%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO145^5 : 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 : 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 09:53:29 AM UTC 2026
% Result : Theorem 1.55s 1.21s
% Output : Refutation 1.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 81 ( 22 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 98 ( 17 ~; 6 |; 6 &; 63 @)
% ( 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 : 6 ( 3 usr; 3 con; 0-2 aty)
% Number of variables : 40 ( 0 ^; 24 !; 16 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cP: $i > $i > $o ).
thf(func_def_4,type,
sK0: $i > $i ).
thf(f15,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f14]) ).
thf(f14,plain,
$true != $true,
inference(superposition,[status(thm)],[f13,f11]) ).
thf(f11,plain,
! [X0: $i] :
( ( cP @ X0 @ ( sK0 @ X0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X0: $i] :
( ( cP @ X0 @ ( sK0 @ X0 ) )
= $true )
& ! [X3: $i,X4: $i] :
( ( ( cP @ X4 @ X3 )
!= $true )
| ( ( cP @ sK1 @ X4 )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f8,f7]) ).
thf(f7,plain,
! [X0: $i] :
( ? [X1: $i] :
( ( cP @ X0 @ X1 )
= $true )
=> ( ( cP @ X0 @ ( sK0 @ X0 ) )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ? [X2: $i] :
! [X3: $i,X4: $i] :
( ( ( cP @ X4 @ X3 )
!= $true )
| ( $true
!= ( cP @ X2 @ X4 ) ) )
=> ! [X4: $i,X3: $i] :
( ( ( cP @ X4 @ X3 )
!= $true )
| ( ( cP @ sK1 @ X4 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
( ! [X0: $i] :
? [X1: $i] :
( ( cP @ X0 @ X1 )
= $true )
& ? [X2: $i] :
! [X3: $i,X4: $i] :
( ( ( cP @ X4 @ X3 )
!= $true )
| ( $true
!= ( cP @ X2 @ X4 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ! [X0: $i] :
? [X1: $i] :
( ( cP @ X0 @ X1 )
= $true )
=> ! [X2: $i] :
? [X3: $i,X4: $i] :
( ( $true
= ( cP @ X2 @ X4 ) )
& ( ( cP @ X4 @ X3 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: $i] :
? [X1: $i] : ( cP @ X0 @ X1 )
=> ! [X2: $i] :
? [X3: $i,X4: $i] :
( ( cP @ X4 @ X3 )
& ( cP @ X2 @ X4 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: $i] :
? [X1: $i] : ( cP @ X0 @ X1 )
=> ! [X0: $i] :
? [X2: $i,X1: $i] :
( ( cP @ X1 @ X2 )
& ( cP @ X0 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X0: $i] :
? [X1: $i] : ( cP @ X0 @ X1 )
=> ! [X0: $i] :
? [X2: $i,X1: $i] :
( ( cP @ X1 @ X2 )
& ( cP @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.o3fZelF5nP/DTF2THF_27742.p',cEXPVAR_BUG) ).
thf(f13,plain,
! [X0: $i] :
( ( cP @ ( sK0 @ sK1 ) @ X0 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: $i] :
( ( ( cP @ ( sK0 @ sK1 ) @ X0 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f10,f11]) ).
thf(f10,plain,
! [X3: $i,X4: $i] :
( ( ( cP @ sK1 @ X4 )
!= $true )
| ( ( cP @ X4 @ X3 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SYO145^5 : 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
% 0.11/0.30 % Computer : n029.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Tue Feb 24 14:24:59 EST 2026
% 0.11/0.30 % CPUTime :
% 0.11/0.30 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.41 ---- Original DTF file ---
% 0.16/0.41 thf(spec,logic,$$dhol).
% 0.16/0.41 %------------------------------------------------------------------------------
% 0.16/0.41 % File : SYO145^5 : TPTP v9.2.1. Released v4.0.0.
% 0.16/0.41 % Domain : Syntactic
% 0.16/0.41 % Problem : TPS problem from BASIC-FO-THMS
% 0.16/0.41 % Version : Especial.
% 0.16/0.41 % English :
% 0.16/0.41
% 0.16/0.41 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.41 % Source : [Bro09]
% 0.16/0.41 % Names : tps_0784 [Bro09]
% 0.16/0.41
% 0.16/0.41 % Status : Theorem
% 0.16/0.41 % 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
% 0.16/0.41 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.16/0.41 % Number of atoms : 3 ( 0 equ; 0 cnn)
% 0.16/0.41 % Maximal formula atoms : 3 ( 3 avg)
% 0.16/0.41 % Number of connectives : 8 ( 0 ~; 0 |; 1 &; 6 @)
% 0.16/0.41 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.16/0.41 % Maximal formula depth : 8 ( 8 avg)
% 0.16/0.41 % Number of types : 2 ( 0 usr)
% 0.16/0.41 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.16/0.41 % Number of symbols : 1 ( 1 usr; 0 con; 2-2 aty)
% 0.16/0.41 % Number of variables : 5 ( 0 ^; 2 !; 3 ?; 5 :)
% 0.16/0.41 % SPC : TH0_THM_NEQ_NAR
% 0.16/0.41
% 0.16/0.41 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.16/0.41 % project in the Department of Mathematical Sciences at Carnegie
% 0.16/0.41 % Mellon University. Distributed under the Creative Commons copyleft
% 0.16/0.41 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.16/0.41 %------------------------------------------------------------------------------
% 0.16/0.41 thf(cP,type,
% 0.16/0.41 cP: $i > $i > $o ).
% 0.16/0.41
% 0.16/0.41 thf(cEXPVAR_BUG,conjecture,
% 0.16/0.41 ( ! [Xx: $i] :
% 0.16/0.41 ? [Xy: $i] : ( cP @ Xx @ Xy )
% 0.16/0.41 => ! [Xx: $i] :
% 0.16/0.41 ? [Xy: $i,Xz: $i] :
% 0.16/0.41 ( ( cP @ Xy @ Xz )
% 0.16/0.41 & ( cP @ Xx @ Xy ) ) ) ).
% 0.16/0.41
% 0.16/0.41 %------------------------------------------------------------------------------
% 0.16/0.41 ------------------------
% 1.45/1.18 ---- Embedded in THF ---
% 1.45/1.18 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.45/1.18 %%% Generated on Tue Feb 24 14:25:00 EST 2026
% 1.45/1.18 %%% using '$$dhol' embedding, version 1.3.0.
% 1.45/1.18 %%% Logic specification used:
% 1.45/1.18 %%% thf(spec, logic, $$dhol).
% 1.45/1.18
% 1.45/1.18 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.o3fZelF5nP/DTF2DTF27742.p
% See solution above
% 1.45/1.18 ------------------------
% 1.45/1.19 ---- Cleaned THF ---
% 1.45/1.19 thf(cP,type,
% 1.45/1.19 cP: $i > $i > $o ).
% 1.45/1.19
% 1.45/1.19 thf(cEXPVAR_BUG,conjecture,
% 1.45/1.19 ( ! [Xx: $i] :
% 1.45/1.19 ? [Xy: $i] : ( cP @ Xx @ Xy )
% 1.45/1.19 => ! [Xx: $i] :
% 1.45/1.19 ? [Xy: $i,Xz: $i] :
% 1.45/1.19 ( ( cP @ Xy @ Xz )
% 1.45/1.19 & ( cP @ Xx @ Xy ) ) ) ).
% 1.45/1.19 ------------------------
% 1.55/1.20 % (27900)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_27742 for (3000ds/183Mi)
% 1.55/1.21 % (27903)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_27742 for (3000ds/2Mi)
% 1.55/1.21 % (27900)First to succeed.
% 1.55/1.21 % (27905)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_27742 for (3000ds/275Mi)
% 1.55/1.21 % (27903)Instruction limit reached!
% 1.55/1.21 % (27903)------------------------------
% 1.55/1.21 % (27903)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.21 % (27903)Termination reason: Unknown
% 1.55/1.21 % (27903)Termination phase: Saturation
% 1.55/1.21
% 1.55/1.21 % (27903)Memory used [KB]: 5500
% 1.55/1.21 % (27903)Time elapsed: 0.002 s
% 1.55/1.21 % (27903)Instructions burned: 2 (million)
% 1.55/1.21 % (27903)------------------------------
% 1.55/1.21 % (27903)------------------------------
% 1.55/1.21 % (27905)Also succeeded, but the first one will report.
% 1.55/1.21 % (27900)Refutation found. Thanks to Tanya!
% 1.55/1.21 % SZS status Theorem for DTF2THF_27742
% 1.55/1.21 % SZS output start Proof for DTF2THF_27742
% 1.55/1.21 thf(func_def_0, type, cP: $i > $i > $o).
% 1.55/1.21 thf(func_def_4, type, sK0: $i > $i).
% 1.55/1.21 thf(f15,plain,(
% 1.55/1.21 $false),
% 1.55/1.21 inference(trivial_inequality_removal,[status(thm)],[f14])).
% 1.55/1.21 thf(f14,plain,(
% 1.55/1.21 ($true != $true)),
% 1.55/1.21 inference(superposition,[status(thm)],[f13,f11])).
% 1.55/1.21 thf(f11,plain,(
% 1.55/1.21 ( ! [X0 : $i] : (((cP @ X0 @ (sK0 @ X0)) = $true)) )),
% 1.55/1.21 inference(cnf_transformation,[status(thm)],[f9])).
% 1.55/1.21 thf(f9,plain,(
% 1.55/1.21 ! [X0 : $i] : ((cP @ X0 @ (sK0 @ X0)) = $true) & ! [X3 : $i,X4 : $i] : (((cP @ X4 @ X3) != $true) | ((cP @ sK1 @ X4) != $true))),
% 1.55/1.21 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f8,f7])).
% 1.55/1.21 thf(f7,plain,(
% 1.55/1.21 ! [X0 : $i] : (? [X1 : $i] : ((cP @ X0 @ X1) = $true) => ((cP @ X0 @ (sK0 @ X0)) = $true))),
% 1.55/1.21 introduced(definition,[],[choice_axiom])).
% 1.55/1.21 thf(f8,plain,(
% 1.55/1.21 ? [X2 : $i] : ! [X3 : $i,X4 : $i] : (((cP @ X4 @ X3) != $true) | ($true != (cP @ X2 @ X4))) => ! [X4 : $i,X3 : $i] : (((cP @ X4 @ X3) != $true) | ((cP @ sK1 @ X4) != $true))),
% 1.55/1.21 introduced(definition,[],[choice_axiom])).
% 1.55/1.21 thf(f6,plain,(
% 1.55/1.21 ! [X0 : $i] : ? [X1 : $i] : ((cP @ X0 @ X1) = $true) & ? [X2 : $i] : ! [X3 : $i,X4 : $i] : (((cP @ X4 @ X3) != $true) | ($true != (cP @ X2 @ X4)))),
% 1.55/1.21 inference(ennf_transformation,[status(thm)],[f5])).
% 1.55/1.21 thf(f5,plain,(
% 1.55/1.21 ~(! [X0 : $i] : ? [X1 : $i] : ((cP @ X0 @ X1) = $true) => ! [X2 : $i] : ? [X3 : $i,X4 : $i] : (($true = (cP @ X2 @ X4)) & ((cP @ X4 @ X3) = $true)))),
% 1.55/1.21 inference(fool_elimination,[status(thm)],[f4])).
% 1.55/1.21 thf(f4,plain,(
% 1.55/1.21 ~(! [X0 : $i] : ? [X1 : $i] : (cP @ X0 @ X1) => ! [X2 : $i] : ? [X3 : $i,X4 : $i] : ((cP @ X4 @ X3) & (cP @ X2 @ X4)))),
% 1.55/1.21 inference(rectify,[status(thm)],[f2])).
% 1.55/1.21 thf(f2,negated_conjecture,(
% 1.55/1.21 ~(! [X0 : $i] : ? [X1 : $i] : (cP @ X0 @ X1) => ! [X0 : $i] : ? [X2 : $i,X1 : $i] : ((cP @ X1 @ X2) & (cP @ X0 @ X1)))),
% 1.55/1.21 inference(negated_conjecture,[status(cth)],[f1])).
% 1.55/1.21 thf(f1,conjecture,(
% 1.55/1.21 ! [X0 : $i] : ? [X1 : $i] : (cP @ X0 @ X1) => ! [X0 : $i] : ? [X2 : $i,X1 : $i] : ((cP @ X1 @ X2) & (cP @ X0 @ X1))),
% 1.55/1.21 file('/export/starexec/sandbox2/tmp/tmp.o3fZelF5nP/DTF2THF_27742.p',cEXPVAR_BUG)).
% 1.55/1.21 thf(f13,plain,(
% 1.55/1.21 ( ! [X0 : $i] : (((cP @ (sK0 @ sK1) @ X0) != $true)) )),
% 1.55/1.21 inference(trivial_inequality_removal,[status(thm)],[f12])).
% 1.55/1.21 thf(f12,plain,(
% 1.55/1.21 ( ! [X0 : $i] : (((cP @ (sK0 @ sK1) @ X0) != $true) | ($true != $true)) )),
% 1.55/1.21 inference(superposition,[status(thm)],[f10,f11])).
% 1.55/1.21 thf(f10,plain,(
% 1.55/1.21 ( ! [X3 : $i,X4 : $i] : (((cP @ sK1 @ X4) != $true) | ((cP @ X4 @ X3) != $true)) )),
% 1.55/1.21 inference(cnf_transformation,[status(thm)],[f9])).
% 1.55/1.21 % SZS output end Proof for DTF2THF_27742
% 1.55/1.21 % (27900)------------------------------
% 1.55/1.21 % (27900)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.21 % (27900)Termination reason: Refutation
% 1.55/1.21
% 1.55/1.21 % (27900)Memory used [KB]: 5500
% 1.55/1.21 % (27900)Time elapsed: 0.004 s
% 1.55/1.21 % (27900)Instructions burned: 2 (million)
% 1.55/1.21 % (27900)------------------------------
% 1.55/1.21 % (27900)------------------------------
% 1.55/1.21 % (27899)Success in time 0.012 s
%------------------------------------------------------------------------------