%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO303^5 : 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 : n020.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 09:53:54 AM UTC 2026
% Result : Theorem 1.60s 1.31s
% Output : Refutation 1.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 7 unt; 0 typ; 2 def)
% Number of atoms : 187 ( 42 equ; 0 cnn)
% Maximal formula atoms : 9 ( 6 avg)
% Number of connectives : 135 ( 31 ~; 25 |; 16 &; 56 @)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 20 ( 0 ^; 20 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
cS: $i > $o ).
thf(func_def_3,type,
cT: $i > $o ).
thf(func_def_6,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_10,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f36,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f21,f31,f35]) ).
thf(f35,plain,
spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f34]) ).
thf(f34,plain,
( $false
| spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f33]) ).
thf(f33,plain,
( ( $true != $true )
| spl0_2 ),
inference(superposition,[status(thm)],[f20,f24]) ).
thf(f24,plain,
! [X0: $i] :
( $true
= ( cT @ X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: $i] :
( ( $true
= ( cT @ X0 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f10,f11]) ).
thf(f11,plain,
( ( cT @ c0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ( cS @ c0 )
= $true )
& ( ( cT @ c0 )
= $true )
& ! [X0: $i > $o] :
( ! [X1: $i] :
( ( X0 @ X1 )
= $true )
| ( ( X0 @ c0 )
!= $true ) )
& ( ( ( cS @ b )
!= $true )
| ( ( cT @ a )
!= $true ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ( cT @ c0 )
= $true )
& ( ( cS @ c0 )
= $true )
& ( ( ( cS @ b )
!= $true )
| ( ( cT @ a )
!= $true ) )
& ! [X0: $i > $o] :
( ! [X1: $i] :
( ( X0 @ X1 )
= $true )
| ( ( X0 @ c0 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ! [X0: $i > $o] :
( ! [X1: $i] :
( ( X0 @ X1 )
= $true )
| ( ( X0 @ c0 )
!= $true ) )
=> ( ~ ( ( ( cT @ c0 )
= $true )
& ( ( cS @ c0 )
= $true ) )
| ( ( ( cS @ b )
= $true )
& ( ( cT @ a )
= $true ) ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ! [X0: $i > $o] :
( ! [X1: $i] :
( ( X0 @ X1 )
= $true )
| ( ( X0 @ c0 )
!= $true ) )
=> ( ~ ( ( ( cT @ c0 )
= $true )
& ( ( cS @ c0 )
= $true ) )
| ( ( ( cS @ b )
= $true )
& ( ( cT @ a )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: $i > $o] :
( ! [X1: $i] : ( X0 @ X1 )
| ~ ( X0 @ c0 ) )
=> ( ~ ( ( cT @ c0 )
& ( cS @ c0 ) )
| ( ( cT @ a )
& ( cS @ b ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: $i > $o] :
( ! [X1: $i] : ( X0 @ X1 )
| ~ ( X0 @ c0 ) )
=> ( ~ ( ( cT @ c0 )
& ( cS @ c0 ) )
| ( ( cT @ a )
& ( cS @ b ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X0: $i > $o] :
( ! [X1: $i] : ( X0 @ X1 )
| ~ ( X0 @ c0 ) )
=> ( ~ ( ( cT @ c0 )
& ( cS @ c0 ) )
| ( ( cT @ a )
& ( cS @ b ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.N8336XnBmK/DTF2THF_5979.p',cMIN_QUAN_BUG) ).
thf(f10,plain,
! [X0: $i > $o,X1: $i] :
( ( ( X0 @ c0 )
!= $true )
| ( ( X0 @ X1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f20,plain,
( ( ( cT @ a )
!= $true )
| spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f18]) ).
thf(f18,definition,
( spl0_2
<=> ( ( cT @ a )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f31,plain,
spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f30]) ).
thf(f30,plain,
( $false
| spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f28]) ).
thf(f28,plain,
( ( $true != $true )
| spl0_1 ),
inference(superposition,[status(thm)],[f16,f25]) ).
thf(f25,plain,
! [X0: $i] :
( ( cS @ X0 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f23]) ).
thf(f23,plain,
! [X0: $i] :
( ( ( cS @ X0 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f10,f12]) ).
thf(f12,plain,
( ( cS @ c0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f16,plain,
( ( ( cS @ b )
!= $true )
| spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f14]) ).
thf(f14,definition,
( spl0_1
<=> ( ( cS @ b )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f21,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f9,f18,f14]) ).
thf(f9,plain,
( ( ( cT @ a )
!= $true )
| ( ( cS @ b )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO303^5 : 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 : n020.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 14:27:57 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.47 ---- Original DTF file ---
% 0.30/0.47 thf(spec,logic,$$dhol).
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 % File : SYO303^5 : TPTP v9.2.1. Released v4.0.0.
% 0.30/0.47 % Domain : Syntactic
% 0.30/0.47 % Problem : TPS problem from BASIC-HO-THMS
% 0.30/0.47 % Version : Especial.
% 0.30/0.47 % English :
% 0.30/0.47
% 0.30/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.30/0.47 % Source : [Bro09]
% 0.30/0.47 % Names : tps_0796 [Bro09]
% 0.30/0.47
% 0.30/0.47 % Status : Theorem
% 0.30/0.47 % Rating : 0.00 v8.1.0, 0.08 v7.4.0, 0.00 v6.2.0, 0.33 v6.1.0, 0.17 v6.0.0, 0.00 v4.0.0
% 0.30/0.47 % Syntax : Number of formulae : 6 ( 0 unt; 5 typ; 0 def)
% 0.30/0.47 % Number of atoms : 4 ( 0 equ; 0 cnn)
% 0.30/0.47 % Maximal formula atoms : 4 ( 4 avg)
% 0.30/0.47 % Number of connectives : 13 ( 2 ~; 2 |; 2 &; 6 @)
% 0.30/0.47 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.30/0.47 % Maximal formula depth : 6 ( 6 avg)
% 0.30/0.47 % Number of types : 2 ( 0 usr)
% 0.30/0.47 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.30/0.47 % Number of symbols : 5 ( 5 usr; 3 con; 0-1 aty)
% 0.30/0.47 % Number of variables : 2 ( 0 ^; 2 !; 0 ?; 2 :)
% 0.30/0.47 % SPC : TH0_THM_NEQ_NAR
% 0.30/0.47
% 0.30/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.30/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.30/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.30/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 thf(b,type,
% 0.30/0.47 b: $i ).
% 0.30/0.47
% 0.30/0.47 thf(cS,type,
% 0.30/0.47 cS: $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(a,type,
% 0.30/0.47 a: $i ).
% 0.30/0.47
% 0.30/0.47 thf(cT,type,
% 0.30/0.47 cT: $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(c0,type,
% 0.30/0.47 c0: $i ).
% 0.30/0.47
% 0.30/0.47 thf(cMIN_QUAN_BUG,conjecture,
% 0.30/0.47 ( ! [P: $i > $o] :
% 0.30/0.47 ( ~ ( P @ c0 )
% 0.30/0.47 | ! [Xx: $i] : ( P @ Xx ) )
% 0.30/0.47 => ( ~ ( ( cS @ c0 )
% 0.30/0.47 & ( cT @ c0 ) )
% 0.30/0.47 | ( ( cT @ a )
% 0.30/0.47 & ( cS @ b ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 ------------------------
% 1.45/1.27 ---- Embedded in THF ---
% 1.45/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.45/1.27 %%% Generated on Tue Feb 24 14:27:58 EST 2026
% 1.45/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.45/1.27 %%% Logic specification used:
% 1.45/1.27 %%% thf(spec, logic, $$dhol).
% 1.45/1.27
% 1.45/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.N8336XnBmK/DTF2DTF5979.p
% See solution above
% 1.45/1.28 ------------------------
% 1.45/1.29 ---- Cleaned THF ---
% 1.45/1.29 thf(b,type,
% 1.45/1.29 b: $i ).
% 1.45/1.29
% 1.45/1.29 thf(cS,type,
% 1.45/1.29 cS: $i > $o ).
% 1.45/1.29
% 1.45/1.29 thf(a,type,
% 1.45/1.29 a: $i ).
% 1.45/1.29
% 1.45/1.29 thf(cT,type,
% 1.45/1.29 cT: $i > $o ).
% 1.45/1.29
% 1.45/1.29 thf(c0,type,
% 1.45/1.29 c0: $i ).
% 1.45/1.29
% 1.45/1.29 thf(cMIN_QUAN_BUG,conjecture,
% 1.45/1.29 ( ! [P: $i > $o] :
% 1.45/1.29 ( ~ ( P @ c0 )
% 1.45/1.29 | ! [Xx: $i] : ( P @ Xx ) )
% 1.45/1.29 => ( ~ ( ( cS @ c0 )
% 1.45/1.29 & ( cT @ c0 ) )
% 1.45/1.29 | ( ( cT @ a )
% 1.45/1.29 & ( cS @ b ) ) ) ) ).
% 1.45/1.29 ------------------------
% 1.60/1.30 % (6311)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_5979 for (2999ds/2Mi)
% 1.60/1.30 % (6312)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_5979 for (2999ds/2Mi)
% 1.60/1.30 % (6311)Instruction limit reached!
% 1.60/1.30 % (6311)------------------------------
% 1.60/1.30 % (6311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.30 % (6311)Termination reason: Unknown
% 1.60/1.30 % (6311)Termination phase: Saturation
% 1.60/1.30
% 1.60/1.30 % (6311)Memory used [KB]: 5500
% 1.60/1.30 % (6311)Time elapsed: 0.003 s
% 1.60/1.30 % (6311)Instructions burned: 3 (million)
% 1.60/1.30 % (6311)------------------------------
% 1.60/1.30 % (6311)------------------------------
% 1.60/1.30 % (6312)Instruction limit reached!
% 1.60/1.30 % (6312)------------------------------
% 1.60/1.30 % (6312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.30 % (6312)Termination reason: Unknown
% 1.60/1.30 % (6312)Termination phase: Saturation
% 1.60/1.30
% 1.60/1.30 % (6312)Memory used [KB]: 5500
% 1.60/1.30 % (6312)Time elapsed: 0.002 s
% 1.60/1.30 % (6312)Instructions burned: 2 (million)
% 1.60/1.30 % (6312)------------------------------
% 1.60/1.30 % (6312)------------------------------
% 1.60/1.31 % (6308)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_5979 for (2999ds/183Mi)
% 1.60/1.31 % (6309)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_5979 for (2999ds/4Mi)
% 1.60/1.31 % (6310)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_5979 for (2999ds/27Mi)
% 1.60/1.31 % (6313)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_5979 for (2999ds/275Mi)
% 1.60/1.31 % (6314)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_5979 for (2999ds/18Mi)
% 1.60/1.31 % (6310)First to succeed.
% 1.60/1.31 % (6309)Instruction limit reached!
% 1.60/1.31 % (6309)------------------------------
% 1.60/1.31 % (6309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.31 % (6309)Termination reason: Unknown
% 1.60/1.31 % (6309)Termination phase: Saturation
% 1.60/1.31
% 1.60/1.31 % (6309)Memory used [KB]: 5500
% 1.60/1.31 % (6309)Time elapsed: 0.005 s
% 1.60/1.31 % (6309)Instructions burned: 4 (million)
% 1.60/1.31 % (6309)------------------------------
% 1.60/1.31 % (6309)------------------------------
% 1.60/1.31 % (6314)Also succeeded, but the first one will report.
% 1.60/1.31 % (6315)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_5979 for (2999ds/3Mi)
% 1.60/1.31 % (6308)Also succeeded, but the first one will report.
% 1.60/1.31 % (6310)Refutation found. Thanks to Tanya!
% 1.60/1.31 % SZS status Theorem for DTF2THF_5979
% 1.60/1.31 % SZS output start Proof for DTF2THF_5979
% 1.60/1.31 thf(func_def_1, type, cS: $i > $o).
% 1.60/1.31 thf(func_def_3, type, cT: $i > $o).
% 1.60/1.31 thf(func_def_6, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.60/1.31 thf(func_def_10, type, ph1: !>[X0: $tType]:(X0)).
% 1.60/1.31 thf(f36,plain,(
% 1.60/1.31 $false),
% 1.60/1.31 inference(avatar_sat_refutation,[status(thm)],[f21,f31,f35])).
% 1.60/1.31 thf(f35,plain,(
% 1.60/1.31 spl0_2),
% 1.60/1.31 inference(avatar_contradiction_clause,[status(thm)],[f34])).
% 1.60/1.31 thf(f34,plain,(
% 1.60/1.31 $false | spl0_2),
% 1.60/1.31 inference(trivial_inequality_removal,[status(thm)],[f33])).
% 1.60/1.31 thf(f33,plain,(
% 1.60/1.31 ($true != $true) | spl0_2),
% 1.60/1.31 inference(superposition,[status(thm)],[f20,f24])).
% 1.60/1.31 thf(f24,plain,(
% 1.60/1.31 ( ! [X0 : $i] : (($true = (cT @ X0))) )),
% 1.60/1.31 inference(trivial_inequality_removal,[status(thm)],[f22])).
% 1.60/1.31 thf(f22,plain,(
% 1.60/1.31 ( ! [X0 : $i] : (($true = (cT @ X0)) | ($true != $true)) )),
% 1.60/1.31 inference(superposition,[status(thm)],[f10,f11])).
% 1.60/1.31 thf(f11,plain,(
% 1.60/1.31 ((cT @ c0) = $true)),
% 1.60/1.31 inference(cnf_transformation,[status(thm)],[f8])).
% 1.60/1.31 thf(f8,plain,(
% 1.60/1.31 ((cS @ c0) = $true) & ((cT @ c0) = $true) & ! [X0 : $i > $o] : (! [X1 : $i] : ((X0 @ X1) = $true) | ((X0 @ c0) != $true)) & (((cS @ b) != $true) | ((cT @ a) != $true))),
% 1.60/1.31 inference(flattening,[status(thm)],[f7])).
% 1.60/1.31 thf(f7,plain,(
% 1.60/1.31 ((((cT @ c0) = $true) & ((cS @ c0) = $true)) & (((cS @ b) != $true) | ((cT @ a) != $true))) & ! [X0 : $i > $o] : (! [X1 : $i] : ((X0 @ X1) = $true) | ((X0 @ c0) != $true))),
% 1.60/1.31 inference(ennf_transformation,[status(thm)],[f6])).
% 1.60/1.31 thf(f6,plain,(
% 1.60/1.31 ~(! [X0 : $i > $o] : (! [X1 : $i] : ((X0 @ X1) = $true) | ((X0 @ c0) != $true)) => (~(((cT @ c0) = $true) & ((cS @ c0) = $true)) | (((cS @ b) = $true) & ((cT @ a) = $true))))),
% 1.60/1.31 inference(flattening,[status(thm)],[f5])).
% 1.60/1.31 thf(f5,plain,(
% 1.60/1.31 ~(! [X0 : $i > $o] : (! [X1 : $i] : ((X0 @ X1) = $true) | ~((X0 @ c0) = $true)) => (~(((cT @ c0) = $true) & ((cS @ c0) = $true)) | (((cS @ b) = $true) & ((cT @ a) = $true))))),
% 1.60/1.31 inference(fool_elimination,[status(thm)],[f4])).
% 1.60/1.31 thf(f4,plain,(
% 1.60/1.31 ~(! [X0 : $i > $o] : (! [X1 : $i] : (X0 @ X1) | ~(X0 @ c0)) => (~((cT @ c0) & (cS @ c0)) | ((cT @ a) & (cS @ b))))),
% 1.60/1.31 inference(rectify,[status(thm)],[f2])).
% 1.60/1.31 thf(f2,negated_conjecture,(
% 1.60/1.31 ~(! [X0 : $i > $o] : (! [X1 : $i] : (X0 @ X1) | ~(X0 @ c0)) => (~((cT @ c0) & (cS @ c0)) | ((cT @ a) & (cS @ b))))),
% 1.60/1.31 inference(negated_conjecture,[status(cth)],[f1])).
% 1.60/1.31 thf(f1,conjecture,(
% 1.60/1.31 ! [X0 : $i > $o] : (! [X1 : $i] : (X0 @ X1) | ~(X0 @ c0)) => (~((cT @ c0) & (cS @ c0)) | ((cT @ a) & (cS @ b)))),
% 1.60/1.31 file('/export/starexec/sandbox/tmp/tmp.N8336XnBmK/DTF2THF_5979.p',cMIN_QUAN_BUG)).
% 1.60/1.31 thf(f10,plain,(
% 1.60/1.31 ( ! [X0 : $i > $o,X1 : $i] : (((X0 @ c0) != $true) | ((X0 @ X1) = $true)) )),
% 1.60/1.31 inference(cnf_transformation,[status(thm)],[f8])).
% 1.60/1.31 thf(f20,plain,(
% 1.60/1.31 ((cT @ a) != $true) | spl0_2),
% 1.60/1.31 inference(avatar_component_clause,[status(thm)],[f18])).
% 1.60/1.31 thf(f18,definition,(
% 1.60/1.31 spl0_2 <=> ((cT @ a) = $true)),
% 1.60/1.31 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.60/1.31 thf(f31,plain,(
% 1.60/1.31 spl0_1),
% 1.60/1.31 inference(avatar_contradiction_clause,[status(thm)],[f30])).
% 1.60/1.31 thf(f30,plain,(
% 1.60/1.31 $false | spl0_1),
% 1.60/1.31 inference(trivial_inequality_removal,[status(thm)],[f28])).
% 1.60/1.31 thf(f28,plain,(
% 1.60/1.31 ($true != $true) | spl0_1),
% 1.60/1.31 inference(superposition,[status(thm)],[f16,f25])).
% 1.60/1.31 thf(f25,plain,(
% 1.60/1.31 ( ! [X0 : $i] : (((cS @ X0) = $true)) )),
% 1.60/1.31 inference(trivial_inequality_removal,[status(thm)],[f23])).
% 1.60/1.31 thf(f23,plain,(
% 1.60/1.31 ( ! [X0 : $i] : (((cS @ X0) = $true) | ($true != $true)) )),
% 1.60/1.31 inference(superposition,[status(thm)],[f10,f12])).
% 1.60/1.31 thf(f12,plain,(
% 1.60/1.31 ((cS @ c0) = $true)),
% 1.60/1.31 inference(cnf_transformation,[status(thm)],[f8])).
% 1.60/1.31 thf(f16,plain,(
% 1.60/1.31 ((cS @ b) != $true) | spl0_1),
% 1.60/1.31 inference(avatar_component_clause,[status(thm)],[f14])).
% 1.60/1.31 thf(f14,definition,(
% 1.60/1.31 spl0_1 <=> ((cS @ b) = $true)),
% 1.60/1.31 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.60/1.31 thf(f21,plain,(
% 1.60/1.31 ~spl0_1 | ~spl0_2),
% 1.60/1.31 inference(avatar_split_clause,[status(thm)],[f9,f18,f14])).
% 1.60/1.31 thf(f9,plain,(
% 1.60/1.31 ((cT @ a) != $true) | ((cS @ b) != $true)),
% 1.60/1.31 inference(cnf_transformation,[status(thm)],[f8])).
% 1.60/1.31 % SZS output end Proof for DTF2THF_5979
% 1.60/1.31 % (6310)------------------------------
% 1.60/1.31 % (6310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.31 % (6310)Termination reason: Refutation
% 1.60/1.31
% 1.60/1.31 % (6310)Memory used [KB]: 5500
% 1.60/1.31 % (6310)Time elapsed: 0.005 s
% 1.60/1.31 % (6310)Instructions burned: 2 (million)
% 1.60/1.31 % (6310)------------------------------
% 1.60/1.31 % (6310)------------------------------
% 1.60/1.31 % (6307)Success in time 0.021 s
%------------------------------------------------------------------------------