%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO384^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n001.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 1.72s 1.47s
% Output : Refutation 1.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 24
% Syntax : Number of formulae : 85 ( 7 unt; 0 typ; 8 def)
% Number of atoms : 1067 ( 285 equ; 0 cnn)
% Maximal formula atoms : 20 ( 12 avg)
% Number of connectives : 1548 ( 197 ~; 182 |; 94 &;1000 @)
% ( 8 <=>; 67 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 28 usr; 14 con; 0-3 aty)
% Number of variables : 452 ( 0 ^; 312 !; 140 ?; 452 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cD: $i > $i > $i > $o ).
thf(func_def_1,type,
cF: $i > $i > $o ).
thf(func_def_2,type,
cS: $i > $i > $o ).
thf(func_def_6,type,
sK0: $i > $i ).
thf(func_def_9,type,
sK3: $i > $i ).
thf(func_def_10,type,
sK4: $i > $i ).
thf(func_def_11,type,
sK5: $i > $i ).
thf(func_def_12,type,
sK6: $i > $i ).
thf(func_def_14,type,
sK8: $i > $i ).
thf(func_def_15,type,
sK9: $i > $i ).
thf(func_def_16,type,
sK10: $i > $i > $i ).
thf(func_def_17,type,
sK11: $i > $i ).
thf(func_def_18,type,
sK12: $i > $i ).
thf(func_def_19,type,
sK13: $i > $i > $i ).
thf(func_def_20,type,
sK14: $i > $i > $i ).
thf(func_def_22,type,
sK16: $i > $i ).
thf(f104,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f51,f55,f59,f66,f67,f68,f69,f70,f79,f82,f87,f103]) ).
thf(f103,plain,
( ~ spl17_4
| ~ spl17_5
| ~ spl17_6
| ~ spl17_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f102]) ).
thf(f102,plain,
( $false
| ~ spl17_4
| ~ spl17_5
| ~ spl17_6
| ~ spl17_7 ),
inference(subsumption_resolution,[status(thm)],[f101,f50]) ).
thf(f50,plain,
( ! [X5: $i] :
( $true
= ( cF @ ( sK4 @ X5 ) @ ( sK5 @ X5 ) ) )
| ~ spl17_4 ),
inference(avatar_component_clause,[status(thm)],[f49]) ).
thf(f49,definition,
( spl17_4
<=> ! [X5: $i] :
( $true
= ( cF @ ( sK4 @ X5 ) @ ( sK5 @ X5 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl17_4])],[avatar_definition]) ).
thf(f101,plain,
( ( ( cF @ ( sK4 @ ( sK11 @ sK2 ) ) @ ( sK5 @ ( sK11 @ sK2 ) ) )
!= $true )
| ~ spl17_5
| ~ spl17_6
| ~ spl17_7 ),
inference(trivial_inequality_removal,[status(thm)],[f100]) ).
thf(f100,plain,
( ( $true != $true )
| ( ( cF @ ( sK4 @ ( sK11 @ sK2 ) ) @ ( sK5 @ ( sK11 @ sK2 ) ) )
!= $true )
| ~ spl17_5
| ~ spl17_6
| ~ spl17_7 ),
inference(superposition,[status(thm)],[f97,f54]) ).
thf(f54,plain,
( ! [X5: $i] :
( ( cF @ ( sK3 @ X5 ) @ ( sK6 @ X5 ) )
= $true )
| ~ spl17_5 ),
inference(avatar_component_clause,[status(thm)],[f53]) ).
thf(f53,definition,
( spl17_5
<=> ! [X5: $i] :
( ( cF @ ( sK3 @ X5 ) @ ( sK6 @ X5 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl17_5])],[avatar_definition]) ).
thf(f97,plain,
( ! [X0: $i] :
( ( $true
!= ( cF @ ( sK3 @ ( sK11 @ sK2 ) ) @ ( sK6 @ X0 ) ) )
| ( ( cF @ ( sK4 @ ( sK11 @ sK2 ) ) @ ( sK5 @ X0 ) )
!= $true ) )
| ~ spl17_6
| ~ spl17_7 ),
inference(trivial_inequality_removal,[status(thm)],[f95]) ).
thf(f95,plain,
( ! [X0: $i] :
( ( $true
!= ( cF @ ( sK3 @ ( sK11 @ sK2 ) ) @ ( sK6 @ X0 ) ) )
| ( $true != $true )
| ( ( cF @ ( sK4 @ ( sK11 @ sK2 ) ) @ ( sK5 @ X0 ) )
!= $true ) )
| ~ spl17_6
| ~ spl17_7 ),
inference(superposition,[status(thm)],[f62,f90]) ).
thf(f90,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( cD @ X1 @ X2 @ X0 ) )
| ( $true
!= ( cF @ ( sK3 @ ( sK11 @ X0 ) ) @ X1 ) )
| ( ( cF @ ( sK4 @ ( sK11 @ X0 ) ) @ X2 )
!= $true ) )
| ~ spl17_6 ),
inference(trivial_inequality_removal,[status(thm)],[f89]) ).
thf(f89,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( cF @ ( sK3 @ ( sK11 @ X0 ) ) @ X1 ) )
| ( $true
= ( cD @ X1 @ X2 @ X0 ) )
| ( ( cF @ ( sK4 @ ( sK11 @ X0 ) ) @ X2 )
!= $true )
| ( $true != $true ) )
| ~ spl17_6 ),
inference(superposition,[status(thm)],[f29,f58]) ).
thf(f58,plain,
( ! [X5: $i] :
( $true
= ( cD @ ( sK3 @ X5 ) @ ( sK4 @ X5 ) @ X5 ) )
| ~ spl17_6 ),
inference(avatar_component_clause,[status(thm)],[f57]) ).
thf(f57,definition,
( spl17_6
<=> ! [X5: $i] :
( $true
= ( cD @ ( sK3 @ X5 ) @ ( sK4 @ X5 ) @ X5 ) ) ),
introduced(definition,[new_symbols(naming,[spl17_6])],[avatar_definition]) ).
thf(f29,plain,
! [X21: $i,X19: $i,X24: $i,X22: $i,X23: $i] :
( ( $true
!= ( cD @ X21 @ X22 @ ( sK11 @ X19 ) ) )
| ( $true
= ( cD @ X23 @ X24 @ X19 ) )
| ( ( cF @ X22 @ X24 )
!= $true )
| ( $true
!= ( cF @ X21 @ X23 ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( ! [X0: $i] :
( ( cF @ X0 @ ( sK0 @ X0 ) )
= $true )
& ( ! [X3: $i] :
( $true
!= ( cF @ sK1 @ X3 ) )
| ! [X5: $i] :
( ( $true
!= ( cD @ ( sK6 @ X5 ) @ ( sK5 @ X5 ) @ sK2 ) )
& ( ( cF @ ( sK3 @ X5 ) @ ( sK6 @ X5 ) )
= $true )
& ( $true
= ( cF @ ( sK4 @ X5 ) @ ( sK5 @ X5 ) ) )
& ( $true
= ( cD @ ( sK3 @ X5 ) @ ( sK4 @ X5 ) @ X5 ) ) )
| ! [X11: $i,X13: $i] :
( ! [X14: $i] :
( ( ( cF @ X13 @ X14 )
!= $true )
| ( $true
= ( cD @ X14 @ sK7 @ X11 ) ) )
| ( ( cS @ ( sK8 @ X11 ) @ X13 )
!= $true ) )
| ! [X15: $i,X17: $i] :
( ( $true
= ( cS @ X17 @ ( sK10 @ X17 @ X15 ) ) )
& ( $true
!= ( cD @ ( sK10 @ X17 @ X15 ) @ X15 @ ( sK9 @ X15 ) ) ) ) )
& ! [X19: $i,X21: $i,X22: $i] :
( ! [X23: $i,X24: $i] :
( ( ( cF @ X22 @ X24 )
!= $true )
| ( $true
!= ( cF @ X21 @ X23 ) )
| ( $true
= ( cD @ X23 @ X24 @ X19 ) ) )
| ( $true
!= ( cD @ X21 @ X22 @ ( sK11 @ X19 ) ) ) )
& ! [X25: $i,X27: $i] :
( ( $true
= ( cS @ X27 @ ( sK13 @ X27 @ X25 ) ) )
& ( ( cD @ ( sK14 @ X27 @ X25 ) @ X25 @ ( sK12 @ X25 ) )
!= $true )
& ( $true
= ( cF @ ( sK13 @ X27 @ X25 ) @ ( sK14 @ X27 @ X25 ) ) ) )
& ! [X31: $i,X33: $i] :
( ( $true
= ( cD @ X33 @ sK15 @ X31 ) )
| ( $true
!= ( cS @ ( sK16 @ X31 ) @ X33 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11,sK12,sK13,sK14,sK15,sK16])],[f8,f23,f22,f21,f20,f19,f18,f17,f16,f15,f14,f13,f12,f11,f10,f9]) ).
thf(f9,plain,
! [X0: $i] :
( ? [X1: $i] :
( ( cF @ X0 @ X1 )
= $true )
=> ( ( cF @ X0 @ ( sK0 @ X0 ) )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X2: $i] :
! [X3: $i] :
( $true
!= ( cF @ X2 @ X3 ) )
=> ! [X3: $i] :
( $true
!= ( cF @ sK1 @ X3 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X4: $i] :
! [X5: $i] :
? [X6: $i,X7: $i] :
( ? [X8: $i,X9: $i] :
( ( ( cD @ X9 @ X8 @ X4 )
!= $true )
& ( $true
= ( cF @ X6 @ X9 ) )
& ( ( cF @ X7 @ X8 )
= $true ) )
& ( ( cD @ X6 @ X7 @ X5 )
= $true ) )
=> ! [X5: $i] :
? [X7: $i,X6: $i] :
( ? [X9: $i,X8: $i] :
( ( $true
!= ( cD @ X9 @ X8 @ sK2 ) )
& ( $true
= ( cF @ X6 @ X9 ) )
& ( ( cF @ X7 @ X8 )
= $true ) )
& ( ( cD @ X6 @ X7 @ X5 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
! [X5: $i] :
( ? [X7: $i,X6: $i] :
( ? [X9: $i,X8: $i] :
( ( $true
!= ( cD @ X9 @ X8 @ sK2 ) )
& ( $true
= ( cF @ X6 @ X9 ) )
& ( ( cF @ X7 @ X8 )
= $true ) )
& ( ( cD @ X6 @ X7 @ X5 )
= $true ) )
=> ( ? [X9: $i,X8: $i] :
( ( $true
!= ( cD @ X9 @ X8 @ sK2 ) )
& ( $true
= ( cF @ ( sK3 @ X5 ) @ X9 ) )
& ( $true
= ( cF @ ( sK4 @ X5 ) @ X8 ) ) )
& ( $true
= ( cD @ ( sK3 @ X5 ) @ ( sK4 @ X5 ) @ X5 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
! [X5: $i] :
( ? [X9: $i,X8: $i] :
( ( $true
!= ( cD @ X9 @ X8 @ sK2 ) )
& ( $true
= ( cF @ ( sK3 @ X5 ) @ X9 ) )
& ( $true
= ( cF @ ( sK4 @ X5 ) @ X8 ) ) )
=> ( ( $true
!= ( cD @ ( sK6 @ X5 ) @ ( sK5 @ X5 ) @ sK2 ) )
& ( ( cF @ ( sK3 @ X5 ) @ ( sK6 @ X5 ) )
= $true )
& ( $true
= ( cF @ ( sK4 @ X5 ) @ ( sK5 @ X5 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
( ? [X10: $i] :
! [X11: $i] :
? [X12: $i] :
! [X13: $i] :
( ! [X14: $i] :
( ( ( cF @ X13 @ X14 )
!= $true )
| ( $true
= ( cD @ X14 @ X10 @ X11 ) ) )
| ( $true
!= ( cS @ X12 @ X13 ) ) )
=> ! [X11: $i] :
? [X12: $i] :
! [X13: $i] :
( ! [X14: $i] :
( ( ( cF @ X13 @ X14 )
!= $true )
| ( $true
= ( cD @ X14 @ sK7 @ X11 ) ) )
| ( $true
!= ( cS @ X12 @ X13 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
! [X11: $i] :
( ? [X12: $i] :
! [X13: $i] :
( ! [X14: $i] :
( ( ( cF @ X13 @ X14 )
!= $true )
| ( $true
= ( cD @ X14 @ sK7 @ X11 ) ) )
| ( $true
!= ( cS @ X12 @ X13 ) ) )
=> ! [X13: $i] :
( ! [X14: $i] :
( ( ( cF @ X13 @ X14 )
!= $true )
| ( $true
= ( cD @ X14 @ sK7 @ X11 ) ) )
| ( ( cS @ ( sK8 @ X11 ) @ X13 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
! [X15: $i] :
( ? [X16: $i] :
! [X17: $i] :
? [X18: $i] :
( ( $true
= ( cS @ X17 @ X18 ) )
& ( $true
!= ( cD @ X18 @ X15 @ X16 ) ) )
=> ! [X17: $i] :
? [X18: $i] :
( ( $true
= ( cS @ X17 @ X18 ) )
& ( $true
!= ( cD @ X18 @ X15 @ ( sK9 @ X15 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
! [X15: $i,X17: $i] :
( ? [X18: $i] :
( ( $true
= ( cS @ X17 @ X18 ) )
& ( $true
!= ( cD @ X18 @ X15 @ ( sK9 @ X15 ) ) ) )
=> ( ( $true
= ( cS @ X17 @ ( sK10 @ X17 @ X15 ) ) )
& ( $true
!= ( cD @ ( sK10 @ X17 @ X15 ) @ X15 @ ( sK9 @ X15 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
! [X19: $i] :
( ? [X20: $i] :
! [X21: $i,X22: $i] :
( ! [X23: $i,X24: $i] :
( ( ( cF @ X22 @ X24 )
!= $true )
| ( $true
!= ( cF @ X21 @ X23 ) )
| ( $true
= ( cD @ X23 @ X24 @ X19 ) ) )
| ( $true
!= ( cD @ X21 @ X22 @ X20 ) ) )
=> ! [X22: $i,X21: $i] :
( ! [X23: $i,X24: $i] :
( ( ( cF @ X22 @ X24 )
!= $true )
| ( $true
!= ( cF @ X21 @ X23 ) )
| ( $true
= ( cD @ X23 @ X24 @ X19 ) ) )
| ( $true
!= ( cD @ X21 @ X22 @ ( sK11 @ X19 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f19,plain,
! [X25: $i] :
( ? [X26: $i] :
! [X27: $i] :
? [X28: $i] :
( ( $true
= ( cS @ X27 @ X28 ) )
& ? [X29: $i] :
( ( $true
!= ( cD @ X29 @ X25 @ X26 ) )
& ( $true
= ( cF @ X28 @ X29 ) ) ) )
=> ! [X27: $i] :
? [X28: $i] :
( ( $true
= ( cS @ X27 @ X28 ) )
& ? [X29: $i] :
( ( ( cD @ X29 @ X25 @ ( sK12 @ X25 ) )
!= $true )
& ( $true
= ( cF @ X28 @ X29 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f20,plain,
! [X25: $i,X27: $i] :
( ? [X28: $i] :
( ( $true
= ( cS @ X27 @ X28 ) )
& ? [X29: $i] :
( ( ( cD @ X29 @ X25 @ ( sK12 @ X25 ) )
!= $true )
& ( $true
= ( cF @ X28 @ X29 ) ) ) )
=> ( ( $true
= ( cS @ X27 @ ( sK13 @ X27 @ X25 ) ) )
& ? [X29: $i] :
( ( ( cD @ X29 @ X25 @ ( sK12 @ X25 ) )
!= $true )
& ( $true
= ( cF @ ( sK13 @ X27 @ X25 ) @ X29 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f21,plain,
! [X25: $i,X27: $i] :
( ? [X29: $i] :
( ( ( cD @ X29 @ X25 @ ( sK12 @ X25 ) )
!= $true )
& ( $true
= ( cF @ ( sK13 @ X27 @ X25 ) @ X29 ) ) )
=> ( ( ( cD @ ( sK14 @ X27 @ X25 ) @ X25 @ ( sK12 @ X25 ) )
!= $true )
& ( $true
= ( cF @ ( sK13 @ X27 @ X25 ) @ ( sK14 @ X27 @ X25 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f22,plain,
( ? [X30: $i] :
! [X31: $i] :
? [X32: $i] :
! [X33: $i] :
( ( ( cD @ X33 @ X30 @ X31 )
= $true )
| ( ( cS @ X32 @ X33 )
!= $true ) )
=> ! [X31: $i] :
? [X32: $i] :
! [X33: $i] :
( ( $true
= ( cD @ X33 @ sK15 @ X31 ) )
| ( ( cS @ X32 @ X33 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f23,plain,
! [X31: $i] :
( ? [X32: $i] :
! [X33: $i] :
( ( $true
= ( cD @ X33 @ sK15 @ X31 ) )
| ( ( cS @ X32 @ X33 )
!= $true ) )
=> ! [X33: $i] :
( ( $true
= ( cD @ X33 @ sK15 @ X31 ) )
| ( $true
!= ( cS @ ( sK16 @ X31 ) @ X33 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ! [X0: $i] :
? [X1: $i] :
( ( cF @ X0 @ X1 )
= $true )
& ( ? [X2: $i] :
! [X3: $i] :
( $true
!= ( cF @ X2 @ X3 ) )
| ? [X4: $i] :
! [X5: $i] :
? [X6: $i,X7: $i] :
( ? [X8: $i,X9: $i] :
( ( ( cD @ X9 @ X8 @ X4 )
!= $true )
& ( $true
= ( cF @ X6 @ X9 ) )
& ( ( cF @ X7 @ X8 )
= $true ) )
& ( ( cD @ X6 @ X7 @ X5 )
= $true ) )
| ? [X10: $i] :
! [X11: $i] :
? [X12: $i] :
! [X13: $i] :
( ! [X14: $i] :
( ( ( cF @ X13 @ X14 )
!= $true )
| ( $true
= ( cD @ X14 @ X10 @ X11 ) ) )
| ( $true
!= ( cS @ X12 @ X13 ) ) )
| ! [X15: $i] :
? [X16: $i] :
! [X17: $i] :
? [X18: $i] :
( ( $true
= ( cS @ X17 @ X18 ) )
& ( $true
!= ( cD @ X18 @ X15 @ X16 ) ) ) )
& ! [X19: $i] :
? [X20: $i] :
! [X21: $i,X22: $i] :
( ! [X23: $i,X24: $i] :
( ( ( cF @ X22 @ X24 )
!= $true )
| ( $true
!= ( cF @ X21 @ X23 ) )
| ( $true
= ( cD @ X23 @ X24 @ X19 ) ) )
| ( $true
!= ( cD @ X21 @ X22 @ X20 ) ) )
& ! [X25: $i] :
? [X26: $i] :
! [X27: $i] :
? [X28: $i] :
( ( $true
= ( cS @ X27 @ X28 ) )
& ? [X29: $i] :
( ( $true
!= ( cD @ X29 @ X25 @ X26 ) )
& ( $true
= ( cF @ X28 @ X29 ) ) ) )
& ? [X30: $i] :
! [X31: $i] :
? [X32: $i] :
! [X33: $i] :
( ( ( cD @ X33 @ X30 @ X31 )
= $true )
| ( ( cS @ X32 @ X33 )
!= $true ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X17: $i] :
? [X18: $i] :
( ( cF @ X17 @ X18 )
= $true )
& ( ? [X4: $i] :
! [X5: $i] :
( ( cF @ X4 @ X5 )
!= $true )
| ? [X6: $i] :
! [X7: $i] :
? [X8: $i,X9: $i] :
( ? [X10: $i,X11: $i] :
( ( $true
!= ( cD @ X11 @ X10 @ X6 ) )
& ( $true
= ( cF @ X8 @ X11 ) )
& ( ( cF @ X9 @ X10 )
= $true ) )
& ( $true
= ( cD @ X8 @ X9 @ X7 ) ) )
| ? [X12: $i] :
! [X13: $i] :
? [X14: $i] :
! [X15: $i] :
( ! [X16: $i] :
( ( $true
!= ( cF @ X15 @ X16 ) )
| ( $true
= ( cD @ X16 @ X12 @ X13 ) ) )
| ( $true
!= ( cS @ X14 @ X15 ) ) )
| ! [X0: $i] :
? [X1: $i] :
! [X2: $i] :
? [X3: $i] :
( ( $true
= ( cS @ X2 @ X3 ) )
& ( $true
!= ( cD @ X3 @ X0 @ X1 ) ) ) )
& ! [X23: $i] :
? [X24: $i] :
! [X25: $i,X26: $i] :
( ! [X27: $i,X28: $i] :
( ( $true
!= ( cF @ X26 @ X28 ) )
| ( $true
!= ( cF @ X25 @ X27 ) )
| ( $true
= ( cD @ X27 @ X28 @ X23 ) ) )
| ( ( cD @ X25 @ X26 @ X24 )
!= $true ) )
& ! [X29: $i] :
? [X30: $i] :
! [X31: $i] :
? [X32: $i] :
( ( $true
= ( cS @ X31 @ X32 ) )
& ? [X33: $i] :
( ( ( cD @ X33 @ X29 @ X30 )
!= $true )
& ( $true
= ( cF @ X32 @ X33 ) ) ) )
& ? [X19: $i] :
! [X20: $i] :
? [X21: $i] :
! [X22: $i] :
( ( $true
= ( cD @ X22 @ X19 @ X20 ) )
| ( $true
!= ( cS @ X21 @ X22 ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X29: $i] :
? [X30: $i] :
! [X31: $i] :
? [X32: $i] :
( ( $true
= ( cS @ X31 @ X32 ) )
& ? [X33: $i] :
( ( ( cD @ X33 @ X29 @ X30 )
!= $true )
& ( $true
= ( cF @ X32 @ X33 ) ) ) )
& ! [X23: $i] :
? [X24: $i] :
! [X26: $i,X25: $i] :
( ! [X28: $i,X27: $i] :
( ( $true
= ( cD @ X27 @ X28 @ X23 ) )
| ( $true
!= ( cF @ X26 @ X28 ) )
| ( $true
!= ( cF @ X25 @ X27 ) ) )
| ( ( cD @ X25 @ X26 @ X24 )
!= $true ) )
& ? [X19: $i] :
! [X20: $i] :
? [X21: $i] :
! [X22: $i] :
( ( $true
= ( cD @ X22 @ X19 @ X20 ) )
| ( $true
!= ( cS @ X21 @ X22 ) ) )
& ! [X17: $i] :
? [X18: $i] :
( ( cF @ X17 @ X18 )
= $true )
& ( ? [X12: $i] :
! [X13: $i] :
? [X14: $i] :
! [X15: $i] :
( ! [X16: $i] :
( ( $true
!= ( cF @ X15 @ X16 ) )
| ( $true
= ( cD @ X16 @ X12 @ X13 ) ) )
| ( $true
!= ( cS @ X14 @ X15 ) ) )
| ? [X6: $i] :
! [X7: $i] :
? [X9: $i,X8: $i] :
( ? [X11: $i,X10: $i] :
( ( $true
!= ( cD @ X11 @ X10 @ X6 ) )
& ( $true
= ( cF @ X8 @ X11 ) )
& ( ( cF @ X9 @ X10 )
= $true ) )
& ( $true
= ( cD @ X8 @ X9 @ X7 ) ) )
| ? [X4: $i] :
! [X5: $i] :
( ( cF @ X4 @ X5 )
!= $true )
| ! [X0: $i] :
? [X1: $i] :
! [X2: $i] :
? [X3: $i] :
( ( $true
= ( cS @ X2 @ X3 ) )
& ( $true
!= ( cD @ X3 @ X0 @ X1 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ( ! [X6: $i] :
? [X7: $i] :
! [X9: $i,X8: $i] :
( ( $true
= ( cD @ X8 @ X9 @ X7 ) )
=> ! [X11: $i,X10: $i] :
( ( ( $true
= ( cF @ X8 @ X11 ) )
& ( ( cF @ X9 @ X10 )
= $true ) )
=> ( $true
= ( cD @ X11 @ X10 @ X6 ) ) ) )
& ! [X4: $i] :
? [X5: $i] :
( ( cF @ X4 @ X5 )
= $true )
& ? [X0: $i] :
! [X1: $i] :
? [X2: $i] :
! [X3: $i] :
( ( $true
= ( cS @ X2 @ X3 ) )
=> ( $true
= ( cD @ X3 @ X0 @ X1 ) ) ) )
=> ? [X12: $i] :
! [X13: $i] :
? [X14: $i] :
! [X15: $i] :
( ( $true
= ( cS @ X14 @ X15 ) )
=> ! [X16: $i] :
( ( $true
= ( cF @ X15 @ X16 ) )
=> ( $true
= ( cD @ X16 @ X12 @ X13 ) ) ) ) )
=> ( ( ! [X23: $i] :
? [X24: $i] :
! [X26: $i,X25: $i] :
( ( ( cD @ X25 @ X26 @ X24 )
= $true )
=> ! [X28: $i,X27: $i] :
( ( ( $true
= ( cF @ X26 @ X28 ) )
& ( $true
= ( cF @ X25 @ X27 ) ) )
=> ( $true
= ( cD @ X27 @ X28 @ X23 ) ) ) )
& ? [X19: $i] :
! [X20: $i] :
? [X21: $i] :
! [X22: $i] :
( ( $true
= ( cS @ X21 @ X22 ) )
=> ( $true
= ( cD @ X22 @ X19 @ X20 ) ) )
& ! [X17: $i] :
? [X18: $i] :
( ( cF @ X17 @ X18 )
= $true ) )
=> ? [X29: $i] :
! [X30: $i] :
? [X31: $i] :
! [X32: $i] :
( ( $true
= ( cS @ X31 @ X32 ) )
=> ! [X33: $i] :
( ( $true
= ( cF @ X32 @ X33 ) )
=> ( ( cD @ X33 @ X29 @ X30 )
= $true ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ( ? [X0: $i] :
! [X1: $i] :
? [X2: $i] :
! [X3: $i] :
( ( cS @ X2 @ X3 )
=> ( cD @ X3 @ X0 @ X1 ) )
& ! [X4: $i] :
? [X5: $i] : ( cF @ X4 @ X5 )
& ! [X6: $i] :
? [X7: $i] :
! [X8: $i,X9: $i] :
( ( cD @ X8 @ X9 @ X7 )
=> ! [X10: $i,X11: $i] :
( ( ( cF @ X8 @ X11 )
& ( cF @ X9 @ X10 ) )
=> ( cD @ X11 @ X10 @ X6 ) ) ) )
=> ? [X12: $i] :
! [X13: $i] :
? [X14: $i] :
! [X15: $i] :
( ( cS @ X14 @ X15 )
=> ! [X16: $i] :
( ( cF @ X15 @ X16 )
=> ( cD @ X16 @ X12 @ X13 ) ) ) )
=> ( ( ! [X17: $i] :
? [X18: $i] : ( cF @ X17 @ X18 )
& ? [X19: $i] :
! [X20: $i] :
? [X21: $i] :
! [X22: $i] :
( ( cS @ X21 @ X22 )
=> ( cD @ X22 @ X19 @ X20 ) )
& ! [X23: $i] :
? [X24: $i] :
! [X25: $i,X26: $i] :
( ( cD @ X25 @ X26 @ X24 )
=> ! [X27: $i,X28: $i] :
( ( ( cF @ X25 @ X27 )
& ( cF @ X26 @ X28 ) )
=> ( cD @ X27 @ X28 @ X23 ) ) ) )
=> ? [X29: $i] :
! [X30: $i] :
? [X31: $i] :
! [X32: $i] :
( ( cS @ X31 @ X32 )
=> ! [X33: $i] :
( ( cF @ X32 @ X33 )
=> ( cD @ X33 @ X29 @ X30 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ( ? [X0: $i] :
! [X2: $i] :
? [X3: $i] :
! [X4: $i] :
( ( cS @ X3 @ X4 )
=> ( cD @ X4 @ X0 @ X2 ) )
& ! [X0: $i] :
? [X1: $i] : ( cF @ X0 @ X1 )
& ! [X2: $i] :
? [X5: $i] :
! [X6: $i,X7: $i] :
( ( cD @ X6 @ X7 @ X5 )
=> ! [X8: $i,X1: $i] :
( ( ( cF @ X6 @ X1 )
& ( cF @ X7 @ X8 ) )
=> ( cD @ X1 @ X8 @ X2 ) ) ) )
=> ? [X1: $i] :
! [X2: $i] :
? [X9: $i] :
! [X4: $i] :
( ( cS @ X9 @ X4 )
=> ! [X8: $i] :
( ( cF @ X4 @ X8 )
=> ( cD @ X8 @ X1 @ X2 ) ) ) )
=> ( ( ! [X0: $i] :
? [X1: $i] : ( cF @ X0 @ X1 )
& ? [X0: $i] :
! [X2: $i] :
? [X3: $i] :
! [X4: $i] :
( ( cS @ X3 @ X4 )
=> ( cD @ X4 @ X0 @ X2 ) )
& ! [X2: $i] :
? [X5: $i] :
! [X6: $i,X7: $i] :
( ( cD @ X6 @ X7 @ X5 )
=> ! [X1: $i,X8: $i] :
( ( ( cF @ X6 @ X1 )
& ( cF @ X7 @ X8 ) )
=> ( cD @ X1 @ X8 @ X2 ) ) ) )
=> ? [X1: $i] :
! [X2: $i] :
? [X9: $i] :
! [X4: $i] :
( ( cS @ X9 @ X4 )
=> ! [X8: $i] :
( ( cF @ X4 @ X8 )
=> ( cD @ X8 @ X1 @ X2 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ( ? [X0: $i] :
! [X2: $i] :
? [X3: $i] :
! [X4: $i] :
( ( cS @ X3 @ X4 )
=> ( cD @ X4 @ X0 @ X2 ) )
& ! [X0: $i] :
? [X1: $i] : ( cF @ X0 @ X1 )
& ! [X2: $i] :
? [X5: $i] :
! [X6: $i,X7: $i] :
( ( cD @ X6 @ X7 @ X5 )
=> ! [X8: $i,X1: $i] :
( ( ( cF @ X6 @ X1 )
& ( cF @ X7 @ X8 ) )
=> ( cD @ X1 @ X8 @ X2 ) ) ) )
=> ? [X1: $i] :
! [X2: $i] :
? [X9: $i] :
! [X4: $i] :
( ( cS @ X9 @ X4 )
=> ! [X8: $i] :
( ( cF @ X4 @ X8 )
=> ( cD @ X8 @ X1 @ X2 ) ) ) )
=> ( ( ! [X0: $i] :
? [X1: $i] : ( cF @ X0 @ X1 )
& ? [X0: $i] :
! [X2: $i] :
? [X3: $i] :
! [X4: $i] :
( ( cS @ X3 @ X4 )
=> ( cD @ X4 @ X0 @ X2 ) )
& ! [X2: $i] :
? [X5: $i] :
! [X6: $i,X7: $i] :
( ( cD @ X6 @ X7 @ X5 )
=> ! [X1: $i,X8: $i] :
( ( ( cF @ X6 @ X1 )
& ( cF @ X7 @ X8 ) )
=> ( cD @ X1 @ X8 @ X2 ) ) ) )
=> ? [X1: $i] :
! [X2: $i] :
? [X9: $i] :
! [X4: $i] :
( ( cS @ X9 @ X4 )
=> ! [X8: $i] :
( ( cF @ X4 @ X8 )
=> ( cD @ X8 @ X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.CRacoZzQkz/DTF2THF_23011.p',cTHM408) ).
thf(f62,plain,
( ! [X5: $i] :
( $true
!= ( cD @ ( sK6 @ X5 ) @ ( sK5 @ X5 ) @ sK2 ) )
| ~ spl17_7 ),
inference(avatar_component_clause,[status(thm)],[f61]) ).
thf(f61,definition,
( spl17_7
<=> ! [X5: $i] :
( $true
!= ( cD @ ( sK6 @ X5 ) @ ( sK5 @ X5 ) @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl17_7])],[avatar_definition]) ).
thf(f87,plain,
( ~ spl17_1
| ~ spl17_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f86]) ).
thf(f86,plain,
( $false
| ~ spl17_1
| ~ spl17_8 ),
inference(trivial_inequality_removal,[status(thm)],[f85]) ).
thf(f85,plain,
( ( $true != $true )
| ~ spl17_1
| ~ spl17_8 ),
inference(superposition,[status(thm)],[f84,f65]) ).
thf(f65,plain,
( ! [X17: $i,X15: $i] :
( $true
= ( cS @ X17 @ ( sK10 @ X17 @ X15 ) ) )
| ~ spl17_8 ),
inference(avatar_component_clause,[status(thm)],[f64]) ).
thf(f64,definition,
( spl17_8
<=> ! [X17: $i,X15: $i] :
( $true
= ( cS @ X17 @ ( sK10 @ X17 @ X15 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl17_8])],[avatar_definition]) ).
thf(f84,plain,
( ! [X0: $i] :
( $true
!= ( cS @ ( sK16 @ ( sK9 @ sK15 ) ) @ ( sK10 @ X0 @ sK15 ) ) )
| ~ spl17_1 ),
inference(trivial_inequality_removal,[status(thm)],[f83]) ).
thf(f83,plain,
( ! [X0: $i] :
( ( $true
!= ( cS @ ( sK16 @ ( sK9 @ sK15 ) ) @ ( sK10 @ X0 @ sK15 ) ) )
| ( $true != $true ) )
| ~ spl17_1 ),
inference(superposition,[status(thm)],[f41,f25]) ).
thf(f25,plain,
! [X31: $i,X33: $i] :
( ( $true
= ( cD @ X33 @ sK15 @ X31 ) )
| ( $true
!= ( cS @ ( sK16 @ X31 ) @ X33 ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f41,plain,
( ! [X17: $i,X15: $i] :
( $true
!= ( cD @ ( sK10 @ X17 @ X15 ) @ X15 @ ( sK9 @ X15 ) ) )
| ~ spl17_1 ),
inference(avatar_component_clause,[status(thm)],[f40]) ).
thf(f40,definition,
( spl17_1
<=> ! [X17: $i,X15: $i] :
( $true
!= ( cD @ ( sK10 @ X17 @ X15 ) @ X15 @ ( sK9 @ X15 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl17_1])],[avatar_definition]) ).
thf(f82,plain,
~ spl17_3,
inference(avatar_contradiction_clause,[status(thm)],[f81]) ).
thf(f81,plain,
( $false
| ~ spl17_3 ),
inference(trivial_inequality_removal,[status(thm)],[f80]) ).
thf(f80,plain,
( ( $true != $true )
| ~ spl17_3 ),
inference(superposition,[status(thm)],[f47,f38]) ).
thf(f38,plain,
! [X0: $i] :
( ( cF @ X0 @ ( sK0 @ X0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f47,plain,
( ! [X3: $i] :
( $true
!= ( cF @ sK1 @ X3 ) )
| ~ spl17_3 ),
inference(avatar_component_clause,[status(thm)],[f46]) ).
thf(f46,definition,
( spl17_3
<=> ! [X3: $i] :
( $true
!= ( cF @ sK1 @ X3 ) ) ),
introduced(definition,[new_symbols(naming,[spl17_3])],[avatar_definition]) ).
thf(f79,plain,
~ spl17_2,
inference(avatar_contradiction_clause,[status(thm)],[f78]) ).
thf(f78,plain,
( $false
| ~ spl17_2 ),
inference(trivial_inequality_removal,[status(thm)],[f77]) ).
thf(f77,plain,
( ( $true != $true )
| ~ spl17_2 ),
inference(superposition,[status(thm)],[f76,f28]) ).
thf(f28,plain,
! [X27: $i,X25: $i] :
( $true
= ( cS @ X27 @ ( sK13 @ X27 @ X25 ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f76,plain,
( ! [X0: $i] :
( $true
!= ( cS @ ( sK8 @ ( sK12 @ sK7 ) ) @ ( sK13 @ X0 @ sK7 ) ) )
| ~ spl17_2 ),
inference(trivial_inequality_removal,[status(thm)],[f75]) ).
thf(f75,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( cS @ ( sK8 @ ( sK12 @ sK7 ) ) @ ( sK13 @ X0 @ sK7 ) ) ) )
| ~ spl17_2 ),
inference(superposition,[status(thm)],[f74,f26]) ).
thf(f26,plain,
! [X27: $i,X25: $i] :
( $true
= ( cF @ ( sK13 @ X27 @ X25 ) @ ( sK14 @ X27 @ X25 ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f74,plain,
( ! [X0: $i,X1: $i] :
( ( ( cF @ X1 @ ( sK14 @ X0 @ sK7 ) )
!= $true )
| ( ( cS @ ( sK8 @ ( sK12 @ sK7 ) ) @ X1 )
!= $true ) )
| ~ spl17_2 ),
inference(trivial_inequality_removal,[status(thm)],[f73]) ).
thf(f73,plain,
( ! [X0: $i,X1: $i] :
( ( ( cS @ ( sK8 @ ( sK12 @ sK7 ) ) @ X1 )
!= $true )
| ( ( cF @ X1 @ ( sK14 @ X0 @ sK7 ) )
!= $true )
| ( $true != $true ) )
| ~ spl17_2 ),
inference(superposition,[status(thm)],[f27,f44]) ).
thf(f44,plain,
( ! [X11: $i,X14: $i,X13: $i] :
( ( $true
= ( cD @ X14 @ sK7 @ X11 ) )
| ( ( cS @ ( sK8 @ X11 ) @ X13 )
!= $true )
| ( ( cF @ X13 @ X14 )
!= $true ) )
| ~ spl17_2 ),
inference(avatar_component_clause,[status(thm)],[f43]) ).
thf(f43,definition,
( spl17_2
<=> ! [X13: $i,X11: $i,X14: $i] :
( ( $true
= ( cD @ X14 @ sK7 @ X11 ) )
| ( ( cF @ X13 @ X14 )
!= $true )
| ( ( cS @ ( sK8 @ X11 ) @ X13 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl17_2])],[avatar_definition]) ).
thf(f27,plain,
! [X27: $i,X25: $i] :
( ( cD @ ( sK14 @ X27 @ X25 ) @ X25 @ ( sK12 @ X25 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f70,plain,
( spl17_8
| spl17_3
| spl17_5
| spl17_2 ),
inference(avatar_split_clause,[status(thm)],[f35,f43,f53,f46,f64]) ).
thf(f35,plain,
! [X3: $i,X11: $i,X14: $i,X17: $i,X15: $i,X5: $i,X13: $i] :
( ( $true
= ( cD @ X14 @ sK7 @ X11 ) )
| ( ( cS @ ( sK8 @ X11 ) @ X13 )
!= $true )
| ( ( cF @ ( sK3 @ X5 ) @ ( sK6 @ X5 ) )
= $true )
| ( ( cF @ X13 @ X14 )
!= $true )
| ( $true
!= ( cF @ sK1 @ X3 ) )
| ( $true
= ( cS @ X17 @ ( sK10 @ X17 @ X15 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f69,plain,
( spl17_2
| spl17_3
| spl17_4
| spl17_8 ),
inference(avatar_split_clause,[status(thm)],[f33,f64,f49,f46,f43]) ).
thf(f33,plain,
! [X3: $i,X11: $i,X14: $i,X17: $i,X15: $i,X5: $i,X13: $i] :
( ( $true
= ( cS @ X17 @ ( sK10 @ X17 @ X15 ) ) )
| ( ( cS @ ( sK8 @ X11 ) @ X13 )
!= $true )
| ( $true
= ( cD @ X14 @ sK7 @ X11 ) )
| ( ( cF @ X13 @ X14 )
!= $true )
| ( $true
!= ( cF @ sK1 @ X3 ) )
| ( $true
= ( cF @ ( sK4 @ X5 ) @ ( sK5 @ X5 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f68,plain,
( spl17_1
| spl17_2
| spl17_3
| spl17_7 ),
inference(avatar_split_clause,[status(thm)],[f36,f61,f46,f43,f40]) ).
thf(f36,plain,
! [X3: $i,X11: $i,X14: $i,X17: $i,X15: $i,X5: $i,X13: $i] :
( ( $true
!= ( cD @ ( sK6 @ X5 ) @ ( sK5 @ X5 ) @ sK2 ) )
| ( $true
!= ( cD @ ( sK10 @ X17 @ X15 ) @ X15 @ ( sK9 @ X15 ) ) )
| ( $true
= ( cD @ X14 @ sK7 @ X11 ) )
| ( $true
!= ( cF @ sK1 @ X3 ) )
| ( ( cS @ ( sK8 @ X11 ) @ X13 )
!= $true )
| ( ( cF @ X13 @ X14 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f67,plain,
( spl17_3
| spl17_2
| spl17_8
| spl17_6 ),
inference(avatar_split_clause,[status(thm)],[f31,f57,f64,f43,f46]) ).
thf(f31,plain,
! [X3: $i,X11: $i,X14: $i,X17: $i,X15: $i,X5: $i,X13: $i] :
( ( $true
!= ( cF @ sK1 @ X3 ) )
| ( $true
= ( cS @ X17 @ ( sK10 @ X17 @ X15 ) ) )
| ( $true
= ( cD @ ( sK3 @ X5 ) @ ( sK4 @ X5 ) @ X5 ) )
| ( $true
= ( cD @ X14 @ sK7 @ X11 ) )
| ( ( cS @ ( sK8 @ X11 ) @ X13 )
!= $true )
| ( ( cF @ X13 @ X14 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f66,plain,
( spl17_3
| spl17_2
| spl17_7
| spl17_8 ),
inference(avatar_split_clause,[status(thm)],[f37,f64,f61,f43,f46]) ).
thf(f37,plain,
! [X3: $i,X11: $i,X14: $i,X17: $i,X15: $i,X5: $i,X13: $i] :
( ( $true
= ( cS @ X17 @ ( sK10 @ X17 @ X15 ) ) )
| ( $true
!= ( cF @ sK1 @ X3 ) )
| ( $true
= ( cD @ X14 @ sK7 @ X11 ) )
| ( ( cF @ X13 @ X14 )
!= $true )
| ( ( cS @ ( sK8 @ X11 ) @ X13 )
!= $true )
| ( $true
!= ( cD @ ( sK6 @ X5 ) @ ( sK5 @ X5 ) @ sK2 ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f59,plain,
( spl17_3
| spl17_2
| spl17_1
| spl17_6 ),
inference(avatar_split_clause,[status(thm)],[f30,f57,f40,f43,f46]) ).
thf(f30,plain,
! [X3: $i,X11: $i,X14: $i,X17: $i,X15: $i,X5: $i,X13: $i] :
( ( $true
!= ( cD @ ( sK10 @ X17 @ X15 ) @ X15 @ ( sK9 @ X15 ) ) )
| ( ( cF @ X13 @ X14 )
!= $true )
| ( $true
= ( cD @ ( sK3 @ X5 ) @ ( sK4 @ X5 ) @ X5 ) )
| ( $true
!= ( cF @ sK1 @ X3 ) )
| ( $true
= ( cD @ X14 @ sK7 @ X11 ) )
| ( ( cS @ ( sK8 @ X11 ) @ X13 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f55,plain,
( spl17_3
| spl17_1
| spl17_5
| spl17_2 ),
inference(avatar_split_clause,[status(thm)],[f34,f43,f53,f40,f46]) ).
thf(f34,plain,
! [X3: $i,X11: $i,X14: $i,X17: $i,X15: $i,X5: $i,X13: $i] :
( ( ( cF @ X13 @ X14 )
!= $true )
| ( $true
!= ( cF @ sK1 @ X3 ) )
| ( $true
!= ( cD @ ( sK10 @ X17 @ X15 ) @ X15 @ ( sK9 @ X15 ) ) )
| ( ( cF @ ( sK3 @ X5 ) @ ( sK6 @ X5 ) )
= $true )
| ( ( cS @ ( sK8 @ X11 ) @ X13 )
!= $true )
| ( $true
= ( cD @ X14 @ sK7 @ X11 ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f51,plain,
( spl17_1
| spl17_2
| spl17_3
| spl17_4 ),
inference(avatar_split_clause,[status(thm)],[f32,f49,f46,f43,f40]) ).
thf(f32,plain,
! [X3: $i,X11: $i,X14: $i,X17: $i,X15: $i,X5: $i,X13: $i] :
( ( $true
= ( cD @ X14 @ sK7 @ X11 ) )
| ( $true
= ( cF @ ( sK4 @ X5 ) @ ( sK5 @ X5 ) ) )
| ( $true
!= ( cD @ ( sK10 @ X17 @ X15 ) @ X15 @ ( sK9 @ X15 ) ) )
| ( ( cS @ ( sK8 @ X11 ) @ X13 )
!= $true )
| ( ( cF @ X13 @ X14 )
!= $true )
| ( $true
!= ( cF @ sK1 @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO384^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.35 % Computer : n001.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Tue Feb 24 14:30:05 EST 2026
% 0.17/0.35 % CPUTime :
% 0.17/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.21/0.46 ---- Original DTF file ---
% 0.21/0.46 thf(spec,logic,$$dhol).
% 0.21/0.46 %------------------------------------------------------------------------------
% 0.21/0.46 % File : SYO384^5 : TPTP v9.2.1. Released v4.0.0.
% 0.21/0.46 % Domain : Syntactic
% 0.21/0.46 % Problem : TPS problem THM408
% 0.21/0.46 % Version : Especial.
% 0.21/0.46 % English :
% 0.21/0.46
% 0.21/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.21/0.46 % Source : [Bro09]
% 0.21/0.46 % Names : tps_0167 [Bro09]
% 0.21/0.46 % : THM408 [TPS]
% 0.21/0.46
% 0.21/0.46 % Status : Theorem
% 0.21/0.46 % Rating : 0.00 v6.2.0, 0.17 v6.1.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.0
% 0.21/0.46 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.21/0.46 % Number of atoms : 20 ( 0 equ; 0 cnn)
% 0.21/0.46 % Maximal formula atoms : 20 ( 20 avg)
% 0.21/0.46 % Number of connectives : 67 ( 0 ~; 0 |; 6 &; 48 @)
% 0.21/0.46 % ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% 0.21/0.46 % Maximal formula depth : 16 ( 16 avg)
% 0.21/0.46 % Number of types : 2 ( 0 usr)
% 0.21/0.46 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.21/0.46 % Number of symbols : 3 ( 3 usr; 0 con; 2-3 aty)
% 0.21/0.46 % Number of variables : 34 ( 0 ^; 22 !; 12 ?; 34 :)
% 0.21/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.21/0.46
% 0.21/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.21/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.21/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.21/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.21/0.46 %------------------------------------------------------------------------------
% 0.21/0.46 thf(cD,type,
% 0.21/0.46 cD: $i > $i > $i > $o ).
% 0.21/0.46
% 0.21/0.46 thf(cF,type,
% 0.21/0.46 cF: $i > $i > $o ).
% 0.21/0.46
% 0.21/0.46 thf(cS,type,
% 0.21/0.46 cS: $i > $i > $o ).
% 0.21/0.46
% 0.21/0.46 thf(cTHM408,conjecture,
% 0.21/0.46 ( ( ( ! [Xx: $i] :
% 0.21/0.46 ? [Xy: $i] : ( cF @ Xx @ Xy )
% 0.21/0.46 & ? [Xx: $i] :
% 0.21/0.46 ! [Xe: $i] :
% 0.21/0.46 ? [Xn: $i] :
% 0.21/0.46 ! [Xw: $i] :
% 0.21/0.46 ( ( cS @ Xn @ Xw )
% 0.21/0.46 => ( cD @ Xw @ Xx @ Xe ) )
% 0.21/0.46 & ! [Xe: $i] :
% 0.21/0.46 ? [Xd: $i] :
% 0.21/0.46 ! [Xa: $i,Xb: $i] :
% 0.21/0.46 ( ( cD @ Xa @ Xb @ Xd )
% 0.21/0.46 => ! [Xy: $i,Xz: $i] :
% 0.21/0.46 ( ( ( cF @ Xa @ Xy )
% 0.21/0.46 & ( cF @ Xb @ Xz ) )
% 0.21/0.46 => ( cD @ Xy @ Xz @ Xe ) ) ) )
% 0.21/0.46 => ? [Xy: $i] :
% 0.21/0.46 ! [Xe: $i] :
% 0.21/0.46 ? [Xm: $i] :
% 0.21/0.46 ! [Xw: $i] :
% 0.21/0.46 ( ( cS @ Xm @ Xw )
% 0.21/0.46 => ! [Xz: $i] :
% 0.21/0.46 ( ( cF @ Xw @ Xz )
% 0.21/0.46 => ( cD @ Xz @ Xy @ Xe ) ) ) )
% 0.21/0.46 => ( ( ! [Xx: $i] :
% 0.21/0.46 ? [Xy: $i] : ( cF @ Xx @ Xy )
% 0.21/0.46 & ? [Xx: $i] :
% 0.21/0.46 ! [Xe: $i] :
% 0.21/0.46 ? [Xn: $i] :
% 0.21/0.46 ! [Xw: $i] :
% 0.21/0.46 ( ( cS @ Xn @ Xw )
% 0.21/0.46 => ( cD @ Xw @ Xx @ Xe ) )
% 0.21/0.46 & ! [Xe: $i] :
% 0.21/0.46 ? [Xd: $i] :
% 0.21/0.46 ! [Xa: $i,Xb: $i] :
% 0.21/0.46 ( ( cD @ Xa @ Xb @ Xd )
% 0.21/0.46 => ! [Xy: $i,Xz: $i] :
% 0.21/0.46 ( ( ( cF @ Xa @ Xy )
% 0.21/0.46 & ( cF @ Xb @ Xz ) )
% 0.21/0.46 => ( cD @ Xy @ Xz @ Xe ) ) ) )
% 0.21/0.46 => ? [Xy: $i] :
% 0.21/0.46 ! [Xe: $i] :
% 0.21/0.46 ? [Xm: $i] :
% 0.21/0.46 ! [Xw: $i] :
% 0.21/0.46 ( ( cS @ Xm @ Xw )
% 0.21/0.46 => ! [Xz: $i] :
% 0.21/0.46 ( ( cF @ Xw @ Xz )
% 0.21/0.46 => ( cD @ Xz @ Xy @ Xe ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 %------------------------------------------------------------------------------
% 0.21/0.46 ------------------------
% 1.72/1.42 ---- Embedded in THF ---
% 1.72/1.42 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.72/1.42 %%% Generated on Tue Feb 24 14:30:06 EST 2026
% 1.72/1.42 %%% using '$$dhol' embedding, version 1.3.0.
% 1.72/1.42 %%% Logic specification used:
% 1.72/1.42 %%% thf(spec, logic, $$dhol).
% 1.72/1.42
% 1.72/1.42 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.CRacoZzQkz/DTF2DTF23011.p
% See solution above
% 1.72/1.42 ------------------------
% 1.72/1.43 ---- Cleaned THF ---
% 1.72/1.43 thf(cD,type,
% 1.72/1.43 cD: $i > $i > $i > $o ).
% 1.72/1.43
% 1.72/1.43 thf(cF,type,
% 1.72/1.43 cF: $i > $i > $o ).
% 1.72/1.43
% 1.72/1.43 thf(cS,type,
% 1.72/1.43 cS: $i > $i > $o ).
% 1.72/1.43
% 1.72/1.43 thf(cTHM408,conjecture,
% 1.72/1.43 ( ( ( ! [Xx: $i] :
% 1.72/1.43 ? [Xy: $i] : ( cF @ Xx @ Xy )
% 1.72/1.43 & ? [Xx: $i] :
% 1.72/1.43 ! [Xe: $i] :
% 1.72/1.43 ? [Xn: $i] :
% 1.72/1.43 ! [Xw: $i] :
% 1.72/1.43 ( ( cS @ Xn @ Xw )
% 1.72/1.43 => ( cD @ Xw @ Xx @ Xe ) )
% 1.72/1.43 & ! [Xe: $i] :
% 1.72/1.43 ? [Xd: $i] :
% 1.72/1.43 ! [Xa: $i,Xb: $i] :
% 1.72/1.43 ( ( cD @ Xa @ Xb @ Xd )
% 1.72/1.43 => ! [Xy: $i,Xz: $i] :
% 1.72/1.43 ( ( ( cF @ Xa @ Xy )
% 1.72/1.43 & ( cF @ Xb @ Xz ) )
% 1.72/1.43 => ( cD @ Xy @ Xz @ Xe ) ) ) )
% 1.72/1.43 => ? [Xy: $i] :
% 1.72/1.43 ! [Xe: $i] :
% 1.72/1.43 ? [Xm: $i] :
% 1.72/1.43 ! [Xw: $i] :
% 1.72/1.43 ( ( cS @ Xm @ Xw )
% 1.72/1.43 => ! [Xz: $i] :
% 1.72/1.43 ( ( cF @ Xw @ Xz )
% 1.72/1.43 => ( cD @ Xz @ Xy @ Xe ) ) ) )
% 1.72/1.43 => ( ( ! [Xx: $i] :
% 1.72/1.43 ? [Xy: $i] : ( cF @ Xx @ Xy )
% 1.72/1.43 & ? [Xx: $i] :
% 1.72/1.43 ! [Xe: $i] :
% 1.72/1.43 ? [Xn: $i] :
% 1.72/1.43 ! [Xw: $i] :
% 1.72/1.43 ( ( cS @ Xn @ Xw )
% 1.72/1.43 => ( cD @ Xw @ Xx @ Xe ) )
% 1.72/1.43 & ! [Xe: $i] :
% 1.72/1.43 ? [Xd: $i] :
% 1.72/1.43 ! [Xa: $i,Xb: $i] :
% 1.72/1.43 ( ( cD @ Xa @ Xb @ Xd )
% 1.72/1.43 => ! [Xy: $i,Xz: $i] :
% 1.72/1.43 ( ( ( cF @ Xa @ Xy )
% 1.72/1.43 & ( cF @ Xb @ Xz ) )
% 1.72/1.43 => ( cD @ Xy @ Xz @ Xe ) ) ) )
% 1.72/1.43 => ? [Xy: $i] :
% 1.72/1.43 ! [Xe: $i] :
% 1.72/1.43 ? [Xm: $i] :
% 1.72/1.43 ! [Xw: $i] :
% 1.72/1.43 ( ( cS @ Xm @ Xw )
% 1.72/1.43 => ! [Xz: $i] :
% 1.72/1.43 ( ( cF @ Xw @ Xz )
% 1.72/1.43 => ( cD @ Xz @ Xy @ Xe ) ) ) ) ) ).
% 1.72/1.43 ------------------------
% 1.72/1.45 % (23109)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_23011 for (2999ds/183Mi)
% 1.72/1.45 % (23115)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_23011 for (2999ds/18Mi)
% 1.72/1.45 % (23110)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_23011 for (2999ds/4Mi)
% 1.72/1.45 % (23111)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_23011 for (2999ds/27Mi)
% 1.72/1.45 % (23113)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_23011 for (2999ds/2Mi)
% 1.72/1.45 % (23112)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_23011 for (2999ds/2Mi)
% 1.72/1.45 % (23114)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_23011 for (2999ds/275Mi)
% 1.72/1.45 % (23112)Instruction limit reached!
% 1.72/1.45 % (23112)------------------------------
% 1.72/1.45 % (23112)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.45 % (23112)Termination reason: Unknown
% 1.72/1.45 % (23112)Termination phase: Preprocessing 3
% 1.72/1.45
% 1.72/1.45 % (23112)Memory used [KB]: 1023
% 1.72/1.45 % (23112)Time elapsed: 0.003 s
% 1.72/1.45 % (23112)Instructions burned: 2 (million)
% 1.72/1.45 % (23112)------------------------------
% 1.72/1.45 % (23112)------------------------------
% 1.72/1.45 % (23113)Instruction limit reached!
% 1.72/1.45 % (23113)------------------------------
% 1.72/1.45 % (23113)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.45 % (23113)Termination reason: Unknown
% 1.72/1.45 % (23113)Termination phase: Property scanning
% 1.72/1.45
% 1.72/1.45 % (23113)Memory used [KB]: 1023
% 1.72/1.45 % (23113)Time elapsed: 0.003 s
% 1.72/1.45 % (23113)Instructions burned: 3 (million)
% 1.72/1.45 % (23113)------------------------------
% 1.72/1.45 % (23113)------------------------------
% 1.72/1.45 % (23110)Instruction limit reached!
% 1.72/1.45 % (23110)------------------------------
% 1.72/1.45 % (23110)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.45 % (23110)Termination reason: Unknown
% 1.72/1.45 % (23110)Termination phase: Property scanning
% 1.72/1.45
% 1.72/1.45 % (23110)Memory used [KB]: 1023
% 1.72/1.45 % (23110)Time elapsed: 0.004 s
% 1.72/1.45 % (23110)Instructions burned: 4 (million)
% 1.72/1.45 % (23110)------------------------------
% 1.72/1.45 % (23110)------------------------------
% 1.72/1.46 % (23109)First to succeed.
% 1.72/1.46 % (23115)Instruction limit reached!
% 1.72/1.46 % (23115)------------------------------
% 1.72/1.46 % (23115)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.46 % (23115)Termination reason: Unknown
% 1.72/1.46 % (23115)Termination phase: Saturation
% 1.72/1.46
% 1.72/1.46 % (23115)Memory used [KB]: 5628
% 1.72/1.46 % (23115)Time elapsed: 0.012 s
% 1.72/1.46 % (23115)Instructions burned: 19 (million)
% 1.72/1.46 % (23115)------------------------------
% 1.72/1.46 % (23115)------------------------------
% 1.72/1.47 % (23114)Also succeeded, but the first one will report.
% 1.72/1.47 % (23111)Also succeeded, but the first one will report.
% 1.72/1.47 % (23109)Refutation found. Thanks to Tanya!
% 1.72/1.47 % SZS status Theorem for DTF2THF_23011
% 1.72/1.47 % SZS output start Proof for DTF2THF_23011
% 1.72/1.47 thf(func_def_0, type, cD: $i > $i > $i > $o).
% 1.72/1.47 thf(func_def_1, type, cF: $i > $i > $o).
% 1.72/1.47 thf(func_def_2, type, cS: $i > $i > $o).
% 1.72/1.47 thf(func_def_6, type, sK0: $i > $i).
% 1.72/1.47 thf(func_def_9, type, sK3: $i > $i).
% 1.72/1.47 thf(func_def_10, type, sK4: $i > $i).
% 1.72/1.47 thf(func_def_11, type, sK5: $i > $i).
% 1.72/1.47 thf(func_def_12, type, sK6: $i > $i).
% 1.72/1.47 thf(func_def_14, type, sK8: $i > $i).
% 1.72/1.47 thf(func_def_15, type, sK9: $i > $i).
% 1.72/1.47 thf(func_def_16, type, sK10: $i > $i > $i).
% 1.72/1.47 thf(func_def_17, type, sK11: $i > $i).
% 1.72/1.47 thf(func_def_18, type, sK12: $i > $i).
% 1.72/1.47 thf(func_def_19, type, sK13: $i > $i > $i).
% 1.72/1.47 thf(func_def_20, type, sK14: $i > $i > $i).
% 1.72/1.47 thf(func_def_22, type, sK16: $i > $i).
% 1.72/1.47 thf(f104,plain,(
% 1.72/1.47 $false),
% 1.72/1.47 inference(avatar_sat_refutation,[status(thm)],[f51,f55,f59,f66,f67,f68,f69,f70,f79,f82,f87,f103])).
% 1.72/1.47 thf(f103,plain,(
% 1.72/1.47 ~spl17_4 | ~spl17_5 | ~spl17_6 | ~spl17_7),
% 1.72/1.47 inference(avatar_contradiction_clause,[status(thm)],[f102])).
% 1.72/1.47 thf(f102,plain,(
% 1.72/1.47 $false | (~spl17_4 | ~spl17_5 | ~spl17_6 | ~spl17_7)),
% 1.72/1.47 inference(subsumption_resolution,[status(thm)],[f101,f50])).
% 1.72/1.47 thf(f50,plain,(
% 1.72/1.47 ( ! [X5 : $i] : (($true = (cF @ (sK4 @ X5) @ (sK5 @ X5)))) ) | ~spl17_4),
% 1.72/1.47 inference(avatar_component_clause,[status(thm)],[f49])).
% 1.72/1.47 thf(f49,definition,(
% 1.72/1.47 spl17_4 <=> ! [X5 : $i] : ($true = (cF @ (sK4 @ X5) @ (sK5 @ X5)))),
% 1.72/1.47 introduced(definition,[new_symbols(naming,[spl17_4])],[avatar_definition])).
% 1.72/1.47 thf(f101,plain,(
% 1.72/1.47 ((cF @ (sK4 @ (sK11 @ sK2)) @ (sK5 @ (sK11 @ sK2))) != $true) | (~spl17_5 | ~spl17_6 | ~spl17_7)),
% 1.72/1.47 inference(trivial_inequality_removal,[status(thm)],[f100])).
% 1.72/1.47 thf(f100,plain,(
% 1.72/1.47 ($true != $true) | ((cF @ (sK4 @ (sK11 @ sK2)) @ (sK5 @ (sK11 @ sK2))) != $true) | (~spl17_5 | ~spl17_6 | ~spl17_7)),
% 1.72/1.47 inference(superposition,[status(thm)],[f97,f54])).
% 1.72/1.47 thf(f54,plain,(
% 1.72/1.47 ( ! [X5 : $i] : (((cF @ (sK3 @ X5) @ (sK6 @ X5)) = $true)) ) | ~spl17_5),
% 1.72/1.47 inference(avatar_component_clause,[status(thm)],[f53])).
% 1.72/1.47 thf(f53,definition,(
% 1.72/1.47 spl17_5 <=> ! [X5 : $i] : ((cF @ (sK3 @ X5) @ (sK6 @ X5)) = $true)),
% 1.72/1.47 introduced(definition,[new_symbols(naming,[spl17_5])],[avatar_definition])).
% 1.72/1.47 thf(f97,plain,(
% 1.72/1.47 ( ! [X0 : $i] : (($true != (cF @ (sK3 @ (sK11 @ sK2)) @ (sK6 @ X0))) | ((cF @ (sK4 @ (sK11 @ sK2)) @ (sK5 @ X0)) != $true)) ) | (~spl17_6 | ~spl17_7)),
% 1.72/1.47 inference(trivial_inequality_removal,[status(thm)],[f95])).
% 1.72/1.47 thf(f95,plain,(
% 1.72/1.47 ( ! [X0 : $i] : (($true != (cF @ (sK3 @ (sK11 @ sK2)) @ (sK6 @ X0))) | ($true != $true) | ((cF @ (sK4 @ (sK11 @ sK2)) @ (sK5 @ X0)) != $true)) ) | (~spl17_6 | ~spl17_7)),
% 1.72/1.47 inference(superposition,[status(thm)],[f62,f90])).
% 1.72/1.47 thf(f90,plain,(
% 1.72/1.47 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (cD @ X1 @ X2 @ X0)) | ($true != (cF @ (sK3 @ (sK11 @ X0)) @ X1)) | ((cF @ (sK4 @ (sK11 @ X0)) @ X2) != $true)) ) | ~spl17_6),
% 1.72/1.47 inference(trivial_inequality_removal,[status(thm)],[f89])).
% 1.72/1.47 thf(f89,plain,(
% 1.72/1.47 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (cF @ (sK3 @ (sK11 @ X0)) @ X1)) | ($true = (cD @ X1 @ X2 @ X0)) | ((cF @ (sK4 @ (sK11 @ X0)) @ X2) != $true) | ($true != $true)) ) | ~spl17_6),
% 1.72/1.47 inference(superposition,[status(thm)],[f29,f58])).
% 1.72/1.47 thf(f58,plain,(
% 1.72/1.47 ( ! [X5 : $i] : (($true = (cD @ (sK3 @ X5) @ (sK4 @ X5) @ X5))) ) | ~spl17_6),
% 1.72/1.47 inference(avatar_component_clause,[status(thm)],[f57])).
% 1.72/1.47 thf(f57,definition,(
% 1.72/1.47 spl17_6 <=> ! [X5 : $i] : ($true = (cD @ (sK3 @ X5) @ (sK4 @ X5) @ X5))),
% 1.72/1.47 introduced(definition,[new_symbols(naming,[spl17_6])],[avatar_definition])).
% 1.72/1.47 thf(f29,plain,(
% 1.72/1.47 ( ! [X21 : $i,X19 : $i,X24 : $i,X22 : $i,X23 : $i] : (($true != (cD @ X21 @ X22 @ (sK11 @ X19))) | ($true = (cD @ X23 @ X24 @ X19)) | ((cF @ X22 @ X24) != $true) | ($true != (cF @ X21 @ X23))) )),
% 1.72/1.47 inference(cnf_transformation,[status(thm)],[f24])).
% 1.72/1.47 thf(f24,plain,(
% 1.72/1.47 ! [X0 : $i] : ((cF @ X0 @ (sK0 @ X0)) = $true) & (! [X3 : $i] : ($true != (cF @ sK1 @ X3)) | ! [X5 : $i] : ((($true != (cD @ (sK6 @ X5) @ (sK5 @ X5) @ sK2)) & ((cF @ (sK3 @ X5) @ (sK6 @ X5)) = $true) & ($true = (cF @ (sK4 @ X5) @ (sK5 @ X5)))) & ($true = (cD @ (sK3 @ X5) @ (sK4 @ X5) @ X5))) | ! [X11 : $i] : ! [X13 : $i] : (! [X14 : $i] : (((cF @ X13 @ X14) != $true) | ($true = (cD @ X14 @ sK7 @ X11))) | ((cS @ (sK8 @ X11) @ X13) != $true)) | ! [X15 : $i] : ! [X17 : $i] : (($true = (cS @ X17 @ (sK10 @ X17 @ X15))) & ($true != (cD @ (sK10 @ X17 @ X15) @ X15 @ (sK9 @ X15))))) & ! [X19 : $i] : ! [X21 : $i,X22 : $i] : (! [X23 : $i,X24 : $i] : (((cF @ X22 @ X24) != $true) | ($true != (cF @ X21 @ X23)) | ($true = (cD @ X23 @ X24 @ X19))) | ($true != (cD @ X21 @ X22 @ (sK11 @ X19)))) & ! [X25 : $i] : ! [X27 : $i] : (($true = (cS @ X27 @ (sK13 @ X27 @ X25))) & (((cD @ (sK14 @ X27 @ X25) @ X25 @ (sK12 @ X25)) != $true) & ($true = (cF @ (sK13 @ X27 @ X25) @ (sK14 @ X27 @ X25))))) & ! [X31 : $i] : ! [X33 : $i] : (($true = (cD @ X33 @ sK15 @ X31)) | ($true != (cS @ (sK16 @ X31) @ X33)))),
% 1.72/1.47 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11,sK12,sK13,sK14,sK15,sK16])],[f8,f23,f22,f21,f20,f19,f18,f17,f16,f15,f14,f13,f12,f11,f10,f9])).
% 1.72/1.47 thf(f9,plain,(
% 1.72/1.47 ! [X0 : $i] : (? [X1 : $i] : ((cF @ X0 @ X1) = $true) => ((cF @ X0 @ (sK0 @ X0)) = $true))),
% 1.72/1.47 introduced(definition,[],[choice_axiom])).
% 1.72/1.47 thf(f10,plain,(
% 1.72/1.47 ? [X2 : $i] : ! [X3 : $i] : ($true != (cF @ X2 @ X3)) => ! [X3 : $i] : ($true != (cF @ sK1 @ X3))),
% 1.72/1.47 introduced(definition,[],[choice_axiom])).
% 1.72/1.47 thf(f11,plain,(
% 1.72/1.47 ? [X4 : $i] : ! [X5 : $i] : ? [X6 : $i,X7 : $i] : (? [X8 : $i,X9 : $i] : (((cD @ X9 @ X8 @ X4) != $true) & ($true = (cF @ X6 @ X9)) & ((cF @ X7 @ X8) = $true)) & ((cD @ X6 @ X7 @ X5) = $true)) => ! [X5 : $i] : ? [X7 : $i,X6 : $i] : (? [X9 : $i,X8 : $i] : (($true != (cD @ X9 @ X8 @ sK2)) & ($true = (cF @ X6 @ X9)) & ((cF @ X7 @ X8) = $true)) & ((cD @ X6 @ X7 @ X5) = $true))),
% 1.72/1.47 introduced(definition,[],[choice_axiom])).
% 1.72/1.47 thf(f12,plain,(
% 1.72/1.47 ! [X5 : $i] : (? [X7 : $i,X6 : $i] : (? [X9 : $i,X8 : $i] : (($true != (cD @ X9 @ X8 @ sK2)) & ($true = (cF @ X6 @ X9)) & ((cF @ X7 @ X8) = $true)) & ((cD @ X6 @ X7 @ X5) = $true)) => (? [X9 : $i,X8 : $i] : (($true != (cD @ X9 @ X8 @ sK2)) & ($true = (cF @ (sK3 @ X5) @ X9)) & ($true = (cF @ (sK4 @ X5) @ X8))) & ($true = (cD @ (sK3 @ X5) @ (sK4 @ X5) @ X5))))),
% 1.72/1.47 introduced(definition,[],[choice_axiom])).
% 1.72/1.47 thf(f13,plain,(
% 1.72/1.47 ! [X5 : $i] : (? [X9 : $i,X8 : $i] : (($true != (cD @ X9 @ X8 @ sK2)) & ($true = (cF @ (sK3 @ X5) @ X9)) & ($true = (cF @ (sK4 @ X5) @ X8))) => (($true != (cD @ (sK6 @ X5) @ (sK5 @ X5) @ sK2)) & ((cF @ (sK3 @ X5) @ (sK6 @ X5)) = $true) & ($true = (cF @ (sK4 @ X5) @ (sK5 @ X5)))))),
% 1.72/1.47 introduced(definition,[],[choice_axiom])).
% 1.72/1.47 thf(f14,plain,(
% 1.72/1.47 ? [X10 : $i] : ! [X11 : $i] : ? [X12 : $i] : ! [X13 : $i] : (! [X14 : $i] : (((cF @ X13 @ X14) != $true) | ($true = (cD @ X14 @ X10 @ X11))) | ($true != (cS @ X12 @ X13))) => ! [X11 : $i] : ? [X12 : $i] : ! [X13 : $i] : (! [X14 : $i] : (((cF @ X13 @ X14) != $true) | ($true = (cD @ X14 @ sK7 @ X11))) | ($true != (cS @ X12 @ X13)))),
% 1.72/1.47 introduced(definition,[],[choice_axiom])).
% 1.72/1.47 thf(f15,plain,(
% 1.72/1.47 ! [X11 : $i] : (? [X12 : $i] : ! [X13 : $i] : (! [X14 : $i] : (((cF @ X13 @ X14) != $true) | ($true = (cD @ X14 @ sK7 @ X11))) | ($true != (cS @ X12 @ X13))) => ! [X13 : $i] : (! [X14 : $i] : (((cF @ X13 @ X14) != $true) | ($true = (cD @ X14 @ sK7 @ X11))) | ((cS @ (sK8 @ X11) @ X13) != $true)))),
% 1.72/1.47 introduced(definition,[],[choice_axiom])).
% 1.72/1.47 thf(f16,plain,(
% 1.72/1.47 ! [X15 : $i] : (? [X16 : $i] : ! [X17 : $i] : ? [X18 : $i] : (($true = (cS @ X17 @ X18)) & ($true != (cD @ X18 @ X15 @ X16))) => ! [X17 : $i] : ? [X18 : $i] : (($true = (cS @ X17 @ X18)) & ($true != (cD @ X18 @ X15 @ (sK9 @ X15)))))),
% 1.72/1.47 introduced(definition,[],[choice_axiom])).
% 1.72/1.47 thf(f17,plain,(
% 1.72/1.47 ! [X15 : $i,X17 : $i] : (? [X18 : $i] : (($true = (cS @ X17 @ X18)) & ($true != (cD @ X18 @ X15 @ (sK9 @ X15)))) => (($true = (cS @ X17 @ (sK10 @ X17 @ X15))) & ($true != (cD @ (sK10 @ X17 @ X15) @ X15 @ (sK9 @ X15)))))),
% 1.72/1.47 introduced(definition,[],[choice_axiom])).
% 1.72/1.47 thf(f18,plain,(
% 1.72/1.47 ! [X19 : $i] : (? [X20 : $i] : ! [X21 : $i,X22 : $i] : (! [X23 : $i,X24 : $i] : (((cF @ X22 @ X24) != $true) | ($true != (cF @ X21 @ X23)) | ($true = (cD @ X23 @ X24 @ X19))) | ($true != (cD @ X21 @ X22 @ X20))) => ! [X22 : $i,X21 : $i] : (! [X23 : $i,X24 : $i] : (((cF @ X22 @ X24) != $true) | ($true != (cF @ X21 @ X23)) | ($true = (cD @ X23 @ X24 @ X19))) | ($true != (cD @ X21 @ X22 @ (sK11 @ X19)))))),
% 1.72/1.47 introduced(definition,[],[choice_axiom])).
% 1.72/1.47 thf(f19,plain,(
% 1.72/1.47 ! [X25 : $i] : (? [X26 : $i] : ! [X27 : $i] : ? [X28 : $i] : (($true = (cS @ X27 @ X28)) & ? [X29 : $i] : (($true != (cD @ X29 @ X25 @ X26)) & ($true = (cF @ X28 @ X29)))) => ! [X27 : $i] : ? [X28 : $i] : (($true = (cS @ X27 @ X28)) & ? [X29 : $i] : (((cD @ X29 @ X25 @ (sK12 @ X25)) != $true) & ($true = (cF @ X28 @ X29)))))),
% 1.72/1.47 introduced(definition,[],[choice_axiom])).
% 1.72/1.47 thf(f20,plain,(
% 1.72/1.47 ! [X25 : $i,X27 : $i] : (? [X28 : $i] : (($true = (cS @ X27 @ X28)) & ? [X29 : $i] : (((cD @ X29 @ X25 @ (sK12 @ X25)) != $true) & ($true = (cF @ X28 @ X29)))) => (($true = (cS @ X27 @ (sK13 @ X27 @ X25))) & ? [X29 : $i] : (((cD @ X29 @ X25 @ (sK12 @ X25)) != $true) & ($true = (cF @ (sK13 @ X27 @ X25) @ X29)))))),
% 1.72/1.47 introduced(definition,[],[choice_axiom])).
% 1.72/1.47 thf(f21,plain,(
% 1.72/1.47 ! [X25 : $i,X27 : $i] : (? [X29 : $i] : (((cD @ X29 @ X25 @ (sK12 @ X25)) != $true) & ($true = (cF @ (sK13 @ X27 @ X25) @ X29))) => (((cD @ (sK14 @ X27 @ X25) @ X25 @ (sK12 @ X25)) != $true) & ($true = (cF @ (sK13 @ X27 @ X25) @ (sK14 @ X27 @ X25)))))),
% 1.72/1.47 introduced(definition,[],[choice_axiom])).
% 1.72/1.47 thf(f22,plain,(
% 1.72/1.47 ? [X30 : $i] : ! [X31 : $i] : ? [X32 : $i] : ! [X33 : $i] : (((cD @ X33 @ X30 @ X31) = $true) | ((cS @ X32 @ X33) != $true)) => ! [X31 : $i] : ? [X32 : $i] : ! [X33 : $i] : (($true = (cD @ X33 @ sK15 @ X31)) | ((cS @ X32 @ X33) != $true))),
% 1.72/1.47 introduced(definition,[],[choice_axiom])).
% 1.72/1.47 thf(f23,plain,(
% 1.72/1.47 ! [X31 : $i] : (? [X32 : $i] : ! [X33 : $i] : (($true = (cD @ X33 @ sK15 @ X31)) | ((cS @ X32 @ X33) != $true)) => ! [X33 : $i] : (($true = (cD @ X33 @ sK15 @ X31)) | ($true != (cS @ (sK16 @ X31) @ X33))))),
% 1.72/1.47 introduced(definition,[],[choice_axiom])).
% 1.72/1.47 thf(f8,plain,(
% 1.72/1.47 ! [X0 : $i] : ? [X1 : $i] : ((cF @ X0 @ X1) = $true) & (? [X2 : $i] : ! [X3 : $i] : ($true != (cF @ X2 @ X3)) | ? [X4 : $i] : ! [X5 : $i] : ? [X6 : $i,X7 : $i] : (? [X8 : $i,X9 : $i] : (((cD @ X9 @ X8 @ X4) != $true) & ($true = (cF @ X6 @ X9)) & ((cF @ X7 @ X8) = $true)) & ((cD @ X6 @ X7 @ X5) = $true)) | ? [X10 : $i] : ! [X11 : $i] : ? [X12 : $i] : ! [X13 : $i] : (! [X14 : $i] : (((cF @ X13 @ X14) != $true) | ($true = (cD @ X14 @ X10 @ X11))) | ($true != (cS @ X12 @ X13))) | ! [X15 : $i] : ? [X16 : $i] : ! [X17 : $i] : ? [X18 : $i] : (($true = (cS @ X17 @ X18)) & ($true != (cD @ X18 @ X15 @ X16)))) & ! [X19 : $i] : ? [X20 : $i] : ! [X21 : $i,X22 : $i] : (! [X23 : $i,X24 : $i] : (((cF @ X22 @ X24) != $true) | ($true != (cF @ X21 @ X23)) | ($true = (cD @ X23 @ X24 @ X19))) | ($true != (cD @ X21 @ X22 @ X20))) & ! [X25 : $i] : ? [X26 : $i] : ! [X27 : $i] : ? [X28 : $i] : (($true = (cS @ X27 @ X28)) & ? [X29 : $i] : (($true != (cD @ X29 @ X25 @ X26)) & ($true = (cF @ X28 @ X29)))) & ? [X30 : $i] : ! [X31 : $i] : ? [X32 : $i] : ! [X33 : $i] : (((cD @ X33 @ X30 @ X31) = $true) | ((cS @ X32 @ X33) != $true))),
% 1.72/1.47 inference(rectify,[status(thm)],[f7])).
% 1.72/1.47 thf(f7,plain,(
% 1.72/1.47 ! [X17 : $i] : ? [X18 : $i] : ((cF @ X17 @ X18) = $true) & (? [X4 : $i] : ! [X5 : $i] : ((cF @ X4 @ X5) != $true) | ? [X6 : $i] : ! [X7 : $i] : ? [X8 : $i,X9 : $i] : (? [X10 : $i,X11 : $i] : (($true != (cD @ X11 @ X10 @ X6)) & ($true = (cF @ X8 @ X11)) & ((cF @ X9 @ X10) = $true)) & ($true = (cD @ X8 @ X9 @ X7))) | ? [X12 : $i] : ! [X13 : $i] : ? [X14 : $i] : ! [X15 : $i] : (! [X16 : $i] : (($true != (cF @ X15 @ X16)) | ($true = (cD @ X16 @ X12 @ X13))) | ($true != (cS @ X14 @ X15))) | ! [X0 : $i] : ? [X1 : $i] : ! [X2 : $i] : ? [X3 : $i] : (($true = (cS @ X2 @ X3)) & ($true != (cD @ X3 @ X0 @ X1)))) & ! [X23 : $i] : ? [X24 : $i] : ! [X25 : $i,X26 : $i] : (! [X27 : $i,X28 : $i] : (($true != (cF @ X26 @ X28)) | ($true != (cF @ X25 @ X27)) | ($true = (cD @ X27 @ X28 @ X23))) | ((cD @ X25 @ X26 @ X24) != $true)) & ! [X29 : $i] : ? [X30 : $i] : ! [X31 : $i] : ? [X32 : $i] : (($true = (cS @ X31 @ X32)) & ? [X33 : $i] : (((cD @ X33 @ X29 @ X30) != $true) & ($true = (cF @ X32 @ X33)))) & ? [X19 : $i] : ! [X20 : $i] : ? [X21 : $i] : ! [X22 : $i] : (($true = (cD @ X22 @ X19 @ X20)) | ($true != (cS @ X21 @ X22)))),
% 1.72/1.47 inference(flattening,[status(thm)],[f6])).
% 1.72/1.47 thf(f6,plain,(
% 1.72/1.47 (! [X29 : $i] : ? [X30 : $i] : ! [X31 : $i] : ? [X32 : $i] : (($true = (cS @ X31 @ X32)) & ? [X33 : $i] : (((cD @ X33 @ X29 @ X30) != $true) & ($true = (cF @ X32 @ X33)))) & (! [X23 : $i] : ? [X24 : $i] : ! [X26 : $i,X25 : $i] : (! [X28 : $i,X27 : $i] : (($true = (cD @ X27 @ X28 @ X23)) | (($true != (cF @ X26 @ X28)) | ($true != (cF @ X25 @ X27)))) | ((cD @ X25 @ X26 @ X24) != $true)) & ? [X19 : $i] : ! [X20 : $i] : ? [X21 : $i] : ! [X22 : $i] : (($true = (cD @ X22 @ X19 @ X20)) | ($true != (cS @ X21 @ X22))) & ! [X17 : $i] : ? [X18 : $i] : ((cF @ X17 @ X18) = $true))) & (? [X12 : $i] : ! [X13 : $i] : ? [X14 : $i] : ! [X15 : $i] : (! [X16 : $i] : (($true != (cF @ X15 @ X16)) | ($true = (cD @ X16 @ X12 @ X13))) | ($true != (cS @ X14 @ X15))) | (? [X6 : $i] : ! [X7 : $i] : ? [X9 : $i,X8 : $i] : (? [X11 : $i,X10 : $i] : (($true != (cD @ X11 @ X10 @ X6)) & (($true = (cF @ X8 @ X11)) & ((cF @ X9 @ X10) = $true))) & ($true = (cD @ X8 @ X9 @ X7))) | ? [X4 : $i] : ! [X5 : $i] : ((cF @ X4 @ X5) != $true) | ! [X0 : $i] : ? [X1 : $i] : ! [X2 : $i] : ? [X3 : $i] : (($true = (cS @ X2 @ X3)) & ($true != (cD @ X3 @ X0 @ X1)))))),
% 1.72/1.47 inference(ennf_transformation,[status(thm)],[f5])).
% 1.72/1.47 thf(f5,plain,(
% 1.72/1.47 ~(((! [X6 : $i] : ? [X7 : $i] : ! [X9 : $i,X8 : $i] : (($true = (cD @ X8 @ X9 @ X7)) => ! [X11 : $i,X10 : $i] : ((($true = (cF @ X8 @ X11)) & ((cF @ X9 @ X10) = $true)) => ($true = (cD @ X11 @ X10 @ X6)))) & ! [X4 : $i] : ? [X5 : $i] : ((cF @ X4 @ X5) = $true) & ? [X0 : $i] : ! [X1 : $i] : ? [X2 : $i] : ! [X3 : $i] : (($true = (cS @ X2 @ X3)) => ($true = (cD @ X3 @ X0 @ X1)))) => ? [X12 : $i] : ! [X13 : $i] : ? [X14 : $i] : ! [X15 : $i] : (($true = (cS @ X14 @ X15)) => ! [X16 : $i] : (($true = (cF @ X15 @ X16)) => ($true = (cD @ X16 @ X12 @ X13))))) => ((! [X23 : $i] : ? [X24 : $i] : ! [X26 : $i,X25 : $i] : (((cD @ X25 @ X26 @ X24) = $true) => ! [X28 : $i,X27 : $i] : ((($true = (cF @ X26 @ X28)) & ($true = (cF @ X25 @ X27))) => ($true = (cD @ X27 @ X28 @ X23)))) & ? [X19 : $i] : ! [X20 : $i] : ? [X21 : $i] : ! [X22 : $i] : (($true = (cS @ X21 @ X22)) => ($true = (cD @ X22 @ X19 @ X20))) & ! [X17 : $i] : ? [X18 : $i] : ((cF @ X17 @ X18) = $true)) => ? [X29 : $i] : ! [X30 : $i] : ? [X31 : $i] : ! [X32 : $i] : (($true = (cS @ X31 @ X32)) => ! [X33 : $i] : (($true = (cF @ X32 @ X33)) => ((cD @ X33 @ X29 @ X30) = $true)))))),
% 1.72/1.47 inference(fool_elimination,[status(thm)],[f4])).
% 1.72/1.47 thf(f4,plain,(
% 1.72/1.47 ~(((? [X0 : $i] : ! [X1 : $i] : ? [X2 : $i] : ! [X3 : $i] : ((cS @ X2 @ X3) => (cD @ X3 @ X0 @ X1)) & ! [X4 : $i] : ? [X5 : $i] : (cF @ X4 @ X5) & ! [X6 : $i] : ? [X7 : $i] : ! [X8 : $i,X9 : $i] : ((cD @ X8 @ X9 @ X7) => ! [X10 : $i,X11 : $i] : (((cF @ X8 @ X11) & (cF @ X9 @ X10)) => (cD @ X11 @ X10 @ X6)))) => ? [X12 : $i] : ! [X13 : $i] : ? [X14 : $i] : ! [X15 : $i] : ((cS @ X14 @ X15) => ! [X16 : $i] : ((cF @ X15 @ X16) => (cD @ X16 @ X12 @ X13)))) => ((! [X17 : $i] : ? [X18 : $i] : (cF @ X17 @ X18) & ? [X19 : $i] : ! [X20 : $i] : ? [X21 : $i] : ! [X22 : $i] : ((cS @ X21 @ X22) => (cD @ X22 @ X19 @ X20)) & ! [X23 : $i] : ? [X24 : $i] : ! [X25 : $i,X26 : $i] : ((cD @ X25 @ X26 @ X24) => ! [X27 : $i,X28 : $i] : (((cF @ X25 @ X27) & (cF @ X26 @ X28)) => (cD @ X27 @ X28 @ X23)))) => ? [X29 : $i] : ! [X30 : $i] : ? [X31 : $i] : ! [X32 : $i] : ((cS @ X31 @ X32) => ! [X33 : $i] : ((cF @ X32 @ X33) => (cD @ X33 @ X29 @ X30)))))),
% 1.72/1.47 inference(rectify,[status(thm)],[f2])).
% 1.72/1.47 thf(f2,negated_conjecture,(
% 1.72/1.47 ~(((? [X0 : $i] : ! [X2 : $i] : ? [X3 : $i] : ! [X4 : $i] : ((cS @ X3 @ X4) => (cD @ X4 @ X0 @ X2)) & ! [X0 : $i] : ? [X1 : $i] : (cF @ X0 @ X1) & ! [X2 : $i] : ? [X5 : $i] : ! [X6 : $i,X7 : $i] : ((cD @ X6 @ X7 @ X5) => ! [X8 : $i,X1 : $i] : (((cF @ X6 @ X1) & (cF @ X7 @ X8)) => (cD @ X1 @ X8 @ X2)))) => ? [X1 : $i] : ! [X2 : $i] : ? [X9 : $i] : ! [X4 : $i] : ((cS @ X9 @ X4) => ! [X8 : $i] : ((cF @ X4 @ X8) => (cD @ X8 @ X1 @ X2)))) => ((! [X0 : $i] : ? [X1 : $i] : (cF @ X0 @ X1) & ? [X0 : $i] : ! [X2 : $i] : ? [X3 : $i] : ! [X4 : $i] : ((cS @ X3 @ X4) => (cD @ X4 @ X0 @ X2)) & ! [X2 : $i] : ? [X5 : $i] : ! [X6 : $i,X7 : $i] : ((cD @ X6 @ X7 @ X5) => ! [X1 : $i,X8 : $i] : (((cF @ X6 @ X1) & (cF @ X7 @ X8)) => (cD @ X1 @ X8 @ X2)))) => ? [X1 : $i] : ! [X2 : $i] : ? [X9 : $i] : ! [X4 : $i] : ((cS @ X9 @ X4) => ! [X8 : $i] : ((cF @ X4 @ X8) => (cD @ X8 @ X1 @ X2)))))),
% 1.72/1.47 inference(negated_conjecture,[status(cth)],[f1])).
% 1.72/1.47 thf(f1,conjecture,(
% 1.72/1.47 ((? [X0 : $i] : ! [X2 : $i] : ? [X3 : $i] : ! [X4 : $i] : ((cS @ X3 @ X4) => (cD @ X4 @ X0 @ X2)) & ! [X0 : $i] : ? [X1 : $i] : (cF @ X0 @ X1) & ! [X2 : $i] : ? [X5 : $i] : ! [X6 : $i,X7 : $i] : ((cD @ X6 @ X7 @ X5) => ! [X8 : $i,X1 : $i] : (((cF @ X6 @ X1) & (cF @ X7 @ X8)) => (cD @ X1 @ X8 @ X2)))) => ? [X1 : $i] : ! [X2 : $i] : ? [X9 : $i] : ! [X4 : $i] : ((cS @ X9 @ X4) => ! [X8 : $i] : ((cF @ X4 @ X8) => (cD @ X8 @ X1 @ X2)))) => ((! [X0 : $i] : ? [X1 : $i] : (cF @ X0 @ X1) & ? [X0 : $i] : ! [X2 : $i] : ? [X3 : $i] : ! [X4 : $i] : ((cS @ X3 @ X4) => (cD @ X4 @ X0 @ X2)) & ! [X2 : $i] : ? [X5 : $i] : ! [X6 : $i,X7 : $i] : ((cD @ X6 @ X7 @ X5) => ! [X1 : $i,X8 : $i] : (((cF @ X6 @ X1) & (cF @ X7 @ X8)) => (cD @ X1 @ X8 @ X2)))) => ? [X1 : $i] : ! [X2 : $i] : ? [X9 : $i] : ! [X4 : $i] : ((cS @ X9 @ X4) => ! [X8 : $i] : ((cF @ X4 @ X8) => (cD @ X8 @ X1 @ X2))))),
% 1.72/1.47 file('/export/starexec/sandbox/tmp/tmp.CRacoZzQkz/DTF2THF_23011.p',cTHM408)).
% 1.72/1.47 thf(f62,plain,(
% 1.72/1.47 ( ! [X5 : $i] : (($true != (cD @ (sK6 @ X5) @ (sK5 @ X5) @ sK2))) ) | ~spl17_7),
% 1.72/1.47 inference(avatar_component_clause,[status(thm)],[f61])).
% 1.72/1.47 thf(f61,definition,(
% 1.72/1.47 spl17_7 <=> ! [X5 : $i] : ($true != (cD @ (sK6 @ X5) @ (sK5 @ X5) @ sK2))),
% 1.72/1.47 introduced(definition,[new_symbols(naming,[spl17_7])],[avatar_definition])).
% 1.72/1.47 thf(f87,plain,(
% 1.72/1.47 ~spl17_1 | ~spl17_8),
% 1.72/1.47 inference(avatar_contradiction_clause,[status(thm)],[f86])).
% 1.72/1.47 thf(f86,plain,(
% 1.72/1.47 $false | (~spl17_1 | ~spl17_8)),
% 1.72/1.47 inference(trivial_inequality_removal,[status(thm)],[f85])).
% 1.72/1.47 thf(f85,plain,(
% 1.72/1.47 ($true != $true) | (~spl17_1 | ~spl17_8)),
% 1.72/1.47 inference(superposition,[status(thm)],[f84,f65])).
% 1.72/1.47 thf(f65,plain,(
% 1.72/1.47 ( ! [X17 : $i,X15 : $i] : (($true = (cS @ X17 @ (sK10 @ X17 @ X15)))) ) | ~spl17_8),
% 1.72/1.47 inference(avatar_component_clause,[status(thm)],[f64])).
% 1.72/1.47 thf(f64,definition,(
% 1.72/1.47 spl17_8 <=> ! [X17 : $i,X15 : $i] : ($true = (cS @ X17 @ (sK10 @ X17 @ X15)))),
% 1.72/1.47 introduced(definition,[new_symbols(naming,[spl17_8])],[avatar_definition])).
% 1.72/1.47 thf(f84,plain,(
% 1.72/1.47 ( ! [X0 : $i] : (($true != (cS @ (sK16 @ (sK9 @ sK15)) @ (sK10 @ X0 @ sK15)))) ) | ~spl17_1),
% 1.72/1.47 inference(trivial_inequality_removal,[status(thm)],[f83])).
% 1.72/1.47 thf(f83,plain,(
% 1.72/1.47 ( ! [X0 : $i] : (($true != (cS @ (sK16 @ (sK9 @ sK15)) @ (sK10 @ X0 @ sK15))) | ($true != $true)) ) | ~spl17_1),
% 1.72/1.47 inference(superposition,[status(thm)],[f41,f25])).
% 1.72/1.47 thf(f25,plain,(
% 1.72/1.47 ( ! [X31 : $i,X33 : $i] : (($true = (cD @ X33 @ sK15 @ X31)) | ($true != (cS @ (sK16 @ X31) @ X33))) )),
% 1.72/1.47 inference(cnf_transformation,[status(thm)],[f24])).
% 1.72/1.47 thf(f41,plain,(
% 1.72/1.47 ( ! [X17 : $i,X15 : $i] : (($true != (cD @ (sK10 @ X17 @ X15) @ X15 @ (sK9 @ X15)))) ) | ~spl17_1),
% 1.72/1.47 inference(avatar_component_clause,[status(thm)],[f40])).
% 1.72/1.47 thf(f40,definition,(
% 1.72/1.47 spl17_1 <=> ! [X17 : $i,X15 : $i] : ($true != (cD @ (sK10 @ X17 @ X15) @ X15 @ (sK9 @ X15)))),
% 1.72/1.47 introduced(definition,[new_symbols(naming,[spl17_1])],[avatar_definition])).
% 1.72/1.47 thf(f82,plain,(
% 1.72/1.47 ~spl17_3),
% 1.72/1.47 inference(avatar_contradiction_clause,[status(thm)],[f81])).
% 1.72/1.47 thf(f81,plain,(
% 1.72/1.47 $false | ~spl17_3),
% 1.72/1.47 inference(trivial_inequality_removal,[status(thm)],[f80])).
% 1.72/1.47 thf(f80,plain,(
% 1.72/1.47 ($true != $true) | ~spl17_3),
% 1.72/1.47 inference(superposition,[status(thm)],[f47,f38])).
% 1.72/1.47 thf(f38,plain,(
% 1.72/1.47 ( ! [X0 : $i] : (((cF @ X0 @ (sK0 @ X0)) = $true)) )),
% 1.72/1.47 inference(cnf_transformation,[status(thm)],[f24])).
% 1.72/1.47 thf(f47,plain,(
% 1.72/1.47 ( ! [X3 : $i] : (($true != (cF @ sK1 @ X3))) ) | ~spl17_3),
% 1.72/1.47 inference(avatar_component_clause,[status(thm)],[f46])).
% 1.72/1.47 thf(f46,definition,(
% 1.72/1.47 spl17_3 <=> ! [X3 : $i] : ($true != (cF @ sK1 @ X3))),
% 1.72/1.47 introduced(definition,[new_symbols(naming,[spl17_3])],[avatar_definition])).
% 1.72/1.47 thf(f79,plain,(
% 1.72/1.47 ~spl17_2),
% 1.72/1.47 inference(avatar_contradiction_clause,[status(thm)],[f78])).
% 1.72/1.47 thf(f78,plain,(
% 1.72/1.47 $false | ~spl17_2),
% 1.72/1.47 inference(trivial_inequality_removal,[status(thm)],[f77])).
% 1.72/1.47 thf(f77,plain,(
% 1.72/1.47 ($true != $true) | ~spl17_2),
% 1.72/1.47 inference(superposition,[status(thm)],[f76,f28])).
% 1.72/1.47 thf(f28,plain,(
% 1.72/1.47 ( ! [X27 : $i,X25 : $i] : (($true = (cS @ X27 @ (sK13 @ X27 @ X25)))) )),
% 1.72/1.47 inference(cnf_transformation,[status(thm)],[f24])).
% 1.72/1.47 thf(f76,plain,(
% 1.72/1.47 ( ! [X0 : $i] : (($true != (cS @ (sK8 @ (sK12 @ sK7)) @ (sK13 @ X0 @ sK7)))) ) | ~spl17_2),
% 1.72/1.47 inference(trivial_inequality_removal,[status(thm)],[f75])).
% 1.72/1.47 thf(f75,plain,(
% 1.72/1.47 ( ! [X0 : $i] : (($true != $true) | ($true != (cS @ (sK8 @ (sK12 @ sK7)) @ (sK13 @ X0 @ sK7)))) ) | ~spl17_2),
% 1.72/1.47 inference(superposition,[status(thm)],[f74,f26])).
% 1.72/1.47 thf(f26,plain,(
% 1.72/1.47 ( ! [X27 : $i,X25 : $i] : (($true = (cF @ (sK13 @ X27 @ X25) @ (sK14 @ X27 @ X25)))) )),
% 1.72/1.47 inference(cnf_transformation,[status(thm)],[f24])).
% 1.72/1.47 thf(f74,plain,(
% 1.72/1.47 ( ! [X0 : $i,X1 : $i] : (((cF @ X1 @ (sK14 @ X0 @ sK7)) != $true) | ((cS @ (sK8 @ (sK12 @ sK7)) @ X1) != $true)) ) | ~spl17_2),
% 1.72/1.47 inference(trivial_inequality_removal,[status(thm)],[f73])).
% 1.72/1.47 thf(f73,plain,(
% 1.72/1.47 ( ! [X0 : $i,X1 : $i] : (((cS @ (sK8 @ (sK12 @ sK7)) @ X1) != $true) | ((cF @ X1 @ (sK14 @ X0 @ sK7)) != $true) | ($true != $true)) ) | ~spl17_2),
% 1.72/1.47 inference(superposition,[status(thm)],[f27,f44])).
% 1.72/1.47 thf(f44,plain,(
% 1.72/1.47 ( ! [X11 : $i,X14 : $i,X13 : $i] : (($true = (cD @ X14 @ sK7 @ X11)) | ((cS @ (sK8 @ X11) @ X13) != $true) | ((cF @ X13 @ X14) != $true)) ) | ~spl17_2),
% 1.72/1.47 inference(avatar_component_clause,[status(thm)],[f43])).
% 1.72/1.47 thf(f43,definition,(
% 1.72/1.47 spl17_2 <=> ! [X13 : $i,X11 : $i,X14 : $i] : (($true = (cD @ X14 @ sK7 @ X11)) | ((cF @ X13 @ X14) != $true) | ((cS @ (sK8 @ X11) @ X13) != $true))),
% 1.72/1.47 introduced(definition,[new_symbols(naming,[spl17_2])],[avatar_definition])).
% 1.72/1.47 thf(f27,plain,(
% 1.72/1.47 ( ! [X27 : $i,X25 : $i] : (((cD @ (sK14 @ X27 @ X25) @ X25 @ (sK12 @ X25)) != $true)) )),
% 1.72/1.47 inference(cnf_transformation,[status(thm)],[f24])).
% 1.72/1.47 thf(f70,plain,(
% 1.72/1.47 spl17_8 | spl17_3 | spl17_5 | spl17_2),
% 1.72/1.47 inference(avatar_split_clause,[status(thm)],[f35,f43,f53,f46,f64])).
% 1.72/1.47 thf(f35,plain,(
% 1.72/1.47 ( ! [X3 : $i,X11 : $i,X14 : $i,X17 : $i,X15 : $i,X5 : $i,X13 : $i] : (($true = (cD @ X14 @ sK7 @ X11)) | ((cS @ (sK8 @ X11) @ X13) != $true) | ((cF @ (sK3 @ X5) @ (sK6 @ X5)) = $true) | ((cF @ X13 @ X14) != $true) | ($true != (cF @ sK1 @ X3)) | ($true = (cS @ X17 @ (sK10 @ X17 @ X15)))) )),
% 1.72/1.47 inference(cnf_transformation,[status(thm)],[f24])).
% 1.72/1.47 thf(f69,plain,(
% 1.72/1.47 spl17_2 | spl17_3 | spl17_4 | spl17_8),
% 1.72/1.47 inference(avatar_split_clause,[status(thm)],[f33,f64,f49,f46,f43])).
% 1.72/1.47 thf(f33,plain,(
% 1.72/1.47 ( ! [X3 : $i,X11 : $i,X14 : $i,X17 : $i,X15 : $i,X5 : $i,X13 : $i] : (($true = (cS @ X17 @ (sK10 @ X17 @ X15))) | ((cS @ (sK8 @ X11) @ X13) != $true) | ($true = (cD @ X14 @ sK7 @ X11)) | ((cF @ X13 @ X14) != $true) | ($true != (cF @ sK1 @ X3)) | ($true = (cF @ (sK4 @ X5) @ (sK5 @ X5)))) )),
% 1.72/1.47 inference(cnf_transformation,[status(thm)],[f24])).
% 1.72/1.47 thf(f68,plain,(
% 1.72/1.47 spl17_1 | spl17_2 | spl17_3 | spl17_7),
% 1.72/1.47 inference(avatar_split_clause,[status(thm)],[f36,f61,f46,f43,f40])).
% 1.72/1.47 thf(f36,plain,(
% 1.72/1.47 ( ! [X3 : $i,X11 : $i,X14 : $i,X17 : $i,X15 : $i,X5 : $i,X13 : $i] : (($true != (cD @ (sK6 @ X5) @ (sK5 @ X5) @ sK2)) | ($true != (cD @ (sK10 @ X17 @ X15) @ X15 @ (sK9 @ X15))) | ($true = (cD @ X14 @ sK7 @ X11)) | ($true != (cF @ sK1 @ X3)) | ((cS @ (sK8 @ X11) @ X13) != $true) | ((cF @ X13 @ X14) != $true)) )),
% 1.72/1.47 inference(cnf_transformation,[status(thm)],[f24])).
% 1.72/1.47 thf(f67,plain,(
% 1.72/1.47 spl17_3 | spl17_2 | spl17_8 | spl17_6),
% 1.72/1.47 inference(avatar_split_clause,[status(thm)],[f31,f57,f64,f43,f46])).
% 1.72/1.47 thf(f31,plain,(
% 1.72/1.47 ( ! [X3 : $i,X11 : $i,X14 : $i,X17 : $i,X15 : $i,X5 : $i,X13 : $i] : (($true != (cF @ sK1 @ X3)) | ($true = (cS @ X17 @ (sK10 @ X17 @ X15))) | ($true = (cD @ (sK3 @ X5) @ (sK4 @ X5) @ X5)) | ($true = (cD @ X14 @ sK7 @ X11)) | ((cS @ (sK8 @ X11) @ X13) != $true) | ((cF @ X13 @ X14) != $true)) )),
% 1.72/1.47 inference(cnf_transformation,[status(thm)],[f24])).
% 1.72/1.47 thf(f66,plain,(
% 1.72/1.47 spl17_3 | spl17_2 | spl17_7 | spl17_8),
% 1.72/1.47 inference(avatar_split_clause,[status(thm)],[f37,f64,f61,f43,f46])).
% 1.72/1.47 thf(f37,plain,(
% 1.72/1.47 ( ! [X3 : $i,X11 : $i,X14 : $i,X17 : $i,X15 : $i,X5 : $i,X13 : $i] : (($true = (cS @ X17 @ (sK10 @ X17 @ X15))) | ($true != (cF @ sK1 @ X3)) | ($true = (cD @ X14 @ sK7 @ X11)) | ((cF @ X13 @ X14) != $true) | ((cS @ (sK8 @ X11) @ X13) != $true) | ($true != (cD @ (sK6 @ X5) @ (sK5 @ X5) @ sK2))) )),
% 1.72/1.47 inference(cnf_transformation,[status(thm)],[f24])).
% 1.72/1.47 thf(f59,plain,(
% 1.72/1.47 spl17_3 | spl17_2 | spl17_1 | spl17_6),
% 1.72/1.47 inference(avatar_split_clause,[status(thm)],[f30,f57,f40,f43,f46])).
% 1.72/1.47 thf(f30,plain,(
% 1.72/1.47 ( ! [X3 : $i,X11 : $i,X14 : $i,X17 : $i,X15 : $i,X5 : $i,X13 : $i] : (($true != (cD @ (sK10 @ X17 @ X15) @ X15 @ (sK9 @ X15))) | ((cF @ X13 @ X14) != $true) | ($true = (cD @ (sK3 @ X5) @ (sK4 @ X5) @ X5)) | ($true != (cF @ sK1 @ X3)) | ($true = (cD @ X14 @ sK7 @ X11)) | ((cS @ (sK8 @ X11) @ X13) != $true)) )),
% 1.72/1.47 inference(cnf_transformation,[status(thm)],[f24])).
% 1.72/1.47 thf(f55,plain,(
% 1.72/1.47 spl17_3 | spl17_1 | spl17_5 | spl17_2),
% 1.72/1.47 inference(avatar_split_clause,[status(thm)],[f34,f43,f53,f40,f46])).
% 1.72/1.47 thf(f34,plain,(
% 1.72/1.47 ( ! [X3 : $i,X11 : $i,X14 : $i,X17 : $i,X15 : $i,X5 : $i,X13 : $i] : (((cF @ X13 @ X14) != $true) | ($true != (cF @ sK1 @ X3)) | ($true != (cD @ (sK10 @ X17 @ X15) @ X15 @ (sK9 @ X15))) | ((cF @ (sK3 @ X5) @ (sK6 @ X5)) = $true) | ((cS @ (sK8 @ X11) @ X13) != $true) | ($true = (cD @ X14 @ sK7 @ X11))) )),
% 1.72/1.47 inference(cnf_transformation,[status(thm)],[f24])).
% 1.72/1.47 thf(f51,plain,(
% 1.72/1.47 spl17_1 | spl17_2 | spl17_3 | spl17_4),
% 1.72/1.47 inference(avatar_split_clause,[status(thm)],[f32,f49,f46,f43,f40])).
% 1.72/1.47 thf(f32,plain,(
% 1.72/1.47 ( ! [X3 : $i,X11 : $i,X14 : $i,X17 : $i,X15 : $i,X5 : $i,X13 : $i] : (($true = (cD @ X14 @ sK7 @ X11)) | ($true = (cF @ (sK4 @ X5) @ (sK5 @ X5))) | ($true != (cD @ (sK10 @ X17 @ X15) @ X15 @ (sK9 @ X15))) | ((cS @ (sK8 @ X11) @ X13) != $true) | ((cF @ X13 @ X14) != $true) | ($true != (cF @ sK1 @ X3))) )),
% 1.72/1.47 inference(cnf_transformation,[status(thm)],[f24])).
% 1.72/1.47 % SZS output end Proof for DTF2THF_23011
% 1.72/1.47 % (23109)------------------------------
% 1.72/1.47 % (23109)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.47 % (23109)Termination reason: Refutation
% 1.72/1.47
% 1.72/1.47 % (23109)Memory used [KB]: 5756
% 1.72/1.47 % (23109)Time elapsed: 0.016 s
% 1.72/1.47 % (23109)Instructions burned: 18 (million)
% 1.72/1.47 % (23109)------------------------------
% 1.72/1.47 % (23109)------------------------------
% 1.72/1.47 % (23108)Success in time 0.031 s
%------------------------------------------------------------------------------