%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV401^5 : 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 : n031.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 09:41:10 AM UTC 2026
% Result : Theorem 1.62s 1.31s
% Output : Refutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 7
% Syntax : Number of formulae : 52 ( 2 unt; 0 typ; 4 def)
% Number of atoms : 473 ( 106 equ; 0 cnn)
% Maximal formula atoms : 10 ( 9 avg)
% Number of connectives : 547 ( 86 ~; 82 |; 26 &; 320 @)
% ( 7 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 52 ( 52 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 100 ( 0 ^; 88 !; 12 ?; 100 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
cF: ( a > $o ) > a > $o ).
thf(func_def_2,type,
cG: ( a > $o ) > a > $o ).
thf(func_def_4,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_7,type,
sK0: a ).
thf(func_def_8,type,
sK1: a > $o ).
thf(func_def_9,type,
sK2: ( a > $o ) > ( a > $o ) > a ).
thf(func_def_11,type,
ph4:
!>[X0: $tType] : X0 ).
thf(f148,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f27,f36,f42,f51,f144,f147]) ).
thf(f147,plain,
( ~ spl3_1
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f146]) ).
thf(f146,plain,
( $false
| ~ spl3_1
| ~ spl3_4 ),
inference(trivial_inequality_removal,[status(thm)],[f145]) ).
thf(f145,plain,
( ( $true = $false )
| ~ spl3_1
| ~ spl3_4 ),
inference(forward_demodulation,[status(thm)],[f22,f35]) ).
thf(f35,plain,
( ( $false
= ( cF @ sK1 @ sK0 ) )
| ~ spl3_4 ),
inference(avatar_component_clause,[status(thm)],[f33]) ).
thf(f33,definition,
( spl3_4
<=> ( $false
= ( cF @ sK1 @ sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition]) ).
thf(f22,plain,
( ( $true
= ( cF @ sK1 @ sK0 ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f20]) ).
thf(f20,definition,
( spl3_1
<=> ( $true
= ( cF @ sK1 @ sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f144,plain,
( ~ spl3_2
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f143]) ).
thf(f143,plain,
( $false
| ~ spl3_2
| ~ spl3_4 ),
inference(trivial_inequality_removal,[status(thm)],[f142]) ).
thf(f142,plain,
( ( $true = $false )
| ~ spl3_2
| ~ spl3_4 ),
inference(forward_demodulation,[status(thm)],[f124,f35]) ).
thf(f124,plain,
( ( $true
= ( cF @ sK1 @ sK0 ) )
| ~ spl3_2
| ~ spl3_4 ),
inference(trivial_inequality_removal,[status(thm)],[f120]) ).
thf(f120,plain,
( ( $true != $true )
| ( $true
= ( cF @ sK1 @ sK0 ) )
| ~ spl3_2
| ~ spl3_4 ),
inference(superposition,[status(thm)],[f113,f26]) ).
thf(f26,plain,
( ( ( cF @ ( cG @ ( cF @ sK1 ) ) @ sK0 )
= $true )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f24]) ).
thf(f24,definition,
( spl3_2
<=> ( ( cF @ ( cG @ ( cF @ sK1 ) ) @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f113,plain,
( ! [X0: a] :
( ( $true
!= ( cF @ ( cG @ ( cF @ sK1 ) ) @ X0 ) )
| ( $true
= ( cF @ sK1 @ X0 ) ) )
| ~ spl3_2
| ~ spl3_4 ),
inference(trivial_inequality_removal,[status(thm)],[f112]) ).
thf(f112,plain,
( ! [X0: a] :
( ( $true = $false )
| ( $true
!= ( cF @ ( cG @ ( cF @ sK1 ) ) @ X0 ) )
| ( $true
= ( cF @ sK1 @ X0 ) ) )
| ~ spl3_2
| ~ spl3_4 ),
inference(forward_demodulation,[status(thm)],[f111,f35]) ).
thf(f111,plain,
( ! [X0: a] :
( ( $true
= ( cF @ sK1 @ sK0 ) )
| ( $true
!= ( cF @ ( cG @ ( cF @ sK1 ) ) @ X0 ) )
| ( $true
= ( cF @ sK1 @ X0 ) ) )
| ~ spl3_2 ),
inference(trivial_inequality_removal,[status(thm)],[f106]) ).
thf(f106,plain,
( ! [X0: a] :
( ( $true
!= ( cF @ ( cG @ ( cF @ sK1 ) ) @ X0 ) )
| ( $true != $true )
| ( $true
= ( cF @ sK1 @ X0 ) )
| ( $true
= ( cF @ sK1 @ sK0 ) ) )
| ~ spl3_2 ),
inference(superposition,[status(thm)],[f12,f81]) ).
thf(f81,plain,
( ! [X0: a > $o] :
( ( $true
= ( cG @ ( cF @ X0 ) @ ( sK2 @ X0 @ ( cG @ ( cF @ sK1 ) ) ) ) )
| ( $true
= ( cF @ X0 @ sK0 ) ) )
| ~ spl3_2 ),
inference(trivial_inequality_removal,[status(thm)],[f78]) ).
thf(f78,plain,
( ! [X0: a > $o] :
( ( $true
= ( cF @ X0 @ sK0 ) )
| ( $true != $true )
| ( $true
= ( cG @ ( cF @ X0 ) @ ( sK2 @ X0 @ ( cG @ ( cF @ sK1 ) ) ) ) ) )
| ~ spl3_2 ),
inference(superposition,[status(thm)],[f14,f70]) ).
thf(f70,plain,
( ! [X0: a > $o] :
( ( $true
= ( X0 @ ( sK2 @ X0 @ ( cG @ ( cF @ sK1 ) ) ) ) )
| ( $true
= ( cF @ X0 @ sK0 ) ) )
| ~ spl3_2 ),
inference(trivial_inequality_removal,[status(thm)],[f68]) ).
thf(f68,plain,
( ! [X0: a > $o] :
( ( $true
= ( cF @ X0 @ sK0 ) )
| ( $true
= ( X0 @ ( sK2 @ X0 @ ( cG @ ( cF @ sK1 ) ) ) ) )
| ( $true != $true ) )
| ~ spl3_2 ),
inference(superposition,[status(thm)],[f13,f26]) ).
thf(f13,plain,
! [X6: a > $o,X9: a,X7: a > $o] :
( ( $true
!= ( cF @ X6 @ X9 ) )
| ( ( cF @ X7 @ X9 )
= $true )
| ( ( X7 @ ( sK2 @ X7 @ X6 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( cF @ ( cG @ ( cF @ sK1 ) ) @ sK0 )
!= ( cF @ sK1 @ sK0 ) )
& ! [X2: a,X3: a > $o] :
( ( $true
!= ( X3 @ X2 ) )
| ( $true
= ( cF @ ( cG @ X3 ) @ X2 ) ) )
& ! [X4: a,X5: a > $o] :
( ( $true
!= ( X5 @ X4 ) )
| ( $true
= ( cG @ ( cF @ X5 ) @ X4 ) ) )
& ! [X6: a > $o,X7: a > $o] :
( ( ( ( X7 @ ( sK2 @ X7 @ X6 ) )
= $true )
& ( $true
!= ( X6 @ ( sK2 @ X7 @ X6 ) ) ) )
| ! [X9: a] :
( ( $true
!= ( cF @ X6 @ X9 ) )
| ( ( cF @ X7 @ X9 )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f10,f9]) ).
thf(f9,plain,
( ? [X0: a,X1: a > $o] :
( ( cF @ ( cG @ ( cF @ X1 ) ) @ X0 )
!= ( cF @ X1 @ X0 ) )
=> ( ( cF @ ( cG @ ( cF @ sK1 ) ) @ sK0 )
!= ( cF @ sK1 @ sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
! [X6: a > $o,X7: a > $o] :
( ? [X8: a] :
( ( ( X7 @ X8 )
= $true )
& ( $true
!= ( X6 @ X8 ) ) )
=> ( ( ( X7 @ ( sK2 @ X7 @ X6 ) )
= $true )
& ( $true
!= ( X6 @ ( sK2 @ X7 @ X6 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ? [X0: a,X1: a > $o] :
( ( cF @ ( cG @ ( cF @ X1 ) ) @ X0 )
!= ( cF @ X1 @ X0 ) )
& ! [X2: a,X3: a > $o] :
( ( $true
!= ( X3 @ X2 ) )
| ( $true
= ( cF @ ( cG @ X3 ) @ X2 ) ) )
& ! [X4: a,X5: a > $o] :
( ( $true
!= ( X5 @ X4 ) )
| ( $true
= ( cG @ ( cF @ X5 ) @ X4 ) ) )
& ! [X6: a > $o,X7: a > $o] :
( ? [X8: a] :
( ( ( X7 @ X8 )
= $true )
& ( $true
!= ( X6 @ X8 ) ) )
| ! [X9: a] :
( ( $true
!= ( cF @ X6 @ X9 ) )
| ( ( cF @ X7 @ X9 )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ? [X8: a,X9: a > $o] :
( ( cF @ ( cG @ ( cF @ X9 ) ) @ X8 )
!= ( cF @ X9 @ X8 ) )
& ! [X1: a,X0: a > $o] :
( ( $true
!= ( X0 @ X1 ) )
| ( $true
= ( cF @ ( cG @ X0 ) @ X1 ) ) )
& ! [X7: a,X6: a > $o] :
( ( $true
!= ( X6 @ X7 ) )
| ( $true
= ( cG @ ( cF @ X6 ) @ X7 ) ) )
& ! [X2: a > $o,X3: a > $o] :
( ? [X4: a] :
( ( $true
= ( X3 @ X4 ) )
& ( $true
!= ( X2 @ X4 ) ) )
| ! [X5: a] :
( ( $true
!= ( cF @ X2 @ X5 ) )
| ( $true
= ( cF @ X3 @ X5 ) ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ? [X8: a,X9: a > $o] :
( ( cF @ ( cG @ ( cF @ X9 ) ) @ X8 )
!= ( cF @ X9 @ X8 ) )
& ! [X7: a,X6: a > $o] :
( ( $true
!= ( X6 @ X7 ) )
| ( $true
= ( cG @ ( cF @ X6 ) @ X7 ) ) )
& ! [X1: a,X0: a > $o] :
( ( $true
!= ( X0 @ X1 ) )
| ( $true
= ( cF @ ( cG @ X0 ) @ X1 ) ) )
& ! [X2: a > $o,X3: a > $o] :
( ? [X4: a] :
( ( $true
= ( X3 @ X4 ) )
& ( $true
!= ( X2 @ X4 ) ) )
| ! [X5: a] :
( ( $true
!= ( cF @ X2 @ X5 ) )
| ( $true
= ( cF @ X3 @ X5 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X6: a > $o,X7: a] :
( ( $true
= ( X6 @ X7 ) )
=> ( $true
= ( cG @ ( cF @ X6 ) @ X7 ) ) )
& ! [X1: a,X0: a > $o] :
( ( $true
= ( X0 @ X1 ) )
=> ( $true
= ( cF @ ( cG @ X0 ) @ X1 ) ) )
& ! [X3: a > $o,X2: a > $o] :
( ! [X4: a] :
( ( $true
= ( X3 @ X4 ) )
=> ( $true
= ( X2 @ X4 ) ) )
=> ! [X5: a] :
( ( $true
= ( cF @ X2 @ X5 ) )
=> ( $true
= ( cF @ X3 @ X5 ) ) ) ) )
=> ! [X8: a,X9: a > $o] :
( ( cF @ ( cG @ ( cF @ X9 ) ) @ X8 )
= ( cF @ X9 @ X8 ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: a > $o,X1: a] :
( ( X0 @ X1 )
=> ( cF @ ( cG @ X0 ) @ X1 ) )
& ! [X2: a > $o,X3: a > $o] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( X2 @ X4 ) )
=> ! [X5: a] :
( ( cF @ X2 @ X5 )
=> ( cF @ X3 @ X5 ) ) )
& ! [X6: a > $o,X7: a] :
( ( X6 @ X7 )
=> ( cG @ ( cF @ X6 ) @ X7 ) ) )
=> ! [X8: a,X9: a > $o] :
( ( cF @ X9 @ X8 )
<=> ( cF @ ( cG @ ( cF @ X9 ) ) @ X8 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X0: a > $o,X2: a] :
( ( X0 @ X2 )
=> ( cF @ ( cG @ X0 ) @ X2 ) )
& ! [X1: a > $o,X0: a > $o] :
( ! [X2: a] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) )
=> ! [X2: a] :
( ( cF @ X1 @ X2 )
=> ( cF @ X0 @ X2 ) ) )
& ! [X0: a > $o,X2: a] :
( ( X0 @ X2 )
=> ( cG @ ( cF @ X0 ) @ X2 ) ) )
=> ! [X2: a,X0: a > $o] :
( ( cF @ X0 @ X2 )
<=> ( cF @ ( cG @ ( cF @ X0 ) ) @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X0: a > $o,X2: a] :
( ( X0 @ X2 )
=> ( cF @ ( cG @ X0 ) @ X2 ) )
& ! [X1: a > $o,X0: a > $o] :
( ! [X2: a] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) )
=> ! [X2: a] :
( ( cF @ X1 @ X2 )
=> ( cF @ X0 @ X2 ) ) )
& ! [X0: a > $o,X2: a] :
( ( X0 @ X2 )
=> ( cG @ ( cF @ X0 ) @ X2 ) ) )
=> ! [X2: a,X0: a > $o] :
( ( cF @ X0 @ X2 )
<=> ( cF @ ( cG @ ( cF @ X0 ) ) @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.k9T8AeD2Lh/DTF2THF_14691.p',cTHM67_pme) ).
thf(f14,plain,
! [X4: a,X5: a > $o] :
( ( $true
!= ( X5 @ X4 ) )
| ( $true
= ( cG @ ( cF @ X5 ) @ X4 ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f12,plain,
! [X6: a > $o,X9: a,X7: a > $o] :
( ( $true
!= ( X6 @ ( sK2 @ X7 @ X6 ) ) )
| ( $true
!= ( cF @ X6 @ X9 ) )
| ( ( cF @ X7 @ X9 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f51,plain,
( ~ spl3_1
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f50]) ).
thf(f50,plain,
( $false
| ~ spl3_1
| ~ spl3_3 ),
inference(trivial_inequality_removal,[status(thm)],[f49]) ).
thf(f49,plain,
( ( $true = $false )
| ~ spl3_1
| ~ spl3_3 ),
inference(forward_demodulation,[status(thm)],[f48,f31]) ).
thf(f31,plain,
( ( ( cF @ ( cG @ ( cF @ sK1 ) ) @ sK0 )
= $false )
| ~ spl3_3 ),
inference(avatar_component_clause,[status(thm)],[f29]) ).
thf(f29,definition,
( spl3_3
<=> ( ( cF @ ( cG @ ( cF @ sK1 ) ) @ sK0 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition]) ).
thf(f48,plain,
( ( ( cF @ ( cG @ ( cF @ sK1 ) ) @ sK0 )
= $true )
| ~ spl3_1 ),
inference(trivial_inequality_removal,[status(thm)],[f45]) ).
thf(f45,plain,
( ( ( cF @ ( cG @ ( cF @ sK1 ) ) @ sK0 )
= $true )
| ( $true != $true )
| ~ spl3_1 ),
inference(superposition,[status(thm)],[f15,f22]) ).
thf(f15,plain,
! [X2: a,X3: a > $o] :
( ( $true
!= ( X3 @ X2 ) )
| ( $true
= ( cF @ ( cG @ X3 ) @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f42,plain,
( ~ spl3_2
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f41]) ).
thf(f41,plain,
( $false
| ~ spl3_2
| ~ spl3_3 ),
inference(trivial_inequality_removal,[status(thm)],[f39]) ).
thf(f39,plain,
( ( $true = $false )
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[status(thm)],[f26,f31]) ).
thf(f36,plain,
( spl3_3
| spl3_4 ),
inference(avatar_split_clause,[status(thm)],[f18,f33,f29]) ).
thf(f18,plain,
( ( $false
= ( cF @ sK1 @ sK0 ) )
| ( ( cF @ ( cG @ ( cF @ sK1 ) ) @ sK0 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
( ( cF @ ( cG @ ( cF @ sK1 ) ) @ sK0 )
!= ( cF @ sK1 @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f27,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f17,f24,f20]) ).
thf(f17,plain,
( ( $true
= ( cF @ sK1 @ sK0 ) )
| ( ( cF @ ( cG @ ( cF @ sK1 ) ) @ sK0 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV401^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n031.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:47:48 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : SEV401^5 : TPTP v9.2.1. Released v4.0.0.
% 0.20/0.46 % Domain : Set Theory
% 0.20/0.46 % Problem : TPS problem THM67
% 0.20/0.46 % Version : Especial.
% 0.20/0.46 % English :
% 0.20/0.46
% 0.20/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.46 % Source : [Bro09]
% 0.20/0.46 % Names : tps_0490 [Bro09]
% 0.20/0.46 % : THM67 [TPS]
% 0.20/0.46
% 0.20/0.46 % Status : Theorem
% 0.20/0.46 % Rating : 0.00 v8.1.0, 0.08 v7.4.0, 0.00 v6.2.0, 0.33 v6.1.0, 0.17 v6.0.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.20/0.46 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.20/0.46 % Number of atoms : 10 ( 0 equ; 0 cnn)
% 0.20/0.46 % Maximal formula atoms : 10 ( 10 avg)
% 0.20/0.46 % Number of connectives : 29 ( 0 ~; 0 |; 2 &; 20 @)
% 0.20/0.46 % ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 10 ( 10 avg)
% 0.20/0.46 % Number of types : 2 ( 1 usr)
% 0.20/0.46 % Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 2 ( 2 usr; 0 con; 2-2 aty)
% 0.20/0.46 % Number of variables : 10 ( 0 ^; 10 !; 0 ?; 10 :)
% 0.20/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.20/0.46
% 0.20/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.20/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.20/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.20/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.20/0.46 % : Polymorphic definitions expanded.
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 thf(a_type,type,
% 0.20/0.46 a: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(cF,type,
% 0.20/0.46 cF: ( a > $o ) > a > $o ).
% 0.20/0.46
% 0.20/0.46 thf(cG,type,
% 0.20/0.46 cG: ( a > $o ) > a > $o ).
% 0.20/0.46
% 0.20/0.46 thf(cTHM67_pme,conjecture,
% 0.20/0.46 ( ( ! [S: a > $o,T: a > $o] :
% 0.20/0.46 ( ! [Xx: a] :
% 0.20/0.46 ( ( S @ Xx )
% 0.20/0.46 => ( T @ Xx ) )
% 0.20/0.46 => ! [Xx: a] :
% 0.20/0.46 ( ( cF @ T @ Xx )
% 0.20/0.46 => ( cF @ S @ Xx ) ) )
% 0.20/0.46 & ! [S: a > $o,Xx: a] :
% 0.20/0.46 ( ( S @ Xx )
% 0.20/0.46 => ( cF @ ( cG @ S ) @ Xx ) )
% 0.20/0.46 & ! [S: a > $o,Xx: a] :
% 0.20/0.46 ( ( S @ Xx )
% 0.20/0.46 => ( cG @ ( cF @ S ) @ Xx ) ) )
% 0.20/0.46 => ! [S: a > $o,Xx: a] :
% 0.20/0.46 ( ( cF @ ( cG @ ( cF @ S ) ) @ Xx )
% 0.20/0.46 <=> ( cF @ S @ Xx ) ) ) ).
% 0.20/0.46
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 ------------------------
% 1.48/1.26 ---- Embedded in THF ---
% 1.48/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.26 %%% Generated on Tue Feb 24 12:47:49 EST 2026
% 1.48/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.26 %%% Logic specification used:
% 1.48/1.26 %%% thf(spec, logic, $$dhol).
% 1.48/1.26
% 1.48/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.k9T8AeD2Lh/DTF2DTF14691.p
% See solution above
% 1.48/1.26 ------------------------
% 1.48/1.27 ---- Cleaned THF ---
% 1.48/1.27 thf(a_type,type,
% 1.48/1.27 a: $tType ).
% 1.48/1.27
% 1.48/1.27 thf(cF,type,
% 1.48/1.27 cF: ( a > $o ) > a > $o ).
% 1.48/1.27
% 1.48/1.27 thf(cG,type,
% 1.48/1.27 cG: ( a > $o ) > a > $o ).
% 1.48/1.27
% 1.48/1.27 thf(cTHM67_pme,conjecture,
% 1.48/1.27 ( ( ! [S: a > $o,T: a > $o] :
% 1.48/1.27 ( ! [Xx: a] :
% 1.48/1.27 ( ( S @ Xx )
% 1.48/1.27 => ( T @ Xx ) )
% 1.48/1.27 => ! [Xx: a] :
% 1.48/1.27 ( ( cF @ T @ Xx )
% 1.48/1.27 => ( cF @ S @ Xx ) ) )
% 1.48/1.27 & ! [S: a > $o,Xx: a] :
% 1.48/1.27 ( ( S @ Xx )
% 1.48/1.27 => ( cF @ ( cG @ S ) @ Xx ) )
% 1.48/1.27 & ! [S: a > $o,Xx: a] :
% 1.48/1.27 ( ( S @ Xx )
% 1.48/1.27 => ( cG @ ( cF @ S ) @ Xx ) ) )
% 1.48/1.27 => ! [S: a > $o,Xx: a] :
% 1.48/1.27 ( ( cF @ ( cG @ ( cF @ S ) ) @ Xx )
% 1.48/1.27 <=> ( cF @ S @ Xx ) ) ) ).
% 1.48/1.27 ------------------------
% 1.48/1.28 % (15016)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_14691 for (2999ds/2Mi)
% 1.48/1.28 % (15013)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_14691 for (2999ds/4Mi)
% 1.48/1.28 % (15016)Instruction limit reached!
% 1.48/1.28 % (15016)------------------------------
% 1.48/1.28 % (15016)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.28 % (15016)Termination reason: Unknown
% 1.48/1.28 % (15016)Termination phase: Saturation
% 1.48/1.28
% 1.48/1.28 % (15016)Memory used [KB]: 895
% 1.48/1.28 % (15016)Time elapsed: 0.002 s
% 1.48/1.28 % (15016)Instructions burned: 2 (million)
% 1.48/1.28 % (15016)------------------------------
% 1.48/1.28 % (15016)------------------------------
% 1.48/1.28 % (15013)Instruction limit reached!
% 1.48/1.28 % (15013)------------------------------
% 1.48/1.28 % (15013)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.28 % (15013)Termination reason: Unknown
% 1.48/1.28 % (15013)Termination phase: Saturation
% 1.48/1.28
% 1.48/1.28 % (15013)Memory used [KB]: 5500
% 1.48/1.28 % (15013)Time elapsed: 0.003 s
% 1.48/1.28 % (15013)Instructions burned: 4 (million)
% 1.48/1.28 % (15013)------------------------------
% 1.48/1.28 % (15013)------------------------------
% 1.48/1.29 % (15012)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_14691 for (2999ds/183Mi)
% 1.48/1.29 % (15014)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_14691 for (2999ds/27Mi)
% 1.48/1.29 % (15015)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_14691 for (2999ds/2Mi)
% 1.48/1.29 % (15017)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_14691 for (2999ds/275Mi)
% 1.48/1.29 % (15018)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_14691 for (2999ds/18Mi)
% 1.48/1.29 % (15015)Instruction limit reached!
% 1.48/1.29 % (15015)------------------------------
% 1.48/1.29 % (15015)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.29 % (15015)Termination reason: Unknown
% 1.48/1.29 % (15015)Termination phase: Preprocessing 3
% 1.48/1.29
% 1.48/1.29 % (15015)Memory used [KB]: 895
% 1.48/1.29 % (15015)Time elapsed: 0.003 s
% 1.48/1.29 % (15015)Instructions burned: 2 (million)
% 1.48/1.29 % (15015)------------------------------
% 1.48/1.29 % (15015)------------------------------
% 1.48/1.29 % (15019)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_14691 for (2999ds/3Mi)
% 1.48/1.29 % (15019)Instruction limit reached!
% 1.48/1.29 % (15019)------------------------------
% 1.48/1.29 % (15019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.29 % (15019)Termination reason: Unknown
% 1.48/1.29 % (15019)Termination phase: Saturation
% 1.48/1.29
% 1.48/1.29 % (15019)Memory used [KB]: 5500
% 1.48/1.29 % (15019)Time elapsed: 0.002 s
% 1.48/1.29 % (15019)Instructions burned: 3 (million)
% 1.48/1.29 % (15019)------------------------------
% 1.48/1.29 % (15019)------------------------------
% 1.48/1.29 % (15020)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_14691 for (2999ds/37Mi)
% 1.62/1.30 % (15022)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_14691 for (2999ds/3Mi)
% 1.62/1.30 % (15018)Instruction limit reached!
% 1.62/1.30 % (15018)------------------------------
% 1.62/1.30 % (15018)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.30 % (15018)Termination reason: Unknown
% 1.62/1.30 % (15018)Termination phase: Saturation
% 1.62/1.30
% 1.62/1.30 % (15018)Memory used [KB]: 5628
% 1.62/1.30 % (15018)Time elapsed: 0.015 s
% 1.62/1.30 % (15018)Instructions burned: 18 (million)
% 1.62/1.30 % (15018)------------------------------
% 1.62/1.30 % (15018)------------------------------
% 1.62/1.30 % (15022)Instruction limit reached!
% 1.62/1.30 % (15022)------------------------------
% 1.62/1.30 % (15022)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.30 % (15022)Termination reason: Unknown
% 1.62/1.30 % (15022)Termination phase: Saturation
% 1.62/1.30
% 1.62/1.30 % (15022)Memory used [KB]: 5500
% 1.62/1.30 % (15022)Time elapsed: 0.003 s
% 1.62/1.30 % (15022)Instructions burned: 5 (million)
% 1.62/1.30 % (15022)------------------------------
% 1.62/1.30 % (15022)------------------------------
% 1.62/1.30 % (15014)First to succeed.
% 1.62/1.31 % (15020)Instruction limit reached!
% 1.62/1.31 % (15020)------------------------------
% 1.62/1.31 % (15020)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.31 % (15020)Termination reason: Unknown
% 1.62/1.31 % (15020)Termination phase: Saturation
% 1.62/1.31
% 1.62/1.31 % (15020)Memory used [KB]: 6140
% 1.62/1.31 % (15020)Time elapsed: 0.014 s
% 1.62/1.31 % (15020)Instructions burned: 39 (million)
% 1.62/1.31 % (15020)------------------------------
% 1.62/1.31 % (15020)------------------------------
% 1.62/1.31 % (15014)Refutation found. Thanks to Tanya!
% 1.62/1.31 % SZS status Theorem for DTF2THF_14691
% 1.62/1.31 % SZS output start Proof for DTF2THF_14691
% 1.62/1.31 thf(type_def_5, type, a: $tType).
% 1.62/1.31 thf(func_def_0, type, a: $tType).
% 1.62/1.31 thf(func_def_1, type, cF: (a > $o) > a > $o).
% 1.62/1.31 thf(func_def_2, type, cG: (a > $o) > a > $o).
% 1.62/1.31 thf(func_def_4, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.62/1.31 thf(func_def_7, type, sK0: a).
% 1.62/1.31 thf(func_def_8, type, sK1: a > $o).
% 1.62/1.31 thf(func_def_9, type, sK2: (a > $o) > (a > $o) > a).
% 1.62/1.31 thf(func_def_11, type, ph4: !>[X0: $tType]:(X0)).
% 1.62/1.31 thf(f148,plain,(
% 1.62/1.31 $false),
% 1.62/1.31 inference(avatar_sat_refutation,[status(thm)],[f27,f36,f42,f51,f144,f147])).
% 1.62/1.31 thf(f147,plain,(
% 1.62/1.31 ~spl3_1 | ~spl3_4),
% 1.62/1.31 inference(avatar_contradiction_clause,[status(thm)],[f146])).
% 1.62/1.31 thf(f146,plain,(
% 1.62/1.31 $false | (~spl3_1 | ~spl3_4)),
% 1.62/1.31 inference(trivial_inequality_removal,[status(thm)],[f145])).
% 1.62/1.31 thf(f145,plain,(
% 1.62/1.31 ($true = $false) | (~spl3_1 | ~spl3_4)),
% 1.62/1.31 inference(forward_demodulation,[status(thm)],[f22,f35])).
% 1.62/1.31 thf(f35,plain,(
% 1.62/1.31 ($false = (cF @ sK1 @ sK0)) | ~spl3_4),
% 1.62/1.31 inference(avatar_component_clause,[status(thm)],[f33])).
% 1.62/1.31 thf(f33,definition,(
% 1.62/1.31 spl3_4 <=> ($false = (cF @ sK1 @ sK0))),
% 1.62/1.31 introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition])).
% 1.62/1.31 thf(f22,plain,(
% 1.62/1.31 ($true = (cF @ sK1 @ sK0)) | ~spl3_1),
% 1.62/1.31 inference(avatar_component_clause,[status(thm)],[f20])).
% 1.62/1.31 thf(f20,definition,(
% 1.62/1.31 spl3_1 <=> ($true = (cF @ sK1 @ sK0))),
% 1.62/1.31 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.62/1.31 thf(f144,plain,(
% 1.62/1.31 ~spl3_2 | ~spl3_4),
% 1.62/1.31 inference(avatar_contradiction_clause,[status(thm)],[f143])).
% 1.62/1.31 thf(f143,plain,(
% 1.62/1.31 $false | (~spl3_2 | ~spl3_4)),
% 1.62/1.31 inference(trivial_inequality_removal,[status(thm)],[f142])).
% 1.62/1.31 thf(f142,plain,(
% 1.62/1.31 ($true = $false) | (~spl3_2 | ~spl3_4)),
% 1.62/1.31 inference(forward_demodulation,[status(thm)],[f124,f35])).
% 1.62/1.31 thf(f124,plain,(
% 1.62/1.31 ($true = (cF @ sK1 @ sK0)) | (~spl3_2 | ~spl3_4)),
% 1.62/1.31 inference(trivial_inequality_removal,[status(thm)],[f120])).
% 1.62/1.31 thf(f120,plain,(
% 1.62/1.31 ($true != $true) | ($true = (cF @ sK1 @ sK0)) | (~spl3_2 | ~spl3_4)),
% 1.62/1.31 inference(superposition,[status(thm)],[f113,f26])).
% 1.62/1.31 thf(f26,plain,(
% 1.62/1.31 ((cF @ (cG @ (cF @ sK1)) @ sK0) = $true) | ~spl3_2),
% 1.62/1.31 inference(avatar_component_clause,[status(thm)],[f24])).
% 1.62/1.31 thf(f24,definition,(
% 1.62/1.31 spl3_2 <=> ((cF @ (cG @ (cF @ sK1)) @ sK0) = $true)),
% 1.62/1.31 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.62/1.31 thf(f113,plain,(
% 1.62/1.31 ( ! [X0 : a] : (($true != (cF @ (cG @ (cF @ sK1)) @ X0)) | ($true = (cF @ sK1 @ X0))) ) | (~spl3_2 | ~spl3_4)),
% 1.62/1.31 inference(trivial_inequality_removal,[status(thm)],[f112])).
% 1.62/1.31 thf(f112,plain,(
% 1.62/1.31 ( ! [X0 : a] : (($true = $false) | ($true != (cF @ (cG @ (cF @ sK1)) @ X0)) | ($true = (cF @ sK1 @ X0))) ) | (~spl3_2 | ~spl3_4)),
% 1.62/1.31 inference(forward_demodulation,[status(thm)],[f111,f35])).
% 1.62/1.31 thf(f111,plain,(
% 1.62/1.31 ( ! [X0 : a] : (($true = (cF @ sK1 @ sK0)) | ($true != (cF @ (cG @ (cF @ sK1)) @ X0)) | ($true = (cF @ sK1 @ X0))) ) | ~spl3_2),
% 1.62/1.31 inference(trivial_inequality_removal,[status(thm)],[f106])).
% 1.62/1.31 thf(f106,plain,(
% 1.62/1.31 ( ! [X0 : a] : (($true != (cF @ (cG @ (cF @ sK1)) @ X0)) | ($true != $true) | ($true = (cF @ sK1 @ X0)) | ($true = (cF @ sK1 @ sK0))) ) | ~spl3_2),
% 1.62/1.31 inference(superposition,[status(thm)],[f12,f81])).
% 1.62/1.31 thf(f81,plain,(
% 1.62/1.31 ( ! [X0 : a > $o] : (($true = (cG @ (cF @ X0) @ (sK2 @ X0 @ (cG @ (cF @ sK1))))) | ($true = (cF @ X0 @ sK0))) ) | ~spl3_2),
% 1.62/1.31 inference(trivial_inequality_removal,[status(thm)],[f78])).
% 1.62/1.31 thf(f78,plain,(
% 1.62/1.31 ( ! [X0 : a > $o] : (($true = (cF @ X0 @ sK0)) | ($true != $true) | ($true = (cG @ (cF @ X0) @ (sK2 @ X0 @ (cG @ (cF @ sK1)))))) ) | ~spl3_2),
% 1.62/1.31 inference(superposition,[status(thm)],[f14,f70])).
% 1.62/1.31 thf(f70,plain,(
% 1.62/1.31 ( ! [X0 : a > $o] : (($true = (X0 @ (sK2 @ X0 @ (cG @ (cF @ sK1))))) | ($true = (cF @ X0 @ sK0))) ) | ~spl3_2),
% 1.62/1.31 inference(trivial_inequality_removal,[status(thm)],[f68])).
% 1.62/1.31 thf(f68,plain,(
% 1.62/1.31 ( ! [X0 : a > $o] : (($true = (cF @ X0 @ sK0)) | ($true = (X0 @ (sK2 @ X0 @ (cG @ (cF @ sK1))))) | ($true != $true)) ) | ~spl3_2),
% 1.62/1.31 inference(superposition,[status(thm)],[f13,f26])).
% 1.62/1.31 thf(f13,plain,(
% 1.62/1.31 ( ! [X6 : a > $o,X9 : a,X7 : a > $o] : (($true != (cF @ X6 @ X9)) | ((cF @ X7 @ X9) = $true) | ((X7 @ (sK2 @ X7 @ X6)) = $true)) )),
% 1.62/1.31 inference(cnf_transformation,[status(thm)],[f11])).
% 1.62/1.31 thf(f11,plain,(
% 1.62/1.31 ((cF @ (cG @ (cF @ sK1)) @ sK0) != (cF @ sK1 @ sK0)) & ! [X2 : a,X3 : a > $o] : (($true != (X3 @ X2)) | ($true = (cF @ (cG @ X3) @ X2))) & ! [X4 : a,X5 : a > $o] : (($true != (X5 @ X4)) | ($true = (cG @ (cF @ X5) @ X4))) & ! [X6 : a > $o,X7 : a > $o] : ((((X7 @ (sK2 @ X7 @ X6)) = $true) & ($true != (X6 @ (sK2 @ X7 @ X6)))) | ! [X9 : a] : (($true != (cF @ X6 @ X9)) | ((cF @ X7 @ X9) = $true)))),
% 1.62/1.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f10,f9])).
% 1.62/1.31 thf(f9,plain,(
% 1.62/1.31 ? [X0 : a,X1 : a > $o] : ((cF @ (cG @ (cF @ X1)) @ X0) != (cF @ X1 @ X0)) => ((cF @ (cG @ (cF @ sK1)) @ sK0) != (cF @ sK1 @ sK0))),
% 1.62/1.31 introduced(definition,[],[choice_axiom])).
% 1.62/1.31 thf(f10,plain,(
% 1.62/1.31 ! [X6 : a > $o,X7 : a > $o] : (? [X8 : a] : (((X7 @ X8) = $true) & ($true != (X6 @ X8))) => (((X7 @ (sK2 @ X7 @ X6)) = $true) & ($true != (X6 @ (sK2 @ X7 @ X6)))))),
% 1.62/1.31 introduced(definition,[],[choice_axiom])).
% 1.62/1.31 thf(f8,plain,(
% 1.62/1.31 ? [X0 : a,X1 : a > $o] : ((cF @ (cG @ (cF @ X1)) @ X0) != (cF @ X1 @ X0)) & ! [X2 : a,X3 : a > $o] : (($true != (X3 @ X2)) | ($true = (cF @ (cG @ X3) @ X2))) & ! [X4 : a,X5 : a > $o] : (($true != (X5 @ X4)) | ($true = (cG @ (cF @ X5) @ X4))) & ! [X6 : a > $o,X7 : a > $o] : (? [X8 : a] : (((X7 @ X8) = $true) & ($true != (X6 @ X8))) | ! [X9 : a] : (($true != (cF @ X6 @ X9)) | ((cF @ X7 @ X9) = $true)))),
% 1.62/1.31 inference(rectify,[status(thm)],[f7])).
% 1.62/1.31 thf(f7,plain,(
% 1.62/1.31 ? [X8 : a,X9 : a > $o] : ((cF @ (cG @ (cF @ X9)) @ X8) != (cF @ X9 @ X8)) & ! [X1 : a,X0 : a > $o] : (($true != (X0 @ X1)) | ($true = (cF @ (cG @ X0) @ X1))) & ! [X7 : a,X6 : a > $o] : (($true != (X6 @ X7)) | ($true = (cG @ (cF @ X6) @ X7))) & ! [X2 : a > $o,X3 : a > $o] : (? [X4 : a] : (($true = (X3 @ X4)) & ($true != (X2 @ X4))) | ! [X5 : a] : (($true != (cF @ X2 @ X5)) | ($true = (cF @ X3 @ X5))))),
% 1.62/1.31 inference(flattening,[status(thm)],[f6])).
% 1.62/1.31 thf(f6,plain,(
% 1.62/1.31 ? [X8 : a,X9 : a > $o] : ((cF @ (cG @ (cF @ X9)) @ X8) != (cF @ X9 @ X8)) & (! [X7 : a,X6 : a > $o] : (($true != (X6 @ X7)) | ($true = (cG @ (cF @ X6) @ X7))) & ! [X1 : a,X0 : a > $o] : (($true != (X0 @ X1)) | ($true = (cF @ (cG @ X0) @ X1))) & ! [X2 : a > $o,X3 : a > $o] : (? [X4 : a] : (($true = (X3 @ X4)) & ($true != (X2 @ X4))) | ! [X5 : a] : (($true != (cF @ X2 @ X5)) | ($true = (cF @ X3 @ X5)))))),
% 1.62/1.31 inference(ennf_transformation,[status(thm)],[f5])).
% 1.62/1.31 thf(f5,plain,(
% 1.62/1.31 ~((! [X6 : a > $o,X7 : a] : (($true = (X6 @ X7)) => ($true = (cG @ (cF @ X6) @ X7))) & ! [X1 : a,X0 : a > $o] : (($true = (X0 @ X1)) => ($true = (cF @ (cG @ X0) @ X1))) & ! [X3 : a > $o,X2 : a > $o] : (! [X4 : a] : (($true = (X3 @ X4)) => ($true = (X2 @ X4))) => ! [X5 : a] : (($true = (cF @ X2 @ X5)) => ($true = (cF @ X3 @ X5))))) => ! [X8 : a,X9 : a > $o] : ((cF @ (cG @ (cF @ X9)) @ X8) = (cF @ X9 @ X8)))),
% 1.62/1.31 inference(fool_elimination,[status(thm)],[f4])).
% 1.62/1.31 thf(f4,plain,(
% 1.62/1.31 ~((! [X0 : a > $o,X1 : a] : ((X0 @ X1) => (cF @ (cG @ X0) @ X1)) & ! [X2 : a > $o,X3 : a > $o] : (! [X4 : a] : ((X3 @ X4) => (X2 @ X4)) => ! [X5 : a] : ((cF @ X2 @ X5) => (cF @ X3 @ X5))) & ! [X6 : a > $o,X7 : a] : ((X6 @ X7) => (cG @ (cF @ X6) @ X7))) => ! [X8 : a,X9 : a > $o] : ((cF @ X9 @ X8) <=> (cF @ (cG @ (cF @ X9)) @ X8)))),
% 1.62/1.31 inference(rectify,[status(thm)],[f2])).
% 1.62/1.31 thf(f2,negated_conjecture,(
% 1.62/1.31 ~((! [X0 : a > $o,X2 : a] : ((X0 @ X2) => (cF @ (cG @ X0) @ X2)) & ! [X1 : a > $o,X0 : a > $o] : (! [X2 : a] : ((X0 @ X2) => (X1 @ X2)) => ! [X2 : a] : ((cF @ X1 @ X2) => (cF @ X0 @ X2))) & ! [X0 : a > $o,X2 : a] : ((X0 @ X2) => (cG @ (cF @ X0) @ X2))) => ! [X2 : a,X0 : a > $o] : ((cF @ X0 @ X2) <=> (cF @ (cG @ (cF @ X0)) @ X2)))),
% 1.62/1.31 inference(negated_conjecture,[status(cth)],[f1])).
% 1.62/1.31 thf(f1,conjecture,(
% 1.62/1.31 (! [X0 : a > $o,X2 : a] : ((X0 @ X2) => (cF @ (cG @ X0) @ X2)) & ! [X1 : a > $o,X0 : a > $o] : (! [X2 : a] : ((X0 @ X2) => (X1 @ X2)) => ! [X2 : a] : ((cF @ X1 @ X2) => (cF @ X0 @ X2))) & ! [X0 : a > $o,X2 : a] : ((X0 @ X2) => (cG @ (cF @ X0) @ X2))) => ! [X2 : a,X0 : a > $o] : ((cF @ X0 @ X2) <=> (cF @ (cG @ (cF @ X0)) @ X2))),
% 1.62/1.31 file('/export/starexec/sandbox/tmp/tmp.k9T8AeD2Lh/DTF2THF_14691.p',cTHM67_pme)).
% 1.62/1.31 thf(f14,plain,(
% 1.62/1.31 ( ! [X4 : a,X5 : a > $o] : (($true != (X5 @ X4)) | ($true = (cG @ (cF @ X5) @ X4))) )),
% 1.62/1.31 inference(cnf_transformation,[status(thm)],[f11])).
% 1.62/1.31 thf(f12,plain,(
% 1.62/1.31 ( ! [X6 : a > $o,X9 : a,X7 : a > $o] : (($true != (X6 @ (sK2 @ X7 @ X6))) | ($true != (cF @ X6 @ X9)) | ((cF @ X7 @ X9) = $true)) )),
% 1.62/1.31 inference(cnf_transformation,[status(thm)],[f11])).
% 1.62/1.31 thf(f51,plain,(
% 1.62/1.31 ~spl3_1 | ~spl3_3),
% 1.62/1.31 inference(avatar_contradiction_clause,[status(thm)],[f50])).
% 1.62/1.31 thf(f50,plain,(
% 1.62/1.31 $false | (~spl3_1 | ~spl3_3)),
% 1.62/1.31 inference(trivial_inequality_removal,[status(thm)],[f49])).
% 1.62/1.31 thf(f49,plain,(
% 1.62/1.31 ($true = $false) | (~spl3_1 | ~spl3_3)),
% 1.62/1.31 inference(forward_demodulation,[status(thm)],[f48,f31])).
% 1.62/1.31 thf(f31,plain,(
% 1.62/1.31 ((cF @ (cG @ (cF @ sK1)) @ sK0) = $false) | ~spl3_3),
% 1.62/1.31 inference(avatar_component_clause,[status(thm)],[f29])).
% 1.62/1.31 thf(f29,definition,(
% 1.62/1.31 spl3_3 <=> ((cF @ (cG @ (cF @ sK1)) @ sK0) = $false)),
% 1.62/1.31 introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition])).
% 1.62/1.31 thf(f48,plain,(
% 1.62/1.31 ((cF @ (cG @ (cF @ sK1)) @ sK0) = $true) | ~spl3_1),
% 1.62/1.31 inference(trivial_inequality_removal,[status(thm)],[f45])).
% 1.62/1.31 thf(f45,plain,(
% 1.62/1.31 ((cF @ (cG @ (cF @ sK1)) @ sK0) = $true) | ($true != $true) | ~spl3_1),
% 1.62/1.31 inference(superposition,[status(thm)],[f15,f22])).
% 1.62/1.31 thf(f15,plain,(
% 1.62/1.31 ( ! [X2 : a,X3 : a > $o] : (($true != (X3 @ X2)) | ($true = (cF @ (cG @ X3) @ X2))) )),
% 1.62/1.31 inference(cnf_transformation,[status(thm)],[f11])).
% 1.62/1.31 thf(f42,plain,(
% 1.62/1.31 ~spl3_2 | ~spl3_3),
% 1.62/1.31 inference(avatar_contradiction_clause,[status(thm)],[f41])).
% 1.62/1.31 thf(f41,plain,(
% 1.62/1.31 $false | (~spl3_2 | ~spl3_3)),
% 1.62/1.31 inference(trivial_inequality_removal,[status(thm)],[f39])).
% 1.62/1.31 thf(f39,plain,(
% 1.62/1.31 ($true = $false) | (~spl3_2 | ~spl3_3)),
% 1.62/1.31 inference(backward_demodulation,[status(thm)],[f26,f31])).
% 1.62/1.31 thf(f36,plain,(
% 1.62/1.31 spl3_3 | spl3_4),
% 1.62/1.31 inference(avatar_split_clause,[status(thm)],[f18,f33,f29])).
% 1.62/1.31 thf(f18,plain,(
% 1.62/1.31 ($false = (cF @ sK1 @ sK0)) | ((cF @ (cG @ (cF @ sK1)) @ sK0) = $false)),
% 1.62/1.31 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 1.62/1.31 thf(f16,plain,(
% 1.62/1.31 ((cF @ (cG @ (cF @ sK1)) @ sK0) != (cF @ sK1 @ sK0))),
% 1.62/1.31 inference(cnf_transformation,[status(thm)],[f11])).
% 1.62/1.31 thf(f27,plain,(
% 1.62/1.31 spl3_1 | spl3_2),
% 1.62/1.31 inference(avatar_split_clause,[status(thm)],[f17,f24,f20])).
% 1.62/1.31 thf(f17,plain,(
% 1.62/1.31 ($true = (cF @ sK1 @ sK0)) | ((cF @ (cG @ (cF @ sK1)) @ sK0) = $true)),
% 1.62/1.31 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 1.62/1.31 % SZS output end Proof for DTF2THF_14691
% 1.62/1.31 % (15014)------------------------------
% 1.62/1.31 % (15014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.31 % (15014)Termination reason: Refutation
% 1.62/1.31
% 1.62/1.31 % (15014)Memory used [KB]: 5628
% 1.62/1.31 % (15014)Time elapsed: 0.019 s
% 1.62/1.31 % (15014)Instructions burned: 22 (million)
% 1.62/1.31 % (15014)------------------------------
% 1.62/1.31 % (15014)------------------------------
% 1.62/1.31 % (15011)Success in time 0.032 s
%------------------------------------------------------------------------------