%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ANA125^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n011.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 08:38:56 AM UTC 2026
% Result : Theorem 0.26s 1.55s
% Output : Refutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 84 ( 29 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 157 ( 17 ~; 4 |; 4 &; 124 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 55 ( 22 ^; 29 !; 4 ?; 55 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
'type/realax/real': $tType ).
thf(func_def_0,type,
'type/realax/real': $tType ).
thf(func_def_1,type,
'const/realax/real_mul': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
thf(func_def_2,type,
'const/iterate/polynomial_function': ( 'type/realax/real' > 'type/realax/real' ) > $o ).
thf(func_def_8,type,
sK0: 'type/realax/real' ).
thf(func_def_9,type,
sK1: 'type/realax/real' > 'type/realax/real' ).
thf(func_def_11,type,
ph3:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
sK4: 'type/realax/real' ).
thf(func_def_13,type,
sK5: 'type/realax/real' > 'type/realax/real' ).
thf(f40,plain,
$false,
inference(equality_resolution,[status(thm)],[f39]) ).
thf(f39,plain,
! [X0: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ sK0 @ ( sK1 @ ( sK5 @ X0 ) ) )
!= ( 'const/realax/real_mul' @ X0 @ ( sK1 @ ( sK5 @ X0 ) ) ) ),
inference(superposition,[status(thm)],[f37,f16]) ).
thf(f16,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ X0 @ X1 )
= ( 'const/realax/real_mul' @ X1 @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ X0 @ X1 )
= ( 'const/realax/real_mul' @ X1 @ X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.noIjEEs3pb/DTF2THF_22343.p','thm/realax/REAL_MUL_SYM_') ).
thf(f37,plain,
! [X0: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ X0 @ ( sK1 @ ( sK5 @ X0 ) ) )
!= ( 'const/realax/real_mul' @ ( sK1 @ ( sK5 @ X0 ) ) @ sK0 ) ),
inference(beta_eta_normalization,[status(thm)],[f36]) ).
thf(f36,plain,
! [X0: 'type/realax/real'] :
( ( ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( sK1 @ Y0 ) @ sK0 )
@ ( sK5 @ X0 ) )
!= ( ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_mul' @ X0 @ ( sK1 @ Y0 ) )
@ ( sK5 @ X0 ) ) ),
inference(negative_extensionality,[status(thm)],[f30]) ).
thf(f30,plain,
! [X0: 'type/realax/real'] :
( ( ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( sK1 @ Y0 ) @ sK0 ) )
!= ( ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_mul' @ X0 @ ( sK1 @ Y0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f26]) ).
thf(f26,plain,
! [X0: 'type/realax/real'] :
( ( $true != $true )
| ( ( ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( sK1 @ Y0 ) @ sK0 ) )
!= ( ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_mul' @ X0 @ ( sK1 @ Y0 ) ) ) ) ),
inference(constrained_superposition,[status(thm)],[f14,f25]) ).
thf(f25,plain,
! [X0: 'type/realax/real'] :
( $true
= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_mul' @ X0 @ ( sK1 @ Y0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f24]) ).
thf(f24,plain,
! [X0: 'type/realax/real'] :
( ( $true != $true )
| ( $true
= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_mul' @ X0 @ ( sK1 @ Y0 ) ) ) ) ),
inference(superposition,[status(thm)],[f17,f15]) ).
thf(f15,plain,
( ( 'const/iterate/polynomial_function' @ sK1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ( 'const/iterate/polynomial_function' @ sK1 )
= $true )
& ( $true
!= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( sK1 @ Y0 ) @ sK0 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f10,f12]) ).
thf(f12,plain,
( ? [X0: 'type/realax/real',X1: 'type/realax/real' > 'type/realax/real'] :
( ( $true
= ( 'const/iterate/polynomial_function' @ X1 ) )
& ( $true
!= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( X1 @ Y0 ) @ X0 ) ) ) )
=> ( ( ( 'const/iterate/polynomial_function' @ sK1 )
= $true )
& ( $true
!= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( sK1 @ Y0 ) @ sK0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
? [X0: 'type/realax/real',X1: 'type/realax/real' > 'type/realax/real'] :
( ( $true
= ( 'const/iterate/polynomial_function' @ X1 ) )
& ( $true
!= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( X1 @ Y0 ) @ X0 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
~ ! [X0: 'type/realax/real',X1: 'type/realax/real' > 'type/realax/real'] :
( ( $true
= ( 'const/iterate/polynomial_function' @ X1 ) )
=> ( $true
= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( X1 @ Y0 ) @ X0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: 'type/realax/real',X1: 'type/realax/real' > 'type/realax/real'] :
( ( 'const/iterate/polynomial_function' @ X1 )
=> ( 'const/iterate/polynomial_function'
@ ^ [X2: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( X1 @ X2 ) @ X0 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ! [X1: 'type/realax/real',X0: 'type/realax/real' > 'type/realax/real'] :
( ( 'const/iterate/polynomial_function' @ X0 )
=> ( 'const/iterate/polynomial_function'
@ ^ [X2: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( X0 @ X2 ) @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
! [X1: 'type/realax/real',X0: 'type/realax/real' > 'type/realax/real'] :
( ( 'const/iterate/polynomial_function' @ X0 )
=> ( 'const/iterate/polynomial_function'
@ ^ [X2: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( X0 @ X2 ) @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.noIjEEs3pb/DTF2THF_22343.p','thm/iterate/POLYNOMIAL_FUNCTION_RMUL_') ).
thf(f17,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real' > 'type/realax/real'] :
( ( $true
!= ( 'const/iterate/polynomial_function' @ X1 ) )
| ( ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_mul' @ X0 @ ( X1 @ Y0 ) ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real' > 'type/realax/real'] :
( ( $true
!= ( 'const/iterate/polynomial_function' @ X1 ) )
| ( ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_mul' @ X0 @ ( X1 @ Y0 ) ) )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real' > 'type/realax/real'] :
( ( $true
= ( 'const/iterate/polynomial_function' @ X1 ) )
=> ( ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_mul' @ X0 @ ( X1 @ Y0 ) ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real' > 'type/realax/real'] :
( ( 'const/iterate/polynomial_function' @ X1 )
=> ( 'const/iterate/polynomial_function'
@ ^ [X2: 'type/realax/real'] : ( 'const/realax/real_mul' @ X0 @ ( X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X1: 'type/realax/real',X0: 'type/realax/real' > 'type/realax/real'] :
( ( 'const/iterate/polynomial_function' @ X0 )
=> ( 'const/iterate/polynomial_function'
@ ^ [X2: 'type/realax/real'] : ( 'const/realax/real_mul' @ X1 @ ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.noIjEEs3pb/DTF2THF_22343.p','thm/iterate/POLYNOMIAL_FUNCTION_LMUL_') ).
thf(f14,plain,
( $true
!= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( sK1 @ Y0 ) @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : ANA125^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.31 % Computer : n011.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Tue Feb 24 03:51:17 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
% 0.16/0.43 ---- Original DTF file ---
% 0.16/0.43 thf(spec,logic,$$dhol).
% 0.16/0.43 %------------------------------------------------------------------------------
% 0.16/0.43 % File : ANA125^1 : TPTP v9.2.1. Released v7.0.0.
% 0.16/0.43 % Domain : Analysis
% 0.16/0.43 % Problem : POLYNOMIAL_FUNCTION_RMUL
% 0.16/0.43 % Version : Especial.
% 0.16/0.43 % English :
% 0.16/0.43
% 0.16/0.43 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.16/0.43 % Source : [Kal16]
% 0.16/0.43 % Names : POLYNOMIAL_FUNCTION_RMUL_.p [Kal16]
% 0.16/0.43
% 0.16/0.43 % Status : Theorem
% 0.16/0.43 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0, 0.36 v7.5.0, 0.29 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0
% 0.16/0.43 % Syntax : Number of formulae : 6 ( 1 unt; 3 typ; 0 def)
% 0.16/0.43 % Number of atoms : 5 ( 1 equ; 0 cnn)
% 0.16/0.43 % Maximal formula atoms : 2 ( 1 avg)
% 0.16/0.43 % Number of connectives : 16 ( 0 ~; 0 |; 0 &; 14 @)
% 0.16/0.43 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.16/0.43 % Maximal formula depth : 9 ( 7 avg)
% 0.16/0.43 % Number of types : 2 ( 1 usr)
% 0.16/0.43 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.16/0.43 % Number of symbols : 3 ( 2 usr; 0 con; 1-2 aty)
% 0.16/0.43 % Number of variables : 8 ( 2 ^; 6 !; 0 ?; 8 :)
% 0.16/0.43 % SPC : TH0_THM_EQU_NAR
% 0.16/0.43
% 0.16/0.43 % Comments : Exported from core HOL Light.
% 0.16/0.43 %------------------------------------------------------------------------------
% 0.16/0.43 thf('thf_type_type/realax/real',type,
% 0.16/0.43 'type/realax/real': $tType ).
% 0.16/0.43
% 0.16/0.43 thf('thf_const_const/realax/real_mul',type,
% 0.16/0.43 'const/realax/real_mul': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
% 0.16/0.43
% 0.16/0.43 thf('thf_const_const/iterate/polynomial_function',type,
% 0.16/0.43 'const/iterate/polynomial_function': ( 'type/realax/real' > 'type/realax/real' ) > $o ).
% 0.16/0.43
% 0.16/0.43 thf('thm/iterate/POLYNOMIAL_FUNCTION_LMUL_',axiom,
% 0.16/0.43 ! [A: 'type/realax/real' > 'type/realax/real',A0: 'type/realax/real'] :
% 0.16/0.43 ( ( 'const/iterate/polynomial_function' @ A )
% 0.16/0.43 => ( 'const/iterate/polynomial_function'
% 0.16/0.43 @ ^ [A1: 'type/realax/real'] : ( 'const/realax/real_mul' @ A0 @ ( A @ A1 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 thf('thm/realax/REAL_MUL_SYM_',axiom,
% 0.16/0.43 ! [A: 'type/realax/real',A0: 'type/realax/real'] :
% 0.16/0.43 ( ( 'const/realax/real_mul' @ A @ A0 )
% 0.16/0.43 = ( 'const/realax/real_mul' @ A0 @ A ) ) ).
% 0.16/0.43
% 0.16/0.43 thf('thm/iterate/POLYNOMIAL_FUNCTION_RMUL_',conjecture,
% 0.16/0.43 ! [A: 'type/realax/real' > 'type/realax/real',A0: 'type/realax/real'] :
% 0.16/0.43 ( ( 'const/iterate/polynomial_function' @ A )
% 0.16/0.43 => ( 'const/iterate/polynomial_function'
% 0.16/0.43 @ ^ [A1: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( A @ A1 ) @ A0 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 %------------------------------------------------------------------------------
% 0.16/0.43 ------------------------
% 0.26/1.50 ---- Embedded in THF ---
% 0.26/1.50 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.26/1.50 %%% Generated on Tue Feb 24 03:51:18 EST 2026
% 0.26/1.50 %%% using '$$dhol' embedding, version 1.3.0.
% 0.26/1.50 %%% Logic specification used:
% 0.26/1.50 %%% thf(spec, logic, $$dhol).
% 0.26/1.50
% 0.26/1.50 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.noIjEEs3pb/DTF2DTF22343.p
% See solution above
% 0.26/1.50 ------------------------
% 0.26/1.51 ---- Cleaned THF ---
% 0.26/1.51 thf('thf_type_type/realax/real',type,
% 0.26/1.51 'type/realax/real': $tType ).
% 0.26/1.51
% 0.26/1.51 thf('thf_const_const/realax/real_mul',type,
% 0.26/1.51 'const/realax/real_mul': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
% 0.26/1.51
% 0.26/1.51 thf('thf_const_const/iterate/polynomial_function',type,
% 0.26/1.51 'const/iterate/polynomial_function': ( 'type/realax/real' > 'type/realax/real' ) > $o ).
% 0.26/1.51
% 0.26/1.51 thf('thm/iterate/POLYNOMIAL_FUNCTION_LMUL_',axiom,
% 0.26/1.51 ! [A: 'type/realax/real' > 'type/realax/real',A0: 'type/realax/real'] :
% 0.26/1.51 ( ( 'const/iterate/polynomial_function' @ A )
% 0.26/1.51 => ( 'const/iterate/polynomial_function'
% 0.26/1.51 @ ^ [A1: 'type/realax/real'] : ( 'const/realax/real_mul' @ A0 @ ( A @ A1 ) ) ) ) ).
% 0.26/1.51
% 0.26/1.51 thf('thm/realax/REAL_MUL_SYM_',axiom,
% 0.26/1.51 ! [A: 'type/realax/real',A0: 'type/realax/real'] :
% 0.26/1.51 ( ( 'const/realax/real_mul' @ A @ A0 )
% 0.26/1.51 = ( 'const/realax/real_mul' @ A0 @ A ) ) ).
% 0.26/1.51
% 0.26/1.51 thf('thm/iterate/POLYNOMIAL_FUNCTION_RMUL_',conjecture,
% 0.26/1.51 ! [A: 'type/realax/real' > 'type/realax/real',A0: 'type/realax/real'] :
% 0.26/1.51 ( ( 'const/iterate/polynomial_function' @ A )
% 0.26/1.51 => ( 'const/iterate/polynomial_function'
% 0.26/1.51 @ ^ [A1: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( A @ A1 ) @ A0 ) ) ) ).
% 0.26/1.51 ------------------------
% 0.26/1.54 % (22444)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_22343 for (2999ds/2Mi)
% 0.26/1.54 % (22441)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_22343 for (2999ds/4Mi)
% 0.26/1.54 % (22444)Instruction limit reached!
% 0.26/1.54 % (22444)------------------------------
% 0.26/1.54 % (22444)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.26/1.54 % (22444)Termination reason: Unknown
% 0.26/1.54 % (22444)Termination phase: Saturation
% 0.26/1.54
% 0.26/1.54 % (22444)Memory used [KB]: 5500
% 0.26/1.54 % (22444)Time elapsed: 0.003 s
% 0.26/1.54 % (22444)Instructions burned: 2 (million)
% 0.26/1.54 % (22444)------------------------------
% 0.26/1.54 % (22444)------------------------------
% 0.26/1.54 % (22441)Instruction limit reached!
% 0.26/1.54 % (22441)------------------------------
% 0.26/1.54 % (22441)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.26/1.54 % (22441)Termination reason: Unknown
% 0.26/1.54 % (22446)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_22343 for (2999ds/18Mi)
% 0.26/1.54 % (22445)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_22343 for (2999ds/275Mi)
% 0.26/1.54 % (22442)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_22343 for (2999ds/27Mi)
% 0.26/1.54 % (22440)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_22343 for (2999ds/183Mi)
% 0.26/1.54 % (22443)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_22343 for (2999ds/2Mi)
% 0.26/1.54 % (22441)Termination phase: Saturation
% 0.26/1.54
% 0.26/1.54 % (22441)Memory used [KB]: 5500
% 0.26/1.54 % (22441)Time elapsed: 0.005 s
% 0.26/1.54 % (22441)Instructions burned: 5 (million)
% 0.26/1.54 % (22441)------------------------------
% 0.26/1.54 % (22441)------------------------------
% 0.26/1.54 % (22443)Instruction limit reached!
% 0.26/1.54 % (22443)------------------------------
% 0.26/1.54 % (22443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.26/1.54 % (22443)Termination reason: Unknown
% 0.26/1.54 % (22443)Termination phase: Saturation
% 0.26/1.54
% 0.26/1.54 % (22443)Memory used [KB]: 5500
% 0.26/1.54 % (22443)Time elapsed: 0.003 s
% 0.26/1.54 % (22443)Instructions burned: 2 (million)
% 0.26/1.54 % (22443)------------------------------
% 0.26/1.54 % (22443)------------------------------
% 0.26/1.54 % (22445)Refutation not found, incomplete strategy
% 0.26/1.54 % (22445)------------------------------
% 0.26/1.54 % (22445)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.26/1.54 % (22445)Termination reason: Refutation not found, incomplete strategy
% 0.26/1.54
% 0.26/1.54
% 0.26/1.54 % (22445)Memory used [KB]: 5500
% 0.26/1.54 % (22445)Time elapsed: 0.003 s
% 0.26/1.54 % (22445)Instructions burned: 2 (million)
% 0.26/1.54 % (22445)------------------------------
% 0.26/1.54 % (22445)------------------------------
% 0.26/1.54 % (22446)First to succeed.
% 0.26/1.54 % (22440)Also succeeded, but the first one will report.
% 0.26/1.55 % (22446)Refutation found. Thanks to Tanya!
% 0.26/1.55 % SZS status Theorem for DTF2THF_22343
% 0.26/1.55 % SZS output start Proof for DTF2THF_22343
% 0.26/1.55 thf(type_def_5, type, 'type/realax/real': $tType).
% 0.26/1.55 thf(func_def_0, type, 'type/realax/real': $tType).
% 0.26/1.55 thf(func_def_1, type, 'const/realax/real_mul': 'type/realax/real' > 'type/realax/real' > 'type/realax/real').
% 0.26/1.55 thf(func_def_2, type, 'const/iterate/polynomial_function': ('type/realax/real' > 'type/realax/real') > $o).
% 0.26/1.55 thf(func_def_8, type, sK0: 'type/realax/real').
% 0.26/1.55 thf(func_def_9, type, sK1: 'type/realax/real' > 'type/realax/real').
% 0.26/1.55 thf(func_def_11, type, ph3: !>[X0: $tType]:(X0)).
% 0.26/1.55 thf(func_def_12, type, sK4: 'type/realax/real').
% 0.26/1.55 thf(func_def_13, type, sK5: 'type/realax/real' > 'type/realax/real').
% 0.26/1.55 thf(f40,plain,(
% 0.26/1.55 $false),
% 0.26/1.55 inference(equality_resolution,[status(thm)],[f39])).
% 0.26/1.55 thf(f39,plain,(
% 0.26/1.55 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_mul' @ sK0 @ (sK1 @ (sK5 @ X0))) != ('const/realax/real_mul' @ X0 @ (sK1 @ (sK5 @ X0))))) )),
% 0.26/1.55 inference(superposition,[status(thm)],[f37,f16])).
% 0.26/1.55 thf(f16,plain,(
% 0.26/1.55 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_mul' @ X0 @ X1) = ('const/realax/real_mul' @ X1 @ X0))) )),
% 0.26/1.55 inference(cnf_transformation,[status(thm)],[f2])).
% 0.26/1.55 thf(f2,axiom,(
% 0.26/1.55 ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/realax/real_mul' @ X0 @ X1) = ('const/realax/real_mul' @ X1 @ X0))),
% 0.26/1.55 file('/export/starexec/sandbox/tmp/tmp.noIjEEs3pb/DTF2THF_22343.p','thm/realax/REAL_MUL_SYM_')).
% 0.26/1.55 thf(f37,plain,(
% 0.26/1.55 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_mul' @ X0 @ (sK1 @ (sK5 @ X0))) != ('const/realax/real_mul' @ (sK1 @ (sK5 @ X0)) @ sK0))) )),
% 0.26/1.55 inference(beta_eta_normalization,[status(thm)],[f36])).
% 0.26/1.55 thf(f36,plain,(
% 0.26/1.55 ( ! [X0 : 'type/realax/real'] : ((((^[Y0 : 'type/realax/real']: ('const/realax/real_mul' @ (sK1 @ Y0) @ sK0)) @ (sK5 @ X0)) != ((^[Y0 : 'type/realax/real']: ('const/realax/real_mul' @ X0 @ (sK1 @ Y0))) @ (sK5 @ X0)))) )),
% 0.26/1.55 inference(negative_extensionality,[status(thm)],[f30])).
% 0.26/1.55 thf(f30,plain,(
% 0.26/1.55 ( ! [X0 : 'type/realax/real'] : (((^[Y0 : 'type/realax/real']: ('const/realax/real_mul' @ (sK1 @ Y0) @ sK0)) != (^[Y0 : 'type/realax/real']: ('const/realax/real_mul' @ X0 @ (sK1 @ Y0))))) )),
% 0.26/1.55 inference(trivial_inequality_removal,[status(thm)],[f26])).
% 0.26/1.55 thf(f26,plain,(
% 0.26/1.55 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ((^[Y0 : 'type/realax/real']: ('const/realax/real_mul' @ (sK1 @ Y0) @ sK0)) != (^[Y0 : 'type/realax/real']: ('const/realax/real_mul' @ X0 @ (sK1 @ Y0))))) )),
% 0.26/1.55 inference(constrained_superposition,[status(thm)],[f14,f25])).
% 0.26/1.55 thf(f25,plain,(
% 0.26/1.55 ( ! [X0 : 'type/realax/real'] : (($true = ('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: ('const/realax/real_mul' @ X0 @ (sK1 @ Y0)))))) )),
% 0.26/1.55 inference(trivial_inequality_removal,[status(thm)],[f24])).
% 0.26/1.55 thf(f24,plain,(
% 0.26/1.55 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = ('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: ('const/realax/real_mul' @ X0 @ (sK1 @ Y0)))))) )),
% 0.26/1.55 inference(superposition,[status(thm)],[f17,f15])).
% 0.26/1.55 thf(f15,plain,(
% 0.26/1.55 (('const/iterate/polynomial_function' @ sK1) = $true)),
% 0.26/1.55 inference(cnf_transformation,[status(thm)],[f13])).
% 0.26/1.55 thf(f13,plain,(
% 0.26/1.55 (('const/iterate/polynomial_function' @ sK1) = $true) & ($true != ('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: ('const/realax/real_mul' @ (sK1 @ Y0) @ sK0))))),
% 0.26/1.55 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f10,f12])).
% 0.26/1.55 thf(f12,plain,(
% 0.26/1.55 ? [X0 : 'type/realax/real',X1 : 'type/realax/real' > 'type/realax/real'] : (($true = ('const/iterate/polynomial_function' @ X1)) & ($true != ('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: ('const/realax/real_mul' @ (X1 @ Y0) @ X0))))) => ((('const/iterate/polynomial_function' @ sK1) = $true) & ($true != ('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: ('const/realax/real_mul' @ (sK1 @ Y0) @ sK0)))))),
% 0.26/1.55 introduced(definition,[],[choice_axiom])).
% 0.26/1.55 thf(f10,plain,(
% 0.26/1.55 ? [X0 : 'type/realax/real',X1 : 'type/realax/real' > 'type/realax/real'] : (($true = ('const/iterate/polynomial_function' @ X1)) & ($true != ('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: ('const/realax/real_mul' @ (X1 @ Y0) @ X0)))))),
% 0.26/1.55 inference(ennf_transformation,[status(thm)],[f7])).
% 0.26/1.55 thf(f7,plain,(
% 0.26/1.55 ~! [X0 : 'type/realax/real',X1 : 'type/realax/real' > 'type/realax/real'] : (($true = ('const/iterate/polynomial_function' @ X1)) => ($true = ('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: ('const/realax/real_mul' @ (X1 @ Y0) @ X0)))))),
% 0.26/1.55 inference(fool_elimination,[status(thm)],[f6])).
% 0.26/1.55 thf(f6,plain,(
% 0.26/1.55 ~! [X0 : 'type/realax/real',X1 : 'type/realax/real' > 'type/realax/real'] : (('const/iterate/polynomial_function' @ X1) => ('const/iterate/polynomial_function' @ (^[X2 : 'type/realax/real'] : ('const/realax/real_mul' @ (X1 @ X2) @ X0))))),
% 0.26/1.55 inference(rectify,[status(thm)],[f4])).
% 0.26/1.55 thf(f4,negated_conjecture,(
% 0.26/1.55 ~! [X1 : 'type/realax/real',X0 : 'type/realax/real' > 'type/realax/real'] : (('const/iterate/polynomial_function' @ X0) => ('const/iterate/polynomial_function' @ (^[X2 : 'type/realax/real'] : ('const/realax/real_mul' @ (X0 @ X2) @ X1))))),
% 0.26/1.55 inference(negated_conjecture,[status(cth)],[f3])).
% 0.26/1.55 thf(f3,conjecture,(
% 0.26/1.55 ! [X1 : 'type/realax/real',X0 : 'type/realax/real' > 'type/realax/real'] : (('const/iterate/polynomial_function' @ X0) => ('const/iterate/polynomial_function' @ (^[X2 : 'type/realax/real'] : ('const/realax/real_mul' @ (X0 @ X2) @ X1))))),
% 0.26/1.55 file('/export/starexec/sandbox/tmp/tmp.noIjEEs3pb/DTF2THF_22343.p','thm/iterate/POLYNOMIAL_FUNCTION_RMUL_')).
% 0.26/1.55 thf(f17,plain,(
% 0.26/1.55 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real' > 'type/realax/real'] : (($true != ('const/iterate/polynomial_function' @ X1)) | (('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: ('const/realax/real_mul' @ X0 @ (X1 @ Y0)))) = $true)) )),
% 0.26/1.55 inference(cnf_transformation,[status(thm)],[f11])).
% 0.26/1.55 thf(f11,plain,(
% 0.26/1.55 ! [X0 : 'type/realax/real',X1 : 'type/realax/real' > 'type/realax/real'] : (($true != ('const/iterate/polynomial_function' @ X1)) | (('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: ('const/realax/real_mul' @ X0 @ (X1 @ Y0)))) = $true))),
% 0.26/1.55 inference(ennf_transformation,[status(thm)],[f9])).
% 0.26/1.55 thf(f9,plain,(
% 0.26/1.55 ! [X0 : 'type/realax/real',X1 : 'type/realax/real' > 'type/realax/real'] : (($true = ('const/iterate/polynomial_function' @ X1)) => (('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: ('const/realax/real_mul' @ X0 @ (X1 @ Y0)))) = $true))),
% 0.26/1.55 inference(fool_elimination,[status(thm)],[f8])).
% 0.26/1.55 thf(f8,plain,(
% 0.26/1.55 ! [X0 : 'type/realax/real',X1 : 'type/realax/real' > 'type/realax/real'] : (('const/iterate/polynomial_function' @ X1) => ('const/iterate/polynomial_function' @ (^[X2 : 'type/realax/real'] : ('const/realax/real_mul' @ X0 @ (X1 @ X2)))))),
% 0.26/1.55 inference(rectify,[status(thm)],[f1])).
% 0.26/1.55 thf(f1,axiom,(
% 0.26/1.55 ! [X1 : 'type/realax/real',X0 : 'type/realax/real' > 'type/realax/real'] : (('const/iterate/polynomial_function' @ X0) => ('const/iterate/polynomial_function' @ (^[X2 : 'type/realax/real'] : ('const/realax/real_mul' @ X1 @ (X0 @ X2)))))),
% 0.26/1.55 file('/export/starexec/sandbox/tmp/tmp.noIjEEs3pb/DTF2THF_22343.p','thm/iterate/POLYNOMIAL_FUNCTION_LMUL_')).
% 0.26/1.55 thf(f14,plain,(
% 0.26/1.55 ($true != ('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: ('const/realax/real_mul' @ (sK1 @ Y0) @ sK0))))),
% 0.26/1.55 inference(cnf_transformation,[status(thm)],[f13])).
% 0.26/1.55 % SZS output end Proof for DTF2THF_22343
% 0.26/1.55 % (22446)------------------------------
% 0.26/1.55 % (22446)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.26/1.55 % (22446)Termination reason: Refutation
% 0.26/1.55
% 0.26/1.55 % (22446)Memory used [KB]: 5500
% 0.26/1.55 % (22446)Time elapsed: 0.007 s
% 0.26/1.55 % (22446)Instructions burned: 6 (million)
% 0.26/1.55 % (22446)------------------------------
% 0.26/1.55 % (22446)------------------------------
% 0.26/1.55 % (22439)Success in time 0.025 s
%------------------------------------------------------------------------------