%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO305^5 : TPTP v9.2.1. Released v4.0.0.
% 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 09:53:54 AM UTC 2026
% Result : Theorem 1.54s 1.44s
% Output : Refutation 1.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 143 ( 42 equ; 0 cnn)
% Maximal formula atoms : 8 ( 8 avg)
% Number of connectives : 126 ( 24 ~; 10 |; 12 &; 58 @)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 0 ^; 24 !; 6 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cB: $i > $o ).
thf(func_def_1,type,
cA: $i > $o ).
thf(func_def_5,type,
sK0: $i > $o ).
thf(f18,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f17,f10]) ).
thf(f10,plain,
( $true
= ( sK0 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X0: $i] :
( ( ( cA @ X0 )
!= $true )
| ( ( cB @ X0 )
= $true ) )
& ! [X2: $i] :
( ( ( cA @ X2 )
= $true )
| ( $true
!= ( sK0 @ X2 ) ) )
& ( ( cB @ sK1 )
!= $true )
& ( $true
= ( sK0 @ sK1 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f8,f7]) ).
thf(f7,plain,
( ? [X1: $i > $o] :
( ! [X2: $i] :
( ( ( cA @ X2 )
= $true )
| ( ( X1 @ X2 )
!= $true ) )
& ? [X3: $i] :
( ( ( cB @ X3 )
!= $true )
& ( ( X1 @ X3 )
= $true ) ) )
=> ( ! [X2: $i] :
( ( ( cA @ X2 )
= $true )
| ( $true
!= ( sK0 @ X2 ) ) )
& ? [X3: $i] :
( ( ( cB @ X3 )
!= $true )
& ( $true
= ( sK0 @ X3 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ? [X3: $i] :
( ( ( cB @ X3 )
!= $true )
& ( $true
= ( sK0 @ X3 ) ) )
=> ( ( ( cB @ sK1 )
!= $true )
& ( $true
= ( sK0 @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
( ! [X0: $i] :
( ( ( cA @ X0 )
!= $true )
| ( ( cB @ X0 )
= $true ) )
& ? [X1: $i > $o] :
( ! [X2: $i] :
( ( ( cA @ X2 )
= $true )
| ( ( X1 @ X2 )
!= $true ) )
& ? [X3: $i] :
( ( ( cB @ X3 )
!= $true )
& ( ( X1 @ X3 )
= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ! [X0: $i] :
( ( ( cA @ X0 )
= $true )
=> ( ( cB @ X0 )
= $true ) )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( ( X1 @ X2 )
= $true )
=> ( ( cA @ X2 )
= $true ) )
=> ! [X3: $i] :
( ( ( X1 @ X3 )
= $true )
=> ( ( cB @ X3 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ( cA @ X2 ) )
=> ! [X3: $i] :
( ( X1 @ X3 )
=> ( cB @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) )
=> ! [X0: $i > $o] :
( ! [X1: $i] :
( ( X0 @ X1 )
=> ( cA @ X1 ) )
=> ! [X1: $i] :
( ( X0 @ X1 )
=> ( cB @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) )
=> ! [X0: $i > $o] :
( ! [X1: $i] :
( ( X0 @ X1 )
=> ( cA @ X1 ) )
=> ! [X1: $i] :
( ( X0 @ X1 )
=> ( cB @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ssbx345PGJ/DTF2THF_13194.p',cSET79_pme) ).
thf(f17,plain,
( $true
!= ( sK0 @ sK1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f16]) ).
thf(f16,plain,
( ( $true
!= ( sK0 @ sK1 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f15,f12]) ).
thf(f12,plain,
! [X2: $i] :
( ( ( cA @ X2 )
= $true )
| ( $true
!= ( sK0 @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f15,plain,
( ( cA @ sK1 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f14]) ).
thf(f14,plain,
( ( $true != $true )
| ( ( cA @ sK1 )
!= $true ) ),
inference(superposition,[status(thm)],[f11,f13]) ).
thf(f13,plain,
! [X0: $i] :
( ( ( cB @ X0 )
= $true )
| ( ( cA @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f11,plain,
( ( cB @ sK1 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYO305^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n016.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 14:28:21 EST 2026
% 0.11/0.30 % CPUTime :
% 0.11/0.30 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/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 : SYO305^5 : TPTP v9.2.1. Released v4.0.0.
% 0.16/0.39 % Domain : Syntactic
% 0.16/0.39 % Problem : TPS problem from BASIC-HO-THMS
% 0.16/0.39 % Version : Especial.
% 0.16/0.39 % English :
% 0.16/0.39
% 0.16/0.39 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.39 % Source : [Bro09]
% 0.16/0.39 % Names : tps_0821 [Bro09]
% 0.16/0.39
% 0.16/0.39 % Status : Theorem
% 0.16/0.39 % Rating : 0.00 v6.2.0, 0.17 v6.1.0, 0.00 v4.0.0
% 0.16/0.39 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.16/0.39 % Number of atoms : 4 ( 0 equ; 0 cnn)
% 0.16/0.39 % Maximal formula atoms : 4 ( 4 avg)
% 0.16/0.39 % Number of connectives : 11 ( 0 ~; 0 |; 0 &; 6 @)
% 0.16/0.39 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.16/0.39 % Maximal formula depth : 7 ( 7 avg)
% 0.16/0.39 % Number of types : 2 ( 0 usr)
% 0.16/0.39 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.16/0.39 % Number of symbols : 2 ( 2 usr; 0 con; 1-1 aty)
% 0.16/0.39 % Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% 0.16/0.39 % SPC : TH0_THM_NEQ_NAR
% 0.16/0.39
% 0.16/0.39 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.16/0.39 % project in the Department of Mathematical Sciences at Carnegie
% 0.16/0.39 % Mellon University. Distributed under the Creative Commons copyleft
% 0.16/0.39 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 thf(cB,type,
% 0.16/0.39 cB: $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(cA,type,
% 0.16/0.39 cA: $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(cSET79_pme,conjecture,
% 0.16/0.39 ( ! [Z1: $i] :
% 0.16/0.39 ( ( cA @ Z1 )
% 0.16/0.39 => ( cB @ Z1 ) )
% 0.16/0.39 => ! [Z1: $i > $o] :
% 0.16/0.39 ( ! [Z3: $i] :
% 0.16/0.39 ( ( Z1 @ Z3 )
% 0.16/0.39 => ( cA @ Z3 ) )
% 0.16/0.39 => ! [Z3: $i] :
% 0.16/0.39 ( ( Z1 @ Z3 )
% 0.16/0.39 => ( cB @ Z3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 ------------------------
% 1.37/1.27 ---- Embedded in THF ---
% 1.37/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.37/1.28 %%% Generated on Tue Feb 24 14:28:21 EST 2026
% 1.37/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.37/1.28 %%% Logic specification used:
% 1.37/1.28 %%% thf(spec, logic, $$dhol).
% 1.37/1.28
% 1.37/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.ssbx345PGJ/DTF2DTF13194.p
% See solution above
% 1.37/1.28 ------------------------
% 1.37/1.28 ---- Cleaned THF ---
% 1.37/1.29 thf(cB,type,
% 1.37/1.29 cB: $i > $o ).
% 1.37/1.29
% 1.37/1.29 thf(cA,type,
% 1.37/1.29 cA: $i > $o ).
% 1.37/1.29
% 1.37/1.29 thf(cSET79_pme,conjecture,
% 1.37/1.29 ( ! [Z1: $i] :
% 1.37/1.29 ( ( cA @ Z1 )
% 1.37/1.29 => ( cB @ Z1 ) )
% 1.37/1.29 => ! [Z1: $i > $o] :
% 1.37/1.29 ( ! [Z3: $i] :
% 1.37/1.29 ( ( Z1 @ Z3 )
% 1.37/1.29 => ( cA @ Z3 ) )
% 1.37/1.29 => ! [Z3: $i] :
% 1.37/1.29 ( ( Z1 @ Z3 )
% 1.37/1.29 => ( cB @ Z3 ) ) ) ) ).
% 1.37/1.29 ------------------------
% 1.54/1.31 ipcrm: permission denied for id (294916)
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% 1.54/1.43 % (13431)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_13194 for (2998ds/18Mi)
% 1.54/1.43 % (13428)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_13194 for (2998ds/2Mi)
% 1.54/1.43 % (13430)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_13194 for (2998ds/275Mi)
% 1.54/1.43 % (13427)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_13194 for (2998ds/27Mi)
% 1.54/1.43 % (13426)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_13194 for (2998ds/4Mi)
% 1.54/1.43 % (13429)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_13194 for (2998ds/2Mi)
% 1.54/1.43 % (13425)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_13194 for (2998ds/183Mi)
% 1.54/1.43 % (13429)Instruction limit reached!
% 1.54/1.43 % (13429)------------------------------
% 1.54/1.43 % (13429)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.43 % (13429)Termination reason: Unknown
% 1.54/1.43 % (13429)Termination phase: Saturation
% 1.54/1.43
% 1.54/1.43 % (13429)Memory used [KB]: 895
% 1.54/1.43 % (13429)Time elapsed: 0.003 s
% 1.54/1.43 % (13429)Instructions burned: 2 (million)
% 1.54/1.43 % (13429)------------------------------
% 1.54/1.43 % (13429)------------------------------
% 1.54/1.43 % (13430)First to succeed.
% 1.54/1.44 % (13425)Also succeeded, but the first one will report.
% 1.54/1.44 % (13426)Also succeeded, but the first one will report.
% 1.54/1.44 % (13430)Refutation found. Thanks to Tanya!
% 1.54/1.44 % SZS status Theorem for DTF2THF_13194
% 1.54/1.44 % SZS output start Proof for DTF2THF_13194
% 1.54/1.44 thf(func_def_0, type, cB: $i > $o).
% 1.54/1.44 thf(func_def_1, type, cA: $i > $o).
% 1.54/1.44 thf(func_def_5, type, sK0: $i > $o).
% 1.54/1.44 thf(f18,plain,(
% 1.54/1.44 $false),
% 1.54/1.44 inference(subsumption_resolution,[status(thm)],[f17,f10])).
% 1.54/1.44 thf(f10,plain,(
% 1.54/1.44 ($true = (sK0 @ sK1))),
% 1.54/1.44 inference(cnf_transformation,[status(thm)],[f9])).
% 1.54/1.44 thf(f9,plain,(
% 1.54/1.44 ! [X0 : $i] : (((cA @ X0) != $true) | ((cB @ X0) = $true)) & (! [X2 : $i] : (((cA @ X2) = $true) | ($true != (sK0 @ X2))) & (((cB @ sK1) != $true) & ($true = (sK0 @ sK1))))),
% 1.54/1.44 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f8,f7])).
% 1.54/1.44 thf(f7,plain,(
% 1.54/1.44 ? [X1 : $i > $o] : (! [X2 : $i] : (((cA @ X2) = $true) | ((X1 @ X2) != $true)) & ? [X3 : $i] : (((cB @ X3) != $true) & ((X1 @ X3) = $true))) => (! [X2 : $i] : (((cA @ X2) = $true) | ($true != (sK0 @ X2))) & ? [X3 : $i] : (((cB @ X3) != $true) & ($true = (sK0 @ X3))))),
% 1.54/1.44 introduced(definition,[],[choice_axiom])).
% 1.54/1.44 thf(f8,plain,(
% 1.54/1.44 ? [X3 : $i] : (((cB @ X3) != $true) & ($true = (sK0 @ X3))) => (((cB @ sK1) != $true) & ($true = (sK0 @ sK1)))),
% 1.54/1.44 introduced(definition,[],[choice_axiom])).
% 1.54/1.44 thf(f6,plain,(
% 1.54/1.44 ! [X0 : $i] : (((cA @ X0) != $true) | ((cB @ X0) = $true)) & ? [X1 : $i > $o] : (! [X2 : $i] : (((cA @ X2) = $true) | ((X1 @ X2) != $true)) & ? [X3 : $i] : (((cB @ X3) != $true) & ((X1 @ X3) = $true)))),
% 1.54/1.44 inference(ennf_transformation,[status(thm)],[f5])).
% 1.54/1.44 thf(f5,plain,(
% 1.54/1.44 ~(! [X0 : $i] : (((cA @ X0) = $true) => ((cB @ X0) = $true)) => ! [X1 : $i > $o] : (! [X2 : $i] : (((X1 @ X2) = $true) => ((cA @ X2) = $true)) => ! [X3 : $i] : (((X1 @ X3) = $true) => ((cB @ X3) = $true))))),
% 1.54/1.44 inference(fool_elimination,[status(thm)],[f4])).
% 1.54/1.44 thf(f4,plain,(
% 1.54/1.44 ~(! [X0 : $i] : ((cA @ X0) => (cB @ X0)) => ! [X1 : $i > $o] : (! [X2 : $i] : ((X1 @ X2) => (cA @ X2)) => ! [X3 : $i] : ((X1 @ X3) => (cB @ X3))))),
% 1.54/1.44 inference(rectify,[status(thm)],[f2])).
% 1.54/1.44 thf(f2,negated_conjecture,(
% 1.54/1.44 ~(! [X0 : $i] : ((cA @ X0) => (cB @ X0)) => ! [X0 : $i > $o] : (! [X1 : $i] : ((X0 @ X1) => (cA @ X1)) => ! [X1 : $i] : ((X0 @ X1) => (cB @ X1))))),
% 1.54/1.44 inference(negated_conjecture,[status(cth)],[f1])).
% 1.54/1.44 thf(f1,conjecture,(
% 1.54/1.44 ! [X0 : $i] : ((cA @ X0) => (cB @ X0)) => ! [X0 : $i > $o] : (! [X1 : $i] : ((X0 @ X1) => (cA @ X1)) => ! [X1 : $i] : ((X0 @ X1) => (cB @ X1)))),
% 1.54/1.44 file('/export/starexec/sandbox/tmp/tmp.ssbx345PGJ/DTF2THF_13194.p',cSET79_pme)).
% 1.54/1.44 thf(f17,plain,(
% 1.54/1.44 ($true != (sK0 @ sK1))),
% 1.54/1.44 inference(trivial_inequality_removal,[status(thm)],[f16])).
% 1.54/1.44 thf(f16,plain,(
% 1.54/1.44 ($true != (sK0 @ sK1)) | ($true != $true)),
% 1.54/1.44 inference(superposition,[status(thm)],[f15,f12])).
% 1.54/1.44 thf(f12,plain,(
% 1.54/1.44 ( ! [X2 : $i] : (((cA @ X2) = $true) | ($true != (sK0 @ X2))) )),
% 1.54/1.44 inference(cnf_transformation,[status(thm)],[f9])).
% 1.54/1.44 thf(f15,plain,(
% 1.54/1.44 ((cA @ sK1) != $true)),
% 1.54/1.44 inference(trivial_inequality_removal,[status(thm)],[f14])).
% 1.54/1.44 thf(f14,plain,(
% 1.54/1.44 ($true != $true) | ((cA @ sK1) != $true)),
% 1.54/1.44 inference(superposition,[status(thm)],[f11,f13])).
% 1.54/1.44 thf(f13,plain,(
% 1.54/1.44 ( ! [X0 : $i] : (((cB @ X0) = $true) | ((cA @ X0) != $true)) )),
% 1.54/1.44 inference(cnf_transformation,[status(thm)],[f9])).
% 1.54/1.44 thf(f11,plain,(
% 1.54/1.44 ((cB @ sK1) != $true)),
% 1.54/1.44 inference(cnf_transformation,[status(thm)],[f9])).
% 1.54/1.44 % SZS output end Proof for DTF2THF_13194
% 1.54/1.44 % (13430)------------------------------
% 1.54/1.44 % (13430)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.44 % (13430)Termination reason: Refutation
% 1.54/1.44
% 1.54/1.44 % (13430)Memory used [KB]: 5500
% 1.54/1.44 % (13430)Time elapsed: 0.004 s
% 1.54/1.44 % (13430)Instructions burned: 1 (million)
% 1.54/1.44 % (13430)------------------------------
% 1.54/1.44 % (13430)------------------------------
% 1.54/1.44 % (13290)Success in time 0.147 s
%------------------------------------------------------------------------------