%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO309^5 : TPTP v9.2.1. Released v4.0.0.
% 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 09:53:55 AM UTC 2026
% Result : Theorem 1.54s 1.24s
% Output : Refutation 1.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 19 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 105 ( 29 equ; 0 cnn)
% Maximal formula atoms : 2 ( 5 avg)
% Number of connectives : 313 ( 29 ~; 0 |; 0 &; 236 @)
% ( 6 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 5 usr; 4 con; 0-2 aty)
% ( 10 !!; 26 ??; 0 @@+; 0 @@-)
% Number of variables : 88 ( 65 ^; 14 !; 9 ?; 88 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cS: $i > $i ).
thf(func_def_1,type,
cQ: $i > $i ).
thf(func_def_2,type,
cR: $i > $i > $o ).
thf(func_def_15,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
sK2: ( $i > $o ) > $i ).
thf(f37,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f36]) ).
thf(f36,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( cR
@ ( sK2
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( cR @ Y1 @ ( cQ @ Y2 ) ) ) )
@ ( cQ @ Y0 ) ) )
!= ( ?? @ $i
@ ^ [Y0: $i] :
( cR
@ ( sK2
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( cR @ Y1 @ ( cQ @ Y2 ) ) ) )
@ ( cQ @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( cR
@ ( sK2
@ ^ [Y1: $i] :
( ?? @ $i
@ ( ^ [Y2: $i,Y3: $i] :
( cR
@ ( ^ [Y4: $i,Y5: $i] : Y4
@ Y2
@ Y3 )
@ ( ^ [Y4: $i,Y5: $i] :
( cQ
@ ( ^ [Y6: $i,Y7: $i] : Y7
@ Y4
@ Y5 ) )
@ Y2
@ Y3 ) )
@ Y1 ) ) )
@ ( cQ @ Y0 ) ) )
!= ( ^ [Y0: $i] :
( ?? @ $i
@ ( ^ [Y1: $i,Y2: $i] :
( cR
@ ( ^ [Y3: $i,Y4: $i] : Y3
@ Y1
@ Y2 )
@ ( ^ [Y3: $i,Y4: $i] :
( cQ
@ ( ^ [Y5: $i,Y6: $i] : Y6
@ Y3
@ Y4 ) )
@ Y1
@ Y2 ) )
@ Y0 ) )
@ ( sK2
@ ^ [Y0: $i] :
( ?? @ $i
@ ( ^ [Y1: $i,Y2: $i] :
( cR
@ ( ^ [Y3: $i,Y4: $i] : Y3
@ Y1
@ Y2 )
@ ( ^ [Y3: $i,Y4: $i] :
( cQ
@ ( ^ [Y5: $i,Y6: $i] : Y6
@ Y3
@ Y4 ) )
@ Y1
@ Y2 ) )
@ Y0 ) ) ) ) ),
inference(superposition,[status(thm)],[f17,f12]) ).
thf(f12,plain,
! [X1: $i] :
( ( ?? @ $i
@ ^ [Y0: $i] : ( cR @ X1 @ ( cQ @ Y0 ) ) )
= ( ~ ( ?? @ $i
@ ^ [Y0: $i] : ( cR @ ( cS @ X1 ) @ ( cQ @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
! [X1: $i] :
( ( ( ?? @ $i
@ ^ [Y0: $i] : ( cR @ X1 @ ( cQ @ Y0 ) ) )
= ( ~ ( ?? @ $i
@ ^ [Y0: $i] : ( cR @ ( cS @ X1 ) @ ( cQ @ Y0 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] : ( cR @ Y0 @ ( cQ @ Y1 ) ) )
= ( ~ ( ?? @ $i
@ ^ [Y1: $i] : ( cR @ ( cS @ Y0 ) @ ( cQ @ Y1 ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f9]) ).
thf(f9,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] : ( cR @ Y0 @ ( cQ @ Y1 ) ) )
= ( ~ ( ?? @ $i
@ ^ [Y1: $i] : ( cR @ ( cS @ Y0 ) @ ( cQ @ Y1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] : ( cR @ Y0 @ ( cQ @ Y1 ) ) )
= ( ~ ( ?? @ $i
@ ^ [Y1: $i] : ( cR @ ( cS @ Y0 ) @ ( cQ @ Y1 ) ) ) ) ) )
=> ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
= ( ~ ( Y0 @ ( cS @ Y1 ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] : ( cR @ Y0 @ ( cQ @ Y1 ) ) )
= ( ~ ( ?? @ $i
@ ^ [Y1: $i] : ( cR @ ( cS @ Y0 ) @ ( cQ @ Y1 ) ) ) ) ) )
=> ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
= ( ~ ( Y0 @ ( cS @ Y1 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] : ( cR @ Y0 @ ( cQ @ Y1 ) ) )
= ( ~ ( ?? @ $i
@ ^ [Y1: $i] : ( cR @ ( cS @ Y0 ) @ ( cQ @ Y1 ) ) ) ) ) )
=> ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
= ( ~ ( Y0 @ ( cS @ Y1 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: $i] :
( ? [X1: $i] : ( cR @ X0 @ ( cQ @ X1 ) )
<=> ~ ? [X2: $i] : ( cR @ ( cS @ X0 ) @ ( cQ @ X2 ) ) )
=> ? [X3: $i > $o] :
! [X4: $i] :
( ( X3 @ X4 )
<=> ~ ( X3 @ ( cS @ X4 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: $i] :
( ? [X1: $i] : ( cR @ X0 @ ( cQ @ X1 ) )
<=> ~ ? [X2: $i] : ( cR @ ( cS @ X0 ) @ ( cQ @ X2 ) ) )
=> ? [X3: $i > $o] :
! [X0: $i] :
( ( X3 @ X0 )
<=> ~ ( X3 @ ( cS @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X0: $i] :
( ? [X1: $i] : ( cR @ X0 @ ( cQ @ X1 ) )
<=> ~ ? [X2: $i] : ( cR @ ( cS @ X0 ) @ ( cQ @ X2 ) ) )
=> ? [X3: $i > $o] :
! [X0: $i] :
( ( X3 @ X0 )
<=> ~ ( X3 @ ( cS @ X0 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ozFSI7NMtX/DTF2THF_23805.p',cEO1) ).
thf(f17,plain,
! [X1: $i > $o] :
( ( ~ ( X1 @ ( cS @ ( sK2 @ X1 ) ) ) )
!= ( X1 @ ( sK2 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
! [X1: $i > $o] :
( ( ( X1 @ ( sK2 @ X1 ) )
= ( ~ ( X1 @ ( cS @ ( sK2 @ X1 ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f15]) ).
thf(f15,plain,
! [X1: $i > $o] :
( $false
= ( ^ [Y0: $i] :
( ( X1 @ Y0 )
= ( ~ ( X1 @ ( cS @ Y0 ) ) ) )
@ ( sK2 @ X1 ) ) ),
inference(sigma_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
! [X1: $i > $o] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
= ( ~ ( X1 @ ( cS @ Y0 ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f13]) ).
thf(f13,plain,
! [X1: $i > $o] :
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
= ( ~ ( Y0 @ ( cS @ Y1 ) ) ) ) )
@ X1 )
= $false ),
inference(pi_clausification,[status(thm)],[f8]) ).
thf(f8,plain,
( $false
= ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
= ( ~ ( Y0 @ ( cS @ Y1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO309^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n006.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % 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 14:27:45 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
% 0.30/0.45 ---- Original DTF file ---
% 0.30/0.45 thf(spec,logic,$$dhol).
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 % File : SYO309^5 : TPTP v9.2.1. Released v4.0.0.
% 0.30/0.45 % Domain : Syntactic
% 0.30/0.45 % Problem : TPS problem from BASIC-HO-THMS
% 0.30/0.45 % Version : Especial.
% 0.30/0.45 % English :
% 0.30/0.45
% 0.30/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.30/0.45 % Source : [Bro09]
% 0.30/0.45 % Names : tps_0833 [Bro09]
% 0.30/0.45
% 0.30/0.45 % Status : Theorem
% 0.30/0.45 % Rating : 0.58 v9.1.0, 0.50 v8.2.0, 0.55 v8.1.0, 0.42 v7.4.0, 0.44 v7.3.0, 0.50 v7.2.0, 0.38 v7.1.0, 0.43 v7.0.0, 0.50 v6.4.0, 0.43 v6.3.0, 0.33 v6.2.0, 0.67 v6.1.0, 0.50 v6.0.0, 0.67 v5.5.0, 0.80 v5.4.0, 0.75 v5.2.0, 0.50 v4.1.0, 0.67 v4.0.0
% 0.30/0.45 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.30/0.45 % Number of atoms : 2 ( 0 equ; 0 cnn)
% 0.30/0.45 % Maximal formula atoms : 2 ( 2 avg)
% 0.30/0.45 % Number of connectives : 15 ( 2 ~; 0 |; 0 &; 10 @)
% 0.30/0.45 % ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% 0.30/0.45 % Maximal formula depth : 9 ( 9 avg)
% 0.30/0.45 % Number of types : 2 ( 0 usr)
% 0.30/0.45 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.30/0.45 % Number of symbols : 3 ( 3 usr; 0 con; 1-2 aty)
% 0.30/0.45 % Number of variables : 5 ( 0 ^; 2 !; 3 ?; 5 :)
% 0.30/0.45 % SPC : TH0_THM_NEQ_NAR
% 0.30/0.45
% 0.30/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.30/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.30/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.30/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 thf(cS,type,
% 0.30/0.45 cS: $i > $i ).
% 0.30/0.45
% 0.30/0.45 thf(cQ,type,
% 0.30/0.45 cQ: $i > $i ).
% 0.30/0.45
% 0.30/0.45 thf(cR,type,
% 0.30/0.45 cR: $i > $i > $o ).
% 0.30/0.45
% 0.30/0.45 thf(cEO1,conjecture,
% 0.30/0.45 ( ! [Xx: $i] :
% 0.30/0.45 ( ? [Xu: $i] : ( cR @ Xx @ ( cQ @ Xu ) )
% 0.30/0.45 <=> ~ ? [Xv: $i] : ( cR @ ( cS @ Xx ) @ ( cQ @ Xv ) ) )
% 0.30/0.45 => ? [A: $i > $o] :
% 0.30/0.45 ! [Xx: $i] :
% 0.30/0.45 ( ( A @ Xx )
% 0.30/0.45 <=> ~ ( A @ ( cS @ Xx ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 ------------------------
% 1.39/1.19 ---- Embedded in THF ---
% 1.39/1.19 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.39/1.19 %%% Generated on Tue Feb 24 14:27:46 EST 2026
% 1.39/1.19 %%% using '$$dhol' embedding, version 1.3.0.
% 1.39/1.19 %%% Logic specification used:
% 1.39/1.19 %%% thf(spec, logic, $$dhol).
% 1.39/1.19
% 1.39/1.19 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.ozFSI7NMtX/DTF2DTF23805.p
% See solution above
% 1.39/1.19 ------------------------
% 1.54/1.20 ---- Cleaned THF ---
% 1.54/1.20 thf(cS,type,
% 1.54/1.20 cS: $i > $i ).
% 1.54/1.20
% 1.54/1.20 thf(cQ,type,
% 1.54/1.20 cQ: $i > $i ).
% 1.54/1.20
% 1.54/1.20 thf(cR,type,
% 1.54/1.20 cR: $i > $i > $o ).
% 1.54/1.20
% 1.54/1.20 thf(cEO1,conjecture,
% 1.54/1.20 ( ! [Xx: $i] :
% 1.54/1.20 ( ? [Xu: $i] : ( cR @ Xx @ ( cQ @ Xu ) )
% 1.54/1.20 <=> ~ ? [Xv: $i] : ( cR @ ( cS @ Xx ) @ ( cQ @ Xv ) ) )
% 1.54/1.20 => ? [A: $i > $o] :
% 1.54/1.20 ! [Xx: $i] :
% 1.54/1.20 ( ( A @ Xx )
% 1.54/1.20 <=> ~ ( A @ ( cS @ Xx ) ) ) ) ).
% 1.54/1.20 ------------------------
% 1.54/1.22 % (23999)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_23805 for (3000ds/4Mi)
% 1.54/1.22 % (24000)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_23805 for (3000ds/27Mi)
% 1.54/1.22 % (24002)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_23805 for (3000ds/2Mi)
% 1.54/1.22 % (24003)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_23805 for (3000ds/275Mi)
% 1.54/1.22 % (24002)Instruction limit reached!
% 1.54/1.22 % (24002)------------------------------
% 1.54/1.22 % (24002)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.22 % (24002)Termination reason: Unknown
% 1.54/1.22 % (24002)Termination phase: Saturation
% 1.54/1.22
% 1.54/1.22 % (24002)Memory used [KB]: 5500
% 1.54/1.22 % (24002)Time elapsed: 0.002 s
% 1.54/1.22 % (24002)Instructions burned: 2 (million)
% 1.54/1.22 % (24002)------------------------------
% 1.54/1.22 % (24002)------------------------------
% 1.54/1.22 % (23999)Instruction limit reached!
% 1.54/1.22 % (23999)------------------------------
% 1.54/1.22 % (23999)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.22 % (23999)Termination reason: Unknown
% 1.54/1.22 % (23999)Termination phase: Saturation
% 1.54/1.22
% 1.54/1.22 % (23999)Memory used [KB]: 5500
% 1.54/1.22 % (23999)Time elapsed: 0.004 s
% 1.54/1.22 % (23999)Instructions burned: 5 (million)
% 1.54/1.22 % (23999)------------------------------
% 1.54/1.22 % (23999)------------------------------
% 1.54/1.22 % (24000)Refutation not found, incomplete strategy
% 1.54/1.22 % (24000)------------------------------
% 1.54/1.22 % (24000)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.22 % (24000)Termination reason: Refutation not found, incomplete strategy
% 1.54/1.22
% 1.54/1.22
% 1.54/1.22 % (24000)Memory used [KB]: 5500
% 1.54/1.22 % (24000)Time elapsed: 0.004 s
% 1.54/1.22 % (24000)Instructions burned: 3 (million)
% 1.54/1.22 % (24000)------------------------------
% 1.54/1.22 % (24000)------------------------------
% 1.54/1.22 % (24003)Refutation not found, incomplete strategy
% 1.54/1.22 % (24003)------------------------------
% 1.54/1.22 % (24003)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.22 % (24003)Termination reason: Refutation not found, incomplete strategy
% 1.54/1.22
% 1.54/1.22
% 1.54/1.22 % (24003)Memory used [KB]: 5500
% 1.54/1.22 % (24003)Time elapsed: 0.005 s
% 1.54/1.22 % (24003)Instructions burned: 10 (million)
% 1.54/1.22 % (24003)------------------------------
% 1.54/1.22 % (24003)------------------------------
% 1.54/1.23 % (24001)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_23805 for (3000ds/2Mi)
% 1.54/1.23 % (23998)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_23805 for (3000ds/183Mi)
% 1.54/1.23 % (24004)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_23805 for (3000ds/18Mi)
% 1.54/1.23 % (24001)Instruction limit reached!
% 1.54/1.23 % (24001)------------------------------
% 1.54/1.23 % (24001)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.23 % (24001)Termination reason: Unknown
% 1.54/1.23 % (24001)Termination phase: Saturation
% 1.54/1.23
% 1.54/1.23 % (24001)Memory used [KB]: 5373
% 1.54/1.23 % (24001)Time elapsed: 0.004 s
% 1.54/1.23 % (24001)Instructions burned: 2 (million)
% 1.54/1.23 % (24001)------------------------------
% 1.54/1.23 % (24001)------------------------------
% 1.54/1.23 % (24017)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_23805 for (2999ds/3Mi)
% 1.54/1.23 % (24017)Instruction limit reached!
% 1.54/1.23 % (24017)------------------------------
% 1.54/1.23 % (24017)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.23 % (24017)Termination reason: Unknown
% 1.54/1.23 % (24017)Termination phase: Saturation
% 1.54/1.23
% 1.54/1.23 % (24017)Memory used [KB]: 5500
% 1.54/1.23 % (24017)Time elapsed: 0.003 s
% 1.54/1.23 % (24017)Instructions burned: 4 (million)
% 1.54/1.23 % (24017)------------------------------
% 1.54/1.23 % (24017)------------------------------
% 1.54/1.24 % (24015)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_23805 for (2999ds/37Mi)
% 1.54/1.24 % (24016)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_23805 for (2999ds/15Mi)
% 1.54/1.24 % (24014)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_23805 for (2999ds/3Mi)
% 1.54/1.24 % (24014)Instruction limit reached!
% 1.54/1.24 % (24014)------------------------------
% 1.54/1.24 % (24014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.24 % (24014)Termination reason: Unknown
% 1.54/1.24 % (24014)Termination phase: Saturation
% 1.54/1.24
% 1.54/1.24 % (24014)Memory used [KB]: 5500
% 1.54/1.24 % (24014)Time elapsed: 0.004 s
% 1.54/1.24 % (24014)Instructions burned: 4 (million)
% 1.54/1.24 % (24014)------------------------------
% 1.54/1.24 % (24014)------------------------------
% 1.54/1.24 % (24015)First to succeed.
% 1.54/1.24 % (24016)Instruction limit reached!
% 1.54/1.24 % (24016)------------------------------
% 1.54/1.24 % (24016)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.24 % (24016)Termination reason: Unknown
% 1.54/1.24 % (24016)Termination phase: Saturation
% 1.54/1.24
% 1.54/1.24 % (24016)Memory used [KB]: 5500
% 1.54/1.24 % (24016)Time elapsed: 0.008 s
% 1.54/1.24 % (24016)Instructions burned: 16 (million)
% 1.54/1.24 % (24016)------------------------------
% 1.54/1.24 % (24016)------------------------------
% 1.54/1.24 % (24015)Refutation found. Thanks to Tanya!
% 1.54/1.24 % SZS status Theorem for DTF2THF_23805
% 1.54/1.24 % SZS output start Proof for DTF2THF_23805
% 1.54/1.24 thf(func_def_0, type, cS: $i > $i).
% 1.54/1.24 thf(func_def_1, type, cQ: $i > $i).
% 1.54/1.24 thf(func_def_2, type, cR: $i > $i > $o).
% 1.54/1.24 thf(func_def_15, type, ph1: !>[X0: $tType]:(X0)).
% 1.54/1.24 thf(func_def_16, type, sK2: ($i > $o) > $i).
% 1.54/1.24 thf(f37,plain,(
% 1.54/1.24 $false),
% 1.54/1.24 inference(trivial_inequality_removal,[status(thm)],[f36])).
% 1.54/1.24 thf(f36,plain,(
% 1.54/1.24 ((?? @ $i @ (^[Y0 : $i]: (cR @ (sK2 @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (cR @ Y1 @ (cQ @ Y2)))))) @ (cQ @ Y0)))) != (?? @ $i @ (^[Y0 : $i]: (cR @ (sK2 @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (cR @ Y1 @ (cQ @ Y2)))))) @ (cQ @ Y0)))))),
% 1.54/1.24 inference(beta_eta_normalization,[status(thm)],[f33])).
% 1.54/1.24 thf(f33,plain,(
% 1.54/1.24 ((?? @ $i @ (^[Y0 : $i]: (cR @ (sK2 @ (^[Y1 : $i]: (?? @ $i @ ((^[Y2 : $i]: ((^[Y3 : $i]: (cR @ ((^[Y4 : $i]: ((^[Y5 : $i]: (Y4)))) @ Y2 @ Y3) @ ((^[Y4 : $i]: ((^[Y5 : $i]: (cQ @ ((^[Y6 : $i]: ((^[Y7 : $i]: (Y7)))) @ Y4 @ Y5))))) @ Y2 @ Y3))))) @ Y1)))) @ (cQ @ Y0)))) != ((^[Y0 : $i]: (?? @ $i @ ((^[Y1 : $i]: ((^[Y2 : $i]: (cR @ ((^[Y3 : $i]: ((^[Y4 : $i]: (Y3)))) @ Y1 @ Y2) @ ((^[Y3 : $i]: ((^[Y4 : $i]: (cQ @ ((^[Y5 : $i]: ((^[Y6 : $i]: (Y6)))) @ Y3 @ Y4))))) @ Y1 @ Y2))))) @ Y0))) @ (sK2 @ (^[Y0 : $i]: (?? @ $i @ ((^[Y1 : $i]: ((^[Y2 : $i]: (cR @ ((^[Y3 : $i]: ((^[Y4 : $i]: (Y3)))) @ Y1 @ Y2) @ ((^[Y3 : $i]: ((^[Y4 : $i]: (cQ @ ((^[Y5 : $i]: ((^[Y6 : $i]: (Y6)))) @ Y3 @ Y4))))) @ Y1 @ Y2))))) @ Y0))))))),
% 1.54/1.24 inference(superposition,[status(thm)],[f17,f12])).
% 1.54/1.24 thf(f12,plain,(
% 1.54/1.24 ( ! [X1 : $i] : (((?? @ $i @ (^[Y0 : $i]: (cR @ X1 @ (cQ @ Y0)))) = (~ (?? @ $i @ (^[Y0 : $i]: (cR @ (cS @ X1) @ (cQ @ Y0))))))) )),
% 1.54/1.24 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.54/1.24 thf(f11,plain,(
% 1.54/1.24 ( ! [X1 : $i] : ((((?? @ $i @ (^[Y0 : $i]: (cR @ X1 @ (cQ @ Y0)))) = (~ (?? @ $i @ (^[Y0 : $i]: (cR @ (cS @ X1) @ (cQ @ Y0)))))) = $true)) )),
% 1.54/1.24 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.54/1.24 thf(f10,plain,(
% 1.54/1.24 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (cR @ Y0 @ (cQ @ Y1)))) = (~ (?? @ $i @ (^[Y1 : $i]: (cR @ (cS @ Y0) @ (cQ @ Y1))))))) @ X1))) )),
% 1.54/1.24 inference(pi_clausification,[status(thm)],[f9])).
% 1.54/1.24 thf(f9,plain,(
% 1.54/1.24 ($true = (!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (cR @ Y0 @ (cQ @ Y1)))) = (~ (?? @ $i @ (^[Y1 : $i]: (cR @ (cS @ Y0) @ (cQ @ Y1)))))))))),
% 1.54/1.24 inference(binary_proxy_clausification,[status(thm)],[f7])).
% 1.54/1.24 thf(f7,plain,(
% 1.54/1.24 (((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (cR @ Y0 @ (cQ @ Y1)))) = (~ (?? @ $i @ (^[Y1 : $i]: (cR @ (cS @ Y0) @ (cQ @ Y1)))))))) => (?? @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) = (~ (Y0 @ (cS @ Y1))))))))) = $false)),
% 1.54/1.24 inference(not_proxy_clausification,[status(thm)],[f6])).
% 1.54/1.24 thf(f6,plain,(
% 1.54/1.24 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (cR @ Y0 @ (cQ @ Y1)))) = (~ (?? @ $i @ (^[Y1 : $i]: (cR @ (cS @ Y0) @ (cQ @ Y1)))))))) => (?? @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) = (~ (Y0 @ (cS @ Y1)))))))))))),
% 1.54/1.24 inference(cnf_transformation,[status(thm)],[f5])).
% 1.54/1.24 thf(f5,plain,(
% 1.54/1.24 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (cR @ Y0 @ (cQ @ Y1)))) = (~ (?? @ $i @ (^[Y1 : $i]: (cR @ (cS @ Y0) @ (cQ @ Y1)))))))) => (?? @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) = (~ (Y0 @ (cS @ Y1)))))))))))),
% 1.54/1.24 inference(fool_elimination,[status(thm)],[f4])).
% 1.54/1.24 thf(f4,plain,(
% 1.54/1.24 ~(! [X0 : $i] : (? [X1 : $i] : (cR @ X0 @ (cQ @ X1)) <=> ~? [X2 : $i] : (cR @ (cS @ X0) @ (cQ @ X2))) => ? [X3 : $i > $o] : ! [X4 : $i] : ((X3 @ X4) <=> ~(X3 @ (cS @ X4))))),
% 1.54/1.24 inference(rectify,[status(thm)],[f2])).
% 1.54/1.24 thf(f2,negated_conjecture,(
% 1.54/1.24 ~(! [X0 : $i] : (? [X1 : $i] : (cR @ X0 @ (cQ @ X1)) <=> ~? [X2 : $i] : (cR @ (cS @ X0) @ (cQ @ X2))) => ? [X3 : $i > $o] : ! [X0 : $i] : ((X3 @ X0) <=> ~(X3 @ (cS @ X0))))),
% 1.54/1.24 inference(negated_conjecture,[status(cth)],[f1])).
% 1.54/1.24 thf(f1,conjecture,(
% 1.54/1.24 ! [X0 : $i] : (? [X1 : $i] : (cR @ X0 @ (cQ @ X1)) <=> ~? [X2 : $i] : (cR @ (cS @ X0) @ (cQ @ X2))) => ? [X3 : $i > $o] : ! [X0 : $i] : ((X3 @ X0) <=> ~(X3 @ (cS @ X0)))),
% 1.54/1.24 file('/export/starexec/sandbox/tmp/tmp.ozFSI7NMtX/DTF2THF_23805.p',cEO1)).
% 1.54/1.24 thf(f17,plain,(
% 1.54/1.24 ( ! [X1 : $i > $o] : (((~ (X1 @ (cS @ (sK2 @ X1)))) != (X1 @ (sK2 @ X1)))) )),
% 1.54/1.24 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 1.54/1.24 thf(f16,plain,(
% 1.54/1.24 ( ! [X1 : $i > $o] : ((((X1 @ (sK2 @ X1)) = (~ (X1 @ (cS @ (sK2 @ X1))))) = $false)) )),
% 1.54/1.24 inference(beta_eta_normalization,[status(thm)],[f15])).
% 1.54/1.24 thf(f15,plain,(
% 1.54/1.24 ( ! [X1 : $i > $o] : (($false = ((^[Y0 : $i]: ((X1 @ Y0) = (~ (X1 @ (cS @ Y0))))) @ (sK2 @ X1)))) )),
% 1.54/1.24 inference(sigma_clausification,[status(thm)],[f14])).
% 1.54/1.24 thf(f14,plain,(
% 1.54/1.24 ( ! [X1 : $i > $o] : (((!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) = (~ (X1 @ (cS @ Y0)))))) = $false)) )),
% 1.54/1.24 inference(beta_eta_normalization,[status(thm)],[f13])).
% 1.54/1.24 thf(f13,plain,(
% 1.54/1.24 ( ! [X1 : $i > $o] : ((((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) = (~ (Y0 @ (cS @ Y1))))))) @ X1) = $false)) )),
% 1.54/1.24 inference(pi_clausification,[status(thm)],[f8])).
% 1.54/1.24 thf(f8,plain,(
% 1.54/1.24 ($false = (?? @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) = (~ (Y0 @ (cS @ Y1)))))))))),
% 1.54/1.24 inference(binary_proxy_clausification,[status(thm)],[f7])).
% 1.54/1.24 % SZS output end Proof for DTF2THF_23805
% 1.54/1.24 % (24015)------------------------------
% 1.54/1.24 % (24015)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.24 % (24015)Termination reason: Refutation
% 1.54/1.24
% 1.54/1.24 % (24015)Memory used [KB]: 5628
% 1.54/1.24 % (24015)Time elapsed: 0.007 s
% 1.54/1.24 % (24015)Instructions burned: 14 (million)
% 1.54/1.24 % (24015)------------------------------
% 1.54/1.24 % (24015)------------------------------
% 1.54/1.24 % (23995)Success in time 0.03 s
%------------------------------------------------------------------------------