%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM814^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n004.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 09:24:50 AM UTC 2026
% Result : Theorem 1.61s 1.35s
% Output : Refutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 5
% Syntax : Number of formulae : 60 ( 38 unt; 0 typ; 0 def)
% Number of atoms : 310 ( 127 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 530 ( 38 ~; 21 |; 35 &; 323 @)
% ( 0 <=>; 57 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 10 usr; 6 con; 0-2 aty)
% ( 56 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 142 ( 77 ^; 61 !; 4 ?; 142 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
cS: $i > $i ).
thf(func_def_2,type,
cEVEN1: $i > $o ).
thf(func_def_4,type,
cODD1: $i > $o ).
thf(func_def_18,type,
sK1: ( $i > $o ) > $i ).
thf(func_def_19,type,
sK2: ( $i > $o ) > $i ).
thf(func_def_20,type,
ph3:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
sK4: $i > $i ).
thf(f862,plain,
$false,
inference(equality_resolution,[status(thm)],[f861]) ).
thf(f861,plain,
! [X0: $i] : ( c0 != X0 ),
inference(subsumption_resolution,[status(thm)],[f860,f53]) ).
thf(f53,plain,
! [X1: $i] :
( c0
!= ( cS @ X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
! [X1: $i] :
( ( c0
= ( cS @ X1 ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
! [X1: $i] :
( ( c0
!= ( cS @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f50]) ).
thf(f50,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( c0
!= ( cS @ Y0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( c0
!= ( cS @ Y0 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( cS @ Y0 )
= ( cS @ Y1 ) )
=> ( Y1 = Y0 ) ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ Y1 ) ) ) )
& ( Y0 @ c0 ) )
=> ( !! @ $i @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( c0
!= ( cS @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f27]) ).
thf(f27,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( cS @ Y0 )
= ( cS @ Y1 ) )
=> ( Y1 = Y0 ) ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ Y1 ) ) ) )
& ( Y0 @ c0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( c0
!= ( cS @ Y0 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f21,f26]) ).
thf(f26,plain,
( cPEANO1
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( cS @ Y0 )
= ( cS @ Y1 ) )
=> ( Y1 = Y0 ) ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ Y1 ) ) ) )
& ( Y0 @ c0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( c0
!= ( cS @ Y0 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f19,f23]) ).
thf(f23,plain,
( cIND
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ Y1 ) ) ) )
& ( Y0 @ c0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( cIND
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ Y1 ) ) ) )
& ( Y0 @ c0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
( cIND
= ( ! [X0: $i > $o] :
( ( ( X0 @ c0 )
& ! [X1: $i] :
( ( X0 @ X1 )
=> ( X0 @ ( cS @ X1 ) ) ) )
=> ! [X2: $i] : ( X0 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( cIND
= ( ! [X1: $i > $o] :
( ( ( X1 @ c0 )
& ! [X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( cS @ X2 ) ) ) )
=> ! [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.L9cmIiQdkO/DTF2THF_16344.p',cIND_def) ).
thf(f19,plain,
( cPEANO1
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( cS @ Y0 )
= ( cS @ Y1 ) )
=> ( Y1 = Y0 ) ) ) )
& cIND
& ( !! @ $i
@ ^ [Y0: $i] :
( c0
!= ( cS @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( cPEANO1
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( cS @ Y0 )
= ( cS @ Y1 ) )
=> ( Y1 = Y0 ) ) ) )
& cIND
& ( !! @ $i
@ ^ [Y0: $i] :
( c0
!= ( cS @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
( ( cPEANO1
= ( ! [X0: $i] :
( c0
!= ( cS @ X0 ) ) ) )
& cIND
& ! [X1: $i,X2: $i] :
( ( ( cS @ X2 )
= ( cS @ X1 ) )
=> ( X1 = X2 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( ( cPEANO1
= ( ! [X3: $i] :
( c0
!= ( cS @ X3 ) ) ) )
& cIND
& ! [X5: $i,X4: $i] :
( ( ( cS @ X4 )
= ( cS @ X5 ) )
=> ( X4 = X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.L9cmIiQdkO/DTF2THF_16344.p',cPEANO1_def) ).
thf(f21,plain,
cPEANO1 = $true,
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ( cPEANO1 = $true )
& ! [X0: $i] :
( ( cODD1 @ X0 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( ( cPEANO1 = $true )
=> ? [X0: $i] :
( ( cODD1 @ X0 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( cPEANO1
=> ? [X0: $i] : ( cODD1 @ X0 ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( cPEANO1
=> ? [X0: $i] : ( cODD1 @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
( cPEANO1
=> ? [X0: $i] : ( cODD1 @ X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.L9cmIiQdkO/DTF2THF_16344.p',cTHM404) ).
thf(f860,plain,
! [X0: $i] :
( ( c0
= ( cS @ X0 ) )
| ( c0 != X0 ) ),
inference(equality_resolution,[status(thm)],[f845]) ).
thf(f845,plain,
! [X0: $i,X1: $i] :
( ( ( cS @ X1 )
!= X0 )
| ( c0 = X0 )
| ( c0 != X1 ) ),
inference(superposition,[status(thm)],[f53,f562]) ).
thf(f562,plain,
! [X0: $i,X1: $i] :
( ( ( cS
@ ( sK2
@ ^ [Y0: $i] : ( X0 != Y0 ) ) )
= X1 )
| ( ( cS @ X1 )
!= X0 )
| ( c0 = X0 ) ),
inference(superposition,[status(thm)],[f40,f303]) ).
thf(f303,plain,
! [X0: $i] :
( ( ( cS
@ ( cS
@ ( sK2
@ ^ [Y0: $i] : ( X0 != Y0 ) ) ) )
= X0 )
| ( c0 = X0 ) ),
inference(equality_proxy_clausification,[status(thm)],[f302]) ).
thf(f302,plain,
! [X0: $i] :
( ( $true
= ( X0 = c0 ) )
| ( ( cS
@ ( cS
@ ( sK2
@ ^ [Y0: $i] : ( X0 != Y0 ) ) ) )
= X0 ) ),
inference(not_proxy_clausification,[status(thm)],[f301]) ).
thf(f301,plain,
! [X0: $i] :
( ( ( X0 != c0 )
= $false )
| ( ( cS
@ ( cS
@ ( sK2
@ ^ [Y0: $i] : ( X0 != Y0 ) ) ) )
= X0 ) ),
inference(beta_eta_normalization,[status(thm)],[f255]) ).
thf(f255,plain,
! [X0: $i] :
( ( ( ^ [Y0: $i] : ( X0 != Y0 )
@ c0 )
= $false )
| ( ( cS
@ ( cS
@ ( sK2
@ ^ [Y0: $i] : ( X0 != Y0 ) ) ) )
= X0 ) ),
inference(leibniz_equality_elimination,[status(thm)],[f62]) ).
thf(f62,plain,
! [X0: $i,X1: $i > $o] :
( ( $false
= ( X1 @ ( cS @ ( cS @ ( sK2 @ X1 ) ) ) ) )
| ( ( X1 @ c0 )
= $false )
| ( ( X1 @ X0 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f61]) ).
thf(f61,plain,
! [X0: $i,X1: $i > $o] :
( ( ( ( X1 @ ( sK2 @ X1 ) )
=> ( X1 @ ( cS @ ( cS @ ( sK2 @ X1 ) ) ) ) )
= $false )
| ( ( X1 @ X0 )
= $true )
| ( ( X1 @ c0 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f60]) ).
thf(f60,plain,
! [X0: $i,X1: $i > $o] :
( ( ( X1 @ X0 )
= $true )
| ( ( X1 @ c0 )
= $false )
| ( ( ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( cS @ ( cS @ Y0 ) ) ) )
@ ( sK2 @ X1 ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
! [X0: $i,X1: $i > $o] :
( ( ( X1 @ X0 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( cS @ ( cS @ Y0 ) ) ) ) )
= $false )
| ( ( X1 @ c0 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f58]) ).
thf(f58,plain,
! [X0: $i,X1: $i > $o] :
( ( ( ( X1 @ c0 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( cS @ ( cS @ Y0 ) ) ) ) ) )
= $false )
| ( ( X1 @ X0 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f57]) ).
thf(f57,plain,
! [X0: $i,X1: $i > $o] :
( ( ( ( X1 @ c0 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( cS @ ( cS @ Y0 ) ) ) ) ) )
=> ( X1 @ X0 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f56]) ).
thf(f56,plain,
! [X0: $i,X1: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( ( ( Y0 @ c0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ ( cS @ Y1 ) ) ) ) ) )
=> ( Y0 @ X0 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
! [X0: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( Y0 @ c0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ ( cS @ Y1 ) ) ) ) ) )
=> ( Y0 @ X0 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
! [X0: $i] :
( ( ~ ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( Y0 @ c0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ ( cS @ Y1 ) ) ) ) ) )
=> ( Y0 @ X0 ) ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f28]) ).
thf(f28,plain,
! [X0: $i] :
( ( ^ [Y0: $i] :
~ ( ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( Y2 @ c0 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cS @ ( cS @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
@ Y0 )
@ X0 )
!= $true ),
inference(definition_unfolding,[status(thm)],[f20,f25]) ).
thf(f25,plain,
( cODD1
= ( ^ [Y0: $i] :
~ ( ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( Y2 @ c0 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cS @ ( cS @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
@ Y0 ) ) ),
inference(definition_unfolding,[status(thm)],[f24,f22]) ).
thf(f22,plain,
( cEVEN1
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( Y1 @ c0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cS @ ( cS @ Y2 ) ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( cEVEN1
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( Y1 @ c0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cS @ ( cS @ Y2 ) ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [X0: $i] :
! [X1: $i > $o] :
( ( ! [X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( cS @ ( cS @ X2 ) ) ) )
& ( X1 @ c0 ) )
=> ( X1 @ X0 ) ) )
= cEVEN1 ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: $i] :
! [X1: $i > $o] :
( ( ! [X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( cS @ ( cS @ X2 ) ) ) )
& ( X1 @ c0 ) )
=> ( X1 @ X0 ) ) )
= cEVEN1 ),
file('/export/starexec/sandbox2/tmp/tmp.L9cmIiQdkO/DTF2THF_16344.p',cEVEN1_def) ).
thf(f24,plain,
( cODD1
= ( ^ [Y0: $i] :
~ ( cEVEN1 @ Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( cODD1
= ( ^ [Y0: $i] :
~ ( cEVEN1 @ Y0 ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
( cODD1
= ( ^ [X0: $i] :
~ ( cEVEN1 @ X0 ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( cODD1
= ( ^ [X0: $i] :
~ ( cEVEN1 @ X0 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.L9cmIiQdkO/DTF2THF_16344.p',cODD1_def) ).
thf(f20,plain,
! [X0: $i] :
( ( cODD1 @ X0 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f40,plain,
! [X2: $i,X1: $i] :
( ( ( cS @ X2 )
!= ( cS @ X1 ) )
| ( X1 = X2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
! [X2: $i,X1: $i] :
( ( X1 = X2 )
| ( ( ( cS @ X1 )
= ( cS @ X2 ) )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
! [X2: $i,X1: $i] :
( ( ( X2 = X1 )
= $true )
| ( ( ( cS @ X1 )
= ( cS @ X2 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
! [X2: $i,X1: $i] :
( ( ( ( cS @ X1 )
= ( cS @ X2 ) )
=> ( X2 = X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f36]) ).
thf(f36,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( cS @ X1 )
= ( cS @ Y0 ) )
=> ( Y0 = X1 ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( cS @ X1 )
= ( cS @ Y0 ) )
=> ( Y0 = X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f34]) ).
thf(f34,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( cS @ Y0 )
= ( cS @ Y1 ) )
=> ( Y1 = Y0 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( cS @ Y0 )
= ( cS @ Y1 ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( cS @ Y0 )
= ( cS @ Y1 ) )
=> ( Y1 = Y0 ) ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ Y1 ) ) ) )
& ( Y0 @ c0 ) )
=> ( !! @ $i @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM814^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% 0.12/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.33 % Computer : n004.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue Feb 24 11:15:26 EST 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : NUM814^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% 0.30/0.46 % Domain : Number Theory (Induction on naturals)
% 0.30/0.46 % Problem : TPS problem from IND-THMS
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English :
% 0.30/0.46
% 0.30/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Bro09]
% 0.30/0.46 % Names : tps_0606 [Bro09]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.33 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.54 v8.1.0, 0.45 v7.5.0, 0.29 v7.4.0, 0.56 v7.3.0, 0.67 v7.2.0, 0.62 v7.0.0, 0.71 v6.4.0, 0.67 v6.3.0, 0.60 v6.2.0, 0.71 v6.1.0, 0.57 v5.5.0, 1.00 v5.2.0
% 0.30/0.46 % Syntax : Number of formulae : 11 ( 4 unt; 6 typ; 4 def)
% 0.30/0.46 % Number of atoms : 15 ( 7 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 2 ( 3 avg)
% 0.30/0.46 % Number of connectives : 28 ( 2 ~; 0 |; 4 &; 16 @)
% 0.30/0.46 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 4 ( 2 avg)
% 0.30/0.46 % Number of types : 2 ( 0 usr)
% 0.30/0.46 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 7 ( 6 usr; 3 con; 0-2 aty)
% 0.30/0.46 % Number of variables : 11 ( 2 ^; 8 !; 1 ?; 11 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.30/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.30/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.30/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.30/0.46 % :
% 0.30/0.46 % Bugfixes : v5.2.0 - Added missing type declarations.
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(c0_type,type,
% 0.30/0.46 c0: $i ).
% 0.30/0.46
% 0.30/0.46 thf(cS_type,type,
% 0.30/0.46 cS: $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(cEVEN1_type,type,
% 0.30/0.46 cEVEN1: $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(cIND_type,type,
% 0.30/0.46 cIND: $o ).
% 0.30/0.46
% 0.30/0.46 thf(cODD1_type,type,
% 0.30/0.46 cODD1: $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(cPEANO1_type,type,
% 0.30/0.46 cPEANO1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(cEVEN1_def,definition,
% 0.30/0.46 ( cEVEN1
% 0.30/0.46 = ( ^ [Xn: $i] :
% 0.30/0.46 ! [Xp: $i > $o] :
% 0.30/0.46 ( ( ( Xp @ c0 )
% 0.30/0.46 & ! [Xx: $i] :
% 0.30/0.46 ( ( Xp @ Xx )
% 0.30/0.46 => ( Xp @ ( cS @ ( cS @ Xx ) ) ) ) )
% 0.30/0.46 => ( Xp @ Xn ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(cIND_def,definition,
% 0.30/0.46 ( cIND
% 0.30/0.46 = ( ! [Xp: $i > $o] :
% 0.30/0.46 ( ( ( Xp @ c0 )
% 0.30/0.46 & ! [Xx: $i] :
% 0.30/0.46 ( ( Xp @ Xx )
% 0.30/0.46 => ( Xp @ ( cS @ Xx ) ) ) )
% 0.30/0.46 => ! [Xx: $i] : ( Xp @ Xx ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(cODD1_def,definition,
% 0.30/0.46 ( cODD1
% 0.30/0.46 = ( ^ [Xn: $i] :
% 0.30/0.46 ~ ( cEVEN1 @ Xn ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(cPEANO1_def,definition,
% 0.30/0.46 ( cPEANO1
% 0.30/0.46 = ( ! [Xu: $i] :
% 0.30/0.46 ( ( cS @ Xu )
% 0.30/0.46 != c0 )
% 0.30/0.46 & ! [Xv: $i,Xw: $i] :
% 0.30/0.46 ( ( ( cS @ Xv )
% 0.30/0.46 = ( cS @ Xw ) )
% 0.30/0.46 => ( Xv = Xw ) )
% 0.30/0.46 & cIND ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(cTHM404,conjecture,
% 0.30/0.46 ( cPEANO1
% 0.30/0.46 => ? [Xn: $i] : ( cODD1 @ Xn ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.47/1.27 ---- Embedded in THF ---
% 1.47/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.27 %%% Generated on Tue Feb 24 11:15:27 EST 2026
% 1.47/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.27 %%% Logic specification used:
% 1.47/1.27 %%% thf(spec, logic, $$dhol).
% 1.47/1.27
% 1.47/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.L9cmIiQdkO/DTF2DTF16344.p
% See solution above
% 1.47/1.27 ------------------------
% 1.47/1.28 ---- Cleaned THF ---
% 1.47/1.28 thf(c0_type,type,
% 1.47/1.28 c0: $i ).
% 1.47/1.28
% 1.47/1.28 thf(cS_type,type,
% 1.47/1.28 cS: $i > $i ).
% 1.47/1.28
% 1.47/1.28 thf(cEVEN1_type,type,
% 1.47/1.28 cEVEN1: $i > $o ).
% 1.47/1.28
% 1.47/1.28 thf(cIND_type,type,
% 1.47/1.28 cIND: $o ).
% 1.47/1.28
% 1.47/1.28 thf(cODD1_type,type,
% 1.47/1.28 cODD1: $i > $o ).
% 1.47/1.28
% 1.47/1.28 thf(cPEANO1_type,type,
% 1.47/1.28 cPEANO1: $o ).
% 1.47/1.28
% 1.47/1.28 thf(cEVEN1_def,definition,
% 1.47/1.28 ( cEVEN1
% 1.47/1.28 = ( ^ [Xn: $i] :
% 1.47/1.28 ! [Xp: $i > $o] :
% 1.47/1.28 ( ( ( Xp @ c0 )
% 1.47/1.28 & ! [Xx: $i] :
% 1.47/1.28 ( ( Xp @ Xx )
% 1.47/1.28 => ( Xp @ ( cS @ ( cS @ Xx ) ) ) ) )
% 1.47/1.28 => ( Xp @ Xn ) ) ) ) ).
% 1.47/1.28
% 1.47/1.28 thf(cIND_def,definition,
% 1.47/1.28 ( cIND
% 1.47/1.28 = ( ! [Xp: $i > $o] :
% 1.47/1.28 ( ( ( Xp @ c0 )
% 1.47/1.28 & ! [Xx: $i] :
% 1.47/1.28 ( ( Xp @ Xx )
% 1.47/1.28 => ( Xp @ ( cS @ Xx ) ) ) )
% 1.47/1.28 => ! [Xx: $i] : ( Xp @ Xx ) ) ) ) ).
% 1.47/1.28
% 1.47/1.28 thf(cODD1_def,definition,
% 1.47/1.28 ( cODD1
% 1.47/1.28 = ( ^ [Xn: $i] :
% 1.47/1.28 ~ ( cEVEN1 @ Xn ) ) ) ).
% 1.47/1.28
% 1.47/1.28 thf(cPEANO1_def,definition,
% 1.47/1.28 ( cPEANO1
% 1.47/1.28 = ( ! [Xu: $i] :
% 1.47/1.28 ( ( cS @ Xu )
% 1.47/1.28 != c0 )
% 1.47/1.28 & ! [Xv: $i,Xw: $i] :
% 1.47/1.28 ( ( ( cS @ Xv )
% 1.47/1.28 = ( cS @ Xw ) )
% 1.47/1.28 => ( Xv = Xw ) )
% 1.47/1.28 & cIND ) ) ).
% 1.47/1.28
% 1.47/1.28 thf(cTHM404,conjecture,
% 1.47/1.28 ( cPEANO1
% 1.47/1.28 => ? [Xn: $i] : ( cODD1 @ Xn ) ) ).
% 1.47/1.28 ------------------------
% 1.47/1.29 % (16561)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_16344 for (2999ds/4Mi)
% 1.47/1.29 % (16562)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_16344 for (2999ds/27Mi)
% 1.47/1.29 % (16561)Instruction limit reached!
% 1.47/1.29 % (16561)------------------------------
% 1.47/1.29 % (16561)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.29 % (16561)Termination reason: Unknown
% 1.47/1.29 % (16561)Termination phase: Saturation
% 1.47/1.29
% 1.47/1.29 % (16561)Memory used [KB]: 5500
% 1.47/1.29 % (16561)Time elapsed: 0.003 s
% 1.47/1.29 % (16561)Instructions burned: 5 (million)
% 1.47/1.29 % (16561)------------------------------
% 1.47/1.29 % (16561)------------------------------
% 1.61/1.30 % (16562)Refutation not found, incomplete strategy
% 1.61/1.30 % (16562)------------------------------
% 1.61/1.30 % (16562)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.30 % (16562)Termination reason: Refutation not found, incomplete strategy
% 1.61/1.30
% 1.61/1.30
% 1.61/1.30 % (16562)Memory used [KB]: 5500
% 1.61/1.30 % (16562)Time elapsed: 0.003 s
% 1.61/1.30 % (16562)Instructions burned: 5 (million)
% 1.61/1.30 % (16562)------------------------------
% 1.61/1.30 % (16562)------------------------------
% 1.61/1.30 % (16560)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_16344 for (2999ds/183Mi)
% 1.61/1.30 % (16563)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_16344 for (2999ds/2Mi)
% 1.61/1.30 % (16564)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_16344 for (2999ds/2Mi)
% 1.61/1.30 % (16565)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_16344 for (2999ds/275Mi)
% 1.61/1.30 % (16566)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_16344 for (2999ds/18Mi)
% 1.61/1.30 % (16563)Instruction limit reached!
% 1.61/1.30 % (16563)------------------------------
% 1.61/1.30 % (16563)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.30 % (16563)Termination reason: Unknown
% 1.61/1.30 % (16563)Termination phase: Property scanning
% 1.61/1.30
% 1.61/1.30 % (16563)Memory used [KB]: 895
% 1.61/1.30 % (16563)Time elapsed: 0.003 s
% 1.61/1.30 % (16563)Instructions burned: 2 (million)
% 1.61/1.30 % (16563)------------------------------
% 1.61/1.30 % (16563)------------------------------
% 1.61/1.30 % (16564)Instruction limit reached!
% 1.61/1.30 % (16564)------------------------------
% 1.61/1.30 % (16564)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.30 % (16564)Termination reason: Unknown
% 1.61/1.30 % (16564)Termination phase: Property scanning
% 1.61/1.30
% 1.61/1.30 % (16564)Memory used [KB]: 895
% 1.61/1.30 % (16564)Time elapsed: 0.003 s
% 1.61/1.30 % (16564)Instructions burned: 2 (million)
% 1.61/1.30 % (16564)------------------------------
% 1.61/1.30 % (16564)------------------------------
% 1.61/1.30 % (16565)Refutation not found, incomplete strategy
% 1.61/1.30 % (16565)------------------------------
% 1.61/1.30 % (16565)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.30 % (16565)Termination reason: Refutation not found, incomplete strategy
% 1.61/1.30
% 1.61/1.30
% 1.61/1.30 % (16565)Memory used [KB]: 5500
% 1.61/1.30 % (16565)Time elapsed: 0.004 s
% 1.61/1.30 % (16565)Instructions burned: 3 (million)
% 1.61/1.30 % (16565)------------------------------
% 1.61/1.30 % (16565)------------------------------
% 1.61/1.30 % (16567)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_16344 for (2999ds/3Mi)
% 1.61/1.30 % (16567)Instruction limit reached!
% 1.61/1.30 % (16567)------------------------------
% 1.61/1.30 % (16567)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.30 % (16567)Termination reason: Unknown
% 1.61/1.30 % (16567)Termination phase: Saturation
% 1.61/1.30
% 1.61/1.30 % (16567)Memory used [KB]: 5500
% 1.61/1.30 % (16567)Time elapsed: 0.002 s
% 1.61/1.30 % (16567)Instructions burned: 3 (million)
% 1.61/1.30 % (16567)------------------------------
% 1.61/1.30 % (16567)------------------------------
% 1.61/1.31 % (16568)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_16344 for (2999ds/37Mi)
% 1.61/1.31 % (16566)Instruction limit reached!
% 1.61/1.31 % (16566)------------------------------
% 1.61/1.31 % (16566)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.31 % (16566)Termination reason: Unknown
% 1.61/1.31 % (16566)Termination phase: Saturation
% 1.61/1.31
% 1.61/1.31 % (16566)Memory used [KB]: 5628
% 1.61/1.31 % (16566)Time elapsed: 0.014 s
% 1.61/1.31 % (16566)Instructions burned: 19 (million)
% 1.61/1.31 % (16566)------------------------------
% 1.61/1.31 % (16566)------------------------------
% 1.61/1.31 % (16572)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_16344 for (2999ds/7Mi)
% 1.61/1.32 % (16572)Instruction limit reached!
% 1.61/1.32 % (16572)------------------------------
% 1.61/1.32 % (16572)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.32 % (16572)Termination reason: Unknown
% 1.61/1.32 % (16572)Termination phase: Saturation
% 1.61/1.32
% 1.61/1.32 % (16572)Memory used [KB]: 1023
% 1.61/1.32 % (16572)Time elapsed: 0.004 s
% 1.61/1.32 % (16572)Instructions burned: 9 (million)
% 1.61/1.32 % (16572)------------------------------
% 1.61/1.32 % (16572)------------------------------
% 1.61/1.32 % (16568)Instruction limit reached!
% 1.61/1.32 % (16568)------------------------------
% 1.61/1.32 % (16568)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.32 % (16568)Termination reason: Unknown
% 1.61/1.32 % (16568)Termination phase: Saturation
% 1.61/1.32
% 1.61/1.32 % (16568)Memory used [KB]: 5884
% 1.61/1.32 % (16568)Time elapsed: 0.014 s
% 1.61/1.32 % (16568)Instructions burned: 39 (million)
% 1.61/1.32 % (16568)------------------------------
% 1.61/1.32 % (16568)------------------------------
% 1.61/1.32 % (16569)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_16344 for (2999ds/15Mi)
% 1.61/1.32 % (16570)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_16344 for (2999ds/3Mi)
% 1.61/1.32 % (16570)Instruction limit reached!
% 1.61/1.32 % (16570)------------------------------
% 1.61/1.32 % (16570)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.32 % (16570)Termination reason: Unknown
% 1.61/1.32 % (16570)Termination phase: Saturation
% 1.61/1.32
% 1.61/1.32 % (16570)Memory used [KB]: 5500
% 1.61/1.32 % (16570)Time elapsed: 0.004 s
% 1.61/1.32 % (16570)Instructions burned: 3 (million)
% 1.61/1.32 % (16570)------------------------------
% 1.61/1.32 % (16570)------------------------------
% 1.61/1.32 % (16571)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_16344 for (2999ds/1041Mi)
% 1.61/1.33 % (16574)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_16344 for (2999ds/3Mi)
% 1.61/1.33 % (16574)Instruction limit reached!
% 1.61/1.33 % (16574)------------------------------
% 1.61/1.33 % (16574)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.33 % (16574)Termination reason: Unknown
% 1.61/1.33 % (16574)Termination phase: Saturation
% 1.61/1.33
% 1.61/1.33 % (16574)Memory used [KB]: 5500
% 1.61/1.33 % (16574)Time elapsed: 0.002 s
% 1.61/1.33 % (16574)Instructions burned: 3 (million)
% 1.61/1.33 % (16574)------------------------------
% 1.61/1.33 % (16574)------------------------------
% 1.61/1.33 % (16575)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_16344 for (2999ds/3Mi)
% 1.61/1.33 % (16569)Instruction limit reached!
% 1.61/1.33 % (16569)------------------------------
% 1.61/1.33 % (16569)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.33 % (16569)Termination reason: Unknown
% 1.61/1.33 % (16569)Termination phase: Saturation
% 1.61/1.33
% 1.61/1.33 % (16569)Memory used [KB]: 5628
% 1.61/1.33 % (16569)Time elapsed: 0.012 s
% 1.61/1.33 % (16569)Instructions burned: 16 (million)
% 1.61/1.33 % (16569)------------------------------
% 1.61/1.33 % (16569)------------------------------
% 1.61/1.33 % (16575)Instruction limit reached!
% 1.61/1.33 % (16575)------------------------------
% 1.61/1.33 % (16575)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.33 % (16575)Termination reason: Unknown
% 1.61/1.33 % (16575)Termination phase: Saturation
% 1.61/1.33
% 1.61/1.33 % (16575)Memory used [KB]: 1023
% 1.61/1.33 % (16575)Time elapsed: 0.003 s
% 1.61/1.33 % (16575)Instructions burned: 4 (million)
% 1.61/1.33 % (16575)------------------------------
% 1.61/1.33 % (16575)------------------------------
% 1.61/1.33 % (16573)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_16344 for (2999ds/16Mi)
% 1.61/1.34 % (16577)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_16344 for (2999ds/3Mi)
% 1.61/1.34 % (16577)Instruction limit reached!
% 1.61/1.34 % (16577)------------------------------
% 1.61/1.34 % (16577)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.34 % (16577)Termination reason: Unknown
% 1.61/1.34 % (16577)Termination phase: Saturation
% 1.61/1.34
% 1.61/1.34 % (16577)Memory used [KB]: 5500
% 1.61/1.34 % (16577)Time elapsed: 0.002 s
% 1.61/1.34 % (16577)Instructions burned: 4 (million)
% 1.61/1.34 % (16577)------------------------------
% 1.61/1.34 % (16577)------------------------------
% 1.61/1.34 % (16576)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_16344 for (2999ds/7Mi)
% 1.61/1.34 % (16579)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_16344 for (2999ds/18Mi)
% 1.61/1.34 % (16573)Instruction limit reached!
% 1.61/1.34 % (16573)------------------------------
% 1.61/1.34 % (16573)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.34 % (16573)Termination reason: Unknown
% 1.61/1.34 % (16573)Termination phase: Saturation
% 1.61/1.34
% 1.61/1.34 % (16573)Memory used [KB]: 5884
% 1.61/1.34 % (16573)Time elapsed: 0.013 s
% 1.61/1.34 % (16573)Instructions burned: 16 (million)
% 1.61/1.34 % (16573)------------------------------
% 1.61/1.34 % (16573)------------------------------
% 1.61/1.34 % (16576)Instruction limit reached!
% 1.61/1.34 % (16576)------------------------------
% 1.61/1.34 % (16576)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.34 % (16576)Termination reason: Unknown
% 1.61/1.34 % (16576)Termination phase: Saturation
% 1.61/1.34
% 1.61/1.34 % (16576)Memory used [KB]: 5500
% 1.61/1.34 % (16576)Time elapsed: 0.006 s
% 1.61/1.34 % (16576)Instructions burned: 8 (million)
% 1.61/1.34 % (16576)------------------------------
% 1.61/1.34 % (16576)------------------------------
% 1.61/1.35 % (16578)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_16344 for (2999ds/4Mi)
% 1.61/1.35 % (16580)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_16344 for (2999ds/710Mi)
% 1.61/1.35 % (16579)Instruction limit reached!
% 1.61/1.35 % (16579)------------------------------
% 1.61/1.35 % (16579)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.35 % (16579)Termination reason: Unknown
% 1.61/1.35 % (16579)Termination phase: Saturation
% 1.61/1.35
% 1.61/1.35 % (16579)Memory used [KB]: 5628
% 1.61/1.35 % (16579)Time elapsed: 0.009 s
% 1.61/1.35 % (16579)Instructions burned: 19 (million)
% 1.61/1.35 % (16579)------------------------------
% 1.61/1.35 % (16579)------------------------------
% 1.61/1.35 % (16560)First to succeed.
% 1.61/1.35 % (16578)Instruction limit reached!
% 1.61/1.35 % (16578)------------------------------
% 1.61/1.35 % (16578)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.35 % (16578)Termination reason: Unknown
% 1.61/1.35 % (16578)Termination phase: Saturation
% 1.61/1.35
% 1.61/1.35 % (16578)Memory used [KB]: 5500
% 1.61/1.35 % (16578)Time elapsed: 0.004 s
% 1.61/1.35 % (16578)Instructions burned: 4 (million)
% 1.61/1.35 % (16578)------------------------------
% 1.61/1.35 % (16578)------------------------------
% 1.61/1.35 % (16560)Refutation found. Thanks to Tanya!
% 1.61/1.35 % SZS status Theorem for DTF2THF_16344
% 1.61/1.35 % SZS output start Proof for DTF2THF_16344
% 1.61/1.35 thf(func_def_1, type, cS: $i > $i).
% 1.61/1.35 thf(func_def_2, type, cEVEN1: $i > $o).
% 1.61/1.35 thf(func_def_4, type, cODD1: $i > $o).
% 1.61/1.35 thf(func_def_18, type, sK1: ($i > $o) > $i).
% 1.61/1.35 thf(func_def_19, type, sK2: ($i > $o) > $i).
% 1.61/1.35 thf(func_def_20, type, ph3: !>[X0: $tType]:(X0)).
% 1.61/1.35 thf(func_def_21, type, sK4: $i > $i).
% 1.61/1.35 thf(f862,plain,(
% 1.61/1.35 $false),
% 1.61/1.35 inference(equality_resolution,[status(thm)],[f861])).
% 1.61/1.35 thf(f861,plain,(
% 1.61/1.35 ( ! [X0 : $i] : ((c0 != X0)) )),
% 1.61/1.35 inference(subsumption_resolution,[status(thm)],[f860,f53])).
% 1.61/1.35 thf(f53,plain,(
% 1.61/1.35 ( ! [X1 : $i] : ((c0 != (cS @ X1))) )),
% 1.61/1.35 inference(equality_proxy_clausification,[status(thm)],[f52])).
% 1.61/1.35 thf(f52,plain,(
% 1.61/1.35 ( ! [X1 : $i] : (((c0 = (cS @ X1)) = $false)) )),
% 1.61/1.35 inference(not_proxy_clausification,[status(thm)],[f51])).
% 1.61/1.35 thf(f51,plain,(
% 1.61/1.35 ( ! [X1 : $i] : (((~ (c0 = (cS @ X1))) = $true)) )),
% 1.61/1.35 inference(beta_eta_normalization,[status(thm)],[f50])).
% 1.61/1.35 thf(f50,plain,(
% 1.61/1.35 ( ! [X1 : $i] : ((((^[Y0 : $i]: (~ (c0 = (cS @ Y0)))) @ X1) = $true)) )),
% 1.61/1.35 inference(pi_clausification,[status(thm)],[f30])).
% 1.61/1.35 thf(f30,plain,(
% 1.61/1.35 ((!! @ $i @ (^[Y0 : $i]: (~ (c0 = (cS @ Y0))))) = $true)),
% 1.61/1.35 inference(binary_proxy_clausification,[status(thm)],[f29])).
% 1.61/1.35 thf(f29,plain,(
% 1.61/1.35 ($true = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((cS @ Y0) = (cS @ Y1)) => (Y1 = Y0)))))) & (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1))))) & (Y0 @ c0)) => (!! @ $i @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: (~ (c0 = (cS @ Y0)))))))),
% 1.61/1.35 inference(beta_eta_normalization,[status(thm)],[f27])).
% 1.61/1.35 thf(f27,plain,(
% 1.61/1.35 ($true = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((cS @ Y0) = (cS @ Y1)) => (Y1 = Y0)))))) & (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1))))) & (Y0 @ c0)) => (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))) & (!! @ $i @ (^[Y0 : $i]: (~ (c0 = (cS @ Y0)))))))),
% 1.61/1.35 inference(definition_unfolding,[status(thm)],[f21,f26])).
% 1.61/1.35 thf(f26,plain,(
% 1.61/1.35 (cPEANO1 = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((cS @ Y0) = (cS @ Y1)) => (Y1 = Y0)))))) & (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1))))) & (Y0 @ c0)) => (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))) & (!! @ $i @ (^[Y0 : $i]: (~ (c0 = (cS @ Y0)))))))),
% 1.61/1.35 inference(definition_unfolding,[status(thm)],[f19,f23])).
% 1.61/1.35 thf(f23,plain,(
% 1.61/1.35 (cIND = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1))))) & (Y0 @ c0)) => (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))))),
% 1.61/1.35 inference(cnf_transformation,[status(thm)],[f13])).
% 1.61/1.35 thf(f13,plain,(
% 1.61/1.35 (cIND = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1))))) & (Y0 @ c0)) => (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))))),
% 1.61/1.35 inference(fool_elimination,[status(thm)],[f12])).
% 1.61/1.35 thf(f12,plain,(
% 1.61/1.35 (cIND = ! [X0 : $i > $o] : (((X0 @ c0) & ! [X1 : $i] : ((X0 @ X1) => (X0 @ (cS @ X1)))) => ! [X2 : $i] : (X0 @ X2)))),
% 1.61/1.35 inference(rectify,[status(thm)],[f2])).
% 1.61/1.35 thf(f2,axiom,(
% 1.61/1.35 (cIND = ! [X1 : $i > $o] : (((X1 @ c0) & ! [X2 : $i] : ((X1 @ X2) => (X1 @ (cS @ X2)))) => ! [X2 : $i] : (X1 @ X2)))),
% 1.61/1.35 file('/export/starexec/sandbox2/tmp/tmp.L9cmIiQdkO/DTF2THF_16344.p',cIND_def)).
% 1.61/1.35 thf(f19,plain,(
% 1.61/1.35 (cPEANO1 = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((cS @ Y0) = (cS @ Y1)) => (Y1 = Y0)))))) & cIND) & (!! @ $i @ (^[Y0 : $i]: (~ (c0 = (cS @ Y0)))))))),
% 1.61/1.35 inference(cnf_transformation,[status(thm)],[f17])).
% 1.61/1.35 thf(f17,plain,(
% 1.61/1.35 (cPEANO1 = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((cS @ Y0) = (cS @ Y1)) => (Y1 = Y0)))))) & cIND) & (!! @ $i @ (^[Y0 : $i]: (~ (c0 = (cS @ Y0)))))))),
% 1.61/1.35 inference(fool_elimination,[status(thm)],[f16])).
% 1.61/1.35 thf(f16,plain,(
% 1.61/1.35 (cPEANO1 = ! [X0 : $i] : (c0 != (cS @ X0)) & cIND & ! [X1 : $i,X2 : $i] : (((cS @ X2) = (cS @ X1)) => (X1 = X2)))),
% 1.61/1.35 inference(rectify,[status(thm)],[f4])).
% 1.61/1.35 thf(f4,axiom,(
% 1.61/1.35 (cPEANO1 = ! [X3 : $i] : (c0 != (cS @ X3)) & cIND & ! [X5 : $i,X4 : $i] : (((cS @ X4) = (cS @ X5)) => (X4 = X5)))),
% 1.61/1.35 file('/export/starexec/sandbox2/tmp/tmp.L9cmIiQdkO/DTF2THF_16344.p',cPEANO1_def)).
% 1.61/1.35 thf(f21,plain,(
% 1.61/1.35 (cPEANO1 = $true)),
% 1.61/1.35 inference(cnf_transformation,[status(thm)],[f18])).
% 1.61/1.35 thf(f18,plain,(
% 1.61/1.35 (cPEANO1 = $true) & ! [X0 : $i] : ((cODD1 @ X0) != $true)),
% 1.61/1.35 inference(ennf_transformation,[status(thm)],[f9])).
% 1.61/1.35 thf(f9,plain,(
% 1.61/1.35 ~((cPEANO1 = $true) => ? [X0 : $i] : ((cODD1 @ X0) = $true))),
% 1.61/1.35 inference(fool_elimination,[status(thm)],[f8])).
% 1.61/1.35 thf(f8,plain,(
% 1.61/1.35 ~(cPEANO1 => ? [X0 : $i] : (cODD1 @ X0))),
% 1.61/1.35 inference(rectify,[status(thm)],[f6])).
% 1.61/1.35 thf(f6,negated_conjecture,(
% 1.61/1.35 ~(cPEANO1 => ? [X0 : $i] : (cODD1 @ X0))),
% 1.61/1.35 inference(negated_conjecture,[status(cth)],[f5])).
% 1.61/1.35 thf(f5,conjecture,(
% 1.61/1.35 cPEANO1 => ? [X0 : $i] : (cODD1 @ X0)),
% 1.61/1.35 file('/export/starexec/sandbox2/tmp/tmp.L9cmIiQdkO/DTF2THF_16344.p',cTHM404)).
% 1.61/1.35 thf(f860,plain,(
% 1.61/1.35 ( ! [X0 : $i] : ((c0 = (cS @ X0)) | (c0 != X0)) )),
% 1.61/1.35 inference(equality_resolution,[status(thm)],[f845])).
% 1.61/1.35 thf(f845,plain,(
% 1.61/1.35 ( ! [X0 : $i,X1 : $i] : (((cS @ X1) != X0) | (c0 = X0) | (c0 != X1)) )),
% 1.61/1.35 inference(superposition,[status(thm)],[f53,f562])).
% 1.61/1.35 thf(f562,plain,(
% 1.61/1.35 ( ! [X0 : $i,X1 : $i] : (((cS @ (sK2 @ (^[Y0 : $i]: (~ (X0 = Y0))))) = X1) | ((cS @ X1) != X0) | (c0 = X0)) )),
% 1.61/1.35 inference(superposition,[status(thm)],[f40,f303])).
% 1.61/1.35 thf(f303,plain,(
% 1.61/1.35 ( ! [X0 : $i] : (((cS @ (cS @ (sK2 @ (^[Y0 : $i]: (~ (X0 = Y0)))))) = X0) | (c0 = X0)) )),
% 1.61/1.35 inference(equality_proxy_clausification,[status(thm)],[f302])).
% 1.61/1.35 thf(f302,plain,(
% 1.61/1.35 ( ! [X0 : $i] : (($true = (X0 = c0)) | ((cS @ (cS @ (sK2 @ (^[Y0 : $i]: (~ (X0 = Y0)))))) = X0)) )),
% 1.61/1.35 inference(not_proxy_clausification,[status(thm)],[f301])).
% 1.61/1.35 thf(f301,plain,(
% 1.61/1.35 ( ! [X0 : $i] : (((~ (X0 = c0)) = $false) | ((cS @ (cS @ (sK2 @ (^[Y0 : $i]: (~ (X0 = Y0)))))) = X0)) )),
% 1.61/1.35 inference(beta_eta_normalization,[status(thm)],[f255])).
% 1.61/1.35 thf(f255,plain,(
% 1.61/1.35 ( ! [X0 : $i] : ((((^[Y0 : $i]: (~ (X0 = Y0))) @ c0) = $false) | ((cS @ (cS @ (sK2 @ (^[Y0 : $i]: (~ (X0 = Y0)))))) = X0)) )),
% 1.61/1.35 inference(leibniz_equality_elimination,[status(thm)],[f62])).
% 1.61/1.35 thf(f62,plain,(
% 1.61/1.35 ( ! [X0 : $i,X1 : $i > $o] : (($false = (X1 @ (cS @ (cS @ (sK2 @ X1))))) | ((X1 @ c0) = $false) | ((X1 @ X0) = $true)) )),
% 1.61/1.35 inference(binary_proxy_clausification,[status(thm)],[f61])).
% 1.61/1.35 thf(f61,plain,(
% 1.61/1.35 ( ! [X0 : $i,X1 : $i > $o] : ((((X1 @ (sK2 @ X1)) => (X1 @ (cS @ (cS @ (sK2 @ X1))))) = $false) | ((X1 @ X0) = $true) | ((X1 @ c0) = $false)) )),
% 1.61/1.35 inference(beta_eta_normalization,[status(thm)],[f60])).
% 1.61/1.35 thf(f60,plain,(
% 1.61/1.35 ( ! [X0 : $i,X1 : $i > $o] : (((X1 @ X0) = $true) | ((X1 @ c0) = $false) | (((^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (cS @ (cS @ Y0))))) @ (sK2 @ X1)) = $false)) )),
% 1.61/1.35 inference(sigma_clausification,[status(thm)],[f59])).
% 1.61/1.35 thf(f59,plain,(
% 1.61/1.35 ( ! [X0 : $i,X1 : $i > $o] : (((X1 @ X0) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (cS @ (cS @ Y0)))))) = $false) | ((X1 @ c0) = $false)) )),
% 1.61/1.35 inference(binary_proxy_clausification,[status(thm)],[f58])).
% 1.61/1.35 thf(f58,plain,(
% 1.61/1.35 ( ! [X0 : $i,X1 : $i > $o] : ((((X1 @ c0) & (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (cS @ (cS @ Y0))))))) = $false) | ((X1 @ X0) = $true)) )),
% 1.61/1.35 inference(binary_proxy_clausification,[status(thm)],[f57])).
% 1.61/1.35 thf(f57,plain,(
% 1.61/1.35 ( ! [X0 : $i,X1 : $i > $o] : (((((X1 @ c0) & (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (cS @ (cS @ Y0))))))) => (X1 @ X0)) = $true)) )),
% 1.61/1.35 inference(beta_eta_normalization,[status(thm)],[f56])).
% 1.61/1.35 thf(f56,plain,(
% 1.61/1.35 ( ! [X0 : $i,X1 : $i > $o] : (($true = ((^[Y0 : $i > $o]: (((Y0 @ c0) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ (cS @ Y1))))))) => (Y0 @ X0))) @ X1))) )),
% 1.61/1.35 inference(pi_clausification,[status(thm)],[f55])).
% 1.61/1.35 thf(f55,plain,(
% 1.61/1.35 ( ! [X0 : $i] : (($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((Y0 @ c0) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ (cS @ Y1))))))) => (Y0 @ X0)))))) )),
% 1.61/1.35 inference(not_proxy_clausification,[status(thm)],[f54])).
% 1.61/1.35 thf(f54,plain,(
% 1.61/1.35 ( ! [X0 : $i] : (((~ (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((Y0 @ c0) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ (cS @ Y1))))))) => (Y0 @ X0))))) != $true)) )),
% 1.61/1.35 inference(beta_eta_normalization,[status(thm)],[f28])).
% 1.61/1.35 thf(f28,plain,(
% 1.61/1.35 ( ! [X0 : $i] : ((((^[Y0 : $i]: (~ ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (((Y2 @ c0) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y2 @ (cS @ (cS @ Y3))))))) => (Y2 @ Y1))))) @ Y0))) @ X0) != $true)) )),
% 1.61/1.35 inference(definition_unfolding,[status(thm)],[f20,f25])).
% 1.61/1.35 thf(f25,plain,(
% 1.61/1.35 (cODD1 = (^[Y0 : $i]: (~ ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (((Y2 @ c0) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y2 @ (cS @ (cS @ Y3))))))) => (Y2 @ Y1))))) @ Y0))))),
% 1.61/1.35 inference(definition_unfolding,[status(thm)],[f24,f22])).
% 1.61/1.35 thf(f22,plain,(
% 1.61/1.35 (cEVEN1 = (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (((Y1 @ c0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y1 @ (cS @ (cS @ Y2))))))) => (Y1 @ Y0))))))),
% 1.61/1.35 inference(cnf_transformation,[status(thm)],[f11])).
% 1.61/1.35 thf(f11,plain,(
% 1.61/1.35 (cEVEN1 = (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (((Y1 @ c0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y1 @ (cS @ (cS @ Y2))))))) => (Y1 @ Y0))))))),
% 1.61/1.35 inference(fool_elimination,[status(thm)],[f10])).
% 1.61/1.35 thf(f10,plain,(
% 1.61/1.35 ((^[X0 : $i] : (! [X1 : $i > $o] : ((! [X2 : $i] : ((X1 @ X2) => (X1 @ (cS @ (cS @ X2)))) & (X1 @ c0)) => (X1 @ X0)))) = cEVEN1)),
% 1.61/1.35 inference(rectify,[status(thm)],[f1])).
% 1.61/1.35 thf(f1,axiom,(
% 1.61/1.35 ((^[X0 : $i] : (! [X1 : $i > $o] : ((! [X2 : $i] : ((X1 @ X2) => (X1 @ (cS @ (cS @ X2)))) & (X1 @ c0)) => (X1 @ X0)))) = cEVEN1)),
% 1.61/1.35 file('/export/starexec/sandbox2/tmp/tmp.L9cmIiQdkO/DTF2THF_16344.p',cEVEN1_def)).
% 1.61/1.35 thf(f24,plain,(
% 1.61/1.35 (cODD1 = (^[Y0 : $i]: (~ (cEVEN1 @ Y0))))),
% 1.61/1.35 inference(cnf_transformation,[status(thm)],[f15])).
% 1.61/1.35 thf(f15,plain,(
% 1.61/1.35 (cODD1 = (^[Y0 : $i]: (~ (cEVEN1 @ Y0))))),
% 1.61/1.35 inference(fool_elimination,[status(thm)],[f14])).
% 1.61/1.35 thf(f14,plain,(
% 1.61/1.35 (cODD1 = (^[X0 : $i] : (~(cEVEN1 @ X0))))),
% 1.61/1.35 inference(rectify,[status(thm)],[f3])).
% 1.61/1.35 thf(f3,axiom,(
% 1.61/1.35 (cODD1 = (^[X0 : $i] : (~(cEVEN1 @ X0))))),
% 1.61/1.35 file('/export/starexec/sandbox2/tmp/tmp.L9cmIiQdkO/DTF2THF_16344.p',cODD1_def)).
% 1.61/1.35 thf(f20,plain,(
% 1.61/1.35 ( ! [X0 : $i] : (((cODD1 @ X0) != $true)) )),
% 1.61/1.35 inference(cnf_transformation,[status(thm)],[f18])).
% 1.61/1.35 thf(f40,plain,(
% 1.61/1.35 ( ! [X2 : $i,X1 : $i] : (((cS @ X2) != (cS @ X1)) | (X1 = X2)) )),
% 1.61/1.35 inference(equality_proxy_clausification,[status(thm)],[f39])).
% 1.61/1.35 thf(f39,plain,(
% 1.61/1.35 ( ! [X2 : $i,X1 : $i] : ((X1 = X2) | (((cS @ X1) = (cS @ X2)) = $false)) )),
% 1.61/1.35 inference(equality_proxy_clausification,[status(thm)],[f38])).
% 1.61/1.35 thf(f38,plain,(
% 1.61/1.35 ( ! [X2 : $i,X1 : $i] : (((X2 = X1) = $true) | (((cS @ X1) = (cS @ X2)) = $false)) )),
% 1.61/1.35 inference(binary_proxy_clausification,[status(thm)],[f37])).
% 1.61/1.35 thf(f37,plain,(
% 1.61/1.35 ( ! [X2 : $i,X1 : $i] : (((((cS @ X1) = (cS @ X2)) => (X2 = X1)) = $true)) )),
% 1.61/1.35 inference(beta_eta_normalization,[status(thm)],[f36])).
% 1.61/1.35 thf(f36,plain,(
% 1.61/1.35 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (((cS @ X1) = (cS @ Y0)) => (Y0 = X1))) @ X2))) )),
% 1.61/1.35 inference(pi_clausification,[status(thm)],[f35])).
% 1.61/1.35 thf(f35,plain,(
% 1.61/1.35 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (((cS @ X1) = (cS @ Y0)) => (Y0 = X1)))))) )),
% 1.61/1.35 inference(beta_eta_normalization,[status(thm)],[f34])).
% 1.61/1.35 thf(f34,plain,(
% 1.61/1.35 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((cS @ Y0) = (cS @ Y1)) => (Y1 = Y0))))) @ X1) = $true)) )),
% 1.61/1.35 inference(pi_clausification,[status(thm)],[f33])).
% 1.61/1.35 thf(f33,plain,(
% 1.61/1.35 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((cS @ Y0) = (cS @ Y1)) => (Y1 = Y0)))))))),
% 1.61/1.35 inference(binary_proxy_clausification,[status(thm)],[f31])).
% 1.61/1.35 thf(f31,plain,(
% 1.61/1.35 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((cS @ Y0) = (cS @ Y1)) => (Y1 = Y0)))))) & (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1))))) & (Y0 @ c0)) => (!! @ $i @ Y0))))))),
% 1.61/1.35 inference(binary_proxy_clausification,[status(thm)],[f29])).
% 1.61/1.35 % SZS output end Proof for DTF2THF_16344
% 1.61/1.35 % (16560)------------------------------
% 1.61/1.35 % (16560)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.35 % (16560)Termination reason: Refutation
% 1.61/1.35
% 1.61/1.35 % (16560)Memory used [KB]: 5756
% 1.61/1.35 % (16560)Time elapsed: 0.050 s
% 1.61/1.35 % (16560)Instructions burned: 90 (million)
% 1.61/1.35 % (16560)------------------------------
% 1.61/1.35 % (16560)------------------------------
% 1.61/1.35 % (16559)Success in time 0.057 s
%------------------------------------------------------------------------------