%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO270^5 : 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 : n020.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 09:53:49 AM UTC 2026
% Result : Theorem 1.51s 1.29s
% Output : Refutation 1.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 11 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 70 ( 20 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 132 ( 9 ~; 0 |; 14 &; 104 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 37 ( 0 ^; 26 !; 11 ?; 37 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
h: $i > $i ).
thf(func_def_1,type,
g: $i > $i ).
thf(func_def_2,type,
cP: $i > $i > $o ).
thf(func_def_6,type,
sK0: ( $i > $i ) > $i > $i ).
thf(f13,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f10,f12]) ).
thf(f12,plain,
! [X3: $i,X0: $i,X1: $i > $i] :
( ( cP @ X3 @ ( X1 @ X0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $i,X1: $i > $i] :
( ! [X3: $i] :
( ( cP @ X3 @ ( X1 @ X0 ) )
= $true )
& ( ( cP @ X0 @ ( sK0 @ X1 @ X0 ) )
= $true )
& ( ( cP @ ( sK0 @ X1 @ X0 ) @ ( g @ ( h @ ( sK0 @ X1 @ X0 ) ) ) )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8]) ).
thf(f8,plain,
! [X0: $i,X1: $i > $i] :
( ? [X2: $i] :
( ! [X3: $i] :
( ( cP @ X3 @ ( X1 @ X0 ) )
= $true )
& ( ( cP @ X0 @ X2 )
= $true )
& ( ( cP @ X2 @ ( g @ ( h @ X2 ) ) )
!= $true ) )
=> ( ! [X3: $i] :
( ( cP @ X3 @ ( X1 @ X0 ) )
= $true )
& ( ( cP @ X0 @ ( sK0 @ X1 @ X0 ) )
= $true )
& ( ( cP @ ( sK0 @ X1 @ X0 ) @ ( g @ ( h @ ( sK0 @ X1 @ X0 ) ) ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
! [X0: $i,X1: $i > $i] :
? [X2: $i] :
( ! [X3: $i] :
( ( cP @ X3 @ ( X1 @ X0 ) )
= $true )
& ( ( cP @ X0 @ X2 )
= $true )
& ( ( cP @ X2 @ ( g @ ( h @ X2 ) ) )
!= $true ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
! [X1: $i > $i,X0: $i] :
? [X2: $i] :
( ( ( cP @ X2 @ ( g @ ( h @ X2 ) ) )
!= $true )
& ! [X3: $i] :
( ( cP @ X3 @ ( X1 @ X0 ) )
= $true )
& ( ( cP @ X0 @ X2 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ? [X1: $i > $i,X0: $i] :
! [X2: $i] :
( ( ! [X3: $i] :
( ( cP @ X3 @ ( X1 @ X0 ) )
= $true )
& ( ( cP @ X0 @ X2 )
= $true ) )
=> ( ( cP @ X2 @ ( g @ ( h @ X2 ) ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ? [X0: $i,X1: $i > $i] :
! [X2: $i] :
( ( ! [X3: $i] : ( cP @ X3 @ ( X1 @ X0 ) )
& ( cP @ X0 @ X2 ) )
=> ( cP @ X2 @ ( g @ ( h @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X0: $i,X1: $i > $i] :
! [X2: $i] :
( ( ! [X3: $i] : ( cP @ X3 @ ( X1 @ X0 ) )
& ( cP @ X0 @ X2 ) )
=> ( cP @ X2 @ ( g @ ( h @ X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X0: $i,X1: $i > $i] :
! [X2: $i] :
( ( ! [X3: $i] : ( cP @ X3 @ ( X1 @ X0 ) )
& ( cP @ X0 @ X2 ) )
=> ( cP @ X2 @ ( g @ ( h @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.VNGgzzedGK/DTF2THF_3410.p',cTHM85) ).
thf(f10,plain,
! [X0: $i,X1: $i > $i] :
( ( cP @ ( sK0 @ X1 @ X0 ) @ ( g @ ( h @ ( sK0 @ X1 @ X0 ) ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO270^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.33 % Computer : n020.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue Feb 24 14:27:27 EST 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.45 ---- Original DTF file ---
% 0.19/0.45 thf(spec,logic,$$dhol).
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 % File : SYO270^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.45 % Domain : Syntactic
% 0.19/0.45 % Problem : TPS problem THM85
% 0.19/0.45 % Version : Especial.
% 0.19/0.45 % English :
% 0.19/0.45
% 0.19/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.45 % Source : [Bro09]
% 0.19/0.45 % Names : tps_0283 [Bro09]
% 0.19/0.45 % : THM85 [TPS]
% 0.19/0.45
% 0.19/0.45 % Status : Theorem
% 0.19/0.45 % Rating : 0.08 v9.1.0, 0.12 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.17 v7.4.0, 0.11 v7.3.0, 0.10 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.2.0, 0.33 v6.1.0, 0.17 v6.0.0, 0.00 v4.0.0
% 0.19/0.45 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.19/0.45 % Number of atoms : 3 ( 0 equ; 0 cnn)
% 0.19/0.45 % Maximal formula atoms : 3 ( 3 avg)
% 0.19/0.45 % Number of connectives : 11 ( 0 ~; 0 |; 1 &; 9 @)
% 0.19/0.45 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.19/0.45 % Maximal formula depth : 9 ( 9 avg)
% 0.19/0.45 % Number of types : 2 ( 0 usr)
% 0.19/0.45 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.19/0.45 % Number of symbols : 3 ( 3 usr; 0 con; 1-2 aty)
% 0.19/0.45 % Number of variables : 4 ( 0 ^; 2 !; 2 ?; 4 :)
% 0.19/0.45 % SPC : TH0_THM_NEQ_NAR
% 0.19/0.45
% 0.19/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 thf(h,type,
% 0.19/0.45 h: $i > $i ).
% 0.19/0.45
% 0.19/0.45 thf(g,type,
% 0.19/0.45 g: $i > $i ).
% 0.19/0.45
% 0.19/0.45 thf(cP,type,
% 0.19/0.45 cP: $i > $i > $o ).
% 0.19/0.45
% 0.19/0.45 thf(cTHM85,conjecture,
% 0.19/0.45 ? [Xx: $i,Xf: $i > $i] :
% 0.19/0.45 ! [Xy: $i] :
% 0.19/0.45 ( ( ! [Xz: $i] : ( cP @ Xz @ ( Xf @ Xx ) )
% 0.19/0.45 & ( cP @ Xx @ Xy ) )
% 0.19/0.45 => ( cP @ Xy @ ( g @ ( h @ Xy ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 ------------------------
% 1.51/1.26 ---- Embedded in THF ---
% 1.51/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.51/1.27 %%% Generated on Tue Feb 24 14:27:28 EST 2026
% 1.51/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.51/1.27 %%% Logic specification used:
% 1.51/1.27 %%% thf(spec, logic, $$dhol).
% 1.51/1.27
% 1.51/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.VNGgzzedGK/DTF2DTF3410.p
% See solution above
% 1.51/1.27 ------------------------
% 1.51/1.28 ---- Cleaned THF ---
% 1.51/1.28 thf(h,type,
% 1.51/1.28 h: $i > $i ).
% 1.51/1.28
% 1.51/1.28 thf(g,type,
% 1.51/1.28 g: $i > $i ).
% 1.51/1.28
% 1.51/1.28 thf(cP,type,
% 1.51/1.28 cP: $i > $i > $o ).
% 1.51/1.28
% 1.51/1.28 thf(cTHM85,conjecture,
% 1.51/1.28 ? [Xx: $i,Xf: $i > $i] :
% 1.51/1.28 ! [Xy: $i] :
% 1.51/1.28 ( ( ! [Xz: $i] : ( cP @ Xz @ ( Xf @ Xx ) )
% 1.51/1.28 & ( cP @ Xx @ Xy ) )
% 1.51/1.28 => ( cP @ Xy @ ( g @ ( h @ Xy ) ) ) ) ).
% 1.51/1.28 ------------------------
% 1.51/1.29 % (3603)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_3410 for (3000ds/275Mi)
% 1.51/1.29 % (3598)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3410 for (3000ds/183Mi)
% 1.51/1.29 % (3603)First to succeed.
% 1.51/1.29 % (3598)Also succeeded, but the first one will report.
% 1.51/1.29 % (3603)Refutation found. Thanks to Tanya!
% 1.51/1.29 % SZS status Theorem for DTF2THF_3410
% 1.51/1.29 % SZS output start Proof for DTF2THF_3410
% 1.51/1.29 thf(func_def_0, type, h: $i > $i).
% 1.51/1.29 thf(func_def_1, type, g: $i > $i).
% 1.51/1.29 thf(func_def_2, type, cP: $i > $i > $o).
% 1.51/1.29 thf(func_def_6, type, sK0: ($i > $i) > $i > $i).
% 1.51/1.29 thf(f13,plain,(
% 1.51/1.29 $false),
% 1.51/1.29 inference(subsumption_resolution,[status(thm)],[f10,f12])).
% 1.51/1.29 thf(f12,plain,(
% 1.51/1.29 ( ! [X3 : $i,X0 : $i,X1 : $i > $i] : (((cP @ X3 @ (X1 @ X0)) = $true)) )),
% 1.51/1.29 inference(cnf_transformation,[status(thm)],[f9])).
% 1.51/1.29 thf(f9,plain,(
% 1.51/1.29 ! [X0 : $i,X1 : $i > $i] : (! [X3 : $i] : ((cP @ X3 @ (X1 @ X0)) = $true) & ((cP @ X0 @ (sK0 @ X1 @ X0)) = $true) & ((cP @ (sK0 @ X1 @ X0) @ (g @ (h @ (sK0 @ X1 @ X0)))) != $true))),
% 1.51/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8])).
% 1.51/1.29 thf(f8,plain,(
% 1.51/1.29 ! [X0 : $i,X1 : $i > $i] : (? [X2 : $i] : (! [X3 : $i] : ((cP @ X3 @ (X1 @ X0)) = $true) & ((cP @ X0 @ X2) = $true) & ((cP @ X2 @ (g @ (h @ X2))) != $true)) => (! [X3 : $i] : ((cP @ X3 @ (X1 @ X0)) = $true) & ((cP @ X0 @ (sK0 @ X1 @ X0)) = $true) & ((cP @ (sK0 @ X1 @ X0) @ (g @ (h @ (sK0 @ X1 @ X0)))) != $true)))),
% 1.51/1.29 introduced(definition,[],[choice_axiom])).
% 1.51/1.29 thf(f7,plain,(
% 1.51/1.29 ! [X0 : $i,X1 : $i > $i] : ? [X2 : $i] : (! [X3 : $i] : ((cP @ X3 @ (X1 @ X0)) = $true) & ((cP @ X0 @ X2) = $true) & ((cP @ X2 @ (g @ (h @ X2))) != $true))),
% 1.51/1.29 inference(flattening,[status(thm)],[f6])).
% 1.51/1.29 thf(f6,plain,(
% 1.51/1.29 ! [X1 : $i > $i,X0 : $i] : ? [X2 : $i] : (((cP @ X2 @ (g @ (h @ X2))) != $true) & (! [X3 : $i] : ((cP @ X3 @ (X1 @ X0)) = $true) & ((cP @ X0 @ X2) = $true)))),
% 1.51/1.29 inference(ennf_transformation,[status(thm)],[f5])).
% 1.51/1.29 thf(f5,plain,(
% 1.51/1.29 ~? [X1 : $i > $i,X0 : $i] : ! [X2 : $i] : ((! [X3 : $i] : ((cP @ X3 @ (X1 @ X0)) = $true) & ((cP @ X0 @ X2) = $true)) => ((cP @ X2 @ (g @ (h @ X2))) = $true))),
% 1.51/1.29 inference(fool_elimination,[status(thm)],[f4])).
% 1.51/1.29 thf(f4,plain,(
% 1.51/1.29 ~? [X0 : $i,X1 : $i > $i] : ! [X2 : $i] : ((! [X3 : $i] : (cP @ X3 @ (X1 @ X0)) & (cP @ X0 @ X2)) => (cP @ X2 @ (g @ (h @ X2))))),
% 1.51/1.29 inference(rectify,[status(thm)],[f2])).
% 1.51/1.29 thf(f2,negated_conjecture,(
% 1.51/1.29 ~? [X0 : $i,X1 : $i > $i] : ! [X2 : $i] : ((! [X3 : $i] : (cP @ X3 @ (X1 @ X0)) & (cP @ X0 @ X2)) => (cP @ X2 @ (g @ (h @ X2))))),
% 1.51/1.29 inference(negated_conjecture,[status(cth)],[f1])).
% 1.51/1.29 thf(f1,conjecture,(
% 1.51/1.29 ? [X0 : $i,X1 : $i > $i] : ! [X2 : $i] : ((! [X3 : $i] : (cP @ X3 @ (X1 @ X0)) & (cP @ X0 @ X2)) => (cP @ X2 @ (g @ (h @ X2))))),
% 1.51/1.29 file('/export/starexec/sandbox/tmp/tmp.VNGgzzedGK/DTF2THF_3410.p',cTHM85)).
% 1.51/1.29 thf(f10,plain,(
% 1.51/1.29 ( ! [X0 : $i,X1 : $i > $i] : (((cP @ (sK0 @ X1 @ X0) @ (g @ (h @ (sK0 @ X1 @ X0)))) != $true)) )),
% 1.51/1.29 inference(cnf_transformation,[status(thm)],[f9])).
% 1.51/1.29 % SZS output end Proof for DTF2THF_3410
% 1.51/1.29 % (3603)------------------------------
% 1.51/1.29 % (3603)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.29 % (3603)Termination reason: Refutation
% 1.51/1.29
% 1.51/1.29 % (3603)Memory used [KB]: 5500
% 1.51/1.29 % (3603)Time elapsed: 0.002 s
% 1.51/1.29 % (3603)Instructions burned: 1 (million)
% 1.51/1.29 % (3603)------------------------------
% 1.51/1.29 % (3603)------------------------------
% 1.51/1.29 % (3597)Success in time 0.007 s
%------------------------------------------------------------------------------