%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO147^5 : 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 : n001.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 09:53:29 AM UTC 2026
% Result : Theorem 1.49s 1.26s
% Output : Refutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 16 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 157 ( 46 equ; 0 cnn)
% Maximal formula atoms : 12 ( 9 avg)
% Number of connectives : 148 ( 23 ~; 13 |; 23 &; 76 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 22 ( 0 ^; 15 !; 7 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cP3: $i > $o ).
thf(func_def_1,type,
cP2: $i > $o ).
thf(func_def_2,type,
cP1: $i > $o ).
thf(func_def_6,type,
sK0: $i > $i ).
thf(f17,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f16,f14]) ).
thf(f14,plain,
! [X0: $i] :
( ( cP2 @ X0 )
!= $true ),
inference(subsumption_resolution,[status(thm)],[f13,f12]) ).
thf(f12,plain,
! [X0: $i] :
( ( cP3 @ X0 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $i] :
( ( ( $true
= ( cP3 @ ( sK0 @ X0 ) ) )
| ( ( cP2 @ X0 )
!= $true ) )
& ( ( cP3 @ X0 )
!= $true )
& ( ( $true
= ( cP2 @ ( sK0 @ X0 ) ) )
| ( ( cP1 @ X0 )
!= $true ) )
& ( ( cP1 @ ( sK0 @ X0 ) )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8]) ).
thf(f8,plain,
! [X0: $i] :
( ? [X1: $i] :
( ( ( ( cP3 @ X1 )
= $true )
| ( ( cP2 @ X0 )
!= $true ) )
& ( ( cP3 @ X0 )
!= $true )
& ( ( ( cP2 @ X1 )
= $true )
| ( ( cP1 @ X0 )
!= $true ) )
& ( ( cP1 @ X1 )
= $true ) )
=> ( ( ( $true
= ( cP3 @ ( sK0 @ X0 ) ) )
| ( ( cP2 @ X0 )
!= $true ) )
& ( ( cP3 @ X0 )
!= $true )
& ( ( $true
= ( cP2 @ ( sK0 @ X0 ) ) )
| ( ( cP1 @ X0 )
!= $true ) )
& ( ( cP1 @ ( sK0 @ X0 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
! [X0: $i] :
? [X1: $i] :
( ( ( ( cP3 @ X1 )
= $true )
| ( ( cP2 @ X0 )
!= $true ) )
& ( ( cP3 @ X0 )
!= $true )
& ( ( ( cP2 @ X1 )
= $true )
| ( ( cP1 @ X0 )
!= $true ) )
& ( ( cP1 @ X1 )
= $true ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: $i] :
? [X1: $i] :
( ( ( cP3 @ X0 )
!= $true )
& ( ( ( cP2 @ X1 )
= $true )
| ( ( cP1 @ X0 )
!= $true ) )
& ( ( ( cP3 @ X1 )
= $true )
| ( ( cP2 @ X0 )
!= $true ) )
& ( ( cP1 @ X1 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ? [X0: $i] :
! [X1: $i] :
( ( ( ( ( cP1 @ X0 )
= $true )
=> ( ( cP2 @ X1 )
= $true ) )
& ( ( ( cP2 @ X0 )
= $true )
=> ( ( cP3 @ X1 )
= $true ) )
& ( ( cP1 @ X1 )
= $true ) )
=> ( ( cP3 @ X0 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ? [X0: $i] :
! [X1: $i] :
( ( ( ( cP1 @ X0 )
=> ( cP2 @ X1 ) )
& ( ( cP2 @ X0 )
=> ( cP3 @ X1 ) )
& ( cP1 @ X1 ) )
=> ( cP3 @ X0 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X0: $i] :
! [X1: $i] :
( ( ( ( cP1 @ X0 )
=> ( cP2 @ X1 ) )
& ( ( cP2 @ X0 )
=> ( cP3 @ X1 ) )
& ( cP1 @ X1 ) )
=> ( cP3 @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X0: $i] :
! [X1: $i] :
( ( ( ( cP1 @ X0 )
=> ( cP2 @ X1 ) )
& ( ( cP2 @ X0 )
=> ( cP3 @ X1 ) )
& ( cP1 @ X1 ) )
=> ( cP3 @ X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.q17Ty8Ud3I/DTF2THF_6417.p',cBAFFLER3) ).
thf(f13,plain,
! [X0: $i] :
( ( $true
= ( cP3 @ ( sK0 @ X0 ) ) )
| ( ( cP2 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f16,plain,
! [X0: $i] :
( ( cP2 @ ( sK0 @ ( sK0 @ X0 ) ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( cP2 @ ( sK0 @ ( sK0 @ X0 ) ) )
= $true ) ),
inference(superposition,[status(thm)],[f11,f10]) ).
thf(f10,plain,
! [X0: $i] :
( ( cP1 @ ( sK0 @ X0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f11,plain,
! [X0: $i] :
( ( ( cP1 @ X0 )
!= $true )
| ( $true
= ( cP2 @ ( sK0 @ X0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO147^5 : 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
% 0.15/0.34 % Computer : n001.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 14:25:35 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.44 ---- Original DTF file ---
% 0.18/0.44 thf(spec,logic,$$dhol).
% 0.18/0.44 %------------------------------------------------------------------------------
% 0.18/0.44 % File : SYO147^5 : TPTP v9.2.1. Released v4.0.0.
% 0.18/0.44 % Domain : Syntactic
% 0.18/0.44 % Problem : TPS problem from BASIC-FO-THMS
% 0.18/0.44 % Version : Especial.
% 0.18/0.44 % English :
% 0.18/0.44
% 0.18/0.44 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.18/0.44 % Source : [Bro09]
% 0.18/0.44 % Names : tps_0791 [Bro09]
% 0.18/0.44
% 0.18/0.44 % Status : Theorem
% 0.18/0.44 % Rating : 0.08 v9.1.0, 0.12 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.08 v7.4.0, 0.11 v7.3.0, 0.10 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.0.0, 0.00 v4.0.0
% 0.18/0.44 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.18/0.44 % Number of atoms : 6 ( 0 equ; 0 cnn)
% 0.18/0.44 % Maximal formula atoms : 6 ( 6 avg)
% 0.18/0.44 % Number of connectives : 11 ( 0 ~; 0 |; 2 &; 6 @)
% 0.18/0.44 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.18/0.44 % Maximal formula depth : 8 ( 8 avg)
% 0.18/0.44 % Number of types : 2 ( 0 usr)
% 0.18/0.44 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.18/0.44 % Number of symbols : 3 ( 3 usr; 0 con; 1-1 aty)
% 0.18/0.44 % Number of variables : 2 ( 0 ^; 1 !; 1 ?; 2 :)
% 0.18/0.44 % SPC : TH0_THM_NEQ_NAR
% 0.18/0.44
% 0.18/0.44 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.18/0.44 % project in the Department of Mathematical Sciences at Carnegie
% 0.18/0.44 % Mellon University. Distributed under the Creative Commons copyleft
% 0.18/0.44 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.18/0.44 %------------------------------------------------------------------------------
% 0.18/0.44 thf(cP3,type,
% 0.18/0.44 cP3: $i > $o ).
% 0.18/0.44
% 0.18/0.44 thf(cP2,type,
% 0.18/0.44 cP2: $i > $o ).
% 0.18/0.44
% 0.18/0.44 thf(cP1,type,
% 0.18/0.44 cP1: $i > $o ).
% 0.18/0.44
% 0.18/0.44 thf(cBAFFLER3,conjecture,
% 0.18/0.44 ? [Xy: $i] :
% 0.18/0.44 ! [Xx: $i] :
% 0.18/0.44 ( ( ( cP1 @ Xx )
% 0.18/0.44 & ( ( cP1 @ Xy )
% 0.18/0.44 => ( cP2 @ Xx ) )
% 0.18/0.44 & ( ( cP2 @ Xy )
% 0.18/0.44 => ( cP3 @ Xx ) ) )
% 0.18/0.44 => ( cP3 @ Xy ) ) ).
% 0.18/0.44
% 0.18/0.44 %------------------------------------------------------------------------------
% 0.18/0.44 ------------------------
% 1.49/1.24 ---- Embedded in THF ---
% 1.49/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.24 %%% Generated on Tue Feb 24 14:25:36 EST 2026
% 1.49/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.24 %%% Logic specification used:
% 1.49/1.24 %%% thf(spec, logic, $$dhol).
% 1.49/1.24
% 1.49/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.q17Ty8Ud3I/DTF2DTF6417.p
% See solution above
% 1.49/1.24 ------------------------
% 1.49/1.25 ---- Cleaned THF ---
% 1.49/1.25 thf(cP3,type,
% 1.49/1.25 cP3: $i > $o ).
% 1.49/1.25
% 1.49/1.25 thf(cP2,type,
% 1.49/1.25 cP2: $i > $o ).
% 1.49/1.25
% 1.49/1.25 thf(cP1,type,
% 1.49/1.25 cP1: $i > $o ).
% 1.49/1.25
% 1.49/1.25 thf(cBAFFLER3,conjecture,
% 1.49/1.25 ? [Xy: $i] :
% 1.49/1.25 ! [Xx: $i] :
% 1.49/1.25 ( ( ( cP1 @ Xx )
% 1.49/1.25 & ( ( cP1 @ Xy )
% 1.49/1.25 => ( cP2 @ Xx ) )
% 1.49/1.25 & ( ( cP2 @ Xy )
% 1.49/1.25 => ( cP3 @ Xx ) ) )
% 1.49/1.25 => ( cP3 @ Xy ) ) ).
% 1.49/1.25 ------------------------
% 1.49/1.26 % (6721)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_6417 for (2999ds/2Mi)
% 1.49/1.26 % (6721)First to succeed.
% 1.49/1.26 % (6721)Refutation found. Thanks to Tanya!
% 1.49/1.26 % SZS status Theorem for DTF2THF_6417
% 1.49/1.26 % SZS output start Proof for DTF2THF_6417
% 1.49/1.26 thf(func_def_0, type, cP3: $i > $o).
% 1.49/1.26 thf(func_def_1, type, cP2: $i > $o).
% 1.49/1.26 thf(func_def_2, type, cP1: $i > $o).
% 1.49/1.26 thf(func_def_6, type, sK0: $i > $i).
% 1.49/1.26 thf(f17,plain,(
% 1.49/1.26 $false),
% 1.49/1.26 inference(subsumption_resolution,[status(thm)],[f16,f14])).
% 1.49/1.26 thf(f14,plain,(
% 1.49/1.26 ( ! [X0 : $i] : (((cP2 @ X0) != $true)) )),
% 1.49/1.26 inference(subsumption_resolution,[status(thm)],[f13,f12])).
% 1.49/1.26 thf(f12,plain,(
% 1.49/1.26 ( ! [X0 : $i] : (((cP3 @ X0) != $true)) )),
% 1.49/1.26 inference(cnf_transformation,[status(thm)],[f9])).
% 1.49/1.26 thf(f9,plain,(
% 1.49/1.26 ! [X0 : $i] : ((($true = (cP3 @ (sK0 @ X0))) | ((cP2 @ X0) != $true)) & ((cP3 @ X0) != $true) & (($true = (cP2 @ (sK0 @ X0))) | ((cP1 @ X0) != $true)) & ((cP1 @ (sK0 @ X0)) = $true))),
% 1.49/1.26 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8])).
% 1.49/1.26 thf(f8,plain,(
% 1.49/1.26 ! [X0 : $i] : (? [X1 : $i] : ((((cP3 @ X1) = $true) | ((cP2 @ X0) != $true)) & ((cP3 @ X0) != $true) & (((cP2 @ X1) = $true) | ((cP1 @ X0) != $true)) & ((cP1 @ X1) = $true)) => ((($true = (cP3 @ (sK0 @ X0))) | ((cP2 @ X0) != $true)) & ((cP3 @ X0) != $true) & (($true = (cP2 @ (sK0 @ X0))) | ((cP1 @ X0) != $true)) & ((cP1 @ (sK0 @ X0)) = $true)))),
% 1.49/1.26 introduced(definition,[],[choice_axiom])).
% 1.49/1.26 thf(f7,plain,(
% 1.49/1.26 ! [X0 : $i] : ? [X1 : $i] : ((((cP3 @ X1) = $true) | ((cP2 @ X0) != $true)) & ((cP3 @ X0) != $true) & (((cP2 @ X1) = $true) | ((cP1 @ X0) != $true)) & ((cP1 @ X1) = $true))),
% 1.49/1.26 inference(flattening,[status(thm)],[f6])).
% 1.49/1.26 thf(f6,plain,(
% 1.49/1.26 ! [X0 : $i] : ? [X1 : $i] : (((cP3 @ X0) != $true) & ((((cP2 @ X1) = $true) | ((cP1 @ X0) != $true)) & (((cP3 @ X1) = $true) | ((cP2 @ X0) != $true)) & ((cP1 @ X1) = $true)))),
% 1.49/1.26 inference(ennf_transformation,[status(thm)],[f5])).
% 1.49/1.26 thf(f5,plain,(
% 1.49/1.26 ~? [X0 : $i] : ! [X1 : $i] : (((((cP1 @ X0) = $true) => ((cP2 @ X1) = $true)) & (((cP2 @ X0) = $true) => ((cP3 @ X1) = $true)) & ((cP1 @ X1) = $true)) => ((cP3 @ X0) = $true))),
% 1.49/1.26 inference(fool_elimination,[status(thm)],[f4])).
% 1.49/1.26 thf(f4,plain,(
% 1.49/1.26 ~? [X0 : $i] : ! [X1 : $i] : ((((cP1 @ X0) => (cP2 @ X1)) & ((cP2 @ X0) => (cP3 @ X1)) & (cP1 @ X1)) => (cP3 @ X0))),
% 1.49/1.26 inference(rectify,[status(thm)],[f2])).
% 1.49/1.26 thf(f2,negated_conjecture,(
% 1.49/1.26 ~? [X0 : $i] : ! [X1 : $i] : ((((cP1 @ X0) => (cP2 @ X1)) & ((cP2 @ X0) => (cP3 @ X1)) & (cP1 @ X1)) => (cP3 @ X0))),
% 1.49/1.26 inference(negated_conjecture,[status(cth)],[f1])).
% 1.49/1.26 thf(f1,conjecture,(
% 1.49/1.26 ? [X0 : $i] : ! [X1 : $i] : ((((cP1 @ X0) => (cP2 @ X1)) & ((cP2 @ X0) => (cP3 @ X1)) & (cP1 @ X1)) => (cP3 @ X0))),
% 1.49/1.26 file('/export/starexec/sandbox/tmp/tmp.q17Ty8Ud3I/DTF2THF_6417.p',cBAFFLER3)).
% 1.49/1.26 thf(f13,plain,(
% 1.49/1.26 ( ! [X0 : $i] : (($true = (cP3 @ (sK0 @ X0))) | ((cP2 @ X0) != $true)) )),
% 1.49/1.26 inference(cnf_transformation,[status(thm)],[f9])).
% 1.49/1.26 thf(f16,plain,(
% 1.49/1.26 ( ! [X0 : $i] : (((cP2 @ (sK0 @ (sK0 @ X0))) = $true)) )),
% 1.49/1.26 inference(trivial_inequality_removal,[status(thm)],[f15])).
% 1.49/1.26 thf(f15,plain,(
% 1.49/1.26 ( ! [X0 : $i] : (($true != $true) | ((cP2 @ (sK0 @ (sK0 @ X0))) = $true)) )),
% 1.49/1.26 inference(superposition,[status(thm)],[f11,f10])).
% 1.49/1.26 thf(f10,plain,(
% 1.49/1.26 ( ! [X0 : $i] : (((cP1 @ (sK0 @ X0)) = $true)) )),
% 1.49/1.26 inference(cnf_transformation,[status(thm)],[f9])).
% 1.49/1.26 thf(f11,plain,(
% 1.49/1.26 ( ! [X0 : $i] : (((cP1 @ X0) != $true) | ($true = (cP2 @ (sK0 @ X0)))) )),
% 1.49/1.26 inference(cnf_transformation,[status(thm)],[f9])).
% 1.49/1.26 % SZS output end Proof for DTF2THF_6417
% 1.49/1.26 % (6721)------------------------------
% 1.49/1.26 % (6721)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.26 % (6721)Termination reason: Refutation
% 1.49/1.26
% 1.49/1.26 % (6721)Memory used [KB]: 5500
% 1.49/1.26 % (6721)Time elapsed: 0.002 s
% 1.49/1.26 % (6721)Instructions burned: 1 (million)
% 1.49/1.26 % (6721)------------------------------
% 1.49/1.26 % (6721)------------------------------
% 1.49/1.26 % (6717)Success in time 0.012 s
%------------------------------------------------------------------------------