& ( $true
= ( morStar @ X1 @ X0 @ X4 @ X4 ) )
& ( $true
= ( morStar @ X0 @ X1 @ X3 @ X3 ) ) ),
inference(ennf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
~ ! [X0: obj,X1: obj,X2: obj,X3: mor,X4: mor] :
( ( $true
= ( morStar @ X0 @ X1 @ X3 @ X3 ) )
=> ( ( $true
= ( morStar @ X1 @ X0 @ X4 @ X4 ) )
=> ( ( ( $true
= ( morStar @ X0 @ X1 @ ( comp @ X1 @ X0 @ X1 @ X4 @ X3 ) @ ( id @ X1 ) ) )
& ( $true
= ( morStar @ X0 @ X0 @ ( comp @ X0 @ X1 @ X0 @ X3 @ X4 ) @ ( id @ X0 ) ) ) )
=> ! [X5: mor] :
( ( $true
= ( morStar @ X0 @ X2 @ X5 @ X5 ) )
=> ( $true
= ( morStar @ X0 @ X2 @ ( comp @ X0 @ X1 @ X2 @ X3 @ ( comp @ X1 @ X0 @ X2 @ X4 @ X5 ) ) @ ( comp @ X0 @ X0 @ X2 @ ( comp @ X0 @ X1 @ X0 @ X3 @ X4 ) @ X5 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f20]) ).
thf(f20,plain,
~ ! [X0: obj,X1: obj,X2: obj,X3: mor,X4: mor] :
( ( morStar @ X0 @ X1 @ X3 @ X3 )
=> ( ( morStar @ X1 @ X0 @ X4 @ X4 )
=> ( ( ( morStar @ X0 @ X1 @ ( comp @ X1 @ X0 @ X1 @ X4 @ X3 ) @ ( id @ X1 ) )
& ( morStar @ X0 @ X0 @ ( comp @ X0 @ X1 @ X0 @ X3 @ X4 ) @ ( id @ X0 ) ) )
=> ! [X5: mor] :
( ( morStar @ X0 @ X2 @ X5 @ X5 )
=> ( morStar @ X0 @ X2 @ ( comp @ X0 @ X1 @ X2 @ X3 @ ( comp @ X1 @ X0 @ X2 @ X4 @ X5 ) ) @ ( comp @ X0 @ X0 @ X2 @ ( comp @ X0 @ X1 @ X0 @ X3 @ X4 ) @ X5 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,negated_conjecture,
~ ! [X2: obj,X3: obj,X4: obj,X12: mor,X13: mor] :
( ( morStar @ X2 @ X3 @ X12 @ X12 )
=> ( ( morStar @ X3 @ X2 @ X13 @ X13 )
=> ( ( ( morStar @ X2 @ X3 @ ( comp @ X3 @ X2 @ X3 @ X13 @ X12 ) @ ( id @ X3 ) )
& ( morStar @ X2 @ X2 @ ( comp @ X2 @ X3 @ X2 @ X12 @ X13 ) @ ( id @ X2 ) ) )
=> ! [X14: mor] :
( ( morStar @ X2 @ X4 @ X14 @ X14 )
=> ( morStar @ X2 @ X4 @ ( comp @ X2 @ X3 @ X4 @ X12 @ ( comp @ X3 @ X2 @ X4 @ X13 @ X14 ) ) @ ( comp @ X2 @ X2 @ X4 @ ( comp @ X2 @ X3 @ X2 @ X12 @ X13 ) @ X14 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
thf(f9,conjecture,
! [X2: obj,X3: obj,X4: obj,X12: mor,X13: mor] :
( ( morStar @ X2 @ X3 @ X12 @ X12 )
=> ( ( morStar @ X3 @ X2 @ X13 @ X13 )
=> ( ( ( morStar @ X2 @ X3 @ ( comp @ X3 @ X2 @ X3 @ X13 @ X12 ) @ ( id @ X3 ) )
& ( morStar @ X2 @ X2 @ ( comp @ X2 @ X3 @ X2 @ X12 @ X13 ) @ ( id @ X2 ) ) )
=> ! [X14: mor] :
( ( morStar @ X2 @ X4 @ X14 @ X14 )
=> ( morStar @ X2 @ X4 @ ( comp @ X2 @ X3 @ X4 @ X12 @ ( comp @ X3 @ X2 @ X4 @ X13 @ X14 ) ) @ ( comp @ X2 @ X2 @ X4 @ ( comp @ X2 @ X3 @ X2 @ X12 @ X13 ) @ X14 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YAg6pGq6WS/DTF2THF_12437.p',conj) ).
thf(f54,plain,
( $true
!= ( morStar @ sK0 @ sK2 @ sK5 @ sK5 ) ),
inference(subsumption_resolution,[status(thm)],[f53,f43]) ).
thf(f43,plain,
( $true
= ( morStar @ sK0 @ sK1 @ sK3 @ sK3 ) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
thf(f53,plain,
( ( $true
!= ( morStar @ sK0 @ sK1 @ sK3 @ sK3 ) )
| ( $true
!= ( morStar @ sK0 @ sK2 @ sK5 @ sK5 ) ) ),
inference(subsumption_resolution,[status(thm)],[f52,f47]) ).
thf(f47,plain,
( $true
= ( morStar @ sK1 @ sK0 @ sK4 @ sK4 ) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
thf(f52,plain,
( ( $true
!= ( morStar @ sK1 @ sK0 @ sK4 @ sK4 ) )
| ( $true
!= ( morStar @ sK0 @ sK2 @ sK5 @ sK5 ) )
| ( $true
!= ( morStar @ sK0 @ sK1 @ sK3 @ sK3 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f51]) ).
thf(f51,plain,
( ( $true
!= ( morStar @ sK0 @ sK2 @ sK5 @ sK5 ) )
| ( $true
!= ( morStar @ sK0 @ sK1 @ sK3 @ sK3 ) )
| ( $true
!= ( morStar @ sK1 @ sK0 @ sK4 @ sK4 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f46,f50]) ).
thf(f50,plain,
! [X2: obj,X3: obj,X0: obj,X1: obj,X6: mor,X4: mor,X5: mor] :
( ( $true
= ( morStar @ X0 @ X3 @ ( comp @ X0 @ X1 @ X3 @ X4 @ ( comp @ X1 @ X2 @ X3 @ X5 @ X6 ) ) @ ( comp @ X0 @ X2 @ X3 @ ( comp @ X0 @ X1 @ X2 @ X4 @ X5 ) @ X6 ) ) )
| ( $true
!= ( morStar @ X1 @ X2 @ X5 @ X5 ) )
| ( $true
!= ( morStar @ X0 @ X1 @ X4 @ X4 ) )
| ( $true
!= ( morStar @ X2 @ X3 @ X6 @ X6 ) ) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
thf(f34,plain,
! [X0: obj,X1: obj,X2: obj,X3: obj,X4: mor,X5: mor,X6: mor] :
( ( $true
= ( morStar @ X0 @ X3 @ ( comp @ X0 @ X1 @ X3 @ X4 @ ( comp @ X1 @ X2 @ X3 @ X5 @ X6 ) ) @ ( comp @ X0 @ X2 @ X3 @ ( comp @ X0 @ X1 @ X2 @ X4 @ X5 ) @ X6 ) ) )
| ( $true
!= ( morStar @ X0 @ X1 @ X4 @ X4 ) )
| ( $true
!= ( morStar @ X1 @ X2 @ X5 @ X5 ) )
| ( $true
!= ( morStar @ X2 @ X3 @ X6 @ X6 ) ) ),
inference(flattening,[status(thm)],[f33]) ).
thf(f33,plain,
! [X0: obj,X1: obj,X2: obj,X3: obj,X4: mor,X5: mor,X6: mor] :
( ( $true
= ( morStar @ X0 @ X3 @ ( comp @ X0 @ X1 @ X3 @ X4 @ ( comp @ X1 @ X2 @ X3 @ X5 @ X6 ) ) @ ( comp @ X0 @ X2 @ X3 @ ( comp @ X0 @ X1 @ X2 @ X4 @ X5 ) @ X6 ) ) )
| ( $true
!= ( morStar @ X2 @ X3 @ X6 @ X6 ) )
| ( $true
!= ( morStar @ X1 @ X2 @ X5 @ X5 ) )
| ( $true
!= ( morStar @ X0 @ X1 @ X4 @ X4 ) ) ),
inference(ennf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
! [X0: obj,X1: obj,X2: obj,X3: obj,X4: mor,X5: mor,X6: mor] :
( ( $true
= ( morStar @ X0 @ X1 @ X4 @ X4 ) )
=> ( ( $true
= ( morStar @ X1 @ X2 @ X5 @ X5 ) )
=> ( ( $true
= ( morStar @ X2 @ X3 @ X6 @ X6 ) )
=> ( $true
= ( morStar @ X0 @ X3 @ ( comp @ X0 @ X1 @ X3 @ X4 @ ( comp @ X1 @ X2 @ X3 @ X5 @ X6 ) ) @ ( comp @ X0 @ X2 @ X3 @ ( comp @ X0 @ X1 @ X2 @ X4 @ X5 ) @ X6 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f28]) ).
thf(f28,plain,
! [X0: obj,X1: obj,X2: obj,X3: obj,X4: mor,X5: mor,X6: mor] :
( ( morStar @ X0 @ X1 @ X4 @ X4 )
=> ( ( morStar @ X1 @ X2 @ X5 @ X5 )
=> ( ( morStar @ X2 @ X3 @ X6 @ X6 )
=> ( morStar @ X0 @ X3 @ ( comp @ X0 @ X1 @ X3 @ X4 @ ( comp @ X1 @ X2 @ X3 @ X5 @ X6 ) ) @ ( comp @ X0 @ X2 @ X3 @ ( comp @ X0 @ X1 @ X2 @ X4 @ X5 ) @ X6 ) ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,axiom,
! [X2: obj,X3: obj,X4: obj,X0: obj,X12: mor,X13: mor,X14: mor] :
( ( morStar @ X2 @ X3 @ X12 @ X12 )
=> ( ( morStar @ X3 @ X4 @ X13 @ X13 )
=> ( ( morStar @ X4 @ X0 @ X14 @ X14 )
=> ( morStar @ X2 @ X0 @ ( comp @ X2 @ X3 @ X0 @ X12 @ ( comp @ X3 @ X4 @ X0 @ X13 @ X14 ) ) @ ( comp @ X2 @ X4 @ X0 @ ( comp @ X2 @ X3 @ X4 @ X12 @ X13 ) @ X14 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YAg6pGq6WS/DTF2THF_12437.p',ax3) ).
thf(f46,plain,
( $true
!= ( morStar @ sK0 @ sK2 @ ( comp @ sK0 @ sK1 @ sK2 @ sK3 @ ( comp @ sK1 @ sK0 @ sK2 @ sK4 @ sK5 ) ) @ ( comp @ sK0 @ sK0 @ sK2 @ ( comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4 ) @ sK5 ) ) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : CAT042^1 : TPTP v9.2.1. Released v9.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n005.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 04:08:29 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 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 : CAT042^1 : TPTP v9.2.1. Released v9.2.0.
% 0.19/0.48 % Domain : Category Theory
% 0.19/0.48 % Problem : Simple problem from category theory dhol_4
% 0.19/0.48 % Version : Especial.
% 0.19/0.48 % English :
% 0.19/0.48
% 0.19/0.48 % Refs : [RRB23] Rothgang et al. (2023), Theorem Proving in Dependently
% 0.19/0.48 % : [Rot25] Rothgang (2025), Email to Geoff Sutcliffe
% 0.19/0.48 % : [RK+25] Ranalter et al. (2025), The Dependently Typed Higher-O
% 0.19/0.48 % Source : [Rot25]
% 0.19/0.48 % Names : CategoryTheory/category-theory-lemmas-dhol_4.p [Rot25]
% 0.19/0.48
% 0.19/0.48 % Status : Theorem
% 0.19/0.48 % Rating : ? v9.2.0
% 0.19/0.48 % Syntax : Number of formulae : 8 ( 3 unt; 4 typ; 0 def)
% 0.19/0.48 % Number of atoms : 6 ( 6 equ; 0 cnn)
% 0.19/0.48 % Maximal formula atoms : 3 ( 1 avg)
% 0.19/0.48 % Number of connectives : 90 ( 0 ~; 0 |; 1 &; 88 @)
% 0.19/0.48 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.19/0.48 % Maximal formula depth : 8 ( 6 avg)
% 0.19/0.48 % Number of types : 1 ( 1 usr)
% 0.19/0.48 % Number of type decls : 4 ( 0 !>P; 2 !>D)
% 0.19/0.48 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.19/0.48 % Number of symbols : 4 ( 3 usr; 0 con; 1-5 aty)
% 0.19/0.48 % Number of variables : 23 ( 0 ^; 19 !; 0 ?; 23 :)
% 0.19/0.48 % ( 4 !>; 0 ?*; 0 @-; 0 @+)
% 0.19/0.48 % SPC : DH0_THM_EQU_NAR
% 0.19/0.48
% 0.19/0.48 % Comments :
% 0.19/0.48 %------------------------------------------------------------------------------
% 0.19/0.48 thf(obj_type,type,
% 0.19/0.48 obj: $tType ).
% 0.19/0.48
% 0.19/0.48 thf(mor_type,type,
% 0.19/0.48 mor: obj > obj > $tType ).
% 0.19/0.48
% 0.19/0.48 thf(id_type,type,
% 0.19/0.48 id:
% 0.19/0.48 !>[X: obj] : ( mor @ X @ X ) ).
% 0.19/0.48
% 0.19/0.48 thf(comp_type,type,
% 0.19/0.48 comp:
% 0.19/0.48 !>[X: obj,Y: obj,Z: obj] : ( ( mor @ X @ Y ) > ( mor @ Y @ Z ) > ( mor @ X @ Z ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(ax1,axiom,
% 0.19/0.48 ! [X: obj,Y: obj,M: mor @ X @ Y] :
% 0.19/0.48 ( ( comp @ X @ X @ Y @ ( id @ X ) @ M )
% 0.19/0.48 = M ) ).
% 0.19/0.48
% 0.19/0.48 thf(ax2,axiom,
% 0.19/0.48 ! [X: obj,Y: obj,M: mor @ X @ Y] :
% 0.19/0.48 ( ( comp @ X @ Y @ Y @ M @ ( id @ Y ) )
% 0.19/0.48 = M ) ).
% 0.19/0.48
% 0.19/0.48 thf(ax3,axiom,
% 0.19/0.48 ! [X: obj,Y: obj,Z: obj,A: obj,F: mor @ X @ Y,G: mor @ Y @ Z,H: mor @ Z @ A] :
% 0.19/0.48 ( ( comp @ X @ Y @ A @ F @ ( comp @ Y @ Z @ A @ G @ H ) )
% 0.19/0.48 = ( comp @ X @ Z @ A @ ( comp @ X @ Y @ Z @ F @ G ) @ H ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(conj,conjecture,
% 0.19/0.48 ! [X: obj,Y: obj,Z: obj,F: mor @ X @ Y,G: mor @ Y @ X] :
% 0.19/0.48 ( ( ( ( comp @ X @ Y @ X @ F @ G )
% 0.19/0.48 = ( id @ X ) )
% 0.19/0.48 & ( ( comp @ Y @ X @ Y @ G @ F )
% 0.19/0.48 = ( id @ Y ) ) )
% 0.19/0.48 => ! [H: mor @ X @ Z] :
% 0.19/0.48 ( ( comp @ X @ Y @ Z @ F @ ( comp @ Y @ X @ Z @ G @ H ) )
% 0.19/0.48 = ( comp @ X @ X @ Z @ ( comp @ X @ Y @ X @ F @ G ) @ H ) ) ) ).
% 0.19/0.48
% 0.19/0.48 %------------------------------------------------------------------------------
% 0.19/0.48 ------------------------
% 1.86/1.53 ---- Embedded in THF ---
% 1.86/1.53 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.86/1.53 %%% Generated on Tue Feb 24 04:08:30 EST 2026
% 1.86/1.53 %%% using '$$dhol' embedding, version 1.3.0.
% 1.86/1.53 %%% Logic specification used:
% 1.86/1.53 %%% thf(spec, logic, $$dhol).
% 1.86/1.53
% 1.86/1.53 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.YAg6pGq6WS/DTF2DTF12437.p
% See solution above
% 1.86/1.53 ------------------------
% 1.86/1.54 ---- Cleaned THF ---
% 1.86/1.54 thf(is_per_type,type,
% 1.86/1.54 isPer:
% 1.86/1.54 !>[A: $tType] : ( ( A > A > $o ) > $o ) ).
% 1.86/1.54
% 1.86/1.54 thf(is_per,definition,
% 1.86/1.54 ! [A: $tType,AStar: A > A > $o] :
% 1.86/1.54 ( ( isPer @ A @ AStar )
% 1.86/1.54 <=> ( ! [X: A,Y: A] :
% 1.86/1.54 ( ( AStar @ X @ Y )
% 1.86/1.54 => ( AStar @ Y @ X ) )
% 1.86/1.54 & ! [X: A,Y: A,Z: A] :
% 1.86/1.54 ( ( AStar @ X @ Y )
% 1.86/1.54 => ( ( AStar @ Y @ Z )
% 1.86/1.54 => ( AStar @ X @ Z ) ) ) ) ) ).
% 1.86/1.54
% 1.86/1.54 thf(obj_type,type,
% 1.86/1.54 obj: $tType ).
% 1.86/1.54
% 1.86/1.54 thf(objStar,type,
% 1.86/1.54 objStar: obj > obj > $o ).
% 1.86/1.54
% 1.86/1.54 thf(objStar_is_eq,axiom,
% 1.86/1.54 ! [X: obj,Y: obj] :
% 1.86/1.54 ( ( objStar @ X @ Y )
% 1.86/1.54 <=> ( X = Y ) ) ).
% 1.86/1.54
% 1.86/1.54 thf(mor_type,type,
% 1.86/1.54 mor: $tType ).
% 1.86/1.54
% 1.86/1.54 thf(morStar,type,
% 1.86/1.54 morStar: obj > obj > mor > mor > $o ).
% 1.86/1.54
% 1.86/1.54 thf('\'morStar\'_is_per',axiom,
% 1.86/1.54 ! [C: obj,C0: obj] : ( isPer @ mor @ ( morStar @ C @ C0 ) ) ).
% 1.86/1.54
% 1.86/1.54 thf(id_type,type,
% 1.86/1.54 id: obj > mor ).
% 1.86/1.54
% 1.86/1.54 thf(id_tp_ax,axiom,
% 1.86/1.54 ! [X: obj] : ( morStar @ X @ X @ ( id @ X ) @ ( id @ X ) ) ).
% 1.86/1.54
% 1.86/1.54 thf(comp_type,type,
% 1.86/1.54 comp: obj > obj > obj > mor > mor > mor ).
% 1.86/1.54
% 1.86/1.54 thf(comp_tp_ax,axiom,
% 1.86/1.54 ! [X: obj,Y: obj,Z: obj,D: mor,D_prime: mor] :
% 1.86/1.54 ( ( morStar @ X @ Y @ D @ D_prime )
% 1.86/1.54 => ! [D0: mor,D0_prime: mor] :
% 1.86/1.54 ( ( morStar @ Y @ Z @ D0 @ D0_prime )
% 1.86/1.54 => ( morStar @ X @ Z @ ( comp @ X @ Y @ Z @ D @ D0 ) @ ( comp @ X @ Y @ Z @ D_prime @ D0_prime ) ) ) ) ).
% 1.86/1.54
% 1.86/1.54 thf(ax1,axiom,
% 1.86/1.54 ! [X: obj,Y: obj,M: mor] :
% 1.86/1.54 ( ( morStar @ X @ Y @ M @ M )
% 1.86/1.54 => ( morStar @ X @ Y @ ( comp @ X @ X @ Y @ ( id @ X ) @ M ) @ M ) ) ).
% 1.86/1.54
% 1.86/1.54 thf(ax2,axiom,
% 1.86/1.54 ! [X: obj,Y: obj,M: mor] :
% 1.86/1.54 ( ( morStar @ X @ Y @ M @ M )
% 1.86/1.54 => ( morStar @ X @ Y @ ( comp @ X @ Y @ Y @ M @ ( id @ Y ) ) @ M ) ) ).
% 1.86/1.54
% 1.86/1.54 thf(ax3,axiom,
% 1.86/1.54 ! [X: obj,Y: obj,Z: obj,A: obj,F: mor,G: mor,H: mor] :
% 1.86/1.54 ( ( morStar @ X @ Y @ F @ F )
% 1.86/1.54 => ( ( morStar @ Y @ Z @ G @ G )
% 1.86/1.54 => ( ( morStar @ Z @ A @ H @ H )
% 1.86/1.54 => ( morStar @ X @ A @ ( comp @ X @ Y @ A @ F @ ( comp @ Y @ Z @ A @ G @ H ) ) @ ( comp @ X @ Z @ A @ ( comp @ X @ Y @ Z @ F @ G ) @ H ) ) ) ) ) ).
% 1.86/1.54
% 1.86/1.54 thf(conj,conjecture,
% 1.86/1.54 ! [X: obj,Y: obj,Z: obj,F: mor,G: mor] :
% 1.86/1.54 ( ( morStar @ X @ Y @ F @ F )
% 1.86/1.54 => ( ( morStar @ Y @ X @ G @ G )
% 1.86/1.54 => ( ( ( morStar @ X @ X @ ( comp @ X @ Y @ X @ F @ G ) @ ( id @ X ) )
% 1.86/1.54 & ( morStar @ X @ Y @ ( comp @ Y @ X @ Y @ G @ F ) @ ( id @ Y ) ) )
% 1.86/1.54 => ! [H: mor] :
% 1.86/1.54 ( ( morStar @ X @ Z @ H @ H )
% 1.86/1.54 => ( morStar @ X @ Z @ ( comp @ X @ Y @ Z @ F @ ( comp @ Y @ X @ Z @ G @ H ) ) @ ( comp @ X @ X @ Z @ ( comp @ X @ Y @ X @ F @ G ) @ H ) ) ) ) ) ) ).
% 1.86/1.54 ------------------------
% 1.86/1.56 % (12576)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_12437 for (2999ds/2Mi)
% 1.86/1.56 % (12574)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_12437 for (2999ds/4Mi)
% 1.86/1.56 % (12573)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_12437 for (2999ds/183Mi)
% 1.86/1.56 % (12577)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_12437 for (2999ds/2Mi)
% 1.86/1.56 % (12578)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_12437 for (2999ds/275Mi)
% 1.86/1.56 % (12575)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_12437 for (2999ds/27Mi)
% 1.86/1.56 % (12579)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_12437 for (2999ds/18Mi)
% 1.86/1.56 % (12576)Instruction limit reached!
% 1.86/1.56 % (12576)------------------------------
% 1.86/1.56 % (12576)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.86/1.56 % (12576)Termination reason: Unknown
% 1.86/1.56 % (12576)Termination phase: shuffling
% 1.86/1.56
% 1.86/1.56 % (12576)Memory used [KB]: 1023
% 1.86/1.56 % (12576)Time elapsed: 0.003 s
% 1.86/1.56 % (12576)Instructions burned: 2 (million)
% 1.86/1.56 % (12576)------------------------------
% 1.86/1.56 % (12576)------------------------------
% 1.86/1.56 % (12577)Instruction limit reached!
% 1.86/1.56 % (12577)------------------------------
% 1.86/1.56 % (12577)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.86/1.56 % (12577)Termination reason: Unknown
% 1.86/1.56 % (12577)Termination phase: shuffling
% 1.86/1.56
% 1.86/1.56 % (12577)Memory used [KB]: 1023
% 1.86/1.56 % (12577)Time elapsed: 0.003 s
% 1.86/1.56 % (12577)Instructions burned: 2 (million)
% 1.86/1.56 % (12577)------------------------------
% 1.86/1.56 % (12577)------------------------------
% 1.86/1.57 % (12574)Instruction limit reached!
% 1.86/1.57 % (12574)------------------------------
% 1.86/1.57 % (12574)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.86/1.57 % (12574)Termination reason: Unknown
% 1.86/1.57 % (12574)Termination phase: Property scanning
% 1.86/1.57
% 1.86/1.57 % (12574)Memory used [KB]: 1023
% 1.86/1.57 % (12574)Time elapsed: 0.004 s
% 1.86/1.57 % (12574)Instructions burned: 4 (million)
% 1.86/1.57 % (12574)------------------------------
% 1.86/1.57 % (12574)------------------------------
% 1.86/1.57 % (12578)First to succeed.
% 1.86/1.57 % (12578)Refutation found. Thanks to Tanya!
% 1.86/1.57 % SZS status Theorem for DTF2THF_12437
% 1.86/1.57 % SZS output start Proof for DTF2THF_12437
% 1.86/1.57 thf(type_def_6, type, obj: $tType).
% 1.86/1.57 thf(type_def_7, type, mor: $tType).
% 1.86/1.57 thf(func_def_0, type, isPer: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 1.86/1.57 thf(func_def_2, type, obj: $tType).
% 1.86/1.57 thf(func_def_3, type, objStar: obj > obj > $o).
% 1.86/1.57 thf(func_def_4, type, mor: $tType).
% 1.86/1.57 thf(func_def_5, type, morStar: obj > obj > mor > mor > $o).
% 1.86/1.57 thf(func_def_6, type, id: obj > mor).
% 1.86/1.57 thf(func_def_7, type, comp: obj > obj > obj > mor > mor > mor).
% 1.86/1.57 thf(func_def_10, type, sK0: obj).
% 1.86/1.57 thf(func_def_11, type, sK1: obj).
% 1.86/1.57 thf(func_def_12, type, sK2: obj).
% 1.86/1.57 thf(func_def_13, type, sK3: mor).
% 1.86/1.57 thf(func_def_14, type, sK4: mor).
% 1.86/1.57 thf(func_def_15, type, sK5: mor).
% 1.86/1.57 thf(f55,plain,(
% 1.86/1.57 $false),
% 1.86/1.57 inference(subsumption_resolution,[status(thm)],[f54,f45])).
% 1.86/1.57 thf(f45,plain,(
% 1.86/1.57 ($true = (morStar @ sK0 @ sK2 @ sK5 @ sK5))),
% 1.86/1.57 inference(cnf_transformation,[status(thm)],[f39])).
% 1.86/1.57 thf(f39,plain,(
% 1.86/1.57 ($true = (morStar @ sK1 @ sK0 @ sK4 @ sK4)) & (($true != (morStar @ sK0 @ sK2 @ (comp @ sK0 @ sK1 @ sK2 @ sK3 @ (comp @ sK1 @ sK0 @ sK2 @ sK4 @ sK5)) @ (comp @ sK0 @ sK0 @ sK2 @ (comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4) @ sK5))) & ($true = (morStar @ sK0 @ sK2 @ sK5 @ sK5))) & ($true = (morStar @ sK0 @ sK0 @ (comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4) @ (id @ sK0))) & ($true = (morStar @ sK0 @ sK1 @ sK3 @ sK3)) & ($true = (morStar @ sK0 @ sK1 @ (comp @ sK1 @ sK0 @ sK1 @ sK4 @ sK3) @ (id @ sK1)))),
% 1.86/1.57 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f31,f38,f37])).
% 1.86/1.57 thf(f37,plain,(
% 1.86/1.57 ? [X0 : obj,X1 : obj,X2 : obj,X3 : mor,X4 : mor] : (($true = (morStar @ X1 @ X0 @ X4 @ X4)) & ? [X5 : mor] : (($true != (morStar @ X0 @ X2 @ (comp @ X0 @ X1 @ X2 @ X3 @ (comp @ X1 @ X0 @ X2 @ X4 @ X5)) @ (comp @ X0 @ X0 @ X2 @ (comp @ X0 @ X1 @ X0 @ X3 @ X4) @ X5))) & ($true = (morStar @ X0 @ X2 @ X5 @ X5))) & ($true = (morStar @ X0 @ X0 @ (comp @ X0 @ X1 @ X0 @ X3 @ X4) @ (id @ X0))) & ($true = (morStar @ X0 @ X1 @ X3 @ X3)) & ($true = (morStar @ X0 @ X1 @ (comp @ X1 @ X0 @ X1 @ X4 @ X3) @ (id @ X1)))) => (($true = (morStar @ sK1 @ sK0 @ sK4 @ sK4)) & ? [X5 : mor] : (($true != (morStar @ sK0 @ sK2 @ (comp @ sK0 @ sK1 @ sK2 @ sK3 @ (comp @ sK1 @ sK0 @ sK2 @ sK4 @ X5)) @ (comp @ sK0 @ sK0 @ sK2 @ (comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4) @ X5))) & ($true = (morStar @ sK0 @ sK2 @ X5 @ X5))) & ($true = (morStar @ sK0 @ sK0 @ (comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4) @ (id @ sK0))) & ($true = (morStar @ sK0 @ sK1 @ sK3 @ sK3)) & ($true = (morStar @ sK0 @ sK1 @ (comp @ sK1 @ sK0 @ sK1 @ sK4 @ sK3) @ (id @ sK1))))),
% 1.86/1.57 introduced(definition,[],[choice_axiom])).
% 1.86/1.57 thf(f38,plain,(
% 1.86/1.57 ? [X5 : mor] : (($true != (morStar @ sK0 @ sK2 @ (comp @ sK0 @ sK1 @ sK2 @ sK3 @ (comp @ sK1 @ sK0 @ sK2 @ sK4 @ X5)) @ (comp @ sK0 @ sK0 @ sK2 @ (comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4) @ X5))) & ($true = (morStar @ sK0 @ sK2 @ X5 @ X5))) => (($true != (morStar @ sK0 @ sK2 @ (comp @ sK0 @ sK1 @ sK2 @ sK3 @ (comp @ sK1 @ sK0 @ sK2 @ sK4 @ sK5)) @ (comp @ sK0 @ sK0 @ sK2 @ (comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4) @ sK5))) & ($true = (morStar @ sK0 @ sK2 @ sK5 @ sK5)))),
% 1.86/1.57 introduced(definition,[],[choice_axiom])).
% 1.86/1.57 thf(f31,plain,(
% 1.86/1.57 ? [X0 : obj,X1 : obj,X2 : obj,X3 : mor,X4 : mor] : (($true = (morStar @ X1 @ X0 @ X4 @ X4)) & ? [X5 : mor] : (($true != (morStar @ X0 @ X2 @ (comp @ X0 @ X1 @ X2 @ X3 @ (comp @ X1 @ X0 @ X2 @ X4 @ X5)) @ (comp @ X0 @ X0 @ X2 @ (comp @ X0 @ X1 @ X0 @ X3 @ X4) @ X5))) & ($true = (morStar @ X0 @ X2 @ X5 @ X5))) & ($true = (morStar @ X0 @ X0 @ (comp @ X0 @ X1 @ X0 @ X3 @ X4) @ (id @ X0))) & ($true = (morStar @ X0 @ X1 @ X3 @ X3)) & ($true = (morStar @ X0 @ X1 @ (comp @ X1 @ X0 @ X1 @ X4 @ X3) @ (id @ X1))))),
% 1.86/1.57 inference(flattening,[status(thm)],[f30])).
% 1.86/1.57 thf(f30,plain,(
% 1.86/1.57 ? [X0 : obj,X1 : obj,X2 : obj,X3 : mor,X4 : mor] : (((? [X5 : mor] : (($true != (morStar @ X0 @ X2 @ (comp @ X0 @ X1 @ X2 @ X3 @ (comp @ X1 @ X0 @ X2 @ X4 @ X5)) @ (comp @ X0 @ X0 @ X2 @ (comp @ X0 @ X1 @ X0 @ X3 @ X4) @ X5))) & ($true = (morStar @ X0 @ X2 @ X5 @ X5))) & (($true = (morStar @ X0 @ X1 @ (comp @ X1 @ X0 @ X1 @ X4 @ X3) @ (id @ X1))) & ($true = (morStar @ X0 @ X0 @ (comp @ X0 @ X1 @ X0 @ X3 @ X4) @ (id @ X0))))) & ($true = (morStar @ X1 @ X0 @ X4 @ X4))) & ($true = (morStar @ X0 @ X1 @ X3 @ X3)))),
% 1.86/1.57 inference(ennf_transformation,[status(thm)],[f21])).
% 1.86/1.57 thf(f21,plain,(
% 1.86/1.57 ~! [X0 : obj,X1 : obj,X2 : obj,X3 : mor,X4 : mor] : (($true = (morStar @ X0 @ X1 @ X3 @ X3)) => (($true = (morStar @ X1 @ X0 @ X4 @ X4)) => ((($true = (morStar @ X0 @ X1 @ (comp @ X1 @ X0 @ X1 @ X4 @ X3) @ (id @ X1))) & ($true = (morStar @ X0 @ X0 @ (comp @ X0 @ X1 @ X0 @ X3 @ X4) @ (id @ X0)))) => ! [X5 : mor] : (($true = (morStar @ X0 @ X2 @ X5 @ X5)) => ($true = (morStar @ X0 @ X2 @ (comp @ X0 @ X1 @ X2 @ X3 @ (comp @ X1 @ X0 @ X2 @ X4 @ X5)) @ (comp @ X0 @ X0 @ X2 @ (comp @ X0 @ X1 @ X0 @ X3 @ X4) @ X5)))))))),
% 1.86/1.57 inference(fool_elimination,[status(thm)],[f20])).
% 1.86/1.57 thf(f20,plain,(
% 1.86/1.57 ~! [X0 : obj,X1 : obj,X2 : obj,X3 : mor,X4 : mor] : ((morStar @ X0 @ X1 @ X3 @ X3) => ((morStar @ X1 @ X0 @ X4 @ X4) => (((morStar @ X0 @ X1 @ (comp @ X1 @ X0 @ X1 @ X4 @ X3) @ (id @ X1)) & (morStar @ X0 @ X0 @ (comp @ X0 @ X1 @ X0 @ X3 @ X4) @ (id @ X0))) => ! [X5 : mor] : ((morStar @ X0 @ X2 @ X5 @ X5) => (morStar @ X0 @ X2 @ (comp @ X0 @ X1 @ X2 @ X3 @ (comp @ X1 @ X0 @ X2 @ X4 @ X5)) @ (comp @ X0 @ X0 @ X2 @ (comp @ X0 @ X1 @ X0 @ X3 @ X4) @ X5))))))),
% 1.86/1.57 inference(rectify,[status(thm)],[f10])).
% 1.86/1.57 thf(f10,negated_conjecture,(
% 1.86/1.57 ~! [X2 : obj,X3 : obj,X4 : obj,X12 : mor,X13 : mor] : ((morStar @ X2 @ X3 @ X12 @ X12) => ((morStar @ X3 @ X2 @ X13 @ X13) => (((morStar @ X2 @ X3 @ (comp @ X3 @ X2 @ X3 @ X13 @ X12) @ (id @ X3)) & (morStar @ X2 @ X2 @ (comp @ X2 @ X3 @ X2 @ X12 @ X13) @ (id @ X2))) => ! [X14 : mor] : ((morStar @ X2 @ X4 @ X14 @ X14) => (morStar @ X2 @ X4 @ (comp @ X2 @ X3 @ X4 @ X12 @ (comp @ X3 @ X2 @ X4 @ X13 @ X14)) @ (comp @ X2 @ X2 @ X4 @ (comp @ X2 @ X3 @ X2 @ X12 @ X13) @ X14))))))),
% 1.86/1.57 inference(negated_conjecture,[status(cth)],[f9])).
% 1.86/1.57 thf(f9,conjecture,(
% 1.86/1.57 ! [X2 : obj,X3 : obj,X4 : obj,X12 : mor,X13 : mor] : ((morStar @ X2 @ X3 @ X12 @ X12) => ((morStar @ X3 @ X2 @ X13 @ X13) => (((morStar @ X2 @ X3 @ (comp @ X3 @ X2 @ X3 @ X13 @ X12) @ (id @ X3)) & (morStar @ X2 @ X2 @ (comp @ X2 @ X3 @ X2 @ X12 @ X13) @ (id @ X2))) => ! [X14 : mor] : ((morStar @ X2 @ X4 @ X14 @ X14) => (morStar @ X2 @ X4 @ (comp @ X2 @ X3 @ X4 @ X12 @ (comp @ X3 @ X2 @ X4 @ X13 @ X14)) @ (comp @ X2 @ X2 @ X4 @ (comp @ X2 @ X3 @ X2 @ X12 @ X13) @ X14))))))),
% 1.86/1.57 file('/export/starexec/sandbox/tmp/tmp.YAg6pGq6WS/DTF2THF_12437.p',conj)).
% 1.86/1.57 thf(f54,plain,(
% 1.86/1.57 ($true != (morStar @ sK0 @ sK2 @ sK5 @ sK5))),
% 1.86/1.57 inference(subsumption_resolution,[status(thm)],[f53,f43])).
% 1.86/1.57 thf(f43,plain,(
% 1.86/1.57 ($true = (morStar @ sK0 @ sK1 @ sK3 @ sK3))),
% 1.86/1.57 inference(cnf_transformation,[status(thm)],[f39])).
% 1.86/1.57 thf(f53,plain,(
% 1.86/1.57 ($true != (morStar @ sK0 @ sK1 @ sK3 @ sK3)) | ($true != (morStar @ sK0 @ sK2 @ sK5 @ sK5))),
% 1.86/1.57 inference(subsumption_resolution,[status(thm)],[f52,f47])).
% 1.86/1.57 thf(f47,plain,(
% 1.86/1.57 ($true = (morStar @ sK1 @ sK0 @ sK4 @ sK4))),
% 1.86/1.57 inference(cnf_transformation,[status(thm)],[f39])).
% 1.86/1.57 thf(f52,plain,(
% 1.86/1.57 ($true != (morStar @ sK1 @ sK0 @ sK4 @ sK4)) | ($true != (morStar @ sK0 @ sK2 @ sK5 @ sK5)) | ($true != (morStar @ sK0 @ sK1 @ sK3 @ sK3))),
% 1.86/1.57 inference(trivial_inequality_removal,[status(thm)],[f51])).
% 1.86/1.57 thf(f51,plain,(
% 1.86/1.57 ($true != (morStar @ sK0 @ sK2 @ sK5 @ sK5)) | ($true != (morStar @ sK0 @ sK1 @ sK3 @ sK3)) | ($true != (morStar @ sK1 @ sK0 @ sK4 @ sK4)) | ($true != $true)),
% 1.86/1.57 inference(superposition,[status(thm)],[f46,f50])).
% 1.86/1.57 thf(f50,plain,(
% 1.86/1.57 ( ! [X2 : obj,X3 : obj,X0 : obj,X1 : obj,X6 : mor,X4 : mor,X5 : mor] : (($true = (morStar @ X0 @ X3 @ (comp @ X0 @ X1 @ X3 @ X4 @ (comp @ X1 @ X2 @ X3 @ X5 @ X6)) @ (comp @ X0 @ X2 @ X3 @ (comp @ X0 @ X1 @ X2 @ X4 @ X5) @ X6))) | ($true != (morStar @ X1 @ X2 @ X5 @ X5)) | ($true != (morStar @ X0 @ X1 @ X4 @ X4)) | ($true != (morStar @ X2 @ X3 @ X6 @ X6))) )),
% 1.86/1.57 inference(cnf_transformation,[status(thm)],[f34])).
% 1.86/1.57 thf(f34,plain,(
% 1.86/1.57 ! [X0 : obj,X1 : obj,X2 : obj,X3 : obj,X4 : mor,X5 : mor,X6 : mor] : (($true = (morStar @ X0 @ X3 @ (comp @ X0 @ X1 @ X3 @ X4 @ (comp @ X1 @ X2 @ X3 @ X5 @ X6)) @ (comp @ X0 @ X2 @ X3 @ (comp @ X0 @ X1 @ X2 @ X4 @ X5) @ X6))) | ($true != (morStar @ X0 @ X1 @ X4 @ X4)) | ($true != (morStar @ X1 @ X2 @ X5 @ X5)) | ($true != (morStar @ X2 @ X3 @ X6 @ X6)))),
% 1.86/1.57 inference(flattening,[status(thm)],[f33])).
% 1.86/1.57 thf(f33,plain,(
% 1.86/1.57 ! [X0 : obj,X1 : obj,X2 : obj,X3 : obj,X4 : mor,X5 : mor,X6 : mor] : (((($true = (morStar @ X0 @ X3 @ (comp @ X0 @ X1 @ X3 @ X4 @ (comp @ X1 @ X2 @ X3 @ X5 @ X6)) @ (comp @ X0 @ X2 @ X3 @ (comp @ X0 @ X1 @ X2 @ X4 @ X5) @ X6))) | ($true != (morStar @ X2 @ X3 @ X6 @ X6))) | ($true != (morStar @ X1 @ X2 @ X5 @ X5))) | ($true != (morStar @ X0 @ X1 @ X4 @ X4)))),
% 1.86/1.57 inference(ennf_transformation,[status(thm)],[f29])).
% 1.86/1.57 thf(f29,plain,(
% 1.86/1.57 ! [X0 : obj,X1 : obj,X2 : obj,X3 : obj,X4 : mor,X5 : mor,X6 : mor] : (($true = (morStar @ X0 @ X1 @ X4 @ X4)) => (($true = (morStar @ X1 @ X2 @ X5 @ X5)) => (($true = (morStar @ X2 @ X3 @ X6 @ X6)) => ($true = (morStar @ X0 @ X3 @ (comp @ X0 @ X1 @ X3 @ X4 @ (comp @ X1 @ X2 @ X3 @ X5 @ X6)) @ (comp @ X0 @ X2 @ X3 @ (comp @ X0 @ X1 @ X2 @ X4 @ X5) @ X6))))))),
% 1.86/1.57 inference(fool_elimination,[status(thm)],[f28])).
% 1.86/1.57 thf(f28,plain,(
% 1.86/1.57 ! [X0 : obj,X1 : obj,X2 : obj,X3 : obj,X4 : mor,X5 : mor,X6 : mor] : ((morStar @ X0 @ X1 @ X4 @ X4) => ((morStar @ X1 @ X2 @ X5 @ X5) => ((morStar @ X2 @ X3 @ X6 @ X6) => (morStar @ X0 @ X3 @ (comp @ X0 @ X1 @ X3 @ X4 @ (comp @ X1 @ X2 @ X3 @ X5 @ X6)) @ (comp @ X0 @ X2 @ X3 @ (comp @ X0 @ X1 @ X2 @ X4 @ X5) @ X6)))))),
% 1.86/1.57 inference(rectify,[status(thm)],[f8])).
% 1.86/1.57 thf(f8,axiom,(
% 1.86/1.57 ! [X2 : obj,X3 : obj,X4 : obj,X0 : obj,X12 : mor,X13 : mor,X14 : mor] : ((morStar @ X2 @ X3 @ X12 @ X12) => ((morStar @ X3 @ X4 @ X13 @ X13) => ((morStar @ X4 @ X0 @ X14 @ X14) => (morStar @ X2 @ X0 @ (comp @ X2 @ X3 @ X0 @ X12 @ (comp @ X3 @ X4 @ X0 @ X13 @ X14)) @ (comp @ X2 @ X4 @ X0 @ (comp @ X2 @ X3 @ X4 @ X12 @ X13) @ X14)))))),
% 1.86/1.57 file('/export/starexec/sandbox/tmp/tmp.YAg6pGq6WS/DTF2THF_12437.p',ax3)).
% 1.86/1.57 thf(f46,plain,(
% 1.86/1.57 ($true != (morStar @ sK0 @ sK2 @ (comp @ sK0 @ sK1 @ sK2 @ sK3 @ (comp @ sK1 @ sK0 @ sK2 @ sK4 @ sK5)) @ (comp @ sK0 @ sK0 @ sK2 @ (comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4) @ sK5)))),
% 1.86/1.57 inference(cnf_transformation,[status(thm)],[f39])).
% 1.86/1.57 % SZS output end Proof for DTF2THF_12437
% 1.86/1.57 % (12578)------------------------------
% 1.86/1.57 % (12578)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.86/1.57 % (12578)Termination reason: Refutation
% 1.86/1.57
% 1.86/1.57 % (12578)Memory used [KB]: 5628
% 1.86/1.57 % (12578)Time elapsed: 0.009 s
% 1.86/1.57 % (12578)Instructions burned: 10 (million)
% 1.86/1.57 % (12578)------------------------------
% 1.86/1.57 % (12578)------------------------------
% 1.86/1.57 % (12572)Success in time 0.024 s
%------------------------------------------------------------------------------