%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO385^5 : 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 : n007.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 09:54:06 AM UTC 2026
% Result : Theorem 1.71s 1.34s
% Output : Refutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of formulae : 59 ( 12 unt; 0 typ; 3 def)
% Number of atoms : 814 ( 185 equ; 0 cnn)
% Maximal formula atoms : 41 ( 13 avg)
% Number of connectives : 1077 ( 205 ~; 157 |; 78 &; 634 @)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 9 con; 0-3 aty)
% Number of variables : 229 ( 0 ^; 229 !; 0 ?; 229 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cQ_3: $i > $i > $i > $o ).
thf(func_def_1,type,
f: $i > $i ).
thf(func_def_2,type,
cP_2: $i > $i > $o ).
thf(func_def_3,type,
cQ_2: $i > $i > $i > $o ).
thf(func_def_8,type,
cP_1: $i > $i > $o ).
thf(func_def_9,type,
cQ_1: $i > $i > $i > $o ).
thf(f65,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f37,f46,f55,f64]) ).
thf(f64,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f63]) ).
thf(f63,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f62]) ).
thf(f62,plain,
( ( $true != $true )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f61,f17]) ).
thf(f17,plain,
( ( cP_2 @ c @ c )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X0: $i] :
( ( cP_1 @ d @ X0 )
= $true )
& ! [X1: $i,X2: $i,X3: $i] :
( $true
!= ( cQ_3 @ X1 @ X2 @ X3 ) )
& ( ( cP_2 @ b @ b )
= $true )
& ! [X4: $i,X5: $i] :
( ( ( cP_1 @ X5 @ X4 )
!= $true )
| ( ( cP_1 @ ( f @ X5 ) @ X4 )
= $true ) )
& ( ( cP_2 @ c @ c )
= $true )
& ( ( cP_1 @ b @ b )
= $true )
& ( ( cP_2 @ a @ a )
= $true )
& ! [X6: $i,X7: $i,X8: $i,X9: $i,X10: $i,X11: $i] :
( ( $true
= ( cQ_3 @ X10 @ X8 @ X11 ) )
| ( ( cP_2 @ ( f @ X9 ) @ X11 )
!= $true )
| ( $true
!= ( cQ_2 @ X7 @ X6 @ X9 ) )
| ( ( cP_2 @ ( f @ X6 ) @ X8 )
!= $true )
| ( $true
!= ( cP_2 @ ( f @ X7 ) @ X10 ) ) )
& ! [X12: $i,X13: $i,X14: $i,X15: $i,X16: $i,X17: $i] :
( ( $true
!= ( cP_1 @ ( f @ X14 ) @ X15 ) )
| ( $true
= ( cQ_2 @ X16 @ X15 @ X17 ) )
| ( $true
!= ( cP_1 @ ( f @ X12 ) @ X17 ) )
| ( $true
!= ( cP_1 @ ( f @ X13 ) @ X16 ) )
| ( ( cQ_1 @ X13 @ X14 @ X12 )
!= $true ) )
& ! [X18: $i,X19: $i] :
( ( ( cP_2 @ X19 @ X18 )
!= $true )
| ( ( cP_2 @ ( f @ X19 ) @ X18 )
= $true ) )
& ! [X20: $i] :
( ( cP_2 @ d @ X20 )
= $true )
& ( ( cQ_1 @ a @ b @ c )
= $true )
& ( ( cP_1 @ a @ a )
= $true )
& ( ( cP_1 @ c @ c )
= $true ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X20: $i] :
( $true
= ( cP_1 @ d @ X20 ) )
& ! [X18: $i,X17: $i,X19: $i] :
( ( cQ_3 @ X18 @ X17 @ X19 )
!= $true )
& ( ( cP_2 @ b @ b )
= $true )
& ! [X15: $i,X16: $i] :
( ( ( cP_1 @ X16 @ X15 )
!= $true )
| ( ( cP_1 @ ( f @ X16 ) @ X15 )
= $true ) )
& ( ( cP_2 @ c @ c )
= $true )
& ( ( cP_1 @ b @ b )
= $true )
& ( ( cP_2 @ a @ a )
= $true )
& ! [X5: $i,X2: $i,X4: $i,X3: $i,X7: $i,X6: $i] :
( ( ( cQ_3 @ X7 @ X4 @ X6 )
= $true )
| ( ( cP_2 @ ( f @ X3 ) @ X6 )
!= $true )
| ( ( cQ_2 @ X2 @ X5 @ X3 )
!= $true )
| ( ( cP_2 @ ( f @ X5 ) @ X4 )
!= $true )
| ( $true
!= ( cP_2 @ ( f @ X2 ) @ X7 ) ) )
& ! [X10: $i,X9: $i,X8: $i,X11: $i,X13: $i,X12: $i] :
( ( $true
!= ( cP_1 @ ( f @ X8 ) @ X11 ) )
| ( $true
= ( cQ_2 @ X13 @ X11 @ X12 ) )
| ( ( cP_1 @ ( f @ X10 ) @ X12 )
!= $true )
| ( ( cP_1 @ ( f @ X9 ) @ X13 )
!= $true )
| ( ( cQ_1 @ X9 @ X8 @ X10 )
!= $true ) )
& ! [X0: $i,X1: $i] :
( ( ( cP_2 @ X1 @ X0 )
!= $true )
| ( $true
= ( cP_2 @ ( f @ X1 ) @ X0 ) ) )
& ! [X14: $i] :
( $true
= ( cP_2 @ d @ X14 ) )
& ( ( cQ_1 @ a @ b @ c )
= $true )
& ( ( cP_1 @ a @ a )
= $true )
& ( ( cP_1 @ c @ c )
= $true ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ~ ( ! [X0: $i,X1: $i] :
( ( ( cP_2 @ X1 @ X0 )
!= $true )
| ( $true
= ( cP_2 @ ( f @ X1 ) @ X0 ) ) )
& ( ( cP_1 @ a @ a )
= $true )
& ( ( cP_1 @ c @ c )
= $true )
& ! [X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( ( ( cP_2 @ ( f @ X5 ) @ X4 )
!= $true )
| ( ( cQ_3 @ X7 @ X4 @ X6 )
= $true )
| ( $true
!= ( cP_2 @ ( f @ X2 ) @ X7 ) )
| ( ( cQ_2 @ X2 @ X5 @ X3 )
!= $true )
| ( ( cP_2 @ ( f @ X3 ) @ X6 )
!= $true ) )
& ( ( cQ_1 @ a @ b @ c )
= $true )
& ( ( cP_2 @ c @ c )
= $true )
& ! [X8: $i,X9: $i,X10: $i,X11: $i,X12: $i,X13: $i] :
( ( ( cP_1 @ ( f @ X9 ) @ X13 )
!= $true )
| ( ( cP_1 @ ( f @ X10 ) @ X12 )
!= $true )
| ( $true
= ( cQ_2 @ X13 @ X11 @ X12 ) )
| ( $true
!= ( cP_1 @ ( f @ X8 ) @ X11 ) )
| ( ( cQ_1 @ X9 @ X8 @ X10 )
!= $true ) )
& ! [X14: $i] :
( $true
= ( cP_2 @ d @ X14 ) )
& ( ( cP_2 @ a @ a )
= $true )
& ( ( cP_2 @ b @ b )
= $true )
& ! [X15: $i,X16: $i] :
( ( ( cP_1 @ ( f @ X16 ) @ X15 )
= $true )
| ( ( cP_1 @ X16 @ X15 )
!= $true ) )
& ! [X17: $i,X18: $i,X19: $i] :
( ( cQ_3 @ X18 @ X17 @ X19 )
!= $true )
& ( ( cP_1 @ b @ b )
= $true )
& ! [X20: $i] :
( $true
= ( cP_1 @ d @ X20 ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ~ ( ! [X0: $i,X1: $i] :
( ~ ( cP_2 @ X1 @ X0 )
| ( cP_2 @ ( f @ X1 ) @ X0 ) )
& ( cP_1 @ a @ a )
& ( cP_1 @ c @ c )
& ! [X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( ~ ( cP_2 @ ( f @ X5 ) @ X4 )
| ( cQ_3 @ X7 @ X4 @ X6 )
| ~ ( cP_2 @ ( f @ X2 ) @ X7 )
| ~ ( cQ_2 @ X2 @ X5 @ X3 )
| ~ ( cP_2 @ ( f @ X3 ) @ X6 ) )
& ( cQ_1 @ a @ b @ c )
& ( cP_2 @ c @ c )
& ! [X8: $i,X9: $i,X10: $i,X11: $i,X12: $i,X13: $i] :
( ~ ( cP_1 @ ( f @ X9 ) @ X13 )
| ~ ( cP_1 @ ( f @ X10 ) @ X12 )
| ( cQ_2 @ X13 @ X11 @ X12 )
| ~ ( cP_1 @ ( f @ X8 ) @ X11 )
| ~ ( cQ_1 @ X9 @ X8 @ X10 ) )
& ! [X14: $i] : ( cP_2 @ d @ X14 )
& ( cP_2 @ a @ a )
& ( cP_2 @ b @ b )
& ! [X15: $i,X16: $i] :
( ( cP_1 @ ( f @ X16 ) @ X15 )
| ~ ( cP_1 @ X16 @ X15 ) )
& ! [X17: $i,X18: $i,X19: $i] :
~ ( cQ_3 @ X18 @ X17 @ X19 )
& ( cP_1 @ b @ b )
& ! [X20: $i] : ( cP_1 @ d @ X20 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ~ ( ! [X1: $i,X0: $i] :
( ~ ( cP_2 @ X0 @ X1 )
| ( cP_2 @ ( f @ X0 ) @ X1 ) )
& ( cP_1 @ a @ a )
& ( cP_1 @ c @ c )
& ! [X0: $i,X2: $i,X4: $i,X1: $i,X5: $i,X3: $i] :
( ~ ( cP_2 @ ( f @ X1 ) @ X4 )
| ( cQ_3 @ X3 @ X4 @ X5 )
| ~ ( cP_2 @ ( f @ X0 ) @ X3 )
| ~ ( cQ_2 @ X0 @ X1 @ X2 )
| ~ ( cP_2 @ ( f @ X2 ) @ X5 ) )
& ( cQ_1 @ a @ b @ c )
& ( cP_2 @ c @ c )
& ! [X1: $i,X0: $i,X2: $i,X4: $i,X5: $i,X3: $i] :
( ~ ( cP_1 @ ( f @ X0 ) @ X3 )
| ~ ( cP_1 @ ( f @ X2 ) @ X5 )
| ( cQ_2 @ X3 @ X4 @ X5 )
| ~ ( cP_1 @ ( f @ X1 ) @ X4 )
| ~ ( cQ_1 @ X0 @ X1 @ X2 ) )
& ! [X0: $i] : ( cP_2 @ d @ X0 )
& ( cP_2 @ a @ a )
& ( cP_2 @ b @ b )
& ! [X1: $i,X0: $i] :
( ( cP_1 @ ( f @ X0 ) @ X1 )
| ~ ( cP_1 @ X0 @ X1 ) )
& ! [X1: $i,X0: $i,X2: $i] :
~ ( cQ_3 @ X0 @ X1 @ X2 )
& ( cP_1 @ b @ b )
& ! [X0: $i] : ( cP_1 @ d @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
~ ( ! [X1: $i,X0: $i] :
( ~ ( cP_2 @ X0 @ X1 )
| ( cP_2 @ ( f @ X0 ) @ X1 ) )
& ( cP_1 @ a @ a )
& ( cP_1 @ c @ c )
& ! [X0: $i,X2: $i,X4: $i,X1: $i,X5: $i,X3: $i] :
( ~ ( cP_2 @ ( f @ X1 ) @ X4 )
| ( cQ_3 @ X3 @ X4 @ X5 )
| ~ ( cP_2 @ ( f @ X0 ) @ X3 )
| ~ ( cQ_2 @ X0 @ X1 @ X2 )
| ~ ( cP_2 @ ( f @ X2 ) @ X5 ) )
& ( cQ_1 @ a @ b @ c )
& ( cP_2 @ c @ c )
& ! [X1: $i,X0: $i,X2: $i,X4: $i,X5: $i,X3: $i] :
( ~ ( cP_1 @ ( f @ X0 ) @ X3 )
| ~ ( cP_1 @ ( f @ X2 ) @ X5 )
| ( cQ_2 @ X3 @ X4 @ X5 )
| ~ ( cP_1 @ ( f @ X1 ) @ X4 )
| ~ ( cQ_1 @ X0 @ X1 @ X2 ) )
& ! [X0: $i] : ( cP_2 @ d @ X0 )
& ( cP_2 @ a @ a )
& ( cP_2 @ b @ b )
& ! [X1: $i,X0: $i] :
( ( cP_1 @ ( f @ X0 ) @ X1 )
| ~ ( cP_1 @ X0 @ X1 ) )
& ! [X1: $i,X0: $i,X2: $i] :
~ ( cQ_3 @ X0 @ X1 @ X2 )
& ( cP_1 @ b @ b )
& ! [X0: $i] : ( cP_1 @ d @ X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.A8xfxfIeB2/DTF2THF_28132.p',cTHM409_2) ).
thf(f61,plain,
( ! [X0: $i] :
( $true
!= ( cP_2 @ c @ X0 ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f60]) ).
thf(f60,plain,
( ! [X0: $i] :
( ( $true
!= ( cP_2 @ c @ X0 ) )
| ( $true != $true ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f59,f8]) ).
thf(f8,plain,
( ( cP_1 @ c @ c )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f59,plain,
( ! [X0: $i,X1: $i] :
( ( $true
!= ( cP_1 @ c @ X0 ) )
| ( ( cP_2 @ X0 @ X1 )
!= $true ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f58]) ).
thf(f58,plain,
( ! [X0: $i,X1: $i] :
( ( $true
!= ( cP_1 @ c @ X0 ) )
| ( $true != $true )
| ( ( cP_2 @ X0 @ X1 )
!= $true ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f57,f12]) ).
thf(f12,plain,
! [X18: $i,X19: $i] :
( ( ( cP_2 @ ( f @ X19 ) @ X18 )
= $true )
| ( ( cP_2 @ X19 @ X18 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f57,plain,
( ! [X0: $i,X1: $i] :
( ( ( cP_2 @ ( f @ X0 ) @ X1 )
!= $true )
| ( $true
!= ( cP_1 @ c @ X0 ) ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f56]) ).
thf(f56,plain,
( ! [X0: $i,X1: $i] :
( ( ( cP_2 @ ( f @ X0 ) @ X1 )
!= $true )
| ( $true != $true )
| ( $true
!= ( cP_1 @ c @ X0 ) ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f30,f18]) ).
thf(f18,plain,
! [X4: $i,X5: $i] :
( ( ( cP_1 @ ( f @ X5 ) @ X4 )
= $true )
| ( ( cP_1 @ X5 @ X4 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f30,plain,
( ! [X3: $i,X4: $i] :
( ( ( cP_1 @ ( f @ c ) @ X3 )
!= $true )
| ( ( cP_2 @ ( f @ X3 ) @ X4 )
!= $true ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f29]) ).
thf(f29,definition,
( spl0_1
<=> ! [X4: $i,X3: $i] :
( ( ( cP_1 @ ( f @ c ) @ X3 )
!= $true )
| ( ( cP_2 @ ( f @ X3 ) @ X4 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f55,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[status(thm)],[f54]) ).
thf(f54,plain,
( $false
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f53]) ).
thf(f53,plain,
( ( $true != $true )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f52,f15]) ).
thf(f15,plain,
( ( cP_2 @ a @ a )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f52,plain,
( ! [X0: $i] :
( $true
!= ( cP_2 @ a @ X0 ) )
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f51]) ).
thf(f51,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( cP_2 @ a @ X0 ) ) )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f50,f9]) ).
thf(f9,plain,
( ( cP_1 @ a @ a )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f50,plain,
( ! [X0: $i,X1: $i] :
( ( ( cP_1 @ a @ X0 )
!= $true )
| ( ( cP_2 @ X0 @ X1 )
!= $true ) )
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f49]) ).
thf(f49,plain,
( ! [X0: $i,X1: $i] :
( ( ( cP_1 @ a @ X0 )
!= $true )
| ( $true != $true )
| ( ( cP_2 @ X0 @ X1 )
!= $true ) )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f48,f12]) ).
thf(f48,plain,
( ! [X0: $i,X1: $i] :
( ( ( cP_2 @ ( f @ X0 ) @ X1 )
!= $true )
| ( ( cP_1 @ a @ X0 )
!= $true ) )
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f47]) ).
thf(f47,plain,
( ! [X0: $i,X1: $i] :
( ( $true != $true )
| ( ( cP_1 @ a @ X0 )
!= $true )
| ( ( cP_2 @ ( f @ X0 ) @ X1 )
!= $true ) )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f36,f18]) ).
thf(f36,plain,
( ! [X2: $i,X5: $i] :
( ( ( cP_1 @ ( f @ a ) @ X2 )
!= $true )
| ( ( cP_2 @ ( f @ X2 ) @ X5 )
!= $true ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f35]) ).
thf(f35,definition,
( spl0_3
<=> ! [X2: $i,X5: $i] :
( ( ( cP_2 @ ( f @ X2 ) @ X5 )
!= $true )
| ( ( cP_1 @ ( f @ a ) @ X2 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f46,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f45]) ).
thf(f45,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f44]) ).
thf(f44,plain,
( ( $true != $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f43,f19]) ).
thf(f19,plain,
( ( cP_2 @ b @ b )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f43,plain,
( ! [X0: $i] :
( ( cP_2 @ b @ X0 )
!= $true )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f42]) ).
thf(f42,plain,
( ! [X0: $i] :
( ( ( cP_2 @ b @ X0 )
!= $true )
| ( $true != $true ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f41,f16]) ).
thf(f16,plain,
( ( cP_1 @ b @ b )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f41,plain,
( ! [X0: $i,X1: $i] :
( ( ( cP_1 @ b @ X0 )
!= $true )
| ( ( cP_2 @ X0 @ X1 )
!= $true ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f40]) ).
thf(f40,plain,
( ! [X0: $i,X1: $i] :
( ( $true != $true )
| ( ( cP_2 @ X0 @ X1 )
!= $true )
| ( ( cP_1 @ b @ X0 )
!= $true ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f39,f12]) ).
thf(f39,plain,
( ! [X0: $i,X1: $i] :
( ( ( cP_2 @ ( f @ X0 ) @ X1 )
!= $true )
| ( ( cP_1 @ b @ X0 )
!= $true ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f38]) ).
thf(f38,plain,
( ! [X0: $i,X1: $i] :
( ( ( cP_1 @ b @ X0 )
!= $true )
| ( $true != $true )
| ( ( cP_2 @ ( f @ X0 ) @ X1 )
!= $true ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f33,f18]) ).
thf(f33,plain,
( ! [X0: $i,X1: $i] :
( ( ( cP_1 @ ( f @ b ) @ X0 )
!= $true )
| ( ( cP_2 @ ( f @ X0 ) @ X1 )
!= $true ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f32]) ).
thf(f32,definition,
( spl0_2
<=> ! [X0: $i,X1: $i] :
( ( ( cP_1 @ ( f @ b ) @ X0 )
!= $true )
| ( ( cP_2 @ ( f @ X0 ) @ X1 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f37,plain,
( spl0_1
| spl0_2
| spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f27,f35,f32,f29]) ).
thf(f27,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( cP_1 @ ( f @ c ) @ X3 )
!= $true )
| ( ( cP_1 @ ( f @ b ) @ X0 )
!= $true )
| ( ( cP_2 @ ( f @ X2 ) @ X5 )
!= $true )
| ( ( cP_2 @ ( f @ X3 ) @ X4 )
!= $true )
| ( ( cP_1 @ ( f @ a ) @ X2 )
!= $true )
| ( ( cP_2 @ ( f @ X0 ) @ X1 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f26]) ).
thf(f26,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( cP_2 @ ( f @ X0 ) @ X1 )
!= $true )
| ( ( cP_2 @ ( f @ X3 ) @ X4 )
!= $true )
| ( ( cP_2 @ ( f @ X2 ) @ X5 )
!= $true )
| ( $true != $true )
| ( ( cP_1 @ ( f @ a ) @ X2 )
!= $true )
| ( ( cP_1 @ ( f @ c ) @ X3 )
!= $true )
| ( ( cP_1 @ ( f @ b ) @ X0 )
!= $true ) ),
inference(superposition,[status(thm)],[f25,f10]) ).
thf(f10,plain,
( ( cQ_1 @ a @ b @ c )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f25,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( cQ_1 @ X7 @ X6 @ X8 )
!= $true )
| ( $true
!= ( cP_2 @ ( f @ X1 ) @ X3 ) )
| ( $true
!= ( cP_1 @ ( f @ X7 ) @ X0 ) )
| ( $true
!= ( cP_1 @ ( f @ X6 ) @ X1 ) )
| ( ( cP_2 @ ( f @ X2 ) @ X5 )
!= $true )
| ( $true
!= ( cP_1 @ ( f @ X8 ) @ X2 ) )
| ( $true
!= ( cP_2 @ ( f @ X0 ) @ X4 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f24]) ).
thf(f24,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_2 @ ( f @ X1 ) @ X3 ) )
| ( $true
!= ( cP_1 @ ( f @ X7 ) @ X0 ) )
| ( $true
!= ( cP_2 @ ( f @ X0 ) @ X4 ) )
| ( ( cQ_1 @ X7 @ X6 @ X8 )
!= $true )
| ( $true
!= ( cP_1 @ ( f @ X6 ) @ X1 ) )
| ( $true != $true )
| ( ( cP_2 @ ( f @ X2 ) @ X5 )
!= $true )
| ( $true
!= ( cP_1 @ ( f @ X8 ) @ X2 ) ) ),
inference(superposition,[status(thm)],[f23,f13]) ).
thf(f13,plain,
! [X16: $i,X14: $i,X17: $i,X15: $i,X12: $i,X13: $i] :
( ( $true
= ( cQ_2 @ X16 @ X15 @ X17 ) )
| ( $true
!= ( cP_1 @ ( f @ X14 ) @ X15 ) )
| ( $true
!= ( cP_1 @ ( f @ X13 ) @ X16 ) )
| ( $true
!= ( cP_1 @ ( f @ X12 ) @ X17 ) )
| ( ( cQ_1 @ X13 @ X14 @ X12 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f23,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( cQ_2 @ X4 @ X3 @ X5 )
!= $true )
| ( ( cP_2 @ ( f @ X3 ) @ X1 )
!= $true )
| ( $true
!= ( cP_2 @ ( f @ X4 ) @ X0 ) )
| ( ( cP_2 @ ( f @ X5 ) @ X2 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f22]) ).
thf(f22,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( cQ_2 @ X4 @ X3 @ X5 )
!= $true )
| ( ( cP_2 @ ( f @ X3 ) @ X1 )
!= $true )
| ( $true != $true )
| ( $true
!= ( cP_2 @ ( f @ X4 ) @ X0 ) )
| ( ( cP_2 @ ( f @ X5 ) @ X2 )
!= $true ) ),
inference(superposition,[status(thm)],[f20,f14]) ).
thf(f14,plain,
! [X10: $i,X11: $i,X8: $i,X6: $i,X9: $i,X7: $i] :
( ( $true
= ( cQ_3 @ X10 @ X8 @ X11 ) )
| ( ( cP_2 @ ( f @ X6 ) @ X8 )
!= $true )
| ( $true
!= ( cP_2 @ ( f @ X7 ) @ X10 ) )
| ( ( cP_2 @ ( f @ X9 ) @ X11 )
!= $true )
| ( $true
!= ( cQ_2 @ X7 @ X6 @ X9 ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f20,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
!= ( cQ_3 @ X1 @ X2 @ X3 ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO385^5 : 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 : n007.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 14:28:53 EST 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.45 ---- Original DTF file ---
% 0.18/0.45 thf(spec,logic,$$dhol).
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 % File : SYO385^5 : TPTP v9.2.1. Released v4.0.0.
% 0.18/0.45 % Domain : Syntactic
% 0.18/0.45 % Problem : TPS problem THM409-2
% 0.18/0.45 % Version : Especial.
% 0.18/0.45 % English :
% 0.18/0.45
% 0.18/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.18/0.45 % Source : [Bro09]
% 0.18/0.45 % Names : tps_0454 [Bro09]
% 0.18/0.45 % : THM409-2 [TPS]
% 0.18/0.45
% 0.18/0.45 % Status : Theorem
% 0.18/0.45 % Rating : 0.17 v9.1.0, 0.12 v9.0.0, 0.17 v8.2.0, 0.18 v8.1.0, 0.17 v7.4.0, 0.22 v7.3.0, 0.20 v7.2.0, 0.25 v7.1.0, 0.29 v7.0.0, 0.25 v6.4.0, 0.29 v6.3.0, 0.33 v6.0.0, 0.17 v5.5.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.0
% 0.18/0.45 % Syntax : Number of formulae : 11 ( 0 unt; 10 typ; 0 def)
% 0.18/0.45 % Number of atoms : 24 ( 0 equ; 0 cnn)
% 0.18/0.45 % Maximal formula atoms : 24 ( 24 avg)
% 0.18/0.45 % Number of connectives : 97 ( 12 ~; 10 |; 13 &; 62 @)
% 0.18/0.45 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.18/0.45 % Maximal formula depth : 29 ( 29 avg)
% 0.18/0.45 % Number of types : 2 ( 0 usr)
% 0.18/0.45 % Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% 0.18/0.45 % Number of symbols : 10 ( 10 usr; 4 con; 0-3 aty)
% 0.18/0.45 % Number of variables : 21 ( 0 ^; 21 !; 0 ?; 21 :)
% 0.18/0.45 % SPC : TH0_THM_NEQ_NAR
% 0.18/0.45
% 0.18/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.18/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.18/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.18/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 thf(cQ_3,type,
% 0.18/0.45 cQ_3: $i > $i > $i > $o ).
% 0.18/0.45
% 0.18/0.45 thf(f,type,
% 0.18/0.45 f: $i > $i ).
% 0.18/0.45
% 0.18/0.45 thf(cP_2,type,
% 0.18/0.45 cP_2: $i > $i > $o ).
% 0.18/0.45
% 0.18/0.45 thf(cQ_2,type,
% 0.18/0.45 cQ_2: $i > $i > $i > $o ).
% 0.18/0.45
% 0.18/0.45 thf(d,type,
% 0.18/0.45 d: $i ).
% 0.18/0.45
% 0.18/0.45 thf(c,type,
% 0.18/0.45 c: $i ).
% 0.18/0.45
% 0.18/0.45 thf(b,type,
% 0.18/0.45 b: $i ).
% 0.18/0.45
% 0.18/0.45 thf(a,type,
% 0.18/0.45 a: $i ).
% 0.18/0.45
% 0.18/0.45 thf(cP_1,type,
% 0.18/0.45 cP_1: $i > $i > $o ).
% 0.18/0.45
% 0.18/0.45 thf(cQ_1,type,
% 0.18/0.45 cQ_1: $i > $i > $i > $o ).
% 0.18/0.45
% 0.18/0.45 thf(cTHM409_2,conjecture,
% 0.18/0.45 ~ ( ( cQ_1 @ a @ b @ c )
% 0.18/0.45 & ( cP_1 @ a @ a )
% 0.18/0.45 & ( cP_1 @ b @ b )
% 0.18/0.45 & ( cP_1 @ c @ c )
% 0.18/0.45 & ! [Xx: $i] : ( cP_1 @ d @ Xx )
% 0.18/0.45 & ! [Xx: $i,Xy: $i] :
% 0.18/0.45 ( ~ ( cP_1 @ Xx @ Xy )
% 0.18/0.45 | ( cP_1 @ ( f @ Xx ) @ Xy ) )
% 0.18/0.45 & ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
% 0.18/0.45 ( ~ ( cQ_1 @ Xx @ Xy @ Xz )
% 0.18/0.45 | ~ ( cP_1 @ ( f @ Xx ) @ Xu )
% 0.18/0.45 | ~ ( cP_1 @ ( f @ Xy ) @ Xv )
% 0.18/0.45 | ~ ( cP_1 @ ( f @ Xz ) @ Xw )
% 0.18/0.45 | ( cQ_2 @ Xu @ Xv @ Xw ) )
% 0.18/0.45 & ( cP_2 @ a @ a )
% 0.18/0.45 & ( cP_2 @ b @ b )
% 0.18/0.45 & ( cP_2 @ c @ c )
% 0.18/0.45 & ! [Xx: $i] : ( cP_2 @ d @ Xx )
% 0.18/0.45 & ! [Xx: $i,Xy: $i] :
% 0.18/0.45 ( ~ ( cP_2 @ Xx @ Xy )
% 0.18/0.45 | ( cP_2 @ ( f @ Xx ) @ Xy ) )
% 0.18/0.45 & ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
% 0.18/0.45 ( ~ ( cQ_2 @ Xx @ Xy @ Xz )
% 0.18/0.45 | ~ ( cP_2 @ ( f @ Xx ) @ Xu )
% 0.18/0.45 | ~ ( cP_2 @ ( f @ Xy ) @ Xv )
% 0.18/0.45 | ~ ( cP_2 @ ( f @ Xz ) @ Xw )
% 0.18/0.45 | ( cQ_3 @ Xu @ Xv @ Xw ) )
% 0.18/0.45 & ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.18/0.45 ~ ( cQ_3 @ Xx @ Xy @ Xz ) ) ).
% 0.18/0.45
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 ------------------------
% 1.52/1.30 ---- Embedded in THF ---
% 1.71/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.71/1.30 %%% Generated on Tue Feb 24 14:28:54 EST 2026
% 1.71/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 1.71/1.30 %%% Logic specification used:
% 1.71/1.30 %%% thf(spec, logic, $$dhol).
% 1.71/1.30
% 1.71/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.A8xfxfIeB2/DTF2DTF28132.p
% See solution above
% 1.71/1.30 ------------------------
% 1.71/1.31 ---- Cleaned THF ---
% 1.71/1.31 thf(cQ_3,type,
% 1.71/1.31 cQ_3: $i > $i > $i > $o ).
% 1.71/1.31
% 1.71/1.31 thf(f,type,
% 1.71/1.31 f: $i > $i ).
% 1.71/1.31
% 1.71/1.31 thf(cP_2,type,
% 1.71/1.31 cP_2: $i > $i > $o ).
% 1.71/1.31
% 1.71/1.31 thf(cQ_2,type,
% 1.71/1.31 cQ_2: $i > $i > $i > $o ).
% 1.71/1.31
% 1.71/1.31 thf(d,type,
% 1.71/1.31 d: $i ).
% 1.71/1.31
% 1.71/1.31 thf(c,type,
% 1.71/1.31 c: $i ).
% 1.71/1.31
% 1.71/1.31 thf(b,type,
% 1.71/1.31 b: $i ).
% 1.71/1.31
% 1.71/1.31 thf(a,type,
% 1.71/1.31 a: $i ).
% 1.71/1.31
% 1.71/1.31 thf(cP_1,type,
% 1.71/1.31 cP_1: $i > $i > $o ).
% 1.71/1.31
% 1.71/1.31 thf(cQ_1,type,
% 1.71/1.31 cQ_1: $i > $i > $i > $o ).
% 1.71/1.31
% 1.71/1.31 thf(cTHM409_2,conjecture,
% 1.71/1.31 ~ ( ( cQ_1 @ a @ b @ c )
% 1.71/1.31 & ( cP_1 @ a @ a )
% 1.71/1.31 & ( cP_1 @ b @ b )
% 1.71/1.31 & ( cP_1 @ c @ c )
% 1.71/1.31 & ! [Xx: $i] : ( cP_1 @ d @ Xx )
% 1.71/1.31 & ! [Xx: $i,Xy: $i] :
% 1.71/1.31 ( ~ ( cP_1 @ Xx @ Xy )
% 1.71/1.31 | ( cP_1 @ ( f @ Xx ) @ Xy ) )
% 1.71/1.31 & ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
% 1.71/1.31 ( ~ ( cQ_1 @ Xx @ Xy @ Xz )
% 1.71/1.31 | ~ ( cP_1 @ ( f @ Xx ) @ Xu )
% 1.71/1.31 | ~ ( cP_1 @ ( f @ Xy ) @ Xv )
% 1.71/1.31 | ~ ( cP_1 @ ( f @ Xz ) @ Xw )
% 1.71/1.31 | ( cQ_2 @ Xu @ Xv @ Xw ) )
% 1.71/1.31 & ( cP_2 @ a @ a )
% 1.71/1.31 & ( cP_2 @ b @ b )
% 1.71/1.31 & ( cP_2 @ c @ c )
% 1.71/1.31 & ! [Xx: $i] : ( cP_2 @ d @ Xx )
% 1.71/1.31 & ! [Xx: $i,Xy: $i] :
% 1.71/1.31 ( ~ ( cP_2 @ Xx @ Xy )
% 1.71/1.31 | ( cP_2 @ ( f @ Xx ) @ Xy ) )
% 1.71/1.31 & ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
% 1.71/1.31 ( ~ ( cQ_2 @ Xx @ Xy @ Xz )
% 1.71/1.31 | ~ ( cP_2 @ ( f @ Xx ) @ Xu )
% 1.71/1.31 | ~ ( cP_2 @ ( f @ Xy ) @ Xv )
% 1.71/1.31 | ~ ( cP_2 @ ( f @ Xz ) @ Xw )
% 1.71/1.31 | ( cQ_3 @ Xu @ Xv @ Xw ) )
% 1.71/1.31 & ! [Xx: $i,Xy: $i,Xz: $i] :
% 1.71/1.31 ~ ( cQ_3 @ Xx @ Xy @ Xz ) ) ).
% 1.71/1.31 ------------------------
% 1.71/1.32 % (28367)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_28132 for (2999ds/2Mi)
% 1.71/1.33 % (28367)Instruction limit reached!
% 1.71/1.33 % (28367)------------------------------
% 1.71/1.33 % (28367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.33 % (28367)Termination reason: Unknown
% 1.71/1.33 % (28367)Termination phase: shuffling
% 1.71/1.33
% 1.71/1.33 % (28367)Memory used [KB]: 1023
% 1.71/1.33 % (28367)Time elapsed: 0.002 s
% 1.71/1.33 % (28367)Instructions burned: 3 (million)
% 1.71/1.33 % (28367)------------------------------
% 1.71/1.33 % (28367)------------------------------
% 1.71/1.33 % (28363)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_28132 for (2999ds/183Mi)
% 1.71/1.33 % (28364)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_28132 for (2999ds/4Mi)
% 1.71/1.33 % (28366)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_28132 for (2999ds/2Mi)
% 1.71/1.33 % (28365)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_28132 for (2999ds/27Mi)
% 1.71/1.33 % (28368)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_28132 for (2999ds/275Mi)
% 1.71/1.33 % (28369)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_28132 for (2999ds/18Mi)
% 1.71/1.33 % (28366)Instruction limit reached!
% 1.71/1.33 % (28366)------------------------------
% 1.71/1.33 % (28366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.33 % (28366)Termination reason: Unknown
% 1.71/1.33 % (28366)Termination phase: Property scanning
% 1.71/1.33
% 1.71/1.33 % (28366)Memory used [KB]: 895
% 1.71/1.33 % (28366)Time elapsed: 0.003 s
% 1.71/1.33 % (28366)Instructions burned: 2 (million)
% 1.71/1.33 % (28366)------------------------------
% 1.71/1.33 % (28366)------------------------------
% 1.71/1.33 % (28364)Instruction limit reached!
% 1.71/1.33 % (28364)------------------------------
% 1.71/1.33 % (28364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.33 % (28364)Termination reason: Unknown
% 1.71/1.33 % (28364)Termination phase: Saturation
% 1.71/1.33
% 1.71/1.33 % (28364)Memory used [KB]: 5500
% 1.71/1.33 % (28364)Time elapsed: 0.005 s
% 1.71/1.33 % (28364)Instructions burned: 4 (million)
% 1.71/1.33 % (28364)------------------------------
% 1.71/1.33 % (28364)------------------------------
% 1.71/1.34 % (28370)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_28132 for (2999ds/3Mi)
% 1.71/1.34 % (28370)Instruction limit reached!
% 1.71/1.34 % (28370)------------------------------
% 1.71/1.34 % (28370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.34 % (28370)Termination reason: Unknown
% 1.71/1.34 % (28370)Termination phase: Saturation
% 1.71/1.34
% 1.71/1.34 % (28370)Memory used [KB]: 5500
% 1.71/1.34 % (28370)Time elapsed: 0.003 s
% 1.71/1.34 % (28370)Instructions burned: 4 (million)
% 1.71/1.34 % (28370)------------------------------
% 1.71/1.34 % (28370)------------------------------
% 1.71/1.34 % (28363)First to succeed.
% 1.71/1.34 % (28368)Also succeeded, but the first one will report.
% 1.71/1.34 % (28363)Refutation found. Thanks to Tanya!
% 1.71/1.34 % SZS status Theorem for DTF2THF_28132
% 1.71/1.34 % SZS output start Proof for DTF2THF_28132
% 1.71/1.34 thf(func_def_0, type, cQ_3: $i > $i > $i > $o).
% 1.71/1.34 thf(func_def_1, type, f: $i > $i).
% 1.71/1.34 thf(func_def_2, type, cP_2: $i > $i > $o).
% 1.71/1.34 thf(func_def_3, type, cQ_2: $i > $i > $i > $o).
% 1.71/1.34 thf(func_def_8, type, cP_1: $i > $i > $o).
% 1.71/1.34 thf(func_def_9, type, cQ_1: $i > $i > $i > $o).
% 1.71/1.34 thf(f65,plain,(
% 1.71/1.34 $false),
% 1.71/1.34 inference(avatar_sat_refutation,[status(thm)],[f37,f46,f55,f64])).
% 1.71/1.34 thf(f64,plain,(
% 1.71/1.34 ~spl0_1),
% 1.71/1.34 inference(avatar_contradiction_clause,[status(thm)],[f63])).
% 1.71/1.34 thf(f63,plain,(
% 1.71/1.34 $false | ~spl0_1),
% 1.71/1.34 inference(trivial_inequality_removal,[status(thm)],[f62])).
% 1.71/1.34 thf(f62,plain,(
% 1.71/1.34 ($true != $true) | ~spl0_1),
% 1.71/1.34 inference(superposition,[status(thm)],[f61,f17])).
% 1.71/1.34 thf(f17,plain,(
% 1.71/1.34 ((cP_2 @ c @ c) = $true)),
% 1.71/1.34 inference(cnf_transformation,[status(thm)],[f7])).
% 1.71/1.34 thf(f7,plain,(
% 1.71/1.34 ! [X0 : $i] : ((cP_1 @ d @ X0) = $true) & ! [X1 : $i,X2 : $i,X3 : $i] : ($true != (cQ_3 @ X1 @ X2 @ X3)) & ((cP_2 @ b @ b) = $true) & ! [X4 : $i,X5 : $i] : (((cP_1 @ X5 @ X4) != $true) | ((cP_1 @ (f @ X5) @ X4) = $true)) & ((cP_2 @ c @ c) = $true) & ((cP_1 @ b @ b) = $true) & ((cP_2 @ a @ a) = $true) & ! [X6 : $i,X7 : $i,X8 : $i,X9 : $i,X10 : $i,X11 : $i] : (($true = (cQ_3 @ X10 @ X8 @ X11)) | ((cP_2 @ (f @ X9) @ X11) != $true) | ($true != (cQ_2 @ X7 @ X6 @ X9)) | ((cP_2 @ (f @ X6) @ X8) != $true) | ($true != (cP_2 @ (f @ X7) @ X10))) & ! [X12 : $i,X13 : $i,X14 : $i,X15 : $i,X16 : $i,X17 : $i] : (($true != (cP_1 @ (f @ X14) @ X15)) | ($true = (cQ_2 @ X16 @ X15 @ X17)) | ($true != (cP_1 @ (f @ X12) @ X17)) | ($true != (cP_1 @ (f @ X13) @ X16)) | ((cQ_1 @ X13 @ X14 @ X12) != $true)) & ! [X18 : $i,X19 : $i] : (((cP_2 @ X19 @ X18) != $true) | ((cP_2 @ (f @ X19) @ X18) = $true)) & ! [X20 : $i] : ((cP_2 @ d @ X20) = $true) & ((cQ_1 @ a @ b @ c) = $true) & ((cP_1 @ a @ a) = $true) & ((cP_1 @ c @ c) = $true)),
% 1.71/1.34 inference(rectify,[status(thm)],[f6])).
% 1.71/1.34 thf(f6,plain,(
% 1.71/1.34 ! [X20 : $i] : ($true = (cP_1 @ d @ X20)) & ! [X18 : $i,X17 : $i,X19 : $i] : ((cQ_3 @ X18 @ X17 @ X19) != $true) & ((cP_2 @ b @ b) = $true) & ! [X15 : $i,X16 : $i] : (((cP_1 @ X16 @ X15) != $true) | ((cP_1 @ (f @ X16) @ X15) = $true)) & ((cP_2 @ c @ c) = $true) & ((cP_1 @ b @ b) = $true) & ((cP_2 @ a @ a) = $true) & ! [X5 : $i,X2 : $i,X4 : $i,X3 : $i,X7 : $i,X6 : $i] : (((cQ_3 @ X7 @ X4 @ X6) = $true) | ((cP_2 @ (f @ X3) @ X6) != $true) | ((cQ_2 @ X2 @ X5 @ X3) != $true) | ((cP_2 @ (f @ X5) @ X4) != $true) | ($true != (cP_2 @ (f @ X2) @ X7))) & ! [X10 : $i,X9 : $i,X8 : $i,X11 : $i,X13 : $i,X12 : $i] : (($true != (cP_1 @ (f @ X8) @ X11)) | ($true = (cQ_2 @ X13 @ X11 @ X12)) | ((cP_1 @ (f @ X10) @ X12) != $true) | ((cP_1 @ (f @ X9) @ X13) != $true) | ((cQ_1 @ X9 @ X8 @ X10) != $true)) & ! [X0 : $i,X1 : $i] : (((cP_2 @ X1 @ X0) != $true) | ($true = (cP_2 @ (f @ X1) @ X0))) & ! [X14 : $i] : ($true = (cP_2 @ d @ X14)) & ((cQ_1 @ a @ b @ c) = $true) & ((cP_1 @ a @ a) = $true) & ((cP_1 @ c @ c) = $true)),
% 1.71/1.34 inference(flattening,[status(thm)],[f5])).
% 1.71/1.34 thf(f5,plain,(
% 1.71/1.34 ~~(! [X0 : $i,X1 : $i] : (~((cP_2 @ X1 @ X0) = $true) | ($true = (cP_2 @ (f @ X1) @ X0))) & ((cP_1 @ a @ a) = $true) & ((cP_1 @ c @ c) = $true) & ! [X2 : $i,X3 : $i,X4 : $i,X5 : $i,X6 : $i,X7 : $i] : (~((cP_2 @ (f @ X5) @ X4) = $true) | ((cQ_3 @ X7 @ X4 @ X6) = $true) | ~($true = (cP_2 @ (f @ X2) @ X7)) | ~((cQ_2 @ X2 @ X5 @ X3) = $true) | ~((cP_2 @ (f @ X3) @ X6) = $true)) & ((cQ_1 @ a @ b @ c) = $true) & ((cP_2 @ c @ c) = $true) & ! [X8 : $i,X9 : $i,X10 : $i,X11 : $i,X12 : $i,X13 : $i] : (~((cP_1 @ (f @ X9) @ X13) = $true) | ~((cP_1 @ (f @ X10) @ X12) = $true) | ($true = (cQ_2 @ X13 @ X11 @ X12)) | ~($true = (cP_1 @ (f @ X8) @ X11)) | ~((cQ_1 @ X9 @ X8 @ X10) = $true)) & ! [X14 : $i] : ($true = (cP_2 @ d @ X14)) & ((cP_2 @ a @ a) = $true) & ((cP_2 @ b @ b) = $true) & ! [X15 : $i,X16 : $i] : (((cP_1 @ (f @ X16) @ X15) = $true) | ~((cP_1 @ X16 @ X15) = $true)) & ! [X17 : $i,X18 : $i,X19 : $i] : ~((cQ_3 @ X18 @ X17 @ X19) = $true) & ((cP_1 @ b @ b) = $true) & ! [X20 : $i] : ($true = (cP_1 @ d @ X20)))),
% 1.71/1.34 inference(fool_elimination,[status(thm)],[f4])).
% 1.71/1.34 thf(f4,plain,(
% 1.71/1.34 ~~(! [X0 : $i,X1 : $i] : (~(cP_2 @ X1 @ X0) | (cP_2 @ (f @ X1) @ X0)) & (cP_1 @ a @ a) & (cP_1 @ c @ c) & ! [X2 : $i,X3 : $i,X4 : $i,X5 : $i,X6 : $i,X7 : $i] : (~(cP_2 @ (f @ X5) @ X4) | (cQ_3 @ X7 @ X4 @ X6) | ~(cP_2 @ (f @ X2) @ X7) | ~(cQ_2 @ X2 @ X5 @ X3) | ~(cP_2 @ (f @ X3) @ X6)) & (cQ_1 @ a @ b @ c) & (cP_2 @ c @ c) & ! [X8 : $i,X9 : $i,X10 : $i,X11 : $i,X12 : $i,X13 : $i] : (~(cP_1 @ (f @ X9) @ X13) | ~(cP_1 @ (f @ X10) @ X12) | (cQ_2 @ X13 @ X11 @ X12) | ~(cP_1 @ (f @ X8) @ X11) | ~(cQ_1 @ X9 @ X8 @ X10)) & ! [X14 : $i] : (cP_2 @ d @ X14) & (cP_2 @ a @ a) & (cP_2 @ b @ b) & ! [X15 : $i,X16 : $i] : ((cP_1 @ (f @ X16) @ X15) | ~(cP_1 @ X16 @ X15)) & ! [X17 : $i,X18 : $i,X19 : $i] : ~(cQ_3 @ X18 @ X17 @ X19) & (cP_1 @ b @ b) & ! [X20 : $i] : (cP_1 @ d @ X20))),
% 1.71/1.34 inference(rectify,[status(thm)],[f2])).
% 1.71/1.34 thf(f2,negated_conjecture,(
% 1.71/1.34 ~~(! [X1 : $i,X0 : $i] : (~(cP_2 @ X0 @ X1) | (cP_2 @ (f @ X0) @ X1)) & (cP_1 @ a @ a) & (cP_1 @ c @ c) & ! [X0 : $i,X2 : $i,X4 : $i,X1 : $i,X5 : $i,X3 : $i] : (~(cP_2 @ (f @ X1) @ X4) | (cQ_3 @ X3 @ X4 @ X5) | ~(cP_2 @ (f @ X0) @ X3) | ~(cQ_2 @ X0 @ X1 @ X2) | ~(cP_2 @ (f @ X2) @ X5)) & (cQ_1 @ a @ b @ c) & (cP_2 @ c @ c) & ! [X1 : $i,X0 : $i,X2 : $i,X4 : $i,X5 : $i,X3 : $i] : (~(cP_1 @ (f @ X0) @ X3) | ~(cP_1 @ (f @ X2) @ X5) | (cQ_2 @ X3 @ X4 @ X5) | ~(cP_1 @ (f @ X1) @ X4) | ~(cQ_1 @ X0 @ X1 @ X2)) & ! [X0 : $i] : (cP_2 @ d @ X0) & (cP_2 @ a @ a) & (cP_2 @ b @ b) & ! [X1 : $i,X0 : $i] : ((cP_1 @ (f @ X0) @ X1) | ~(cP_1 @ X0 @ X1)) & ! [X1 : $i,X0 : $i,X2 : $i] : ~(cQ_3 @ X0 @ X1 @ X2) & (cP_1 @ b @ b) & ! [X0 : $i] : (cP_1 @ d @ X0))),
% 1.71/1.34 inference(negated_conjecture,[status(cth)],[f1])).
% 1.71/1.34 thf(f1,conjecture,(
% 1.71/1.34 ~(! [X1 : $i,X0 : $i] : (~(cP_2 @ X0 @ X1) | (cP_2 @ (f @ X0) @ X1)) & (cP_1 @ a @ a) & (cP_1 @ c @ c) & ! [X0 : $i,X2 : $i,X4 : $i,X1 : $i,X5 : $i,X3 : $i] : (~(cP_2 @ (f @ X1) @ X4) | (cQ_3 @ X3 @ X4 @ X5) | ~(cP_2 @ (f @ X0) @ X3) | ~(cQ_2 @ X0 @ X1 @ X2) | ~(cP_2 @ (f @ X2) @ X5)) & (cQ_1 @ a @ b @ c) & (cP_2 @ c @ c) & ! [X1 : $i,X0 : $i,X2 : $i,X4 : $i,X5 : $i,X3 : $i] : (~(cP_1 @ (f @ X0) @ X3) | ~(cP_1 @ (f @ X2) @ X5) | (cQ_2 @ X3 @ X4 @ X5) | ~(cP_1 @ (f @ X1) @ X4) | ~(cQ_1 @ X0 @ X1 @ X2)) & ! [X0 : $i] : (cP_2 @ d @ X0) & (cP_2 @ a @ a) & (cP_2 @ b @ b) & ! [X1 : $i,X0 : $i] : ((cP_1 @ (f @ X0) @ X1) | ~(cP_1 @ X0 @ X1)) & ! [X1 : $i,X0 : $i,X2 : $i] : ~(cQ_3 @ X0 @ X1 @ X2) & (cP_1 @ b @ b) & ! [X0 : $i] : (cP_1 @ d @ X0))),
% 1.71/1.34 file('/export/starexec/sandbox2/tmp/tmp.A8xfxfIeB2/DTF2THF_28132.p',cTHM409_2)).
% 1.71/1.34 thf(f61,plain,(
% 1.71/1.34 ( ! [X0 : $i] : (($true != (cP_2 @ c @ X0))) ) | ~spl0_1),
% 1.71/1.34 inference(trivial_inequality_removal,[status(thm)],[f60])).
% 1.71/1.34 thf(f60,plain,(
% 1.71/1.34 ( ! [X0 : $i] : (($true != (cP_2 @ c @ X0)) | ($true != $true)) ) | ~spl0_1),
% 1.71/1.34 inference(superposition,[status(thm)],[f59,f8])).
% 1.71/1.34 thf(f8,plain,(
% 1.71/1.34 ((cP_1 @ c @ c) = $true)),
% 1.71/1.34 inference(cnf_transformation,[status(thm)],[f7])).
% 1.71/1.34 thf(f59,plain,(
% 1.71/1.34 ( ! [X0 : $i,X1 : $i] : (($true != (cP_1 @ c @ X0)) | ((cP_2 @ X0 @ X1) != $true)) ) | ~spl0_1),
% 1.71/1.34 inference(trivial_inequality_removal,[status(thm)],[f58])).
% 1.71/1.34 thf(f58,plain,(
% 1.71/1.34 ( ! [X0 : $i,X1 : $i] : (($true != (cP_1 @ c @ X0)) | ($true != $true) | ((cP_2 @ X0 @ X1) != $true)) ) | ~spl0_1),
% 1.71/1.34 inference(superposition,[status(thm)],[f57,f12])).
% 1.71/1.34 thf(f12,plain,(
% 1.71/1.34 ( ! [X18 : $i,X19 : $i] : (((cP_2 @ (f @ X19) @ X18) = $true) | ((cP_2 @ X19 @ X18) != $true)) )),
% 1.71/1.34 inference(cnf_transformation,[status(thm)],[f7])).
% 1.71/1.34 thf(f57,plain,(
% 1.71/1.34 ( ! [X0 : $i,X1 : $i] : (((cP_2 @ (f @ X0) @ X1) != $true) | ($true != (cP_1 @ c @ X0))) ) | ~spl0_1),
% 1.71/1.34 inference(trivial_inequality_removal,[status(thm)],[f56])).
% 1.71/1.34 thf(f56,plain,(
% 1.71/1.34 ( ! [X0 : $i,X1 : $i] : (((cP_2 @ (f @ X0) @ X1) != $true) | ($true != $true) | ($true != (cP_1 @ c @ X0))) ) | ~spl0_1),
% 1.71/1.34 inference(superposition,[status(thm)],[f30,f18])).
% 1.71/1.34 thf(f18,plain,(
% 1.71/1.34 ( ! [X4 : $i,X5 : $i] : (((cP_1 @ (f @ X5) @ X4) = $true) | ((cP_1 @ X5 @ X4) != $true)) )),
% 1.71/1.34 inference(cnf_transformation,[status(thm)],[f7])).
% 1.71/1.34 thf(f30,plain,(
% 1.71/1.34 ( ! [X3 : $i,X4 : $i] : (((cP_1 @ (f @ c) @ X3) != $true) | ((cP_2 @ (f @ X3) @ X4) != $true)) ) | ~spl0_1),
% 1.71/1.34 inference(avatar_component_clause,[status(thm)],[f29])).
% 1.71/1.34 thf(f29,definition,(
% 1.71/1.34 spl0_1 <=> ! [X4 : $i,X3 : $i] : (((cP_1 @ (f @ c) @ X3) != $true) | ((cP_2 @ (f @ X3) @ X4) != $true))),
% 1.71/1.34 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.71/1.34 thf(f55,plain,(
% 1.71/1.34 ~spl0_3),
% 1.71/1.34 inference(avatar_contradiction_clause,[status(thm)],[f54])).
% 1.71/1.34 thf(f54,plain,(
% 1.71/1.34 $false | ~spl0_3),
% 1.71/1.34 inference(trivial_inequality_removal,[status(thm)],[f53])).
% 1.71/1.34 thf(f53,plain,(
% 1.71/1.34 ($true != $true) | ~spl0_3),
% 1.71/1.34 inference(superposition,[status(thm)],[f52,f15])).
% 1.71/1.34 thf(f15,plain,(
% 1.71/1.34 ((cP_2 @ a @ a) = $true)),
% 1.71/1.34 inference(cnf_transformation,[status(thm)],[f7])).
% 1.71/1.34 thf(f52,plain,(
% 1.71/1.34 ( ! [X0 : $i] : (($true != (cP_2 @ a @ X0))) ) | ~spl0_3),
% 1.71/1.34 inference(trivial_inequality_removal,[status(thm)],[f51])).
% 1.71/1.34 thf(f51,plain,(
% 1.71/1.34 ( ! [X0 : $i] : (($true != $true) | ($true != (cP_2 @ a @ X0))) ) | ~spl0_3),
% 1.71/1.34 inference(superposition,[status(thm)],[f50,f9])).
% 1.71/1.34 thf(f9,plain,(
% 1.71/1.34 ((cP_1 @ a @ a) = $true)),
% 1.71/1.34 inference(cnf_transformation,[status(thm)],[f7])).
% 1.71/1.34 thf(f50,plain,(
% 1.71/1.34 ( ! [X0 : $i,X1 : $i] : (((cP_1 @ a @ X0) != $true) | ((cP_2 @ X0 @ X1) != $true)) ) | ~spl0_3),
% 1.71/1.34 inference(trivial_inequality_removal,[status(thm)],[f49])).
% 1.71/1.34 thf(f49,plain,(
% 1.71/1.34 ( ! [X0 : $i,X1 : $i] : (((cP_1 @ a @ X0) != $true) | ($true != $true) | ((cP_2 @ X0 @ X1) != $true)) ) | ~spl0_3),
% 1.71/1.34 inference(superposition,[status(thm)],[f48,f12])).
% 1.71/1.34 thf(f48,plain,(
% 1.71/1.34 ( ! [X0 : $i,X1 : $i] : (((cP_2 @ (f @ X0) @ X1) != $true) | ((cP_1 @ a @ X0) != $true)) ) | ~spl0_3),
% 1.71/1.34 inference(trivial_inequality_removal,[status(thm)],[f47])).
% 1.71/1.34 thf(f47,plain,(
% 1.71/1.34 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ((cP_1 @ a @ X0) != $true) | ((cP_2 @ (f @ X0) @ X1) != $true)) ) | ~spl0_3),
% 1.71/1.34 inference(superposition,[status(thm)],[f36,f18])).
% 1.71/1.34 thf(f36,plain,(
% 1.71/1.34 ( ! [X2 : $i,X5 : $i] : (((cP_1 @ (f @ a) @ X2) != $true) | ((cP_2 @ (f @ X2) @ X5) != $true)) ) | ~spl0_3),
% 1.71/1.34 inference(avatar_component_clause,[status(thm)],[f35])).
% 1.71/1.34 thf(f35,definition,(
% 1.71/1.34 spl0_3 <=> ! [X2 : $i,X5 : $i] : (((cP_2 @ (f @ X2) @ X5) != $true) | ((cP_1 @ (f @ a) @ X2) != $true))),
% 1.71/1.34 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.71/1.34 thf(f46,plain,(
% 1.71/1.34 ~spl0_2),
% 1.71/1.34 inference(avatar_contradiction_clause,[status(thm)],[f45])).
% 1.71/1.34 thf(f45,plain,(
% 1.71/1.34 $false | ~spl0_2),
% 1.71/1.34 inference(trivial_inequality_removal,[status(thm)],[f44])).
% 1.71/1.34 thf(f44,plain,(
% 1.71/1.34 ($true != $true) | ~spl0_2),
% 1.71/1.34 inference(superposition,[status(thm)],[f43,f19])).
% 1.71/1.34 thf(f19,plain,(
% 1.71/1.34 ((cP_2 @ b @ b) = $true)),
% 1.71/1.34 inference(cnf_transformation,[status(thm)],[f7])).
% 1.71/1.34 thf(f43,plain,(
% 1.71/1.34 ( ! [X0 : $i] : (((cP_2 @ b @ X0) != $true)) ) | ~spl0_2),
% 1.71/1.34 inference(trivial_inequality_removal,[status(thm)],[f42])).
% 1.71/1.34 thf(f42,plain,(
% 1.71/1.34 ( ! [X0 : $i] : (((cP_2 @ b @ X0) != $true) | ($true != $true)) ) | ~spl0_2),
% 1.71/1.34 inference(superposition,[status(thm)],[f41,f16])).
% 1.71/1.34 thf(f16,plain,(
% 1.71/1.34 ((cP_1 @ b @ b) = $true)),
% 1.71/1.34 inference(cnf_transformation,[status(thm)],[f7])).
% 1.71/1.34 thf(f41,plain,(
% 1.71/1.34 ( ! [X0 : $i,X1 : $i] : (((cP_1 @ b @ X0) != $true) | ((cP_2 @ X0 @ X1) != $true)) ) | ~spl0_2),
% 1.71/1.34 inference(trivial_inequality_removal,[status(thm)],[f40])).
% 1.71/1.34 thf(f40,plain,(
% 1.71/1.34 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ((cP_2 @ X0 @ X1) != $true) | ((cP_1 @ b @ X0) != $true)) ) | ~spl0_2),
% 1.71/1.34 inference(superposition,[status(thm)],[f39,f12])).
% 1.71/1.34 thf(f39,plain,(
% 1.71/1.34 ( ! [X0 : $i,X1 : $i] : (((cP_2 @ (f @ X0) @ X1) != $true) | ((cP_1 @ b @ X0) != $true)) ) | ~spl0_2),
% 1.71/1.34 inference(trivial_inequality_removal,[status(thm)],[f38])).
% 1.71/1.34 thf(f38,plain,(
% 1.71/1.34 ( ! [X0 : $i,X1 : $i] : (((cP_1 @ b @ X0) != $true) | ($true != $true) | ((cP_2 @ (f @ X0) @ X1) != $true)) ) | ~spl0_2),
% 1.71/1.34 inference(superposition,[status(thm)],[f33,f18])).
% 1.71/1.34 thf(f33,plain,(
% 1.71/1.34 ( ! [X0 : $i,X1 : $i] : (((cP_1 @ (f @ b) @ X0) != $true) | ((cP_2 @ (f @ X0) @ X1) != $true)) ) | ~spl0_2),
% 1.71/1.34 inference(avatar_component_clause,[status(thm)],[f32])).
% 1.71/1.34 thf(f32,definition,(
% 1.71/1.34 spl0_2 <=> ! [X0 : $i,X1 : $i] : (((cP_1 @ (f @ b) @ X0) != $true) | ((cP_2 @ (f @ X0) @ X1) != $true))),
% 1.71/1.34 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.71/1.34 thf(f37,plain,(
% 1.71/1.34 spl0_1 | spl0_2 | spl0_3),
% 1.71/1.34 inference(avatar_split_clause,[status(thm)],[f27,f35,f32,f29])).
% 1.71/1.34 thf(f27,plain,(
% 1.71/1.34 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (((cP_1 @ (f @ c) @ X3) != $true) | ((cP_1 @ (f @ b) @ X0) != $true) | ((cP_2 @ (f @ X2) @ X5) != $true) | ((cP_2 @ (f @ X3) @ X4) != $true) | ((cP_1 @ (f @ a) @ X2) != $true) | ((cP_2 @ (f @ X0) @ X1) != $true)) )),
% 1.71/1.34 inference(trivial_inequality_removal,[status(thm)],[f26])).
% 1.71/1.34 thf(f26,plain,(
% 1.71/1.34 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (((cP_2 @ (f @ X0) @ X1) != $true) | ((cP_2 @ (f @ X3) @ X4) != $true) | ((cP_2 @ (f @ X2) @ X5) != $true) | ($true != $true) | ((cP_1 @ (f @ a) @ X2) != $true) | ((cP_1 @ (f @ c) @ X3) != $true) | ((cP_1 @ (f @ b) @ X0) != $true)) )),
% 1.71/1.34 inference(superposition,[status(thm)],[f25,f10])).
% 1.71/1.34 thf(f10,plain,(
% 1.71/1.34 ((cQ_1 @ a @ b @ c) = $true)),
% 1.71/1.34 inference(cnf_transformation,[status(thm)],[f7])).
% 1.71/1.34 thf(f25,plain,(
% 1.71/1.34 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((cQ_1 @ X7 @ X6 @ X8) != $true) | ($true != (cP_2 @ (f @ X1) @ X3)) | ($true != (cP_1 @ (f @ X7) @ X0)) | ($true != (cP_1 @ (f @ X6) @ X1)) | ((cP_2 @ (f @ X2) @ X5) != $true) | ($true != (cP_1 @ (f @ X8) @ X2)) | ($true != (cP_2 @ (f @ X0) @ X4))) )),
% 1.71/1.34 inference(trivial_inequality_removal,[status(thm)],[f24])).
% 1.71/1.34 thf(f24,plain,(
% 1.71/1.34 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true != (cP_2 @ (f @ X1) @ X3)) | ($true != (cP_1 @ (f @ X7) @ X0)) | ($true != (cP_2 @ (f @ X0) @ X4)) | ((cQ_1 @ X7 @ X6 @ X8) != $true) | ($true != (cP_1 @ (f @ X6) @ X1)) | ($true != $true) | ((cP_2 @ (f @ X2) @ X5) != $true) | ($true != (cP_1 @ (f @ X8) @ X2))) )),
% 1.71/1.34 inference(superposition,[status(thm)],[f23,f13])).
% 1.71/1.34 thf(f13,plain,(
% 1.71/1.34 ( ! [X16 : $i,X14 : $i,X17 : $i,X15 : $i,X12 : $i,X13 : $i] : (($true = (cQ_2 @ X16 @ X15 @ X17)) | ($true != (cP_1 @ (f @ X14) @ X15)) | ($true != (cP_1 @ (f @ X13) @ X16)) | ($true != (cP_1 @ (f @ X12) @ X17)) | ((cQ_1 @ X13 @ X14 @ X12) != $true)) )),
% 1.71/1.34 inference(cnf_transformation,[status(thm)],[f7])).
% 1.71/1.34 thf(f23,plain,(
% 1.71/1.34 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (((cQ_2 @ X4 @ X3 @ X5) != $true) | ((cP_2 @ (f @ X3) @ X1) != $true) | ($true != (cP_2 @ (f @ X4) @ X0)) | ((cP_2 @ (f @ X5) @ X2) != $true)) )),
% 1.71/1.34 inference(trivial_inequality_removal,[status(thm)],[f22])).
% 1.71/1.34 thf(f22,plain,(
% 1.71/1.34 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (((cQ_2 @ X4 @ X3 @ X5) != $true) | ((cP_2 @ (f @ X3) @ X1) != $true) | ($true != $true) | ($true != (cP_2 @ (f @ X4) @ X0)) | ((cP_2 @ (f @ X5) @ X2) != $true)) )),
% 1.71/1.34 inference(superposition,[status(thm)],[f20,f14])).
% 1.71/1.34 thf(f14,plain,(
% 1.71/1.34 ( ! [X10 : $i,X11 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (($true = (cQ_3 @ X10 @ X8 @ X11)) | ((cP_2 @ (f @ X6) @ X8) != $true) | ($true != (cP_2 @ (f @ X7) @ X10)) | ((cP_2 @ (f @ X9) @ X11) != $true) | ($true != (cQ_2 @ X7 @ X6 @ X9))) )),
% 1.71/1.34 inference(cnf_transformation,[status(thm)],[f7])).
% 1.71/1.34 thf(f20,plain,(
% 1.71/1.34 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true != (cQ_3 @ X1 @ X2 @ X3))) )),
% 1.71/1.34 inference(cnf_transformation,[status(thm)],[f7])).
% 1.71/1.34 % SZS output end Proof for DTF2THF_28132
% 1.71/1.34 % (28363)------------------------------
% 1.71/1.34 % (28363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.34 % (28363)Termination reason: Refutation
% 1.71/1.34
% 1.71/1.34 % (28363)Memory used [KB]: 5628
% 1.71/1.34 % (28363)Time elapsed: 0.013 s
% 1.71/1.34 % (28363)Instructions burned: 12 (million)
% 1.71/1.34 % (28363)------------------------------
% 1.71/1.34 % (28363)------------------------------
% 1.71/1.34 % (28362)Success in time 0.027 s
%------------------------------------------------------------------------------