%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYN356^5 : 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 : 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 09:50:50 AM UTC 2026
% Result : Theorem 1.51s 1.26s
% Output : Refutation 1.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 3
% Syntax : Number of formulae : 34 ( 4 unt; 0 typ; 2 def)
% Number of atoms : 301 ( 62 equ; 0 cnn)
% Maximal formula atoms : 14 ( 8 avg)
% Number of connectives : 276 ( 41 ~; 35 |; 28 &; 158 @)
% ( 2 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 6 con; 0-2 aty)
% Number of variables : 44 ( 0 ^; 44 !; 0 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
cQ: $i > $i > $o ).
thf(func_def_3,type,
cR: $i > $i > $o ).
thf(f53,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f22,f37,f51]) ).
thf(f51,plain,
spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f50]) ).
thf(f50,plain,
( $false
| spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f48]) ).
thf(f48,plain,
( ( $true != $true )
| spl0_2 ),
inference(superposition,[status(thm)],[f46,f13]) ).
thf(f13,plain,
( ( cR @ cA @ cB )
= $true ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ( cR @ cA @ cB )
= $true )
& ! [X0: $i,X1: $i] :
( ( ( cR @ X0 @ X1 )
!= $true )
| ( ( ( cQ @ X0 @ X1 )
= $true )
& ( ( cR @ X1 @ X0 )
= $true ) ) )
& ( ( ( cQ @ cA @ cA )
!= $true )
| ( ( cQ @ cB @ cB )
!= $true ) )
& ! [X2: $i,X3: $i] :
( ( $true
!= ( cQ @ X3 @ X2 ) )
| ( $true
= ( cQ @ X3 @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ( cR @ cA @ cB )
= $true )
& ! [X3: $i,X2: $i] :
( ( $true
!= ( cR @ X3 @ X2 ) )
| ( ( $true
= ( cQ @ X3 @ X2 ) )
& ( $true
= ( cR @ X2 @ X3 ) ) ) )
& ( ( ( cQ @ cA @ cA )
!= $true )
| ( ( cQ @ cB @ cB )
!= $true ) )
& ! [X1: $i,X0: $i] :
( ( ( cQ @ X0 @ X1 )
!= $true )
| ( $true
= ( cQ @ X0 @ X0 ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ( ( cQ @ cA @ cA )
!= $true )
| ( ( cQ @ cB @ cB )
!= $true ) )
& ( ( cR @ cA @ cB )
= $true )
& ! [X1: $i,X0: $i] :
( ( ( cQ @ X0 @ X1 )
!= $true )
| ( $true
= ( cQ @ X0 @ X0 ) ) )
& ! [X3: $i,X2: $i] :
( ( $true
!= ( cR @ X3 @ X2 ) )
| ( ( $true
= ( cQ @ X3 @ X2 ) )
& ( $true
= ( cR @ X2 @ X3 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ( ( cR @ cA @ cB )
= $true )
& ! [X0: $i,X1: $i] :
( ( ( cQ @ X0 @ X1 )
= $true )
=> ( $true
= ( cQ @ X0 @ X0 ) ) )
& ! [X3: $i,X2: $i] :
( ( $true
= ( cR @ X3 @ X2 ) )
=> ( ( $true
= ( cQ @ X3 @ X2 ) )
& ( $true
= ( cR @ X2 @ X3 ) ) ) ) )
=> ( ( ( cQ @ cB @ cB )
= $true )
& ( ( cQ @ cA @ cA )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ( cR @ cA @ cB )
& ! [X0: $i,X1: $i] :
( ( cQ @ X0 @ X1 )
=> ( cQ @ X0 @ X0 ) )
& ! [X2: $i,X3: $i] :
( ( cR @ X3 @ X2 )
=> ( ( cQ @ X3 @ X2 )
& ( cR @ X2 @ X3 ) ) ) )
=> ( ( cQ @ cA @ cA )
& ( cQ @ cB @ cB ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ( cR @ cA @ cB )
& ! [X2: $i,X3: $i] :
( ( cQ @ X2 @ X3 )
=> ( cQ @ X2 @ X2 ) )
& ! [X1: $i,X0: $i] :
( ( cR @ X0 @ X1 )
=> ( ( cQ @ X0 @ X1 )
& ( cR @ X1 @ X0 ) ) ) )
=> ( ( cQ @ cA @ cA )
& ( cQ @ cB @ cB ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ( cR @ cA @ cB )
& ! [X2: $i,X3: $i] :
( ( cQ @ X2 @ X3 )
=> ( cQ @ X2 @ X2 ) )
& ! [X1: $i,X0: $i] :
( ( cR @ X0 @ X1 )
=> ( ( cQ @ X0 @ X1 )
& ( cR @ X1 @ X0 ) ) ) )
=> ( ( cQ @ cA @ cA )
& ( cQ @ cB @ cB ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.eyLHmTH8db/DTF2THF_27465.p',cLX2107) ).
thf(f46,plain,
( ! [X0: $i] :
( ( cR @ cA @ X0 )
!= $true )
| spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f45]) ).
thf(f45,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( ( cR @ cA @ X0 )
!= $true ) )
| spl0_2 ),
inference(superposition,[status(thm)],[f41,f12]) ).
thf(f12,plain,
! [X0: $i,X1: $i] :
( ( ( cQ @ X0 @ X1 )
= $true )
| ( ( cR @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f41,plain,
( ! [X0: $i] :
( $true
!= ( cQ @ cA @ X0 ) )
| spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f38]) ).
thf(f38,plain,
( ! [X0: $i] :
( ( $true
!= ( cQ @ cA @ X0 ) )
| ( $true != $true ) )
| spl0_2 ),
inference(superposition,[status(thm)],[f21,f9]) ).
thf(f9,plain,
! [X2: $i,X3: $i] :
( ( $true
= ( cQ @ X3 @ X3 ) )
| ( $true
!= ( cQ @ X3 @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f21,plain,
( ( ( cQ @ cA @ cA )
!= $true )
| spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f19]) ).
thf(f19,definition,
( spl0_2
<=> ( ( cQ @ cA @ cA )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f37,plain,
spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f36]) ).
thf(f36,plain,
( $false
| spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f33]) ).
thf(f33,plain,
( ( $true != $true )
| spl0_1 ),
inference(superposition,[status(thm)],[f32,f13]) ).
thf(f32,plain,
( ! [X0: $i] :
( ( cR @ X0 @ cB )
!= $true )
| spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f31]) ).
thf(f31,plain,
( ! [X0: $i] :
( ( ( cR @ X0 @ cB )
!= $true )
| ( $true != $true ) )
| spl0_1 ),
inference(superposition,[status(thm)],[f30,f11]) ).
thf(f11,plain,
! [X0: $i,X1: $i] :
( ( ( cR @ X1 @ X0 )
= $true )
| ( ( cR @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f30,plain,
( ! [X0: $i] :
( $true
!= ( cR @ cB @ X0 ) )
| spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f28]) ).
thf(f28,plain,
( ! [X0: $i] :
( ( $true
!= ( cR @ cB @ X0 ) )
| ( $true != $true ) )
| spl0_1 ),
inference(superposition,[status(thm)],[f24,f12]) ).
thf(f24,plain,
( ! [X0: $i] :
( $true
!= ( cQ @ cB @ X0 ) )
| spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f23]) ).
thf(f23,plain,
( ! [X0: $i] :
( ( $true
!= ( cQ @ cB @ X0 ) )
| ( $true != $true ) )
| spl0_1 ),
inference(superposition,[status(thm)],[f17,f9]) ).
thf(f17,plain,
( ( ( cQ @ cB @ cB )
!= $true )
| spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f15]) ).
thf(f15,definition,
( spl0_1
<=> ( ( cQ @ cB @ cB )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f22,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f10,f19,f15]) ).
thf(f10,plain,
( ( ( cQ @ cB @ cB )
!= $true )
| ( ( cQ @ cA @ cA )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYN356^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n020.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
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 13:55:57 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/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 : SYN356^5 : TPTP v9.2.1. Released v4.0.0.
% 0.30/0.45 % Domain : Syntactic
% 0.30/0.45 % Problem : TPS problem from BASIC-FO-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_0893 [Bro09]
% 0.30/0.45 % : tps_0319 [Bro09]
% 0.30/0.45 % : THM45 [TPS]
% 0.30/0.45
% 0.30/0.45 % Status : Theorem
% 0.30/0.45 % Rating : 0.08 v9.1.0, 0.12 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.08 v7.4.0, 0.11 v7.3.0, 0.10 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.0.0, 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v4.0.0
% 0.30/0.45 % Syntax : Number of formulae : 5 ( 0 unt; 4 typ; 0 def)
% 0.30/0.45 % Number of atoms : 8 ( 0 equ; 0 cnn)
% 0.30/0.45 % Maximal formula atoms : 8 ( 8 avg)
% 0.30/0.45 % Number of connectives : 23 ( 0 ~; 0 |; 4 &; 16 @)
% 0.30/0.45 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.30/0.45 % Maximal formula depth : 10 ( 10 avg)
% 0.30/0.45 % Number of types : 2 ( 0 usr)
% 0.30/0.45 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.30/0.45 % Number of symbols : 4 ( 4 usr; 2 con; 0-2 aty)
% 0.30/0.45 % Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% 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 %------------------------------------------------------------------------------
% 0.30/0.45 thf(cB,type,
% 0.30/0.45 cB: $i ).
% 0.30/0.45
% 0.30/0.45 thf(cQ,type,
% 0.30/0.45 cQ: $i > $i > $o ).
% 0.30/0.45
% 0.30/0.45 thf(cA,type,
% 0.30/0.45 cA: $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(cLX2107,conjecture,
% 0.30/0.45 ( ( ( cR @ cA @ cB )
% 0.30/0.45 & ! [X: $i,Y: $i] :
% 0.30/0.45 ( ( cR @ X @ Y )
% 0.30/0.45 => ( ( cR @ Y @ X )
% 0.30/0.45 & ( cQ @ X @ Y ) ) )
% 0.30/0.45 & ! [U: $i,V: $i] :
% 0.30/0.45 ( ( cQ @ U @ V )
% 0.30/0.45 => ( cQ @ U @ U ) ) )
% 0.30/0.45 => ( ( cQ @ cA @ cA )
% 0.30/0.45 & ( cQ @ cB @ cB ) ) ) ).
% 0.30/0.45
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 ------------------------
% 1.51/1.23 ---- Embedded in THF ---
% 1.51/1.23 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.51/1.23 %%% Generated on Tue Feb 24 13:55:58 EST 2026
% 1.51/1.23 %%% using '$$dhol' embedding, version 1.3.0.
% 1.51/1.23 %%% Logic specification used:
% 1.51/1.23 %%% thf(spec, logic, $$dhol).
% 1.51/1.23
% 1.51/1.23 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.eyLHmTH8db/DTF2DTF27465.p
% See solution above
% 1.51/1.23 ------------------------
% 1.51/1.24 ---- Cleaned THF ---
% 1.51/1.24 thf(cB,type,
% 1.51/1.24 cB: $i ).
% 1.51/1.24
% 1.51/1.24 thf(cQ,type,
% 1.51/1.24 cQ: $i > $i > $o ).
% 1.51/1.24
% 1.51/1.24 thf(cA,type,
% 1.51/1.24 cA: $i ).
% 1.51/1.24
% 1.51/1.24 thf(cR,type,
% 1.51/1.24 cR: $i > $i > $o ).
% 1.51/1.24
% 1.51/1.24 thf(cLX2107,conjecture,
% 1.51/1.24 ( ( ( cR @ cA @ cB )
% 1.51/1.24 & ! [X: $i,Y: $i] :
% 1.51/1.24 ( ( cR @ X @ Y )
% 1.51/1.24 => ( ( cR @ Y @ X )
% 1.51/1.24 & ( cQ @ X @ Y ) ) )
% 1.51/1.24 & ! [U: $i,V: $i] :
% 1.51/1.24 ( ( cQ @ U @ V )
% 1.51/1.24 => ( cQ @ U @ U ) ) )
% 1.51/1.24 => ( ( cQ @ cA @ cA )
% 1.51/1.24 & ( cQ @ cB @ cB ) ) ) ).
% 1.51/1.24 ------------------------
% 1.51/1.26 % (27580)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_27465 for (2999ds/183Mi)
% 1.51/1.26 % (27585)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_27465 for (2999ds/275Mi)
% 1.51/1.26 % (27580)First to succeed.
% 1.51/1.26 % (27581)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_27465 for (2999ds/4Mi)
% 1.51/1.26 % (27585)Also succeeded, but the first one will report.
% 1.51/1.26 % (27580)Refutation found. Thanks to Tanya!
% 1.51/1.26 % SZS status Theorem for DTF2THF_27465
% 1.51/1.26 % SZS output start Proof for DTF2THF_27465
% 1.51/1.26 thf(func_def_1, type, cQ: $i > $i > $o).
% 1.51/1.26 thf(func_def_3, type, cR: $i > $i > $o).
% 1.51/1.26 thf(f53,plain,(
% 1.51/1.26 $false),
% 1.51/1.26 inference(avatar_sat_refutation,[status(thm)],[f22,f37,f51])).
% 1.51/1.26 thf(f51,plain,(
% 1.51/1.26 spl0_2),
% 1.51/1.26 inference(avatar_contradiction_clause,[status(thm)],[f50])).
% 1.51/1.26 thf(f50,plain,(
% 1.51/1.26 $false | spl0_2),
% 1.51/1.26 inference(trivial_inequality_removal,[status(thm)],[f48])).
% 1.51/1.26 thf(f48,plain,(
% 1.51/1.26 ($true != $true) | spl0_2),
% 1.51/1.26 inference(superposition,[status(thm)],[f46,f13])).
% 1.51/1.26 thf(f13,plain,(
% 1.51/1.26 ((cR @ cA @ cB) = $true)),
% 1.51/1.26 inference(cnf_transformation,[status(thm)],[f8])).
% 1.51/1.26 thf(f8,plain,(
% 1.51/1.26 ((cR @ cA @ cB) = $true) & ! [X0 : $i,X1 : $i] : (((cR @ X0 @ X1) != $true) | (((cQ @ X0 @ X1) = $true) & ((cR @ X1 @ X0) = $true))) & (((cQ @ cA @ cA) != $true) | ((cQ @ cB @ cB) != $true)) & ! [X2 : $i,X3 : $i] : (($true != (cQ @ X3 @ X2)) | ($true = (cQ @ X3 @ X3)))),
% 1.51/1.26 inference(rectify,[status(thm)],[f7])).
% 1.51/1.26 thf(f7,plain,(
% 1.51/1.26 ((cR @ cA @ cB) = $true) & ! [X3 : $i,X2 : $i] : (($true != (cR @ X3 @ X2)) | (($true = (cQ @ X3 @ X2)) & ($true = (cR @ X2 @ X3)))) & (((cQ @ cA @ cA) != $true) | ((cQ @ cB @ cB) != $true)) & ! [X1 : $i,X0 : $i] : (((cQ @ X0 @ X1) != $true) | ($true = (cQ @ X0 @ X0)))),
% 1.51/1.26 inference(flattening,[status(thm)],[f6])).
% 1.51/1.26 thf(f6,plain,(
% 1.51/1.26 (((cQ @ cA @ cA) != $true) | ((cQ @ cB @ cB) != $true)) & (((cR @ cA @ cB) = $true) & ! [X1 : $i,X0 : $i] : (((cQ @ X0 @ X1) != $true) | ($true = (cQ @ X0 @ X0))) & ! [X3 : $i,X2 : $i] : (($true != (cR @ X3 @ X2)) | (($true = (cQ @ X3 @ X2)) & ($true = (cR @ X2 @ X3)))))),
% 1.51/1.26 inference(ennf_transformation,[status(thm)],[f5])).
% 1.51/1.26 thf(f5,plain,(
% 1.51/1.26 ~((((cR @ cA @ cB) = $true) & ! [X0 : $i,X1 : $i] : (((cQ @ X0 @ X1) = $true) => ($true = (cQ @ X0 @ X0))) & ! [X3 : $i,X2 : $i] : (($true = (cR @ X3 @ X2)) => (($true = (cQ @ X3 @ X2)) & ($true = (cR @ X2 @ X3))))) => (((cQ @ cB @ cB) = $true) & ((cQ @ cA @ cA) = $true)))),
% 1.51/1.26 inference(fool_elimination,[status(thm)],[f4])).
% 1.51/1.26 thf(f4,plain,(
% 1.51/1.26 ~(((cR @ cA @ cB) & ! [X0 : $i,X1 : $i] : ((cQ @ X0 @ X1) => (cQ @ X0 @ X0)) & ! [X2 : $i,X3 : $i] : ((cR @ X3 @ X2) => ((cQ @ X3 @ X2) & (cR @ X2 @ X3)))) => ((cQ @ cA @ cA) & (cQ @ cB @ cB)))),
% 1.51/1.26 inference(rectify,[status(thm)],[f2])).
% 1.51/1.26 thf(f2,negated_conjecture,(
% 1.51/1.26 ~(((cR @ cA @ cB) & ! [X2 : $i,X3 : $i] : ((cQ @ X2 @ X3) => (cQ @ X2 @ X2)) & ! [X1 : $i,X0 : $i] : ((cR @ X0 @ X1) => ((cQ @ X0 @ X1) & (cR @ X1 @ X0)))) => ((cQ @ cA @ cA) & (cQ @ cB @ cB)))),
% 1.51/1.26 inference(negated_conjecture,[status(cth)],[f1])).
% 1.51/1.26 thf(f1,conjecture,(
% 1.51/1.26 ((cR @ cA @ cB) & ! [X2 : $i,X3 : $i] : ((cQ @ X2 @ X3) => (cQ @ X2 @ X2)) & ! [X1 : $i,X0 : $i] : ((cR @ X0 @ X1) => ((cQ @ X0 @ X1) & (cR @ X1 @ X0)))) => ((cQ @ cA @ cA) & (cQ @ cB @ cB))),
% 1.51/1.26 file('/export/starexec/sandbox2/tmp/tmp.eyLHmTH8db/DTF2THF_27465.p',cLX2107)).
% 1.51/1.26 thf(f46,plain,(
% 1.51/1.26 ( ! [X0 : $i] : (((cR @ cA @ X0) != $true)) ) | spl0_2),
% 1.51/1.26 inference(trivial_inequality_removal,[status(thm)],[f45])).
% 1.51/1.26 thf(f45,plain,(
% 1.51/1.26 ( ! [X0 : $i] : (($true != $true) | ((cR @ cA @ X0) != $true)) ) | spl0_2),
% 1.51/1.26 inference(superposition,[status(thm)],[f41,f12])).
% 1.51/1.26 thf(f12,plain,(
% 1.51/1.26 ( ! [X0 : $i,X1 : $i] : (((cQ @ X0 @ X1) = $true) | ((cR @ X0 @ X1) != $true)) )),
% 1.51/1.26 inference(cnf_transformation,[status(thm)],[f8])).
% 1.51/1.26 thf(f41,plain,(
% 1.51/1.26 ( ! [X0 : $i] : (($true != (cQ @ cA @ X0))) ) | spl0_2),
% 1.51/1.26 inference(trivial_inequality_removal,[status(thm)],[f38])).
% 1.51/1.26 thf(f38,plain,(
% 1.51/1.26 ( ! [X0 : $i] : (($true != (cQ @ cA @ X0)) | ($true != $true)) ) | spl0_2),
% 1.51/1.26 inference(superposition,[status(thm)],[f21,f9])).
% 1.51/1.26 thf(f9,plain,(
% 1.51/1.26 ( ! [X2 : $i,X3 : $i] : (($true = (cQ @ X3 @ X3)) | ($true != (cQ @ X3 @ X2))) )),
% 1.51/1.26 inference(cnf_transformation,[status(thm)],[f8])).
% 1.51/1.26 thf(f21,plain,(
% 1.51/1.26 ((cQ @ cA @ cA) != $true) | spl0_2),
% 1.51/1.26 inference(avatar_component_clause,[status(thm)],[f19])).
% 1.51/1.26 thf(f19,definition,(
% 1.51/1.26 spl0_2 <=> ((cQ @ cA @ cA) = $true)),
% 1.51/1.26 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.51/1.26 thf(f37,plain,(
% 1.51/1.26 spl0_1),
% 1.51/1.26 inference(avatar_contradiction_clause,[status(thm)],[f36])).
% 1.51/1.26 thf(f36,plain,(
% 1.51/1.26 $false | spl0_1),
% 1.51/1.26 inference(trivial_inequality_removal,[status(thm)],[f33])).
% 1.51/1.26 thf(f33,plain,(
% 1.51/1.26 ($true != $true) | spl0_1),
% 1.51/1.26 inference(superposition,[status(thm)],[f32,f13])).
% 1.51/1.26 thf(f32,plain,(
% 1.51/1.26 ( ! [X0 : $i] : (((cR @ X0 @ cB) != $true)) ) | spl0_1),
% 1.51/1.26 inference(trivial_inequality_removal,[status(thm)],[f31])).
% 1.51/1.26 thf(f31,plain,(
% 1.51/1.26 ( ! [X0 : $i] : (((cR @ X0 @ cB) != $true) | ($true != $true)) ) | spl0_1),
% 1.51/1.26 inference(superposition,[status(thm)],[f30,f11])).
% 1.51/1.26 thf(f11,plain,(
% 1.51/1.26 ( ! [X0 : $i,X1 : $i] : (((cR @ X1 @ X0) = $true) | ((cR @ X0 @ X1) != $true)) )),
% 1.51/1.26 inference(cnf_transformation,[status(thm)],[f8])).
% 1.51/1.26 thf(f30,plain,(
% 1.51/1.26 ( ! [X0 : $i] : (($true != (cR @ cB @ X0))) ) | spl0_1),
% 1.51/1.26 inference(trivial_inequality_removal,[status(thm)],[f28])).
% 1.51/1.26 thf(f28,plain,(
% 1.51/1.26 ( ! [X0 : $i] : (($true != (cR @ cB @ X0)) | ($true != $true)) ) | spl0_1),
% 1.51/1.26 inference(superposition,[status(thm)],[f24,f12])).
% 1.51/1.26 thf(f24,plain,(
% 1.51/1.26 ( ! [X0 : $i] : (($true != (cQ @ cB @ X0))) ) | spl0_1),
% 1.51/1.26 inference(trivial_inequality_removal,[status(thm)],[f23])).
% 1.51/1.26 thf(f23,plain,(
% 1.51/1.26 ( ! [X0 : $i] : (($true != (cQ @ cB @ X0)) | ($true != $true)) ) | spl0_1),
% 1.51/1.26 inference(superposition,[status(thm)],[f17,f9])).
% 1.51/1.26 thf(f17,plain,(
% 1.51/1.26 ((cQ @ cB @ cB) != $true) | spl0_1),
% 1.51/1.26 inference(avatar_component_clause,[status(thm)],[f15])).
% 1.51/1.26 thf(f15,definition,(
% 1.51/1.26 spl0_1 <=> ((cQ @ cB @ cB) = $true)),
% 1.51/1.26 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.51/1.26 thf(f22,plain,(
% 1.51/1.26 ~spl0_1 | ~spl0_2),
% 1.51/1.26 inference(avatar_split_clause,[status(thm)],[f10,f19,f15])).
% 1.51/1.26 thf(f10,plain,(
% 1.51/1.26 ((cQ @ cB @ cB) != $true) | ((cQ @ cA @ cA) != $true)),
% 1.51/1.26 inference(cnf_transformation,[status(thm)],[f8])).
% 1.51/1.26 % SZS output end Proof for DTF2THF_27465
% 1.51/1.26 % (27580)------------------------------
% 1.51/1.26 % (27580)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.26 % (27580)Termination reason: Refutation
% 1.51/1.26
% 1.51/1.26 % (27580)Memory used [KB]: 5500
% 1.51/1.26 % (27580)Time elapsed: 0.004 s
% 1.51/1.26 % (27580)Instructions burned: 4 (million)
% 1.51/1.26 % (27580)------------------------------
% 1.51/1.26 % (27580)------------------------------
% 1.51/1.26 % (27579)Success in time 0.007 s
%------------------------------------------------------------------------------