%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO379^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n002.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 09:54:05 AM UTC 2026
% Result : Theorem 1.50s 1.39s
% Output : Refutation 1.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 86 ( 39 equ; 4 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 59 ( 10 ~; 3 |; 7 &; 32 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 4 usr; 5 con; 0-2 aty)
% ( 0 !!; 7 ??; 0 @@+; 0 @@-)
% Number of variables : 31 ( 15 ^; 10 !; 6 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
cQDP0: $i > $o ).
thf(func_def_2,type,
cQDP1: ( $i > $o ) > $o ).
thf(func_def_13,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f23,plain,
$false,
inference(equality_resolution,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: $i] : ( c != X0 ),
inference(equality_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: $i] :
( ( c = X0 )
= $false ),
inference(equality_resolution,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: $i > $o,X1: $i] :
( ( ( (=) @ c )
!= X0 )
| ( ( X0 @ X1 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: $i > $o] :
( ( ( (=) @ c )
!= X0 )
| ( $false
= ( ?? @ $i @ X0 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: $i > $o] :
( ( ( ( (=) @ c )
= X0 )
= $false )
| ( $false
= ( ?? @ $i @ X0 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: $i > $o] :
( $true
!= ( ( ( (=) @ c )
= X0 )
& ( ?? @ $i @ X0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: $i > $o] :
( ( ^ [Y0: $i > $o] :
( ( ( ^ [Y1: $i] : ( c = Y1 ) )
= Y0 )
& ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) )
@ X0 )
!= $true ),
inference(definition_unfolding,[status(thm)],[f14,f15]) ).
thf(f15,plain,
( cQDP1
= ( ^ [Y0: $i > $o] :
( ( ( ^ [Y1: $i] : ( c = Y1 ) )
= Y0 )
& ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f13,f12]) ).
thf(f12,plain,
( cQDP0
= ( ^ [Y0: $i] : ( c = Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( cQDP0
= ( ^ [Y0: $i] : ( c = Y0 ) ) ),
inference(fool_elimination,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: $i] : ( c = X0 ) )
= cQDP0 ),
file('/export/starexec/sandbox2/tmp/tmp.Mb2Y8VMETo/DTF2THF_24359.p',cQDP0_def) ).
thf(f13,plain,
( cQDP1
= ( ^ [Y0: $i > $o] :
( ( cQDP0 = Y0 )
& ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( cQDP1
= ( ^ [Y0: $i > $o] :
( ( cQDP0 = Y0 )
& ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ^ [X0: $i > $o] :
( ? [X1: $i] : ( X0 @ X1 )
& ( cQDP0 = X0 ) ) )
= cQDP1 ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( ( ^ [X0: $i > $o] :
( ? [X1: $i] : ( X0 @ X1 )
& ( cQDP0 = X0 ) ) )
= cQDP1 ),
file('/export/starexec/sandbox2/tmp/tmp.Mb2Y8VMETo/DTF2THF_24359.p',cQDP1_def) ).
thf(f14,plain,
! [X0: $i > $o] :
( ( cQDP1 @ X0 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $i > $o] :
( ( cQDP1 @ X0 )
!= $true ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
~ ? [X0: $i > $o] :
( ( cQDP1 @ X0 )
= $true ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
~ ? [X0: $i > $o] : ( cQDP1 @ X0 ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ? [X2: $i > $o] : ( cQDP1 @ X2 ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
? [X2: $i > $o] : ( cQDP1 @ X2 ),
file('/export/starexec/sandbox2/tmp/tmp.Mb2Y8VMETo/DTF2THF_24359.p',cQDTHM1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SYO379^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% 0.00/0.10 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.13/0.31 % Computer : n002.cluster.edu
% 0.13/0.31 % Model : x86_64 x86_64
% 0.13/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.31 % Memory : 8042.1875MB
% 0.13/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.31 % CPULimit : 300
% 0.13/0.31 % WCLimit : 300
% 0.13/0.31 % DateTime : Tue Feb 24 14:29:18 EST 2026
% 0.13/0.31 % CPUTime :
% 0.13/0.31 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.41 ---- Original DTF file ---
% 0.18/0.41 thf(spec,logic,$$dhol).
% 0.18/0.41 %------------------------------------------------------------------------------
% 0.18/0.41 % File : SYO379^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% 0.18/0.41 % Domain : Syntactic
% 0.18/0.41 % Problem : TPS problem from QUANTDEPTH-THMS
% 0.18/0.41 % Version : Especial.
% 0.18/0.41 % English :
% 0.18/0.41
% 0.18/0.41 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.18/0.41 % Source : [Bro09]
% 0.18/0.41 % Names : tps_0590 [Bro09]
% 0.18/0.41
% 0.18/0.41 % Status : Theorem
% 0.18/0.41 % Rating : 0.00 v9.0.0, 0.10 v8.2.0, 0.31 v8.1.0, 0.27 v7.5.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.2.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.40 v5.2.0
% 0.18/0.41 % Syntax : Number of formulae : 6 ( 3 unt; 3 typ; 2 def)
% 0.18/0.41 % Number of atoms : 8 ( 4 equ; 0 cnn)
% 0.18/0.41 % Maximal formula atoms : 1 ( 2 avg)
% 0.18/0.41 % Number of connectives : 3 ( 0 ~; 0 |; 1 &; 2 @)
% 0.18/0.41 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.18/0.41 % Maximal formula depth : 3 ( 2 avg)
% 0.18/0.41 % Number of types : 2 ( 0 usr)
% 0.18/0.41 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.18/0.41 % Number of symbols : 4 ( 3 usr; 1 con; 0-2 aty)
% 0.18/0.41 % Number of variables : 4 ( 2 ^; 0 !; 2 ?; 4 :)
% 0.18/0.41 % SPC : TH0_THM_EQU_NAR
% 0.18/0.41
% 0.18/0.41 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.18/0.41 % project in the Department of Mathematical Sciences at Carnegie
% 0.18/0.41 % Mellon University. Distributed under the Creative Commons copyleft
% 0.18/0.41 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.18/0.41 % Bugfixes : v5.2.0 - Added missing type declarations.
% 0.18/0.41 %------------------------------------------------------------------------------
% 0.18/0.41 thf(c_type,type,
% 0.18/0.41 c: $i ).
% 0.18/0.41
% 0.18/0.41 thf(cQDP0_type,type,
% 0.18/0.41 cQDP0: $i > $o ).
% 0.18/0.41
% 0.18/0.41 thf(cQDP1_type,type,
% 0.18/0.41 cQDP1: ( $i > $o ) > $o ).
% 0.18/0.41
% 0.18/0.41 thf(cQDP0_def,definition,
% 0.18/0.41 ( cQDP0
% 0.18/0.41 = ( ^ [Xz: $i] : ( Xz = c ) ) ) ).
% 0.18/0.41
% 0.18/0.41 thf(cQDP1_def,definition,
% 0.18/0.41 ( cQDP1
% 0.18/0.41 = ( ^ [Xz: $i > $o] :
% 0.18/0.41 ( ( Xz = cQDP0 )
% 0.18/0.41 & ? [Xt: $i] : ( Xz @ Xt ) ) ) ) ).
% 0.18/0.41
% 0.18/0.41 thf(cQDTHM1,conjecture,
% 0.18/0.41 ? [Xs: $i > $o] : ( cQDP1 @ Xs ) ).
% 0.18/0.41
% 0.18/0.41 %------------------------------------------------------------------------------
% 0.18/0.41 ------------------------
% 1.50/1.35 ---- Embedded in THF ---
% 1.50/1.36 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.36 %%% Generated on Tue Feb 24 14:29:19 EST 2026
% 1.50/1.36 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.36 %%% Logic specification used:
% 1.50/1.36 %%% thf(spec, logic, $$dhol).
% 1.50/1.36
% 1.50/1.36 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.Mb2Y8VMETo/DTF2DTF24359.p
% See solution above
% 1.50/1.36 ------------------------
% 1.50/1.36 ---- Cleaned THF ---
% 1.50/1.37 thf(c_type,type,
% 1.50/1.37 c: $i ).
% 1.50/1.37
% 1.50/1.37 thf(cQDP0_type,type,
% 1.50/1.37 cQDP0: $i > $o ).
% 1.50/1.37
% 1.50/1.37 thf(cQDP1_type,type,
% 1.50/1.37 cQDP1: ( $i > $o ) > $o ).
% 1.50/1.37
% 1.50/1.37 thf(cQDP0_def,definition,
% 1.50/1.37 ( cQDP0
% 1.50/1.37 = ( ^ [Xz: $i] : ( Xz = c ) ) ) ).
% 1.50/1.37
% 1.50/1.37 thf(cQDP1_def,definition,
% 1.50/1.37 ( cQDP1
% 1.50/1.37 = ( ^ [Xz: $i > $o] :
% 1.50/1.37 ( ( Xz = cQDP0 )
% 1.50/1.37 & ? [Xt: $i] : ( Xz @ Xt ) ) ) ) ).
% 1.50/1.37
% 1.50/1.37 thf(cQDTHM1,conjecture,
% 1.50/1.37 ? [Xs: $i > $o] : ( cQDP1 @ Xs ) ).
% 1.50/1.37 ------------------------
% 1.50/1.39 % (24456)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_24359 for (3000ds/183Mi)
% 1.50/1.39 % (24462)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_24359 for (3000ds/18Mi)
% 1.50/1.39 % (24457)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_24359 for (3000ds/4Mi)
% 1.50/1.39 % (24460)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_24359 for (3000ds/2Mi)
% 1.50/1.39 % (24459)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_24359 for (3000ds/2Mi)
% 1.50/1.39 % (24461)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_24359 for (3000ds/275Mi)
% 1.50/1.39 % (24458)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_24359 for (3000ds/27Mi)
% 1.50/1.39 % (24460)Instruction limit reached!
% 1.50/1.39 % (24460)------------------------------
% 1.50/1.39 % (24460)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.39 % (24460)Termination reason: Unknown
% 1.50/1.39 % (24460)Termination phase: Saturation
% 1.50/1.39
% 1.50/1.39 % (24460)Memory used [KB]: 895
% 1.50/1.39 % (24460)Time elapsed: 0.003 s
% 1.50/1.39 % (24460)Instructions burned: 2 (million)
% 1.50/1.39 % (24460)------------------------------
% 1.50/1.39 % (24460)------------------------------
% 1.50/1.39 % (24461)Refutation not found, incomplete strategy
% 1.50/1.39 % (24461)------------------------------
% 1.50/1.39 % (24461)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.39 % (24461)Termination reason: Refutation not found, incomplete strategy
% 1.50/1.39
% 1.50/1.39
% 1.50/1.39 % (24461)Memory used [KB]: 5373
% 1.50/1.39 % (24461)Time elapsed: 0.002 s
% 1.50/1.39 % (24461)Instructions burned: 1 (million)
% 1.50/1.39 % (24461)------------------------------
% 1.50/1.39 % (24461)------------------------------
% 1.50/1.39 % (24456)First to succeed.
% 1.50/1.39 % (24457)Also succeeded, but the first one will report.
% 1.50/1.39 % (24456)Refutation found. Thanks to Tanya!
% 1.50/1.39 % SZS status Theorem for DTF2THF_24359
% 1.50/1.39 % SZS output start Proof for DTF2THF_24359
% 1.50/1.39 thf(func_def_1, type, cQDP0: $i > $o).
% 1.50/1.39 thf(func_def_2, type, cQDP1: ($i > $o) > $o).
% 1.50/1.39 thf(func_def_13, type, ph1: !>[X0: $tType]:(X0)).
% 1.50/1.39 thf(f23,plain,(
% 1.50/1.39 $false),
% 1.50/1.39 inference(equality_resolution,[status(thm)],[f22])).
% 1.50/1.39 thf(f22,plain,(
% 1.50/1.39 ( ! [X0 : $i] : ((c != X0)) )),
% 1.50/1.39 inference(equality_proxy_clausification,[status(thm)],[f21])).
% 1.50/1.39 thf(f21,plain,(
% 1.50/1.39 ( ! [X0 : $i] : (((c = X0) = $false)) )),
% 1.50/1.39 inference(equality_resolution,[status(thm)],[f20])).
% 1.50/1.39 thf(f20,plain,(
% 1.50/1.39 ( ! [X0 : $i > $o,X1 : $i] : (((= @ c) != X0) | ((X0 @ X1) = $false)) )),
% 1.50/1.39 inference(pi_clausification,[status(thm)],[f19])).
% 1.50/1.39 thf(f19,plain,(
% 1.50/1.39 ( ! [X0 : $i > $o] : (((= @ c) != X0) | ($false = (?? @ $i @ X0))) )),
% 1.50/1.39 inference(equality_proxy_clausification,[status(thm)],[f18])).
% 1.50/1.39 thf(f18,plain,(
% 1.50/1.39 ( ! [X0 : $i > $o] : ((((= @ c) = X0) = $false) | ($false = (?? @ $i @ X0))) )),
% 1.50/1.39 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.50/1.39 thf(f17,plain,(
% 1.50/1.39 ( ! [X0 : $i > $o] : (($true != (((= @ c) = X0) & (?? @ $i @ X0)))) )),
% 1.50/1.39 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.50/1.39 thf(f16,plain,(
% 1.50/1.39 ( ! [X0 : $i > $o] : ((((^[Y0 : $i > $o]: (((^[Y1 : $i]: (c = Y1)) = Y0) & (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) @ X0) != $true)) )),
% 1.50/1.39 inference(definition_unfolding,[status(thm)],[f14,f15])).
% 1.50/1.39 thf(f15,plain,(
% 1.50/1.39 (cQDP1 = (^[Y0 : $i > $o]: (((^[Y1 : $i]: (c = Y1)) = Y0) & (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
% 1.50/1.39 inference(definition_unfolding,[status(thm)],[f13,f12])).
% 1.50/1.39 thf(f12,plain,(
% 1.50/1.39 (cQDP0 = (^[Y0 : $i]: (c = Y0)))),
% 1.50/1.39 inference(cnf_transformation,[status(thm)],[f8])).
% 1.50/1.39 thf(f8,plain,(
% 1.50/1.39 (cQDP0 = (^[Y0 : $i]: (c = Y0)))),
% 1.50/1.39 inference(fool_elimination,[status(thm)],[f1])).
% 1.50/1.39 thf(f1,axiom,(
% 1.50/1.39 ((^[X0 : $i] : ((c = X0))) = cQDP0)),
% 1.50/1.39 file('/export/starexec/sandbox2/tmp/tmp.Mb2Y8VMETo/DTF2THF_24359.p',cQDP0_def)).
% 1.50/1.39 thf(f13,plain,(
% 1.50/1.39 (cQDP1 = (^[Y0 : $i > $o]: ((cQDP0 = Y0) & (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
% 1.50/1.39 inference(cnf_transformation,[status(thm)],[f10])).
% 1.50/1.39 thf(f10,plain,(
% 1.50/1.39 (cQDP1 = (^[Y0 : $i > $o]: ((cQDP0 = Y0) & (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
% 1.50/1.39 inference(fool_elimination,[status(thm)],[f9])).
% 1.50/1.39 thf(f9,plain,(
% 1.50/1.39 ((^[X0 : $i > $o] : (? [X1 : $i] : (X0 @ X1) & (cQDP0 = X0))) = cQDP1)),
% 1.50/1.39 inference(rectify,[status(thm)],[f2])).
% 1.50/1.39 thf(f2,axiom,(
% 1.50/1.39 ((^[X0 : $i > $o] : (? [X1 : $i] : (X0 @ X1) & (cQDP0 = X0))) = cQDP1)),
% 1.50/1.39 file('/export/starexec/sandbox2/tmp/tmp.Mb2Y8VMETo/DTF2THF_24359.p',cQDP1_def)).
% 1.50/1.39 thf(f14,plain,(
% 1.50/1.39 ( ! [X0 : $i > $o] : (((cQDP1 @ X0) != $true)) )),
% 1.50/1.39 inference(cnf_transformation,[status(thm)],[f11])).
% 1.50/1.39 thf(f11,plain,(
% 1.50/1.39 ! [X0 : $i > $o] : ((cQDP1 @ X0) != $true)),
% 1.50/1.39 inference(ennf_transformation,[status(thm)],[f7])).
% 1.50/1.39 thf(f7,plain,(
% 1.50/1.39 ~? [X0 : $i > $o] : ((cQDP1 @ X0) = $true)),
% 1.50/1.39 inference(fool_elimination,[status(thm)],[f6])).
% 1.50/1.39 thf(f6,plain,(
% 1.50/1.39 ~? [X0 : $i > $o] : (cQDP1 @ X0)),
% 1.50/1.39 inference(rectify,[status(thm)],[f4])).
% 1.50/1.39 thf(f4,negated_conjecture,(
% 1.50/1.39 ~? [X2 : $i > $o] : (cQDP1 @ X2)),
% 1.50/1.39 inference(negated_conjecture,[status(cth)],[f3])).
% 1.50/1.39 thf(f3,conjecture,(
% 1.50/1.39 ? [X2 : $i > $o] : (cQDP1 @ X2)),
% 1.50/1.39 file('/export/starexec/sandbox2/tmp/tmp.Mb2Y8VMETo/DTF2THF_24359.p',cQDTHM1)).
% 1.50/1.39 % SZS output end Proof for DTF2THF_24359
% 1.50/1.39 % (24456)------------------------------
% 1.50/1.39 % (24456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.39 % (24456)Termination reason: Refutation
% 1.50/1.39
% 1.50/1.39 % (24456)Memory used [KB]: 5500
% 1.50/1.39 % (24456)Time elapsed: 0.004 s
% 1.50/1.39 % (24456)Instructions burned: 1 (million)
% 1.50/1.39 % (24456)------------------------------
% 1.50/1.39 % (24456)------------------------------
% 1.50/1.39 % (24455)Success in time 0.017 s
%------------------------------------------------------------------------------