%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET626^5 : 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 : n025.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 09:31:58 AM UTC 2026
% Result : Theorem 1.50s 1.23s
% Output : Refutation 1.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 120 ( 44 equ; 0 cnn)
% Maximal formula atoms : 10 ( 7 avg)
% Number of connectives : 120 ( 19 ~; 7 |; 31 &; 57 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 33 ( 0 ^; 14 !; 19 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
cZ: a > $o ).
thf(func_def_3,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_6,type,
sK0: a > $o ).
thf(func_def_7,type,
sK1: a > $o ).
thf(func_def_8,type,
sK2: a ).
thf(f18,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f17]) ).
thf(f17,plain,
$true != $true,
inference(superposition,[status(thm)],[f16,f11]) ).
thf(f11,plain,
( $true
= ( sK0 @ sK2 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ! [X2: a] :
( ( $true
!= ( sK0 @ X2 ) )
| ( $true
!= ( sK1 @ X2 ) ) )
& ( $true
= ( cZ @ sK2 ) )
& ( $true
= ( sK1 @ sK2 ) )
& ( $true
= ( sK0 @ sK2 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f7,f9,f8]) ).
thf(f8,plain,
( ? [X0: a > $o,X1: a > $o] :
( ! [X2: a] :
( ( ( X0 @ X2 )
!= $true )
| ( ( X1 @ X2 )
!= $true ) )
& ? [X3: a] :
( ( $true
= ( cZ @ X3 ) )
& ( $true
= ( X1 @ X3 ) )
& ( $true
= ( X0 @ X3 ) ) ) )
=> ( ! [X2: a] :
( ( $true
!= ( sK0 @ X2 ) )
| ( $true
!= ( sK1 @ X2 ) ) )
& ? [X3: a] :
( ( $true
= ( cZ @ X3 ) )
& ( $true
= ( sK1 @ X3 ) )
& ( $true
= ( sK0 @ X3 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ? [X3: a] :
( ( $true
= ( cZ @ X3 ) )
& ( $true
= ( sK1 @ X3 ) )
& ( $true
= ( sK0 @ X3 ) ) )
=> ( ( $true
= ( cZ @ sK2 ) )
& ( $true
= ( sK1 @ sK2 ) )
& ( $true
= ( sK0 @ sK2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
? [X0: a > $o,X1: a > $o] :
( ! [X2: a] :
( ( ( X0 @ X2 )
!= $true )
| ( ( X1 @ X2 )
!= $true ) )
& ? [X3: a] :
( ( $true
= ( cZ @ X3 ) )
& ( $true
= ( X1 @ X3 ) )
& ( $true
= ( X0 @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o] :
( ! [X3: a] :
( ( $true
!= ( X0 @ X3 ) )
| ( $true
!= ( X1 @ X3 ) ) )
& ? [X2: a] :
( ( ( cZ @ X2 )
= $true )
& ( ( X1 @ X2 )
= $true )
& ( ( X0 @ X2 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X1: a > $o,X0: a > $o] :
( ? [X2: a] :
( ( ( cZ @ X2 )
= $true )
& ( ( X1 @ X2 )
= $true )
& ( ( X0 @ X2 )
= $true ) )
=> ? [X3: a] :
( ( $true
= ( X0 @ X3 ) )
& ( $true
= ( X1 @ X3 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ? [X2: a] :
( ( cZ @ X2 )
& ( X0 @ X2 )
& ( X1 @ X2 ) )
=> ? [X3: a] :
( ( X1 @ X3 )
& ( X0 @ X3 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X1: a > $o] :
( ? [X2: a] :
( ( cZ @ X2 )
& ( X0 @ X2 )
& ( X1 @ X2 ) )
=> ? [X2: a] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a > $o,X1: a > $o] :
( ? [X2: a] :
( ( cZ @ X2 )
& ( X0 @ X2 )
& ( X1 @ X2 ) )
=> ? [X2: a] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ZjlS5YgwEk/DTF2THF_3344.p',cBOOL_PROP_102_pme) ).
thf(f16,plain,
( $true
!= ( sK0 @ sK2 ) ),
inference(trivial_inequality_removal,[status(thm)],[f15]) ).
thf(f15,plain,
( ( $true
!= ( sK0 @ sK2 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f14,f12]) ).
thf(f12,plain,
( $true
= ( sK1 @ sK2 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f14,plain,
! [X2: a] :
( ( $true
!= ( sK1 @ X2 ) )
| ( $true
!= ( sK0 @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET626^5 : 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 : n025.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 12:00:57 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
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SET626^5 : TPTP v9.2.1. Released v4.0.0.
% 0.30/0.46 % Domain : Set Theory
% 0.30/0.46 % Problem : TPS problem BOOL-PROP-102
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English : Trybulec's 102th Boolean property of sets
% 0.30/0.46
% 0.30/0.46 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.30/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Bro09]
% 0.30/0.46 % Names : tps_0204 [Bro09]
% 0.30/0.46 % : BOOL-PROP-102 [TPS]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v4.0.0
% 0.30/0.46 % Syntax : Number of formulae : 3 ( 1 unt; 2 typ; 0 def)
% 0.30/0.46 % Number of atoms : 1 ( 0 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 1 ( 1 avg)
% 0.30/0.46 % Number of connectives : 9 ( 0 ~; 0 |; 3 &; 5 @)
% 0.30/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 8 ( 8 avg)
% 0.30/0.46 % Number of types : 2 ( 1 usr)
% 0.30/0.46 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 1 ( 1 usr; 0 con; 1-1 aty)
% 0.30/0.46 % Number of variables : 4 ( 0 ^; 2 !; 2 ?; 4 :)
% 0.30/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.30/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.30/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.30/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.30/0.46 % : Polymorphic definitions expanded.
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(a_type,type,
% 0.30/0.46 a: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(cZ,type,
% 0.30/0.46 cZ: a > $o ).
% 0.30/0.46
% 0.30/0.46 thf(cBOOL_PROP_102_pme,conjecture,
% 0.30/0.46 ! [X: a > $o,Y: a > $o] :
% 0.30/0.46 ( ? [Xx: a] :
% 0.30/0.46 ( ( X @ Xx )
% 0.30/0.46 & ( Y @ Xx )
% 0.30/0.46 & ( cZ @ Xx ) )
% 0.30/0.46 => ? [Xx: a] :
% 0.30/0.46 ( ( X @ Xx )
% 0.30/0.46 & ( Y @ Xx ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.35/1.20 ---- Embedded in THF ---
% 1.50/1.20 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.20 %%% Generated on Tue Feb 24 12:00:58 EST 2026
% 1.50/1.20 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.20 %%% Logic specification used:
% 1.50/1.20 %%% thf(spec, logic, $$dhol).
% 1.50/1.20
% 1.50/1.20 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.ZjlS5YgwEk/DTF2DTF3344.p
% See solution above
% 1.50/1.20 ------------------------
% 1.50/1.21 ---- Cleaned THF ---
% 1.50/1.21 thf(a_type,type,
% 1.50/1.21 a: $tType ).
% 1.50/1.21
% 1.50/1.21 thf(cZ,type,
% 1.50/1.21 cZ: a > $o ).
% 1.50/1.21
% 1.50/1.21 thf(cBOOL_PROP_102_pme,conjecture,
% 1.50/1.21 ! [X: a > $o,Y: a > $o] :
% 1.50/1.21 ( ? [Xx: a] :
% 1.50/1.21 ( ( X @ Xx )
% 1.50/1.21 & ( Y @ Xx )
% 1.50/1.21 & ( cZ @ Xx ) )
% 1.50/1.21 => ? [Xx: a] :
% 1.50/1.21 ( ( X @ Xx )
% 1.50/1.21 & ( Y @ Xx ) ) ) ).
% 1.50/1.21 ------------------------
% 1.50/1.22 % (3443)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_3344 for (2999ds/27Mi)
% 1.50/1.22 % (3445)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_3344 for (2999ds/2Mi)
% 1.50/1.22 % (3443)First to succeed.
% 1.50/1.22 % (3445)Instruction limit reached!
% 1.50/1.22 % (3445)------------------------------
% 1.50/1.22 % (3445)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.22 % (3445)Termination reason: Unknown
% 1.50/1.22 % (3445)Termination phase: Saturation
% 1.50/1.22
% 1.50/1.22 % (3445)Memory used [KB]: 5500
% 1.50/1.22 % (3445)Time elapsed: 0.002 s
% 1.50/1.22 % (3445)Instructions burned: 3 (million)
% 1.50/1.22 % (3445)------------------------------
% 1.50/1.22 % (3445)------------------------------
% 1.50/1.23 % (3443)Refutation found. Thanks to Tanya!
% 1.50/1.23 % SZS status Theorem for DTF2THF_3344
% 1.50/1.23 % SZS output start Proof for DTF2THF_3344
% 1.50/1.23 thf(type_def_5, type, a: $tType).
% 1.50/1.23 thf(func_def_0, type, a: $tType).
% 1.50/1.23 thf(func_def_1, type, cZ: a > $o).
% 1.50/1.23 thf(func_def_3, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.50/1.23 thf(func_def_6, type, sK0: a > $o).
% 1.50/1.23 thf(func_def_7, type, sK1: a > $o).
% 1.50/1.23 thf(func_def_8, type, sK2: a).
% 1.50/1.23 thf(f18,plain,(
% 1.50/1.23 $false),
% 1.50/1.23 inference(trivial_inequality_removal,[status(thm)],[f17])).
% 1.50/1.23 thf(f17,plain,(
% 1.50/1.23 ($true != $true)),
% 1.50/1.23 inference(superposition,[status(thm)],[f16,f11])).
% 1.50/1.23 thf(f11,plain,(
% 1.50/1.23 ($true = (sK0 @ sK2))),
% 1.50/1.23 inference(cnf_transformation,[status(thm)],[f10])).
% 1.50/1.23 thf(f10,plain,(
% 1.50/1.23 ! [X2 : a] : (($true != (sK0 @ X2)) | ($true != (sK1 @ X2))) & (($true = (cZ @ sK2)) & ($true = (sK1 @ sK2)) & ($true = (sK0 @ sK2)))),
% 1.50/1.23 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f7,f9,f8])).
% 1.50/1.23 thf(f8,plain,(
% 1.50/1.23 ? [X0 : a > $o,X1 : a > $o] : (! [X2 : a] : (((X0 @ X2) != $true) | ((X1 @ X2) != $true)) & ? [X3 : a] : (($true = (cZ @ X3)) & ($true = (X1 @ X3)) & ($true = (X0 @ X3)))) => (! [X2 : a] : (($true != (sK0 @ X2)) | ($true != (sK1 @ X2))) & ? [X3 : a] : (($true = (cZ @ X3)) & ($true = (sK1 @ X3)) & ($true = (sK0 @ X3))))),
% 1.50/1.23 introduced(definition,[],[choice_axiom])).
% 1.50/1.23 thf(f9,plain,(
% 1.50/1.23 ? [X3 : a] : (($true = (cZ @ X3)) & ($true = (sK1 @ X3)) & ($true = (sK0 @ X3))) => (($true = (cZ @ sK2)) & ($true = (sK1 @ sK2)) & ($true = (sK0 @ sK2)))),
% 1.50/1.23 introduced(definition,[],[choice_axiom])).
% 1.50/1.23 thf(f7,plain,(
% 1.50/1.23 ? [X0 : a > $o,X1 : a > $o] : (! [X2 : a] : (((X0 @ X2) != $true) | ((X1 @ X2) != $true)) & ? [X3 : a] : (($true = (cZ @ X3)) & ($true = (X1 @ X3)) & ($true = (X0 @ X3))))),
% 1.50/1.23 inference(rectify,[status(thm)],[f6])).
% 1.50/1.23 thf(f6,plain,(
% 1.50/1.23 ? [X0 : a > $o,X1 : a > $o] : (! [X3 : a] : (($true != (X0 @ X3)) | ($true != (X1 @ X3))) & ? [X2 : a] : (((cZ @ X2) = $true) & ((X1 @ X2) = $true) & ((X0 @ X2) = $true)))),
% 1.50/1.23 inference(ennf_transformation,[status(thm)],[f5])).
% 1.50/1.23 thf(f5,plain,(
% 1.50/1.23 ~! [X1 : a > $o,X0 : a > $o] : (? [X2 : a] : (((cZ @ X2) = $true) & ((X1 @ X2) = $true) & ((X0 @ X2) = $true)) => ? [X3 : a] : (($true = (X0 @ X3)) & ($true = (X1 @ X3))))),
% 1.50/1.23 inference(fool_elimination,[status(thm)],[f4])).
% 1.50/1.23 thf(f4,plain,(
% 1.50/1.23 ~! [X0 : a > $o,X1 : a > $o] : (? [X2 : a] : ((cZ @ X2) & (X0 @ X2) & (X1 @ X2)) => ? [X3 : a] : ((X1 @ X3) & (X0 @ X3)))),
% 1.50/1.23 inference(rectify,[status(thm)],[f2])).
% 1.50/1.23 thf(f2,negated_conjecture,(
% 1.50/1.23 ~! [X0 : a > $o,X1 : a > $o] : (? [X2 : a] : ((cZ @ X2) & (X0 @ X2) & (X1 @ X2)) => ? [X2 : a] : ((X1 @ X2) & (X0 @ X2)))),
% 1.50/1.23 inference(negated_conjecture,[status(cth)],[f1])).
% 1.50/1.23 thf(f1,conjecture,(
% 1.50/1.23 ! [X0 : a > $o,X1 : a > $o] : (? [X2 : a] : ((cZ @ X2) & (X0 @ X2) & (X1 @ X2)) => ? [X2 : a] : ((X1 @ X2) & (X0 @ X2)))),
% 1.50/1.23 file('/export/starexec/sandbox/tmp/tmp.ZjlS5YgwEk/DTF2THF_3344.p',cBOOL_PROP_102_pme)).
% 1.50/1.23 thf(f16,plain,(
% 1.50/1.23 ($true != (sK0 @ sK2))),
% 1.50/1.23 inference(trivial_inequality_removal,[status(thm)],[f15])).
% 1.50/1.23 thf(f15,plain,(
% 1.50/1.23 ($true != (sK0 @ sK2)) | ($true != $true)),
% 1.50/1.23 inference(superposition,[status(thm)],[f14,f12])).
% 1.50/1.23 thf(f12,plain,(
% 1.50/1.23 ($true = (sK1 @ sK2))),
% 1.50/1.23 inference(cnf_transformation,[status(thm)],[f10])).
% 1.50/1.23 thf(f14,plain,(
% 1.50/1.23 ( ! [X2 : a] : (($true != (sK1 @ X2)) | ($true != (sK0 @ X2))) )),
% 1.50/1.23 inference(cnf_transformation,[status(thm)],[f10])).
% 1.50/1.23 % SZS output end Proof for DTF2THF_3344
% 1.50/1.23 % (3443)------------------------------
% 1.50/1.23 % (3443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.23 % (3443)Termination reason: Refutation
% 1.50/1.23
% 1.50/1.23 % (3443)Memory used [KB]: 5500
% 1.50/1.23 % (3443)Time elapsed: 0.003 s
% 1.50/1.23 % (3443)Instructions burned: 1 (million)
% 1.50/1.23 % (3443)------------------------------
% 1.50/1.23 % (3443)------------------------------
% 1.50/1.23 % (3440)Success in time 0.003 s
%------------------------------------------------------------------------------