%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO034^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n014.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 09:53:11 AM UTC 2026
% Result : Theorem 1.53s 1.32s
% Output : Refutation 1.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 1
% Syntax : Number of formulae : 14 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 42 ( 17 equ; 0 cnn)
% Maximal formula atoms : 1 ( 3 avg)
% Number of connectives : 57 ( 7 ~; 0 |; 0 &; 39 @)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 2 usr; 4 con; 0-2 aty)
% ( 5 !!; 3 ??; 0 @@+; 0 @@-)
% Number of variables : 26 ( 15 ^; 8 !; 3 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_11,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
sK2: ( $o > $o ) > $o ).
thf(f20,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f19]) ).
thf(f19,plain,
( ( sK2
@ ^ [Y0: $o] : Y0 )
!= ( sK2
@ ^ [Y0: $o] : Y0 ) ),
inference(beta_eta_normalization,[status(thm)],[f13]) ).
thf(f13,plain,
( ( sK2
@ ^ [Y0: $o] : Y0 )
!= ( ^ [Y0: $o] : Y0
@ ( sK2
@ ^ [Y0: $o] : Y0 ) ) ),
inference(primitive_instantiation,[status(thm)],[f12]) ).
thf(f12,plain,
! [X1: $o > $o] :
( ( sK2 @ X1 )
!= ( X1 @ ( sK2 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
! [X1: $o > $o] :
( ( ( X1 @ ( sK2 @ X1 ) )
= ( sK2 @ X1 ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
! [X1: $o > $o] :
( $false
= ( ^ [Y0: $o] :
( ( X1 @ Y0 )
= Y0 )
@ ( sK2 @ X1 ) ) ),
inference(sigma_clausification,[status(thm)],[f9]) ).
thf(f9,plain,
! [X1: $o > $o] :
( $false
= ( !! @ $o
@ ^ [Y0: $o] :
( ( X1 @ Y0 )
= Y0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f8]) ).
thf(f8,plain,
! [X1: $o > $o] :
( $false
= ( ^ [Y0: $o > $o] :
( !! @ $o
@ ^ [Y1: $o] :
( ( Y0 @ Y1 )
= Y1 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ?? @ ( $o > $o )
@ ^ [Y0: $o > $o] :
( !! @ $o
@ ^ [Y1: $o] :
( ( Y0 @ Y1 )
= Y1 ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( ?? @ ( $o > $o )
@ ^ [Y0: $o > $o] :
( !! @ $o
@ ^ [Y1: $o] :
( ( Y0 @ Y1 )
= Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( ?? @ ( $o > $o )
@ ^ [Y0: $o > $o] :
( !! @ $o
@ ^ [Y1: $o] :
( ( Y0 @ Y1 )
= Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ? [X0: $o > $o] :
! [X1: $o] :
( ( X0 @ X1 )
<=> X1 ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X0: $o > $o] :
! [X1: $o] :
( ( X0 @ X1 )
<=> X1 ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X0: $o > $o] :
! [X1: $o] :
( ( X0 @ X1 )
<=> X1 ),
file('/export/starexec/sandbox2/tmp/tmp.3zqjiIRXF6/DTF2THF_18320.p',conj) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYO034^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.10 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.30 % Computer : n014.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Tue Feb 24 14:22:12 EST 2026
% 0.11/0.30 % CPUTime :
% 0.11/0.30 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.39 ---- Original DTF file ---
% 0.16/0.39 thf(spec,logic,$$dhol).
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 % File : SYO034^1 : TPTP v9.2.1. Released v3.7.0.
% 0.16/0.39 % Domain : Syntactic
% 0.16/0.39 % Problem : Formula not making use of projection
% 0.16/0.39 % Version : Especial.
% 0.16/0.39 % English :
% 0.16/0.39
% 0.16/0.39 % Refs : [BB05] Benzmueller & Brown (2005), A Structured Set of Higher
% 0.16/0.39 % : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% 0.16/0.39 % Source : [Ben09]
% 0.16/0.39 % Names : Example 29 [BB05]
% 0.16/0.39
% 0.16/0.39 % Status : Theorem
% 0.16/0.39 % Rating : 0.00 v8.1.0, 0.08 v7.4.0, 0.00 v6.2.0, 0.33 v6.1.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.1, 0.33 v4.0.0, 0.00 v3.7.0
% 0.16/0.39 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.16/0.39 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.16/0.39 % Maximal formula atoms : 0 ( 0 avg)
% 0.16/0.39 % Number of connectives : 2 ( 0 ~; 0 |; 0 &; 1 @)
% 0.16/0.39 % ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% 0.16/0.39 % Maximal formula depth : 5 ( 5 avg)
% 0.16/0.39 % Number of types : 1 ( 0 usr)
% 0.16/0.39 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.16/0.39 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.16/0.39 % Number of variables : 2 ( 0 ^; 1 !; 1 ?; 2 :)
% 0.16/0.39 % SPC : TH0_THM_NEQ_NAR
% 0.16/0.39
% 0.16/0.39 % Comments : Requires set comprehension, and set instantiation with projection
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 thf(conj,conjecture,
% 0.16/0.39 ? [N: $o > $o] :
% 0.16/0.39 ! [P: $o] :
% 0.16/0.39 ( ( N @ P )
% 0.16/0.39 <=> P ) ).
% 0.16/0.39
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 ------------------------
% 1.34/1.29 ---- Embedded in THF ---
% 1.34/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.34/1.29 %%% Generated on Tue Feb 24 14:22:13 EST 2026
% 1.34/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.34/1.29 %%% Logic specification used:
% 1.34/1.29 %%% thf(spec, logic, $$dhol).
% 1.34/1.29
% 1.34/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.3zqjiIRXF6/DTF2DTF18320.p
% See solution above
% 1.34/1.29 ------------------------
% 1.53/1.30 ---- Cleaned THF ---
% 1.53/1.30 thf(conj,conjecture,
% 1.53/1.30 ? [N: $o > $o] :
% 1.53/1.30 ! [P: $o] :
% 1.53/1.30 ( ( N @ P )
% 1.53/1.30 <=> P ) ).
% 1.53/1.30 ------------------------
% 1.53/1.32 % (18420)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_18320 for (3000ds/27Mi)
% 1.53/1.32 % (18424)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_18320 for (3000ds/18Mi)
% 1.53/1.32 % (18422)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_18320 for (3000ds/2Mi)
% 1.53/1.32 % (18418)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_18320 for (3000ds/183Mi)
% 1.53/1.32 % (18419)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_18320 for (3000ds/4Mi)
% 1.53/1.32 % (18421)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_18320 for (3000ds/2Mi)
% 1.53/1.32 % (18423)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_18320 for (3000ds/275Mi)
% 1.53/1.32 % (18421)Instruction limit reached!
% 1.53/1.32 % (18421)------------------------------
% 1.53/1.32 % (18421)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.32 % (18421)Termination reason: Unknown
% 1.53/1.32 % (18421)Termination phase: Saturation
% 1.53/1.32
% 1.53/1.32 % (18421)Memory used [KB]: 5500
% 1.53/1.32 % (18421)Time elapsed: 0.004 s
% 1.53/1.32 % (18421)Instructions burned: 3 (million)
% 1.53/1.32 % (18421)------------------------------
% 1.53/1.32 % (18421)------------------------------
% 1.53/1.32 % (18422)First to succeed.
% 1.53/1.32 % (18420)Refutation not found, incomplete strategy
% 1.53/1.32 % (18420)------------------------------
% 1.53/1.32 % (18420)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.32 % (18420)Termination reason: Refutation not found, incomplete strategy
% 1.53/1.32
% 1.53/1.32
% 1.53/1.32 % (18420)Memory used [KB]: 5500
% 1.53/1.32 % (18420)Time elapsed: 0.004 s
% 1.53/1.32 % (18420)Instructions burned: 3 (million)
% 1.53/1.32 % (18420)------------------------------
% 1.53/1.32 % (18420)------------------------------
% 1.53/1.32 % (18423)Also succeeded, but the first one will report.
% 1.53/1.32 % (18419)Instruction limit reached!
% 1.53/1.32 % (18419)------------------------------
% 1.53/1.32 % (18419)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.32 % (18419)Termination reason: Unknown
% 1.53/1.32 % (18419)Termination phase: Saturation
% 1.53/1.32
% 1.53/1.32 % (18419)Memory used [KB]: 5500
% 1.53/1.32 % (18419)Time elapsed: 0.005 s
% 1.53/1.32 % (18419)Instructions burned: 5 (million)
% 1.53/1.32 % (18419)------------------------------
% 1.53/1.32 % (18419)------------------------------
% 1.53/1.32 % (18422)Refutation found. Thanks to Tanya!
% 1.53/1.32 % SZS status Theorem for DTF2THF_18320
% 1.53/1.32 % SZS output start Proof for DTF2THF_18320
% 1.53/1.32 thf(func_def_11, type, ph1: !>[X0: $tType]:(X0)).
% 1.53/1.32 thf(func_def_12, type, sK2: ($o > $o) > $o).
% 1.53/1.32 thf(f20,plain,(
% 1.53/1.32 $false),
% 1.53/1.32 inference(trivial_inequality_removal,[status(thm)],[f19])).
% 1.53/1.32 thf(f19,plain,(
% 1.53/1.32 ((sK2 @ (^[Y0 : $o]: (Y0))) != (sK2 @ (^[Y0 : $o]: (Y0))))),
% 1.53/1.32 inference(beta_eta_normalization,[status(thm)],[f13])).
% 1.53/1.32 thf(f13,plain,(
% 1.53/1.32 ((sK2 @ (^[Y0 : $o]: (Y0))) != ((^[Y0 : $o]: (Y0)) @ (sK2 @ (^[Y0 : $o]: (Y0)))))),
% 1.53/1.32 inference(primitive_instantiation,[status(thm)],[f12])).
% 1.53/1.32 thf(f12,plain,(
% 1.53/1.32 ( ! [X1 : $o > $o] : (((sK2 @ X1) != (X1 @ (sK2 @ X1)))) )),
% 1.53/1.32 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.53/1.32 thf(f11,plain,(
% 1.53/1.32 ( ! [X1 : $o > $o] : ((((X1 @ (sK2 @ X1)) = (sK2 @ X1)) = $false)) )),
% 1.53/1.32 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.53/1.32 thf(f10,plain,(
% 1.53/1.32 ( ! [X1 : $o > $o] : (($false = ((^[Y0 : $o]: ((X1 @ Y0) = Y0)) @ (sK2 @ X1)))) )),
% 1.53/1.32 inference(sigma_clausification,[status(thm)],[f9])).
% 1.53/1.32 thf(f9,plain,(
% 1.53/1.32 ( ! [X1 : $o > $o] : (($false = (!! @ $o @ (^[Y0 : $o]: ((X1 @ Y0) = Y0))))) )),
% 1.53/1.32 inference(beta_eta_normalization,[status(thm)],[f8])).
% 1.53/1.32 thf(f8,plain,(
% 1.53/1.32 ( ! [X1 : $o > $o] : (($false = ((^[Y0 : $o > $o]: (!! @ $o @ (^[Y1 : $o]: ((Y0 @ Y1) = Y1)))) @ X1))) )),
% 1.53/1.32 inference(pi_clausification,[status(thm)],[f7])).
% 1.53/1.32 thf(f7,plain,(
% 1.53/1.32 ((?? @ ($o > $o) @ (^[Y0 : $o > $o]: (!! @ $o @ (^[Y1 : $o]: ((Y0 @ Y1) = Y1))))) = $false)),
% 1.53/1.32 inference(not_proxy_clausification,[status(thm)],[f6])).
% 1.53/1.32 thf(f6,plain,(
% 1.53/1.32 ($true = (~ (?? @ ($o > $o) @ (^[Y0 : $o > $o]: (!! @ $o @ (^[Y1 : $o]: ((Y0 @ Y1) = Y1)))))))),
% 1.53/1.32 inference(cnf_transformation,[status(thm)],[f5])).
% 1.53/1.32 thf(f5,plain,(
% 1.53/1.32 ($true = (~ (?? @ ($o > $o) @ (^[Y0 : $o > $o]: (!! @ $o @ (^[Y1 : $o]: ((Y0 @ Y1) = Y1)))))))),
% 1.53/1.32 inference(fool_elimination,[status(thm)],[f4])).
% 1.53/1.32 thf(f4,plain,(
% 1.53/1.32 ~? [X0 : $o > $o] : ! [X1 : $o] : ((X0 @ X1) <=> X1)),
% 1.53/1.32 inference(rectify,[status(thm)],[f2])).
% 1.53/1.32 thf(f2,negated_conjecture,(
% 1.53/1.32 ~? [X0 : $o > $o] : ! [X1 : $o] : ((X0 @ X1) <=> X1)),
% 1.53/1.32 inference(negated_conjecture,[status(cth)],[f1])).
% 1.53/1.32 thf(f1,conjecture,(
% 1.53/1.32 ? [X0 : $o > $o] : ! [X1 : $o] : ((X0 @ X1) <=> X1)),
% 1.53/1.32 file('/export/starexec/sandbox2/tmp/tmp.3zqjiIRXF6/DTF2THF_18320.p',conj)).
% 1.53/1.32 % SZS output end Proof for DTF2THF_18320
% 1.53/1.32 % (18422)------------------------------
% 1.53/1.32 % (18422)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.32 % (18422)Termination reason: Refutation
% 1.53/1.32
% 1.53/1.32 % (18422)Memory used [KB]: 5500
% 1.53/1.32 % (18422)Time elapsed: 0.004 s
% 1.53/1.32 % (18422)Instructions burned: 1 (million)
% 1.53/1.32 % (18422)------------------------------
% 1.53/1.32 % (18422)------------------------------
% 1.53/1.32 % (18417)Success in time 0.018 s
%------------------------------------------------------------------------------