%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV398^5 : 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 : n002.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 1.79s 1.57s
% Output : Refutation 1.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 7
% Syntax : Number of formulae : 47 ( 2 unt; 0 typ; 4 def)
% Number of atoms : 455 ( 104 equ; 0 cnn)
% Maximal formula atoms : 10 ( 9 avg)
% Number of connectives : 527 ( 75 ~; 73 |; 26 &; 320 @)
% ( 7 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 44 ( 44 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 92 ( 0 ^; 80 !; 12 ?; 92 :)
% 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 > $o ).
thf(func_def_8,type,
sK1: a ).
thf(func_def_9,type,
sK2: ( a > $o ) > ( a > $o ) > a ).
thf(func_def_11,type,
ph4:
!>[X0: $tType] : X0 ).
thf(f161,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f27,f36,f43,f55,f146]) ).
thf(f146,plain,
( ~ spl3_1
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f145]) ).
thf(f145,plain,
( $false
| ~ spl3_1
| ~ spl3_4 ),
inference(trivial_inequality_removal,[status(thm)],[f144]) ).
thf(f144,plain,
( ( $false = $true )
| ~ spl3_1
| ~ spl3_4 ),
inference(forward_demodulation,[status(thm)],[f142,f35]) ).
thf(f35,plain,
( ( $false
= ( cF @ sK0 @ sK1 ) )
| ~ spl3_4 ),
inference(avatar_component_clause,[status(thm)],[f33]) ).
thf(f33,definition,
( spl3_4
<=> ( $false
= ( cF @ sK0 @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition]) ).
thf(f142,plain,
( ( ( cF @ sK0 @ sK1 )
= $true )
| ~ spl3_1
| ~ spl3_4 ),
inference(trivial_inequality_removal,[status(thm)],[f134]) ).
thf(f134,plain,
( ( $true != $true )
| ( ( cF @ sK0 @ sK1 )
= $true )
| ~ spl3_1
| ~ spl3_4 ),
inference(superposition,[status(thm)],[f127,f22]) ).
thf(f22,plain,
( ( ( cF @ ( cG @ ( cF @ sK0 ) ) @ sK1 )
= $true )
| ~ spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f20]) ).
thf(f20,definition,
( spl3_1
<=> ( ( cF @ ( cG @ ( cF @ sK0 ) ) @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f127,plain,
( ! [X0: a] :
( ( ( cF @ ( cG @ ( cF @ sK0 ) ) @ X0 )
!= $true )
| ( ( cF @ sK0 @ X0 )
= $true ) )
| ~ spl3_1
| ~ spl3_4 ),
inference(trivial_inequality_removal,[status(thm)],[f126]) ).
thf(f126,plain,
( ! [X0: a] :
( ( $false = $true )
| ( ( cF @ sK0 @ X0 )
= $true )
| ( ( cF @ ( cG @ ( cF @ sK0 ) ) @ X0 )
!= $true ) )
| ~ spl3_1
| ~ spl3_4 ),
inference(forward_demodulation,[status(thm)],[f124,f35]) ).
thf(f124,plain,
( ! [X0: a] :
( ( ( cF @ sK0 @ X0 )
= $true )
| ( ( cF @ ( cG @ ( cF @ sK0 ) ) @ X0 )
!= $true )
| ( ( cF @ sK0 @ sK1 )
= $true ) )
| ~ spl3_1 ),
inference(trivial_inequality_removal,[status(thm)],[f120]) ).
thf(f120,plain,
( ! [X0: a] :
( ( ( cF @ sK0 @ sK1 )
= $true )
| ( ( cF @ sK0 @ X0 )
= $true )
| ( ( cF @ ( cG @ ( cF @ sK0 ) ) @ X0 )
!= $true )
| ( $true != $true ) )
| ~ spl3_1 ),
inference(superposition,[status(thm)],[f12,f92]) ).
thf(f92,plain,
( ! [X0: a > $o] :
( ( ( cG @ ( cF @ X0 ) @ ( sK2 @ ( cG @ ( cF @ sK0 ) ) @ X0 ) )
= $true )
| ( ( cF @ X0 @ sK1 )
= $true ) )
| ~ spl3_1 ),
inference(trivial_inequality_removal,[status(thm)],[f88]) ).
thf(f88,plain,
( ! [X0: a > $o] :
( ( $true != $true )
| ( ( cF @ X0 @ sK1 )
= $true )
| ( ( cG @ ( cF @ X0 ) @ ( sK2 @ ( cG @ ( cF @ sK0 ) ) @ X0 ) )
= $true ) )
| ~ spl3_1 ),
inference(superposition,[status(thm)],[f15,f49]) ).
thf(f49,plain,
( ! [X0: a > $o] :
( ( ( X0 @ ( sK2 @ ( cG @ ( cF @ sK0 ) ) @ X0 ) )
= $true )
| ( ( cF @ X0 @ sK1 )
= $true ) )
| ~ spl3_1 ),
inference(trivial_inequality_removal,[status(thm)],[f44]) ).
thf(f44,plain,
( ! [X0: a > $o] :
( ( ( cF @ X0 @ sK1 )
= $true )
| ( ( X0 @ ( sK2 @ ( cG @ ( cF @ sK0 ) ) @ X0 ) )
= $true )
| ( $true != $true ) )
| ~ spl3_1 ),
inference(superposition,[status(thm)],[f13,f22]) ).
thf(f13,plain,
! [X8: a,X6: a > $o,X5: a > $o] :
( ( $true
!= ( cF @ X6 @ X8 ) )
| ( ( cF @ X5 @ X8 )
= $true )
| ( ( X5 @ ( sK2 @ X6 @ X5 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ! [X0: a > $o] :
( ! [X1: a] :
( ( $true
!= ( X0 @ X1 ) )
| ( ( cF @ ( cG @ X0 ) @ X1 )
= $true ) )
& ! [X2: a] :
( ( ( X0 @ X2 )
!= $true )
| ( ( cG @ ( cF @ X0 ) @ X2 )
= $true ) ) )
& ( ( cF @ ( cG @ ( cF @ sK0 ) ) @ sK1 )
!= ( cF @ sK0 @ sK1 ) )
& ! [X5: a > $o,X6: a > $o] :
( ( ( ( X5 @ ( sK2 @ X6 @ X5 ) )
= $true )
& ( ( X6 @ ( sK2 @ X6 @ X5 ) )
!= $true ) )
| ! [X8: a] :
( ( $true
!= ( cF @ X6 @ X8 ) )
| ( ( cF @ X5 @ X8 )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f10,f9]) ).
thf(f9,plain,
( ? [X3: a > $o,X4: a] :
( ( cF @ ( cG @ ( cF @ X3 ) ) @ X4 )
!= ( cF @ X3 @ X4 ) )
=> ( ( cF @ ( cG @ ( cF @ sK0 ) ) @ sK1 )
!= ( cF @ sK0 @ sK1 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
! [X5: a > $o,X6: a > $o] :
( ? [X7: a] :
( ( $true
= ( X5 @ X7 ) )
& ( ( X6 @ X7 )
!= $true ) )
=> ( ( ( X5 @ ( sK2 @ X6 @ X5 ) )
= $true )
& ( ( X6 @ ( sK2 @ X6 @ X5 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ! [X0: a > $o] :
( ! [X1: a] :
( ( $true
!= ( X0 @ X1 ) )
| ( ( cF @ ( cG @ X0 ) @ X1 )
= $true ) )
& ! [X2: a] :
( ( ( X0 @ X2 )
!= $true )
| ( ( cG @ ( cF @ X0 ) @ X2 )
= $true ) ) )
& ? [X3: a > $o,X4: a] :
( ( cF @ ( cG @ ( cF @ X3 ) ) @ X4 )
!= ( cF @ X3 @ X4 ) )
& ! [X5: a > $o,X6: a > $o] :
( ? [X7: a] :
( ( $true
= ( X5 @ X7 ) )
& ( ( X6 @ X7 )
!= $true ) )
| ! [X8: a] :
( ( $true
!= ( cF @ X6 @ X8 ) )
| ( ( cF @ X5 @ X8 )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X0: a > $o] :
( ! [X1: a] :
( ( $true
!= ( X0 @ X1 ) )
| ( ( cF @ ( cG @ X0 ) @ X1 )
= $true ) )
& ! [X2: a] :
( ( ( X0 @ X2 )
!= $true )
| ( ( cG @ ( cF @ X0 ) @ X2 )
= $true ) ) )
& ? [X7: a > $o,X8: a] :
( ( cF @ X7 @ X8 )
!= ( cF @ ( cG @ ( cF @ X7 ) ) @ X8 ) )
& ! [X4: a > $o,X3: a > $o] :
( ? [X5: a] :
( ( ( X4 @ X5 )
= $true )
& ( ( X3 @ X5 )
!= $true ) )
| ! [X6: a] :
( ( ( cF @ X3 @ X6 )
!= $true )
| ( ( cF @ X4 @ X6 )
= $true ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ? [X7: a > $o,X8: a] :
( ( cF @ X7 @ X8 )
!= ( cF @ ( cG @ ( cF @ X7 ) ) @ X8 ) )
& ! [X4: a > $o,X3: a > $o] :
( ? [X5: a] :
( ( ( X4 @ X5 )
= $true )
& ( ( X3 @ X5 )
!= $true ) )
| ! [X6: a] :
( ( ( cF @ X3 @ X6 )
!= $true )
| ( ( cF @ X4 @ X6 )
= $true ) ) )
& ! [X0: a > $o] :
( ! [X1: a] :
( ( $true
!= ( X0 @ X1 ) )
| ( ( cF @ ( cG @ X0 ) @ X1 )
= $true ) )
& ! [X2: a] :
( ( ( X0 @ X2 )
!= $true )
| ( ( cG @ ( cF @ X0 ) @ X2 )
= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X4: a > $o,X3: a > $o] :
( ! [X5: a] :
( ( ( X4 @ X5 )
= $true )
=> ( ( X3 @ X5 )
= $true ) )
=> ! [X6: a] :
( ( ( cF @ X3 @ X6 )
= $true )
=> ( ( cF @ X4 @ X6 )
= $true ) ) )
& ! [X0: a > $o] :
( ! [X1: a] :
( ( $true
= ( X0 @ X1 ) )
=> ( ( cF @ ( cG @ X0 ) @ X1 )
= $true ) )
& ! [X2: a] :
( ( ( X0 @ X2 )
= $true )
=> ( ( cG @ ( cF @ X0 ) @ X2 )
= $true ) ) ) )
=> ! [X7: a > $o,X8: a] :
( ( cF @ X7 @ X8 )
= ( cF @ ( cG @ ( cF @ X7 ) ) @ X8 ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: a > $o] :
( ! [X1: a] :
( ( X0 @ X1 )
=> ( cF @ ( cG @ X0 ) @ X1 ) )
& ! [X2: a] :
( ( X0 @ X2 )
=> ( cG @ ( cF @ X0 ) @ X2 ) ) )
& ! [X3: a > $o,X4: a > $o] :
( ! [X5: a] :
( ( X4 @ X5 )
=> ( X3 @ X5 ) )
=> ! [X6: a] :
( ( cF @ X3 @ X6 )
=> ( cF @ X4 @ X6 ) ) ) )
=> ! [X7: a > $o,X8: a] :
( ( cF @ X7 @ X8 )
<=> ( cF @ ( cG @ ( cF @ X7 ) ) @ X8 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X0: a > $o] :
( ! [X2: a] :
( ( X0 @ X2 )
=> ( cF @ ( cG @ X0 ) @ X2 ) )
& ! [X2: a] :
( ( X0 @ X2 )
=> ( cG @ ( cF @ 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] :
( ( 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 ) )
& ! [X2: a] :
( ( X0 @ X2 )
=> ( cG @ ( cF @ 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] :
( ( cF @ X0 @ X2 )
<=> ( cF @ ( cG @ ( cF @ X0 ) ) @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.1GhvNZ3Iez/DTF2THF_22939.p',cTHM67A_pme) ).
thf(f15,plain,
! [X2: a,X0: a > $o] :
( ( ( X0 @ X2 )
!= $true )
| ( ( cG @ ( cF @ X0 ) @ X2 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f12,plain,
! [X8: a,X6: a > $o,X5: a > $o] :
( ( ( X6 @ ( sK2 @ X6 @ X5 ) )
!= $true )
| ( ( cF @ X5 @ X8 )
= $true )
| ( $true
!= ( cF @ X6 @ X8 ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f55,plain,
( ~ spl3_1
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f54]) ).
thf(f54,plain,
( $false
| ~ spl3_1
| ~ spl3_3 ),
inference(trivial_inequality_removal,[status(thm)],[f50]) ).
thf(f50,plain,
( ( $false = $true )
| ~ spl3_1
| ~ spl3_3 ),
inference(backward_demodulation,[status(thm)],[f22,f31]) ).
thf(f31,plain,
( ( $false
= ( cF @ ( cG @ ( cF @ sK0 ) ) @ sK1 ) )
| ~ spl3_3 ),
inference(avatar_component_clause,[status(thm)],[f29]) ).
thf(f29,definition,
( spl3_3
<=> ( $false
= ( cF @ ( cG @ ( cF @ sK0 ) ) @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition]) ).
thf(f43,plain,
( spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f42,f24,f20]) ).
thf(f24,definition,
( spl3_2
<=> ( ( cF @ sK0 @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f42,plain,
( ( ( cF @ ( cG @ ( cF @ sK0 ) ) @ sK1 )
= $true )
| ~ spl3_2 ),
inference(trivial_inequality_removal,[status(thm)],[f41]) ).
thf(f41,plain,
( ( ( cF @ ( cG @ ( cF @ sK0 ) ) @ sK1 )
= $true )
| ( $true != $true )
| ~ spl3_2 ),
inference(superposition,[status(thm)],[f16,f26]) ).
thf(f26,plain,
( ( ( cF @ sK0 @ sK1 )
= $true )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f24]) ).
thf(f16,plain,
! [X0: a > $o,X1: a] :
( ( $true
!= ( X0 @ X1 ) )
| ( ( cF @ ( cG @ X0 ) @ X1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f36,plain,
( spl3_3
| spl3_4 ),
inference(avatar_split_clause,[status(thm)],[f18,f33,f29]) ).
thf(f18,plain,
( ( $false
= ( cF @ ( cG @ ( cF @ sK0 ) ) @ sK1 ) )
| ( $false
= ( cF @ sK0 @ sK1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
( ( cF @ ( cG @ ( cF @ sK0 ) ) @ sK1 )
!= ( cF @ sK0 @ sK1 ) ),
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,
( ( ( cF @ sK0 @ sK1 )
= $true )
| ( ( cF @ ( cG @ ( cF @ sK0 ) ) @ sK1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV398^5 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/0.34 % Computer : n002.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Feb 24 12:46:18 EST 2026
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.48 ---- Original DTF file ---
% 0.19/0.49 thf(spec,logic,$$dhol).
% 0.19/0.49 %------------------------------------------------------------------------------
% 0.19/0.49 % File : SEV398^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.49 % Domain : Set Theory
% 0.19/0.49 % Problem : TPS problem THM67A
% 0.19/0.49 % Version : Especial.
% 0.19/0.49 % English :
% 0.19/0.49
% 0.19/0.49 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.49 % Source : [Bro09]
% 0.19/0.49 % Names : tps_0437 [Bro09]
% 0.19/0.49 % : THM67A [TPS]
% 0.19/0.49
% 0.19/0.49 % Status : Theorem
% 0.19/0.49 % 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
% 0.19/0.49 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.19/0.49 % Number of atoms : 10 ( 0 equ; 0 cnn)
% 0.19/0.49 % Maximal formula atoms : 10 ( 10 avg)
% 0.19/0.49 % Number of connectives : 29 ( 0 ~; 0 |; 2 &; 20 @)
% 0.19/0.49 % ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% 0.19/0.49 % Maximal formula depth : 10 ( 10 avg)
% 0.19/0.49 % Number of types : 2 ( 1 usr)
% 0.19/0.49 % Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% 0.19/0.49 % Number of symbols : 2 ( 2 usr; 0 con; 2-2 aty)
% 0.19/0.49 % Number of variables : 9 ( 0 ^; 9 !; 0 ?; 9 :)
% 0.19/0.49 % SPC : TH0_THM_NEQ_NAR
% 0.19/0.49
% 0.19/0.49 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.49 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.49 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.49 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.49 % : Polymorphic definitions expanded.
% 0.19/0.49 %------------------------------------------------------------------------------
% 0.19/0.49 thf(a_type,type,
% 0.19/0.49 a: $tType ).
% 0.19/0.49
% 0.19/0.49 thf(cF,type,
% 0.19/0.49 cF: ( a > $o ) > a > $o ).
% 0.19/0.49
% 0.19/0.49 thf(cG,type,
% 0.19/0.49 cG: ( a > $o ) > a > $o ).
% 0.19/0.49
% 0.19/0.49 thf(cTHM67A_pme,conjecture,
% 0.19/0.49 ( ( ! [S: a > $o,T: a > $o] :
% 0.19/0.49 ( ! [Xx: a] :
% 0.19/0.49 ( ( S @ Xx )
% 0.19/0.49 => ( T @ Xx ) )
% 0.19/0.49 => ! [Xx: a] :
% 0.19/0.49 ( ( cF @ T @ Xx )
% 0.19/0.49 => ( cF @ S @ Xx ) ) )
% 0.19/0.49 & ! [S: a > $o] :
% 0.19/0.49 ( ! [Xx: a] :
% 0.19/0.49 ( ( S @ Xx )
% 0.19/0.49 => ( cF @ ( cG @ S ) @ Xx ) )
% 0.19/0.49 & ! [Xx: a] :
% 0.19/0.49 ( ( S @ Xx )
% 0.19/0.49 => ( cG @ ( cF @ S ) @ Xx ) ) ) )
% 0.19/0.49 => ! [S: a > $o,Xx: a] :
% 0.19/0.49 ( ( cF @ ( cG @ ( cF @ S ) ) @ Xx )
% 0.19/0.49 <=> ( cF @ S @ Xx ) ) ) ).
% 0.19/0.49
% 0.19/0.49 %------------------------------------------------------------------------------
% 0.19/0.49 ------------------------
% 1.79/1.52 ---- Embedded in THF ---
% 1.79/1.52 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.79/1.52 %%% Generated on Tue Feb 24 12:46:19 EST 2026
% 1.79/1.52 %%% using '$$dhol' embedding, version 1.3.0.
% 1.79/1.52 %%% Logic specification used:
% 1.79/1.52 %%% thf(spec, logic, $$dhol).
% 1.79/1.52
% 1.79/1.52 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.1GhvNZ3Iez/DTF2DTF22939.p
% See solution above
% 1.79/1.52 ------------------------
% 1.79/1.53 ---- Cleaned THF ---
% 1.79/1.53 thf(a_type,type,
% 1.79/1.53 a: $tType ).
% 1.79/1.53
% 1.79/1.53 thf(cF,type,
% 1.79/1.53 cF: ( a > $o ) > a > $o ).
% 1.79/1.53
% 1.79/1.53 thf(cG,type,
% 1.79/1.53 cG: ( a > $o ) > a > $o ).
% 1.79/1.53
% 1.79/1.53 thf(cTHM67A_pme,conjecture,
% 1.79/1.53 ( ( ! [S: a > $o,T: a > $o] :
% 1.79/1.53 ( ! [Xx: a] :
% 1.79/1.53 ( ( S @ Xx )
% 1.79/1.53 => ( T @ Xx ) )
% 1.79/1.53 => ! [Xx: a] :
% 1.79/1.53 ( ( cF @ T @ Xx )
% 1.79/1.53 => ( cF @ S @ Xx ) ) )
% 1.79/1.53 & ! [S: a > $o] :
% 1.79/1.53 ( ! [Xx: a] :
% 1.79/1.53 ( ( S @ Xx )
% 1.79/1.53 => ( cF @ ( cG @ S ) @ Xx ) )
% 1.79/1.53 & ! [Xx: a] :
% 1.79/1.53 ( ( S @ Xx )
% 1.79/1.53 => ( cG @ ( cF @ S ) @ Xx ) ) ) )
% 1.79/1.53 => ! [S: a > $o,Xx: a] :
% 1.79/1.53 ( ( cF @ ( cG @ ( cF @ S ) ) @ Xx )
% 1.79/1.53 <=> ( cF @ S @ Xx ) ) ) ).
% 1.79/1.53 ------------------------
% 1.79/1.55 % (23055)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_22939 for (3000ds/2Mi)
% 1.79/1.55 % (23052)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_22939 for (3000ds/4Mi)
% 1.79/1.55 % (23057)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_22939 for (3000ds/18Mi)
% 1.79/1.55 % (23051)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_22939 for (3000ds/183Mi)
% 1.79/1.55 % (23053)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_22939 for (3000ds/27Mi)
% 1.79/1.55 % (23056)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_22939 for (3000ds/275Mi)
% 1.79/1.55 % (23054)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_22939 for (3000ds/2Mi)
% 1.79/1.56 % (23055)Instruction limit reached!
% 1.79/1.56 % (23055)------------------------------
% 1.79/1.56 % (23055)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.56 % (23055)Termination reason: Unknown
% 1.79/1.56 % (23055)Termination phase: Property scanning
% 1.79/1.56
% 1.79/1.56 % (23055)Memory used [KB]: 895
% 1.79/1.56 % (23055)Time elapsed: 0.003 s
% 1.79/1.56 % (23055)Instructions burned: 2 (million)
% 1.79/1.56 % (23055)------------------------------
% 1.79/1.56 % (23055)------------------------------
% 1.79/1.56 % (23054)Instruction limit reached!
% 1.79/1.56 % (23054)------------------------------
% 1.79/1.56 % (23054)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.56 % (23054)Termination reason: Unknown
% 1.79/1.56 % (23054)Termination phase: Saturation
% 1.79/1.56
% 1.79/1.56 % (23054)Memory used [KB]: 5500
% 1.79/1.56 % (23054)Time elapsed: 0.003 s
% 1.79/1.56 % (23054)Instructions burned: 2 (million)
% 1.79/1.56 % (23054)------------------------------
% 1.79/1.56 % (23054)------------------------------
% 1.79/1.56 % (23052)Instruction limit reached!
% 1.79/1.56 % (23052)------------------------------
% 1.79/1.56 % (23052)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.56 % (23052)Termination reason: Unknown
% 1.79/1.56 % (23052)Termination phase: Saturation
% 1.79/1.56
% 1.79/1.56 % (23052)Memory used [KB]: 5500
% 1.79/1.56 % (23052)Time elapsed: 0.004 s
% 1.79/1.56 % (23052)Instructions burned: 4 (million)
% 1.79/1.56 % (23052)------------------------------
% 1.79/1.56 % (23052)------------------------------
% 1.79/1.57 % (23057)Instruction limit reached!
% 1.79/1.57 % (23057)------------------------------
% 1.79/1.57 % (23057)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.57 % (23057)Termination reason: Unknown
% 1.79/1.57 % (23057)Termination phase: Saturation
% 1.79/1.57
% 1.79/1.57 % (23057)Memory used [KB]: 5628
% 1.79/1.57 % (23057)Time elapsed: 0.013 s
% 1.79/1.57 % (23057)Instructions burned: 19 (million)
% 1.79/1.57 % (23057)------------------------------
% 1.79/1.57 % (23057)------------------------------
% 1.79/1.57 % (23053)First to succeed.
% 1.79/1.57 % (23053)Refutation found. Thanks to Tanya!
% 1.79/1.57 % SZS status Theorem for DTF2THF_22939
% 1.79/1.57 % SZS output start Proof for DTF2THF_22939
% 1.79/1.57 thf(type_def_5, type, a: $tType).
% 1.79/1.57 thf(func_def_0, type, a: $tType).
% 1.79/1.57 thf(func_def_1, type, cF: (a > $o) > a > $o).
% 1.79/1.57 thf(func_def_2, type, cG: (a > $o) > a > $o).
% 1.79/1.57 thf(func_def_4, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.79/1.57 thf(func_def_7, type, sK0: a > $o).
% 1.79/1.57 thf(func_def_8, type, sK1: a).
% 1.79/1.57 thf(func_def_9, type, sK2: (a > $o) > (a > $o) > a).
% 1.79/1.57 thf(func_def_11, type, ph4: !>[X0: $tType]:(X0)).
% 1.79/1.57 thf(f161,plain,(
% 1.79/1.57 $false),
% 1.79/1.57 inference(avatar_sat_refutation,[status(thm)],[f27,f36,f43,f55,f146])).
% 1.79/1.57 thf(f146,plain,(
% 1.79/1.57 ~spl3_1 | ~spl3_4),
% 1.79/1.57 inference(avatar_contradiction_clause,[status(thm)],[f145])).
% 1.79/1.57 thf(f145,plain,(
% 1.79/1.57 $false | (~spl3_1 | ~spl3_4)),
% 1.79/1.57 inference(trivial_inequality_removal,[status(thm)],[f144])).
% 1.79/1.57 thf(f144,plain,(
% 1.79/1.57 ($false = $true) | (~spl3_1 | ~spl3_4)),
% 1.79/1.57 inference(forward_demodulation,[status(thm)],[f142,f35])).
% 1.79/1.57 thf(f35,plain,(
% 1.79/1.57 ($false = (cF @ sK0 @ sK1)) | ~spl3_4),
% 1.79/1.57 inference(avatar_component_clause,[status(thm)],[f33])).
% 1.79/1.57 thf(f33,definition,(
% 1.79/1.57 spl3_4 <=> ($false = (cF @ sK0 @ sK1))),
% 1.79/1.57 introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition])).
% 1.79/1.57 thf(f142,plain,(
% 1.79/1.57 ((cF @ sK0 @ sK1) = $true) | (~spl3_1 | ~spl3_4)),
% 1.79/1.57 inference(trivial_inequality_removal,[status(thm)],[f134])).
% 1.79/1.57 thf(f134,plain,(
% 1.79/1.57 ($true != $true) | ((cF @ sK0 @ sK1) = $true) | (~spl3_1 | ~spl3_4)),
% 1.79/1.57 inference(superposition,[status(thm)],[f127,f22])).
% 1.79/1.57 thf(f22,plain,(
% 1.79/1.57 ((cF @ (cG @ (cF @ sK0)) @ sK1) = $true) | ~spl3_1),
% 1.79/1.57 inference(avatar_component_clause,[status(thm)],[f20])).
% 1.79/1.57 thf(f20,definition,(
% 1.79/1.57 spl3_1 <=> ((cF @ (cG @ (cF @ sK0)) @ sK1) = $true)),
% 1.79/1.57 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.79/1.57 thf(f127,plain,(
% 1.79/1.57 ( ! [X0 : a] : (((cF @ (cG @ (cF @ sK0)) @ X0) != $true) | ((cF @ sK0 @ X0) = $true)) ) | (~spl3_1 | ~spl3_4)),
% 1.79/1.57 inference(trivial_inequality_removal,[status(thm)],[f126])).
% 1.79/1.57 thf(f126,plain,(
% 1.79/1.57 ( ! [X0 : a] : (($false = $true) | ((cF @ sK0 @ X0) = $true) | ((cF @ (cG @ (cF @ sK0)) @ X0) != $true)) ) | (~spl3_1 | ~spl3_4)),
% 1.79/1.57 inference(forward_demodulation,[status(thm)],[f124,f35])).
% 1.79/1.57 thf(f124,plain,(
% 1.79/1.57 ( ! [X0 : a] : (((cF @ sK0 @ X0) = $true) | ((cF @ (cG @ (cF @ sK0)) @ X0) != $true) | ((cF @ sK0 @ sK1) = $true)) ) | ~spl3_1),
% 1.79/1.57 inference(trivial_inequality_removal,[status(thm)],[f120])).
% 1.79/1.57 thf(f120,plain,(
% 1.79/1.57 ( ! [X0 : a] : (((cF @ sK0 @ sK1) = $true) | ((cF @ sK0 @ X0) = $true) | ((cF @ (cG @ (cF @ sK0)) @ X0) != $true) | ($true != $true)) ) | ~spl3_1),
% 1.79/1.57 inference(superposition,[status(thm)],[f12,f92])).
% 1.79/1.57 thf(f92,plain,(
% 1.79/1.57 ( ! [X0 : a > $o] : (((cG @ (cF @ X0) @ (sK2 @ (cG @ (cF @ sK0)) @ X0)) = $true) | ((cF @ X0 @ sK1) = $true)) ) | ~spl3_1),
% 1.79/1.57 inference(trivial_inequality_removal,[status(thm)],[f88])).
% 1.79/1.57 thf(f88,plain,(
% 1.79/1.57 ( ! [X0 : a > $o] : (($true != $true) | ((cF @ X0 @ sK1) = $true) | ((cG @ (cF @ X0) @ (sK2 @ (cG @ (cF @ sK0)) @ X0)) = $true)) ) | ~spl3_1),
% 1.79/1.57 inference(superposition,[status(thm)],[f15,f49])).
% 1.79/1.57 thf(f49,plain,(
% 1.79/1.57 ( ! [X0 : a > $o] : (((X0 @ (sK2 @ (cG @ (cF @ sK0)) @ X0)) = $true) | ((cF @ X0 @ sK1) = $true)) ) | ~spl3_1),
% 1.79/1.57 inference(trivial_inequality_removal,[status(thm)],[f44])).
% 1.79/1.57 thf(f44,plain,(
% 1.79/1.57 ( ! [X0 : a > $o] : (((cF @ X0 @ sK1) = $true) | ((X0 @ (sK2 @ (cG @ (cF @ sK0)) @ X0)) = $true) | ($true != $true)) ) | ~spl3_1),
% 1.79/1.57 inference(superposition,[status(thm)],[f13,f22])).
% 1.79/1.57 thf(f13,plain,(
% 1.79/1.57 ( ! [X8 : a,X6 : a > $o,X5 : a > $o] : (($true != (cF @ X6 @ X8)) | ((cF @ X5 @ X8) = $true) | ((X5 @ (sK2 @ X6 @ X5)) = $true)) )),
% 1.79/1.57 inference(cnf_transformation,[status(thm)],[f11])).
% 1.79/1.57 thf(f11,plain,(
% 1.79/1.57 ! [X0 : a > $o] : (! [X1 : a] : (($true != (X0 @ X1)) | ((cF @ (cG @ X0) @ X1) = $true)) & ! [X2 : a] : (((X0 @ X2) != $true) | ((cG @ (cF @ X0) @ X2) = $true))) & ((cF @ (cG @ (cF @ sK0)) @ sK1) != (cF @ sK0 @ sK1)) & ! [X5 : a > $o,X6 : a > $o] : ((((X5 @ (sK2 @ X6 @ X5)) = $true) & ((X6 @ (sK2 @ X6 @ X5)) != $true)) | ! [X8 : a] : (($true != (cF @ X6 @ X8)) | ((cF @ X5 @ X8) = $true)))),
% 1.79/1.57 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f10,f9])).
% 1.79/1.57 thf(f9,plain,(
% 1.79/1.57 ? [X3 : a > $o,X4 : a] : ((cF @ (cG @ (cF @ X3)) @ X4) != (cF @ X3 @ X4)) => ((cF @ (cG @ (cF @ sK0)) @ sK1) != (cF @ sK0 @ sK1))),
% 1.79/1.57 introduced(definition,[],[choice_axiom])).
% 1.79/1.57 thf(f10,plain,(
% 1.79/1.57 ! [X5 : a > $o,X6 : a > $o] : (? [X7 : a] : (($true = (X5 @ X7)) & ((X6 @ X7) != $true)) => (((X5 @ (sK2 @ X6 @ X5)) = $true) & ((X6 @ (sK2 @ X6 @ X5)) != $true)))),
% 1.79/1.57 introduced(definition,[],[choice_axiom])).
% 1.79/1.57 thf(f8,plain,(
% 1.79/1.57 ! [X0 : a > $o] : (! [X1 : a] : (($true != (X0 @ X1)) | ((cF @ (cG @ X0) @ X1) = $true)) & ! [X2 : a] : (((X0 @ X2) != $true) | ((cG @ (cF @ X0) @ X2) = $true))) & ? [X3 : a > $o,X4 : a] : ((cF @ (cG @ (cF @ X3)) @ X4) != (cF @ X3 @ X4)) & ! [X5 : a > $o,X6 : a > $o] : (? [X7 : a] : (($true = (X5 @ X7)) & ((X6 @ X7) != $true)) | ! [X8 : a] : (($true != (cF @ X6 @ X8)) | ((cF @ X5 @ X8) = $true)))),
% 1.79/1.57 inference(rectify,[status(thm)],[f7])).
% 1.79/1.57 thf(f7,plain,(
% 1.79/1.57 ! [X0 : a > $o] : (! [X1 : a] : (($true != (X0 @ X1)) | ((cF @ (cG @ X0) @ X1) = $true)) & ! [X2 : a] : (((X0 @ X2) != $true) | ((cG @ (cF @ X0) @ X2) = $true))) & ? [X7 : a > $o,X8 : a] : ((cF @ X7 @ X8) != (cF @ (cG @ (cF @ X7)) @ X8)) & ! [X4 : a > $o,X3 : a > $o] : (? [X5 : a] : (((X4 @ X5) = $true) & ((X3 @ X5) != $true)) | ! [X6 : a] : (((cF @ X3 @ X6) != $true) | ((cF @ X4 @ X6) = $true)))),
% 1.79/1.57 inference(flattening,[status(thm)],[f6])).
% 1.79/1.57 thf(f6,plain,(
% 1.79/1.57 ? [X7 : a > $o,X8 : a] : ((cF @ X7 @ X8) != (cF @ (cG @ (cF @ X7)) @ X8)) & (! [X4 : a > $o,X3 : a > $o] : (? [X5 : a] : (((X4 @ X5) = $true) & ((X3 @ X5) != $true)) | ! [X6 : a] : (((cF @ X3 @ X6) != $true) | ((cF @ X4 @ X6) = $true))) & ! [X0 : a > $o] : (! [X1 : a] : (($true != (X0 @ X1)) | ((cF @ (cG @ X0) @ X1) = $true)) & ! [X2 : a] : (((X0 @ X2) != $true) | ((cG @ (cF @ X0) @ X2) = $true))))),
% 1.79/1.57 inference(ennf_transformation,[status(thm)],[f5])).
% 1.79/1.57 thf(f5,plain,(
% 1.79/1.57 ~((! [X4 : a > $o,X3 : a > $o] : (! [X5 : a] : (((X4 @ X5) = $true) => ((X3 @ X5) = $true)) => ! [X6 : a] : (((cF @ X3 @ X6) = $true) => ((cF @ X4 @ X6) = $true))) & ! [X0 : a > $o] : (! [X1 : a] : (($true = (X0 @ X1)) => ((cF @ (cG @ X0) @ X1) = $true)) & ! [X2 : a] : (((X0 @ X2) = $true) => ((cG @ (cF @ X0) @ X2) = $true)))) => ! [X7 : a > $o,X8 : a] : ((cF @ X7 @ X8) = (cF @ (cG @ (cF @ X7)) @ X8)))),
% 1.79/1.57 inference(fool_elimination,[status(thm)],[f4])).
% 1.79/1.57 thf(f4,plain,(
% 1.79/1.57 ~((! [X0 : a > $o] : (! [X1 : a] : ((X0 @ X1) => (cF @ (cG @ X0) @ X1)) & ! [X2 : a] : ((X0 @ X2) => (cG @ (cF @ X0) @ X2))) & ! [X3 : a > $o,X4 : a > $o] : (! [X5 : a] : ((X4 @ X5) => (X3 @ X5)) => ! [X6 : a] : ((cF @ X3 @ X6) => (cF @ X4 @ X6)))) => ! [X7 : a > $o,X8 : a] : ((cF @ X7 @ X8) <=> (cF @ (cG @ (cF @ X7)) @ X8)))),
% 1.79/1.57 inference(rectify,[status(thm)],[f2])).
% 1.79/1.57 thf(f2,negated_conjecture,(
% 1.79/1.57 ~((! [X0 : a > $o] : (! [X2 : a] : ((X0 @ X2) => (cF @ (cG @ X0) @ X2)) & ! [X2 : a] : ((X0 @ X2) => (cG @ (cF @ 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] : ((cF @ X0 @ X2) <=> (cF @ (cG @ (cF @ X0)) @ X2)))),
% 1.79/1.57 inference(negated_conjecture,[status(cth)],[f1])).
% 1.79/1.57 thf(f1,conjecture,(
% 1.79/1.57 (! [X0 : a > $o] : (! [X2 : a] : ((X0 @ X2) => (cF @ (cG @ X0) @ X2)) & ! [X2 : a] : ((X0 @ X2) => (cG @ (cF @ 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] : ((cF @ X0 @ X2) <=> (cF @ (cG @ (cF @ X0)) @ X2))),
% 1.79/1.57 file('/export/starexec/sandbox/tmp/tmp.1GhvNZ3Iez/DTF2THF_22939.p',cTHM67A_pme)).
% 1.79/1.57 thf(f15,plain,(
% 1.79/1.57 ( ! [X2 : a,X0 : a > $o] : (((X0 @ X2) != $true) | ((cG @ (cF @ X0) @ X2) = $true)) )),
% 1.79/1.57 inference(cnf_transformation,[status(thm)],[f11])).
% 1.79/1.57 thf(f12,plain,(
% 1.79/1.57 ( ! [X8 : a,X6 : a > $o,X5 : a > $o] : (((X6 @ (sK2 @ X6 @ X5)) != $true) | ((cF @ X5 @ X8) = $true) | ($true != (cF @ X6 @ X8))) )),
% 1.79/1.57 inference(cnf_transformation,[status(thm)],[f11])).
% 1.79/1.57 thf(f55,plain,(
% 1.79/1.57 ~spl3_1 | ~spl3_3),
% 1.79/1.57 inference(avatar_contradiction_clause,[status(thm)],[f54])).
% 1.79/1.57 thf(f54,plain,(
% 1.79/1.57 $false | (~spl3_1 | ~spl3_3)),
% 1.79/1.57 inference(trivial_inequality_removal,[status(thm)],[f50])).
% 1.79/1.57 thf(f50,plain,(
% 1.79/1.57 ($false = $true) | (~spl3_1 | ~spl3_3)),
% 1.79/1.57 inference(backward_demodulation,[status(thm)],[f22,f31])).
% 1.79/1.57 thf(f31,plain,(
% 1.79/1.57 ($false = (cF @ (cG @ (cF @ sK0)) @ sK1)) | ~spl3_3),
% 1.79/1.57 inference(avatar_component_clause,[status(thm)],[f29])).
% 1.79/1.57 thf(f29,definition,(
% 1.79/1.57 spl3_3 <=> ($false = (cF @ (cG @ (cF @ sK0)) @ sK1))),
% 1.79/1.57 introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition])).
% 1.79/1.57 thf(f43,plain,(
% 1.79/1.57 spl3_1 | ~spl3_2),
% 1.79/1.57 inference(avatar_split_clause,[status(thm)],[f42,f24,f20])).
% 1.79/1.57 thf(f24,definition,(
% 1.79/1.57 spl3_2 <=> ((cF @ sK0 @ sK1) = $true)),
% 1.79/1.57 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.79/1.57 thf(f42,plain,(
% 1.79/1.57 ((cF @ (cG @ (cF @ sK0)) @ sK1) = $true) | ~spl3_2),
% 1.79/1.57 inference(trivial_inequality_removal,[status(thm)],[f41])).
% 1.79/1.57 thf(f41,plain,(
% 1.79/1.57 ((cF @ (cG @ (cF @ sK0)) @ sK1) = $true) | ($true != $true) | ~spl3_2),
% 1.79/1.57 inference(superposition,[status(thm)],[f16,f26])).
% 1.79/1.57 thf(f26,plain,(
% 1.79/1.57 ((cF @ sK0 @ sK1) = $true) | ~spl3_2),
% 1.79/1.57 inference(avatar_component_clause,[status(thm)],[f24])).
% 1.79/1.57 thf(f16,plain,(
% 1.79/1.57 ( ! [X0 : a > $o,X1 : a] : (($true != (X0 @ X1)) | ((cF @ (cG @ X0) @ X1) = $true)) )),
% 1.79/1.57 inference(cnf_transformation,[status(thm)],[f11])).
% 1.79/1.57 thf(f36,plain,(
% 1.79/1.57 spl3_3 | spl3_4),
% 1.79/1.57 inference(avatar_split_clause,[status(thm)],[f18,f33,f29])).
% 1.79/1.57 thf(f18,plain,(
% 1.79/1.57 ($false = (cF @ (cG @ (cF @ sK0)) @ sK1)) | ($false = (cF @ sK0 @ sK1))),
% 1.79/1.57 inference(binary_proxy_clausification,[status(thm)],[f14])).
% 1.79/1.57 thf(f14,plain,(
% 1.79/1.57 ((cF @ (cG @ (cF @ sK0)) @ sK1) != (cF @ sK0 @ sK1))),
% 1.79/1.57 inference(cnf_transformation,[status(thm)],[f11])).
% 1.79/1.57 thf(f27,plain,(
% 1.79/1.57 spl3_1 | spl3_2),
% 1.79/1.57 inference(avatar_split_clause,[status(thm)],[f17,f24,f20])).
% 1.79/1.57 thf(f17,plain,(
% 1.79/1.57 ((cF @ sK0 @ sK1) = $true) | ((cF @ (cG @ (cF @ sK0)) @ sK1) = $true)),
% 1.79/1.57 inference(binary_proxy_clausification,[status(thm)],[f14])).
% 1.79/1.57 % SZS output end Proof for DTF2THF_22939
% 1.79/1.57 % (23053)------------------------------
% 1.79/1.57 % (23053)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.57 % (23053)Termination reason: Refutation
% 1.79/1.57
% 1.79/1.57 % (23053)Memory used [KB]: 5628
% 1.79/1.57 % (23053)Time elapsed: 0.018 s
% 1.79/1.57 % (23053)Instructions burned: 25 (million)
% 1.79/1.57 % (23053)------------------------------
% 1.79/1.57 % (23053)------------------------------
% 1.79/1.57 % (23050)Success in time 0.029 s
%------------------------------------------------------------------------------