%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV236^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n017.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 09:40:37 AM UTC 2026
% Result : Theorem 1.51s 1.29s
% Output : Refutation 1.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 1
% Syntax : Number of formulae : 28 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 186 ( 24 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 436 ( 5 ~; 0 |; 17 &; 281 @)
% ( 0 <=>; 72 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 62 ( 62 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 6 usr; 7 con; 0-2 aty)
% ( 50 !!; 11 ??; 0 @@+; 0 @@-)
% Number of variables : 103 ( 74 ^; 26 !; 3 ?; 103 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
cS: a > $o ).
thf(func_def_2,type,
cK: ( a > $o ) > a > $o ).
thf(func_def_16,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
sK2: a ).
thf(func_def_18,type,
sK3: a ).
thf(func_def_19,type,
sK4: a ).
thf(f53,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f52]) ).
thf(f52,plain,
$true = $false,
inference(beta_eta_normalization,[status(thm)],[f51]) ).
thf(f51,plain,
( ( ^ [Y0: a] : $true
@ sK4 )
= $false ),
inference(sigma_clausification,[status(thm)],[f50]) ).
thf(f50,plain,
( ( !! @ a
@ ^ [Y0: a] : $true )
= $false ),
inference(boolean_simplification,[status(thm)],[f49]) ).
thf(f49,plain,
( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( cS @ Y0 )
=> ( cS @ Y0 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f48]) ).
thf(f48,plain,
( $false
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( ( cS @ Y0 )
=> ( cS @ Y0 ) ) ) ) ),
inference(superposition,[status(thm)],[f46,f40]) ).
thf(f40,plain,
( ( cS @ sK3 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
( ( ( cS @ sK3 )
=> ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK3 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cS @ Y1 ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f37]) ).
thf(f37,plain,
( ( ^ [Y0: a] :
( ( cS @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cS @ Y2 ) ) ) ) ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( cS @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cS @ Y2 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
( $true
= ( ~ ( !! @ a
@ ^ [Y0: a] :
( ( cS @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cS @ Y2 ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f32]) ).
thf(f32,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( cS @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cS @ Y2 ) ) ) ) ) ) )
=> $false )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( cS @ Y0 )
=> ( ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y1 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cS @ Y3 ) ) ) ) )
@ Y0 ) ) )
=> $false )
= $true ),
inference(superposition,[status(thm)],[f27,f10]) ).
thf(f10,plain,
( ( !! @ a
@ ^ [Y0: a] :
( ( cK @ cS @ Y0 )
=> ( cK
@ ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y1 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cS @ Y3 ) ) ) ) )
@ Y0 ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( $false
= ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( cK @ Y0 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y0: a] :
( ( cK @ cS @ Y0 )
=> ( cK
@ ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y1 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cS @ Y3 ) ) ) ) )
@ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ~ ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( cK @ Y0 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y0: a] :
( ( cK @ cS @ Y0 )
=> ( cK
@ ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y1 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cS @ Y3 ) ) ) ) )
@ Y0 ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ~ ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( cK @ Y0 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y0: a] :
( ( cK @ cS @ Y0 )
=> ( cK
@ ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y1 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cS @ Y3 ) ) ) ) )
@ Y0 ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: a > $o,X1: a > $o] :
( ! [X2: a] :
( ( X1 @ X2 )
=> ( X0 @ X2 ) )
=> ! [X3: a] :
( ( cK @ X1 @ X3 )
=> ( cK @ X0 @ X3 ) ) )
=> ! [X4: a] :
( ( cK @ cS @ X4 )
=> ( cK
@ ^ [X5: a] :
? [X6: a > $o] :
( ! [X7: a] :
( ( X6 @ X7 )
=> ( cS @ X7 ) )
& ( X6 @ X5 ) )
@ X4 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X1: a > $o,X0: a > $o] :
( ! [X2: a] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) )
=> ! [X2: a] :
( ( cK @ X0 @ X2 )
=> ( cK @ X1 @ X2 ) ) )
=> ! [X2: a] :
( ( cK @ cS @ X2 )
=> ( cK
@ ^ [X3: a] :
? [X4: a > $o] :
( ! [X5: a] :
( ( X4 @ X5 )
=> ( cS @ X5 ) )
& ( X4 @ X3 ) )
@ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X1: a > $o,X0: a > $o] :
( ! [X2: a] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) )
=> ! [X2: a] :
( ( cK @ X0 @ X2 )
=> ( cK @ X1 @ X2 ) ) )
=> ! [X2: a] :
( ( cK @ cS @ X2 )
=> ( cK
@ ^ [X3: a] :
? [X4: a > $o] :
( ! [X5: a] :
( ( X4 @ X5 )
=> ( cS @ X5 ) )
& ( X4 @ X3 ) )
@ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.TTDOxoUNhA/DTF2THF_26628.p',cTHM91_pme) ).
thf(f27,plain,
! [X2: a > $o,X1: a > $o] :
( ( ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( X2 @ Y0 ) ) )
=> ( !! @ a
@ ^ [Y0: a] :
( ( cK @ X1 @ Y0 )
=> ( cK @ X2 @ Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f26]) ).
thf(f26,plain,
! [X2: a > $o,X1: a > $o] :
( ( ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( ( X1 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( cK @ X1 @ Y1 )
=> ( cK @ Y0 @ Y1 ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
! [X1: a > $o] :
( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( ( X1 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( cK @ X1 @ Y1 )
=> ( cK @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f24]) ).
thf(f24,plain,
! [X1: a > $o] :
( ( ^ [Y0: a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( cK @ Y0 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( cK @ Y0 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f7]) ).
thf(f46,plain,
! [X1: a > $o] :
( ( ( X1 @ sK3 )
& ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( cS @ Y0 ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f45]) ).
thf(f45,plain,
! [X1: a > $o] :
( ( ^ [Y0: a > $o] :
( ( Y0 @ sK3 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cS @ Y1 ) ) ) )
@ X1 )
= $false ),
inference(pi_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
( ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK3 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cS @ Y1 ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV236^5 : TPTP v9.2.1. Released v4.0.0.
% 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n017.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 12:40:56 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
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.46 thf(spec,logic,$$dhol).
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % File : SEV236^5 : TPTP v9.2.1. Released v4.0.0.
% 0.31/0.46 % Domain : Set Theory (Sets of sets)
% 0.31/0.46 % Problem : TPS problem THM91
% 0.31/0.46 % Version : Especial.
% 0.31/0.46 % English :
% 0.31/0.46
% 0.31/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.31/0.46 % Source : [Bro09]
% 0.31/0.46 % Names : tps_0463 [Bro09]
% 0.31/0.46 % : THM91 [TPS]
% 0.31/0.46
% 0.31/0.46 % Status : Theorem
% 0.31/0.46 % Rating : 0.00 v8.1.0, 0.08 v7.4.0, 0.00 v6.2.0, 0.17 v6.1.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.1.0, 0.33 v4.0.0
% 0.31/0.46 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.31/0.46 % Number of atoms : 6 ( 0 equ; 0 cnn)
% 0.31/0.46 % Maximal formula atoms : 6 ( 6 avg)
% 0.31/0.46 % Number of connectives : 20 ( 0 ~; 0 |; 1 &; 13 @)
% 0.31/0.46 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 0.31/0.46 % Maximal formula depth : 12 ( 12 avg)
% 0.31/0.46 % Number of types : 2 ( 1 usr)
% 0.31/0.46 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.31/0.46 % Number of symbols : 2 ( 2 usr; 0 con; 1-2 aty)
% 0.31/0.46 % Number of variables : 8 ( 1 ^; 6 !; 1 ?; 8 :)
% 0.31/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.31/0.46
% 0.31/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.31/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.31/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.31/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.31/0.46 % : Polymorphic definitions expanded.
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 thf(a_type,type,
% 0.31/0.46 a: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(cS,type,
% 0.31/0.46 cS: a > $o ).
% 0.31/0.46
% 0.31/0.46 thf(cK,type,
% 0.31/0.46 cK: ( a > $o ) > a > $o ).
% 0.31/0.46
% 0.31/0.46 thf(cTHM91_pme,conjecture,
% 0.31/0.46 ( ! [X: a > $o,Y: a > $o] :
% 0.31/0.46 ( ! [Xx: a] :
% 0.31/0.46 ( ( X @ Xx )
% 0.31/0.46 => ( Y @ Xx ) )
% 0.31/0.46 => ! [Xx: a] :
% 0.31/0.46 ( ( cK @ X @ Xx )
% 0.31/0.46 => ( cK @ Y @ Xx ) ) )
% 0.31/0.46 => ! [Xx: a] :
% 0.31/0.46 ( ( cK @ cS @ Xx )
% 0.31/0.46 => ( cK
% 0.31/0.46 @ ^ [Xx0: a] :
% 0.31/0.46 ? [S_3: a > $o] :
% 0.31/0.46 ( ! [Xx1: a] :
% 0.31/0.46 ( ( S_3 @ Xx1 )
% 0.31/0.46 => ( cS @ Xx1 ) )
% 0.31/0.46 & ( S_3 @ Xx0 ) )
% 0.31/0.46 @ Xx ) ) ) ).
% 0.31/0.46
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 ------------------------
% 1.51/1.22 ---- Embedded in THF ---
% 1.51/1.22 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.51/1.22 %%% Generated on Tue Feb 24 12:40:57 EST 2026
% 1.51/1.22 %%% using '$$dhol' embedding, version 1.3.0.
% 1.51/1.22 %%% Logic specification used:
% 1.51/1.22 %%% thf(spec, logic, $$dhol).
% 1.51/1.22
% 1.51/1.22 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.TTDOxoUNhA/DTF2DTF26628.p
% See solution above
% 1.51/1.22 ------------------------
% 1.51/1.23 ---- Cleaned THF ---
% 1.51/1.23 thf(a_type,type,
% 1.51/1.23 a: $tType ).
% 1.51/1.23
% 1.51/1.23 thf(cS,type,
% 1.51/1.23 cS: a > $o ).
% 1.51/1.23
% 1.51/1.23 thf(cK,type,
% 1.51/1.23 cK: ( a > $o ) > a > $o ).
% 1.51/1.23
% 1.51/1.23 thf(cTHM91_pme,conjecture,
% 1.51/1.23 ( ! [X: a > $o,Y: a > $o] :
% 1.51/1.23 ( ! [Xx: a] :
% 1.51/1.23 ( ( X @ Xx )
% 1.51/1.23 => ( Y @ Xx ) )
% 1.51/1.23 => ! [Xx: a] :
% 1.51/1.23 ( ( cK @ X @ Xx )
% 1.51/1.23 => ( cK @ Y @ Xx ) ) )
% 1.51/1.23 => ! [Xx: a] :
% 1.51/1.23 ( ( cK @ cS @ Xx )
% 1.51/1.23 => ( cK
% 1.51/1.23 @ ^ [Xx0: a] :
% 1.51/1.23 ? [S_3: a > $o] :
% 1.51/1.23 ( ! [Xx1: a] :
% 1.51/1.23 ( ( S_3 @ Xx1 )
% 1.51/1.23 => ( cS @ Xx1 ) )
% 1.51/1.23 & ( S_3 @ Xx0 ) )
% 1.51/1.23 @ Xx ) ) ) ).
% 1.51/1.23 ------------------------
% 1.51/1.24 % (26773)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_26628 for (2999ds/183Mi)
% 1.51/1.24 % (26779)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_26628 for (2999ds/18Mi)
% 1.51/1.24 % (26777)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_26628 for (2999ds/2Mi)
% 1.51/1.24 % (26777)Instruction limit reached!
% 1.51/1.24 % (26777)------------------------------
% 1.51/1.24 % (26777)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.24 % (26777)Termination reason: Unknown
% 1.51/1.24 % (26777)Termination phase: Saturation
% 1.51/1.24
% 1.51/1.24 % (26777)Memory used [KB]: 5500
% 1.51/1.24 % (26777)Time elapsed: 0.002 s
% 1.51/1.24 % (26777)Instructions burned: 2 (million)
% 1.51/1.24 % (26777)------------------------------
% 1.51/1.24 % (26777)------------------------------
% 1.51/1.25 % (26774)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_26628 for (2999ds/4Mi)
% 1.51/1.25 % (26779)Instruction limit reached!
% 1.51/1.25 % (26779)------------------------------
% 1.51/1.25 % (26779)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.25 % (26779)Termination reason: Unknown
% 1.51/1.25 % (26779)Termination phase: Saturation
% 1.51/1.25
% 1.51/1.25 % (26779)Memory used [KB]: 5628
% 1.51/1.25 % (26779)Time elapsed: 0.008 s
% 1.51/1.25 % (26779)Instructions burned: 20 (million)
% 1.51/1.25 % (26779)------------------------------
% 1.51/1.25 % (26779)------------------------------
% 1.51/1.25 % (26775)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_26628 for (2999ds/27Mi)
% 1.51/1.25 % (26778)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_26628 for (2999ds/275Mi)
% 1.51/1.25 % (26776)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_26628 for (2999ds/2Mi)
% 1.51/1.25 % (26774)Instruction limit reached!
% 1.51/1.25 % (26774)------------------------------
% 1.51/1.25 % (26774)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.25 % (26774)Termination reason: Unknown
% 1.51/1.25 % (26774)Termination phase: Saturation
% 1.51/1.25
% 1.51/1.25 % (26774)Memory used [KB]: 5500
% 1.51/1.25 % (26774)Time elapsed: 0.005 s
% 1.51/1.25 % (26774)Instructions burned: 4 (million)
% 1.51/1.25 % (26774)------------------------------
% 1.51/1.25 % (26774)------------------------------
% 1.51/1.25 % (26775)Refutation not found, incomplete strategy
% 1.51/1.25 % (26775)------------------------------
% 1.51/1.25 % (26775)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.25 % (26775)Termination reason: Refutation not found, incomplete strategy
% 1.51/1.25
% 1.51/1.25
% 1.51/1.25 % (26775)Memory used [KB]: 5500
% 1.51/1.25 % (26775)Time elapsed: 0.005 s
% 1.51/1.25 % (26775)Instructions burned: 2 (million)
% 1.51/1.25 % (26775)------------------------------
% 1.51/1.25 % (26775)------------------------------
% 1.51/1.25 % (26776)Instruction limit reached!
% 1.51/1.25 % (26776)------------------------------
% 1.51/1.25 % (26776)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.25 % (26776)Termination reason: Unknown
% 1.51/1.25 % (26776)Termination phase: Saturation
% 1.51/1.25
% 1.51/1.25 % (26776)Memory used [KB]: 5500
% 1.51/1.25 % (26776)Time elapsed: 0.004 s
% 1.51/1.25 % (26776)Instructions burned: 2 (million)
% 1.51/1.25 % (26776)------------------------------
% 1.51/1.25 % (26776)------------------------------
% 1.51/1.26 % (26783)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_26628 for (2999ds/37Mi)
% 1.51/1.26 % (26780)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_26628 for (2999ds/3Mi)
% 1.51/1.26 % (26780)Instruction limit reached!
% 1.51/1.26 % (26780)------------------------------
% 1.51/1.26 % (26780)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.26 % (26780)Termination reason: Unknown
% 1.51/1.26 % (26780)Termination phase: Saturation
% 1.51/1.26
% 1.51/1.26 % (26780)Memory used [KB]: 5500
% 1.51/1.26 % (26780)Time elapsed: 0.006 s
% 1.51/1.26 % (26780)Instructions burned: 3 (million)
% 1.51/1.26 % (26780)------------------------------
% 1.51/1.26 % (26780)------------------------------
% 1.51/1.27 % (26788)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_26628 for (2999ds/3Mi)
% 1.51/1.27 % (26788)Instruction limit reached!
% 1.51/1.27 % (26788)------------------------------
% 1.51/1.27 % (26788)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.27 % (26788)Termination reason: Unknown
% 1.51/1.27 % (26788)Termination phase: Saturation
% 1.51/1.27
% 1.51/1.27 % (26788)Memory used [KB]: 5500
% 1.51/1.27 % (26788)Time elapsed: 0.004 s
% 1.51/1.27 % (26788)Instructions burned: 4 (million)
% 1.51/1.27 % (26788)------------------------------
% 1.51/1.27 % (26788)------------------------------
% 1.51/1.27 % (26787)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_26628 for (2999ds/15Mi)
% 1.51/1.27 % (26783)Instruction limit reached!
% 1.51/1.27 % (26783)------------------------------
% 1.51/1.27 % (26783)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.27 % (26783)Termination reason: Unknown
% 1.51/1.27 % (26783)Termination phase: Saturation
% 1.51/1.27
% 1.51/1.27 % (26783)Memory used [KB]: 6012
% 1.51/1.27 % (26783)Time elapsed: 0.017 s
% 1.51/1.27 % (26783)Instructions burned: 37 (million)
% 1.51/1.27 % (26783)------------------------------
% 1.51/1.27 % (26783)------------------------------
% 1.51/1.28 % (26789)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_26628 for (2999ds/1041Mi)
% 1.51/1.28 % (26787)Instruction limit reached!
% 1.51/1.28 % (26787)------------------------------
% 1.51/1.28 % (26787)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.28 % (26787)Termination reason: Unknown
% 1.51/1.28 % (26787)Termination phase: Saturation
% 1.51/1.28
% 1.51/1.28 % (26787)Memory used [KB]: 5628
% 1.51/1.28 % (26787)Time elapsed: 0.012 s
% 1.51/1.28 % (26787)Instructions burned: 16 (million)
% 1.51/1.28 % (26787)------------------------------
% 1.51/1.28 % (26787)------------------------------
% 1.51/1.28 % (26789)First to succeed.
% 1.51/1.28 % (26802)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_26628 for (2999ds/3Mi)
% 1.51/1.29 % (26799)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_26628 for (2999ds/7Mi)
% 1.51/1.29 % (26802)Instruction limit reached!
% 1.51/1.29 % (26802)------------------------------
% 1.51/1.29 % (26802)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.29 % (26802)Termination reason: Unknown
% 1.51/1.29 % (26802)Termination phase: Saturation
% 1.51/1.29
% 1.51/1.29 % (26802)Memory used [KB]: 5500
% 1.51/1.29 % (26802)Time elapsed: 0.003 s
% 1.51/1.29 % (26802)Instructions burned: 5 (million)
% 1.51/1.29 % (26802)------------------------------
% 1.51/1.29 % (26802)------------------------------
% 1.51/1.29 % (26789)Refutation found. Thanks to Tanya!
% 1.51/1.29 % SZS status Theorem for DTF2THF_26628
% 1.51/1.29 % SZS output start Proof for DTF2THF_26628
% 1.51/1.29 thf(type_def_5, type, a: $tType).
% 1.51/1.29 thf(func_def_0, type, a: $tType).
% 1.51/1.29 thf(func_def_1, type, cS: a > $o).
% 1.51/1.29 thf(func_def_2, type, cK: (a > $o) > a > $o).
% 1.51/1.29 thf(func_def_16, type, ph1: !>[X0: $tType]:(X0)).
% 1.51/1.29 thf(func_def_17, type, sK2: a).
% 1.51/1.29 thf(func_def_18, type, sK3: a).
% 1.51/1.29 thf(func_def_19, type, sK4: a).
% 1.51/1.29 thf(f53,plain,(
% 1.51/1.29 $false),
% 1.51/1.29 inference(trivial_inequality_removal,[status(thm)],[f52])).
% 1.51/1.29 thf(f52,plain,(
% 1.51/1.29 ($true = $false)),
% 1.51/1.29 inference(beta_eta_normalization,[status(thm)],[f51])).
% 1.51/1.29 thf(f51,plain,(
% 1.51/1.29 (((^[Y0 : a]: ($true)) @ sK4) = $false)),
% 1.51/1.29 inference(sigma_clausification,[status(thm)],[f50])).
% 1.51/1.29 thf(f50,plain,(
% 1.51/1.29 ((!! @ a @ (^[Y0 : a]: ($true))) = $false)),
% 1.51/1.29 inference(boolean_simplification,[status(thm)],[f49])).
% 1.51/1.29 thf(f49,plain,(
% 1.51/1.29 ($false = (!! @ a @ (^[Y0 : a]: ((cS @ Y0) => (cS @ Y0)))))),
% 1.51/1.29 inference(boolean_simplification,[status(thm)],[f48])).
% 1.51/1.29 thf(f48,plain,(
% 1.51/1.29 ($false = ($true & (!! @ a @ (^[Y0 : a]: ((cS @ Y0) => (cS @ Y0))))))),
% 1.51/1.29 inference(superposition,[status(thm)],[f46,f40])).
% 1.51/1.29 thf(f40,plain,(
% 1.51/1.29 ((cS @ sK3) = $true)),
% 1.51/1.29 inference(binary_proxy_clausification,[status(thm)],[f38])).
% 1.51/1.29 thf(f38,plain,(
% 1.51/1.29 (((cS @ sK3) => (?? @ (a > $o) @ (^[Y0 : a > $o]: ((Y0 @ sK3) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (cS @ Y1)))))))) = $false)),
% 1.51/1.29 inference(beta_eta_normalization,[status(thm)],[f37])).
% 1.51/1.29 thf(f37,plain,(
% 1.51/1.29 (((^[Y0 : a]: ((cS @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cS @ Y2))))))))) @ sK3) = $false)),
% 1.51/1.29 inference(sigma_clausification,[status(thm)],[f34])).
% 1.51/1.29 thf(f34,plain,(
% 1.51/1.29 ($false = (!! @ a @ (^[Y0 : a]: ((cS @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cS @ Y2)))))))))))),
% 1.51/1.29 inference(not_proxy_clausification,[status(thm)],[f33])).
% 1.51/1.29 thf(f33,plain,(
% 1.51/1.29 ($true = (~ (!! @ a @ (^[Y0 : a]: ((cS @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cS @ Y2))))))))))))),
% 1.51/1.29 inference(boolean_simplification,[status(thm)],[f32])).
% 1.51/1.29 thf(f32,plain,(
% 1.51/1.29 (((!! @ a @ (^[Y0 : a]: ((cS @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cS @ Y2)))))))))) => $false) = $true)),
% 1.51/1.29 inference(beta_eta_normalization,[status(thm)],[f29])).
% 1.51/1.29 thf(f29,plain,(
% 1.51/1.29 (((!! @ a @ (^[Y0 : a]: ((cS @ Y0) => ((^[Y1 : a]: (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y2 @ Y1) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (cS @ Y3)))))))) @ Y0)))) => $false) = $true)),
% 1.51/1.29 inference(superposition,[status(thm)],[f27,f10])).
% 1.51/1.29 thf(f10,plain,(
% 1.51/1.29 ((!! @ a @ (^[Y0 : a]: ((cK @ cS @ Y0) => (cK @ (^[Y1 : a]: (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y2 @ Y1) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (cS @ Y3)))))))) @ Y0)))) = $false)),
% 1.51/1.29 inference(binary_proxy_clausification,[status(thm)],[f7])).
% 1.51/1.29 thf(f7,plain,(
% 1.51/1.29 ($false = ((!! @ (a > $o) @ (^[Y0 : a > $o]: (!! @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y0 @ Y2) => (Y1 @ Y2)))) => (!! @ a @ (^[Y2 : a]: ((cK @ Y0 @ Y2) => (cK @ Y1 @ Y2))))))))) => (!! @ a @ (^[Y0 : a]: ((cK @ cS @ Y0) => (cK @ (^[Y1 : a]: (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y2 @ Y1) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (cS @ Y3)))))))) @ Y0))))))),
% 1.51/1.29 inference(not_proxy_clausification,[status(thm)],[f6])).
% 1.51/1.29 thf(f6,plain,(
% 1.51/1.29 ((~ ((!! @ (a > $o) @ (^[Y0 : a > $o]: (!! @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y0 @ Y2) => (Y1 @ Y2)))) => (!! @ a @ (^[Y2 : a]: ((cK @ Y0 @ Y2) => (cK @ Y1 @ Y2))))))))) => (!! @ a @ (^[Y0 : a]: ((cK @ cS @ Y0) => (cK @ (^[Y1 : a]: (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y2 @ Y1) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (cS @ Y3)))))))) @ Y0)))))) = $true)),
% 1.51/1.29 inference(cnf_transformation,[status(thm)],[f5])).
% 1.51/1.29 thf(f5,plain,(
% 1.51/1.29 ((~ ((!! @ (a > $o) @ (^[Y0 : a > $o]: (!! @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y0 @ Y2) => (Y1 @ Y2)))) => (!! @ a @ (^[Y2 : a]: ((cK @ Y0 @ Y2) => (cK @ Y1 @ Y2))))))))) => (!! @ a @ (^[Y0 : a]: ((cK @ cS @ Y0) => (cK @ (^[Y1 : a]: (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y2 @ Y1) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (cS @ Y3)))))))) @ Y0)))))) = $true)),
% 1.51/1.29 inference(fool_elimination,[status(thm)],[f4])).
% 1.51/1.29 thf(f4,plain,(
% 1.51/1.29 ~(! [X0 : a > $o,X1 : a > $o] : (! [X2 : a] : ((X1 @ X2) => (X0 @ X2)) => ! [X3 : a] : ((cK @ X1 @ X3) => (cK @ X0 @ X3))) => ! [X4 : a] : ((cK @ cS @ X4) => (cK @ (^[X5 : a] : (? [X6 : a > $o] : (! [X7 : a] : ((X6 @ X7) => (cS @ X7)) & (X6 @ X5)))) @ X4)))),
% 1.51/1.29 inference(rectify,[status(thm)],[f2])).
% 1.51/1.29 thf(f2,negated_conjecture,(
% 1.51/1.29 ~(! [X1 : a > $o,X0 : a > $o] : (! [X2 : a] : ((X0 @ X2) => (X1 @ X2)) => ! [X2 : a] : ((cK @ X0 @ X2) => (cK @ X1 @ X2))) => ! [X2 : a] : ((cK @ cS @ X2) => (cK @ (^[X3 : a] : (? [X4 : a > $o] : (! [X5 : a] : ((X4 @ X5) => (cS @ X5)) & (X4 @ X3)))) @ X2)))),
% 1.51/1.29 inference(negated_conjecture,[status(cth)],[f1])).
% 1.51/1.29 thf(f1,conjecture,(
% 1.51/1.29 ! [X1 : a > $o,X0 : a > $o] : (! [X2 : a] : ((X0 @ X2) => (X1 @ X2)) => ! [X2 : a] : ((cK @ X0 @ X2) => (cK @ X1 @ X2))) => ! [X2 : a] : ((cK @ cS @ X2) => (cK @ (^[X3 : a] : (? [X4 : a > $o] : (! [X5 : a] : ((X4 @ X5) => (cS @ X5)) & (X4 @ X3)))) @ X2))),
% 1.51/1.29 file('/export/starexec/sandbox2/tmp/tmp.TTDOxoUNhA/DTF2THF_26628.p',cTHM91_pme)).
% 1.51/1.29 thf(f27,plain,(
% 1.51/1.29 ( ! [X2 : a > $o,X1 : a > $o] : ((((!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (X2 @ Y0)))) => (!! @ a @ (^[Y0 : a]: ((cK @ X1 @ Y0) => (cK @ X2 @ Y0))))) = $true)) )),
% 1.51/1.29 inference(beta_eta_normalization,[status(thm)],[f26])).
% 1.51/1.29 thf(f26,plain,(
% 1.51/1.29 ( ! [X2 : a > $o,X1 : a > $o] : ((((^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((X1 @ Y1) => (Y0 @ Y1)))) => (!! @ a @ (^[Y1 : a]: ((cK @ X1 @ Y1) => (cK @ Y0 @ Y1)))))) @ X2) = $true)) )),
% 1.51/1.29 inference(pi_clausification,[status(thm)],[f25])).
% 1.51/1.29 thf(f25,plain,(
% 1.51/1.29 ( ! [X1 : a > $o] : (((!! @ (a > $o) @ (^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((X1 @ Y1) => (Y0 @ Y1)))) => (!! @ a @ (^[Y1 : a]: ((cK @ X1 @ Y1) => (cK @ Y0 @ Y1))))))) = $true)) )),
% 1.51/1.29 inference(beta_eta_normalization,[status(thm)],[f24])).
% 1.51/1.29 thf(f24,plain,(
% 1.51/1.29 ( ! [X1 : a > $o] : ((((^[Y0 : a > $o]: (!! @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y0 @ Y2) => (Y1 @ Y2)))) => (!! @ a @ (^[Y2 : a]: ((cK @ Y0 @ Y2) => (cK @ Y1 @ Y2)))))))) @ X1) = $true)) )),
% 1.51/1.29 inference(pi_clausification,[status(thm)],[f11])).
% 1.51/1.29 thf(f11,plain,(
% 1.51/1.29 ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (!! @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y0 @ Y2) => (Y1 @ Y2)))) => (!! @ a @ (^[Y2 : a]: ((cK @ Y0 @ Y2) => (cK @ Y1 @ Y2))))))))))),
% 1.51/1.29 inference(binary_proxy_clausification,[status(thm)],[f7])).
% 1.51/1.29 thf(f46,plain,(
% 1.51/1.29 ( ! [X1 : a > $o] : ((((X1 @ sK3) & (!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (cS @ Y0))))) = $false)) )),
% 1.51/1.29 inference(beta_eta_normalization,[status(thm)],[f45])).
% 1.51/1.29 thf(f45,plain,(
% 1.51/1.29 ( ! [X1 : a > $o] : ((((^[Y0 : a > $o]: ((Y0 @ sK3) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (cS @ Y1)))))) @ X1) = $false)) )),
% 1.51/1.29 inference(pi_clausification,[status(thm)],[f39])).
% 1.51/1.29 thf(f39,plain,(
% 1.51/1.29 ((?? @ (a > $o) @ (^[Y0 : a > $o]: ((Y0 @ sK3) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (cS @ Y1))))))) = $false)),
% 1.51/1.29 inference(binary_proxy_clausification,[status(thm)],[f38])).
% 1.51/1.29 % SZS output end Proof for DTF2THF_26628
% 1.51/1.29 % (26789)------------------------------
% 1.51/1.29 % (26789)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.29 % (26789)Termination reason: Refutation
% 1.51/1.29
% 1.51/1.29 % (26789)Memory used [KB]: 5500
% 1.51/1.29 % (26789)Time elapsed: 0.013 s
% 1.51/1.29 % (26789)Instructions burned: 12 (million)
% 1.51/1.29 % (26789)------------------------------
% 1.51/1.29 % (26789)------------------------------
% 1.51/1.29 % (26772)Success in time 0.05 s
%------------------------------------------------------------------------------