%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO233^5 : 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 : n031.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 09:53:43 AM UTC 2026
% Result : Theorem 1.58s 1.32s
% Output : Refutation 1.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 12 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 31 ( 18 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 58 ( 11 ~; 3 |; 2 &; 34 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 15 ( 0 ^; 15 !; 0 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cN: $i > $i ).
thf(func_def_1,type,
cM: $i > $i ).
thf(func_def_6,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f22,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f21]) ).
thf(f21,plain,
( ( cN @ sK2 )
!= ( cN @ sK2 ) ),
inference(superposition,[status(thm)],[f10,f12]) ).
thf(f12,plain,
! [X0: $i] :
( ( cM @ X0 )
= ( cN @ X0 ) ),
inference(leibniz_equality_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $i > $o,X1: $i] :
( ( ( X0 @ ( cN @ X1 ) )
= $true )
| ( ( X0 @ ( cM @ X1 ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X0: $i > $o,X1: $i] :
( ( ( X0 @ ( cM @ X1 ) )
!= $true )
| ( ( X0 @ ( cN @ X1 ) )
= $true ) )
& ( cM != cN ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X1: $i > $o,X0: $i] :
( ( ( X1 @ ( cM @ X0 ) )
!= $true )
| ( ( X1 @ ( cN @ X0 ) )
= $true ) )
& ( cM != cN ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ! [X1: $i > $o,X0: $i] :
( ( ( X1 @ ( cM @ X0 ) )
= $true )
=> ( ( X1 @ ( cN @ X0 ) )
= $true ) )
=> ( cM = cN ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: $i,X1: $i > $o] :
( ( X1 @ ( cM @ X0 ) )
=> ( X1 @ ( cN @ X0 ) ) )
=> ( cM = cN ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: $i,X1: $i > $o] :
( ( X1 @ ( cM @ X0 ) )
=> ( X1 @ ( cN @ X0 ) ) )
=> ( cM = cN ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X0: $i,X1: $i > $o] :
( ( X1 @ ( cM @ X0 ) )
=> ( X1 @ ( cN @ X0 ) ) )
=> ( cM = cN ) ),
file('/export/starexec/sandbox/tmp/tmp.JyLd2VZodT/DTF2THF_19952.p',cLEIBNIZ) ).
thf(f10,plain,
( ( cM @ sK2 )
!= ( cN @ sK2 ) ),
inference(negative_extensionality,[status(thm)],[f8]) ).
thf(f8,plain,
cM != cN,
inference(cnf_transformation,[status(thm)],[f7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYO233^5 : 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
% 0.11/0.30 % Computer : n031.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 14:27:33 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
% 0.17/0.39 ---- Original DTF file ---
% 0.17/0.39 thf(spec,logic,$$dhol).
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 % File : SYO233^5 : TPTP v9.2.1. Released v4.0.0.
% 0.17/0.39 % Domain : Syntactic
% 0.17/0.39 % Problem : TPS problem from BASIC-HO-EQ-THMS
% 0.17/0.39 % Version : Especial.
% 0.17/0.39 % English :
% 0.17/0.39
% 0.17/0.39 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.17/0.39 % Source : [Bro09]
% 0.17/0.39 % Names : tps_0698 [Bro09]
% 0.17/0.39
% 0.17/0.39 % Status : Theorem
% 0.17/0.39 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.38 v8.1.0, 0.45 v7.5.0, 0.14 v7.4.0, 0.00 v6.2.0, 0.29 v6.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% 0.17/0.39 % Syntax : Number of formulae : 3 ( 1 unt; 2 typ; 0 def)
% 0.17/0.39 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.17/0.39 % Maximal formula atoms : 1 ( 1 avg)
% 0.17/0.39 % Number of connectives : 6 ( 0 ~; 0 |; 0 &; 4 @)
% 0.17/0.39 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.17/0.39 % Maximal formula depth : 7 ( 7 avg)
% 0.17/0.39 % Number of types : 2 ( 0 usr)
% 0.17/0.39 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.17/0.39 % Number of symbols : 3 ( 2 usr; 0 con; 1-2 aty)
% 0.17/0.39 % Number of variables : 2 ( 0 ^; 2 !; 0 ?; 2 :)
% 0.17/0.39 % SPC : TH0_THM_EQU_NAR
% 0.17/0.39
% 0.17/0.39 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.17/0.39 % project in the Department of Mathematical Sciences at Carnegie
% 0.17/0.39 % Mellon University. Distributed under the Creative Commons copyleft
% 0.17/0.39 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 thf(cN,type,
% 0.17/0.39 cN: $i > $i ).
% 0.17/0.39
% 0.17/0.39 thf(cM,type,
% 0.17/0.39 cM: $i > $i ).
% 0.17/0.39
% 0.17/0.39 thf(cLEIBNIZ,conjecture,
% 0.17/0.39 ( ! [Xx: $i,Xp: $i > $o] :
% 0.17/0.39 ( ( Xp @ ( cM @ Xx ) )
% 0.17/0.39 => ( Xp @ ( cN @ Xx ) ) )
% 0.17/0.39 => ( cM = cN ) ) ).
% 0.17/0.39
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 ------------------------
% 1.38/1.29 ---- Embedded in THF ---
% 1.38/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.38/1.29 %%% Generated on Tue Feb 24 14:27:34 EST 2026
% 1.38/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.38/1.29 %%% Logic specification used:
% 1.38/1.29 %%% thf(spec, logic, $$dhol).
% 1.38/1.29
% 1.38/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.JyLd2VZodT/DTF2DTF19952.p
% See solution above
% 1.38/1.29 ------------------------
% 1.58/1.30 ---- Cleaned THF ---
% 1.58/1.30 thf(cN,type,
% 1.58/1.30 cN: $i > $i ).
% 1.58/1.30
% 1.58/1.30 thf(cM,type,
% 1.58/1.30 cM: $i > $i ).
% 1.58/1.30
% 1.58/1.30 thf(cLEIBNIZ,conjecture,
% 1.58/1.30 ( ! [Xx: $i,Xp: $i > $o] :
% 1.58/1.30 ( ( Xp @ ( cM @ Xx ) )
% 1.58/1.30 => ( Xp @ ( cN @ Xx ) ) )
% 1.58/1.30 => ( cM = cN ) ) ).
% 1.58/1.30 ------------------------
% 1.58/1.32 % (20051)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_19952 for (3000ds/4Mi)
% 1.58/1.32 % (20052)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_19952 for (3000ds/27Mi)
% 1.58/1.32 % (20054)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_19952 for (3000ds/2Mi)
% 1.58/1.32 % (20050)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_19952 for (3000ds/183Mi)
% 1.58/1.32 % (20055)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_19952 for (3000ds/275Mi)
% 1.58/1.32 % (20056)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_19952 for (3000ds/18Mi)
% 1.58/1.32 % (20053)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_19952 for (3000ds/2Mi)
% 1.58/1.32 % (20052)Refutation not found, incomplete strategy
% 1.58/1.32 % (20052)------------------------------
% 1.58/1.32 % (20052)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.32 % (20052)Termination reason: Refutation not found, incomplete strategy
% 1.58/1.32
% 1.58/1.32
% 1.58/1.32 % (20052)Memory used [KB]: 5500
% 1.58/1.32 % (20052)Time elapsed: 0.003 s
% 1.58/1.32 % (20052)Instructions burned: 1 (million)
% 1.58/1.32 % (20052)------------------------------
% 1.58/1.32 % (20052)------------------------------
% 1.58/1.32 % (20055)First to succeed.
% 1.58/1.32 % (20054)Instruction limit reached!
% 1.58/1.32 % (20054)------------------------------
% 1.58/1.32 % (20054)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.32 % (20054)Termination reason: Unknown
% 1.58/1.32 % (20054)Termination phase: Saturation
% 1.58/1.32
% 1.58/1.32 % (20054)Memory used [KB]: 5500
% 1.58/1.32 % (20054)Time elapsed: 0.004 s
% 1.58/1.32 % (20054)Instructions burned: 3 (million)
% 1.58/1.32 % (20054)------------------------------
% 1.58/1.32 % (20054)------------------------------
% 1.58/1.32 % (20050)Also succeeded, but the first one will report.
% 1.58/1.32 % (20055)Refutation found. Thanks to Tanya!
% 1.58/1.32 % SZS status Theorem for DTF2THF_19952
% 1.58/1.32 % SZS output start Proof for DTF2THF_19952
% 1.58/1.32 thf(func_def_0, type, cN: $i > $i).
% 1.58/1.32 thf(func_def_1, type, cM: $i > $i).
% 1.58/1.32 thf(func_def_6, type, ph1: !>[X0: $tType]:(X0)).
% 1.58/1.32 thf(f22,plain,(
% 1.58/1.32 $false),
% 1.58/1.32 inference(trivial_inequality_removal,[status(thm)],[f21])).
% 1.58/1.32 thf(f21,plain,(
% 1.58/1.32 ((cN @ sK2) != (cN @ sK2))),
% 1.58/1.32 inference(superposition,[status(thm)],[f10,f12])).
% 1.58/1.32 thf(f12,plain,(
% 1.58/1.32 ( ! [X0 : $i] : (((cM @ X0) = (cN @ X0))) )),
% 1.58/1.32 inference(leibniz_equality_elimination,[status(thm)],[f9])).
% 1.58/1.32 thf(f9,plain,(
% 1.58/1.32 ( ! [X0 : $i > $o,X1 : $i] : (((X0 @ (cN @ X1)) = $true) | ((X0 @ (cM @ X1)) != $true)) )),
% 1.58/1.32 inference(cnf_transformation,[status(thm)],[f7])).
% 1.58/1.32 thf(f7,plain,(
% 1.58/1.32 ! [X0 : $i > $o,X1 : $i] : (((X0 @ (cM @ X1)) != $true) | ((X0 @ (cN @ X1)) = $true)) & (cM != cN)),
% 1.58/1.32 inference(rectify,[status(thm)],[f6])).
% 1.58/1.32 thf(f6,plain,(
% 1.58/1.32 ! [X1 : $i > $o,X0 : $i] : (((X1 @ (cM @ X0)) != $true) | ((X1 @ (cN @ X0)) = $true)) & (cM != cN)),
% 1.58/1.32 inference(ennf_transformation,[status(thm)],[f5])).
% 1.58/1.32 thf(f5,plain,(
% 1.58/1.32 ~(! [X1 : $i > $o,X0 : $i] : (((X1 @ (cM @ X0)) = $true) => ((X1 @ (cN @ X0)) = $true)) => (cM = cN))),
% 1.58/1.32 inference(fool_elimination,[status(thm)],[f4])).
% 1.58/1.32 thf(f4,plain,(
% 1.58/1.32 ~(! [X0 : $i,X1 : $i > $o] : ((X1 @ (cM @ X0)) => (X1 @ (cN @ X0))) => (cM = cN))),
% 1.58/1.32 inference(rectify,[status(thm)],[f2])).
% 1.58/1.32 thf(f2,negated_conjecture,(
% 1.58/1.32 ~(! [X0 : $i,X1 : $i > $o] : ((X1 @ (cM @ X0)) => (X1 @ (cN @ X0))) => (cM = cN))),
% 1.58/1.32 inference(negated_conjecture,[status(cth)],[f1])).
% 1.58/1.32 thf(f1,conjecture,(
% 1.58/1.32 ! [X0 : $i,X1 : $i > $o] : ((X1 @ (cM @ X0)) => (X1 @ (cN @ X0))) => (cM = cN)),
% 1.58/1.32 file('/export/starexec/sandbox/tmp/tmp.JyLd2VZodT/DTF2THF_19952.p',cLEIBNIZ)).
% 1.58/1.32 thf(f10,plain,(
% 1.58/1.32 ((cM @ sK2) != (cN @ sK2))),
% 1.58/1.32 inference(negative_extensionality,[status(thm)],[f8])).
% 1.58/1.32 thf(f8,plain,(
% 1.58/1.32 (cM != cN)),
% 1.58/1.32 inference(cnf_transformation,[status(thm)],[f7])).
% 1.58/1.32 % SZS output end Proof for DTF2THF_19952
% 1.58/1.32 % (20055)------------------------------
% 1.58/1.32 % (20055)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.32 % (20055)Termination reason: Refutation
% 1.58/1.32
% 1.58/1.32 % (20055)Memory used [KB]: 5500
% 1.58/1.32 % (20055)Time elapsed: 0.004 s
% 1.58/1.32 % (20055)Instructions burned: 1 (million)
% 1.58/1.32 % (20055)------------------------------
% 1.58/1.32 % (20055)------------------------------
% 1.58/1.32 % (20049)Success in time 0.018 s
%------------------------------------------------------------------------------