%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV412^5 : 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 : n004.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 1.31s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 41 ( 3 unt; 0 typ; 5 def)
% Number of atoms : 389 ( 98 equ; 0 cnn)
% Maximal formula atoms : 9 ( 9 avg)
% Number of connectives : 252 ( 50 ~; 62 |; 20 &; 85 @)
% ( 5 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 10 con; 0-2 aty)
% Number of variables : 25 ( 0 ^; 17 !; 8 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
cB: $i > $o ).
thf(func_def_2,type,
cA: $i > $o ).
thf(f54,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f34,f39,f44,f45,f46,f51,f53]) ).
thf(f53,plain,
( ~ spl2_2
| spl2_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f52]) ).
thf(f52,plain,
( $false
| ~ spl2_2
| spl2_4 ),
inference(subsumption_resolution,[status(thm)],[f49,f29]) ).
thf(f29,plain,
( ( ( cA @ sK1 )
= $true )
| ~ spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f27]) ).
thf(f27,definition,
( spl2_2
<=> ( ( cA @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f49,plain,
( ( ( cA @ sK1 )
!= $true )
| spl2_4 ),
inference(trivial_inequality_removal,[status(thm)],[f48]) ).
thf(f48,plain,
( ( ( cA @ sK1 )
!= $true )
| ( $true != $true )
| spl2_4 ),
inference(superposition,[status(thm)],[f38,f16]) ).
thf(f16,plain,
! [X0: $i] :
( ( ( cB @ X0 )
= $true )
| ( ( cA @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( cG != $true )
& ! [X0: $i] :
( ( ( cA @ X0 )
!= $true )
| ( ( cB @ X0 )
= $true ) )
& ( ( ( $true
= ( cA @ sK0 ) )
& ( $true
!= ( cB @ sK0 ) ) )
| ( cG = $true )
| ( cG = $true )
| ( ( ( cA @ sK1 )
= $true )
& ( $true
!= ( cB @ sK1 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f8,f10,f9]) ).
thf(f9,plain,
( ? [X1: $i] :
( ( $true
= ( cA @ X1 ) )
& ( $true
!= ( cB @ X1 ) ) )
=> ( ( $true
= ( cA @ sK0 ) )
& ( $true
!= ( cB @ sK0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X2: $i] :
( ( $true
= ( cA @ X2 ) )
& ( $true
!= ( cB @ X2 ) ) )
=> ( ( ( cA @ sK1 )
= $true )
& ( $true
!= ( cB @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ( cG != $true )
& ! [X0: $i] :
( ( ( cA @ X0 )
!= $true )
| ( ( cB @ X0 )
= $true ) )
& ( ? [X1: $i] :
( ( $true
= ( cA @ X1 ) )
& ( $true
!= ( cB @ X1 ) ) )
| ( cG = $true )
| ( cG = $true )
| ? [X2: $i] :
( ( $true
= ( cA @ X2 ) )
& ( $true
!= ( cB @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ( cG != $true )
& ! [X2: $i] :
( ( $true
!= ( cA @ X2 ) )
| ( $true
= ( cB @ X2 ) ) )
& ( ? [X0: $i] :
( ( ( cA @ X0 )
= $true )
& ( ( cB @ X0 )
!= $true ) )
| ( cG = $true )
| ( cG = $true )
| ? [X1: $i] :
( ( $true
= ( cA @ X1 ) )
& ( $true
!= ( cB @ X1 ) ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ( cG != $true )
& ! [X2: $i] :
( ( $true
!= ( cA @ X2 ) )
| ( $true
= ( cB @ X2 ) ) )
& ( ( cG = $true )
| ? [X0: $i] :
( ( ( cA @ X0 )
= $true )
& ( ( cB @ X0 )
!= $true ) )
| ( cG = $true )
| ? [X1: $i] :
( ( $true
= ( cA @ X1 ) )
& ( $true
!= ( cB @ X1 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ( ! [X0: $i] :
( ( ( cA @ X0 )
= $true )
=> ( ( cB @ X0 )
= $true ) )
=> ( cG = $true ) )
| ( ! [X1: $i] :
( ( $true
= ( cA @ X1 ) )
=> ( $true
= ( cB @ X1 ) ) )
=> ( cG = $true ) ) )
=> ( ! [X2: $i] :
( ( $true
= ( cA @ X2 ) )
=> ( $true
= ( cB @ X2 ) ) )
=> ( cG = $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ( ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) )
=> cG )
| ( ! [X1: $i] :
( ( cA @ X1 )
=> ( cB @ X1 ) )
=> cG ) )
=> ( ! [X2: $i] :
( ( cA @ X2 )
=> ( cB @ X2 ) )
=> cG ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ( ! [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 ) )
=> cG )
| ( ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) )
=> cG ) )
=> ( ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) )
=> cG ) ),
file('/export/starexec/sandbox2/tmp/tmp.73YrD6BFLG/DTF2THF_30624.p',cDUAL_EG2_pme) ).
thf(f38,plain,
( ( $true
!= ( cB @ sK1 ) )
| spl2_4 ),
inference(avatar_component_clause,[status(thm)],[f36]) ).
thf(f36,definition,
( spl2_4
<=> ( $true
= ( cB @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition]) ).
thf(f51,plain,
( ~ spl2_5
| spl2_1 ),
inference(avatar_split_clause,[status(thm)],[f50,f23,f41]) ).
thf(f41,definition,
( spl2_5
<=> ( $true
= ( cA @ sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_5])],[avatar_definition]) ).
thf(f23,definition,
( spl2_1
<=> ( $true
= ( cB @ sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f50,plain,
( ( $true
!= ( cA @ sK0 ) )
| spl2_1 ),
inference(trivial_inequality_removal,[status(thm)],[f47]) ).
thf(f47,plain,
( ( $true
!= ( cA @ sK0 ) )
| ( $true != $true )
| spl2_1 ),
inference(superposition,[status(thm)],[f25,f16]) ).
thf(f25,plain,
( ( $true
!= ( cB @ sK0 ) )
| spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f23]) ).
thf(f46,plain,
~ spl2_3,
inference(avatar_split_clause,[status(thm)],[f17,f31]) ).
thf(f31,definition,
( spl2_3
<=> ( cG = $true ) ),
introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition]) ).
thf(f17,plain,
cG != $true,
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f45,plain,
( spl2_5
| ~ spl2_4
| spl2_3 ),
inference(avatar_split_clause,[status(thm)],[f18,f31,f36,f41]) ).
thf(f18,plain,
( ( $true
= ( cA @ sK0 ) )
| ( cG = $true )
| ( $true
!= ( cB @ sK1 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f14]) ).
thf(f14,plain,
( ( cG = $true )
| ( cG = $true )
| ( $true
= ( cA @ sK0 ) )
| ( $true
!= ( cB @ sK1 ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f44,plain,
( spl2_3
| spl2_5
| spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f19,f27,f41,f31]) ).
thf(f19,plain,
( ( ( cA @ sK1 )
= $true )
| ( cG = $true )
| ( $true
= ( cA @ sK0 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f15]) ).
thf(f15,plain,
( ( $true
= ( cA @ sK0 ) )
| ( cG = $true )
| ( ( cA @ sK1 )
= $true )
| ( cG = $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f39,plain,
( ~ spl2_4
| ~ spl2_1
| spl2_3 ),
inference(avatar_split_clause,[status(thm)],[f20,f31,f23,f36]) ).
thf(f20,plain,
( ( $true
!= ( cB @ sK1 ) )
| ( cG = $true )
| ( $true
!= ( cB @ sK0 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f12]) ).
thf(f12,plain,
( ( $true
!= ( cB @ sK1 ) )
| ( cG = $true )
| ( $true
!= ( cB @ sK0 ) )
| ( cG = $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f34,plain,
( ~ spl2_1
| spl2_2
| spl2_3 ),
inference(avatar_split_clause,[status(thm)],[f21,f31,f27,f23]) ).
thf(f21,plain,
( ( cG = $true )
| ( ( cA @ sK1 )
= $true )
| ( $true
!= ( cB @ sK0 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f13]) ).
thf(f13,plain,
( ( $true
!= ( cB @ sK0 ) )
| ( cG = $true )
| ( ( cA @ sK1 )
= $true )
| ( cG = $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV412^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n004.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 12:46:11 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.46 ---- Original DTF file ---
% 0.19/0.46 thf(spec,logic,$$dhol).
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % File : SEV412^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.46 % Domain : Set Theory
% 0.19/0.46 % Problem : TPS problem from SETS-THMS
% 0.19/0.46 % Version : Especial.
% 0.19/0.46 % English :
% 0.19/0.46
% 0.19/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.46 % Source : [Bro09]
% 0.19/0.46 % Names : tps_0836 [Bro09]
% 0.19/0.46
% 0.19/0.46 % Status : Theorem
% 0.19/0.46 % Rating : 0.00 v6.2.0, 0.17 v6.1.0, 0.00 v4.0.0
% 0.19/0.46 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.19/0.46 % Number of atoms : 9 ( 0 equ; 0 cnn)
% 0.19/0.46 % Maximal formula atoms : 9 ( 9 avg)
% 0.19/0.46 % Number of connectives : 14 ( 0 ~; 1 |; 0 &; 6 @)
% 0.19/0.46 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.19/0.46 % Maximal formula depth : 7 ( 7 avg)
% 0.19/0.46 % Number of types : 2 ( 0 usr)
% 0.19/0.46 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.19/0.46 % Number of symbols : 3 ( 3 usr; 1 con; 0-1 aty)
% 0.19/0.46 % Number of variables : 3 ( 0 ^; 3 !; 0 ?; 3 :)
% 0.19/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.19/0.46
% 0.19/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 thf(cG,type,
% 0.19/0.46 cG: $o ).
% 0.19/0.46
% 0.19/0.46 thf(cB,type,
% 0.19/0.46 cB: $i > $o ).
% 0.19/0.46
% 0.19/0.46 thf(cA,type,
% 0.19/0.46 cA: $i > $o ).
% 0.19/0.46
% 0.19/0.46 thf(cDUAL_EG2_pme,conjecture,
% 0.19/0.46 ( ( ( ! [Xx: $i] :
% 0.19/0.46 ( ( cA @ Xx )
% 0.19/0.46 => ( cB @ Xx ) )
% 0.19/0.46 => cG )
% 0.19/0.46 | ( ! [Xx: $i] :
% 0.19/0.46 ( ( cA @ Xx )
% 0.19/0.46 => ( cB @ Xx ) )
% 0.19/0.46 => cG ) )
% 0.19/0.46 => ( ! [Xx: $i] :
% 0.19/0.46 ( ( cA @ Xx )
% 0.19/0.46 => ( cB @ Xx ) )
% 0.19/0.46 => cG ) ) ).
% 0.19/0.46
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 ------------------------
% 1.49/1.28 ---- Embedded in THF ---
% 1.49/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.28 %%% Generated on Tue Feb 24 12:46:12 EST 2026
% 1.49/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.28 %%% Logic specification used:
% 1.49/1.28 %%% thf(spec, logic, $$dhol).
% 1.49/1.28
% 1.49/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.73YrD6BFLG/DTF2DTF30624.p
% See solution above
% 1.49/1.28 ------------------------
% 1.49/1.29 ---- Cleaned THF ---
% 1.49/1.29 thf(cG,type,
% 1.49/1.29 cG: $o ).
% 1.49/1.29
% 1.49/1.29 thf(cB,type,
% 1.49/1.29 cB: $i > $o ).
% 1.49/1.29
% 1.49/1.29 thf(cA,type,
% 1.49/1.29 cA: $i > $o ).
% 1.49/1.29
% 1.49/1.29 thf(cDUAL_EG2_pme,conjecture,
% 1.49/1.29 ( ( ( ! [Xx: $i] :
% 1.49/1.29 ( ( cA @ Xx )
% 1.49/1.29 => ( cB @ Xx ) )
% 1.49/1.29 => cG )
% 1.49/1.29 | ( ! [Xx: $i] :
% 1.49/1.29 ( ( cA @ Xx )
% 1.49/1.29 => ( cB @ Xx ) )
% 1.49/1.29 => cG ) )
% 1.49/1.29 => ( ! [Xx: $i] :
% 1.49/1.29 ( ( cA @ Xx )
% 1.49/1.29 => ( cB @ Xx ) )
% 1.49/1.29 => cG ) ) ).
% 1.49/1.29 ------------------------
% 1.65/1.30 % (30797)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30624 for (3000ds/183Mi)
% 1.65/1.30 % (30797)First to succeed.
% 1.65/1.31 % (30797)Refutation found. Thanks to Tanya!
% 1.65/1.31 % SZS status Theorem for DTF2THF_30624
% 1.65/1.31 % SZS output start Proof for DTF2THF_30624
% 1.65/1.31 thf(func_def_1, type, cB: $i > $o).
% 1.65/1.31 thf(func_def_2, type, cA: $i > $o).
% 1.65/1.31 thf(f54,plain,(
% 1.65/1.31 $false),
% 1.65/1.31 inference(avatar_sat_refutation,[status(thm)],[f34,f39,f44,f45,f46,f51,f53])).
% 1.65/1.31 thf(f53,plain,(
% 1.65/1.31 ~spl2_2 | spl2_4),
% 1.65/1.31 inference(avatar_contradiction_clause,[status(thm)],[f52])).
% 1.65/1.31 thf(f52,plain,(
% 1.65/1.31 $false | (~spl2_2 | spl2_4)),
% 1.65/1.31 inference(subsumption_resolution,[status(thm)],[f49,f29])).
% 1.65/1.31 thf(f29,plain,(
% 1.65/1.31 ((cA @ sK1) = $true) | ~spl2_2),
% 1.65/1.31 inference(avatar_component_clause,[status(thm)],[f27])).
% 1.65/1.31 thf(f27,definition,(
% 1.65/1.31 spl2_2 <=> ((cA @ sK1) = $true)),
% 1.65/1.31 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.65/1.31 thf(f49,plain,(
% 1.65/1.31 ((cA @ sK1) != $true) | spl2_4),
% 1.65/1.31 inference(trivial_inequality_removal,[status(thm)],[f48])).
% 1.65/1.31 thf(f48,plain,(
% 1.65/1.31 ((cA @ sK1) != $true) | ($true != $true) | spl2_4),
% 1.65/1.31 inference(superposition,[status(thm)],[f38,f16])).
% 1.65/1.31 thf(f16,plain,(
% 1.65/1.31 ( ! [X0 : $i] : (((cB @ X0) = $true) | ((cA @ X0) != $true)) )),
% 1.65/1.31 inference(cnf_transformation,[status(thm)],[f11])).
% 1.65/1.31 thf(f11,plain,(
% 1.65/1.31 (cG != $true) & ! [X0 : $i] : (((cA @ X0) != $true) | ((cB @ X0) = $true)) & ((($true = (cA @ sK0)) & ($true != (cB @ sK0))) | (cG = $true) | (cG = $true) | (((cA @ sK1) = $true) & ($true != (cB @ sK1))))),
% 1.65/1.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f8,f10,f9])).
% 1.65/1.31 thf(f9,plain,(
% 1.65/1.31 ? [X1 : $i] : (($true = (cA @ X1)) & ($true != (cB @ X1))) => (($true = (cA @ sK0)) & ($true != (cB @ sK0)))),
% 1.65/1.31 introduced(definition,[],[choice_axiom])).
% 1.65/1.31 thf(f10,plain,(
% 1.65/1.31 ? [X2 : $i] : (($true = (cA @ X2)) & ($true != (cB @ X2))) => (((cA @ sK1) = $true) & ($true != (cB @ sK1)))),
% 1.65/1.31 introduced(definition,[],[choice_axiom])).
% 1.65/1.31 thf(f8,plain,(
% 1.65/1.31 (cG != $true) & ! [X0 : $i] : (((cA @ X0) != $true) | ((cB @ X0) = $true)) & (? [X1 : $i] : (($true = (cA @ X1)) & ($true != (cB @ X1))) | (cG = $true) | (cG = $true) | ? [X2 : $i] : (($true = (cA @ X2)) & ($true != (cB @ X2))))),
% 1.65/1.31 inference(rectify,[status(thm)],[f7])).
% 1.65/1.31 thf(f7,plain,(
% 1.65/1.31 (cG != $true) & ! [X2 : $i] : (($true != (cA @ X2)) | ($true = (cB @ X2))) & (? [X0 : $i] : (((cA @ X0) = $true) & ((cB @ X0) != $true)) | (cG = $true) | (cG = $true) | ? [X1 : $i] : (($true = (cA @ X1)) & ($true != (cB @ X1))))),
% 1.65/1.31 inference(flattening,[status(thm)],[f6])).
% 1.65/1.31 thf(f6,plain,(
% 1.65/1.31 ((cG != $true) & ! [X2 : $i] : (($true != (cA @ X2)) | ($true = (cB @ X2)))) & (((cG = $true) | ? [X0 : $i] : (((cA @ X0) = $true) & ((cB @ X0) != $true))) | ((cG = $true) | ? [X1 : $i] : (($true = (cA @ X1)) & ($true != (cB @ X1)))))),
% 1.65/1.31 inference(ennf_transformation,[status(thm)],[f5])).
% 1.65/1.31 thf(f5,plain,(
% 1.65/1.31 ~(((! [X0 : $i] : (((cA @ X0) = $true) => ((cB @ X0) = $true)) => (cG = $true)) | (! [X1 : $i] : (($true = (cA @ X1)) => ($true = (cB @ X1))) => (cG = $true))) => (! [X2 : $i] : (($true = (cA @ X2)) => ($true = (cB @ X2))) => (cG = $true)))),
% 1.65/1.31 inference(fool_elimination,[status(thm)],[f4])).
% 1.65/1.31 thf(f4,plain,(
% 1.65/1.31 ~(((! [X0 : $i] : ((cA @ X0) => (cB @ X0)) => cG) | (! [X1 : $i] : ((cA @ X1) => (cB @ X1)) => cG)) => (! [X2 : $i] : ((cA @ X2) => (cB @ X2)) => cG))),
% 1.65/1.31 inference(rectify,[status(thm)],[f2])).
% 1.65/1.31 thf(f2,negated_conjecture,(
% 1.65/1.31 ~(((! [X0 : $i] : ((cA @ X0) => (cB @ X0)) => cG) | (! [X0 : $i] : ((cA @ X0) => (cB @ X0)) => cG)) => (! [X0 : $i] : ((cA @ X0) => (cB @ X0)) => cG))),
% 1.65/1.31 inference(negated_conjecture,[status(cth)],[f1])).
% 1.65/1.31 thf(f1,conjecture,(
% 1.65/1.31 ((! [X0 : $i] : ((cA @ X0) => (cB @ X0)) => cG) | (! [X0 : $i] : ((cA @ X0) => (cB @ X0)) => cG)) => (! [X0 : $i] : ((cA @ X0) => (cB @ X0)) => cG)),
% 1.65/1.31 file('/export/starexec/sandbox2/tmp/tmp.73YrD6BFLG/DTF2THF_30624.p',cDUAL_EG2_pme)).
% 1.65/1.31 thf(f38,plain,(
% 1.65/1.31 ($true != (cB @ sK1)) | spl2_4),
% 1.65/1.31 inference(avatar_component_clause,[status(thm)],[f36])).
% 1.65/1.31 thf(f36,definition,(
% 1.65/1.31 spl2_4 <=> ($true = (cB @ sK1))),
% 1.65/1.31 introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition])).
% 1.65/1.31 thf(f51,plain,(
% 1.65/1.31 ~spl2_5 | spl2_1),
% 1.65/1.31 inference(avatar_split_clause,[status(thm)],[f50,f23,f41])).
% 1.65/1.31 thf(f41,definition,(
% 1.65/1.31 spl2_5 <=> ($true = (cA @ sK0))),
% 1.65/1.31 introduced(definition,[new_symbols(naming,[spl2_5])],[avatar_definition])).
% 1.65/1.31 thf(f23,definition,(
% 1.65/1.31 spl2_1 <=> ($true = (cB @ sK0))),
% 1.65/1.31 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.65/1.31 thf(f50,plain,(
% 1.65/1.31 ($true != (cA @ sK0)) | spl2_1),
% 1.65/1.31 inference(trivial_inequality_removal,[status(thm)],[f47])).
% 1.65/1.31 thf(f47,plain,(
% 1.65/1.31 ($true != (cA @ sK0)) | ($true != $true) | spl2_1),
% 1.65/1.31 inference(superposition,[status(thm)],[f25,f16])).
% 1.65/1.31 thf(f25,plain,(
% 1.65/1.31 ($true != (cB @ sK0)) | spl2_1),
% 1.65/1.31 inference(avatar_component_clause,[status(thm)],[f23])).
% 1.65/1.31 thf(f46,plain,(
% 1.65/1.31 ~spl2_3),
% 1.65/1.31 inference(avatar_split_clause,[status(thm)],[f17,f31])).
% 1.65/1.31 thf(f31,definition,(
% 1.65/1.31 spl2_3 <=> (cG = $true)),
% 1.65/1.31 introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition])).
% 1.65/1.31 thf(f17,plain,(
% 1.65/1.31 (cG != $true)),
% 1.65/1.31 inference(cnf_transformation,[status(thm)],[f11])).
% 1.65/1.31 thf(f45,plain,(
% 1.65/1.31 spl2_5 | ~spl2_4 | spl2_3),
% 1.65/1.31 inference(avatar_split_clause,[status(thm)],[f18,f31,f36,f41])).
% 1.65/1.31 thf(f18,plain,(
% 1.65/1.31 ($true = (cA @ sK0)) | (cG = $true) | ($true != (cB @ sK1))),
% 1.65/1.31 inference(duplicate_literal_removal,[status(thm)],[f14])).
% 1.65/1.31 thf(f14,plain,(
% 1.65/1.31 (cG = $true) | (cG = $true) | ($true = (cA @ sK0)) | ($true != (cB @ sK1))),
% 1.65/1.31 inference(cnf_transformation,[status(thm)],[f11])).
% 1.65/1.31 thf(f44,plain,(
% 1.65/1.31 spl2_3 | spl2_5 | spl2_2),
% 1.65/1.31 inference(avatar_split_clause,[status(thm)],[f19,f27,f41,f31])).
% 1.65/1.31 thf(f19,plain,(
% 1.65/1.31 ((cA @ sK1) = $true) | (cG = $true) | ($true = (cA @ sK0))),
% 1.65/1.31 inference(duplicate_literal_removal,[status(thm)],[f15])).
% 1.65/1.31 thf(f15,plain,(
% 1.65/1.31 ($true = (cA @ sK0)) | (cG = $true) | ((cA @ sK1) = $true) | (cG = $true)),
% 1.65/1.31 inference(cnf_transformation,[status(thm)],[f11])).
% 1.65/1.31 thf(f39,plain,(
% 1.65/1.31 ~spl2_4 | ~spl2_1 | spl2_3),
% 1.65/1.31 inference(avatar_split_clause,[status(thm)],[f20,f31,f23,f36])).
% 1.65/1.31 thf(f20,plain,(
% 1.65/1.31 ($true != (cB @ sK1)) | (cG = $true) | ($true != (cB @ sK0))),
% 1.65/1.31 inference(duplicate_literal_removal,[status(thm)],[f12])).
% 1.65/1.31 thf(f12,plain,(
% 1.65/1.31 ($true != (cB @ sK1)) | (cG = $true) | ($true != (cB @ sK0)) | (cG = $true)),
% 1.65/1.31 inference(cnf_transformation,[status(thm)],[f11])).
% 1.65/1.31 thf(f34,plain,(
% 1.65/1.31 ~spl2_1 | spl2_2 | spl2_3),
% 1.65/1.31 inference(avatar_split_clause,[status(thm)],[f21,f31,f27,f23])).
% 1.65/1.31 thf(f21,plain,(
% 1.65/1.31 (cG = $true) | ((cA @ sK1) = $true) | ($true != (cB @ sK0))),
% 1.65/1.31 inference(duplicate_literal_removal,[status(thm)],[f13])).
% 1.65/1.31 thf(f13,plain,(
% 1.65/1.31 ($true != (cB @ sK0)) | (cG = $true) | ((cA @ sK1) = $true) | (cG = $true)),
% 1.65/1.31 inference(cnf_transformation,[status(thm)],[f11])).
% 1.65/1.31 % SZS output end Proof for DTF2THF_30624
% 1.65/1.31 % (30797)------------------------------
% 1.65/1.31 % (30797)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.31 % (30797)Termination reason: Refutation
% 1.65/1.31
% 1.65/1.31 % (30797)Memory used [KB]: 5500
% 1.65/1.31 % (30797)Time elapsed: 0.003 s
% 1.65/1.31 % (30797)Instructions burned: 1 (million)
% 1.65/1.31 % (30797)------------------------------
% 1.65/1.31 % (30797)------------------------------
% 1.65/1.31 % (30796)Success in time 0.012 s
%------------------------------------------------------------------------------