%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU852^5 : 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 : n009.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 09:37:35 AM UTC 2026
% Result : Theorem 0.31s 1.32s
% Output : Refutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 49 ( 1 unt; 0 typ; 6 def)
% Number of atoms : 529 ( 195 equ; 0 cnn)
% Maximal formula atoms : 32 ( 10 avg)
% Number of connectives : 568 ( 121 ~; 114 |; 69 &; 223 @)
% ( 11 <=>; 28 =>; 0 <=; 2 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 33 ( 33 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 10 con; 0-2 aty)
% Number of variables : 107 ( 0 ^; 77 !; 30 ?; 107 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_4,type,
sK0: a > $o ).
thf(func_def_5,type,
sK1: a > $o ).
thf(func_def_6,type,
sK2: a > $o ).
thf(func_def_7,type,
sK3: a ).
thf(func_def_8,type,
sK4: a ).
thf(f73,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f51,f58,f60,f61,f62,f64,f68,f72]) ).
thf(f72,plain,
( spl5_2
| ~ spl5_5
| ~ spl5_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f71]) ).
thf(f71,plain,
( $false
| spl5_2
| ~ spl5_5
| ~ spl5_7 ),
inference(subsumption_resolution,[status(thm)],[f70,f50]) ).
thf(f50,plain,
( ( ( sK0 @ sK4 )
= $true )
| ~ spl5_5 ),
inference(avatar_component_clause,[status(thm)],[f48]) ).
thf(f48,definition,
( spl5_5
<=> ( ( sK0 @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl5_5])],[avatar_definition]) ).
thf(f70,plain,
( ( ( sK0 @ sK4 )
!= $true )
| spl5_2
| ~ spl5_7 ),
inference(trivial_inequality_removal,[status(thm)],[f69]) ).
thf(f69,plain,
( ( $true != $true )
| ( ( sK0 @ sK4 )
!= $true )
| spl5_2
| ~ spl5_7 ),
inference(superposition,[status(thm)],[f35,f57]) ).
thf(f57,plain,
( ! [X5: a] :
( ( ( sK2 @ X5 )
= $true )
| ( ( sK0 @ X5 )
!= $true ) )
| ~ spl5_7 ),
inference(avatar_component_clause,[status(thm)],[f56]) ).
thf(f56,definition,
( spl5_7
<=> ! [X5: a] :
( ( ( sK2 @ X5 )
= $true )
| ( ( sK0 @ X5 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl5_7])],[avatar_definition]) ).
thf(f35,plain,
( ( ( sK2 @ sK4 )
!= $true )
| spl5_2 ),
inference(avatar_component_clause,[status(thm)],[f33]) ).
thf(f33,definition,
( spl5_2
<=> ( ( sK2 @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl5_2])],[avatar_definition]) ).
thf(f68,plain,
( spl5_1
| ~ spl5_3
| ~ spl5_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f67]) ).
thf(f67,plain,
( $false
| spl5_1
| ~ spl5_3
| ~ spl5_7 ),
inference(subsumption_resolution,[status(thm)],[f66,f40]) ).
thf(f40,plain,
( ( ( sK0 @ sK3 )
= $true )
| ~ spl5_3 ),
inference(avatar_component_clause,[status(thm)],[f38]) ).
thf(f38,definition,
( spl5_3
<=> ( ( sK0 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl5_3])],[avatar_definition]) ).
thf(f66,plain,
( ( ( sK0 @ sK3 )
!= $true )
| spl5_1
| ~ spl5_7 ),
inference(trivial_inequality_removal,[status(thm)],[f65]) ).
thf(f65,plain,
( ( $true != $true )
| ( ( sK0 @ sK3 )
!= $true )
| spl5_1
| ~ spl5_7 ),
inference(superposition,[status(thm)],[f31,f57]) ).
thf(f31,plain,
( ( ( sK2 @ sK3 )
!= $true )
| spl5_1 ),
inference(avatar_component_clause,[status(thm)],[f29]) ).
thf(f29,definition,
( spl5_1
<=> ( ( sK2 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl5_1])],[avatar_definition]) ).
thf(f64,plain,
( spl5_7
| ~ spl5_6 ),
inference(avatar_split_clause,[status(thm)],[f63,f53,f56]) ).
thf(f53,definition,
( spl5_6
<=> ! [X6: a] :
( ( ( sK1 @ X6 )
!= $true )
| ( ( sK2 @ X6 )
= $true )
| ( ( sK0 @ X6 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl5_6])],[avatar_definition]) ).
thf(f63,plain,
( ! [X6: a] :
( ( ( sK0 @ X6 )
!= $true )
| ( ( sK2 @ X6 )
= $true ) )
| ~ spl5_6 ),
inference(subsumption_resolution,[status(thm)],[f54,f17]) ).
thf(f17,plain,
! [X7: a] :
( ( ( sK1 @ X7 )
= $true )
| ( ( sK0 @ X7 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ( ( ( sK0 @ sK3 )
= $true )
& ( ( sK2 @ sK3 )
!= $true ) )
| ( ( ( sK1 @ sK4 )
= $true )
& ( ( sK0 @ sK4 )
= $true )
& ( ( sK2 @ sK4 )
!= $true )
& ( ( sK2 @ sK4 )
!= $true ) ) )
& ( ! [X5: a] :
( ( ( sK0 @ X5 )
!= $true )
| ( ( sK2 @ X5 )
= $true ) )
| ! [X6: a] :
( ( ( sK1 @ X6 )
!= $true )
| ( ( sK0 @ X6 )
!= $true )
| ( ( sK2 @ X6 )
= $true )
| ( ( sK2 @ X6 )
= $true ) ) )
& ! [X7: a] :
( ( ( sK0 @ X7 )
!= $true )
| ( ( sK1 @ X7 )
= $true ) )
& ! [X8: a] :
( ( ( sK2 @ X8 )
!= $true )
| ( ( sK1 @ X8 )
= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f11,f14,f13,f12]) ).
thf(f12,plain,
( ? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ? [X3: a] :
( ( ( X0 @ X3 )
= $true )
& ( ( X2 @ X3 )
!= $true ) )
| ? [X4: a] :
( ( ( X1 @ X4 )
= $true )
& ( ( X0 @ X4 )
= $true )
& ( ( X2 @ X4 )
!= $true )
& ( ( X2 @ X4 )
!= $true ) ) )
& ( ! [X5: a] :
( ( ( X0 @ X5 )
!= $true )
| ( ( X2 @ X5 )
= $true ) )
| ! [X6: a] :
( ( ( X1 @ X6 )
!= $true )
| ( ( X0 @ X6 )
!= $true )
| ( ( X2 @ X6 )
= $true )
| ( ( X2 @ X6 )
= $true ) ) )
& ! [X7: a] :
( ( ( X0 @ X7 )
!= $true )
| ( ( X1 @ X7 )
= $true ) )
& ! [X8: a] :
( ( ( X2 @ X8 )
!= $true )
| ( ( X1 @ X8 )
= $true ) ) )
=> ( ( ? [X3: a] :
( ( ( sK0 @ X3 )
= $true )
& ( ( sK2 @ X3 )
!= $true ) )
| ? [X4: a] :
( ( ( sK1 @ X4 )
= $true )
& ( ( sK0 @ X4 )
= $true )
& ( ( sK2 @ X4 )
!= $true )
& ( ( sK2 @ X4 )
!= $true ) ) )
& ( ! [X5: a] :
( ( ( sK0 @ X5 )
!= $true )
| ( ( sK2 @ X5 )
= $true ) )
| ! [X6: a] :
( ( ( sK1 @ X6 )
!= $true )
| ( ( sK0 @ X6 )
!= $true )
| ( ( sK2 @ X6 )
= $true )
| ( ( sK2 @ X6 )
= $true ) ) )
& ! [X7: a] :
( ( ( sK0 @ X7 )
!= $true )
| ( ( sK1 @ X7 )
= $true ) )
& ! [X8: a] :
( ( ( sK2 @ X8 )
!= $true )
| ( ( sK1 @ X8 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ? [X3: a] :
( ( ( sK0 @ X3 )
= $true )
& ( ( sK2 @ X3 )
!= $true ) )
=> ( ( ( sK0 @ sK3 )
= $true )
& ( ( sK2 @ sK3 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
( ? [X4: a] :
( ( ( sK1 @ X4 )
= $true )
& ( ( sK0 @ X4 )
= $true )
& ( ( sK2 @ X4 )
!= $true )
& ( ( sK2 @ X4 )
!= $true ) )
=> ( ( ( sK1 @ sK4 )
= $true )
& ( ( sK0 @ sK4 )
= $true )
& ( ( sK2 @ sK4 )
!= $true )
& ( ( sK2 @ sK4 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ? [X3: a] :
( ( ( X0 @ X3 )
= $true )
& ( ( X2 @ X3 )
!= $true ) )
| ? [X4: a] :
( ( ( X1 @ X4 )
= $true )
& ( ( X0 @ X4 )
= $true )
& ( ( X2 @ X4 )
!= $true )
& ( ( X2 @ X4 )
!= $true ) ) )
& ( ! [X5: a] :
( ( ( X0 @ X5 )
!= $true )
| ( ( X2 @ X5 )
= $true ) )
| ! [X6: a] :
( ( ( X1 @ X6 )
!= $true )
| ( ( X0 @ X6 )
!= $true )
| ( ( X2 @ X6 )
= $true )
| ( ( X2 @ X6 )
= $true ) ) )
& ! [X7: a] :
( ( ( X0 @ X7 )
!= $true )
| ( ( X1 @ X7 )
= $true ) )
& ! [X8: a] :
( ( ( X2 @ X8 )
!= $true )
| ( ( X1 @ X8 )
= $true ) ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,plain,
? [X1: a > $o,X2: a > $o,X0: a > $o] :
( ( ? [X6: a] :
( ( ( X1 @ X6 )
= $true )
& ( ( X0 @ X6 )
!= $true ) )
| ? [X5: a] :
( ( ( X2 @ X5 )
= $true )
& ( ( X1 @ X5 )
= $true )
& ( ( X0 @ X5 )
!= $true )
& ( ( X0 @ X5 )
!= $true ) ) )
& ( ! [X6: a] :
( ( ( X1 @ X6 )
!= $true )
| ( ( X0 @ X6 )
= $true ) )
| ! [X5: a] :
( ( ( X2 @ X5 )
!= $true )
| ( ( X1 @ X5 )
!= $true )
| ( ( X0 @ X5 )
= $true )
| ( ( X0 @ X5 )
= $true ) ) )
& ! [X4: a] :
( ( ( X1 @ X4 )
!= $true )
| ( ( X2 @ X4 )
= $true ) )
& ! [X3: a] :
( ( ( X0 @ X3 )
!= $true )
| ( ( X2 @ X3 )
= $true ) ) ),
inference(flattening,[status(thm)],[f9]) ).
thf(f9,plain,
? [X1: a > $o,X2: a > $o,X0: a > $o] :
( ( ? [X6: a] :
( ( ( X1 @ X6 )
= $true )
& ( ( X0 @ X6 )
!= $true ) )
| ? [X5: a] :
( ( ( X2 @ X5 )
= $true )
& ( ( X1 @ X5 )
= $true )
& ( ( X0 @ X5 )
!= $true )
& ( ( X0 @ X5 )
!= $true ) ) )
& ( ! [X6: a] :
( ( ( X1 @ X6 )
!= $true )
| ( ( X0 @ X6 )
= $true ) )
| ! [X5: a] :
( ( ( X2 @ X5 )
!= $true )
| ( ( X1 @ X5 )
!= $true )
| ( ( X0 @ X5 )
= $true )
| ( ( X0 @ X5 )
= $true ) ) )
& ! [X4: a] :
( ( ( X1 @ X4 )
!= $true )
| ( ( X2 @ X4 )
= $true ) )
& ! [X3: a] :
( ( ( X0 @ X3 )
!= $true )
| ( ( X2 @ X3 )
= $true ) ) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
? [X1: a > $o,X2: a > $o,X0: a > $o] :
( ( ! [X5: a] :
( ( ( X2 @ X5 )
!= $true )
| ( ( X1 @ X5 )
!= $true )
| ( ( X0 @ X5 )
= $true )
| ( ( X0 @ X5 )
= $true ) )
<~> ! [X6: a] :
( ( ( X1 @ X6 )
!= $true )
| ( ( X0 @ X6 )
= $true ) ) )
& ! [X4: a] :
( ( ( X1 @ X4 )
!= $true )
| ( ( X2 @ X4 )
= $true ) )
& ! [X3: a] :
( ( ( X0 @ X3 )
!= $true )
| ( ( X2 @ X3 )
= $true ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
? [X1: a > $o,X0: a > $o,X2: a > $o] :
( ( ! [X6: a] :
( ( ( X1 @ X6 )
!= $true )
| ( ( X0 @ X6 )
= $true ) )
<~> ! [X5: a] :
( ( ( X0 @ X5 )
= $true )
| ( ( X0 @ X5 )
= $true )
| ( ( X1 @ X5 )
!= $true )
| ( ( X2 @ X5 )
!= $true ) ) )
& ! [X4: a] :
( ( ( X1 @ X4 )
!= $true )
| ( ( X2 @ X4 )
= $true ) )
& ! [X3: a] :
( ( ( X0 @ X3 )
!= $true )
| ( ( X2 @ X3 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X1: a > $o,X0: a > $o,X2: a > $o] :
( ( ! [X4: a] :
( ( ( X1 @ X4 )
= $true )
=> ( ( X2 @ X4 )
= $true ) )
& ! [X3: a] :
( ( ( X0 @ X3 )
= $true )
=> ( ( X2 @ X3 )
= $true ) ) )
=> ( ! [X6: a] :
( ( ( X1 @ X6 )
= $true )
=> ( ( X0 @ X6 )
= $true ) )
<=> ! [X5: a] :
( ( ( ( X0 @ X5 )
!= $true )
& ( ( X1 @ X5 )
= $true )
& ( ( X2 @ X5 )
= $true ) )
=> ( ( X0 @ X5 )
= $true ) ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X4: a] :
( ( ( X1 @ X4 )
= $true )
=> ( ( X2 @ X4 )
= $true ) )
& ! [X3: a] :
( ( ( X0 @ X3 )
= $true )
=> ( ( X2 @ X3 )
= $true ) ) )
=> ( ! [X5: a] :
( ( ( ( X0 @ X5 )
!= $true )
& ( ( X1 @ X5 )
= $true )
& ( ( X2 @ X5 )
= $true ) )
=> ( ( X0 @ X5 )
= $true ) )
<=> ! [X6: a] :
( ( ( X1 @ X6 )
= $true )
=> ( ( X0 @ X6 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( X0 @ X3 )
=> ( X2 @ X3 ) )
& ! [X4: a] :
( ( X1 @ X4 )
=> ( X2 @ X4 ) ) )
=> ( ! [X5: a] :
( ( ~ ( X0 @ X5 )
& ( X1 @ X5 )
& ( X2 @ X5 ) )
=> ( X0 @ X5 ) )
<=> ! [X6: a] :
( ( X1 @ X6 )
=> ( X0 @ X6 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a > $o,X0: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( X2 @ X3 ) ) )
=> ( ! [X3: a] :
( ( ~ ( X1 @ X3 )
& ( X0 @ X3 )
& ( X2 @ X3 ) )
=> ( X1 @ X3 ) )
<=> ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: a > $o,X0: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( X2 @ X3 ) ) )
=> ( ! [X3: a] :
( ( ~ ( X1 @ X3 )
& ( X0 @ X3 )
& ( X2 @ X3 ) )
=> ( X1 @ X3 ) )
<=> ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.WBbRyWuNj4/DTF2THF_5714.p',cGAZING_THM36_pme) ).
thf(f54,plain,
( ! [X6: a] :
( ( ( sK0 @ X6 )
!= $true )
| ( ( sK2 @ X6 )
= $true )
| ( ( sK1 @ X6 )
!= $true ) )
| ~ spl5_6 ),
inference(avatar_component_clause,[status(thm)],[f53]) ).
thf(f62,plain,
( ~ spl5_2
| spl5_3 ),
inference(avatar_split_clause,[status(thm)],[f23,f38,f33]) ).
thf(f23,plain,
( ( ( sK2 @ sK4 )
!= $true )
| ( ( sK0 @ sK3 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f61,plain,
( spl5_3
| spl5_5 ),
inference(avatar_split_clause,[status(thm)],[f25,f48,f38]) ).
thf(f25,plain,
( ( ( sK0 @ sK3 )
= $true )
| ( ( sK0 @ sK4 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f60,plain,
( ~ spl5_2
| ~ spl5_1 ),
inference(avatar_split_clause,[status(thm)],[f20,f29,f33]) ).
thf(f20,plain,
( ( ( sK2 @ sK4 )
!= $true )
| ( ( sK2 @ sK3 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f58,plain,
( spl5_6
| spl5_7 ),
inference(avatar_split_clause,[status(thm)],[f27,f56,f53]) ).
thf(f27,plain,
! [X6: a,X5: a] :
( ( ( sK1 @ X6 )
!= $true )
| ( ( sK0 @ X6 )
!= $true )
| ( ( sK2 @ X5 )
= $true )
| ( ( sK2 @ X6 )
= $true )
| ( ( sK0 @ X5 )
!= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f18]) ).
thf(f18,plain,
! [X6: a,X5: a] :
( ( ( sK2 @ X6 )
= $true )
| ( ( sK0 @ X6 )
!= $true )
| ( ( sK0 @ X5 )
!= $true )
| ( ( sK1 @ X6 )
!= $true )
| ( ( sK2 @ X5 )
= $true )
| ( ( sK2 @ X6 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f51,plain,
( spl5_5
| ~ spl5_1 ),
inference(avatar_split_clause,[status(thm)],[f21,f29,f48]) ).
thf(f21,plain,
( ( ( sK2 @ sK3 )
!= $true )
| ( ( sK0 @ sK4 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU852^5 : 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 : n009.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:35:25 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
% 0.31/0.45 ---- Original DTF file ---
% 0.31/0.45 thf(spec,logic,$$dhol).
% 0.31/0.45 %------------------------------------------------------------------------------
% 0.31/0.45 % File : SEU852^5 : TPTP v9.2.1. Released v4.0.0.
% 0.31/0.45 % Domain : Set Theory
% 0.31/0.45 % Problem : TPS problem GAZING-THM36
% 0.31/0.45 % Version : Especial.
% 0.31/0.45 % English :
% 0.31/0.45
% 0.31/0.45 % Refs : [Bar92] Barker-Plummer D (1992), Gazing: An Approach to the Pr
% 0.31/0.45 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.31/0.45 % Source : [Bro09]
% 0.31/0.45 % Names : tps_0394 [Bro09]
% 0.31/0.45 % : 36 [Bar92]
% 0.31/0.45 % : GAZING-THM36 [TPS]
% 0.31/0.45
% 0.31/0.45 % Status : Theorem
% 0.31/0.45 % 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 v6.2.0, 0.00 v6.1.0, 0.17 v6.0.0, 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v4.0.0
% 0.31/0.45 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.31/0.45 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.31/0.45 % Maximal formula atoms : 0 ( 0 avg)
% 0.31/0.45 % Number of connectives : 20 ( 1 ~; 0 |; 3 &; 10 @)
% 0.31/0.45 % ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% 0.31/0.46 % Maximal formula depth : 12 ( 12 avg)
% 0.31/0.46 % Number of types : 2 ( 1 usr)
% 0.31/0.46 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.31/0.46 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.31/0.46 % Number of variables : 7 ( 0 ^; 7 !; 0 ?; 7 :)
% 0.31/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.31/0.46
% 0.31/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.31/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.31/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.31/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.31/0.46 % : Polymorphic definitions expanded.
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 thf(a_type,type,
% 0.31/0.46 a: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(cGAZING_THM36_pme,conjecture,
% 0.31/0.46 ! [S: a > $o,T: a > $o,U: a > $o] :
% 0.31/0.46 ( ( ! [Xx: a] :
% 0.31/0.46 ( ( S @ Xx )
% 0.31/0.46 => ( U @ Xx ) )
% 0.31/0.46 & ! [Xx: a] :
% 0.31/0.46 ( ( T @ Xx )
% 0.31/0.46 => ( U @ Xx ) ) )
% 0.31/0.46 => ( ! [Xx: a] :
% 0.31/0.46 ( ( S @ Xx )
% 0.31/0.46 => ( T @ Xx ) )
% 0.31/0.46 <=> ! [Xx: a] :
% 0.31/0.46 ( ( ( S @ Xx )
% 0.31/0.46 & ( U @ Xx )
% 0.31/0.46 & ~ ( T @ Xx ) )
% 0.31/0.46 => ( T @ Xx ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 ------------------------
% 0.31/1.30 ---- Embedded in THF ---
% 0.31/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.31/1.30 %%% Generated on Tue Feb 24 12:35:26 EST 2026
% 0.31/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 0.31/1.30 %%% Logic specification used:
% 0.31/1.30 %%% thf(spec, logic, $$dhol).
% 0.31/1.30
% 0.31/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.WBbRyWuNj4/DTF2DTF5714.p
% See solution above
% 0.31/1.30 ------------------------
% 0.31/1.31 ---- Cleaned THF ---
% 0.31/1.31 thf(a_type,type,
% 0.31/1.31 a: $tType ).
% 0.31/1.31
% 0.31/1.31 thf(cGAZING_THM36_pme,conjecture,
% 0.31/1.31 ! [S: a > $o,T: a > $o,U: a > $o] :
% 0.31/1.31 ( ( ! [Xx: a] :
% 0.31/1.31 ( ( S @ Xx )
% 0.31/1.31 => ( U @ Xx ) )
% 0.31/1.31 & ! [Xx: a] :
% 0.31/1.31 ( ( T @ Xx )
% 0.31/1.31 => ( U @ Xx ) ) )
% 0.31/1.31 => ( ! [Xx: a] :
% 0.31/1.31 ( ( S @ Xx )
% 0.31/1.31 => ( T @ Xx ) )
% 0.31/1.31 <=> ! [Xx: a] :
% 0.31/1.31 ( ( ( S @ Xx )
% 0.31/1.31 & ( U @ Xx )
% 0.31/1.31 & ~ ( T @ Xx ) )
% 0.31/1.31 => ( T @ Xx ) ) ) ) ).
% 0.31/1.31 ------------------------
% 0.31/1.32 % (5923)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_5714 for (2999ds/275Mi)
% 0.31/1.32 % (5918)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_5714 for (2999ds/4Mi)
% 0.31/1.32 % (5923)First to succeed.
% 0.31/1.32 % (5918)Instruction limit reached!
% 0.31/1.32 % (5918)------------------------------
% 0.31/1.32 % (5918)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.32 % (5918)Termination reason: Unknown
% 0.31/1.32 % (5918)Termination phase: Saturation
% 0.31/1.32
% 0.31/1.32 % (5918)Memory used [KB]: 5500
% 0.31/1.32 % (5918)Time elapsed: 0.003 s
% 0.31/1.32 % (5918)Instructions burned: 5 (million)
% 0.31/1.32 % (5918)------------------------------
% 0.31/1.32 % (5918)------------------------------
% 0.31/1.32 % (5917)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_5714 for (2999ds/183Mi)
% 0.31/1.32 % (5923)Refutation found. Thanks to Tanya!
% 0.31/1.32 % SZS status Theorem for DTF2THF_5714
% 0.31/1.32 % SZS output start Proof for DTF2THF_5714
% 0.31/1.32 thf(type_def_5, type, a: $tType).
% 0.31/1.32 thf(func_def_0, type, a: $tType).
% 0.31/1.32 thf(func_def_4, type, sK0: a > $o).
% 0.31/1.32 thf(func_def_5, type, sK1: a > $o).
% 0.31/1.32 thf(func_def_6, type, sK2: a > $o).
% 0.31/1.32 thf(func_def_7, type, sK3: a).
% 0.31/1.32 thf(func_def_8, type, sK4: a).
% 0.31/1.32 thf(f73,plain,(
% 0.31/1.32 $false),
% 0.31/1.32 inference(avatar_sat_refutation,[status(thm)],[f51,f58,f60,f61,f62,f64,f68,f72])).
% 0.31/1.32 thf(f72,plain,(
% 0.31/1.32 spl5_2 | ~spl5_5 | ~spl5_7),
% 0.31/1.32 inference(avatar_contradiction_clause,[status(thm)],[f71])).
% 0.31/1.32 thf(f71,plain,(
% 0.31/1.32 $false | (spl5_2 | ~spl5_5 | ~spl5_7)),
% 0.31/1.32 inference(subsumption_resolution,[status(thm)],[f70,f50])).
% 0.31/1.32 thf(f50,plain,(
% 0.31/1.32 ((sK0 @ sK4) = $true) | ~spl5_5),
% 0.31/1.32 inference(avatar_component_clause,[status(thm)],[f48])).
% 0.31/1.32 thf(f48,definition,(
% 0.31/1.32 spl5_5 <=> ((sK0 @ sK4) = $true)),
% 0.31/1.32 introduced(definition,[new_symbols(naming,[spl5_5])],[avatar_definition])).
% 0.31/1.32 thf(f70,plain,(
% 0.31/1.32 ((sK0 @ sK4) != $true) | (spl5_2 | ~spl5_7)),
% 0.31/1.32 inference(trivial_inequality_removal,[status(thm)],[f69])).
% 0.31/1.32 thf(f69,plain,(
% 0.31/1.32 ($true != $true) | ((sK0 @ sK4) != $true) | (spl5_2 | ~spl5_7)),
% 0.31/1.32 inference(superposition,[status(thm)],[f35,f57])).
% 0.31/1.32 thf(f57,plain,(
% 0.31/1.32 ( ! [X5 : a] : (((sK2 @ X5) = $true) | ((sK0 @ X5) != $true)) ) | ~spl5_7),
% 0.31/1.32 inference(avatar_component_clause,[status(thm)],[f56])).
% 0.31/1.32 thf(f56,definition,(
% 0.31/1.32 spl5_7 <=> ! [X5 : a] : (((sK2 @ X5) = $true) | ((sK0 @ X5) != $true))),
% 0.31/1.32 introduced(definition,[new_symbols(naming,[spl5_7])],[avatar_definition])).
% 0.31/1.32 thf(f35,plain,(
% 0.31/1.32 ((sK2 @ sK4) != $true) | spl5_2),
% 0.31/1.32 inference(avatar_component_clause,[status(thm)],[f33])).
% 0.31/1.32 thf(f33,definition,(
% 0.31/1.32 spl5_2 <=> ((sK2 @ sK4) = $true)),
% 0.31/1.32 introduced(definition,[new_symbols(naming,[spl5_2])],[avatar_definition])).
% 0.31/1.32 thf(f68,plain,(
% 0.31/1.32 spl5_1 | ~spl5_3 | ~spl5_7),
% 0.31/1.32 inference(avatar_contradiction_clause,[status(thm)],[f67])).
% 0.31/1.32 thf(f67,plain,(
% 0.31/1.32 $false | (spl5_1 | ~spl5_3 | ~spl5_7)),
% 0.31/1.32 inference(subsumption_resolution,[status(thm)],[f66,f40])).
% 0.31/1.32 thf(f40,plain,(
% 0.31/1.32 ((sK0 @ sK3) = $true) | ~spl5_3),
% 0.31/1.32 inference(avatar_component_clause,[status(thm)],[f38])).
% 0.31/1.32 thf(f38,definition,(
% 0.31/1.32 spl5_3 <=> ((sK0 @ sK3) = $true)),
% 0.31/1.32 introduced(definition,[new_symbols(naming,[spl5_3])],[avatar_definition])).
% 0.31/1.32 thf(f66,plain,(
% 0.31/1.32 ((sK0 @ sK3) != $true) | (spl5_1 | ~spl5_7)),
% 0.31/1.32 inference(trivial_inequality_removal,[status(thm)],[f65])).
% 0.31/1.32 thf(f65,plain,(
% 0.31/1.32 ($true != $true) | ((sK0 @ sK3) != $true) | (spl5_1 | ~spl5_7)),
% 0.31/1.32 inference(superposition,[status(thm)],[f31,f57])).
% 0.31/1.32 thf(f31,plain,(
% 0.31/1.32 ((sK2 @ sK3) != $true) | spl5_1),
% 0.31/1.32 inference(avatar_component_clause,[status(thm)],[f29])).
% 0.31/1.32 thf(f29,definition,(
% 0.31/1.32 spl5_1 <=> ((sK2 @ sK3) = $true)),
% 0.31/1.32 introduced(definition,[new_symbols(naming,[spl5_1])],[avatar_definition])).
% 0.31/1.32 thf(f64,plain,(
% 0.31/1.32 spl5_7 | ~spl5_6),
% 0.31/1.32 inference(avatar_split_clause,[status(thm)],[f63,f53,f56])).
% 0.31/1.32 thf(f53,definition,(
% 0.31/1.32 spl5_6 <=> ! [X6 : a] : (((sK1 @ X6) != $true) | ((sK2 @ X6) = $true) | ((sK0 @ X6) != $true))),
% 0.31/1.32 introduced(definition,[new_symbols(naming,[spl5_6])],[avatar_definition])).
% 0.31/1.32 thf(f63,plain,(
% 0.31/1.32 ( ! [X6 : a] : (((sK0 @ X6) != $true) | ((sK2 @ X6) = $true)) ) | ~spl5_6),
% 0.31/1.32 inference(subsumption_resolution,[status(thm)],[f54,f17])).
% 0.31/1.32 thf(f17,plain,(
% 0.31/1.32 ( ! [X7 : a] : (((sK1 @ X7) = $true) | ((sK0 @ X7) != $true)) )),
% 0.31/1.32 inference(cnf_transformation,[status(thm)],[f15])).
% 0.31/1.32 thf(f15,plain,(
% 0.31/1.32 ((((sK0 @ sK3) = $true) & ((sK2 @ sK3) != $true)) | (((sK1 @ sK4) = $true) & ((sK0 @ sK4) = $true) & ((sK2 @ sK4) != $true) & ((sK2 @ sK4) != $true))) & (! [X5 : a] : (((sK0 @ X5) != $true) | ((sK2 @ X5) = $true)) | ! [X6 : a] : (((sK1 @ X6) != $true) | ((sK0 @ X6) != $true) | ((sK2 @ X6) = $true) | ((sK2 @ X6) = $true))) & ! [X7 : a] : (((sK0 @ X7) != $true) | ((sK1 @ X7) = $true)) & ! [X8 : a] : (((sK2 @ X8) != $true) | ((sK1 @ X8) = $true))),
% 0.31/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f11,f14,f13,f12])).
% 0.31/1.32 thf(f12,plain,(
% 0.31/1.32 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((? [X3 : a] : (((X0 @ X3) = $true) & ((X2 @ X3) != $true)) | ? [X4 : a] : (((X1 @ X4) = $true) & ((X0 @ X4) = $true) & ((X2 @ X4) != $true) & ((X2 @ X4) != $true))) & (! [X5 : a] : (((X0 @ X5) != $true) | ((X2 @ X5) = $true)) | ! [X6 : a] : (((X1 @ X6) != $true) | ((X0 @ X6) != $true) | ((X2 @ X6) = $true) | ((X2 @ X6) = $true))) & ! [X7 : a] : (((X0 @ X7) != $true) | ((X1 @ X7) = $true)) & ! [X8 : a] : (((X2 @ X8) != $true) | ((X1 @ X8) = $true))) => ((? [X3 : a] : (((sK0 @ X3) = $true) & ((sK2 @ X3) != $true)) | ? [X4 : a] : (((sK1 @ X4) = $true) & ((sK0 @ X4) = $true) & ((sK2 @ X4) != $true) & ((sK2 @ X4) != $true))) & (! [X5 : a] : (((sK0 @ X5) != $true) | ((sK2 @ X5) = $true)) | ! [X6 : a] : (((sK1 @ X6) != $true) | ((sK0 @ X6) != $true) | ((sK2 @ X6) = $true) | ((sK2 @ X6) = $true))) & ! [X7 : a] : (((sK0 @ X7) != $true) | ((sK1 @ X7) = $true)) & ! [X8 : a] : (((sK2 @ X8) != $true) | ((sK1 @ X8) = $true)))),
% 0.31/1.32 introduced(definition,[],[choice_axiom])).
% 0.31/1.32 thf(f13,plain,(
% 0.31/1.32 ? [X3 : a] : (((sK0 @ X3) = $true) & ((sK2 @ X3) != $true)) => (((sK0 @ sK3) = $true) & ((sK2 @ sK3) != $true))),
% 0.31/1.32 introduced(definition,[],[choice_axiom])).
% 0.31/1.32 thf(f14,plain,(
% 0.31/1.32 ? [X4 : a] : (((sK1 @ X4) = $true) & ((sK0 @ X4) = $true) & ((sK2 @ X4) != $true) & ((sK2 @ X4) != $true)) => (((sK1 @ sK4) = $true) & ((sK0 @ sK4) = $true) & ((sK2 @ sK4) != $true) & ((sK2 @ sK4) != $true))),
% 0.31/1.32 introduced(definition,[],[choice_axiom])).
% 0.31/1.32 thf(f11,plain,(
% 0.31/1.32 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((? [X3 : a] : (((X0 @ X3) = $true) & ((X2 @ X3) != $true)) | ? [X4 : a] : (((X1 @ X4) = $true) & ((X0 @ X4) = $true) & ((X2 @ X4) != $true) & ((X2 @ X4) != $true))) & (! [X5 : a] : (((X0 @ X5) != $true) | ((X2 @ X5) = $true)) | ! [X6 : a] : (((X1 @ X6) != $true) | ((X0 @ X6) != $true) | ((X2 @ X6) = $true) | ((X2 @ X6) = $true))) & ! [X7 : a] : (((X0 @ X7) != $true) | ((X1 @ X7) = $true)) & ! [X8 : a] : (((X2 @ X8) != $true) | ((X1 @ X8) = $true)))),
% 0.31/1.32 inference(rectify,[status(thm)],[f10])).
% 0.31/1.32 thf(f10,plain,(
% 0.31/1.32 ? [X1 : a > $o,X2 : a > $o,X0 : a > $o] : ((? [X6 : a] : (((X1 @ X6) = $true) & ((X0 @ X6) != $true)) | ? [X5 : a] : (((X2 @ X5) = $true) & ((X1 @ X5) = $true) & ((X0 @ X5) != $true) & ((X0 @ X5) != $true))) & (! [X6 : a] : (((X1 @ X6) != $true) | ((X0 @ X6) = $true)) | ! [X5 : a] : (((X2 @ X5) != $true) | ((X1 @ X5) != $true) | ((X0 @ X5) = $true) | ((X0 @ X5) = $true))) & ! [X4 : a] : (((X1 @ X4) != $true) | ((X2 @ X4) = $true)) & ! [X3 : a] : (((X0 @ X3) != $true) | ((X2 @ X3) = $true)))),
% 0.31/1.32 inference(flattening,[status(thm)],[f9])).
% 0.31/1.32 thf(f9,plain,(
% 0.31/1.32 ? [X1 : a > $o,X2 : a > $o,X0 : a > $o] : (((? [X6 : a] : (((X1 @ X6) = $true) & ((X0 @ X6) != $true)) | ? [X5 : a] : (((X2 @ X5) = $true) & ((X1 @ X5) = $true) & ((X0 @ X5) != $true) & ((X0 @ X5) != $true))) & (! [X6 : a] : (((X1 @ X6) != $true) | ((X0 @ X6) = $true)) | ! [X5 : a] : (((X2 @ X5) != $true) | ((X1 @ X5) != $true) | ((X0 @ X5) = $true) | ((X0 @ X5) = $true)))) & ! [X4 : a] : (((X1 @ X4) != $true) | ((X2 @ X4) = $true)) & ! [X3 : a] : (((X0 @ X3) != $true) | ((X2 @ X3) = $true)))),
% 0.31/1.32 inference(nnf_transformation,[status(thm)],[f8])).
% 0.31/1.32 thf(f8,plain,(
% 0.31/1.32 ? [X1 : a > $o,X2 : a > $o,X0 : a > $o] : ((! [X5 : a] : (((X2 @ X5) != $true) | ((X1 @ X5) != $true) | ((X0 @ X5) = $true) | ((X0 @ X5) = $true)) <~> ! [X6 : a] : (((X1 @ X6) != $true) | ((X0 @ X6) = $true))) & ! [X4 : a] : (((X1 @ X4) != $true) | ((X2 @ X4) = $true)) & ! [X3 : a] : (((X0 @ X3) != $true) | ((X2 @ X3) = $true)))),
% 0.31/1.32 inference(flattening,[status(thm)],[f7])).
% 0.31/1.32 thf(f7,plain,(
% 0.31/1.32 ? [X1 : a > $o,X0 : a > $o,X2 : a > $o] : ((! [X6 : a] : (((X1 @ X6) != $true) | ((X0 @ X6) = $true)) <~> ! [X5 : a] : (((X0 @ X5) = $true) | (((X0 @ X5) = $true) | ((X1 @ X5) != $true) | ((X2 @ X5) != $true)))) & (! [X4 : a] : (((X1 @ X4) != $true) | ((X2 @ X4) = $true)) & ! [X3 : a] : (((X0 @ X3) != $true) | ((X2 @ X3) = $true))))),
% 0.31/1.32 inference(ennf_transformation,[status(thm)],[f6])).
% 0.31/1.32 thf(f6,plain,(
% 0.31/1.32 ~! [X1 : a > $o,X0 : a > $o,X2 : a > $o] : ((! [X4 : a] : (((X1 @ X4) = $true) => ((X2 @ X4) = $true)) & ! [X3 : a] : (((X0 @ X3) = $true) => ((X2 @ X3) = $true))) => (! [X6 : a] : (((X1 @ X6) = $true) => ((X0 @ X6) = $true)) <=> ! [X5 : a] : ((((X0 @ X5) != $true) & ((X1 @ X5) = $true) & ((X2 @ X5) = $true)) => ((X0 @ X5) = $true))))),
% 0.31/1.32 inference(flattening,[status(thm)],[f5])).
% 0.31/1.32 thf(f5,plain,(
% 0.31/1.32 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((! [X4 : a] : (((X1 @ X4) = $true) => ((X2 @ X4) = $true)) & ! [X3 : a] : (((X0 @ X3) = $true) => ((X2 @ X3) = $true))) => (! [X5 : a] : ((~((X0 @ X5) = $true) & ((X1 @ X5) = $true) & ((X2 @ X5) = $true)) => ((X0 @ X5) = $true)) <=> ! [X6 : a] : (((X1 @ X6) = $true) => ((X0 @ X6) = $true))))),
% 0.31/1.32 inference(fool_elimination,[status(thm)],[f4])).
% 0.31/1.32 thf(f4,plain,(
% 0.31/1.32 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((! [X3 : a] : ((X0 @ X3) => (X2 @ X3)) & ! [X4 : a] : ((X1 @ X4) => (X2 @ X4))) => (! [X5 : a] : ((~(X0 @ X5) & (X1 @ X5) & (X2 @ X5)) => (X0 @ X5)) <=> ! [X6 : a] : ((X1 @ X6) => (X0 @ X6))))),
% 0.31/1.32 inference(rectify,[status(thm)],[f2])).
% 0.31/1.32 thf(f2,negated_conjecture,(
% 0.31/1.32 ~! [X1 : a > $o,X0 : a > $o,X2 : a > $o] : ((! [X3 : a] : ((X1 @ X3) => (X2 @ X3)) & ! [X3 : a] : ((X0 @ X3) => (X2 @ X3))) => (! [X3 : a] : ((~(X1 @ X3) & (X0 @ X3) & (X2 @ X3)) => (X1 @ X3)) <=> ! [X3 : a] : ((X0 @ X3) => (X1 @ X3))))),
% 0.31/1.32 inference(negated_conjecture,[status(cth)],[f1])).
% 0.31/1.32 thf(f1,conjecture,(
% 0.31/1.32 ! [X1 : a > $o,X0 : a > $o,X2 : a > $o] : ((! [X3 : a] : ((X1 @ X3) => (X2 @ X3)) & ! [X3 : a] : ((X0 @ X3) => (X2 @ X3))) => (! [X3 : a] : ((~(X1 @ X3) & (X0 @ X3) & (X2 @ X3)) => (X1 @ X3)) <=> ! [X3 : a] : ((X0 @ X3) => (X1 @ X3))))),
% 0.31/1.32 file('/export/starexec/sandbox/tmp/tmp.WBbRyWuNj4/DTF2THF_5714.p',cGAZING_THM36_pme)).
% 0.31/1.32 thf(f54,plain,(
% 0.31/1.32 ( ! [X6 : a] : (((sK0 @ X6) != $true) | ((sK2 @ X6) = $true) | ((sK1 @ X6) != $true)) ) | ~spl5_6),
% 0.31/1.32 inference(avatar_component_clause,[status(thm)],[f53])).
% 0.31/1.32 thf(f62,plain,(
% 0.31/1.32 ~spl5_2 | spl5_3),
% 0.31/1.32 inference(avatar_split_clause,[status(thm)],[f23,f38,f33])).
% 0.31/1.32 thf(f23,plain,(
% 0.31/1.32 ((sK2 @ sK4) != $true) | ((sK0 @ sK3) = $true)),
% 0.31/1.32 inference(cnf_transformation,[status(thm)],[f15])).
% 0.31/1.32 thf(f61,plain,(
% 0.31/1.32 spl5_3 | spl5_5),
% 0.31/1.32 inference(avatar_split_clause,[status(thm)],[f25,f48,f38])).
% 0.31/1.32 thf(f25,plain,(
% 0.31/1.32 ((sK0 @ sK3) = $true) | ((sK0 @ sK4) = $true)),
% 0.31/1.32 inference(cnf_transformation,[status(thm)],[f15])).
% 0.31/1.32 thf(f60,plain,(
% 0.31/1.32 ~spl5_2 | ~spl5_1),
% 0.31/1.32 inference(avatar_split_clause,[status(thm)],[f20,f29,f33])).
% 0.31/1.32 thf(f20,plain,(
% 0.31/1.32 ((sK2 @ sK4) != $true) | ((sK2 @ sK3) != $true)),
% 0.31/1.32 inference(cnf_transformation,[status(thm)],[f15])).
% 0.31/1.32 thf(f58,plain,(
% 0.31/1.32 spl5_6 | spl5_7),
% 0.31/1.32 inference(avatar_split_clause,[status(thm)],[f27,f56,f53])).
% 0.31/1.32 thf(f27,plain,(
% 0.31/1.32 ( ! [X6 : a,X5 : a] : (((sK1 @ X6) != $true) | ((sK0 @ X6) != $true) | ((sK2 @ X5) = $true) | ((sK2 @ X6) = $true) | ((sK0 @ X5) != $true)) )),
% 0.31/1.32 inference(duplicate_literal_removal,[status(thm)],[f18])).
% 0.31/1.32 thf(f18,plain,(
% 0.31/1.32 ( ! [X6 : a,X5 : a] : (((sK2 @ X6) = $true) | ((sK0 @ X6) != $true) | ((sK0 @ X5) != $true) | ((sK1 @ X6) != $true) | ((sK2 @ X5) = $true) | ((sK2 @ X6) = $true)) )),
% 0.31/1.32 inference(cnf_transformation,[status(thm)],[f15])).
% 0.31/1.32 thf(f51,plain,(
% 0.31/1.32 spl5_5 | ~spl5_1),
% 0.31/1.32 inference(avatar_split_clause,[status(thm)],[f21,f29,f48])).
% 0.31/1.32 thf(f21,plain,(
% 0.31/1.32 ((sK2 @ sK3) != $true) | ((sK0 @ sK4) = $true)),
% 0.31/1.32 inference(cnf_transformation,[status(thm)],[f15])).
% 0.31/1.32 % SZS output end Proof for DTF2THF_5714
% 0.31/1.32 % (5923)------------------------------
% 0.31/1.32 % (5923)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.32 % (5923)Termination reason: Refutation
% 0.31/1.32
% 0.31/1.32 % (5923)Memory used [KB]: 5500
% 0.31/1.32 % (5923)Time elapsed: 0.004 s
% 0.31/1.32 % (5923)Instructions burned: 2 (million)
% 0.31/1.32 % (5923)------------------------------
% 0.31/1.32 % (5923)------------------------------
% 0.31/1.32 % (5916)Success in time 0.014 s
%------------------------------------------------------------------------------