%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO091^5 : 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 : n017.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 09:53:21 AM UTC 2026
% Result : Theorem 1.64s 1.44s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 84 ( 1 unt; 0 typ; 5 def)
% Number of atoms : 586 ( 168 equ)
% Maximal formula atoms : 32 ( 6 avg)
% Number of connectives : 430 ( 162 ~; 216 |; 25 &)
% ( 25 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 354 ( 252 fml; 102 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 8 usr; 10 prp; 0-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 24 ( 12 !; 12 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
tff(f110,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f35,f36,f37,f38,f39,f40,f41,f42,f51,f61,f66,f73,f81,f83,f86,f92,f96,f109]) ).
tff(f109,plain,
( ~ spl3_3
| ~ spl3_4
| ~ spl3_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f108]) ).
tff(f108,plain,
( $false
| ~ spl3_3
| ~ spl3_4
| ~ spl3_5 ),
inference(trivial_inequality_removal,[status(thm)],[f107]) ).
tff(f107,plain,
( ( $false = $true )
| ~ spl3_3
| ~ spl3_4
| ~ spl3_5 ),
inference(backward_demodulation,[status(thm)],[f34,f103]) ).
tff(f103,plain,
( ( $false = sK0 )
| ~ spl3_3
| ~ spl3_5 ),
inference(superposition,[status(thm)],[f65,f29]) ).
tff(f29,plain,
( ( sK2 = sK0 )
| ~ spl3_3 ),
inference(avatar_component_clause,[status(thm)],[f28]) ).
tff(f28,definition,
( spl3_3
<=> ( sK2 = sK0 ) ),
introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition]) ).
tff(f65,plain,
( ( $false = sK2 )
| ~ spl3_5 ),
inference(avatar_component_clause,[status(thm)],[f63]) ).
tff(f63,definition,
( spl3_5
<=> ( $false = sK2 ) ),
introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition]) ).
tff(f34,plain,
( ( $true = sK0 )
| ~ spl3_4 ),
inference(avatar_component_clause,[status(thm)],[f32]) ).
tff(f32,definition,
( spl3_4
<=> ( $true = sK0 ) ),
introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition]) ).
tff(f96,plain,
( spl3_1
| spl3_2
| ~ spl3_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f95]) ).
tff(f95,plain,
( $false
| spl3_1
| spl3_2
| ~ spl3_5 ),
inference(subsumption_resolution,[status(thm)],[f94,f88]) ).
tff(f88,plain,
( ( $false != sK1 )
| spl3_2
| ~ spl3_5 ),
inference(backward_demodulation,[status(thm)],[f26,f65]) ).
tff(f26,plain,
( ( sK1 != sK2 )
| spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f24]) ).
tff(f24,definition,
( spl3_2
<=> ( sK1 = sK2 ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
tff(f94,plain,
( ( $false = sK1 )
| spl3_1 ),
inference(trivial_inequality_removal,[status(thm)],[f93]) ).
tff(f93,plain,
( ( $true != $true )
| ( $false = sK1 )
| spl3_1 ),
inference(fool_paramodulation,[status(thm)],[f21]) ).
tff(f21,plain,
( ( sK1 != $true )
| spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f20]) ).
tff(f20,definition,
( spl3_1
<=> ( sK1 = $true ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
tff(f92,plain,
( spl3_3
| spl3_4
| ~ spl3_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f91]) ).
tff(f91,plain,
( $false
| spl3_3
| spl3_4
| ~ spl3_5 ),
inference(subsumption_resolution,[status(thm)],[f90,f87]) ).
tff(f87,plain,
( ( $false != sK0 )
| spl3_3
| ~ spl3_5 ),
inference(backward_demodulation,[status(thm)],[f30,f65]) ).
tff(f30,plain,
( ( sK2 != sK0 )
| spl3_3 ),
inference(avatar_component_clause,[status(thm)],[f28]) ).
tff(f90,plain,
( ( $false = sK0 )
| spl3_4 ),
inference(trivial_inequality_removal,[status(thm)],[f89]) ).
tff(f89,plain,
( ( $true != $true )
| ( $false = sK0 )
| spl3_4 ),
inference(fool_paramodulation,[status(thm)],[f33]) ).
tff(f33,plain,
( ( $true != sK0 )
| spl3_4 ),
inference(avatar_component_clause,[status(thm)],[f32]) ).
tff(f86,plain,
( spl3_5
| ~ spl3_1
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f85,f24,f20,f63]) ).
tff(f85,plain,
( ( $false = sK2 )
| ~ spl3_1
| spl3_2 ),
inference(subsumption_resolution,[status(thm)],[f84,f22]) ).
tff(f22,plain,
( ( sK1 = $true )
| ~ spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f20]) ).
tff(f84,plain,
( ( sK1 != $true )
| ( $false = sK2 )
| spl3_2 ),
inference(fool_paramodulation,[status(thm)],[f26]) ).
tff(f83,plain,
( ~ spl3_1
| ~ spl3_2
| spl3_3
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f82]) ).
tff(f82,plain,
( $false
| ~ spl3_1
| ~ spl3_2
| spl3_3
| ~ spl3_4 ),
inference(subsumption_resolution,[status(thm)],[f79,f22]) ).
tff(f79,plain,
( ( sK1 != $true )
| ~ spl3_2
| spl3_3
| ~ spl3_4 ),
inference(superposition,[status(thm)],[f74,f25]) ).
tff(f25,plain,
( ( sK1 = sK2 )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f24]) ).
tff(f74,plain,
( ( $true != sK2 )
| spl3_3
| ~ spl3_4 ),
inference(backward_demodulation,[status(thm)],[f30,f34]) ).
tff(f81,plain,
( spl3_5
| spl3_3
| ~ spl3_4 ),
inference(avatar_split_clause,[status(thm)],[f80,f32,f28,f63]) ).
tff(f80,plain,
( ( $false = sK2 )
| spl3_3
| ~ spl3_4 ),
inference(trivial_inequality_removal,[status(thm)],[f78]) ).
tff(f78,plain,
( ( $true != $true )
| ( $false = sK2 )
| spl3_3
| ~ spl3_4 ),
inference(fool_paramodulation,[status(thm)],[f74]) ).
tff(f73,plain,
( ~ spl3_1
| ~ spl3_2
| ~ spl3_3
| ~ spl3_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f72]) ).
tff(f72,plain,
( $false
| ~ spl3_1
| ~ spl3_2
| ~ spl3_3
| ~ spl3_5 ),
inference(trivial_inequality_removal,[status(thm)],[f71]) ).
tff(f71,plain,
( ( $false = $true )
| ~ spl3_1
| ~ spl3_2
| ~ spl3_3
| ~ spl3_5 ),
inference(backward_demodulation,[status(thm)],[f22,f69]) ).
tff(f69,plain,
( ( $false = sK1 )
| ~ spl3_2
| ~ spl3_3
| ~ spl3_5 ),
inference(backward_demodulation,[status(thm)],[f67,f68]) ).
tff(f68,plain,
( ( $false = sK0 )
| ~ spl3_3
| ~ spl3_5 ),
inference(backward_demodulation,[status(thm)],[f29,f65]) ).
tff(f67,plain,
( ( sK1 = sK0 )
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[status(thm)],[f25,f29]) ).
tff(f66,plain,
( spl3_5
| spl3_4
| ~ spl3_3 ),
inference(avatar_split_clause,[status(thm)],[f52,f28,f32,f63]) ).
tff(f52,plain,
( ( $true = sK0 )
| ( $false = sK2 )
| ~ spl3_3 ),
inference(fool_paramodulation,[status(thm)],[f29]) ).
tff(f61,plain,
( spl3_1
| ~ spl3_2
| ~ spl3_3
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f60]) ).
tff(f60,plain,
( $false
| spl3_1
| ~ spl3_2
| ~ spl3_3
| ~ spl3_4 ),
inference(trivial_inequality_removal,[status(thm)],[f59]) ).
tff(f59,plain,
( ( $false = $true )
| spl3_1
| ~ spl3_2
| ~ spl3_3
| ~ spl3_4 ),
inference(backward_demodulation,[status(thm)],[f34,f55]) ).
tff(f55,plain,
( ( $false = sK0 )
| spl3_1
| ~ spl3_2
| ~ spl3_3 ),
inference(superposition,[status(thm)],[f45,f29]) ).
tff(f45,plain,
( ( $false = sK2 )
| spl3_1
| ~ spl3_2 ),
inference(backward_demodulation,[status(thm)],[f25,f44]) ).
tff(f44,plain,
( ( $false = sK1 )
| spl3_1 ),
inference(trivial_inequality_removal,[status(thm)],[f43]) ).
tff(f43,plain,
( ( $true != $true )
| ( $false = sK1 )
| spl3_1 ),
inference(fool_paramodulation,[status(thm)],[f21]) ).
tff(f51,plain,
( spl3_1
| ~ spl3_2
| spl3_3
| spl3_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f50]) ).
tff(f50,plain,
( $false
| spl3_1
| ~ spl3_2
| spl3_3
| spl3_4 ),
inference(subsumption_resolution,[status(thm)],[f49,f47]) ).
tff(f47,plain,
( ( $false != sK0 )
| spl3_1
| ~ spl3_2
| spl3_3 ),
inference(backward_demodulation,[status(thm)],[f30,f45]) ).
tff(f49,plain,
( ( $false = sK0 )
| spl3_4 ),
inference(trivial_inequality_removal,[status(thm)],[f48]) ).
tff(f48,plain,
( ( $true != $true )
| ( $false = sK0 )
| spl3_4 ),
inference(fool_paramodulation,[status(thm)],[f33]) ).
tff(f42,plain,
( spl3_4
| spl3_3
| ~ spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f13,f24,f20,f28,f32]) ).
tff(f13,plain,
( ( $true = sK0 )
| ( sK1 != sK2 )
| ( sK2 = sK0 )
| ( sK1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
tff(f10,plain,
( ( ( ( ( sK1 != sK2 )
| ( $true != sK0 ) )
& ( ( sK1 = sK2 )
| ( $true = sK0 ) ) )
| ( ( ( sK2 != sK0 )
| ( sK1 != $true ) )
& ( ( sK2 = sK0 )
| ( sK1 = $true ) ) ) )
& ( ( ( ( $true = sK0 )
| ( sK1 != sK2 ) )
& ( ( sK1 = sK2 )
| ( $true != sK0 ) ) )
| ( ( ( sK1 = $true )
| ( sK2 != sK0 ) )
& ( ( sK2 = sK0 )
| ( sK1 != $true ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f9]) ).
tff(f9,plain,
( ? [X0: $o,X1: $o,X2: $o] :
( ( ( ( ( (X1) != (X2) )
| ( $true != (X0) ) )
& ( ( (X1) = (X2) )
| ( $true = (X0) ) ) )
| ( ( ( (X0) != (X2) )
| ( $true != (X1) ) )
& ( ( (X0) = (X2) )
| ( $true = (X1) ) ) ) )
& ( ( ( ( $true = (X0) )
| ( (X1) != (X2) ) )
& ( ( (X1) = (X2) )
| ( $true != (X0) ) ) )
| ( ( ( $true = (X1) )
| ( (X0) != (X2) ) )
& ( ( (X0) = (X2) )
| ( $true != (X1) ) ) ) ) )
=> ( ( ( ( ( sK1 != sK2 )
| ( $true != sK0 ) )
& ( ( sK1 = sK2 )
| ( $true = sK0 ) ) )
| ( ( ( sK2 != sK0 )
| ( sK1 != $true ) )
& ( ( sK2 = sK0 )
| ( sK1 = $true ) ) ) )
& ( ( ( ( $true = sK0 )
| ( sK1 != sK2 ) )
& ( ( sK1 = sK2 )
| ( $true != sK0 ) ) )
| ( ( ( sK1 = $true )
| ( sK2 != sK0 ) )
& ( ( sK2 = sK0 )
| ( sK1 != $true ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
tff(f8,plain,
? [X0: $o,X1: $o,X2: $o] :
( ( ( ( ( (X1) != (X2) )
| ( $true != (X0) ) )
& ( ( (X1) = (X2) )
| ( $true = (X0) ) ) )
| ( ( ( (X0) != (X2) )
| ( $true != (X1) ) )
& ( ( (X0) = (X2) )
| ( $true = (X1) ) ) ) )
& ( ( ( ( $true = (X0) )
| ( (X1) != (X2) ) )
& ( ( (X1) = (X2) )
| ( $true != (X0) ) ) )
| ( ( ( $true = (X1) )
| ( (X0) != (X2) ) )
& ( ( (X0) = (X2) )
| ( $true != (X1) ) ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
tff(f7,plain,
? [X2: $o,X1: $o,X0: $o] :
( ( ( ( ( (X0) != (X1) )
| ( $true != (X2) ) )
& ( ( (X0) = (X1) )
| ( $true = (X2) ) ) )
| ( ( ( (X0) != (X2) )
| ( $true != (X1) ) )
& ( ( (X0) = (X2) )
| ( $true = (X1) ) ) ) )
& ( ( ( ( $true = (X2) )
| ( (X0) != (X1) ) )
& ( ( (X0) = (X1) )
| ( $true != (X2) ) ) )
| ( ( ( $true = (X1) )
| ( (X0) != (X2) ) )
& ( ( (X0) = (X2) )
| ( $true != (X1) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
tff(f6,plain,
? [X2: $o,X1: $o,X0: $o] :
( ( ( $true = (X1) )
<=> ( (X0) = (X2) ) )
<~> ( ( $true = (X2) )
<=> ( (X0) = (X1) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
tff(f5,plain,
~ ! [X2: $o,X0: $o,X1: $o] :
( ( ( $true = (X1) )
<=> ( (X0) = (X2) ) )
<=> ( ( $true = (X2) )
<=> ( (X0) = (X1) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
tff(f4,plain,
~ ! [X0: $o,X1: $o,X2: $o] :
( ( ( (X1)
<=> (X0) )
<=> (X2) )
<=> ( ( (X0)
<=> (X2) )
<=> (X1) ) ),
inference(rectify,[status(thm)],[f2]) ).
tff(f2,negated_conjecture,
~ ! [X1: $o,X0: $o,X2: $o] :
( ( ( (X0)
<=> (X1) )
<=> (X2) )
<=> ( ( (X1)
<=> (X2) )
<=> (X0) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f1,conjecture,
! [X1: $o,X0: $o,X2: $o] :
( ( ( (X0)
<=> (X1) )
<=> (X2) )
<=> ( ( (X1)
<=> (X2) )
<=> (X0) ) ),
file('/export/starexec/sandbox/tmp/tmp.vUHBJ673Wd/DTF2THF_14529.p',cTHM50Q) ).
tff(f41,plain,
( spl3_2
| ~ spl3_4
| spl3_3
| ~ spl3_1 ),
inference(avatar_split_clause,[status(thm)],[f11,f20,f28,f32,f24]) ).
tff(f11,plain,
( ( sK1 = sK2 )
| ( $true != sK0 )
| ( sK1 != $true )
| ( sK2 = sK0 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
tff(f40,plain,
( ~ spl3_1
| ~ spl3_3
| spl3_2
| spl3_4 ),
inference(avatar_split_clause,[status(thm)],[f16,f32,f24,f28,f20]) ).
tff(f16,plain,
( ( sK1 = sK2 )
| ( sK1 != $true )
| ( sK2 != sK0 )
| ( $true = sK0 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
tff(f39,plain,
( ~ spl3_4
| spl3_1
| ~ spl3_2
| spl3_3 ),
inference(avatar_split_clause,[status(thm)],[f17,f28,f24,f20,f32]) ).
tff(f17,plain,
( ( sK2 = sK0 )
| ( sK1 = $true )
| ( sK1 != sK2 )
| ( $true != sK0 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
tff(f38,plain,
( ~ spl3_4
| ~ spl3_2
| ~ spl3_1
| ~ spl3_3 ),
inference(avatar_split_clause,[status(thm)],[f18,f28,f20,f24,f32]) ).
tff(f18,plain,
( ( sK1 != sK2 )
| ( sK1 != $true )
| ( $true != sK0 )
| ( sK2 != sK0 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
tff(f37,plain,
( spl3_3
| spl3_4
| spl3_2
| spl3_1 ),
inference(avatar_split_clause,[status(thm)],[f15,f20,f24,f32,f28]) ).
tff(f15,plain,
( ( $true = sK0 )
| ( sK1 = $true )
| ( sK2 = sK0 )
| ( sK1 = sK2 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
tff(f36,plain,
( ~ spl3_3
| ~ spl3_4
| spl3_1
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f12,f24,f20,f32,f28]) ).
tff(f12,plain,
( ( sK1 = $true )
| ( sK2 != sK0 )
| ( sK1 = sK2 )
| ( $true != sK0 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
tff(f35,plain,
( spl3_1
| ~ spl3_2
| ~ spl3_3
| spl3_4 ),
inference(avatar_split_clause,[status(thm)],[f14,f32,f28,f24,f20]) ).
tff(f14,plain,
( ( sK1 = $true )
| ( sK2 != sK0 )
| ( $true = sK0 )
| ( sK1 != sK2 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO091^5 : TPTP v9.2.1. Released v4.0.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n017.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 14:22:41 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
% 0.33/0.48 ---- Original DTF file ---
% 0.33/0.48 thf(spec,logic,$$dhol).
% 0.33/0.48 %------------------------------------------------------------------------------
% 0.33/0.48 % File : SYO091^5 : TPTP v9.2.1. Released v4.0.0.
% 0.33/0.48 % Domain : Syntactic
% 0.33/0.48 % Problem : TPS problem THM50Q
% 0.33/0.48 % Version : Especial.
% 0.33/0.48 % English :
% 0.33/0.48
% 0.33/0.48 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.33/0.48 % Source : [Bro09]
% 0.33/0.48 % Names : tps_0185 [Bro09]
% 0.33/0.48 % : THM50Q [TPS]
% 0.33/0.48
% 0.33/0.48 % Status : Theorem
% 0.33/0.48 % Rating : 0.17 v9.1.0, 0.12 v9.0.0, 0.17 v8.2.0, 0.18 v8.1.0, 0.17 v7.4.0, 0.22 v7.3.0, 0.20 v7.2.0, 0.25 v7.1.0, 0.29 v7.0.0, 0.25 v6.4.0, 0.29 v6.3.0, 0.33 v6.2.0, 0.50 v6.1.0, 0.33 v6.0.0, 0.17 v5.5.0, 0.00 v4.0.0
% 0.33/0.48 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.33/0.48 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.33/0.48 % Maximal formula atoms : 0 ( 0 avg)
% 0.33/0.48 % Number of connectives : 5 ( 0 ~; 0 |; 0 &; 0 @)
% 0.33/0.48 % ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% 0.33/0.48 % Maximal formula depth : 7 ( 7 avg)
% 0.33/0.48 % Number of types : 1 ( 0 usr)
% 0.33/0.48 % Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% 0.33/0.48 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.33/0.48 % Number of variables : 3 ( 0 ^; 3 !; 0 ?; 3 :)
% 0.33/0.48 % SPC : TH0_THM_NEQ_NAR
% 0.33/0.48
% 0.33/0.48 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.33/0.48 % project in the Department of Mathematical Sciences at Carnegie
% 0.33/0.48 % Mellon University. Distributed under the Creative Commons copyleft
% 0.33/0.48 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.33/0.48 %------------------------------------------------------------------------------
% 0.33/0.48 thf(cTHM50Q,conjecture,
% 0.33/0.48 ! [P: $o,Q: $o,R: $o] :
% 0.33/0.48 ( ( ( P
% 0.33/0.48 <=> Q )
% 0.33/0.48 <=> R )
% 0.33/0.48 <=> ( P
% 0.33/0.48 <=> ( Q
% 0.33/0.48 <=> R ) ) ) ).
% 0.33/0.48
% 0.33/0.48 %------------------------------------------------------------------------------
% 0.33/0.48 ------------------------
% 1.64/1.40 ---- Embedded in THF ---
% 1.64/1.40 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.64/1.40 %%% Generated on Tue Feb 24 14:22:42 EST 2026
% 1.64/1.40 %%% using '$$dhol' embedding, version 1.3.0.
% 1.64/1.40 %%% Logic specification used:
% 1.64/1.40 %%% thf(spec, logic, $$dhol).
% 1.64/1.40
% 1.64/1.40 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.vUHBJ673Wd/DTF2DTF14529.p
% See solution above
% 1.64/1.40 ------------------------
% 1.64/1.41 ---- Cleaned THF ---
% 1.64/1.41 thf(cTHM50Q,conjecture,
% 1.64/1.41 ! [P: $o,Q: $o,R: $o] :
% 1.64/1.41 ( ( ( P
% 1.64/1.41 <=> Q )
% 1.64/1.41 <=> R )
% 1.64/1.41 <=> ( P
% 1.64/1.41 <=> ( Q
% 1.64/1.41 <=> R ) ) ) ).
% 1.64/1.41 ------------------------
% 1.64/1.43 % (14645)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_14529 for (3000ds/2Mi)
% 1.64/1.43 % (14644)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_14529 for (3000ds/2Mi)
% 1.64/1.43 % (14646)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_14529 for (3000ds/275Mi)
% 1.64/1.43 % (14641)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_14529 for (3000ds/183Mi)
% 1.64/1.43 % (14642)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_14529 for (3000ds/4Mi)
% 1.64/1.43 % (14643)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_14529 for (3000ds/27Mi)
% 1.64/1.43 % (14647)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_14529 for (3000ds/18Mi)
% 1.64/1.43 % (14645)Instruction limit reached!
% 1.64/1.43 % (14645)------------------------------
% 1.64/1.43 % (14645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.43 % (14645)Termination reason: Unknown
% 1.64/1.43 % (14645)Termination phase: Saturation
% 1.64/1.43
% 1.64/1.43 % (14645)Memory used [KB]: 5500
% 1.64/1.43 % (14645)Time elapsed: 0.003 s
% 1.64/1.43 % (14645)Instructions burned: 2 (million)
% 1.64/1.43 % (14645)------------------------------
% 1.64/1.43 % (14645)------------------------------
% 1.64/1.43 % (14646)Refutation not found, incomplete strategy
% 1.64/1.43 % (14646)------------------------------
% 1.64/1.43 % (14646)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.43 % (14646)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.43
% 1.64/1.43
% 1.64/1.43 % (14646)Memory used [KB]: 5500
% 1.64/1.43 % (14646)Time elapsed: 0.003 s
% 1.64/1.43 % (14646)Instructions burned: 2 (million)
% 1.64/1.43 % (14646)------------------------------
% 1.64/1.43 % (14646)------------------------------
% 1.64/1.43 % (14644)Instruction limit reached!
% 1.64/1.43 % (14644)------------------------------
% 1.64/1.43 % (14644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.43 % (14644)Termination reason: Unknown
% 1.64/1.43 % (14644)Termination phase: Saturation
% 1.64/1.43
% 1.64/1.43 % (14644)Memory used [KB]: 5500
% 1.64/1.43 % (14644)Time elapsed: 0.004 s
% 1.64/1.43 % (14644)Instructions burned: 3 (million)
% 1.64/1.43 % (14644)------------------------------
% 1.64/1.43 % (14644)------------------------------
% 1.64/1.44 % (14642)First to succeed.
% 1.64/1.44 % (14647)Also succeeded, but the first one will report.
% 1.64/1.44 % (14642)Refutation found. Thanks to Tanya!
% 1.64/1.44 % SZS status Theorem for DTF2THF_14529
% 1.64/1.44 % SZS output start Proof for DTF2THF_14529
% 1.64/1.44 tff(f110,plain,(
% 1.64/1.44 $false),
% 1.64/1.44 inference(avatar_sat_refutation,[status(thm)],[f35,f36,f37,f38,f39,f40,f41,f42,f51,f61,f66,f73,f81,f83,f86,f92,f96,f109])).
% 1.64/1.44 tff(f109,plain,(
% 1.64/1.44 ~spl3_3 | ~spl3_4 | ~spl3_5),
% 1.64/1.44 inference(avatar_contradiction_clause,[status(thm)],[f108])).
% 1.64/1.44 tff(f108,plain,(
% 1.64/1.44 $false | (~spl3_3 | ~spl3_4 | ~spl3_5)),
% 1.64/1.44 inference(trivial_inequality_removal,[status(thm)],[f107])).
% 1.64/1.44 tff(f107,plain,(
% 1.64/1.44 ($false = $true) | (~spl3_3 | ~spl3_4 | ~spl3_5)),
% 1.64/1.44 inference(backward_demodulation,[status(thm)],[f34,f103])).
% 1.64/1.44 tff(f103,plain,(
% 1.64/1.44 ($false = sK0) | (~spl3_3 | ~spl3_5)),
% 1.64/1.44 inference(superposition,[status(thm)],[f65,f29])).
% 1.64/1.44 tff(f29,plain,(
% 1.64/1.44 (sK2 = sK0) | ~spl3_3),
% 1.64/1.44 inference(avatar_component_clause,[status(thm)],[f28])).
% 1.64/1.44 tff(f28,definition,(
% 1.64/1.44 spl3_3 <=> (sK2 = sK0)),
% 1.64/1.44 introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition])).
% 1.64/1.44 tff(f65,plain,(
% 1.64/1.44 ($false = sK2) | ~spl3_5),
% 1.64/1.44 inference(avatar_component_clause,[status(thm)],[f63])).
% 1.64/1.44 tff(f63,definition,(
% 1.64/1.44 spl3_5 <=> ($false = sK2)),
% 1.64/1.44 introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition])).
% 1.64/1.44 tff(f34,plain,(
% 1.64/1.44 ($true = sK0) | ~spl3_4),
% 1.64/1.44 inference(avatar_component_clause,[status(thm)],[f32])).
% 1.64/1.44 tff(f32,definition,(
% 1.64/1.44 spl3_4 <=> ($true = sK0)),
% 1.64/1.44 introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition])).
% 1.64/1.44 tff(f96,plain,(
% 1.64/1.44 spl3_1 | spl3_2 | ~spl3_5),
% 1.64/1.44 inference(avatar_contradiction_clause,[status(thm)],[f95])).
% 1.64/1.44 tff(f95,plain,(
% 1.64/1.44 $false | (spl3_1 | spl3_2 | ~spl3_5)),
% 1.64/1.44 inference(subsumption_resolution,[status(thm)],[f94,f88])).
% 1.64/1.44 tff(f88,plain,(
% 1.64/1.44 ($false != sK1) | (spl3_2 | ~spl3_5)),
% 1.64/1.44 inference(backward_demodulation,[status(thm)],[f26,f65])).
% 1.64/1.44 tff(f26,plain,(
% 1.64/1.44 (sK1 != sK2) | spl3_2),
% 1.64/1.44 inference(avatar_component_clause,[status(thm)],[f24])).
% 1.64/1.44 tff(f24,definition,(
% 1.64/1.44 spl3_2 <=> (sK1 = sK2)),
% 1.64/1.44 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.64/1.44 tff(f94,plain,(
% 1.64/1.44 ($false = sK1) | spl3_1),
% 1.64/1.44 inference(trivial_inequality_removal,[status(thm)],[f93])).
% 1.64/1.44 tff(f93,plain,(
% 1.64/1.44 ($true != $true) | ($false = sK1) | spl3_1),
% 1.64/1.44 inference(fool_paramodulation,[status(thm)],[f21])).
% 1.64/1.44 tff(f21,plain,(
% 1.64/1.44 (sK1 != $true) | spl3_1),
% 1.64/1.44 inference(avatar_component_clause,[status(thm)],[f20])).
% 1.64/1.44 tff(f20,definition,(
% 1.64/1.44 spl3_1 <=> (sK1 = $true)),
% 1.64/1.44 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.64/1.44 tff(f92,plain,(
% 1.64/1.44 spl3_3 | spl3_4 | ~spl3_5),
% 1.64/1.44 inference(avatar_contradiction_clause,[status(thm)],[f91])).
% 1.64/1.44 tff(f91,plain,(
% 1.64/1.44 $false | (spl3_3 | spl3_4 | ~spl3_5)),
% 1.64/1.44 inference(subsumption_resolution,[status(thm)],[f90,f87])).
% 1.64/1.44 tff(f87,plain,(
% 1.64/1.44 ($false != sK0) | (spl3_3 | ~spl3_5)),
% 1.64/1.44 inference(backward_demodulation,[status(thm)],[f30,f65])).
% 1.64/1.44 tff(f30,plain,(
% 1.64/1.44 (sK2 != sK0) | spl3_3),
% 1.64/1.44 inference(avatar_component_clause,[status(thm)],[f28])).
% 1.64/1.44 tff(f90,plain,(
% 1.64/1.44 ($false = sK0) | spl3_4),
% 1.64/1.44 inference(trivial_inequality_removal,[status(thm)],[f89])).
% 1.64/1.44 tff(f89,plain,(
% 1.64/1.44 ($true != $true) | ($false = sK0) | spl3_4),
% 1.64/1.44 inference(fool_paramodulation,[status(thm)],[f33])).
% 1.64/1.44 tff(f33,plain,(
% 1.64/1.44 ($true != sK0) | spl3_4),
% 1.64/1.44 inference(avatar_component_clause,[status(thm)],[f32])).
% 1.64/1.44 tff(f86,plain,(
% 1.64/1.44 spl3_5 | ~spl3_1 | spl3_2),
% 1.64/1.44 inference(avatar_split_clause,[status(thm)],[f85,f24,f20,f63])).
% 1.64/1.44 tff(f85,plain,(
% 1.64/1.44 ($false = sK2) | (~spl3_1 | spl3_2)),
% 1.64/1.44 inference(subsumption_resolution,[status(thm)],[f84,f22])).
% 1.64/1.44 tff(f22,plain,(
% 1.64/1.44 (sK1 = $true) | ~spl3_1),
% 1.64/1.44 inference(avatar_component_clause,[status(thm)],[f20])).
% 1.64/1.44 tff(f84,plain,(
% 1.64/1.44 (sK1 != $true) | ($false = sK2) | spl3_2),
% 1.64/1.44 inference(fool_paramodulation,[status(thm)],[f26])).
% 1.64/1.44 tff(f83,plain,(
% 1.64/1.44 ~spl3_1 | ~spl3_2 | spl3_3 | ~spl3_4),
% 1.64/1.44 inference(avatar_contradiction_clause,[status(thm)],[f82])).
% 1.64/1.44 tff(f82,plain,(
% 1.64/1.44 $false | (~spl3_1 | ~spl3_2 | spl3_3 | ~spl3_4)),
% 1.64/1.44 inference(subsumption_resolution,[status(thm)],[f79,f22])).
% 1.64/1.44 tff(f79,plain,(
% 1.64/1.44 (sK1 != $true) | (~spl3_2 | spl3_3 | ~spl3_4)),
% 1.64/1.44 inference(superposition,[status(thm)],[f74,f25])).
% 1.64/1.44 tff(f25,plain,(
% 1.64/1.44 (sK1 = sK2) | ~spl3_2),
% 1.64/1.44 inference(avatar_component_clause,[status(thm)],[f24])).
% 1.64/1.44 tff(f74,plain,(
% 1.64/1.44 ($true != sK2) | (spl3_3 | ~spl3_4)),
% 1.64/1.44 inference(backward_demodulation,[status(thm)],[f30,f34])).
% 1.64/1.44 tff(f81,plain,(
% 1.64/1.44 spl3_5 | spl3_3 | ~spl3_4),
% 1.64/1.44 inference(avatar_split_clause,[status(thm)],[f80,f32,f28,f63])).
% 1.64/1.44 tff(f80,plain,(
% 1.64/1.44 ($false = sK2) | (spl3_3 | ~spl3_4)),
% 1.64/1.44 inference(trivial_inequality_removal,[status(thm)],[f78])).
% 1.64/1.44 tff(f78,plain,(
% 1.64/1.44 ($true != $true) | ($false = sK2) | (spl3_3 | ~spl3_4)),
% 1.64/1.44 inference(fool_paramodulation,[status(thm)],[f74])).
% 1.64/1.44 tff(f73,plain,(
% 1.64/1.44 ~spl3_1 | ~spl3_2 | ~spl3_3 | ~spl3_5),
% 1.64/1.44 inference(avatar_contradiction_clause,[status(thm)],[f72])).
% 1.64/1.44 tff(f72,plain,(
% 1.64/1.44 $false | (~spl3_1 | ~spl3_2 | ~spl3_3 | ~spl3_5)),
% 1.64/1.44 inference(trivial_inequality_removal,[status(thm)],[f71])).
% 1.64/1.44 tff(f71,plain,(
% 1.64/1.44 ($false = $true) | (~spl3_1 | ~spl3_2 | ~spl3_3 | ~spl3_5)),
% 1.64/1.44 inference(backward_demodulation,[status(thm)],[f22,f69])).
% 1.64/1.44 tff(f69,plain,(
% 1.64/1.44 ($false = sK1) | (~spl3_2 | ~spl3_3 | ~spl3_5)),
% 1.64/1.44 inference(backward_demodulation,[status(thm)],[f67,f68])).
% 1.64/1.44 tff(f68,plain,(
% 1.64/1.44 ($false = sK0) | (~spl3_3 | ~spl3_5)),
% 1.64/1.44 inference(backward_demodulation,[status(thm)],[f29,f65])).
% 1.64/1.44 tff(f67,plain,(
% 1.64/1.44 (sK1 = sK0) | (~spl3_2 | ~spl3_3)),
% 1.64/1.44 inference(backward_demodulation,[status(thm)],[f25,f29])).
% 1.64/1.44 tff(f66,plain,(
% 1.64/1.44 spl3_5 | spl3_4 | ~spl3_3),
% 1.64/1.44 inference(avatar_split_clause,[status(thm)],[f52,f28,f32,f63])).
% 1.64/1.44 tff(f52,plain,(
% 1.64/1.44 ($true = sK0) | ($false = sK2) | ~spl3_3),
% 1.64/1.44 inference(fool_paramodulation,[status(thm)],[f29])).
% 1.64/1.44 tff(f61,plain,(
% 1.64/1.44 spl3_1 | ~spl3_2 | ~spl3_3 | ~spl3_4),
% 1.64/1.44 inference(avatar_contradiction_clause,[status(thm)],[f60])).
% 1.64/1.44 tff(f60,plain,(
% 1.64/1.44 $false | (spl3_1 | ~spl3_2 | ~spl3_3 | ~spl3_4)),
% 1.64/1.44 inference(trivial_inequality_removal,[status(thm)],[f59])).
% 1.64/1.44 tff(f59,plain,(
% 1.64/1.44 ($false = $true) | (spl3_1 | ~spl3_2 | ~spl3_3 | ~spl3_4)),
% 1.64/1.44 inference(backward_demodulation,[status(thm)],[f34,f55])).
% 1.64/1.44 tff(f55,plain,(
% 1.64/1.44 ($false = sK0) | (spl3_1 | ~spl3_2 | ~spl3_3)),
% 1.64/1.44 inference(superposition,[status(thm)],[f45,f29])).
% 1.64/1.44 tff(f45,plain,(
% 1.64/1.44 ($false = sK2) | (spl3_1 | ~spl3_2)),
% 1.64/1.44 inference(backward_demodulation,[status(thm)],[f25,f44])).
% 1.64/1.44 tff(f44,plain,(
% 1.64/1.44 ($false = sK1) | spl3_1),
% 1.64/1.44 inference(trivial_inequality_removal,[status(thm)],[f43])).
% 1.64/1.44 tff(f43,plain,(
% 1.64/1.44 ($true != $true) | ($false = sK1) | spl3_1),
% 1.64/1.44 inference(fool_paramodulation,[status(thm)],[f21])).
% 1.64/1.44 tff(f51,plain,(
% 1.64/1.44 spl3_1 | ~spl3_2 | spl3_3 | spl3_4),
% 1.64/1.44 inference(avatar_contradiction_clause,[status(thm)],[f50])).
% 1.64/1.44 tff(f50,plain,(
% 1.64/1.44 $false | (spl3_1 | ~spl3_2 | spl3_3 | spl3_4)),
% 1.64/1.44 inference(subsumption_resolution,[status(thm)],[f49,f47])).
% 1.64/1.44 tff(f47,plain,(
% 1.64/1.44 ($false != sK0) | (spl3_1 | ~spl3_2 | spl3_3)),
% 1.64/1.44 inference(backward_demodulation,[status(thm)],[f30,f45])).
% 1.64/1.44 tff(f49,plain,(
% 1.64/1.44 ($false = sK0) | spl3_4),
% 1.64/1.44 inference(trivial_inequality_removal,[status(thm)],[f48])).
% 1.64/1.44 tff(f48,plain,(
% 1.64/1.44 ($true != $true) | ($false = sK0) | spl3_4),
% 1.64/1.44 inference(fool_paramodulation,[status(thm)],[f33])).
% 1.64/1.44 tff(f42,plain,(
% 1.64/1.44 spl3_4 | spl3_3 | ~spl3_1 | ~spl3_2),
% 1.64/1.44 inference(avatar_split_clause,[status(thm)],[f13,f24,f20,f28,f32])).
% 1.64/1.44 tff(f13,plain,(
% 1.64/1.44 ($true = sK0) | (sK1 != sK2) | (sK2 = sK0) | (sK1 != $true)),
% 1.64/1.44 inference(cnf_transformation,[status(thm)],[f10])).
% 1.64/1.44 tff(f10,plain,(
% 1.64/1.44 ((((sK1 != sK2) | ($true != sK0)) & ((sK1 = sK2) | ($true = sK0))) | (((sK2 != sK0) | (sK1 != $true)) & ((sK2 = sK0) | (sK1 = $true)))) & (((($true = sK0) | (sK1 != sK2)) & ((sK1 = sK2) | ($true != sK0))) | (((sK1 = $true) | (sK2 != sK0)) & ((sK2 = sK0) | (sK1 != $true))))),
% 1.64/1.44 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f9])).
% 1.64/1.44 tff(f9,plain,(
% 1.64/1.44 ? [X0 : $o,X1 : $o,X2 : $o] : (((((X1 != X2) | ($true != X0)) & ((X1 = X2) | ($true = X0))) | (((X0 != X2) | ($true != X1)) & ((X0 = X2) | ($true = X1)))) & (((($true = X0) | (X1 != X2)) & ((X1 = X2) | ($true != X0))) | ((($true = X1) | (X0 != X2)) & ((X0 = X2) | ($true != X1))))) => (((((sK1 != sK2) | ($true != sK0)) & ((sK1 = sK2) | ($true = sK0))) | (((sK2 != sK0) | (sK1 != $true)) & ((sK2 = sK0) | (sK1 = $true)))) & (((($true = sK0) | (sK1 != sK2)) & ((sK1 = sK2) | ($true != sK0))) | (((sK1 = $true) | (sK2 != sK0)) & ((sK2 = sK0) | (sK1 != $true)))))),
% 1.64/1.44 introduced(definition,[],[choice_axiom])).
% 1.64/1.44 tff(f8,plain,(
% 1.64/1.44 ? [X0 : $o,X1 : $o,X2 : $o] : (((((X1 != X2) | ($true != X0)) & ((X1 = X2) | ($true = X0))) | (((X0 != X2) | ($true != X1)) & ((X0 = X2) | ($true = X1)))) & (((($true = X0) | (X1 != X2)) & ((X1 = X2) | ($true != X0))) | ((($true = X1) | (X0 != X2)) & ((X0 = X2) | ($true != X1)))))),
% 1.64/1.44 inference(rectify,[status(thm)],[f7])).
% 1.64/1.44 tff(f7,plain,(
% 1.64/1.44 ? [X2 : $o,X1 : $o,X0 : $o] : (((((X0 != X1) | ($true != X2)) & ((X0 = X1) | ($true = X2))) | (((X0 != X2) | ($true != X1)) & ((X0 = X2) | ($true = X1)))) & (((($true = X2) | (X0 != X1)) & ((X0 = X1) | ($true != X2))) | ((($true = X1) | (X0 != X2)) & ((X0 = X2) | ($true != X1)))))),
% 1.64/1.44 inference(nnf_transformation,[status(thm)],[f6])).
% 1.64/1.44 tff(f6,plain,(
% 1.64/1.44 ? [X2 : $o,X1 : $o,X0 : $o] : ((($true = X1) <=> (X0 = X2)) <~> (($true = X2) <=> (X0 = X1)))),
% 1.64/1.44 inference(ennf_transformation,[status(thm)],[f5])).
% 1.64/1.44 tff(f5,plain,(
% 1.64/1.44 ~! [X2 : $o,X0 : $o,X1 : $o] : ((($true = X1) <=> (X0 = X2)) <=> (($true = X2) <=> (X0 = X1)))),
% 1.64/1.44 inference(fool_elimination,[status(thm)],[f4])).
% 1.64/1.44 tff(f4,plain,(
% 1.64/1.44 ~! [X0 : $o,X1 : $o,X2 : $o] : (((X1 <=> X0) <=> X2) <=> ((X0 <=> X2) <=> X1))),
% 1.64/1.44 inference(rectify,[status(thm)],[f2])).
% 1.64/1.44 tff(f2,negated_conjecture,(
% 1.64/1.44 ~! [X1 : $o,X0 : $o,X2 : $o] : (((X0 <=> X1) <=> X2) <=> ((X1 <=> X2) <=> X0))),
% 1.64/1.44 inference(negated_conjecture,[status(cth)],[f1])).
% 1.64/1.44 tff(f1,conjecture,(
% 1.64/1.44 ! [X1 : $o,X0 : $o,X2 : $o] : (((X0 <=> X1) <=> X2) <=> ((X1 <=> X2) <=> X0))),
% 1.64/1.44 file('/export/starexec/sandbox/tmp/tmp.vUHBJ673Wd/DTF2THF_14529.p',cTHM50Q)).
% 1.64/1.44 tff(f41,plain,(
% 1.64/1.44 spl3_2 | ~spl3_4 | spl3_3 | ~spl3_1),
% 1.64/1.44 inference(avatar_split_clause,[status(thm)],[f11,f20,f28,f32,f24])).
% 1.64/1.44 tff(f11,plain,(
% 1.64/1.44 (sK1 = sK2) | ($true != sK0) | (sK1 != $true) | (sK2 = sK0)),
% 1.64/1.44 inference(cnf_transformation,[status(thm)],[f10])).
% 1.64/1.44 tff(f40,plain,(
% 1.64/1.44 ~spl3_1 | ~spl3_3 | spl3_2 | spl3_4),
% 1.64/1.44 inference(avatar_split_clause,[status(thm)],[f16,f32,f24,f28,f20])).
% 1.64/1.44 tff(f16,plain,(
% 1.64/1.44 (sK1 = sK2) | (sK1 != $true) | (sK2 != sK0) | ($true = sK0)),
% 1.64/1.44 inference(cnf_transformation,[status(thm)],[f10])).
% 1.64/1.44 tff(f39,plain,(
% 1.64/1.44 ~spl3_4 | spl3_1 | ~spl3_2 | spl3_3),
% 1.64/1.44 inference(avatar_split_clause,[status(thm)],[f17,f28,f24,f20,f32])).
% 1.64/1.44 tff(f17,plain,(
% 1.64/1.44 (sK2 = sK0) | (sK1 = $true) | (sK1 != sK2) | ($true != sK0)),
% 1.64/1.44 inference(cnf_transformation,[status(thm)],[f10])).
% 1.64/1.44 tff(f38,plain,(
% 1.64/1.44 ~spl3_4 | ~spl3_2 | ~spl3_1 | ~spl3_3),
% 1.64/1.44 inference(avatar_split_clause,[status(thm)],[f18,f28,f20,f24,f32])).
% 1.64/1.44 tff(f18,plain,(
% 1.64/1.44 (sK1 != sK2) | (sK1 != $true) | ($true != sK0) | (sK2 != sK0)),
% 1.64/1.44 inference(cnf_transformation,[status(thm)],[f10])).
% 1.64/1.44 tff(f37,plain,(
% 1.64/1.44 spl3_3 | spl3_4 | spl3_2 | spl3_1),
% 1.64/1.44 inference(avatar_split_clause,[status(thm)],[f15,f20,f24,f32,f28])).
% 1.64/1.44 tff(f15,plain,(
% 1.64/1.44 ($true = sK0) | (sK1 = $true) | (sK2 = sK0) | (sK1 = sK2)),
% 1.64/1.44 inference(cnf_transformation,[status(thm)],[f10])).
% 1.64/1.44 tff(f36,plain,(
% 1.64/1.44 ~spl3_3 | ~spl3_4 | spl3_1 | spl3_2),
% 1.64/1.44 inference(avatar_split_clause,[status(thm)],[f12,f24,f20,f32,f28])).
% 1.64/1.44 tff(f12,plain,(
% 1.64/1.44 (sK1 = $true) | (sK2 != sK0) | (sK1 = sK2) | ($true != sK0)),
% 1.64/1.44 inference(cnf_transformation,[status(thm)],[f10])).
% 1.64/1.44 tff(f35,plain,(
% 1.64/1.44 spl3_1 | ~spl3_2 | ~spl3_3 | spl3_4),
% 1.64/1.44 inference(avatar_split_clause,[status(thm)],[f14,f32,f28,f24,f20])).
% 1.64/1.44 tff(f14,plain,(
% 1.64/1.44 (sK1 = $true) | (sK2 != sK0) | ($true = sK0) | (sK1 != sK2)),
% 1.64/1.44 inference(cnf_transformation,[status(thm)],[f10])).
% 1.64/1.44 % SZS output end Proof for DTF2THF_14529
% 1.64/1.44 % (14642)------------------------------
% 1.64/1.44 % (14642)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.44 % (14642)Termination reason: Refutation
% 1.64/1.44
% 1.64/1.44 % (14642)Memory used [KB]: 5500
% 1.64/1.44 % (14642)Time elapsed: 0.005 s
% 1.64/1.44 % (14642)Instructions burned: 3 (million)
% 1.64/1.44 % (14642)------------------------------
% 1.64/1.44 % (14642)------------------------------
% 1.64/1.44 % (14640)Success in time 0.019 s
%------------------------------------------------------------------------------