%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV091^5 : 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 : n027.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 09:40:15 AM UTC 2026
% Result : Theorem 1.32s 1.14s
% Output : Refutation 1.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 5
% Syntax : Number of formulae : 62 ( 6 unt; 0 typ; 2 def)
% Number of atoms : 619 ( 150 equ; 0 cnn)
% Maximal formula atoms : 12 ( 9 avg)
% Number of connectives : 601 ( 104 ~; 101 |; 40 &; 336 @)
% ( 2 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 8 con; 0-2 aty)
% Number of variables : 136 ( 0 ^; 120 !; 16 ?; 136 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cQ: $i > $i > $o ).
thf(func_def_1,type,
cP: $i > $i > $o ).
thf(f137,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f56,f94,f136]) ).
thf(f136,plain,
spl4_2,
inference(avatar_contradiction_clause,[status(thm)],[f135]) ).
thf(f135,plain,
( $false
| spl4_2 ),
inference(subsumption_resolution,[status(thm)],[f133,f104]) ).
thf(f104,plain,
( ( $true
= ( cQ @ sK2 @ sK0 ) )
| spl4_2 ),
inference(trivial_inequality_removal,[status(thm)],[f102]) ).
thf(f102,plain,
( ( $true
= ( cQ @ sK2 @ sK0 ) )
| ( $true != $true )
| spl4_2 ),
inference(superposition,[status(thm)],[f99,f12]) ).
thf(f12,plain,
! [X12: $i,X13: $i] :
( ( $true
= ( cP @ X13 @ X12 ) )
| ( $true
= ( cQ @ X13 @ X12 ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( cP @ X0 @ X2 )
!= $true )
| ( $true
!= ( cP @ X2 @ X1 ) )
| ( ( cP @ X0 @ X1 )
= $true ) )
& ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( cQ @ X4 @ X3 ) )
| ( $true
= ( cQ @ X5 @ X3 ) )
| ( $true
!= ( cQ @ X5 @ X4 ) ) )
& ( $true
!= ( cP @ sK1 @ sK0 ) )
& ! [X8: $i,X9: $i] :
( ( $true
!= ( cQ @ X9 @ X8 ) )
| ( $true
= ( cQ @ X8 @ X9 ) ) )
& ( $true
!= ( cQ @ sK3 @ sK2 ) )
& ! [X12: $i,X13: $i] :
( ( $true
= ( cP @ X13 @ X12 ) )
| ( $true
= ( cQ @ X13 @ X12 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f10,f9]) ).
thf(f9,plain,
( ? [X6: $i,X7: $i] :
( $true
!= ( cP @ X7 @ X6 ) )
=> ( $true
!= ( cP @ sK1 @ sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X10: $i,X11: $i] :
( $true
!= ( cQ @ X11 @ X10 ) )
=> ( $true
!= ( cQ @ sK3 @ sK2 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( cP @ X0 @ X2 )
!= $true )
| ( $true
!= ( cP @ X2 @ X1 ) )
| ( ( cP @ X0 @ X1 )
= $true ) )
& ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( cQ @ X4 @ X3 ) )
| ( $true
= ( cQ @ X5 @ X3 ) )
| ( $true
!= ( cQ @ X5 @ X4 ) ) )
& ? [X6: $i,X7: $i] :
( $true
!= ( cP @ X7 @ X6 ) )
& ! [X8: $i,X9: $i] :
( ( $true
!= ( cQ @ X9 @ X8 ) )
| ( $true
= ( cQ @ X8 @ X9 ) ) )
& ? [X10: $i,X11: $i] :
( $true
!= ( cQ @ X11 @ X10 ) )
& ! [X12: $i,X13: $i] :
( ( $true
= ( cP @ X13 @ X12 ) )
| ( $true
= ( cQ @ X13 @ X12 ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X3: $i,X2: $i,X4: $i] :
( ( $true
!= ( cP @ X3 @ X4 ) )
| ( $true
!= ( cP @ X4 @ X2 ) )
| ( $true
= ( cP @ X3 @ X2 ) ) )
& ! [X8: $i,X7: $i,X9: $i] :
( ( $true
!= ( cQ @ X7 @ X8 ) )
| ( $true
= ( cQ @ X9 @ X8 ) )
| ( $true
!= ( cQ @ X9 @ X7 ) ) )
& ? [X10: $i,X11: $i] :
( $true
!= ( cP @ X11 @ X10 ) )
& ! [X6: $i,X5: $i] :
( ( $true
!= ( cQ @ X5 @ X6 ) )
| ( $true
= ( cQ @ X6 @ X5 ) ) )
& ? [X13: $i,X12: $i] :
( $true
!= ( cQ @ X12 @ X13 ) )
& ! [X0: $i,X1: $i] :
( ( $true
= ( cP @ X1 @ X0 ) )
| ( ( cQ @ X1 @ X0 )
= $true ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ? [X13: $i,X12: $i] :
( $true
!= ( cQ @ X12 @ X13 ) )
& ? [X10: $i,X11: $i] :
( $true
!= ( cP @ X11 @ X10 ) )
& ! [X6: $i,X5: $i] :
( ( $true
!= ( cQ @ X5 @ X6 ) )
| ( $true
= ( cQ @ X6 @ X5 ) ) )
& ! [X9: $i,X7: $i,X8: $i] :
( ( $true
= ( cQ @ X9 @ X8 ) )
| ( $true
!= ( cQ @ X9 @ X7 ) )
| ( $true
!= ( cQ @ X7 @ X8 ) ) )
& ! [X4: $i,X2: $i,X3: $i] :
( ( $true
= ( cP @ X3 @ X2 ) )
| ( $true
!= ( cP @ X3 @ X4 ) )
| ( $true
!= ( cP @ X4 @ X2 ) ) )
& ! [X0: $i,X1: $i] :
( ( $true
= ( cP @ X1 @ X0 ) )
| ( ( cQ @ X1 @ X0 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X6: $i,X5: $i] :
( ( $true
= ( cQ @ X5 @ X6 ) )
=> ( $true
= ( cQ @ X6 @ X5 ) ) )
& ! [X9: $i,X7: $i,X8: $i] :
( ( ( $true
= ( cQ @ X9 @ X7 ) )
& ( $true
= ( cQ @ X7 @ X8 ) ) )
=> ( $true
= ( cQ @ X9 @ X8 ) ) )
& ! [X4: $i,X2: $i,X3: $i] :
( ( ( $true
= ( cP @ X3 @ X4 ) )
& ( $true
= ( cP @ X4 @ X2 ) ) )
=> ( $true
= ( cP @ X3 @ X2 ) ) )
& ! [X0: $i,X1: $i] :
( ( $true
= ( cP @ X1 @ X0 ) )
| ( ( cQ @ X1 @ X0 )
= $true ) ) )
=> ( ! [X12: $i,X13: $i] :
( $true
= ( cQ @ X12 @ X13 ) )
| ! [X10: $i,X11: $i] :
( $true
= ( cP @ X11 @ X10 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: $i,X1: $i] :
( ( cQ @ X1 @ X0 )
| ( cP @ X1 @ X0 ) )
& ! [X2: $i,X3: $i,X4: $i] :
( ( ( cP @ X3 @ X4 )
& ( cP @ X4 @ X2 ) )
=> ( cP @ X3 @ X2 ) )
& ! [X5: $i,X6: $i] :
( ( cQ @ X5 @ X6 )
=> ( cQ @ X6 @ X5 ) )
& ! [X7: $i,X8: $i,X9: $i] :
( ( ( cQ @ X7 @ X8 )
& ( cQ @ X9 @ X7 ) )
=> ( cQ @ X9 @ X8 ) ) )
=> ( ! [X10: $i,X11: $i] : ( cP @ X11 @ X10 )
| ! [X12: $i,X13: $i] : ( cQ @ X12 @ X13 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X1: $i,X0: $i] :
( ( cQ @ X0 @ X1 )
| ( cP @ X0 @ X1 ) )
& ! [X2: $i,X0: $i,X1: $i] :
( ( ( cP @ X0 @ X1 )
& ( cP @ X1 @ X2 ) )
=> ( cP @ X0 @ X2 ) )
& ! [X0: $i,X1: $i] :
( ( cQ @ X0 @ X1 )
=> ( cQ @ X1 @ X0 ) )
& ! [X1: $i,X2: $i,X0: $i] :
( ( ( cQ @ X1 @ X2 )
& ( cQ @ X0 @ X1 ) )
=> ( cQ @ X0 @ X2 ) ) )
=> ( ! [X1: $i,X0: $i] : ( cP @ X0 @ X1 )
| ! [X0: $i,X1: $i] : ( cQ @ X0 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X1: $i,X0: $i] :
( ( cQ @ X0 @ X1 )
| ( cP @ X0 @ X1 ) )
& ! [X2: $i,X0: $i,X1: $i] :
( ( ( cP @ X0 @ X1 )
& ( cP @ X1 @ X2 ) )
=> ( cP @ X0 @ X2 ) )
& ! [X0: $i,X1: $i] :
( ( cQ @ X0 @ X1 )
=> ( cQ @ X1 @ X0 ) )
& ! [X1: $i,X2: $i,X0: $i] :
( ( ( cQ @ X1 @ X2 )
& ( cQ @ X0 @ X1 ) )
=> ( cQ @ X0 @ X2 ) ) )
=> ( ! [X1: $i,X0: $i] : ( cP @ X0 @ X1 )
| ! [X0: $i,X1: $i] : ( cQ @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.jHK11XZ5Jg/DTF2THF_17994.p',cCADE13_pme) ).
thf(f99,plain,
( ( $true
!= ( cP @ sK2 @ sK0 ) )
| spl4_2 ),
inference(trivial_inequality_removal,[status(thm)],[f95]) ).
thf(f95,plain,
( ( $true != $true )
| ( $true
!= ( cP @ sK2 @ sK0 ) )
| spl4_2 ),
inference(superposition,[status(thm)],[f55,f41]) ).
thf(f41,plain,
! [X0: $i] :
( ( $true
= ( cQ @ sK1 @ X0 ) )
| ( $true
!= ( cP @ X0 @ sK0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f39]) ).
thf(f39,plain,
! [X0: $i] :
( ( $true != $true )
| ( $true
= ( cQ @ sK1 @ X0 ) )
| ( $true
!= ( cP @ X0 @ sK0 ) ) ),
inference(superposition,[status(thm)],[f37,f12]) ).
thf(f37,plain,
! [X0: $i] :
( ( $true
!= ( cP @ sK1 @ X0 ) )
| ( $true
!= ( cP @ X0 @ sK0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f36]) ).
thf(f36,plain,
! [X0: $i] :
( ( $true
!= ( cP @ sK1 @ X0 ) )
| ( $true
!= ( cP @ X0 @ sK0 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f15,f17]) ).
thf(f17,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( cP @ X0 @ X1 )
= $true )
| ( $true
!= ( cP @ X2 @ X1 ) )
| ( ( cP @ X0 @ X2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f15,plain,
( $true
!= ( cP @ sK1 @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f55,plain,
( ( $true
!= ( cQ @ sK1 @ sK2 ) )
| spl4_2 ),
inference(avatar_component_clause,[status(thm)],[f53]) ).
thf(f53,definition,
( spl4_2
<=> ( $true
= ( cQ @ sK1 @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition]) ).
thf(f133,plain,
( ( $true
!= ( cQ @ sK2 @ sK0 ) )
| spl4_2 ),
inference(trivial_inequality_removal,[status(thm)],[f132]) ).
thf(f132,plain,
( ( $true
!= ( cQ @ sK2 @ sK0 ) )
| ( $true != $true )
| spl4_2 ),
inference(superposition,[status(thm)],[f127,f14]) ).
thf(f14,plain,
! [X8: $i,X9: $i] :
( ( $true
= ( cQ @ X8 @ X9 ) )
| ( $true
!= ( cQ @ X9 @ X8 ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f127,plain,
( ( $true
!= ( cQ @ sK0 @ sK2 ) )
| spl4_2 ),
inference(trivial_inequality_removal,[status(thm)],[f123]) ).
thf(f123,plain,
( ( $true != $true )
| ( $true
!= ( cQ @ sK0 @ sK2 ) )
| spl4_2 ),
inference(superposition,[status(thm)],[f98,f19]) ).
thf(f19,plain,
( $true
= ( cQ @ sK1 @ sK0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f18]) ).
thf(f18,plain,
( ( $true != $true )
| ( $true
= ( cQ @ sK1 @ sK0 ) ) ),
inference(superposition,[status(thm)],[f15,f12]) ).
thf(f98,plain,
( ! [X0: $i] :
( ( $true
!= ( cQ @ sK1 @ X0 ) )
| ( $true
!= ( cQ @ X0 @ sK2 ) ) )
| spl4_2 ),
inference(trivial_inequality_removal,[status(thm)],[f96]) ).
thf(f96,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( cQ @ sK1 @ X0 ) )
| ( $true
!= ( cQ @ X0 @ sK2 ) ) )
| spl4_2 ),
inference(superposition,[status(thm)],[f55,f16]) ).
thf(f16,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( cQ @ X5 @ X3 ) )
| ( $true
!= ( cQ @ X4 @ X3 ) )
| ( $true
!= ( cQ @ X5 @ X4 ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f94,plain,
spl4_1,
inference(avatar_contradiction_clause,[status(thm)],[f93]) ).
thf(f93,plain,
( $false
| spl4_1 ),
inference(subsumption_resolution,[status(thm)],[f91,f66]) ).
thf(f66,plain,
( ( $true
!= ( cQ @ sK2 @ sK0 ) )
| spl4_1 ),
inference(trivial_inequality_removal,[status(thm)],[f64]) ).
thf(f64,plain,
( ( $true
!= ( cQ @ sK2 @ sK0 ) )
| ( $true != $true )
| spl4_1 ),
inference(superposition,[status(thm)],[f62,f14]) ).
thf(f62,plain,
( ( $true
!= ( cQ @ sK0 @ sK2 ) )
| spl4_1 ),
inference(trivial_inequality_removal,[status(thm)],[f61]) ).
thf(f61,plain,
( ( $true
!= ( cQ @ sK0 @ sK2 ) )
| ( $true != $true )
| spl4_1 ),
inference(superposition,[status(thm)],[f27,f59]) ).
thf(f59,plain,
( ( $true
= ( cQ @ sK3 @ sK0 ) )
| spl4_1 ),
inference(trivial_inequality_removal,[status(thm)],[f58]) ).
thf(f58,plain,
( ( $true != $true )
| ( $true
= ( cQ @ sK3 @ sK0 ) )
| spl4_1 ),
inference(superposition,[status(thm)],[f51,f12]) ).
thf(f51,plain,
( ( $true
!= ( cP @ sK3 @ sK0 ) )
| spl4_1 ),
inference(avatar_component_clause,[status(thm)],[f49]) ).
thf(f49,definition,
( spl4_1
<=> ( $true
= ( cP @ sK3 @ sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition]) ).
thf(f27,plain,
! [X0: $i] :
( ( $true
!= ( cQ @ sK3 @ X0 ) )
| ( $true
!= ( cQ @ X0 @ sK2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f25]) ).
thf(f25,plain,
! [X0: $i] :
( ( $true
!= ( cQ @ sK3 @ X0 ) )
| ( $true != $true )
| ( $true
!= ( cQ @ X0 @ sK2 ) ) ),
inference(superposition,[status(thm)],[f13,f16]) ).
thf(f13,plain,
( $true
!= ( cQ @ sK3 @ sK2 ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f91,plain,
( ( $true
= ( cQ @ sK2 @ sK0 ) )
| spl4_1 ),
inference(trivial_inequality_removal,[status(thm)],[f90]) ).
thf(f90,plain,
( ( $true != $true )
| ( $true
= ( cQ @ sK2 @ sK0 ) )
| spl4_1 ),
inference(superposition,[status(thm)],[f86,f12]) ).
thf(f86,plain,
( ( $true
!= ( cP @ sK2 @ sK0 ) )
| spl4_1 ),
inference(trivial_inequality_removal,[status(thm)],[f81]) ).
thf(f81,plain,
( ( $true != $true )
| ( $true
!= ( cP @ sK2 @ sK0 ) )
| spl4_1 ),
inference(superposition,[status(thm)],[f13,f74]) ).
thf(f74,plain,
( ! [X0: $i] :
( ( $true
= ( cQ @ sK3 @ X0 ) )
| ( $true
!= ( cP @ X0 @ sK0 ) ) )
| spl4_1 ),
inference(trivial_inequality_removal,[status(thm)],[f72]) ).
thf(f72,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( $true
= ( cQ @ sK3 @ X0 ) )
| ( $true
!= ( cP @ X0 @ sK0 ) ) )
| spl4_1 ),
inference(superposition,[status(thm)],[f60,f12]) ).
thf(f60,plain,
( ! [X0: $i] :
( ( $true
!= ( cP @ sK3 @ X0 ) )
| ( $true
!= ( cP @ X0 @ sK0 ) ) )
| spl4_1 ),
inference(trivial_inequality_removal,[status(thm)],[f57]) ).
thf(f57,plain,
( ! [X0: $i] :
( ( $true
!= ( cP @ X0 @ sK0 ) )
| ( $true != $true )
| ( $true
!= ( cP @ sK3 @ X0 ) ) )
| spl4_1 ),
inference(superposition,[status(thm)],[f51,f17]) ).
thf(f56,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[status(thm)],[f47,f53,f49]) ).
thf(f47,plain,
( ( $true
!= ( cP @ sK3 @ sK0 ) )
| ( $true
!= ( cQ @ sK1 @ sK2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f46]) ).
thf(f46,plain,
( ( $true != $true )
| ( $true
!= ( cP @ sK3 @ sK0 ) )
| ( $true
!= ( cQ @ sK1 @ sK2 ) ) ),
inference(superposition,[status(thm)],[f31,f41]) ).
thf(f31,plain,
! [X0: $i] :
( ( $true
!= ( cQ @ X0 @ sK3 ) )
| ( $true
!= ( cQ @ X0 @ sK2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f29]) ).
thf(f29,plain,
! [X0: $i] :
( ( $true
!= ( cQ @ X0 @ sK2 ) )
| ( $true != $true )
| ( $true
!= ( cQ @ X0 @ sK3 ) ) ),
inference(superposition,[status(thm)],[f27,f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEV091^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.31 % Computer : n027.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue Feb 24 12:40:22 EST 2026
% 0.12/0.32 % CPUTime :
% 0.12/0.32 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.41 ---- Original DTF file ---
% 0.15/0.41 thf(spec,logic,$$dhol).
% 0.15/0.41 %------------------------------------------------------------------------------
% 0.15/0.41 % File : SEV091^5 : TPTP v9.2.1. Released v4.0.0.
% 0.15/0.41 % Domain : Set Theory (Relations)
% 0.15/0.41 % Problem : TPS problem from RELN-THMS
% 0.15/0.41 % Version : Especial.
% 0.15/0.41 % English :
% 0.15/0.41
% 0.15/0.41 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.15/0.41 % Source : [Bro09]
% 0.15/0.41 % Names : tps_1029 [Bro09]
% 0.15/0.41
% 0.15/0.41 % Status : Theorem
% 0.15/0.41 % Rating : 0.25 v8.2.0, 0.27 v8.1.0, 0.25 v7.4.0, 0.33 v7.3.0, 0.30 v7.2.0, 0.38 v7.1.0, 0.43 v7.0.0, 0.38 v6.4.0, 0.43 v6.3.0, 0.50 v6.0.0, 0.33 v5.5.0, 0.20 v5.4.0, 0.25 v5.1.0, 0.50 v5.0.0, 0.25 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% 0.15/0.41 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.15/0.41 % Number of atoms : 12 ( 0 equ; 0 cnn)
% 0.15/0.41 % Maximal formula atoms : 12 ( 12 avg)
% 0.15/0.41 % Number of connectives : 35 ( 0 ~; 2 |; 5 &; 24 @)
% 0.15/0.41 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.15/0.41 % Maximal formula depth : 11 ( 11 avg)
% 0.15/0.41 % Number of types : 2 ( 0 usr)
% 0.15/0.41 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.15/0.41 % Number of symbols : 2 ( 2 usr; 0 con; 2-2 aty)
% 0.15/0.41 % Number of variables : 14 ( 0 ^; 14 !; 0 ?; 14 :)
% 0.15/0.41 % SPC : TH0_THM_NEQ_NAR
% 0.15/0.41
% 0.15/0.41 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.15/0.41 % project in the Department of Mathematical Sciences at Carnegie
% 0.15/0.41 % Mellon University. Distributed under the Creative Commons copyleft
% 0.15/0.41 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.15/0.41 %------------------------------------------------------------------------------
% 0.15/0.41 thf(cQ,type,
% 0.15/0.41 cQ: $i > $i > $o ).
% 0.15/0.41
% 0.15/0.41 thf(cP,type,
% 0.15/0.41 cP: $i > $i > $o ).
% 0.15/0.41
% 0.15/0.41 thf(cCADE13_pme,conjecture,
% 0.15/0.41 ( ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.15/0.41 ( ( ( cP @ Xx @ Xy )
% 0.15/0.41 & ( cP @ Xy @ Xz ) )
% 0.15/0.41 => ( cP @ Xx @ Xz ) )
% 0.15/0.41 & ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.15/0.41 ( ( ( cQ @ Xx @ Xy )
% 0.15/0.41 & ( cQ @ Xy @ Xz ) )
% 0.15/0.41 => ( cQ @ Xx @ Xz ) )
% 0.15/0.41 & ! [Xx: $i,Xy: $i] :
% 0.15/0.41 ( ( cQ @ Xx @ Xy )
% 0.15/0.41 => ( cQ @ Xy @ Xx ) )
% 0.15/0.41 & ! [Xx: $i,Xy: $i] :
% 0.15/0.41 ( ( cP @ Xx @ Xy )
% 0.15/0.41 | ( cQ @ Xx @ Xy ) ) )
% 0.15/0.41 => ( ! [Xx: $i,Xy: $i] : ( cP @ Xx @ Xy )
% 0.15/0.41 | ! [Xx: $i,Xy: $i] : ( cQ @ Xx @ Xy ) ) ) ).
% 0.15/0.41
% 0.15/0.41 %------------------------------------------------------------------------------
% 0.15/0.41 ------------------------
% 1.14/1.11 ---- Embedded in THF ---
% 1.14/1.11 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.14/1.11 %%% Generated on Tue Feb 24 12:40:22 EST 2026
% 1.14/1.11 %%% using '$$dhol' embedding, version 1.3.0.
% 1.14/1.11 %%% Logic specification used:
% 1.14/1.11 %%% thf(spec, logic, $$dhol).
% 1.14/1.11
% 1.14/1.11 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.jHK11XZ5Jg/DTF2DTF17994.p
% See solution above
% 1.14/1.11 ------------------------
% 1.32/1.12 ---- Cleaned THF ---
% 1.32/1.12 thf(cQ,type,
% 1.32/1.12 cQ: $i > $i > $o ).
% 1.32/1.12
% 1.32/1.12 thf(cP,type,
% 1.32/1.12 cP: $i > $i > $o ).
% 1.32/1.12
% 1.32/1.12 thf(cCADE13_pme,conjecture,
% 1.32/1.12 ( ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 1.32/1.12 ( ( ( cP @ Xx @ Xy )
% 1.32/1.12 & ( cP @ Xy @ Xz ) )
% 1.32/1.12 => ( cP @ Xx @ Xz ) )
% 1.32/1.12 & ! [Xx: $i,Xy: $i,Xz: $i] :
% 1.32/1.12 ( ( ( cQ @ Xx @ Xy )
% 1.32/1.12 & ( cQ @ Xy @ Xz ) )
% 1.32/1.12 => ( cQ @ Xx @ Xz ) )
% 1.32/1.12 & ! [Xx: $i,Xy: $i] :
% 1.32/1.12 ( ( cQ @ Xx @ Xy )
% 1.32/1.12 => ( cQ @ Xy @ Xx ) )
% 1.32/1.12 & ! [Xx: $i,Xy: $i] :
% 1.32/1.12 ( ( cP @ Xx @ Xy )
% 1.32/1.12 | ( cQ @ Xx @ Xy ) ) )
% 1.32/1.12 => ( ! [Xx: $i,Xy: $i] : ( cP @ Xx @ Xy )
% 1.32/1.12 | ! [Xx: $i,Xy: $i] : ( cQ @ Xx @ Xy ) ) ) ).
% 1.32/1.12 ------------------------
% 1.32/1.13 % (18093)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_17994 for (3000ds/183Mi)
% 1.32/1.13 % (18096)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_17994 for (3000ds/2Mi)
% 1.32/1.13 % (18095)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_17994 for (3000ds/27Mi)
% 1.32/1.13 % (18094)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_17994 for (3000ds/4Mi)
% 1.32/1.13 % (18097)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_17994 for (3000ds/2Mi)
% 1.32/1.13 % (18099)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_17994 for (3000ds/18Mi)
% 1.32/1.13 % (18098)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_17994 for (3000ds/275Mi)
% 1.32/1.13 % (18096)Instruction limit reached!
% 1.32/1.13 % (18096)------------------------------
% 1.32/1.13 % (18096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.32/1.13 % (18096)Termination reason: Unknown
% 1.32/1.13 % (18097)Instruction limit reached!
% 1.32/1.13 % (18097)------------------------------
% 1.32/1.13 % (18097)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.32/1.13 % (18097)Termination reason: Unknown
% 1.32/1.13 % (18097)Termination phase: Property scanning
% 1.32/1.13
% 1.32/1.13 % (18097)Memory used [KB]: 895
% 1.32/1.13 % (18097)Time elapsed: 0.002 s
% 1.32/1.13 % (18097)Instructions burned: 2 (million)
% 1.32/1.13 % (18097)------------------------------
% 1.32/1.13 % (18097)------------------------------
% 1.32/1.13 % (18096)Termination phase: Preprocessing 3
% 1.32/1.13
% 1.32/1.13 % (18096)Memory used [KB]: 895
% 1.32/1.13 % (18096)Time elapsed: 0.002 s
% 1.32/1.13 % (18096)Instructions burned: 2 (million)
% 1.32/1.13 % (18096)------------------------------
% 1.32/1.13 % (18096)------------------------------
% 1.32/1.14 % (18093)First to succeed.
% 1.32/1.14 % (18094)Instruction limit reached!
% 1.32/1.14 % (18094)------------------------------
% 1.32/1.14 % (18094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.32/1.14 % (18094)Termination reason: Unknown
% 1.32/1.14 % (18094)Termination phase: Saturation
% 1.32/1.14
% 1.32/1.14 % (18094)Memory used [KB]: 5500
% 1.32/1.14 % (18094)Time elapsed: 0.004 s
% 1.32/1.14 % (18094)Instructions burned: 4 (million)
% 1.32/1.14 % (18094)------------------------------
% 1.32/1.14 % (18094)------------------------------
% 1.32/1.14 % (18093)Refutation found. Thanks to Tanya!
% 1.32/1.14 % SZS status Theorem for DTF2THF_17994
% 1.32/1.14 % SZS output start Proof for DTF2THF_17994
% 1.32/1.14 thf(func_def_0, type, cQ: $i > $i > $o).
% 1.32/1.14 thf(func_def_1, type, cP: $i > $i > $o).
% 1.32/1.14 thf(f137,plain,(
% 1.32/1.14 $false),
% 1.32/1.14 inference(avatar_sat_refutation,[status(thm)],[f56,f94,f136])).
% 1.32/1.14 thf(f136,plain,(
% 1.32/1.14 spl4_2),
% 1.32/1.14 inference(avatar_contradiction_clause,[status(thm)],[f135])).
% 1.32/1.14 thf(f135,plain,(
% 1.32/1.14 $false | spl4_2),
% 1.32/1.14 inference(subsumption_resolution,[status(thm)],[f133,f104])).
% 1.32/1.14 thf(f104,plain,(
% 1.32/1.14 ($true = (cQ @ sK2 @ sK0)) | spl4_2),
% 1.32/1.14 inference(trivial_inequality_removal,[status(thm)],[f102])).
% 1.32/1.14 thf(f102,plain,(
% 1.32/1.14 ($true = (cQ @ sK2 @ sK0)) | ($true != $true) | spl4_2),
% 1.32/1.14 inference(superposition,[status(thm)],[f99,f12])).
% 1.32/1.14 thf(f12,plain,(
% 1.32/1.14 ( ! [X12 : $i,X13 : $i] : (($true = (cP @ X13 @ X12)) | ($true = (cQ @ X13 @ X12))) )),
% 1.32/1.14 inference(cnf_transformation,[status(thm)],[f11])).
% 1.32/1.14 thf(f11,plain,(
% 1.32/1.14 ! [X0 : $i,X1 : $i,X2 : $i] : (((cP @ X0 @ X2) != $true) | ($true != (cP @ X2 @ X1)) | ((cP @ X0 @ X1) = $true)) & ! [X3 : $i,X4 : $i,X5 : $i] : (($true != (cQ @ X4 @ X3)) | ($true = (cQ @ X5 @ X3)) | ($true != (cQ @ X5 @ X4))) & ($true != (cP @ sK1 @ sK0)) & ! [X8 : $i,X9 : $i] : (($true != (cQ @ X9 @ X8)) | ($true = (cQ @ X8 @ X9))) & ($true != (cQ @ sK3 @ sK2)) & ! [X12 : $i,X13 : $i] : (($true = (cP @ X13 @ X12)) | ($true = (cQ @ X13 @ X12)))),
% 1.32/1.14 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f10,f9])).
% 1.32/1.14 thf(f9,plain,(
% 1.32/1.14 ? [X6 : $i,X7 : $i] : ($true != (cP @ X7 @ X6)) => ($true != (cP @ sK1 @ sK0))),
% 1.32/1.14 introduced(definition,[],[choice_axiom])).
% 1.32/1.14 thf(f10,plain,(
% 1.32/1.14 ? [X10 : $i,X11 : $i] : ($true != (cQ @ X11 @ X10)) => ($true != (cQ @ sK3 @ sK2))),
% 1.32/1.14 introduced(definition,[],[choice_axiom])).
% 1.32/1.14 thf(f8,plain,(
% 1.32/1.14 ! [X0 : $i,X1 : $i,X2 : $i] : (((cP @ X0 @ X2) != $true) | ($true != (cP @ X2 @ X1)) | ((cP @ X0 @ X1) = $true)) & ! [X3 : $i,X4 : $i,X5 : $i] : (($true != (cQ @ X4 @ X3)) | ($true = (cQ @ X5 @ X3)) | ($true != (cQ @ X5 @ X4))) & ? [X6 : $i,X7 : $i] : ($true != (cP @ X7 @ X6)) & ! [X8 : $i,X9 : $i] : (($true != (cQ @ X9 @ X8)) | ($true = (cQ @ X8 @ X9))) & ? [X10 : $i,X11 : $i] : ($true != (cQ @ X11 @ X10)) & ! [X12 : $i,X13 : $i] : (($true = (cP @ X13 @ X12)) | ($true = (cQ @ X13 @ X12)))),
% 1.32/1.14 inference(rectify,[status(thm)],[f7])).
% 1.32/1.14 thf(f7,plain,(
% 1.32/1.14 ! [X3 : $i,X2 : $i,X4 : $i] : (($true != (cP @ X3 @ X4)) | ($true != (cP @ X4 @ X2)) | ($true = (cP @ X3 @ X2))) & ! [X8 : $i,X7 : $i,X9 : $i] : (($true != (cQ @ X7 @ X8)) | ($true = (cQ @ X9 @ X8)) | ($true != (cQ @ X9 @ X7))) & ? [X10 : $i,X11 : $i] : ($true != (cP @ X11 @ X10)) & ! [X6 : $i,X5 : $i] : (($true != (cQ @ X5 @ X6)) | ($true = (cQ @ X6 @ X5))) & ? [X13 : $i,X12 : $i] : ($true != (cQ @ X12 @ X13)) & ! [X0 : $i,X1 : $i] : (($true = (cP @ X1 @ X0)) | ((cQ @ X1 @ X0) = $true))),
% 1.32/1.14 inference(flattening,[status(thm)],[f6])).
% 1.32/1.14 thf(f6,plain,(
% 1.32/1.14 (? [X13 : $i,X12 : $i] : ($true != (cQ @ X12 @ X13)) & ? [X10 : $i,X11 : $i] : ($true != (cP @ X11 @ X10))) & (! [X6 : $i,X5 : $i] : (($true != (cQ @ X5 @ X6)) | ($true = (cQ @ X6 @ X5))) & ! [X9 : $i,X7 : $i,X8 : $i] : (($true = (cQ @ X9 @ X8)) | (($true != (cQ @ X9 @ X7)) | ($true != (cQ @ X7 @ X8)))) & ! [X4 : $i,X2 : $i,X3 : $i] : (($true = (cP @ X3 @ X2)) | (($true != (cP @ X3 @ X4)) | ($true != (cP @ X4 @ X2)))) & ! [X0 : $i,X1 : $i] : (($true = (cP @ X1 @ X0)) | ((cQ @ X1 @ X0) = $true)))),
% 1.32/1.14 inference(ennf_transformation,[status(thm)],[f5])).
% 1.32/1.14 thf(f5,plain,(
% 1.32/1.14 ~((! [X6 : $i,X5 : $i] : (($true = (cQ @ X5 @ X6)) => ($true = (cQ @ X6 @ X5))) & ! [X9 : $i,X7 : $i,X8 : $i] : ((($true = (cQ @ X9 @ X7)) & ($true = (cQ @ X7 @ X8))) => ($true = (cQ @ X9 @ X8))) & ! [X4 : $i,X2 : $i,X3 : $i] : ((($true = (cP @ X3 @ X4)) & ($true = (cP @ X4 @ X2))) => ($true = (cP @ X3 @ X2))) & ! [X0 : $i,X1 : $i] : (($true = (cP @ X1 @ X0)) | ((cQ @ X1 @ X0) = $true))) => (! [X12 : $i,X13 : $i] : ($true = (cQ @ X12 @ X13)) | ! [X10 : $i,X11 : $i] : ($true = (cP @ X11 @ X10))))),
% 1.32/1.14 inference(fool_elimination,[status(thm)],[f4])).
% 1.32/1.14 thf(f4,plain,(
% 1.32/1.14 ~((! [X0 : $i,X1 : $i] : ((cQ @ X1 @ X0) | (cP @ X1 @ X0)) & ! [X2 : $i,X3 : $i,X4 : $i] : (((cP @ X3 @ X4) & (cP @ X4 @ X2)) => (cP @ X3 @ X2)) & ! [X5 : $i,X6 : $i] : ((cQ @ X5 @ X6) => (cQ @ X6 @ X5)) & ! [X7 : $i,X8 : $i,X9 : $i] : (((cQ @ X7 @ X8) & (cQ @ X9 @ X7)) => (cQ @ X9 @ X8))) => (! [X10 : $i,X11 : $i] : (cP @ X11 @ X10) | ! [X12 : $i,X13 : $i] : (cQ @ X12 @ X13)))),
% 1.32/1.14 inference(rectify,[status(thm)],[f2])).
% 1.32/1.14 thf(f2,negated_conjecture,(
% 1.32/1.14 ~((! [X1 : $i,X0 : $i] : ((cQ @ X0 @ X1) | (cP @ X0 @ X1)) & ! [X2 : $i,X0 : $i,X1 : $i] : (((cP @ X0 @ X1) & (cP @ X1 @ X2)) => (cP @ X0 @ X2)) & ! [X0 : $i,X1 : $i] : ((cQ @ X0 @ X1) => (cQ @ X1 @ X0)) & ! [X1 : $i,X2 : $i,X0 : $i] : (((cQ @ X1 @ X2) & (cQ @ X0 @ X1)) => (cQ @ X0 @ X2))) => (! [X1 : $i,X0 : $i] : (cP @ X0 @ X1) | ! [X0 : $i,X1 : $i] : (cQ @ X0 @ X1)))),
% 1.32/1.14 inference(negated_conjecture,[status(cth)],[f1])).
% 1.32/1.14 thf(f1,conjecture,(
% 1.32/1.14 (! [X1 : $i,X0 : $i] : ((cQ @ X0 @ X1) | (cP @ X0 @ X1)) & ! [X2 : $i,X0 : $i,X1 : $i] : (((cP @ X0 @ X1) & (cP @ X1 @ X2)) => (cP @ X0 @ X2)) & ! [X0 : $i,X1 : $i] : ((cQ @ X0 @ X1) => (cQ @ X1 @ X0)) & ! [X1 : $i,X2 : $i,X0 : $i] : (((cQ @ X1 @ X2) & (cQ @ X0 @ X1)) => (cQ @ X0 @ X2))) => (! [X1 : $i,X0 : $i] : (cP @ X0 @ X1) | ! [X0 : $i,X1 : $i] : (cQ @ X0 @ X1))),
% 1.32/1.14 file('/export/starexec/sandbox2/tmp/tmp.jHK11XZ5Jg/DTF2THF_17994.p',cCADE13_pme)).
% 1.32/1.14 thf(f99,plain,(
% 1.32/1.14 ($true != (cP @ sK2 @ sK0)) | spl4_2),
% 1.32/1.14 inference(trivial_inequality_removal,[status(thm)],[f95])).
% 1.32/1.14 thf(f95,plain,(
% 1.32/1.14 ($true != $true) | ($true != (cP @ sK2 @ sK0)) | spl4_2),
% 1.32/1.14 inference(superposition,[status(thm)],[f55,f41])).
% 1.32/1.14 thf(f41,plain,(
% 1.32/1.14 ( ! [X0 : $i] : (($true = (cQ @ sK1 @ X0)) | ($true != (cP @ X0 @ sK0))) )),
% 1.32/1.14 inference(trivial_inequality_removal,[status(thm)],[f39])).
% 1.32/1.14 thf(f39,plain,(
% 1.32/1.14 ( ! [X0 : $i] : (($true != $true) | ($true = (cQ @ sK1 @ X0)) | ($true != (cP @ X0 @ sK0))) )),
% 1.32/1.14 inference(superposition,[status(thm)],[f37,f12])).
% 1.32/1.14 thf(f37,plain,(
% 1.32/1.14 ( ! [X0 : $i] : (($true != (cP @ sK1 @ X0)) | ($true != (cP @ X0 @ sK0))) )),
% 1.32/1.14 inference(trivial_inequality_removal,[status(thm)],[f36])).
% 1.32/1.14 thf(f36,plain,(
% 1.32/1.14 ( ! [X0 : $i] : (($true != (cP @ sK1 @ X0)) | ($true != (cP @ X0 @ sK0)) | ($true != $true)) )),
% 1.32/1.14 inference(superposition,[status(thm)],[f15,f17])).
% 1.32/1.14 thf(f17,plain,(
% 1.32/1.14 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((cP @ X0 @ X1) = $true) | ($true != (cP @ X2 @ X1)) | ((cP @ X0 @ X2) != $true)) )),
% 1.32/1.14 inference(cnf_transformation,[status(thm)],[f11])).
% 1.32/1.14 thf(f15,plain,(
% 1.32/1.14 ($true != (cP @ sK1 @ sK0))),
% 1.32/1.14 inference(cnf_transformation,[status(thm)],[f11])).
% 1.32/1.14 thf(f55,plain,(
% 1.32/1.14 ($true != (cQ @ sK1 @ sK2)) | spl4_2),
% 1.32/1.14 inference(avatar_component_clause,[status(thm)],[f53])).
% 1.32/1.14 thf(f53,definition,(
% 1.32/1.14 spl4_2 <=> ($true = (cQ @ sK1 @ sK2))),
% 1.32/1.14 introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition])).
% 1.32/1.14 thf(f133,plain,(
% 1.32/1.14 ($true != (cQ @ sK2 @ sK0)) | spl4_2),
% 1.32/1.14 inference(trivial_inequality_removal,[status(thm)],[f132])).
% 1.32/1.14 thf(f132,plain,(
% 1.32/1.14 ($true != (cQ @ sK2 @ sK0)) | ($true != $true) | spl4_2),
% 1.32/1.14 inference(superposition,[status(thm)],[f127,f14])).
% 1.32/1.14 thf(f14,plain,(
% 1.32/1.14 ( ! [X8 : $i,X9 : $i] : (($true = (cQ @ X8 @ X9)) | ($true != (cQ @ X9 @ X8))) )),
% 1.32/1.14 inference(cnf_transformation,[status(thm)],[f11])).
% 1.32/1.14 thf(f127,plain,(
% 1.32/1.14 ($true != (cQ @ sK0 @ sK2)) | spl4_2),
% 1.32/1.14 inference(trivial_inequality_removal,[status(thm)],[f123])).
% 1.32/1.14 thf(f123,plain,(
% 1.32/1.14 ($true != $true) | ($true != (cQ @ sK0 @ sK2)) | spl4_2),
% 1.32/1.14 inference(superposition,[status(thm)],[f98,f19])).
% 1.32/1.14 thf(f19,plain,(
% 1.32/1.14 ($true = (cQ @ sK1 @ sK0))),
% 1.32/1.14 inference(trivial_inequality_removal,[status(thm)],[f18])).
% 1.32/1.14 thf(f18,plain,(
% 1.32/1.14 ($true != $true) | ($true = (cQ @ sK1 @ sK0))),
% 1.32/1.14 inference(superposition,[status(thm)],[f15,f12])).
% 1.32/1.14 thf(f98,plain,(
% 1.32/1.14 ( ! [X0 : $i] : (($true != (cQ @ sK1 @ X0)) | ($true != (cQ @ X0 @ sK2))) ) | spl4_2),
% 1.32/1.14 inference(trivial_inequality_removal,[status(thm)],[f96])).
% 1.32/1.14 thf(f96,plain,(
% 1.32/1.14 ( ! [X0 : $i] : (($true != $true) | ($true != (cQ @ sK1 @ X0)) | ($true != (cQ @ X0 @ sK2))) ) | spl4_2),
% 1.32/1.14 inference(superposition,[status(thm)],[f55,f16])).
% 1.32/1.14 thf(f16,plain,(
% 1.32/1.14 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true = (cQ @ X5 @ X3)) | ($true != (cQ @ X4 @ X3)) | ($true != (cQ @ X5 @ X4))) )),
% 1.32/1.14 inference(cnf_transformation,[status(thm)],[f11])).
% 1.32/1.14 thf(f94,plain,(
% 1.32/1.14 spl4_1),
% 1.32/1.14 inference(avatar_contradiction_clause,[status(thm)],[f93])).
% 1.32/1.14 thf(f93,plain,(
% 1.32/1.14 $false | spl4_1),
% 1.32/1.14 inference(subsumption_resolution,[status(thm)],[f91,f66])).
% 1.32/1.14 thf(f66,plain,(
% 1.32/1.14 ($true != (cQ @ sK2 @ sK0)) | spl4_1),
% 1.32/1.14 inference(trivial_inequality_removal,[status(thm)],[f64])).
% 1.32/1.14 thf(f64,plain,(
% 1.32/1.14 ($true != (cQ @ sK2 @ sK0)) | ($true != $true) | spl4_1),
% 1.32/1.14 inference(superposition,[status(thm)],[f62,f14])).
% 1.32/1.14 thf(f62,plain,(
% 1.32/1.14 ($true != (cQ @ sK0 @ sK2)) | spl4_1),
% 1.32/1.14 inference(trivial_inequality_removal,[status(thm)],[f61])).
% 1.32/1.14 thf(f61,plain,(
% 1.32/1.14 ($true != (cQ @ sK0 @ sK2)) | ($true != $true) | spl4_1),
% 1.32/1.14 inference(superposition,[status(thm)],[f27,f59])).
% 1.32/1.14 thf(f59,plain,(
% 1.32/1.14 ($true = (cQ @ sK3 @ sK0)) | spl4_1),
% 1.32/1.14 inference(trivial_inequality_removal,[status(thm)],[f58])).
% 1.32/1.14 thf(f58,plain,(
% 1.32/1.14 ($true != $true) | ($true = (cQ @ sK3 @ sK0)) | spl4_1),
% 1.32/1.14 inference(superposition,[status(thm)],[f51,f12])).
% 1.32/1.14 thf(f51,plain,(
% 1.32/1.14 ($true != (cP @ sK3 @ sK0)) | spl4_1),
% 1.32/1.14 inference(avatar_component_clause,[status(thm)],[f49])).
% 1.32/1.14 thf(f49,definition,(
% 1.32/1.14 spl4_1 <=> ($true = (cP @ sK3 @ sK0))),
% 1.32/1.14 introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition])).
% 1.32/1.14 thf(f27,plain,(
% 1.32/1.14 ( ! [X0 : $i] : (($true != (cQ @ sK3 @ X0)) | ($true != (cQ @ X0 @ sK2))) )),
% 1.32/1.14 inference(trivial_inequality_removal,[status(thm)],[f25])).
% 1.32/1.14 thf(f25,plain,(
% 1.32/1.14 ( ! [X0 : $i] : (($true != (cQ @ sK3 @ X0)) | ($true != $true) | ($true != (cQ @ X0 @ sK2))) )),
% 1.32/1.14 inference(superposition,[status(thm)],[f13,f16])).
% 1.32/1.14 thf(f13,plain,(
% 1.32/1.14 ($true != (cQ @ sK3 @ sK2))),
% 1.32/1.14 inference(cnf_transformation,[status(thm)],[f11])).
% 1.32/1.14 thf(f91,plain,(
% 1.32/1.14 ($true = (cQ @ sK2 @ sK0)) | spl4_1),
% 1.32/1.14 inference(trivial_inequality_removal,[status(thm)],[f90])).
% 1.32/1.14 thf(f90,plain,(
% 1.32/1.14 ($true != $true) | ($true = (cQ @ sK2 @ sK0)) | spl4_1),
% 1.32/1.14 inference(superposition,[status(thm)],[f86,f12])).
% 1.32/1.14 thf(f86,plain,(
% 1.32/1.14 ($true != (cP @ sK2 @ sK0)) | spl4_1),
% 1.32/1.14 inference(trivial_inequality_removal,[status(thm)],[f81])).
% 1.32/1.14 thf(f81,plain,(
% 1.32/1.14 ($true != $true) | ($true != (cP @ sK2 @ sK0)) | spl4_1),
% 1.32/1.14 inference(superposition,[status(thm)],[f13,f74])).
% 1.32/1.14 thf(f74,plain,(
% 1.32/1.14 ( ! [X0 : $i] : (($true = (cQ @ sK3 @ X0)) | ($true != (cP @ X0 @ sK0))) ) | spl4_1),
% 1.32/1.14 inference(trivial_inequality_removal,[status(thm)],[f72])).
% 1.32/1.14 thf(f72,plain,(
% 1.32/1.14 ( ! [X0 : $i] : (($true != $true) | ($true = (cQ @ sK3 @ X0)) | ($true != (cP @ X0 @ sK0))) ) | spl4_1),
% 1.32/1.14 inference(superposition,[status(thm)],[f60,f12])).
% 1.32/1.14 thf(f60,plain,(
% 1.32/1.14 ( ! [X0 : $i] : (($true != (cP @ sK3 @ X0)) | ($true != (cP @ X0 @ sK0))) ) | spl4_1),
% 1.32/1.14 inference(trivial_inequality_removal,[status(thm)],[f57])).
% 1.32/1.14 thf(f57,plain,(
% 1.32/1.14 ( ! [X0 : $i] : (($true != (cP @ X0 @ sK0)) | ($true != $true) | ($true != (cP @ sK3 @ X0))) ) | spl4_1),
% 1.32/1.14 inference(superposition,[status(thm)],[f51,f17])).
% 1.32/1.14 thf(f56,plain,(
% 1.32/1.14 ~spl4_1 | ~spl4_2),
% 1.32/1.14 inference(avatar_split_clause,[status(thm)],[f47,f53,f49])).
% 1.32/1.14 thf(f47,plain,(
% 1.32/1.14 ($true != (cP @ sK3 @ sK0)) | ($true != (cQ @ sK1 @ sK2))),
% 1.32/1.14 inference(trivial_inequality_removal,[status(thm)],[f46])).
% 1.32/1.14 thf(f46,plain,(
% 1.32/1.14 ($true != $true) | ($true != (cP @ sK3 @ sK0)) | ($true != (cQ @ sK1 @ sK2))),
% 1.32/1.14 inference(superposition,[status(thm)],[f31,f41])).
% 1.32/1.14 thf(f31,plain,(
% 1.32/1.14 ( ! [X0 : $i] : (($true != (cQ @ X0 @ sK3)) | ($true != (cQ @ X0 @ sK2))) )),
% 1.32/1.14 inference(trivial_inequality_removal,[status(thm)],[f29])).
% 1.32/1.14 thf(f29,plain,(
% 1.32/1.14 ( ! [X0 : $i] : (($true != (cQ @ X0 @ sK2)) | ($true != $true) | ($true != (cQ @ X0 @ sK3))) )),
% 1.32/1.14 inference(superposition,[status(thm)],[f27,f14])).
% 1.32/1.14 % SZS output end Proof for DTF2THF_17994
% 1.32/1.14 % (18093)------------------------------
% 1.32/1.14 % (18093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.32/1.14 % (18093)Termination reason: Refutation
% 1.32/1.14
% 1.32/1.14 % (18093)Memory used [KB]: 5628
% 1.32/1.14 % (18093)Time elapsed: 0.009 s
% 1.32/1.14 % (18093)Instructions burned: 18 (million)
% 1.32/1.14 % (18093)------------------------------
% 1.32/1.14 % (18093)------------------------------
% 1.32/1.14 % (18092)Success in time 0.017 s
%------------------------------------------------------------------------------