%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO105^5 : 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 : n023.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 09:53:23 AM UTC 2026
% Result : Theorem 1.54s 1.35s
% Output : Refutation 1.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 19
% Syntax : Number of formulae : 67 ( 1 unt; 0 typ; 10 def)
% Number of atoms : 673 ( 147 equ; 0 cnn)
% Maximal formula atoms : 12 ( 10 avg)
% Number of connectives : 685 ( 155 ~; 103 |; 32 &; 351 @)
% ( 15 <=>; 28 =>; 0 <=; 1 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 22 usr; 17 con; 0-3 aty)
% Number of variables : 167 ( 0 ^; 105 !; 62 ?; 167 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cR: $i > $o ).
thf(func_def_2,type,
cP: $i > $i > $i > $o ).
thf(func_def_3,type,
cQ: $i > $i > $o ).
thf(func_def_9,type,
sK2: $i > $i ).
thf(func_def_10,type,
sK3: $i > $i > $i ).
thf(func_def_11,type,
sK4: $i > $i ).
thf(func_def_14,type,
sK7: $i > $i ).
thf(f89,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f58,f59,f63,f67,f70,f72,f74,f76,f79,f82,f85,f88]) ).
thf(f88,plain,
( ~ spl8_7
| ~ spl8_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f87]) ).
thf(f87,plain,
( $false
| ~ spl8_7
| ~ spl8_9 ),
inference(trivial_inequality_removal,[status(thm)],[f86]) ).
thf(f86,plain,
( ( $true != $true )
| ~ spl8_7
| ~ spl8_9 ),
inference(superposition,[status(thm)],[f52,f62]) ).
thf(f62,plain,
( ! [X1: $i] :
( ( cP @ X1 @ y @ sK0 )
= $true )
| ~ spl8_9 ),
inference(avatar_component_clause,[status(thm)],[f61]) ).
thf(f61,definition,
( spl8_9
<=> ! [X1: $i] :
( ( cP @ X1 @ y @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl8_9])],[avatar_definition]) ).
thf(f52,plain,
( ! [X13: $i] :
( $true
!= ( cP @ ( sK7 @ X13 ) @ y @ X13 ) )
| ~ spl8_7 ),
inference(avatar_component_clause,[status(thm)],[f51]) ).
thf(f51,definition,
( spl8_7
<=> ! [X13: $i] :
( $true
!= ( cP @ ( sK7 @ X13 ) @ y @ X13 ) ) ),
introduced(definition,[new_symbols(naming,[spl8_7])],[avatar_definition]) ).
thf(f85,plain,
( spl8_2
| ~ spl8_3
| ~ spl8_7 ),
inference(avatar_split_clause,[status(thm)],[f84,f51,f36,f33]) ).
thf(f33,definition,
( spl8_2
<=> ! [X3: $i] :
( ( cQ @ X3 @ y )
!= $true ) ),
introduced(definition,[new_symbols(naming,[spl8_2])],[avatar_definition]) ).
thf(f36,definition,
( spl8_3
<=> ! [X6: $i,X4: $i] :
( ( ( cP @ X6 @ y @ ( sK2 @ X4 ) )
= $true )
| ( $true
!= ( cQ @ X4 @ y ) ) ) ),
introduced(definition,[new_symbols(naming,[spl8_3])],[avatar_definition]) ).
thf(f84,plain,
( ! [X0: $i] :
( ( cQ @ X0 @ y )
!= $true )
| ~ spl8_3
| ~ spl8_7 ),
inference(trivial_inequality_removal,[status(thm)],[f83]) ).
thf(f83,plain,
( ! [X0: $i] :
( ( ( cQ @ X0 @ y )
!= $true )
| ( $true != $true ) )
| ~ spl8_3
| ~ spl8_7 ),
inference(superposition,[status(thm)],[f52,f37]) ).
thf(f37,plain,
( ! [X6: $i,X4: $i] :
( ( ( cP @ X6 @ y @ ( sK2 @ X4 ) )
= $true )
| ( $true
!= ( cQ @ X4 @ y ) ) )
| ~ spl8_3 ),
inference(avatar_component_clause,[status(thm)],[f36]) ).
thf(f82,plain,
( spl8_2
| ~ spl8_3
| ~ spl8_4 ),
inference(avatar_split_clause,[status(thm)],[f81,f40,f36,f33]) ).
thf(f40,definition,
( spl8_4
<=> ! [X8: $i] :
( $true
!= ( cP @ ( sK4 @ X8 ) @ y @ X8 ) ) ),
introduced(definition,[new_symbols(naming,[spl8_4])],[avatar_definition]) ).
thf(f81,plain,
( ! [X0: $i] :
( ( cQ @ X0 @ y )
!= $true )
| ~ spl8_3
| ~ spl8_4 ),
inference(trivial_inequality_removal,[status(thm)],[f80]) ).
thf(f80,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( ( cQ @ X0 @ y )
!= $true ) )
| ~ spl8_3
| ~ spl8_4 ),
inference(superposition,[status(thm)],[f41,f37]) ).
thf(f41,plain,
( ! [X8: $i] :
( $true
!= ( cP @ ( sK4 @ X8 ) @ y @ X8 ) )
| ~ spl8_4 ),
inference(avatar_component_clause,[status(thm)],[f40]) ).
thf(f79,plain,
( ~ spl8_4
| ~ spl8_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f78]) ).
thf(f78,plain,
( $false
| ~ spl8_4
| ~ spl8_9 ),
inference(trivial_inequality_removal,[status(thm)],[f77]) ).
thf(f77,plain,
( ( $true != $true )
| ~ spl8_4
| ~ spl8_9 ),
inference(superposition,[status(thm)],[f41,f62]) ).
thf(f76,plain,
( ~ spl8_1
| ~ spl8_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f75]) ).
thf(f75,plain,
( $false
| ~ spl8_1
| ~ spl8_5 ),
inference(subsumption_resolution,[status(thm)],[f31,f44]) ).
thf(f44,plain,
( ! [X10: $i] :
( $true
!= ( cR @ X10 ) )
| ~ spl8_5 ),
inference(avatar_component_clause,[status(thm)],[f43]) ).
thf(f43,definition,
( spl8_5
<=> ! [X10: $i] :
( $true
!= ( cR @ X10 ) ) ),
introduced(definition,[new_symbols(naming,[spl8_5])],[avatar_definition]) ).
thf(f31,plain,
( ( ( cR @ sK1 )
= $true )
| ~ spl8_1 ),
inference(avatar_component_clause,[status(thm)],[f29]) ).
thf(f29,definition,
( spl8_1
<=> ( ( cR @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl8_1])],[avatar_definition]) ).
thf(f74,plain,
( spl8_2
| ~ spl8_5
| ~ spl8_10 ),
inference(avatar_split_clause,[status(thm)],[f73,f65,f43,f33]) ).
thf(f65,definition,
( spl8_10
<=> ! [X6: $i,X4: $i] :
( ( $true
!= ( cQ @ X4 @ y ) )
| ( ( cR @ ( sK3 @ X6 @ X4 ) )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl8_10])],[avatar_definition]) ).
thf(f73,plain,
( ! [X4: $i] :
( $true
!= ( cQ @ X4 @ y ) )
| ~ spl8_5
| ~ spl8_10 ),
inference(subsumption_resolution,[status(thm)],[f66,f44]) ).
thf(f66,plain,
( ! [X6: $i,X4: $i] :
( ( ( cR @ ( sK3 @ X6 @ X4 ) )
= $true )
| ( $true
!= ( cQ @ X4 @ y ) ) )
| ~ spl8_10 ),
inference(avatar_component_clause,[status(thm)],[f65]) ).
thf(f72,plain,
( ~ spl8_2
| ~ spl8_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f71]) ).
thf(f71,plain,
( $false
| ~ spl8_2
| ~ spl8_8 ),
inference(subsumption_resolution,[status(thm)],[f56,f34]) ).
thf(f34,plain,
( ! [X3: $i] :
( ( cQ @ X3 @ y )
!= $true )
| ~ spl8_2 ),
inference(avatar_component_clause,[status(thm)],[f33]) ).
thf(f56,plain,
( ( ( cQ @ sK5 @ y )
= $true )
| ~ spl8_8 ),
inference(avatar_component_clause,[status(thm)],[f54]) ).
thf(f54,definition,
( spl8_8
<=> ( ( cQ @ sK5 @ y )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl8_8])],[avatar_definition]) ).
thf(f70,plain,
( ~ spl8_2
| ~ spl8_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f69]) ).
thf(f69,plain,
( $false
| ~ spl8_2
| ~ spl8_6 ),
inference(subsumption_resolution,[status(thm)],[f48,f34]) ).
thf(f48,plain,
( ( ( cQ @ sK6 @ y )
= $true )
| ~ spl8_6 ),
inference(avatar_component_clause,[status(thm)],[f46]) ).
thf(f46,definition,
( spl8_6
<=> ( ( cQ @ sK6 @ y )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl8_6])],[avatar_definition]) ).
thf(f67,plain,
( spl8_2
| spl8_10
| spl8_1 ),
inference(avatar_split_clause,[status(thm)],[f24,f29,f65,f33]) ).
thf(f24,plain,
! [X3: $i,X6: $i,X4: $i] :
( ( $true
!= ( cQ @ X4 @ y ) )
| ( ( cR @ sK1 )
= $true )
| ( ( cQ @ X3 @ y )
!= $true )
| ( ( cR @ ( sK3 @ X6 @ X4 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ( ! [X1: $i] :
( ( cP @ X1 @ y @ sK0 )
= $true )
& ( ( cR @ sK1 )
= $true ) )
| ! [X3: $i] :
( ( cQ @ X3 @ y )
!= $true )
| ! [X4: $i,X6: $i] :
( ( $true
!= ( cQ @ X4 @ y ) )
| ( ( ( cP @ X6 @ y @ ( sK2 @ X4 ) )
= $true )
& ( ( cR @ ( sK3 @ X6 @ X4 ) )
= $true ) ) ) )
& ( ( ! [X8: $i] :
( ( $true
!= ( cP @ ( sK4 @ X8 ) @ y @ X8 ) )
| ! [X10: $i] :
( $true
!= ( cR @ X10 ) ) )
& ( ( cQ @ sK5 @ y )
= $true ) )
| ! [X13: $i,X15: $i] :
( ( ( cQ @ sK6 @ y )
= $true )
& ( ( $true
!= ( cP @ ( sK7 @ X13 ) @ y @ X13 ) )
| ( ( cR @ X15 )
!= $true ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7])],[f10,f18,f17,f16,f15,f14,f13,f12,f11]) ).
thf(f11,plain,
( ? [X0: $i] :
( ! [X1: $i] :
( ( cP @ X1 @ y @ X0 )
= $true )
& ? [X2: $i] :
( $true
= ( cR @ X2 ) ) )
=> ( ! [X1: $i] :
( ( cP @ X1 @ y @ sK0 )
= $true )
& ? [X2: $i] :
( $true
= ( cR @ X2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ? [X2: $i] :
( $true
= ( cR @ X2 ) )
=> ( ( cR @ sK1 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
! [X4: $i] :
( ? [X5: $i] :
! [X6: $i] :
? [X7: $i] :
( ( $true
!= ( cQ @ X4 @ y ) )
| ( ( $true
= ( cP @ X6 @ y @ X5 ) )
& ( ( cR @ X7 )
= $true ) ) )
=> ! [X6: $i] :
? [X7: $i] :
( ( $true
!= ( cQ @ X4 @ y ) )
| ( ( ( cP @ X6 @ y @ ( sK2 @ X4 ) )
= $true )
& ( ( cR @ X7 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
! [X4: $i,X6: $i] :
( ? [X7: $i] :
( ( $true
!= ( cQ @ X4 @ y ) )
| ( ( ( cP @ X6 @ y @ ( sK2 @ X4 ) )
= $true )
& ( ( cR @ X7 )
= $true ) ) )
=> ( ( $true
!= ( cQ @ X4 @ y ) )
| ( ( ( cP @ X6 @ y @ ( sK2 @ X4 ) )
= $true )
& ( ( cR @ ( sK3 @ X6 @ X4 ) )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
! [X8: $i] :
( ? [X9: $i] :
( $true
!= ( cP @ X9 @ y @ X8 ) )
=> ( $true
!= ( cP @ ( sK4 @ X8 ) @ y @ X8 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
( ? [X11: $i] :
( ( cQ @ X11 @ y )
= $true )
=> ( ( cQ @ sK5 @ y )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
( ? [X12: $i] :
! [X13: $i] :
? [X14: $i] :
! [X15: $i] :
( ( ( cQ @ X12 @ y )
= $true )
& ( ( $true
!= ( cP @ X14 @ y @ X13 ) )
| ( ( cR @ X15 )
!= $true ) ) )
=> ! [X13: $i] :
? [X14: $i] :
! [X15: $i] :
( ( ( cQ @ sK6 @ y )
= $true )
& ( ( $true
!= ( cP @ X14 @ y @ X13 ) )
| ( ( cR @ X15 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
! [X13: $i] :
( ? [X14: $i] :
! [X15: $i] :
( ( ( cQ @ sK6 @ y )
= $true )
& ( ( $true
!= ( cP @ X14 @ y @ X13 ) )
| ( ( cR @ X15 )
!= $true ) ) )
=> ! [X15: $i] :
( ( ( cQ @ sK6 @ y )
= $true )
& ( ( $true
!= ( cP @ ( sK7 @ X13 ) @ y @ X13 ) )
| ( ( cR @ X15 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ( ? [X0: $i] :
( ! [X1: $i] :
( ( cP @ X1 @ y @ X0 )
= $true )
& ? [X2: $i] :
( $true
= ( cR @ X2 ) ) )
| ! [X3: $i] :
( ( cQ @ X3 @ y )
!= $true )
| ! [X4: $i] :
? [X5: $i] :
! [X6: $i] :
? [X7: $i] :
( ( $true
!= ( cQ @ X4 @ y ) )
| ( ( $true
= ( cP @ X6 @ y @ X5 ) )
& ( ( cR @ X7 )
= $true ) ) ) )
& ( ( ! [X8: $i] :
( ? [X9: $i] :
( $true
!= ( cP @ X9 @ y @ X8 ) )
| ! [X10: $i] :
( $true
!= ( cR @ X10 ) ) )
& ? [X11: $i] :
( ( cQ @ X11 @ y )
= $true ) )
| ? [X12: $i] :
! [X13: $i] :
? [X14: $i] :
! [X15: $i] :
( ( ( cQ @ X12 @ y )
= $true )
& ( ( $true
!= ( cP @ X14 @ y @ X13 ) )
| ( ( cR @ X15 )
!= $true ) ) ) ) ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ? [X5: $i] :
( ! [X6: $i] :
( $true
= ( cP @ X6 @ y @ X5 ) )
& ? [X7: $i] :
( ( cR @ X7 )
= $true ) )
| ! [X4: $i] :
( $true
!= ( cQ @ X4 @ y ) )
| ! [X0: $i] :
? [X1: $i] :
! [X2: $i] :
? [X3: $i] :
( ( ( cQ @ X0 @ y )
!= $true )
| ( ( ( cP @ X2 @ y @ X1 )
= $true )
& ( ( cR @ X3 )
= $true ) ) ) )
& ( ( ! [X5: $i] :
( ? [X6: $i] :
( $true
!= ( cP @ X6 @ y @ X5 ) )
| ! [X7: $i] :
( ( cR @ X7 )
!= $true ) )
& ? [X4: $i] :
( $true
= ( cQ @ X4 @ y ) ) )
| ? [X0: $i] :
! [X1: $i] :
? [X2: $i] :
! [X3: $i] :
( ( ( cQ @ X0 @ y )
= $true )
& ( ( ( cP @ X2 @ y @ X1 )
!= $true )
| ( ( cR @ X3 )
!= $true ) ) ) ) ),
inference(flattening,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ? [X5: $i] :
( ! [X6: $i] :
( $true
= ( cP @ X6 @ y @ X5 ) )
& ? [X7: $i] :
( ( cR @ X7 )
= $true ) )
| ! [X4: $i] :
( $true
!= ( cQ @ X4 @ y ) )
| ! [X0: $i] :
? [X1: $i] :
! [X2: $i] :
? [X3: $i] :
( ( ( cQ @ X0 @ y )
!= $true )
| ( ( ( cP @ X2 @ y @ X1 )
= $true )
& ( ( cR @ X3 )
= $true ) ) ) )
& ( ( ! [X5: $i] :
( ? [X6: $i] :
( $true
!= ( cP @ X6 @ y @ X5 ) )
| ! [X7: $i] :
( ( cR @ X7 )
!= $true ) )
& ? [X4: $i] :
( $true
= ( cQ @ X4 @ y ) ) )
| ? [X0: $i] :
! [X1: $i] :
? [X2: $i] :
! [X3: $i] :
( ( ( cQ @ X0 @ y )
= $true )
& ( ( ( cP @ X2 @ y @ X1 )
!= $true )
| ( ( cR @ X3 )
!= $true ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ? [X0: $i] :
! [X1: $i] :
? [X2: $i] :
! [X3: $i] :
( ( ( cQ @ X0 @ y )
= $true )
& ( ( ( cP @ X2 @ y @ X1 )
!= $true )
| ( ( cR @ X3 )
!= $true ) ) )
<~> ( ! [X5: $i] :
( ? [X6: $i] :
( $true
!= ( cP @ X6 @ y @ X5 ) )
| ! [X7: $i] :
( ( cR @ X7 )
!= $true ) )
& ? [X4: $i] :
( $true
= ( cQ @ X4 @ y ) ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ? [X0: $i] :
! [X1: $i] :
? [X2: $i] :
! [X3: $i] :
~ ( ( ( cQ @ X0 @ y )
= $true )
=> ~ ( ( ( cP @ X2 @ y @ X1 )
= $true )
=> ( ( cR @ X3 )
!= $true ) ) )
<=> ~ ( ? [X4: $i] :
( $true
= ( cQ @ X4 @ y ) )
=> ~ ! [X5: $i] :
( ! [X6: $i] :
( $true
= ( cP @ X6 @ y @ X5 ) )
=> ~ ? [X7: $i] :
( ( cR @ X7 )
= $true ) ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ? [X0: $i] :
! [X1: $i] :
? [X2: $i] :
! [X3: $i] :
~ ( ( ( cQ @ X0 @ y )
= $true )
=> ~ ( ( ( cP @ X2 @ y @ X1 )
= $true )
=> ( ( cR @ X3 )
!= $true ) ) )
<=> ~ ( ? [X4: $i] :
( $true
= ( cQ @ X4 @ y ) )
=> ~ ! [X5: $i] :
( ! [X6: $i] :
( $true
= ( cP @ X6 @ y @ X5 ) )
=> ~ ? [X7: $i] :
( ( cR @ X7 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ? [X0: $i] :
! [X1: $i] :
? [X2: $i] :
! [X3: $i] :
~ ( ( cQ @ X0 @ y )
=> ~ ( ( cP @ X2 @ y @ X1 )
=> ~ ( cR @ X3 ) ) )
<=> ~ ( ? [X4: $i] : ( cQ @ X4 @ y )
=> ~ ! [X5: $i] :
( ! [X6: $i] : ( cP @ X6 @ y @ X5 )
=> ~ ? [X7: $i] : ( cR @ X7 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ? [X0: $i] :
! [X1: $i] :
? [X2: $i] :
! [X3: $i] :
~ ( ( cQ @ X0 @ y )
=> ~ ( ( cP @ X2 @ y @ X1 )
=> ~ ( cR @ X3 ) ) )
<=> ~ ( ? [X0: $i] : ( cQ @ X0 @ y )
=> ~ ! [X1: $i] :
( ! [X2: $i] : ( cP @ X2 @ y @ X1 )
=> ~ ? [X3: $i] : ( cR @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ? [X0: $i] :
! [X1: $i] :
? [X2: $i] :
! [X3: $i] :
~ ( ( cQ @ X0 @ y )
=> ~ ( ( cP @ X2 @ y @ X1 )
=> ~ ( cR @ X3 ) ) )
<=> ~ ( ? [X0: $i] : ( cQ @ X0 @ y )
=> ~ ! [X1: $i] :
( ! [X2: $i] : ( cP @ X2 @ y @ X1 )
=> ~ ? [X3: $i] : ( cR @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Ojf7M1sxBm/DTF2THF_31665.p',cX2201TEST) ).
thf(f63,plain,
( spl8_2
| spl8_3
| spl8_9 ),
inference(avatar_split_clause,[status(thm)],[f27,f61,f36,f33]) ).
thf(f27,plain,
! [X3: $i,X1: $i,X6: $i,X4: $i] :
( ( ( cP @ X6 @ y @ ( sK2 @ X4 ) )
= $true )
| ( ( cP @ X1 @ y @ sK0 )
= $true )
| ( ( cQ @ X3 @ y )
!= $true )
| ( $true
!= ( cQ @ X4 @ y ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f59,plain,
( spl8_7
| spl8_5
| spl8_4
| spl8_5 ),
inference(avatar_split_clause,[status(thm)],[f22,f43,f40,f43,f51]) ).
thf(f22,plain,
! [X10: $i,X8: $i,X15: $i,X13: $i] :
( ( $true
!= ( cR @ X10 ) )
| ( ( cR @ X15 )
!= $true )
| ( $true
!= ( cP @ ( sK7 @ X13 ) @ y @ X13 ) )
| ( $true
!= ( cP @ ( sK4 @ X8 ) @ y @ X8 ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f58,plain,
( spl8_6
| spl8_8 ),
inference(avatar_split_clause,[status(thm)],[f21,f54,f46]) ).
thf(f21,plain,
( ( ( cQ @ sK5 @ y )
= $true )
| ( ( cQ @ sK6 @ y )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYO105^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.10 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n023.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 14:25:04 EST 2026
% 0.11/0.30 % CPUTime :
% 0.11/0.30 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.39 ---- Original DTF file ---
% 0.18/0.39 thf(spec,logic,$$dhol).
% 0.18/0.39 %------------------------------------------------------------------------------
% 0.18/0.39 % File : SYO105^5 : TPTP v9.2.1. Released v4.0.0.
% 0.18/0.39 % Domain : Syntactic
% 0.18/0.39 % Problem : TPS problem X2201TEST
% 0.18/0.39 % Version : Especial.
% 0.18/0.39 % English :
% 0.18/0.39
% 0.18/0.39 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.18/0.39 % Source : [Bro09]
% 0.18/0.39 % Names : tps_0395 [Bro09]
% 0.18/0.39 % : X2201TEST [TPS]
% 0.18/0.39
% 0.18/0.39 % Status : Theorem
% 0.18/0.39 % Rating : 0.17 v9.1.0, 0.12 v9.0.0, 0.17 v8.2.0, 0.18 v8.1.0, 0.08 v7.4.0, 0.11 v7.3.0, 0.10 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.33 v6.1.0, 0.17 v6.0.0, 0.00 v5.2.0, 0.25 v4.1.0, 0.00 v4.0.0
% 0.18/0.39 % Syntax : Number of formulae : 5 ( 0 unt; 4 typ; 0 def)
% 0.18/0.39 % Number of atoms : 6 ( 0 equ; 0 cnn)
% 0.18/0.39 % Maximal formula atoms : 6 ( 6 avg)
% 0.18/0.39 % Number of connectives : 23 ( 6 ~; 0 |; 0 &; 12 @)
% 0.18/0.39 % ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% 0.18/0.39 % Maximal formula depth : 13 ( 13 avg)
% 0.18/0.39 % Number of types : 2 ( 0 usr)
% 0.18/0.39 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.18/0.39 % Number of symbols : 4 ( 4 usr; 1 con; 0-3 aty)
% 0.18/0.39 % Number of variables : 8 ( 0 ^; 4 !; 4 ?; 8 :)
% 0.18/0.39 % SPC : TH0_THM_NEQ_NAR
% 0.18/0.39
% 0.18/0.39 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.18/0.39 % project in the Department of Mathematical Sciences at Carnegie
% 0.18/0.39 % Mellon University. Distributed under the Creative Commons copyleft
% 0.18/0.39 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.18/0.39 %------------------------------------------------------------------------------
% 0.18/0.39 thf(cR,type,
% 0.18/0.39 cR: $i > $o ).
% 0.18/0.39
% 0.18/0.39 thf(y,type,
% 0.18/0.39 y: $i ).
% 0.18/0.39
% 0.18/0.39 thf(cP,type,
% 0.18/0.39 cP: $i > $i > $i > $o ).
% 0.18/0.39
% 0.18/0.39 thf(cQ,type,
% 0.18/0.39 cQ: $i > $i > $o ).
% 0.18/0.39
% 0.18/0.39 thf(cX2201TEST,conjecture,
% 0.18/0.39 ( ~ ( ? [Xx: $i] : ( cQ @ Xx @ y )
% 0.18/0.39 => ~ ! [Xz: $i] :
% 0.18/0.39 ( ! [Xu: $i] : ( cP @ Xu @ y @ Xz )
% 0.18/0.39 => ~ ? [Xv: $i] : ( cR @ Xv ) ) )
% 0.18/0.39 <=> ? [Xx: $i] :
% 0.18/0.39 ! [Xz: $i] :
% 0.18/0.39 ? [Xu: $i] :
% 0.18/0.39 ! [Xv: $i] :
% 0.18/0.39 ~ ( ( cQ @ Xx @ y )
% 0.18/0.39 => ~ ( ( cP @ Xu @ y @ Xz )
% 0.18/0.39 => ~ ( cR @ Xv ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 %------------------------------------------------------------------------------
% 0.18/0.39 ------------------------
% 1.54/1.31 ---- Embedded in THF ---
% 1.54/1.31 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.54/1.31 %%% Generated on Tue Feb 24 14:25:05 EST 2026
% 1.54/1.31 %%% using '$$dhol' embedding, version 1.3.0.
% 1.54/1.31 %%% Logic specification used:
% 1.54/1.31 %%% thf(spec, logic, $$dhol).
% 1.54/1.31
% 1.54/1.31 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.Ojf7M1sxBm/DTF2DTF31665.p
% See solution above
% 1.54/1.31 ------------------------
% 1.54/1.32 ---- Cleaned THF ---
% 1.54/1.32 thf(cR,type,
% 1.54/1.32 cR: $i > $o ).
% 1.54/1.32
% 1.54/1.32 thf(y,type,
% 1.54/1.32 y: $i ).
% 1.54/1.32
% 1.54/1.32 thf(cP,type,
% 1.54/1.32 cP: $i > $i > $i > $o ).
% 1.54/1.32
% 1.54/1.32 thf(cQ,type,
% 1.54/1.32 cQ: $i > $i > $o ).
% 1.54/1.32
% 1.54/1.32 thf(cX2201TEST,conjecture,
% 1.54/1.32 ( ~ ( ? [Xx: $i] : ( cQ @ Xx @ y )
% 1.54/1.32 => ~ ! [Xz: $i] :
% 1.54/1.32 ( ! [Xu: $i] : ( cP @ Xu @ y @ Xz )
% 1.54/1.32 => ~ ? [Xv: $i] : ( cR @ Xv ) ) )
% 1.54/1.32 <=> ? [Xx: $i] :
% 1.54/1.32 ! [Xz: $i] :
% 1.54/1.32 ? [Xu: $i] :
% 1.54/1.32 ! [Xv: $i] :
% 1.54/1.32 ~ ( ( cQ @ Xx @ y )
% 1.54/1.32 => ~ ( ( cP @ Xu @ y @ Xz )
% 1.54/1.32 => ~ ( cR @ Xv ) ) ) ) ).
% 1.54/1.32 ------------------------
% 1.54/1.34 % (31767)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_31665 for (2999ds/275Mi)
% 1.54/1.34 % (31768)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_31665 for (2999ds/18Mi)
% 1.54/1.34 % (31766)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_31665 for (2999ds/2Mi)
% 1.54/1.34 % (31762)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_31665 for (2999ds/183Mi)
% 1.54/1.34 % (31764)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_31665 for (2999ds/27Mi)
% 1.54/1.34 % (31763)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_31665 for (2999ds/4Mi)
% 1.54/1.34 % (31765)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_31665 for (2999ds/2Mi)
% 1.54/1.34 % (31765)Instruction limit reached!
% 1.54/1.34 % (31765)------------------------------
% 1.54/1.34 % (31765)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.34 % (31765)Termination reason: Unknown
% 1.54/1.34 % (31765)Termination phase: Saturation
% 1.54/1.34
% 1.54/1.34 % (31765)Memory used [KB]: 1023
% 1.54/1.34 % (31765)Time elapsed: 0.003 s
% 1.54/1.34 % (31765)Instructions burned: 2 (million)
% 1.54/1.34 % (31765)------------------------------
% 1.54/1.34 % (31765)------------------------------
% 1.54/1.34 % (31766)Instruction limit reached!
% 1.54/1.34 % (31766)------------------------------
% 1.54/1.34 % (31766)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.34 % (31766)Termination reason: Unknown
% 1.54/1.34 % (31766)Termination phase: Saturation
% 1.54/1.34
% 1.54/1.34 % (31766)Memory used [KB]: 5373
% 1.54/1.34 % (31766)Time elapsed: 0.003 s
% 1.54/1.34 % (31766)Instructions burned: 2 (million)
% 1.54/1.34 % (31766)------------------------------
% 1.54/1.34 % (31766)------------------------------
% 1.54/1.34 % (31763)Instruction limit reached!
% 1.54/1.34 % (31763)------------------------------
% 1.54/1.34 % (31763)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.34 % (31763)Termination reason: Unknown
% 1.54/1.34 % (31763)Termination phase: Saturation
% 1.54/1.34
% 1.54/1.34 % (31763)Memory used [KB]: 5500
% 1.54/1.34 % (31763)Time elapsed: 0.005 s
% 1.54/1.34 % (31763)Instructions burned: 5 (million)
% 1.54/1.34 % (31763)------------------------------
% 1.54/1.34 % (31763)------------------------------
% 1.54/1.34 % (31762)First to succeed.
% 1.54/1.35 % (31767)Also succeeded, but the first one will report.
% 1.54/1.35 % (31768)Also succeeded, but the first one will report.
% 1.54/1.35 % (31762)Refutation found. Thanks to Tanya!
% 1.54/1.35 % SZS status Theorem for DTF2THF_31665
% 1.54/1.35 % SZS output start Proof for DTF2THF_31665
% 1.54/1.35 thf(func_def_0, type, cR: $i > $o).
% 1.54/1.35 thf(func_def_2, type, cP: $i > $i > $i > $o).
% 1.54/1.35 thf(func_def_3, type, cQ: $i > $i > $o).
% 1.54/1.35 thf(func_def_9, type, sK2: $i > $i).
% 1.54/1.35 thf(func_def_10, type, sK3: $i > $i > $i).
% 1.54/1.35 thf(func_def_11, type, sK4: $i > $i).
% 1.54/1.35 thf(func_def_14, type, sK7: $i > $i).
% 1.54/1.35 thf(f89,plain,(
% 1.54/1.35 $false),
% 1.54/1.35 inference(avatar_sat_refutation,[status(thm)],[f58,f59,f63,f67,f70,f72,f74,f76,f79,f82,f85,f88])).
% 1.54/1.35 thf(f88,plain,(
% 1.54/1.35 ~spl8_7 | ~spl8_9),
% 1.54/1.35 inference(avatar_contradiction_clause,[status(thm)],[f87])).
% 1.54/1.35 thf(f87,plain,(
% 1.54/1.35 $false | (~spl8_7 | ~spl8_9)),
% 1.54/1.35 inference(trivial_inequality_removal,[status(thm)],[f86])).
% 1.54/1.35 thf(f86,plain,(
% 1.54/1.35 ($true != $true) | (~spl8_7 | ~spl8_9)),
% 1.54/1.35 inference(superposition,[status(thm)],[f52,f62])).
% 1.54/1.35 thf(f62,plain,(
% 1.54/1.35 ( ! [X1 : $i] : (((cP @ X1 @ y @ sK0) = $true)) ) | ~spl8_9),
% 1.54/1.35 inference(avatar_component_clause,[status(thm)],[f61])).
% 1.54/1.35 thf(f61,definition,(
% 1.54/1.35 spl8_9 <=> ! [X1 : $i] : ((cP @ X1 @ y @ sK0) = $true)),
% 1.54/1.35 introduced(definition,[new_symbols(naming,[spl8_9])],[avatar_definition])).
% 1.54/1.35 thf(f52,plain,(
% 1.54/1.35 ( ! [X13 : $i] : (($true != (cP @ (sK7 @ X13) @ y @ X13))) ) | ~spl8_7),
% 1.54/1.35 inference(avatar_component_clause,[status(thm)],[f51])).
% 1.54/1.35 thf(f51,definition,(
% 1.54/1.35 spl8_7 <=> ! [X13 : $i] : ($true != (cP @ (sK7 @ X13) @ y @ X13))),
% 1.54/1.35 introduced(definition,[new_symbols(naming,[spl8_7])],[avatar_definition])).
% 1.54/1.35 thf(f85,plain,(
% 1.54/1.35 spl8_2 | ~spl8_3 | ~spl8_7),
% 1.54/1.35 inference(avatar_split_clause,[status(thm)],[f84,f51,f36,f33])).
% 1.54/1.35 thf(f33,definition,(
% 1.54/1.35 spl8_2 <=> ! [X3 : $i] : ((cQ @ X3 @ y) != $true)),
% 1.54/1.35 introduced(definition,[new_symbols(naming,[spl8_2])],[avatar_definition])).
% 1.54/1.35 thf(f36,definition,(
% 1.54/1.35 spl8_3 <=> ! [X6 : $i,X4 : $i] : (((cP @ X6 @ y @ (sK2 @ X4)) = $true) | ($true != (cQ @ X4 @ y)))),
% 1.54/1.35 introduced(definition,[new_symbols(naming,[spl8_3])],[avatar_definition])).
% 1.54/1.35 thf(f84,plain,(
% 1.54/1.35 ( ! [X0 : $i] : (((cQ @ X0 @ y) != $true)) ) | (~spl8_3 | ~spl8_7)),
% 1.54/1.35 inference(trivial_inequality_removal,[status(thm)],[f83])).
% 1.54/1.35 thf(f83,plain,(
% 1.54/1.35 ( ! [X0 : $i] : (((cQ @ X0 @ y) != $true) | ($true != $true)) ) | (~spl8_3 | ~spl8_7)),
% 1.54/1.35 inference(superposition,[status(thm)],[f52,f37])).
% 1.54/1.35 thf(f37,plain,(
% 1.54/1.35 ( ! [X6 : $i,X4 : $i] : (((cP @ X6 @ y @ (sK2 @ X4)) = $true) | ($true != (cQ @ X4 @ y))) ) | ~spl8_3),
% 1.54/1.35 inference(avatar_component_clause,[status(thm)],[f36])).
% 1.54/1.35 thf(f82,plain,(
% 1.54/1.35 spl8_2 | ~spl8_3 | ~spl8_4),
% 1.54/1.35 inference(avatar_split_clause,[status(thm)],[f81,f40,f36,f33])).
% 1.54/1.35 thf(f40,definition,(
% 1.54/1.35 spl8_4 <=> ! [X8 : $i] : ($true != (cP @ (sK4 @ X8) @ y @ X8))),
% 1.54/1.35 introduced(definition,[new_symbols(naming,[spl8_4])],[avatar_definition])).
% 1.54/1.35 thf(f81,plain,(
% 1.54/1.35 ( ! [X0 : $i] : (((cQ @ X0 @ y) != $true)) ) | (~spl8_3 | ~spl8_4)),
% 1.54/1.35 inference(trivial_inequality_removal,[status(thm)],[f80])).
% 1.54/1.35 thf(f80,plain,(
% 1.54/1.35 ( ! [X0 : $i] : (($true != $true) | ((cQ @ X0 @ y) != $true)) ) | (~spl8_3 | ~spl8_4)),
% 1.54/1.35 inference(superposition,[status(thm)],[f41,f37])).
% 1.54/1.35 thf(f41,plain,(
% 1.54/1.35 ( ! [X8 : $i] : (($true != (cP @ (sK4 @ X8) @ y @ X8))) ) | ~spl8_4),
% 1.54/1.35 inference(avatar_component_clause,[status(thm)],[f40])).
% 1.54/1.35 thf(f79,plain,(
% 1.54/1.35 ~spl8_4 | ~spl8_9),
% 1.54/1.35 inference(avatar_contradiction_clause,[status(thm)],[f78])).
% 1.54/1.35 thf(f78,plain,(
% 1.54/1.35 $false | (~spl8_4 | ~spl8_9)),
% 1.54/1.35 inference(trivial_inequality_removal,[status(thm)],[f77])).
% 1.54/1.35 thf(f77,plain,(
% 1.54/1.35 ($true != $true) | (~spl8_4 | ~spl8_9)),
% 1.54/1.35 inference(superposition,[status(thm)],[f41,f62])).
% 1.54/1.35 thf(f76,plain,(
% 1.54/1.35 ~spl8_1 | ~spl8_5),
% 1.54/1.35 inference(avatar_contradiction_clause,[status(thm)],[f75])).
% 1.54/1.35 thf(f75,plain,(
% 1.54/1.35 $false | (~spl8_1 | ~spl8_5)),
% 1.54/1.35 inference(subsumption_resolution,[status(thm)],[f31,f44])).
% 1.54/1.35 thf(f44,plain,(
% 1.54/1.35 ( ! [X10 : $i] : (($true != (cR @ X10))) ) | ~spl8_5),
% 1.54/1.35 inference(avatar_component_clause,[status(thm)],[f43])).
% 1.54/1.35 thf(f43,definition,(
% 1.54/1.35 spl8_5 <=> ! [X10 : $i] : ($true != (cR @ X10))),
% 1.54/1.35 introduced(definition,[new_symbols(naming,[spl8_5])],[avatar_definition])).
% 1.54/1.35 thf(f31,plain,(
% 1.54/1.35 ((cR @ sK1) = $true) | ~spl8_1),
% 1.54/1.35 inference(avatar_component_clause,[status(thm)],[f29])).
% 1.54/1.35 thf(f29,definition,(
% 1.54/1.35 spl8_1 <=> ((cR @ sK1) = $true)),
% 1.54/1.35 introduced(definition,[new_symbols(naming,[spl8_1])],[avatar_definition])).
% 1.54/1.35 thf(f74,plain,(
% 1.54/1.35 spl8_2 | ~spl8_5 | ~spl8_10),
% 1.54/1.35 inference(avatar_split_clause,[status(thm)],[f73,f65,f43,f33])).
% 1.54/1.35 thf(f65,definition,(
% 1.54/1.35 spl8_10 <=> ! [X6 : $i,X4 : $i] : (($true != (cQ @ X4 @ y)) | ((cR @ (sK3 @ X6 @ X4)) = $true))),
% 1.54/1.35 introduced(definition,[new_symbols(naming,[spl8_10])],[avatar_definition])).
% 1.54/1.35 thf(f73,plain,(
% 1.54/1.35 ( ! [X4 : $i] : (($true != (cQ @ X4 @ y))) ) | (~spl8_5 | ~spl8_10)),
% 1.54/1.35 inference(subsumption_resolution,[status(thm)],[f66,f44])).
% 1.54/1.35 thf(f66,plain,(
% 1.54/1.35 ( ! [X6 : $i,X4 : $i] : (((cR @ (sK3 @ X6 @ X4)) = $true) | ($true != (cQ @ X4 @ y))) ) | ~spl8_10),
% 1.54/1.35 inference(avatar_component_clause,[status(thm)],[f65])).
% 1.54/1.35 thf(f72,plain,(
% 1.54/1.35 ~spl8_2 | ~spl8_8),
% 1.54/1.35 inference(avatar_contradiction_clause,[status(thm)],[f71])).
% 1.54/1.35 thf(f71,plain,(
% 1.54/1.35 $false | (~spl8_2 | ~spl8_8)),
% 1.54/1.35 inference(subsumption_resolution,[status(thm)],[f56,f34])).
% 1.54/1.35 thf(f34,plain,(
% 1.54/1.35 ( ! [X3 : $i] : (((cQ @ X3 @ y) != $true)) ) | ~spl8_2),
% 1.54/1.35 inference(avatar_component_clause,[status(thm)],[f33])).
% 1.54/1.35 thf(f56,plain,(
% 1.54/1.35 ((cQ @ sK5 @ y) = $true) | ~spl8_8),
% 1.54/1.35 inference(avatar_component_clause,[status(thm)],[f54])).
% 1.54/1.35 thf(f54,definition,(
% 1.54/1.35 spl8_8 <=> ((cQ @ sK5 @ y) = $true)),
% 1.54/1.35 introduced(definition,[new_symbols(naming,[spl8_8])],[avatar_definition])).
% 1.54/1.35 thf(f70,plain,(
% 1.54/1.35 ~spl8_2 | ~spl8_6),
% 1.54/1.35 inference(avatar_contradiction_clause,[status(thm)],[f69])).
% 1.54/1.35 thf(f69,plain,(
% 1.54/1.35 $false | (~spl8_2 | ~spl8_6)),
% 1.54/1.35 inference(subsumption_resolution,[status(thm)],[f48,f34])).
% 1.54/1.35 thf(f48,plain,(
% 1.54/1.35 ((cQ @ sK6 @ y) = $true) | ~spl8_6),
% 1.54/1.35 inference(avatar_component_clause,[status(thm)],[f46])).
% 1.54/1.35 thf(f46,definition,(
% 1.54/1.35 spl8_6 <=> ((cQ @ sK6 @ y) = $true)),
% 1.54/1.35 introduced(definition,[new_symbols(naming,[spl8_6])],[avatar_definition])).
% 1.54/1.35 thf(f67,plain,(
% 1.54/1.35 spl8_2 | spl8_10 | spl8_1),
% 1.54/1.35 inference(avatar_split_clause,[status(thm)],[f24,f29,f65,f33])).
% 1.54/1.35 thf(f24,plain,(
% 1.54/1.35 ( ! [X3 : $i,X6 : $i,X4 : $i] : (($true != (cQ @ X4 @ y)) | ((cR @ sK1) = $true) | ((cQ @ X3 @ y) != $true) | ((cR @ (sK3 @ X6 @ X4)) = $true)) )),
% 1.54/1.35 inference(cnf_transformation,[status(thm)],[f19])).
% 1.54/1.35 thf(f19,plain,(
% 1.54/1.35 ((! [X1 : $i] : ((cP @ X1 @ y @ sK0) = $true) & ((cR @ sK1) = $true)) | ! [X3 : $i] : ((cQ @ X3 @ y) != $true) | ! [X4 : $i] : ! [X6 : $i] : (($true != (cQ @ X4 @ y)) | (((cP @ X6 @ y @ (sK2 @ X4)) = $true) & ((cR @ (sK3 @ X6 @ X4)) = $true)))) & ((! [X8 : $i] : (($true != (cP @ (sK4 @ X8) @ y @ X8)) | ! [X10 : $i] : ($true != (cR @ X10))) & ((cQ @ sK5 @ y) = $true)) | ! [X13 : $i] : ! [X15 : $i] : (((cQ @ sK6 @ y) = $true) & (($true != (cP @ (sK7 @ X13) @ y @ X13)) | ((cR @ X15) != $true))))),
% 1.54/1.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7])],[f10,f18,f17,f16,f15,f14,f13,f12,f11])).
% 1.54/1.35 thf(f11,plain,(
% 1.54/1.35 ? [X0 : $i] : (! [X1 : $i] : ((cP @ X1 @ y @ X0) = $true) & ? [X2 : $i] : ($true = (cR @ X2))) => (! [X1 : $i] : ((cP @ X1 @ y @ sK0) = $true) & ? [X2 : $i] : ($true = (cR @ X2)))),
% 1.54/1.35 introduced(definition,[],[choice_axiom])).
% 1.54/1.35 thf(f12,plain,(
% 1.54/1.35 ? [X2 : $i] : ($true = (cR @ X2)) => ((cR @ sK1) = $true)),
% 1.54/1.35 introduced(definition,[],[choice_axiom])).
% 1.54/1.35 thf(f13,plain,(
% 1.54/1.35 ! [X4 : $i] : (? [X5 : $i] : ! [X6 : $i] : ? [X7 : $i] : (($true != (cQ @ X4 @ y)) | (($true = (cP @ X6 @ y @ X5)) & ((cR @ X7) = $true))) => ! [X6 : $i] : ? [X7 : $i] : (($true != (cQ @ X4 @ y)) | (((cP @ X6 @ y @ (sK2 @ X4)) = $true) & ((cR @ X7) = $true))))),
% 1.54/1.35 introduced(definition,[],[choice_axiom])).
% 1.54/1.35 thf(f14,plain,(
% 1.54/1.35 ! [X4 : $i,X6 : $i] : (? [X7 : $i] : (($true != (cQ @ X4 @ y)) | (((cP @ X6 @ y @ (sK2 @ X4)) = $true) & ((cR @ X7) = $true))) => (($true != (cQ @ X4 @ y)) | (((cP @ X6 @ y @ (sK2 @ X4)) = $true) & ((cR @ (sK3 @ X6 @ X4)) = $true))))),
% 1.54/1.35 introduced(definition,[],[choice_axiom])).
% 1.54/1.35 thf(f15,plain,(
% 1.54/1.35 ! [X8 : $i] : (? [X9 : $i] : ($true != (cP @ X9 @ y @ X8)) => ($true != (cP @ (sK4 @ X8) @ y @ X8)))),
% 1.54/1.35 introduced(definition,[],[choice_axiom])).
% 1.54/1.35 thf(f16,plain,(
% 1.54/1.35 ? [X11 : $i] : ((cQ @ X11 @ y) = $true) => ((cQ @ sK5 @ y) = $true)),
% 1.54/1.35 introduced(definition,[],[choice_axiom])).
% 1.54/1.35 thf(f17,plain,(
% 1.54/1.35 ? [X12 : $i] : ! [X13 : $i] : ? [X14 : $i] : ! [X15 : $i] : (((cQ @ X12 @ y) = $true) & (($true != (cP @ X14 @ y @ X13)) | ((cR @ X15) != $true))) => ! [X13 : $i] : ? [X14 : $i] : ! [X15 : $i] : (((cQ @ sK6 @ y) = $true) & (($true != (cP @ X14 @ y @ X13)) | ((cR @ X15) != $true)))),
% 1.54/1.35 introduced(definition,[],[choice_axiom])).
% 1.54/1.35 thf(f18,plain,(
% 1.54/1.35 ! [X13 : $i] : (? [X14 : $i] : ! [X15 : $i] : (((cQ @ sK6 @ y) = $true) & (($true != (cP @ X14 @ y @ X13)) | ((cR @ X15) != $true))) => ! [X15 : $i] : (((cQ @ sK6 @ y) = $true) & (($true != (cP @ (sK7 @ X13) @ y @ X13)) | ((cR @ X15) != $true))))),
% 1.54/1.35 introduced(definition,[],[choice_axiom])).
% 1.54/1.35 thf(f10,plain,(
% 1.54/1.35 (? [X0 : $i] : (! [X1 : $i] : ((cP @ X1 @ y @ X0) = $true) & ? [X2 : $i] : ($true = (cR @ X2))) | ! [X3 : $i] : ((cQ @ X3 @ y) != $true) | ! [X4 : $i] : ? [X5 : $i] : ! [X6 : $i] : ? [X7 : $i] : (($true != (cQ @ X4 @ y)) | (($true = (cP @ X6 @ y @ X5)) & ((cR @ X7) = $true)))) & ((! [X8 : $i] : (? [X9 : $i] : ($true != (cP @ X9 @ y @ X8)) | ! [X10 : $i] : ($true != (cR @ X10))) & ? [X11 : $i] : ((cQ @ X11 @ y) = $true)) | ? [X12 : $i] : ! [X13 : $i] : ? [X14 : $i] : ! [X15 : $i] : (((cQ @ X12 @ y) = $true) & (($true != (cP @ X14 @ y @ X13)) | ((cR @ X15) != $true))))),
% 1.54/1.35 inference(rectify,[status(thm)],[f9])).
% 1.54/1.35 thf(f9,plain,(
% 1.54/1.35 (? [X5 : $i] : (! [X6 : $i] : ($true = (cP @ X6 @ y @ X5)) & ? [X7 : $i] : ((cR @ X7) = $true)) | ! [X4 : $i] : ($true != (cQ @ X4 @ y)) | ! [X0 : $i] : ? [X1 : $i] : ! [X2 : $i] : ? [X3 : $i] : (((cQ @ X0 @ y) != $true) | (((cP @ X2 @ y @ X1) = $true) & ((cR @ X3) = $true)))) & ((! [X5 : $i] : (? [X6 : $i] : ($true != (cP @ X6 @ y @ X5)) | ! [X7 : $i] : ((cR @ X7) != $true)) & ? [X4 : $i] : ($true = (cQ @ X4 @ y))) | ? [X0 : $i] : ! [X1 : $i] : ? [X2 : $i] : ! [X3 : $i] : (((cQ @ X0 @ y) = $true) & (((cP @ X2 @ y @ X1) != $true) | ((cR @ X3) != $true))))),
% 1.54/1.35 inference(flattening,[status(thm)],[f8])).
% 1.54/1.35 thf(f8,plain,(
% 1.54/1.35 ((? [X5 : $i] : (! [X6 : $i] : ($true = (cP @ X6 @ y @ X5)) & ? [X7 : $i] : ((cR @ X7) = $true)) | ! [X4 : $i] : ($true != (cQ @ X4 @ y))) | ! [X0 : $i] : ? [X1 : $i] : ! [X2 : $i] : ? [X3 : $i] : (((cQ @ X0 @ y) != $true) | (((cP @ X2 @ y @ X1) = $true) & ((cR @ X3) = $true)))) & ((! [X5 : $i] : (? [X6 : $i] : ($true != (cP @ X6 @ y @ X5)) | ! [X7 : $i] : ((cR @ X7) != $true)) & ? [X4 : $i] : ($true = (cQ @ X4 @ y))) | ? [X0 : $i] : ! [X1 : $i] : ? [X2 : $i] : ! [X3 : $i] : (((cQ @ X0 @ y) = $true) & (((cP @ X2 @ y @ X1) != $true) | ((cR @ X3) != $true))))),
% 1.54/1.35 inference(nnf_transformation,[status(thm)],[f7])).
% 1.54/1.35 thf(f7,plain,(
% 1.54/1.35 ? [X0 : $i] : ! [X1 : $i] : ? [X2 : $i] : ! [X3 : $i] : (((cQ @ X0 @ y) = $true) & (((cP @ X2 @ y @ X1) != $true) | ((cR @ X3) != $true))) <~> (! [X5 : $i] : (? [X6 : $i] : ($true != (cP @ X6 @ y @ X5)) | ! [X7 : $i] : ((cR @ X7) != $true)) & ? [X4 : $i] : ($true = (cQ @ X4 @ y)))),
% 1.54/1.35 inference(ennf_transformation,[status(thm)],[f6])).
% 1.54/1.35 thf(f6,plain,(
% 1.54/1.35 ~(? [X0 : $i] : ! [X1 : $i] : ? [X2 : $i] : ! [X3 : $i] : ~(((cQ @ X0 @ y) = $true) => ~(((cP @ X2 @ y @ X1) = $true) => ((cR @ X3) != $true))) <=> ~(? [X4 : $i] : ($true = (cQ @ X4 @ y)) => ~! [X5 : $i] : (! [X6 : $i] : ($true = (cP @ X6 @ y @ X5)) => ~? [X7 : $i] : ((cR @ X7) = $true))))),
% 1.54/1.35 inference(flattening,[status(thm)],[f5])).
% 1.54/1.35 thf(f5,plain,(
% 1.54/1.35 ~(? [X0 : $i] : ! [X1 : $i] : ? [X2 : $i] : ! [X3 : $i] : ~(((cQ @ X0 @ y) = $true) => ~(((cP @ X2 @ y @ X1) = $true) => ~((cR @ X3) = $true))) <=> ~(? [X4 : $i] : ($true = (cQ @ X4 @ y)) => ~! [X5 : $i] : (! [X6 : $i] : ($true = (cP @ X6 @ y @ X5)) => ~? [X7 : $i] : ((cR @ X7) = $true))))),
% 1.54/1.35 inference(fool_elimination,[status(thm)],[f4])).
% 1.54/1.35 thf(f4,plain,(
% 1.54/1.35 ~(? [X0 : $i] : ! [X1 : $i] : ? [X2 : $i] : ! [X3 : $i] : ~((cQ @ X0 @ y) => ~((cP @ X2 @ y @ X1) => ~(cR @ X3))) <=> ~(? [X4 : $i] : (cQ @ X4 @ y) => ~! [X5 : $i] : (! [X6 : $i] : (cP @ X6 @ y @ X5) => ~? [X7 : $i] : (cR @ X7))))),
% 1.54/1.35 inference(rectify,[status(thm)],[f2])).
% 1.54/1.35 thf(f2,negated_conjecture,(
% 1.54/1.35 ~(? [X0 : $i] : ! [X1 : $i] : ? [X2 : $i] : ! [X3 : $i] : ~((cQ @ X0 @ y) => ~((cP @ X2 @ y @ X1) => ~(cR @ X3))) <=> ~(? [X0 : $i] : (cQ @ X0 @ y) => ~! [X1 : $i] : (! [X2 : $i] : (cP @ X2 @ y @ X1) => ~? [X3 : $i] : (cR @ X3))))),
% 1.54/1.35 inference(negated_conjecture,[status(cth)],[f1])).
% 1.54/1.35 thf(f1,conjecture,(
% 1.54/1.35 ? [X0 : $i] : ! [X1 : $i] : ? [X2 : $i] : ! [X3 : $i] : ~((cQ @ X0 @ y) => ~((cP @ X2 @ y @ X1) => ~(cR @ X3))) <=> ~(? [X0 : $i] : (cQ @ X0 @ y) => ~! [X1 : $i] : (! [X2 : $i] : (cP @ X2 @ y @ X1) => ~? [X3 : $i] : (cR @ X3)))),
% 1.54/1.35 file('/export/starexec/sandbox2/tmp/tmp.Ojf7M1sxBm/DTF2THF_31665.p',cX2201TEST)).
% 1.54/1.35 thf(f63,plain,(
% 1.54/1.35 spl8_2 | spl8_3 | spl8_9),
% 1.54/1.35 inference(avatar_split_clause,[status(thm)],[f27,f61,f36,f33])).
% 1.54/1.35 thf(f27,plain,(
% 1.54/1.35 ( ! [X3 : $i,X1 : $i,X6 : $i,X4 : $i] : (((cP @ X6 @ y @ (sK2 @ X4)) = $true) | ((cP @ X1 @ y @ sK0) = $true) | ((cQ @ X3 @ y) != $true) | ($true != (cQ @ X4 @ y))) )),
% 1.54/1.35 inference(cnf_transformation,[status(thm)],[f19])).
% 1.54/1.35 thf(f59,plain,(
% 1.54/1.35 spl8_7 | spl8_5 | spl8_4 | spl8_5),
% 1.54/1.35 inference(avatar_split_clause,[status(thm)],[f22,f43,f40,f43,f51])).
% 1.54/1.35 thf(f22,plain,(
% 1.54/1.35 ( ! [X10 : $i,X8 : $i,X15 : $i,X13 : $i] : (($true != (cR @ X10)) | ((cR @ X15) != $true) | ($true != (cP @ (sK7 @ X13) @ y @ X13)) | ($true != (cP @ (sK4 @ X8) @ y @ X8))) )),
% 1.54/1.35 inference(cnf_transformation,[status(thm)],[f19])).
% 1.54/1.35 thf(f58,plain,(
% 1.54/1.35 spl8_6 | spl8_8),
% 1.54/1.35 inference(avatar_split_clause,[status(thm)],[f21,f54,f46])).
% 1.54/1.35 thf(f21,plain,(
% 1.54/1.35 ((cQ @ sK5 @ y) = $true) | ((cQ @ sK6 @ y) = $true)),
% 1.54/1.35 inference(cnf_transformation,[status(thm)],[f19])).
% 1.54/1.35 % SZS output end Proof for DTF2THF_31665
% 1.54/1.35 % (31762)------------------------------
% 1.54/1.35 % (31762)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.35 % (31762)Termination reason: Refutation
% 1.54/1.35
% 1.54/1.35 % (31762)Memory used [KB]: 5628
% 1.54/1.35 % (31762)Time elapsed: 0.008 s
% 1.54/1.35 % (31762)Instructions burned: 6 (million)
% 1.54/1.35 % (31762)------------------------------
% 1.54/1.35 % (31762)------------------------------
% 1.54/1.35 % (31761)Success in time 0.023 s
%------------------------------------------------------------------------------