%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV225^5 : TPTP v9.2.1. Bugfixed v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n031.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 09:40:36 AM UTC 2026
% Result : Theorem 1.17s 1.11s
% Output : Refutation 1.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 79 ( 29 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 75 ( 14 ~; 0 |; 10 &; 43 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 4 usr; 6 con; 0-2 aty)
% ( 3 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 15 ( 4 ^; 9 !; 2 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
r: $tType ).
thf(func_def_0,type,
r: $tType ).
thf(func_def_1,type,
c0: r ).
thf(func_def_2,type,
less: r > r > $o ).
thf(func_def_11,type,
sK0: r ).
thf(f23,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f21]) ).
thf(f21,plain,
$true = $false,
inference(superposition,[status(thm)],[f20,f17]) ).
thf(f17,plain,
( $true
= ( less @ sK0 @ sK0 ) ),
inference(definition_unfolding,[status(thm)],[f13,f14]) ).
thf(f14,plain,
c0 = sK0,
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( cIRREFLEXIVE_LAW = $true )
& ( c0 = sK0 )
& ( $true
= ( less @ sK0 @ c0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f9,f10]) ).
thf(f10,plain,
( ? [X0: r] :
( ( c0 = X0 )
& ( ( less @ X0 @ c0 )
= $true ) )
=> ( ( c0 = sK0 )
& ( $true
= ( less @ sK0 @ c0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ( cIRREFLEXIVE_LAW = $true )
& ? [X0: r] :
( ( c0 = X0 )
& ( ( less @ X0 @ c0 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ( cIRREFLEXIVE_LAW = $true )
=> ! [X0: r] :
~ ( ( c0 = X0 )
& ( ( less @ X0 @ c0 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( cIRREFLEXIVE_LAW
=> ! [X0: r] :
~ ( ( less @ X0 @ c0 )
& ( c0 = X0 ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ( cIRREFLEXIVE_LAW
=> ! [X0: r] :
~ ( ( less @ X0 @ c0 )
& ( c0 = X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( cIRREFLEXIVE_LAW
=> ! [X0: r] :
~ ( ( less @ X0 @ c0 )
& ( c0 = X0 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.yFCGtYyIyK/DTF2THF_32547.p',cPARNAS_FIG3_A) ).
thf(f13,plain,
( $true
= ( less @ sK0 @ c0 ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f20,plain,
! [X1: r] :
( $false
= ( less @ X1 @ X1 ) ),
inference(not_proxy_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
! [X1: r] :
( $true
= ( ~ ( less @ X1 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f18]) ).
thf(f18,plain,
! [X1: r] :
( ( ^ [Y0: r] :
~ ( less @ Y0 @ Y0 )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
( ( !! @ r
@ ^ [Y0: r] :
~ ( less @ Y0 @ Y0 ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f15,f12]) ).
thf(f12,plain,
( cIRREFLEXIVE_LAW
= ( !! @ r
@ ^ [Y0: r] :
~ ( less @ Y0 @ Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( cIRREFLEXIVE_LAW
= ( !! @ r
@ ^ [Y0: r] :
~ ( less @ Y0 @ Y0 ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( cIRREFLEXIVE_LAW
= ( ! [X0: r] :
~ ( less @ X0 @ X0 ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( cIRREFLEXIVE_LAW
= ( ! [X0: r] :
~ ( less @ X0 @ X0 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.yFCGtYyIyK/DTF2THF_32547.p',cIRREFLEXIVE_LAW_def) ).
thf(f15,plain,
cIRREFLEXIVE_LAW = $true,
inference(cnf_transformation,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEV225^5 : TPTP v9.2.1. Bugfixed v5.3.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.32 % Computer : n031.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue Feb 24 12:43:18 EST 2026
% 0.12/0.32 % CPUTime :
% 0.12/0.32 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.43 ---- Original DTF file ---
% 0.15/0.43 thf(spec,logic,$$dhol).
% 0.15/0.43 %------------------------------------------------------------------------------
% 0.15/0.43 % File : SEV225^5 : TPTP v9.2.1. Bugfixed v5.3.0.
% 0.15/0.43 % Domain : Set Theory (Sets of sets)
% 0.15/0.43 % Problem : TPS problem from REALS-THMS
% 0.15/0.43 % Version : Especial.
% 0.15/0.43 % English :
% 0.15/0.43
% 0.15/0.43 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.15/0.43 % Source : [Bro09]
% 0.15/0.43 % Names : tps_0676 [Bro09]
% 0.15/0.43
% 0.15/0.43 % Status : Theorem
% 0.15/0.43 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v6.2.0, 0.14 v6.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.33 v5.4.0, 0.20 v5.3.0
% 0.15/0.43 % Syntax : Number of formulae : 6 ( 1 unt; 4 typ; 1 def)
% 0.15/0.43 % Number of atoms : 6 ( 2 equ; 0 cnn)
% 0.15/0.43 % Maximal formula atoms : 3 ( 3 avg)
% 0.15/0.43 % Number of connectives : 8 ( 2 ~; 0 |; 1 &; 4 @)
% 0.15/0.43 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.15/0.43 % Maximal formula depth : 7 ( 4 avg)
% 0.15/0.43 % Number of types : 2 ( 1 usr)
% 0.15/0.43 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.15/0.43 % Number of symbols : 4 ( 3 usr; 2 con; 0-2 aty)
% 0.15/0.43 % Number of variables : 2 ( 0 ^; 2 !; 0 ?; 2 :)
% 0.15/0.43 % SPC : TH0_THM_EQU_NAR
% 0.15/0.43
% 0.15/0.43 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.15/0.43 % project in the Department of Mathematical Sciences at Carnegie
% 0.15/0.43 % Mellon University. Distributed under the Creative Commons copyleft
% 0.15/0.43 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.15/0.43 % Bugfixes : v5.2.0 - Added missing type declarations.
% 0.15/0.43 % : v5.3.0 - Fixed tType to $tType from last bugfixes.
% 0.15/0.43 %------------------------------------------------------------------------------
% 0.15/0.43 thf(r_type,type,
% 0.15/0.43 r: $tType ).
% 0.15/0.43
% 0.15/0.43 thf(c0_type,type,
% 0.15/0.43 c0: r ).
% 0.15/0.43
% 0.15/0.43 thf(less_type,type,
% 0.15/0.43 less: r > r > $o ).
% 0.15/0.43
% 0.15/0.43 thf(cIRREFLEXIVE_LAW_type,type,
% 0.15/0.43 cIRREFLEXIVE_LAW: $o ).
% 0.15/0.43
% 0.15/0.43 thf(cIRREFLEXIVE_LAW_def,definition,
% 0.15/0.43 ( cIRREFLEXIVE_LAW
% 0.15/0.43 = ( ! [Xx: r] :
% 0.15/0.43 ~ ( less @ Xx @ Xx ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(cPARNAS_FIG3_A,conjecture,
% 0.15/0.43 ( cIRREFLEXIVE_LAW
% 0.15/0.43 => ! [Xx: r] :
% 0.15/0.43 ~ ( ( less @ Xx @ c0 )
% 0.15/0.43 & ( Xx = c0 ) ) ) ).
% 0.15/0.43
% 0.15/0.43 %------------------------------------------------------------------------------
% 0.15/0.43 ------------------------
% 1.17/1.08 ---- Embedded in THF ---
% 1.17/1.08 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.17/1.08 %%% Generated on Tue Feb 24 12:43:18 EST 2026
% 1.17/1.08 %%% using '$$dhol' embedding, version 1.3.0.
% 1.17/1.08 %%% Logic specification used:
% 1.17/1.08 %%% thf(spec, logic, $$dhol).
% 1.17/1.08
% 1.17/1.08 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.yFCGtYyIyK/DTF2DTF32547.p
% See solution above
% 1.17/1.08 ------------------------
% 1.17/1.09 ---- Cleaned THF ---
% 1.17/1.09 thf(r_type,type,
% 1.17/1.09 r: $tType ).
% 1.17/1.09
% 1.17/1.09 thf(c0_type,type,
% 1.17/1.09 c0: r ).
% 1.17/1.09
% 1.17/1.09 thf(less_type,type,
% 1.17/1.09 less: r > r > $o ).
% 1.17/1.09
% 1.17/1.09 thf(cIRREFLEXIVE_LAW_type,type,
% 1.17/1.09 cIRREFLEXIVE_LAW: $o ).
% 1.17/1.09
% 1.17/1.09 thf(cIRREFLEXIVE_LAW_def,definition,
% 1.17/1.09 ( cIRREFLEXIVE_LAW
% 1.17/1.09 = ( ! [Xx: r] :
% 1.17/1.09 ~ ( less @ Xx @ Xx ) ) ) ).
% 1.17/1.09
% 1.17/1.09 thf(cPARNAS_FIG3_A,conjecture,
% 1.17/1.09 ( cIRREFLEXIVE_LAW
% 1.17/1.09 => ! [Xx: r] :
% 1.17/1.09 ~ ( ( less @ Xx @ c0 )
% 1.17/1.09 & ( Xx = c0 ) ) ) ).
% 1.17/1.09 ------------------------
% 1.17/1.11 % (32644)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_32547 for (3000ds/183Mi)
% 1.17/1.11 % (32644)First to succeed.
% 1.17/1.11 % (32644)Refutation found. Thanks to Tanya!
% 1.17/1.11 % SZS status Theorem for DTF2THF_32547
% 1.17/1.11 % SZS output start Proof for DTF2THF_32547
% 1.17/1.11 thf(type_def_5, type, r: $tType).
% 1.17/1.11 thf(func_def_0, type, r: $tType).
% 1.17/1.11 thf(func_def_1, type, c0: r).
% 1.17/1.11 thf(func_def_2, type, less: r > r > $o).
% 1.17/1.11 thf(func_def_11, type, sK0: r).
% 1.17/1.11 thf(f23,plain,(
% 1.17/1.11 $false),
% 1.17/1.11 inference(trivial_inequality_removal,[status(thm)],[f21])).
% 1.17/1.11 thf(f21,plain,(
% 1.17/1.11 ($true = $false)),
% 1.17/1.11 inference(superposition,[status(thm)],[f20,f17])).
% 1.17/1.11 thf(f17,plain,(
% 1.17/1.11 ($true = (less @ sK0 @ sK0))),
% 1.17/1.11 inference(definition_unfolding,[status(thm)],[f13,f14])).
% 1.17/1.11 thf(f14,plain,(
% 1.17/1.11 (c0 = sK0)),
% 1.17/1.11 inference(cnf_transformation,[status(thm)],[f11])).
% 1.17/1.11 thf(f11,plain,(
% 1.17/1.11 (cIRREFLEXIVE_LAW = $true) & ((c0 = sK0) & ($true = (less @ sK0 @ c0)))),
% 1.17/1.11 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f9,f10])).
% 1.17/1.11 thf(f10,plain,(
% 1.17/1.11 ? [X0 : r] : ((c0 = X0) & ((less @ X0 @ c0) = $true)) => ((c0 = sK0) & ($true = (less @ sK0 @ c0)))),
% 1.17/1.11 introduced(definition,[],[choice_axiom])).
% 1.17/1.11 thf(f9,plain,(
% 1.17/1.11 (cIRREFLEXIVE_LAW = $true) & ? [X0 : r] : ((c0 = X0) & ((less @ X0 @ c0) = $true))),
% 1.17/1.11 inference(ennf_transformation,[status(thm)],[f6])).
% 1.17/1.11 thf(f6,plain,(
% 1.17/1.11 ~((cIRREFLEXIVE_LAW = $true) => ! [X0 : r] : ~((c0 = X0) & ((less @ X0 @ c0) = $true)))),
% 1.17/1.11 inference(fool_elimination,[status(thm)],[f5])).
% 1.17/1.11 thf(f5,plain,(
% 1.17/1.11 ~(cIRREFLEXIVE_LAW => ! [X0 : r] : ~((less @ X0 @ c0) & (c0 = X0)))),
% 1.17/1.11 inference(rectify,[status(thm)],[f3])).
% 1.17/1.11 thf(f3,negated_conjecture,(
% 1.17/1.11 ~(cIRREFLEXIVE_LAW => ! [X0 : r] : ~((less @ X0 @ c0) & (c0 = X0)))),
% 1.17/1.11 inference(negated_conjecture,[status(cth)],[f2])).
% 1.17/1.11 thf(f2,conjecture,(
% 1.17/1.11 cIRREFLEXIVE_LAW => ! [X0 : r] : ~((less @ X0 @ c0) & (c0 = X0))),
% 1.17/1.11 file('/export/starexec/sandbox2/tmp/tmp.yFCGtYyIyK/DTF2THF_32547.p',cPARNAS_FIG3_A)).
% 1.17/1.11 thf(f13,plain,(
% 1.17/1.11 ($true = (less @ sK0 @ c0))),
% 1.17/1.11 inference(cnf_transformation,[status(thm)],[f11])).
% 1.17/1.11 thf(f20,plain,(
% 1.17/1.11 ( ! [X1 : r] : (($false = (less @ X1 @ X1))) )),
% 1.17/1.11 inference(not_proxy_clausification,[status(thm)],[f19])).
% 1.17/1.11 thf(f19,plain,(
% 1.17/1.11 ( ! [X1 : r] : (($true = (~ (less @ X1 @ X1)))) )),
% 1.17/1.11 inference(beta_eta_normalization,[status(thm)],[f18])).
% 1.17/1.11 thf(f18,plain,(
% 1.17/1.11 ( ! [X1 : r] : ((((^[Y0 : r]: (~ (less @ Y0 @ Y0))) @ X1) = $true)) )),
% 1.17/1.11 inference(pi_clausification,[status(thm)],[f16])).
% 1.17/1.11 thf(f16,plain,(
% 1.17/1.11 ((!! @ r @ (^[Y0 : r]: (~ (less @ Y0 @ Y0)))) = $true)),
% 1.17/1.11 inference(definition_unfolding,[status(thm)],[f15,f12])).
% 1.17/1.11 thf(f12,plain,(
% 1.17/1.11 (cIRREFLEXIVE_LAW = (!! @ r @ (^[Y0 : r]: (~ (less @ Y0 @ Y0)))))),
% 1.17/1.11 inference(cnf_transformation,[status(thm)],[f8])).
% 1.17/1.11 thf(f8,plain,(
% 1.17/1.11 (cIRREFLEXIVE_LAW = (!! @ r @ (^[Y0 : r]: (~ (less @ Y0 @ Y0)))))),
% 1.17/1.11 inference(fool_elimination,[status(thm)],[f7])).
% 1.17/1.11 thf(f7,plain,(
% 1.17/1.11 (cIRREFLEXIVE_LAW = ! [X0 : r] : ~(less @ X0 @ X0))),
% 1.17/1.11 inference(rectify,[status(thm)],[f1])).
% 1.17/1.11 thf(f1,axiom,(
% 1.17/1.11 (cIRREFLEXIVE_LAW = ! [X0 : r] : ~(less @ X0 @ X0))),
% 1.17/1.11 file('/export/starexec/sandbox2/tmp/tmp.yFCGtYyIyK/DTF2THF_32547.p',cIRREFLEXIVE_LAW_def)).
% 1.17/1.11 thf(f15,plain,(
% 1.17/1.11 (cIRREFLEXIVE_LAW = $true)),
% 1.17/1.11 inference(cnf_transformation,[status(thm)],[f11])).
% 1.17/1.11 % SZS output end Proof for DTF2THF_32547
% 1.17/1.11 % (32644)------------------------------
% 1.17/1.11 % (32644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.17/1.11 % (32644)Termination reason: Refutation
% 1.17/1.11
% 1.17/1.11 % (32644)Memory used [KB]: 5500
% 1.17/1.11 % (32644)Time elapsed: 0.002 s
% 1.17/1.11 % (32644)Instructions burned: 1 (million)
% 1.17/1.11 % (32644)------------------------------
% 1.17/1.11 % (32644)------------------------------
% 1.17/1.11 % (32643)Success in time 0.011 s
%------------------------------------------------------------------------------