%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO173^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:53:34 AM UTC 2026
% Result : Theorem 1.66s 1.53s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 3
% Syntax : Number of formulae : 64 ( 14 unt; 0 typ; 1 def)
% Number of atoms : 497 ( 140 equ; 0 cnn)
% Maximal formula atoms : 7 ( 7 avg)
% Number of connectives : 824 ( 113 ~; 77 |; 28 &; 604 @)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 153 ( 0 ^; 146 !; 7 ?; 153 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
nt: $i > $i ).
thf(func_def_1,type,
imp: $i > $i > $i ).
thf(func_def_2,type,
cT: $i > $o ).
thf(f2501,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f2261,f2473]) ).
thf(f2473,plain,
~ spl1_3,
inference(avatar_contradiction_clause,[status(thm)],[f2472]) ).
thf(f2472,plain,
( $false
| ~ spl1_3 ),
inference(trivial_inequality_removal,[status(thm)],[f2423]) ).
thf(f2423,plain,
( ( $false = $true )
| ~ spl1_3 ),
inference(backward_demodulation,[status(thm)],[f14,f2328]) ).
thf(f2328,plain,
( ! [X0: $i] :
( ( cT @ X0 )
= $false )
| ~ spl1_3 ),
inference(trivial_inequality_removal,[status(thm)],[f2265]) ).
thf(f2265,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( ( cT @ X0 )
= $false ) )
| ~ spl1_3 ),
inference(fool_paramodulation,[status(thm)],[f168]) ).
thf(f168,plain,
( ! [X0: $i] :
( ( cT @ X0 )
!= $true )
| ~ spl1_3 ),
inference(avatar_component_clause,[status(thm)],[f167]) ).
thf(f167,definition,
( spl1_3
<=> ! [X0: $i] :
( ( cT @ X0 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[spl1_3])],[avatar_definition]) ).
thf(f14,plain,
! [X2: $i,X0: $i,X1: $i] :
( $true
= ( cT @ ( imp @ ( imp @ X1 @ ( imp @ X0 @ X2 ) ) @ ( imp @ ( imp @ X1 @ X0 ) @ ( imp @ X1 @ X2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( $true
= ( cT @ ( imp @ ( imp @ X1 @ ( imp @ X0 @ X2 ) ) @ ( imp @ ( imp @ X1 @ X0 ) @ ( imp @ X1 @ X2 ) ) ) ) )
& ! [X3: $i,X4: $i] :
( $true
= ( cT @ ( imp @ ( imp @ ( nt @ X3 ) @ ( nt @ X4 ) ) @ ( imp @ X4 @ X3 ) ) ) )
& ! [X5: $i,X6: $i] :
( ( $true
!= ( cT @ X6 ) )
| ( $true
!= ( cT @ ( imp @ X6 @ X5 ) ) )
| ( $true
= ( cT @ X5 ) ) )
& ! [X7: $i,X8: $i] :
( $true
= ( cT @ ( imp @ X7 @ ( imp @ X8 @ X7 ) ) ) )
& ( $true
!= ( cT @ ( imp @ ( nt @ ( nt @ sK0 ) ) @ sK0 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8]) ).
thf(f8,plain,
( ? [X9: $i] :
( ( cT @ ( imp @ ( nt @ ( nt @ X9 ) ) @ X9 ) )
!= $true )
=> ( $true
!= ( cT @ ( imp @ ( nt @ ( nt @ sK0 ) ) @ sK0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( $true
= ( cT @ ( imp @ ( imp @ X1 @ ( imp @ X0 @ X2 ) ) @ ( imp @ ( imp @ X1 @ X0 ) @ ( imp @ X1 @ X2 ) ) ) ) )
& ! [X3: $i,X4: $i] :
( $true
= ( cT @ ( imp @ ( imp @ ( nt @ X3 ) @ ( nt @ X4 ) ) @ ( imp @ X4 @ X3 ) ) ) )
& ! [X5: $i,X6: $i] :
( ( $true
!= ( cT @ X6 ) )
| ( $true
!= ( cT @ ( imp @ X6 @ X5 ) ) )
| ( $true
= ( cT @ X5 ) ) )
& ! [X7: $i,X8: $i] :
( $true
= ( cT @ ( imp @ X7 @ ( imp @ X8 @ X7 ) ) ) )
& ? [X9: $i] :
( ( cT @ ( imp @ ( nt @ ( nt @ X9 ) ) @ X9 ) )
!= $true ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X9: $i,X8: $i,X7: $i] :
( $true
= ( cT @ ( imp @ ( imp @ X8 @ ( imp @ X9 @ X7 ) ) @ ( imp @ ( imp @ X8 @ X9 ) @ ( imp @ X8 @ X7 ) ) ) ) )
& ! [X2: $i,X3: $i] :
( $true
= ( cT @ ( imp @ ( imp @ ( nt @ X2 ) @ ( nt @ X3 ) ) @ ( imp @ X3 @ X2 ) ) ) )
& ! [X4: $i,X5: $i] :
( ( $true
!= ( cT @ X5 ) )
| ( ( cT @ ( imp @ X5 @ X4 ) )
!= $true )
| ( $true
= ( cT @ X4 ) ) )
& ! [X1: $i,X0: $i] :
( $true
= ( cT @ ( imp @ X1 @ ( imp @ X0 @ X1 ) ) ) )
& ? [X6: $i] :
( ( cT @ ( imp @ ( nt @ ( nt @ X6 ) ) @ X6 ) )
!= $true ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ~ ( ! [X1: $i,X0: $i] :
( $true
= ( cT @ ( imp @ X1 @ ( imp @ X0 @ X1 ) ) ) )
& ! [X2: $i,X3: $i] :
( $true
= ( cT @ ( imp @ ( imp @ ( nt @ X2 ) @ ( nt @ X3 ) ) @ ( imp @ X3 @ X2 ) ) ) )
& ! [X4: $i,X5: $i] :
( ( $true
!= ( cT @ X5 ) )
| ( $true
= ( cT @ X4 ) )
| ( ( cT @ ( imp @ X5 @ X4 ) )
!= $true ) )
& ? [X6: $i] :
( ( cT @ ( imp @ ( nt @ ( nt @ X6 ) ) @ X6 ) )
!= $true )
& ! [X9: $i,X8: $i,X7: $i] :
( $true
= ( cT @ ( imp @ ( imp @ X8 @ ( imp @ X9 @ X7 ) ) @ ( imp @ ( imp @ X8 @ X9 ) @ ( imp @ X8 @ X7 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ~ ( ! [X0: $i,X1: $i] : ( cT @ ( imp @ X1 @ ( imp @ X0 @ X1 ) ) )
& ! [X2: $i,X3: $i] : ( cT @ ( imp @ ( imp @ ( nt @ X2 ) @ ( nt @ X3 ) ) @ ( imp @ X3 @ X2 ) ) )
& ! [X4: $i,X5: $i] :
( ~ ( cT @ X5 )
| ( cT @ X4 )
| ~ ( cT @ ( imp @ X5 @ X4 ) ) )
& ? [X6: $i] :
~ ( cT @ ( imp @ ( nt @ ( nt @ X6 ) ) @ X6 ) )
& ! [X7: $i,X8: $i,X9: $i] : ( cT @ ( imp @ ( imp @ X8 @ ( imp @ X9 @ X7 ) ) @ ( imp @ ( imp @ X8 @ X9 ) @ ( imp @ X8 @ X7 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ~ ( ! [X1: $i,X0: $i] : ( cT @ ( imp @ X0 @ ( imp @ X1 @ X0 ) ) )
& ! [X0: $i,X1: $i] : ( cT @ ( imp @ ( imp @ ( nt @ X0 ) @ ( nt @ X1 ) ) @ ( imp @ X1 @ X0 ) ) )
& ! [X1: $i,X0: $i] :
( ~ ( cT @ X0 )
| ( cT @ X1 )
| ~ ( cT @ ( imp @ X0 @ X1 ) ) )
& ? [X3: $i] :
~ ( cT @ ( imp @ ( nt @ ( nt @ X3 ) ) @ X3 ) )
& ! [X2: $i,X0: $i,X1: $i] : ( cT @ ( imp @ ( imp @ X0 @ ( imp @ X1 @ X2 ) ) @ ( imp @ ( imp @ X0 @ X1 ) @ ( imp @ X0 @ X2 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
~ ( ! [X1: $i,X0: $i] : ( cT @ ( imp @ X0 @ ( imp @ X1 @ X0 ) ) )
& ! [X0: $i,X1: $i] : ( cT @ ( imp @ ( imp @ ( nt @ X0 ) @ ( nt @ X1 ) ) @ ( imp @ X1 @ X0 ) ) )
& ! [X1: $i,X0: $i] :
( ~ ( cT @ X0 )
| ( cT @ X1 )
| ~ ( cT @ ( imp @ X0 @ X1 ) ) )
& ? [X3: $i] :
~ ( cT @ ( imp @ ( nt @ ( nt @ X3 ) ) @ X3 ) )
& ! [X2: $i,X0: $i,X1: $i] : ( cT @ ( imp @ ( imp @ X0 @ ( imp @ X1 @ X2 ) ) @ ( imp @ ( imp @ X0 @ X1 ) @ ( imp @ X0 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.tL6P2LiOfW/DTF2THF_15574.p',cLCL077_1) ).
thf(f2261,plain,
spl1_3,
inference(avatar_split_clause,[status(thm)],[f2254,f167]) ).
thf(f2254,plain,
! [X0: $i] :
( ( cT @ X0 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f2237]) ).
thf(f2237,plain,
! [X0: $i] :
( ( ( cT @ X0 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f2229,f24]) ).
thf(f24,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( cT @ ( imp @ X1 @ X0 ) ) )
| ( ( cT @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f23]) ).
thf(f23,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( ( cT @ X0 )
!= $true )
| ( $true
= ( cT @ ( imp @ X1 @ X0 ) ) ) ),
inference(superposition,[status(thm)],[f12,f11]) ).
thf(f11,plain,
! [X8: $i,X7: $i] :
( $true
= ( cT @ ( imp @ X7 @ ( imp @ X8 @ X7 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f12,plain,
! [X6: $i,X5: $i] :
( ( $true
!= ( cT @ ( imp @ X6 @ X5 ) ) )
| ( $true
!= ( cT @ X6 ) )
| ( $true
= ( cT @ X5 ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f2229,plain,
! [X0: $i] :
( $true
!= ( cT @ ( imp @ ( imp @ X0 @ sK0 ) @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f2228]) ).
thf(f2228,plain,
! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( cT @ ( imp @ ( imp @ X0 @ sK0 ) @ X0 ) ) ) ),
inference(forward_demodulation,[status(thm)],[f2222,f284]) ).
thf(f284,plain,
! [X0: $i] :
( $true
= ( cT @ ( imp @ X0 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f274]) ).
thf(f274,plain,
! [X0: $i] :
( ( $true
= ( cT @ ( imp @ X0 @ X0 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f270,f11]) ).
thf(f270,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( cT @ ( imp @ ( nt @ X0 ) @ X1 ) ) )
| ( $true
= ( cT @ ( imp @ X0 @ X0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f263]) ).
thf(f263,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
= ( cT @ ( imp @ X0 @ X0 ) ) )
| ( $true
!= ( cT @ ( imp @ ( nt @ X0 ) @ X1 ) ) ) ),
inference(superposition,[status(thm)],[f53,f252]) ).
thf(f252,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( cT @ ( imp @ X0 @ X0 ) ) )
| ( ( cT @ ( imp @ X0 @ X1 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f246]) ).
thf(f246,plain,
! [X0: $i,X1: $i] :
( ( ( cT @ ( imp @ X0 @ X1 ) )
!= $true )
| ( $true != $true )
| ( $true
= ( cT @ ( imp @ X0 @ X0 ) ) ) ),
inference(superposition,[status(thm)],[f241,f11]) ).
thf(f241,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( cT @ ( imp @ X0 @ ( imp @ X1 @ X2 ) ) )
!= $true )
| ( ( cT @ ( imp @ X0 @ X1 ) )
!= $true )
| ( $true
= ( cT @ ( imp @ X0 @ X2 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f238]) ).
thf(f238,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
= ( cT @ ( imp @ X0 @ X2 ) ) )
| ( ( cT @ ( imp @ X0 @ ( imp @ X1 @ X2 ) ) )
!= $true )
| ( ( cT @ ( imp @ X0 @ X1 ) )
!= $true ) ),
inference(superposition,[status(thm)],[f12,f234]) ).
thf(f234,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( cT @ ( imp @ ( imp @ X0 @ X1 ) @ ( imp @ X0 @ X2 ) ) ) )
| ( ( cT @ ( imp @ X0 @ ( imp @ X1 @ X2 ) ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f230]) ).
thf(f230,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false = $true )
| ( $true
= ( cT @ ( imp @ ( imp @ X0 @ X1 ) @ ( imp @ X0 @ X2 ) ) ) )
| ( ( cT @ ( imp @ X0 @ ( imp @ X1 @ X2 ) ) )
!= $true ) ),
inference(superposition,[status(thm)],[f25,f14]) ).
thf(f25,plain,
! [X6: $i,X5: $i] :
( ( $false
= ( cT @ ( imp @ X6 @ X5 ) ) )
| ( $true
!= ( cT @ X6 ) )
| ( $true
= ( cT @ X5 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f21]) ).
thf(f21,plain,
! [X6: $i,X5: $i] :
( ( $true != $true )
| ( $true
!= ( cT @ X6 ) )
| ( $true
= ( cT @ X5 ) )
| ( $false
= ( cT @ ( imp @ X6 @ X5 ) ) ) ),
inference(fool_paramodulation,[status(thm)],[f12]) ).
thf(f53,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( cT @ ( imp @ ( nt @ X0 ) @ ( nt @ X1 ) ) ) )
| ( $true
= ( cT @ ( imp @ X1 @ X0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f50]) ).
thf(f50,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( cT @ ( imp @ X1 @ X0 ) ) )
| ( $true != $true )
| ( $true
!= ( cT @ ( imp @ ( nt @ X0 ) @ ( nt @ X1 ) ) ) ) ),
inference(superposition,[status(thm)],[f12,f13]) ).
thf(f13,plain,
! [X3: $i,X4: $i] :
( $true
= ( cT @ ( imp @ ( imp @ ( nt @ X3 ) @ ( nt @ X4 ) ) @ ( imp @ X4 @ X3 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f2222,plain,
! [X0: $i] :
( ( ( cT @ ( imp @ sK0 @ sK0 ) )
!= $true )
| ( $true
!= ( cT @ ( imp @ ( imp @ X0 @ sK0 ) @ X0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f2156]) ).
thf(f2156,plain,
! [X0: $i] :
( ( $true
!= ( cT @ ( imp @ ( imp @ X0 @ sK0 ) @ X0 ) ) )
| ( ( cT @ ( imp @ sK0 @ sK0 ) )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f1531,f297]) ).
thf(f297,plain,
! [X0: $i,X1: $i] :
( ( ( cT @ ( imp @ ( imp @ X0 @ X1 ) @ X1 ) )
= $true )
| ( $true
!= ( cT @ ( imp @ ( imp @ X0 @ X1 ) @ X0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f292]) ).
thf(f292,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( cT @ ( imp @ ( imp @ X0 @ X1 ) @ X0 ) ) )
| ( $true != $true )
| ( ( cT @ ( imp @ ( imp @ X0 @ X1 ) @ X1 ) )
= $true ) ),
inference(superposition,[status(thm)],[f241,f284]) ).
thf(f1531,plain,
! [X0: $i,X1: $i] :
( ( ( cT @ ( imp @ ( imp @ X0 @ sK0 ) @ X1 ) )
!= $true )
| ( $true
!= ( cT @ ( imp @ X1 @ sK0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f1525]) ).
thf(f1525,plain,
! [X0: $i,X1: $i] :
( ( ( cT @ ( imp @ ( imp @ X0 @ sK0 ) @ X1 ) )
!= $true )
| ( $true != $true )
| ( $true
!= ( cT @ ( imp @ X1 @ sK0 ) ) ) ),
inference(superposition,[status(thm)],[f1506,f255]) ).
thf(f255,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( cT @ ( imp @ X0 @ X2 ) ) )
| ( $true
!= ( cT @ ( imp @ X1 @ X2 ) ) )
| ( ( cT @ ( imp @ X0 @ X1 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f250]) ).
thf(f250,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( cT @ ( imp @ X0 @ X2 ) ) )
| ( $true != $true )
| ( ( cT @ ( imp @ X0 @ X1 ) )
!= $true )
| ( $true
!= ( cT @ ( imp @ X1 @ X2 ) ) ) ),
inference(superposition,[status(thm)],[f241,f24]) ).
thf(f1506,plain,
! [X0: $i] :
( $true
!= ( cT @ ( imp @ ( imp @ X0 @ sK0 ) @ sK0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f1476]) ).
thf(f1476,plain,
! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( cT @ ( imp @ ( imp @ X0 @ sK0 ) @ sK0 ) ) ) ),
inference(superposition,[status(thm)],[f1339,f13]) ).
thf(f1339,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( cT @ ( imp @ ( imp @ ( nt @ sK0 ) @ X0 ) @ X1 ) ) )
| ( $true
!= ( cT @ ( imp @ X1 @ sK0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f1329]) ).
thf(f1329,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( cT @ ( imp @ ( imp @ ( nt @ sK0 ) @ X0 ) @ X1 ) ) )
| ( $true
!= ( cT @ ( imp @ X1 @ sK0 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f1305,f255]) ).
thf(f1305,plain,
! [X0: $i] :
( $true
!= ( cT @ ( imp @ ( imp @ ( nt @ sK0 ) @ X0 ) @ sK0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f1285]) ).
thf(f1285,plain,
! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( cT @ ( imp @ ( imp @ ( nt @ sK0 ) @ X0 ) @ sK0 ) ) ) ),
inference(superposition,[status(thm)],[f476,f13]) ).
thf(f476,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( cT @ ( imp @ ( imp @ X0 @ ( nt @ ( nt @ sK0 ) ) ) @ X1 ) ) )
| ( $true
!= ( cT @ ( imp @ X1 @ sK0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f468]) ).
thf(f468,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( cT @ ( imp @ X1 @ sK0 ) ) )
| ( $true
!= ( cT @ ( imp @ ( imp @ X0 @ ( nt @ ( nt @ sK0 ) ) ) @ X1 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f337,f255]) ).
thf(f337,plain,
! [X0: $i] :
( ( cT @ ( imp @ ( imp @ X0 @ ( nt @ ( nt @ sK0 ) ) ) @ sK0 ) )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f324]) ).
thf(f324,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( cT @ ( imp @ ( imp @ X0 @ ( nt @ ( nt @ sK0 ) ) ) @ sK0 ) )
!= $true ) ),
inference(superposition,[status(thm)],[f318,f11]) ).
thf(f318,plain,
! [X0: $i] :
( ( $true
!= ( cT @ ( imp @ ( nt @ ( nt @ sK0 ) ) @ X0 ) ) )
| ( $true
!= ( cT @ ( imp @ X0 @ sK0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f301]) ).
thf(f301,plain,
! [X0: $i] :
( ( $true
!= ( cT @ ( imp @ X0 @ sK0 ) ) )
| ( $true
!= ( cT @ ( imp @ ( nt @ ( nt @ sK0 ) ) @ X0 ) ) )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f255,f16]) ).
thf(f16,plain,
( $false
= ( cT @ ( imp @ ( nt @ ( nt @ sK0 ) ) @ sK0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f15]) ).
thf(f15,plain,
( ( $false
= ( cT @ ( imp @ ( nt @ ( nt @ sK0 ) ) @ sK0 ) ) )
| ( $true != $true ) ),
inference(fool_paramodulation,[status(thm)],[f10]) ).
thf(f10,plain,
( $true
!= ( cT @ ( imp @ ( nt @ ( nt @ sK0 ) ) @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO173^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.14/0.33 % Computer : n006.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue Feb 24 14:25:15 EST 2026
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.20/0.45 ---- Original DTF file ---
% 0.20/0.45 thf(spec,logic,$$dhol).
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 % File : SYO173^5 : TPTP v9.2.1. Released v4.0.0.
% 0.20/0.45 % Domain : Syntactic
% 0.20/0.45 % Problem : TPS problem from BASIC-FO-THMS
% 0.20/0.45 % Version : Especial.
% 0.20/0.45 % English :
% 0.20/0.45
% 0.20/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.45 % Source : [Bro09]
% 0.20/0.45 % Names : tps_1028 [Bro09]
% 0.20/0.45
% 0.20/0.45 % Status : Theorem
% 0.20/0.45 % Rating : 0.42 v9.1.0, 0.38 v9.0.0, 0.33 v8.2.0, 0.36 v8.1.0, 0.33 v7.3.0, 0.30 v7.2.0, 0.38 v7.1.0, 0.43 v7.0.0, 0.50 v6.4.0, 0.57 v6.3.0, 0.67 v6.1.0, 0.50 v6.0.0, 0.33 v5.5.0, 0.40 v5.4.0, 0.50 v5.1.0, 0.75 v5.0.0, 0.50 v4.1.0, 0.33 v4.0.0
% 0.20/0.45 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.20/0.45 % Number of atoms : 7 ( 0 equ; 0 cnn)
% 0.20/0.45 % Maximal formula atoms : 7 ( 7 avg)
% 0.20/0.45 % Number of connectives : 47 ( 4 ~; 2 |; 4 &; 37 @)
% 0.20/0.45 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.20/0.45 % Maximal formula depth : 14 ( 14 avg)
% 0.20/0.45 % Number of types : 2 ( 0 usr)
% 0.20/0.45 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.20/0.45 % Number of symbols : 3 ( 3 usr; 0 con; 1-2 aty)
% 0.20/0.45 % Number of variables : 10 ( 0 ^; 9 !; 1 ?; 10 :)
% 0.20/0.45 % SPC : TH0_THM_NEQ_NAR
% 0.20/0.45
% 0.20/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.20/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.20/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.20/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 thf(nt,type,
% 0.20/0.45 nt: $i > $i ).
% 0.20/0.45
% 0.20/0.45 thf(imp,type,
% 0.20/0.45 imp: $i > $i > $i ).
% 0.20/0.45
% 0.20/0.45 thf(cT,type,
% 0.20/0.45 cT: $i > $o ).
% 0.20/0.45
% 0.20/0.45 thf(cLCL077_1,conjecture,
% 0.20/0.45 ~ ( ! [Xp: $i,Xq: $i] :
% 0.20/0.45 ( ~ ( cT @ ( imp @ Xp @ Xq ) )
% 0.20/0.45 | ~ ( cT @ Xp )
% 0.20/0.45 | ( cT @ Xq ) )
% 0.20/0.45 & ! [Xp: $i,Xq: $i] : ( cT @ ( imp @ Xp @ ( imp @ Xq @ Xp ) ) )
% 0.20/0.45 & ! [Xp: $i,Xq: $i,Xr: $i] : ( cT @ ( imp @ ( imp @ Xp @ ( imp @ Xq @ Xr ) ) @ ( imp @ ( imp @ Xp @ Xq ) @ ( imp @ Xp @ Xr ) ) ) )
% 0.20/0.45 & ! [Xp: $i,Xq: $i] : ( cT @ ( imp @ ( imp @ ( nt @ Xp ) @ ( nt @ Xq ) ) @ ( imp @ Xq @ Xp ) ) )
% 0.20/0.45 & ? [Xa: $i] :
% 0.20/0.45 ~ ( cT @ ( imp @ ( nt @ ( nt @ Xa ) ) @ Xa ) ) ) ).
% 0.20/0.45
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 ------------------------
% 1.45/1.29 ---- Embedded in THF ---
% 1.45/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.45/1.29 %%% Generated on Tue Feb 24 14:25:16 EST 2026
% 1.45/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.45/1.29 %%% Logic specification used:
% 1.45/1.29 %%% thf(spec, logic, $$dhol).
% 1.45/1.29
% 1.45/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.tL6P2LiOfW/DTF2DTF15574.p
% See solution above
% 1.45/1.29 ------------------------
% 1.63/1.30 ---- Cleaned THF ---
% 1.63/1.30 thf(nt,type,
% 1.63/1.30 nt: $i > $i ).
% 1.63/1.30
% 1.63/1.30 thf(imp,type,
% 1.63/1.30 imp: $i > $i > $i ).
% 1.63/1.30
% 1.63/1.30 thf(cT,type,
% 1.63/1.30 cT: $i > $o ).
% 1.63/1.30
% 1.63/1.30 thf(cLCL077_1,conjecture,
% 1.63/1.30 ~ ( ! [Xp: $i,Xq: $i] :
% 1.63/1.30 ( ~ ( cT @ ( imp @ Xp @ Xq ) )
% 1.63/1.30 | ~ ( cT @ Xp )
% 1.63/1.30 | ( cT @ Xq ) )
% 1.63/1.30 & ! [Xp: $i,Xq: $i] : ( cT @ ( imp @ Xp @ ( imp @ Xq @ Xp ) ) )
% 1.63/1.30 & ! [Xp: $i,Xq: $i,Xr: $i] : ( cT @ ( imp @ ( imp @ Xp @ ( imp @ Xq @ Xr ) ) @ ( imp @ ( imp @ Xp @ Xq ) @ ( imp @ Xp @ Xr ) ) ) )
% 1.63/1.30 & ! [Xp: $i,Xq: $i] : ( cT @ ( imp @ ( imp @ ( nt @ Xp ) @ ( nt @ Xq ) ) @ ( imp @ Xq @ Xp ) ) )
% 1.63/1.30 & ? [Xa: $i] :
% 1.63/1.30 ~ ( cT @ ( imp @ ( nt @ ( nt @ Xa ) ) @ Xa ) ) ) ).
% 1.63/1.30 ------------------------
% 1.63/1.31 % (15748)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_15574 for (3000ds/4Mi)
% 1.63/1.31 % (15748)Instruction limit reached!
% 1.63/1.31 % (15748)------------------------------
% 1.63/1.31 % (15748)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.31 % (15748)Termination reason: Unknown
% 1.63/1.31 % (15748)Termination phase: Saturation
% 1.63/1.31
% 1.63/1.31 % (15748)Memory used [KB]: 5500
% 1.63/1.31 % (15748)Time elapsed: 0.003 s
% 1.63/1.31 % (15748)Instructions burned: 4 (million)
% 1.63/1.31 % (15748)------------------------------
% 1.63/1.31 % (15748)------------------------------
% 1.63/1.32 % (15747)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_15574 for (3000ds/183Mi)
% 1.63/1.32 % (15749)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_15574 for (3000ds/27Mi)
% 1.63/1.32 % (15750)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_15574 for (3000ds/2Mi)
% 1.63/1.32 % (15754)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_15574 for (3000ds/18Mi)
% 1.63/1.32 % (15753)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_15574 for (3000ds/275Mi)
% 1.63/1.32 % (15752)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_15574 for (3000ds/2Mi)
% 1.63/1.32 % (15750)Instruction limit reached!
% 1.63/1.32 % (15750)------------------------------
% 1.63/1.32 % (15750)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.32 % (15750)Termination reason: Unknown
% 1.63/1.32 % (15750)Termination phase: Preprocessing 3
% 1.63/1.32
% 1.63/1.32 % (15750)Memory used [KB]: 895
% 1.63/1.32 % (15750)Time elapsed: 0.003 s
% 1.63/1.32 % (15750)Instructions burned: 2 (million)
% 1.63/1.32 % (15750)------------------------------
% 1.63/1.32 % (15750)------------------------------
% 1.63/1.32 % (15752)Instruction limit reached!
% 1.63/1.32 % (15752)------------------------------
% 1.63/1.32 % (15752)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.32 % (15752)Termination reason: Unknown
% 1.63/1.32 % (15752)Termination phase: Saturation
% 1.63/1.32
% 1.63/1.32 % (15752)Memory used [KB]: 5500
% 1.63/1.32 % (15752)Time elapsed: 0.003 s
% 1.63/1.32 % (15752)Instructions burned: 3 (million)
% 1.63/1.32 % (15752)------------------------------
% 1.63/1.32 % (15752)------------------------------
% 1.63/1.32 % (15760)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_15574 for (2999ds/3Mi)
% 1.63/1.32 % (15760)Instruction limit reached!
% 1.63/1.32 % (15760)------------------------------
% 1.63/1.32 % (15760)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.32 % (15760)Termination reason: Unknown
% 1.63/1.32 % (15760)Termination phase: Saturation
% 1.63/1.32
% 1.63/1.32 % (15760)Memory used [KB]: 5500
% 1.63/1.32 % (15760)Time elapsed: 0.003 s
% 1.63/1.32 % (15760)Instructions burned: 3 (million)
% 1.63/1.32 % (15760)------------------------------
% 1.63/1.32 % (15760)------------------------------
% 1.63/1.33 % (15754)Instruction limit reached!
% 1.63/1.33 % (15754)------------------------------
% 1.63/1.33 % (15754)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.33 % (15754)Termination reason: Unknown
% 1.63/1.33 % (15754)Termination phase: Saturation
% 1.63/1.33
% 1.63/1.33 % (15754)Memory used [KB]: 5628
% 1.63/1.33 % (15754)Time elapsed: 0.013 s
% 1.63/1.33 % (15754)Instructions burned: 18 (million)
% 1.63/1.33 % (15754)------------------------------
% 1.63/1.33 % (15754)------------------------------
% 1.63/1.33 % (15769)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_15574 for (2999ds/3Mi)
% 1.63/1.33 % (15749)Instruction limit reached!
% 1.63/1.33 % (15749)------------------------------
% 1.63/1.33 % (15749)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.33 % (15749)Termination reason: Unknown
% 1.63/1.33 % (15749)Termination phase: Saturation
% 1.63/1.33
% 1.63/1.33 % (15749)Memory used [KB]: 5628
% 1.63/1.33 % (15749)Time elapsed: 0.019 s
% 1.63/1.33 % (15749)Instructions burned: 28 (million)
% 1.63/1.33 % (15749)------------------------------
% 1.63/1.33 % (15749)------------------------------
% 1.63/1.34 % (15769)Instruction limit reached!
% 1.63/1.34 % (15769)------------------------------
% 1.63/1.34 % (15769)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.34 % (15769)Termination reason: Unknown
% 1.63/1.34 % (15769)Termination phase: Saturation
% 1.63/1.34
% 1.63/1.34 % (15769)Memory used [KB]: 5500
% 1.63/1.34 % (15769)Time elapsed: 0.003 s
% 1.63/1.34 % (15769)Instructions burned: 4 (million)
% 1.63/1.34 % (15769)------------------------------
% 1.63/1.34 % (15769)------------------------------
% 1.63/1.34 % (15764)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_15574 for (2999ds/37Mi)
% 1.63/1.34 % (15766)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_15574 for (2999ds/15Mi)
% 1.63/1.35 % (15779)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_15574 for (2999ds/16Mi)
% 1.63/1.35 % (15772)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_15574 for (2999ds/1041Mi)
% 1.63/1.35 % (15766)Instruction limit reached!
% 1.63/1.35 % (15766)------------------------------
% 1.63/1.35 % (15766)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.35 % (15766)Termination reason: Unknown
% 1.63/1.35 % (15766)Termination phase: Saturation
% 1.63/1.35
% 1.63/1.35 % (15766)Memory used [KB]: 5628
% 1.63/1.35 % (15766)Time elapsed: 0.012 s
% 1.63/1.35 % (15766)Instructions burned: 16 (million)
% 1.63/1.35 % (15766)------------------------------
% 1.63/1.35 % (15766)------------------------------
% 1.63/1.35 % (15778)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_15574 for (2999ds/7Mi)
% 1.63/1.35 % (15779)Instruction limit reached!
% 1.63/1.35 % (15779)------------------------------
% 1.63/1.35 % (15779)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.35 % (15779)Termination reason: Unknown
% 1.63/1.35 % (15779)Termination phase: Saturation
% 1.63/1.35
% 1.63/1.35 % (15779)Memory used [KB]: 5628
% 1.63/1.35 % (15779)Time elapsed: 0.008 s
% 1.63/1.35 % (15779)Instructions burned: 17 (million)
% 1.63/1.35 % (15779)------------------------------
% 1.63/1.35 % (15779)------------------------------
% 1.63/1.35 % (15778)Instruction limit reached!
% 1.63/1.35 % (15778)------------------------------
% 1.63/1.35 % (15778)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.35 % (15778)Termination reason: Unknown
% 1.63/1.35 % (15778)Termination phase: Saturation
% 1.63/1.35
% 1.63/1.35 % (15778)Memory used [KB]: 1023
% 1.63/1.35 % (15778)Time elapsed: 0.006 s
% 1.63/1.35 % (15778)Instructions burned: 8 (million)
% 1.63/1.35 % (15778)------------------------------
% 1.63/1.35 % (15778)------------------------------
% 1.63/1.36 % (15764)Instruction limit reached!
% 1.63/1.36 % (15764)------------------------------
% 1.63/1.36 % (15764)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.36 % (15764)Termination reason: Unknown
% 1.63/1.36 % (15764)Termination phase: Saturation
% 1.63/1.36
% 1.63/1.36 % (15764)Memory used [KB]: 5756
% 1.63/1.36 % (15764)Time elapsed: 0.024 s
% 1.63/1.36 % (15764)Instructions burned: 37 (million)
% 1.63/1.36 % (15764)------------------------------
% 1.63/1.36 % (15764)------------------------------
% 1.63/1.36 % (15788)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_15574 for (2999ds/3Mi)
% 1.63/1.36 % (15788)Instruction limit reached!
% 1.63/1.36 % (15788)------------------------------
% 1.63/1.36 % (15788)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.36 % (15788)Termination reason: Unknown
% 1.63/1.36 % (15788)Termination phase: Saturation
% 1.63/1.36
% 1.63/1.36 % (15788)Memory used [KB]: 1023
% 1.63/1.36 % (15788)Time elapsed: 0.003 s
% 1.63/1.36 % (15788)Instructions burned: 4 (million)
% 1.63/1.36 % (15788)------------------------------
% 1.63/1.36 % (15788)------------------------------
% 1.63/1.36 % (15786)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_15574 for (2999ds/3Mi)
% 1.63/1.37 % (15789)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_15574 for (2999ds/7Mi)
% 1.63/1.37 % (15786)Instruction limit reached!
% 1.63/1.37 % (15786)------------------------------
% 1.63/1.37 % (15786)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.37 % (15786)Termination reason: Unknown
% 1.63/1.37 % (15786)Termination phase: Twee Goal Transformation
% 1.63/1.37
% 1.63/1.37 % (15786)Memory used [KB]: 1023
% 1.63/1.37 % (15786)Time elapsed: 0.004 s
% 1.63/1.37 % (15786)Instructions burned: 4 (million)
% 1.63/1.37 % (15786)------------------------------
% 1.63/1.37 % (15786)------------------------------
% 1.63/1.37 % (15789)Refutation not found, incomplete strategy
% 1.63/1.37 % (15789)------------------------------
% 1.63/1.37 % (15789)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.37 % (15789)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.37
% 1.63/1.37
% 1.63/1.37 % (15789)Memory used [KB]: 5500
% 1.63/1.37 % (15789)Time elapsed: 0.002 s
% 1.63/1.37 % (15789)Instructions burned: 2 (million)
% 1.63/1.37 % (15789)------------------------------
% 1.63/1.37 % (15789)------------------------------
% 1.63/1.37 % (15795)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_15574 for (2999ds/4Mi)
% 1.63/1.38 % (15795)Instruction limit reached!
% 1.63/1.38 % (15795)------------------------------
% 1.63/1.38 % (15795)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.38 % (15795)Termination reason: Unknown
% 1.63/1.38 % (15795)Termination phase: Saturation
% 1.63/1.38
% 1.63/1.38 % (15795)Memory used [KB]: 5500
% 1.63/1.38 % (15795)Time elapsed: 0.004 s
% 1.63/1.38 % (15795)Instructions burned: 6 (million)
% 1.63/1.38 % (15795)------------------------------
% 1.63/1.38 % (15795)------------------------------
% 1.63/1.38 % (15792)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_15574 for (2999ds/3Mi)
% 1.63/1.38 % (15792)Instruction limit reached!
% 1.63/1.38 % (15792)------------------------------
% 1.63/1.38 % (15792)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.38 % (15792)Termination reason: Unknown
% 1.63/1.38 % (15792)Termination phase: Saturation
% 1.63/1.38
% 1.63/1.38 % (15792)Memory used [KB]: 5500
% 1.63/1.38 % (15792)Time elapsed: 0.004 s
% 1.63/1.38 % (15792)Instructions burned: 4 (million)
% 1.63/1.38 % (15792)------------------------------
% 1.63/1.38 % (15792)------------------------------
% 1.63/1.38 % (15799)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_15574 for (2999ds/710Mi)
% 1.63/1.38 % (15798)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_15574 for (2999ds/18Mi)
% 1.63/1.38 % (15747)Instruction limit reached!
% 1.63/1.38 % (15747)------------------------------
% 1.63/1.38 % (15747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.38 % (15747)Termination reason: Unknown
% 1.63/1.38 % (15747)Termination phase: Saturation
% 1.63/1.38
% 1.63/1.38 % (15747)Memory used [KB]: 6140
% 1.63/1.38 % (15747)Time elapsed: 0.068 s
% 1.63/1.38 % (15747)Instructions burned: 184 (million)
% 1.63/1.38 % (15747)------------------------------
% 1.63/1.38 % (15747)------------------------------
% 1.63/1.39 % (15804)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_15574 for (2999ds/6Mi)
% 1.63/1.39 % (15804)Instruction limit reached!
% 1.63/1.39 % (15804)------------------------------
% 1.63/1.39 % (15804)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.39 % (15804)Termination reason: Unknown
% 1.63/1.39 % (15804)Termination phase: Saturation
% 1.63/1.39
% 1.63/1.39 % (15804)Memory used [KB]: 5500
% 1.63/1.39 % (15804)Time elapsed: 0.004 s
% 1.63/1.39 % (15804)Instructions burned: 6 (million)
% 1.63/1.39 % (15804)------------------------------
% 1.63/1.39 % (15804)------------------------------
% 1.63/1.39 % (15798)Instruction limit reached!
% 1.63/1.39 % (15798)------------------------------
% 1.63/1.39 % (15798)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.39 % (15798)Termination reason: Unknown
% 1.63/1.39 % (15798)Termination phase: Saturation
% 1.63/1.39
% 1.63/1.39 % (15798)Memory used [KB]: 5500
% 1.63/1.39 % (15798)Time elapsed: 0.009 s
% 1.63/1.39 % (15798)Instructions burned: 19 (million)
% 1.63/1.39 % (15798)------------------------------
% 1.63/1.39 % (15798)------------------------------
% 1.63/1.39 % (15809)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_15574 for (2999ds/21Mi)
% 1.63/1.39 % (15806)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_15574 for (2999ds/902Mi)
% 1.66/1.40 % (15812)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_15574 for (2999ds/5Mi)
% 1.66/1.40 % (15812)Instruction limit reached!
% 1.66/1.40 % (15812)------------------------------
% 1.66/1.40 % (15812)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.40 % (15812)Termination reason: Unknown
% 1.66/1.40 % (15812)Termination phase: Saturation
% 1.66/1.40
% 1.66/1.40 % (15812)Memory used [KB]: 5500
% 1.66/1.40 % (15812)Time elapsed: 0.004 s
% 1.66/1.40 % (15812)Instructions burned: 7 (million)
% 1.66/1.40 % (15812)------------------------------
% 1.66/1.40 % (15812)------------------------------
% 1.66/1.40 % (15813)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_15574 for (2999ds/6Mi)
% 1.66/1.40 % (15809)Instruction limit reached!
% 1.66/1.40 % (15809)------------------------------
% 1.66/1.40 % (15809)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.40 % (15809)Termination reason: Unknown
% 1.66/1.40 % (15809)Termination phase: Saturation
% 1.66/1.40
% 1.66/1.40 % (15809)Memory used [KB]: 5628
% 1.66/1.40 % (15809)Time elapsed: 0.010 s
% 1.66/1.40 % (15809)Instructions burned: 22 (million)
% 1.66/1.40 % (15809)------------------------------
% 1.66/1.40 % (15809)------------------------------
% 1.66/1.40 % (15813)Instruction limit reached!
% 1.66/1.40 % (15813)------------------------------
% 1.66/1.40 % (15813)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.40 % (15813)Termination reason: Unknown
% 1.66/1.40 % (15813)Termination phase: Saturation
% 1.66/1.40
% 1.66/1.40 % (15813)Memory used [KB]: 5500
% 1.66/1.40 % (15813)Time elapsed: 0.003 s
% 1.66/1.40 % (15813)Instructions burned: 7 (million)
% 1.66/1.40 % (15813)------------------------------
% 1.66/1.40 % (15813)------------------------------
% 1.66/1.41 % (15816)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_15574 for (2999ds/377Mi)
% 1.66/1.41 % (15817)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_15574 for (2999ds/779Mi)
% 1.66/1.41 % (15818)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_15574 for (2999ds/19Mi)
% 1.66/1.42 % (15818)Refutation not found, incomplete strategy
% 1.66/1.42 % (15818)------------------------------
% 1.66/1.42 % (15818)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.42 % (15818)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.42
% 1.66/1.42
% 1.66/1.42 % (15818)Memory used [KB]: 5500
% 1.66/1.42 % (15818)Time elapsed: 0.004 s
% 1.66/1.42 % (15818)Instructions burned: 7 (million)
% 1.66/1.42 % (15818)------------------------------
% 1.66/1.42 % (15818)------------------------------
% 1.66/1.43 % (15827)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_15574 for (2998ds/879Mi)
% 1.66/1.46 % (15753)Instruction limit reached!
% 1.66/1.46 % (15753)------------------------------
% 1.66/1.46 % (15753)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.46 % (15753)Termination reason: Unknown
% 1.66/1.46 % (15753)Termination phase: Saturation
% 1.66/1.46
% 1.66/1.46 % (15753)Memory used [KB]: 5884
% 1.66/1.46 % (15753)Time elapsed: 0.141 s
% 1.66/1.46 % (15753)Instructions burned: 275 (million)
% 1.66/1.46 % (15753)------------------------------
% 1.66/1.46 % (15753)------------------------------
% 1.66/1.47 % (15849)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_15574 for (2998ds/17Mi)
% 1.66/1.47 % (15849)Instruction limit reached!
% 1.66/1.47 % (15849)------------------------------
% 1.66/1.47 % (15849)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.47 % (15849)Termination reason: Unknown
% 1.66/1.47 % (15849)Termination phase: Saturation
% 1.66/1.47
% 1.66/1.47 % (15849)Memory used [KB]: 5628
% 1.66/1.47 % (15849)Time elapsed: 0.008 s
% 1.66/1.47 % (15849)Instructions burned: 17 (million)
% 1.66/1.47 % (15849)------------------------------
% 1.66/1.47 % (15849)------------------------------
% 1.66/1.48 % (15852)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_15574 for (2998ds/3Mi)
% 1.66/1.48 % (15852)Instruction limit reached!
% 1.66/1.48 % (15852)------------------------------
% 1.66/1.48 % (15852)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.48 % (15852)Termination reason: Unknown
% 1.66/1.48 % (15852)Termination phase: Saturation
% 1.66/1.48
% 1.66/1.48 % (15852)Memory used [KB]: 1023
% 1.66/1.48 % (15852)Time elapsed: 0.003 s
% 1.66/1.48 % (15852)Instructions burned: 4 (million)
% 1.66/1.48 % (15852)------------------------------
% 1.66/1.48 % (15852)------------------------------
% 1.66/1.49 % (15864)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_15574 for (2998ds/30Mi)
% 1.66/1.50 % (15864)Instruction limit reached!
% 1.66/1.50 % (15864)------------------------------
% 1.66/1.50 % (15864)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.50 % (15864)Termination reason: Unknown
% 1.66/1.50 % (15864)Termination phase: Saturation
% 1.66/1.50
% 1.66/1.50 % (15864)Memory used [KB]: 5628
% 1.66/1.50 % (15864)Time elapsed: 0.012 s
% 1.66/1.50 % (15864)Instructions burned: 30 (million)
% 1.66/1.50 % (15864)------------------------------
% 1.66/1.50 % (15864)------------------------------
% 1.66/1.51 % (15876)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_15574 for (2998ds/127Mi)
% 1.66/1.53 % (15816)First to succeed.
% 1.66/1.53 % (15816)Refutation found. Thanks to Tanya!
% 1.66/1.53 % SZS status Theorem for DTF2THF_15574
% 1.66/1.53 % SZS output start Proof for DTF2THF_15574
% 1.66/1.53 thf(func_def_0, type, nt: $i > $i).
% 1.66/1.53 thf(func_def_1, type, imp: $i > $i > $i).
% 1.66/1.53 thf(func_def_2, type, cT: $i > $o).
% 1.66/1.53 thf(f2501,plain,(
% 1.66/1.53 $false),
% 1.66/1.53 inference(avatar_sat_refutation,[status(thm)],[f2261,f2473])).
% 1.66/1.53 thf(f2473,plain,(
% 1.66/1.53 ~spl1_3),
% 1.66/1.53 inference(avatar_contradiction_clause,[status(thm)],[f2472])).
% 1.66/1.53 thf(f2472,plain,(
% 1.66/1.53 $false | ~spl1_3),
% 1.66/1.53 inference(trivial_inequality_removal,[status(thm)],[f2423])).
% 1.66/1.53 thf(f2423,plain,(
% 1.66/1.53 ($false = $true) | ~spl1_3),
% 1.66/1.53 inference(backward_demodulation,[status(thm)],[f14,f2328])).
% 1.66/1.53 thf(f2328,plain,(
% 1.66/1.53 ( ! [X0 : $i] : (((cT @ X0) = $false)) ) | ~spl1_3),
% 1.66/1.53 inference(trivial_inequality_removal,[status(thm)],[f2265])).
% 1.66/1.53 thf(f2265,plain,(
% 1.66/1.53 ( ! [X0 : $i] : (($true != $true) | ((cT @ X0) = $false)) ) | ~spl1_3),
% 1.66/1.53 inference(fool_paramodulation,[status(thm)],[f168])).
% 1.66/1.53 thf(f168,plain,(
% 1.66/1.53 ( ! [X0 : $i] : (((cT @ X0) != $true)) ) | ~spl1_3),
% 1.66/1.53 inference(avatar_component_clause,[status(thm)],[f167])).
% 1.66/1.53 thf(f167,definition,(
% 1.66/1.53 spl1_3 <=> ! [X0 : $i] : ((cT @ X0) != $true)),
% 1.66/1.53 introduced(definition,[new_symbols(naming,[spl1_3])],[avatar_definition])).
% 1.66/1.53 thf(f14,plain,(
% 1.66/1.53 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (cT @ (imp @ (imp @ X1 @ (imp @ X0 @ X2)) @ (imp @ (imp @ X1 @ X0) @ (imp @ X1 @ X2)))))) )),
% 1.66/1.53 inference(cnf_transformation,[status(thm)],[f9])).
% 1.66/1.53 thf(f9,plain,(
% 1.66/1.53 ! [X0 : $i,X1 : $i,X2 : $i] : ($true = (cT @ (imp @ (imp @ X1 @ (imp @ X0 @ X2)) @ (imp @ (imp @ X1 @ X0) @ (imp @ X1 @ X2))))) & ! [X3 : $i,X4 : $i] : ($true = (cT @ (imp @ (imp @ (nt @ X3) @ (nt @ X4)) @ (imp @ X4 @ X3)))) & ! [X5 : $i,X6 : $i] : (($true != (cT @ X6)) | ($true != (cT @ (imp @ X6 @ X5))) | ($true = (cT @ X5))) & ! [X7 : $i,X8 : $i] : ($true = (cT @ (imp @ X7 @ (imp @ X8 @ X7)))) & ($true != (cT @ (imp @ (nt @ (nt @ sK0)) @ sK0)))),
% 1.66/1.53 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8])).
% 1.66/1.53 thf(f8,plain,(
% 1.66/1.53 ? [X9 : $i] : ((cT @ (imp @ (nt @ (nt @ X9)) @ X9)) != $true) => ($true != (cT @ (imp @ (nt @ (nt @ sK0)) @ sK0)))),
% 1.66/1.53 introduced(definition,[],[choice_axiom])).
% 1.66/1.53 thf(f7,plain,(
% 1.66/1.53 ! [X0 : $i,X1 : $i,X2 : $i] : ($true = (cT @ (imp @ (imp @ X1 @ (imp @ X0 @ X2)) @ (imp @ (imp @ X1 @ X0) @ (imp @ X1 @ X2))))) & ! [X3 : $i,X4 : $i] : ($true = (cT @ (imp @ (imp @ (nt @ X3) @ (nt @ X4)) @ (imp @ X4 @ X3)))) & ! [X5 : $i,X6 : $i] : (($true != (cT @ X6)) | ($true != (cT @ (imp @ X6 @ X5))) | ($true = (cT @ X5))) & ! [X7 : $i,X8 : $i] : ($true = (cT @ (imp @ X7 @ (imp @ X8 @ X7)))) & ? [X9 : $i] : ((cT @ (imp @ (nt @ (nt @ X9)) @ X9)) != $true)),
% 1.66/1.53 inference(rectify,[status(thm)],[f6])).
% 1.66/1.53 thf(f6,plain,(
% 1.66/1.53 ! [X9 : $i,X8 : $i,X7 : $i] : ($true = (cT @ (imp @ (imp @ X8 @ (imp @ X9 @ X7)) @ (imp @ (imp @ X8 @ X9) @ (imp @ X8 @ X7))))) & ! [X2 : $i,X3 : $i] : ($true = (cT @ (imp @ (imp @ (nt @ X2) @ (nt @ X3)) @ (imp @ X3 @ X2)))) & ! [X4 : $i,X5 : $i] : (($true != (cT @ X5)) | ((cT @ (imp @ X5 @ X4)) != $true) | ($true = (cT @ X4))) & ! [X1 : $i,X0 : $i] : ($true = (cT @ (imp @ X1 @ (imp @ X0 @ X1)))) & ? [X6 : $i] : ((cT @ (imp @ (nt @ (nt @ X6)) @ X6)) != $true)),
% 1.66/1.53 inference(flattening,[status(thm)],[f5])).
% 1.66/1.53 thf(f5,plain,(
% 1.66/1.53 ~~(! [X1 : $i,X0 : $i] : ($true = (cT @ (imp @ X1 @ (imp @ X0 @ X1)))) & ! [X2 : $i,X3 : $i] : ($true = (cT @ (imp @ (imp @ (nt @ X2) @ (nt @ X3)) @ (imp @ X3 @ X2)))) & ! [X4 : $i,X5 : $i] : (~($true = (cT @ X5)) | ($true = (cT @ X4)) | ~((cT @ (imp @ X5 @ X4)) = $true)) & ? [X6 : $i] : ~((cT @ (imp @ (nt @ (nt @ X6)) @ X6)) = $true) & ! [X9 : $i,X8 : $i,X7 : $i] : ($true = (cT @ (imp @ (imp @ X8 @ (imp @ X9 @ X7)) @ (imp @ (imp @ X8 @ X9) @ (imp @ X8 @ X7))))))),
% 1.66/1.53 inference(fool_elimination,[status(thm)],[f4])).
% 1.66/1.53 thf(f4,plain,(
% 1.66/1.53 ~~(! [X0 : $i,X1 : $i] : (cT @ (imp @ X1 @ (imp @ X0 @ X1))) & ! [X2 : $i,X3 : $i] : (cT @ (imp @ (imp @ (nt @ X2) @ (nt @ X3)) @ (imp @ X3 @ X2))) & ! [X4 : $i,X5 : $i] : (~(cT @ X5) | (cT @ X4) | ~(cT @ (imp @ X5 @ X4))) & ? [X6 : $i] : ~(cT @ (imp @ (nt @ (nt @ X6)) @ X6)) & ! [X7 : $i,X8 : $i,X9 : $i] : (cT @ (imp @ (imp @ X8 @ (imp @ X9 @ X7)) @ (imp @ (imp @ X8 @ X9) @ (imp @ X8 @ X7)))))),
% 1.66/1.53 inference(rectify,[status(thm)],[f2])).
% 1.66/1.53 thf(f2,negated_conjecture,(
% 1.66/1.53 ~~(! [X1 : $i,X0 : $i] : (cT @ (imp @ X0 @ (imp @ X1 @ X0))) & ! [X0 : $i,X1 : $i] : (cT @ (imp @ (imp @ (nt @ X0) @ (nt @ X1)) @ (imp @ X1 @ X0))) & ! [X1 : $i,X0 : $i] : (~(cT @ X0) | (cT @ X1) | ~(cT @ (imp @ X0 @ X1))) & ? [X3 : $i] : ~(cT @ (imp @ (nt @ (nt @ X3)) @ X3)) & ! [X2 : $i,X0 : $i,X1 : $i] : (cT @ (imp @ (imp @ X0 @ (imp @ X1 @ X2)) @ (imp @ (imp @ X0 @ X1) @ (imp @ X0 @ X2)))))),
% 1.66/1.53 inference(negated_conjecture,[status(cth)],[f1])).
% 1.66/1.53 thf(f1,conjecture,(
% 1.66/1.53 ~(! [X1 : $i,X0 : $i] : (cT @ (imp @ X0 @ (imp @ X1 @ X0))) & ! [X0 : $i,X1 : $i] : (cT @ (imp @ (imp @ (nt @ X0) @ (nt @ X1)) @ (imp @ X1 @ X0))) & ! [X1 : $i,X0 : $i] : (~(cT @ X0) | (cT @ X1) | ~(cT @ (imp @ X0 @ X1))) & ? [X3 : $i] : ~(cT @ (imp @ (nt @ (nt @ X3)) @ X3)) & ! [X2 : $i,X0 : $i,X1 : $i] : (cT @ (imp @ (imp @ X0 @ (imp @ X1 @ X2)) @ (imp @ (imp @ X0 @ X1) @ (imp @ X0 @ X2)))))),
% 1.66/1.53 file('/export/starexec/sandbox2/tmp/tmp.tL6P2LiOfW/DTF2THF_15574.p',cLCL077_1)).
% 1.66/1.53 thf(f2261,plain,(
% 1.66/1.53 spl1_3),
% 1.66/1.53 inference(avatar_split_clause,[status(thm)],[f2254,f167])).
% 1.66/1.53 thf(f2254,plain,(
% 1.66/1.53 ( ! [X0 : $i] : (((cT @ X0) != $true)) )),
% 1.66/1.53 inference(trivial_inequality_removal,[status(thm)],[f2237])).
% 1.66/1.53 thf(f2237,plain,(
% 1.66/1.53 ( ! [X0 : $i] : (((cT @ X0) != $true) | ($true != $true)) )),
% 1.66/1.53 inference(superposition,[status(thm)],[f2229,f24])).
% 1.66/1.53 thf(f24,plain,(
% 1.66/1.53 ( ! [X0 : $i,X1 : $i] : (($true = (cT @ (imp @ X1 @ X0))) | ((cT @ X0) != $true)) )),
% 1.66/1.53 inference(trivial_inequality_removal,[status(thm)],[f23])).
% 1.66/1.53 thf(f23,plain,(
% 1.66/1.53 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ((cT @ X0) != $true) | ($true = (cT @ (imp @ X1 @ X0)))) )),
% 1.66/1.53 inference(superposition,[status(thm)],[f12,f11])).
% 1.66/1.53 thf(f11,plain,(
% 1.66/1.53 ( ! [X8 : $i,X7 : $i] : (($true = (cT @ (imp @ X7 @ (imp @ X8 @ X7))))) )),
% 1.66/1.53 inference(cnf_transformation,[status(thm)],[f9])).
% 1.66/1.53 thf(f12,plain,(
% 1.66/1.53 ( ! [X6 : $i,X5 : $i] : (($true != (cT @ (imp @ X6 @ X5))) | ($true != (cT @ X6)) | ($true = (cT @ X5))) )),
% 1.66/1.53 inference(cnf_transformation,[status(thm)],[f9])).
% 1.66/1.53 thf(f2229,plain,(
% 1.66/1.53 ( ! [X0 : $i] : (($true != (cT @ (imp @ (imp @ X0 @ sK0) @ X0)))) )),
% 1.66/1.53 inference(trivial_inequality_removal,[status(thm)],[f2228])).
% 1.66/1.53 thf(f2228,plain,(
% 1.66/1.53 ( ! [X0 : $i] : (($true != $true) | ($true != (cT @ (imp @ (imp @ X0 @ sK0) @ X0)))) )),
% 1.66/1.53 inference(forward_demodulation,[status(thm)],[f2222,f284])).
% 1.66/1.53 thf(f284,plain,(
% 1.66/1.53 ( ! [X0 : $i] : (($true = (cT @ (imp @ X0 @ X0)))) )),
% 1.66/1.53 inference(trivial_inequality_removal,[status(thm)],[f274])).
% 1.66/1.53 thf(f274,plain,(
% 1.66/1.53 ( ! [X0 : $i] : (($true = (cT @ (imp @ X0 @ X0))) | ($true != $true)) )),
% 1.66/1.53 inference(superposition,[status(thm)],[f270,f11])).
% 1.66/1.53 thf(f270,plain,(
% 1.66/1.53 ( ! [X0 : $i,X1 : $i] : (($true != (cT @ (imp @ (nt @ X0) @ X1))) | ($true = (cT @ (imp @ X0 @ X0)))) )),
% 1.66/1.53 inference(trivial_inequality_removal,[status(thm)],[f263])).
% 1.66/1.53 thf(f263,plain,(
% 1.66/1.53 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ($true = (cT @ (imp @ X0 @ X0))) | ($true != (cT @ (imp @ (nt @ X0) @ X1)))) )),
% 1.66/1.53 inference(superposition,[status(thm)],[f53,f252])).
% 1.66/1.53 thf(f252,plain,(
% 1.66/1.53 ( ! [X0 : $i,X1 : $i] : (($true = (cT @ (imp @ X0 @ X0))) | ((cT @ (imp @ X0 @ X1)) != $true)) )),
% 1.66/1.53 inference(trivial_inequality_removal,[status(thm)],[f246])).
% 1.66/1.53 thf(f246,plain,(
% 1.66/1.53 ( ! [X0 : $i,X1 : $i] : (((cT @ (imp @ X0 @ X1)) != $true) | ($true != $true) | ($true = (cT @ (imp @ X0 @ X0)))) )),
% 1.66/1.53 inference(superposition,[status(thm)],[f241,f11])).
% 1.66/1.53 thf(f241,plain,(
% 1.66/1.53 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((cT @ (imp @ X0 @ (imp @ X1 @ X2))) != $true) | ((cT @ (imp @ X0 @ X1)) != $true) | ($true = (cT @ (imp @ X0 @ X2)))) )),
% 1.66/1.53 inference(trivial_inequality_removal,[status(thm)],[f238])).
% 1.66/1.53 thf(f238,plain,(
% 1.66/1.53 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ($true = (cT @ (imp @ X0 @ X2))) | ((cT @ (imp @ X0 @ (imp @ X1 @ X2))) != $true) | ((cT @ (imp @ X0 @ X1)) != $true)) )),
% 1.66/1.53 inference(superposition,[status(thm)],[f12,f234])).
% 1.66/1.53 thf(f234,plain,(
% 1.66/1.53 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (cT @ (imp @ (imp @ X0 @ X1) @ (imp @ X0 @ X2)))) | ((cT @ (imp @ X0 @ (imp @ X1 @ X2))) != $true)) )),
% 1.66/1.53 inference(trivial_inequality_removal,[status(thm)],[f230])).
% 1.66/1.53 thf(f230,plain,(
% 1.66/1.53 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = $true) | ($true = (cT @ (imp @ (imp @ X0 @ X1) @ (imp @ X0 @ X2)))) | ((cT @ (imp @ X0 @ (imp @ X1 @ X2))) != $true)) )),
% 1.66/1.53 inference(superposition,[status(thm)],[f25,f14])).
% 1.66/1.53 thf(f25,plain,(
% 1.66/1.53 ( ! [X6 : $i,X5 : $i] : (($false = (cT @ (imp @ X6 @ X5))) | ($true != (cT @ X6)) | ($true = (cT @ X5))) )),
% 1.66/1.53 inference(trivial_inequality_removal,[status(thm)],[f21])).
% 1.66/1.53 thf(f21,plain,(
% 1.66/1.53 ( ! [X6 : $i,X5 : $i] : (($true != $true) | ($true != (cT @ X6)) | ($true = (cT @ X5)) | ($false = (cT @ (imp @ X6 @ X5)))) )),
% 1.66/1.53 inference(fool_paramodulation,[status(thm)],[f12])).
% 1.66/1.53 thf(f53,plain,(
% 1.66/1.53 ( ! [X0 : $i,X1 : $i] : (($true != (cT @ (imp @ (nt @ X0) @ (nt @ X1)))) | ($true = (cT @ (imp @ X1 @ X0)))) )),
% 1.66/1.53 inference(trivial_inequality_removal,[status(thm)],[f50])).
% 1.66/1.53 thf(f50,plain,(
% 1.66/1.53 ( ! [X0 : $i,X1 : $i] : (($true = (cT @ (imp @ X1 @ X0))) | ($true != $true) | ($true != (cT @ (imp @ (nt @ X0) @ (nt @ X1))))) )),
% 1.66/1.53 inference(superposition,[status(thm)],[f12,f13])).
% 1.66/1.53 thf(f13,plain,(
% 1.66/1.53 ( ! [X3 : $i,X4 : $i] : (($true = (cT @ (imp @ (imp @ (nt @ X3) @ (nt @ X4)) @ (imp @ X4 @ X3))))) )),
% 1.66/1.53 inference(cnf_transformation,[status(thm)],[f9])).
% 1.66/1.53 thf(f2222,plain,(
% 1.66/1.53 ( ! [X0 : $i] : (((cT @ (imp @ sK0 @ sK0)) != $true) | ($true != (cT @ (imp @ (imp @ X0 @ sK0) @ X0)))) )),
% 1.66/1.53 inference(trivial_inequality_removal,[status(thm)],[f2156])).
% 1.66/1.53 thf(f2156,plain,(
% 1.66/1.53 ( ! [X0 : $i] : (($true != (cT @ (imp @ (imp @ X0 @ sK0) @ X0))) | ((cT @ (imp @ sK0 @ sK0)) != $true) | ($true != $true)) )),
% 1.66/1.53 inference(superposition,[status(thm)],[f1531,f297])).
% 1.66/1.53 thf(f297,plain,(
% 1.66/1.53 ( ! [X0 : $i,X1 : $i] : (((cT @ (imp @ (imp @ X0 @ X1) @ X1)) = $true) | ($true != (cT @ (imp @ (imp @ X0 @ X1) @ X0)))) )),
% 1.66/1.53 inference(trivial_inequality_removal,[status(thm)],[f292])).
% 1.66/1.53 thf(f292,plain,(
% 1.66/1.53 ( ! [X0 : $i,X1 : $i] : (($true != (cT @ (imp @ (imp @ X0 @ X1) @ X0))) | ($true != $true) | ((cT @ (imp @ (imp @ X0 @ X1) @ X1)) = $true)) )),
% 1.66/1.53 inference(superposition,[status(thm)],[f241,f284])).
% 1.66/1.53 thf(f1531,plain,(
% 1.66/1.53 ( ! [X0 : $i,X1 : $i] : (((cT @ (imp @ (imp @ X0 @ sK0) @ X1)) != $true) | ($true != (cT @ (imp @ X1 @ sK0)))) )),
% 1.66/1.53 inference(trivial_inequality_removal,[status(thm)],[f1525])).
% 1.66/1.53 thf(f1525,plain,(
% 1.66/1.53 ( ! [X0 : $i,X1 : $i] : (((cT @ (imp @ (imp @ X0 @ sK0) @ X1)) != $true) | ($true != $true) | ($true != (cT @ (imp @ X1 @ sK0)))) )),
% 1.66/1.53 inference(superposition,[status(thm)],[f1506,f255])).
% 1.66/1.53 thf(f255,plain,(
% 1.66/1.53 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (cT @ (imp @ X0 @ X2))) | ($true != (cT @ (imp @ X1 @ X2))) | ((cT @ (imp @ X0 @ X1)) != $true)) )),
% 1.66/1.53 inference(trivial_inequality_removal,[status(thm)],[f250])).
% 1.66/1.53 thf(f250,plain,(
% 1.66/1.53 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (cT @ (imp @ X0 @ X2))) | ($true != $true) | ((cT @ (imp @ X0 @ X1)) != $true) | ($true != (cT @ (imp @ X1 @ X2)))) )),
% 1.66/1.53 inference(superposition,[status(thm)],[f241,f24])).
% 1.66/1.53 thf(f1506,plain,(
% 1.66/1.53 ( ! [X0 : $i] : (($true != (cT @ (imp @ (imp @ X0 @ sK0) @ sK0)))) )),
% 1.66/1.53 inference(trivial_inequality_removal,[status(thm)],[f1476])).
% 1.66/1.53 thf(f1476,plain,(
% 1.66/1.53 ( ! [X0 : $i] : (($true != $true) | ($true != (cT @ (imp @ (imp @ X0 @ sK0) @ sK0)))) )),
% 1.66/1.53 inference(superposition,[status(thm)],[f1339,f13])).
% 1.66/1.53 thf(f1339,plain,(
% 1.66/1.53 ( ! [X0 : $i,X1 : $i] : (($true != (cT @ (imp @ (imp @ (nt @ sK0) @ X0) @ X1))) | ($true != (cT @ (imp @ X1 @ sK0)))) )),
% 1.66/1.53 inference(trivial_inequality_removal,[status(thm)],[f1329])).
% 1.66/1.53 thf(f1329,plain,(
% 1.66/1.53 ( ! [X0 : $i,X1 : $i] : (($true != (cT @ (imp @ (imp @ (nt @ sK0) @ X0) @ X1))) | ($true != (cT @ (imp @ X1 @ sK0))) | ($true != $true)) )),
% 1.66/1.53 inference(superposition,[status(thm)],[f1305,f255])).
% 1.66/1.53 thf(f1305,plain,(
% 1.66/1.53 ( ! [X0 : $i] : (($true != (cT @ (imp @ (imp @ (nt @ sK0) @ X0) @ sK0)))) )),
% 1.66/1.53 inference(trivial_inequality_removal,[status(thm)],[f1285])).
% 1.66/1.53 thf(f1285,plain,(
% 1.66/1.53 ( ! [X0 : $i] : (($true != $true) | ($true != (cT @ (imp @ (imp @ (nt @ sK0) @ X0) @ sK0)))) )),
% 1.66/1.53 inference(superposition,[status(thm)],[f476,f13])).
% 1.66/1.53 thf(f476,plain,(
% 1.66/1.53 ( ! [X0 : $i,X1 : $i] : (($true != (cT @ (imp @ (imp @ X0 @ (nt @ (nt @ sK0))) @ X1))) | ($true != (cT @ (imp @ X1 @ sK0)))) )),
% 1.66/1.53 inference(trivial_inequality_removal,[status(thm)],[f468])).
% 1.66/1.53 thf(f468,plain,(
% 1.66/1.53 ( ! [X0 : $i,X1 : $i] : (($true != (cT @ (imp @ X1 @ sK0))) | ($true != (cT @ (imp @ (imp @ X0 @ (nt @ (nt @ sK0))) @ X1))) | ($true != $true)) )),
% 1.66/1.53 inference(superposition,[status(thm)],[f337,f255])).
% 1.66/1.53 thf(f337,plain,(
% 1.66/1.53 ( ! [X0 : $i] : (((cT @ (imp @ (imp @ X0 @ (nt @ (nt @ sK0))) @ sK0)) != $true)) )),
% 1.66/1.53 inference(trivial_inequality_removal,[status(thm)],[f324])).
% 1.66/1.53 thf(f324,plain,(
% 1.66/1.53 ( ! [X0 : $i] : (($true != $true) | ((cT @ (imp @ (imp @ X0 @ (nt @ (nt @ sK0))) @ sK0)) != $true)) )),
% 1.66/1.53 inference(superposition,[status(thm)],[f318,f11])).
% 1.66/1.53 thf(f318,plain,(
% 1.66/1.53 ( ! [X0 : $i] : (($true != (cT @ (imp @ (nt @ (nt @ sK0)) @ X0))) | ($true != (cT @ (imp @ X0 @ sK0)))) )),
% 1.66/1.53 inference(trivial_inequality_removal,[status(thm)],[f301])).
% 1.66/1.53 thf(f301,plain,(
% 1.66/1.53 ( ! [X0 : $i] : (($true != (cT @ (imp @ X0 @ sK0))) | ($true != (cT @ (imp @ (nt @ (nt @ sK0)) @ X0))) | ($false = $true)) )),
% 1.66/1.53 inference(superposition,[status(thm)],[f255,f16])).
% 1.66/1.53 thf(f16,plain,(
% 1.66/1.53 ($false = (cT @ (imp @ (nt @ (nt @ sK0)) @ sK0)))),
% 1.66/1.53 inference(trivial_inequality_removal,[status(thm)],[f15])).
% 1.66/1.53 thf(f15,plain,(
% 1.66/1.53 ($false = (cT @ (imp @ (nt @ (nt @ sK0)) @ sK0))) | ($true != $true)),
% 1.66/1.53 inference(fool_paramodulation,[status(thm)],[f10])).
% 1.66/1.53 thf(f10,plain,(
% 1.66/1.53 ($true != (cT @ (imp @ (nt @ (nt @ sK0)) @ sK0)))),
% 1.66/1.53 inference(cnf_transformation,[status(thm)],[f9])).
% 1.66/1.53 % SZS output end Proof for DTF2THF_15574
% 1.66/1.53 % (15816)------------------------------
% 1.66/1.53 % (15816)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.53 % (15816)Termination reason: Refutation
% 1.66/1.53
% 1.66/1.53 % (15816)Memory used [KB]: 6012
% 1.66/1.53 % (15816)Time elapsed: 0.125 s
% 1.66/1.53 % (15816)Instructions burned: 371 (million)
% 1.66/1.53 % (15816)------------------------------
% 1.66/1.53 % (15816)------------------------------
% 1.66/1.53 % (15745)Success in time 0.221 s
%------------------------------------------------------------------------------