%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO287^5 : 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 : n025.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 09:53:51 AM UTC 2026
% Result : Theorem 1.49s 1.28s
% Output : Refutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1
% Syntax : Number of formulae : 12 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 64 ( 15 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 109 ( 5 ~; 11 |; 0 &; 82 @)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 5 usr; 5 con; 0-2 aty)
% ( 5 !!; 3 ??; 0 @@+; 0 @@-)
% Number of variables : 21 ( 10 ^; 8 !; 3 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cB: $i > $i > $o ).
thf(func_def_1,type,
cA: $i > $o ).
thf(func_def_15,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
sK2: ( $i > $i > $o ) > $i ).
thf(f20,plain,
$false,
inference(equality_resolution,[status(thm)],[f12]) ).
thf(f12,plain,
! [X1: $i > $i > $o] :
( ( ( cA @ ( sK2 @ X1 ) )
| ( cB @ ( sK2 @ X1 ) @ ( sK2 @ X1 ) ) )
!= ( X1 @ ( sK2 @ X1 ) @ c0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
! [X1: $i > $i > $o] :
( ( ( X1 @ ( sK2 @ X1 ) @ c0 )
= ( ( cA @ ( sK2 @ X1 ) )
| ( cB @ ( sK2 @ X1 ) @ ( sK2 @ X1 ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
! [X1: $i > $i > $o] :
( ( ^ [Y0: $i] :
( ( X1 @ Y0 @ c0 )
= ( ( cA @ Y0 )
| ( cB @ Y0 @ Y0 ) ) )
@ ( sK2 @ X1 ) )
= $false ),
inference(sigma_clausification,[status(thm)],[f9]) ).
thf(f9,plain,
! [X1: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 @ c0 )
= ( ( cA @ Y0 )
| ( cB @ Y0 @ Y0 ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f8]) ).
thf(f8,plain,
! [X1: $i > $i > $o] :
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 @ c0 )
= ( ( cA @ Y1 )
| ( cB @ Y1 @ Y1 ) ) ) )
@ X1 )
= $false ),
inference(pi_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( $false
= ( ?? @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 @ c0 )
= ( ( cA @ Y1 )
| ( cB @ Y1 @ Y1 ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( ?? @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 @ c0 )
= ( ( cA @ Y1 )
| ( cB @ Y1 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( ?? @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 @ c0 )
= ( ( cA @ Y1 )
| ( cB @ Y1 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ? [X0: $i > $i > $o] :
! [X1: $i] :
( ( X0 @ X1 @ c0 )
<=> ( ( cB @ X1 @ X1 )
| ( cA @ X1 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X0: $i > $i > $o] :
! [X1: $i] :
( ( X0 @ X1 @ c0 )
<=> ( ( cB @ X1 @ X1 )
| ( cA @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X0: $i > $i > $o] :
! [X1: $i] :
( ( X0 @ X1 @ c0 )
<=> ( ( cB @ X1 @ X1 )
| ( cA @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Qqsoi7wQO3/DTF2THF_14972.p',cSV9) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO287^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n025.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 14:27:42 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.45 ---- Original DTF file ---
% 0.19/0.45 thf(spec,logic,$$dhol).
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 % File : SYO287^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.45 % Domain : Syntactic
% 0.19/0.45 % Problem : TPS problem from BASIC-HO-THMS
% 0.19/0.45 % Version : Especial.
% 0.19/0.45 % English :
% 0.19/0.45
% 0.19/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.45 % Source : [Bro09]
% 0.19/0.45 % Names : tps_0693 [Bro09]
% 0.19/0.45
% 0.19/0.45 % Status : Theorem
% 0.19/0.45 % Rating : 0.42 v9.1.0, 0.50 v9.0.0, 0.42 v8.2.0, 0.36 v8.1.0, 0.42 v7.4.0, 0.33 v7.3.0, 0.40 v7.2.0, 0.25 v7.1.0, 0.29 v7.0.0, 0.50 v6.4.0, 0.43 v6.3.0, 0.33 v6.2.0, 0.50 v6.1.0, 0.33 v6.0.0, 0.50 v5.5.0, 0.60 v5.4.0, 0.75 v4.1.0, 0.67 v4.0.0
% 0.19/0.45 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.19/0.45 % Number of atoms : 2 ( 0 equ; 0 cnn)
% 0.19/0.45 % Maximal formula atoms : 2 ( 2 avg)
% 0.19/0.45 % Number of connectives : 7 ( 0 ~; 1 |; 0 &; 5 @)
% 0.19/0.45 % ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% 0.19/0.45 % Maximal formula depth : 7 ( 7 avg)
% 0.19/0.45 % Number of types : 2 ( 0 usr)
% 0.19/0.45 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.19/0.45 % Number of symbols : 3 ( 3 usr; 1 con; 0-2 aty)
% 0.19/0.45 % Number of variables : 2 ( 0 ^; 1 !; 1 ?; 2 :)
% 0.19/0.45 % SPC : TH0_THM_NEQ_NAR
% 0.19/0.45
% 0.19/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 thf(cB,type,
% 0.19/0.45 cB: $i > $i > $o ).
% 0.19/0.45
% 0.19/0.45 thf(cA,type,
% 0.19/0.45 cA: $i > $o ).
% 0.19/0.45
% 0.19/0.45 thf(c0,type,
% 0.19/0.45 c0: $i ).
% 0.19/0.45
% 0.19/0.45 thf(cSV9,conjecture,
% 0.19/0.45 ? [Xv: $i > $i > $o] :
% 0.19/0.45 ! [Xx: $i] :
% 0.19/0.45 ( ( Xv @ Xx @ c0 )
% 0.19/0.45 <=> ( ( cA @ Xx )
% 0.19/0.45 | ( cB @ Xx @ Xx ) ) ) ).
% 0.19/0.45
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 ------------------------
% 1.49/1.23 ---- Embedded in THF ---
% 1.49/1.23 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.23 %%% Generated on Tue Feb 24 14:27:43 EST 2026
% 1.49/1.23 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.23 %%% Logic specification used:
% 1.49/1.23 %%% thf(spec, logic, $$dhol).
% 1.49/1.23
% 1.49/1.23 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.Qqsoi7wQO3/DTF2DTF14972.p
% See solution above
% 1.49/1.23 ------------------------
% 1.49/1.23 ---- Cleaned THF ---
% 1.49/1.24 thf(cB,type,
% 1.49/1.24 cB: $i > $i > $o ).
% 1.49/1.24
% 1.49/1.24 thf(cA,type,
% 1.49/1.24 cA: $i > $o ).
% 1.49/1.24
% 1.49/1.24 thf(c0,type,
% 1.49/1.24 c0: $i ).
% 1.49/1.24
% 1.49/1.24 thf(cSV9,conjecture,
% 1.49/1.24 ? [Xv: $i > $i > $o] :
% 1.49/1.24 ! [Xx: $i] :
% 1.49/1.24 ( ( Xv @ Xx @ c0 )
% 1.49/1.24 <=> ( ( cA @ Xx )
% 1.49/1.24 | ( cB @ Xx @ Xx ) ) ) ).
% 1.49/1.24 ------------------------
% 1.49/1.25 % (15190)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_14972 for (3000ds/4Mi)
% 1.49/1.25 % (15190)Instruction limit reached!
% 1.49/1.25 % (15190)------------------------------
% 1.49/1.25 % (15190)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.25 % (15190)Termination reason: Unknown
% 1.49/1.25 % (15190)Termination phase: Saturation
% 1.49/1.25
% 1.49/1.25 % (15190)Memory used [KB]: 5500
% 1.49/1.25 % (15190)Time elapsed: 0.003 s
% 1.49/1.25 % (15190)Instructions burned: 4 (million)
% 1.49/1.25 % (15190)------------------------------
% 1.49/1.25 % (15190)------------------------------
% 1.49/1.26 % (15189)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_14972 for (3000ds/183Mi)
% 1.49/1.26 % (15191)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_14972 for (3000ds/27Mi)
% 1.49/1.26 % (15192)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_14972 for (3000ds/2Mi)
% 1.49/1.26 % (15193)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_14972 for (3000ds/2Mi)
% 1.49/1.26 % (15195)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_14972 for (3000ds/18Mi)
% 1.49/1.26 % (15194)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_14972 for (3000ds/275Mi)
% 1.49/1.26 % (15192)Instruction limit reached!
% 1.49/1.26 % (15192)------------------------------
% 1.49/1.26 % (15192)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.26 % (15192)Termination reason: Unknown
% 1.49/1.26 % (15192)Termination phase: Saturation
% 1.49/1.26
% 1.49/1.26 % (15192)Memory used [KB]: 5500
% 1.49/1.26 % (15192)Time elapsed: 0.004 s
% 1.49/1.26 % (15192)Instructions burned: 2 (million)
% 1.49/1.26 % (15192)------------------------------
% 1.49/1.26 % (15192)------------------------------
% 1.49/1.26 % (15193)Instruction limit reached!
% 1.49/1.26 % (15193)------------------------------
% 1.49/1.26 % (15193)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.26 % (15193)Termination reason: Unknown
% 1.49/1.26 % (15193)Termination phase: Saturation
% 1.49/1.26
% 1.49/1.26 % (15193)Memory used [KB]: 5500
% 1.49/1.26 % (15193)Time elapsed: 0.004 s
% 1.49/1.26 % (15193)Instructions burned: 3 (million)
% 1.49/1.26 % (15193)------------------------------
% 1.49/1.26 % (15193)------------------------------
% 1.49/1.26 % (15191)Refutation not found, incomplete strategy
% 1.49/1.26 % (15191)------------------------------
% 1.49/1.26 % (15191)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.26 % (15191)Termination reason: Refutation not found, incomplete strategy
% 1.49/1.26
% 1.49/1.26
% 1.49/1.26 % (15191)Memory used [KB]: 5500
% 1.49/1.26 % (15191)Time elapsed: 0.004 s
% 1.49/1.26 % (15191)Instructions burned: 2 (million)
% 1.49/1.26 % (15191)------------------------------
% 1.49/1.26 % (15191)------------------------------
% 1.49/1.26 % (15196)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_14972 for (2999ds/3Mi)
% 1.49/1.26 % (15196)Instruction limit reached!
% 1.49/1.26 % (15196)------------------------------
% 1.49/1.26 % (15196)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.26 % (15196)Termination reason: Unknown
% 1.49/1.26 % (15196)Termination phase: Saturation
% 1.49/1.26
% 1.49/1.26 % (15196)Memory used [KB]: 5500
% 1.49/1.26 % (15196)Time elapsed: 0.002 s
% 1.49/1.26 % (15196)Instructions burned: 3 (million)
% 1.49/1.26 % (15196)------------------------------
% 1.49/1.26 % (15196)------------------------------
% 1.49/1.26 % (15194)Refutation not found, incomplete strategy
% 1.49/1.26 % (15194)------------------------------
% 1.49/1.26 % (15194)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.26 % (15194)Termination reason: Refutation not found, incomplete strategy
% 1.49/1.26
% 1.49/1.26
% 1.49/1.26 % (15194)Memory used [KB]: 5500
% 1.49/1.26 % (15194)Time elapsed: 0.006 s
% 1.49/1.26 % (15194)Instructions burned: 5 (million)
% 1.49/1.26 % (15194)------------------------------
% 1.49/1.26 % (15194)------------------------------
% 1.49/1.27 % (15195)Instruction limit reached!
% 1.49/1.27 % (15195)------------------------------
% 1.49/1.27 % (15195)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.27 % (15195)Termination reason: Unknown
% 1.49/1.27 % (15195)Termination phase: Saturation
% 1.49/1.27
% 1.49/1.27 % (15195)Memory used [KB]: 5628
% 1.49/1.27 % (15195)Time elapsed: 0.013 s
% 1.49/1.27 % (15195)Instructions burned: 19 (million)
% 1.49/1.27 % (15195)------------------------------
% 1.49/1.27 % (15195)------------------------------
% 1.49/1.27 % (15200)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_14972 for (2999ds/1041Mi)
% 1.49/1.27 % (15197)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_14972 for (2999ds/37Mi)
% 1.49/1.27 % (15198)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_14972 for (2999ds/15Mi)
% 1.49/1.28 % (15199)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_14972 for (2999ds/3Mi)
% 1.49/1.28 % (15197)First to succeed.
% 1.49/1.28 % (15199)Instruction limit reached!
% 1.49/1.28 % (15199)------------------------------
% 1.49/1.28 % (15199)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.28 % (15199)Termination reason: Unknown
% 1.49/1.28 % (15199)Termination phase: Saturation
% 1.49/1.28
% 1.49/1.28 % (15199)Memory used [KB]: 5500
% 1.49/1.28 % (15199)Time elapsed: 0.004 s
% 1.49/1.28 % (15199)Instructions burned: 3 (million)
% 1.49/1.28 % (15199)------------------------------
% 1.49/1.28 % (15199)------------------------------
% 1.49/1.28 % (15201)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_14972 for (2999ds/7Mi)
% 1.49/1.28 % (15197)Refutation found. Thanks to Tanya!
% 1.49/1.28 % SZS status Theorem for DTF2THF_14972
% 1.49/1.28 % SZS output start Proof for DTF2THF_14972
% 1.49/1.28 thf(func_def_0, type, cB: $i > $i > $o).
% 1.49/1.28 thf(func_def_1, type, cA: $i > $o).
% 1.49/1.28 thf(func_def_15, type, ph1: !>[X0: $tType]:(X0)).
% 1.49/1.28 thf(func_def_16, type, sK2: ($i > $i > $o) > $i).
% 1.49/1.28 thf(f20,plain,(
% 1.49/1.28 $false),
% 1.49/1.28 inference(equality_resolution,[status(thm)],[f12])).
% 1.49/1.28 thf(f12,plain,(
% 1.49/1.28 ( ! [X1 : $i > $i > $o] : ((((cA @ (sK2 @ X1)) | (cB @ (sK2 @ X1) @ (sK2 @ X1))) != (X1 @ (sK2 @ X1) @ c0))) )),
% 1.49/1.28 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.49/1.28 thf(f11,plain,(
% 1.49/1.28 ( ! [X1 : $i > $i > $o] : ((((X1 @ (sK2 @ X1) @ c0) = ((cA @ (sK2 @ X1)) | (cB @ (sK2 @ X1) @ (sK2 @ X1)))) = $false)) )),
% 1.49/1.28 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.49/1.28 thf(f10,plain,(
% 1.49/1.28 ( ! [X1 : $i > $i > $o] : ((((^[Y0 : $i]: ((X1 @ Y0 @ c0) = ((cA @ Y0) | (cB @ Y0 @ Y0)))) @ (sK2 @ X1)) = $false)) )),
% 1.49/1.28 inference(sigma_clausification,[status(thm)],[f9])).
% 1.49/1.28 thf(f9,plain,(
% 1.49/1.28 ( ! [X1 : $i > $i > $o] : (((!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0 @ c0) = ((cA @ Y0) | (cB @ Y0 @ Y0))))) = $false)) )),
% 1.49/1.28 inference(beta_eta_normalization,[status(thm)],[f8])).
% 1.49/1.28 thf(f8,plain,(
% 1.49/1.28 ( ! [X1 : $i > $i > $o] : ((((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1 @ c0) = ((cA @ Y1) | (cB @ Y1 @ Y1)))))) @ X1) = $false)) )),
% 1.49/1.28 inference(pi_clausification,[status(thm)],[f7])).
% 1.49/1.28 thf(f7,plain,(
% 1.49/1.28 ($false = (?? @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1 @ c0) = ((cA @ Y1) | (cB @ Y1 @ Y1))))))))),
% 1.49/1.28 inference(not_proxy_clausification,[status(thm)],[f6])).
% 1.49/1.28 thf(f6,plain,(
% 1.49/1.28 ($true = (~ (?? @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1 @ c0) = ((cA @ Y1) | (cB @ Y1 @ Y1)))))))))),
% 1.49/1.28 inference(cnf_transformation,[status(thm)],[f5])).
% 1.49/1.28 thf(f5,plain,(
% 1.49/1.28 ($true = (~ (?? @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1 @ c0) = ((cA @ Y1) | (cB @ Y1 @ Y1)))))))))),
% 1.49/1.28 inference(fool_elimination,[status(thm)],[f4])).
% 1.49/1.28 thf(f4,plain,(
% 1.49/1.28 ~? [X0 : $i > $i > $o] : ! [X1 : $i] : ((X0 @ X1 @ c0) <=> ((cB @ X1 @ X1) | (cA @ X1)))),
% 1.49/1.28 inference(rectify,[status(thm)],[f2])).
% 1.49/1.28 thf(f2,negated_conjecture,(
% 1.49/1.28 ~? [X0 : $i > $i > $o] : ! [X1 : $i] : ((X0 @ X1 @ c0) <=> ((cB @ X1 @ X1) | (cA @ X1)))),
% 1.49/1.28 inference(negated_conjecture,[status(cth)],[f1])).
% 1.49/1.28 thf(f1,conjecture,(
% 1.49/1.28 ? [X0 : $i > $i > $o] : ! [X1 : $i] : ((X0 @ X1 @ c0) <=> ((cB @ X1 @ X1) | (cA @ X1)))),
% 1.49/1.28 file('/export/starexec/sandbox2/tmp/tmp.Qqsoi7wQO3/DTF2THF_14972.p',cSV9)).
% 1.49/1.28 % SZS output end Proof for DTF2THF_14972
% 1.49/1.28 % (15197)------------------------------
% 1.49/1.28 % (15197)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.28 % (15197)Termination reason: Refutation
% 1.49/1.28
% 1.49/1.28 % (15197)Memory used [KB]: 5500
% 1.49/1.28 % (15197)Time elapsed: 0.004 s
% 1.49/1.28 % (15197)Instructions burned: 3 (million)
% 1.49/1.28 % (15197)------------------------------
% 1.49/1.28 % (15197)------------------------------
% 1.49/1.28 % (15188)Success in time 0.036 s
%------------------------------------------------------------------------------