%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO301^5 : 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 : n025.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 1.45s 1.29s
% Output : Refutation 1.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 3 unt; 0 typ; 1 def)
% Number of atoms : 109 ( 33 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 132 ( 26 ~; 12 |; 12 &; 72 @)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 32 ( 0 ^; 21 !; 11 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
f: $i > $i ).
thf(func_def_1,type,
cP: $i > $o ).
thf(func_def_6,type,
sK0: ( $i > $o ) > $i ).
thf(func_def_9,type,
ph2:
!>[X0: $tType] : X0 ).
thf(f31,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f27,f30]) ).
thf(f30,plain,
~ spl1_1,
inference(avatar_contradiction_clause,[status(thm)],[f29]) ).
thf(f29,plain,
( $false
| ~ spl1_1 ),
inference(trivial_inequality_removal,[status(thm)],[f28]) ).
thf(f28,plain,
( ( $true != $true )
| ~ spl1_1 ),
inference(superposition,[status(thm)],[f26,f10]) ).
thf(f10,plain,
( ( cP @ ( f @ b ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X0: $i > $o,X1: $i] :
( ( $true
!= ( X0 @ ( f @ X1 ) ) )
| ( ( ( X0 @ ( sK0 @ X0 ) )
= $true )
& ( $true
!= ( cP @ ( sK0 @ X0 ) ) ) ) )
& ( ( cP @ ( f @ b ) )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8]) ).
thf(f8,plain,
! [X0: $i > $o] :
( ? [X2: $i] :
( ( $true
= ( X0 @ X2 ) )
& ( ( cP @ X2 )
!= $true ) )
=> ( ( ( X0 @ ( sK0 @ X0 ) )
= $true )
& ( $true
!= ( cP @ ( sK0 @ X0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
( ! [X0: $i > $o,X1: $i] :
( ( $true
!= ( X0 @ ( f @ X1 ) ) )
| ? [X2: $i] :
( ( $true
= ( X0 @ X2 ) )
& ( ( cP @ X2 )
!= $true ) ) )
& ( ( cP @ ( f @ b ) )
= $true ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X1: $i > $o,X0: $i] :
( ( ( X1 @ ( f @ X0 ) )
!= $true )
| ? [X2: $i] :
( ( ( X1 @ X2 )
= $true )
& ( ( cP @ X2 )
!= $true ) ) )
& ( ( cP @ ( f @ b ) )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ( cP @ ( f @ b ) )
= $true )
=> ? [X1: $i > $o,X0: $i] :
( ( ( X1 @ ( f @ X0 ) )
= $true )
& ! [X2: $i] :
( ( ( X1 @ X2 )
= $true )
=> ( ( cP @ X2 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( cP @ ( f @ b ) )
=> ? [X0: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ( cP @ X2 ) )
& ( X1 @ ( f @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( cP @ ( f @ b ) )
=> ? [X0: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ( cP @ X2 ) )
& ( X1 @ ( f @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( cP @ ( f @ b ) )
=> ? [X0: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ( cP @ X2 ) )
& ( X1 @ ( f @ X0 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.bAlT9J71nX/DTF2THF_16213.p',cBLEDSOE5) ).
thf(f26,plain,
( ! [X0: $i] :
( $true
!= ( cP @ ( f @ X0 ) ) )
| ~ spl1_1 ),
inference(avatar_component_clause,[status(thm)],[f25]) ).
thf(f25,definition,
( spl1_1
<=> ! [X0: $i] :
( $true
!= ( cP @ ( f @ X0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition]) ).
thf(f27,plain,
( spl1_1
| spl1_1 ),
inference(avatar_split_clause,[status(thm)],[f19,f25,f25]) ).
thf(f19,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( cP @ ( f @ X0 ) ) )
| ( $true
!= ( cP @ ( f @ X1 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( cP @ ( f @ X1 ) ) )
| ( $true != $true )
| ( $true
!= ( cP @ ( f @ X0 ) ) ) ),
inference(superposition,[status(thm)],[f11,f12]) ).
thf(f12,plain,
! [X0: $i > $o,X1: $i] :
( ( ( X0 @ ( sK0 @ X0 ) )
= $true )
| ( $true
!= ( X0 @ ( f @ X1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f11,plain,
! [X0: $i > $o,X1: $i] :
( ( $true
!= ( cP @ ( sK0 @ X0 ) ) )
| ( $true
!= ( X0 @ ( f @ X1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO301^5 : 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
% 0.16/0.34 % Computer : n025.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 14:27:57 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : SYO301^5 : TPTP v9.2.1. Released v4.0.0.
% 0.29/0.46 % Domain : Syntactic
% 0.29/0.46 % Problem : TPS problem from BASIC-HO-THMS
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English :
% 0.29/0.46
% 0.29/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.46 % Source : [Bro09]
% 0.29/0.46 % Names : tps_0775 [Bro09]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % 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, 0.10 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 v6.2.0, 0.33 v6.1.0, 0.17 v6.0.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.0
% 0.29/0.46 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.29/0.46 % Number of atoms : 2 ( 0 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 2 ( 2 avg)
% 0.29/0.46 % Number of connectives : 9 ( 0 ~; 0 |; 1 &; 6 @)
% 0.29/0.46 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 8 ( 8 avg)
% 0.29/0.46 % Number of types : 2 ( 0 usr)
% 0.29/0.46 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 3 ( 3 usr; 1 con; 0-1 aty)
% 0.29/0.46 % Number of variables : 3 ( 0 ^; 1 !; 2 ?; 3 :)
% 0.29/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.29/0.46
% 0.29/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.29/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.29/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.29/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 thf(f,type,
% 0.29/0.46 f: $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(cP,type,
% 0.29/0.46 cP: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(b,type,
% 0.29/0.46 b: $i ).
% 0.29/0.46
% 0.29/0.46 thf(cBLEDSOE5,conjecture,
% 0.29/0.46 ( ( cP @ ( f @ b ) )
% 0.29/0.46 => ? [Xs: $i,A: $i > $o] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( A @ Xx )
% 0.29/0.46 => ( cP @ Xx ) )
% 0.29/0.46 & ( A @ ( f @ Xs ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 1.45/1.26 ---- Embedded in THF ---
% 1.45/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.45/1.26 %%% Generated on Tue Feb 24 14:27:58 EST 2026
% 1.45/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.45/1.26 %%% Logic specification used:
% 1.45/1.26 %%% thf(spec, logic, $$dhol).
% 1.45/1.26
% 1.45/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.bAlT9J71nX/DTF2DTF16213.p
% See solution above
% 1.45/1.26 ------------------------
% 1.45/1.27 ---- Cleaned THF ---
% 1.45/1.27 thf(f,type,
% 1.45/1.27 f: $i > $i ).
% 1.45/1.27
% 1.45/1.27 thf(cP,type,
% 1.45/1.27 cP: $i > $o ).
% 1.45/1.27
% 1.45/1.27 thf(b,type,
% 1.45/1.27 b: $i ).
% 1.45/1.27
% 1.45/1.27 thf(cBLEDSOE5,conjecture,
% 1.45/1.27 ( ( cP @ ( f @ b ) )
% 1.45/1.27 => ? [Xs: $i,A: $i > $o] :
% 1.45/1.27 ( ! [Xx: $i] :
% 1.45/1.27 ( ( A @ Xx )
% 1.45/1.27 => ( cP @ Xx ) )
% 1.45/1.27 & ( A @ ( f @ Xs ) ) ) ) ).
% 1.45/1.27 ------------------------
% 1.45/1.28 % (16494)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_16213 for (2999ds/275Mi)
% 1.45/1.28 % (16493)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_16213 for (2999ds/2Mi)
% 1.45/1.28 % (16493)Instruction limit reached!
% 1.45/1.28 % (16493)------------------------------
% 1.45/1.28 % (16493)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.28 % (16493)Termination reason: Unknown
% 1.45/1.28 % (16493)Termination phase: Saturation
% 1.45/1.28
% 1.45/1.28 % (16493)Memory used [KB]: 5500
% 1.45/1.28 % (16493)Time elapsed: 0.002 s
% 1.45/1.28 % (16493)Instructions burned: 2 (million)
% 1.45/1.28 % (16493)------------------------------
% 1.45/1.28 % (16493)------------------------------
% 1.45/1.28 % (16494)First to succeed.
% 1.45/1.29 % (16494)Refutation found. Thanks to Tanya!
% 1.45/1.29 % SZS status Theorem for DTF2THF_16213
% 1.45/1.29 % SZS output start Proof for DTF2THF_16213
% 1.45/1.29 thf(func_def_0, type, f: $i > $i).
% 1.45/1.29 thf(func_def_1, type, cP: $i > $o).
% 1.45/1.29 thf(func_def_6, type, sK0: ($i > $o) > $i).
% 1.45/1.29 thf(func_def_9, type, ph2: !>[X0: $tType]:(X0)).
% 1.45/1.29 thf(f31,plain,(
% 1.45/1.29 $false),
% 1.45/1.29 inference(avatar_sat_refutation,[status(thm)],[f27,f30])).
% 1.45/1.29 thf(f30,plain,(
% 1.45/1.29 ~spl1_1),
% 1.45/1.29 inference(avatar_contradiction_clause,[status(thm)],[f29])).
% 1.45/1.29 thf(f29,plain,(
% 1.45/1.29 $false | ~spl1_1),
% 1.45/1.29 inference(trivial_inequality_removal,[status(thm)],[f28])).
% 1.45/1.29 thf(f28,plain,(
% 1.45/1.29 ($true != $true) | ~spl1_1),
% 1.45/1.29 inference(superposition,[status(thm)],[f26,f10])).
% 1.45/1.29 thf(f10,plain,(
% 1.45/1.29 ((cP @ (f @ b)) = $true)),
% 1.45/1.29 inference(cnf_transformation,[status(thm)],[f9])).
% 1.45/1.29 thf(f9,plain,(
% 1.45/1.29 ! [X0 : $i > $o,X1 : $i] : (($true != (X0 @ (f @ X1))) | (((X0 @ (sK0 @ X0)) = $true) & ($true != (cP @ (sK0 @ X0))))) & ((cP @ (f @ b)) = $true)),
% 1.45/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8])).
% 1.45/1.29 thf(f8,plain,(
% 1.45/1.29 ! [X0 : $i > $o] : (? [X2 : $i] : (($true = (X0 @ X2)) & ((cP @ X2) != $true)) => (((X0 @ (sK0 @ X0)) = $true) & ($true != (cP @ (sK0 @ X0)))))),
% 1.45/1.29 introduced(definition,[],[choice_axiom])).
% 1.45/1.29 thf(f7,plain,(
% 1.45/1.29 ! [X0 : $i > $o,X1 : $i] : (($true != (X0 @ (f @ X1))) | ? [X2 : $i] : (($true = (X0 @ X2)) & ((cP @ X2) != $true))) & ((cP @ (f @ b)) = $true)),
% 1.45/1.29 inference(rectify,[status(thm)],[f6])).
% 1.45/1.29 thf(f6,plain,(
% 1.45/1.29 ! [X1 : $i > $o,X0 : $i] : (((X1 @ (f @ X0)) != $true) | ? [X2 : $i] : (((X1 @ X2) = $true) & ((cP @ X2) != $true))) & ((cP @ (f @ b)) = $true)),
% 1.45/1.29 inference(ennf_transformation,[status(thm)],[f5])).
% 1.45/1.29 thf(f5,plain,(
% 1.45/1.29 ~(((cP @ (f @ b)) = $true) => ? [X1 : $i > $o,X0 : $i] : (((X1 @ (f @ X0)) = $true) & ! [X2 : $i] : (((X1 @ X2) = $true) => ((cP @ X2) = $true))))),
% 1.45/1.29 inference(fool_elimination,[status(thm)],[f4])).
% 1.45/1.29 thf(f4,plain,(
% 1.45/1.29 ~((cP @ (f @ b)) => ? [X0 : $i,X1 : $i > $o] : (! [X2 : $i] : ((X1 @ X2) => (cP @ X2)) & (X1 @ (f @ X0))))),
% 1.45/1.29 inference(rectify,[status(thm)],[f2])).
% 1.45/1.29 thf(f2,negated_conjecture,(
% 1.45/1.29 ~((cP @ (f @ b)) => ? [X0 : $i,X1 : $i > $o] : (! [X2 : $i] : ((X1 @ X2) => (cP @ X2)) & (X1 @ (f @ X0))))),
% 1.45/1.29 inference(negated_conjecture,[status(cth)],[f1])).
% 1.45/1.29 thf(f1,conjecture,(
% 1.45/1.29 (cP @ (f @ b)) => ? [X0 : $i,X1 : $i > $o] : (! [X2 : $i] : ((X1 @ X2) => (cP @ X2)) & (X1 @ (f @ X0)))),
% 1.45/1.29 file('/export/starexec/sandbox/tmp/tmp.bAlT9J71nX/DTF2THF_16213.p',cBLEDSOE5)).
% 1.45/1.29 thf(f26,plain,(
% 1.45/1.29 ( ! [X0 : $i] : (($true != (cP @ (f @ X0)))) ) | ~spl1_1),
% 1.45/1.29 inference(avatar_component_clause,[status(thm)],[f25])).
% 1.45/1.29 thf(f25,definition,(
% 1.45/1.29 spl1_1 <=> ! [X0 : $i] : ($true != (cP @ (f @ X0)))),
% 1.45/1.29 introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition])).
% 1.45/1.29 thf(f27,plain,(
% 1.45/1.29 spl1_1 | spl1_1),
% 1.45/1.29 inference(avatar_split_clause,[status(thm)],[f19,f25,f25])).
% 1.45/1.29 thf(f19,plain,(
% 1.45/1.29 ( ! [X0 : $i,X1 : $i] : (($true != (cP @ (f @ X0))) | ($true != (cP @ (f @ X1)))) )),
% 1.45/1.29 inference(trivial_inequality_removal,[status(thm)],[f17])).
% 1.45/1.29 thf(f17,plain,(
% 1.45/1.29 ( ! [X0 : $i,X1 : $i] : (($true != (cP @ (f @ X1))) | ($true != $true) | ($true != (cP @ (f @ X0)))) )),
% 1.45/1.29 inference(superposition,[status(thm)],[f11,f12])).
% 1.45/1.29 thf(f12,plain,(
% 1.45/1.29 ( ! [X0 : $i > $o,X1 : $i] : (((X0 @ (sK0 @ X0)) = $true) | ($true != (X0 @ (f @ X1)))) )),
% 1.45/1.29 inference(cnf_transformation,[status(thm)],[f9])).
% 1.45/1.29 thf(f11,plain,(
% 1.45/1.29 ( ! [X0 : $i > $o,X1 : $i] : (($true != (cP @ (sK0 @ X0))) | ($true != (X0 @ (f @ X1)))) )),
% 1.45/1.29 inference(cnf_transformation,[status(thm)],[f9])).
% 1.45/1.29 % SZS output end Proof for DTF2THF_16213
% 1.45/1.29 % (16494)------------------------------
% 1.45/1.29 % (16494)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.29 % (16494)Termination reason: Refutation
% 1.45/1.29
% 1.45/1.29 % (16494)Memory used [KB]: 5500
% 1.45/1.29 % (16494)Time elapsed: 0.003 s
% 1.45/1.29 % (16494)Instructions burned: 3 (million)
% 1.45/1.29 % (16494)------------------------------
% 1.45/1.29 % (16494)------------------------------
% 1.45/1.29 % (16488)Success in time 0.012 s
%------------------------------------------------------------------------------