%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO013^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n016.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 09:53:08 AM UTC 2026
% Result : Theorem 1.52s 1.26s
% Output : Refutation 1.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 13 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 83 ( 18 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 41 ( 7 ~; 0 |; 14 &; 16 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_2,type,
p: $o > $o ).
thf(f14,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f13,f12]) ).
thf(f12,plain,
( ( p @ $true )
!= $true ),
inference(definition_unfolding,[status(thm)],[f11,f10]) ).
thf(f10,plain,
b = $true,
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ( p @ b )
!= $true )
& ( b = $true )
& ( ( p @ a )
= $true )
& ( a = $true ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ( p @ b )
!= $true )
& ( ( p @ a )
= $true )
& ( a = $true )
& ( b = $true ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ( ( p @ a )
= $true )
& ( a = $true )
& ( b = $true ) )
=> ( ( p @ b )
= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( b
& ( p @ a )
& a )
=> ( p @ b ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( b
& ( p @ a )
& a )
=> ( p @ b ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( b
& ( p @ a )
& a )
=> ( p @ b ) ),
file('/export/starexec/sandbox/tmp/tmp.a2pGKkK4Gz/DTF2THF_17075.p',conj) ).
thf(f11,plain,
( ( p @ b )
!= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f13,plain,
( ( p @ $true )
= $true ),
inference(definition_unfolding,[status(thm)],[f9,f8]) ).
thf(f8,plain,
a = $true,
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f9,plain,
( ( p @ a )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO013^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n016.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 14:21:51 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.45 ---- Original DTF file ---
% 0.19/0.45 thf(spec,logic,$$dhol).
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 % File : SYO013^1 : TPTP v9.2.1. Released v3.7.0.
% 0.19/0.45 % Domain : Syntactic
% 0.19/0.45 % Problem : Formula valid with Boolean extentionality 2
% 0.19/0.45 % Version : Especial.
% 0.19/0.45 % English :
% 0.19/0.45
% 0.19/0.45 % Refs : [BB05] Benzmueller & Brown (2005), A Structured Set of Higher
% 0.19/0.45 % : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% 0.19/0.45 % Source : [Ben09]
% 0.19/0.45 % Names : Example 15b [BB05]
% 0.19/0.45
% 0.19/0.45 % Status : Theorem
% 0.19/0.45 % : Without Boolean extensionality : CounterSatisfiable
% 0.19/0.45 % Rating : 0.08 v9.1.0, 0.12 v9.0.0, 0.08 v8.2.0, 0.09 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 v6.0.0, 0.00 v5.3.0, 0.25 v4.1.0, 0.33 v4.0.0, 0.00 v3.7.0
% 0.19/0.45 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.19/0.45 % Number of atoms : 6 ( 0 equ; 0 cnn)
% 0.19/0.45 % Maximal formula atoms : 6 ( 6 avg)
% 0.19/0.45 % Number of connectives : 5 ( 0 ~; 0 |; 2 &; 2 @)
% 0.19/0.45 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.19/0.45 % Maximal formula depth : 5 ( 5 avg)
% 0.19/0.45 % Number of types : 1 ( 0 usr)
% 0.19/0.45 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.19/0.45 % Number of symbols : 3 ( 3 usr; 2 con; 0-1 aty)
% 0.19/0.45 % Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% 0.19/0.45 % SPC : TH0_THM_NEQ_NAR
% 0.19/0.45
% 0.19/0.45 % Comments :
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 thf(a_type,type,
% 0.19/0.45 a: $o ).
% 0.19/0.45
% 0.19/0.45 thf(b_type,type,
% 0.19/0.45 b: $o ).
% 0.19/0.45
% 0.19/0.45 thf(p_type,type,
% 0.19/0.45 p: $o > $o ).
% 0.19/0.45
% 0.19/0.45 thf(conj,conjecture,
% 0.19/0.45 ( ( a
% 0.19/0.45 & b
% 0.19/0.45 & ( p @ a ) )
% 0.19/0.45 => ( p @ b ) ) ).
% 0.19/0.45
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 ------------------------
% 1.52/1.23 ---- Embedded in THF ---
% 1.52/1.23 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.52/1.23 %%% Generated on Tue Feb 24 14:21:51 EST 2026
% 1.52/1.23 %%% using '$$dhol' embedding, version 1.3.0.
% 1.52/1.23 %%% Logic specification used:
% 1.52/1.23 %%% thf(spec, logic, $$dhol).
% 1.52/1.23
% 1.52/1.23 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.a2pGKkK4Gz/DTF2DTF17075.p
% See solution above
% 1.52/1.23 ------------------------
% 1.52/1.24 ---- Cleaned THF ---
% 1.52/1.24 thf(a_type,type,
% 1.52/1.24 a: $o ).
% 1.52/1.24
% 1.52/1.24 thf(b_type,type,
% 1.52/1.24 b: $o ).
% 1.52/1.24
% 1.52/1.24 thf(p_type,type,
% 1.52/1.24 p: $o > $o ).
% 1.52/1.24
% 1.52/1.24 thf(conj,conjecture,
% 1.52/1.24 ( ( a
% 1.52/1.24 & b
% 1.52/1.24 & ( p @ a ) )
% 1.52/1.24 => ( p @ b ) ) ).
% 1.52/1.24 ------------------------
% 1.52/1.26 % (17267)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_17075 for (2999ds/2Mi)
% 1.52/1.26 % (17268)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_17075 for (2999ds/275Mi)
% 1.52/1.26 % (17268)First to succeed.
% 1.52/1.26 % (17266)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_17075 for (2999ds/2Mi)
% 1.52/1.26 % (17267)Instruction limit reached!
% 1.52/1.26 % (17267)------------------------------
% 1.52/1.26 % (17267)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.26 % (17267)Termination reason: Unknown
% 1.52/1.26 % (17267)Termination phase: Saturation
% 1.52/1.26
% 1.52/1.26 % (17267)Memory used [KB]: 5500
% 1.52/1.26 % (17267)Time elapsed: 0.002 s
% 1.52/1.26 % (17267)Instructions burned: 2 (million)
% 1.52/1.26 % (17267)------------------------------
% 1.52/1.26 % (17267)------------------------------
% 1.52/1.26 % (17266)Also succeeded, but the first one will report.
% 1.52/1.26 % (17268)Refutation found. Thanks to Tanya!
% 1.52/1.26 % SZS status Theorem for DTF2THF_17075
% 1.52/1.26 % SZS output start Proof for DTF2THF_17075
% 1.52/1.26 thf(func_def_2, type, p: $o > $o).
% 1.52/1.26 thf(f14,plain,(
% 1.52/1.26 $false),
% 1.52/1.26 inference(subsumption_resolution,[status(thm)],[f13,f12])).
% 1.52/1.26 thf(f12,plain,(
% 1.52/1.26 ((p @ $true) != $true)),
% 1.52/1.26 inference(definition_unfolding,[status(thm)],[f11,f10])).
% 1.52/1.26 thf(f10,plain,(
% 1.52/1.26 (b = $true)),
% 1.52/1.26 inference(cnf_transformation,[status(thm)],[f7])).
% 1.52/1.26 thf(f7,plain,(
% 1.52/1.26 ((p @ b) != $true) & (b = $true) & ((p @ a) = $true) & (a = $true)),
% 1.52/1.26 inference(flattening,[status(thm)],[f6])).
% 1.52/1.26 thf(f6,plain,(
% 1.52/1.26 ((p @ b) != $true) & (((p @ a) = $true) & (a = $true) & (b = $true))),
% 1.52/1.26 inference(ennf_transformation,[status(thm)],[f5])).
% 1.52/1.26 thf(f5,plain,(
% 1.52/1.26 ~((((p @ a) = $true) & (a = $true) & (b = $true)) => ((p @ b) = $true))),
% 1.52/1.26 inference(fool_elimination,[status(thm)],[f4])).
% 1.52/1.26 thf(f4,plain,(
% 1.52/1.26 ~((b & (p @ a) & a) => (p @ b))),
% 1.52/1.26 inference(rectify,[status(thm)],[f2])).
% 1.52/1.26 thf(f2,negated_conjecture,(
% 1.52/1.26 ~((b & (p @ a) & a) => (p @ b))),
% 1.52/1.26 inference(negated_conjecture,[status(cth)],[f1])).
% 1.52/1.26 thf(f1,conjecture,(
% 1.52/1.26 (b & (p @ a) & a) => (p @ b)),
% 1.52/1.26 file('/export/starexec/sandbox/tmp/tmp.a2pGKkK4Gz/DTF2THF_17075.p',conj)).
% 1.52/1.26 thf(f11,plain,(
% 1.52/1.26 ((p @ b) != $true)),
% 1.52/1.26 inference(cnf_transformation,[status(thm)],[f7])).
% 1.52/1.26 thf(f13,plain,(
% 1.52/1.26 ((p @ $true) = $true)),
% 1.52/1.26 inference(definition_unfolding,[status(thm)],[f9,f8])).
% 1.52/1.26 thf(f8,plain,(
% 1.52/1.26 (a = $true)),
% 1.52/1.26 inference(cnf_transformation,[status(thm)],[f7])).
% 1.52/1.26 thf(f9,plain,(
% 1.52/1.26 ((p @ a) = $true)),
% 1.52/1.26 inference(cnf_transformation,[status(thm)],[f7])).
% 1.52/1.26 % SZS output end Proof for DTF2THF_17075
% 1.52/1.26 % (17268)------------------------------
% 1.52/1.26 % (17268)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.26 % (17268)Termination reason: Refutation
% 1.52/1.26
% 1.52/1.26 % (17268)Memory used [KB]: 5373
% 1.52/1.26 % (17268)Time elapsed: 0.002 s
% 1.52/1.26 % (17268)------------------------------
% 1.52/1.26 % (17268)------------------------------
% 1.52/1.26 % (17262)Success in time 0.011 s
%------------------------------------------------------------------------------