%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO256^5 : 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 : n014.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 09:53:47 AM UTC 2026
% Result : Theorem 1.57s 1.32s
% Output : Refutation 1.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 14 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 58 ( 13 equ; 0 cnn)
% Maximal formula atoms : 2 ( 4 avg)
% Number of connectives : 107 ( 8 ~; 15 |; 0 &; 70 @)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 3 usr; 3 con; 0-2 aty)
% ( 10 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 42 ( 10 ^; 22 !; 10 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_8,type,
sK0: a > $o ).
thf(func_def_9,type,
sK1: a > $o ).
thf(func_def_10,type,
sK2: $o > $o ).
thf(f15,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f14]) ).
thf(f14,plain,
$true = $false,
inference(backward_demodulation,[status(thm)],[f13,f12]) ).
thf(f12,plain,
( ( sK2
@ ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) ) ) )
= $false ),
inference(condensation,[status(thm)],[f11]) ).
thf(f11,plain,
! [X3: $o] :
( ( ( sK2 @ X3 )
= $false )
| ( ( sK2
@ ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f9]) ).
thf(f9,plain,
! [X3: $o] :
( ( sK2 @ X3 )
!= ( sK2
@ ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
! [X3: $o] :
( ( sK2 @ X3 )
!= ( sK2
@ ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f6,f7]) ).
thf(f7,plain,
( ? [X0: a > $o,X1: a > $o,X2: $o > $o] :
! [X3: $o] :
( ( X2
@ ( !! @ a
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 @ Y0 ) ) ) )
!= ( X2 @ X3 ) )
=> ! [X3: $o] :
( ( sK2 @ X3 )
!= ( sK2
@ ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o,X2: $o > $o] :
! [X3: $o] :
( ( X2
@ ( !! @ a
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 @ Y0 ) ) ) )
!= ( X2 @ X3 ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o,X2: $o > $o] :
? [X3: $o] :
( ( X2
@ ( !! @ a
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 @ Y0 ) ) ) )
= ( X2 @ X3 ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: $o > $o] :
? [X3: $o] :
( ( X2 @ X3 )
<=> ( X2
@ ! [X4: a] :
( ( X1 @ X4 )
| ( X0 @ X4 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X2: a > $o,X1: a > $o,X0: $o > $o] :
? [X3: $o] :
( ( X0 @ X3 )
<=> ( X0
@ ! [X4: a] :
( ( X1 @ X4 )
| ( X2 @ X4 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X2: a > $o,X1: a > $o,X0: $o > $o] :
? [X3: $o] :
( ( X0 @ X3 )
<=> ( X0
@ ! [X4: a] :
( ( X1 @ X4 )
| ( X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.8SL8zOusUF/DTF2THF_3244.p',cTHM121) ).
thf(f13,plain,
( ( sK2
@ ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) ) ) )
= $true ),
inference(condensation,[status(thm)],[f10]) ).
thf(f10,plain,
! [X3: $o] :
( ( ( sK2
@ ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) ) ) )
= $true )
| ( ( sK2 @ X3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYO256^5 : 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
% 0.11/0.29 % Computer : n014.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 14:26:57 EST 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.39 ---- Original DTF file ---
% 0.17/0.39 thf(spec,logic,$$dhol).
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 % File : SYO256^5 : TPTP v9.2.1. Released v4.0.0.
% 0.17/0.39 % Domain : Syntactic
% 0.17/0.39 % Problem : TPS problem THM121
% 0.17/0.39 % Version : Especial.
% 0.17/0.39 % English : Test theorem for nested primitive substitutions.
% 0.17/0.39
% 0.17/0.39 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.17/0.39 % Source : [Bro09]
% 0.17/0.39 % Names : tps_0106 [Bro09]
% 0.17/0.39 % : THM121 [TPS]
% 0.17/0.39
% 0.17/0.39 % Status : Theorem
% 0.17/0.39 % Rating : 0.00 v6.2.0, 0.17 v6.1.0, 0.00 v4.0.0
% 0.17/0.39 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.17/0.39 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.17/0.39 % Maximal formula atoms : 0 ( 0 avg)
% 0.17/0.39 % Number of connectives : 6 ( 0 ~; 1 |; 0 &; 4 @)
% 0.17/0.39 % ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% 0.17/0.39 % Maximal formula depth : 10 ( 10 avg)
% 0.17/0.39 % Number of types : 2 ( 1 usr)
% 0.17/0.39 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.17/0.39 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.17/0.39 % Number of variables : 5 ( 0 ^; 4 !; 1 ?; 5 :)
% 0.17/0.39 % SPC : TH0_THM_NEQ_NAR
% 0.17/0.39
% 0.17/0.39 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.17/0.39 % project in the Department of Mathematical Sciences at Carnegie
% 0.17/0.39 % Mellon University. Distributed under the Creative Commons copyleft
% 0.17/0.39 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 thf(a_type,type,
% 0.17/0.39 a: $tType ).
% 0.17/0.39
% 0.17/0.39 thf(cTHM121,conjecture,
% 0.17/0.39 ! [Xr: $o > $o,Xp: a > $o,Xq: a > $o] :
% 0.17/0.39 ? [Xh: $o] :
% 0.17/0.39 ( ( Xr @ Xh )
% 0.17/0.39 <=> ( Xr
% 0.17/0.39 @ ! [Xx: a] :
% 0.17/0.39 ( ( Xp @ Xx )
% 0.17/0.39 | ( Xq @ Xx ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 ------------------------
% 1.37/1.28 ---- Embedded in THF ---
% 1.37/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.37/1.28 %%% Generated on Tue Feb 24 14:26:58 EST 2026
% 1.37/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.37/1.28 %%% Logic specification used:
% 1.37/1.28 %%% thf(spec, logic, $$dhol).
% 1.37/1.28
% 1.37/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.8SL8zOusUF/DTF2DTF3244.p
% See solution above
% 1.37/1.28 ------------------------
% 1.37/1.29 ---- Cleaned THF ---
% 1.37/1.29 thf(a_type,type,
% 1.37/1.29 a: $tType ).
% 1.37/1.29
% 1.37/1.29 thf(cTHM121,conjecture,
% 1.37/1.29 ! [Xr: $o > $o,Xp: a > $o,Xq: a > $o] :
% 1.37/1.29 ? [Xh: $o] :
% 1.37/1.29 ( ( Xr @ Xh )
% 1.37/1.29 <=> ( Xr
% 1.37/1.29 @ ! [Xx: a] :
% 1.37/1.29 ( ( Xp @ Xx )
% 1.37/1.29 | ( Xq @ Xx ) ) ) ) ).
% 1.37/1.29 ------------------------
% 1.57/1.31 % (3346)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_3244 for (3000ds/275Mi)
% 1.57/1.31 % (3341)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3244 for (3000ds/183Mi)
% 1.57/1.31 % (3344)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3244 for (3000ds/2Mi)
% 1.57/1.31 % (3345)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_3244 for (3000ds/2Mi)
% 1.57/1.31 % (3347)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3244 for (3000ds/18Mi)
% 1.57/1.31 % (3342)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_3244 for (3000ds/4Mi)
% 1.57/1.31 % (3343)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_3244 for (3000ds/27Mi)
% 1.57/1.31 % (3344)Instruction limit reached!
% 1.57/1.31 % (3344)------------------------------
% 1.57/1.31 % (3344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.31 % (3344)Termination reason: Unknown
% 1.57/1.31 % (3345)Instruction limit reached!
% 1.57/1.31 % (3345)------------------------------
% 1.57/1.31 % (3345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.31 % (3345)Termination reason: Unknown
% 1.57/1.31 % (3345)Termination phase: Saturation
% 1.57/1.31
% 1.57/1.31 % (3345)Memory used [KB]: 5500
% 1.57/1.31 % (3345)Time elapsed: 0.003 s
% 1.57/1.31 % (3345)Instructions burned: 2 (million)
% 1.57/1.31 % (3345)------------------------------
% 1.57/1.31 % (3345)------------------------------
% 1.57/1.31 % (3344)Termination phase: Saturation
% 1.57/1.31
% 1.57/1.31 % (3344)Memory used [KB]: 5500
% 1.57/1.31 % (3344)Time elapsed: 0.003 s
% 1.57/1.31 % (3344)Instructions burned: 2 (million)
% 1.57/1.31 % (3344)------------------------------
% 1.57/1.31 % (3344)------------------------------
% 1.57/1.31 % (3347)First to succeed.
% 1.57/1.32 % (3343)Also succeeded, but the first one will report.
% 1.57/1.32 % (3346)Also succeeded, but the first one will report.
% 1.57/1.32 % (3347)Refutation found. Thanks to Tanya!
% 1.57/1.32 % SZS status Theorem for DTF2THF_3244
% 1.57/1.32 % SZS output start Proof for DTF2THF_3244
% 1.57/1.32 thf(type_def_6, type, a: $tType).
% 1.57/1.32 thf(func_def_0, type, a: $tType).
% 1.57/1.32 thf(func_def_8, type, sK0: a > $o).
% 1.57/1.32 thf(func_def_9, type, sK1: a > $o).
% 1.57/1.32 thf(func_def_10, type, sK2: $o > $o).
% 1.57/1.32 thf(f15,plain,(
% 1.57/1.32 $false),
% 1.57/1.32 inference(trivial_inequality_removal,[status(thm)],[f14])).
% 1.57/1.32 thf(f14,plain,(
% 1.57/1.32 ($true = $false)),
% 1.57/1.32 inference(backward_demodulation,[status(thm)],[f13,f12])).
% 1.57/1.32 thf(f12,plain,(
% 1.57/1.32 ((sK2 @ (!! @ a @ (^[Y0 : a]: ((sK0 @ Y0) | (sK1 @ Y0))))) = $false)),
% 1.57/1.32 inference(condensation,[status(thm)],[f11])).
% 1.57/1.32 thf(f11,plain,(
% 1.57/1.32 ( ! [X3 : $o] : (((sK2 @ X3) = $false) | ((sK2 @ (!! @ a @ (^[Y0 : a]: ((sK0 @ Y0) | (sK1 @ Y0))))) = $false)) )),
% 1.57/1.32 inference(binary_proxy_clausification,[status(thm)],[f9])).
% 1.57/1.32 thf(f9,plain,(
% 1.57/1.32 ( ! [X3 : $o] : (((sK2 @ X3) != (sK2 @ (!! @ a @ (^[Y0 : a]: ((sK0 @ Y0) | (sK1 @ Y0))))))) )),
% 1.57/1.32 inference(cnf_transformation,[status(thm)],[f8])).
% 1.57/1.32 thf(f8,plain,(
% 1.57/1.32 ! [X3 : $o] : ((sK2 @ X3) != (sK2 @ (!! @ a @ (^[Y0 : a]: ((sK0 @ Y0) | (sK1 @ Y0))))))),
% 1.57/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f6,f7])).
% 1.57/1.32 thf(f7,plain,(
% 1.57/1.32 ? [X0 : a > $o,X1 : a > $o,X2 : $o > $o] : ! [X3 : $o] : ((X2 @ (!! @ a @ (^[Y0 : a]: ((X0 @ Y0) | (X1 @ Y0))))) != (X2 @ X3)) => ! [X3 : $o] : ((sK2 @ X3) != (sK2 @ (!! @ a @ (^[Y0 : a]: ((sK0 @ Y0) | (sK1 @ Y0))))))),
% 1.57/1.32 introduced(definition,[],[choice_axiom])).
% 1.57/1.32 thf(f6,plain,(
% 1.57/1.32 ? [X0 : a > $o,X1 : a > $o,X2 : $o > $o] : ! [X3 : $o] : ((X2 @ (!! @ a @ (^[Y0 : a]: ((X0 @ Y0) | (X1 @ Y0))))) != (X2 @ X3))),
% 1.57/1.32 inference(ennf_transformation,[status(thm)],[f5])).
% 1.57/1.32 thf(f5,plain,(
% 1.57/1.32 ~! [X0 : a > $o,X1 : a > $o,X2 : $o > $o] : ? [X3 : $o] : ((X2 @ (!! @ a @ (^[Y0 : a]: ((X0 @ Y0) | (X1 @ Y0))))) = (X2 @ X3))),
% 1.57/1.32 inference(fool_elimination,[status(thm)],[f4])).
% 1.57/1.32 thf(f4,plain,(
% 1.57/1.32 ~! [X0 : a > $o,X1 : a > $o,X2 : $o > $o] : ? [X3 : $o] : ((X2 @ X3) <=> (X2 @ ! [X4 : a] : ((X1 @ X4) | (X0 @ X4))))),
% 1.57/1.32 inference(rectify,[status(thm)],[f2])).
% 1.57/1.32 thf(f2,negated_conjecture,(
% 1.57/1.32 ~! [X2 : a > $o,X1 : a > $o,X0 : $o > $o] : ? [X3 : $o] : ((X0 @ X3) <=> (X0 @ ! [X4 : a] : ((X1 @ X4) | (X2 @ X4))))),
% 1.57/1.32 inference(negated_conjecture,[status(cth)],[f1])).
% 1.57/1.32 thf(f1,conjecture,(
% 1.57/1.32 ! [X2 : a > $o,X1 : a > $o,X0 : $o > $o] : ? [X3 : $o] : ((X0 @ X3) <=> (X0 @ ! [X4 : a] : ((X1 @ X4) | (X2 @ X4))))),
% 1.57/1.32 file('/export/starexec/sandbox/tmp/tmp.8SL8zOusUF/DTF2THF_3244.p',cTHM121)).
% 1.57/1.32 thf(f13,plain,(
% 1.57/1.32 ((sK2 @ (!! @ a @ (^[Y0 : a]: ((sK0 @ Y0) | (sK1 @ Y0))))) = $true)),
% 1.57/1.32 inference(condensation,[status(thm)],[f10])).
% 1.57/1.32 thf(f10,plain,(
% 1.57/1.32 ( ! [X3 : $o] : (((sK2 @ (!! @ a @ (^[Y0 : a]: ((sK0 @ Y0) | (sK1 @ Y0))))) = $true) | ((sK2 @ X3) = $true)) )),
% 1.57/1.32 inference(binary_proxy_clausification,[status(thm)],[f9])).
% 1.57/1.32 % SZS output end Proof for DTF2THF_3244
% 1.57/1.32 % (3347)------------------------------
% 1.57/1.32 % (3347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.32 % (3347)Termination reason: Refutation
% 1.57/1.32
% 1.57/1.32 % (3347)Memory used [KB]: 5500
% 1.57/1.32 % (3347)Time elapsed: 0.003 s
% 1.57/1.32 % (3347)Instructions burned: 1 (million)
% 1.57/1.32 % (3347)------------------------------
% 1.57/1.32 % (3347)------------------------------
% 1.57/1.32 % (3340)Success in time 0.018 s
%------------------------------------------------------------------------------