%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : CAT040^1 : 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 : n031.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 1.87s 1.60s
% Output : Refutation 1.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 9
% Syntax : Number of formulae : 63 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 509 ( 193 equ; 0 cnn)
% Maximal formula atoms : 14 ( 8 avg)
% Number of connectives : 1183 ( 89 ~; 61 |; 73 &; 922 @)
% ( 5 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 7 con; 0-5 aty)
% Number of variables : 197 ( 0 ^; 162 !; 35 ?; 197 :)
% 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:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
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_21,type,
ph11:
!>[X0: $tType] : X0 ).
thf(f202,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f198]) ).
thf(f198,plain,
$true != $true,
inference(superposition,[status(thm)],[f179,f49]) ).
thf(f49,plain,
! [X0: obj] :
( $true
= ( morStar @ X0 @ X0 @ ( id @ X0 ) @ ( id @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: obj] :
( $true
= ( morStar @ X0 @ X0 @ ( id @ X0 ) @ ( id @ X0 ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: obj] : ( morStar @ X0 @ X0 @ ( id @ X0 ) @ ( id @ X0 ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X2: obj] : ( morStar @ X2 @ X2 @ ( id @ X2 ) @ ( id @ X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.lEGYaQ07tq/DTF2THF_28409.p',id_tp_ax) ).
thf(f179,plain,
( ( morStar @ sK0 @ sK0 @ ( id @ sK0 ) @ ( id @ sK0 ) )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f178]) ).
thf(f178,plain,
( ( ( morStar @ sK0 @ sK0 @ ( id @ sK0 ) @ ( id @ sK0 ) )
!= $true )
| ( $true != $true ) ),
inference(forward_demodulation,[status(thm)],[f177,f79]) ).
thf(f79,plain,
( $true
= ( morStar @ sK0 @ sK0 @ sK4 @ ( id @ sK0 ) ) ),
inference(forward_demodulation,[status(thm)],[f78,f53]) ).
thf(f53,plain,
sK1 = sK0,
inference(cnf_transformation,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ( morStar @ sK0 @ sK2 @ ( comp @ sK0 @ sK1 @ sK2 @ sK3 @ sK4 ) @ ( id @ sK2 ) )
!= $true )
& ( $true
= ( morStar @ sK0 @ sK1 @ sK3 @ sK3 ) )
& ( $true
= ( morStar @ sK1 @ sK2 @ sK4 @ sK4 ) )
& ( sK1 = sK0 )
& ( ( morStar @ sK1 @ sK2 @ sK4 @ ( id @ sK1 ) )
= $true )
& ( sK2 = sK1 )
& ( $true
= ( morStar @ sK0 @ sK1 @ sK3 @ ( id @ sK0 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f31,f39]) ).
thf(f39,plain,
( ? [X0: obj,X1: obj,X2: obj,X3: mor,X4: mor] :
( ( ( morStar @ X0 @ X2 @ ( comp @ X0 @ X1 @ X2 @ X3 @ X4 ) @ ( id @ X2 ) )
!= $true )
& ( $true
= ( morStar @ X0 @ X1 @ X3 @ X3 ) )
& ( $true
= ( morStar @ X1 @ X2 @ X4 @ X4 ) )
& ( X0 = X1 )
& ( $true
= ( morStar @ X1 @ X2 @ X4 @ ( id @ X1 ) ) )
& ( X1 = X2 )
& ( $true
= ( morStar @ X0 @ X1 @ X3 @ ( id @ X0 ) ) ) )
=> ( ( ( morStar @ sK0 @ sK2 @ ( comp @ sK0 @ sK1 @ sK2 @ sK3 @ sK4 ) @ ( id @ sK2 ) )
!= $true )
& ( $true
= ( morStar @ sK0 @ sK1 @ sK3 @ sK3 ) )
& ( $true
= ( morStar @ sK1 @ sK2 @ sK4 @ sK4 ) )
& ( sK1 = sK0 )
& ( ( morStar @ sK1 @ sK2 @ sK4 @ ( id @ sK1 ) )
= $true )
& ( sK2 = sK1 )
& ( $true
= ( morStar @ sK0 @ sK1 @ sK3 @ ( id @ sK0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f31,plain,
? [X0: obj,X1: obj,X2: obj,X3: mor,X4: mor] :
( ( ( morStar @ X0 @ X2 @ ( comp @ X0 @ X1 @ X2 @ X3 @ X4 ) @ ( id @ X2 ) )
!= $true )
& ( $true
= ( morStar @ X0 @ X1 @ X3 @ X3 ) )
& ( $true
= ( morStar @ X1 @ X2 @ X4 @ X4 ) )
& ( X0 = X1 )
& ( $true
= ( morStar @ X1 @ X2 @ X4 @ ( id @ X1 ) ) )
& ( X1 = X2 )
& ( $true
= ( morStar @ X0 @ X1 @ X3 @ ( id @ X0 ) ) ) ),
inference(flattening,[status(thm)],[f30]) ).
thf(f30,plain,
? [X0: obj,X1: obj,X2: obj,X3: mor,X4: mor] :
( ( ( morStar @ X0 @ X2 @ ( comp @ X0 @ X1 @ X2 @ X3 @ X4 ) @ ( id @ X2 ) )
!= $true )
& ( $true
= ( morStar @ X0 @ X1 @ X3 @ ( id @ X0 ) ) )
& ( X1 = X2 )
& ( X0 = X1 )
& ( $true
= ( morStar @ X1 @ X2 @ X4 @ ( id @ X1 ) ) )
& ( $true
= ( morStar @ X1 @ X2 @ X4 @ X4 ) )
& ( $true
= ( morStar @ X0 @ X1 @ X3 @ X3 ) ) ),
inference(ennf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
~ ! [X0: obj,X1: obj,X2: obj,X3: mor,X4: mor] :
( ( $true
= ( morStar @ X0 @ X1 @ X3 @ X3 ) )
=> ( ( $true
= ( morStar @ X1 @ X2 @ X4 @ X4 ) )
=> ( ( ( $true
= ( morStar @ X0 @ X1 @ X3 @ ( id @ X0 ) ) )
& ( X1 = X2 )
& ( X0 = X1 )
& ( $true
= ( morStar @ X1 @ X2 @ X4 @ ( id @ X1 ) ) ) )
=> ( ( morStar @ X0 @ X2 @ ( comp @ X0 @ X1 @ X2 @ X3 @ X4 ) @ ( id @ X2 ) )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f24]) ).
thf(f24,plain,
~ ! [X0: obj,X1: obj,X2: obj,X3: mor,X4: mor] :
( ( morStar @ X0 @ X1 @ X3 @ X3 )
=> ( ( morStar @ X1 @ X2 @ X4 @ X4 )
=> ( ( ( X0 = X1 )
& ( morStar @ X0 @ X1 @ X3 @ ( id @ X0 ) )
& ( X1 = X2 )
& ( morStar @ X1 @ X2 @ X4 @ ( id @ X1 ) ) )
=> ( morStar @ X0 @ X2 @ ( comp @ X0 @ X1 @ X2 @ X3 @ X4 ) @ ( id @ X2 ) ) ) ) ),
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 @ X4 @ X13 @ X13 )
=> ( ( ( X2 = X3 )
& ( morStar @ X2 @ X3 @ X12 @ ( id @ X2 ) )
& ( X3 = X4 )
& ( morStar @ X3 @ X4 @ X13 @ ( id @ X3 ) ) )
=> ( morStar @ X2 @ X4 @ ( comp @ X2 @ X3 @ X4 @ X12 @ X13 ) @ ( id @ X4 ) ) ) ) ),
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 @ X4 @ X13 @ X13 )
=> ( ( ( X2 = X3 )
& ( morStar @ X2 @ X3 @ X12 @ ( id @ X2 ) )
& ( X3 = X4 )
& ( morStar @ X3 @ X4 @ X13 @ ( id @ X3 ) ) )
=> ( morStar @ X2 @ X4 @ ( comp @ X2 @ X3 @ X4 @ X12 @ X13 ) @ ( id @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.lEGYaQ07tq/DTF2THF_28409.p',conj) ).
thf(f78,plain,
( $true
= ( morStar @ sK0 @ sK1 @ sK4 @ ( id @ sK0 ) ) ),
inference(forward_demodulation,[status(thm)],[f77,f51]) ).
thf(f51,plain,
sK2 = sK1,
inference(cnf_transformation,[status(thm)],[f40]) ).
thf(f77,plain,
( ( morStar @ sK0 @ sK2 @ sK4 @ ( id @ sK0 ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f52,f53]) ).
thf(f52,plain,
( ( morStar @ sK1 @ sK2 @ sK4 @ ( id @ sK1 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f40]) ).
thf(f177,plain,
( ( $true
!= ( morStar @ sK0 @ sK0 @ sK4 @ ( id @ sK0 ) ) )
| ( ( morStar @ sK0 @ sK0 @ ( id @ sK0 ) @ ( id @ sK0 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f176]) ).
thf(f176,plain,
( ( $true
!= ( morStar @ sK0 @ sK0 @ sK4 @ ( id @ sK0 ) ) )
| ( $true != $true )
| ( ( morStar @ sK0 @ sK0 @ ( id @ sK0 ) @ ( id @ sK0 ) )
!= $true ) ),
inference(forward_demodulation,[status(thm)],[f175,f76]) ).
thf(f76,plain,
( ( morStar @ sK0 @ sK0 @ sK3 @ ( id @ sK0 ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f50,f53]) ).
thf(f50,plain,
( $true
= ( morStar @ sK0 @ sK1 @ sK3 @ ( id @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
thf(f175,plain,
( ( ( morStar @ sK0 @ sK0 @ sK3 @ ( id @ sK0 ) )
!= $true )
| ( $true
!= ( morStar @ sK0 @ sK0 @ sK4 @ ( id @ sK0 ) ) )
| ( ( morStar @ sK0 @ sK0 @ ( id @ sK0 ) @ ( id @ sK0 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f168]) ).
thf(f168,plain,
( ( ( morStar @ sK0 @ sK0 @ ( id @ sK0 ) @ ( id @ sK0 ) )
!= $true )
| ( $true != $true )
| ( $true
!= ( morStar @ sK0 @ sK0 @ sK4 @ ( id @ sK0 ) ) )
| ( ( morStar @ sK0 @ sK0 @ sK3 @ ( id @ sK0 ) )
!= $true ) ),
inference(superposition,[status(thm)],[f111,f57]) ).
thf(f57,plain,
! [X2: mor,X0: obj,X1: obj] :
( ( ( morStar @ X0 @ X1 @ ( comp @ X0 @ X0 @ X1 @ ( id @ X0 ) @ X2 ) @ X2 )
= $true )
| ( $true
!= ( morStar @ X0 @ X1 @ X2 @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
thf(f34,plain,
! [X0: obj,X1: obj,X2: mor] :
( ( ( morStar @ X0 @ X1 @ ( comp @ X0 @ X0 @ X1 @ ( id @ X0 ) @ X2 ) @ X2 )
= $true )
| ( $true
!= ( morStar @ X0 @ X1 @ X2 @ X2 ) ) ),
inference(ennf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
! [X0: obj,X1: obj,X2: mor] :
( ( $true
= ( morStar @ X0 @ X1 @ X2 @ X2 ) )
=> ( ( morStar @ X0 @ X1 @ ( comp @ X0 @ X0 @ X1 @ ( id @ X0 ) @ X2 ) @ X2 )
= $true ) ),
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.lEGYaQ07tq/DTF2THF_28409.p',ax1) ).
thf(f111,plain,
! [X0: mor,X1: mor] :
( ( $true
!= ( morStar @ sK0 @ sK0 @ ( comp @ sK0 @ sK0 @ sK0 @ X0 @ X1 ) @ ( id @ sK0 ) ) )
| ( ( morStar @ sK0 @ sK0 @ sK4 @ X1 )
!= $true )
| ( $true
!= ( morStar @ sK0 @ sK0 @ sK3 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f106]) ).
thf(f106,plain,
! [X0: mor,X1: mor] :
( ( ( morStar @ sK0 @ sK0 @ sK4 @ X1 )
!= $true )
| ( $true
!= ( morStar @ sK0 @ sK0 @ ( comp @ sK0 @ sK0 @ sK0 @ X0 @ X1 ) @ ( id @ sK0 ) ) )
| ( $true
!= ( morStar @ sK0 @ sK0 @ sK3 @ X0 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f89,f58]) ).
thf(f58,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 @ X0 @ X1 @ X3 @ X4 ) )
| ( $true
!= ( morStar @ X1 @ X2 @ X5 @ X6 ) ) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
thf(f35,plain,
! [X0: obj,X1: obj,X2: obj,X3: mor,X4: mor] :
( ( $true
!= ( morStar @ X0 @ X1 @ X3 @ X4 ) )
| ! [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(ennf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: obj,X1: obj,X2: obj,X3: mor,X4: mor] :
( ( $true
= ( morStar @ X0 @ X1 @ X3 @ X4 ) )
=> ! [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)],[f18]) ).
thf(f18,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.lEGYaQ07tq/DTF2THF_28409.p',comp_tp_ax) ).
thf(f89,plain,
! [X0: mor] :
( ( $true
!= ( morStar @ sK0 @ sK0 @ ( comp @ sK0 @ sK0 @ sK0 @ sK3 @ sK4 ) @ X0 ) )
| ( ( morStar @ sK0 @ sK0 @ X0 @ ( id @ sK0 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f88]) ).
thf(f88,plain,
! [X0: mor] :
( ( $true != $true )
| ( ( morStar @ sK0 @ sK0 @ X0 @ ( id @ sK0 ) )
!= $true )
| ( $true
!= ( morStar @ sK0 @ sK0 @ ( comp @ sK0 @ sK0 @ sK0 @ sK3 @ sK4 ) @ X0 ) ) ),
inference(forward_demodulation,[status(thm)],[f84,f70]) ).
thf(f70,plain,
! [X0: obj,X1: obj] :
( $true
= ( isPer @ mor @ ( morStar @ X0 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: obj,X1: obj] :
( $true
= ( isPer @ mor @ ( morStar @ X0 @ X1 ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,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.lEGYaQ07tq/DTF2THF_28409.p','\'morStar\'_is_per') ).
thf(f84,plain,
! [X0: mor] :
( ( $true
!= ( morStar @ sK0 @ sK0 @ ( comp @ sK0 @ sK0 @ sK0 @ sK3 @ sK4 ) @ X0 ) )
| ( $true
!= ( isPer @ mor @ ( morStar @ sK0 @ sK0 ) ) )
| ( ( morStar @ sK0 @ sK0 @ X0 @ ( id @ sK0 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f83]) ).
thf(f83,plain,
! [X0: mor] :
( ( ( morStar @ sK0 @ sK0 @ X0 @ ( id @ sK0 ) )
!= $true )
| ( $true
!= ( morStar @ sK0 @ sK0 @ ( comp @ sK0 @ sK0 @ sK0 @ sK3 @ sK4 ) @ X0 ) )
| ( $true
!= ( isPer @ mor @ ( morStar @ sK0 @ sK0 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f81,f66]) ).
thf(f66,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0 > X0 > $o,X4: X0] :
( ( ( X1 @ X2 @ X4 )
= $true )
| ( ( X1 @ X2 @ X3 )
!= $true )
| ( ( isPer @ X0 @ X1 )
!= $true )
| ( ( X1 @ X3 @ X4 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
thf(f46,plain,
! [X0: $tType,X1: X0 > X0 > $o] :
( ( ( ! [X2: X0,X3: X0,X4: X0] :
( ( ( X1 @ X2 @ X3 )
!= $true )
| ( ( X1 @ X2 @ X4 )
= $true )
| ( ( X1 @ X3 @ X4 )
!= $true ) )
& ! [X5: X0,X6: X0] :
( ( $true
!= ( X1 @ X5 @ X6 ) )
| ( ( X1 @ X6 @ X5 )
= $true ) ) )
| ( ( isPer @ X0 @ X1 )
!= $true ) )
& ( ( ( isPer @ X0 @ X1 )
= $true )
| ( ( $true
= ( X1 @ ( sK5 @ X0 @ X1 ) @ ( sK6 @ X0 @ X1 ) ) )
& ( $true
!= ( X1 @ ( sK5 @ X0 @ X1 ) @ ( sK7 @ X0 @ X1 ) ) )
& ( ( X1 @ ( sK6 @ X0 @ X1 ) @ ( sK7 @ X0 @ X1 ) )
= $true ) )
| ( ( $true
= ( X1 @ ( sK8 @ X0 @ X1 ) @ ( sK9 @ X0 @ X1 ) ) )
& ( ( X1 @ ( sK9 @ X0 @ X1 ) @ ( sK8 @ X0 @ X1 ) )
!= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8,sK9])],[f43,f45,f44]) ).
thf(f44,plain,
! [X0: $tType,X1: X0 > X0 > $o] :
( ? [X7: X0,X8: X0,X9: X0] :
( ( ( X1 @ X7 @ X8 )
= $true )
& ( $true
!= ( X1 @ X7 @ X9 ) )
& ( ( X1 @ X8 @ X9 )
= $true ) )
=> ( ( $true
= ( X1 @ ( sK5 @ X0 @ X1 ) @ ( sK6 @ X0 @ X1 ) ) )
& ( $true
!= ( X1 @ ( sK5 @ X0 @ X1 ) @ ( sK7 @ X0 @ X1 ) ) )
& ( ( X1 @ ( sK6 @ X0 @ X1 ) @ ( sK7 @ X0 @ X1 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f45,plain,
! [X0: $tType,X1: X0 > X0 > $o] :
( ? [X10: X0,X11: X0] :
( ( $true
= ( X1 @ X10 @ X11 ) )
& ( $true
!= ( X1 @ X11 @ X10 ) ) )
=> ( ( $true
= ( X1 @ ( sK8 @ X0 @ X1 ) @ ( sK9 @ X0 @ X1 ) ) )
& ( ( X1 @ ( sK9 @ X0 @ X1 ) @ ( sK8 @ X0 @ X1 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f43,plain,
! [X0: $tType,X1: X0 > X0 > $o] :
( ( ( ! [X2: X0,X3: X0,X4: X0] :
( ( ( X1 @ X2 @ X3 )
!= $true )
| ( ( X1 @ X2 @ X4 )
= $true )
| ( ( X1 @ X3 @ X4 )
!= $true ) )
& ! [X5: X0,X6: X0] :
( ( $true
!= ( X1 @ X5 @ X6 ) )
| ( ( X1 @ X6 @ X5 )
= $true ) ) )
| ( ( isPer @ X0 @ X1 )
!= $true ) )
& ( ( ( isPer @ X0 @ X1 )
= $true )
| ? [X7: X0,X8: X0,X9: X0] :
( ( ( X1 @ X7 @ X8 )
= $true )
& ( $true
!= ( X1 @ X7 @ X9 ) )
& ( ( X1 @ X8 @ X9 )
= $true ) )
| ? [X10: X0,X11: X0] :
( ( $true
= ( X1 @ X10 @ X11 ) )
& ( $true
!= ( X1 @ X11 @ X10 ) ) ) ) ),
inference(rectify,[status(thm)],[f42]) ).
thf(f42,plain,
! [X0: $tType,X1: X0 > X0 > $o] :
( ( ( ! [X4: X0,X5: X0,X6: X0] :
( ( $true
!= ( X1 @ X4 @ X5 ) )
| ( $true
= ( X1 @ X4 @ X6 ) )
| ( $true
!= ( X1 @ X5 @ X6 ) ) )
& ! [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 @ X4 @ X5 ) )
& ( $true
!= ( X1 @ X4 @ X6 ) )
& ( $true
= ( X1 @ X5 @ X6 ) ) )
| ? [X2: X0,X3: X0] :
( ( ( X1 @ X2 @ X3 )
= $true )
& ( ( X1 @ X3 @ X2 )
!= $true ) ) ) ),
inference(flattening,[status(thm)],[f41]) ).
thf(f41,plain,
! [X0: $tType,X1: X0 > X0 > $o] :
( ( ( ! [X4: X0,X5: X0,X6: X0] :
( ( $true
!= ( X1 @ X4 @ X5 ) )
| ( $true
= ( X1 @ X4 @ X6 ) )
| ( $true
!= ( X1 @ X5 @ X6 ) ) )
& ! [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 @ X4 @ X5 ) )
& ( $true
!= ( X1 @ X4 @ X6 ) )
& ( $true
= ( X1 @ X5 @ X6 ) ) )
| ? [X2: X0,X3: X0] :
( ( ( X1 @ X2 @ X3 )
= $true )
& ( ( X1 @ X3 @ X2 )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f33]) ).
thf(f33,plain,
! [X0: $tType,X1: X0 > X0 > $o] :
( ( ! [X4: X0,X5: X0,X6: X0] :
( ( $true
!= ( X1 @ X4 @ X5 ) )
| ( $true
= ( X1 @ X4 @ X6 ) )
| ( $true
!= ( X1 @ X5 @ X6 ) ) )
& ! [X2: X0,X3: X0] :
( ( ( X1 @ X2 @ X3 )
!= $true )
| ( ( X1 @ X3 @ X2 )
= $true ) ) )
<=> ( ( isPer @ X0 @ X1 )
= $true ) ),
inference(flattening,[status(thm)],[f32]) ).
thf(f32,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] :
( ( $true
= ( X1 @ X4 @ X6 ) )
| ( $true
!= ( X1 @ X5 @ X6 ) )
| ( $true
!= ( X1 @ X4 @ X5 ) ) ) )
<=> ( ( isPer @ X0 @ X1 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,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] :
( ( $true
= ( X1 @ X4 @ X5 ) )
=> ( ( $true
= ( X1 @ X5 @ X6 ) )
=> ( $true
= ( X1 @ X4 @ X6 ) ) ) ) )
<=> ( ( isPer @ X0 @ X1 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,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.lEGYaQ07tq/DTF2THF_28409.p',is_per) ).
thf(f81,plain,
( $true
!= ( morStar @ sK0 @ sK0 @ ( comp @ sK0 @ sK0 @ sK0 @ sK3 @ sK4 ) @ ( id @ sK0 ) ) ),
inference(forward_demodulation,[status(thm)],[f80,f53]) ).
thf(f80,plain,
( $true
!= ( morStar @ sK0 @ sK1 @ ( comp @ sK0 @ sK1 @ sK1 @ sK3 @ sK4 ) @ ( id @ sK1 ) ) ),
inference(forward_demodulation,[status(thm)],[f56,f51]) ).
thf(f56,plain,
( ( morStar @ sK0 @ sK2 @ ( comp @ sK0 @ sK1 @ sK2 @ sK3 @ sK4 ) @ ( id @ sK2 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : CAT040^1 : TPTP v9.2.1. Released v9.2.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n031.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 04:09:33 EST 2026
% 0.17/0.35 % CPUTime :
% 0.17/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.48 ---- Original DTF file ---
% 0.20/0.48 thf(spec,logic,$$dhol).
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 % File : CAT040^1 : TPTP v9.2.1. Released v9.2.0.
% 0.20/0.48 % Domain : Category Theory
% 0.20/0.48 % Problem : Simple problem from category theory dhol_2
% 0.20/0.48 % Version : Especial.
% 0.20/0.48 % English :
% 0.20/0.48
% 0.20/0.48 % Refs : [RRB23] Rothgang et al. (2023), Theorem Proving in Dependently
% 0.20/0.48 % : [Rot25] Rothgang (2025), Email to Geoff Sutcliffe
% 0.20/0.48 % : [RK+25] Ranalter et al. (2025), The Dependently Typed Higher-O
% 0.20/0.48 % Source : [Rot25]
% 0.20/0.48 % Names : CategoryTheory/category-theory-lemmas-dhol_2.p [Rot25]
% 0.20/0.48
% 0.20/0.48 % Status : Theorem
% 0.20/0.48 % Rating : ? v9.2.0
% 0.20/0.48 % Syntax : Number of formulae : 8 ( 3 unt; 4 typ; 0 def)
% 0.20/0.48 % Number of atoms : 8 ( 8 equ; 0 cnn)
% 0.20/0.48 % Maximal formula atoms : 5 ( 2 avg)
% 0.20/0.48 % Number of connectives : 66 ( 0 ~; 0 |; 3 &; 62 @)
% 0.20/0.48 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.20/0.48 % Maximal formula depth : 10 ( 7 avg)
% 0.20/0.48 % Number of types : 1 ( 1 usr)
% 0.20/0.48 % Number of type decls : 4 ( 0 !>P; 2 !>D)
% 0.20/0.48 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.20/0.48 % Number of symbols : 4 ( 3 usr; 0 con; 1-5 aty)
% 0.20/0.48 % Number of variables : 22 ( 0 ^; 18 !; 0 ?; 22 :)
% 0.20/0.48 % ( 4 !>; 0 ?*; 0 @-; 0 @+)
% 0.20/0.48 % SPC : DH0_THM_EQU_NAR
% 0.20/0.48
% 0.20/0.48 % Comments :
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 thf(obj_type,type,
% 0.20/0.48 obj: $tType ).
% 0.20/0.48
% 0.20/0.48 thf(mor_type,type,
% 0.20/0.48 mor: obj > obj > $tType ).
% 0.20/0.48
% 0.20/0.48 thf(id_type,type,
% 0.20/0.48 id:
% 0.20/0.48 !>[X: obj] : ( mor @ X @ X ) ).
% 0.20/0.48
% 0.20/0.48 thf(comp_type,type,
% 0.20/0.48 comp:
% 0.20/0.48 !>[X: obj,Y: obj,Z: obj] : ( ( mor @ X @ Y ) > ( mor @ Y @ Z ) > ( mor @ X @ Z ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(ax1,axiom,
% 0.20/0.48 ! [X: obj,Y: obj,M: mor @ X @ Y] :
% 0.20/0.48 ( ( comp @ X @ X @ Y @ ( id @ X ) @ M )
% 0.20/0.48 = M ) ).
% 0.20/0.48
% 0.20/0.48 thf(ax2,axiom,
% 0.20/0.48 ! [X: obj,Y: obj,M: mor @ X @ Y] :
% 0.20/0.48 ( ( comp @ X @ Y @ Y @ M @ ( id @ Y ) )
% 0.20/0.48 = M ) ).
% 0.20/0.48
% 0.20/0.48 thf(ax3,axiom,
% 0.20/0.48 ! [X: obj,Y: obj,Z: obj,A: obj,F: mor @ X @ Y,G: mor @ Y @ Z,H: mor @ Z @ A] :
% 0.20/0.48 ( ( comp @ X @ Y @ A @ F @ ( comp @ Y @ Z @ A @ G @ H ) )
% 0.20/0.48 = ( comp @ X @ Z @ A @ ( comp @ X @ Y @ Z @ F @ G ) @ H ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(conj,conjecture,
% 0.20/0.48 ! [X: obj,Y: obj,Z: obj,F: mor @ X @ Y,G: mor @ Y @ Z] :
% 0.20/0.48 ( ( ( X = Y )
% 0.20/0.48 & ( Y = Z )
% 0.20/0.48 & ( F
% 0.20/0.48 = ( id @ X ) )
% 0.20/0.48 & ( G
% 0.20/0.48 = ( id @ Y ) ) )
% 0.20/0.48 => ( ( comp @ X @ Y @ Z @ F @ G )
% 0.20/0.48 = ( id @ Z ) ) ) ).
% 0.20/0.48
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 ------------------------
% 1.69/1.48 ---- Embedded in THF ---
% 1.69/1.48 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.69/1.48 %%% Generated on Tue Feb 24 04:09:34 EST 2026
% 1.69/1.48 %%% using '$$dhol' embedding, version 1.3.0.
% 1.69/1.48 %%% Logic specification used:
% 1.69/1.48 %%% thf(spec, logic, $$dhol).
% 1.69/1.48
% 1.69/1.48 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.lEGYaQ07tq/DTF2DTF28409.p
% See solution above
% 1.69/1.48 ------------------------
% 1.69/1.49 ---- Cleaned THF ---
% 1.69/1.49 thf(is_per_type,type,
% 1.69/1.49 isPer:
% 1.69/1.49 !>[A: $tType] : ( ( A > A > $o ) > $o ) ).
% 1.69/1.49
% 1.69/1.49 thf(is_per,definition,
% 1.69/1.49 ! [A: $tType,AStar: A > A > $o] :
% 1.69/1.49 ( ( isPer @ A @ AStar )
% 1.69/1.49 <=> ( ! [X: A,Y: A] :
% 1.69/1.49 ( ( AStar @ X @ Y )
% 1.69/1.49 => ( AStar @ Y @ X ) )
% 1.69/1.49 & ! [X: A,Y: A,Z: A] :
% 1.69/1.49 ( ( AStar @ X @ Y )
% 1.69/1.49 => ( ( AStar @ Y @ Z )
% 1.69/1.49 => ( AStar @ X @ Z ) ) ) ) ) ).
% 1.69/1.49
% 1.69/1.49 thf(obj_type,type,
% 1.69/1.49 obj: $tType ).
% 1.69/1.49
% 1.69/1.49 thf(objStar,type,
% 1.69/1.49 objStar: obj > obj > $o ).
% 1.69/1.49
% 1.69/1.49 thf(objStar_is_eq,axiom,
% 1.69/1.49 ! [X: obj,Y: obj] :
% 1.69/1.49 ( ( objStar @ X @ Y )
% 1.69/1.49 <=> ( X = Y ) ) ).
% 1.69/1.49
% 1.69/1.49 thf(mor_type,type,
% 1.69/1.49 mor: $tType ).
% 1.69/1.49
% 1.69/1.49 thf(morStar,type,
% 1.69/1.49 morStar: obj > obj > mor > mor > $o ).
% 1.69/1.49
% 1.69/1.49 thf('\'morStar\'_is_per',axiom,
% 1.69/1.49 ! [C: obj,C0: obj] : ( isPer @ mor @ ( morStar @ C @ C0 ) ) ).
% 1.69/1.49
% 1.69/1.49 thf(id_type,type,
% 1.69/1.49 id: obj > mor ).
% 1.69/1.49
% 1.69/1.49 thf(id_tp_ax,axiom,
% 1.69/1.49 ! [X: obj] : ( morStar @ X @ X @ ( id @ X ) @ ( id @ X ) ) ).
% 1.69/1.49
% 1.69/1.49 thf(comp_type,type,
% 1.69/1.49 comp: obj > obj > obj > mor > mor > mor ).
% 1.69/1.49
% 1.69/1.49 thf(comp_tp_ax,axiom,
% 1.69/1.49 ! [X: obj,Y: obj,Z: obj,D: mor,D_prime: mor] :
% 1.69/1.49 ( ( morStar @ X @ Y @ D @ D_prime )
% 1.69/1.49 => ! [D0: mor,D0_prime: mor] :
% 1.69/1.49 ( ( morStar @ Y @ Z @ D0 @ D0_prime )
% 1.69/1.49 => ( morStar @ X @ Z @ ( comp @ X @ Y @ Z @ D @ D0 ) @ ( comp @ X @ Y @ Z @ D_prime @ D0_prime ) ) ) ) ).
% 1.69/1.49
% 1.69/1.49 thf(ax1,axiom,
% 1.69/1.49 ! [X: obj,Y: obj,M: mor] :
% 1.69/1.49 ( ( morStar @ X @ Y @ M @ M )
% 1.69/1.49 => ( morStar @ X @ Y @ ( comp @ X @ X @ Y @ ( id @ X ) @ M ) @ M ) ) ).
% 1.69/1.49
% 1.69/1.49 thf(ax2,axiom,
% 1.69/1.49 ! [X: obj,Y: obj,M: mor] :
% 1.69/1.49 ( ( morStar @ X @ Y @ M @ M )
% 1.69/1.49 => ( morStar @ X @ Y @ ( comp @ X @ Y @ Y @ M @ ( id @ Y ) ) @ M ) ) ).
% 1.69/1.49
% 1.69/1.49 thf(ax3,axiom,
% 1.69/1.49 ! [X: obj,Y: obj,Z: obj,A: obj,F: mor,G: mor,H: mor] :
% 1.69/1.49 ( ( morStar @ X @ Y @ F @ F )
% 1.69/1.49 => ( ( morStar @ Y @ Z @ G @ G )
% 1.69/1.49 => ( ( morStar @ Z @ A @ H @ H )
% 1.69/1.49 => ( 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 ) ) ) ) ) ).
% 1.69/1.49
% 1.69/1.49 thf(conj,conjecture,
% 1.69/1.49 ! [X: obj,Y: obj,Z: obj,F: mor,G: mor] :
% 1.69/1.49 ( ( morStar @ X @ Y @ F @ F )
% 1.69/1.49 => ( ( morStar @ Y @ Z @ G @ G )
% 1.69/1.49 => ( ( ( X = Y )
% 1.69/1.49 & ( Y = Z )
% 1.69/1.49 & ( morStar @ X @ Y @ F @ ( id @ X ) )
% 1.69/1.49 & ( morStar @ Y @ Z @ G @ ( id @ Y ) ) )
% 1.69/1.49 => ( morStar @ X @ Z @ ( comp @ X @ Y @ Z @ F @ G ) @ ( id @ Z ) ) ) ) ) ).
% 1.69/1.49 ------------------------
% 1.87/1.51 % (28511)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_28409 for (2999ds/2Mi)
% 1.87/1.51 % (28512)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_28409 for (2999ds/275Mi)
% 1.87/1.51 % (28508)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_28409 for (2999ds/4Mi)
% 1.87/1.51 % (28510)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_28409 for (2999ds/2Mi)
% 1.87/1.51 % (28509)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_28409 for (2999ds/27Mi)
% 1.87/1.51 % (28507)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_28409 for (2999ds/183Mi)
% 1.87/1.51 % (28513)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_28409 for (2999ds/18Mi)
% 1.87/1.51 % (28510)Instruction limit reached!
% 1.87/1.51 % (28510)------------------------------
% 1.87/1.51 % (28510)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/1.51 % (28510)Termination reason: Unknown
% 1.87/1.51 % (28510)Termination phase: shuffling
% 1.87/1.51
% 1.87/1.51 % (28511)Instruction limit reached!
% 1.87/1.51 % (28511)------------------------------
% 1.87/1.51 % (28511)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/1.51 % (28511)Termination reason: Unknown
% 1.87/1.51 % (28511)Termination phase: shuffling
% 1.87/1.51
% 1.87/1.51 % (28511)Memory used [KB]: 1023
% 1.87/1.51 % (28511)Time elapsed: 0.003 s
% 1.87/1.51 % (28511)Instructions burned: 2 (million)
% 1.87/1.51 % (28511)------------------------------
% 1.87/1.51 % (28511)------------------------------
% 1.87/1.51 % (28510)Memory used [KB]: 1023
% 1.87/1.51 % (28510)Time elapsed: 0.003 s
% 1.87/1.51 % (28510)Instructions burned: 2 (million)
% 1.87/1.51 % (28510)------------------------------
% 1.87/1.51 % (28510)------------------------------
% 1.87/1.51 % (28508)Instruction limit reached!
% 1.87/1.51 % (28508)------------------------------
% 1.87/1.51 % (28508)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/1.51 % (28508)Termination reason: Unknown
% 1.87/1.51 % (28508)Termination phase: Property scanning
% 1.87/1.51
% 1.87/1.51 % (28508)Memory used [KB]: 1023
% 1.87/1.51 % (28508)Time elapsed: 0.004 s
% 1.87/1.51 % (28508)Instructions burned: 4 (million)
% 1.87/1.51 % (28508)------------------------------
% 1.87/1.51 % (28508)------------------------------
% 1.87/1.52 % (28512)Refutation not found, incomplete strategy
% 1.87/1.52 % (28512)------------------------------
% 1.87/1.52 % (28512)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/1.52 % (28512)Termination reason: Refutation not found, incomplete strategy
% 1.87/1.52
% 1.87/1.52
% 1.87/1.52 % (28512)Memory used [KB]: 5500
% 1.87/1.52 % (28512)Time elapsed: 0.006 s
% 1.87/1.52 % (28512)Instructions burned: 8 (million)
% 1.87/1.52 % (28512)------------------------------
% 1.87/1.52 % (28512)------------------------------
% 1.87/1.52 % (28513)Instruction limit reached!
% 1.87/1.52 % (28513)------------------------------
% 1.87/1.52 % (28513)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/1.52 % (28513)Termination reason: Unknown
% 1.87/1.52 % (28513)Termination phase: Saturation
% 1.87/1.52
% 1.87/1.52 % (28513)Memory used [KB]: 5628
% 1.87/1.52 % (28513)Time elapsed: 0.011 s
% 1.87/1.52 % (28513)Instructions burned: 18 (million)
% 1.87/1.52 % (28513)------------------------------
% 1.87/1.52 % (28513)------------------------------
% 1.87/1.53 % (28509)Instruction limit reached!
% 1.87/1.53 % (28509)------------------------------
% 1.87/1.53 % (28509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/1.53 % (28509)Termination reason: Unknown
% 1.87/1.53 % (28509)Termination phase: Saturation
% 1.87/1.53
% 1.87/1.53 % (28509)Memory used [KB]: 5628
% 1.87/1.53 % (28509)Time elapsed: 0.017 s
% 1.87/1.53 % (28509)Instructions burned: 28 (million)
% 1.87/1.53 % (28509)------------------------------
% 1.87/1.53 % (28509)------------------------------
% 1.87/1.53 % (28514)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_28409 for (2999ds/3Mi)
% 1.87/1.53 % (28515)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_28409 for (2999ds/37Mi)
% 1.87/1.53 % (28516)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_28409 for (2999ds/15Mi)
% 1.87/1.53 % (28514)Instruction limit reached!
% 1.87/1.53 % (28514)------------------------------
% 1.87/1.53 % (28514)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/1.53 % (28514)Termination reason: Unknown
% 1.87/1.53 % (28514)Termination phase: Property scanning
% 1.87/1.53
% 1.87/1.53 % (28514)Memory used [KB]: 1023
% 1.87/1.53 % (28514)Time elapsed: 0.003 s
% 1.87/1.53 % (28514)Instructions burned: 3 (million)
% 1.87/1.53 % (28514)------------------------------
% 1.87/1.53 % (28514)------------------------------
% 1.87/1.53 % (28517)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_28409 for (2999ds/3Mi)
% 1.87/1.53 % (28517)Instruction limit reached!
% 1.87/1.53 % (28517)------------------------------
% 1.87/1.53 % (28517)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/1.53 % (28517)Termination reason: Unknown
% 1.87/1.53 % (28517)Termination phase: Preprocessing 1
% 1.87/1.53
% 1.87/1.53 % (28517)Memory used [KB]: 1023
% 1.87/1.53 % (28517)Time elapsed: 0.003 s
% 1.87/1.53 % (28517)Instructions burned: 4 (million)
% 1.87/1.53 % (28517)------------------------------
% 1.87/1.53 % (28517)------------------------------
% 1.87/1.54 % (28518)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_28409 for (2999ds/1041Mi)
% 1.87/1.54 % (28516)Instruction limit reached!
% 1.87/1.54 % (28516)------------------------------
% 1.87/1.54 % (28516)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/1.54 % (28516)Termination reason: Unknown
% 1.87/1.54 % (28516)Termination phase: Saturation
% 1.87/1.54
% 1.87/1.54 % (28516)Memory used [KB]: 5756
% 1.87/1.54 % (28516)Time elapsed: 0.009 s
% 1.87/1.54 % (28516)Instructions burned: 15 (million)
% 1.87/1.54 % (28516)------------------------------
% 1.87/1.54 % (28516)------------------------------
% 1.87/1.54 % (28519)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_28409 for (2999ds/7Mi)
% 1.87/1.55 % (28519)Instruction limit reached!
% 1.87/1.55 % (28519)------------------------------
% 1.87/1.55 % (28519)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/1.55 % (28519)Termination reason: Unknown
% 1.87/1.55 % (28519)Termination phase: Property scanning
% 1.87/1.55
% 1.87/1.55 % (28519)Memory used [KB]: 1023
% 1.87/1.55 % (28519)Time elapsed: 0.005 s
% 1.87/1.55 % (28519)Instructions burned: 7 (million)
% 1.87/1.55 % (28519)------------------------------
% 1.87/1.55 % (28519)------------------------------
% 1.87/1.55 % (28520)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_28409 for (2999ds/16Mi)
% 1.87/1.55 % (28515)Instruction limit reached!
% 1.87/1.55 % (28515)------------------------------
% 1.87/1.55 % (28515)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/1.55 % (28515)Termination reason: Unknown
% 1.87/1.55 % (28515)Termination phase: Saturation
% 1.87/1.55
% 1.87/1.55 % (28515)Memory used [KB]: 5884
% 1.87/1.55 % (28515)Time elapsed: 0.020 s
% 1.87/1.55 % (28515)Instructions burned: 39 (million)
% 1.87/1.55 % (28515)------------------------------
% 1.87/1.55 % (28515)------------------------------
% 1.87/1.55 % (28521)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_28409 for (2999ds/3Mi)
% 1.87/1.55 % (28521)Instruction limit reached!
% 1.87/1.55 % (28521)------------------------------
% 1.87/1.55 % (28521)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/1.55 % (28521)Termination reason: Unknown
% 1.87/1.55 % (28521)Termination phase: Property scanning
% 1.87/1.55
% 1.87/1.55 % (28521)Memory used [KB]: 1023
% 1.87/1.55 % (28521)Time elapsed: 0.003 s
% 1.87/1.55 % (28521)Instructions burned: 4 (million)
% 1.87/1.55 % (28521)------------------------------
% 1.87/1.55 % (28521)------------------------------
% 1.87/1.55 % (28522)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_28409 for (2999ds/3Mi)
% 1.87/1.56 % (28522)Instruction limit reached!
% 1.87/1.56 % (28522)------------------------------
% 1.87/1.56 % (28522)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/1.56 % (28522)Termination reason: Unknown
% 1.87/1.56 % (28522)Termination phase: Property scanning
% 1.87/1.56
% 1.87/1.56 % (28522)Memory used [KB]: 1023
% 1.87/1.56 % (28522)Time elapsed: 0.003 s
% 1.87/1.56 % (28522)Instructions burned: 4 (million)
% 1.87/1.56 % (28522)------------------------------
% 1.87/1.56 % (28522)------------------------------
% 1.87/1.56 % (28520)Instruction limit reached!
% 1.87/1.56 % (28520)------------------------------
% 1.87/1.56 % (28520)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/1.56 % (28520)Termination reason: Unknown
% 1.87/1.56 % (28520)Termination phase: Saturation
% 1.87/1.56
% 1.87/1.56 % (28520)Memory used [KB]: 5756
% 1.87/1.56 % (28520)Time elapsed: 0.010 s
% 1.87/1.56 % (28520)Instructions burned: 17 (million)
% 1.87/1.56 % (28520)------------------------------
% 1.87/1.56 % (28520)------------------------------
% 1.87/1.56 % (28523)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_28409 for (2999ds/7Mi)
% 1.87/1.56 % (28524)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_28409 for (2999ds/3Mi)
% 1.87/1.57 % (28524)Instruction limit reached!
% 1.87/1.57 % (28524)------------------------------
% 1.87/1.57 % (28524)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/1.57 % (28524)Termination reason: Unknown
% 1.87/1.57 % (28524)Termination phase: Property scanning
% 1.87/1.57
% 1.87/1.57 % (28524)Memory used [KB]: 1023
% 1.87/1.57 % (28524)Time elapsed: 0.003 s
% 1.87/1.57 % (28524)Instructions burned: 4 (million)
% 1.87/1.57 % (28524)------------------------------
% 1.87/1.57 % (28524)------------------------------
% 1.87/1.57 % (28523)Instruction limit reached!
% 1.87/1.57 % (28523)------------------------------
% 1.87/1.57 % (28523)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/1.57 % (28523)Termination reason: Unknown
% 1.87/1.57 % (28523)Termination phase: Saturation
% 1.87/1.57
% 1.87/1.57 % (28523)Memory used [KB]: 5500
% 1.87/1.57 % (28523)Time elapsed: 0.005 s
% 1.87/1.57 % (28523)Instructions burned: 7 (million)
% 1.87/1.57 % (28523)------------------------------
% 1.87/1.57 % (28523)------------------------------
% 1.87/1.57 % (28525)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_28409 for (2999ds/4Mi)
% 1.87/1.57 % (28525)Instruction limit reached!
% 1.87/1.57 % (28525)------------------------------
% 1.87/1.57 % (28525)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/1.57 % (28525)Termination reason: Unknown
% 1.87/1.57 % (28525)Termination phase: Property scanning
% 1.87/1.57
% 1.87/1.57 % (28525)Memory used [KB]: 1023
% 1.87/1.57 % (28525)Time elapsed: 0.003 s
% 1.87/1.57 % (28525)Instructions burned: 4 (million)
% 1.87/1.57 % (28525)------------------------------
% 1.87/1.57 % (28525)------------------------------
% 1.87/1.57 % (28526)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_28409 for (2999ds/18Mi)
% 1.87/1.57 % (28527)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_28409 for (2999ds/710Mi)
% 1.87/1.58 % (28526)Instruction limit reached!
% 1.87/1.58 % (28526)------------------------------
% 1.87/1.58 % (28526)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/1.58 % (28526)Termination reason: Unknown
% 1.87/1.58 % (28526)Termination phase: Saturation
% 1.87/1.58
% 1.87/1.58 % (28526)Memory used [KB]: 5628
% 1.87/1.58 % (28526)Time elapsed: 0.011 s
% 1.87/1.58 % (28526)Instructions burned: 18 (million)
% 1.87/1.58 % (28526)------------------------------
% 1.87/1.58 % (28526)------------------------------
% 1.87/1.58 % (28529)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_28409 for (2999ds/902Mi)
% 1.87/1.58 % (28528)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_28409 for (2999ds/6Mi)
% 1.87/1.59 % (28530)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_28409 for (2999ds/21Mi)
% 1.87/1.59 % (28528)Instruction limit reached!
% 1.87/1.59 % (28528)------------------------------
% 1.87/1.59 % (28528)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/1.59 % (28528)Termination reason: Unknown
% 1.87/1.59 % (28528)Termination phase: Saturation
% 1.87/1.59
% 1.87/1.59 % (28528)Memory used [KB]: 5500
% 1.87/1.59 % (28528)Time elapsed: 0.005 s
% 1.87/1.59 % (28528)Instructions burned: 7 (million)
% 1.87/1.59 % (28528)------------------------------
% 1.87/1.59 % (28528)------------------------------
% 1.87/1.59 % (28507)Instruction limit reached!
% 1.87/1.59 % (28507)------------------------------
% 1.87/1.59 % (28507)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/1.59 % (28507)Termination reason: Unknown
% 1.87/1.59 % (28507)Termination phase: Saturation
% 1.87/1.59
% 1.87/1.59 % (28507)Memory used [KB]: 7164
% 1.87/1.59 % (28507)Time elapsed: 0.083 s
% 1.87/1.59 % (28507)Instructions burned: 183 (million)
% 1.87/1.59 % (28507)------------------------------
% 1.87/1.59 % (28507)------------------------------
% 1.87/1.60 % (28529)First to succeed.
% 1.87/1.60 % (28530)Instruction limit reached!
% 1.87/1.60 % (28530)------------------------------
% 1.87/1.60 % (28530)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/1.60 % (28530)Termination reason: Unknown
% 1.87/1.60 % (28530)Termination phase: Saturation
% 1.87/1.60 % (28531)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_28409 for (2999ds/5Mi)
% 1.87/1.60
% 1.87/1.60 % (28530)Memory used [KB]: 5628
% 1.87/1.60 % (28530)Time elapsed: 0.013 s
% 1.87/1.60 % (28530)Instructions burned: 22 (million)
% 1.87/1.60 % (28530)------------------------------
% 1.87/1.60 % (28530)------------------------------
% 1.87/1.60 % (28531)Instruction limit reached!
% 1.87/1.60 % (28531)------------------------------
% 1.87/1.60 % (28531)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/1.60 % (28531)Termination reason: Unknown
% 1.87/1.60 % (28531)Termination phase: Property scanning
% 1.87/1.60
% 1.87/1.60 % (28531)Memory used [KB]: 1023
% 1.87/1.60 % (28531)Time elapsed: 0.004 s
% 1.87/1.60 % (28531)Instructions burned: 5 (million)
% 1.87/1.60 % (28531)------------------------------
% 1.87/1.60 % (28531)------------------------------
% 1.87/1.60 % (28529)Refutation found. Thanks to Tanya!
% 1.87/1.60 % SZS status Theorem for DTF2THF_28409
% 1.87/1.60 % SZS output start Proof for DTF2THF_28409
% 1.87/1.60 thf(type_def_6, type, obj: $tType).
% 1.87/1.60 thf(type_def_7, type, mor: $tType).
% 1.87/1.60 thf(func_def_0, type, isPer: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 1.87/1.60 thf(func_def_2, type, obj: $tType).
% 1.87/1.60 thf(func_def_3, type, objStar: obj > obj > $o).
% 1.87/1.60 thf(func_def_4, type, mor: $tType).
% 1.87/1.60 thf(func_def_5, type, morStar: obj > obj > mor > mor > $o).
% 1.87/1.60 thf(func_def_6, type, id: obj > mor).
% 1.87/1.60 thf(func_def_7, type, comp: obj > obj > obj > mor > mor > mor).
% 1.87/1.60 thf(func_def_10, type, sK0: obj).
% 1.87/1.60 thf(func_def_11, type, sK1: obj).
% 1.87/1.60 thf(func_def_12, type, sK2: obj).
% 1.87/1.60 thf(func_def_13, type, sK3: mor).
% 1.87/1.60 thf(func_def_14, type, sK4: mor).
% 1.87/1.60 thf(func_def_15, type, sK5: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.87/1.60 thf(func_def_16, type, sK6: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.87/1.60 thf(func_def_17, type, sK7: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.87/1.60 thf(func_def_18, type, sK8: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.87/1.60 thf(func_def_19, type, sK9: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.87/1.60 thf(func_def_21, type, ph11: !>[X0: $tType]:(X0)).
% 1.87/1.60 thf(f202,plain,(
% 1.87/1.60 $false),
% 1.87/1.60 inference(trivial_inequality_removal,[status(thm)],[f198])).
% 1.87/1.60 thf(f198,plain,(
% 1.87/1.60 ($true != $true)),
% 1.87/1.60 inference(superposition,[status(thm)],[f179,f49])).
% 1.87/1.60 thf(f49,plain,(
% 1.87/1.60 ( ! [X0 : obj] : (($true = (morStar @ X0 @ X0 @ (id @ X0) @ (id @ X0)))) )),
% 1.87/1.60 inference(cnf_transformation,[status(thm)],[f15])).
% 1.87/1.60 thf(f15,plain,(
% 1.87/1.60 ! [X0 : obj] : ($true = (morStar @ X0 @ X0 @ (id @ X0) @ (id @ X0)))),
% 1.87/1.60 inference(fool_elimination,[status(thm)],[f14])).
% 1.87/1.60 thf(f14,plain,(
% 1.87/1.60 ! [X0 : obj] : (morStar @ X0 @ X0 @ (id @ X0) @ (id @ X0))),
% 1.87/1.60 inference(rectify,[status(thm)],[f4])).
% 1.87/1.60 thf(f4,axiom,(
% 1.87/1.60 ! [X2 : obj] : (morStar @ X2 @ X2 @ (id @ X2) @ (id @ X2))),
% 1.87/1.60 file('/export/starexec/sandbox/tmp/tmp.lEGYaQ07tq/DTF2THF_28409.p',id_tp_ax)).
% 1.87/1.60 thf(f179,plain,(
% 1.87/1.60 ((morStar @ sK0 @ sK0 @ (id @ sK0) @ (id @ sK0)) != $true)),
% 1.87/1.60 inference(trivial_inequality_removal,[status(thm)],[f178])).
% 1.87/1.60 thf(f178,plain,(
% 1.87/1.60 ((morStar @ sK0 @ sK0 @ (id @ sK0) @ (id @ sK0)) != $true) | ($true != $true)),
% 1.87/1.60 inference(forward_demodulation,[status(thm)],[f177,f79])).
% 1.87/1.60 thf(f79,plain,(
% 1.87/1.60 ($true = (morStar @ sK0 @ sK0 @ sK4 @ (id @ sK0)))),
% 1.87/1.60 inference(forward_demodulation,[status(thm)],[f78,f53])).
% 1.87/1.60 thf(f53,plain,(
% 1.87/1.60 (sK1 = sK0)),
% 1.87/1.60 inference(cnf_transformation,[status(thm)],[f40])).
% 1.87/1.60 thf(f40,plain,(
% 1.87/1.60 ((morStar @ sK0 @ sK2 @ (comp @ sK0 @ sK1 @ sK2 @ sK3 @ sK4) @ (id @ sK2)) != $true) & ($true = (morStar @ sK0 @ sK1 @ sK3 @ sK3)) & ($true = (morStar @ sK1 @ sK2 @ sK4 @ sK4)) & (sK1 = sK0) & ((morStar @ sK1 @ sK2 @ sK4 @ (id @ sK1)) = $true) & (sK2 = sK1) & ($true = (morStar @ sK0 @ sK1 @ sK3 @ (id @ sK0)))),
% 1.87/1.60 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f31,f39])).
% 1.87/1.60 thf(f39,plain,(
% 1.87/1.60 ? [X0 : obj,X1 : obj,X2 : obj,X3 : mor,X4 : mor] : (((morStar @ X0 @ X2 @ (comp @ X0 @ X1 @ X2 @ X3 @ X4) @ (id @ X2)) != $true) & ($true = (morStar @ X0 @ X1 @ X3 @ X3)) & ($true = (morStar @ X1 @ X2 @ X4 @ X4)) & (X0 = X1) & ($true = (morStar @ X1 @ X2 @ X4 @ (id @ X1))) & (X1 = X2) & ($true = (morStar @ X0 @ X1 @ X3 @ (id @ X0)))) => (((morStar @ sK0 @ sK2 @ (comp @ sK0 @ sK1 @ sK2 @ sK3 @ sK4) @ (id @ sK2)) != $true) & ($true = (morStar @ sK0 @ sK1 @ sK3 @ sK3)) & ($true = (morStar @ sK1 @ sK2 @ sK4 @ sK4)) & (sK1 = sK0) & ((morStar @ sK1 @ sK2 @ sK4 @ (id @ sK1)) = $true) & (sK2 = sK1) & ($true = (morStar @ sK0 @ sK1 @ sK3 @ (id @ sK0))))),
% 1.87/1.60 introduced(definition,[],[choice_axiom])).
% 1.87/1.60 thf(f31,plain,(
% 1.87/1.60 ? [X0 : obj,X1 : obj,X2 : obj,X3 : mor,X4 : mor] : (((morStar @ X0 @ X2 @ (comp @ X0 @ X1 @ X2 @ X3 @ X4) @ (id @ X2)) != $true) & ($true = (morStar @ X0 @ X1 @ X3 @ X3)) & ($true = (morStar @ X1 @ X2 @ X4 @ X4)) & (X0 = X1) & ($true = (morStar @ X1 @ X2 @ X4 @ (id @ X1))) & (X1 = X2) & ($true = (morStar @ X0 @ X1 @ X3 @ (id @ X0))))),
% 1.87/1.60 inference(flattening,[status(thm)],[f30])).
% 1.87/1.60 thf(f30,plain,(
% 1.87/1.60 ? [X0 : obj,X1 : obj,X2 : obj,X3 : mor,X4 : mor] : (((((morStar @ X0 @ X2 @ (comp @ X0 @ X1 @ X2 @ X3 @ X4) @ (id @ X2)) != $true) & (($true = (morStar @ X0 @ X1 @ X3 @ (id @ X0))) & (X1 = X2) & (X0 = X1) & ($true = (morStar @ X1 @ X2 @ X4 @ (id @ X1))))) & ($true = (morStar @ X1 @ X2 @ X4 @ X4))) & ($true = (morStar @ X0 @ X1 @ X3 @ X3)))),
% 1.87/1.60 inference(ennf_transformation,[status(thm)],[f25])).
% 1.87/1.60 thf(f25,plain,(
% 1.87/1.60 ~! [X0 : obj,X1 : obj,X2 : obj,X3 : mor,X4 : mor] : (($true = (morStar @ X0 @ X1 @ X3 @ X3)) => (($true = (morStar @ X1 @ X2 @ X4 @ X4)) => ((($true = (morStar @ X0 @ X1 @ X3 @ (id @ X0))) & (X1 = X2) & (X0 = X1) & ($true = (morStar @ X1 @ X2 @ X4 @ (id @ X1)))) => ((morStar @ X0 @ X2 @ (comp @ X0 @ X1 @ X2 @ X3 @ X4) @ (id @ X2)) = $true))))),
% 1.87/1.60 inference(fool_elimination,[status(thm)],[f24])).
% 1.87/1.60 thf(f24,plain,(
% 1.87/1.60 ~! [X0 : obj,X1 : obj,X2 : obj,X3 : mor,X4 : mor] : ((morStar @ X0 @ X1 @ X3 @ X3) => ((morStar @ X1 @ X2 @ X4 @ X4) => (((X0 = X1) & (morStar @ X0 @ X1 @ X3 @ (id @ X0)) & (X1 = X2) & (morStar @ X1 @ X2 @ X4 @ (id @ X1))) => (morStar @ X0 @ X2 @ (comp @ X0 @ X1 @ X2 @ X3 @ X4) @ (id @ X2)))))),
% 1.87/1.60 inference(rectify,[status(thm)],[f10])).
% 1.87/1.60 thf(f10,negated_conjecture,(
% 1.87/1.60 ~! [X2 : obj,X3 : obj,X4 : obj,X12 : mor,X13 : mor] : ((morStar @ X2 @ X3 @ X12 @ X12) => ((morStar @ X3 @ X4 @ X13 @ X13) => (((X2 = X3) & (morStar @ X2 @ X3 @ X12 @ (id @ X2)) & (X3 = X4) & (morStar @ X3 @ X4 @ X13 @ (id @ X3))) => (morStar @ X2 @ X4 @ (comp @ X2 @ X3 @ X4 @ X12 @ X13) @ (id @ X4)))))),
% 1.87/1.60 inference(negated_conjecture,[status(cth)],[f9])).
% 1.87/1.60 thf(f9,conjecture,(
% 1.87/1.60 ! [X2 : obj,X3 : obj,X4 : obj,X12 : mor,X13 : mor] : ((morStar @ X2 @ X3 @ X12 @ X12) => ((morStar @ X3 @ X4 @ X13 @ X13) => (((X2 = X3) & (morStar @ X2 @ X3 @ X12 @ (id @ X2)) & (X3 = X4) & (morStar @ X3 @ X4 @ X13 @ (id @ X3))) => (morStar @ X2 @ X4 @ (comp @ X2 @ X3 @ X4 @ X12 @ X13) @ (id @ X4)))))),
% 1.87/1.60 file('/export/starexec/sandbox/tmp/tmp.lEGYaQ07tq/DTF2THF_28409.p',conj)).
% 1.87/1.60 thf(f78,plain,(
% 1.87/1.60 ($true = (morStar @ sK0 @ sK1 @ sK4 @ (id @ sK0)))),
% 1.87/1.60 inference(forward_demodulation,[status(thm)],[f77,f51])).
% 1.87/1.60 thf(f51,plain,(
% 1.87/1.60 (sK2 = sK1)),
% 1.87/1.60 inference(cnf_transformation,[status(thm)],[f40])).
% 1.87/1.60 thf(f77,plain,(
% 1.87/1.60 ((morStar @ sK0 @ sK2 @ sK4 @ (id @ sK0)) = $true)),
% 1.87/1.60 inference(forward_demodulation,[status(thm)],[f52,f53])).
% 1.87/1.60 thf(f52,plain,(
% 1.87/1.60 ((morStar @ sK1 @ sK2 @ sK4 @ (id @ sK1)) = $true)),
% 1.87/1.60 inference(cnf_transformation,[status(thm)],[f40])).
% 1.87/1.60 thf(f177,plain,(
% 1.87/1.60 ($true != (morStar @ sK0 @ sK0 @ sK4 @ (id @ sK0))) | ((morStar @ sK0 @ sK0 @ (id @ sK0) @ (id @ sK0)) != $true)),
% 1.87/1.60 inference(trivial_inequality_removal,[status(thm)],[f176])).
% 1.87/1.60 thf(f176,plain,(
% 1.87/1.60 ($true != (morStar @ sK0 @ sK0 @ sK4 @ (id @ sK0))) | ($true != $true) | ((morStar @ sK0 @ sK0 @ (id @ sK0) @ (id @ sK0)) != $true)),
% 1.87/1.60 inference(forward_demodulation,[status(thm)],[f175,f76])).
% 1.87/1.60 thf(f76,plain,(
% 1.87/1.60 ((morStar @ sK0 @ sK0 @ sK3 @ (id @ sK0)) = $true)),
% 1.87/1.60 inference(forward_demodulation,[status(thm)],[f50,f53])).
% 1.87/1.60 thf(f50,plain,(
% 1.87/1.60 ($true = (morStar @ sK0 @ sK1 @ sK3 @ (id @ sK0)))),
% 1.87/1.60 inference(cnf_transformation,[status(thm)],[f40])).
% 1.87/1.60 thf(f175,plain,(
% 1.87/1.60 ((morStar @ sK0 @ sK0 @ sK3 @ (id @ sK0)) != $true) | ($true != (morStar @ sK0 @ sK0 @ sK4 @ (id @ sK0))) | ((morStar @ sK0 @ sK0 @ (id @ sK0) @ (id @ sK0)) != $true)),
% 1.87/1.60 inference(trivial_inequality_removal,[status(thm)],[f168])).
% 1.87/1.60 thf(f168,plain,(
% 1.87/1.60 ((morStar @ sK0 @ sK0 @ (id @ sK0) @ (id @ sK0)) != $true) | ($true != $true) | ($true != (morStar @ sK0 @ sK0 @ sK4 @ (id @ sK0))) | ((morStar @ sK0 @ sK0 @ sK3 @ (id @ sK0)) != $true)),
% 1.87/1.60 inference(superposition,[status(thm)],[f111,f57])).
% 1.87/1.60 thf(f57,plain,(
% 1.87/1.60 ( ! [X2 : mor,X0 : obj,X1 : obj] : (((morStar @ X0 @ X1 @ (comp @ X0 @ X0 @ X1 @ (id @ X0) @ X2) @ X2) = $true) | ($true != (morStar @ X0 @ X1 @ X2 @ X2))) )),
% 1.87/1.60 inference(cnf_transformation,[status(thm)],[f34])).
% 1.87/1.60 thf(f34,plain,(
% 1.87/1.60 ! [X0 : obj,X1 : obj,X2 : mor] : (((morStar @ X0 @ X1 @ (comp @ X0 @ X0 @ X1 @ (id @ X0) @ X2) @ X2) = $true) | ($true != (morStar @ X0 @ X1 @ X2 @ X2)))),
% 1.87/1.60 inference(ennf_transformation,[status(thm)],[f27])).
% 1.87/1.60 thf(f27,plain,(
% 1.87/1.60 ! [X0 : obj,X1 : obj,X2 : mor] : (($true = (morStar @ X0 @ X1 @ X2 @ X2)) => ((morStar @ X0 @ X1 @ (comp @ X0 @ X0 @ X1 @ (id @ X0) @ X2) @ X2) = $true))),
% 1.87/1.60 inference(fool_elimination,[status(thm)],[f26])).
% 1.87/1.60 thf(f26,plain,(
% 1.87/1.60 ! [X0 : obj,X1 : obj,X2 : mor] : ((morStar @ X0 @ X1 @ X2 @ X2) => (morStar @ X0 @ X1 @ (comp @ X0 @ X0 @ X1 @ (id @ X0) @ X2) @ X2))),
% 1.87/1.60 inference(rectify,[status(thm)],[f6])).
% 1.87/1.60 thf(f6,axiom,(
% 1.87/1.60 ! [X2 : obj,X3 : obj,X11 : mor] : ((morStar @ X2 @ X3 @ X11 @ X11) => (morStar @ X2 @ X3 @ (comp @ X2 @ X2 @ X3 @ (id @ X2) @ X11) @ X11))),
% 1.87/1.60 file('/export/starexec/sandbox/tmp/tmp.lEGYaQ07tq/DTF2THF_28409.p',ax1)).
% 1.87/1.60 thf(f111,plain,(
% 1.87/1.60 ( ! [X0 : mor,X1 : mor] : (($true != (morStar @ sK0 @ sK0 @ (comp @ sK0 @ sK0 @ sK0 @ X0 @ X1) @ (id @ sK0))) | ((morStar @ sK0 @ sK0 @ sK4 @ X1) != $true) | ($true != (morStar @ sK0 @ sK0 @ sK3 @ X0))) )),
% 1.87/1.60 inference(trivial_inequality_removal,[status(thm)],[f106])).
% 1.87/1.60 thf(f106,plain,(
% 1.87/1.60 ( ! [X0 : mor,X1 : mor] : (((morStar @ sK0 @ sK0 @ sK4 @ X1) != $true) | ($true != (morStar @ sK0 @ sK0 @ (comp @ sK0 @ sK0 @ sK0 @ X0 @ X1) @ (id @ sK0))) | ($true != (morStar @ sK0 @ sK0 @ sK3 @ X0)) | ($true != $true)) )),
% 1.87/1.60 inference(superposition,[status(thm)],[f89,f58])).
% 1.87/1.60 thf(f58,plain,(
% 1.87/1.60 ( ! [X2 : obj,X3 : mor,X0 : obj,X1 : obj,X6 : mor,X4 : mor,X5 : mor] : (($true = (morStar @ X0 @ X2 @ (comp @ X0 @ X1 @ X2 @ X3 @ X5) @ (comp @ X0 @ X1 @ X2 @ X4 @ X6))) | ($true != (morStar @ X0 @ X1 @ X3 @ X4)) | ($true != (morStar @ X1 @ X2 @ X5 @ X6))) )),
% 1.87/1.60 inference(cnf_transformation,[status(thm)],[f35])).
% 1.87/1.60 thf(f35,plain,(
% 1.87/1.60 ! [X0 : obj,X1 : obj,X2 : obj,X3 : mor,X4 : mor] : (($true != (morStar @ X0 @ X1 @ X3 @ X4)) | ! [X5 : mor,X6 : mor] : (($true != (morStar @ X1 @ X2 @ X5 @ X6)) | ($true = (morStar @ X0 @ X2 @ (comp @ X0 @ X1 @ X2 @ X3 @ X5) @ (comp @ X0 @ X1 @ X2 @ X4 @ X6)))))),
% 1.87/1.60 inference(ennf_transformation,[status(thm)],[f19])).
% 1.87/1.60 thf(f19,plain,(
% 1.87/1.60 ! [X0 : obj,X1 : obj,X2 : obj,X3 : mor,X4 : mor] : (($true = (morStar @ X0 @ X1 @ X3 @ X4)) => ! [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)))))),
% 1.87/1.60 inference(fool_elimination,[status(thm)],[f18])).
% 1.87/1.60 thf(f18,plain,(
% 1.87/1.60 ! [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))))),
% 1.87/1.60 inference(rectify,[status(thm)],[f5])).
% 1.87/1.60 thf(f5,axiom,(
% 1.87/1.60 ! [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))))),
% 1.87/1.60 file('/export/starexec/sandbox/tmp/tmp.lEGYaQ07tq/DTF2THF_28409.p',comp_tp_ax)).
% 1.87/1.60 thf(f89,plain,(
% 1.87/1.60 ( ! [X0 : mor] : (($true != (morStar @ sK0 @ sK0 @ (comp @ sK0 @ sK0 @ sK0 @ sK3 @ sK4) @ X0)) | ((morStar @ sK0 @ sK0 @ X0 @ (id @ sK0)) != $true)) )),
% 1.87/1.60 inference(trivial_inequality_removal,[status(thm)],[f88])).
% 1.87/1.60 thf(f88,plain,(
% 1.87/1.60 ( ! [X0 : mor] : (($true != $true) | ((morStar @ sK0 @ sK0 @ X0 @ (id @ sK0)) != $true) | ($true != (morStar @ sK0 @ sK0 @ (comp @ sK0 @ sK0 @ sK0 @ sK3 @ sK4) @ X0))) )),
% 1.87/1.60 inference(forward_demodulation,[status(thm)],[f84,f70])).
% 1.87/1.60 thf(f70,plain,(
% 1.87/1.60 ( ! [X0 : obj,X1 : obj] : (($true = (isPer @ mor @ (morStar @ X0 @ X1)))) )),
% 1.87/1.60 inference(cnf_transformation,[status(thm)],[f17])).
% 1.87/1.60 thf(f17,plain,(
% 1.87/1.60 ! [X0 : obj,X1 : obj] : ($true = (isPer @ mor @ (morStar @ X0 @ X1)))),
% 1.87/1.60 inference(fool_elimination,[status(thm)],[f16])).
% 1.87/1.60 thf(f16,plain,(
% 1.87/1.60 ! [X0 : obj,X1 : obj] : (isPer @ mor @ (morStar @ X0 @ X1))),
% 1.87/1.60 inference(rectify,[status(thm)],[f3])).
% 1.87/1.60 thf(f3,axiom,(
% 1.87/1.60 ! [X5 : obj,X6 : obj] : (isPer @ mor @ (morStar @ X5 @ X6))),
% 1.87/1.60 file('/export/starexec/sandbox/tmp/tmp.lEGYaQ07tq/DTF2THF_28409.p','\'morStar\'_is_per')).
% 1.87/1.60 thf(f84,plain,(
% 1.87/1.60 ( ! [X0 : mor] : (($true != (morStar @ sK0 @ sK0 @ (comp @ sK0 @ sK0 @ sK0 @ sK3 @ sK4) @ X0)) | ($true != (isPer @ mor @ (morStar @ sK0 @ sK0))) | ((morStar @ sK0 @ sK0 @ X0 @ (id @ sK0)) != $true)) )),
% 1.87/1.60 inference(trivial_inequality_removal,[status(thm)],[f83])).
% 1.87/1.60 thf(f83,plain,(
% 1.87/1.60 ( ! [X0 : mor] : (((morStar @ sK0 @ sK0 @ X0 @ (id @ sK0)) != $true) | ($true != (morStar @ sK0 @ sK0 @ (comp @ sK0 @ sK0 @ sK0 @ sK3 @ sK4) @ X0)) | ($true != (isPer @ mor @ (morStar @ sK0 @ sK0))) | ($true != $true)) )),
% 1.87/1.60 inference(superposition,[status(thm)],[f81,f66])).
% 1.87/1.60 thf(f66,plain,(
% 1.87/1.60 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > X0 > $o,X4 : X0] : (((X1 @ X2 @ X4) = $true) | ((X1 @ X2 @ X3) != $true) | ((isPer @ X0 @ X1) != $true) | ((X1 @ X3 @ X4) != $true)) )),
% 1.87/1.60 inference(cnf_transformation,[status(thm)],[f46])).
% 1.87/1.60 thf(f46,plain,(
% 1.87/1.60 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((! [X2 : X0,X3 : X0,X4 : X0] : (((X1 @ X2 @ X3) != $true) | ((X1 @ X2 @ X4) = $true) | ((X1 @ X3 @ X4) != $true)) & ! [X5 : X0,X6 : X0] : (($true != (X1 @ X5 @ X6)) | ((X1 @ X6 @ X5) = $true))) | ((isPer @ X0 @ X1) != $true)) & (((isPer @ X0 @ X1) = $true) | (($true = (X1 @ (sK5 @ X0 @ X1) @ (sK6 @ X0 @ X1))) & ($true != (X1 @ (sK5 @ X0 @ X1) @ (sK7 @ X0 @ X1))) & ((X1 @ (sK6 @ X0 @ X1) @ (sK7 @ X0 @ X1)) = $true)) | (($true = (X1 @ (sK8 @ X0 @ X1) @ (sK9 @ X0 @ X1))) & ((X1 @ (sK9 @ X0 @ X1) @ (sK8 @ X0 @ X1)) != $true))))),
% 1.87/1.60 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8,sK9])],[f43,f45,f44])).
% 1.87/1.60 thf(f44,plain,(
% 1.87/1.60 ! [X0 : $tType,X1 : X0 > X0 > $o] : (? [X7 : X0,X8 : X0,X9 : X0] : (((X1 @ X7 @ X8) = $true) & ($true != (X1 @ X7 @ X9)) & ((X1 @ X8 @ X9) = $true)) => (($true = (X1 @ (sK5 @ X0 @ X1) @ (sK6 @ X0 @ X1))) & ($true != (X1 @ (sK5 @ X0 @ X1) @ (sK7 @ X0 @ X1))) & ((X1 @ (sK6 @ X0 @ X1) @ (sK7 @ X0 @ X1)) = $true)))),
% 1.87/1.60 introduced(definition,[],[choice_axiom])).
% 1.87/1.60 thf(f45,plain,(
% 1.87/1.60 ! [X0 : $tType,X1 : X0 > X0 > $o] : (? [X10 : X0,X11 : X0] : (($true = (X1 @ X10 @ X11)) & ($true != (X1 @ X11 @ X10))) => (($true = (X1 @ (sK8 @ X0 @ X1) @ (sK9 @ X0 @ X1))) & ((X1 @ (sK9 @ X0 @ X1) @ (sK8 @ X0 @ X1)) != $true)))),
% 1.87/1.60 introduced(definition,[],[choice_axiom])).
% 1.87/1.60 thf(f43,plain,(
% 1.87/1.60 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((! [X2 : X0,X3 : X0,X4 : X0] : (((X1 @ X2 @ X3) != $true) | ((X1 @ X2 @ X4) = $true) | ((X1 @ X3 @ X4) != $true)) & ! [X5 : X0,X6 : X0] : (($true != (X1 @ X5 @ X6)) | ((X1 @ X6 @ X5) = $true))) | ((isPer @ X0 @ X1) != $true)) & (((isPer @ X0 @ X1) = $true) | ? [X7 : X0,X8 : X0,X9 : X0] : (((X1 @ X7 @ X8) = $true) & ($true != (X1 @ X7 @ X9)) & ((X1 @ X8 @ X9) = $true)) | ? [X10 : X0,X11 : X0] : (($true = (X1 @ X10 @ X11)) & ($true != (X1 @ X11 @ X10)))))),
% 1.87/1.60 inference(rectify,[status(thm)],[f42])).
% 1.87/1.60 thf(f42,plain,(
% 1.87/1.60 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((! [X4 : X0,X5 : X0,X6 : X0] : (($true != (X1 @ X4 @ X5)) | ($true = (X1 @ X4 @ X6)) | ($true != (X1 @ X5 @ X6))) & ! [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 @ X4 @ X5)) & ($true != (X1 @ X4 @ X6)) & ($true = (X1 @ X5 @ X6))) | ? [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3) = $true) & ((X1 @ X3 @ X2) != $true))))),
% 1.87/1.60 inference(flattening,[status(thm)],[f41])).
% 1.87/1.60 thf(f41,plain,(
% 1.87/1.60 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((! [X4 : X0,X5 : X0,X6 : X0] : (($true != (X1 @ X4 @ X5)) | ($true = (X1 @ X4 @ X6)) | ($true != (X1 @ X5 @ X6))) & ! [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 @ X4 @ X5)) & ($true != (X1 @ X4 @ X6)) & ($true = (X1 @ X5 @ X6))) | ? [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3) = $true) & ((X1 @ X3 @ X2) != $true)))))),
% 1.87/1.60 inference(nnf_transformation,[status(thm)],[f33])).
% 1.87/1.60 thf(f33,plain,(
% 1.87/1.60 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((! [X4 : X0,X5 : X0,X6 : X0] : (($true != (X1 @ X4 @ X5)) | ($true = (X1 @ X4 @ X6)) | ($true != (X1 @ X5 @ X6))) & ! [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3) != $true) | ((X1 @ X3 @ X2) = $true))) <=> ((isPer @ X0 @ X1) = $true))),
% 1.87/1.60 inference(flattening,[status(thm)],[f32])).
% 1.87/1.60 thf(f32,plain,(
% 1.87/1.60 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((! [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3) != $true) | ((X1 @ X3 @ X2) = $true)) & ! [X4 : X0,X5 : X0,X6 : X0] : ((($true = (X1 @ X4 @ X6)) | ($true != (X1 @ X5 @ X6))) | ($true != (X1 @ X4 @ X5)))) <=> ((isPer @ X0 @ X1) = $true))),
% 1.87/1.60 inference(ennf_transformation,[status(thm)],[f13])).
% 1.87/1.60 thf(f13,plain,(
% 1.87/1.60 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((! [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3) = $true) => ((X1 @ X3 @ X2) = $true)) & ! [X4 : X0,X5 : X0,X6 : X0] : (($true = (X1 @ X4 @ X5)) => (($true = (X1 @ X5 @ X6)) => ($true = (X1 @ X4 @ X6))))) <=> ((isPer @ X0 @ X1) = $true))),
% 1.87/1.60 inference(fool_elimination,[status(thm)],[f12])).
% 1.87/1.60 thf(f12,plain,(
% 1.87/1.60 ! [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))),
% 1.87/1.60 inference(rectify,[status(thm)],[f1])).
% 1.87/1.60 thf(f1,axiom,(
% 1.87/1.60 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((! [X2 : X0,X3 : X0] : ((X1 @ X2 @ X3) => (X1 @ X3 @ X2)) & ! [X2 : X0,X3 : X0,X4 : X0] : ((X1 @ X2 @ X3) => ((X1 @ X3 @ X4) => (X1 @ X2 @ X4)))) <=> (isPer @ X0 @ X1))),
% 1.87/1.60 file('/export/starexec/sandbox/tmp/tmp.lEGYaQ07tq/DTF2THF_28409.p',is_per)).
% 1.87/1.60 thf(f81,plain,(
% 1.87/1.60 ($true != (morStar @ sK0 @ sK0 @ (comp @ sK0 @ sK0 @ sK0 @ sK3 @ sK4) @ (id @ sK0)))),
% 1.87/1.60 inference(forward_demodulation,[status(thm)],[f80,f53])).
% 1.87/1.60 thf(f80,plain,(
% 1.87/1.60 ($true != (morStar @ sK0 @ sK1 @ (comp @ sK0 @ sK1 @ sK1 @ sK3 @ sK4) @ (id @ sK1)))),
% 1.87/1.60 inference(forward_demodulation,[status(thm)],[f56,f51])).
% 1.87/1.60 thf(f56,plain,(
% 1.87/1.60 ((morStar @ sK0 @ sK2 @ (comp @ sK0 @ sK1 @ sK2 @ sK3 @ sK4) @ (id @ sK2)) != $true)),
% 1.87/1.60 inference(cnf_transformation,[status(thm)],[f40])).
% 1.87/1.60 % SZS output end Proof for DTF2THF_28409
% 1.87/1.60 % (28529)------------------------------
% 1.87/1.60 % (28529)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/1.60 % (28529)Termination reason: Refutation
% 1.87/1.60
% 1.87/1.60 % (28529)Memory used [KB]: 5628
% 1.87/1.60 % (28529)Time elapsed: 0.017 s
% 1.87/1.60 % (28529)Instructions burned: 25 (million)
% 1.87/1.60 % (28529)------------------------------
% 1.87/1.60 % (28529)------------------------------
% 1.87/1.60 % (28506)Success in time 0.106 s
%------------------------------------------------------------------------------