%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : CAT041^1 : 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 : n017.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 08:40:55 AM UTC 2026
% Result : Theorem 1.74s 1.57s
% Output : Refutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 10
% Syntax : Number of formulae : 71 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 659 ( 226 equ; 0 cnn)
% Maximal formula atoms : 12 ( 9 avg)
% Number of connectives : 1889 ( 131 ~; 92 |; 62 &;1552 @)
% ( 5 <=>; 47 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 8 con; 0-5 aty)
% Number of variables : 248 ( 0 ^; 208 !; 40 ?; 248 :)
% 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(func_def_16,type,
sK6:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_17,type,
sK7:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_18,type,
sK8:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_19,type,
sK9:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_20,type,
sK10:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_22,type,
ph12:
!>[X0: $tType] : X0 ).
thf(f960,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f957]) ).
thf(f957,plain,
$true != $true,
inference(superposition,[status(thm)],[f934,f56]) ).
thf(f56,plain,
( $true
= ( morStar @ sK0 @ sK0 @ ( comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4 ) @ ( id @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
thf(f41,plain,
( ( $true
= ( morStar @ sK0 @ sK2 @ sK5 @ sK5 ) )
& ( ( morStar @ sK0 @ sK2 @ ( comp @ sK0 @ sK1 @ sK2 @ sK3 @ ( comp @ sK1 @ sK0 @ sK2 @ sK4 @ sK5 ) ) @ sK5 )
!= $true )
& ( $true
= ( morStar @ sK0 @ sK1 @ ( comp @ sK1 @ sK0 @ sK1 @ sK4 @ sK3 ) @ ( id @ sK1 ) ) )
& ( $true
= ( morStar @ sK0 @ sK0 @ ( comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4 ) @ ( id @ sK0 ) ) )
& ( $true
= ( morStar @ sK1 @ sK0 @ sK4 @ sK4 ) )
& ( $true
= ( morStar @ sK0 @ sK1 @ sK3 @ sK3 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f38,f40,f39]) ).
thf(f39,plain,
( ? [X0: obj,X1: obj,X2: obj,X3: mor,X4: mor] :
( ? [X5: mor] :
( ( ( morStar @ X0 @ X2 @ X5 @ X5 )
= $true )
& ( $true
!= ( morStar @ X0 @ X2 @ ( comp @ X0 @ X1 @ X2 @ X3 @ ( comp @ X1 @ X0 @ X2 @ X4 @ X5 ) ) @ X5 ) ) )
& ( ( morStar @ X0 @ X1 @ ( comp @ X1 @ X0 @ X1 @ X4 @ X3 ) @ ( id @ X1 ) )
= $true )
& ( $true
= ( morStar @ X0 @ X0 @ ( comp @ X0 @ X1 @ X0 @ X3 @ X4 ) @ ( id @ X0 ) ) )
& ( $true
= ( morStar @ X1 @ X0 @ X4 @ X4 ) )
& ( $true
= ( morStar @ X0 @ X1 @ X3 @ X3 ) ) )
=> ( ? [X5: mor] :
( ( ( morStar @ sK0 @ sK2 @ X5 @ X5 )
= $true )
& ( $true
!= ( morStar @ sK0 @ sK2 @ ( comp @ sK0 @ sK1 @ sK2 @ sK3 @ ( comp @ sK1 @ sK0 @ sK2 @ sK4 @ X5 ) ) @ X5 ) ) )
& ( $true
= ( morStar @ sK0 @ sK1 @ ( comp @ sK1 @ sK0 @ sK1 @ sK4 @ sK3 ) @ ( id @ sK1 ) ) )
& ( $true
= ( morStar @ sK0 @ sK0 @ ( comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4 ) @ ( id @ sK0 ) ) )
& ( $true
= ( morStar @ sK1 @ sK0 @ sK4 @ sK4 ) )
& ( $true
= ( morStar @ sK0 @ sK1 @ sK3 @ sK3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f40,plain,
( ? [X5: mor] :
( ( ( morStar @ sK0 @ sK2 @ X5 @ X5 )
= $true )
& ( $true
!= ( morStar @ sK0 @ sK2 @ ( comp @ sK0 @ sK1 @ sK2 @ sK3 @ ( comp @ sK1 @ sK0 @ sK2 @ sK4 @ X5 ) ) @ X5 ) ) )
=> ( ( $true
= ( morStar @ sK0 @ sK2 @ sK5 @ sK5 ) )
& ( ( morStar @ sK0 @ sK2 @ ( comp @ sK0 @ sK1 @ sK2 @ sK3 @ ( comp @ sK1 @ sK0 @ sK2 @ sK4 @ sK5 ) ) @ sK5 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f38,plain,
? [X0: obj,X1: obj,X2: obj,X3: mor,X4: mor] :
( ? [X5: mor] :
( ( ( morStar @ X0 @ X2 @ X5 @ X5 )
= $true )
& ( $true
!= ( morStar @ X0 @ X2 @ ( comp @ X0 @ X1 @ X2 @ X3 @ ( comp @ X1 @ X0 @ X2 @ X4 @ X5 ) ) @ X5 ) ) )
& ( ( morStar @ X0 @ X1 @ ( comp @ X1 @ X0 @ X1 @ X4 @ X3 ) @ ( id @ X1 ) )
= $true )
& ( $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(flattening,[status(thm)],[f37]) ).
thf(f37,plain,
? [X0: obj,X1: obj,X2: obj,X3: mor,X4: mor] :
( ? [X5: mor] :
( ( ( morStar @ X0 @ X2 @ X5 @ X5 )
= $true )
& ( $true
!= ( morStar @ X0 @ X2 @ ( comp @ X0 @ X1 @ X2 @ X3 @ ( comp @ X1 @ X0 @ X2 @ X4 @ X5 ) ) @ X5 ) ) )
& ( ( morStar @ X0 @ X1 @ ( comp @ X1 @ X0 @ X1 @ X4 @ X3 ) @ ( id @ X1 ) )
= $true )
& ( $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)],[f15]) ).
thf(f15,plain,
~ ! [X0: obj,X1: obj,X2: obj,X3: mor,X4: mor] :
( ( $true
= ( morStar @ X0 @ X1 @ X3 @ X3 ) )
=> ( ( $true
= ( morStar @ X1 @ X0 @ X4 @ X4 ) )
=> ( ( ( ( morStar @ X0 @ X1 @ ( comp @ X1 @ X0 @ X1 @ X4 @ X3 ) @ ( id @ X1 ) )
= $true )
& ( $true
= ( morStar @ X0 @ X0 @ ( comp @ X0 @ X1 @ X0 @ X3 @ X4 ) @ ( id @ X0 ) ) ) )
=> ! [X5: mor] :
( ( ( morStar @ X0 @ X2 @ X5 @ X5 )
= $true )
=> ( $true
= ( morStar @ X0 @ X2 @ ( comp @ X0 @ X1 @ X2 @ X3 @ ( comp @ X1 @ X0 @ X2 @ X4 @ X5 ) ) @ X5 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
~ ! [X0: obj,X1: obj,X2: obj,X3: mor,X4: mor] :
( ( morStar @ X0 @ X1 @ X3 @ X3 )
=> ( ( morStar @ X1 @ X0 @ X4 @ X4 )
=> ( ( ( morStar @ X0 @ X0 @ ( comp @ X0 @ X1 @ X0 @ X3 @ X4 ) @ ( id @ X0 ) )
& ( morStar @ X0 @ X1 @ ( comp @ X1 @ X0 @ X1 @ X4 @ X3 ) @ ( id @ X1 ) ) )
=> ! [X5: mor] :
( ( morStar @ X0 @ X2 @ X5 @ X5 )
=> ( morStar @ X0 @ X2 @ ( comp @ X0 @ X1 @ X2 @ X3 @ ( comp @ X1 @ X0 @ X2 @ X4 @ X5 ) ) @ 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 @ X2 @ ( comp @ X2 @ X3 @ X2 @ X12 @ X13 ) @ ( id @ X2 ) )
& ( morStar @ X2 @ X3 @ ( comp @ X3 @ X2 @ X3 @ X13 @ X12 ) @ ( id @ X3 ) ) )
=> ! [X14: mor] :
( ( morStar @ X2 @ X4 @ X14 @ X14 )
=> ( morStar @ X2 @ X4 @ ( comp @ X2 @ X3 @ X4 @ X12 @ ( comp @ X3 @ X2 @ X4 @ X13 @ X14 ) ) @ 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 @ X2 @ ( comp @ X2 @ X3 @ X2 @ X12 @ X13 ) @ ( id @ X2 ) )
& ( morStar @ X2 @ X3 @ ( comp @ X3 @ X2 @ X3 @ X13 @ X12 ) @ ( id @ X3 ) ) )
=> ! [X14: mor] :
( ( morStar @ X2 @ X4 @ X14 @ X14 )
=> ( morStar @ X2 @ X4 @ ( comp @ X2 @ X3 @ X4 @ X12 @ ( comp @ X3 @ X2 @ X4 @ X13 @ X14 ) ) @ X14 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.2hUijUb1Os/DTF2THF_31277.p',conj) ).
thf(f934,plain,
( $true
!= ( morStar @ sK0 @ sK0 @ ( comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4 ) @ ( id @ sK0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f933]) ).
thf(f933,plain,
( ( $true
!= ( morStar @ sK0 @ sK0 @ ( comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4 ) @ ( id @ sK0 ) ) )
| ( $true != $true ) ),
inference(forward_demodulation,[status(thm)],[f932,f59]) ).
thf(f59,plain,
( $true
= ( morStar @ sK0 @ sK2 @ sK5 @ sK5 ) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
thf(f932,plain,
( ( $true
!= ( morStar @ sK0 @ sK2 @ sK5 @ sK5 ) )
| ( $true
!= ( morStar @ sK0 @ sK0 @ ( comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4 ) @ ( id @ sK0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f931]) ).
thf(f931,plain,
( ( $true
!= ( morStar @ sK0 @ sK0 @ ( comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4 ) @ ( id @ sK0 ) ) )
| ( $true
!= ( morStar @ sK0 @ sK2 @ sK5 @ sK5 ) )
| ( $true != $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f926]) ).
thf(f926,plain,
( ( $true != $true )
| ( $true
!= ( morStar @ sK0 @ sK0 @ ( comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4 ) @ ( id @ sK0 ) ) )
| ( $true
!= ( morStar @ sK0 @ sK2 @ sK5 @ sK5 ) )
| ( $true
!= ( morStar @ sK0 @ sK2 @ sK5 @ sK5 ) ) ),
inference(superposition,[status(thm)],[f239,f50]) ).
thf(f50,plain,
! [X2: mor,X0: obj,X1: obj] :
( ( $true
= ( morStar @ X0 @ X1 @ ( comp @ X0 @ X0 @ X1 @ ( id @ X0 ) @ X2 ) @ X2 ) )
| ( ( morStar @ X0 @ X1 @ X2 @ X2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
thf(f36,plain,
! [X0: obj,X1: obj,X2: mor] :
( ( ( morStar @ X0 @ X1 @ X2 @ X2 )
!= $true )
| ( $true
= ( morStar @ X0 @ X1 @ ( comp @ X0 @ X0 @ X1 @ ( id @ X0 ) @ X2 ) @ X2 ) ) ),
inference(ennf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
! [X0: obj,X1: obj,X2: mor] :
( ( ( morStar @ X0 @ X1 @ X2 @ X2 )
= $true )
=> ( $true
= ( morStar @ X0 @ X1 @ ( comp @ X0 @ X0 @ X1 @ ( id @ X0 ) @ X2 ) @ X2 ) ) ),
inference(fool_elimination,[status(thm)],[f26]) ).
thf(f26,plain,
! [X0: obj,X1: obj,X2: mor] :
( ( morStar @ X0 @ X1 @ X2 @ X2 )
=> ( morStar @ X0 @ X1 @ ( comp @ X0 @ X0 @ X1 @ ( id @ X0 ) @ X2 ) @ X2 ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
! [X2: obj,X3: obj,X11: mor] :
( ( morStar @ X2 @ X3 @ X11 @ X11 )
=> ( morStar @ X2 @ X3 @ ( comp @ X2 @ X2 @ X3 @ ( id @ X2 ) @ X11 ) @ X11 ) ),
file('/export/starexec/sandbox/tmp/tmp.2hUijUb1Os/DTF2THF_31277.p',ax1) ).
thf(f239,plain,
! [X0: mor,X1: mor] :
( ( $true
!= ( morStar @ sK0 @ sK2 @ ( comp @ sK0 @ sK0 @ sK2 @ X0 @ X1 ) @ sK5 ) )
| ( $true
!= ( morStar @ sK0 @ sK0 @ ( comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4 ) @ X0 ) )
| ( $true
!= ( morStar @ sK0 @ sK2 @ sK5 @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f236]) ).
thf(f236,plain,
! [X0: mor,X1: mor] :
( ( $true != $true )
| ( $true
!= ( morStar @ sK0 @ sK2 @ sK5 @ X1 ) )
| ( $true
!= ( morStar @ sK0 @ sK2 @ ( comp @ sK0 @ sK0 @ sK2 @ X0 @ X1 ) @ sK5 ) )
| ( $true
!= ( morStar @ sK0 @ sK0 @ ( comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4 ) @ X0 ) ) ),
inference(superposition,[status(thm)],[f119,f53]) ).
thf(f53,plain,
! [X2: obj,X3: mor,X0: obj,X1: obj,X6: mor,X4: mor,X5: mor] :
( ( $true
= ( morStar @ X0 @ X2 @ ( comp @ X0 @ X1 @ X2 @ X3 @ X5 ) @ ( comp @ X0 @ X1 @ X2 @ X4 @ X6 ) ) )
| ( $true
!= ( morStar @ X1 @ X2 @ X5 @ X6 ) )
| ( ( morStar @ X0 @ X1 @ X3 @ X4 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f30,plain,
! [X0: obj,X1: obj,X2: obj,X3: mor,X4: mor] :
( ( ( morStar @ X0 @ X1 @ X3 @ X4 )
!= $true )
| ! [X5: mor,X6: mor] :
( ( $true
= ( morStar @ X0 @ X2 @ ( comp @ X0 @ X1 @ X2 @ X3 @ X5 ) @ ( comp @ X0 @ X1 @ X2 @ X4 @ X6 ) ) )
| ( $true
!= ( morStar @ X1 @ X2 @ X5 @ X6 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: obj,X1: obj,X2: obj,X3: mor,X4: mor] :
( ( ( morStar @ X0 @ X1 @ X3 @ X4 )
= $true )
=> ! [X5: mor,X6: mor] :
( ( $true
= ( morStar @ X1 @ X2 @ X5 @ X6 ) )
=> ( $true
= ( morStar @ X0 @ X2 @ ( comp @ X0 @ X1 @ X2 @ X3 @ X5 ) @ ( comp @ X0 @ X1 @ X2 @ X4 @ X6 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: obj,X1: obj,X2: obj,X3: mor,X4: mor] :
( ( morStar @ X0 @ X1 @ X3 @ X4 )
=> ! [X5: mor,X6: mor] :
( ( morStar @ X1 @ X2 @ X5 @ X6 )
=> ( morStar @ X0 @ X2 @ ( comp @ X0 @ X1 @ X2 @ X3 @ X5 ) @ ( comp @ X0 @ X1 @ X2 @ X4 @ X6 ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X2: obj,X3: obj,X4: obj,X7: mor,X8: mor] :
( ( morStar @ X2 @ X3 @ X7 @ X8 )
=> ! [X9: mor,X10: mor] :
( ( morStar @ X3 @ X4 @ X9 @ X10 )
=> ( morStar @ X2 @ X4 @ ( comp @ X2 @ X3 @ X4 @ X7 @ X9 ) @ ( comp @ X2 @ X3 @ X4 @ X8 @ X10 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.2hUijUb1Os/DTF2THF_31277.p',comp_tp_ax) ).
thf(f119,plain,
! [X0: mor] :
( ( ( morStar @ sK0 @ sK2 @ ( comp @ sK0 @ sK0 @ sK2 @ ( comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4 ) @ sK5 ) @ X0 )
!= $true )
| ( $true
!= ( morStar @ sK0 @ sK2 @ X0 @ sK5 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f118]) ).
thf(f118,plain,
! [X0: mor] :
( ( ( morStar @ sK0 @ sK2 @ ( comp @ sK0 @ sK0 @ sK2 @ ( comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4 ) @ sK5 ) @ X0 )
!= $true )
| ( $true
!= ( morStar @ sK0 @ sK2 @ X0 @ sK5 ) )
| ( $true != $true ) ),
inference(forward_demodulation,[status(thm)],[f117,f52]) ).
thf(f52,plain,
! [X0: obj,X1: obj] :
( $true
= ( isPer @ mor @ ( morStar @ X0 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: obj,X1: obj] :
( $true
= ( isPer @ mor @ ( morStar @ X0 @ X1 ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: obj,X1: obj] : ( isPer @ mor @ ( morStar @ X0 @ X1 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X5: obj,X6: obj] : ( isPer @ mor @ ( morStar @ X5 @ X6 ) ),
file('/export/starexec/sandbox/tmp/tmp.2hUijUb1Os/DTF2THF_31277.p','\'morStar\'_is_per') ).
thf(f117,plain,
! [X0: mor] :
( ( $true
!= ( morStar @ sK0 @ sK2 @ X0 @ sK5 ) )
| ( ( morStar @ sK0 @ sK2 @ ( comp @ sK0 @ sK0 @ sK2 @ ( comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4 ) @ sK5 ) @ X0 )
!= $true )
| ( ( isPer @ mor @ ( morStar @ sK0 @ sK2 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f115]) ).
thf(f115,plain,
! [X0: mor] :
( ( $true
!= ( morStar @ sK0 @ sK2 @ X0 @ sK5 ) )
| ( ( morStar @ sK0 @ sK2 @ ( comp @ sK0 @ sK0 @ sK2 @ ( comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4 ) @ sK5 ) @ X0 )
!= $true )
| ( ( isPer @ mor @ ( morStar @ sK0 @ sK2 ) )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f113,f68]) ).
thf(f68,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0 > X0 > $o,X4: X0] :
( ( ( X1 @ X2 @ X4 )
= $true )
| ( ( X1 @ X3 @ X4 )
!= $true )
| ( ( X1 @ X2 @ X3 )
!= $true )
| ( ( isPer @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
thf(f47,plain,
! [X0: $tType,X1: X0 > X0 > $o] :
( ( ( ! [X2: X0,X3: X0,X4: X0] :
( ( ( X1 @ X3 @ X4 )
!= $true )
| ( ( X1 @ X2 @ X3 )
!= $true )
| ( ( X1 @ X2 @ X4 )
= $true ) )
& ! [X5: X0,X6: X0] :
( ( $true
!= ( X1 @ X5 @ X6 ) )
| ( $true
= ( X1 @ X6 @ X5 ) ) ) )
| ( ( isPer @ X0 @ X1 )
!= $true ) )
& ( ( ( isPer @ X0 @ X1 )
= $true )
| ( ( $true
= ( X1 @ ( sK7 @ X0 @ X1 ) @ ( sK8 @ X0 @ X1 ) ) )
& ( ( X1 @ ( sK6 @ X0 @ X1 ) @ ( sK7 @ X0 @ X1 ) )
= $true )
& ( $true
!= ( X1 @ ( sK6 @ X0 @ X1 ) @ ( sK8 @ X0 @ X1 ) ) ) )
| ( ( $true
= ( X1 @ ( sK9 @ X0 @ X1 ) @ ( sK10 @ X0 @ X1 ) ) )
& ( $true
!= ( X1 @ ( sK10 @ X0 @ X1 ) @ ( sK9 @ X0 @ X1 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9,sK10])],[f44,f46,f45]) ).
thf(f45,plain,
! [X0: $tType,X1: X0 > X0 > $o] :
( ? [X7: X0,X8: X0,X9: X0] :
( ( $true
= ( X1 @ X8 @ X9 ) )
& ( $true
= ( X1 @ X7 @ X8 ) )
& ( ( X1 @ X7 @ X9 )
!= $true ) )
=> ( ( $true
= ( X1 @ ( sK7 @ X0 @ X1 ) @ ( sK8 @ X0 @ X1 ) ) )
& ( ( X1 @ ( sK6 @ X0 @ X1 ) @ ( sK7 @ X0 @ X1 ) )
= $true )
& ( $true
!= ( X1 @ ( sK6 @ X0 @ X1 ) @ ( sK8 @ X0 @ X1 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f46,plain,
! [X0: $tType,X1: X0 > X0 > $o] :
( ? [X10: X0,X11: X0] :
( ( $true
= ( X1 @ X10 @ X11 ) )
& ( $true
!= ( X1 @ X11 @ X10 ) ) )
=> ( ( $true
= ( X1 @ ( sK9 @ X0 @ X1 ) @ ( sK10 @ X0 @ X1 ) ) )
& ( $true
!= ( X1 @ ( sK10 @ X0 @ X1 ) @ ( sK9 @ X0 @ X1 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f44,plain,
! [X0: $tType,X1: X0 > X0 > $o] :
( ( ( ! [X2: X0,X3: X0,X4: X0] :
( ( ( X1 @ X3 @ X4 )
!= $true )
| ( ( X1 @ X2 @ X3 )
!= $true )
| ( ( X1 @ X2 @ X4 )
= $true ) )
& ! [X5: X0,X6: X0] :
( ( $true
!= ( X1 @ X5 @ X6 ) )
| ( $true
= ( X1 @ X6 @ X5 ) ) ) )
| ( ( isPer @ X0 @ X1 )
!= $true ) )
& ( ( ( isPer @ X0 @ X1 )
= $true )
| ? [X7: X0,X8: X0,X9: X0] :
( ( $true
= ( X1 @ X8 @ X9 ) )
& ( $true
= ( X1 @ X7 @ X8 ) )
& ( ( X1 @ X7 @ X9 )
!= $true ) )
| ? [X10: X0,X11: X0] :
( ( $true
= ( X1 @ X10 @ X11 ) )
& ( $true
!= ( X1 @ X11 @ X10 ) ) ) ) ),
inference(rectify,[status(thm)],[f43]) ).
thf(f43,plain,
! [X0: $tType,X1: X0 > X0 > $o] :
( ( ( ! [X4: X0,X5: X0,X6: X0] :
( ( $true
!= ( X1 @ X5 @ X6 ) )
| ( ( X1 @ X4 @ X5 )
!= $true )
| ( ( X1 @ X4 @ X6 )
= $true ) )
& ! [X2: X0,X3: X0] :
( ( ( X1 @ X2 @ X3 )
!= $true )
| ( ( X1 @ X3 @ X2 )
= $true ) ) )
| ( ( isPer @ X0 @ X1 )
!= $true ) )
& ( ( ( isPer @ X0 @ X1 )
= $true )
| ? [X4: X0,X5: X0,X6: X0] :
( ( $true
= ( X1 @ X5 @ X6 ) )
& ( ( X1 @ X4 @ X5 )
= $true )
& ( ( X1 @ X4 @ X6 )
!= $true ) )
| ? [X2: X0,X3: X0] :
( ( ( X1 @ X2 @ X3 )
= $true )
& ( ( X1 @ X3 @ X2 )
!= $true ) ) ) ),
inference(flattening,[status(thm)],[f42]) ).
thf(f42,plain,
! [X0: $tType,X1: X0 > X0 > $o] :
( ( ( ! [X4: X0,X5: X0,X6: X0] :
( ( $true
!= ( X1 @ X5 @ X6 ) )
| ( ( X1 @ X4 @ X5 )
!= $true )
| ( ( X1 @ X4 @ X6 )
= $true ) )
& ! [X2: X0,X3: X0] :
( ( ( X1 @ X2 @ X3 )
!= $true )
| ( ( X1 @ X3 @ X2 )
= $true ) ) )
| ( ( isPer @ X0 @ X1 )
!= $true ) )
& ( ( ( isPer @ X0 @ X1 )
= $true )
| ? [X4: X0,X5: X0,X6: X0] :
( ( $true
= ( X1 @ X5 @ X6 ) )
& ( ( X1 @ X4 @ X5 )
= $true )
& ( ( X1 @ X4 @ X6 )
!= $true ) )
| ? [X2: X0,X3: X0] :
( ( ( X1 @ X2 @ X3 )
= $true )
& ( ( X1 @ X3 @ X2 )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f32]) ).
thf(f32,plain,
! [X0: $tType,X1: X0 > X0 > $o] :
( ( ! [X4: X0,X5: X0,X6: X0] :
( ( $true
!= ( X1 @ X5 @ X6 ) )
| ( ( X1 @ X4 @ X5 )
!= $true )
| ( ( X1 @ X4 @ X6 )
= $true ) )
& ! [X2: X0,X3: X0] :
( ( ( X1 @ X2 @ X3 )
!= $true )
| ( ( X1 @ X3 @ X2 )
= $true ) ) )
<=> ( ( isPer @ X0 @ X1 )
= $true ) ),
inference(flattening,[status(thm)],[f31]) ).
thf(f31,plain,
! [X0: $tType,X1: X0 > X0 > $o] :
( ( ! [X2: X0,X3: X0] :
( ( ( X1 @ X2 @ X3 )
!= $true )
| ( ( X1 @ X3 @ X2 )
= $true ) )
& ! [X4: X0,X5: X0,X6: X0] :
( ( ( X1 @ X4 @ X6 )
= $true )
| ( $true
!= ( X1 @ X5 @ X6 ) )
| ( ( X1 @ X4 @ X5 )
!= $true ) ) )
<=> ( ( isPer @ X0 @ X1 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: $tType,X1: X0 > X0 > $o] :
( ( ! [X2: X0,X3: X0] :
( ( ( X1 @ X2 @ X3 )
= $true )
=> ( ( X1 @ X3 @ X2 )
= $true ) )
& ! [X4: X0,X5: X0,X6: X0] :
( ( ( X1 @ X4 @ X5 )
= $true )
=> ( ( $true
= ( X1 @ X5 @ X6 ) )
=> ( ( X1 @ X4 @ X6 )
= $true ) ) ) )
<=> ( ( isPer @ X0 @ X1 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: $tType,X1: X0 > X0 > $o] :
( ( ! [X2: X0,X3: X0] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) )
& ! [X4: X0,X5: X0,X6: X0] :
( ( X1 @ X4 @ X5 )
=> ( ( X1 @ X5 @ X6 )
=> ( X1 @ X4 @ X6 ) ) ) )
<=> ( isPer @ X0 @ X1 ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $tType,X1: X0 > X0 > $o] :
( ( ! [X2: X0,X3: X0] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) )
& ! [X2: X0,X3: X0,X4: X0] :
( ( X1 @ X2 @ X3 )
=> ( ( X1 @ X3 @ X4 )
=> ( X1 @ X2 @ X4 ) ) ) )
<=> ( isPer @ X0 @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.2hUijUb1Os/DTF2THF_31277.p',is_per) ).
thf(f113,plain,
( $true
!= ( morStar @ sK0 @ sK2 @ ( comp @ sK0 @ sK0 @ sK2 @ ( comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4 ) @ sK5 ) @ sK5 ) ),
inference(trivial_inequality_removal,[status(thm)],[f112]) ).
thf(f112,plain,
( ( $true != $true )
| ( $true
!= ( morStar @ sK0 @ sK2 @ ( comp @ sK0 @ sK0 @ sK2 @ ( comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4 ) @ sK5 ) @ sK5 ) ) ),
inference(forward_demodulation,[status(thm)],[f111,f54]) ).
thf(f54,plain,
( $true
= ( morStar @ sK0 @ sK1 @ sK3 @ sK3 ) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
thf(f111,plain,
( ( $true
!= ( morStar @ sK0 @ sK2 @ ( comp @ sK0 @ sK0 @ sK2 @ ( comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4 ) @ sK5 ) @ sK5 ) )
| ( $true
!= ( morStar @ sK0 @ sK1 @ sK3 @ sK3 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f110]) ).
thf(f110,plain,
( ( $true
!= ( morStar @ sK0 @ sK1 @ sK3 @ sK3 ) )
| ( $true != $true )
| ( $true
!= ( morStar @ sK0 @ sK2 @ ( comp @ sK0 @ sK0 @ sK2 @ ( comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4 ) @ sK5 ) @ sK5 ) ) ),
inference(forward_demodulation,[status(thm)],[f109,f55]) ).
thf(f55,plain,
( $true
= ( morStar @ sK1 @ sK0 @ sK4 @ sK4 ) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
thf(f109,plain,
( ( $true
!= ( morStar @ sK1 @ sK0 @ sK4 @ sK4 ) )
| ( $true
!= ( morStar @ sK0 @ sK2 @ ( comp @ sK0 @ sK0 @ sK2 @ ( comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4 ) @ sK5 ) @ sK5 ) )
| ( $true
!= ( morStar @ sK0 @ sK1 @ sK3 @ sK3 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f108]) ).
thf(f108,plain,
( ( $true
!= ( morStar @ sK0 @ sK2 @ ( comp @ sK0 @ sK0 @ sK2 @ ( comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4 ) @ sK5 ) @ sK5 ) )
| ( $true != $true )
| ( $true
!= ( morStar @ sK0 @ sK1 @ sK3 @ sK3 ) )
| ( $true
!= ( morStar @ sK1 @ sK0 @ sK4 @ sK4 ) ) ),
inference(forward_demodulation,[status(thm)],[f100,f59]) ).
thf(f100,plain,
( ( $true
!= ( morStar @ sK0 @ sK2 @ sK5 @ sK5 ) )
| ( $true
!= ( morStar @ sK1 @ sK0 @ sK4 @ sK4 ) )
| ( $true
!= ( morStar @ sK0 @ sK1 @ sK3 @ sK3 ) )
| ( $true
!= ( morStar @ sK0 @ sK2 @ ( comp @ sK0 @ sK0 @ sK2 @ ( comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4 ) @ sK5 ) @ sK5 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f97]) ).
thf(f97,plain,
( ( $true != $true )
| ( $true
!= ( morStar @ sK0 @ sK2 @ sK5 @ sK5 ) )
| ( $true
!= ( morStar @ sK1 @ sK0 @ sK4 @ sK4 ) )
| ( $true
!= ( morStar @ sK0 @ sK2 @ ( comp @ sK0 @ sK0 @ sK2 @ ( comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4 ) @ sK5 ) @ sK5 ) )
| ( $true
!= ( morStar @ sK0 @ sK1 @ sK3 @ sK3 ) ) ),
inference(superposition,[status(thm)],[f77,f49]) ).
thf(f49,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 @ X2 @ X3 @ X6 @ X6 ) )
| ( $true
!= ( morStar @ X1 @ X2 @ X5 @ X5 ) )
| ( $true
!= ( morStar @ X0 @ X1 @ X4 @ X4 ) ) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
thf(f35,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 @ 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 ) ) ),
inference(flattening,[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 @ X2 @ X3 @ X6 @ X6 ) )
| ( $true
!= ( morStar @ X1 @ X2 @ X5 @ X5 ) )
| ( $true
!= ( morStar @ X0 @ X1 @ X4 @ X4 ) ) ),
inference(ennf_transformation,[status(thm)],[f25]) ).
thf(f25,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)],[f24]) ).
thf(f24,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.2hUijUb1Os/DTF2THF_31277.p',ax3) ).
thf(f77,plain,
! [X0: mor] :
( ( $true
!= ( morStar @ sK0 @ sK2 @ ( comp @ sK0 @ sK1 @ sK2 @ sK3 @ ( comp @ sK1 @ sK0 @ sK2 @ sK4 @ sK5 ) ) @ X0 ) )
| ( $true
!= ( morStar @ sK0 @ sK2 @ X0 @ sK5 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f76]) ).
thf(f76,plain,
! [X0: mor] :
( ( $true != $true )
| ( $true
!= ( morStar @ sK0 @ sK2 @ X0 @ sK5 ) )
| ( $true
!= ( morStar @ sK0 @ sK2 @ ( comp @ sK0 @ sK1 @ sK2 @ sK3 @ ( comp @ sK1 @ sK0 @ sK2 @ sK4 @ sK5 ) ) @ X0 ) ) ),
inference(forward_demodulation,[status(thm)],[f75,f52]) ).
thf(f75,plain,
! [X0: mor] :
( ( $true
!= ( morStar @ sK0 @ sK2 @ X0 @ sK5 ) )
| ( $true
!= ( morStar @ sK0 @ sK2 @ ( comp @ sK0 @ sK1 @ sK2 @ sK3 @ ( comp @ sK1 @ sK0 @ sK2 @ sK4 @ sK5 ) ) @ X0 ) )
| ( ( isPer @ mor @ ( morStar @ sK0 @ sK2 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f73]) ).
thf(f73,plain,
! [X0: mor] :
( ( ( isPer @ mor @ ( morStar @ sK0 @ sK2 ) )
!= $true )
| ( $true
!= ( morStar @ sK0 @ sK2 @ X0 @ sK5 ) )
| ( $true
!= ( morStar @ sK0 @ sK2 @ ( comp @ sK0 @ sK1 @ sK2 @ sK3 @ ( comp @ sK1 @ sK0 @ sK2 @ sK4 @ sK5 ) ) @ X0 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f58,f68]) ).
thf(f58,plain,
( ( morStar @ sK0 @ sK2 @ ( comp @ sK0 @ sK1 @ sK2 @ sK3 @ ( comp @ sK1 @ sK0 @ sK2 @ sK4 @ sK5 ) ) @ sK5 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : CAT041^1 : TPTP v9.2.1. Released v9.2.0.
% 0.00/0.09 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.29 % Computer : n017.cluster.edu
% 0.12/0.29 % Model : x86_64 x86_64
% 0.12/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.29 % Memory : 8042.1875MB
% 0.12/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.29 % CPULimit : 300
% 0.12/0.29 % WCLimit : 300
% 0.12/0.29 % DateTime : Tue Feb 24 04:07:11 EST 2026
% 0.12/0.29 % CPUTime :
% 0.12/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.39 ---- Original DTF file ---
% 0.19/0.39 thf(spec,logic,$$dhol).
% 0.19/0.39 %------------------------------------------------------------------------------
% 0.19/0.39 % File : CAT041^1 : TPTP v9.2.1. Released v9.2.0.
% 0.19/0.39 % Domain : Category Theory
% 0.19/0.39 % Problem : Simple problem from category theory dhol_3
% 0.19/0.39 % Version : Especial.
% 0.19/0.39 % English :
% 0.19/0.39
% 0.19/0.39 % Refs : [RRB23] Rothgang et al. (2023), Theorem Proving in Dependently
% 0.19/0.39 % : [Rot25] Rothgang (2025), Email to Geoff Sutcliffe
% 0.19/0.39 % : [RK+25] Ranalter et al. (2025), The Dependently Typed Higher-O
% 0.19/0.39 % Source : [Rot25]
% 0.19/0.39 % Names : CategoryTheory/category-theory-lemmas-dhol_3.p [Rot25]
% 0.19/0.39
% 0.19/0.39 % Status : Theorem
% 0.19/0.39 % Rating : ? v9.2.0
% 0.19/0.39 % Syntax : Number of formulae : 8 ( 3 unt; 4 typ; 0 def)
% 0.19/0.39 % Number of atoms : 6 ( 6 equ; 0 cnn)
% 0.19/0.39 % Maximal formula atoms : 3 ( 1 avg)
% 0.19/0.39 % Number of connectives : 80 ( 0 ~; 0 |; 1 &; 78 @)
% 0.19/0.39 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.19/0.39 % Maximal formula depth : 8 ( 6 avg)
% 0.19/0.39 % Number of types : 1 ( 1 usr)
% 0.19/0.39 % Number of type decls : 4 ( 0 !>P; 2 !>D)
% 0.19/0.39 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.19/0.39 % Number of symbols : 4 ( 3 usr; 0 con; 1-5 aty)
% 0.19/0.39 % Number of variables : 23 ( 0 ^; 19 !; 0 ?; 23 :)
% 0.19/0.39 % ( 4 !>; 0 ?*; 0 @-; 0 @+)
% 0.19/0.39 % SPC : DH0_THM_EQU_NAR
% 0.19/0.39
% 0.19/0.39 % Comments :
% 0.19/0.39 %------------------------------------------------------------------------------
% 0.19/0.39 thf(obj_type,type,
% 0.19/0.39 obj: $tType ).
% 0.19/0.39
% 0.19/0.39 thf(mor_type,type,
% 0.19/0.39 mor: obj > obj > $tType ).
% 0.19/0.39
% 0.19/0.39 thf(id_type,type,
% 0.19/0.39 id:
% 0.19/0.39 !>[X: obj] : ( mor @ X @ X ) ).
% 0.19/0.39
% 0.19/0.39 thf(comp_type,type,
% 0.19/0.39 comp:
% 0.19/0.39 !>[X: obj,Y: obj,Z: obj] : ( ( mor @ X @ Y ) > ( mor @ Y @ Z ) > ( mor @ X @ Z ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(ax1,axiom,
% 0.19/0.39 ! [X: obj,Y: obj,M: mor @ X @ Y] :
% 0.19/0.39 ( ( comp @ X @ X @ Y @ ( id @ X ) @ M )
% 0.19/0.39 = M ) ).
% 0.19/0.39
% 0.19/0.39 thf(ax2,axiom,
% 0.19/0.39 ! [X: obj,Y: obj,M: mor @ X @ Y] :
% 0.19/0.39 ( ( comp @ X @ Y @ Y @ M @ ( id @ Y ) )
% 0.19/0.39 = M ) ).
% 0.19/0.39
% 0.19/0.39 thf(ax3,axiom,
% 0.19/0.39 ! [X: obj,Y: obj,Z: obj,A: obj,F: mor @ X @ Y,G: mor @ Y @ Z,H: mor @ Z @ A] :
% 0.19/0.39 ( ( comp @ X @ Y @ A @ F @ ( comp @ Y @ Z @ A @ G @ H ) )
% 0.19/0.39 = ( comp @ X @ Z @ A @ ( comp @ X @ Y @ Z @ F @ G ) @ H ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(conj,conjecture,
% 0.19/0.39 ! [X: obj,Y: obj,Z: obj,F: mor @ X @ Y,G: mor @ Y @ X] :
% 0.19/0.39 ( ( ( ( comp @ X @ Y @ X @ F @ G )
% 0.19/0.39 = ( id @ X ) )
% 0.19/0.39 & ( ( comp @ Y @ X @ Y @ G @ F )
% 0.19/0.39 = ( id @ Y ) ) )
% 0.19/0.39 => ! [H: mor @ X @ Z] :
% 0.19/0.39 ( ( comp @ X @ Y @ Z @ F @ ( comp @ Y @ X @ Z @ G @ H ) )
% 0.19/0.39 = H ) ) ).
% 0.19/0.39
% 0.19/0.39 %------------------------------------------------------------------------------
% 0.19/0.39 ------------------------
% 1.58/1.38 ---- Embedded in THF ---
% 1.58/1.38 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.58/1.38 %%% Generated on Tue Feb 24 04:07:12 EST 2026
% 1.58/1.38 %%% using '$$dhol' embedding, version 1.3.0.
% 1.58/1.38 %%% Logic specification used:
% 1.58/1.38 %%% thf(spec, logic, $$dhol).
% 1.58/1.38
% 1.58/1.38 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.2hUijUb1Os/DTF2DTF31277.p
% See solution above
% 1.58/1.38 ------------------------
% 1.58/1.39 ---- Cleaned THF ---
% 1.58/1.39 thf(is_per_type,type,
% 1.58/1.39 isPer:
% 1.58/1.39 !>[A: $tType] : ( ( A > A > $o ) > $o ) ).
% 1.58/1.39
% 1.58/1.39 thf(is_per,definition,
% 1.58/1.39 ! [A: $tType,AStar: A > A > $o] :
% 1.58/1.39 ( ( isPer @ A @ AStar )
% 1.58/1.39 <=> ( ! [X: A,Y: A] :
% 1.58/1.39 ( ( AStar @ X @ Y )
% 1.58/1.39 => ( AStar @ Y @ X ) )
% 1.58/1.39 & ! [X: A,Y: A,Z: A] :
% 1.58/1.39 ( ( AStar @ X @ Y )
% 1.58/1.39 => ( ( AStar @ Y @ Z )
% 1.58/1.39 => ( AStar @ X @ Z ) ) ) ) ) ).
% 1.58/1.39
% 1.58/1.39 thf(obj_type,type,
% 1.58/1.39 obj: $tType ).
% 1.58/1.39
% 1.58/1.39 thf(objStar,type,
% 1.58/1.39 objStar: obj > obj > $o ).
% 1.58/1.39
% 1.58/1.39 thf(objStar_is_eq,axiom,
% 1.58/1.39 ! [X: obj,Y: obj] :
% 1.58/1.39 ( ( objStar @ X @ Y )
% 1.58/1.39 <=> ( X = Y ) ) ).
% 1.58/1.39
% 1.58/1.39 thf(mor_type,type,
% 1.58/1.39 mor: $tType ).
% 1.58/1.39
% 1.58/1.39 thf(morStar,type,
% 1.58/1.39 morStar: obj > obj > mor > mor > $o ).
% 1.58/1.39
% 1.58/1.39 thf('\'morStar\'_is_per',axiom,
% 1.58/1.39 ! [C: obj,C0: obj] : ( isPer @ mor @ ( morStar @ C @ C0 ) ) ).
% 1.58/1.39
% 1.58/1.39 thf(id_type,type,
% 1.58/1.39 id: obj > mor ).
% 1.58/1.39
% 1.58/1.39 thf(id_tp_ax,axiom,
% 1.58/1.39 ! [X: obj] : ( morStar @ X @ X @ ( id @ X ) @ ( id @ X ) ) ).
% 1.58/1.39
% 1.58/1.39 thf(comp_type,type,
% 1.58/1.39 comp: obj > obj > obj > mor > mor > mor ).
% 1.58/1.39
% 1.58/1.39 thf(comp_tp_ax,axiom,
% 1.58/1.39 ! [X: obj,Y: obj,Z: obj,D: mor,D_prime: mor] :
% 1.58/1.39 ( ( morStar @ X @ Y @ D @ D_prime )
% 1.58/1.39 => ! [D0: mor,D0_prime: mor] :
% 1.58/1.39 ( ( morStar @ Y @ Z @ D0 @ D0_prime )
% 1.58/1.39 => ( morStar @ X @ Z @ ( comp @ X @ Y @ Z @ D @ D0 ) @ ( comp @ X @ Y @ Z @ D_prime @ D0_prime ) ) ) ) ).
% 1.58/1.39
% 1.58/1.39 thf(ax1,axiom,
% 1.58/1.39 ! [X: obj,Y: obj,M: mor] :
% 1.58/1.39 ( ( morStar @ X @ Y @ M @ M )
% 1.58/1.39 => ( morStar @ X @ Y @ ( comp @ X @ X @ Y @ ( id @ X ) @ M ) @ M ) ) ).
% 1.58/1.39
% 1.58/1.39 thf(ax2,axiom,
% 1.58/1.39 ! [X: obj,Y: obj,M: mor] :
% 1.58/1.39 ( ( morStar @ X @ Y @ M @ M )
% 1.58/1.39 => ( morStar @ X @ Y @ ( comp @ X @ Y @ Y @ M @ ( id @ Y ) ) @ M ) ) ).
% 1.58/1.39
% 1.58/1.39 thf(ax3,axiom,
% 1.58/1.39 ! [X: obj,Y: obj,Z: obj,A: obj,F: mor,G: mor,H: mor] :
% 1.58/1.39 ( ( morStar @ X @ Y @ F @ F )
% 1.58/1.39 => ( ( morStar @ Y @ Z @ G @ G )
% 1.58/1.39 => ( ( morStar @ Z @ A @ H @ H )
% 1.58/1.39 => ( 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 ) ) ) ) ) ).
% 1.58/1.39
% 1.58/1.39 thf(conj,conjecture,
% 1.58/1.39 ! [X: obj,Y: obj,Z: obj,F: mor,G: mor] :
% 1.58/1.39 ( ( morStar @ X @ Y @ F @ F )
% 1.58/1.39 => ( ( morStar @ Y @ X @ G @ G )
% 1.58/1.39 => ( ( ( morStar @ X @ X @ ( comp @ X @ Y @ X @ F @ G ) @ ( id @ X ) )
% 1.58/1.39 & ( morStar @ X @ Y @ ( comp @ Y @ X @ Y @ G @ F ) @ ( id @ Y ) ) )
% 1.58/1.39 => ! [H: mor] :
% 1.58/1.39 ( ( morStar @ X @ Z @ H @ H )
% 1.58/1.39 => ( morStar @ X @ Z @ ( comp @ X @ Y @ Z @ F @ ( comp @ Y @ X @ Z @ G @ H ) ) @ H ) ) ) ) ) ).
% 1.58/1.39 ------------------------
% 1.74/1.41 % (31377)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_31277 for (2999ds/2Mi)
% 1.74/1.41 % (31374)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_31277 for (2999ds/183Mi)
% 1.74/1.41 % (31375)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_31277 for (2999ds/4Mi)
% 1.74/1.41 % (31376)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_31277 for (2999ds/27Mi)
% 1.74/1.41 % (31378)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_31277 for (2999ds/2Mi)
% 1.74/1.41 % (31379)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_31277 for (2999ds/275Mi)
% 1.74/1.41 % (31380)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_31277 for (2999ds/18Mi)
% 1.74/1.41 % (31377)Instruction limit reached!
% 1.74/1.41 % (31377)------------------------------
% 1.74/1.41 % (31377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.41 % (31377)Termination reason: Unknown
% 1.74/1.41 % (31377)Termination phase: Property scanning
% 1.74/1.41 % (31378)Instruction limit reached!
% 1.74/1.41 % (31378)------------------------------
% 1.74/1.41 % (31378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.41 % (31378)Termination reason: Unknown
% 1.74/1.41 % (31378)Termination phase: shuffling
% 1.74/1.41
% 1.74/1.41 % (31378)Memory used [KB]: 1023
% 1.74/1.41 % (31378)Time elapsed: 0.003 s
% 1.74/1.41 % (31378)Instructions burned: 3 (million)
% 1.74/1.41 % (31378)------------------------------
% 1.74/1.41 % (31378)------------------------------
% 1.74/1.41
% 1.74/1.41 % (31377)Memory used [KB]: 1023
% 1.74/1.41 % (31377)Time elapsed: 0.003 s
% 1.74/1.41 % (31377)Instructions burned: 3 (million)
% 1.74/1.41 % (31377)------------------------------
% 1.74/1.41 % (31377)------------------------------
% 1.74/1.41 % (31375)Instruction limit reached!
% 1.74/1.41 % (31375)------------------------------
% 1.74/1.41 % (31375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.41 % (31375)Termination reason: Unknown
% 1.74/1.41 % (31375)Termination phase: Preprocessing 3
% 1.74/1.41
% 1.74/1.41 % (31375)Memory used [KB]: 1023
% 1.74/1.41 % (31375)Time elapsed: 0.004 s
% 1.74/1.41 % (31375)Instructions burned: 5 (million)
% 1.74/1.41 % (31375)------------------------------
% 1.74/1.41 % (31375)------------------------------
% 1.74/1.42 % (31379)Refutation not found, incomplete strategy
% 1.74/1.42 % (31379)------------------------------
% 1.74/1.42 % (31379)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.42 % (31379)Termination reason: Refutation not found, incomplete strategy
% 1.74/1.42
% 1.74/1.42
% 1.74/1.42 % (31379)Memory used [KB]: 5628
% 1.74/1.42 % (31379)Time elapsed: 0.006 s
% 1.74/1.42 % (31379)Instructions burned: 8 (million)
% 1.74/1.42 % (31379)------------------------------
% 1.74/1.42 % (31379)------------------------------
% 1.74/1.42 % (31380)Instruction limit reached!
% 1.74/1.42 % (31380)------------------------------
% 1.74/1.42 % (31380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.42 % (31380)Termination reason: Unknown
% 1.74/1.42 % (31380)Termination phase: Saturation
% 1.74/1.42
% 1.74/1.42 % (31380)Memory used [KB]: 5628
% 1.74/1.42 % (31380)Time elapsed: 0.011 s
% 1.74/1.42 % (31380)Instructions burned: 19 (million)
% 1.74/1.42 % (31380)------------------------------
% 1.74/1.42 % (31380)------------------------------
% 1.74/1.43 % (31376)Instruction limit reached!
% 1.74/1.43 % (31376)------------------------------
% 1.74/1.43 % (31376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.43 % (31376)Termination reason: Unknown
% 1.74/1.43 % (31376)Termination phase: Saturation
% 1.74/1.43
% 1.74/1.43 % (31376)Memory used [KB]: 5628
% 1.74/1.43 % (31376)Time elapsed: 0.016 s
% 1.74/1.43 % (31376)Instructions burned: 27 (million)
% 1.74/1.43 % (31376)------------------------------
% 1.74/1.43 % (31376)------------------------------
% 1.74/1.43 % (31382)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_31277 for (2999ds/37Mi)
% 1.74/1.43 % (31381)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_31277 for (2999ds/3Mi)
% 1.74/1.43 % (31383)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_31277 for (2999ds/15Mi)
% 1.74/1.43 % (31381)Instruction limit reached!
% 1.74/1.43 % (31381)------------------------------
% 1.74/1.43 % (31381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.43 % (31381)Termination reason: Unknown
% 1.74/1.43 % (31381)Termination phase: Property scanning
% 1.74/1.43
% 1.74/1.43 % (31381)Memory used [KB]: 1023
% 1.74/1.43 % (31381)Time elapsed: 0.003 s
% 1.74/1.43 % (31381)Instructions burned: 4 (million)
% 1.74/1.43 % (31381)------------------------------
% 1.74/1.43 % (31381)------------------------------
% 1.74/1.43 % (31384)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_31277 for (2999ds/3Mi)
% 1.74/1.43 % (31384)Instruction limit reached!
% 1.74/1.43 % (31384)------------------------------
% 1.74/1.43 % (31384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.43 % (31384)Termination reason: Unknown
% 1.74/1.43 % (31384)Termination phase: Property scanning
% 1.74/1.43
% 1.74/1.43 % (31384)Memory used [KB]: 1023
% 1.74/1.43 % (31384)Time elapsed: 0.003 s
% 1.74/1.43 % (31384)Instructions burned: 4 (million)
% 1.74/1.43 % (31384)------------------------------
% 1.74/1.43 % (31384)------------------------------
% 1.74/1.44 % (31385)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_31277 for (2999ds/1041Mi)
% 1.74/1.44 % (31383)Instruction limit reached!
% 1.74/1.44 % (31383)------------------------------
% 1.74/1.44 % (31383)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.44 % (31383)Termination reason: Unknown
% 1.74/1.44 % (31383)Termination phase: Saturation
% 1.74/1.44
% 1.74/1.44 % (31383)Memory used [KB]: 5756
% 1.74/1.44 % (31383)Time elapsed: 0.009 s
% 1.74/1.44 % (31383)Instructions burned: 15 (million)
% 1.74/1.44 % (31383)------------------------------
% 1.74/1.44 % (31383)------------------------------
% 1.74/1.44 % (31386)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_31277 for (2999ds/7Mi)
% 1.74/1.45 % (31386)Instruction limit reached!
% 1.74/1.45 % (31386)------------------------------
% 1.74/1.45 % (31386)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.45 % (31386)Termination reason: Unknown
% 1.74/1.45 % (31386)Termination phase: Saturation
% 1.74/1.45
% 1.74/1.45 % (31386)Memory used [KB]: 1023
% 1.74/1.45 % (31386)Time elapsed: 0.005 s
% 1.74/1.45 % (31386)Instructions burned: 8 (million)
% 1.74/1.45 % (31386)------------------------------
% 1.74/1.45 % (31386)------------------------------
% 1.74/1.45 % (31387)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_31277 for (2999ds/16Mi)
% 1.74/1.45 % (31382)Instruction limit reached!
% 1.74/1.45 % (31382)------------------------------
% 1.74/1.45 % (31382)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.45 % (31382)Termination reason: Unknown
% 1.74/1.45 % (31382)Termination phase: Saturation
% 1.74/1.45
% 1.74/1.45 % (31382)Memory used [KB]: 5756
% 1.74/1.45 % (31382)Time elapsed: 0.020 s
% 1.74/1.45 % (31382)Instructions burned: 38 (million)
% 1.74/1.45 % (31382)------------------------------
% 1.74/1.45 % (31382)------------------------------
% 1.74/1.45 % (31388)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_31277 for (2999ds/3Mi)
% 1.74/1.45 % (31388)Instruction limit reached!
% 1.74/1.45 % (31388)------------------------------
% 1.74/1.45 % (31388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.45 % (31388)Termination reason: Unknown
% 1.74/1.45 % (31388)Termination phase: Property scanning
% 1.74/1.45
% 1.74/1.45 % (31388)Memory used [KB]: 1023
% 1.74/1.45 % (31388)Time elapsed: 0.003 s
% 1.74/1.45 % (31388)Instructions burned: 4 (million)
% 1.74/1.45 % (31388)------------------------------
% 1.74/1.45 % (31388)------------------------------
% 1.74/1.45 % (31389)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_31277 for (2999ds/3Mi)
% 1.74/1.46 % (31389)Instruction limit reached!
% 1.74/1.46 % (31389)------------------------------
% 1.74/1.46 % (31389)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.46 % (31389)Termination reason: Unknown
% 1.74/1.46 % (31389)Termination phase: Property scanning
% 1.74/1.46
% 1.74/1.46 % (31389)Memory used [KB]: 1023
% 1.74/1.46 % (31389)Time elapsed: 0.003 s
% 1.74/1.46 % (31389)Instructions burned: 4 (million)
% 1.74/1.46 % (31389)------------------------------
% 1.74/1.46 % (31389)------------------------------
% 1.74/1.46 % (31387)Instruction limit reached!
% 1.74/1.46 % (31387)------------------------------
% 1.74/1.46 % (31387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.46 % (31387)Termination reason: Unknown
% 1.74/1.46 % (31387)Termination phase: Saturation
% 1.74/1.46
% 1.74/1.46 % (31387)Memory used [KB]: 5884
% 1.74/1.46 % (31387)Time elapsed: 0.010 s
% 1.74/1.46 % (31387)Instructions burned: 17 (million)
% 1.74/1.46 % (31387)------------------------------
% 1.74/1.46 % (31387)------------------------------
% 1.74/1.46 % (31390)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_31277 for (2999ds/7Mi)
% 1.74/1.46 % (31391)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_31277 for (2999ds/3Mi)
% 1.74/1.47 % (31390)Instruction limit reached!
% 1.74/1.47 % (31390)------------------------------
% 1.74/1.47 % (31390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.47 % (31390)Termination reason: Unknown
% 1.74/1.47 % (31390)Termination phase: Saturation
% 1.74/1.47
% 1.74/1.47 % (31390)Memory used [KB]: 5500
% 1.74/1.47 % (31390)Time elapsed: 0.005 s
% 1.74/1.47 % (31390)Instructions burned: 8 (million)
% 1.74/1.47 % (31390)------------------------------
% 1.74/1.47 % (31390)------------------------------
% 1.74/1.47 % (31391)Instruction limit reached!
% 1.74/1.47 % (31391)------------------------------
% 1.74/1.47 % (31391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.47 % (31391)Termination reason: Unknown
% 1.74/1.47 % (31391)Termination phase: Property scanning
% 1.74/1.47
% 1.74/1.47 % (31391)Memory used [KB]: 1023
% 1.74/1.47 % (31391)Time elapsed: 0.003 s
% 1.74/1.47 % (31391)Instructions burned: 4 (million)
% 1.74/1.47 % (31391)------------------------------
% 1.74/1.47 % (31391)------------------------------
% 1.74/1.47 % (31392)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_31277 for (2999ds/4Mi)
% 1.74/1.47 % (31392)Instruction limit reached!
% 1.74/1.47 % (31392)------------------------------
% 1.74/1.47 % (31392)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.47 % (31392)Termination reason: Unknown
% 1.74/1.47 % (31392)Termination phase: Property scanning
% 1.74/1.47
% 1.74/1.47 % (31392)Memory used [KB]: 1023
% 1.74/1.47 % (31392)Time elapsed: 0.003 s
% 1.74/1.47 % (31392)Instructions burned: 4 (million)
% 1.74/1.47 % (31392)------------------------------
% 1.74/1.47 % (31392)------------------------------
% 1.74/1.47 % (31393)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_31277 for (2999ds/18Mi)
% 1.74/1.47 % (31394)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_31277 for (2999ds/710Mi)
% 1.74/1.48 % (31393)Instruction limit reached!
% 1.74/1.48 % (31393)------------------------------
% 1.74/1.48 % (31393)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.48 % (31393)Termination reason: Unknown
% 1.74/1.48 % (31393)Termination phase: Saturation
% 1.74/1.48
% 1.74/1.48 % (31393)Memory used [KB]: 5628
% 1.74/1.48 % (31393)Time elapsed: 0.011 s
% 1.74/1.48 % (31393)Instructions burned: 19 (million)
% 1.74/1.48 % (31393)------------------------------
% 1.74/1.48 % (31393)------------------------------
% 1.74/1.48 % (31395)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_31277 for (2999ds/6Mi)
% 1.74/1.48 % (31396)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_31277 for (2999ds/902Mi)
% 1.74/1.48 % (31395)Instruction limit reached!
% 1.74/1.48 % (31395)------------------------------
% 1.74/1.48 % (31395)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.48 % (31395)Termination reason: Unknown
% 1.74/1.48 % (31395)Termination phase: Property scanning
% 1.74/1.48
% 1.74/1.48 % (31395)Memory used [KB]: 1023
% 1.74/1.48 % (31395)Time elapsed: 0.004 s
% 1.74/1.48 % (31395)Instructions burned: 6 (million)
% 1.74/1.48 % (31395)------------------------------
% 1.74/1.48 % (31395)------------------------------
% 1.74/1.49 % (31397)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_31277 for (2999ds/21Mi)
% 1.74/1.49 % (31374)Instruction limit reached!
% 1.74/1.49 % (31374)------------------------------
% 1.74/1.49 % (31374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.49 % (31374)Termination reason: Unknown
% 1.74/1.49 % (31374)Termination phase: Saturation
% 1.74/1.49
% 1.74/1.49 % (31374)Memory used [KB]: 7036
% 1.74/1.49 % (31374)Time elapsed: 0.077 s
% 1.74/1.49 % (31374)Instructions burned: 184 (million)
% 1.74/1.49 % (31374)------------------------------
% 1.74/1.49 % (31374)------------------------------
% 1.74/1.50 % (31398)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_31277 for (2999ds/5Mi)
% 1.74/1.50 % (31397)Instruction limit reached!
% 1.74/1.50 % (31397)------------------------------
% 1.74/1.50 % (31397)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.50 % (31397)Termination reason: Unknown
% 1.74/1.50 % (31397)Termination phase: Saturation
% 1.74/1.50
% 1.74/1.50 % (31397)Memory used [KB]: 5628
% 1.74/1.50 % (31397)Time elapsed: 0.013 s
% 1.74/1.50 % (31397)Instructions burned: 22 (million)
% 1.74/1.50 % (31397)------------------------------
% 1.74/1.50 % (31397)------------------------------
% 1.74/1.50 % (31398)Instruction limit reached!
% 1.74/1.50 % (31398)------------------------------
% 1.74/1.50 % (31398)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.50 % (31398)Termination reason: Unknown
% 1.74/1.50 % (31398)Termination phase: Property scanning
% 1.74/1.50
% 1.74/1.50 % (31398)Memory used [KB]: 1023
% 1.74/1.50 % (31398)Time elapsed: 0.004 s
% 1.74/1.50 % (31398)Instructions burned: 6 (million)
% 1.74/1.50 % (31398)------------------------------
% 1.74/1.50 % (31398)------------------------------
% 1.74/1.50 % (31399)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_31277 for (2999ds/6Mi)
% 1.74/1.50 % (31399)Instruction limit reached!
% 1.74/1.50 % (31399)------------------------------
% 1.74/1.50 % (31399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.50 % (31399)Termination reason: Unknown
% 1.74/1.50 % (31399)Termination phase: Preprocessing 1
% 1.74/1.50
% 1.74/1.50 % (31399)Memory used [KB]: 1023
% 1.74/1.50 % (31399)Time elapsed: 0.004 s
% 1.74/1.50 % (31399)Instructions burned: 6 (million)
% 1.74/1.50 % (31399)------------------------------
% 1.74/1.50 % (31399)------------------------------
% 1.74/1.50 % (31400)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_31277 for (2999ds/377Mi)
% 1.74/1.51 % (31401)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_31277 for (2999ds/779Mi)
% 1.74/1.52 % (31402)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_31277 for (2999ds/19Mi)
% 1.74/1.52 % (31403)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_31277 for (2999ds/879Mi)
% 1.74/1.52 % (31402)Instruction limit reached!
% 1.74/1.52 % (31402)------------------------------
% 1.74/1.52 % (31402)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.52 % (31402)Termination reason: Unknown
% 1.74/1.52 % (31402)Termination phase: Saturation
% 1.74/1.52
% 1.74/1.52 % (31402)Memory used [KB]: 5628
% 1.74/1.52 % (31402)Time elapsed: 0.011 s
% 1.74/1.52 % (31402)Instructions burned: 20 (million)
% 1.74/1.52 % (31402)------------------------------
% 1.74/1.52 % (31402)------------------------------
% 1.74/1.54 % (31404)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_31277 for (2998ds/17Mi)
% 1.74/1.55 % (31404)Instruction limit reached!
% 1.74/1.55 % (31404)------------------------------
% 1.74/1.55 % (31404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.55 % (31404)Termination reason: Unknown
% 1.74/1.55 % (31404)Termination phase: Saturation
% 1.74/1.55
% 1.74/1.55 % (31404)Memory used [KB]: 5756
% 1.74/1.55 % (31404)Time elapsed: 0.032 s
% 1.74/1.55 % (31404)Instructions burned: 18 (million)
% 1.74/1.55 % (31404)------------------------------
% 1.74/1.55 % (31404)------------------------------
% 1.74/1.56 % (31396)First to succeed.
% 1.74/1.57 % (31396)Refutation found. Thanks to Tanya!
% 1.74/1.57 % SZS status Theorem for DTF2THF_31277
% 1.74/1.57 % SZS output start Proof for DTF2THF_31277
% 1.74/1.57 thf(type_def_6, type, obj: $tType).
% 1.74/1.57 thf(type_def_7, type, mor: $tType).
% 1.74/1.57 thf(func_def_0, type, isPer: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 1.74/1.57 thf(func_def_2, type, obj: $tType).
% 1.74/1.57 thf(func_def_3, type, objStar: obj > obj > $o).
% 1.74/1.57 thf(func_def_4, type, mor: $tType).
% 1.74/1.57 thf(func_def_5, type, morStar: obj > obj > mor > mor > $o).
% 1.74/1.57 thf(func_def_6, type, id: obj > mor).
% 1.74/1.57 thf(func_def_7, type, comp: obj > obj > obj > mor > mor > mor).
% 1.74/1.57 thf(func_def_10, type, sK0: obj).
% 1.74/1.57 thf(func_def_11, type, sK1: obj).
% 1.74/1.57 thf(func_def_12, type, sK2: obj).
% 1.74/1.57 thf(func_def_13, type, sK3: mor).
% 1.74/1.57 thf(func_def_14, type, sK4: mor).
% 1.74/1.57 thf(func_def_15, type, sK5: mor).
% 1.74/1.57 thf(func_def_16, type, sK6: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.74/1.57 thf(func_def_17, type, sK7: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.74/1.57 thf(func_def_18, type, sK8: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.74/1.57 thf(func_def_19, type, sK9: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.74/1.57 thf(func_def_20, type, sK10: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.74/1.57 thf(func_def_22, type, ph12: !>[X0: $tType]:(X0)).
% 1.74/1.57 thf(f960,plain,(
% 1.74/1.57 $false),
% 1.74/1.57 inference(trivial_inequality_removal,[status(thm)],[f957])).
% 1.74/1.57 thf(f957,plain,(
% 1.74/1.57 ($true != $true)),
% 1.74/1.57 inference(superposition,[status(thm)],[f934,f56])).
% 1.74/1.57 thf(f56,plain,(
% 1.74/1.57 ($true = (morStar @ sK0 @ sK0 @ (comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4) @ (id @ sK0)))),
% 1.74/1.57 inference(cnf_transformation,[status(thm)],[f41])).
% 1.74/1.57 thf(f41,plain,(
% 1.74/1.57 (($true = (morStar @ sK0 @ sK2 @ sK5 @ sK5)) & ((morStar @ sK0 @ sK2 @ (comp @ sK0 @ sK1 @ sK2 @ sK3 @ (comp @ sK1 @ sK0 @ sK2 @ sK4 @ sK5)) @ sK5) != $true)) & ($true = (morStar @ sK0 @ sK1 @ (comp @ sK1 @ sK0 @ sK1 @ sK4 @ sK3) @ (id @ sK1))) & ($true = (morStar @ sK0 @ sK0 @ (comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4) @ (id @ sK0))) & ($true = (morStar @ sK1 @ sK0 @ sK4 @ sK4)) & ($true = (morStar @ sK0 @ sK1 @ sK3 @ sK3))),
% 1.74/1.57 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f38,f40,f39])).
% 1.74/1.57 thf(f39,plain,(
% 1.74/1.57 ? [X0 : obj,X1 : obj,X2 : obj,X3 : mor,X4 : mor] : (? [X5 : mor] : (((morStar @ X0 @ X2 @ X5 @ X5) = $true) & ($true != (morStar @ X0 @ X2 @ (comp @ X0 @ X1 @ X2 @ X3 @ (comp @ X1 @ X0 @ X2 @ X4 @ X5)) @ X5))) & ((morStar @ X0 @ X1 @ (comp @ X1 @ X0 @ X1 @ X4 @ X3) @ (id @ X1)) = $true) & ($true = (morStar @ X0 @ X0 @ (comp @ X0 @ X1 @ X0 @ X3 @ X4) @ (id @ X0))) & ($true = (morStar @ X1 @ X0 @ X4 @ X4)) & ($true = (morStar @ X0 @ X1 @ X3 @ X3))) => (? [X5 : mor] : (((morStar @ sK0 @ sK2 @ X5 @ X5) = $true) & ($true != (morStar @ sK0 @ sK2 @ (comp @ sK0 @ sK1 @ sK2 @ sK3 @ (comp @ sK1 @ sK0 @ sK2 @ sK4 @ X5)) @ X5))) & ($true = (morStar @ sK0 @ sK1 @ (comp @ sK1 @ sK0 @ sK1 @ sK4 @ sK3) @ (id @ sK1))) & ($true = (morStar @ sK0 @ sK0 @ (comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4) @ (id @ sK0))) & ($true = (morStar @ sK1 @ sK0 @ sK4 @ sK4)) & ($true = (morStar @ sK0 @ sK1 @ sK3 @ sK3)))),
% 1.74/1.57 introduced(definition,[],[choice_axiom])).
% 1.74/1.57 thf(f40,plain,(
% 1.74/1.57 ? [X5 : mor] : (((morStar @ sK0 @ sK2 @ X5 @ X5) = $true) & ($true != (morStar @ sK0 @ sK2 @ (comp @ sK0 @ sK1 @ sK2 @ sK3 @ (comp @ sK1 @ sK0 @ sK2 @ sK4 @ X5)) @ X5))) => (($true = (morStar @ sK0 @ sK2 @ sK5 @ sK5)) & ((morStar @ sK0 @ sK2 @ (comp @ sK0 @ sK1 @ sK2 @ sK3 @ (comp @ sK1 @ sK0 @ sK2 @ sK4 @ sK5)) @ sK5) != $true))),
% 1.74/1.57 introduced(definition,[],[choice_axiom])).
% 1.74/1.57 thf(f38,plain,(
% 1.74/1.57 ? [X0 : obj,X1 : obj,X2 : obj,X3 : mor,X4 : mor] : (? [X5 : mor] : (((morStar @ X0 @ X2 @ X5 @ X5) = $true) & ($true != (morStar @ X0 @ X2 @ (comp @ X0 @ X1 @ X2 @ X3 @ (comp @ X1 @ X0 @ X2 @ X4 @ X5)) @ X5))) & ((morStar @ X0 @ X1 @ (comp @ X1 @ X0 @ X1 @ X4 @ X3) @ (id @ X1)) = $true) & ($true = (morStar @ X0 @ X0 @ (comp @ X0 @ X1 @ X0 @ X3 @ X4) @ (id @ X0))) & ($true = (morStar @ X1 @ X0 @ X4 @ X4)) & ($true = (morStar @ X0 @ X1 @ X3 @ X3)))),
% 1.74/1.57 inference(flattening,[status(thm)],[f37])).
% 1.74/1.57 thf(f37,plain,(
% 1.74/1.57 ? [X0 : obj,X1 : obj,X2 : obj,X3 : mor,X4 : mor] : (((? [X5 : mor] : (((morStar @ X0 @ X2 @ X5 @ X5) = $true) & ($true != (morStar @ X0 @ X2 @ (comp @ X0 @ X1 @ X2 @ X3 @ (comp @ X1 @ X0 @ X2 @ X4 @ X5)) @ X5))) & (((morStar @ X0 @ X1 @ (comp @ X1 @ X0 @ X1 @ X4 @ X3) @ (id @ X1)) = $true) & ($true = (morStar @ X0 @ X0 @ (comp @ X0 @ X1 @ X0 @ X3 @ X4) @ (id @ X0))))) & ($true = (morStar @ X1 @ X0 @ X4 @ X4))) & ($true = (morStar @ X0 @ X1 @ X3 @ X3)))),
% 1.74/1.57 inference(ennf_transformation,[status(thm)],[f15])).
% 1.74/1.57 thf(f15,plain,(
% 1.74/1.57 ~! [X0 : obj,X1 : obj,X2 : obj,X3 : mor,X4 : mor] : (($true = (morStar @ X0 @ X1 @ X3 @ X3)) => (($true = (morStar @ X1 @ X0 @ X4 @ X4)) => ((((morStar @ X0 @ X1 @ (comp @ X1 @ X0 @ X1 @ X4 @ X3) @ (id @ X1)) = $true) & ($true = (morStar @ X0 @ X0 @ (comp @ X0 @ X1 @ X0 @ X3 @ X4) @ (id @ X0)))) => ! [X5 : mor] : (((morStar @ X0 @ X2 @ X5 @ X5) = $true) => ($true = (morStar @ X0 @ X2 @ (comp @ X0 @ X1 @ X2 @ X3 @ (comp @ X1 @ X0 @ X2 @ X4 @ X5)) @ X5))))))),
% 1.74/1.57 inference(fool_elimination,[status(thm)],[f14])).
% 1.74/1.57 thf(f14,plain,(
% 1.74/1.57 ~! [X0 : obj,X1 : obj,X2 : obj,X3 : mor,X4 : mor] : ((morStar @ X0 @ X1 @ X3 @ X3) => ((morStar @ X1 @ X0 @ X4 @ X4) => (((morStar @ X0 @ X0 @ (comp @ X0 @ X1 @ X0 @ X3 @ X4) @ (id @ X0)) & (morStar @ X0 @ X1 @ (comp @ X1 @ X0 @ X1 @ X4 @ X3) @ (id @ X1))) => ! [X5 : mor] : ((morStar @ X0 @ X2 @ X5 @ X5) => (morStar @ X0 @ X2 @ (comp @ X0 @ X1 @ X2 @ X3 @ (comp @ X1 @ X0 @ X2 @ X4 @ X5)) @ X5)))))),
% 1.74/1.57 inference(rectify,[status(thm)],[f10])).
% 1.74/1.57 thf(f10,negated_conjecture,(
% 1.74/1.57 ~! [X2 : obj,X3 : obj,X4 : obj,X12 : mor,X13 : mor] : ((morStar @ X2 @ X3 @ X12 @ X12) => ((morStar @ X3 @ X2 @ X13 @ X13) => (((morStar @ X2 @ X2 @ (comp @ X2 @ X3 @ X2 @ X12 @ X13) @ (id @ X2)) & (morStar @ X2 @ X3 @ (comp @ X3 @ X2 @ X3 @ X13 @ X12) @ (id @ X3))) => ! [X14 : mor] : ((morStar @ X2 @ X4 @ X14 @ X14) => (morStar @ X2 @ X4 @ (comp @ X2 @ X3 @ X4 @ X12 @ (comp @ X3 @ X2 @ X4 @ X13 @ X14)) @ X14)))))),
% 1.74/1.57 inference(negated_conjecture,[status(cth)],[f9])).
% 1.74/1.57 thf(f9,conjecture,(
% 1.74/1.57 ! [X2 : obj,X3 : obj,X4 : obj,X12 : mor,X13 : mor] : ((morStar @ X2 @ X3 @ X12 @ X12) => ((morStar @ X3 @ X2 @ X13 @ X13) => (((morStar @ X2 @ X2 @ (comp @ X2 @ X3 @ X2 @ X12 @ X13) @ (id @ X2)) & (morStar @ X2 @ X3 @ (comp @ X3 @ X2 @ X3 @ X13 @ X12) @ (id @ X3))) => ! [X14 : mor] : ((morStar @ X2 @ X4 @ X14 @ X14) => (morStar @ X2 @ X4 @ (comp @ X2 @ X3 @ X4 @ X12 @ (comp @ X3 @ X2 @ X4 @ X13 @ X14)) @ X14)))))),
% 1.74/1.57 file('/export/starexec/sandbox/tmp/tmp.2hUijUb1Os/DTF2THF_31277.p',conj)).
% 1.74/1.57 thf(f934,plain,(
% 1.74/1.57 ($true != (morStar @ sK0 @ sK0 @ (comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4) @ (id @ sK0)))),
% 1.74/1.57 inference(trivial_inequality_removal,[status(thm)],[f933])).
% 1.74/1.57 thf(f933,plain,(
% 1.74/1.57 ($true != (morStar @ sK0 @ sK0 @ (comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4) @ (id @ sK0))) | ($true != $true)),
% 1.74/1.57 inference(forward_demodulation,[status(thm)],[f932,f59])).
% 1.74/1.57 thf(f59,plain,(
% 1.74/1.57 ($true = (morStar @ sK0 @ sK2 @ sK5 @ sK5))),
% 1.74/1.57 inference(cnf_transformation,[status(thm)],[f41])).
% 1.74/1.57 thf(f932,plain,(
% 1.74/1.57 ($true != (morStar @ sK0 @ sK2 @ sK5 @ sK5)) | ($true != (morStar @ sK0 @ sK0 @ (comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4) @ (id @ sK0)))),
% 1.74/1.57 inference(trivial_inequality_removal,[status(thm)],[f931])).
% 1.74/1.57 thf(f931,plain,(
% 1.74/1.57 ($true != (morStar @ sK0 @ sK0 @ (comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4) @ (id @ sK0))) | ($true != (morStar @ sK0 @ sK2 @ sK5 @ sK5)) | ($true != $true)),
% 1.74/1.57 inference(duplicate_literal_removal,[status(thm)],[f926])).
% 1.74/1.57 thf(f926,plain,(
% 1.74/1.57 ($true != $true) | ($true != (morStar @ sK0 @ sK0 @ (comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4) @ (id @ sK0))) | ($true != (morStar @ sK0 @ sK2 @ sK5 @ sK5)) | ($true != (morStar @ sK0 @ sK2 @ sK5 @ sK5))),
% 1.74/1.57 inference(superposition,[status(thm)],[f239,f50])).
% 1.74/1.57 thf(f50,plain,(
% 1.74/1.57 ( ! [X2 : mor,X0 : obj,X1 : obj] : (($true = (morStar @ X0 @ X1 @ (comp @ X0 @ X0 @ X1 @ (id @ X0) @ X2) @ X2)) | ((morStar @ X0 @ X1 @ X2 @ X2) != $true)) )),
% 1.74/1.57 inference(cnf_transformation,[status(thm)],[f36])).
% 1.74/1.57 thf(f36,plain,(
% 1.74/1.57 ! [X0 : obj,X1 : obj,X2 : mor] : (((morStar @ X0 @ X1 @ X2 @ X2) != $true) | ($true = (morStar @ X0 @ X1 @ (comp @ X0 @ X0 @ X1 @ (id @ X0) @ X2) @ X2)))),
% 1.74/1.57 inference(ennf_transformation,[status(thm)],[f27])).
% 1.74/1.57 thf(f27,plain,(
% 1.74/1.57 ! [X0 : obj,X1 : obj,X2 : mor] : (((morStar @ X0 @ X1 @ X2 @ X2) = $true) => ($true = (morStar @ X0 @ X1 @ (comp @ X0 @ X0 @ X1 @ (id @ X0) @ X2) @ X2)))),
% 1.74/1.57 inference(fool_elimination,[status(thm)],[f26])).
% 1.74/1.57 thf(f26,plain,(
% 1.74/1.57 ! [X0 : obj,X1 : obj,X2 : mor] : ((morStar @ X0 @ X1 @ X2 @ X2) => (morStar @ X0 @ X1 @ (comp @ X0 @ X0 @ X1 @ (id @ X0) @ X2) @ X2))),
% 1.74/1.57 inference(rectify,[status(thm)],[f6])).
% 1.74/1.57 thf(f6,axiom,(
% 1.74/1.57 ! [X2 : obj,X3 : obj,X11 : mor] : ((morStar @ X2 @ X3 @ X11 @ X11) => (morStar @ X2 @ X3 @ (comp @ X2 @ X2 @ X3 @ (id @ X2) @ X11) @ X11))),
% 1.74/1.57 file('/export/starexec/sandbox/tmp/tmp.2hUijUb1Os/DTF2THF_31277.p',ax1)).
% 1.74/1.57 thf(f239,plain,(
% 1.74/1.57 ( ! [X0 : mor,X1 : mor] : (($true != (morStar @ sK0 @ sK2 @ (comp @ sK0 @ sK0 @ sK2 @ X0 @ X1) @ sK5)) | ($true != (morStar @ sK0 @ sK0 @ (comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4) @ X0)) | ($true != (morStar @ sK0 @ sK2 @ sK5 @ X1))) )),
% 1.74/1.57 inference(trivial_inequality_removal,[status(thm)],[f236])).
% 1.74/1.57 thf(f236,plain,(
% 1.74/1.57 ( ! [X0 : mor,X1 : mor] : (($true != $true) | ($true != (morStar @ sK0 @ sK2 @ sK5 @ X1)) | ($true != (morStar @ sK0 @ sK2 @ (comp @ sK0 @ sK0 @ sK2 @ X0 @ X1) @ sK5)) | ($true != (morStar @ sK0 @ sK0 @ (comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4) @ X0))) )),
% 1.74/1.57 inference(superposition,[status(thm)],[f119,f53])).
% 1.74/1.57 thf(f53,plain,(
% 1.74/1.57 ( ! [X2 : obj,X3 : mor,X0 : obj,X1 : obj,X6 : mor,X4 : mor,X5 : mor] : (($true = (morStar @ X0 @ X2 @ (comp @ X0 @ X1 @ X2 @ X3 @ X5) @ (comp @ X0 @ X1 @ X2 @ X4 @ X6))) | ($true != (morStar @ X1 @ X2 @ X5 @ X6)) | ((morStar @ X0 @ X1 @ X3 @ X4) != $true)) )),
% 1.74/1.57 inference(cnf_transformation,[status(thm)],[f30])).
% 1.74/1.57 thf(f30,plain,(
% 1.74/1.57 ! [X0 : obj,X1 : obj,X2 : obj,X3 : mor,X4 : mor] : (((morStar @ X0 @ X1 @ X3 @ X4) != $true) | ! [X5 : mor,X6 : mor] : (($true = (morStar @ X0 @ X2 @ (comp @ X0 @ X1 @ X2 @ X3 @ X5) @ (comp @ X0 @ X1 @ X2 @ X4 @ X6))) | ($true != (morStar @ X1 @ X2 @ X5 @ X6))))),
% 1.74/1.57 inference(ennf_transformation,[status(thm)],[f17])).
% 1.74/1.57 thf(f17,plain,(
% 1.74/1.57 ! [X0 : obj,X1 : obj,X2 : obj,X3 : mor,X4 : mor] : (((morStar @ X0 @ X1 @ X3 @ X4) = $true) => ! [X5 : mor,X6 : mor] : (($true = (morStar @ X1 @ X2 @ X5 @ X6)) => ($true = (morStar @ X0 @ X2 @ (comp @ X0 @ X1 @ X2 @ X3 @ X5) @ (comp @ X0 @ X1 @ X2 @ X4 @ X6)))))),
% 1.74/1.57 inference(fool_elimination,[status(thm)],[f16])).
% 1.74/1.57 thf(f16,plain,(
% 1.74/1.57 ! [X0 : obj,X1 : obj,X2 : obj,X3 : mor,X4 : mor] : ((morStar @ X0 @ X1 @ X3 @ X4) => ! [X5 : mor,X6 : mor] : ((morStar @ X1 @ X2 @ X5 @ X6) => (morStar @ X0 @ X2 @ (comp @ X0 @ X1 @ X2 @ X3 @ X5) @ (comp @ X0 @ X1 @ X2 @ X4 @ X6))))),
% 1.74/1.57 inference(rectify,[status(thm)],[f5])).
% 1.74/1.57 thf(f5,axiom,(
% 1.74/1.57 ! [X2 : obj,X3 : obj,X4 : obj,X7 : mor,X8 : mor] : ((morStar @ X2 @ X3 @ X7 @ X8) => ! [X9 : mor,X10 : mor] : ((morStar @ X3 @ X4 @ X9 @ X10) => (morStar @ X2 @ X4 @ (comp @ X2 @ X3 @ X4 @ X7 @ X9) @ (comp @ X2 @ X3 @ X4 @ X8 @ X10))))),
% 1.74/1.57 file('/export/starexec/sandbox/tmp/tmp.2hUijUb1Os/DTF2THF_31277.p',comp_tp_ax)).
% 1.74/1.57 thf(f119,plain,(
% 1.74/1.57 ( ! [X0 : mor] : (((morStar @ sK0 @ sK2 @ (comp @ sK0 @ sK0 @ sK2 @ (comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4) @ sK5) @ X0) != $true) | ($true != (morStar @ sK0 @ sK2 @ X0 @ sK5))) )),
% 1.74/1.57 inference(trivial_inequality_removal,[status(thm)],[f118])).
% 1.74/1.57 thf(f118,plain,(
% 1.74/1.57 ( ! [X0 : mor] : (((morStar @ sK0 @ sK2 @ (comp @ sK0 @ sK0 @ sK2 @ (comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4) @ sK5) @ X0) != $true) | ($true != (morStar @ sK0 @ sK2 @ X0 @ sK5)) | ($true != $true)) )),
% 1.74/1.57 inference(forward_demodulation,[status(thm)],[f117,f52])).
% 1.74/1.57 thf(f52,plain,(
% 1.74/1.57 ( ! [X0 : obj,X1 : obj] : (($true = (isPer @ mor @ (morStar @ X0 @ X1)))) )),
% 1.74/1.57 inference(cnf_transformation,[status(thm)],[f13])).
% 1.74/1.57 thf(f13,plain,(
% 1.74/1.57 ! [X0 : obj,X1 : obj] : ($true = (isPer @ mor @ (morStar @ X0 @ X1)))),
% 1.74/1.57 inference(fool_elimination,[status(thm)],[f12])).
% 1.74/1.57 thf(f12,plain,(
% 1.74/1.57 ! [X0 : obj,X1 : obj] : (isPer @ mor @ (morStar @ X0 @ X1))),
% 1.74/1.57 inference(rectify,[status(thm)],[f3])).
% 1.74/1.57 thf(f3,axiom,(
% 1.74/1.57 ! [X5 : obj,X6 : obj] : (isPer @ mor @ (morStar @ X5 @ X6))),
% 1.74/1.57 file('/export/starexec/sandbox/tmp/tmp.2hUijUb1Os/DTF2THF_31277.p','\'morStar\'_is_per')).
% 1.74/1.57 thf(f117,plain,(
% 1.74/1.57 ( ! [X0 : mor] : (($true != (morStar @ sK0 @ sK2 @ X0 @ sK5)) | ((morStar @ sK0 @ sK2 @ (comp @ sK0 @ sK0 @ sK2 @ (comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4) @ sK5) @ X0) != $true) | ((isPer @ mor @ (morStar @ sK0 @ sK2)) != $true)) )),
% 1.74/1.57 inference(trivial_inequality_removal,[status(thm)],[f115])).
% 1.74/1.57 thf(f115,plain,(
% 1.74/1.57 ( ! [X0 : mor] : (($true != (morStar @ sK0 @ sK2 @ X0 @ sK5)) | ((morStar @ sK0 @ sK2 @ (comp @ sK0 @ sK0 @ sK2 @ (comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4) @ sK5) @ X0) != $true) | ((isPer @ mor @ (morStar @ sK0 @ sK2)) != $true) | ($true != $true)) )),
% 1.74/1.57 inference(superposition,[status(thm)],[f113,f68])).
% 1.74/1.57 thf(f68,plain,(
% 1.74/1.57 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > X0 > $o,X4 : X0] : (((X1 @ X2 @ X4) = $true) | ((X1 @ X3 @ X4) != $true) | ((X1 @ X2 @ X3) != $true) | ((isPer @ X0 @ X1) != $true)) )),
% 1.74/1.57 inference(cnf_transformation,[status(thm)],[f47])).
% 1.74/1.57 thf(f47,plain,(
% 1.74/1.57 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((! [X2 : X0,X3 : X0,X4 : X0] : (((X1 @ X3 @ X4) != $true) | ((X1 @ X2 @ X3) != $true) | ((X1 @ X2 @ X4) = $true)) & ! [X5 : X0,X6 : X0] : (($true != (X1 @ X5 @ X6)) | ($true = (X1 @ X6 @ X5)))) | ((isPer @ X0 @ X1) != $true)) & (((isPer @ X0 @ X1) = $true) | (($true = (X1 @ (sK7 @ X0 @ X1) @ (sK8 @ X0 @ X1))) & ((X1 @ (sK6 @ X0 @ X1) @ (sK7 @ X0 @ X1)) = $true) & ($true != (X1 @ (sK6 @ X0 @ X1) @ (sK8 @ X0 @ X1)))) | (($true = (X1 @ (sK9 @ X0 @ X1) @ (sK10 @ X0 @ X1))) & ($true != (X1 @ (sK10 @ X0 @ X1) @ (sK9 @ X0 @ X1))))))),
% 1.74/1.57 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9,sK10])],[f44,f46,f45])).
% 1.74/1.57 thf(f45,plain,(
% 1.74/1.57 ! [X0 : $tType,X1 : X0 > X0 > $o] : (? [X7 : X0,X8 : X0,X9 : X0] : (($true = (X1 @ X8 @ X9)) & ($true = (X1 @ X7 @ X8)) & ((X1 @ X7 @ X9) != $true)) => (($true = (X1 @ (sK7 @ X0 @ X1) @ (sK8 @ X0 @ X1))) & ((X1 @ (sK6 @ X0 @ X1) @ (sK7 @ X0 @ X1)) = $true) & ($true != (X1 @ (sK6 @ X0 @ X1) @ (sK8 @ X0 @ X1)))))),
% 1.74/1.57 introduced(definition,[],[choice_axiom])).
% 1.74/1.57 thf(f46,plain,(
% 1.74/1.57 ! [X0 : $tType,X1 : X0 > X0 > $o] : (? [X10 : X0,X11 : X0] : (($true = (X1 @ X10 @ X11)) & ($true != (X1 @ X11 @ X10))) => (($true = (X1 @ (sK9 @ X0 @ X1) @ (sK10 @ X0 @ X1))) & ($true != (X1 @ (sK10 @ X0 @ X1) @ (sK9 @ X0 @ X1)))))),
% 1.74/1.57 introduced(definition,[],[choice_axiom])).
% 1.74/1.57 thf(f44,plain,(
% 1.74/1.57 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((! [X2 : X0,X3 : X0,X4 : X0] : (((X1 @ X3 @ X4) != $true) | ((X1 @ X2 @ X3) != $true) | ((X1 @ X2 @ X4) = $true)) & ! [X5 : X0,X6 : X0] : (($true != (X1 @ X5 @ X6)) | ($true = (X1 @ X6 @ X5)))) | ((isPer @ X0 @ X1) != $true)) & (((isPer @ X0 @ X1) = $true) | ? [X7 : X0,X8 : X0,X9 : X0] : (($true = (X1 @ X8 @ X9)) & ($true = (X1 @ X7 @ X8)) & ((X1 @ X7 @ X9) != $true)) | ? [X10 : X0,X11 : X0] : (($true = (X1 @ X10 @ X11)) & ($true != (X1 @ X11 @ X10)))))),
% 1.74/1.57 inference(rectify,[status(thm)],[f43])).
% 1.74/1.57 thf(f43,plain,(
% 1.74/1.57 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((! [X4 : X0,X5 : X0,X6 : X0] : (($true != (X1 @ X5 @ X6)) | ((X1 @ X4 @ X5) != $true) | ((X1 @ X4 @ X6) = $true)) & ! [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3) != $true) | ((X1 @ X3 @ X2) = $true))) | ((isPer @ X0 @ X1) != $true)) & (((isPer @ X0 @ X1) = $true) | ? [X4 : X0,X5 : X0,X6 : X0] : (($true = (X1 @ X5 @ X6)) & ((X1 @ X4 @ X5) = $true) & ((X1 @ X4 @ X6) != $true)) | ? [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3) = $true) & ((X1 @ X3 @ X2) != $true))))),
% 1.74/1.57 inference(flattening,[status(thm)],[f42])).
% 1.74/1.57 thf(f42,plain,(
% 1.74/1.57 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((! [X4 : X0,X5 : X0,X6 : X0] : (($true != (X1 @ X5 @ X6)) | ((X1 @ X4 @ X5) != $true) | ((X1 @ X4 @ X6) = $true)) & ! [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3) != $true) | ((X1 @ X3 @ X2) = $true))) | ((isPer @ X0 @ X1) != $true)) & (((isPer @ X0 @ X1) = $true) | (? [X4 : X0,X5 : X0,X6 : X0] : (($true = (X1 @ X5 @ X6)) & ((X1 @ X4 @ X5) = $true) & ((X1 @ X4 @ X6) != $true)) | ? [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3) = $true) & ((X1 @ X3 @ X2) != $true)))))),
% 1.74/1.57 inference(nnf_transformation,[status(thm)],[f32])).
% 1.74/1.57 thf(f32,plain,(
% 1.74/1.57 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((! [X4 : X0,X5 : X0,X6 : X0] : (($true != (X1 @ X5 @ X6)) | ((X1 @ X4 @ X5) != $true) | ((X1 @ X4 @ X6) = $true)) & ! [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3) != $true) | ((X1 @ X3 @ X2) = $true))) <=> ((isPer @ X0 @ X1) = $true))),
% 1.74/1.57 inference(flattening,[status(thm)],[f31])).
% 1.74/1.57 thf(f31,plain,(
% 1.74/1.57 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((! [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3) != $true) | ((X1 @ X3 @ X2) = $true)) & ! [X4 : X0,X5 : X0,X6 : X0] : ((((X1 @ X4 @ X6) = $true) | ($true != (X1 @ X5 @ X6))) | ((X1 @ X4 @ X5) != $true))) <=> ((isPer @ X0 @ X1) = $true))),
% 1.74/1.57 inference(ennf_transformation,[status(thm)],[f21])).
% 1.74/1.57 thf(f21,plain,(
% 1.74/1.57 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((! [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3) = $true) => ((X1 @ X3 @ X2) = $true)) & ! [X4 : X0,X5 : X0,X6 : X0] : (((X1 @ X4 @ X5) = $true) => (($true = (X1 @ X5 @ X6)) => ((X1 @ X4 @ X6) = $true)))) <=> ((isPer @ X0 @ X1) = $true))),
% 1.74/1.57 inference(fool_elimination,[status(thm)],[f20])).
% 1.74/1.57 thf(f20,plain,(
% 1.74/1.57 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((! [X2 : X0,X3 : X0] : ((X1 @ X2 @ X3) => (X1 @ X3 @ X2)) & ! [X4 : X0,X5 : X0,X6 : X0] : ((X1 @ X4 @ X5) => ((X1 @ X5 @ X6) => (X1 @ X4 @ X6)))) <=> (isPer @ X0 @ X1))),
% 1.74/1.57 inference(rectify,[status(thm)],[f1])).
% 1.74/1.57 thf(f1,axiom,(
% 1.74/1.57 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((! [X2 : X0,X3 : X0] : ((X1 @ X2 @ X3) => (X1 @ X3 @ X2)) & ! [X2 : X0,X3 : X0,X4 : X0] : ((X1 @ X2 @ X3) => ((X1 @ X3 @ X4) => (X1 @ X2 @ X4)))) <=> (isPer @ X0 @ X1))),
% 1.74/1.57 file('/export/starexec/sandbox/tmp/tmp.2hUijUb1Os/DTF2THF_31277.p',is_per)).
% 1.74/1.57 thf(f113,plain,(
% 1.74/1.57 ($true != (morStar @ sK0 @ sK2 @ (comp @ sK0 @ sK0 @ sK2 @ (comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4) @ sK5) @ sK5))),
% 1.74/1.57 inference(trivial_inequality_removal,[status(thm)],[f112])).
% 1.74/1.57 thf(f112,plain,(
% 1.74/1.57 ($true != $true) | ($true != (morStar @ sK0 @ sK2 @ (comp @ sK0 @ sK0 @ sK2 @ (comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4) @ sK5) @ sK5))),
% 1.74/1.57 inference(forward_demodulation,[status(thm)],[f111,f54])).
% 1.74/1.57 thf(f54,plain,(
% 1.74/1.57 ($true = (morStar @ sK0 @ sK1 @ sK3 @ sK3))),
% 1.74/1.57 inference(cnf_transformation,[status(thm)],[f41])).
% 1.74/1.57 thf(f111,plain,(
% 1.74/1.57 ($true != (morStar @ sK0 @ sK2 @ (comp @ sK0 @ sK0 @ sK2 @ (comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4) @ sK5) @ sK5)) | ($true != (morStar @ sK0 @ sK1 @ sK3 @ sK3))),
% 1.74/1.57 inference(trivial_inequality_removal,[status(thm)],[f110])).
% 1.74/1.57 thf(f110,plain,(
% 1.74/1.57 ($true != (morStar @ sK0 @ sK1 @ sK3 @ sK3)) | ($true != $true) | ($true != (morStar @ sK0 @ sK2 @ (comp @ sK0 @ sK0 @ sK2 @ (comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4) @ sK5) @ sK5))),
% 1.74/1.57 inference(forward_demodulation,[status(thm)],[f109,f55])).
% 1.74/1.57 thf(f55,plain,(
% 1.74/1.57 ($true = (morStar @ sK1 @ sK0 @ sK4 @ sK4))),
% 1.74/1.57 inference(cnf_transformation,[status(thm)],[f41])).
% 1.74/1.57 thf(f109,plain,(
% 1.74/1.57 ($true != (morStar @ sK1 @ sK0 @ sK4 @ sK4)) | ($true != (morStar @ sK0 @ sK2 @ (comp @ sK0 @ sK0 @ sK2 @ (comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4) @ sK5) @ sK5)) | ($true != (morStar @ sK0 @ sK1 @ sK3 @ sK3))),
% 1.74/1.57 inference(trivial_inequality_removal,[status(thm)],[f108])).
% 1.74/1.57 thf(f108,plain,(
% 1.74/1.57 ($true != (morStar @ sK0 @ sK2 @ (comp @ sK0 @ sK0 @ sK2 @ (comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4) @ sK5) @ sK5)) | ($true != $true) | ($true != (morStar @ sK0 @ sK1 @ sK3 @ sK3)) | ($true != (morStar @ sK1 @ sK0 @ sK4 @ sK4))),
% 1.74/1.57 inference(forward_demodulation,[status(thm)],[f100,f59])).
% 1.74/1.57 thf(f100,plain,(
% 1.74/1.57 ($true != (morStar @ sK0 @ sK2 @ sK5 @ sK5)) | ($true != (morStar @ sK1 @ sK0 @ sK4 @ sK4)) | ($true != (morStar @ sK0 @ sK1 @ sK3 @ sK3)) | ($true != (morStar @ sK0 @ sK2 @ (comp @ sK0 @ sK0 @ sK2 @ (comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4) @ sK5) @ sK5))),
% 1.74/1.57 inference(trivial_inequality_removal,[status(thm)],[f97])).
% 1.74/1.57 thf(f97,plain,(
% 1.74/1.57 ($true != $true) | ($true != (morStar @ sK0 @ sK2 @ sK5 @ sK5)) | ($true != (morStar @ sK1 @ sK0 @ sK4 @ sK4)) | ($true != (morStar @ sK0 @ sK2 @ (comp @ sK0 @ sK0 @ sK2 @ (comp @ sK0 @ sK1 @ sK0 @ sK3 @ sK4) @ sK5) @ sK5)) | ($true != (morStar @ sK0 @ sK1 @ sK3 @ sK3))),
% 1.74/1.57 inference(superposition,[status(thm)],[f77,f49])).
% 1.74/1.57 thf(f49,plain,(
% 1.74/1.57 ( ! [X2 : obj,X3 : obj,X0 : obj,X1 : obj,X6 : mor,X4 : mor,X5 : mor] : (($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))) | ($true != (morStar @ X2 @ X3 @ X6 @ X6)) | ($true != (morStar @ X1 @ X2 @ X5 @ X5)) | ($true != (morStar @ X0 @ X1 @ X4 @ X4))) )),
% 1.74/1.57 inference(cnf_transformation,[status(thm)],[f35])).
% 1.74/1.57 thf(f35,plain,(
% 1.74/1.57 ! [X0 : obj,X1 : obj,X2 : obj,X3 : obj,X4 : mor,X5 : mor,X6 : mor] : (($true != (morStar @ X0 @ X1 @ X4 @ X4)) | ($true != (morStar @ X1 @ X2 @ X5 @ X5)) | ($true = (morStar @ X0 @ X3 @ (comp @ X0 @ X1 @ X3 @ X4 @ (comp @ X1 @ X2 @ X3 @ X5 @ X6)) @ (comp @ X0 @ X2 @ X3 @ (comp @ X0 @ X1 @ X2 @ X4 @ X5) @ X6))) | ($true != (morStar @ X2 @ X3 @ X6 @ X6)))),
% 1.74/1.57 inference(flattening,[status(thm)],[f34])).
% 1.74/1.57 thf(f34,plain,(
% 1.74/1.57 ! [X0 : obj,X1 : obj,X2 : obj,X3 : obj,X4 : mor,X5 : mor,X6 : mor] : (((($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))) | ($true != (morStar @ X0 @ X1 @ X4 @ X4)))),
% 1.74/1.57 inference(ennf_transformation,[status(thm)],[f25])).
% 1.74/1.57 thf(f25,plain,(
% 1.74/1.57 ! [X0 : obj,X1 : obj,X2 : obj,X3 : obj,X4 : mor,X5 : mor,X6 : mor] : (($true = (morStar @ X0 @ X1 @ X4 @ X4)) => (($true = (morStar @ X1 @ X2 @ X5 @ X5)) => (($true = (morStar @ X2 @ X3 @ X6 @ X6)) => ($true = (morStar @ X0 @ X3 @ (comp @ X0 @ X1 @ X3 @ X4 @ (comp @ X1 @ X2 @ X3 @ X5 @ X6)) @ (comp @ X0 @ X2 @ X3 @ (comp @ X0 @ X1 @ X2 @ X4 @ X5) @ X6))))))),
% 1.74/1.57 inference(fool_elimination,[status(thm)],[f24])).
% 1.74/1.57 thf(f24,plain,(
% 1.74/1.57 ! [X0 : obj,X1 : obj,X2 : obj,X3 : obj,X4 : mor,X5 : mor,X6 : mor] : ((morStar @ X0 @ X1 @ X4 @ X4) => ((morStar @ X1 @ X2 @ X5 @ X5) => ((morStar @ X2 @ X3 @ X6 @ X6) => (morStar @ X0 @ X3 @ (comp @ X0 @ X1 @ X3 @ X4 @ (comp @ X1 @ X2 @ X3 @ X5 @ X6)) @ (comp @ X0 @ X2 @ X3 @ (comp @ X0 @ X1 @ X2 @ X4 @ X5) @ X6)))))),
% 1.74/1.57 inference(rectify,[status(thm)],[f8])).
% 1.74/1.57 thf(f8,axiom,(
% 1.74/1.57 ! [X2 : obj,X3 : obj,X4 : obj,X0 : obj,X12 : mor,X13 : mor,X14 : mor] : ((morStar @ X2 @ X3 @ X12 @ X12) => ((morStar @ X3 @ X4 @ X13 @ X13) => ((morStar @ X4 @ X0 @ X14 @ X14) => (morStar @ X2 @ X0 @ (comp @ X2 @ X3 @ X0 @ X12 @ (comp @ X3 @ X4 @ X0 @ X13 @ X14)) @ (comp @ X2 @ X4 @ X0 @ (comp @ X2 @ X3 @ X4 @ X12 @ X13) @ X14)))))),
% 1.74/1.57 file('/export/starexec/sandbox/tmp/tmp.2hUijUb1Os/DTF2THF_31277.p',ax3)).
% 1.74/1.57 thf(f77,plain,(
% 1.74/1.57 ( ! [X0 : mor] : (($true != (morStar @ sK0 @ sK2 @ (comp @ sK0 @ sK1 @ sK2 @ sK3 @ (comp @ sK1 @ sK0 @ sK2 @ sK4 @ sK5)) @ X0)) | ($true != (morStar @ sK0 @ sK2 @ X0 @ sK5))) )),
% 1.74/1.57 inference(trivial_inequality_removal,[status(thm)],[f76])).
% 1.74/1.57 thf(f76,plain,(
% 1.74/1.57 ( ! [X0 : mor] : (($true != $true) | ($true != (morStar @ sK0 @ sK2 @ X0 @ sK5)) | ($true != (morStar @ sK0 @ sK2 @ (comp @ sK0 @ sK1 @ sK2 @ sK3 @ (comp @ sK1 @ sK0 @ sK2 @ sK4 @ sK5)) @ X0))) )),
% 1.74/1.57 inference(forward_demodulation,[status(thm)],[f75,f52])).
% 1.74/1.57 thf(f75,plain,(
% 1.74/1.57 ( ! [X0 : mor] : (($true != (morStar @ sK0 @ sK2 @ X0 @ sK5)) | ($true != (morStar @ sK0 @ sK2 @ (comp @ sK0 @ sK1 @ sK2 @ sK3 @ (comp @ sK1 @ sK0 @ sK2 @ sK4 @ sK5)) @ X0)) | ((isPer @ mor @ (morStar @ sK0 @ sK2)) != $true)) )),
% 1.74/1.57 inference(trivial_inequality_removal,[status(thm)],[f73])).
% 1.74/1.57 thf(f73,plain,(
% 1.74/1.57 ( ! [X0 : mor] : (((isPer @ mor @ (morStar @ sK0 @ sK2)) != $true) | ($true != (morStar @ sK0 @ sK2 @ X0 @ sK5)) | ($true != (morStar @ sK0 @ sK2 @ (comp @ sK0 @ sK1 @ sK2 @ sK3 @ (comp @ sK1 @ sK0 @ sK2 @ sK4 @ sK5)) @ X0)) | ($true != $true)) )),
% 1.74/1.57 inference(superposition,[status(thm)],[f58,f68])).
% 1.74/1.57 thf(f58,plain,(
% 1.74/1.57 ((morStar @ sK0 @ sK2 @ (comp @ sK0 @ sK1 @ sK2 @ sK3 @ (comp @ sK1 @ sK0 @ sK2 @ sK4 @ sK5)) @ sK5) != $true)),
% 1.74/1.57 inference(cnf_transformation,[status(thm)],[f41])).
% 1.74/1.57 % SZS output end Proof for DTF2THF_31277
% 1.74/1.57 % (31396)------------------------------
% 1.74/1.57 % (31396)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.57 % (31396)Termination reason: Refutation
% 1.74/1.57
% 1.74/1.57 % (31396)Memory used [KB]: 6012
% 1.74/1.57 % (31396)Time elapsed: 0.085 s
% 1.74/1.57 % (31396)Instructions burned: 164 (million)
% 1.74/1.57 % (31396)------------------------------
% 1.74/1.57 % (31396)------------------------------
% 1.74/1.57 % (31373)Success in time 0.156 s
%------------------------------------------------------------------------------