%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM830^5 : TPTP v9.2.1. Bugfixed v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n010.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 09:24:52 AM UTC 2026
% Result : Theorem 1.38s 1.23s
% Output : Refutation 1.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 5
% Syntax : Number of formulae : 53 ( 47 unt; 0 typ; 0 def)
% Number of atoms : 187 ( 92 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 424 ( 10 ~; 0 |; 20 &; 368 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 8 usr; 8 con; 0-2 aty)
% ( 22 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 61 ( 28 ^; 33 !; 0 ?; 61 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
n: $tType ).
thf(func_def_0,type,
n: $tType ).
thf(func_def_1,type,
c0: n ).
thf(func_def_2,type,
cS: n > n ).
thf(func_def_3,type,
c_plus: n > n > n ).
thf(func_def_4,type,
c_star: n > n > n ).
thf(f660,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f659]) ).
thf(f659,plain,
( ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) )
!= ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ),
inference(superposition,[status(thm)],[f658,f41]) ).
thf(f41,plain,
! [X1: n] :
( ( c_plus @ X1 @ c0 )
= X1 ),
inference(equality_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
! [X1: n] :
( $true
= ( ( c_plus @ X1 @ c0 )
= X1 ) ),
inference(beta_eta_normalization,[status(thm)],[f39]) ).
thf(f39,plain,
! [X1: n] :
( $true
= ( ^ [Y0: n] :
( ( c_plus @ Y0 @ c0 )
= Y0 )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( $true
= ( !! @ n
@ ^ [Y0: n] :
( ( c_plus @ Y0 @ c0 )
= Y0 ) ) ),
inference(definition_unfolding,[status(thm)],[f20,f16]) ).
thf(f16,plain,
( cPA_1
= ( !! @ n
@ ^ [Y0: n] :
( ( c_plus @ Y0 @ c0 )
= Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( cPA_1
= ( !! @ n
@ ^ [Y0: n] :
( ( c_plus @ Y0 @ c0 )
= Y0 ) ) ),
inference(fool_elimination,[status(thm)],[f1]) ).
thf(f1,axiom,
( cPA_1
= ( ! [X0: n] :
( ( c_plus @ X0 @ c0 )
= X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.e2rdlGzodo/DTF2THF_5538.p',cPA_1_def) ).
thf(f20,plain,
cPA_1 = $true,
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( cPA_2 = $true )
& ( cPA_1 = $true )
& ( cPA_3 = $true )
& ( cPA_4 = $true )
& ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
!= ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ) ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
!= ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) )
& ( cPA_1 = $true )
& ( cPA_4 = $true )
& ( cPA_3 = $true )
& ( cPA_2 = $true ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
~ ( ( ( cPA_1 = $true )
& ( cPA_4 = $true )
& ( cPA_3 = $true )
& ( cPA_2 = $true ) )
=> ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
= ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( ( cPA_2
& cPA_1
& cPA_3
& cPA_4 )
=> ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
= ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( ( cPA_2
& cPA_1
& cPA_3
& cPA_4 )
=> ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
= ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
( ( cPA_2
& cPA_1
& cPA_3
& cPA_4 )
=> ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
= ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.e2rdlGzodo/DTF2THF_5538.p',cPA_THM1) ).
thf(f658,plain,
( ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) )
!= ( cS @ ( cS @ ( c_plus @ ( cS @ ( cS @ c0 ) ) @ c0 ) ) ) ),
inference(superposition,[status(thm)],[f657,f33]) ).
thf(f33,plain,
! [X2: n,X1: n] :
( ( c_plus @ X2 @ ( cS @ X1 ) )
= ( cS @ ( c_plus @ X2 @ X1 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
! [X2: n,X1: n] :
( ( ( c_plus @ X2 @ ( cS @ X1 ) )
= ( cS @ ( c_plus @ X2 @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f31]) ).
thf(f31,plain,
! [X2: n,X1: n] :
( ( ^ [Y0: n] :
( ( c_plus @ Y0 @ ( cS @ X1 ) )
= ( cS @ ( c_plus @ Y0 @ X1 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
! [X1: n] :
( ( !! @ n
@ ^ [Y0: n] :
( ( c_plus @ Y0 @ ( cS @ X1 ) )
= ( cS @ ( c_plus @ Y0 @ X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f29]) ).
thf(f29,plain,
! [X1: n] :
( $true
= ( ^ [Y0: n] :
( !! @ n
@ ^ [Y1: n] :
( ( c_plus @ Y1 @ ( cS @ Y0 ) )
= ( cS @ ( c_plus @ Y1 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
( ( !! @ n
@ ^ [Y0: n] :
( !! @ n
@ ^ [Y1: n] :
( ( c_plus @ Y1 @ ( cS @ Y0 ) )
= ( cS @ ( c_plus @ Y1 @ Y0 ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f24,f21]) ).
thf(f21,plain,
cPA_2 = $true,
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f24,plain,
( cPA_2
= ( !! @ n
@ ^ [Y0: n] :
( !! @ n
@ ^ [Y1: n] :
( ( c_plus @ Y1 @ ( cS @ Y0 ) )
= ( cS @ ( c_plus @ Y1 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( cPA_2
= ( !! @ n
@ ^ [Y0: n] :
( !! @ n
@ ^ [Y1: n] :
( ( c_plus @ Y1 @ ( cS @ Y0 ) )
= ( cS @ ( c_plus @ Y1 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: n,X1: n] :
( ( ( c_plus @ X0 @ ( cS @ X1 ) )
= ( cS @ ( c_plus @ X0 @ X1 ) ) )
= cPA_2 ),
file('/export/starexec/sandbox/tmp/tmp.e2rdlGzodo/DTF2THF_5538.p',cPA_2_def) ).
thf(f657,plain,
( ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) )
!= ( cS @ ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ c0 ) ) ) ),
inference(superposition,[status(thm)],[f656,f33]) ).
thf(f656,plain,
( ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
!= ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ),
inference(superposition,[status(thm)],[f17,f654]) ).
thf(f654,plain,
( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
= ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ),
inference(superposition,[status(thm)],[f193,f648]) ).
thf(f648,plain,
( ( cS @ ( cS @ c0 ) )
= ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ c0 ) ) ),
inference(superposition,[status(thm)],[f193,f44]) ).
thf(f44,plain,
! [X1: n] :
( c0
= ( c_star @ X1 @ c0 ) ),
inference(equality_proxy_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
! [X1: n] :
( $true
= ( c0
= ( c_star @ X1 @ c0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f42]) ).
thf(f42,plain,
! [X1: n] :
( $true
= ( ^ [Y0: n] :
( c0
= ( c_star @ Y0 @ c0 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
( ( !! @ n
@ ^ [Y0: n] :
( c0
= ( c_star @ Y0 @ c0 ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f23,f19]) ).
thf(f19,plain,
cPA_3 = $true,
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f23,plain,
( cPA_3
= ( !! @ n
@ ^ [Y0: n] :
( c0
= ( c_star @ Y0 @ c0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( cPA_3
= ( !! @ n
@ ^ [Y0: n] :
( c0
= ( c_star @ Y0 @ c0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: n] :
( ( c0
= ( c_star @ X0 @ c0 ) )
= cPA_3 ),
file('/export/starexec/sandbox/tmp/tmp.e2rdlGzodo/DTF2THF_5538.p',cPA_3_def) ).
thf(f193,plain,
! [X0: n] :
( ( cS @ ( cS @ ( c_star @ ( cS @ ( cS @ c0 ) ) @ X0 ) ) )
= ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ X0 ) ) ),
inference(superposition,[status(thm)],[f118,f41]) ).
thf(f118,plain,
! [X0: n,X1: n] :
( ( cS @ ( cS @ ( c_plus @ ( c_star @ ( cS @ ( cS @ X0 ) ) @ X1 ) @ X0 ) ) )
= ( c_star @ ( cS @ ( cS @ X0 ) ) @ ( cS @ X1 ) ) ),
inference(superposition,[status(thm)],[f49,f33]) ).
thf(f49,plain,
! [X0: n,X1: n] :
( ( cS @ ( c_plus @ ( c_star @ ( cS @ X0 ) @ X1 ) @ X0 ) )
= ( c_star @ ( cS @ X0 ) @ ( cS @ X1 ) ) ),
inference(superposition,[status(thm)],[f33,f38]) ).
thf(f38,plain,
! [X2: n,X1: n] :
( ( c_plus @ ( c_star @ X2 @ X1 ) @ X2 )
= ( c_star @ X2 @ ( cS @ X1 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
! [X2: n,X1: n] :
( $true
= ( ( c_star @ X2 @ ( cS @ X1 ) )
= ( c_plus @ ( c_star @ X2 @ X1 ) @ X2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f36]) ).
thf(f36,plain,
! [X2: n,X1: n] :
( ( ^ [Y0: n] :
( ( c_star @ Y0 @ ( cS @ X1 ) )
= ( c_plus @ ( c_star @ Y0 @ X1 ) @ Y0 ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
! [X1: n] :
( ( !! @ n
@ ^ [Y0: n] :
( ( c_star @ Y0 @ ( cS @ X1 ) )
= ( c_plus @ ( c_star @ Y0 @ X1 ) @ Y0 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f34]) ).
thf(f34,plain,
! [X1: n] :
( ( ^ [Y0: n] :
( !! @ n
@ ^ [Y1: n] :
( ( c_star @ Y1 @ ( cS @ Y0 ) )
= ( c_plus @ ( c_star @ Y1 @ Y0 ) @ Y1 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
( ( !! @ n
@ ^ [Y0: n] :
( !! @ n
@ ^ [Y1: n] :
( ( c_star @ Y1 @ ( cS @ Y0 ) )
= ( c_plus @ ( c_star @ Y1 @ Y0 ) @ Y1 ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f22,f18]) ).
thf(f18,plain,
cPA_4 = $true,
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f22,plain,
( cPA_4
= ( !! @ n
@ ^ [Y0: n] :
( !! @ n
@ ^ [Y1: n] :
( ( c_star @ Y1 @ ( cS @ Y0 ) )
= ( c_plus @ ( c_star @ Y1 @ Y0 ) @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( cPA_4
= ( !! @ n
@ ^ [Y0: n] :
( !! @ n
@ ^ [Y1: n] :
( ( c_star @ Y1 @ ( cS @ Y0 ) )
= ( c_plus @ ( c_star @ Y1 @ Y0 ) @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X0: n,X1: n] :
( ( ( c_star @ X0 @ ( cS @ X1 ) )
= ( c_plus @ ( c_star @ X0 @ X1 ) @ X0 ) )
= cPA_4 ),
file('/export/starexec/sandbox/tmp/tmp.e2rdlGzodo/DTF2THF_5538.p',cPA_4_def) ).
thf(f17,plain,
( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
!= ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : NUM830^5 : TPTP v9.2.1. Bugfixed v5.3.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.32 % Computer : n010.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue Feb 24 11:14:48 EST 2026
% 0.12/0.32 % CPUTime :
% 0.12/0.32 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.42 ---- Original DTF file ---
% 0.16/0.42 thf(spec,logic,$$dhol).
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 % File : NUM830^5 : TPTP v9.2.1. Bugfixed v5.3.0.
% 0.16/0.42 % Domain : Number Theory (Induction on naturals)
% 0.16/0.42 % Problem : TPS problem from PA-THMS
% 0.16/0.42 % Version : Especial.
% 0.16/0.42 % English :
% 0.16/0.42
% 0.16/0.42 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.42 % Source : [Bro09]
% 0.16/0.42 % Names : tps_0798 [Bro09]
% 0.16/0.42
% 0.16/0.42 % Status : Theorem
% 0.16/0.42 % Rating : 0.00 v9.0.0, 0.10 v8.2.0, 0.15 v8.1.0, 0.09 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.14 v6.1.0, 0.29 v5.5.0, 0.17 v5.4.0, 0.40 v5.3.0
% 0.16/0.42 % Syntax : Number of formulae : 14 ( 4 unt; 9 typ; 4 def)
% 0.16/0.42 % Number of atoms : 17 ( 9 equ; 0 cnn)
% 0.16/0.42 % Maximal formula atoms : 5 ( 3 avg)
% 0.16/0.42 % Number of connectives : 33 ( 0 ~; 0 |; 3 &; 29 @)
% 0.16/0.42 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.16/0.42 % Maximal formula depth : 5 ( 2 avg)
% 0.16/0.42 % Number of types : 2 ( 1 usr)
% 0.16/0.42 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.16/0.42 % Number of symbols : 9 ( 8 usr; 5 con; 0-2 aty)
% 0.16/0.42 % Number of variables : 6 ( 0 ^; 6 !; 0 ?; 6 :)
% 0.16/0.42 % SPC : TH0_THM_EQU_NAR
% 0.16/0.42
% 0.16/0.42 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.16/0.42 % project in the Department of Mathematical Sciences at Carnegie
% 0.16/0.42 % Mellon University. Distributed under the Creative Commons copyleft
% 0.16/0.42 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.16/0.42 % :
% 0.16/0.42 % Bugfixes : v5.2.0 - Added missing type declarations.
% 0.16/0.42 % : v5.3.0 - Fixed tType to $tType from last bugfixes.
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 thf(n_type,type,
% 0.16/0.42 n: $tType ).
% 0.16/0.42
% 0.16/0.42 thf(c0_type,type,
% 0.16/0.42 c0: n ).
% 0.16/0.42
% 0.16/0.42 thf(cS_type,type,
% 0.16/0.42 cS: n > n ).
% 0.16/0.42
% 0.16/0.42 thf(c_plus_type,type,
% 0.16/0.42 c_plus: n > n > n ).
% 0.16/0.42
% 0.16/0.42 thf(c_star_type,type,
% 0.16/0.42 c_star: n > n > n ).
% 0.16/0.42
% 0.16/0.42 thf(cPA_1_type,type,
% 0.16/0.42 cPA_1: $o ).
% 0.16/0.42
% 0.16/0.42 thf(cPA_2_type,type,
% 0.16/0.42 cPA_2: $o ).
% 0.16/0.42
% 0.16/0.42 thf(cPA_3_type,type,
% 0.16/0.42 cPA_3: $o ).
% 0.16/0.42
% 0.16/0.42 thf(cPA_4_type,type,
% 0.16/0.42 cPA_4: $o ).
% 0.16/0.42
% 0.16/0.42 thf(cPA_1_def,definition,
% 0.16/0.42 ( cPA_1
% 0.16/0.42 = ( ! [Xx: n] :
% 0.16/0.42 ( ( c_plus @ Xx @ c0 )
% 0.16/0.42 = Xx ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(cPA_2_def,definition,
% 0.16/0.42 ( cPA_2
% 0.16/0.42 = ( ! [Xx: n,Xy: n] :
% 0.16/0.42 ( ( c_plus @ Xx @ ( cS @ Xy ) )
% 0.16/0.42 = ( cS @ ( c_plus @ Xx @ Xy ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(cPA_3_def,definition,
% 0.16/0.42 ( cPA_3
% 0.16/0.42 = ( ! [Xx: n] :
% 0.16/0.42 ( ( c_star @ Xx @ c0 )
% 0.16/0.42 = c0 ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(cPA_4_def,definition,
% 0.16/0.42 ( cPA_4
% 0.16/0.42 = ( ! [Xx: n,Xy: n] :
% 0.16/0.42 ( ( c_star @ Xx @ ( cS @ Xy ) )
% 0.16/0.42 = ( c_plus @ ( c_star @ Xx @ Xy ) @ Xx ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(cPA_THM1,conjecture,
% 0.16/0.42 ( ( cPA_1
% 0.16/0.42 & cPA_2
% 0.16/0.42 & cPA_3
% 0.16/0.42 & cPA_4 )
% 0.16/0.42 => ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
% 0.16/0.42 = ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 ------------------------
% 1.30/1.15 ---- Embedded in THF ---
% 1.30/1.15 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.30/1.15 %%% Generated on Tue Feb 24 11:14:48 EST 2026
% 1.30/1.15 %%% using '$$dhol' embedding, version 1.3.0.
% 1.30/1.15 %%% Logic specification used:
% 1.30/1.15 %%% thf(spec, logic, $$dhol).
% 1.30/1.15
% 1.30/1.15 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.e2rdlGzodo/DTF2DTF5538.p
% See solution above
% 1.30/1.15 ------------------------
% 1.30/1.16 ---- Cleaned THF ---
% 1.30/1.16 thf(n_type,type,
% 1.30/1.16 n: $tType ).
% 1.30/1.16
% 1.30/1.16 thf(c0_type,type,
% 1.30/1.16 c0: n ).
% 1.30/1.16
% 1.30/1.16 thf(cS_type,type,
% 1.30/1.16 cS: n > n ).
% 1.30/1.16
% 1.30/1.16 thf(c_plus_type,type,
% 1.30/1.16 c_plus: n > n > n ).
% 1.30/1.16
% 1.30/1.16 thf(c_star_type,type,
% 1.30/1.16 c_star: n > n > n ).
% 1.30/1.16
% 1.30/1.16 thf(cPA_1_type,type,
% 1.30/1.16 cPA_1: $o ).
% 1.30/1.16
% 1.30/1.16 thf(cPA_2_type,type,
% 1.30/1.16 cPA_2: $o ).
% 1.30/1.16
% 1.30/1.16 thf(cPA_3_type,type,
% 1.30/1.16 cPA_3: $o ).
% 1.30/1.16
% 1.30/1.16 thf(cPA_4_type,type,
% 1.30/1.16 cPA_4: $o ).
% 1.30/1.16
% 1.30/1.16 thf(cPA_1_def,definition,
% 1.30/1.16 ( cPA_1
% 1.30/1.16 = ( ! [Xx: n] :
% 1.30/1.16 ( ( c_plus @ Xx @ c0 )
% 1.30/1.16 = Xx ) ) ) ).
% 1.30/1.16
% 1.30/1.16 thf(cPA_2_def,definition,
% 1.30/1.16 ( cPA_2
% 1.30/1.16 = ( ! [Xx: n,Xy: n] :
% 1.30/1.16 ( ( c_plus @ Xx @ ( cS @ Xy ) )
% 1.30/1.16 = ( cS @ ( c_plus @ Xx @ Xy ) ) ) ) ) ).
% 1.30/1.16
% 1.30/1.16 thf(cPA_3_def,definition,
% 1.30/1.16 ( cPA_3
% 1.30/1.16 = ( ! [Xx: n] :
% 1.30/1.16 ( ( c_star @ Xx @ c0 )
% 1.30/1.16 = c0 ) ) ) ).
% 1.30/1.16
% 1.30/1.16 thf(cPA_4_def,definition,
% 1.30/1.16 ( cPA_4
% 1.30/1.16 = ( ! [Xx: n,Xy: n] :
% 1.30/1.16 ( ( c_star @ Xx @ ( cS @ Xy ) )
% 1.30/1.16 = ( c_plus @ ( c_star @ Xx @ Xy ) @ Xx ) ) ) ) ).
% 1.30/1.16
% 1.30/1.16 thf(cPA_THM1,conjecture,
% 1.30/1.16 ( ( cPA_1
% 1.30/1.16 & cPA_2
% 1.30/1.16 & cPA_3
% 1.30/1.16 & cPA_4 )
% 1.30/1.16 => ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
% 1.30/1.16 = ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ) ) ).
% 1.30/1.16 ------------------------
% 1.30/1.17 % (5636)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_5538 for (3000ds/183Mi)
% 1.30/1.18 % (5638)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_5538 for (3000ds/27Mi)
% 1.30/1.18 % (5637)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_5538 for (3000ds/4Mi)
% 1.30/1.18 % (5639)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_5538 for (3000ds/2Mi)
% 1.30/1.18 % (5640)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_5538 for (3000ds/2Mi)
% 1.30/1.18 % (5641)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_5538 for (3000ds/275Mi)
% 1.30/1.18 % (5642)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_5538 for (3000ds/18Mi)
% 1.30/1.18 % (5639)Instruction limit reached!
% 1.30/1.18 % (5639)------------------------------
% 1.30/1.18 % (5639)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.30/1.18 % (5639)Termination reason: Unknown
% 1.30/1.18 % (5640)Instruction limit reached!
% 1.30/1.18 % (5640)------------------------------
% 1.30/1.18 % (5640)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.30/1.18 % (5640)Termination reason: Unknown
% 1.30/1.18 % (5640)Termination phase: Saturation
% 1.30/1.18
% 1.30/1.18 % (5640)Memory used [KB]: 5500
% 1.30/1.18 % (5640)Time elapsed: 0.003 s
% 1.30/1.18 % (5640)Instructions burned: 3 (million)
% 1.30/1.18 % (5640)------------------------------
% 1.30/1.18 % (5640)------------------------------
% 1.30/1.18 % (5639)Termination phase: Saturation
% 1.30/1.18
% 1.30/1.18 % (5639)Memory used [KB]: 5500
% 1.30/1.18 % (5639)Time elapsed: 0.003 s
% 1.30/1.18 % (5639)Instructions burned: 3 (million)
% 1.30/1.18 % (5639)------------------------------
% 1.30/1.18 % (5639)------------------------------
% 1.30/1.18 % (5637)Instruction limit reached!
% 1.30/1.18 % (5637)------------------------------
% 1.30/1.18 % (5637)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.30/1.18 % (5637)Termination reason: Unknown
% 1.30/1.18 % (5637)Termination phase: Saturation
% 1.30/1.18
% 1.30/1.18 % (5637)Memory used [KB]: 5500
% 1.30/1.18 % (5637)Time elapsed: 0.004 s
% 1.30/1.18 % (5637)Instructions burned: 4 (million)
% 1.30/1.18 % (5637)------------------------------
% 1.30/1.18 % (5637)------------------------------
% 1.30/1.19 % (5642)Instruction limit reached!
% 1.30/1.19 % (5642)------------------------------
% 1.30/1.19 % (5642)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.30/1.19 % (5642)Termination reason: Unknown
% 1.30/1.19 % (5642)Termination phase: Saturation
% 1.30/1.19
% 1.30/1.19 % (5642)Memory used [KB]: 5500
% 1.30/1.19 % (5642)Time elapsed: 0.011 s
% 1.30/1.19 % (5642)Instructions burned: 18 (million)
% 1.30/1.19 % (5642)------------------------------
% 1.30/1.19 % (5642)------------------------------
% 1.30/1.19 % (5638)Instruction limit reached!
% 1.30/1.19 % (5638)------------------------------
% 1.30/1.19 % (5638)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.30/1.19 % (5638)Termination reason: Unknown
% 1.30/1.19 % (5638)Termination phase: Saturation
% 1.30/1.19
% 1.30/1.19 % (5638)Memory used [KB]: 5628
% 1.30/1.19 % (5638)Time elapsed: 0.015 s
% 1.30/1.19 % (5638)Instructions burned: 27 (million)
% 1.30/1.19 % (5638)------------------------------
% 1.30/1.19 % (5638)------------------------------
% 1.38/1.20 % (5644)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_5538 for (2999ds/37Mi)
% 1.38/1.20 % (5643)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_5538 for (2999ds/3Mi)
% 1.38/1.20 % (5643)Instruction limit reached!
% 1.38/1.20 % (5643)------------------------------
% 1.38/1.20 % (5643)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.38/1.20 % (5643)Termination reason: Unknown
% 1.38/1.20 % (5643)Termination phase: Saturation
% 1.38/1.20
% 1.38/1.20 % (5643)Memory used [KB]: 5500
% 1.38/1.20 % (5643)Time elapsed: 0.003 s
% 1.38/1.20 % (5643)Instructions burned: 3 (million)
% 1.38/1.20 % (5643)------------------------------
% 1.38/1.20 % (5643)------------------------------
% 1.38/1.20 % (5645)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_5538 for (2999ds/15Mi)
% 1.38/1.21 % (5646)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_5538 for (2999ds/3Mi)
% 1.38/1.21 % (5645)Instruction limit reached!
% 1.38/1.21 % (5645)------------------------------
% 1.38/1.21 % (5645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.38/1.21 % (5645)Termination reason: Unknown
% 1.38/1.21 % (5645)Termination phase: Saturation
% 1.38/1.21
% 1.38/1.21 % (5645)Memory used [KB]: 5500
% 1.38/1.21 % (5645)Time elapsed: 0.009 s
% 1.38/1.21 % (5645)Instructions burned: 15 (million)
% 1.38/1.21 % (5645)------------------------------
% 1.38/1.21 % (5645)------------------------------
% 1.38/1.21 % (5646)Instruction limit reached!
% 1.38/1.21 % (5646)------------------------------
% 1.38/1.21 % (5646)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.38/1.21 % (5646)Termination reason: Unknown
% 1.38/1.21 % (5646)Termination phase: Saturation
% 1.38/1.21
% 1.38/1.21 % (5646)Memory used [KB]: 5500
% 1.38/1.21 % (5646)Time elapsed: 0.003 s
% 1.38/1.21 % (5646)Instructions burned: 3 (million)
% 1.38/1.21 % (5646)------------------------------
% 1.38/1.21 % (5646)------------------------------
% 1.38/1.21 % (5647)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_5538 for (2999ds/1041Mi)
% 1.38/1.22 % (5648)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_5538 for (2999ds/7Mi)
% 1.38/1.22 % (5644)Instruction limit reached!
% 1.38/1.22 % (5644)------------------------------
% 1.38/1.22 % (5644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.38/1.22 % (5644)Termination reason: Unknown
% 1.38/1.22 % (5644)Termination phase: Saturation
% 1.38/1.22
% 1.38/1.22 % (5644)Memory used [KB]: 5756
% 1.38/1.22 % (5644)Time elapsed: 0.021 s
% 1.38/1.22 % (5644)Instructions burned: 39 (million)
% 1.38/1.22 % (5644)------------------------------
% 1.38/1.22 % (5644)------------------------------
% 1.38/1.22 % (5648)Instruction limit reached!
% 1.38/1.22 % (5648)------------------------------
% 1.38/1.22 % (5648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.38/1.22 % (5648)Termination reason: Unknown
% 1.38/1.22 % (5648)Termination phase: Saturation
% 1.38/1.22
% 1.38/1.22 % (5648)Memory used [KB]: 1023
% 1.38/1.22 % (5648)Time elapsed: 0.006 s
% 1.38/1.22 % (5648)Instructions burned: 8 (million)
% 1.38/1.22 % (5648)------------------------------
% 1.38/1.22 % (5648)------------------------------
% 1.38/1.22 % (5649)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_5538 for (2999ds/16Mi)
% 1.38/1.23 % (5636)First to succeed.
% 1.38/1.23 % (5650)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_5538 for (2999ds/3Mi)
% 1.38/1.23 % (5650)Instruction limit reached!
% 1.38/1.23 % (5650)------------------------------
% 1.38/1.23 % (5650)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.38/1.23 % (5650)Termination reason: Unknown
% 1.38/1.23 % (5650)Termination phase: Saturation
% 1.38/1.23
% 1.38/1.23 % (5650)Memory used [KB]: 5500
% 1.38/1.23 % (5650)Time elapsed: 0.003 s
% 1.38/1.23 % (5650)Instructions burned: 3 (million)
% 1.38/1.23 % (5650)------------------------------
% 1.38/1.23 % (5650)------------------------------
% 1.38/1.23 % (5636)Refutation found. Thanks to Tanya!
% 1.38/1.23 % SZS status Theorem for DTF2THF_5538
% 1.38/1.23 % SZS output start Proof for DTF2THF_5538
% 1.38/1.23 thf(type_def_5, type, n: $tType).
% 1.38/1.23 thf(func_def_0, type, n: $tType).
% 1.38/1.23 thf(func_def_1, type, c0: n).
% 1.38/1.23 thf(func_def_2, type, cS: n > n).
% 1.38/1.23 thf(func_def_3, type, c_plus: n > n > n).
% 1.38/1.23 thf(func_def_4, type, c_star: n > n > n).
% 1.38/1.23 thf(f660,plain,(
% 1.38/1.23 $false),
% 1.38/1.23 inference(trivial_inequality_removal,[status(thm)],[f659])).
% 1.38/1.23 thf(f659,plain,(
% 1.38/1.23 ((cS @ (cS @ (cS @ (cS @ c0)))) != (cS @ (cS @ (cS @ (cS @ c0)))))),
% 1.38/1.23 inference(superposition,[status(thm)],[f658,f41])).
% 1.38/1.23 thf(f41,plain,(
% 1.38/1.23 ( ! [X1 : n] : (((c_plus @ X1 @ c0) = X1)) )),
% 1.38/1.23 inference(equality_proxy_clausification,[status(thm)],[f40])).
% 1.38/1.23 thf(f40,plain,(
% 1.38/1.23 ( ! [X1 : n] : (($true = ((c_plus @ X1 @ c0) = X1))) )),
% 1.38/1.23 inference(beta_eta_normalization,[status(thm)],[f39])).
% 1.38/1.23 thf(f39,plain,(
% 1.38/1.23 ( ! [X1 : n] : (($true = ((^[Y0 : n]: ((c_plus @ Y0 @ c0) = Y0)) @ X1))) )),
% 1.38/1.23 inference(pi_clausification,[status(thm)],[f25])).
% 1.38/1.23 thf(f25,plain,(
% 1.38/1.23 ($true = (!! @ n @ (^[Y0 : n]: ((c_plus @ Y0 @ c0) = Y0))))),
% 1.38/1.23 inference(definition_unfolding,[status(thm)],[f20,f16])).
% 1.38/1.23 thf(f16,plain,(
% 1.38/1.23 (cPA_1 = (!! @ n @ (^[Y0 : n]: ((c_plus @ Y0 @ c0) = Y0))))),
% 1.38/1.23 inference(cnf_transformation,[status(thm)],[f10])).
% 1.38/1.23 thf(f10,plain,(
% 1.38/1.23 (cPA_1 = (!! @ n @ (^[Y0 : n]: ((c_plus @ Y0 @ c0) = Y0))))),
% 1.38/1.23 inference(fool_elimination,[status(thm)],[f1])).
% 1.38/1.23 thf(f1,axiom,(
% 1.38/1.23 (cPA_1 = ! [X0 : n] : ((c_plus @ X0 @ c0) = X0))),
% 1.38/1.23 file('/export/starexec/sandbox/tmp/tmp.e2rdlGzodo/DTF2THF_5538.p',cPA_1_def)).
% 1.38/1.23 thf(f20,plain,(
% 1.38/1.23 (cPA_1 = $true)),
% 1.38/1.23 inference(cnf_transformation,[status(thm)],[f15])).
% 1.38/1.23 thf(f15,plain,(
% 1.38/1.23 (cPA_2 = $true) & (cPA_1 = $true) & (cPA_3 = $true) & (cPA_4 = $true) & ((c_star @ (cS @ (cS @ c0)) @ (cS @ (cS @ c0))) != (c_plus @ (cS @ (cS @ c0)) @ (cS @ (cS @ c0))))),
% 1.38/1.23 inference(flattening,[status(thm)],[f14])).
% 1.38/1.23 thf(f14,plain,(
% 1.38/1.23 ((c_star @ (cS @ (cS @ c0)) @ (cS @ (cS @ c0))) != (c_plus @ (cS @ (cS @ c0)) @ (cS @ (cS @ c0)))) & ((cPA_1 = $true) & (cPA_4 = $true) & (cPA_3 = $true) & (cPA_2 = $true))),
% 1.38/1.23 inference(ennf_transformation,[status(thm)],[f12])).
% 1.38/1.23 thf(f12,plain,(
% 1.38/1.23 ~(((cPA_1 = $true) & (cPA_4 = $true) & (cPA_3 = $true) & (cPA_2 = $true)) => ((c_star @ (cS @ (cS @ c0)) @ (cS @ (cS @ c0))) = (c_plus @ (cS @ (cS @ c0)) @ (cS @ (cS @ c0)))))),
% 1.38/1.23 inference(fool_elimination,[status(thm)],[f11])).
% 1.38/1.23 thf(f11,plain,(
% 1.38/1.23 ~((cPA_2 & cPA_1 & cPA_3 & cPA_4) => ((c_star @ (cS @ (cS @ c0)) @ (cS @ (cS @ c0))) = (c_plus @ (cS @ (cS @ c0)) @ (cS @ (cS @ c0)))))),
% 1.38/1.23 inference(rectify,[status(thm)],[f6])).
% 1.38/1.23 thf(f6,negated_conjecture,(
% 1.38/1.23 ~((cPA_2 & cPA_1 & cPA_3 & cPA_4) => ((c_star @ (cS @ (cS @ c0)) @ (cS @ (cS @ c0))) = (c_plus @ (cS @ (cS @ c0)) @ (cS @ (cS @ c0)))))),
% 1.38/1.23 inference(negated_conjecture,[status(cth)],[f5])).
% 1.38/1.23 thf(f5,conjecture,(
% 1.38/1.23 (cPA_2 & cPA_1 & cPA_3 & cPA_4) => ((c_star @ (cS @ (cS @ c0)) @ (cS @ (cS @ c0))) = (c_plus @ (cS @ (cS @ c0)) @ (cS @ (cS @ c0))))),
% 1.38/1.23 file('/export/starexec/sandbox/tmp/tmp.e2rdlGzodo/DTF2THF_5538.p',cPA_THM1)).
% 1.38/1.23 thf(f658,plain,(
% 1.38/1.23 ((cS @ (cS @ (cS @ (cS @ c0)))) != (cS @ (cS @ (c_plus @ (cS @ (cS @ c0)) @ c0))))),
% 1.38/1.23 inference(superposition,[status(thm)],[f657,f33])).
% 1.38/1.23 thf(f33,plain,(
% 1.38/1.23 ( ! [X2 : n,X1 : n] : (((c_plus @ X2 @ (cS @ X1)) = (cS @ (c_plus @ X2 @ X1)))) )),
% 1.38/1.23 inference(equality_proxy_clausification,[status(thm)],[f32])).
% 1.38/1.23 thf(f32,plain,(
% 1.38/1.23 ( ! [X2 : n,X1 : n] : ((((c_plus @ X2 @ (cS @ X1)) = (cS @ (c_plus @ X2 @ X1))) = $true)) )),
% 1.38/1.23 inference(beta_eta_normalization,[status(thm)],[f31])).
% 1.38/1.23 thf(f31,plain,(
% 1.38/1.23 ( ! [X2 : n,X1 : n] : ((((^[Y0 : n]: ((c_plus @ Y0 @ (cS @ X1)) = (cS @ (c_plus @ Y0 @ X1)))) @ X2) = $true)) )),
% 1.38/1.23 inference(pi_clausification,[status(thm)],[f30])).
% 1.38/1.23 thf(f30,plain,(
% 1.38/1.23 ( ! [X1 : n] : (((!! @ n @ (^[Y0 : n]: ((c_plus @ Y0 @ (cS @ X1)) = (cS @ (c_plus @ Y0 @ X1))))) = $true)) )),
% 1.38/1.23 inference(beta_eta_normalization,[status(thm)],[f29])).
% 1.38/1.23 thf(f29,plain,(
% 1.38/1.23 ( ! [X1 : n] : (($true = ((^[Y0 : n]: (!! @ n @ (^[Y1 : n]: ((c_plus @ Y1 @ (cS @ Y0)) = (cS @ (c_plus @ Y1 @ Y0)))))) @ X1))) )),
% 1.38/1.23 inference(pi_clausification,[status(thm)],[f28])).
% 1.38/1.23 thf(f28,plain,(
% 1.38/1.23 ((!! @ n @ (^[Y0 : n]: (!! @ n @ (^[Y1 : n]: ((c_plus @ Y1 @ (cS @ Y0)) = (cS @ (c_plus @ Y1 @ Y0))))))) = $true)),
% 1.38/1.23 inference(definition_unfolding,[status(thm)],[f24,f21])).
% 1.38/1.23 thf(f21,plain,(
% 1.38/1.23 (cPA_2 = $true)),
% 1.38/1.23 inference(cnf_transformation,[status(thm)],[f15])).
% 1.38/1.23 thf(f24,plain,(
% 1.38/1.23 (cPA_2 = (!! @ n @ (^[Y0 : n]: (!! @ n @ (^[Y1 : n]: ((c_plus @ Y1 @ (cS @ Y0)) = (cS @ (c_plus @ Y1 @ Y0))))))))),
% 1.38/1.23 inference(cnf_transformation,[status(thm)],[f9])).
% 1.38/1.23 thf(f9,plain,(
% 1.38/1.23 (cPA_2 = (!! @ n @ (^[Y0 : n]: (!! @ n @ (^[Y1 : n]: ((c_plus @ Y1 @ (cS @ Y0)) = (cS @ (c_plus @ Y1 @ Y0))))))))),
% 1.38/1.23 inference(fool_elimination,[status(thm)],[f2])).
% 1.38/1.23 thf(f2,axiom,(
% 1.38/1.23 (! [X0 : n,X1 : n] : ((c_plus @ X0 @ (cS @ X1)) = (cS @ (c_plus @ X0 @ X1))) = cPA_2)),
% 1.38/1.23 file('/export/starexec/sandbox/tmp/tmp.e2rdlGzodo/DTF2THF_5538.p',cPA_2_def)).
% 1.38/1.23 thf(f657,plain,(
% 1.38/1.23 ((cS @ (cS @ (cS @ (cS @ c0)))) != (cS @ (c_plus @ (cS @ (cS @ c0)) @ (cS @ c0))))),
% 1.38/1.23 inference(superposition,[status(thm)],[f656,f33])).
% 1.38/1.23 thf(f656,plain,(
% 1.38/1.23 ((c_plus @ (cS @ (cS @ c0)) @ (cS @ (cS @ c0))) != (cS @ (cS @ (cS @ (cS @ c0)))))),
% 1.38/1.23 inference(superposition,[status(thm)],[f17,f654])).
% 1.38/1.23 thf(f654,plain,(
% 1.38/1.23 ((c_star @ (cS @ (cS @ c0)) @ (cS @ (cS @ c0))) = (cS @ (cS @ (cS @ (cS @ c0)))))),
% 1.38/1.23 inference(superposition,[status(thm)],[f193,f648])).
% 1.38/1.23 thf(f648,plain,(
% 1.38/1.23 ((cS @ (cS @ c0)) = (c_star @ (cS @ (cS @ c0)) @ (cS @ c0)))),
% 1.38/1.23 inference(superposition,[status(thm)],[f193,f44])).
% 1.38/1.23 thf(f44,plain,(
% 1.38/1.23 ( ! [X1 : n] : ((c0 = (c_star @ X1 @ c0))) )),
% 1.38/1.23 inference(equality_proxy_clausification,[status(thm)],[f43])).
% 1.38/1.23 thf(f43,plain,(
% 1.38/1.23 ( ! [X1 : n] : (($true = (c0 = (c_star @ X1 @ c0)))) )),
% 1.38/1.23 inference(beta_eta_normalization,[status(thm)],[f42])).
% 1.38/1.23 thf(f42,plain,(
% 1.38/1.23 ( ! [X1 : n] : (($true = ((^[Y0 : n]: (c0 = (c_star @ Y0 @ c0))) @ X1))) )),
% 1.38/1.23 inference(pi_clausification,[status(thm)],[f27])).
% 1.38/1.23 thf(f27,plain,(
% 1.38/1.23 ((!! @ n @ (^[Y0 : n]: (c0 = (c_star @ Y0 @ c0)))) = $true)),
% 1.38/1.23 inference(definition_unfolding,[status(thm)],[f23,f19])).
% 1.38/1.23 thf(f19,plain,(
% 1.38/1.23 (cPA_3 = $true)),
% 1.38/1.23 inference(cnf_transformation,[status(thm)],[f15])).
% 1.38/1.23 thf(f23,plain,(
% 1.38/1.23 (cPA_3 = (!! @ n @ (^[Y0 : n]: (c0 = (c_star @ Y0 @ c0)))))),
% 1.38/1.23 inference(cnf_transformation,[status(thm)],[f13])).
% 1.38/1.23 thf(f13,plain,(
% 1.38/1.23 (cPA_3 = (!! @ n @ (^[Y0 : n]: (c0 = (c_star @ Y0 @ c0)))))),
% 1.38/1.23 inference(fool_elimination,[status(thm)],[f3])).
% 1.38/1.23 thf(f3,axiom,(
% 1.38/1.23 (! [X0 : n] : (c0 = (c_star @ X0 @ c0)) = cPA_3)),
% 1.38/1.23 file('/export/starexec/sandbox/tmp/tmp.e2rdlGzodo/DTF2THF_5538.p',cPA_3_def)).
% 1.38/1.23 thf(f193,plain,(
% 1.38/1.23 ( ! [X0 : n] : (((cS @ (cS @ (c_star @ (cS @ (cS @ c0)) @ X0))) = (c_star @ (cS @ (cS @ c0)) @ (cS @ X0)))) )),
% 1.38/1.23 inference(superposition,[status(thm)],[f118,f41])).
% 1.38/1.23 thf(f118,plain,(
% 1.38/1.23 ( ! [X0 : n,X1 : n] : (((cS @ (cS @ (c_plus @ (c_star @ (cS @ (cS @ X0)) @ X1) @ X0))) = (c_star @ (cS @ (cS @ X0)) @ (cS @ X1)))) )),
% 1.38/1.23 inference(superposition,[status(thm)],[f49,f33])).
% 1.38/1.23 thf(f49,plain,(
% 1.38/1.23 ( ! [X0 : n,X1 : n] : (((cS @ (c_plus @ (c_star @ (cS @ X0) @ X1) @ X0)) = (c_star @ (cS @ X0) @ (cS @ X1)))) )),
% 1.38/1.23 inference(superposition,[status(thm)],[f33,f38])).
% 1.38/1.23 thf(f38,plain,(
% 1.38/1.23 ( ! [X2 : n,X1 : n] : (((c_plus @ (c_star @ X2 @ X1) @ X2) = (c_star @ X2 @ (cS @ X1)))) )),
% 1.38/1.23 inference(equality_proxy_clausification,[status(thm)],[f37])).
% 1.38/1.23 thf(f37,plain,(
% 1.38/1.23 ( ! [X2 : n,X1 : n] : (($true = ((c_star @ X2 @ (cS @ X1)) = (c_plus @ (c_star @ X2 @ X1) @ X2)))) )),
% 1.38/1.23 inference(beta_eta_normalization,[status(thm)],[f36])).
% 1.38/1.23 thf(f36,plain,(
% 1.38/1.23 ( ! [X2 : n,X1 : n] : ((((^[Y0 : n]: ((c_star @ Y0 @ (cS @ X1)) = (c_plus @ (c_star @ Y0 @ X1) @ Y0))) @ X2) = $true)) )),
% 1.38/1.23 inference(pi_clausification,[status(thm)],[f35])).
% 1.38/1.23 thf(f35,plain,(
% 1.38/1.23 ( ! [X1 : n] : (((!! @ n @ (^[Y0 : n]: ((c_star @ Y0 @ (cS @ X1)) = (c_plus @ (c_star @ Y0 @ X1) @ Y0)))) = $true)) )),
% 1.38/1.23 inference(beta_eta_normalization,[status(thm)],[f34])).
% 1.38/1.23 thf(f34,plain,(
% 1.38/1.23 ( ! [X1 : n] : ((((^[Y0 : n]: (!! @ n @ (^[Y1 : n]: ((c_star @ Y1 @ (cS @ Y0)) = (c_plus @ (c_star @ Y1 @ Y0) @ Y1))))) @ X1) = $true)) )),
% 1.38/1.23 inference(pi_clausification,[status(thm)],[f26])).
% 1.38/1.23 thf(f26,plain,(
% 1.38/1.23 ((!! @ n @ (^[Y0 : n]: (!! @ n @ (^[Y1 : n]: ((c_star @ Y1 @ (cS @ Y0)) = (c_plus @ (c_star @ Y1 @ Y0) @ Y1)))))) = $true)),
% 1.38/1.23 inference(definition_unfolding,[status(thm)],[f22,f18])).
% 1.38/1.23 thf(f18,plain,(
% 1.38/1.23 (cPA_4 = $true)),
% 1.38/1.23 inference(cnf_transformation,[status(thm)],[f15])).
% 1.38/1.23 thf(f22,plain,(
% 1.38/1.23 (cPA_4 = (!! @ n @ (^[Y0 : n]: (!! @ n @ (^[Y1 : n]: ((c_star @ Y1 @ (cS @ Y0)) = (c_plus @ (c_star @ Y1 @ Y0) @ Y1)))))))),
% 1.38/1.23 inference(cnf_transformation,[status(thm)],[f8])).
% 1.38/1.23 thf(f8,plain,(
% 1.38/1.23 (cPA_4 = (!! @ n @ (^[Y0 : n]: (!! @ n @ (^[Y1 : n]: ((c_star @ Y1 @ (cS @ Y0)) = (c_plus @ (c_star @ Y1 @ Y0) @ Y1)))))))),
% 1.38/1.23 inference(fool_elimination,[status(thm)],[f4])).
% 1.38/1.23 thf(f4,axiom,(
% 1.38/1.23 (! [X0 : n,X1 : n] : ((c_star @ X0 @ (cS @ X1)) = (c_plus @ (c_star @ X0 @ X1) @ X0)) = cPA_4)),
% 1.38/1.23 file('/export/starexec/sandbox/tmp/tmp.e2rdlGzodo/DTF2THF_5538.p',cPA_4_def)).
% 1.38/1.23 thf(f17,plain,(
% 1.38/1.23 ((c_star @ (cS @ (cS @ c0)) @ (cS @ (cS @ c0))) != (c_plus @ (cS @ (cS @ c0)) @ (cS @ (cS @ c0))))),
% 1.38/1.23 inference(cnf_transformation,[status(thm)],[f15])).
% 1.38/1.23 % SZS output end Proof for DTF2THF_5538
% 1.38/1.23 % (5636)------------------------------
% 1.38/1.23 % (5636)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.38/1.23 % (5636)Termination reason: Refutation
% 1.38/1.23
% 1.38/1.23 % (5636)Memory used [KB]: 6652
% 1.38/1.23 % (5636)Time elapsed: 0.057 s
% 1.38/1.23 % (5636)Instructions burned: 182 (million)
% 1.38/1.23 % (5636)------------------------------
% 1.38/1.23 % (5636)------------------------------
% 1.38/1.23 % (5635)Success in time 0.061 s
%------------------------------------------------------------------------------