%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO307^5 : 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 : n021.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 09:53:54 AM UTC 2026
% Result : Theorem 1.62s 1.31s
% Output : Refutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of formulae : 14 ( 2 unt; 0 typ; 0 def)
% Number of atoms : 160 ( 56 equ; 0 cnn)
% Maximal formula atoms : 14 ( 11 avg)
% Number of connectives : 183 ( 27 ~; 29 |; 30 &; 92 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 38 ( 4 ^; 18 !; 16 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cT: $i > $o ).
thf(func_def_1,type,
q: $i > $o ).
thf(func_def_2,type,
cR: $i > $o ).
thf(func_def_3,type,
p: $i > $o ).
thf(func_def_7,type,
sK0: ( $i > $o ) > $i ).
thf(func_def_8,type,
sK1: ( $i > $o ) > $i ).
thf(func_def_9,type,
sK2: ( $i > $o ) > $i ).
thf(func_def_12,type,
ph4:
!>[X0: $tType] : X0 ).
thf(f25,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f24]) ).
thf(f24,plain,
$false = $true,
inference(duplicate_literal_removal,[status(thm)],[f23]) ).
thf(f23,plain,
( ( $false = $true )
| ( $false = $true ) ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ( ^ [Y0: $i] : $false
@ ( sK2
@ ^ [Y0: $i] : $false ) )
= $true )
| ( $true
= ( ^ [Y0: $i] : $false
@ ( sK1
@ ^ [Y0: $i] : $false ) ) ) ),
inference(primitive_instantiation,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: $i > $o] :
( ( $true
= ( X0 @ ( sK2 @ X0 ) ) )
| ( $true
= ( X0 @ ( sK1 @ X0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $i > $o] :
( ( ( ( q @ ( sK1 @ X0 ) )
!= $true )
| ( $true
!= ( cT @ ( sK0 @ X0 ) ) ) )
& ( ( $true
= ( X0 @ ( sK1 @ X0 ) ) )
| ( ( $true
= ( X0 @ ( sK0 @ X0 ) ) )
& ( $true
= ( X0 @ ( sK2 @ X0 ) ) ) ) )
& ( ( ( cR @ ( sK2 @ X0 ) )
!= $true )
| ( ( p @ ( sK1 @ X0 ) )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f9]) ).
thf(f9,plain,
! [X0: $i > $o] :
( ? [X1: $i,X2: $i,X3: $i] :
( ( ( ( q @ X2 )
!= $true )
| ( ( cT @ X1 )
!= $true ) )
& ( ( ( X0 @ X2 )
= $true )
| ( ( ( X0 @ X1 )
= $true )
& ( ( X0 @ X3 )
= $true ) ) )
& ( ( $true
!= ( cR @ X3 ) )
| ( ( p @ X2 )
!= $true ) ) )
=> ( ( ( ( q @ ( sK1 @ X0 ) )
!= $true )
| ( $true
!= ( cT @ ( sK0 @ X0 ) ) ) )
& ( ( $true
= ( X0 @ ( sK1 @ X0 ) ) )
| ( ( $true
= ( X0 @ ( sK0 @ X0 ) ) )
& ( $true
= ( X0 @ ( sK2 @ X0 ) ) ) ) )
& ( ( ( cR @ ( sK2 @ X0 ) )
!= $true )
| ( ( p @ ( sK1 @ X0 ) )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
! [X0: $i > $o] :
? [X1: $i,X2: $i,X3: $i] :
( ( ( ( q @ X2 )
!= $true )
| ( ( cT @ X1 )
!= $true ) )
& ( ( ( X0 @ X2 )
= $true )
| ( ( ( X0 @ X1 )
= $true )
& ( ( X0 @ X3 )
= $true ) ) )
& ( ( $true
!= ( cR @ X3 ) )
| ( ( p @ X2 )
!= $true ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: $i > $o] :
? [X3: $i,X2: $i,X1: $i] :
( ( ( ( q @ X2 )
!= $true )
| ( ( cT @ X3 )
!= $true ) )
& ( ( ( X0 @ X2 )
= $true )
| ( ( ( X0 @ X3 )
= $true )
& ( ( X0 @ X1 )
= $true ) ) )
& ( ( $true
!= ( cR @ X1 ) )
| ( ( p @ X2 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: $i > $o] :
? [X2: $i,X3: $i,X1: $i] :
( ( ( ( q @ X2 )
!= $true )
| ( ( cT @ X3 )
!= $true ) )
& ( ( $true
!= ( cR @ X1 ) )
| ( ( p @ X2 )
!= $true ) )
& ( ( ( X0 @ X2 )
= $true )
| ( ( ( X0 @ X3 )
= $true )
& ( ( X0 @ X1 )
= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ? [X0: $i > $o] :
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( X0 @ X2 )
= $true )
| ( ( ( X0 @ X3 )
= $true )
& ( ( X0 @ X1 )
= $true ) ) )
=> ( ( ( ( q @ X2 )
= $true )
& ( ( cT @ X3 )
= $true ) )
| ( ( ( p @ X2 )
= $true )
& ( $true
= ( cR @ X1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ? [X0: $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( ( X0 @ X1 )
& ( X0 @ X3 ) )
| ( X0 @ X2 ) )
=> ( ( ( cR @ X1 )
& ( p @ X2 ) )
| ( ( cT @ X3 )
& ( q @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X0: $i > $o] :
! [X2: $i,X1: $i,X3: $i] :
( ( ( ( X0 @ X2 )
& ( X0 @ X3 ) )
| ( X0 @ X1 ) )
=> ( ( ( cR @ X2 )
& ( p @ X1 ) )
| ( ( cT @ X3 )
& ( q @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X0: $i > $o] :
! [X2: $i,X1: $i,X3: $i] :
( ( ( ( X0 @ X2 )
& ( X0 @ X3 ) )
| ( X0 @ X1 ) )
=> ( ( ( cR @ X2 )
& ( p @ X1 ) )
| ( ( cT @ X3 )
& ( q @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.IhcpBojbYp/DTF2THF_10542.p',cBLEDSOE5F) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO307^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n021.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 14:27:54 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.45 ---- Original DTF file ---
% 0.18/0.45 thf(spec,logic,$$dhol).
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 % File : SYO307^5 : TPTP v9.2.1. Released v4.0.0.
% 0.18/0.45 % Domain : Syntactic
% 0.18/0.45 % Problem : TPS problem from BASIC-HO-THMS
% 0.18/0.45 % Version : Especial.
% 0.18/0.45 % English :
% 0.18/0.45
% 0.18/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.18/0.45 % Source : [Bro09]
% 0.18/0.45 % Names : tps_0829 [Bro09]
% 0.18/0.45
% 0.18/0.45 % Status : Theorem
% 0.18/0.45 % Rating : 0.08 v9.1.0, 0.12 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.17 v7.4.0, 0.11 v7.3.0, 0.20 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 v6.2.0, 0.33 v6.1.0, 0.17 v6.0.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.18/0.45 % Syntax : Number of formulae : 5 ( 0 unt; 4 typ; 0 def)
% 0.18/0.45 % Number of atoms : 4 ( 0 equ; 0 cnn)
% 0.18/0.45 % Maximal formula atoms : 4 ( 4 avg)
% 0.18/0.45 % Number of connectives : 13 ( 0 ~; 2 |; 3 &; 7 @)
% 0.18/0.45 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.18/0.45 % Maximal formula depth : 9 ( 9 avg)
% 0.18/0.45 % Number of types : 2 ( 0 usr)
% 0.18/0.45 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.18/0.45 % Number of symbols : 4 ( 4 usr; 0 con; 1-1 aty)
% 0.18/0.45 % Number of variables : 4 ( 0 ^; 3 !; 1 ?; 4 :)
% 0.18/0.45 % SPC : TH0_THM_NEQ_NAR
% 0.18/0.45
% 0.18/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.18/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.18/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.18/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 thf(cT,type,
% 0.18/0.45 cT: $i > $o ).
% 0.18/0.45
% 0.18/0.45 thf(q,type,
% 0.18/0.45 q: $i > $o ).
% 0.18/0.45
% 0.18/0.45 thf(cR,type,
% 0.18/0.45 cR: $i > $o ).
% 0.18/0.45
% 0.18/0.45 thf(p,type,
% 0.18/0.45 p: $i > $o ).
% 0.18/0.45
% 0.18/0.45 thf(cBLEDSOE5F,conjecture,
% 0.18/0.45 ? [A: $i > $o] :
% 0.18/0.45 ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.18/0.45 ( ( ( A @ Xx )
% 0.18/0.45 | ( ( A @ Xy )
% 0.18/0.45 & ( A @ Xz ) ) )
% 0.18/0.45 => ( ( ( p @ Xx )
% 0.18/0.45 & ( cR @ Xy ) )
% 0.18/0.45 | ( ( q @ Xx )
% 0.18/0.45 & ( cT @ Xz ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 ------------------------
% 1.43/1.28 ---- Embedded in THF ---
% 1.43/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.43/1.28 %%% Generated on Tue Feb 24 14:27:54 EST 2026
% 1.43/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.43/1.28 %%% Logic specification used:
% 1.43/1.28 %%% thf(spec, logic, $$dhol).
% 1.43/1.28
% 1.43/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.IhcpBojbYp/DTF2DTF10542.p
% See solution above
% 1.43/1.28 ------------------------
% 1.43/1.29 ---- Cleaned THF ---
% 1.43/1.29 thf(cT,type,
% 1.43/1.29 cT: $i > $o ).
% 1.43/1.29
% 1.43/1.29 thf(q,type,
% 1.43/1.29 q: $i > $o ).
% 1.43/1.29
% 1.43/1.29 thf(cR,type,
% 1.43/1.29 cR: $i > $o ).
% 1.43/1.29
% 1.43/1.29 thf(p,type,
% 1.43/1.29 p: $i > $o ).
% 1.43/1.29
% 1.43/1.29 thf(cBLEDSOE5F,conjecture,
% 1.43/1.29 ? [A: $i > $o] :
% 1.43/1.29 ! [Xx: $i,Xy: $i,Xz: $i] :
% 1.43/1.29 ( ( ( A @ Xx )
% 1.43/1.29 | ( ( A @ Xy )
% 1.43/1.29 & ( A @ Xz ) ) )
% 1.43/1.29 => ( ( ( p @ Xx )
% 1.43/1.29 & ( cR @ Xy ) )
% 1.43/1.29 | ( ( q @ Xx )
% 1.43/1.29 & ( cT @ Xz ) ) ) ) ).
% 1.43/1.29 ------------------------
% 1.62/1.30 % (10719)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_10542 for (2999ds/183Mi)
% 1.62/1.30 % (10720)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_10542 for (2999ds/4Mi)
% 1.62/1.31 % (10719)First to succeed.
% 1.62/1.31 % (10724)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_10542 for (2999ds/275Mi)
% 1.62/1.31 % (10720)Also succeeded, but the first one will report.
% 1.62/1.31 % (10724)Also succeeded, but the first one will report.
% 1.62/1.31 % (10719)Refutation found. Thanks to Tanya!
% 1.62/1.31 % SZS status Theorem for DTF2THF_10542
% 1.62/1.31 % SZS output start Proof for DTF2THF_10542
% 1.62/1.31 thf(func_def_0, type, cT: $i > $o).
% 1.62/1.31 thf(func_def_1, type, q: $i > $o).
% 1.62/1.31 thf(func_def_2, type, cR: $i > $o).
% 1.62/1.31 thf(func_def_3, type, p: $i > $o).
% 1.62/1.31 thf(func_def_7, type, sK0: ($i > $o) > $i).
% 1.62/1.31 thf(func_def_8, type, sK1: ($i > $o) > $i).
% 1.62/1.31 thf(func_def_9, type, sK2: ($i > $o) > $i).
% 1.62/1.31 thf(func_def_12, type, ph4: !>[X0: $tType]:(X0)).
% 1.62/1.31 thf(f25,plain,(
% 1.62/1.31 $false),
% 1.62/1.31 inference(trivial_inequality_removal,[status(thm)],[f24])).
% 1.62/1.31 thf(f24,plain,(
% 1.62/1.31 ($false = $true)),
% 1.62/1.31 inference(duplicate_literal_removal,[status(thm)],[f23])).
% 1.62/1.31 thf(f23,plain,(
% 1.62/1.31 ($false = $true) | ($false = $true)),
% 1.62/1.31 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.62/1.31 thf(f16,plain,(
% 1.62/1.31 (((^[Y0 : $i]: ($false)) @ (sK2 @ (^[Y0 : $i]: ($false)))) = $true) | ($true = ((^[Y0 : $i]: ($false)) @ (sK1 @ (^[Y0 : $i]: ($false)))))),
% 1.62/1.31 inference(primitive_instantiation,[status(thm)],[f12])).
% 1.62/1.31 thf(f12,plain,(
% 1.62/1.31 ( ! [X0 : $i > $o] : (($true = (X0 @ (sK2 @ X0))) | ($true = (X0 @ (sK1 @ X0)))) )),
% 1.62/1.31 inference(cnf_transformation,[status(thm)],[f10])).
% 1.62/1.31 thf(f10,plain,(
% 1.62/1.31 ! [X0 : $i > $o] : ((((q @ (sK1 @ X0)) != $true) | ($true != (cT @ (sK0 @ X0)))) & (($true = (X0 @ (sK1 @ X0))) | (($true = (X0 @ (sK0 @ X0))) & ($true = (X0 @ (sK2 @ X0))))) & (((cR @ (sK2 @ X0)) != $true) | ((p @ (sK1 @ X0)) != $true)))),
% 1.62/1.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f9])).
% 1.62/1.31 thf(f9,plain,(
% 1.62/1.31 ! [X0 : $i > $o] : (? [X1 : $i,X2 : $i,X3 : $i] : ((((q @ X2) != $true) | ((cT @ X1) != $true)) & (((X0 @ X2) = $true) | (((X0 @ X1) = $true) & ((X0 @ X3) = $true))) & (($true != (cR @ X3)) | ((p @ X2) != $true))) => ((((q @ (sK1 @ X0)) != $true) | ($true != (cT @ (sK0 @ X0)))) & (($true = (X0 @ (sK1 @ X0))) | (($true = (X0 @ (sK0 @ X0))) & ($true = (X0 @ (sK2 @ X0))))) & (((cR @ (sK2 @ X0)) != $true) | ((p @ (sK1 @ X0)) != $true))))),
% 1.62/1.31 introduced(definition,[],[choice_axiom])).
% 1.62/1.31 thf(f8,plain,(
% 1.62/1.31 ! [X0 : $i > $o] : ? [X1 : $i,X2 : $i,X3 : $i] : ((((q @ X2) != $true) | ((cT @ X1) != $true)) & (((X0 @ X2) = $true) | (((X0 @ X1) = $true) & ((X0 @ X3) = $true))) & (($true != (cR @ X3)) | ((p @ X2) != $true)))),
% 1.62/1.31 inference(rectify,[status(thm)],[f7])).
% 1.62/1.31 thf(f7,plain,(
% 1.62/1.31 ! [X0 : $i > $o] : ? [X3 : $i,X2 : $i,X1 : $i] : ((((q @ X2) != $true) | ((cT @ X3) != $true)) & (((X0 @ X2) = $true) | (((X0 @ X3) = $true) & ((X0 @ X1) = $true))) & (($true != (cR @ X1)) | ((p @ X2) != $true)))),
% 1.62/1.31 inference(flattening,[status(thm)],[f6])).
% 1.62/1.31 thf(f6,plain,(
% 1.62/1.31 ! [X0 : $i > $o] : ? [X2 : $i,X3 : $i,X1 : $i] : (((((q @ X2) != $true) | ((cT @ X3) != $true)) & (($true != (cR @ X1)) | ((p @ X2) != $true))) & (((X0 @ X2) = $true) | (((X0 @ X3) = $true) & ((X0 @ X1) = $true))))),
% 1.62/1.31 inference(ennf_transformation,[status(thm)],[f5])).
% 1.62/1.31 thf(f5,plain,(
% 1.62/1.31 ~? [X0 : $i > $o] : ! [X2 : $i,X3 : $i,X1 : $i] : ((((X0 @ X2) = $true) | (((X0 @ X3) = $true) & ((X0 @ X1) = $true))) => ((((q @ X2) = $true) & ((cT @ X3) = $true)) | (((p @ X2) = $true) & ($true = (cR @ X1)))))),
% 1.62/1.31 inference(fool_elimination,[status(thm)],[f4])).
% 1.62/1.31 thf(f4,plain,(
% 1.62/1.31 ~? [X0 : $i > $o] : ! [X1 : $i,X2 : $i,X3 : $i] : ((((X0 @ X1) & (X0 @ X3)) | (X0 @ X2)) => (((cR @ X1) & (p @ X2)) | ((cT @ X3) & (q @ X2))))),
% 1.62/1.31 inference(rectify,[status(thm)],[f2])).
% 1.62/1.31 thf(f2,negated_conjecture,(
% 1.62/1.31 ~? [X0 : $i > $o] : ! [X2 : $i,X1 : $i,X3 : $i] : ((((X0 @ X2) & (X0 @ X3)) | (X0 @ X1)) => (((cR @ X2) & (p @ X1)) | ((cT @ X3) & (q @ X1))))),
% 1.62/1.31 inference(negated_conjecture,[status(cth)],[f1])).
% 1.62/1.31 thf(f1,conjecture,(
% 1.62/1.31 ? [X0 : $i > $o] : ! [X2 : $i,X1 : $i,X3 : $i] : ((((X0 @ X2) & (X0 @ X3)) | (X0 @ X1)) => (((cR @ X2) & (p @ X1)) | ((cT @ X3) & (q @ X1))))),
% 1.62/1.31 file('/export/starexec/sandbox2/tmp/tmp.IhcpBojbYp/DTF2THF_10542.p',cBLEDSOE5F)).
% 1.62/1.31 % SZS output end Proof for DTF2THF_10542
% 1.62/1.31 % (10719)------------------------------
% 1.62/1.31 % (10719)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.31 % (10719)Termination reason: Refutation
% 1.62/1.31
% 1.62/1.31 % (10719)Memory used [KB]: 5500
% 1.62/1.31 % (10719)Time elapsed: 0.003 s
% 1.62/1.31 % (10719)Instructions burned: 2 (million)
% 1.62/1.31 % (10719)------------------------------
% 1.62/1.31 % (10719)------------------------------
% 1.62/1.31 % (10718)Success in time 0.005 s
%------------------------------------------------------------------------------