%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO146^5 : 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 : n011.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 1.78s 1.41s
% Output : Refutation 1.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 5 unt; 0 typ; 2 def)
% Number of atoms : 203 ( 38 equ; 0 cnn)
% Maximal formula atoms : 10 ( 7 avg)
% Number of connectives : 138 ( 19 ~; 31 |; 8 &; 74 @)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 7 con; 0-2 aty)
% Number of variables : 14 ( 0 ^; 14 !; 0 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
cQ: $i > $o ).
thf(func_def_3,type,
cP: $i > $i > $o ).
thf(f55,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f19,f41,f54]) ).
thf(f54,plain,
spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f53]) ).
thf(f53,plain,
( $false
| spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f49]) ).
thf(f49,plain,
( ( $false = $true )
| spl0_2 ),
inference(superposition,[status(thm)],[f45,f21]) ).
thf(f21,plain,
( ( cQ @ a )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f20]) ).
thf(f20,plain,
( ( $true != $true )
| ( ( cQ @ a )
= $false ) ),
inference(fool_paramodulation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( cQ @ a )
!= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ( cQ @ a )
!= $true )
& ! [X0: $i] :
( ! [X1: $i] :
( ( cP @ X0 @ X1 )
= $true )
| ( ( cQ @ X0 )
= $true ) )
& ( ( ( cP @ a @ c )
!= $true )
| ( ( cP @ a @ b )
!= $true ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ( cQ @ a )
!= $true )
& ( ( ( cP @ a @ c )
!= $true )
| ( ( cP @ a @ b )
!= $true ) )
& ! [X0: $i] :
( ! [X1: $i] :
( ( cP @ X0 @ X1 )
= $true )
| ( ( cQ @ X0 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ! [X0: $i] :
( ! [X1: $i] :
( ( cP @ X0 @ X1 )
= $true )
| ( ( cQ @ X0 )
= $true ) )
=> ( ( ( cQ @ a )
= $true )
| ( ( ( cP @ a @ b )
= $true )
& ( ( cP @ a @ c )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: $i] :
( ( cQ @ X0 )
| ! [X1: $i] : ( cP @ X0 @ X1 ) )
=> ( ( ( cP @ a @ c )
& ( cP @ a @ b ) )
| ( cQ @ a ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: $i] :
( ( cQ @ X0 )
| ! [X1: $i] : ( cP @ X0 @ X1 ) )
=> ( ( ( cP @ a @ c )
& ( cP @ a @ b ) )
| ( cQ @ a ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X0: $i] :
( ( cQ @ X0 )
| ! [X1: $i] : ( cP @ X0 @ X1 ) )
=> ( ( ( cP @ a @ c )
& ( cP @ a @ b ) )
| ( cQ @ a ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Nqlc8esKAk/DTF2THF_30669.p',cDUP_EXPL_1) ).
thf(f45,plain,
( ( ( cQ @ a )
= $true )
| spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f44]) ).
thf(f44,plain,
( ( $true != $true )
| ( ( cQ @ a )
= $true )
| spl0_2 ),
inference(superposition,[status(thm)],[f18,f9]) ).
thf(f9,plain,
! [X0: $i,X1: $i] :
( ( ( cP @ X0 @ X1 )
= $true )
| ( ( cQ @ X0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f18,plain,
( ( ( cP @ a @ b )
!= $true )
| spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f16]) ).
thf(f16,definition,
( spl0_2
<=> ( ( cP @ a @ b )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f41,plain,
spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f40]) ).
thf(f40,plain,
( $false
| spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f37]) ).
thf(f37,plain,
( ( $false = $true )
| spl0_1 ),
inference(superposition,[status(thm)],[f21,f34]) ).
thf(f34,plain,
( ( ( cQ @ a )
= $true )
| spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f31]) ).
thf(f31,plain,
( ( ( cQ @ a )
= $true )
| ( $false = $true )
| spl0_1 ),
inference(superposition,[status(thm)],[f9,f26]) ).
thf(f26,plain,
( ( ( cP @ a @ c )
= $false )
| spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ( cP @ a @ c )
= $false )
| ( $true != $true )
| spl0_1 ),
inference(fool_paramodulation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ( cP @ a @ c )
!= $true )
| spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f12]) ).
thf(f12,definition,
( spl0_1
<=> ( ( cP @ a @ c )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f19,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f8,f16,f12]) ).
thf(f8,plain,
( ( ( cP @ a @ b )
!= $true )
| ( ( cP @ a @ c )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO146^5 : 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 : n011.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 14:24:32 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
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.46 thf(spec,logic,$$dhol).
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % File : SYO146^5 : TPTP v9.2.1. Released v4.0.0.
% 0.31/0.46 % Domain : Syntactic
% 0.31/0.46 % Problem : TPS problem from BASIC-FO-THMS
% 0.31/0.46 % Version : Especial.
% 0.31/0.46 % English :
% 0.31/0.46
% 0.31/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.31/0.46 % Source : [Bro09]
% 0.31/0.46 % Names : tps_0785 [Bro09]
% 0.31/0.46
% 0.31/0.46 % Status : Theorem
% 0.31/0.46 % Rating : 0.00 v6.2.0, 0.17 v6.0.0, 0.00 v4.0.0
% 0.31/0.46 % Syntax : Number of formulae : 6 ( 0 unt; 5 typ; 0 def)
% 0.31/0.46 % Number of atoms : 5 ( 0 equ; 0 cnn)
% 0.31/0.46 % Maximal formula atoms : 5 ( 5 avg)
% 0.31/0.46 % Number of connectives : 12 ( 0 ~; 2 |; 1 &; 8 @)
% 0.31/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.31/0.46 % Maximal formula depth : 7 ( 7 avg)
% 0.31/0.46 % Number of types : 2 ( 0 usr)
% 0.31/0.46 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.31/0.46 % Number of symbols : 5 ( 5 usr; 3 con; 0-2 aty)
% 0.31/0.46 % Number of variables : 2 ( 0 ^; 2 !; 0 ?; 2 :)
% 0.31/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.31/0.46
% 0.31/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.31/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.31/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.31/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 thf(a,type,
% 0.31/0.46 a: $i ).
% 0.31/0.46
% 0.31/0.46 thf(cQ,type,
% 0.31/0.46 cQ: $i > $o ).
% 0.31/0.46
% 0.31/0.46 thf(c,type,
% 0.31/0.46 c: $i ).
% 0.31/0.46
% 0.31/0.46 thf(cP,type,
% 0.31/0.46 cP: $i > $i > $o ).
% 0.31/0.46
% 0.31/0.46 thf(b,type,
% 0.31/0.46 b: $i ).
% 0.31/0.46
% 0.31/0.46 thf(cDUP_EXPL_1,conjecture,
% 0.31/0.46 ( ! [Xx: $i] :
% 0.31/0.46 ( ! [Xy: $i] : ( cP @ Xx @ Xy )
% 0.31/0.46 | ( cQ @ Xx ) )
% 0.31/0.46 => ( ( ( cP @ a @ b )
% 0.31/0.46 & ( cP @ a @ c ) )
% 0.31/0.46 | ( cQ @ a ) ) ) ).
% 0.31/0.46
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 ------------------------
% 1.60/1.38 ---- Embedded in THF ---
% 1.60/1.38 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.60/1.38 %%% Generated on Tue Feb 24 14:24:33 EST 2026
% 1.60/1.38 %%% using '$$dhol' embedding, version 1.3.0.
% 1.60/1.38 %%% Logic specification used:
% 1.60/1.38 %%% thf(spec, logic, $$dhol).
% 1.60/1.38
% 1.60/1.38 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.Nqlc8esKAk/DTF2DTF30669.p
% See solution above
% 1.60/1.38 ------------------------
% 1.60/1.39 ---- Cleaned THF ---
% 1.60/1.39 thf(a,type,
% 1.60/1.39 a: $i ).
% 1.60/1.39
% 1.60/1.39 thf(cQ,type,
% 1.60/1.39 cQ: $i > $o ).
% 1.60/1.39
% 1.60/1.39 thf(c,type,
% 1.60/1.39 c: $i ).
% 1.60/1.39
% 1.60/1.39 thf(cP,type,
% 1.60/1.39 cP: $i > $i > $o ).
% 1.60/1.39
% 1.60/1.39 thf(b,type,
% 1.60/1.39 b: $i ).
% 1.60/1.39
% 1.60/1.39 thf(cDUP_EXPL_1,conjecture,
% 1.60/1.39 ( ! [Xx: $i] :
% 1.60/1.39 ( ! [Xy: $i] : ( cP @ Xx @ Xy )
% 1.60/1.39 | ( cQ @ Xx ) )
% 1.60/1.39 => ( ( ( cP @ a @ b )
% 1.60/1.39 & ( cP @ a @ c ) )
% 1.60/1.39 | ( cQ @ a ) ) ) ).
% 1.60/1.39 ------------------------
% 1.78/1.41 % (30887)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_30669 for (2999ds/2Mi)
% 1.78/1.41 % (30887)Instruction limit reached!
% 1.78/1.41 % (30887)------------------------------
% 1.78/1.41 % (30887)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.41 % (30887)Termination reason: Unknown
% 1.78/1.41 % (30887)Termination phase: Saturation
% 1.78/1.41
% 1.78/1.41 % (30887)Memory used [KB]: 5500
% 1.78/1.41 % (30887)Time elapsed: 0.003 s
% 1.78/1.41 % (30887)Instructions burned: 2 (million)
% 1.78/1.41 % (30887)------------------------------
% 1.78/1.41 % (30887)------------------------------
% 1.78/1.41 % (30884)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_30669 for (2999ds/4Mi)
% 1.78/1.41 % (30884)First to succeed.
% 1.78/1.41 % (30885)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_30669 for (2999ds/27Mi)
% 1.78/1.41 % (30884)Refutation found. Thanks to Tanya!
% 1.78/1.41 % SZS status Theorem for DTF2THF_30669
% 1.78/1.41 % SZS output start Proof for DTF2THF_30669
% 1.78/1.41 thf(func_def_1, type, cQ: $i > $o).
% 1.78/1.41 thf(func_def_3, type, cP: $i > $i > $o).
% 1.78/1.41 thf(f55,plain,(
% 1.78/1.41 $false),
% 1.78/1.41 inference(avatar_sat_refutation,[status(thm)],[f19,f41,f54])).
% 1.78/1.41 thf(f54,plain,(
% 1.78/1.41 spl0_2),
% 1.78/1.41 inference(avatar_contradiction_clause,[status(thm)],[f53])).
% 1.78/1.41 thf(f53,plain,(
% 1.78/1.41 $false | spl0_2),
% 1.78/1.41 inference(trivial_inequality_removal,[status(thm)],[f49])).
% 1.78/1.41 thf(f49,plain,(
% 1.78/1.41 ($false = $true) | spl0_2),
% 1.78/1.41 inference(superposition,[status(thm)],[f45,f21])).
% 1.78/1.41 thf(f21,plain,(
% 1.78/1.41 ((cQ @ a) = $false)),
% 1.78/1.41 inference(trivial_inequality_removal,[status(thm)],[f20])).
% 1.78/1.41 thf(f20,plain,(
% 1.78/1.41 ($true != $true) | ((cQ @ a) = $false)),
% 1.78/1.41 inference(fool_paramodulation,[status(thm)],[f10])).
% 1.78/1.41 thf(f10,plain,(
% 1.78/1.41 ((cQ @ a) != $true)),
% 1.78/1.41 inference(cnf_transformation,[status(thm)],[f7])).
% 1.78/1.41 thf(f7,plain,(
% 1.78/1.41 ((cQ @ a) != $true) & ! [X0 : $i] : (! [X1 : $i] : ((cP @ X0 @ X1) = $true) | ((cQ @ X0) = $true)) & (((cP @ a @ c) != $true) | ((cP @ a @ b) != $true))),
% 1.78/1.41 inference(flattening,[status(thm)],[f6])).
% 1.78/1.41 thf(f6,plain,(
% 1.78/1.41 (((cQ @ a) != $true) & (((cP @ a @ c) != $true) | ((cP @ a @ b) != $true))) & ! [X0 : $i] : (! [X1 : $i] : ((cP @ X0 @ X1) = $true) | ((cQ @ X0) = $true))),
% 1.78/1.41 inference(ennf_transformation,[status(thm)],[f5])).
% 1.78/1.41 thf(f5,plain,(
% 1.78/1.41 ~(! [X0 : $i] : (! [X1 : $i] : ((cP @ X0 @ X1) = $true) | ((cQ @ X0) = $true)) => (((cQ @ a) = $true) | (((cP @ a @ b) = $true) & ((cP @ a @ c) = $true))))),
% 1.78/1.41 inference(fool_elimination,[status(thm)],[f4])).
% 1.78/1.41 thf(f4,plain,(
% 1.78/1.41 ~(! [X0 : $i] : ((cQ @ X0) | ! [X1 : $i] : (cP @ X0 @ X1)) => (((cP @ a @ c) & (cP @ a @ b)) | (cQ @ a)))),
% 1.78/1.41 inference(rectify,[status(thm)],[f2])).
% 1.78/1.41 thf(f2,negated_conjecture,(
% 1.78/1.41 ~(! [X0 : $i] : ((cQ @ X0) | ! [X1 : $i] : (cP @ X0 @ X1)) => (((cP @ a @ c) & (cP @ a @ b)) | (cQ @ a)))),
% 1.78/1.41 inference(negated_conjecture,[status(cth)],[f1])).
% 1.78/1.41 thf(f1,conjecture,(
% 1.78/1.41 ! [X0 : $i] : ((cQ @ X0) | ! [X1 : $i] : (cP @ X0 @ X1)) => (((cP @ a @ c) & (cP @ a @ b)) | (cQ @ a))),
% 1.78/1.41 file('/export/starexec/sandbox/tmp/tmp.Nqlc8esKAk/DTF2THF_30669.p',cDUP_EXPL_1)).
% 1.78/1.41 thf(f45,plain,(
% 1.78/1.41 ((cQ @ a) = $true) | spl0_2),
% 1.78/1.41 inference(trivial_inequality_removal,[status(thm)],[f44])).
% 1.78/1.41 thf(f44,plain,(
% 1.78/1.41 ($true != $true) | ((cQ @ a) = $true) | spl0_2),
% 1.78/1.41 inference(superposition,[status(thm)],[f18,f9])).
% 1.78/1.41 thf(f9,plain,(
% 1.78/1.41 ( ! [X0 : $i,X1 : $i] : (((cP @ X0 @ X1) = $true) | ((cQ @ X0) = $true)) )),
% 1.78/1.41 inference(cnf_transformation,[status(thm)],[f7])).
% 1.78/1.41 thf(f18,plain,(
% 1.78/1.41 ((cP @ a @ b) != $true) | spl0_2),
% 1.78/1.41 inference(avatar_component_clause,[status(thm)],[f16])).
% 1.78/1.41 thf(f16,definition,(
% 1.78/1.41 spl0_2 <=> ((cP @ a @ b) = $true)),
% 1.78/1.41 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.78/1.41 thf(f41,plain,(
% 1.78/1.41 spl0_1),
% 1.78/1.41 inference(avatar_contradiction_clause,[status(thm)],[f40])).
% 1.78/1.41 thf(f40,plain,(
% 1.78/1.41 $false | spl0_1),
% 1.78/1.41 inference(trivial_inequality_removal,[status(thm)],[f37])).
% 1.78/1.41 thf(f37,plain,(
% 1.78/1.41 ($false = $true) | spl0_1),
% 1.78/1.41 inference(superposition,[status(thm)],[f21,f34])).
% 1.78/1.41 thf(f34,plain,(
% 1.78/1.41 ((cQ @ a) = $true) | spl0_1),
% 1.78/1.41 inference(trivial_inequality_removal,[status(thm)],[f31])).
% 1.78/1.41 thf(f31,plain,(
% 1.78/1.41 ((cQ @ a) = $true) | ($false = $true) | spl0_1),
% 1.78/1.41 inference(superposition,[status(thm)],[f9,f26])).
% 1.78/1.41 thf(f26,plain,(
% 1.78/1.41 ((cP @ a @ c) = $false) | spl0_1),
% 1.78/1.41 inference(trivial_inequality_removal,[status(thm)],[f25])).
% 1.78/1.41 thf(f25,plain,(
% 1.78/1.41 ((cP @ a @ c) = $false) | ($true != $true) | spl0_1),
% 1.78/1.41 inference(fool_paramodulation,[status(thm)],[f14])).
% 1.78/1.41 thf(f14,plain,(
% 1.78/1.41 ((cP @ a @ c) != $true) | spl0_1),
% 1.78/1.41 inference(avatar_component_clause,[status(thm)],[f12])).
% 1.78/1.41 thf(f12,definition,(
% 1.78/1.41 spl0_1 <=> ((cP @ a @ c) = $true)),
% 1.78/1.41 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.78/1.41 thf(f19,plain,(
% 1.78/1.41 ~spl0_1 | ~spl0_2),
% 1.78/1.41 inference(avatar_split_clause,[status(thm)],[f8,f16,f12])).
% 1.78/1.41 thf(f8,plain,(
% 1.78/1.41 ((cP @ a @ b) != $true) | ((cP @ a @ c) != $true)),
% 1.78/1.41 inference(cnf_transformation,[status(thm)],[f7])).
% 1.78/1.41 % SZS output end Proof for DTF2THF_30669
% 1.78/1.41 % (30884)------------------------------
% 1.78/1.41 % (30884)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.41 % (30884)Termination reason: Refutation
% 1.78/1.41
% 1.78/1.41 % (30884)Memory used [KB]: 5500
% 1.78/1.41 % (30884)Time elapsed: 0.004 s
% 1.78/1.41 % (30884)Instructions burned: 3 (million)
% 1.78/1.41 % (30884)------------------------------
% 1.78/1.41 % (30884)------------------------------
% 1.78/1.41 % (30881)Success in time 0.017 s
%------------------------------------------------------------------------------