%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO503^1 : TPTP v9.2.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n006.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 09:54:24 AM UTC 2026
% Result : Theorem 1.47s 1.38s
% Output : Refutation 1.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 103 ( 10 unt; 0 typ; 9 def)
% Number of atoms : 576 ( 119 equ; 0 cnn)
% Maximal formula atoms : 13 ( 5 avg)
% Number of connectives : 396 ( 161 ~; 161 |; 6 &; 59 @)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 14 con; 0-2 aty)
% Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_3,type,
f: $o > $o ).
thf(func_def_4,type,
g: $o > $o ).
thf(func_def_5,type,
p: ( $o > $o ) > $o ).
thf(func_def_10,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f252,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f25,f34,f61,f98,f100,f101,f126,f143,f146,f147,f151,f162,f171,f190,f209,f244,f248,f251]) ).
thf(f251,plain,
( spl0_2
| ~ spl0_7
| spl0_10 ),
inference(avatar_contradiction_clause,[status(thm)],[f250]) ).
thf(f250,plain,
( $false
| spl0_2
| ~ spl0_7
| spl0_10 ),
inference(subsumption_resolution,[status(thm)],[f249,f23]) ).
thf(f23,plain,
( ( b != $true )
| spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f22]) ).
thf(f22,definition,
( spl0_2
<=> ( b = $true ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f249,plain,
( ( b = $true )
| ~ spl0_7
| spl0_10 ),
inference(subsumption_resolution,[status(thm)],[f224,f93]) ).
thf(f93,plain,
( ( sK2 != $true )
| spl0_10 ),
inference(avatar_component_clause,[status(thm)],[f92]) ).
thf(f92,definition,
( spl0_10
<=> ( sK2 = $true ) ),
introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition]) ).
thf(f224,plain,
( ( sK2 = $true )
| ( b = $true )
| ~ spl0_7 ),
inference(binary_proxy_clausification,[status(thm)],[f223]) ).
thf(f223,plain,
( ( b != sK2 )
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f218]) ).
thf(f218,plain,
( ( b != sK2 )
| ( $false = $true )
| ~ spl0_7 ),
inference(constrained_superposition,[status(thm)],[f14,f56]) ).
thf(f56,plain,
( ( $false
= ( f @ sK2 ) )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f54]) ).
thf(f54,definition,
( spl0_7
<=> ( $false
= ( f @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f14,plain,
( ( f @ b )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ( f @ b )
= $true )
& ( ( p @ g )
!= $true )
& ( ( g @ a )
= $true )
& ( ( f @ a )
= $true )
& ( a != b )
& ( ( g @ b )
= $true )
& ( ( p @ f )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ( ( g @ b )
!= $true )
| ( ( g @ a )
!= $true )
| ( ( p @ g )
= $true )
| ( ( f @ b )
!= $true )
| ( ( f @ a )
!= $true )
| ( ( p @ f )
!= $true )
| ( a = b ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( a = b )
| ( ( f @ b )
!= $true )
| ( ( g @ a )
!= $true )
| ( ( g @ b )
!= $true )
| ( ( f @ a )
!= $true )
| ( ( p @ f )
!= $true )
| ( ( p @ g )
= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( a = b )
| ~ ( f @ b )
| ~ ( g @ a )
| ~ ( g @ b )
| ~ ( f @ a )
| ~ ( p @ f )
| ( p @ g ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( a = b )
| ~ ( f @ b )
| ~ ( g @ a )
| ~ ( g @ b )
| ~ ( f @ a )
| ~ ( p @ f )
| ( p @ g ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( a = b )
| ~ ( f @ b )
| ~ ( g @ a )
| ~ ( g @ b )
| ~ ( f @ a )
| ~ ( p @ f )
| ( p @ g ) ),
file('/export/starexec/sandbox/tmp/tmp.iVjheRs3o4/DTF2THF_10596.p',claim) ).
thf(f248,plain,
( ~ spl0_9
| ~ spl0_4
| ~ spl0_7 ),
inference(avatar_split_clause,[status(thm)],[f227,f54,f31,f87]) ).
thf(f87,definition,
( spl0_9
<=> ( $false = sK2 ) ),
introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition]) ).
thf(f31,definition,
( spl0_4
<=> ( b = $false ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f227,plain,
( ( $false != sK2 )
| ~ spl0_4
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f216]) ).
thf(f216,plain,
( ( $false = $true )
| ( $false != sK2 )
| ~ spl0_4
| ~ spl0_7 ),
inference(constrained_superposition,[status(thm)],[f156,f56]) ).
thf(f156,plain,
( ( ( f @ $false )
= $true )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f14,f33]) ).
thf(f33,plain,
( ( b = $false )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f31]) ).
thf(f244,plain,
( spl0_9
| spl0_3
| ~ spl0_7 ),
inference(avatar_split_clause,[status(thm)],[f243,f54,f27,f87]) ).
thf(f27,definition,
( spl0_3
<=> ( a = $false ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f243,plain,
( ( $false = sK2 )
| spl0_3
| ~ spl0_7 ),
inference(subsumption_resolution,[status(thm)],[f233,f28]) ).
thf(f28,plain,
( ( a != $false )
| spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f27]) ).
thf(f233,plain,
( ( $false = sK2 )
| ( a = $false )
| ~ spl0_7 ),
inference(binary_proxy_clausification,[status(thm)],[f231]) ).
thf(f231,plain,
( ( a != sK2 )
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f214]) ).
thf(f214,plain,
( ( a != sK2 )
| ( $false = $true )
| ~ spl0_7 ),
inference(constrained_superposition,[status(thm)],[f56,f11]) ).
thf(f11,plain,
( ( f @ a )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f209,plain,
( ~ spl0_9
| ~ spl0_4
| spl0_5 ),
inference(avatar_split_clause,[status(thm)],[f196,f45,f31,f87]) ).
thf(f45,definition,
( spl0_5
<=> ( $true
= ( g @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f196,plain,
( ( $false != sK2 )
| ~ spl0_4
| spl0_5 ),
inference(trivial_inequality_removal,[status(thm)],[f192]) ).
thf(f192,plain,
( ( $true != $true )
| ( $false != sK2 )
| ~ spl0_4
| spl0_5 ),
inference(constrained_superposition,[status(thm)],[f46,f158]) ).
thf(f158,plain,
( ( $true
= ( g @ $false ) )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f9,f33]) ).
thf(f9,plain,
( ( g @ b )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f46,plain,
( ( $true
!= ( g @ sK2 ) )
| spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f45]) ).
thf(f190,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f189]) ).
thf(f189,plain,
( $false
| ~ spl0_1
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f183]) ).
thf(f183,plain,
( ( $false = $true )
| ~ spl0_1
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f29,f20]) ).
thf(f20,plain,
( ( a = $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f18]) ).
thf(f18,definition,
( spl0_1
<=> ( a = $true ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f29,plain,
( ( a = $false )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f27]) ).
thf(f171,plain,
( spl0_10
| spl0_2
| ~ spl0_8 ),
inference(avatar_split_clause,[status(thm)],[f170,f58,f22,f92]) ).
thf(f58,definition,
( spl0_8
<=> ( $false
= ( g @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition]) ).
thf(f170,plain,
( ( sK2 = $true )
| spl0_2
| ~ spl0_8 ),
inference(subsumption_resolution,[status(thm)],[f121,f23]) ).
thf(f121,plain,
( ( sK2 = $true )
| ( b = $true )
| ~ spl0_8 ),
inference(binary_proxy_clausification,[status(thm)],[f120]) ).
thf(f120,plain,
( ( b != sK2 )
| ~ spl0_8 ),
inference(trivial_inequality_removal,[status(thm)],[f114]) ).
thf(f114,plain,
( ( b != sK2 )
| ( $false = $true )
| ~ spl0_8 ),
inference(constrained_superposition,[status(thm)],[f60,f9]) ).
thf(f60,plain,
( ( $false
= ( g @ sK2 ) )
| ~ spl0_8 ),
inference(avatar_component_clause,[status(thm)],[f58]) ).
thf(f162,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f161]) ).
thf(f161,plain,
( $false
| ~ spl0_2
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f155]) ).
thf(f155,plain,
( ( $false = $true )
| ~ spl0_2
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f33,f24]) ).
thf(f24,plain,
( ( b = $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f22]) ).
thf(f151,plain,
( spl0_9
| spl0_3
| ~ spl0_8 ),
inference(avatar_split_clause,[status(thm)],[f150,f58,f27,f87]) ).
thf(f150,plain,
( ( $false = sK2 )
| spl0_3
| ~ spl0_8 ),
inference(subsumption_resolution,[status(thm)],[f130,f28]) ).
thf(f130,plain,
( ( a = $false )
| ( $false = sK2 )
| ~ spl0_8 ),
inference(binary_proxy_clausification,[status(thm)],[f128]) ).
thf(f128,plain,
( ( a != sK2 )
| ~ spl0_8 ),
inference(trivial_inequality_removal,[status(thm)],[f118]) ).
thf(f118,plain,
( ( $false = $true )
| ( a != sK2 )
| ~ spl0_8 ),
inference(constrained_superposition,[status(thm)],[f12,f60]) ).
thf(f12,plain,
( ( g @ a )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f147,plain,
( spl0_9
| spl0_4
| ~ spl0_8 ),
inference(avatar_split_clause,[status(thm)],[f122,f58,f31,f87]) ).
thf(f122,plain,
( ( $false = sK2 )
| ( b = $false )
| ~ spl0_8 ),
inference(binary_proxy_clausification,[status(thm)],[f120]) ).
thf(f146,plain,
( ~ spl0_9
| ~ spl0_3
| ~ spl0_8 ),
inference(avatar_split_clause,[status(thm)],[f127,f58,f27,f87]) ).
thf(f127,plain,
( ( $false != sK2 )
| ~ spl0_3
| ~ spl0_8 ),
inference(trivial_inequality_removal,[status(thm)],[f111]) ).
thf(f111,plain,
( ( $false != sK2 )
| ( $false = $true )
| ~ spl0_3
| ~ spl0_8 ),
inference(constrained_superposition,[status(thm)],[f60,f37]) ).
thf(f37,plain,
( ( $true
= ( g @ $false ) )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f12,f29]) ).
thf(f143,plain,
( ~ spl0_10
| ~ spl0_2
| ~ spl0_8 ),
inference(avatar_split_clause,[status(thm)],[f134,f58,f22,f92]) ).
thf(f134,plain,
( ( sK2 != $true )
| ~ spl0_2
| ~ spl0_8 ),
inference(trivial_inequality_removal,[status(thm)],[f117]) ).
thf(f117,plain,
( ( $false = $true )
| ( sK2 != $true )
| ~ spl0_2
| ~ spl0_8 ),
inference(constrained_superposition,[status(thm)],[f35,f60]) ).
thf(f35,plain,
( ( $true
= ( g @ $true ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f9,f24]) ).
thf(f126,plain,
( ~ spl0_5
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f125]) ).
thf(f125,plain,
( $false
| ~ spl0_5
| ~ spl0_8 ),
inference(trivial_inequality_removal,[status(thm)],[f110]) ).
thf(f110,plain,
( ( $false = $true )
| ~ spl0_5
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f60,f47]) ).
thf(f47,plain,
( ( $true
= ( g @ sK2 ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f45]) ).
thf(f101,plain,
( ~ spl0_10
| ~ spl0_2
| ~ spl0_7 ),
inference(avatar_split_clause,[status(thm)],[f70,f54,f22,f92]) ).
thf(f70,plain,
( ( sK2 != $true )
| ~ spl0_2
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f62]) ).
thf(f62,plain,
( ( sK2 != $true )
| ( $false = $true )
| ~ spl0_2
| ~ spl0_7 ),
inference(constrained_superposition,[status(thm)],[f56,f38]) ).
thf(f38,plain,
( ( ( f @ $true )
= $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f14,f24]) ).
thf(f100,plain,
( spl0_9
| spl0_4
| ~ spl0_7 ),
inference(avatar_split_clause,[status(thm)],[f73,f54,f31,f87]) ).
thf(f73,plain,
( ( b = $false )
| ( $false = sK2 )
| ~ spl0_7 ),
inference(binary_proxy_clausification,[status(thm)],[f71]) ).
thf(f71,plain,
( ( b != sK2 )
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f64]) ).
thf(f64,plain,
( ( b != sK2 )
| ( $false = $true )
| ~ spl0_7 ),
inference(constrained_superposition,[status(thm)],[f56,f14]) ).
thf(f98,plain,
( ~ spl0_9
| ~ spl0_3
| ~ spl0_7 ),
inference(avatar_split_clause,[status(thm)],[f77,f54,f27,f87]) ).
thf(f77,plain,
( ( $false != sK2 )
| ~ spl0_3
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f63]) ).
thf(f63,plain,
( ( $false = $true )
| ( $false != sK2 )
| ~ spl0_3
| ~ spl0_7 ),
inference(constrained_superposition,[status(thm)],[f56,f36]) ).
thf(f36,plain,
( ( ( f @ $false )
= $true )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f11,f29]) ).
thf(f61,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[status(thm)],[f43,f58,f54]) ).
thf(f43,plain,
( ( $false
= ( f @ sK2 ) )
| ( $false
= ( g @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
( ( f @ sK2 )
!= ( g @ sK2 ) ),
inference(negative_extensionality,[status(thm)],[f40]) ).
thf(f40,plain,
f != g,
inference(trivial_inequality_removal,[status(thm)],[f39]) ).
thf(f39,plain,
( ( $true != $true )
| ( f != g ) ),
inference(constrained_superposition,[status(thm)],[f13,f8]) ).
thf(f8,plain,
( ( p @ f )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f13,plain,
( ( p @ g )
!= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f34,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f16,f31,f27]) ).
thf(f16,plain,
( ( b = $false )
| ( a = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f10]) ).
thf(f10,plain,
a != b,
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f25,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f15,f22,f18]) ).
thf(f15,plain,
( ( b = $true )
| ( a = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO503^1 : TPTP v9.2.1. Released v4.1.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/0.33 % Computer : n006.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue Feb 24 14:32:45 EST 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.44 ---- Original DTF file ---
% 0.17/0.44 thf(spec,logic,$$dhol).
% 0.17/0.44 %------------------------------------------------------------------------------
% 0.17/0.44 % File : SYO503^1 : TPTP v9.2.1. Released v4.1.0.
% 0.17/0.44 % Domain : Syntactic
% 0.17/0.44 % Problem : Tableau with two branches
% 0.17/0.44 % Version : Especial.
% 0.17/0.44 % English :
% 0.17/0.44
% 0.17/0.44 % Refs : [BS09a] Brown & Smolka (2009), Terminating Tableaux for the Ba
% 0.17/0.44 % : [BS09b] Brown E. & Smolka (2009), Extended First-Order Logic
% 0.17/0.44 % : [Bro09] Brown E. (2009), Email to Geoff Sutcliffe
% 0.17/0.44 % Source : [Bro09]
% 0.17/0.44 % Names : Example 3.4 [BS09a]
% 0.17/0.44 % : basic9 [Bro09]
% 0.17/0.44
% 0.17/0.44 % Status : Theorem
% 0.17/0.44 % Rating : 0.00 v9.0.0, 0.10 v8.2.0, 0.31 v8.1.0, 0.27 v7.5.0, 0.14 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.43 v6.1.0, 0.29 v5.5.0, 0.17 v5.4.0, 0.40 v5.3.0, 0.60 v5.1.0, 0.80 v5.0.0, 0.60 v4.1.0
% 0.17/0.44 % Syntax : Number of formulae : 7 ( 0 unt; 6 typ; 0 def)
% 0.17/0.44 % Number of atoms : 15 ( 1 equ; 0 cnn)
% 0.17/0.44 % Maximal formula atoms : 13 ( 15 avg)
% 0.17/0.44 % Number of connectives : 17 ( 5 ~; 6 |; 0 &; 6 @)
% 0.17/0.44 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.17/0.44 % Maximal formula depth : 9 ( 9 avg)
% 0.17/0.44 % Number of types : 1 ( 0 usr)
% 0.17/0.44 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.17/0.44 % Number of symbols : 7 ( 6 usr; 3 con; 0-2 aty)
% 0.17/0.44 % Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% 0.17/0.44 % SPC : TH0_THM_EQU_NAR
% 0.17/0.44
% 0.17/0.44 % Comments : The fragment of simple type theory that restricts equations to
% 0.17/0.44 % base types and disallows lambda abstraction and quantification is
% 0.17/0.44 % decidable. This is an example.
% 0.17/0.44 %------------------------------------------------------------------------------
% 0.17/0.44 thf(a,type,
% 0.17/0.44 a: $o ).
% 0.17/0.44
% 0.17/0.44 thf(b,type,
% 0.17/0.44 b: $o ).
% 0.17/0.44
% 0.17/0.44 thf(c,type,
% 0.17/0.44 c: $o ).
% 0.17/0.44
% 0.17/0.44 thf(f,type,
% 0.17/0.44 f: $o > $o ).
% 0.17/0.44
% 0.17/0.44 thf(g,type,
% 0.17/0.44 g: $o > $o ).
% 0.17/0.44
% 0.17/0.44 thf(p,type,
% 0.17/0.44 p: ( $o > $o ) > $o ).
% 0.17/0.44
% 0.17/0.44 thf(claim,conjecture,
% 0.17/0.44 ( ( a = b )
% 0.17/0.44 | ~ ( f @ a )
% 0.17/0.44 | ~ ( f @ b )
% 0.17/0.44 | ~ ( g @ a )
% 0.17/0.44 | ~ ( g @ b )
% 0.17/0.44 | ~ ( p @ f )
% 0.17/0.44 | ( p @ g ) ) ).
% 0.17/0.44
% 0.17/0.44 %------------------------------------------------------------------------------
% 0.17/0.44 ------------------------
% 1.47/1.35 ---- Embedded in THF ---
% 1.47/1.35 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.35 %%% Generated on Tue Feb 24 14:32:46 EST 2026
% 1.47/1.35 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.35 %%% Logic specification used:
% 1.47/1.35 %%% thf(spec, logic, $$dhol).
% 1.47/1.35
% 1.47/1.35 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.iVjheRs3o4/DTF2DTF10596.p
% See solution above
% 1.47/1.35 ------------------------
% 1.47/1.36 ---- Cleaned THF ---
% 1.47/1.36 thf(a,type,
% 1.47/1.36 a: $o ).
% 1.47/1.36
% 1.47/1.36 thf(b,type,
% 1.47/1.36 b: $o ).
% 1.47/1.36
% 1.47/1.36 thf(c,type,
% 1.47/1.36 c: $o ).
% 1.47/1.36
% 1.47/1.36 thf(f,type,
% 1.47/1.36 f: $o > $o ).
% 1.47/1.36
% 1.47/1.36 thf(g,type,
% 1.47/1.36 g: $o > $o ).
% 1.47/1.36
% 1.47/1.36 thf(p,type,
% 1.47/1.36 p: ( $o > $o ) > $o ).
% 1.47/1.36
% 1.47/1.36 thf(claim,conjecture,
% 1.47/1.36 ( ( a = b )
% 1.47/1.36 | ~ ( f @ a )
% 1.47/1.36 | ~ ( f @ b )
% 1.47/1.36 | ~ ( g @ a )
% 1.47/1.36 | ~ ( g @ b )
% 1.47/1.36 | ~ ( p @ f )
% 1.47/1.36 | ( p @ g ) ) ).
% 1.47/1.36 ------------------------
% 1.47/1.38 % (10693)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_10596 for (2999ds/183Mi)
% 1.47/1.38 % (10693)First to succeed.
% 1.47/1.38 % (10693)Refutation found. Thanks to Tanya!
% 1.47/1.38 % SZS status Theorem for DTF2THF_10596
% 1.47/1.38 % SZS output start Proof for DTF2THF_10596
% 1.47/1.38 thf(func_def_3, type, f: $o > $o).
% 1.47/1.38 thf(func_def_4, type, g: $o > $o).
% 1.47/1.38 thf(func_def_5, type, p: ($o > $o) > $o).
% 1.47/1.38 thf(func_def_10, type, ph1: !>[X0: $tType]:(X0)).
% 1.47/1.38 thf(f252,plain,(
% 1.47/1.38 $false),
% 1.47/1.38 inference(avatar_sat_refutation,[status(thm)],[f25,f34,f61,f98,f100,f101,f126,f143,f146,f147,f151,f162,f171,f190,f209,f244,f248,f251])).
% 1.47/1.38 thf(f251,plain,(
% 1.47/1.38 spl0_2 | ~spl0_7 | spl0_10),
% 1.47/1.38 inference(avatar_contradiction_clause,[status(thm)],[f250])).
% 1.47/1.38 thf(f250,plain,(
% 1.47/1.38 $false | (spl0_2 | ~spl0_7 | spl0_10)),
% 1.47/1.38 inference(subsumption_resolution,[status(thm)],[f249,f23])).
% 1.47/1.38 thf(f23,plain,(
% 1.47/1.38 (b != $true) | spl0_2),
% 1.47/1.38 inference(avatar_component_clause,[status(thm)],[f22])).
% 1.47/1.38 thf(f22,definition,(
% 1.47/1.38 spl0_2 <=> (b = $true)),
% 1.47/1.38 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.47/1.38 thf(f249,plain,(
% 1.47/1.38 (b = $true) | (~spl0_7 | spl0_10)),
% 1.47/1.38 inference(subsumption_resolution,[status(thm)],[f224,f93])).
% 1.47/1.38 thf(f93,plain,(
% 1.47/1.38 (sK2 != $true) | spl0_10),
% 1.47/1.38 inference(avatar_component_clause,[status(thm)],[f92])).
% 1.47/1.38 thf(f92,definition,(
% 1.47/1.38 spl0_10 <=> (sK2 = $true)),
% 1.47/1.38 introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition])).
% 1.47/1.38 thf(f224,plain,(
% 1.47/1.38 (sK2 = $true) | (b = $true) | ~spl0_7),
% 1.47/1.38 inference(binary_proxy_clausification,[status(thm)],[f223])).
% 1.47/1.38 thf(f223,plain,(
% 1.47/1.38 (b != sK2) | ~spl0_7),
% 1.47/1.38 inference(trivial_inequality_removal,[status(thm)],[f218])).
% 1.47/1.38 thf(f218,plain,(
% 1.47/1.38 (b != sK2) | ($false = $true) | ~spl0_7),
% 1.47/1.38 inference(constrained_superposition,[status(thm)],[f14,f56])).
% 1.47/1.38 thf(f56,plain,(
% 1.47/1.38 ($false = (f @ sK2)) | ~spl0_7),
% 1.47/1.38 inference(avatar_component_clause,[status(thm)],[f54])).
% 1.47/1.38 thf(f54,definition,(
% 1.47/1.38 spl0_7 <=> ($false = (f @ sK2))),
% 1.47/1.38 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 1.47/1.38 thf(f14,plain,(
% 1.47/1.38 ((f @ b) = $true)),
% 1.47/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 1.47/1.38 thf(f7,plain,(
% 1.47/1.38 ((f @ b) = $true) & ((p @ g) != $true) & ((g @ a) = $true) & ((f @ a) = $true) & (a != b) & ((g @ b) = $true) & ((p @ f) = $true)),
% 1.47/1.38 inference(ennf_transformation,[status(thm)],[f6])).
% 1.47/1.38 thf(f6,plain,(
% 1.47/1.38 ~(((g @ b) != $true) | ((g @ a) != $true) | ((p @ g) = $true) | ((f @ b) != $true) | ((f @ a) != $true) | ((p @ f) != $true) | (a = b))),
% 1.47/1.38 inference(flattening,[status(thm)],[f5])).
% 1.47/1.38 thf(f5,plain,(
% 1.47/1.38 ~((a = b) | ~((f @ b) = $true) | ~((g @ a) = $true) | ~((g @ b) = $true) | ~((f @ a) = $true) | ~((p @ f) = $true) | ((p @ g) = $true))),
% 1.47/1.38 inference(fool_elimination,[status(thm)],[f4])).
% 1.47/1.38 thf(f4,plain,(
% 1.47/1.38 ~((a = b) | ~(f @ b) | ~(g @ a) | ~(g @ b) | ~(f @ a) | ~(p @ f) | (p @ g))),
% 1.47/1.38 inference(rectify,[status(thm)],[f2])).
% 1.47/1.38 thf(f2,negated_conjecture,(
% 1.47/1.38 ~((a = b) | ~(f @ b) | ~(g @ a) | ~(g @ b) | ~(f @ a) | ~(p @ f) | (p @ g))),
% 1.47/1.38 inference(negated_conjecture,[status(cth)],[f1])).
% 1.47/1.38 thf(f1,conjecture,(
% 1.47/1.38 (a = b) | ~(f @ b) | ~(g @ a) | ~(g @ b) | ~(f @ a) | ~(p @ f) | (p @ g)),
% 1.47/1.38 file('/export/starexec/sandbox/tmp/tmp.iVjheRs3o4/DTF2THF_10596.p',claim)).
% 1.47/1.38 thf(f248,plain,(
% 1.47/1.38 ~spl0_9 | ~spl0_4 | ~spl0_7),
% 1.47/1.38 inference(avatar_split_clause,[status(thm)],[f227,f54,f31,f87])).
% 1.47/1.38 thf(f87,definition,(
% 1.47/1.38 spl0_9 <=> ($false = sK2)),
% 1.47/1.38 introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition])).
% 1.47/1.38 thf(f31,definition,(
% 1.47/1.38 spl0_4 <=> (b = $false)),
% 1.47/1.38 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.47/1.38 thf(f227,plain,(
% 1.47/1.38 ($false != sK2) | (~spl0_4 | ~spl0_7)),
% 1.47/1.38 inference(trivial_inequality_removal,[status(thm)],[f216])).
% 1.47/1.38 thf(f216,plain,(
% 1.47/1.38 ($false = $true) | ($false != sK2) | (~spl0_4 | ~spl0_7)),
% 1.47/1.38 inference(constrained_superposition,[status(thm)],[f156,f56])).
% 1.47/1.38 thf(f156,plain,(
% 1.47/1.38 ((f @ $false) = $true) | ~spl0_4),
% 1.47/1.38 inference(superposition,[status(thm)],[f14,f33])).
% 1.47/1.38 thf(f33,plain,(
% 1.47/1.38 (b = $false) | ~spl0_4),
% 1.47/1.38 inference(avatar_component_clause,[status(thm)],[f31])).
% 1.47/1.38 thf(f244,plain,(
% 1.47/1.38 spl0_9 | spl0_3 | ~spl0_7),
% 1.47/1.38 inference(avatar_split_clause,[status(thm)],[f243,f54,f27,f87])).
% 1.47/1.38 thf(f27,definition,(
% 1.47/1.38 spl0_3 <=> (a = $false)),
% 1.47/1.38 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.47/1.38 thf(f243,plain,(
% 1.47/1.38 ($false = sK2) | (spl0_3 | ~spl0_7)),
% 1.47/1.38 inference(subsumption_resolution,[status(thm)],[f233,f28])).
% 1.47/1.38 thf(f28,plain,(
% 1.47/1.38 (a != $false) | spl0_3),
% 1.47/1.38 inference(avatar_component_clause,[status(thm)],[f27])).
% 1.47/1.38 thf(f233,plain,(
% 1.47/1.38 ($false = sK2) | (a = $false) | ~spl0_7),
% 1.47/1.38 inference(binary_proxy_clausification,[status(thm)],[f231])).
% 1.47/1.38 thf(f231,plain,(
% 1.47/1.38 (a != sK2) | ~spl0_7),
% 1.47/1.38 inference(trivial_inequality_removal,[status(thm)],[f214])).
% 1.47/1.38 thf(f214,plain,(
% 1.47/1.38 (a != sK2) | ($false = $true) | ~spl0_7),
% 1.47/1.38 inference(constrained_superposition,[status(thm)],[f56,f11])).
% 1.47/1.38 thf(f11,plain,(
% 1.47/1.38 ((f @ a) = $true)),
% 1.47/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 1.47/1.38 thf(f209,plain,(
% 1.47/1.38 ~spl0_9 | ~spl0_4 | spl0_5),
% 1.47/1.38 inference(avatar_split_clause,[status(thm)],[f196,f45,f31,f87])).
% 1.47/1.38 thf(f45,definition,(
% 1.47/1.38 spl0_5 <=> ($true = (g @ sK2))),
% 1.47/1.38 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 1.47/1.38 thf(f196,plain,(
% 1.47/1.38 ($false != sK2) | (~spl0_4 | spl0_5)),
% 1.47/1.38 inference(trivial_inequality_removal,[status(thm)],[f192])).
% 1.47/1.38 thf(f192,plain,(
% 1.47/1.38 ($true != $true) | ($false != sK2) | (~spl0_4 | spl0_5)),
% 1.47/1.38 inference(constrained_superposition,[status(thm)],[f46,f158])).
% 1.47/1.38 thf(f158,plain,(
% 1.47/1.38 ($true = (g @ $false)) | ~spl0_4),
% 1.47/1.38 inference(superposition,[status(thm)],[f9,f33])).
% 1.47/1.38 thf(f9,plain,(
% 1.47/1.38 ((g @ b) = $true)),
% 1.47/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 1.47/1.38 thf(f46,plain,(
% 1.47/1.38 ($true != (g @ sK2)) | spl0_5),
% 1.47/1.38 inference(avatar_component_clause,[status(thm)],[f45])).
% 1.47/1.38 thf(f190,plain,(
% 1.47/1.38 ~spl0_1 | ~spl0_3),
% 1.47/1.38 inference(avatar_contradiction_clause,[status(thm)],[f189])).
% 1.47/1.38 thf(f189,plain,(
% 1.47/1.38 $false | (~spl0_1 | ~spl0_3)),
% 1.47/1.38 inference(trivial_inequality_removal,[status(thm)],[f183])).
% 1.47/1.38 thf(f183,plain,(
% 1.47/1.38 ($false = $true) | (~spl0_1 | ~spl0_3)),
% 1.47/1.38 inference(superposition,[status(thm)],[f29,f20])).
% 1.47/1.38 thf(f20,plain,(
% 1.47/1.38 (a = $true) | ~spl0_1),
% 1.47/1.38 inference(avatar_component_clause,[status(thm)],[f18])).
% 1.47/1.38 thf(f18,definition,(
% 1.47/1.38 spl0_1 <=> (a = $true)),
% 1.47/1.38 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.47/1.38 thf(f29,plain,(
% 1.47/1.38 (a = $false) | ~spl0_3),
% 1.47/1.38 inference(avatar_component_clause,[status(thm)],[f27])).
% 1.47/1.38 thf(f171,plain,(
% 1.47/1.38 spl0_10 | spl0_2 | ~spl0_8),
% 1.47/1.38 inference(avatar_split_clause,[status(thm)],[f170,f58,f22,f92])).
% 1.47/1.38 thf(f58,definition,(
% 1.47/1.38 spl0_8 <=> ($false = (g @ sK2))),
% 1.47/1.38 introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition])).
% 1.47/1.38 thf(f170,plain,(
% 1.47/1.38 (sK2 = $true) | (spl0_2 | ~spl0_8)),
% 1.47/1.38 inference(subsumption_resolution,[status(thm)],[f121,f23])).
% 1.47/1.38 thf(f121,plain,(
% 1.47/1.38 (sK2 = $true) | (b = $true) | ~spl0_8),
% 1.47/1.38 inference(binary_proxy_clausification,[status(thm)],[f120])).
% 1.47/1.38 thf(f120,plain,(
% 1.47/1.38 (b != sK2) | ~spl0_8),
% 1.47/1.38 inference(trivial_inequality_removal,[status(thm)],[f114])).
% 1.47/1.38 thf(f114,plain,(
% 1.47/1.38 (b != sK2) | ($false = $true) | ~spl0_8),
% 1.47/1.38 inference(constrained_superposition,[status(thm)],[f60,f9])).
% 1.47/1.38 thf(f60,plain,(
% 1.47/1.38 ($false = (g @ sK2)) | ~spl0_8),
% 1.47/1.38 inference(avatar_component_clause,[status(thm)],[f58])).
% 1.47/1.38 thf(f162,plain,(
% 1.47/1.38 ~spl0_2 | ~spl0_4),
% 1.47/1.38 inference(avatar_contradiction_clause,[status(thm)],[f161])).
% 1.47/1.38 thf(f161,plain,(
% 1.47/1.38 $false | (~spl0_2 | ~spl0_4)),
% 1.47/1.38 inference(trivial_inequality_removal,[status(thm)],[f155])).
% 1.47/1.38 thf(f155,plain,(
% 1.47/1.38 ($false = $true) | (~spl0_2 | ~spl0_4)),
% 1.47/1.38 inference(superposition,[status(thm)],[f33,f24])).
% 1.47/1.38 thf(f24,plain,(
% 1.47/1.38 (b = $true) | ~spl0_2),
% 1.47/1.38 inference(avatar_component_clause,[status(thm)],[f22])).
% 1.47/1.38 thf(f151,plain,(
% 1.47/1.38 spl0_9 | spl0_3 | ~spl0_8),
% 1.47/1.38 inference(avatar_split_clause,[status(thm)],[f150,f58,f27,f87])).
% 1.47/1.38 thf(f150,plain,(
% 1.47/1.38 ($false = sK2) | (spl0_3 | ~spl0_8)),
% 1.47/1.38 inference(subsumption_resolution,[status(thm)],[f130,f28])).
% 1.47/1.38 thf(f130,plain,(
% 1.47/1.38 (a = $false) | ($false = sK2) | ~spl0_8),
% 1.47/1.38 inference(binary_proxy_clausification,[status(thm)],[f128])).
% 1.47/1.38 thf(f128,plain,(
% 1.47/1.38 (a != sK2) | ~spl0_8),
% 1.47/1.38 inference(trivial_inequality_removal,[status(thm)],[f118])).
% 1.47/1.38 thf(f118,plain,(
% 1.47/1.38 ($false = $true) | (a != sK2) | ~spl0_8),
% 1.47/1.38 inference(constrained_superposition,[status(thm)],[f12,f60])).
% 1.47/1.38 thf(f12,plain,(
% 1.47/1.38 ((g @ a) = $true)),
% 1.47/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 1.47/1.38 thf(f147,plain,(
% 1.47/1.38 spl0_9 | spl0_4 | ~spl0_8),
% 1.47/1.38 inference(avatar_split_clause,[status(thm)],[f122,f58,f31,f87])).
% 1.47/1.38 thf(f122,plain,(
% 1.47/1.38 ($false = sK2) | (b = $false) | ~spl0_8),
% 1.47/1.38 inference(binary_proxy_clausification,[status(thm)],[f120])).
% 1.47/1.38 thf(f146,plain,(
% 1.47/1.38 ~spl0_9 | ~spl0_3 | ~spl0_8),
% 1.47/1.38 inference(avatar_split_clause,[status(thm)],[f127,f58,f27,f87])).
% 1.47/1.38 thf(f127,plain,(
% 1.47/1.38 ($false != sK2) | (~spl0_3 | ~spl0_8)),
% 1.47/1.38 inference(trivial_inequality_removal,[status(thm)],[f111])).
% 1.47/1.38 thf(f111,plain,(
% 1.47/1.38 ($false != sK2) | ($false = $true) | (~spl0_3 | ~spl0_8)),
% 1.47/1.38 inference(constrained_superposition,[status(thm)],[f60,f37])).
% 1.47/1.38 thf(f37,plain,(
% 1.47/1.38 ($true = (g @ $false)) | ~spl0_3),
% 1.47/1.38 inference(superposition,[status(thm)],[f12,f29])).
% 1.47/1.38 thf(f143,plain,(
% 1.47/1.38 ~spl0_10 | ~spl0_2 | ~spl0_8),
% 1.47/1.38 inference(avatar_split_clause,[status(thm)],[f134,f58,f22,f92])).
% 1.47/1.38 thf(f134,plain,(
% 1.47/1.38 (sK2 != $true) | (~spl0_2 | ~spl0_8)),
% 1.47/1.38 inference(trivial_inequality_removal,[status(thm)],[f117])).
% 1.47/1.38 thf(f117,plain,(
% 1.47/1.38 ($false = $true) | (sK2 != $true) | (~spl0_2 | ~spl0_8)),
% 1.47/1.38 inference(constrained_superposition,[status(thm)],[f35,f60])).
% 1.47/1.38 thf(f35,plain,(
% 1.47/1.38 ($true = (g @ $true)) | ~spl0_2),
% 1.47/1.38 inference(superposition,[status(thm)],[f9,f24])).
% 1.47/1.38 thf(f126,plain,(
% 1.47/1.38 ~spl0_5 | ~spl0_8),
% 1.47/1.38 inference(avatar_contradiction_clause,[status(thm)],[f125])).
% 1.47/1.38 thf(f125,plain,(
% 1.47/1.38 $false | (~spl0_5 | ~spl0_8)),
% 1.47/1.38 inference(trivial_inequality_removal,[status(thm)],[f110])).
% 1.47/1.38 thf(f110,plain,(
% 1.47/1.38 ($false = $true) | (~spl0_5 | ~spl0_8)),
% 1.47/1.38 inference(superposition,[status(thm)],[f60,f47])).
% 1.47/1.38 thf(f47,plain,(
% 1.47/1.38 ($true = (g @ sK2)) | ~spl0_5),
% 1.47/1.38 inference(avatar_component_clause,[status(thm)],[f45])).
% 1.47/1.38 thf(f101,plain,(
% 1.47/1.38 ~spl0_10 | ~spl0_2 | ~spl0_7),
% 1.47/1.38 inference(avatar_split_clause,[status(thm)],[f70,f54,f22,f92])).
% 1.47/1.38 thf(f70,plain,(
% 1.47/1.38 (sK2 != $true) | (~spl0_2 | ~spl0_7)),
% 1.47/1.38 inference(trivial_inequality_removal,[status(thm)],[f62])).
% 1.47/1.38 thf(f62,plain,(
% 1.47/1.38 (sK2 != $true) | ($false = $true) | (~spl0_2 | ~spl0_7)),
% 1.47/1.38 inference(constrained_superposition,[status(thm)],[f56,f38])).
% 1.47/1.38 thf(f38,plain,(
% 1.47/1.38 ((f @ $true) = $true) | ~spl0_2),
% 1.47/1.38 inference(superposition,[status(thm)],[f14,f24])).
% 1.47/1.38 thf(f100,plain,(
% 1.47/1.38 spl0_9 | spl0_4 | ~spl0_7),
% 1.47/1.38 inference(avatar_split_clause,[status(thm)],[f73,f54,f31,f87])).
% 1.47/1.38 thf(f73,plain,(
% 1.47/1.38 (b = $false) | ($false = sK2) | ~spl0_7),
% 1.47/1.38 inference(binary_proxy_clausification,[status(thm)],[f71])).
% 1.47/1.38 thf(f71,plain,(
% 1.47/1.38 (b != sK2) | ~spl0_7),
% 1.47/1.38 inference(trivial_inequality_removal,[status(thm)],[f64])).
% 1.47/1.38 thf(f64,plain,(
% 1.47/1.38 (b != sK2) | ($false = $true) | ~spl0_7),
% 1.47/1.38 inference(constrained_superposition,[status(thm)],[f56,f14])).
% 1.47/1.38 thf(f98,plain,(
% 1.47/1.38 ~spl0_9 | ~spl0_3 | ~spl0_7),
% 1.47/1.38 inference(avatar_split_clause,[status(thm)],[f77,f54,f27,f87])).
% 1.47/1.38 thf(f77,plain,(
% 1.47/1.38 ($false != sK2) | (~spl0_3 | ~spl0_7)),
% 1.47/1.38 inference(trivial_inequality_removal,[status(thm)],[f63])).
% 1.47/1.38 thf(f63,plain,(
% 1.47/1.38 ($false = $true) | ($false != sK2) | (~spl0_3 | ~spl0_7)),
% 1.47/1.38 inference(constrained_superposition,[status(thm)],[f56,f36])).
% 1.47/1.38 thf(f36,plain,(
% 1.47/1.38 ((f @ $false) = $true) | ~spl0_3),
% 1.47/1.38 inference(superposition,[status(thm)],[f11,f29])).
% 1.47/1.38 thf(f61,plain,(
% 1.47/1.38 spl0_7 | spl0_8),
% 1.47/1.38 inference(avatar_split_clause,[status(thm)],[f43,f58,f54])).
% 1.47/1.38 thf(f43,plain,(
% 1.47/1.38 ($false = (f @ sK2)) | ($false = (g @ sK2))),
% 1.47/1.38 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 1.47/1.38 thf(f41,plain,(
% 1.47/1.38 ((f @ sK2) != (g @ sK2))),
% 1.47/1.38 inference(negative_extensionality,[status(thm)],[f40])).
% 1.47/1.38 thf(f40,plain,(
% 1.47/1.38 (f != g)),
% 1.47/1.38 inference(trivial_inequality_removal,[status(thm)],[f39])).
% 1.47/1.38 thf(f39,plain,(
% 1.47/1.38 ($true != $true) | (f != g)),
% 1.47/1.38 inference(constrained_superposition,[status(thm)],[f13,f8])).
% 1.47/1.38 thf(f8,plain,(
% 1.47/1.38 ((p @ f) = $true)),
% 1.47/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 1.47/1.38 thf(f13,plain,(
% 1.47/1.38 ((p @ g) != $true)),
% 1.47/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 1.47/1.38 thf(f34,plain,(
% 1.47/1.38 spl0_3 | spl0_4),
% 1.47/1.38 inference(avatar_split_clause,[status(thm)],[f16,f31,f27])).
% 1.47/1.38 thf(f16,plain,(
% 1.47/1.38 (b = $false) | (a = $false)),
% 1.47/1.38 inference(binary_proxy_clausification,[status(thm)],[f10])).
% 1.47/1.38 thf(f10,plain,(
% 1.47/1.38 (a != b)),
% 1.47/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 1.47/1.38 thf(f25,plain,(
% 1.47/1.38 spl0_1 | spl0_2),
% 1.47/1.38 inference(avatar_split_clause,[status(thm)],[f15,f22,f18])).
% 1.47/1.38 thf(f15,plain,(
% 1.47/1.38 (b = $true) | (a = $true)),
% 1.47/1.38 inference(binary_proxy_clausification,[status(thm)],[f10])).
% 1.47/1.38 % SZS output end Proof for DTF2THF_10596
% 1.47/1.38 % (10693)------------------------------
% 1.47/1.38 % (10693)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.38 % (10693)Termination reason: Refutation
% 1.47/1.38
% 1.47/1.38 % (10693)Memory used [KB]: 5628
% 1.47/1.38 % (10693)Time elapsed: 0.007 s
% 1.47/1.38 % (10693)Instructions burned: 9 (million)
% 1.47/1.38 % (10693)------------------------------
% 1.47/1.38 % (10693)------------------------------
% 1.47/1.38 % (10692)Success in time 0.017 s
%------------------------------------------------------------------------------