%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO281^5 : 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 : n024.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 09:53:50 AM UTC 2026
% Result : Theorem 1.01s 0.90s
% Output : Refutation 1.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 42 ( 17 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 52 ( 12 ~; 0 |; 6 &; 28 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 26 ( 2 ^; 14 !; 10 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_3,type,
sK0: $i > $o ).
thf(func_def_4,type,
sK1: ( $i > $o ) > $i ).
thf(func_def_7,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f16,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f15]) ).
thf(f15,plain,
$true != $true,
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
( $true
!= ( ^ [Y0: $i] : $true
@ ( sK1
@ ^ [Y0: $i] : $true ) ) ),
inference(primitive_instantiation,[status(thm)],[f10]) ).
thf(f10,plain,
! [X1: $i > $o] :
( ( X1 @ ( sK1 @ X1 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X1: $i > $o] :
( ( ( sK0 @ ( sK1 @ X1 ) )
= $true )
& ( ( X1 @ ( sK1 @ X1 ) )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f8,f7]) ).
thf(f7,plain,
( ? [X0: $i > $o] :
! [X1: $i > $o] :
? [X2: $i] :
( ( ( X0 @ X2 )
= $true )
& ( ( X1 @ X2 )
!= $true ) )
=> ! [X1: $i > $o] :
? [X2: $i] :
( ( ( sK0 @ X2 )
= $true )
& ( ( X1 @ X2 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
! [X1: $i > $o] :
( ? [X2: $i] :
( ( ( sK0 @ X2 )
= $true )
& ( ( X1 @ X2 )
!= $true ) )
=> ( ( ( sK0 @ ( sK1 @ X1 ) )
= $true )
& ( ( X1 @ ( sK1 @ X1 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
? [X0: $i > $o] :
! [X1: $i > $o] :
? [X2: $i] :
( ( ( X0 @ X2 )
= $true )
& ( ( X1 @ X2 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: $i > $o] :
? [X1: $i > $o] :
! [X2: $i] :
( ( ( X0 @ X2 )
= $true )
=> ( ( X1 @ X2 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: $i > $o] :
? [X1: $i > $o] :
! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: $i > $o] :
? [X1: $i > $o] :
! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: $i > $o] :
? [X1: $i > $o] :
! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.m5H1qwe6Dw/DTF2THF_7602.p',cTRIV3) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SYO281^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.25 % Computer : n024.cluster.edu
% 0.08/0.25 % Model : x86_64 x86_64
% 0.08/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.25 % Memory : 8042.1875MB
% 0.08/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.25 % CPULimit : 300
% 0.08/0.25 % WCLimit : 300
% 0.08/0.25 % DateTime : Tue Feb 24 09:27:10 EST 2026
% 0.08/0.25 % CPUTime :
% 0.08/0.25 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.31 ---- Original DTF file ---
% 0.08/0.31 thf(spec,logic,$$dhol).
% 0.08/0.31 %------------------------------------------------------------------------------
% 0.08/0.31 % File : SYO281^5 : TPTP v9.2.1. Released v4.0.0.
% 0.08/0.31 % Domain : Syntactic
% 0.08/0.31 % Problem : TPS problem from BASIC-HO-THMS
% 0.08/0.31 % Version : Especial.
% 0.08/0.31 % English :
% 0.08/0.31
% 0.08/0.31 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.08/0.31 % Source : [Bro09]
% 0.08/0.31 % Names : tps_0658 [Bro09]
% 0.08/0.31
% 0.08/0.31 % Status : Theorem
% 0.08/0.31 % Rating : 0.00 v8.1.0, 0.08 v7.4.0, 0.00 v6.2.0, 0.17 v6.1.0, 0.00 v4.0.0
% 0.08/0.31 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.08/0.31 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.08/0.31 % Maximal formula atoms : 0 ( 0 avg)
% 0.08/0.31 % Number of connectives : 3 ( 0 ~; 0 |; 0 &; 2 @)
% 0.08/0.31 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.08/0.31 % Maximal formula depth : 6 ( 6 avg)
% 0.08/0.31 % Number of types : 2 ( 0 usr)
% 0.08/0.31 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.08/0.31 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.08/0.31 % Number of variables : 3 ( 0 ^; 2 !; 1 ?; 3 :)
% 0.08/0.31 % SPC : TH0_THM_NEQ_NAR
% 0.08/0.31
% 0.08/0.31 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.08/0.31 % project in the Department of Mathematical Sciences at Carnegie
% 0.08/0.31 % Mellon University. Distributed under the Creative Commons copyleft
% 0.08/0.31 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.08/0.31 %------------------------------------------------------------------------------
% 0.08/0.31 thf(cTRIV3,conjecture,
% 0.08/0.31 ! [Xp: $i > $o] :
% 0.08/0.31 ? [Xq: $i > $o] :
% 0.08/0.31 ! [Xx: $i] :
% 0.08/0.31 ( ( Xp @ Xx )
% 0.08/0.31 => ( Xq @ Xx ) ) ).
% 0.08/0.31
% 0.08/0.31 %------------------------------------------------------------------------------
% 0.08/0.31 ------------------------
% 0.84/0.88 ---- Embedded in THF ---
% 0.84/0.88 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.84/0.88 %%% Generated on Tue Feb 24 09:27:11 EST 2026
% 0.84/0.88 %%% using '$$dhol' embedding, version 1.3.0.
% 0.84/0.88 %%% Logic specification used:
% 0.84/0.88 %%% thf(spec, logic, $$dhol).
% 0.84/0.88
% 0.84/0.88 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.m5H1qwe6Dw/DTF2DTF7602.p
% See solution above
% 0.84/0.88 ------------------------
% 0.84/0.89 ---- Cleaned THF ---
% 0.84/0.89 thf(cTRIV3,conjecture,
% 0.84/0.89 ! [Xp: $i > $o] :
% 0.84/0.89 ? [Xq: $i > $o] :
% 0.84/0.89 ! [Xx: $i] :
% 0.84/0.89 ( ( Xp @ Xx )
% 0.84/0.89 => ( Xq @ Xx ) ) ).
% 0.84/0.89 ------------------------
% 1.01/0.90 % (7791)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7602 for (3000ds/183Mi)
% 1.01/0.90 % (7793)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_7602 for (3000ds/27Mi)
% 1.01/0.90 % (7794)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7602 for (3000ds/2Mi)
% 1.01/0.90 % (7794)First to succeed.
% 1.01/0.90 % (7792)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_7602 for (3000ds/4Mi)
% 1.01/0.90 % (7791)Also succeeded, but the first one will report.
% 1.01/0.90 % (7795)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_7602 for (3000ds/2Mi)
% 1.01/0.90 % (7793)Also succeeded, but the first one will report.
% 1.01/0.90 % (7794)Refutation found. Thanks to Tanya!
% 1.01/0.90 % SZS status Theorem for DTF2THF_7602
% 1.01/0.90 % SZS output start Proof for DTF2THF_7602
% 1.01/0.90 thf(func_def_3, type, sK0: $i > $o).
% 1.01/0.90 thf(func_def_4, type, sK1: ($i > $o) > $i).
% 1.01/0.90 thf(func_def_7, type, ph3: !>[X0: $tType]:(X0)).
% 1.01/0.90 thf(f16,plain,(
% 1.01/0.90 $false),
% 1.01/0.90 inference(trivial_inequality_removal,[status(thm)],[f15])).
% 1.01/0.90 thf(f15,plain,(
% 1.01/0.90 ($true != $true)),
% 1.01/0.90 inference(beta_eta_normalization,[status(thm)],[f12])).
% 1.01/0.90 thf(f12,plain,(
% 1.01/0.90 ($true != ((^[Y0 : $i]: ($true)) @ (sK1 @ (^[Y0 : $i]: ($true)))))),
% 1.01/0.90 inference(primitive_instantiation,[status(thm)],[f10])).
% 1.01/0.90 thf(f10,plain,(
% 1.01/0.90 ( ! [X1 : $i > $o] : (((X1 @ (sK1 @ X1)) != $true)) )),
% 1.01/0.90 inference(cnf_transformation,[status(thm)],[f9])).
% 1.01/0.90 thf(f9,plain,(
% 1.01/0.90 ! [X1 : $i > $o] : (((sK0 @ (sK1 @ X1)) = $true) & ((X1 @ (sK1 @ X1)) != $true))),
% 1.01/0.90 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f8,f7])).
% 1.01/0.90 thf(f7,plain,(
% 1.01/0.90 ? [X0 : $i > $o] : ! [X1 : $i > $o] : ? [X2 : $i] : (((X0 @ X2) = $true) & ((X1 @ X2) != $true)) => ! [X1 : $i > $o] : ? [X2 : $i] : (((sK0 @ X2) = $true) & ((X1 @ X2) != $true))),
% 1.01/0.90 introduced(definition,[],[choice_axiom])).
% 1.01/0.90 thf(f8,plain,(
% 1.01/0.90 ! [X1 : $i > $o] : (? [X2 : $i] : (((sK0 @ X2) = $true) & ((X1 @ X2) != $true)) => (((sK0 @ (sK1 @ X1)) = $true) & ((X1 @ (sK1 @ X1)) != $true)))),
% 1.01/0.90 introduced(definition,[],[choice_axiom])).
% 1.01/0.90 thf(f6,plain,(
% 1.01/0.90 ? [X0 : $i > $o] : ! [X1 : $i > $o] : ? [X2 : $i] : (((X0 @ X2) = $true) & ((X1 @ X2) != $true))),
% 1.01/0.90 inference(ennf_transformation,[status(thm)],[f5])).
% 1.01/0.90 thf(f5,plain,(
% 1.01/0.90 ~! [X0 : $i > $o] : ? [X1 : $i > $o] : ! [X2 : $i] : (((X0 @ X2) = $true) => ((X1 @ X2) = $true))),
% 1.01/0.90 inference(fool_elimination,[status(thm)],[f4])).
% 1.01/0.90 thf(f4,plain,(
% 1.01/0.90 ~! [X0 : $i > $o] : ? [X1 : $i > $o] : ! [X2 : $i] : ((X0 @ X2) => (X1 @ X2))),
% 1.01/0.90 inference(rectify,[status(thm)],[f2])).
% 1.01/0.90 thf(f2,negated_conjecture,(
% 1.01/0.90 ~! [X0 : $i > $o] : ? [X1 : $i > $o] : ! [X2 : $i] : ((X0 @ X2) => (X1 @ X2))),
% 1.01/0.90 inference(negated_conjecture,[status(cth)],[f1])).
% 1.01/0.90 thf(f1,conjecture,(
% 1.01/0.90 ! [X0 : $i > $o] : ? [X1 : $i > $o] : ! [X2 : $i] : ((X0 @ X2) => (X1 @ X2))),
% 1.01/0.90 file('/export/starexec/sandbox/tmp/tmp.m5H1qwe6Dw/DTF2THF_7602.p',cTRIV3)).
% 1.01/0.90 % SZS output end Proof for DTF2THF_7602
% 1.01/0.90 % (7794)------------------------------
% 1.01/0.90 % (7794)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.01/0.90 % (7794)Termination reason: Refutation
% 1.01/0.90
% 1.01/0.90 % (7794)Memory used [KB]: 5500
% 1.01/0.90 % (7794)Time elapsed: 0.002 s
% 1.01/0.90 % (7794)------------------------------
% 1.01/0.90 % (7794)------------------------------
% 1.01/0.90 % (7790)Success in time 0.006 s
%------------------------------------------------------------------------------