%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO365^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n005.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 09:54:03 AM UTC 2026
% Result : Theorem 1.46s 1.29s
% Output : Refutation 1.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 90 ( 27 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 83 ( 18 ~; 0 |; 0 &; 32 @)
% ( 2 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 4 usr; 6 con; 0-2 aty)
% ( 10 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 14 ( 10 ^; 4 !; 0 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
cC: $o > $o ).
thf(f20,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f19]) ).
thf(f19,plain,
$false = $true,
inference(boolean_simplification,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ~ $true ) = $true ),
inference(boolean_simplification,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ~ ( ( !! @ $o
@ ^ [Y0: $o] :
( !! @ $o
@ ^ [Y1: $o] :
( ( Y1 = Y0 )
=> ( Y1 = Y0 ) ) ) )
=> $true ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ~ ( ( !! @ $o
@ ^ [Y0: $o] :
( !! @ $o
@ ^ [Y1: $o] :
( ( Y1 = Y0 )
=> ( Y1 = Y0 ) ) ) )
=> ( ( cC @ cA )
=> ( cC @ cA ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ~ ( ( !! @ $o
@ ^ [Y0: $o] :
( !! @ $o
@ ^ [Y1: $o] :
( ( Y1 = Y0 )
=> ( Y1 = Y0 ) ) ) )
=> ( ( cC @ cA )
=> ( cC
@ ~ ~ cA ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f13,f14,f12]) ).
thf(f12,plain,
( cEXT2
= ( ( cC @ cA )
=> ( cC
@ ~ ~ cA ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( cEXT2
= ( ( cC @ cA )
=> ( cC
@ ~ ~ cA ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
( ( cEXT2
= ( cC @ cA ) )
=> ( cC
@ ~ ~ cA ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( cEXT2
= ( cC @ cA ) )
=> ( cC
@ ~ ~ cA ) ),
file('/export/starexec/sandbox/tmp/tmp.VkePvbxk5i/DTF2THF_1267.p',cEXT2_def) ).
thf(f14,plain,
( cEXT_eq_0
= ( !! @ $o
@ ^ [Y0: $o] :
( !! @ $o
@ ^ [Y1: $o] :
( ( Y1 = Y0 )
=> ( Y1 = Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( cEXT_eq_0
= ( !! @ $o
@ ^ [Y0: $o] :
( !! @ $o
@ ^ [Y1: $o] :
( ( Y1 = Y0 )
=> ( Y1 = Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $o,X1: $o] :
( ( ( X0
<=> X1 )
=> ( X0 = X1 ) )
= cEXT_eq_0 ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $o,X1: $o] :
( ( ( X0
<=> X1 )
=> ( X0 = X1 ) )
= cEXT_eq_0 ),
file('/export/starexec/sandbox/tmp/tmp.VkePvbxk5i/DTF2THF_1267.p',cEXT_eq_0_def) ).
thf(f13,plain,
( ( ~ ( cEXT_eq_0
=> cEXT2 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ~ ( cEXT_eq_0
=> cEXT2 ) )
= $true ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( cEXT_eq_0
=> cEXT2 ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( cEXT_eq_0
=> cEXT2 ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( cEXT_eq_0
=> cEXT2 ),
file('/export/starexec/sandbox/tmp/tmp.VkePvbxk5i/DTF2THF_1267.p',cEXT2A) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO365^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n005.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 14:28:44 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
% 0.31/0.47 ---- Original DTF file ---
% 0.31/0.47 thf(spec,logic,$$dhol).
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 % File : SYO365^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% 0.31/0.47 % Domain : Syntactic
% 0.31/0.47 % Problem : TPS problem from EXTENSIONALITY
% 0.31/0.47 % Version : Especial.
% 0.31/0.47 % English :
% 0.31/0.47
% 0.31/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.31/0.47 % Source : [Bro09]
% 0.31/0.47 % Names : tps_0585 [Bro09]
% 0.31/0.47
% 0.31/0.47 % Status : Theorem
% 0.31/0.47 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.15 v8.1.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0
% 0.31/0.47 % Syntax : Number of formulae : 7 ( 2 unt; 4 typ; 2 def)
% 0.31/0.47 % Number of atoms : 11 ( 3 equ; 0 cnn)
% 0.31/0.47 % Maximal formula atoms : 2 ( 3 avg)
% 0.31/0.47 % Number of connectives : 8 ( 2 ~; 0 |; 0 &; 2 @)
% 0.31/0.47 % ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% 0.31/0.47 % Maximal formula depth : 2 ( 1 avg)
% 0.31/0.47 % Number of types : 1 ( 0 usr)
% 0.31/0.47 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.31/0.47 % Number of symbols : 5 ( 4 usr; 3 con; 0-2 aty)
% 0.31/0.47 % Number of variables : 2 ( 0 ^; 2 !; 0 ?; 2 :)
% 0.31/0.47 % SPC : TH0_THM_EQU_NAR
% 0.31/0.47
% 0.31/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.31/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.31/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.31/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.31/0.47 % Bugfixes : v5.2.0 - Added missing type declarations.
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 thf(cA_type,type,
% 0.31/0.47 cA: $o ).
% 0.31/0.47
% 0.31/0.47 thf(cC_type,type,
% 0.31/0.47 cC: $o > $o ).
% 0.31/0.47
% 0.31/0.47 thf(cEXT2_type,type,
% 0.31/0.47 cEXT2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(cEXT_eq_0_type,type,
% 0.31/0.47 cEXT_eq_0: $o ).
% 0.31/0.47
% 0.31/0.47 thf(cEXT2_def,definition,
% 0.31/0.47 ( cEXT2
% 0.31/0.47 = ( ( cC @ cA )
% 0.31/0.47 => ( cC
% 0.31/0.47 @ ~ ~ cA ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(cEXT_eq_0_def,definition,
% 0.31/0.47 ( cEXT_eq_0
% 0.31/0.47 = ( ! [Xp: $o,Xq: $o] :
% 0.31/0.47 ( ( Xp
% 0.31/0.47 <=> Xq )
% 0.31/0.47 => ( Xp = Xq ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(cEXT2A,conjecture,
% 0.31/0.47 ( cEXT_eq_0
% 0.31/0.47 => cEXT2 ) ).
% 0.31/0.47
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 ------------------------
% 1.46/1.26 ---- Embedded in THF ---
% 1.46/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.26 %%% Generated on Tue Feb 24 14:28:45 EST 2026
% 1.46/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.26 %%% Logic specification used:
% 1.46/1.26 %%% thf(spec, logic, $$dhol).
% 1.46/1.26
% 1.46/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.VkePvbxk5i/DTF2DTF1267.p
% See solution above
% 1.46/1.26 ------------------------
% 1.46/1.27 ---- Cleaned THF ---
% 1.46/1.27 thf(cA_type,type,
% 1.46/1.27 cA: $o ).
% 1.46/1.27
% 1.46/1.27 thf(cC_type,type,
% 1.46/1.27 cC: $o > $o ).
% 1.46/1.27
% 1.46/1.27 thf(cEXT2_type,type,
% 1.46/1.27 cEXT2: $o ).
% 1.46/1.27
% 1.46/1.27 thf(cEXT_eq_0_type,type,
% 1.46/1.27 cEXT_eq_0: $o ).
% 1.46/1.27
% 1.46/1.27 thf(cEXT2_def,definition,
% 1.46/1.27 ( cEXT2
% 1.46/1.27 = ( ( cC @ cA )
% 1.46/1.27 => ( cC
% 1.46/1.27 @ ~ ~ cA ) ) ) ).
% 1.46/1.27
% 1.46/1.27 thf(cEXT_eq_0_def,definition,
% 1.46/1.27 ( cEXT_eq_0
% 1.46/1.27 = ( ! [Xp: $o,Xq: $o] :
% 1.46/1.27 ( ( Xp
% 1.46/1.27 <=> Xq )
% 1.46/1.27 => ( Xp = Xq ) ) ) ) ).
% 1.46/1.27
% 1.46/1.27 thf(cEXT2A,conjecture,
% 1.46/1.27 ( cEXT_eq_0
% 1.46/1.27 => cEXT2 ) ).
% 1.46/1.27 ------------------------
% 1.46/1.29 % (1604)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_1267 for (2999ds/275Mi)
% 1.46/1.29 % (1603)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_1267 for (2999ds/2Mi)
% 1.46/1.29 % (1604)Refutation not found, incomplete strategy
% 1.46/1.29 % (1604)------------------------------
% 1.46/1.29 % (1604)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.29 % (1604)Termination reason: Refutation not found, incomplete strategy
% 1.46/1.29
% 1.46/1.29
% 1.46/1.29 % (1604)Memory used [KB]: 5373
% 1.46/1.29 % (1604)Time elapsed: 0.002 s
% 1.46/1.29 % (1604)Instructions burned: 1 (million)
% 1.46/1.29 % (1604)------------------------------
% 1.46/1.29 % (1604)------------------------------
% 1.46/1.29 % (1603)First to succeed.
% 1.46/1.29 % (1603)Refutation found. Thanks to Tanya!
% 1.46/1.29 % SZS status Theorem for DTF2THF_1267
% 1.46/1.29 % SZS output start Proof for DTF2THF_1267
% 1.46/1.29 thf(func_def_1, type, cC: $o > $o).
% 1.46/1.29 thf(f20,plain,(
% 1.46/1.29 $false),
% 1.46/1.29 inference(trivial_inequality_removal,[status(thm)],[f19])).
% 1.46/1.29 thf(f19,plain,(
% 1.46/1.29 ($false = $true)),
% 1.46/1.29 inference(boolean_simplification,[status(thm)],[f18])).
% 1.46/1.29 thf(f18,plain,(
% 1.46/1.29 ((~ $true) = $true)),
% 1.46/1.29 inference(boolean_simplification,[status(thm)],[f17])).
% 1.46/1.29 thf(f17,plain,(
% 1.46/1.29 ((~ ((!! @ $o @ (^[Y0 : $o]: (!! @ $o @ (^[Y1 : $o]: ((Y1 = Y0) => (Y1 = Y0)))))) => $true)) = $true)),
% 1.46/1.29 inference(boolean_simplification,[status(thm)],[f16])).
% 1.46/1.29 thf(f16,plain,(
% 1.46/1.29 ((~ ((!! @ $o @ (^[Y0 : $o]: (!! @ $o @ (^[Y1 : $o]: ((Y1 = Y0) => (Y1 = Y0)))))) => ((cC @ cA) => (cC @ cA)))) = $true)),
% 1.46/1.29 inference(boolean_simplification,[status(thm)],[f15])).
% 1.46/1.29 thf(f15,plain,(
% 1.46/1.29 ((~ ((!! @ $o @ (^[Y0 : $o]: (!! @ $o @ (^[Y1 : $o]: ((Y1 = Y0) => (Y1 = Y0)))))) => ((cC @ cA) => (cC @ (~ (~ cA)))))) = $true)),
% 1.46/1.29 inference(definition_unfolding,[status(thm)],[f13,f14,f12])).
% 1.46/1.29 thf(f12,plain,(
% 1.46/1.29 (cEXT2 = ((cC @ cA) => (cC @ (~ (~ cA)))))),
% 1.46/1.29 inference(cnf_transformation,[status(thm)],[f7])).
% 1.46/1.29 thf(f7,plain,(
% 1.46/1.29 (cEXT2 = ((cC @ cA) => (cC @ (~ (~ cA)))))),
% 1.46/1.29 inference(fool_elimination,[status(thm)],[f6])).
% 1.46/1.29 thf(f6,plain,(
% 1.46/1.29 (cEXT2 = (cC @ cA) => (cC @ ~~cA))),
% 1.46/1.29 inference(rectify,[status(thm)],[f1])).
% 1.46/1.29 thf(f1,axiom,(
% 1.46/1.29 (cEXT2 = (cC @ cA) => (cC @ ~~cA))),
% 1.46/1.29 file('/export/starexec/sandbox/tmp/tmp.VkePvbxk5i/DTF2THF_1267.p',cEXT2_def)).
% 1.46/1.29 thf(f14,plain,(
% 1.46/1.29 (cEXT_eq_0 = (!! @ $o @ (^[Y0 : $o]: (!! @ $o @ (^[Y1 : $o]: ((Y1 = Y0) => (Y1 = Y0)))))))),
% 1.46/1.29 inference(cnf_transformation,[status(thm)],[f11])).
% 1.46/1.29 thf(f11,plain,(
% 1.46/1.29 (cEXT_eq_0 = (!! @ $o @ (^[Y0 : $o]: (!! @ $o @ (^[Y1 : $o]: ((Y1 = Y0) => (Y1 = Y0)))))))),
% 1.46/1.29 inference(fool_elimination,[status(thm)],[f10])).
% 1.46/1.29 thf(f10,plain,(
% 1.46/1.29 (! [X0 : $o,X1 : $o] : ((X0 <=> X1) => (X0 = X1)) = cEXT_eq_0)),
% 1.46/1.29 inference(rectify,[status(thm)],[f2])).
% 1.46/1.29 thf(f2,axiom,(
% 1.46/1.29 (! [X0 : $o,X1 : $o] : ((X0 <=> X1) => (X0 = X1)) = cEXT_eq_0)),
% 1.46/1.29 file('/export/starexec/sandbox/tmp/tmp.VkePvbxk5i/DTF2THF_1267.p',cEXT_eq_0_def)).
% 1.46/1.29 thf(f13,plain,(
% 1.46/1.29 ((~ (cEXT_eq_0 => cEXT2)) = $true)),
% 1.46/1.29 inference(cnf_transformation,[status(thm)],[f9])).
% 1.46/1.29 thf(f9,plain,(
% 1.46/1.29 ((~ (cEXT_eq_0 => cEXT2)) = $true)),
% 1.46/1.29 inference(fool_elimination,[status(thm)],[f8])).
% 1.46/1.29 thf(f8,plain,(
% 1.46/1.29 ~(cEXT_eq_0 => cEXT2)),
% 1.46/1.29 inference(rectify,[status(thm)],[f4])).
% 1.46/1.29 thf(f4,negated_conjecture,(
% 1.46/1.29 ~(cEXT_eq_0 => cEXT2)),
% 1.46/1.29 inference(negated_conjecture,[status(cth)],[f3])).
% 1.46/1.29 thf(f3,conjecture,(
% 1.46/1.29 cEXT_eq_0 => cEXT2),
% 1.46/1.29 file('/export/starexec/sandbox/tmp/tmp.VkePvbxk5i/DTF2THF_1267.p',cEXT2A)).
% 1.46/1.29 % SZS output end Proof for DTF2THF_1267
% 1.46/1.29 % (1603)------------------------------
% 1.46/1.29 % (1603)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.29 % (1603)Termination reason: Refutation
% 1.46/1.29
% 1.46/1.29 % (1603)Memory used [KB]: 5373
% 1.46/1.29 % (1603)Time elapsed: 0.002 s
% 1.46/1.29 % (1603)------------------------------
% 1.46/1.29 % (1603)------------------------------
% 1.46/1.29 % (1598)Success in time 0.012 s
%------------------------------------------------------------------------------