%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYN382^5 : 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 09:50:53 AM UTC 2026
% Result : Theorem 1.49s 1.28s
% Output : Refutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 105 ( 28 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 125 ( 15 ~; 14 |; 6 &; 84 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 41 ( 0 ^; 29 !; 12 ?; 41 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cQ: $i > $i > $o ).
thf(func_def_1,type,
cP: $i > $i > $o ).
thf(func_def_5,type,
sK0: $i > $i ).
thf(f16,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f15]) ).
thf(f15,plain,
$true != $true,
inference(superposition,[status(thm)],[f10,f14]) ).
thf(f14,plain,
! [X0: $i] :
( ( cP @ ( sK0 @ sK1 ) @ X0 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: $i] :
( ( ( cP @ ( sK0 @ sK1 ) @ X0 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f11,f12]) ).
thf(f12,plain,
! [X2: $i,X0: $i] :
( ( $true
= ( cQ @ ( sK0 @ X0 ) @ X0 ) )
| ( ( cP @ ( sK0 @ X0 ) @ X2 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X0: $i] :
( ! [X2: $i] :
( ( cP @ ( sK0 @ X0 ) @ X2 )
= $true )
| ( $true
= ( cQ @ ( sK0 @ X0 ) @ X0 ) ) )
& ! [X4: $i] :
( ( $true
!= ( cQ @ X4 @ sK1 ) )
& ( $true
!= ( cP @ X4 @ sK1 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f8,f7]) ).
thf(f7,plain,
! [X0: $i] :
( ? [X1: $i] :
( ! [X2: $i] :
( ( cP @ X1 @ X2 )
= $true )
| ( ( cQ @ X1 @ X0 )
= $true ) )
=> ( ! [X2: $i] :
( ( cP @ ( sK0 @ X0 ) @ X2 )
= $true )
| ( $true
= ( cQ @ ( sK0 @ X0 ) @ X0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ? [X3: $i] :
! [X4: $i] :
( ( $true
!= ( cQ @ X4 @ X3 ) )
& ( ( cP @ X4 @ X3 )
!= $true ) )
=> ! [X4: $i] :
( ( $true
!= ( cQ @ X4 @ sK1 ) )
& ( $true
!= ( cP @ X4 @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
( ! [X0: $i] :
? [X1: $i] :
( ! [X2: $i] :
( ( cP @ X1 @ X2 )
= $true )
| ( ( cQ @ X1 @ X0 )
= $true ) )
& ? [X3: $i] :
! [X4: $i] :
( ( $true
!= ( cQ @ X4 @ X3 ) )
& ( ( cP @ X4 @ X3 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ! [X0: $i] :
? [X1: $i] :
( ! [X2: $i] :
( ( cP @ X1 @ X2 )
= $true )
| ( ( cQ @ X1 @ X0 )
= $true ) )
=> ! [X3: $i] :
? [X4: $i] :
( ( $true
= ( cQ @ X4 @ X3 ) )
| ( ( cP @ X4 @ X3 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: $i] :
? [X1: $i] :
( ( cQ @ X1 @ X0 )
| ! [X2: $i] : ( cP @ X1 @ X2 ) )
=> ! [X3: $i] :
? [X4: $i] :
( ( cQ @ X4 @ X3 )
| ( cP @ X4 @ X3 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: $i] :
? [X1: $i] :
( ( cQ @ X1 @ X0 )
| ! [X2: $i] : ( cP @ X1 @ X2 ) )
=> ! [X2: $i] :
? [X1: $i] :
( ( cQ @ X1 @ X2 )
| ( cP @ X1 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X0: $i] :
? [X1: $i] :
( ( cQ @ X1 @ X0 )
| ! [X2: $i] : ( cP @ X1 @ X2 ) )
=> ! [X2: $i] :
? [X1: $i] :
( ( cQ @ X1 @ X2 )
| ( cP @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.QqeX8nqJ6d/DTF2THF_3584.p',cX2134) ).
thf(f11,plain,
! [X4: $i] :
( $true
!= ( cQ @ X4 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f10,plain,
! [X4: $i] :
( $true
!= ( cP @ X4 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN382^5 : 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
% 0.17/0.34 % Computer : n029.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 13:56:44 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.28/0.46 ---- Original DTF file ---
% 0.28/0.46 thf(spec,logic,$$dhol).
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 % File : SYN382^5 : TPTP v9.2.1. Released v4.0.0.
% 0.28/0.46 % Domain : Syntactic
% 0.28/0.46 % Problem : TPS problem X2134
% 0.28/0.46 % Version : Especial.
% 0.28/0.46 % English :
% 0.28/0.46
% 0.28/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.28/0.46 % Source : [Bro09]
% 0.28/0.46 % Names : tps_0126 [Bro09]
% 0.28/0.46 % : X2134 [TPS]
% 0.28/0.46
% 0.28/0.46 % Status : Theorem
% 0.28/0.46 % Rating : 0.00 v6.2.0, 0.17 v6.0.0, 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v4.0.0
% 0.28/0.46 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.28/0.46 % Number of atoms : 4 ( 0 equ; 0 cnn)
% 0.28/0.46 % Maximal formula atoms : 4 ( 4 avg)
% 0.28/0.46 % Number of connectives : 11 ( 0 ~; 2 |; 0 &; 8 @)
% 0.28/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.28/0.46 % Maximal formula depth : 8 ( 8 avg)
% 0.28/0.46 % Number of types : 2 ( 0 usr)
% 0.28/0.46 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.28/0.46 % Number of symbols : 2 ( 2 usr; 0 con; 2-2 aty)
% 0.28/0.46 % Number of variables : 5 ( 0 ^; 3 !; 2 ?; 5 :)
% 0.28/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.28/0.46
% 0.28/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.28/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.28/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.28/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.28/0.46 % :
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 thf(cQ,type,
% 0.28/0.46 cQ: $i > $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(cP,type,
% 0.28/0.46 cP: $i > $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(cX2134,conjecture,
% 0.28/0.46 ( ! [Xz: $i] :
% 0.28/0.46 ? [Xx: $i] :
% 0.28/0.46 ( ! [Xy: $i] : ( cP @ Xx @ Xy )
% 0.28/0.46 | ( cQ @ Xx @ Xz ) )
% 0.28/0.46 => ! [Xy: $i] :
% 0.28/0.46 ? [Xx: $i] :
% 0.28/0.46 ( ( cP @ Xx @ Xy )
% 0.28/0.46 | ( cQ @ Xx @ Xy ) ) ) ).
% 0.28/0.46
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 ------------------------
% 1.49/1.25 ---- Embedded in THF ---
% 1.49/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.25 %%% Generated on Tue Feb 24 13:56:45 EST 2026
% 1.49/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.25 %%% Logic specification used:
% 1.49/1.25 %%% thf(spec, logic, $$dhol).
% 1.49/1.25
% 1.49/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.QqeX8nqJ6d/DTF2DTF3584.p
% See solution above
% 1.49/1.25 ------------------------
% 1.49/1.26 ---- Cleaned THF ---
% 1.49/1.26 thf(cQ,type,
% 1.49/1.26 cQ: $i > $i > $o ).
% 1.49/1.26
% 1.49/1.26 thf(cP,type,
% 1.49/1.26 cP: $i > $i > $o ).
% 1.49/1.26
% 1.49/1.26 thf(cX2134,conjecture,
% 1.49/1.26 ( ! [Xz: $i] :
% 1.49/1.26 ? [Xx: $i] :
% 1.49/1.26 ( ! [Xy: $i] : ( cP @ Xx @ Xy )
% 1.49/1.26 | ( cQ @ Xx @ Xz ) )
% 1.49/1.26 => ! [Xy: $i] :
% 1.49/1.26 ? [Xx: $i] :
% 1.49/1.26 ( ( cP @ Xx @ Xy )
% 1.49/1.26 | ( cQ @ Xx @ Xy ) ) ) ).
% 1.49/1.26 ------------------------
% 1.49/1.27 % (3863)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3584 for (2999ds/183Mi)
% 1.49/1.27 % (3864)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_3584 for (2999ds/4Mi)
% 1.49/1.27 % (3863)First to succeed.
% 1.49/1.28 % (3864)Also succeeded, but the first one will report.
% 1.49/1.28 % (3863)Refutation found. Thanks to Tanya!
% 1.49/1.28 % SZS status Theorem for DTF2THF_3584
% 1.49/1.28 % SZS output start Proof for DTF2THF_3584
% 1.49/1.28 thf(func_def_0, type, cQ: $i > $i > $o).
% 1.49/1.28 thf(func_def_1, type, cP: $i > $i > $o).
% 1.49/1.28 thf(func_def_5, type, sK0: $i > $i).
% 1.49/1.28 thf(f16,plain,(
% 1.49/1.28 $false),
% 1.49/1.28 inference(trivial_inequality_removal,[status(thm)],[f15])).
% 1.49/1.28 thf(f15,plain,(
% 1.49/1.28 ($true != $true)),
% 1.49/1.28 inference(superposition,[status(thm)],[f10,f14])).
% 1.49/1.28 thf(f14,plain,(
% 1.49/1.28 ( ! [X0 : $i] : (((cP @ (sK0 @ sK1) @ X0) = $true)) )),
% 1.49/1.28 inference(trivial_inequality_removal,[status(thm)],[f13])).
% 1.49/1.28 thf(f13,plain,(
% 1.49/1.28 ( ! [X0 : $i] : (((cP @ (sK0 @ sK1) @ X0) = $true) | ($true != $true)) )),
% 1.49/1.28 inference(superposition,[status(thm)],[f11,f12])).
% 1.49/1.28 thf(f12,plain,(
% 1.49/1.28 ( ! [X2 : $i,X0 : $i] : (($true = (cQ @ (sK0 @ X0) @ X0)) | ((cP @ (sK0 @ X0) @ X2) = $true)) )),
% 1.49/1.28 inference(cnf_transformation,[status(thm)],[f9])).
% 1.49/1.28 thf(f9,plain,(
% 1.49/1.28 ! [X0 : $i] : (! [X2 : $i] : ((cP @ (sK0 @ X0) @ X2) = $true) | ($true = (cQ @ (sK0 @ X0) @ X0))) & ! [X4 : $i] : (($true != (cQ @ X4 @ sK1)) & ($true != (cP @ X4 @ sK1)))),
% 1.49/1.28 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f8,f7])).
% 1.49/1.28 thf(f7,plain,(
% 1.49/1.28 ! [X0 : $i] : (? [X1 : $i] : (! [X2 : $i] : ((cP @ X1 @ X2) = $true) | ((cQ @ X1 @ X0) = $true)) => (! [X2 : $i] : ((cP @ (sK0 @ X0) @ X2) = $true) | ($true = (cQ @ (sK0 @ X0) @ X0))))),
% 1.49/1.28 introduced(definition,[],[choice_axiom])).
% 1.49/1.28 thf(f8,plain,(
% 1.49/1.28 ? [X3 : $i] : ! [X4 : $i] : (($true != (cQ @ X4 @ X3)) & ((cP @ X4 @ X3) != $true)) => ! [X4 : $i] : (($true != (cQ @ X4 @ sK1)) & ($true != (cP @ X4 @ sK1)))),
% 1.49/1.28 introduced(definition,[],[choice_axiom])).
% 1.49/1.28 thf(f6,plain,(
% 1.49/1.28 ! [X0 : $i] : ? [X1 : $i] : (! [X2 : $i] : ((cP @ X1 @ X2) = $true) | ((cQ @ X1 @ X0) = $true)) & ? [X3 : $i] : ! [X4 : $i] : (($true != (cQ @ X4 @ X3)) & ((cP @ X4 @ X3) != $true))),
% 1.49/1.28 inference(ennf_transformation,[status(thm)],[f5])).
% 1.49/1.28 thf(f5,plain,(
% 1.49/1.28 ~(! [X0 : $i] : ? [X1 : $i] : (! [X2 : $i] : ((cP @ X1 @ X2) = $true) | ((cQ @ X1 @ X0) = $true)) => ! [X3 : $i] : ? [X4 : $i] : (($true = (cQ @ X4 @ X3)) | ((cP @ X4 @ X3) = $true)))),
% 1.49/1.28 inference(fool_elimination,[status(thm)],[f4])).
% 1.49/1.28 thf(f4,plain,(
% 1.49/1.28 ~(! [X0 : $i] : ? [X1 : $i] : ((cQ @ X1 @ X0) | ! [X2 : $i] : (cP @ X1 @ X2)) => ! [X3 : $i] : ? [X4 : $i] : ((cQ @ X4 @ X3) | (cP @ X4 @ X3)))),
% 1.49/1.28 inference(rectify,[status(thm)],[f2])).
% 1.49/1.28 thf(f2,negated_conjecture,(
% 1.49/1.28 ~(! [X0 : $i] : ? [X1 : $i] : ((cQ @ X1 @ X0) | ! [X2 : $i] : (cP @ X1 @ X2)) => ! [X2 : $i] : ? [X1 : $i] : ((cQ @ X1 @ X2) | (cP @ X1 @ X2)))),
% 1.49/1.28 inference(negated_conjecture,[status(cth)],[f1])).
% 1.49/1.28 thf(f1,conjecture,(
% 1.49/1.28 ! [X0 : $i] : ? [X1 : $i] : ((cQ @ X1 @ X0) | ! [X2 : $i] : (cP @ X1 @ X2)) => ! [X2 : $i] : ? [X1 : $i] : ((cQ @ X1 @ X2) | (cP @ X1 @ X2))),
% 1.49/1.28 file('/export/starexec/sandbox/tmp/tmp.QqeX8nqJ6d/DTF2THF_3584.p',cX2134)).
% 1.49/1.28 thf(f11,plain,(
% 1.49/1.28 ( ! [X4 : $i] : (($true != (cQ @ X4 @ sK1))) )),
% 1.49/1.28 inference(cnf_transformation,[status(thm)],[f9])).
% 1.49/1.28 thf(f10,plain,(
% 1.49/1.28 ( ! [X4 : $i] : (($true != (cP @ X4 @ sK1))) )),
% 1.49/1.28 inference(cnf_transformation,[status(thm)],[f9])).
% 1.49/1.28 % SZS output end Proof for DTF2THF_3584
% 1.49/1.28 % (3863)------------------------------
% 1.49/1.28 % (3863)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.28 % (3863)Termination reason: Refutation
% 1.49/1.28
% 1.49/1.28 % (3863)Memory used [KB]: 5500
% 1.49/1.28 % (3863)Time elapsed: 0.003 s
% 1.49/1.28 % (3863)Instructions burned: 1 (million)
% 1.49/1.28 % (3863)------------------------------
% 1.49/1.28 % (3863)------------------------------
% 1.49/1.28 % (3862)Success in time 0.012 s
%------------------------------------------------------------------------------