%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV410^5 : 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 : 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 09:41:12 AM UTC 2026
% Result : Theorem 1.61s 1.36s
% Output : Refutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 2
% Syntax : Number of formulae : 19 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 138 ( 34 equ; 0 cnn)
% Maximal formula atoms : 5 ( 7 avg)
% Number of connectives : 155 ( 18 ~; 24 |; 11 &; 91 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 34 ( 17 ^; 10 !; 7 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cA: $i > $o ).
thf(func_def_1,type,
cP: ( $i > $o ) > $o ).
thf(func_def_2,type,
cB: $i > $o ).
thf(func_def_9,type,
sK0: ( $i > $o ) > $i ).
thf(func_def_12,type,
ph2:
!>[X0: $tType] : X0 ).
thf(f21,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f20]) ).
thf(f20,plain,
$false = $true,
inference(forward_demodulation,[status(thm)],[f15,f18]) ).
thf(f18,plain,
( $false
= ( cA
@ ( sK0
@ ^ [Y0: $i] :
( ( cB @ Y0 )
| ( cA @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( $true
!= ( ( cB
@ ( sK0
@ ^ [Y0: $i] :
( ( cB @ Y0 )
| ( cA @ Y0 ) ) ) )
| ( cA
@ ( sK0
@ ^ [Y0: $i] :
( ( cB @ Y0 )
| ( cA @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
( $true
!= ( ^ [Y0: $i] :
( ( cB @ Y0 )
| ( cA @ Y0 ) )
@ ( sK0
@ ^ [Y0: $i] :
( ( cB @ Y0 )
| ( cA @ Y0 ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f14]) ).
thf(f14,plain,
( ( $true
!= ( ^ [Y0: $i] :
( ( cB @ Y0 )
| ( cA @ Y0 ) )
@ ( sK0
@ ^ [Y0: $i] :
( ( cB @ Y0 )
| ( cA @ Y0 ) ) ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f11,f10]) ).
thf(f10,plain,
( ( cP
@ ^ [Y0: $i] :
( ( cB @ Y0 )
| ( cA @ Y0 ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X0: $i > $o] :
( ( ( cP @ X0 )
!= $true )
| ( ( $true
= ( cA @ ( sK0 @ X0 ) ) )
& ( $true
!= ( X0 @ ( sK0 @ X0 ) ) ) ) )
& ( ( cP
@ ^ [Y0: $i] :
( ( cB @ Y0 )
| ( cA @ Y0 ) ) )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8]) ).
thf(f8,plain,
! [X0: $i > $o] :
( ? [X1: $i] :
( ( $true
= ( cA @ X1 ) )
& ( $true
!= ( X0 @ X1 ) ) )
=> ( ( $true
= ( cA @ ( sK0 @ X0 ) ) )
& ( $true
!= ( X0 @ ( sK0 @ X0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
( ! [X0: $i > $o] :
( ( ( cP @ X0 )
!= $true )
| ? [X1: $i] :
( ( $true
= ( cA @ X1 ) )
& ( $true
!= ( X0 @ X1 ) ) ) )
& ( ( cP
@ ^ [Y0: $i] :
( ( cB @ Y0 )
| ( cA @ Y0 ) ) )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ( ( cP
@ ^ [Y0: $i] :
( ( cB @ Y0 )
| ( cA @ Y0 ) ) )
= $true )
=> ? [X0: $i > $o] :
( ! [X1: $i] :
( ( $true
= ( cA @ X1 ) )
=> ( $true
= ( X0 @ X1 ) ) )
& ( ( cP @ X0 )
= $true ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ( cP
@ ^ [Y0: $i] :
( ( cB @ Y0 )
| ( cA @ Y0 ) ) )
= $true )
=> ? [X1: $i > $o] :
( ( ( cP @ X1 )
= $true )
& ! [X2: $i] :
( ( $true
= ( cA @ X2 ) )
=> ( ( X1 @ X2 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( cP
@ ^ [X0: $i] :
( ( cA @ X0 )
| ( cB @ X0 ) ) )
=> ? [X1: $i > $o] :
( ( cP @ X1 )
& ! [X2: $i] :
( ( cA @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( cP
@ ^ [X0: $i] :
( ( cA @ X0 )
| ( cB @ X0 ) ) )
=> ? [X1: $i > $o] :
( ( cP @ X1 )
& ! [X0: $i] :
( ( cA @ X0 )
=> ( X1 @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( cP
@ ^ [X0: $i] :
( ( cA @ X0 )
| ( cB @ X0 ) ) )
=> ? [X1: $i > $o] :
( ( cP @ X1 )
& ! [X0: $i] :
( ( cA @ X0 )
=> ( X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.t09wXrP3VB/DTF2THF_14987.p',cSV1_pme) ).
thf(f11,plain,
! [X0: $i > $o] :
( ( ( cP @ X0 )
!= $true )
| ( $true
!= ( X0 @ ( sK0 @ X0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f15,plain,
( $true
= ( cA
@ ( sK0
@ ^ [Y0: $i] :
( ( cB @ Y0 )
| ( cA @ Y0 ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f13]) ).
thf(f13,plain,
( ( $true
= ( cA
@ ( sK0
@ ^ [Y0: $i] :
( ( cB @ Y0 )
| ( cA @ Y0 ) ) ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f12,f10]) ).
thf(f12,plain,
! [X0: $i > $o] :
( ( ( cP @ X0 )
!= $true )
| ( $true
= ( cA @ ( sK0 @ X0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV410^5 : 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
% 0.17/0.34 % Computer : n025.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:46:27 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.47 thf(spec,logic,$$dhol).
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 % File : SEV410^5 : TPTP v9.2.1. Released v4.0.0.
% 0.20/0.47 % Domain : Set Theory
% 0.20/0.47 % Problem : TPS problem from SETS-THMS
% 0.20/0.47 % Version : Especial.
% 0.20/0.47 % English :
% 0.20/0.47
% 0.20/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.47 % Source : [Bro09]
% 0.20/0.47 % Names : tps_0790 [Bro09]
% 0.20/0.47
% 0.20/0.47 % Status : Theorem
% 0.20/0.47 % Rating : 0.00 v8.1.0, 0.08 v7.4.0, 0.00 v7.3.0, 0.10 v7.2.0, 0.00 v6.2.0, 0.17 v6.1.0, 0.00 v5.5.0, 0.20 v5.4.0, 0.25 v4.1.0, 0.33 v4.0.0
% 0.20/0.47 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.20/0.47 % Number of atoms : 5 ( 0 equ; 0 cnn)
% 0.20/0.47 % Maximal formula atoms : 5 ( 5 avg)
% 0.20/0.47 % Number of connectives : 10 ( 0 ~; 1 |; 1 &; 6 @)
% 0.20/0.47 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.20/0.47 % Maximal formula depth : 7 ( 7 avg)
% 0.20/0.47 % Number of types : 2 ( 0 usr)
% 0.20/0.47 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.20/0.47 % Number of symbols : 3 ( 3 usr; 0 con; 1-1 aty)
% 0.20/0.47 % Number of variables : 3 ( 1 ^; 1 !; 1 ?; 3 :)
% 0.20/0.47 % SPC : TH0_THM_NEQ_NAR
% 0.20/0.47
% 0.20/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.20/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.20/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.20/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 thf(cA,type,
% 0.20/0.47 cA: $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(cP,type,
% 0.20/0.47 cP: ( $i > $o ) > $o ).
% 0.20/0.47
% 0.20/0.47 thf(cB,type,
% 0.20/0.47 cB: $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(cSV1_pme,conjecture,
% 0.20/0.47 ( ( cP
% 0.20/0.47 @ ^ [Xx: $i] :
% 0.20/0.47 ( ( cA @ Xx )
% 0.20/0.47 | ( cB @ Xx ) ) )
% 0.20/0.47 => ? [Xu: $i > $o] :
% 0.20/0.47 ( ( cP @ Xu )
% 0.20/0.47 & ! [Xx: $i] :
% 0.20/0.47 ( ( cA @ Xx )
% 0.20/0.47 => ( Xu @ Xx ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 ------------------------
% 1.61/1.32 ---- Embedded in THF ---
% 1.61/1.32 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.61/1.32 %%% Generated on Tue Feb 24 12:46:28 EST 2026
% 1.61/1.32 %%% using '$$dhol' embedding, version 1.3.0.
% 1.61/1.32 %%% Logic specification used:
% 1.61/1.32 %%% thf(spec, logic, $$dhol).
% 1.61/1.32
% 1.61/1.32 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.t09wXrP3VB/DTF2DTF14987.p
% See solution above
% 1.61/1.32 ------------------------
% 1.61/1.33 ---- Cleaned THF ---
% 1.61/1.33 thf(cA,type,
% 1.61/1.33 cA: $i > $o ).
% 1.61/1.33
% 1.61/1.33 thf(cP,type,
% 1.61/1.33 cP: ( $i > $o ) > $o ).
% 1.61/1.33
% 1.61/1.33 thf(cB,type,
% 1.61/1.33 cB: $i > $o ).
% 1.61/1.33
% 1.61/1.33 thf(cSV1_pme,conjecture,
% 1.61/1.33 ( ( cP
% 1.61/1.33 @ ^ [Xx: $i] :
% 1.61/1.33 ( ( cA @ Xx )
% 1.61/1.33 | ( cB @ Xx ) ) )
% 1.61/1.33 => ? [Xu: $i > $o] :
% 1.61/1.33 ( ( cP @ Xu )
% 1.61/1.33 & ! [Xx: $i] :
% 1.61/1.33 ( ( cA @ Xx )
% 1.61/1.33 => ( Xu @ Xx ) ) ) ) ).
% 1.61/1.33 ------------------------
% 1.61/1.35 % (15318)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_14987 for (3000ds/2Mi)
% 1.61/1.35 % (15316)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_14987 for (3000ds/4Mi)
% 1.61/1.35 % (15315)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_14987 for (3000ds/183Mi)
% 1.61/1.35 % (15319)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_14987 for (3000ds/2Mi)
% 1.61/1.35 % (15321)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_14987 for (3000ds/18Mi)
% 1.61/1.35 % (15320)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_14987 for (3000ds/275Mi)
% 1.61/1.35 % (15317)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_14987 for (3000ds/27Mi)
% 1.61/1.35 % (15318)Instruction limit reached!
% 1.61/1.35 % (15318)------------------------------
% 1.61/1.35 % (15318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.35 % (15318)Termination reason: Unknown
% 1.61/1.35 % (15318)Termination phase: Saturation
% 1.61/1.35
% 1.61/1.35 % (15318)Memory used [KB]: 5500
% 1.61/1.35 % (15318)Time elapsed: 0.004 s
% 1.61/1.35 % (15318)Instructions burned: 2 (million)
% 1.61/1.35 % (15318)------------------------------
% 1.61/1.35 % (15318)------------------------------
% 1.61/1.35 % (15319)Instruction limit reached!
% 1.61/1.35 % (15319)------------------------------
% 1.61/1.35 % (15319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.35 % (15319)Termination reason: Unknown
% 1.61/1.35 % (15319)Termination phase: Saturation
% 1.61/1.35
% 1.61/1.35 % (15319)Memory used [KB]: 5500
% 1.61/1.35 % (15319)Time elapsed: 0.004 s
% 1.61/1.35 % (15319)Instructions burned: 2 (million)
% 1.61/1.35 % (15319)------------------------------
% 1.61/1.35 % (15319)------------------------------
% 1.61/1.36 % (15317)Refutation not found, incomplete strategy
% 1.61/1.36 % (15317)------------------------------
% 1.61/1.36 % (15317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.36 % (15317)Termination reason: Refutation not found, incomplete strategy
% 1.61/1.36
% 1.61/1.36
% 1.61/1.36 % (15317)Memory used [KB]: 5500
% 1.61/1.36 % (15317)Time elapsed: 0.004 s
% 1.61/1.36 % (15317)Instructions burned: 2 (million)
% 1.61/1.36 % (15317)------------------------------
% 1.61/1.36 % (15317)------------------------------
% 1.61/1.36 % (15321)First to succeed.
% 1.61/1.36 % (15316)Instruction limit reached!
% 1.61/1.36 % (15316)------------------------------
% 1.61/1.36 % (15316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.36 % (15316)Termination reason: Unknown
% 1.61/1.36 % (15316)Termination phase: Saturation
% 1.61/1.36
% 1.61/1.36 % (15316)Memory used [KB]: 5500
% 1.61/1.36 % (15316)Time elapsed: 0.006 s
% 1.61/1.36 % (15316)Instructions burned: 5 (million)
% 1.61/1.36 % (15316)------------------------------
% 1.61/1.36 % (15316)------------------------------
% 1.61/1.36 % (15320)Refutation not found, incomplete strategy
% 1.61/1.36 % (15320)------------------------------
% 1.61/1.36 % (15320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.36 % (15320)Termination reason: Refutation not found, incomplete strategy
% 1.61/1.36
% 1.61/1.36
% 1.61/1.36 % (15320)Memory used [KB]: 5500
% 1.61/1.36 % (15320)Time elapsed: 0.006 s
% 1.61/1.36 % (15320)Instructions burned: 5 (million)
% 1.61/1.36 % (15320)------------------------------
% 1.61/1.36 % (15320)------------------------------
% 1.61/1.36 % (15321)Refutation found. Thanks to Tanya!
% 1.61/1.36 % SZS status Theorem for DTF2THF_14987
% 1.61/1.36 % SZS output start Proof for DTF2THF_14987
% 1.61/1.36 thf(func_def_0, type, cA: $i > $o).
% 1.61/1.36 thf(func_def_1, type, cP: ($i > $o) > $o).
% 1.61/1.36 thf(func_def_2, type, cB: $i > $o).
% 1.61/1.36 thf(func_def_9, type, sK0: ($i > $o) > $i).
% 1.61/1.36 thf(func_def_12, type, ph2: !>[X0: $tType]:(X0)).
% 1.61/1.36 thf(f21,plain,(
% 1.61/1.36 $false),
% 1.61/1.36 inference(trivial_inequality_removal,[status(thm)],[f20])).
% 1.61/1.36 thf(f20,plain,(
% 1.61/1.36 ($false = $true)),
% 1.61/1.36 inference(forward_demodulation,[status(thm)],[f15,f18])).
% 1.61/1.36 thf(f18,plain,(
% 1.61/1.36 ($false = (cA @ (sK0 @ (^[Y0 : $i]: ((cB @ Y0) | (cA @ Y0))))))),
% 1.61/1.36 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.61/1.36 thf(f17,plain,(
% 1.61/1.36 ($true != ((cB @ (sK0 @ (^[Y0 : $i]: ((cB @ Y0) | (cA @ Y0))))) | (cA @ (sK0 @ (^[Y0 : $i]: ((cB @ Y0) | (cA @ Y0)))))))),
% 1.61/1.36 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.61/1.36 thf(f16,plain,(
% 1.61/1.36 ($true != ((^[Y0 : $i]: ((cB @ Y0) | (cA @ Y0))) @ (sK0 @ (^[Y0 : $i]: ((cB @ Y0) | (cA @ Y0))))))),
% 1.61/1.36 inference(trivial_inequality_removal,[status(thm)],[f14])).
% 1.61/1.36 thf(f14,plain,(
% 1.61/1.36 ($true != ((^[Y0 : $i]: ((cB @ Y0) | (cA @ Y0))) @ (sK0 @ (^[Y0 : $i]: ((cB @ Y0) | (cA @ Y0)))))) | ($true != $true)),
% 1.61/1.36 inference(superposition,[status(thm)],[f11,f10])).
% 1.61/1.36 thf(f10,plain,(
% 1.61/1.36 ((cP @ (^[Y0 : $i]: ((cB @ Y0) | (cA @ Y0)))) = $true)),
% 1.61/1.36 inference(cnf_transformation,[status(thm)],[f9])).
% 1.61/1.36 thf(f9,plain,(
% 1.61/1.36 ! [X0 : $i > $o] : (((cP @ X0) != $true) | (($true = (cA @ (sK0 @ X0))) & ($true != (X0 @ (sK0 @ X0))))) & ((cP @ (^[Y0 : $i]: ((cB @ Y0) | (cA @ Y0)))) = $true)),
% 1.61/1.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8])).
% 1.61/1.36 thf(f8,plain,(
% 1.61/1.36 ! [X0 : $i > $o] : (? [X1 : $i] : (($true = (cA @ X1)) & ($true != (X0 @ X1))) => (($true = (cA @ (sK0 @ X0))) & ($true != (X0 @ (sK0 @ X0)))))),
% 1.61/1.36 introduced(definition,[],[choice_axiom])).
% 1.61/1.36 thf(f7,plain,(
% 1.61/1.36 ! [X0 : $i > $o] : (((cP @ X0) != $true) | ? [X1 : $i] : (($true = (cA @ X1)) & ($true != (X0 @ X1)))) & ((cP @ (^[Y0 : $i]: ((cB @ Y0) | (cA @ Y0)))) = $true)),
% 1.61/1.36 inference(ennf_transformation,[status(thm)],[f6])).
% 1.61/1.36 thf(f6,plain,(
% 1.61/1.36 ~(((cP @ (^[Y0 : $i]: ((cB @ Y0) | (cA @ Y0)))) = $true) => ? [X0 : $i > $o] : (! [X1 : $i] : (($true = (cA @ X1)) => ($true = (X0 @ X1))) & ((cP @ X0) = $true)))),
% 1.61/1.36 inference(rectify,[status(thm)],[f5])).
% 1.61/1.36 thf(f5,plain,(
% 1.61/1.36 ~(((cP @ (^[Y0 : $i]: ((cB @ Y0) | (cA @ Y0)))) = $true) => ? [X1 : $i > $o] : (((cP @ X1) = $true) & ! [X2 : $i] : (($true = (cA @ X2)) => ((X1 @ X2) = $true))))),
% 1.61/1.36 inference(fool_elimination,[status(thm)],[f4])).
% 1.61/1.36 thf(f4,plain,(
% 1.61/1.36 ~((cP @ (^[X0 : $i] : ((cA @ X0) | (cB @ X0)))) => ? [X1 : $i > $o] : ((cP @ X1) & ! [X2 : $i] : ((cA @ X2) => (X1 @ X2))))),
% 1.61/1.36 inference(rectify,[status(thm)],[f2])).
% 1.61/1.36 thf(f2,negated_conjecture,(
% 1.61/1.36 ~((cP @ (^[X0 : $i] : ((cA @ X0) | (cB @ X0)))) => ? [X1 : $i > $o] : ((cP @ X1) & ! [X0 : $i] : ((cA @ X0) => (X1 @ X0))))),
% 1.61/1.36 inference(negated_conjecture,[status(cth)],[f1])).
% 1.61/1.36 thf(f1,conjecture,(
% 1.61/1.36 (cP @ (^[X0 : $i] : ((cA @ X0) | (cB @ X0)))) => ? [X1 : $i > $o] : ((cP @ X1) & ! [X0 : $i] : ((cA @ X0) => (X1 @ X0)))),
% 1.61/1.36 file('/export/starexec/sandbox/tmp/tmp.t09wXrP3VB/DTF2THF_14987.p',cSV1_pme)).
% 1.61/1.36 thf(f11,plain,(
% 1.61/1.36 ( ! [X0 : $i > $o] : (((cP @ X0) != $true) | ($true != (X0 @ (sK0 @ X0)))) )),
% 1.61/1.36 inference(cnf_transformation,[status(thm)],[f9])).
% 1.61/1.36 thf(f15,plain,(
% 1.61/1.36 ($true = (cA @ (sK0 @ (^[Y0 : $i]: ((cB @ Y0) | (cA @ Y0))))))),
% 1.61/1.36 inference(trivial_inequality_removal,[status(thm)],[f13])).
% 1.61/1.36 thf(f13,plain,(
% 1.61/1.36 ($true = (cA @ (sK0 @ (^[Y0 : $i]: ((cB @ Y0) | (cA @ Y0)))))) | ($true != $true)),
% 1.61/1.36 inference(superposition,[status(thm)],[f12,f10])).
% 1.61/1.36 thf(f12,plain,(
% 1.61/1.36 ( ! [X0 : $i > $o] : (((cP @ X0) != $true) | ($true = (cA @ (sK0 @ X0)))) )),
% 1.61/1.36 inference(cnf_transformation,[status(thm)],[f9])).
% 1.61/1.36 % SZS output end Proof for DTF2THF_14987
% 1.61/1.36 % (15321)------------------------------
% 1.61/1.36 % (15321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.36 % (15321)Termination reason: Refutation
% 1.61/1.36
% 1.61/1.36 % (15321)Memory used [KB]: 5500
% 1.61/1.36 % (15321)Time elapsed: 0.005 s
% 1.61/1.36 % (15321)Instructions burned: 2 (million)
% 1.61/1.36 % (15321)------------------------------
% 1.61/1.36 % (15321)------------------------------
% 1.61/1.36 % (15314)Success in time 0.019 s
%------------------------------------------------------------------------------