%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO507^1 : TPTP v9.2.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n010.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 09:54:25 AM UTC 2026
% Result : Theorem 1.46s 1.28s
% Output : Refutation 1.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 10 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 45 ( 8 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 53 ( 27 ~; 0 |; 5 &; 21 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 2 usr; 2 con; 0-2 aty)
% Number of variables : 7 ( 7 ^; 0 !; 0 ?; 7 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
f: $i > $o ).
thf(func_def_1,type,
p: ( $i > $o ) > $o ).
thf(f11,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f8,f10]) ).
thf(f10,plain,
( ( p @ f )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f9]) ).
thf(f9,plain,
( ( p
@ ^ [Y0: $i] : ( f @ Y0 ) )
!= $true ),
inference(boolean_simplification,[status(thm)],[f7]) ).
thf(f7,plain,
( ( p
@ ^ [Y0: $i] :
~ ~ ( f @ Y0 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ( p @ f )
= $true )
& ( ( p
@ ^ [Y0: $i] :
~ ~ ( f @ Y0 ) )
!= $true ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ~ ( ( ( p
@ ^ [Y0: $i] :
~ ~ ( f @ Y0 ) )
!= $true )
& ( ( p @ f )
= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ~ ( ~ ( p
@ ^ [X0: $i] :
~ ~ ( f @ X0 ) )
& ( p @ f ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ~ ( ~ ( p
@ ^ [X0: $i] :
~ ~ ( f @ X0 ) )
& ( p @ f ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
~ ( ~ ( p
@ ^ [X0: $i] :
~ ~ ( f @ X0 ) )
& ( p @ f ) ),
file('/export/starexec/sandbox/tmp/tmp.54UP2cPMHH/DTF2THF_15929.p',claim) ).
thf(f8,plain,
( ( p @ f )
= $true ),
inference(cnf_transformation,[status(thm)],[f6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO507^1 : TPTP v9.2.1. Released v4.1.0.
% 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.35 % Computer : n010.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Tue Feb 24 14:32:48 EST 2026
% 0.16/0.35 % CPUTime :
% 0.16/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.47 ---- Original DTF file ---
% 0.30/0.47 thf(spec,logic,$$dhol).
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 % File : SYO507^1 : TPTP v9.2.1. Released v4.1.0.
% 0.30/0.47 % Domain : Syntactic
% 0.30/0.47 % Problem : Example 4.1
% 0.30/0.47 % Version : Especial.
% 0.30/0.47 % English :
% 0.30/0.47
% 0.30/0.47 % Refs : [Bro09] Brown E. (2009), Email to Geoff Sutcliffe
% 0.30/0.47 % : [BS09] Brown E. & Smolka (2009), Extended First-Order Logic
% 0.30/0.47 % Source : [Bro09]
% 0.30/0.47 % Names : efo2 [Bro09]
% 0.30/0.47 % : Example 4.1 [BS09]
% 0.30/0.47
% 0.30/0.47 % Status : Theorem
% 0.30/0.47 % Rating : 0.17 v9.1.0, 0.12 v9.0.0, 0.17 v8.2.0, 0.18 v8.1.0, 0.08 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 v5.3.0, 0.25 v4.1.0
% 0.30/0.47 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.30/0.47 % Number of atoms : 4 ( 0 equ; 0 cnn)
% 0.30/0.47 % Maximal formula atoms : 4 ( 4 avg)
% 0.30/0.47 % Number of connectives : 8 ( 4 ~; 0 |; 1 &; 3 @)
% 0.30/0.47 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.30/0.47 % Maximal formula depth : 9 ( 9 avg)
% 0.30/0.47 % Number of types : 2 ( 0 usr)
% 0.30/0.47 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.30/0.47 % Number of symbols : 2 ( 2 usr; 0 con; 1-1 aty)
% 0.30/0.47 % Number of variables : 1 ( 1 ^; 0 !; 0 ?; 1 :)
% 0.30/0.47 % SPC : TH0_THM_NEQ_NAR
% 0.30/0.47
% 0.30/0.47 % Comments :
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 thf(f,type,
% 0.30/0.47 f: $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(p,type,
% 0.30/0.47 p: ( $i > $o ) > $o ).
% 0.30/0.47
% 0.30/0.47 thf(claim,conjecture,
% 0.30/0.47 ~ ( ( p @ f )
% 0.30/0.47 & ~ ( p
% 0.30/0.47 @ ^ [X: $i] :
% 0.30/0.47 ~ ~ ( f @ X ) ) ) ).
% 0.30/0.47
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 ------------------------
% 1.46/1.25 ---- Embedded in THF ---
% 1.46/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.25 %%% Generated on Tue Feb 24 14:32:49 EST 2026
% 1.46/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.25 %%% Logic specification used:
% 1.46/1.25 %%% thf(spec, logic, $$dhol).
% 1.46/1.25
% 1.46/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.54UP2cPMHH/DTF2DTF15929.p
% See solution above
% 1.46/1.25 ------------------------
% 1.46/1.26 ---- Cleaned THF ---
% 1.46/1.27 thf(f,type,
% 1.46/1.27 f: $i > $o ).
% 1.46/1.27
% 1.46/1.27 thf(p,type,
% 1.46/1.27 p: ( $i > $o ) > $o ).
% 1.46/1.27
% 1.46/1.27 thf(claim,conjecture,
% 1.46/1.27 ~ ( ( p @ f )
% 1.46/1.27 & ~ ( p
% 1.46/1.27 @ ^ [X: $i] :
% 1.46/1.27 ~ ~ ( f @ X ) ) ) ).
% 1.46/1.27 ------------------------
% 1.46/1.28 % (16261)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_15929 for (2999ds/275Mi)
% 1.46/1.28 % (16261)First to succeed.
% 1.46/1.28 % (16261)Refutation found. Thanks to Tanya!
% 1.46/1.28 % SZS status Theorem for DTF2THF_15929
% 1.46/1.28 % SZS output start Proof for DTF2THF_15929
% 1.46/1.28 thf(func_def_0, type, f: $i > $o).
% 1.46/1.28 thf(func_def_1, type, p: ($i > $o) > $o).
% 1.46/1.28 thf(f11,plain,(
% 1.46/1.28 $false),
% 1.46/1.28 inference(subsumption_resolution,[status(thm)],[f8,f10])).
% 1.46/1.28 thf(f10,plain,(
% 1.46/1.28 ((p @ f) != $true)),
% 1.46/1.28 inference(beta_eta_normalization,[status(thm)],[f9])).
% 1.46/1.28 thf(f9,plain,(
% 1.46/1.28 ((p @ (^[Y0 : $i]: (f @ Y0))) != $true)),
% 1.46/1.28 inference(boolean_simplification,[status(thm)],[f7])).
% 1.46/1.28 thf(f7,plain,(
% 1.46/1.28 ((p @ (^[Y0 : $i]: (~ (~ (f @ Y0))))) != $true)),
% 1.46/1.28 inference(cnf_transformation,[status(thm)],[f6])).
% 1.46/1.28 thf(f6,plain,(
% 1.46/1.28 ((p @ f) = $true) & ((p @ (^[Y0 : $i]: (~ (~ (f @ Y0))))) != $true)),
% 1.46/1.28 inference(flattening,[status(thm)],[f5])).
% 1.46/1.28 thf(f5,plain,(
% 1.46/1.28 ~~(~((p @ (^[Y0 : $i]: (~ (~ (f @ Y0))))) = $true) & ((p @ f) = $true))),
% 1.46/1.28 inference(fool_elimination,[status(thm)],[f4])).
% 1.46/1.28 thf(f4,plain,(
% 1.46/1.28 ~~(~(p @ (^[X0 : $i] : (~~(f @ X0)))) & (p @ f))),
% 1.46/1.28 inference(rectify,[status(thm)],[f2])).
% 1.46/1.28 thf(f2,negated_conjecture,(
% 1.46/1.28 ~~(~(p @ (^[X0 : $i] : (~~(f @ X0)))) & (p @ f))),
% 1.46/1.28 inference(negated_conjecture,[status(cth)],[f1])).
% 1.46/1.28 thf(f1,conjecture,(
% 1.46/1.28 ~(~(p @ (^[X0 : $i] : (~~(f @ X0)))) & (p @ f))),
% 1.46/1.28 file('/export/starexec/sandbox/tmp/tmp.54UP2cPMHH/DTF2THF_15929.p',claim)).
% 1.46/1.28 thf(f8,plain,(
% 1.46/1.28 ((p @ f) = $true)),
% 1.46/1.28 inference(cnf_transformation,[status(thm)],[f6])).
% 1.46/1.28 % SZS output end Proof for DTF2THF_15929
% 1.46/1.28 % (16261)------------------------------
% 1.46/1.28 % (16261)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.28 % (16261)Termination reason: Refutation
% 1.46/1.28
% 1.46/1.28 % (16261)Memory used [KB]: 5373
% 1.46/1.28 % (16261)Time elapsed: 0.002 s
% 1.46/1.28 % (16261)------------------------------
% 1.46/1.28 % (16261)------------------------------
% 1.46/1.28 % (16255)Success in time 0.012 s
%------------------------------------------------------------------------------