%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV065^5 : 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 : n014.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 09:40:12 AM UTC 2026
% Result : Theorem 0.22s 1.15s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of formulae : 56 ( 10 unt; 0 typ; 4 def)
% Number of atoms : 311 ( 164 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 313 ( 56 ~; 68 |; 60 &; 120 @)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 10 con; 0-2 aty)
% Number of variables : 40 ( 22 ^; 12 !; 6 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
b: $tType ).
thf(type_def_6,type,
a: $tType ).
thf(func_def_0,type,
b: $tType ).
thf(func_def_1,type,
a: $tType ).
thf(func_def_12,type,
sK0: b ).
thf(func_def_13,type,
sK1: b > a > $o ).
thf(func_def_14,type,
sK2: a ).
thf(func_def_16,type,
ph4:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
sK5: b ).
thf(func_def_18,type,
sK6: a ).
thf(f83,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f53,f58,f63,f64,f65,f71,f82]) ).
thf(f82,plain,
( ~ spl3_1
| spl3_2
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f81]) ).
thf(f81,plain,
( $false
| ~ spl3_1
| spl3_2
| ~ spl3_3 ),
inference(subsumption_resolution,[status(thm)],[f79,f9]) ).
thf(f9,plain,
( $true
= ( sK1 @ sK0 @ sK2 ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ( ^ [Y0: b,Y1: a] :
( ( ( sK1 @ Y0 @ Y1 )
& ~ ( ( sK2 = Y1 )
& ( sK0 = Y0 ) ) )
| ( ( sK0 = Y0 )
& ( sK2 = Y1 ) ) ) )
!= sK1 )
& ( $true
= ( sK1 @ sK0 @ sK2 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f6,f7]) ).
thf(f7,plain,
( ? [X0: b,X1: b > a > $o,X2: a] :
( ( ( ^ [Y0: b,Y1: a] :
( ( ( X1 @ Y0 @ Y1 )
& ~ ( ( X2 = Y1 )
& ( X0 = Y0 ) ) )
| ( ( X0 = Y0 )
& ( X2 = Y1 ) ) ) )
!= X1 )
& ( ( X1 @ X0 @ X2 )
= $true ) )
=> ( ( ( ^ [Y0: b,Y1: a] :
( ( ( sK1 @ Y0 @ Y1 )
& ~ ( ( sK2 = Y1 )
& ( sK0 = Y0 ) ) )
| ( ( sK0 = Y0 )
& ( sK2 = Y1 ) ) ) )
!= sK1 )
& ( $true
= ( sK1 @ sK0 @ sK2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
? [X0: b,X1: b > a > $o,X2: a] :
( ( ( ^ [Y0: b,Y1: a] :
( ( ( X1 @ Y0 @ Y1 )
& ~ ( ( X2 = Y1 )
& ( X0 = Y0 ) ) )
| ( ( X0 = Y0 )
& ( X2 = Y1 ) ) ) )
!= X1 )
& ( ( X1 @ X0 @ X2 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: b,X1: b > a > $o,X2: a] :
( ( ( X1 @ X0 @ X2 )
= $true )
=> ( ( ^ [Y0: b,Y1: a] :
( ( ( X1 @ Y0 @ Y1 )
& ~ ( ( X2 = Y1 )
& ( X0 = Y0 ) ) )
| ( ( X0 = Y0 )
& ( X2 = Y1 ) ) ) )
= X1 ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: b,X1: b > a > $o,X2: a] :
( ( X1 @ X0 @ X2 )
=> ( ( ^ [X3: b,X4: a] :
( ( ( X2 = X4 )
& ( X0 = X3 ) )
| ( ~ ( ( X0 = X3 )
& ( X2 = X4 ) )
& ( X1 @ X3 @ X4 ) ) ) )
= X1 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: b,X2: b > a > $o,X1: a] :
( ( X2 @ X0 @ X1 )
=> ( ( ^ [X3: b,X4: a] :
( ( ( X1 = X4 )
& ( X0 = X3 ) )
| ( ~ ( ( X0 = X3 )
& ( X1 = X4 ) )
& ( X2 @ X3 @ X4 ) ) ) )
= X2 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: b,X2: b > a > $o,X1: a] :
( ( X2 @ X0 @ X1 )
=> ( ( ^ [X3: b,X4: a] :
( ( ( X1 = X4 )
& ( X0 = X3 ) )
| ( ~ ( ( X0 = X3 )
& ( X1 = X4 ) )
& ( X2 @ X3 @ X4 ) ) ) )
= X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.jrBxDCT3lx/DTF2THF_30943.p',cTHM177_pme) ).
thf(f79,plain,
( ( $true
!= ( sK1 @ sK0 @ sK2 ) )
| ~ spl3_1
| spl3_2
| ~ spl3_3 ),
inference(superposition,[status(thm)],[f74,f57]) ).
thf(f57,plain,
( ( sK0 = sK5 )
| ~ spl3_3 ),
inference(avatar_component_clause,[status(thm)],[f55]) ).
thf(f55,definition,
( spl3_3
<=> ( sK0 = sK5 ) ),
introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition]) ).
thf(f74,plain,
( ( ( sK1 @ sK5 @ sK2 )
!= $true )
| ~ spl3_1
| spl3_2 ),
inference(superposition,[status(thm)],[f51,f48]) ).
thf(f48,plain,
( ( sK2 = sK6 )
| ~ spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f46]) ).
thf(f46,definition,
( spl3_1
<=> ( sK2 = sK6 ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f51,plain,
( ( ( sK1 @ sK5 @ sK6 )
!= $true )
| spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f50]) ).
thf(f50,definition,
( spl3_2
<=> ( ( sK1 @ sK5 @ sK6 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f71,plain,
( ~ spl3_2
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f70]) ).
thf(f70,plain,
( $false
| ~ spl3_2
| ~ spl3_4 ),
inference(trivial_inequality_removal,[status(thm)],[f66]) ).
thf(f66,plain,
( ( $true = $false )
| ~ spl3_2
| ~ spl3_4 ),
inference(superposition,[status(thm)],[f52,f62]) ).
thf(f62,plain,
( ( ( sK1 @ sK5 @ sK6 )
= $false )
| ~ spl3_4 ),
inference(avatar_component_clause,[status(thm)],[f60]) ).
thf(f60,definition,
( spl3_4
<=> ( ( sK1 @ sK5 @ sK6 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition]) ).
thf(f52,plain,
( ( ( sK1 @ sK5 @ sK6 )
= $true )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f50]) ).
thf(f65,plain,
( spl3_1
| spl3_4 ),
inference(avatar_split_clause,[status(thm)],[f24,f60,f46]) ).
thf(f24,plain,
( ( sK2 = sK6 )
| ( ( sK1 @ sK5 @ sK6 )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ( sK2 = sK6 )
= $true )
| ( ( sK1 @ sK5 @ sK6 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( ( $true
= ( ( sK2 = sK6 )
& ( sK0 = sK5 ) ) )
| ( ( sK1 @ sK5 @ sK6 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ( sK1 @ sK5 @ sK6 )
= $false )
| ( $false
= ( ~ ( ( sK2 = sK6 )
& ( sK0 = sK5 ) ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ( sK1 @ sK5 @ sK6 )
= $false )
| ( ( sK1 @ sK5 @ sK6 )
= $false )
| ( $false
= ( ~ ( ( sK2 = sK6 )
& ( sK0 = sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ( sK1 @ sK5 @ sK6 )
= $false )
| ( ( ( sK1 @ sK5 @ sK6 )
& ~ ( ( sK2 = sK6 )
& ( sK0 = sK5 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
( ( $false
= ( ( ( sK1 @ sK5 @ sK6 )
& ~ ( ( sK2 = sK6 )
& ( sK0 = sK5 ) ) )
| ( ( sK0 = sK5 )
& ( sK2 = sK6 ) ) ) )
| ( ( sK1 @ sK5 @ sK6 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
( ( sK1 @ sK5 @ sK6 )
!= ( ( ( sK1 @ sK5 @ sK6 )
& ~ ( ( sK2 = sK6 )
& ( sK0 = sK5 ) ) )
| ( ( sK0 = sK5 )
& ( sK2 = sK6 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f13]) ).
thf(f13,plain,
( ( sK1 @ sK5 @ sK6 )
!= ( ^ [Y0: a] :
( ( ( sK1 @ sK5 @ Y0 )
& ~ ( ( sK2 = Y0 )
& ( sK0 = sK5 ) ) )
| ( ( sK0 = sK5 )
& ( sK2 = Y0 ) ) )
@ sK6 ) ),
inference(negative_extensionality,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ^ [Y0: a] :
( ( ( sK1 @ sK5 @ Y0 )
& ~ ( ( sK2 = Y0 )
& ( sK0 = sK5 ) ) )
| ( ( sK0 = sK5 )
& ( sK2 = Y0 ) ) ) )
!= ( sK1 @ sK5 ) ),
inference(beta_eta_normalization,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ^ [Y0: b,Y1: a] :
( ( ( sK1 @ Y0 @ Y1 )
& ~ ( ( sK2 = Y1 )
& ( sK0 = Y0 ) ) )
| ( ( sK0 = Y0 )
& ( sK2 = Y1 ) ) )
@ sK5 )
!= ( sK1 @ sK5 ) ),
inference(negative_extensionality,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: b,Y1: a] :
( ( ( sK1 @ Y0 @ Y1 )
& ~ ( ( sK2 = Y1 )
& ( sK0 = Y0 ) ) )
| ( ( sK0 = Y0 )
& ( sK2 = Y1 ) ) ) )
!= sK1 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f64,plain,
( spl3_3
| spl3_4 ),
inference(avatar_split_clause,[status(thm)],[f25,f60,f55]) ).
thf(f25,plain,
( ( ( sK1 @ sK5 @ sK6 )
= $false )
| ( sK0 = sK5 ) ),
inference(equality_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
( ( $true
= ( sK0 = sK5 ) )
| ( ( sK1 @ sK5 @ sK6 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f63,plain,
( ~ spl3_3
| spl3_4
| ~ spl3_1 ),
inference(avatar_split_clause,[status(thm)],[f28,f46,f60,f55]) ).
thf(f28,plain,
( ( sK2 != sK6 )
| ( sK0 != sK5 )
| ( ( sK1 @ sK5 @ sK6 )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ( sK1 @ sK5 @ sK6 )
= $false )
| ( $false
= ( sK0 = sK5 ) )
| ( sK2 != sK6 ) ),
inference(equality_proxy_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ( sK1 @ sK5 @ sK6 )
= $false )
| ( ( sK2 = sK6 )
= $false )
| ( $false
= ( sK0 = sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( ( $false
= ( ( sK0 = sK5 )
& ( sK2 = sK6 ) ) )
| ( ( sK1 @ sK5 @ sK6 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f58,plain,
( spl3_3
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f35,f50,f55]) ).
thf(f35,plain,
( ( ( sK1 @ sK5 @ sK6 )
= $true )
| ( sK0 = sK5 ) ),
inference(equality_proxy_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
( ( ( sK1 @ sK5 @ sK6 )
= $true )
| ( $true
= ( sK0 = sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
( ( ( sK1 @ sK5 @ sK6 )
= $true )
| ( $true
= ( ( sK0 = sK5 )
& ( sK2 = sK6 ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f31]) ).
thf(f31,plain,
( ( ( sK1 @ sK5 @ sK6 )
= $true )
| ( ( sK1 @ sK5 @ sK6 )
= $true )
| ( $true
= ( ( sK0 = sK5 )
& ( sK2 = sK6 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ( ( sK1 @ sK5 @ sK6 )
& ~ ( ( sK2 = sK6 )
& ( sK0 = sK5 ) ) )
= $true )
| ( $true
= ( ( sK0 = sK5 )
& ( sK2 = sK6 ) ) )
| ( ( sK1 @ sK5 @ sK6 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( ( $true
= ( ( ( sK1 @ sK5 @ sK6 )
& ~ ( ( sK2 = sK6 )
& ( sK0 = sK5 ) ) )
| ( ( sK0 = sK5 )
& ( sK2 = sK6 ) ) ) )
| ( ( sK1 @ sK5 @ sK6 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f14]) ).
thf(f53,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f36,f50,f46]) ).
thf(f36,plain,
( ( ( sK1 @ sK5 @ sK6 )
= $true )
| ( sK2 = sK6 ) ),
inference(equality_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ( sK1 @ sK5 @ sK6 )
= $true )
| ( ( sK2 = sK6 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEV065^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.13/0.31 % Computer : n014.cluster.edu
% 0.13/0.31 % Model : x86_64 x86_64
% 0.13/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.31 % Memory : 8042.1875MB
% 0.13/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.31 % CPULimit : 300
% 0.13/0.31 % WCLimit : 300
% 0.13/0.31 % DateTime : Tue Feb 24 12:39:42 EST 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.32 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.40 ---- Original DTF file ---
% 0.15/0.40 thf(spec,logic,$$dhol).
% 0.15/0.40 %------------------------------------------------------------------------------
% 0.15/0.40 % File : SEV065^5 : TPTP v9.2.1. Released v4.0.0.
% 0.15/0.40 % Domain : Set Theory (Relations)
% 0.15/0.40 % Problem : TPS problem THM177
% 0.15/0.40 % Version : Especial.
% 0.15/0.40 % English :
% 0.15/0.40
% 0.15/0.40 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.15/0.40 % Source : [Bro09]
% 0.15/0.40 % Names : tps_0417 [Bro09]
% 0.15/0.40 % : THM177 [TPS]
% 0.15/0.40
% 0.15/0.40 % Status : Theorem
% 0.15/0.40 % Rating : 0.00 v9.0.0, 0.10 v8.2.0, 0.15 v8.1.0, 0.09 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 v5.5.0, 0.17 v5.4.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.33 v4.0.0
% 0.15/0.40 % Syntax : Number of formulae : 3 ( 1 unt; 2 typ; 0 def)
% 0.15/0.40 % Number of atoms : 5 ( 5 equ; 0 cnn)
% 0.15/0.40 % Maximal formula atoms : 1 ( 5 avg)
% 0.15/0.40 % Number of connectives : 10 ( 1 ~; 1 |; 3 &; 4 @)
% 0.15/0.40 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.15/0.40 % Maximal formula depth : 7 ( 7 avg)
% 0.15/0.40 % Number of types : 3 ( 2 usr)
% 0.15/0.40 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.15/0.40 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.15/0.40 % Number of variables : 5 ( 2 ^; 3 !; 0 ?; 5 :)
% 0.15/0.40 % SPC : TH0_THM_EQU_NAR
% 0.15/0.40
% 0.15/0.40 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.15/0.40 % project in the Department of Mathematical Sciences at Carnegie
% 0.15/0.40 % Mellon University. Distributed under the Creative Commons copyleft
% 0.15/0.40 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.15/0.40 % : Polymorphic definitions expanded.
% 0.15/0.40 %------------------------------------------------------------------------------
% 0.15/0.40 thf(b_type,type,
% 0.15/0.40 b: $tType ).
% 0.15/0.40
% 0.15/0.40 thf(a_type,type,
% 0.15/0.40 a: $tType ).
% 0.15/0.40
% 0.15/0.40 thf(cTHM177_pme,conjecture,
% 0.15/0.40 ! [Xx: b,Xy: a,Xk: b > a > $o] :
% 0.15/0.40 ( ( Xk @ Xx @ Xy )
% 0.15/0.40 => ( ( ^ [Xu: b,Xv: a] :
% 0.15/0.40 ( ( ( Xk @ Xu @ Xv )
% 0.15/0.40 & ~ ( ( Xu = Xx )
% 0.15/0.40 & ( Xv = Xy ) ) )
% 0.15/0.40 | ( ( Xu = Xx )
% 0.15/0.40 & ( Xv = Xy ) ) ) )
% 0.15/0.40 = Xk ) ) ).
% 0.15/0.40
% 0.15/0.40 %------------------------------------------------------------------------------
% 0.15/0.40 ------------------------
% 1.12/1.13 ---- Embedded in THF ---
% 0.22/1.13 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.22/1.13 %%% Generated on Tue Feb 24 12:39:43 EST 2026
% 0.22/1.13 %%% using '$$dhol' embedding, version 1.3.0.
% 0.22/1.13 %%% Logic specification used:
% 0.22/1.13 %%% thf(spec, logic, $$dhol).
% 0.22/1.13
% 0.22/1.13 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.jrBxDCT3lx/DTF2DTF30943.p
% See solution above
% 0.22/1.13 ------------------------
% 0.22/1.13 ---- Cleaned THF ---
% 0.22/1.13 thf(b_type,type,
% 0.22/1.13 b: $tType ).
% 0.22/1.13
% 0.22/1.13 thf(a_type,type,
% 0.22/1.13 a: $tType ).
% 0.22/1.13
% 0.22/1.13 thf(cTHM177_pme,conjecture,
% 0.22/1.13 ! [Xx: b,Xy: a,Xk: b > a > $o] :
% 0.22/1.13 ( ( Xk @ Xx @ Xy )
% 0.22/1.13 => ( ( ^ [Xu: b,Xv: a] :
% 0.22/1.13 ( ( ( Xk @ Xu @ Xv )
% 0.22/1.13 & ~ ( ( Xu = Xx )
% 0.22/1.13 & ( Xv = Xy ) ) )
% 0.22/1.13 | ( ( Xu = Xx )
% 0.22/1.13 & ( Xv = Xy ) ) ) )
% 0.22/1.13 = Xk ) ) ).
% 0.22/1.13 ------------------------
% 0.22/1.15 % (31043)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30943 for (3000ds/183Mi)
% 0.22/1.15 % (31043)First to succeed.
% 0.22/1.15 % (31043)Refutation found. Thanks to Tanya!
% 0.22/1.15 % SZS status Theorem for DTF2THF_30943
% 0.22/1.15 % SZS output start Proof for DTF2THF_30943
% 0.22/1.15 thf(type_def_5, type, b: $tType).
% 0.22/1.15 thf(type_def_6, type, a: $tType).
% 0.22/1.15 thf(func_def_0, type, b: $tType).
% 0.22/1.15 thf(func_def_1, type, a: $tType).
% 0.22/1.15 thf(func_def_12, type, sK0: b).
% 0.22/1.15 thf(func_def_13, type, sK1: b > a > $o).
% 0.22/1.15 thf(func_def_14, type, sK2: a).
% 0.22/1.15 thf(func_def_16, type, ph4: !>[X0: $tType]:(X0)).
% 0.22/1.15 thf(func_def_17, type, sK5: b).
% 0.22/1.15 thf(func_def_18, type, sK6: a).
% 0.22/1.15 thf(f83,plain,(
% 0.22/1.15 $false),
% 0.22/1.15 inference(avatar_sat_refutation,[status(thm)],[f53,f58,f63,f64,f65,f71,f82])).
% 0.22/1.15 thf(f82,plain,(
% 0.22/1.15 ~spl3_1 | spl3_2 | ~spl3_3),
% 0.22/1.15 inference(avatar_contradiction_clause,[status(thm)],[f81])).
% 0.22/1.15 thf(f81,plain,(
% 0.22/1.15 $false | (~spl3_1 | spl3_2 | ~spl3_3)),
% 0.22/1.15 inference(subsumption_resolution,[status(thm)],[f79,f9])).
% 0.22/1.15 thf(f9,plain,(
% 0.22/1.15 ($true = (sK1 @ sK0 @ sK2))),
% 0.22/1.15 inference(cnf_transformation,[status(thm)],[f8])).
% 0.22/1.15 thf(f8,plain,(
% 0.22/1.15 ((^[Y0 : b]: ((^[Y1 : a]: (((sK1 @ Y0 @ Y1) & (~ ((sK2 = Y1) & (sK0 = Y0)))) | ((sK0 = Y0) & (sK2 = Y1)))))) != sK1) & ($true = (sK1 @ sK0 @ sK2))),
% 0.22/1.15 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f6,f7])).
% 0.22/1.15 thf(f7,plain,(
% 0.22/1.15 ? [X0 : b,X1 : b > a > $o,X2 : a] : (((^[Y0 : b]: ((^[Y1 : a]: (((X1 @ Y0 @ Y1) & (~ ((X2 = Y1) & (X0 = Y0)))) | ((X0 = Y0) & (X2 = Y1)))))) != X1) & ((X1 @ X0 @ X2) = $true)) => (((^[Y0 : b]: ((^[Y1 : a]: (((sK1 @ Y0 @ Y1) & (~ ((sK2 = Y1) & (sK0 = Y0)))) | ((sK0 = Y0) & (sK2 = Y1)))))) != sK1) & ($true = (sK1 @ sK0 @ sK2)))),
% 0.22/1.15 introduced(definition,[],[choice_axiom])).
% 0.22/1.15 thf(f6,plain,(
% 0.22/1.15 ? [X0 : b,X1 : b > a > $o,X2 : a] : (((^[Y0 : b]: ((^[Y1 : a]: (((X1 @ Y0 @ Y1) & (~ ((X2 = Y1) & (X0 = Y0)))) | ((X0 = Y0) & (X2 = Y1)))))) != X1) & ((X1 @ X0 @ X2) = $true))),
% 0.22/1.15 inference(ennf_transformation,[status(thm)],[f5])).
% 0.22/1.15 thf(f5,plain,(
% 0.22/1.15 ~! [X0 : b,X1 : b > a > $o,X2 : a] : (((X1 @ X0 @ X2) = $true) => ((^[Y0 : b]: ((^[Y1 : a]: (((X1 @ Y0 @ Y1) & (~ ((X2 = Y1) & (X0 = Y0)))) | ((X0 = Y0) & (X2 = Y1)))))) = X1))),
% 0.22/1.15 inference(fool_elimination,[status(thm)],[f4])).
% 0.22/1.15 thf(f4,plain,(
% 0.22/1.15 ~! [X0 : b,X1 : b > a > $o,X2 : a] : ((X1 @ X0 @ X2) => ((^[X3 : b, X4 : a] : (((X2 = X4) & (X0 = X3)) | (~((X0 = X3) & (X2 = X4)) & (X1 @ X3 @ X4)))) = X1))),
% 0.22/1.15 inference(rectify,[status(thm)],[f2])).
% 0.22/1.15 thf(f2,negated_conjecture,(
% 0.22/1.15 ~! [X0 : b,X2 : b > a > $o,X1 : a] : ((X2 @ X0 @ X1) => ((^[X3 : b, X4 : a] : (((X1 = X4) & (X0 = X3)) | (~((X0 = X3) & (X1 = X4)) & (X2 @ X3 @ X4)))) = X2))),
% 0.22/1.15 inference(negated_conjecture,[status(cth)],[f1])).
% 0.22/1.15 thf(f1,conjecture,(
% 0.22/1.15 ! [X0 : b,X2 : b > a > $o,X1 : a] : ((X2 @ X0 @ X1) => ((^[X3 : b, X4 : a] : (((X1 = X4) & (X0 = X3)) | (~((X0 = X3) & (X1 = X4)) & (X2 @ X3 @ X4)))) = X2))),
% 0.22/1.15 file('/export/starexec/sandbox2/tmp/tmp.jrBxDCT3lx/DTF2THF_30943.p',cTHM177_pme)).
% 0.22/1.15 thf(f79,plain,(
% 0.22/1.15 ($true != (sK1 @ sK0 @ sK2)) | (~spl3_1 | spl3_2 | ~spl3_3)),
% 0.22/1.15 inference(superposition,[status(thm)],[f74,f57])).
% 0.22/1.15 thf(f57,plain,(
% 0.22/1.15 (sK0 = sK5) | ~spl3_3),
% 0.22/1.15 inference(avatar_component_clause,[status(thm)],[f55])).
% 0.22/1.15 thf(f55,definition,(
% 0.22/1.15 spl3_3 <=> (sK0 = sK5)),
% 0.22/1.15 introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition])).
% 0.22/1.15 thf(f74,plain,(
% 0.22/1.15 ((sK1 @ sK5 @ sK2) != $true) | (~spl3_1 | spl3_2)),
% 0.22/1.15 inference(superposition,[status(thm)],[f51,f48])).
% 0.22/1.15 thf(f48,plain,(
% 0.22/1.15 (sK2 = sK6) | ~spl3_1),
% 0.22/1.15 inference(avatar_component_clause,[status(thm)],[f46])).
% 0.22/1.15 thf(f46,definition,(
% 0.22/1.15 spl3_1 <=> (sK2 = sK6)),
% 0.22/1.15 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 0.22/1.15 thf(f51,plain,(
% 0.22/1.15 ((sK1 @ sK5 @ sK6) != $true) | spl3_2),
% 0.22/1.15 inference(avatar_component_clause,[status(thm)],[f50])).
% 0.22/1.15 thf(f50,definition,(
% 0.22/1.15 spl3_2 <=> ((sK1 @ sK5 @ sK6) = $true)),
% 0.22/1.15 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 0.22/1.15 thf(f71,plain,(
% 0.22/1.15 ~spl3_2 | ~spl3_4),
% 0.22/1.15 inference(avatar_contradiction_clause,[status(thm)],[f70])).
% 0.22/1.15 thf(f70,plain,(
% 0.22/1.15 $false | (~spl3_2 | ~spl3_4)),
% 0.22/1.15 inference(trivial_inequality_removal,[status(thm)],[f66])).
% 0.22/1.15 thf(f66,plain,(
% 0.22/1.15 ($true = $false) | (~spl3_2 | ~spl3_4)),
% 0.22/1.15 inference(superposition,[status(thm)],[f52,f62])).
% 0.22/1.15 thf(f62,plain,(
% 0.22/1.15 ((sK1 @ sK5 @ sK6) = $false) | ~spl3_4),
% 0.22/1.15 inference(avatar_component_clause,[status(thm)],[f60])).
% 0.22/1.15 thf(f60,definition,(
% 0.22/1.15 spl3_4 <=> ((sK1 @ sK5 @ sK6) = $false)),
% 0.22/1.15 introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition])).
% 0.22/1.15 thf(f52,plain,(
% 0.22/1.15 ((sK1 @ sK5 @ sK6) = $true) | ~spl3_2),
% 0.22/1.15 inference(avatar_component_clause,[status(thm)],[f50])).
% 0.22/1.15 thf(f65,plain,(
% 0.22/1.15 spl3_1 | spl3_4),
% 0.22/1.15 inference(avatar_split_clause,[status(thm)],[f24,f60,f46])).
% 0.22/1.15 thf(f24,plain,(
% 0.22/1.15 (sK2 = sK6) | ((sK1 @ sK5 @ sK6) = $false)),
% 0.22/1.15 inference(equality_proxy_clausification,[status(thm)],[f23])).
% 0.22/1.15 thf(f23,plain,(
% 0.22/1.15 ((sK2 = sK6) = $true) | ((sK1 @ sK5 @ sK6) = $false)),
% 0.22/1.15 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 0.22/1.15 thf(f21,plain,(
% 0.22/1.15 ($true = ((sK2 = sK6) & (sK0 = sK5))) | ((sK1 @ sK5 @ sK6) = $false)),
% 0.22/1.15 inference(not_proxy_clausification,[status(thm)],[f20])).
% 0.22/1.15 thf(f20,plain,(
% 0.22/1.15 ((sK1 @ sK5 @ sK6) = $false) | ($false = (~ ((sK2 = sK6) & (sK0 = sK5))))),
% 0.22/1.15 inference(duplicate_literal_removal,[status(thm)],[f19])).
% 0.22/1.15 thf(f19,plain,(
% 0.22/1.15 ((sK1 @ sK5 @ sK6) = $false) | ((sK1 @ sK5 @ sK6) = $false) | ($false = (~ ((sK2 = sK6) & (sK0 = sK5))))),
% 0.22/1.15 inference(binary_proxy_clausification,[status(thm)],[f18])).
% 0.22/1.15 thf(f18,plain,(
% 0.22/1.15 ((sK1 @ sK5 @ sK6) = $false) | (((sK1 @ sK5 @ sK6) & (~ ((sK2 = sK6) & (sK0 = sK5)))) = $false)),
% 0.22/1.15 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 0.22/1.15 thf(f16,plain,(
% 0.22/1.15 ($false = (((sK1 @ sK5 @ sK6) & (~ ((sK2 = sK6) & (sK0 = sK5)))) | ((sK0 = sK5) & (sK2 = sK6)))) | ((sK1 @ sK5 @ sK6) = $false)),
% 0.22/1.15 inference(binary_proxy_clausification,[status(thm)],[f14])).
% 0.22/1.15 thf(f14,plain,(
% 0.22/1.15 ((sK1 @ sK5 @ sK6) != (((sK1 @ sK5 @ sK6) & (~ ((sK2 = sK6) & (sK0 = sK5)))) | ((sK0 = sK5) & (sK2 = sK6))))),
% 0.22/1.15 inference(beta_eta_normalization,[status(thm)],[f13])).
% 0.22/1.15 thf(f13,plain,(
% 0.22/1.15 ((sK1 @ sK5 @ sK6) != ((^[Y0 : a]: (((sK1 @ sK5 @ Y0) & (~ ((sK2 = Y0) & (sK0 = sK5)))) | ((sK0 = sK5) & (sK2 = Y0)))) @ sK6))),
% 0.22/1.15 inference(negative_extensionality,[status(thm)],[f12])).
% 0.22/1.15 thf(f12,plain,(
% 0.22/1.15 ((^[Y0 : a]: (((sK1 @ sK5 @ Y0) & (~ ((sK2 = Y0) & (sK0 = sK5)))) | ((sK0 = sK5) & (sK2 = Y0)))) != (sK1 @ sK5))),
% 0.22/1.15 inference(beta_eta_normalization,[status(thm)],[f11])).
% 0.22/1.15 thf(f11,plain,(
% 0.22/1.15 (((^[Y0 : b]: ((^[Y1 : a]: (((sK1 @ Y0 @ Y1) & (~ ((sK2 = Y1) & (sK0 = Y0)))) | ((sK0 = Y0) & (sK2 = Y1)))))) @ sK5) != (sK1 @ sK5))),
% 0.22/1.15 inference(negative_extensionality,[status(thm)],[f10])).
% 0.22/1.15 thf(f10,plain,(
% 0.22/1.15 ((^[Y0 : b]: ((^[Y1 : a]: (((sK1 @ Y0 @ Y1) & (~ ((sK2 = Y1) & (sK0 = Y0)))) | ((sK0 = Y0) & (sK2 = Y1)))))) != sK1)),
% 0.22/1.15 inference(cnf_transformation,[status(thm)],[f8])).
% 0.22/1.15 thf(f64,plain,(
% 0.22/1.15 spl3_3 | spl3_4),
% 0.22/1.15 inference(avatar_split_clause,[status(thm)],[f25,f60,f55])).
% 0.22/1.15 thf(f25,plain,(
% 0.22/1.15 ((sK1 @ sK5 @ sK6) = $false) | (sK0 = sK5)),
% 0.22/1.15 inference(equality_proxy_clausification,[status(thm)],[f22])).
% 0.22/1.15 thf(f22,plain,(
% 0.22/1.15 ($true = (sK0 = sK5)) | ((sK1 @ sK5 @ sK6) = $false)),
% 0.22/1.15 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 0.22/1.15 thf(f63,plain,(
% 0.22/1.15 ~spl3_3 | spl3_4 | ~spl3_1),
% 0.22/1.15 inference(avatar_split_clause,[status(thm)],[f28,f46,f60,f55])).
% 0.22/1.15 thf(f28,plain,(
% 0.22/1.15 (sK2 != sK6) | (sK0 != sK5) | ((sK1 @ sK5 @ sK6) = $false)),
% 0.22/1.15 inference(equality_proxy_clausification,[status(thm)],[f27])).
% 0.22/1.15 thf(f27,plain,(
% 0.22/1.15 ((sK1 @ sK5 @ sK6) = $false) | ($false = (sK0 = sK5)) | (sK2 != sK6)),
% 0.22/1.15 inference(equality_proxy_clausification,[status(thm)],[f26])).
% 0.22/1.15 thf(f26,plain,(
% 0.22/1.15 ((sK1 @ sK5 @ sK6) = $false) | ((sK2 = sK6) = $false) | ($false = (sK0 = sK5))),
% 0.22/1.15 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 0.22/1.15 thf(f17,plain,(
% 0.22/1.15 ($false = ((sK0 = sK5) & (sK2 = sK6))) | ((sK1 @ sK5 @ sK6) = $false)),
% 0.22/1.15 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 0.22/1.15 thf(f58,plain,(
% 0.22/1.15 spl3_3 | spl3_2),
% 0.22/1.15 inference(avatar_split_clause,[status(thm)],[f35,f50,f55])).
% 0.22/1.15 thf(f35,plain,(
% 0.22/1.15 ((sK1 @ sK5 @ sK6) = $true) | (sK0 = sK5)),
% 0.22/1.15 inference(equality_proxy_clausification,[status(thm)],[f34])).
% 0.22/1.15 thf(f34,plain,(
% 0.22/1.15 ((sK1 @ sK5 @ sK6) = $true) | ($true = (sK0 = sK5))),
% 0.22/1.15 inference(binary_proxy_clausification,[status(thm)],[f32])).
% 0.22/1.15 thf(f32,plain,(
% 0.22/1.15 ((sK1 @ sK5 @ sK6) = $true) | ($true = ((sK0 = sK5) & (sK2 = sK6)))),
% 0.22/1.15 inference(duplicate_literal_removal,[status(thm)],[f31])).
% 0.22/1.15 thf(f31,plain,(
% 0.22/1.15 ((sK1 @ sK5 @ sK6) = $true) | ((sK1 @ sK5 @ sK6) = $true) | ($true = ((sK0 = sK5) & (sK2 = sK6)))),
% 0.22/1.15 inference(binary_proxy_clausification,[status(thm)],[f29])).
% 0.22/1.15 thf(f29,plain,(
% 0.22/1.15 (((sK1 @ sK5 @ sK6) & (~ ((sK2 = sK6) & (sK0 = sK5)))) = $true) | ($true = ((sK0 = sK5) & (sK2 = sK6))) | ((sK1 @ sK5 @ sK6) = $true)),
% 0.22/1.15 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 0.22/1.15 thf(f15,plain,(
% 0.22/1.15 ($true = (((sK1 @ sK5 @ sK6) & (~ ((sK2 = sK6) & (sK0 = sK5)))) | ((sK0 = sK5) & (sK2 = sK6)))) | ((sK1 @ sK5 @ sK6) = $true)),
% 0.22/1.15 inference(binary_proxy_clausification,[status(thm)],[f14])).
% 0.22/1.15 thf(f53,plain,(
% 0.22/1.15 spl3_1 | spl3_2),
% 0.22/1.15 inference(avatar_split_clause,[status(thm)],[f36,f50,f46])).
% 0.22/1.15 thf(f36,plain,(
% 0.22/1.15 ((sK1 @ sK5 @ sK6) = $true) | (sK2 = sK6)),
% 0.22/1.15 inference(equality_proxy_clausification,[status(thm)],[f33])).
% 0.22/1.15 thf(f33,plain,(
% 0.22/1.15 ((sK1 @ sK5 @ sK6) = $true) | ((sK2 = sK6) = $true)),
% 0.22/1.15 inference(binary_proxy_clausification,[status(thm)],[f32])).
% 0.22/1.15 % SZS output end Proof for DTF2THF_30943
% 0.22/1.15 % (31043)------------------------------
% 0.22/1.15 % (31043)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.15 % (31043)Termination reason: Refutation
% 0.22/1.15
% 0.22/1.15 % (31043)Memory used [KB]: 5500
% 0.22/1.15 % (31043)Time elapsed: 0.004 s
% 0.22/1.15 % (31043)Instructions burned: 3 (million)
% 0.22/1.15 % (31043)------------------------------
% 0.22/1.15 % (31043)------------------------------
% 0.22/1.15 % (31042)Success in time 0.013 s
%------------------------------------------------------------------------------