%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO296^5 : 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 : n004.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 09:53:53 AM UTC 2026
% Result : Theorem 1.53s 1.37s
% Output : Refutation 1.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 13 ( 2 unt; 0 typ; 0 def)
% Number of atoms : 88 ( 31 equ; 0 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 96 ( 13 ~; 17 |; 9 &; 52 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 27 ( 4 ^; 13 !; 10 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
q: $i > $o ).
thf(func_def_1,type,
p: $i > $o ).
thf(func_def_5,type,
sK0: ( $i > $o ) > $i ).
thf(func_def_6,type,
sK1: ( $i > $o ) > $i ).
thf(func_def_9,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f17,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f16]) ).
thf(f16,plain,
$true = $false,
inference(duplicate_literal_removal,[status(thm)],[f15]) ).
thf(f15,plain,
( ( $true = $false )
| ( $true = $false ) ),
inference(beta_eta_normalization,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ( ^ [Y0: $i] : $false
@ ( sK1
@ ^ [Y0: $i] : $false ) )
= $true )
| ( ( ^ [Y0: $i] : $false
@ ( sK0
@ ^ [Y0: $i] : $false ) )
= $true ) ),
inference(primitive_instantiation,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $i > $o] :
( ( ( X0 @ ( sK1 @ X0 ) )
= $true )
| ( ( X0 @ ( sK0 @ X0 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $i > $o] :
( ( ( ( X0 @ ( sK1 @ X0 ) )
= $true )
| ( ( X0 @ ( sK0 @ X0 ) )
= $true ) )
& ( ( ( q @ ( sK1 @ X0 ) )
!= $true )
| ( ( p @ ( sK0 @ X0 ) )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f8]) ).
thf(f8,plain,
! [X0: $i > $o] :
( ? [X1: $i,X2: $i] :
( ( ( ( X0 @ X2 )
= $true )
| ( ( X0 @ X1 )
= $true ) )
& ( ( ( q @ X2 )
!= $true )
| ( ( p @ X1 )
!= $true ) ) )
=> ( ( ( ( X0 @ ( sK1 @ X0 ) )
= $true )
| ( ( X0 @ ( sK0 @ X0 ) )
= $true ) )
& ( ( ( q @ ( sK1 @ X0 ) )
!= $true )
| ( ( p @ ( sK0 @ X0 ) )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
! [X0: $i > $o] :
? [X1: $i,X2: $i] :
( ( ( ( X0 @ X2 )
= $true )
| ( ( X0 @ X1 )
= $true ) )
& ( ( ( q @ X2 )
!= $true )
| ( ( p @ X1 )
!= $true ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: $i > $o] :
? [X2: $i,X1: $i] :
( ( ( ( X0 @ X1 )
= $true )
| ( ( X0 @ X2 )
= $true ) )
& ( ( ( q @ X1 )
!= $true )
| ( $true
!= ( p @ X2 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ? [X0: $i > $o] :
! [X1: $i,X2: $i] :
( ( ( ( X0 @ X1 )
= $true )
| ( ( X0 @ X2 )
= $true ) )
=> ( ( $true
= ( p @ X2 ) )
& ( ( q @ X1 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ? [X0: $i > $o] :
! [X1: $i,X2: $i] :
( ( ( X0 @ X2 )
| ( X0 @ X1 ) )
=> ( ( q @ X1 )
& ( p @ X2 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X0: $i > $o] :
! [X2: $i,X1: $i] :
( ( ( X0 @ X1 )
| ( X0 @ X2 ) )
=> ( ( q @ X2 )
& ( p @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X0: $i > $o] :
! [X2: $i,X1: $i] :
( ( ( X0 @ X1 )
| ( X0 @ X2 ) )
=> ( ( q @ X2 )
& ( p @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AK4AcwwHnh/DTF2THF_21259.p',cBLEDSOE5D) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYO296^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/0.30 % Computer : n004.cluster.edu
% 0.13/0.30 % Model : x86_64 x86_64
% 0.13/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.30 % Memory : 8042.1875MB
% 0.13/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.30 % CPULimit : 300
% 0.13/0.30 % WCLimit : 300
% 0.13/0.30 % DateTime : Tue Feb 24 14:27:26 EST 2026
% 0.13/0.30 % CPUTime :
% 0.13/0.30 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.40 ---- Original DTF file ---
% 0.18/0.40 thf(spec,logic,$$dhol).
% 0.18/0.40 %------------------------------------------------------------------------------
% 0.18/0.40 % File : SYO296^5 : TPTP v9.2.1. Released v4.0.0.
% 0.18/0.40 % Domain : Syntactic
% 0.18/0.40 % Problem : TPS problem from BASIC-HO-THMS
% 0.18/0.40 % Version : Especial.
% 0.18/0.40 % English :
% 0.18/0.40
% 0.18/0.40 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.18/0.40 % Source : [Bro09]
% 0.18/0.40 % Names : tps_0746 [Bro09]
% 0.18/0.40
% 0.18/0.40 % Status : Theorem
% 0.18/0.40 % 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
% 0.18/0.40 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.18/0.40 % Number of atoms : 2 ( 0 equ; 0 cnn)
% 0.18/0.40 % Maximal formula atoms : 2 ( 2 avg)
% 0.18/0.40 % Number of connectives : 7 ( 0 ~; 1 |; 1 &; 4 @)
% 0.18/0.40 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.18/0.40 % Maximal formula depth : 7 ( 7 avg)
% 0.18/0.40 % Number of types : 2 ( 0 usr)
% 0.18/0.40 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.18/0.40 % Number of symbols : 2 ( 2 usr; 0 con; 1-1 aty)
% 0.18/0.40 % Number of variables : 3 ( 0 ^; 2 !; 1 ?; 3 :)
% 0.18/0.40 % SPC : TH0_THM_NEQ_NAR
% 0.18/0.40
% 0.18/0.40 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.18/0.40 % project in the Department of Mathematical Sciences at Carnegie
% 0.18/0.40 % Mellon University. Distributed under the Creative Commons copyleft
% 0.18/0.40 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.18/0.40 %------------------------------------------------------------------------------
% 0.18/0.40 thf(q,type,
% 0.18/0.40 q: $i > $o ).
% 0.18/0.40
% 0.18/0.40 thf(p,type,
% 0.18/0.40 p: $i > $o ).
% 0.18/0.40
% 0.18/0.40 thf(cBLEDSOE5D,conjecture,
% 0.18/0.40 ? [A: $i > $o] :
% 0.18/0.40 ! [Xx: $i,Xy: $i] :
% 0.18/0.40 ( ( ( A @ Xx )
% 0.18/0.40 | ( A @ Xy ) )
% 0.18/0.40 => ( ( p @ Xx )
% 0.18/0.40 & ( q @ Xy ) ) ) ).
% 0.18/0.40
% 0.18/0.40 %------------------------------------------------------------------------------
% 0.18/0.40 ------------------------
% 1.53/1.34 ---- Embedded in THF ---
% 1.53/1.34 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.53/1.34 %%% Generated on Tue Feb 24 14:27:27 EST 2026
% 1.53/1.34 %%% using '$$dhol' embedding, version 1.3.0.
% 1.53/1.34 %%% Logic specification used:
% 1.53/1.34 %%% thf(spec, logic, $$dhol).
% 1.53/1.34
% 1.53/1.34 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.AK4AcwwHnh/DTF2DTF21259.p
% See solution above
% 1.53/1.34 ------------------------
% 1.53/1.35 ---- Cleaned THF ---
% 1.53/1.35 thf(q,type,
% 1.53/1.35 q: $i > $o ).
% 1.53/1.35
% 1.53/1.35 thf(p,type,
% 1.53/1.35 p: $i > $o ).
% 1.53/1.35
% 1.53/1.35 thf(cBLEDSOE5D,conjecture,
% 1.53/1.35 ? [A: $i > $o] :
% 1.53/1.35 ! [Xx: $i,Xy: $i] :
% 1.53/1.35 ( ( ( A @ Xx )
% 1.53/1.35 | ( A @ Xy ) )
% 1.53/1.35 => ( ( p @ Xx )
% 1.53/1.35 & ( q @ Xy ) ) ) ).
% 1.53/1.35 ------------------------
% 1.53/1.37 % (21356)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_21259 for (3000ds/183Mi)
% 1.53/1.37 % (21357)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_21259 for (3000ds/4Mi)
% 1.53/1.37 % (21358)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_21259 for (3000ds/27Mi)
% 1.53/1.37 % (21362)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_21259 for (3000ds/18Mi)
% 1.53/1.37 % (21360)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_21259 for (3000ds/2Mi)
% 1.53/1.37 % (21359)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_21259 for (3000ds/2Mi)
% 1.53/1.37 % (21361)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_21259 for (3000ds/275Mi)
% 1.53/1.37 % (21359)First to succeed.
% 1.53/1.37 % (21358)Refutation not found, incomplete strategy
% 1.53/1.37 % (21358)------------------------------
% 1.53/1.37 % (21358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.37 % (21358)Termination reason: Refutation not found, incomplete strategy
% 1.53/1.37
% 1.53/1.37
% 1.53/1.37 % (21358)Memory used [KB]: 5500
% 1.53/1.37 % (21358)Time elapsed: 0.004 s
% 1.53/1.37 % (21358)Instructions burned: 1 (million)
% 1.53/1.37 % (21358)------------------------------
% 1.53/1.37 % (21358)------------------------------
% 1.53/1.37 % (21360)Instruction limit reached!
% 1.53/1.37 % (21360)------------------------------
% 1.53/1.37 % (21360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.37 % (21360)Termination reason: Unknown
% 1.53/1.37 % (21360)Termination phase: Saturation
% 1.53/1.37
% 1.53/1.37 % (21360)Memory used [KB]: 5500
% 1.53/1.37 % (21360)Time elapsed: 0.004 s
% 1.53/1.37 % (21360)Instructions burned: 3 (million)
% 1.53/1.37 % (21360)------------------------------
% 1.53/1.37 % (21360)------------------------------
% 1.53/1.37 % (21356)Also succeeded, but the first one will report.
% 1.53/1.37 % (21359)Refutation found. Thanks to Tanya!
% 1.53/1.37 % SZS status Theorem for DTF2THF_21259
% 1.53/1.37 % SZS output start Proof for DTF2THF_21259
% 1.53/1.37 thf(func_def_0, type, q: $i > $o).
% 1.53/1.37 thf(func_def_1, type, p: $i > $o).
% 1.53/1.37 thf(func_def_5, type, sK0: ($i > $o) > $i).
% 1.53/1.37 thf(func_def_6, type, sK1: ($i > $o) > $i).
% 1.53/1.37 thf(func_def_9, type, ph3: !>[X0: $tType]:(X0)).
% 1.53/1.37 thf(f17,plain,(
% 1.53/1.37 $false),
% 1.53/1.37 inference(trivial_inequality_removal,[status(thm)],[f16])).
% 1.53/1.37 thf(f16,plain,(
% 1.53/1.37 ($true = $false)),
% 1.53/1.37 inference(duplicate_literal_removal,[status(thm)],[f15])).
% 1.53/1.37 thf(f15,plain,(
% 1.53/1.37 ($true = $false) | ($true = $false)),
% 1.53/1.37 inference(beta_eta_normalization,[status(thm)],[f13])).
% 1.53/1.37 thf(f13,plain,(
% 1.53/1.37 (((^[Y0 : $i]: ($false)) @ (sK1 @ (^[Y0 : $i]: ($false)))) = $true) | (((^[Y0 : $i]: ($false)) @ (sK0 @ (^[Y0 : $i]: ($false)))) = $true)),
% 1.53/1.37 inference(primitive_instantiation,[status(thm)],[f11])).
% 1.53/1.37 thf(f11,plain,(
% 1.53/1.37 ( ! [X0 : $i > $o] : (((X0 @ (sK1 @ X0)) = $true) | ((X0 @ (sK0 @ X0)) = $true)) )),
% 1.53/1.37 inference(cnf_transformation,[status(thm)],[f9])).
% 1.53/1.37 thf(f9,plain,(
% 1.53/1.37 ! [X0 : $i > $o] : ((((X0 @ (sK1 @ X0)) = $true) | ((X0 @ (sK0 @ X0)) = $true)) & (((q @ (sK1 @ X0)) != $true) | ((p @ (sK0 @ X0)) != $true)))),
% 1.53/1.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f8])).
% 1.53/1.37 thf(f8,plain,(
% 1.53/1.37 ! [X0 : $i > $o] : (? [X1 : $i,X2 : $i] : ((((X0 @ X2) = $true) | ((X0 @ X1) = $true)) & (((q @ X2) != $true) | ((p @ X1) != $true))) => ((((X0 @ (sK1 @ X0)) = $true) | ((X0 @ (sK0 @ X0)) = $true)) & (((q @ (sK1 @ X0)) != $true) | ((p @ (sK0 @ X0)) != $true))))),
% 1.53/1.37 introduced(definition,[],[choice_axiom])).
% 1.53/1.37 thf(f7,plain,(
% 1.53/1.37 ! [X0 : $i > $o] : ? [X1 : $i,X2 : $i] : ((((X0 @ X2) = $true) | ((X0 @ X1) = $true)) & (((q @ X2) != $true) | ((p @ X1) != $true)))),
% 1.53/1.37 inference(rectify,[status(thm)],[f6])).
% 1.53/1.37 thf(f6,plain,(
% 1.53/1.37 ! [X0 : $i > $o] : ? [X2 : $i,X1 : $i] : ((((X0 @ X1) = $true) | ((X0 @ X2) = $true)) & (((q @ X1) != $true) | ($true != (p @ X2))))),
% 1.53/1.37 inference(ennf_transformation,[status(thm)],[f5])).
% 1.53/1.37 thf(f5,plain,(
% 1.53/1.37 ~? [X0 : $i > $o] : ! [X1 : $i,X2 : $i] : ((((X0 @ X1) = $true) | ((X0 @ X2) = $true)) => (($true = (p @ X2)) & ((q @ X1) = $true)))),
% 1.53/1.37 inference(fool_elimination,[status(thm)],[f4])).
% 1.53/1.37 thf(f4,plain,(
% 1.53/1.37 ~? [X0 : $i > $o] : ! [X1 : $i,X2 : $i] : (((X0 @ X2) | (X0 @ X1)) => ((q @ X1) & (p @ X2)))),
% 1.53/1.37 inference(rectify,[status(thm)],[f2])).
% 1.53/1.37 thf(f2,negated_conjecture,(
% 1.53/1.37 ~? [X0 : $i > $o] : ! [X2 : $i,X1 : $i] : (((X0 @ X1) | (X0 @ X2)) => ((q @ X2) & (p @ X1)))),
% 1.53/1.37 inference(negated_conjecture,[status(cth)],[f1])).
% 1.53/1.37 thf(f1,conjecture,(
% 1.53/1.37 ? [X0 : $i > $o] : ! [X2 : $i,X1 : $i] : (((X0 @ X1) | (X0 @ X2)) => ((q @ X2) & (p @ X1)))),
% 1.53/1.37 file('/export/starexec/sandbox/tmp/tmp.AK4AcwwHnh/DTF2THF_21259.p',cBLEDSOE5D)).
% 1.53/1.37 % SZS output end Proof for DTF2THF_21259
% 1.53/1.37 % (21359)------------------------------
% 1.53/1.37 % (21359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.37 % (21359)Termination reason: Refutation
% 1.53/1.37
% 1.53/1.37 % (21359)Memory used [KB]: 5500
% 1.53/1.37 % (21359)Time elapsed: 0.004 s
% 1.53/1.37 % (21359)Instructions burned: 1 (million)
% 1.53/1.37 % (21359)------------------------------
% 1.53/1.37 % (21359)------------------------------
% 1.53/1.37 % (21355)Success in time 0.018 s
%------------------------------------------------------------------------------