%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV416^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n001.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 09:41:12 AM UTC 2026
% Result : Theorem 1.65s 1.32s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 62 ( 3 unt; 0 typ; 7 def)
% Number of atoms : 663 ( 163 equ; 0 cnn)
% Maximal formula atoms : 11 ( 10 avg)
% Number of connectives : 428 ( 87 ~; 126 |; 30 &; 143 @)
% ( 7 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 13 con; 0-2 aty)
% Number of variables : 33 ( 0 ^; 21 !; 12 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
cB: $i > $o ).
thf(func_def_2,type,
cA: $i > $o ).
thf(f79,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f47,f56,f57,f58,f63,f64,f65,f66,f67,f72,f74,f78]) ).
thf(f78,plain,
( ~ spl3_4
| spl3_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f77]) ).
thf(f77,plain,
( $false
| ~ spl3_4
| spl3_6 ),
inference(subsumption_resolution,[status(thm)],[f76,f46]) ).
thf(f46,plain,
( ( $true
= ( cA @ sK2 ) )
| ~ spl3_4 ),
inference(avatar_component_clause,[status(thm)],[f44]) ).
thf(f44,definition,
( spl3_4
<=> ( $true
= ( cA @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition]) ).
thf(f76,plain,
( ( $true
!= ( cA @ sK2 ) )
| spl3_6 ),
inference(trivial_inequality_removal,[status(thm)],[f75]) ).
thf(f75,plain,
( ( $true
!= ( cA @ sK2 ) )
| ( $true != $true )
| spl3_6 ),
inference(superposition,[status(thm)],[f55,f22]) ).
thf(f22,plain,
! [X0: $i] :
( ( ( cB @ X0 )
= $true )
| ( ( cA @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ! [X0: $i] :
( ( ( cB @ X0 )
= $true )
| ( ( cA @ X0 )
!= $true ) )
& ( ( ( ( cB @ sK0 )
!= $true )
& ( ( cA @ sK0 )
= $true ) )
| ( cG = $true )
| ( ( ( cB @ sK1 )
!= $true )
& ( $true
= ( cA @ sK1 ) ) )
| ( cG = $true )
| ( ( $true
!= ( cB @ sK2 ) )
& ( $true
= ( cA @ sK2 ) ) ) )
& ( cG != $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f11,f10,f9]) ).
thf(f9,plain,
( ? [X1: $i] :
( ( $true
!= ( cB @ X1 ) )
& ( ( cA @ X1 )
= $true ) )
=> ( ( ( cB @ sK0 )
!= $true )
& ( ( cA @ sK0 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X2: $i] :
( ( $true
!= ( cB @ X2 ) )
& ( $true
= ( cA @ X2 ) ) )
=> ( ( ( cB @ sK1 )
!= $true )
& ( $true
= ( cA @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X3: $i] :
( ( $true
!= ( cB @ X3 ) )
& ( $true
= ( cA @ X3 ) ) )
=> ( ( $true
!= ( cB @ sK2 ) )
& ( $true
= ( cA @ sK2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ! [X0: $i] :
( ( ( cB @ X0 )
= $true )
| ( ( cA @ X0 )
!= $true ) )
& ( ? [X1: $i] :
( ( $true
!= ( cB @ X1 ) )
& ( ( cA @ X1 )
= $true ) )
| ( cG = $true )
| ? [X2: $i] :
( ( $true
!= ( cB @ X2 ) )
& ( $true
= ( cA @ X2 ) ) )
| ( cG = $true )
| ? [X3: $i] :
( ( $true
!= ( cB @ X3 ) )
& ( $true
= ( cA @ X3 ) ) ) )
& ( cG != $true ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X3: $i] :
( ( $true
= ( cB @ X3 ) )
| ( $true
!= ( cA @ X3 ) ) )
& ( ? [X1: $i] :
( ( $true
!= ( cB @ X1 ) )
& ( ( cA @ X1 )
= $true ) )
| ( cG = $true )
| ? [X2: $i] :
( ( $true
!= ( cB @ X2 ) )
& ( $true
= ( cA @ X2 ) ) )
| ( cG = $true )
| ? [X0: $i] :
( ( ( cB @ X0 )
!= $true )
& ( ( cA @ X0 )
= $true ) ) )
& ( cG != $true ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ( cG != $true )
& ! [X3: $i] :
( ( $true
= ( cB @ X3 ) )
| ( $true
!= ( cA @ X3 ) ) )
& ( ( cG = $true )
| ? [X1: $i] :
( ( $true
!= ( cB @ X1 ) )
& ( ( cA @ X1 )
= $true ) )
| ? [X0: $i] :
( ( ( cB @ X0 )
!= $true )
& ( ( cA @ X0 )
= $true ) )
| ( cG = $true )
| ? [X2: $i] :
( ( $true
!= ( cB @ X2 ) )
& ( $true
= ( cA @ X2 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ( ( ! [X1: $i] :
( ( ( cA @ X1 )
= $true )
=> ( $true
= ( cB @ X1 ) ) )
& ! [X0: $i] :
( ( ( cA @ X0 )
= $true )
=> ( ( cB @ X0 )
= $true ) ) )
=> ( cG = $true ) )
| ( ! [X2: $i] :
( ( $true
= ( cA @ X2 ) )
=> ( $true
= ( cB @ X2 ) ) )
=> ( cG = $true ) ) )
=> ( ! [X3: $i] :
( ( $true
= ( cA @ X3 ) )
=> ( $true
= ( cB @ X3 ) ) )
=> ( cG = $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ( ( ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) )
& ! [X1: $i] :
( ( cA @ X1 )
=> ( cB @ X1 ) ) )
=> cG )
| ( ! [X2: $i] :
( ( cA @ X2 )
=> ( cB @ X2 ) )
=> cG ) )
=> ( ! [X3: $i] :
( ( cA @ X3 )
=> ( cB @ X3 ) )
=> cG ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ( ( ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) )
& ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) ) )
=> cG )
| ( ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) )
=> cG ) )
=> ( ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) )
=> cG ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ( ( ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) )
& ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) ) )
=> cG )
| ( ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) )
=> cG ) )
=> ( ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) )
=> cG ) ),
file('/export/starexec/sandbox2/tmp/tmp.onvUxnuSsf/DTF2THF_24623.p',cDUAL_EG3_pme) ).
thf(f55,plain,
( ( $true
!= ( cB @ sK2 ) )
| spl3_6 ),
inference(avatar_component_clause,[status(thm)],[f53]) ).
thf(f53,definition,
( spl3_6
<=> ( $true
= ( cB @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition]) ).
thf(f74,plain,
( ~ spl3_3
| spl3_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f73]) ).
thf(f73,plain,
( $false
| ~ spl3_3
| spl3_5 ),
inference(subsumption_resolution,[status(thm)],[f70,f42]) ).
thf(f42,plain,
( ( $true
= ( cA @ sK1 ) )
| ~ spl3_3 ),
inference(avatar_component_clause,[status(thm)],[f40]) ).
thf(f40,definition,
( spl3_3
<=> ( $true
= ( cA @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition]) ).
thf(f70,plain,
( ( $true
!= ( cA @ sK1 ) )
| spl3_5 ),
inference(trivial_inequality_removal,[status(thm)],[f69]) ).
thf(f69,plain,
( ( $true != $true )
| ( $true
!= ( cA @ sK1 ) )
| spl3_5 ),
inference(superposition,[status(thm)],[f51,f22]) ).
thf(f51,plain,
( ( ( cB @ sK1 )
!= $true )
| spl3_5 ),
inference(avatar_component_clause,[status(thm)],[f49]) ).
thf(f49,definition,
( spl3_5
<=> ( ( cB @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition]) ).
thf(f72,plain,
( ~ spl3_7
| spl3_1 ),
inference(avatar_split_clause,[status(thm)],[f71,f32,f60]) ).
thf(f60,definition,
( spl3_7
<=> ( ( cA @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_7])],[avatar_definition]) ).
thf(f32,definition,
( spl3_1
<=> ( ( cB @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f71,plain,
( ( ( cA @ sK0 )
!= $true )
| spl3_1 ),
inference(trivial_inequality_removal,[status(thm)],[f68]) ).
thf(f68,plain,
( ( ( cA @ sK0 )
!= $true )
| ( $true != $true )
| spl3_1 ),
inference(superposition,[status(thm)],[f34,f22]) ).
thf(f34,plain,
( ( ( cB @ sK0 )
!= $true )
| spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f32]) ).
thf(f67,plain,
( spl3_7
| ~ spl3_6
| spl3_2
| spl3_3 ),
inference(avatar_split_clause,[status(thm)],[f23,f40,f36,f53,f60]) ).
thf(f36,definition,
( spl3_2
<=> ( cG = $true ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f23,plain,
( ( $true
!= ( cB @ sK2 ) )
| ( ( cA @ sK0 )
= $true )
| ( cG = $true )
| ( $true
= ( cA @ sK1 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f15]) ).
thf(f15,plain,
( ( cG = $true )
| ( $true
= ( cA @ sK1 ) )
| ( ( cA @ sK0 )
= $true )
| ( $true
!= ( cB @ sK2 ) )
| ( cG = $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f66,plain,
( ~ spl3_5
| spl3_4
| spl3_2
| spl3_7 ),
inference(avatar_split_clause,[status(thm)],[f24,f60,f36,f44,f49]) ).
thf(f24,plain,
( ( ( cA @ sK0 )
= $true )
| ( cG = $true )
| ( ( cB @ sK1 )
!= $true )
| ( $true
= ( cA @ sK2 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f16]) ).
thf(f16,plain,
( ( $true
= ( cA @ sK2 ) )
| ( ( cA @ sK0 )
= $true )
| ( ( cB @ sK1 )
!= $true )
| ( cG = $true )
| ( cG = $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f65,plain,
( spl3_3
| ~ spl3_6
| ~ spl3_1
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f25,f36,f32,f53,f40]) ).
thf(f25,plain,
( ( ( cB @ sK0 )
!= $true )
| ( $true
!= ( cB @ sK2 ) )
| ( cG = $true )
| ( $true
= ( cA @ sK1 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ( cB @ sK0 )
!= $true )
| ( $true
= ( cA @ sK1 ) )
| ( $true
!= ( cB @ sK2 ) )
| ( cG = $true )
| ( cG = $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f64,plain,
( spl3_4
| spl3_2
| spl3_7
| spl3_3 ),
inference(avatar_split_clause,[status(thm)],[f26,f40,f60,f36,f44]) ).
thf(f26,plain,
( ( ( cA @ sK0 )
= $true )
| ( $true
= ( cA @ sK1 ) )
| ( cG = $true )
| ( $true
= ( cA @ sK2 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f14]) ).
thf(f14,plain,
( ( cG = $true )
| ( cG = $true )
| ( $true
= ( cA @ sK2 ) )
| ( ( cA @ sK0 )
= $true )
| ( $true
= ( cA @ sK1 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f63,plain,
( ~ spl3_5
| ~ spl3_6
| spl3_7
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f27,f36,f60,f53,f49]) ).
thf(f27,plain,
( ( ( cB @ sK1 )
!= $true )
| ( ( cA @ sK0 )
= $true )
| ( cG = $true )
| ( $true
!= ( cB @ sK2 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f17]) ).
thf(f17,plain,
( ( cG = $true )
| ( ( cB @ sK1 )
!= $true )
| ( cG = $true )
| ( $true
!= ( cB @ sK2 ) )
| ( ( cA @ sK0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f58,plain,
( ~ spl3_1
| spl3_4
| ~ spl3_5
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f28,f36,f49,f44,f32]) ).
thf(f28,plain,
( ( cG = $true )
| ( ( cB @ sK0 )
!= $true )
| ( $true
= ( cA @ sK2 ) )
| ( ( cB @ sK1 )
!= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f20]) ).
thf(f20,plain,
( ( $true
= ( cA @ sK2 ) )
| ( ( cB @ sK0 )
!= $true )
| ( cG = $true )
| ( cG = $true )
| ( ( cB @ sK1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f57,plain,
~ spl3_2,
inference(avatar_split_clause,[status(thm)],[f13,f36]) ).
thf(f13,plain,
cG != $true,
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f56,plain,
( ~ spl3_5
| ~ spl3_1
| spl3_2
| ~ spl3_6 ),
inference(avatar_split_clause,[status(thm)],[f29,f53,f36,f32,f49]) ).
thf(f29,plain,
( ( ( cB @ sK1 )
!= $true )
| ( $true
!= ( cB @ sK2 ) )
| ( ( cB @ sK0 )
!= $true )
| ( cG = $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f21]) ).
thf(f21,plain,
( ( cG = $true )
| ( ( cB @ sK0 )
!= $true )
| ( ( cB @ sK1 )
!= $true )
| ( cG = $true )
| ( $true
!= ( cB @ sK2 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f47,plain,
( ~ spl3_1
| spl3_2
| spl3_3
| spl3_4 ),
inference(avatar_split_clause,[status(thm)],[f30,f44,f40,f36,f32]) ).
thf(f30,plain,
( ( $true
= ( cA @ sK1 ) )
| ( cG = $true )
| ( ( cB @ sK0 )
!= $true )
| ( $true
= ( cA @ sK2 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ( cB @ sK0 )
!= $true )
| ( cG = $true )
| ( $true
= ( cA @ sK2 ) )
| ( $true
= ( cA @ sK1 ) )
| ( cG = $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV416^5 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n001.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 12:47:05 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.27/0.47 ---- Original DTF file ---
% 0.27/0.47 thf(spec,logic,$$dhol).
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 % File : SEV416^5 : TPTP v9.2.1. Released v4.0.0.
% 0.27/0.47 % Domain : Set Theory
% 0.27/0.47 % Problem : TPS problem from SETS-THMS
% 0.27/0.47 % Version : Especial.
% 0.27/0.47 % English :
% 0.27/0.47
% 0.27/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.27/0.47 % Source : [Bro09]
% 0.27/0.47 % Names : tps_0880 [Bro09]
% 0.27/0.47
% 0.27/0.47 % Status : Theorem
% 0.27/0.47 % Rating : 0.00 v6.2.0, 0.17 v6.1.0, 0.00 v4.0.0
% 0.27/0.47 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.27/0.47 % Number of atoms : 11 ( 0 equ; 0 cnn)
% 0.27/0.47 % Maximal formula atoms : 11 ( 11 avg)
% 0.27/0.47 % Number of connectives : 18 ( 0 ~; 1 |; 1 &; 8 @)
% 0.27/0.47 % ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% 0.27/0.47 % Maximal formula depth : 8 ( 8 avg)
% 0.27/0.47 % Number of types : 2 ( 0 usr)
% 0.27/0.47 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.27/0.47 % Number of symbols : 3 ( 3 usr; 1 con; 0-1 aty)
% 0.27/0.47 % Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% 0.27/0.47 % SPC : TH0_THM_NEQ_NAR
% 0.27/0.47
% 0.27/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.27/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.27/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.27/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 thf(cG,type,
% 0.27/0.47 cG: $o ).
% 0.27/0.47
% 0.27/0.47 thf(cB,type,
% 0.27/0.47 cB: $i > $o ).
% 0.27/0.47
% 0.27/0.47 thf(cA,type,
% 0.27/0.47 cA: $i > $o ).
% 0.27/0.47
% 0.27/0.47 thf(cDUAL_EG3_pme,conjecture,
% 0.27/0.47 ( ( ( ( ! [Xx: $i] :
% 0.27/0.47 ( ( cA @ Xx )
% 0.27/0.47 => ( cB @ Xx ) )
% 0.27/0.47 & ! [Xx: $i] :
% 0.27/0.47 ( ( cA @ Xx )
% 0.27/0.47 => ( cB @ Xx ) ) )
% 0.27/0.47 => cG )
% 0.27/0.47 | ( ! [Xx: $i] :
% 0.27/0.47 ( ( cA @ Xx )
% 0.27/0.47 => ( cB @ Xx ) )
% 0.27/0.47 => cG ) )
% 0.27/0.47 => ( ! [Xx: $i] :
% 0.27/0.47 ( ( cA @ Xx )
% 0.27/0.47 => ( cB @ Xx ) )
% 0.27/0.47 => cG ) ) ).
% 0.27/0.47
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 ------------------------
% 1.46/1.28 ---- Embedded in THF ---
% 1.46/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.29 %%% Generated on Tue Feb 24 12:47:06 EST 2026
% 1.46/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.29 %%% Logic specification used:
% 1.46/1.29 %%% thf(spec, logic, $$dhol).
% 1.46/1.29
% 1.46/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.onvUxnuSsf/DTF2DTF24623.p
% See solution above
% 1.46/1.29 ------------------------
% 1.65/1.30 ---- Cleaned THF ---
% 1.65/1.30 thf(cG,type,
% 1.65/1.30 cG: $o ).
% 1.65/1.30
% 1.65/1.30 thf(cB,type,
% 1.65/1.30 cB: $i > $o ).
% 1.65/1.30
% 1.65/1.30 thf(cA,type,
% 1.65/1.30 cA: $i > $o ).
% 1.65/1.30
% 1.65/1.30 thf(cDUAL_EG3_pme,conjecture,
% 1.65/1.30 ( ( ( ( ! [Xx: $i] :
% 1.65/1.30 ( ( cA @ Xx )
% 1.65/1.30 => ( cB @ Xx ) )
% 1.65/1.30 & ! [Xx: $i] :
% 1.65/1.30 ( ( cA @ Xx )
% 1.65/1.30 => ( cB @ Xx ) ) )
% 1.65/1.30 => cG )
% 1.65/1.30 | ( ! [Xx: $i] :
% 1.65/1.30 ( ( cA @ Xx )
% 1.65/1.30 => ( cB @ Xx ) )
% 1.65/1.30 => cG ) )
% 1.65/1.30 => ( ! [Xx: $i] :
% 1.65/1.30 ( ( cA @ Xx )
% 1.65/1.30 => ( cB @ Xx ) )
% 1.65/1.30 => cG ) ) ).
% 1.65/1.30 ------------------------
% 1.65/1.31 % (24897)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_24623 for (2999ds/183Mi)
% 1.65/1.31 % (24899)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_24623 for (2999ds/27Mi)
% 1.65/1.31 % (24897)First to succeed.
% 1.65/1.32 % (24899)Also succeeded, but the first one will report.
% 1.65/1.32 % (24897)Refutation found. Thanks to Tanya!
% 1.65/1.32 % SZS status Theorem for DTF2THF_24623
% 1.65/1.32 % SZS output start Proof for DTF2THF_24623
% 1.65/1.32 thf(func_def_1, type, cB: $i > $o).
% 1.65/1.32 thf(func_def_2, type, cA: $i > $o).
% 1.65/1.32 thf(f79,plain,(
% 1.65/1.32 $false),
% 1.65/1.32 inference(avatar_sat_refutation,[status(thm)],[f47,f56,f57,f58,f63,f64,f65,f66,f67,f72,f74,f78])).
% 1.65/1.32 thf(f78,plain,(
% 1.65/1.32 ~spl3_4 | spl3_6),
% 1.65/1.32 inference(avatar_contradiction_clause,[status(thm)],[f77])).
% 1.65/1.32 thf(f77,plain,(
% 1.65/1.32 $false | (~spl3_4 | spl3_6)),
% 1.65/1.32 inference(subsumption_resolution,[status(thm)],[f76,f46])).
% 1.65/1.32 thf(f46,plain,(
% 1.65/1.32 ($true = (cA @ sK2)) | ~spl3_4),
% 1.65/1.32 inference(avatar_component_clause,[status(thm)],[f44])).
% 1.65/1.32 thf(f44,definition,(
% 1.65/1.32 spl3_4 <=> ($true = (cA @ sK2))),
% 1.65/1.32 introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition])).
% 1.65/1.32 thf(f76,plain,(
% 1.65/1.32 ($true != (cA @ sK2)) | spl3_6),
% 1.65/1.32 inference(trivial_inequality_removal,[status(thm)],[f75])).
% 1.65/1.32 thf(f75,plain,(
% 1.65/1.32 ($true != (cA @ sK2)) | ($true != $true) | spl3_6),
% 1.65/1.32 inference(superposition,[status(thm)],[f55,f22])).
% 1.65/1.32 thf(f22,plain,(
% 1.65/1.32 ( ! [X0 : $i] : (((cB @ X0) = $true) | ((cA @ X0) != $true)) )),
% 1.65/1.32 inference(cnf_transformation,[status(thm)],[f12])).
% 1.65/1.32 thf(f12,plain,(
% 1.65/1.32 ! [X0 : $i] : (((cB @ X0) = $true) | ((cA @ X0) != $true)) & ((((cB @ sK0) != $true) & ((cA @ sK0) = $true)) | (cG = $true) | (((cB @ sK1) != $true) & ($true = (cA @ sK1))) | (cG = $true) | (($true != (cB @ sK2)) & ($true = (cA @ sK2)))) & (cG != $true)),
% 1.65/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f11,f10,f9])).
% 1.65/1.32 thf(f9,plain,(
% 1.65/1.32 ? [X1 : $i] : (($true != (cB @ X1)) & ((cA @ X1) = $true)) => (((cB @ sK0) != $true) & ((cA @ sK0) = $true))),
% 1.65/1.32 introduced(definition,[],[choice_axiom])).
% 1.65/1.32 thf(f10,plain,(
% 1.65/1.32 ? [X2 : $i] : (($true != (cB @ X2)) & ($true = (cA @ X2))) => (((cB @ sK1) != $true) & ($true = (cA @ sK1)))),
% 1.65/1.32 introduced(definition,[],[choice_axiom])).
% 1.65/1.32 thf(f11,plain,(
% 1.65/1.32 ? [X3 : $i] : (($true != (cB @ X3)) & ($true = (cA @ X3))) => (($true != (cB @ sK2)) & ($true = (cA @ sK2)))),
% 1.65/1.32 introduced(definition,[],[choice_axiom])).
% 1.65/1.32 thf(f8,plain,(
% 1.65/1.32 ! [X0 : $i] : (((cB @ X0) = $true) | ((cA @ X0) != $true)) & (? [X1 : $i] : (($true != (cB @ X1)) & ((cA @ X1) = $true)) | (cG = $true) | ? [X2 : $i] : (($true != (cB @ X2)) & ($true = (cA @ X2))) | (cG = $true) | ? [X3 : $i] : (($true != (cB @ X3)) & ($true = (cA @ X3)))) & (cG != $true)),
% 1.65/1.32 inference(rectify,[status(thm)],[f7])).
% 1.65/1.32 thf(f7,plain,(
% 1.65/1.32 ! [X3 : $i] : (($true = (cB @ X3)) | ($true != (cA @ X3))) & (? [X1 : $i] : (($true != (cB @ X1)) & ((cA @ X1) = $true)) | (cG = $true) | ? [X2 : $i] : (($true != (cB @ X2)) & ($true = (cA @ X2))) | (cG = $true) | ? [X0 : $i] : (((cB @ X0) != $true) & ((cA @ X0) = $true))) & (cG != $true)),
% 1.65/1.32 inference(flattening,[status(thm)],[f6])).
% 1.65/1.32 thf(f6,plain,(
% 1.65/1.32 ((cG != $true) & ! [X3 : $i] : (($true = (cB @ X3)) | ($true != (cA @ X3)))) & (((cG = $true) | (? [X1 : $i] : (($true != (cB @ X1)) & ((cA @ X1) = $true)) | ? [X0 : $i] : (((cB @ X0) != $true) & ((cA @ X0) = $true)))) | ((cG = $true) | ? [X2 : $i] : (($true != (cB @ X2)) & ($true = (cA @ X2)))))),
% 1.65/1.32 inference(ennf_transformation,[status(thm)],[f5])).
% 1.65/1.32 thf(f5,plain,(
% 1.65/1.32 ~((((! [X1 : $i] : (((cA @ X1) = $true) => ($true = (cB @ X1))) & ! [X0 : $i] : (((cA @ X0) = $true) => ((cB @ X0) = $true))) => (cG = $true)) | (! [X2 : $i] : (($true = (cA @ X2)) => ($true = (cB @ X2))) => (cG = $true))) => (! [X3 : $i] : (($true = (cA @ X3)) => ($true = (cB @ X3))) => (cG = $true)))),
% 1.65/1.32 inference(fool_elimination,[status(thm)],[f4])).
% 1.65/1.32 thf(f4,plain,(
% 1.65/1.32 ~((((! [X0 : $i] : ((cA @ X0) => (cB @ X0)) & ! [X1 : $i] : ((cA @ X1) => (cB @ X1))) => cG) | (! [X2 : $i] : ((cA @ X2) => (cB @ X2)) => cG)) => (! [X3 : $i] : ((cA @ X3) => (cB @ X3)) => cG))),
% 1.65/1.32 inference(rectify,[status(thm)],[f2])).
% 1.65/1.32 thf(f2,negated_conjecture,(
% 1.65/1.32 ~((((! [X0 : $i] : ((cA @ X0) => (cB @ X0)) & ! [X0 : $i] : ((cA @ X0) => (cB @ X0))) => cG) | (! [X0 : $i] : ((cA @ X0) => (cB @ X0)) => cG)) => (! [X0 : $i] : ((cA @ X0) => (cB @ X0)) => cG))),
% 1.65/1.32 inference(negated_conjecture,[status(cth)],[f1])).
% 1.65/1.32 thf(f1,conjecture,(
% 1.65/1.32 (((! [X0 : $i] : ((cA @ X0) => (cB @ X0)) & ! [X0 : $i] : ((cA @ X0) => (cB @ X0))) => cG) | (! [X0 : $i] : ((cA @ X0) => (cB @ X0)) => cG)) => (! [X0 : $i] : ((cA @ X0) => (cB @ X0)) => cG)),
% 1.65/1.32 file('/export/starexec/sandbox2/tmp/tmp.onvUxnuSsf/DTF2THF_24623.p',cDUAL_EG3_pme)).
% 1.65/1.32 thf(f55,plain,(
% 1.65/1.32 ($true != (cB @ sK2)) | spl3_6),
% 1.65/1.32 inference(avatar_component_clause,[status(thm)],[f53])).
% 1.65/1.32 thf(f53,definition,(
% 1.65/1.32 spl3_6 <=> ($true = (cB @ sK2))),
% 1.65/1.32 introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition])).
% 1.65/1.32 thf(f74,plain,(
% 1.65/1.32 ~spl3_3 | spl3_5),
% 1.65/1.32 inference(avatar_contradiction_clause,[status(thm)],[f73])).
% 1.65/1.32 thf(f73,plain,(
% 1.65/1.32 $false | (~spl3_3 | spl3_5)),
% 1.65/1.32 inference(subsumption_resolution,[status(thm)],[f70,f42])).
% 1.65/1.32 thf(f42,plain,(
% 1.65/1.32 ($true = (cA @ sK1)) | ~spl3_3),
% 1.65/1.32 inference(avatar_component_clause,[status(thm)],[f40])).
% 1.65/1.32 thf(f40,definition,(
% 1.65/1.32 spl3_3 <=> ($true = (cA @ sK1))),
% 1.65/1.32 introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition])).
% 1.65/1.32 thf(f70,plain,(
% 1.65/1.32 ($true != (cA @ sK1)) | spl3_5),
% 1.65/1.32 inference(trivial_inequality_removal,[status(thm)],[f69])).
% 1.65/1.32 thf(f69,plain,(
% 1.65/1.32 ($true != $true) | ($true != (cA @ sK1)) | spl3_5),
% 1.65/1.32 inference(superposition,[status(thm)],[f51,f22])).
% 1.65/1.32 thf(f51,plain,(
% 1.65/1.32 ((cB @ sK1) != $true) | spl3_5),
% 1.65/1.32 inference(avatar_component_clause,[status(thm)],[f49])).
% 1.65/1.32 thf(f49,definition,(
% 1.65/1.32 spl3_5 <=> ((cB @ sK1) = $true)),
% 1.65/1.32 introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition])).
% 1.65/1.32 thf(f72,plain,(
% 1.65/1.32 ~spl3_7 | spl3_1),
% 1.65/1.32 inference(avatar_split_clause,[status(thm)],[f71,f32,f60])).
% 1.65/1.32 thf(f60,definition,(
% 1.65/1.32 spl3_7 <=> ((cA @ sK0) = $true)),
% 1.65/1.32 introduced(definition,[new_symbols(naming,[spl3_7])],[avatar_definition])).
% 1.65/1.32 thf(f32,definition,(
% 1.65/1.32 spl3_1 <=> ((cB @ sK0) = $true)),
% 1.65/1.32 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.65/1.32 thf(f71,plain,(
% 1.65/1.32 ((cA @ sK0) != $true) | spl3_1),
% 1.65/1.32 inference(trivial_inequality_removal,[status(thm)],[f68])).
% 1.65/1.32 thf(f68,plain,(
% 1.65/1.32 ((cA @ sK0) != $true) | ($true != $true) | spl3_1),
% 1.65/1.32 inference(superposition,[status(thm)],[f34,f22])).
% 1.65/1.32 thf(f34,plain,(
% 1.65/1.32 ((cB @ sK0) != $true) | spl3_1),
% 1.65/1.32 inference(avatar_component_clause,[status(thm)],[f32])).
% 1.65/1.32 thf(f67,plain,(
% 1.65/1.32 spl3_7 | ~spl3_6 | spl3_2 | spl3_3),
% 1.65/1.32 inference(avatar_split_clause,[status(thm)],[f23,f40,f36,f53,f60])).
% 1.65/1.32 thf(f36,definition,(
% 1.65/1.32 spl3_2 <=> (cG = $true)),
% 1.65/1.32 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.65/1.32 thf(f23,plain,(
% 1.65/1.32 ($true != (cB @ sK2)) | ((cA @ sK0) = $true) | (cG = $true) | ($true = (cA @ sK1))),
% 1.65/1.32 inference(duplicate_literal_removal,[status(thm)],[f15])).
% 1.65/1.32 thf(f15,plain,(
% 1.65/1.32 (cG = $true) | ($true = (cA @ sK1)) | ((cA @ sK0) = $true) | ($true != (cB @ sK2)) | (cG = $true)),
% 1.65/1.32 inference(cnf_transformation,[status(thm)],[f12])).
% 1.65/1.32 thf(f66,plain,(
% 1.65/1.32 ~spl3_5 | spl3_4 | spl3_2 | spl3_7),
% 1.65/1.32 inference(avatar_split_clause,[status(thm)],[f24,f60,f36,f44,f49])).
% 1.65/1.32 thf(f24,plain,(
% 1.65/1.32 ((cA @ sK0) = $true) | (cG = $true) | ((cB @ sK1) != $true) | ($true = (cA @ sK2))),
% 1.65/1.32 inference(duplicate_literal_removal,[status(thm)],[f16])).
% 1.65/1.32 thf(f16,plain,(
% 1.65/1.32 ($true = (cA @ sK2)) | ((cA @ sK0) = $true) | ((cB @ sK1) != $true) | (cG = $true) | (cG = $true)),
% 1.65/1.32 inference(cnf_transformation,[status(thm)],[f12])).
% 1.65/1.32 thf(f65,plain,(
% 1.65/1.32 spl3_3 | ~spl3_6 | ~spl3_1 | spl3_2),
% 1.65/1.32 inference(avatar_split_clause,[status(thm)],[f25,f36,f32,f53,f40])).
% 1.65/1.32 thf(f25,plain,(
% 1.65/1.32 ((cB @ sK0) != $true) | ($true != (cB @ sK2)) | (cG = $true) | ($true = (cA @ sK1))),
% 1.65/1.32 inference(duplicate_literal_removal,[status(thm)],[f19])).
% 1.65/1.32 thf(f19,plain,(
% 1.65/1.32 ((cB @ sK0) != $true) | ($true = (cA @ sK1)) | ($true != (cB @ sK2)) | (cG = $true) | (cG = $true)),
% 1.65/1.32 inference(cnf_transformation,[status(thm)],[f12])).
% 1.65/1.32 thf(f64,plain,(
% 1.65/1.32 spl3_4 | spl3_2 | spl3_7 | spl3_3),
% 1.65/1.32 inference(avatar_split_clause,[status(thm)],[f26,f40,f60,f36,f44])).
% 1.65/1.32 thf(f26,plain,(
% 1.65/1.32 ((cA @ sK0) = $true) | ($true = (cA @ sK1)) | (cG = $true) | ($true = (cA @ sK2))),
% 1.65/1.32 inference(duplicate_literal_removal,[status(thm)],[f14])).
% 1.65/1.32 thf(f14,plain,(
% 1.65/1.32 (cG = $true) | (cG = $true) | ($true = (cA @ sK2)) | ((cA @ sK0) = $true) | ($true = (cA @ sK1))),
% 1.65/1.32 inference(cnf_transformation,[status(thm)],[f12])).
% 1.65/1.32 thf(f63,plain,(
% 1.65/1.32 ~spl3_5 | ~spl3_6 | spl3_7 | spl3_2),
% 1.65/1.32 inference(avatar_split_clause,[status(thm)],[f27,f36,f60,f53,f49])).
% 1.65/1.32 thf(f27,plain,(
% 1.65/1.32 ((cB @ sK1) != $true) | ((cA @ sK0) = $true) | (cG = $true) | ($true != (cB @ sK2))),
% 1.65/1.32 inference(duplicate_literal_removal,[status(thm)],[f17])).
% 1.65/1.32 thf(f17,plain,(
% 1.65/1.32 (cG = $true) | ((cB @ sK1) != $true) | (cG = $true) | ($true != (cB @ sK2)) | ((cA @ sK0) = $true)),
% 1.65/1.32 inference(cnf_transformation,[status(thm)],[f12])).
% 1.65/1.32 thf(f58,plain,(
% 1.65/1.32 ~spl3_1 | spl3_4 | ~spl3_5 | spl3_2),
% 1.65/1.32 inference(avatar_split_clause,[status(thm)],[f28,f36,f49,f44,f32])).
% 1.65/1.32 thf(f28,plain,(
% 1.65/1.32 (cG = $true) | ((cB @ sK0) != $true) | ($true = (cA @ sK2)) | ((cB @ sK1) != $true)),
% 1.65/1.32 inference(duplicate_literal_removal,[status(thm)],[f20])).
% 1.65/1.32 thf(f20,plain,(
% 1.65/1.32 ($true = (cA @ sK2)) | ((cB @ sK0) != $true) | (cG = $true) | (cG = $true) | ((cB @ sK1) != $true)),
% 1.65/1.32 inference(cnf_transformation,[status(thm)],[f12])).
% 1.65/1.32 thf(f57,plain,(
% 1.65/1.32 ~spl3_2),
% 1.65/1.32 inference(avatar_split_clause,[status(thm)],[f13,f36])).
% 1.65/1.32 thf(f13,plain,(
% 1.65/1.32 (cG != $true)),
% 1.65/1.32 inference(cnf_transformation,[status(thm)],[f12])).
% 1.65/1.32 thf(f56,plain,(
% 1.65/1.32 ~spl3_5 | ~spl3_1 | spl3_2 | ~spl3_6),
% 1.65/1.32 inference(avatar_split_clause,[status(thm)],[f29,f53,f36,f32,f49])).
% 1.65/1.32 thf(f29,plain,(
% 1.65/1.32 ((cB @ sK1) != $true) | ($true != (cB @ sK2)) | ((cB @ sK0) != $true) | (cG = $true)),
% 1.65/1.32 inference(duplicate_literal_removal,[status(thm)],[f21])).
% 1.65/1.32 thf(f21,plain,(
% 1.65/1.32 (cG = $true) | ((cB @ sK0) != $true) | ((cB @ sK1) != $true) | (cG = $true) | ($true != (cB @ sK2))),
% 1.65/1.32 inference(cnf_transformation,[status(thm)],[f12])).
% 1.65/1.32 thf(f47,plain,(
% 1.65/1.32 ~spl3_1 | spl3_2 | spl3_3 | spl3_4),
% 1.65/1.32 inference(avatar_split_clause,[status(thm)],[f30,f44,f40,f36,f32])).
% 1.65/1.32 thf(f30,plain,(
% 1.65/1.32 ($true = (cA @ sK1)) | (cG = $true) | ((cB @ sK0) != $true) | ($true = (cA @ sK2))),
% 1.65/1.32 inference(duplicate_literal_removal,[status(thm)],[f18])).
% 1.65/1.32 thf(f18,plain,(
% 1.65/1.32 ((cB @ sK0) != $true) | (cG = $true) | ($true = (cA @ sK2)) | ($true = (cA @ sK1)) | (cG = $true)),
% 1.65/1.32 inference(cnf_transformation,[status(thm)],[f12])).
% 1.65/1.32 % SZS output end Proof for DTF2THF_24623
% 1.65/1.32 % (24897)------------------------------
% 1.65/1.32 % (24897)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.32 % (24897)Termination reason: Refutation
% 1.65/1.32
% 1.65/1.32 % (24897)Memory used [KB]: 5500
% 1.65/1.32 % (24897)Time elapsed: 0.003 s
% 1.65/1.32 % (24897)Instructions burned: 3 (million)
% 1.65/1.32 % (24897)------------------------------
% 1.65/1.32 % (24897)------------------------------
% 1.65/1.32 % (24896)Success in time 0.013 s
%------------------------------------------------------------------------------