%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : PUZ102^5 : 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 : n002.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 09:28:29 AM UTC 2026
% Result : Theorem 1.60s 1.33s
% Output : Refutation 1.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 115 ( 26 equ; 0 cnn)
% Maximal formula atoms : 2 ( 4 avg)
% Number of connectives : 201 ( 10 ~; 2 |; 9 &; 147 @)
% ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 4 usr; 4 con; 0-2 aty)
% ( 12 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 37 ( 24 ^; 11 !; 2 ?; 37 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
s: $i > $i ).
thf(func_def_1,type,
cCKB_E2: $i > $i > $o ).
thf(func_def_14,type,
sK2: $i > $o ).
thf(f31,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f29]) ).
thf(f29,plain,
$true = $false,
inference(superposition,[status(thm)],[f28,f20]) ).
thf(f20,plain,
( ( sK2 @ sK0 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
=> ( sK2 @ ( s @ ( s @ Y0 ) ) ) ) )
& ( sK2 @ sK0 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( $false
= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
=> ( sK2 @ ( s @ ( s @ Y0 ) ) ) ) )
& ( sK2 @ sK0 ) )
=> ( sK2 @ ( s @ ( s @ sK0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ ( s @ Y1 ) ) ) ) )
& ( Y0 @ sK0 ) )
=> ( Y0 @ ( s @ ( s @ sK0 ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( $true
!= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ ( s @ Y1 ) ) ) ) )
& ( Y0 @ sK0 ) )
=> ( Y0 @ ( s @ ( s @ sK0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( s @ ( s @ Y3 ) ) ) ) )
& ( Y2 @ Y0 ) )
=> ( Y2 @ Y1 ) ) )
@ sK0
@ ( s @ ( s @ sK0 ) ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f13,f12]) ).
thf(f12,plain,
( cCKB_E2
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( s @ ( s @ Y3 ) ) ) ) )
& ( Y2 @ Y0 ) )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( cCKB_E2
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( s @ ( s @ Y3 ) ) ) ) )
& ( Y2 @ Y0 ) )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ^ [X0: $i,X1: $i] :
! [X2: $i > $o] :
( ( ( X2 @ X0 )
& ! [X3: $i] :
( ( X2 @ X3 )
=> ( X2 @ ( s @ ( s @ X3 ) ) ) ) )
=> ( X2 @ X1 ) ) )
= cCKB_E2 ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: $i,X1: $i] :
! [X2: $i > $o] :
( ( ( X2 @ X0 )
& ! [X3: $i] :
( ( X2 @ X3 )
=> ( X2 @ ( s @ ( s @ X3 ) ) ) ) )
=> ( X2 @ X1 ) ) )
= cCKB_E2 ),
file('/export/starexec/sandbox2/tmp/tmp.BwFSWdykzk/DTF2THF_19364.p',cCKB_E2_def) ).
thf(f13,plain,
( $true
!= ( cCKB_E2 @ sK0 @ ( s @ ( s @ sK0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( $true
!= ( cCKB_E2 @ sK0 @ ( s @ ( s @ sK0 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f9,f10]) ).
thf(f10,plain,
( ? [X0: $i] :
( ( cCKB_E2 @ X0 @ ( s @ ( s @ X0 ) ) )
!= $true )
=> ( $true
!= ( cCKB_E2 @ sK0 @ ( s @ ( s @ sK0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
? [X0: $i] :
( ( cCKB_E2 @ X0 @ ( s @ ( s @ X0 ) ) )
!= $true ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
~ ! [X0: $i] :
( ( cCKB_E2 @ X0 @ ( s @ ( s @ X0 ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ! [X0: $i] : ( cCKB_E2 @ X0 @ ( s @ ( s @ X0 ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ! [X0: $i] : ( cCKB_E2 @ X0 @ ( s @ ( s @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
! [X0: $i] : ( cCKB_E2 @ X0 @ ( s @ ( s @ X0 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.BwFSWdykzk/DTF2THF_19364.p',cCKB_L33000) ).
thf(f28,plain,
( ( sK2 @ sK0 )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ( sK2 @ sK0 )
= $false )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f24,f18]) ).
thf(f18,plain,
( ( sK2 @ ( s @ ( s @ sK0 ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f24,plain,
! [X1: $i] :
( ( ( sK2 @ ( s @ ( s @ X1 ) ) )
= $true )
| ( $false
= ( sK2 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
! [X1: $i] :
( $true
= ( ( sK2 @ X1 )
=> ( sK2 @ ( s @ ( s @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f22]) ).
thf(f22,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( sK2 @ Y0 )
=> ( sK2 @ ( s @ ( s @ Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
=> ( sK2 @ ( s @ ( s @ Y0 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : PUZ102^5 : 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
% 0.16/0.34 % Computer : n002.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 11:33:03 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 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 : PUZ102^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% 0.30/0.46 % Domain : Puzzles
% 0.30/0.46 % Problem : TPS problem from CHECKERBOARD-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_0612 [Bro09]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.2.0
% 0.30/0.46 % Syntax : Number of formulae : 4 ( 2 unt; 2 typ; 1 def)
% 0.30/0.46 % Number of atoms : 3 ( 1 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 1 ( 1 avg)
% 0.30/0.46 % Number of connectives : 13 ( 0 ~; 0 |; 1 &; 10 @)
% 0.30/0.46 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 5 ( 3 avg)
% 0.30/0.46 % Number of types : 2 ( 0 usr)
% 0.30/0.46 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 3 ( 2 usr; 0 con; 1-2 aty)
% 0.30/0.46 % Number of variables : 5 ( 2 ^; 3 !; 0 ?; 5 :)
% 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 % Bugfixes : v5.2.0 - Added missing type declarations.
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(s_type,type,
% 0.30/0.46 s: $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(cCKB_E2_type,type,
% 0.30/0.46 cCKB_E2: $i > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(cCKB_E2_def,definition,
% 0.30/0.46 ( cCKB_E2
% 0.30/0.46 = ( ^ [Xx: $i,Xy: $i] :
% 0.30/0.46 ! [Xp: $i > $o] :
% 0.30/0.46 ( ( ( Xp @ Xx )
% 0.30/0.46 & ! [Xu: $i] :
% 0.30/0.46 ( ( Xp @ Xu )
% 0.30/0.46 => ( Xp @ ( s @ ( s @ Xu ) ) ) ) )
% 0.30/0.46 => ( Xp @ Xy ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(cCKB_L33000,conjecture,
% 0.30/0.46 ! [Xx: $i] : ( cCKB_E2 @ Xx @ ( s @ ( s @ Xx ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.43/1.29 ---- Embedded in THF ---
% 1.43/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.43/1.29 %%% Generated on Tue Feb 24 11:33:04 EST 2026
% 1.43/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.43/1.29 %%% Logic specification used:
% 1.43/1.29 %%% thf(spec, logic, $$dhol).
% 1.43/1.29
% 1.43/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.BwFSWdykzk/DTF2DTF19364.p
% See solution above
% 1.43/1.29 ------------------------
% 1.60/1.31 ---- Cleaned THF ---
% 1.60/1.31 thf(s_type,type,
% 1.60/1.31 s: $i > $i ).
% 1.60/1.31
% 1.60/1.31 thf(cCKB_E2_type,type,
% 1.60/1.31 cCKB_E2: $i > $i > $o ).
% 1.60/1.31
% 1.60/1.31 thf(cCKB_E2_def,definition,
% 1.60/1.31 ( cCKB_E2
% 1.60/1.31 = ( ^ [Xx: $i,Xy: $i] :
% 1.60/1.31 ! [Xp: $i > $o] :
% 1.60/1.31 ( ( ( Xp @ Xx )
% 1.60/1.31 & ! [Xu: $i] :
% 1.60/1.31 ( ( Xp @ Xu )
% 1.60/1.31 => ( Xp @ ( s @ ( s @ Xu ) ) ) ) )
% 1.60/1.31 => ( Xp @ Xy ) ) ) ) ).
% 1.60/1.31
% 1.60/1.31 thf(cCKB_L33000,conjecture,
% 1.60/1.31 ! [Xx: $i] : ( cCKB_E2 @ Xx @ ( s @ ( s @ Xx ) ) ) ).
% 1.60/1.31 ------------------------
% 1.60/1.32 % (19645)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_19364 for (2999ds/275Mi)
% 1.60/1.32 % (19645)Refutation not found, incomplete strategy
% 1.60/1.32 % (19645)------------------------------
% 1.60/1.32 % (19645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.32 % (19645)Termination reason: Refutation not found, incomplete strategy
% 1.60/1.32
% 1.60/1.32
% 1.60/1.32 % (19645)Memory used [KB]: 5373
% 1.60/1.32 % (19645)Time elapsed: 0.002 s
% 1.60/1.32 % (19645)Instructions burned: 1 (million)
% 1.60/1.32 % (19645)------------------------------
% 1.60/1.32 % (19645)------------------------------
% 1.60/1.33 % (19644)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_19364 for (2999ds/2Mi)
% 1.60/1.33 % (19644)Instruction limit reached!
% 1.60/1.33 % (19644)------------------------------
% 1.60/1.33 % (19644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.33 % (19644)Termination reason: Unknown
% 1.60/1.33 % (19644)Termination phase: Saturation
% 1.60/1.33
% 1.60/1.33 % (19644)Memory used [KB]: 5500
% 1.60/1.33 % (19644)Time elapsed: 0.003 s
% 1.60/1.33 % (19644)Instructions burned: 2 (million)
% 1.60/1.33 % (19644)------------------------------
% 1.60/1.33 % (19644)------------------------------
% 1.60/1.33 % (19640)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_19364 for (2999ds/183Mi)
% 1.60/1.33 % (19641)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_19364 for (2999ds/4Mi)
% 1.60/1.33 % (19642)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_19364 for (2999ds/27Mi)
% 1.60/1.33 % (19643)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_19364 for (2999ds/2Mi)
% 1.60/1.33 % (19646)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_19364 for (2999ds/18Mi)
% 1.60/1.33 % (19643)Instruction limit reached!
% 1.60/1.33 % (19643)------------------------------
% 1.60/1.33 % (19643)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.33 % (19643)Termination reason: Unknown
% 1.60/1.33 % (19643)Termination phase: Saturation
% 1.60/1.33
% 1.60/1.33 % (19643)Memory used [KB]: 5500
% 1.60/1.33 % (19643)Time elapsed: 0.004 s
% 1.60/1.33 % (19643)Instructions burned: 2 (million)
% 1.60/1.33 % (19643)------------------------------
% 1.60/1.33 % (19643)------------------------------
% 1.60/1.33 % (19640)First to succeed.
% 1.60/1.33 % (19641)Also succeeded, but the first one will report.
% 1.60/1.33 % (19647)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_19364 for (2999ds/3Mi)
% 1.60/1.33 % (19640)Refutation found. Thanks to Tanya!
% 1.60/1.33 % SZS status Theorem for DTF2THF_19364
% 1.60/1.33 % SZS output start Proof for DTF2THF_19364
% 1.60/1.33 thf(func_def_0, type, s: $i > $i).
% 1.60/1.33 thf(func_def_1, type, cCKB_E2: $i > $i > $o).
% 1.60/1.33 thf(func_def_14, type, sK2: $i > $o).
% 1.60/1.33 thf(f31,plain,(
% 1.60/1.33 $false),
% 1.60/1.33 inference(trivial_inequality_removal,[status(thm)],[f29])).
% 1.60/1.33 thf(f29,plain,(
% 1.60/1.33 ($true = $false)),
% 1.60/1.33 inference(superposition,[status(thm)],[f28,f20])).
% 1.60/1.33 thf(f20,plain,(
% 1.60/1.33 ((sK2 @ sK0) = $true)),
% 1.60/1.33 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.60/1.33 thf(f19,plain,(
% 1.60/1.33 ($true = ((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) => (sK2 @ (s @ (s @ Y0)))))) & (sK2 @ sK0)))),
% 1.60/1.33 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.60/1.33 thf(f17,plain,(
% 1.60/1.33 ($false = (((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) => (sK2 @ (s @ (s @ Y0)))))) & (sK2 @ sK0)) => (sK2 @ (s @ (s @ sK0)))))),
% 1.60/1.33 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.60/1.33 thf(f16,plain,(
% 1.60/1.33 (((^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (s @ (s @ Y1)))))) & (Y0 @ sK0)) => (Y0 @ (s @ (s @ sK0))))) @ sK2) = $false)),
% 1.60/1.33 inference(sigma_clausification,[status(thm)],[f15])).
% 1.60/1.33 thf(f15,plain,(
% 1.60/1.33 ($true != (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (s @ (s @ Y1)))))) & (Y0 @ sK0)) => (Y0 @ (s @ (s @ sK0)))))))),
% 1.60/1.33 inference(beta_eta_normalization,[status(thm)],[f14])).
% 1.60/1.33 thf(f14,plain,(
% 1.60/1.33 (((^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y2 @ (s @ (s @ Y3)))))) & (Y2 @ Y0)) => (Y2 @ Y1))))))) @ sK0 @ (s @ (s @ sK0))) != $true)),
% 1.60/1.33 inference(definition_unfolding,[status(thm)],[f13,f12])).
% 1.60/1.33 thf(f12,plain,(
% 1.60/1.33 (cCKB_E2 = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y2 @ (s @ (s @ Y3)))))) & (Y2 @ Y0)) => (Y2 @ Y1))))))))),
% 1.60/1.33 inference(cnf_transformation,[status(thm)],[f6])).
% 1.60/1.33 thf(f6,plain,(
% 1.60/1.33 (cCKB_E2 = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y2 @ (s @ (s @ Y3)))))) & (Y2 @ Y0)) => (Y2 @ Y1))))))))),
% 1.60/1.33 inference(fool_elimination,[status(thm)],[f5])).
% 1.60/1.33 thf(f5,plain,(
% 1.60/1.33 ((^[X0 : $i, X1 : $i] : (! [X2 : $i > $o] : (((X2 @ X0) & ! [X3 : $i] : ((X2 @ X3) => (X2 @ (s @ (s @ X3))))) => (X2 @ X1)))) = cCKB_E2)),
% 1.60/1.33 inference(rectify,[status(thm)],[f1])).
% 1.60/1.33 thf(f1,axiom,(
% 1.60/1.33 ((^[X0 : $i, X1 : $i] : (! [X2 : $i > $o] : (((X2 @ X0) & ! [X3 : $i] : ((X2 @ X3) => (X2 @ (s @ (s @ X3))))) => (X2 @ X1)))) = cCKB_E2)),
% 1.60/1.33 file('/export/starexec/sandbox2/tmp/tmp.BwFSWdykzk/DTF2THF_19364.p',cCKB_E2_def)).
% 1.60/1.33 thf(f13,plain,(
% 1.60/1.33 ($true != (cCKB_E2 @ sK0 @ (s @ (s @ sK0))))),
% 1.60/1.33 inference(cnf_transformation,[status(thm)],[f11])).
% 1.60/1.33 thf(f11,plain,(
% 1.60/1.33 ($true != (cCKB_E2 @ sK0 @ (s @ (s @ sK0))))),
% 1.60/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f9,f10])).
% 1.60/1.33 thf(f10,plain,(
% 1.60/1.33 ? [X0 : $i] : ((cCKB_E2 @ X0 @ (s @ (s @ X0))) != $true) => ($true != (cCKB_E2 @ sK0 @ (s @ (s @ sK0))))),
% 1.60/1.33 introduced(definition,[],[choice_axiom])).
% 1.60/1.33 thf(f9,plain,(
% 1.60/1.33 ? [X0 : $i] : ((cCKB_E2 @ X0 @ (s @ (s @ X0))) != $true)),
% 1.60/1.33 inference(ennf_transformation,[status(thm)],[f8])).
% 1.60/1.33 thf(f8,plain,(
% 1.60/1.33 ~! [X0 : $i] : ((cCKB_E2 @ X0 @ (s @ (s @ X0))) = $true)),
% 1.60/1.33 inference(fool_elimination,[status(thm)],[f7])).
% 1.60/1.33 thf(f7,plain,(
% 1.60/1.33 ~! [X0 : $i] : (cCKB_E2 @ X0 @ (s @ (s @ X0)))),
% 1.60/1.33 inference(rectify,[status(thm)],[f3])).
% 1.60/1.33 thf(f3,negated_conjecture,(
% 1.60/1.33 ~! [X0 : $i] : (cCKB_E2 @ X0 @ (s @ (s @ X0)))),
% 1.60/1.33 inference(negated_conjecture,[status(cth)],[f2])).
% 1.60/1.33 thf(f2,conjecture,(
% 1.60/1.33 ! [X0 : $i] : (cCKB_E2 @ X0 @ (s @ (s @ X0)))),
% 1.60/1.33 file('/export/starexec/sandbox2/tmp/tmp.BwFSWdykzk/DTF2THF_19364.p',cCKB_L33000)).
% 1.60/1.33 thf(f28,plain,(
% 1.60/1.33 ((sK2 @ sK0) = $false)),
% 1.60/1.33 inference(trivial_inequality_removal,[status(thm)],[f25])).
% 1.60/1.33 thf(f25,plain,(
% 1.60/1.33 ((sK2 @ sK0) = $false) | ($true = $false)),
% 1.60/1.33 inference(superposition,[status(thm)],[f24,f18])).
% 1.60/1.33 thf(f18,plain,(
% 1.60/1.33 ((sK2 @ (s @ (s @ sK0))) = $false)),
% 1.60/1.33 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.60/1.33 thf(f24,plain,(
% 1.60/1.33 ( ! [X1 : $i] : (((sK2 @ (s @ (s @ X1))) = $true) | ($false = (sK2 @ X1))) )),
% 1.60/1.33 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 1.60/1.33 thf(f23,plain,(
% 1.60/1.33 ( ! [X1 : $i] : (($true = ((sK2 @ X1) => (sK2 @ (s @ (s @ X1)))))) )),
% 1.60/1.33 inference(beta_eta_normalization,[status(thm)],[f22])).
% 1.60/1.33 thf(f22,plain,(
% 1.60/1.33 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((sK2 @ Y0) => (sK2 @ (s @ (s @ Y0))))) @ X1) = $true)) )),
% 1.60/1.33 inference(pi_clausification,[status(thm)],[f21])).
% 1.60/1.33 thf(f21,plain,(
% 1.60/1.33 ((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) => (sK2 @ (s @ (s @ Y0)))))) = $true)),
% 1.60/1.33 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.60/1.33 % SZS output end Proof for DTF2THF_19364
% 1.60/1.33 % (19640)------------------------------
% 1.60/1.33 % (19640)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.33 % (19640)Termination reason: Refutation
% 1.60/1.33
% 1.60/1.33 % (19640)Memory used [KB]: 5500
% 1.60/1.33 % (19640)Time elapsed: 0.005 s
% 1.60/1.33 % (19640)Instructions burned: 2 (million)
% 1.60/1.33 % (19640)------------------------------
% 1.60/1.33 % (19640)------------------------------
% 1.60/1.33 % (19639)Success in time 0.021 s
%------------------------------------------------------------------------------