%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYN057^5 : 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 : n029.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 09:50:27 AM UTC 2026
% Result : Theorem 1.49s 1.26s
% Output : Refutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 5
% Syntax : Number of formulae : 39 ( 7 unt; 0 typ; 2 def)
% Number of atoms : 471 ( 130 equ; 0 cnn)
% Maximal formula atoms : 13 ( 12 avg)
% Number of connectives : 424 ( 107 ~; 62 |; 58 &; 163 @)
% ( 2 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 67 ( 0 ^; 49 !; 18 ?; 67 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cI: $i > $o ).
thf(func_def_1,type,
cJ: $i > $o ).
thf(func_def_2,type,
cH: $i > $o ).
thf(func_def_3,type,
cG: $i > $o ).
thf(func_def_4,type,
cF: $i > $o ).
thf(f44,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f26,f37,f43]) ).
thf(f43,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[status(thm)],[f42]) ).
thf(f42,plain,
( $false
| ~ spl2_1 ),
inference(subsumption_resolution,[status(thm)],[f41,f18]) ).
thf(f18,plain,
( ( cF @ sK0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ! [X0: $i] :
( ( ( cH @ X0 )
= $true )
| ( ( cF @ X0 )
!= $true ) )
& ( ( cF @ sK0 )
= $true )
& ( ( cG @ sK0 )
!= $true )
& ! [X2: $i] :
( ( $true
= ( cF @ X2 ) )
| ( $true
!= ( cI @ X2 ) )
| ( ( cJ @ X2 )
!= $true ) )
& ( $true
= ( cI @ sK1 ) )
& ( $true
= ( cJ @ sK1 ) )
& ( ! [X4: $i] :
( ( $true
!= ( cH @ X4 ) )
| ( ( cI @ X4 )
!= $true ) )
| ! [X5: $i] :
( ( ( cH @ X5 )
!= $true )
| ( $true
= ( cG @ X5 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f9,f11,f10]) ).
thf(f10,plain,
( ? [X1: $i] :
( ( $true
= ( cF @ X1 ) )
& ( $true
!= ( cG @ X1 ) ) )
=> ( ( ( cF @ sK0 )
= $true )
& ( ( cG @ sK0 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X3: $i] :
( ( ( cI @ X3 )
= $true )
& ( $true
= ( cJ @ X3 ) ) )
=> ( ( $true
= ( cI @ sK1 ) )
& ( $true
= ( cJ @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ! [X0: $i] :
( ( ( cH @ X0 )
= $true )
| ( ( cF @ X0 )
!= $true ) )
& ? [X1: $i] :
( ( $true
= ( cF @ X1 ) )
& ( $true
!= ( cG @ X1 ) ) )
& ! [X2: $i] :
( ( $true
= ( cF @ X2 ) )
| ( $true
!= ( cI @ X2 ) )
| ( ( cJ @ X2 )
!= $true ) )
& ? [X3: $i] :
( ( ( cI @ X3 )
= $true )
& ( $true
= ( cJ @ X3 ) ) )
& ( ! [X4: $i] :
( ( $true
!= ( cH @ X4 ) )
| ( ( cI @ X4 )
!= $true ) )
| ! [X5: $i] :
( ( ( cH @ X5 )
!= $true )
| ( $true
= ( cG @ X5 ) ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
( ! [X4: $i] :
( ( $true
= ( cH @ X4 ) )
| ( ( cF @ X4 )
!= $true ) )
& ? [X2: $i] :
( ( $true
= ( cF @ X2 ) )
& ( $true
!= ( cG @ X2 ) ) )
& ! [X3: $i] :
( ( $true
= ( cF @ X3 ) )
| ( ( cI @ X3 )
!= $true )
| ( $true
!= ( cJ @ X3 ) ) )
& ? [X5: $i] :
( ( $true
= ( cI @ X5 ) )
& ( ( cJ @ X5 )
= $true ) )
& ( ! [X1: $i] :
( ( $true
!= ( cH @ X1 ) )
| ( ( cI @ X1 )
!= $true ) )
| ! [X0: $i] :
( ( ( cH @ X0 )
!= $true )
| ( ( cG @ X0 )
= $true ) ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
( ? [X5: $i] :
( ( $true
= ( cI @ X5 ) )
& ( ( cJ @ X5 )
= $true ) )
& ! [X4: $i] :
( ( $true
= ( cH @ X4 ) )
| ( ( cF @ X4 )
!= $true ) )
& ! [X3: $i] :
( ( $true
= ( cF @ X3 ) )
| ( $true
!= ( cJ @ X3 ) )
| ( ( cI @ X3 )
!= $true ) )
& ? [X2: $i] :
( ( $true
= ( cF @ X2 ) )
& ( $true
!= ( cG @ X2 ) ) )
& ( ! [X1: $i] :
( ( $true
!= ( cH @ X1 ) )
| ( ( cI @ X1 )
!= $true ) )
| ! [X0: $i] :
( ( ( cH @ X0 )
!= $true )
| ( ( cG @ X0 )
= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ( ! [X4: $i] :
( ( ( cF @ X4 )
= $true )
=> ( $true
= ( cH @ X4 ) ) )
& ! [X3: $i] :
( ( ( $true
= ( cJ @ X3 ) )
& ( ( cI @ X3 )
= $true ) )
=> ( $true
= ( cF @ X3 ) ) )
& ? [X2: $i] :
( ( $true
= ( cF @ X2 ) )
& ( $true
!= ( cG @ X2 ) ) )
& ( ? [X0: $i] :
( ( ( cG @ X0 )
!= $true )
& ( ( cH @ X0 )
= $true ) )
=> ! [X1: $i] :
( ( ( cI @ X1 )
= $true )
=> ( $true
!= ( cH @ X1 ) ) ) ) )
=> ! [X5: $i] :
( ( ( cJ @ X5 )
= $true )
=> ( $true
!= ( cI @ X5 ) ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ( ? [X0: $i] :
( ( ( cG @ X0 )
!= $true )
& ( ( cH @ X0 )
= $true ) )
=> ! [X1: $i] :
( ( ( cI @ X1 )
= $true )
=> ( $true
!= ( cH @ X1 ) ) ) )
& ? [X2: $i] :
( ( $true
!= ( cG @ X2 ) )
& ( $true
= ( cF @ X2 ) ) )
& ! [X3: $i] :
( ( ( $true
= ( cJ @ X3 ) )
& ( ( cI @ X3 )
= $true ) )
=> ( $true
= ( cF @ X3 ) ) )
& ! [X4: $i] :
( ( ( cF @ X4 )
= $true )
=> ( $true
= ( cH @ X4 ) ) ) )
=> ! [X5: $i] :
( ( ( cJ @ X5 )
= $true )
=> ( $true
!= ( cI @ X5 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ( ? [X0: $i] :
( ~ ( cG @ X0 )
& ( cH @ X0 ) )
=> ! [X1: $i] :
( ( cI @ X1 )
=> ~ ( cH @ X1 ) ) )
& ? [X2: $i] :
( ~ ( cG @ X2 )
& ( cF @ X2 ) )
& ! [X3: $i] :
( ( ( cI @ X3 )
& ( cJ @ X3 ) )
=> ( cF @ X3 ) )
& ! [X4: $i] :
( ( cF @ X4 )
=> ( cH @ X4 ) ) )
=> ! [X5: $i] :
( ( cJ @ X5 )
=> ~ ( cI @ X5 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ( ? [X0: $i] :
( ~ ( cG @ X0 )
& ( cH @ X0 ) )
=> ! [X0: $i] :
( ( cI @ X0 )
=> ~ ( cH @ X0 ) ) )
& ? [X0: $i] :
( ~ ( cG @ X0 )
& ( cF @ X0 ) )
& ! [X0: $i] :
( ( ( cI @ X0 )
& ( cJ @ X0 ) )
=> ( cF @ X0 ) )
& ! [X0: $i] :
( ( cF @ X0 )
=> ( cH @ X0 ) ) )
=> ! [X0: $i] :
( ( cJ @ X0 )
=> ~ ( cI @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ( ? [X0: $i] :
( ~ ( cG @ X0 )
& ( cH @ X0 ) )
=> ! [X0: $i] :
( ( cI @ X0 )
=> ~ ( cH @ X0 ) ) )
& ? [X0: $i] :
( ~ ( cG @ X0 )
& ( cF @ X0 ) )
& ! [X0: $i] :
( ( ( cI @ X0 )
& ( cJ @ X0 ) )
=> ( cF @ X0 ) )
& ! [X0: $i] :
( ( cF @ X0 )
=> ( cH @ X0 ) ) )
=> ! [X0: $i] :
( ( cJ @ X0 )
=> ~ ( cI @ X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ccuVYuDgjE/DTF2THF_9683.p',cPELL27) ).
thf(f41,plain,
( ( ( cF @ sK0 )
!= $true )
| ~ spl2_1 ),
inference(trivial_inequality_removal,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ( cF @ sK0 )
!= $true )
| ( $true != $true )
| ~ spl2_1 ),
inference(superposition,[status(thm)],[f39,f19]) ).
thf(f19,plain,
! [X0: $i] :
( ( ( cH @ X0 )
= $true )
| ( ( cF @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f39,plain,
( ( $true
!= ( cH @ sK0 ) )
| ~ spl2_1 ),
inference(trivial_inequality_removal,[status(thm)],[f38]) ).
thf(f38,plain,
( ( $true
!= ( cH @ sK0 ) )
| ( $true != $true )
| ~ spl2_1 ),
inference(superposition,[status(thm)],[f17,f22]) ).
thf(f22,plain,
( ! [X5: $i] :
( ( $true
= ( cG @ X5 ) )
| ( ( cH @ X5 )
!= $true ) )
| ~ spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f21]) ).
thf(f21,definition,
( spl2_1
<=> ! [X5: $i] :
( ( ( cH @ X5 )
!= $true )
| ( $true
= ( cG @ X5 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f17,plain,
( ( cG @ sK0 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f37,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[status(thm)],[f36]) ).
thf(f36,plain,
( $false
| ~ spl2_2 ),
inference(subsumption_resolution,[status(thm)],[f35,f15]) ).
thf(f15,plain,
( $true
= ( cI @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f35,plain,
( ( $true
!= ( cI @ sK1 ) )
| ~ spl2_2 ),
inference(trivial_inequality_removal,[status(thm)],[f34]) ).
thf(f34,plain,
( ( $true != $true )
| ( $true
!= ( cI @ sK1 ) )
| ~ spl2_2 ),
inference(superposition,[status(thm)],[f33,f14]) ).
thf(f14,plain,
( $true
= ( cJ @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f33,plain,
( ! [X0: $i] :
( ( ( cJ @ X0 )
!= $true )
| ( ( cI @ X0 )
!= $true ) )
| ~ spl2_2 ),
inference(trivial_inequality_removal,[status(thm)],[f32]) ).
thf(f32,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( ( cI @ X0 )
!= $true )
| ( ( cJ @ X0 )
!= $true ) )
| ~ spl2_2 ),
inference(duplicate_literal_removal,[status(thm)],[f31]) ).
thf(f31,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( ( cI @ X0 )
!= $true )
| ( ( cJ @ X0 )
!= $true )
| ( ( cI @ X0 )
!= $true ) )
| ~ spl2_2 ),
inference(superposition,[status(thm)],[f28,f16]) ).
thf(f16,plain,
! [X2: $i] :
( ( $true
= ( cF @ X2 ) )
| ( $true
!= ( cI @ X2 ) )
| ( ( cJ @ X2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f28,plain,
( ! [X0: $i] :
( ( ( cF @ X0 )
!= $true )
| ( ( cI @ X0 )
!= $true ) )
| ~ spl2_2 ),
inference(trivial_inequality_removal,[status(thm)],[f27]) ).
thf(f27,plain,
( ! [X0: $i] :
( ( ( cI @ X0 )
!= $true )
| ( ( cF @ X0 )
!= $true )
| ( $true != $true ) )
| ~ spl2_2 ),
inference(superposition,[status(thm)],[f25,f19]) ).
thf(f25,plain,
( ! [X4: $i] :
( ( $true
!= ( cH @ X4 ) )
| ( ( cI @ X4 )
!= $true ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f24]) ).
thf(f24,definition,
( spl2_2
<=> ! [X4: $i] :
( ( ( cI @ X4 )
!= $true )
| ( $true
!= ( cH @ X4 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f26,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f13,f24,f21]) ).
thf(f13,plain,
! [X4: $i,X5: $i] :
( ( ( cH @ X5 )
!= $true )
| ( ( cI @ X4 )
!= $true )
| ( $true
!= ( cH @ X4 ) )
| ( $true
= ( cG @ X5 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN057^5 : 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 : n029.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 13:50:44 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
% 0.26/0.46 ---- Original DTF file ---
% 0.26/0.46 thf(spec,logic,$$dhol).
% 0.26/0.46 %------------------------------------------------------------------------------
% 0.26/0.46 % File : SYN057^5 : TPTP v9.2.1. Released v4.0.0.
% 0.26/0.46 % Domain : Syntactic
% 0.26/0.46 % Problem : TPS problem PELL27
% 0.26/0.46 % Version : Especial.
% 0.26/0.46 % English :
% 0.26/0.46
% 0.26/0.46 % Refs : [Pel86] Pelletier (1986), Seventy-five Problems for Testing Au
% 0.26/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.26/0.46 % Source : [Bro09]
% 0.26/0.46 % Names : tps_0332 [Bro09]
% 0.26/0.46 % : PELL27 [TPS]
% 0.26/0.46 % : Pelletier 27 [Pel86]
% 0.26/0.46
% 0.26/0.46 % Status : Theorem
% 0.26/0.46 % Rating : 0.00 v6.2.0, 0.17 v6.0.0, 0.00 v4.0.0
% 0.26/0.46 % Syntax : Number of formulae : 6 ( 0 unt; 5 typ; 0 def)
% 0.26/0.46 % Number of atoms : 13 ( 0 equ; 0 cnn)
% 0.26/0.46 % Maximal formula atoms : 13 ( 13 avg)
% 0.26/0.46 % Number of connectives : 29 ( 4 ~; 0 |; 6 &; 13 @)
% 0.26/0.46 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 0.26/0.46 % Maximal formula depth : 10 ( 10 avg)
% 0.26/0.46 % Number of types : 2 ( 0 usr)
% 0.26/0.46 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.26/0.46 % Number of symbols : 5 ( 5 usr; 0 con; 1-1 aty)
% 0.26/0.46 % Number of variables : 6 ( 0 ^; 4 !; 2 ?; 6 :)
% 0.26/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.26/0.46
% 0.26/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.26/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.26/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.26/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.26/0.46 % :
% 0.26/0.46 %------------------------------------------------------------------------------
% 0.26/0.46 thf(cI,type,
% 0.26/0.46 cI: $i > $o ).
% 0.26/0.46
% 0.26/0.46 thf(cJ,type,
% 0.26/0.46 cJ: $i > $o ).
% 0.26/0.46
% 0.26/0.46 thf(cH,type,
% 0.26/0.46 cH: $i > $o ).
% 0.26/0.46
% 0.26/0.46 thf(cG,type,
% 0.26/0.46 cG: $i > $o ).
% 0.26/0.46
% 0.26/0.46 thf(cF,type,
% 0.26/0.46 cF: $i > $o ).
% 0.26/0.46
% 0.26/0.46 thf(cPELL27,conjecture,
% 0.26/0.46 ( ( ? [Xx: $i] :
% 0.26/0.46 ( ( cF @ Xx )
% 0.26/0.46 & ~ ( cG @ Xx ) )
% 0.26/0.46 & ! [Xx: $i] :
% 0.26/0.46 ( ( cF @ Xx )
% 0.26/0.46 => ( cH @ Xx ) )
% 0.26/0.46 & ! [Xx: $i] :
% 0.26/0.46 ( ( ( cJ @ Xx )
% 0.26/0.46 & ( cI @ Xx ) )
% 0.26/0.46 => ( cF @ Xx ) )
% 0.26/0.46 & ( ? [Xx: $i] :
% 0.26/0.46 ( ( cH @ Xx )
% 0.26/0.46 & ~ ( cG @ Xx ) )
% 0.26/0.46 => ! [Xx: $i] :
% 0.26/0.46 ( ( cI @ Xx )
% 0.26/0.46 => ~ ( cH @ Xx ) ) ) )
% 0.26/0.46 => ! [Xx: $i] :
% 0.26/0.46 ( ( cJ @ Xx )
% 0.26/0.46 => ~ ( cI @ Xx ) ) ) ).
% 0.26/0.46
% 0.26/0.46 %------------------------------------------------------------------------------
% 0.26/0.46 ------------------------
% 1.49/1.23 ---- Embedded in THF ---
% 1.49/1.23 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.23 %%% Generated on Tue Feb 24 13:50:45 EST 2026
% 1.49/1.23 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.23 %%% Logic specification used:
% 1.49/1.23 %%% thf(spec, logic, $$dhol).
% 1.49/1.23
% 1.49/1.23 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.ccuVYuDgjE/DTF2DTF9683.p
% See solution above
% 1.49/1.23 ------------------------
% 1.49/1.24 ---- Cleaned THF ---
% 1.49/1.24 thf(cI,type,
% 1.49/1.24 cI: $i > $o ).
% 1.49/1.24
% 1.49/1.24 thf(cJ,type,
% 1.49/1.24 cJ: $i > $o ).
% 1.49/1.24
% 1.49/1.24 thf(cH,type,
% 1.49/1.24 cH: $i > $o ).
% 1.49/1.24
% 1.49/1.24 thf(cG,type,
% 1.49/1.24 cG: $i > $o ).
% 1.49/1.24
% 1.49/1.24 thf(cF,type,
% 1.49/1.24 cF: $i > $o ).
% 1.49/1.24
% 1.49/1.24 thf(cPELL27,conjecture,
% 1.49/1.24 ( ( ? [Xx: $i] :
% 1.49/1.24 ( ( cF @ Xx )
% 1.49/1.24 & ~ ( cG @ Xx ) )
% 1.49/1.24 & ! [Xx: $i] :
% 1.49/1.24 ( ( cF @ Xx )
% 1.49/1.24 => ( cH @ Xx ) )
% 1.49/1.24 & ! [Xx: $i] :
% 1.49/1.24 ( ( ( cJ @ Xx )
% 1.49/1.24 & ( cI @ Xx ) )
% 1.49/1.24 => ( cF @ Xx ) )
% 1.49/1.24 & ( ? [Xx: $i] :
% 1.49/1.24 ( ( cH @ Xx )
% 1.49/1.24 & ~ ( cG @ Xx ) )
% 1.49/1.24 => ! [Xx: $i] :
% 1.49/1.24 ( ( cI @ Xx )
% 1.49/1.24 => ~ ( cH @ Xx ) ) ) )
% 1.49/1.24 => ! [Xx: $i] :
% 1.49/1.24 ( ( cJ @ Xx )
% 1.49/1.24 => ~ ( cI @ Xx ) ) ) ).
% 1.49/1.24 ------------------------
% 1.49/1.26 % (9790)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_9683 for (2999ds/183Mi)
% 1.49/1.26 % (9792)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_9683 for (2999ds/27Mi)
% 1.49/1.26 % (9790)First to succeed.
% 1.49/1.26 % (9792)Also succeeded, but the first one will report.
% 1.49/1.26 % (9790)Refutation found. Thanks to Tanya!
% 1.49/1.26 % SZS status Theorem for DTF2THF_9683
% 1.49/1.26 % SZS output start Proof for DTF2THF_9683
% 1.49/1.26 thf(func_def_0, type, cI: $i > $o).
% 1.49/1.26 thf(func_def_1, type, cJ: $i > $o).
% 1.49/1.26 thf(func_def_2, type, cH: $i > $o).
% 1.49/1.26 thf(func_def_3, type, cG: $i > $o).
% 1.49/1.26 thf(func_def_4, type, cF: $i > $o).
% 1.49/1.26 thf(f44,plain,(
% 1.49/1.26 $false),
% 1.49/1.26 inference(avatar_sat_refutation,[status(thm)],[f26,f37,f43])).
% 1.49/1.26 thf(f43,plain,(
% 1.49/1.26 ~spl2_1),
% 1.49/1.26 inference(avatar_contradiction_clause,[status(thm)],[f42])).
% 1.49/1.26 thf(f42,plain,(
% 1.49/1.26 $false | ~spl2_1),
% 1.49/1.26 inference(subsumption_resolution,[status(thm)],[f41,f18])).
% 1.49/1.26 thf(f18,plain,(
% 1.49/1.26 ((cF @ sK0) = $true)),
% 1.49/1.26 inference(cnf_transformation,[status(thm)],[f12])).
% 1.49/1.26 thf(f12,plain,(
% 1.49/1.26 ! [X0 : $i] : (((cH @ X0) = $true) | ((cF @ X0) != $true)) & (((cF @ sK0) = $true) & ((cG @ sK0) != $true)) & ! [X2 : $i] : (($true = (cF @ X2)) | ($true != (cI @ X2)) | ((cJ @ X2) != $true)) & (($true = (cI @ sK1)) & ($true = (cJ @ sK1))) & (! [X4 : $i] : (($true != (cH @ X4)) | ((cI @ X4) != $true)) | ! [X5 : $i] : (((cH @ X5) != $true) | ($true = (cG @ X5))))),
% 1.49/1.26 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f9,f11,f10])).
% 1.49/1.26 thf(f10,plain,(
% 1.49/1.26 ? [X1 : $i] : (($true = (cF @ X1)) & ($true != (cG @ X1))) => (((cF @ sK0) = $true) & ((cG @ sK0) != $true))),
% 1.49/1.26 introduced(definition,[],[choice_axiom])).
% 1.49/1.26 thf(f11,plain,(
% 1.49/1.26 ? [X3 : $i] : (((cI @ X3) = $true) & ($true = (cJ @ X3))) => (($true = (cI @ sK1)) & ($true = (cJ @ sK1)))),
% 1.49/1.26 introduced(definition,[],[choice_axiom])).
% 1.49/1.26 thf(f9,plain,(
% 1.49/1.26 ! [X0 : $i] : (((cH @ X0) = $true) | ((cF @ X0) != $true)) & ? [X1 : $i] : (($true = (cF @ X1)) & ($true != (cG @ X1))) & ! [X2 : $i] : (($true = (cF @ X2)) | ($true != (cI @ X2)) | ((cJ @ X2) != $true)) & ? [X3 : $i] : (((cI @ X3) = $true) & ($true = (cJ @ X3))) & (! [X4 : $i] : (($true != (cH @ X4)) | ((cI @ X4) != $true)) | ! [X5 : $i] : (((cH @ X5) != $true) | ($true = (cG @ X5))))),
% 1.49/1.26 inference(rectify,[status(thm)],[f8])).
% 1.49/1.26 thf(f8,plain,(
% 1.49/1.26 ! [X4 : $i] : (($true = (cH @ X4)) | ((cF @ X4) != $true)) & ? [X2 : $i] : (($true = (cF @ X2)) & ($true != (cG @ X2))) & ! [X3 : $i] : (($true = (cF @ X3)) | ((cI @ X3) != $true) | ($true != (cJ @ X3))) & ? [X5 : $i] : (($true = (cI @ X5)) & ((cJ @ X5) = $true)) & (! [X1 : $i] : (($true != (cH @ X1)) | ((cI @ X1) != $true)) | ! [X0 : $i] : (((cH @ X0) != $true) | ((cG @ X0) = $true)))),
% 1.49/1.26 inference(flattening,[status(thm)],[f7])).
% 1.49/1.26 thf(f7,plain,(
% 1.49/1.26 ? [X5 : $i] : (($true = (cI @ X5)) & ((cJ @ X5) = $true)) & (! [X4 : $i] : (($true = (cH @ X4)) | ((cF @ X4) != $true)) & ! [X3 : $i] : (($true = (cF @ X3)) | (($true != (cJ @ X3)) | ((cI @ X3) != $true))) & ? [X2 : $i] : (($true = (cF @ X2)) & ($true != (cG @ X2))) & (! [X1 : $i] : (($true != (cH @ X1)) | ((cI @ X1) != $true)) | ! [X0 : $i] : (((cH @ X0) != $true) | ((cG @ X0) = $true))))),
% 1.49/1.26 inference(ennf_transformation,[status(thm)],[f6])).
% 1.49/1.26 thf(f6,plain,(
% 1.49/1.26 ~((! [X4 : $i] : (((cF @ X4) = $true) => ($true = (cH @ X4))) & ! [X3 : $i] : ((($true = (cJ @ X3)) & ((cI @ X3) = $true)) => ($true = (cF @ X3))) & ? [X2 : $i] : (($true = (cF @ X2)) & ($true != (cG @ X2))) & (? [X0 : $i] : (((cG @ X0) != $true) & ((cH @ X0) = $true)) => ! [X1 : $i] : (((cI @ X1) = $true) => ($true != (cH @ X1))))) => ! [X5 : $i] : (((cJ @ X5) = $true) => ($true != (cI @ X5))))),
% 1.49/1.26 inference(flattening,[status(thm)],[f5])).
% 1.49/1.26 thf(f5,plain,(
% 1.49/1.26 ~(((? [X0 : $i] : (~((cG @ X0) = $true) & ((cH @ X0) = $true)) => ! [X1 : $i] : (((cI @ X1) = $true) => ~($true = (cH @ X1)))) & ? [X2 : $i] : (~($true = (cG @ X2)) & ($true = (cF @ X2))) & ! [X3 : $i] : ((($true = (cJ @ X3)) & ((cI @ X3) = $true)) => ($true = (cF @ X3))) & ! [X4 : $i] : (((cF @ X4) = $true) => ($true = (cH @ X4)))) => ! [X5 : $i] : (((cJ @ X5) = $true) => ~($true = (cI @ X5))))),
% 1.49/1.26 inference(fool_elimination,[status(thm)],[f4])).
% 1.49/1.26 thf(f4,plain,(
% 1.49/1.26 ~(((? [X0 : $i] : (~(cG @ X0) & (cH @ X0)) => ! [X1 : $i] : ((cI @ X1) => ~(cH @ X1))) & ? [X2 : $i] : (~(cG @ X2) & (cF @ X2)) & ! [X3 : $i] : (((cI @ X3) & (cJ @ X3)) => (cF @ X3)) & ! [X4 : $i] : ((cF @ X4) => (cH @ X4))) => ! [X5 : $i] : ((cJ @ X5) => ~(cI @ X5)))),
% 1.49/1.26 inference(rectify,[status(thm)],[f2])).
% 1.49/1.26 thf(f2,negated_conjecture,(
% 1.49/1.26 ~(((? [X0 : $i] : (~(cG @ X0) & (cH @ X0)) => ! [X0 : $i] : ((cI @ X0) => ~(cH @ X0))) & ? [X0 : $i] : (~(cG @ X0) & (cF @ X0)) & ! [X0 : $i] : (((cI @ X0) & (cJ @ X0)) => (cF @ X0)) & ! [X0 : $i] : ((cF @ X0) => (cH @ X0))) => ! [X0 : $i] : ((cJ @ X0) => ~(cI @ X0)))),
% 1.49/1.26 inference(negated_conjecture,[status(cth)],[f1])).
% 1.49/1.26 thf(f1,conjecture,(
% 1.49/1.26 ((? [X0 : $i] : (~(cG @ X0) & (cH @ X0)) => ! [X0 : $i] : ((cI @ X0) => ~(cH @ X0))) & ? [X0 : $i] : (~(cG @ X0) & (cF @ X0)) & ! [X0 : $i] : (((cI @ X0) & (cJ @ X0)) => (cF @ X0)) & ! [X0 : $i] : ((cF @ X0) => (cH @ X0))) => ! [X0 : $i] : ((cJ @ X0) => ~(cI @ X0))),
% 1.49/1.26 file('/export/starexec/sandbox/tmp/tmp.ccuVYuDgjE/DTF2THF_9683.p',cPELL27)).
% 1.49/1.26 thf(f41,plain,(
% 1.49/1.26 ((cF @ sK0) != $true) | ~spl2_1),
% 1.49/1.26 inference(trivial_inequality_removal,[status(thm)],[f40])).
% 1.49/1.26 thf(f40,plain,(
% 1.49/1.26 ((cF @ sK0) != $true) | ($true != $true) | ~spl2_1),
% 1.49/1.26 inference(superposition,[status(thm)],[f39,f19])).
% 1.49/1.26 thf(f19,plain,(
% 1.49/1.26 ( ! [X0 : $i] : (((cH @ X0) = $true) | ((cF @ X0) != $true)) )),
% 1.49/1.26 inference(cnf_transformation,[status(thm)],[f12])).
% 1.49/1.26 thf(f39,plain,(
% 1.49/1.26 ($true != (cH @ sK0)) | ~spl2_1),
% 1.49/1.26 inference(trivial_inequality_removal,[status(thm)],[f38])).
% 1.49/1.26 thf(f38,plain,(
% 1.49/1.26 ($true != (cH @ sK0)) | ($true != $true) | ~spl2_1),
% 1.49/1.26 inference(superposition,[status(thm)],[f17,f22])).
% 1.49/1.26 thf(f22,plain,(
% 1.49/1.26 ( ! [X5 : $i] : (($true = (cG @ X5)) | ((cH @ X5) != $true)) ) | ~spl2_1),
% 1.49/1.26 inference(avatar_component_clause,[status(thm)],[f21])).
% 1.49/1.26 thf(f21,definition,(
% 1.49/1.26 spl2_1 <=> ! [X5 : $i] : (((cH @ X5) != $true) | ($true = (cG @ X5)))),
% 1.49/1.26 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.49/1.26 thf(f17,plain,(
% 1.49/1.26 ((cG @ sK0) != $true)),
% 1.49/1.26 inference(cnf_transformation,[status(thm)],[f12])).
% 1.49/1.26 thf(f37,plain,(
% 1.49/1.26 ~spl2_2),
% 1.49/1.26 inference(avatar_contradiction_clause,[status(thm)],[f36])).
% 1.49/1.26 thf(f36,plain,(
% 1.49/1.26 $false | ~spl2_2),
% 1.49/1.26 inference(subsumption_resolution,[status(thm)],[f35,f15])).
% 1.49/1.26 thf(f15,plain,(
% 1.49/1.26 ($true = (cI @ sK1))),
% 1.49/1.26 inference(cnf_transformation,[status(thm)],[f12])).
% 1.49/1.26 thf(f35,plain,(
% 1.49/1.26 ($true != (cI @ sK1)) | ~spl2_2),
% 1.49/1.26 inference(trivial_inequality_removal,[status(thm)],[f34])).
% 1.49/1.26 thf(f34,plain,(
% 1.49/1.26 ($true != $true) | ($true != (cI @ sK1)) | ~spl2_2),
% 1.49/1.26 inference(superposition,[status(thm)],[f33,f14])).
% 1.49/1.26 thf(f14,plain,(
% 1.49/1.26 ($true = (cJ @ sK1))),
% 1.49/1.26 inference(cnf_transformation,[status(thm)],[f12])).
% 1.49/1.26 thf(f33,plain,(
% 1.49/1.26 ( ! [X0 : $i] : (((cJ @ X0) != $true) | ((cI @ X0) != $true)) ) | ~spl2_2),
% 1.49/1.26 inference(trivial_inequality_removal,[status(thm)],[f32])).
% 1.49/1.26 thf(f32,plain,(
% 1.49/1.26 ( ! [X0 : $i] : (($true != $true) | ((cI @ X0) != $true) | ((cJ @ X0) != $true)) ) | ~spl2_2),
% 1.49/1.26 inference(duplicate_literal_removal,[status(thm)],[f31])).
% 1.49/1.26 thf(f31,plain,(
% 1.49/1.26 ( ! [X0 : $i] : (($true != $true) | ((cI @ X0) != $true) | ((cJ @ X0) != $true) | ((cI @ X0) != $true)) ) | ~spl2_2),
% 1.49/1.26 inference(superposition,[status(thm)],[f28,f16])).
% 1.49/1.26 thf(f16,plain,(
% 1.49/1.26 ( ! [X2 : $i] : (($true = (cF @ X2)) | ($true != (cI @ X2)) | ((cJ @ X2) != $true)) )),
% 1.49/1.26 inference(cnf_transformation,[status(thm)],[f12])).
% 1.49/1.26 thf(f28,plain,(
% 1.49/1.26 ( ! [X0 : $i] : (((cF @ X0) != $true) | ((cI @ X0) != $true)) ) | ~spl2_2),
% 1.49/1.26 inference(trivial_inequality_removal,[status(thm)],[f27])).
% 1.49/1.26 thf(f27,plain,(
% 1.49/1.26 ( ! [X0 : $i] : (((cI @ X0) != $true) | ((cF @ X0) != $true) | ($true != $true)) ) | ~spl2_2),
% 1.49/1.26 inference(superposition,[status(thm)],[f25,f19])).
% 1.49/1.26 thf(f25,plain,(
% 1.49/1.26 ( ! [X4 : $i] : (($true != (cH @ X4)) | ((cI @ X4) != $true)) ) | ~spl2_2),
% 1.49/1.26 inference(avatar_component_clause,[status(thm)],[f24])).
% 1.49/1.26 thf(f24,definition,(
% 1.49/1.26 spl2_2 <=> ! [X4 : $i] : (((cI @ X4) != $true) | ($true != (cH @ X4)))),
% 1.49/1.26 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.49/1.26 thf(f26,plain,(
% 1.49/1.26 spl2_1 | spl2_2),
% 1.49/1.26 inference(avatar_split_clause,[status(thm)],[f13,f24,f21])).
% 1.49/1.26 thf(f13,plain,(
% 1.49/1.26 ( ! [X4 : $i,X5 : $i] : (((cH @ X5) != $true) | ((cI @ X4) != $true) | ($true != (cH @ X4)) | ($true = (cG @ X5))) )),
% 1.49/1.26 inference(cnf_transformation,[status(thm)],[f12])).
% 1.49/1.26 % SZS output end Proof for DTF2THF_9683
% 1.49/1.26 % (9790)------------------------------
% 1.49/1.26 % (9790)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.26 % (9790)Termination reason: Refutation
% 1.49/1.26
% 1.49/1.26 % (9790)Memory used [KB]: 5500
% 1.49/1.26 % (9790)Time elapsed: 0.003 s
% 1.49/1.26 % (9790)Instructions burned: 4 (million)
% 1.49/1.26 % (9790)------------------------------
% 1.49/1.26 % (9790)------------------------------
% 1.49/1.26 % (9789)Success in time 0.003 s
%------------------------------------------------------------------------------