%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM812^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n006.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 09:24:49 AM UTC 2026
% Result : Theorem 1.60s 1.30s
% Output : Refutation 1.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 3
% Syntax : Number of formulae : 31 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 168 ( 66 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 237 ( 22 ~; 21 |; 15 &; 131 @)
% ( 0 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 6 usr; 6 con; 0-2 aty)
% ( 23 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 57 ( 22 ^; 29 !; 6 ?; 57 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
cS: $i > $i ).
thf(func_def_14,type,
sK2: ( $i > $o ) > $i ).
thf(func_def_16,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f185,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f182]) ).
thf(f182,plain,
( ( sK0 != sK0 )
| ( c0 != c0 ) ),
inference(superposition,[status(thm)],[f15,f167]) ).
thf(f167,plain,
! [X0: $i] :
( ( c0 = X0 )
| ( sK0 != X0 ) ),
inference(superposition,[status(thm)],[f14,f83]) ).
thf(f83,plain,
! [X0: $i] :
( ( ( cS
@ ( sK2
@ ^ [Y0: $i] : ( X0 != Y0 ) ) )
= X0 )
| ( c0 = X0 ) ),
inference(equality_proxy_clausification,[status(thm)],[f82]) ).
thf(f82,plain,
! [X0: $i] :
( ( ( X0 = c0 )
= $true )
| ( ( cS
@ ( sK2
@ ^ [Y0: $i] : ( X0 != Y0 ) ) )
= X0 ) ),
inference(not_proxy_clausification,[status(thm)],[f81]) ).
thf(f81,plain,
! [X0: $i] :
( ( $false
= ( X0 != c0 ) )
| ( ( cS
@ ( sK2
@ ^ [Y0: $i] : ( X0 != Y0 ) ) )
= X0 ) ),
inference(beta_eta_normalization,[status(thm)],[f63]) ).
thf(f63,plain,
! [X0: $i] :
( ( $false
= ( ^ [Y0: $i] : ( X0 != Y0 )
@ c0 ) )
| ( ( cS
@ ( sK2
@ ^ [Y0: $i] : ( X0 != Y0 ) ) )
= X0 ) ),
inference(leibniz_equality_elimination,[status(thm)],[f27]) ).
thf(f27,plain,
! [X2: $i,X1: $i > $o] :
( ( $false
= ( X1 @ ( cS @ ( sK2 @ X1 ) ) ) )
| ( $true
= ( X1 @ X2 ) )
| ( ( X1 @ c0 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
! [X1: $i > $o] :
( ( $true
= ( !! @ $i @ X1 ) )
| ( ( X1 @ c0 )
= $false )
| ( $false
= ( X1 @ ( cS @ ( sK2 @ X1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
! [X1: $i > $o] :
( ( $false
= ( ( X1 @ ( sK2 @ X1 ) )
=> ( X1 @ ( cS @ ( sK2 @ X1 ) ) ) ) )
| ( ( X1 @ c0 )
= $false )
| ( $true
= ( !! @ $i @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f22]) ).
thf(f22,plain,
! [X1: $i > $o] :
( ( ( X1 @ c0 )
= $false )
| ( $true
= ( !! @ $i @ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( cS @ Y0 ) ) )
@ ( sK2 @ X1 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
! [X1: $i > $o] :
( ( ( X1 @ c0 )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( cS @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
! [X1: $i > $o] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( cS @ Y0 ) ) ) )
& ( X1 @ c0 ) )
= $false )
| ( $true
= ( !! @ $i @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
! [X1: $i > $o] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( cS @ Y0 ) ) ) )
& ( X1 @ c0 ) )
=> ( !! @ $i @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f18]) ).
thf(f18,plain,
! [X1: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ Y1 ) ) ) )
& ( Y0 @ c0 ) )
=> ( !! @ $i @ Y0 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ Y1 ) ) ) )
& ( Y0 @ c0 ) )
=> ( !! @ $i @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ Y1 ) ) ) )
& ( Y0 @ c0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f13,f12]) ).
thf(f12,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)],[f8]) ).
thf(f8,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)],[f7]) ).
thf(f7,plain,
! [X0: $i > $o] :
( ( ( ( X0 @ c0 )
& ! [X1: $i] :
( ( X0 @ X1 )
=> ( X0 @ ( cS @ X1 ) ) ) )
=> ! [X2: $i] : ( X0 @ X2 ) )
= cIND ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i > $o] :
( ( ( ( X0 @ c0 )
& ! [X1: $i] :
( ( X0 @ X1 )
=> ( X0 @ ( cS @ X1 ) ) ) )
=> ! [X1: $i] : ( X0 @ X1 ) )
= cIND ),
file('/export/starexec/sandbox/tmp/tmp.co3plJG88Y/DTF2THF_17551.p',cIND_def) ).
thf(f13,plain,
cIND = $true,
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( c0 != sK0 )
& ! [X1: $i] :
( ( cS @ X1 )
!= sK0 )
& ( cIND = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f9,f10]) ).
thf(f10,plain,
( ? [X0: $i] :
( ( c0 != X0 )
& ! [X1: $i] :
( ( cS @ X1 )
!= X0 ) )
=> ( ( c0 != sK0 )
& ! [X1: $i] :
( ( cS @ X1 )
!= sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ? [X0: $i] :
( ( c0 != X0 )
& ! [X1: $i] :
( ( cS @ X1 )
!= X0 ) )
& ( cIND = $true ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ( cIND = $true )
=> ! [X0: $i] :
( ( c0 = X0 )
| ? [X1: $i] :
( ( cS @ X1 )
= X0 ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( cIND
=> ! [X0: $i] :
( ? [X1: $i] :
( ( cS @ X1 )
= X0 )
| ( c0 = X0 ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ( cIND
=> ! [X2: $i] :
( ? [X3: $i] :
( ( cS @ X3 )
= X2 )
| ( c0 = X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( cIND
=> ! [X2: $i] :
( ? [X3: $i] :
( ( cS @ X3 )
= X2 )
| ( c0 = X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.co3plJG88Y/DTF2THF_17551.p',cTHM578) ).
thf(f14,plain,
! [X1: $i] :
( ( cS @ X1 )
!= sK0 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f15,plain,
c0 != sK0,
inference(cnf_transformation,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM812^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n006.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 11:15:30 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : NUM812^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% 0.20/0.46 % Domain : Number Theory (Induction on naturals)
% 0.20/0.46 % Problem : TPS problem THM578
% 0.20/0.46 % Version : Especial.
% 0.20/0.46 % English : Variant of THM6104, including induction in the hypothesis.
% 0.20/0.46
% 0.20/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.46 % Source : [Bro09]
% 0.20/0.46 % Names : tps_0443 [Bro09]
% 0.20/0.46 % : THM578 [TPS]
% 0.20/0.46
% 0.20/0.46 % Status : Theorem
% 0.20/0.46 % 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, 0.11 v7.2.0, 0.12 v7.0.0, 0.00 v6.2.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.40 v5.3.0, 0.60 v5.2.0
% 0.20/0.46 % Syntax : Number of formulae : 5 ( 1 unt; 3 typ; 1 def)
% 0.20/0.46 % Number of atoms : 5 ( 3 equ; 0 cnn)
% 0.20/0.46 % Maximal formula atoms : 3 ( 2 avg)
% 0.20/0.46 % Number of connectives : 11 ( 0 ~; 1 |; 1 &; 6 @)
% 0.20/0.46 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 5 ( 3 avg)
% 0.20/0.46 % Number of types : 2 ( 0 usr)
% 0.20/0.46 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 4 ( 3 usr; 2 con; 0-2 aty)
% 0.20/0.46 % Number of variables : 5 ( 0 ^; 4 !; 1 ?; 5 :)
% 0.20/0.46 % SPC : TH0_THM_EQU_NAR
% 0.20/0.46
% 0.20/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.20/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.20/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.20/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.20/0.46 % :
% 0.20/0.46 % Bugfixes : v5.2.0 - Added missing type declarations.
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 thf(c0_type,type,
% 0.20/0.46 c0: $i ).
% 0.20/0.46
% 0.20/0.46 thf(cS_type,type,
% 0.20/0.46 cS: $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(cIND_type,type,
% 0.20/0.46 cIND: $o ).
% 0.20/0.46
% 0.20/0.46 thf(cIND_def,definition,
% 0.20/0.46 ( cIND
% 0.20/0.46 = ( ! [Xp: $i > $o] :
% 0.20/0.46 ( ( ( Xp @ c0 )
% 0.20/0.46 & ! [Xx: $i] :
% 0.20/0.46 ( ( Xp @ Xx )
% 0.20/0.46 => ( Xp @ ( cS @ Xx ) ) ) )
% 0.20/0.46 => ! [Xx: $i] : ( Xp @ Xx ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(cTHM578,conjecture,
% 0.20/0.46 ( cIND
% 0.20/0.46 => ! [Xn: $i] :
% 0.20/0.46 ( ( Xn = c0 )
% 0.20/0.46 | ? [Xm: $i] :
% 0.20/0.46 ( Xn
% 0.20/0.46 = ( cS @ Xm ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 ------------------------
% 1.46/1.26 ---- Embedded in THF ---
% 1.46/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.26 %%% Generated on Tue Feb 24 11:15:31 EST 2026
% 1.46/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.26 %%% Logic specification used:
% 1.46/1.26 %%% thf(spec, logic, $$dhol).
% 1.46/1.26
% 1.46/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.co3plJG88Y/DTF2DTF17551.p
% See solution above
% 1.46/1.26 ------------------------
% 1.46/1.27 ---- Cleaned THF ---
% 1.46/1.27 thf(c0_type,type,
% 1.46/1.27 c0: $i ).
% 1.46/1.27
% 1.46/1.27 thf(cS_type,type,
% 1.46/1.27 cS: $i > $i ).
% 1.46/1.27
% 1.46/1.27 thf(cIND_type,type,
% 1.46/1.27 cIND: $o ).
% 1.46/1.27
% 1.46/1.27 thf(cIND_def,definition,
% 1.46/1.27 ( cIND
% 1.46/1.27 = ( ! [Xp: $i > $o] :
% 1.46/1.27 ( ( ( Xp @ c0 )
% 1.46/1.27 & ! [Xx: $i] :
% 1.46/1.27 ( ( Xp @ Xx )
% 1.46/1.27 => ( Xp @ ( cS @ Xx ) ) ) )
% 1.46/1.27 => ! [Xx: $i] : ( Xp @ Xx ) ) ) ) ).
% 1.46/1.27
% 1.46/1.27 thf(cTHM578,conjecture,
% 1.46/1.27 ( cIND
% 1.46/1.27 => ! [Xn: $i] :
% 1.46/1.27 ( ( Xn = c0 )
% 1.46/1.27 | ? [Xm: $i] :
% 1.46/1.27 ( Xn
% 1.46/1.27 = ( cS @ Xm ) ) ) ) ).
% 1.46/1.27 ------------------------
% 1.46/1.28 % (17882)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_17551 for (2999ds/2Mi)
% 1.46/1.28 % (17882)Instruction limit reached!
% 1.46/1.28 % (17882)------------------------------
% 1.46/1.28 % (17882)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.28 % (17882)Termination reason: Unknown
% 1.46/1.28 % (17882)Termination phase: Function definition elimination
% 1.46/1.28
% 1.46/1.28 % (17882)Memory used [KB]: 895
% 1.46/1.28 % (17882)Time elapsed: 0.002 s
% 1.46/1.28 % (17882)Instructions burned: 2 (million)
% 1.46/1.28 % (17882)------------------------------
% 1.46/1.28 % (17882)------------------------------
% 1.46/1.28 % (17880)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_17551 for (2999ds/27Mi)
% 1.46/1.28 % (17880)Refutation not found, incomplete strategy
% 1.46/1.28 % (17880)------------------------------
% 1.46/1.28 % (17880)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.28 % (17880)Termination reason: Refutation not found, incomplete strategy
% 1.46/1.28
% 1.46/1.28
% 1.46/1.28 % (17880)Memory used [KB]: 5500
% 1.46/1.28 % (17880)Time elapsed: 0.003 s
% 1.46/1.28 % (17880)Instructions burned: 2 (million)
% 1.46/1.28 % (17880)------------------------------
% 1.46/1.28 % (17880)------------------------------
% 1.46/1.29 % (17878)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_17551 for (2999ds/183Mi)
% 1.46/1.29 % (17879)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_17551 for (2999ds/4Mi)
% 1.46/1.29 % (17881)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_17551 for (2999ds/2Mi)
% 1.46/1.29 % (17883)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_17551 for (2999ds/275Mi)
% 1.46/1.29 % (17884)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_17551 for (2999ds/18Mi)
% 1.46/1.29 % (17881)Instruction limit reached!
% 1.46/1.29 % (17881)------------------------------
% 1.46/1.29 % (17881)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.29 % (17881)Termination reason: Unknown
% 1.46/1.29 % (17881)Termination phase: Property scanning
% 1.46/1.29
% 1.46/1.29 % (17881)Memory used [KB]: 895
% 1.46/1.29 % (17881)Time elapsed: 0.003 s
% 1.46/1.29 % (17881)Instructions burned: 2 (million)
% 1.46/1.29 % (17881)------------------------------
% 1.46/1.29 % (17881)------------------------------
% 1.46/1.29 % (17883)Refutation not found, incomplete strategy
% 1.46/1.29 % (17883)------------------------------
% 1.46/1.29 % (17883)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.29 % (17883)Termination reason: Refutation not found, incomplete strategy
% 1.46/1.29
% 1.46/1.29
% 1.46/1.29 % (17883)Memory used [KB]: 5373
% 1.46/1.29 % (17883)Time elapsed: 0.003 s
% 1.46/1.29 % (17883)Instructions burned: 1 (million)
% 1.46/1.29 % (17883)------------------------------
% 1.46/1.29 % (17883)------------------------------
% 1.46/1.29 % (17885)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_17551 for (2999ds/3Mi)
% 1.46/1.29 % (17879)Instruction limit reached!
% 1.46/1.29 % (17879)------------------------------
% 1.46/1.29 % (17879)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.29 % (17879)Termination reason: Unknown
% 1.46/1.29 % (17879)Termination phase: Saturation
% 1.46/1.29
% 1.46/1.29 % (17879)Memory used [KB]: 5500
% 1.46/1.29 % (17879)Time elapsed: 0.005 s
% 1.46/1.29 % (17879)Instructions burned: 4 (million)
% 1.46/1.29 % (17879)------------------------------
% 1.46/1.29 % (17879)------------------------------
% 1.46/1.29 % (17885)Refutation not found, incomplete strategy
% 1.46/1.29 % (17885)------------------------------
% 1.46/1.29 % (17885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.29 % (17885)Termination reason: Refutation not found, incomplete strategy
% 1.46/1.29
% 1.46/1.29
% 1.46/1.29 % (17885)Memory used [KB]: 5500
% 1.46/1.29 % (17885)Time elapsed: 0.001 s
% 1.46/1.29 % (17885)Instructions burned: 1 (million)
% 1.46/1.29 % (17885)------------------------------
% 1.46/1.29 % (17885)------------------------------
% 1.46/1.30 % (17886)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_17551 for (2999ds/37Mi)
% 1.60/1.30 % (17878)First to succeed.
% 1.60/1.30 % (17878)Refutation found. Thanks to Tanya!
% 1.60/1.30 % SZS status Theorem for DTF2THF_17551
% 1.60/1.30 % SZS output start Proof for DTF2THF_17551
% 1.60/1.30 thf(func_def_1, type, cS: $i > $i).
% 1.60/1.30 thf(func_def_14, type, sK2: ($i > $o) > $i).
% 1.60/1.30 thf(func_def_16, type, ph3: !>[X0: $tType]:(X0)).
% 1.60/1.30 thf(f185,plain,(
% 1.60/1.30 $false),
% 1.60/1.30 inference(trivial_inequality_removal,[status(thm)],[f182])).
% 1.60/1.30 thf(f182,plain,(
% 1.60/1.30 (sK0 != sK0) | (c0 != c0)),
% 1.60/1.30 inference(superposition,[status(thm)],[f15,f167])).
% 1.60/1.30 thf(f167,plain,(
% 1.60/1.30 ( ! [X0 : $i] : ((c0 = X0) | (sK0 != X0)) )),
% 1.60/1.30 inference(superposition,[status(thm)],[f14,f83])).
% 1.60/1.30 thf(f83,plain,(
% 1.60/1.30 ( ! [X0 : $i] : (((cS @ (sK2 @ (^[Y0 : $i]: (~ (X0 = Y0))))) = X0) | (c0 = X0)) )),
% 1.60/1.30 inference(equality_proxy_clausification,[status(thm)],[f82])).
% 1.60/1.30 thf(f82,plain,(
% 1.60/1.30 ( ! [X0 : $i] : (((X0 = c0) = $true) | ((cS @ (sK2 @ (^[Y0 : $i]: (~ (X0 = Y0))))) = X0)) )),
% 1.60/1.30 inference(not_proxy_clausification,[status(thm)],[f81])).
% 1.60/1.30 thf(f81,plain,(
% 1.60/1.30 ( ! [X0 : $i] : (($false = (~ (X0 = c0))) | ((cS @ (sK2 @ (^[Y0 : $i]: (~ (X0 = Y0))))) = X0)) )),
% 1.60/1.30 inference(beta_eta_normalization,[status(thm)],[f63])).
% 1.60/1.30 thf(f63,plain,(
% 1.60/1.30 ( ! [X0 : $i] : (($false = ((^[Y0 : $i]: (~ (X0 = Y0))) @ c0)) | ((cS @ (sK2 @ (^[Y0 : $i]: (~ (X0 = Y0))))) = X0)) )),
% 1.60/1.30 inference(leibniz_equality_elimination,[status(thm)],[f27])).
% 1.60/1.30 thf(f27,plain,(
% 1.60/1.30 ( ! [X2 : $i,X1 : $i > $o] : (($false = (X1 @ (cS @ (sK2 @ X1)))) | ($true = (X1 @ X2)) | ((X1 @ c0) = $false)) )),
% 1.60/1.30 inference(pi_clausification,[status(thm)],[f24])).
% 1.60/1.30 thf(f24,plain,(
% 1.60/1.30 ( ! [X1 : $i > $o] : (($true = (!! @ $i @ X1)) | ((X1 @ c0) = $false) | ($false = (X1 @ (cS @ (sK2 @ X1))))) )),
% 1.60/1.30 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 1.60/1.30 thf(f23,plain,(
% 1.60/1.30 ( ! [X1 : $i > $o] : (($false = ((X1 @ (sK2 @ X1)) => (X1 @ (cS @ (sK2 @ X1))))) | ((X1 @ c0) = $false) | ($true = (!! @ $i @ X1))) )),
% 1.60/1.30 inference(beta_eta_normalization,[status(thm)],[f22])).
% 1.60/1.30 thf(f22,plain,(
% 1.60/1.30 ( ! [X1 : $i > $o] : (((X1 @ c0) = $false) | ($true = (!! @ $i @ X1)) | ($false = ((^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (cS @ Y0)))) @ (sK2 @ X1)))) )),
% 1.60/1.30 inference(sigma_clausification,[status(thm)],[f21])).
% 1.60/1.30 thf(f21,plain,(
% 1.60/1.30 ( ! [X1 : $i > $o] : (((X1 @ c0) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (cS @ Y0)))))) | ($true = (!! @ $i @ X1))) )),
% 1.60/1.30 inference(binary_proxy_clausification,[status(thm)],[f20])).
% 1.60/1.30 thf(f20,plain,(
% 1.60/1.30 ( ! [X1 : $i > $o] : ((((!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (cS @ Y0))))) & (X1 @ c0)) = $false) | ($true = (!! @ $i @ X1))) )),
% 1.60/1.30 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.60/1.30 thf(f19,plain,(
% 1.60/1.30 ( ! [X1 : $i > $o] : (((((!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (cS @ Y0))))) & (X1 @ c0)) => (!! @ $i @ X1)) = $true)) )),
% 1.60/1.30 inference(beta_eta_normalization,[status(thm)],[f18])).
% 1.60/1.30 thf(f18,plain,(
% 1.60/1.30 ( ! [X1 : $i > $o] : (($true = ((^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1))))) & (Y0 @ c0)) => (!! @ $i @ Y0))) @ X1))) )),
% 1.60/1.30 inference(pi_clausification,[status(thm)],[f17])).
% 1.60/1.30 thf(f17,plain,(
% 1.60/1.30 ($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1))))) & (Y0 @ c0)) => (!! @ $i @ Y0)))))),
% 1.60/1.30 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.60/1.30 thf(f16,plain,(
% 1.60/1.30 ($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1))))) & (Y0 @ c0)) => (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))))),
% 1.60/1.30 inference(definition_unfolding,[status(thm)],[f13,f12])).
% 1.60/1.30 thf(f12,plain,(
% 1.60/1.30 (cIND = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1))))) & (Y0 @ c0)) => (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))))),
% 1.60/1.30 inference(cnf_transformation,[status(thm)],[f8])).
% 1.60/1.30 thf(f8,plain,(
% 1.60/1.30 (cIND = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1))))) & (Y0 @ c0)) => (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))))),
% 1.60/1.30 inference(fool_elimination,[status(thm)],[f7])).
% 1.60/1.30 thf(f7,plain,(
% 1.60/1.30 (! [X0 : $i > $o] : (((X0 @ c0) & ! [X1 : $i] : ((X0 @ X1) => (X0 @ (cS @ X1)))) => ! [X2 : $i] : (X0 @ X2)) = cIND)),
% 1.60/1.30 inference(rectify,[status(thm)],[f1])).
% 1.60/1.30 thf(f1,axiom,(
% 1.60/1.30 (! [X0 : $i > $o] : (((X0 @ c0) & ! [X1 : $i] : ((X0 @ X1) => (X0 @ (cS @ X1)))) => ! [X1 : $i] : (X0 @ X1)) = cIND)),
% 1.60/1.30 file('/export/starexec/sandbox/tmp/tmp.co3plJG88Y/DTF2THF_17551.p',cIND_def)).
% 1.60/1.30 thf(f13,plain,(
% 1.60/1.30 (cIND = $true)),
% 1.60/1.30 inference(cnf_transformation,[status(thm)],[f11])).
% 1.60/1.30 thf(f11,plain,(
% 1.60/1.30 ((c0 != sK0) & ! [X1 : $i] : ((cS @ X1) != sK0)) & (cIND = $true)),
% 1.60/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f9,f10])).
% 1.60/1.30 thf(f10,plain,(
% 1.60/1.30 ? [X0 : $i] : ((c0 != X0) & ! [X1 : $i] : ((cS @ X1) != X0)) => ((c0 != sK0) & ! [X1 : $i] : ((cS @ X1) != sK0))),
% 1.60/1.30 introduced(definition,[],[choice_axiom])).
% 1.60/1.30 thf(f9,plain,(
% 1.60/1.30 ? [X0 : $i] : ((c0 != X0) & ! [X1 : $i] : ((cS @ X1) != X0)) & (cIND = $true)),
% 1.60/1.30 inference(ennf_transformation,[status(thm)],[f6])).
% 1.60/1.30 thf(f6,plain,(
% 1.60/1.30 ~((cIND = $true) => ! [X0 : $i] : ((c0 = X0) | ? [X1 : $i] : ((cS @ X1) = X0)))),
% 1.60/1.30 inference(fool_elimination,[status(thm)],[f5])).
% 1.60/1.30 thf(f5,plain,(
% 1.60/1.30 ~(cIND => ! [X0 : $i] : (? [X1 : $i] : ((cS @ X1) = X0) | (c0 = X0)))),
% 1.60/1.30 inference(rectify,[status(thm)],[f3])).
% 1.60/1.30 thf(f3,negated_conjecture,(
% 1.60/1.30 ~(cIND => ! [X2 : $i] : (? [X3 : $i] : ((cS @ X3) = X2) | (c0 = X2)))),
% 1.60/1.30 inference(negated_conjecture,[status(cth)],[f2])).
% 1.60/1.30 thf(f2,conjecture,(
% 1.60/1.30 cIND => ! [X2 : $i] : (? [X3 : $i] : ((cS @ X3) = X2) | (c0 = X2))),
% 1.60/1.30 file('/export/starexec/sandbox/tmp/tmp.co3plJG88Y/DTF2THF_17551.p',cTHM578)).
% 1.60/1.30 thf(f14,plain,(
% 1.60/1.30 ( ! [X1 : $i] : (((cS @ X1) != sK0)) )),
% 1.60/1.30 inference(cnf_transformation,[status(thm)],[f11])).
% 1.60/1.30 thf(f15,plain,(
% 1.60/1.30 (c0 != sK0)),
% 1.60/1.30 inference(cnf_transformation,[status(thm)],[f11])).
% 1.60/1.30 % SZS output end Proof for DTF2THF_17551
% 1.60/1.30 % (17878)------------------------------
% 1.60/1.30 % (17878)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.30 % (17878)Termination reason: Refutation
% 1.60/1.30
% 1.60/1.30 % (17878)Memory used [KB]: 5500
% 1.60/1.30 % (17878)Time elapsed: 0.011 s
% 1.60/1.30 % (17878)Instructions burned: 12 (million)
% 1.60/1.30 % (17878)------------------------------
% 1.60/1.30 % (17878)------------------------------
% 1.60/1.30 % (17877)Success in time 0.024 s
%------------------------------------------------------------------------------