%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYN386^5 : 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 : n022.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 09:50:53 AM UTC 2026
% Result : Theorem 1.65s 1.31s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 31 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 383 ( 113 equ; 0 cnn)
% Maximal formula atoms : 10 ( 12 avg)
% Number of connectives : 578 ( 55 ~; 40 |; 42 &; 410 @)
% ( 0 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 204 ( 0 ^; 144 !; 60 ?; 204 :)
% 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_4,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_7,type,
sK0: $i > $i ).
thf(func_def_8,type,
sK1: $i > $i ).
thf(func_def_9,type,
sK2: $i > $i > $i ).
thf(func_def_10,type,
sK3: $i > $i > $i ).
thf(func_def_12,type,
sK5: $i > $i ).
thf(func_def_13,type,
sK6: $i > $i ).
thf(f36,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f33]) ).
thf(f33,plain,
$true != $true,
inference(superposition,[status(thm)],[f20,f32]) ).
thf(f32,plain,
! [X0: $i,X1: $i] :
( ( cD @ ( sK3 @ ( sK5 @ ( sK0 @ X0 ) ) @ X1 ) @ ( sK6 @ sK4 ) @ X0 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f31]) ).
thf(f31,plain,
! [X0: $i,X1: $i] :
( ( ( cD @ ( sK3 @ ( sK5 @ ( sK0 @ X0 ) ) @ X1 ) @ ( sK6 @ sK4 ) @ X0 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f29,f17]) ).
thf(f17,plain,
! [X15: $i] :
( ( cF @ X15 @ ( sK6 @ X15 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ! [X0: $i,X2: $i,X3: $i] :
( ( $true
!= ( cD @ X3 @ X2 @ ( sK0 @ X0 ) ) )
| ! [X4: $i,X5: $i] :
( ( $true
!= ( cF @ X3 @ X4 ) )
| ( $true
= ( cD @ X4 @ X5 @ X0 ) )
| ( ( cF @ X2 @ X5 )
!= $true ) ) )
& ! [X6: $i,X8: $i] :
( ( ( cF @ ( sK2 @ X8 @ X6 ) @ ( sK3 @ X8 @ X6 ) )
= $true )
& ( ( cD @ ( sK3 @ X8 @ X6 ) @ X6 @ ( sK1 @ X6 ) )
!= $true )
& ( $true
= ( cS @ X8 @ ( sK2 @ X8 @ X6 ) ) ) )
& ! [X12: $i,X14: $i] :
( ( $true
= ( cD @ X14 @ sK4 @ X12 ) )
| ( $true
!= ( cS @ ( sK5 @ X12 ) @ X14 ) ) )
& ! [X15: $i] :
( ( cF @ X15 @ ( sK6 @ X15 ) )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6])],[f8,f15,f14,f13,f12,f11,f10,f9]) ).
thf(f9,plain,
! [X0: $i] :
( ? [X1: $i] :
! [X2: $i,X3: $i] :
( ( ( cD @ X3 @ X2 @ X1 )
!= $true )
| ! [X4: $i,X5: $i] :
( ( $true
!= ( cF @ X3 @ X4 ) )
| ( $true
= ( cD @ X4 @ X5 @ X0 ) )
| ( ( cF @ X2 @ X5 )
!= $true ) ) )
=> ! [X3: $i,X2: $i] :
( ( $true
!= ( cD @ X3 @ X2 @ ( sK0 @ X0 ) ) )
| ! [X4: $i,X5: $i] :
( ( $true
!= ( cF @ X3 @ X4 ) )
| ( $true
= ( cD @ X4 @ X5 @ X0 ) )
| ( ( cF @ X2 @ X5 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
! [X6: $i] :
( ? [X7: $i] :
! [X8: $i] :
? [X9: $i] :
( ? [X10: $i] :
( ( ( cF @ X9 @ X10 )
= $true )
& ( $true
!= ( cD @ X10 @ X6 @ X7 ) ) )
& ( $true
= ( cS @ X8 @ X9 ) ) )
=> ! [X8: $i] :
? [X9: $i] :
( ? [X10: $i] :
( ( ( cF @ X9 @ X10 )
= $true )
& ( ( cD @ X10 @ X6 @ ( sK1 @ X6 ) )
!= $true ) )
& ( $true
= ( cS @ X8 @ X9 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
! [X6: $i,X8: $i] :
( ? [X9: $i] :
( ? [X10: $i] :
( ( ( cF @ X9 @ X10 )
= $true )
& ( ( cD @ X10 @ X6 @ ( sK1 @ X6 ) )
!= $true ) )
& ( $true
= ( cS @ X8 @ X9 ) ) )
=> ( ? [X10: $i] :
( ( $true
= ( cF @ ( sK2 @ X8 @ X6 ) @ X10 ) )
& ( ( cD @ X10 @ X6 @ ( sK1 @ X6 ) )
!= $true ) )
& ( $true
= ( cS @ X8 @ ( sK2 @ X8 @ X6 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
! [X6: $i,X8: $i] :
( ? [X10: $i] :
( ( $true
= ( cF @ ( sK2 @ X8 @ X6 ) @ X10 ) )
& ( ( cD @ X10 @ X6 @ ( sK1 @ X6 ) )
!= $true ) )
=> ( ( ( cF @ ( sK2 @ X8 @ X6 ) @ ( sK3 @ X8 @ X6 ) )
= $true )
& ( ( cD @ ( sK3 @ X8 @ X6 ) @ X6 @ ( sK1 @ X6 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ? [X11: $i] :
! [X12: $i] :
? [X13: $i] :
! [X14: $i] :
( ( $true
= ( cD @ X14 @ X11 @ X12 ) )
| ( ( cS @ X13 @ X14 )
!= $true ) )
=> ! [X12: $i] :
? [X13: $i] :
! [X14: $i] :
( ( $true
= ( cD @ X14 @ sK4 @ X12 ) )
| ( ( cS @ X13 @ X14 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
! [X12: $i] :
( ? [X13: $i] :
! [X14: $i] :
( ( $true
= ( cD @ X14 @ sK4 @ X12 ) )
| ( ( cS @ X13 @ X14 )
!= $true ) )
=> ! [X14: $i] :
( ( $true
= ( cD @ X14 @ sK4 @ X12 ) )
| ( $true
!= ( cS @ ( sK5 @ X12 ) @ X14 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
! [X15: $i] :
( ? [X16: $i] :
( $true
= ( cF @ X15 @ X16 ) )
=> ( ( cF @ X15 @ ( sK6 @ X15 ) )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ! [X0: $i] :
? [X1: $i] :
! [X2: $i,X3: $i] :
( ( ( cD @ X3 @ X2 @ X1 )
!= $true )
| ! [X4: $i,X5: $i] :
( ( $true
!= ( cF @ X3 @ X4 ) )
| ( $true
= ( cD @ X4 @ X5 @ X0 ) )
| ( ( cF @ X2 @ X5 )
!= $true ) ) )
& ! [X6: $i] :
? [X7: $i] :
! [X8: $i] :
? [X9: $i] :
( ? [X10: $i] :
( ( ( cF @ X9 @ X10 )
= $true )
& ( $true
!= ( cD @ X10 @ X6 @ X7 ) ) )
& ( $true
= ( cS @ X8 @ X9 ) ) )
& ? [X11: $i] :
! [X12: $i] :
? [X13: $i] :
! [X14: $i] :
( ( $true
= ( cD @ X14 @ X11 @ X12 ) )
| ( ( cS @ X13 @ X14 )
!= $true ) )
& ! [X15: $i] :
? [X16: $i] :
( $true
= ( cF @ X15 @ X16 ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X6: $i] :
? [X7: $i] :
! [X9: $i,X8: $i] :
( ( ( cD @ X8 @ X9 @ X7 )
!= $true )
| ! [X10: $i,X11: $i] :
( ( ( cF @ X8 @ X10 )
!= $true )
| ( ( cD @ X10 @ X11 @ X6 )
= $true )
| ( $true
!= ( cF @ X9 @ X11 ) ) ) )
& ! [X12: $i] :
? [X13: $i] :
! [X14: $i] :
? [X15: $i] :
( ? [X16: $i] :
( ( $true
= ( cF @ X15 @ X16 ) )
& ( ( cD @ X16 @ X12 @ X13 )
!= $true ) )
& ( ( cS @ X14 @ X15 )
= $true ) )
& ? [X0: $i] :
! [X1: $i] :
? [X2: $i] :
! [X3: $i] :
( ( $true
= ( cD @ X3 @ X0 @ X1 ) )
| ( $true
!= ( cS @ X2 @ X3 ) ) )
& ! [X4: $i] :
? [X5: $i] :
( ( cF @ X4 @ X5 )
= $true ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X12: $i] :
? [X13: $i] :
! [X14: $i] :
? [X15: $i] :
( ? [X16: $i] :
( ( $true
= ( cF @ X15 @ X16 ) )
& ( ( cD @ X16 @ X12 @ X13 )
!= $true ) )
& ( ( cS @ X14 @ X15 )
= $true ) )
& ! [X4: $i] :
? [X5: $i] :
( ( cF @ X4 @ X5 )
= $true )
& ? [X0: $i] :
! [X1: $i] :
? [X2: $i] :
! [X3: $i] :
( ( $true
= ( cD @ X3 @ X0 @ X1 ) )
| ( $true
!= ( cS @ X2 @ X3 ) ) )
& ! [X6: $i] :
? [X7: $i] :
! [X8: $i,X9: $i] :
( ! [X10: $i,X11: $i] :
( ( ( cD @ X10 @ X11 @ X6 )
= $true )
| ( ( cF @ X8 @ X10 )
!= $true )
| ( $true
!= ( cF @ X9 @ X11 ) ) )
| ( ( cD @ X8 @ X9 @ X7 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [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 ) ) )
& ! [X6: $i] :
? [X7: $i] :
! [X8: $i,X9: $i] :
( ( ( cD @ X8 @ X9 @ X7 )
= $true )
=> ! [X10: $i,X11: $i] :
( ( ( ( cF @ X8 @ X10 )
= $true )
& ( $true
= ( cF @ X9 @ X11 ) ) )
=> ( ( cD @ X10 @ X11 @ X6 )
= $true ) ) ) )
=> ? [X12: $i] :
! [X13: $i] :
? [X14: $i] :
! [X15: $i] :
( ( ( cS @ X14 @ X15 )
= $true )
=> ! [X16: $i] :
( ( $true
= ( cF @ X15 @ X16 ) )
=> ( ( cD @ X16 @ X12 @ X13 )
= $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 @ X9 @ X11 )
& ( cF @ X8 @ X10 ) )
=> ( cD @ X10 @ X11 @ X6 ) ) ) )
=> ? [X12: $i] :
! [X13: $i] :
? [X14: $i] :
! [X15: $i] :
( ( cS @ X14 @ X15 )
=> ! [X16: $i] :
( ( cF @ X15 @ X16 )
=> ( cD @ X16 @ X12 @ X13 ) ) ) ),
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 )
=> ! [X1: $i,X8: $i] :
( ( ( cF @ X7 @ X8 )
& ( cF @ X6 @ X1 ) )
=> ( 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 )
=> ! [X1: $i,X8: $i] :
( ( ( cF @ X7 @ X8 )
& ( cF @ X6 @ X1 ) )
=> ( 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.cog6E7hg1A/DTF2THF_4842.p',cX2138) ).
thf(f29,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( cF @ sK4 @ X2 ) )
| ( $true
= ( cD @ ( sK3 @ ( sK5 @ ( sK0 @ X0 ) ) @ X1 ) @ X2 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f27]) ).
thf(f27,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( cD @ ( sK3 @ ( sK5 @ ( sK0 @ X0 ) ) @ X1 ) @ X2 @ X0 ) )
| ( $true
!= ( cF @ sK4 @ X2 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f26,f21]) ).
thf(f21,plain,
! [X8: $i,X6: $i] :
( ( cF @ ( sK2 @ X8 @ X6 ) @ ( sK3 @ X8 @ X6 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f26,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( cF @ ( sK2 @ ( sK5 @ ( sK0 @ X0 ) ) @ X1 ) @ X2 ) )
| ( $true
!= ( cF @ sK4 @ X3 ) )
| ( ( cD @ X2 @ X3 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f25]) ).
thf(f25,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( cF @ sK4 @ X3 ) )
| ( $true
!= ( cF @ ( sK2 @ ( sK5 @ ( sK0 @ X0 ) ) @ X1 ) @ X2 ) )
| ( ( cD @ X2 @ X3 @ X0 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f22,f24]) ).
thf(f24,plain,
! [X0: $i,X1: $i] :
( $true
= ( cD @ ( sK2 @ ( sK5 @ X0 ) @ X1 ) @ sK4 @ X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f23]) ).
thf(f23,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
= ( cD @ ( sK2 @ ( sK5 @ X0 ) @ X1 ) @ sK4 @ X0 ) ) ),
inference(superposition,[status(thm)],[f18,f19]) ).
thf(f19,plain,
! [X8: $i,X6: $i] :
( $true
= ( cS @ X8 @ ( sK2 @ X8 @ X6 ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f18,plain,
! [X14: $i,X12: $i] :
( ( $true
!= ( cS @ ( sK5 @ X12 ) @ X14 ) )
| ( $true
= ( cD @ X14 @ sK4 @ X12 ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f22,plain,
! [X2: $i,X3: $i,X0: $i,X4: $i,X5: $i] :
( ( $true
!= ( cD @ X3 @ X2 @ ( sK0 @ X0 ) ) )
| ( $true
!= ( cF @ X3 @ X4 ) )
| ( $true
= ( cD @ X4 @ X5 @ X0 ) )
| ( ( cF @ X2 @ X5 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f20,plain,
! [X8: $i,X6: $i] :
( ( cD @ ( sK3 @ X8 @ X6 ) @ X6 @ ( sK1 @ X6 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN386^5 : 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
% 0.17/0.34 % Computer : n022.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 13:56:36 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
% 0.29/0.47 ---- Original DTF file ---
% 0.29/0.47 thf(spec,logic,$$dhol).
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 % File : SYN386^5 : TPTP v9.2.1. Released v4.0.0.
% 0.29/0.47 % Domain : Syntactic
% 0.29/0.47 % Problem : TPS problem X2138
% 0.29/0.47 % Version : Especial.
% 0.29/0.47 % English :
% 0.29/0.47
% 0.29/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.47 % Source : [Bro09]
% 0.29/0.47 % Names : tps_0369 [Bro09]
% 0.29/0.47 % : tps_0402 [Bro09]
% 0.29/0.47 % : X2138 [TPS]
% 0.29/0.47 % : THM82 [TPS]
% 0.29/0.47 % : THM82A [TPS]
% 0.29/0.47
% 0.29/0.47 % Status : Theorem
% 0.29/0.47 % Rating : 0.25 v9.0.0, 0.17 v8.2.0, 0.18 v8.1.0, 0.17 v7.4.0, 0.11 v7.3.0, 0.10 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.25 v6.4.0, 0.29 v6.3.0, 0.33 v6.1.0, 0.17 v6.0.0, 0.00 v5.5.0, 0.20 v5.4.0, 0.25 v5.3.0, 0.50 v5.2.0, 0.25 v5.1.0, 0.50 v5.0.0, 0.25 v4.1.0, 0.00 v4.0.0
% 0.29/0.47 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.29/0.47 % Number of atoms : 10 ( 0 equ; 0 cnn)
% 0.29/0.47 % Maximal formula atoms : 10 ( 10 avg)
% 0.29/0.47 % Number of connectives : 33 ( 0 ~; 0 |; 3 &; 24 @)
% 0.29/0.47 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 0.29/0.47 % Maximal formula depth : 15 ( 15 avg)
% 0.29/0.47 % Number of types : 2 ( 0 usr)
% 0.29/0.47 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.29/0.47 % Number of symbols : 3 ( 3 usr; 0 con; 2-3 aty)
% 0.29/0.47 % Number of variables : 17 ( 0 ^; 11 !; 6 ?; 17 :)
% 0.29/0.47 % SPC : TH0_THM_NEQ_NAR
% 0.29/0.47
% 0.29/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.29/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.29/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.29/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.29/0.47 % :
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 thf(cD,type,
% 0.29/0.47 cD: $i > $i > $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(cF,type,
% 0.29/0.47 cF: $i > $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(cS,type,
% 0.29/0.47 cS: $i > $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(cX2138,conjecture,
% 0.29/0.47 ( ( ! [Xx: $i] :
% 0.29/0.47 ? [Xy: $i] : ( cF @ Xx @ Xy )
% 0.29/0.47 & ? [Xx: $i] :
% 0.29/0.47 ! [Xe: $i] :
% 0.29/0.47 ? [Xn: $i] :
% 0.29/0.47 ! [Xw: $i] :
% 0.29/0.47 ( ( cS @ Xn @ Xw )
% 0.29/0.47 => ( cD @ Xw @ Xx @ Xe ) )
% 0.29/0.47 & ! [Xe: $i] :
% 0.29/0.47 ? [Xd: $i] :
% 0.29/0.47 ! [Xa: $i,Xb: $i] :
% 0.29/0.47 ( ( cD @ Xa @ Xb @ Xd )
% 0.29/0.47 => ! [Xy: $i,Xz: $i] :
% 0.29/0.47 ( ( ( cF @ Xa @ Xy )
% 0.29/0.47 & ( cF @ Xb @ Xz ) )
% 0.29/0.47 => ( cD @ Xy @ Xz @ Xe ) ) ) )
% 0.29/0.47 => ? [Xy: $i] :
% 0.29/0.47 ! [Xe: $i] :
% 0.29/0.47 ? [Xm: $i] :
% 0.29/0.47 ! [Xw: $i] :
% 0.29/0.47 ( ( cS @ Xm @ Xw )
% 0.29/0.47 => ! [Xz: $i] :
% 0.29/0.47 ( ( cF @ Xw @ Xz )
% 0.29/0.47 => ( cD @ Xz @ Xy @ Xe ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 ------------------------
% 1.45/1.28 ---- Embedded in THF ---
% 1.45/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.45/1.28 %%% Generated on Tue Feb 24 13:56:37 EST 2026
% 1.45/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.45/1.28 %%% Logic specification used:
% 1.45/1.28 %%% thf(spec, logic, $$dhol).
% 1.45/1.28
% 1.45/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.cog6E7hg1A/DTF2DTF4842.p
% See solution above
% 1.45/1.28 ------------------------
% 1.45/1.29 ---- Cleaned THF ---
% 1.45/1.29 thf(cD,type,
% 1.45/1.29 cD: $i > $i > $i > $o ).
% 1.45/1.29
% 1.45/1.29 thf(cF,type,
% 1.45/1.29 cF: $i > $i > $o ).
% 1.45/1.29
% 1.45/1.29 thf(cS,type,
% 1.45/1.29 cS: $i > $i > $o ).
% 1.45/1.29
% 1.45/1.29 thf(cX2138,conjecture,
% 1.45/1.29 ( ( ! [Xx: $i] :
% 1.45/1.29 ? [Xy: $i] : ( cF @ Xx @ Xy )
% 1.45/1.29 & ? [Xx: $i] :
% 1.45/1.29 ! [Xe: $i] :
% 1.45/1.29 ? [Xn: $i] :
% 1.45/1.29 ! [Xw: $i] :
% 1.45/1.29 ( ( cS @ Xn @ Xw )
% 1.45/1.29 => ( cD @ Xw @ Xx @ Xe ) )
% 1.45/1.29 & ! [Xe: $i] :
% 1.45/1.29 ? [Xd: $i] :
% 1.45/1.29 ! [Xa: $i,Xb: $i] :
% 1.45/1.29 ( ( cD @ Xa @ Xb @ Xd )
% 1.45/1.29 => ! [Xy: $i,Xz: $i] :
% 1.45/1.29 ( ( ( cF @ Xa @ Xy )
% 1.45/1.29 & ( cF @ Xb @ Xz ) )
% 1.45/1.29 => ( cD @ Xy @ Xz @ Xe ) ) ) )
% 1.45/1.29 => ? [Xy: $i] :
% 1.45/1.29 ! [Xe: $i] :
% 1.45/1.29 ? [Xm: $i] :
% 1.45/1.29 ! [Xw: $i] :
% 1.45/1.29 ( ( cS @ Xm @ Xw )
% 1.45/1.29 => ! [Xz: $i] :
% 1.45/1.29 ( ( cF @ Xw @ Xz )
% 1.45/1.29 => ( cD @ Xz @ Xy @ Xe ) ) ) ) ).
% 1.45/1.29 ------------------------
% 1.65/1.31 % (4952)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_4842 for (2999ds/2Mi)
% 1.65/1.31 % (4952)Instruction limit reached!
% 1.65/1.31 % (4952)------------------------------
% 1.65/1.31 % (4952)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.31 % (4952)Termination reason: Unknown
% 1.65/1.31 % (4952)Termination phase: Property scanning
% 1.65/1.31
% 1.65/1.31 % (4952)Memory used [KB]: 1023
% 1.65/1.31 % (4952)Time elapsed: 0.002 s
% 1.65/1.31 % (4952)Instructions burned: 2 (million)
% 1.65/1.31 % (4952)------------------------------
% 1.65/1.31 % (4952)------------------------------
% 1.65/1.31 % (4951)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_4842 for (2999ds/27Mi)
% 1.65/1.31 % (4951)First to succeed.
% 1.65/1.31 % (4951)Refutation found. Thanks to Tanya!
% 1.65/1.31 % SZS status Theorem for DTF2THF_4842
% 1.65/1.31 % SZS output start Proof for DTF2THF_4842
% 1.65/1.31 thf(func_def_0, type, cD: $i > $i > $i > $o).
% 1.65/1.31 thf(func_def_1, type, cF: $i > $i > $o).
% 1.65/1.31 thf(func_def_2, type, cS: $i > $i > $o).
% 1.65/1.31 thf(func_def_4, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.65/1.31 thf(func_def_7, type, sK0: $i > $i).
% 1.65/1.31 thf(func_def_8, type, sK1: $i > $i).
% 1.65/1.31 thf(func_def_9, type, sK2: $i > $i > $i).
% 1.65/1.31 thf(func_def_10, type, sK3: $i > $i > $i).
% 1.65/1.31 thf(func_def_12, type, sK5: $i > $i).
% 1.65/1.31 thf(func_def_13, type, sK6: $i > $i).
% 1.65/1.31 thf(f36,plain,(
% 1.65/1.31 $false),
% 1.65/1.31 inference(trivial_inequality_removal,[status(thm)],[f33])).
% 1.65/1.31 thf(f33,plain,(
% 1.65/1.31 ($true != $true)),
% 1.65/1.31 inference(superposition,[status(thm)],[f20,f32])).
% 1.65/1.31 thf(f32,plain,(
% 1.65/1.31 ( ! [X0 : $i,X1 : $i] : (((cD @ (sK3 @ (sK5 @ (sK0 @ X0)) @ X1) @ (sK6 @ sK4) @ X0) = $true)) )),
% 1.65/1.31 inference(trivial_inequality_removal,[status(thm)],[f31])).
% 1.65/1.31 thf(f31,plain,(
% 1.65/1.31 ( ! [X0 : $i,X1 : $i] : (((cD @ (sK3 @ (sK5 @ (sK0 @ X0)) @ X1) @ (sK6 @ sK4) @ X0) = $true) | ($true != $true)) )),
% 1.65/1.31 inference(superposition,[status(thm)],[f29,f17])).
% 1.65/1.31 thf(f17,plain,(
% 1.65/1.31 ( ! [X15 : $i] : (((cF @ X15 @ (sK6 @ X15)) = $true)) )),
% 1.65/1.31 inference(cnf_transformation,[status(thm)],[f16])).
% 1.65/1.31 thf(f16,plain,(
% 1.65/1.31 ! [X0 : $i] : ! [X2 : $i,X3 : $i] : (($true != (cD @ X3 @ X2 @ (sK0 @ X0))) | ! [X4 : $i,X5 : $i] : (($true != (cF @ X3 @ X4)) | ($true = (cD @ X4 @ X5 @ X0)) | ((cF @ X2 @ X5) != $true))) & ! [X6 : $i] : ! [X8 : $i] : ((((cF @ (sK2 @ X8 @ X6) @ (sK3 @ X8 @ X6)) = $true) & ((cD @ (sK3 @ X8 @ X6) @ X6 @ (sK1 @ X6)) != $true)) & ($true = (cS @ X8 @ (sK2 @ X8 @ X6)))) & ! [X12 : $i] : ! [X14 : $i] : (($true = (cD @ X14 @ sK4 @ X12)) | ($true != (cS @ (sK5 @ X12) @ X14))) & ! [X15 : $i] : ((cF @ X15 @ (sK6 @ X15)) = $true)),
% 1.65/1.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6])],[f8,f15,f14,f13,f12,f11,f10,f9])).
% 1.65/1.31 thf(f9,plain,(
% 1.65/1.31 ! [X0 : $i] : (? [X1 : $i] : ! [X2 : $i,X3 : $i] : (((cD @ X3 @ X2 @ X1) != $true) | ! [X4 : $i,X5 : $i] : (($true != (cF @ X3 @ X4)) | ($true = (cD @ X4 @ X5 @ X0)) | ((cF @ X2 @ X5) != $true))) => ! [X3 : $i,X2 : $i] : (($true != (cD @ X3 @ X2 @ (sK0 @ X0))) | ! [X4 : $i,X5 : $i] : (($true != (cF @ X3 @ X4)) | ($true = (cD @ X4 @ X5 @ X0)) | ((cF @ X2 @ X5) != $true))))),
% 1.65/1.31 introduced(definition,[],[choice_axiom])).
% 1.65/1.31 thf(f10,plain,(
% 1.65/1.31 ! [X6 : $i] : (? [X7 : $i] : ! [X8 : $i] : ? [X9 : $i] : (? [X10 : $i] : (((cF @ X9 @ X10) = $true) & ($true != (cD @ X10 @ X6 @ X7))) & ($true = (cS @ X8 @ X9))) => ! [X8 : $i] : ? [X9 : $i] : (? [X10 : $i] : (((cF @ X9 @ X10) = $true) & ((cD @ X10 @ X6 @ (sK1 @ X6)) != $true)) & ($true = (cS @ X8 @ X9))))),
% 1.65/1.31 introduced(definition,[],[choice_axiom])).
% 1.65/1.31 thf(f11,plain,(
% 1.65/1.31 ! [X6 : $i,X8 : $i] : (? [X9 : $i] : (? [X10 : $i] : (((cF @ X9 @ X10) = $true) & ((cD @ X10 @ X6 @ (sK1 @ X6)) != $true)) & ($true = (cS @ X8 @ X9))) => (? [X10 : $i] : (($true = (cF @ (sK2 @ X8 @ X6) @ X10)) & ((cD @ X10 @ X6 @ (sK1 @ X6)) != $true)) & ($true = (cS @ X8 @ (sK2 @ X8 @ X6)))))),
% 1.65/1.31 introduced(definition,[],[choice_axiom])).
% 1.65/1.31 thf(f12,plain,(
% 1.65/1.31 ! [X6 : $i,X8 : $i] : (? [X10 : $i] : (($true = (cF @ (sK2 @ X8 @ X6) @ X10)) & ((cD @ X10 @ X6 @ (sK1 @ X6)) != $true)) => (((cF @ (sK2 @ X8 @ X6) @ (sK3 @ X8 @ X6)) = $true) & ((cD @ (sK3 @ X8 @ X6) @ X6 @ (sK1 @ X6)) != $true)))),
% 1.65/1.31 introduced(definition,[],[choice_axiom])).
% 1.65/1.31 thf(f13,plain,(
% 1.65/1.31 ? [X11 : $i] : ! [X12 : $i] : ? [X13 : $i] : ! [X14 : $i] : (($true = (cD @ X14 @ X11 @ X12)) | ((cS @ X13 @ X14) != $true)) => ! [X12 : $i] : ? [X13 : $i] : ! [X14 : $i] : (($true = (cD @ X14 @ sK4 @ X12)) | ((cS @ X13 @ X14) != $true))),
% 1.65/1.31 introduced(definition,[],[choice_axiom])).
% 1.65/1.31 thf(f14,plain,(
% 1.65/1.31 ! [X12 : $i] : (? [X13 : $i] : ! [X14 : $i] : (($true = (cD @ X14 @ sK4 @ X12)) | ((cS @ X13 @ X14) != $true)) => ! [X14 : $i] : (($true = (cD @ X14 @ sK4 @ X12)) | ($true != (cS @ (sK5 @ X12) @ X14))))),
% 1.65/1.31 introduced(definition,[],[choice_axiom])).
% 1.65/1.31 thf(f15,plain,(
% 1.65/1.31 ! [X15 : $i] : (? [X16 : $i] : ($true = (cF @ X15 @ X16)) => ((cF @ X15 @ (sK6 @ X15)) = $true))),
% 1.65/1.31 introduced(definition,[],[choice_axiom])).
% 1.65/1.31 thf(f8,plain,(
% 1.65/1.31 ! [X0 : $i] : ? [X1 : $i] : ! [X2 : $i,X3 : $i] : (((cD @ X3 @ X2 @ X1) != $true) | ! [X4 : $i,X5 : $i] : (($true != (cF @ X3 @ X4)) | ($true = (cD @ X4 @ X5 @ X0)) | ((cF @ X2 @ X5) != $true))) & ! [X6 : $i] : ? [X7 : $i] : ! [X8 : $i] : ? [X9 : $i] : (? [X10 : $i] : (((cF @ X9 @ X10) = $true) & ($true != (cD @ X10 @ X6 @ X7))) & ($true = (cS @ X8 @ X9))) & ? [X11 : $i] : ! [X12 : $i] : ? [X13 : $i] : ! [X14 : $i] : (($true = (cD @ X14 @ X11 @ X12)) | ((cS @ X13 @ X14) != $true)) & ! [X15 : $i] : ? [X16 : $i] : ($true = (cF @ X15 @ X16))),
% 1.65/1.31 inference(rectify,[status(thm)],[f7])).
% 1.65/1.31 thf(f7,plain,(
% 1.65/1.31 ! [X6 : $i] : ? [X7 : $i] : ! [X9 : $i,X8 : $i] : (((cD @ X8 @ X9 @ X7) != $true) | ! [X10 : $i,X11 : $i] : (((cF @ X8 @ X10) != $true) | ((cD @ X10 @ X11 @ X6) = $true) | ($true != (cF @ X9 @ X11)))) & ! [X12 : $i] : ? [X13 : $i] : ! [X14 : $i] : ? [X15 : $i] : (? [X16 : $i] : (($true = (cF @ X15 @ X16)) & ((cD @ X16 @ X12 @ X13) != $true)) & ((cS @ X14 @ X15) = $true)) & ? [X0 : $i] : ! [X1 : $i] : ? [X2 : $i] : ! [X3 : $i] : (($true = (cD @ X3 @ X0 @ X1)) | ($true != (cS @ X2 @ X3))) & ! [X4 : $i] : ? [X5 : $i] : ((cF @ X4 @ X5) = $true)),
% 1.65/1.31 inference(flattening,[status(thm)],[f6])).
% 1.65/1.31 thf(f6,plain,(
% 1.65/1.31 ! [X12 : $i] : ? [X13 : $i] : ! [X14 : $i] : ? [X15 : $i] : (? [X16 : $i] : (($true = (cF @ X15 @ X16)) & ((cD @ X16 @ X12 @ X13) != $true)) & ((cS @ X14 @ X15) = $true)) & (! [X4 : $i] : ? [X5 : $i] : ((cF @ X4 @ X5) = $true) & ? [X0 : $i] : ! [X1 : $i] : ? [X2 : $i] : ! [X3 : $i] : (($true = (cD @ X3 @ X0 @ X1)) | ($true != (cS @ X2 @ X3))) & ! [X6 : $i] : ? [X7 : $i] : ! [X8 : $i,X9 : $i] : (! [X10 : $i,X11 : $i] : (((cD @ X10 @ X11 @ X6) = $true) | (((cF @ X8 @ X10) != $true) | ($true != (cF @ X9 @ X11)))) | ((cD @ X8 @ X9 @ X7) != $true)))),
% 1.65/1.31 inference(ennf_transformation,[status(thm)],[f5])).
% 1.65/1.31 thf(f5,plain,(
% 1.65/1.31 ~((! [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))) & ! [X6 : $i] : ? [X7 : $i] : ! [X8 : $i,X9 : $i] : (((cD @ X8 @ X9 @ X7) = $true) => ! [X10 : $i,X11 : $i] : ((((cF @ X8 @ X10) = $true) & ($true = (cF @ X9 @ X11))) => ((cD @ X10 @ X11 @ X6) = $true)))) => ? [X12 : $i] : ! [X13 : $i] : ? [X14 : $i] : ! [X15 : $i] : (((cS @ X14 @ X15) = $true) => ! [X16 : $i] : (($true = (cF @ X15 @ X16)) => ((cD @ X16 @ X12 @ X13) = $true))))),
% 1.65/1.31 inference(fool_elimination,[status(thm)],[f4])).
% 1.65/1.31 thf(f4,plain,(
% 1.65/1.31 ~((? [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 @ X9 @ X11) & (cF @ X8 @ X10)) => (cD @ X10 @ X11 @ X6)))) => ? [X12 : $i] : ! [X13 : $i] : ? [X14 : $i] : ! [X15 : $i] : ((cS @ X14 @ X15) => ! [X16 : $i] : ((cF @ X15 @ X16) => (cD @ X16 @ X12 @ X13))))),
% 1.65/1.31 inference(rectify,[status(thm)],[f2])).
% 1.65/1.31 thf(f2,negated_conjecture,(
% 1.65/1.31 ~((? [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) => ! [X1 : $i,X8 : $i] : (((cF @ X7 @ X8) & (cF @ X6 @ X1)) => (cD @ X1 @ X8 @ X2)))) => ? [X1 : $i] : ! [X2 : $i] : ? [X9 : $i] : ! [X4 : $i] : ((cS @ X9 @ X4) => ! [X8 : $i] : ((cF @ X4 @ X8) => (cD @ X8 @ X1 @ X2))))),
% 1.65/1.31 inference(negated_conjecture,[status(cth)],[f1])).
% 1.65/1.31 thf(f1,conjecture,(
% 1.65/1.31 (? [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) => ! [X1 : $i,X8 : $i] : (((cF @ X7 @ X8) & (cF @ X6 @ X1)) => (cD @ X1 @ X8 @ X2)))) => ? [X1 : $i] : ! [X2 : $i] : ? [X9 : $i] : ! [X4 : $i] : ((cS @ X9 @ X4) => ! [X8 : $i] : ((cF @ X4 @ X8) => (cD @ X8 @ X1 @ X2)))),
% 1.65/1.31 file('/export/starexec/sandbox/tmp/tmp.cog6E7hg1A/DTF2THF_4842.p',cX2138)).
% 1.65/1.31 thf(f29,plain,(
% 1.65/1.31 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (cF @ sK4 @ X2)) | ($true = (cD @ (sK3 @ (sK5 @ (sK0 @ X0)) @ X1) @ X2 @ X0))) )),
% 1.65/1.31 inference(trivial_inequality_removal,[status(thm)],[f27])).
% 1.65/1.31 thf(f27,plain,(
% 1.65/1.31 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (cD @ (sK3 @ (sK5 @ (sK0 @ X0)) @ X1) @ X2 @ X0)) | ($true != (cF @ sK4 @ X2)) | ($true != $true)) )),
% 1.65/1.31 inference(superposition,[status(thm)],[f26,f21])).
% 1.65/1.31 thf(f21,plain,(
% 1.65/1.31 ( ! [X8 : $i,X6 : $i] : (((cF @ (sK2 @ X8 @ X6) @ (sK3 @ X8 @ X6)) = $true)) )),
% 1.65/1.31 inference(cnf_transformation,[status(thm)],[f16])).
% 1.65/1.31 thf(f26,plain,(
% 1.65/1.31 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (cF @ (sK2 @ (sK5 @ (sK0 @ X0)) @ X1) @ X2)) | ($true != (cF @ sK4 @ X3)) | ((cD @ X2 @ X3 @ X0) = $true)) )),
% 1.65/1.31 inference(trivial_inequality_removal,[status(thm)],[f25])).
% 1.65/1.31 thf(f25,plain,(
% 1.65/1.31 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (cF @ sK4 @ X3)) | ($true != (cF @ (sK2 @ (sK5 @ (sK0 @ X0)) @ X1) @ X2)) | ((cD @ X2 @ X3 @ X0) = $true) | ($true != $true)) )),
% 1.65/1.31 inference(superposition,[status(thm)],[f22,f24])).
% 1.65/1.31 thf(f24,plain,(
% 1.65/1.31 ( ! [X0 : $i,X1 : $i] : (($true = (cD @ (sK2 @ (sK5 @ X0) @ X1) @ sK4 @ X0))) )),
% 1.65/1.31 inference(trivial_inequality_removal,[status(thm)],[f23])).
% 1.65/1.31 thf(f23,plain,(
% 1.65/1.31 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ($true = (cD @ (sK2 @ (sK5 @ X0) @ X1) @ sK4 @ X0))) )),
% 1.65/1.31 inference(superposition,[status(thm)],[f18,f19])).
% 1.65/1.31 thf(f19,plain,(
% 1.65/1.31 ( ! [X8 : $i,X6 : $i] : (($true = (cS @ X8 @ (sK2 @ X8 @ X6)))) )),
% 1.65/1.31 inference(cnf_transformation,[status(thm)],[f16])).
% 1.65/1.31 thf(f18,plain,(
% 1.65/1.31 ( ! [X14 : $i,X12 : $i] : (($true != (cS @ (sK5 @ X12) @ X14)) | ($true = (cD @ X14 @ sK4 @ X12))) )),
% 1.65/1.31 inference(cnf_transformation,[status(thm)],[f16])).
% 1.65/1.31 thf(f22,plain,(
% 1.65/1.31 ( ! [X2 : $i,X3 : $i,X0 : $i,X4 : $i,X5 : $i] : (($true != (cD @ X3 @ X2 @ (sK0 @ X0))) | ($true != (cF @ X3 @ X4)) | ($true = (cD @ X4 @ X5 @ X0)) | ((cF @ X2 @ X5) != $true)) )),
% 1.65/1.31 inference(cnf_transformation,[status(thm)],[f16])).
% 1.65/1.31 thf(f20,plain,(
% 1.65/1.31 ( ! [X8 : $i,X6 : $i] : (((cD @ (sK3 @ X8 @ X6) @ X6 @ (sK1 @ X6)) != $true)) )),
% 1.65/1.31 inference(cnf_transformation,[status(thm)],[f16])).
% 1.65/1.31 % SZS output end Proof for DTF2THF_4842
% 1.65/1.31 % (4951)------------------------------
% 1.65/1.31 % (4951)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.31 % (4951)Termination reason: Refutation
% 1.65/1.31
% 1.65/1.31 % (4951)Memory used [KB]: 5500
% 1.65/1.31 % (4951)Time elapsed: 0.005 s
% 1.65/1.31 % (4951)Instructions burned: 7 (million)
% 1.65/1.31 % (4951)------------------------------
% 1.65/1.31 % (4951)------------------------------
% 1.65/1.31 % (4948)Success in time 0.016 s
%------------------------------------------------------------------------------