%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO293^5 : 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 : n019.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 09:53:52 AM UTC 2026
% Result : Theorem 1.46s 1.29s
% Output : Refutation 1.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 12 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 55 ( 21 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 75 ( 8 ~; 0 |; 14 &; 48 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 25 ( 2 ^; 13 !; 10 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cP: $i > $i > $o ).
thf(func_def_4,type,
sK0: ( $i > $o ) > $i ).
thf(func_def_5,type,
sK1: ( $i > $o ) > $i ).
thf(func_def_8,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f17,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f16]) ).
thf(f16,plain,
$true = $false,
inference(beta_eta_normalization,[status(thm)],[f14]) ).
thf(f14,plain,
( $true
= ( ^ [Y0: $i] : $false
@ ( sK1
@ ^ [Y0: $i] : $false ) ) ),
inference(primitive_instantiation,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $i > $o] :
( $true
= ( X0 @ ( sK1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $i > $o] :
( ( $true
= ( X0 @ ( sK0 @ X0 ) ) )
& ( $true
!= ( cP @ ( sK1 @ X0 ) @ ( sK0 @ X0 ) ) )
& ( $true
= ( X0 @ ( sK1 @ X0 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f8]) ).
thf(f8,plain,
! [X0: $i > $o] :
( ? [X1: $i,X2: $i] :
( ( ( X0 @ X1 )
= $true )
& ( $true
!= ( cP @ X2 @ X1 ) )
& ( ( X0 @ X2 )
= $true ) )
=> ( ( $true
= ( X0 @ ( sK0 @ X0 ) ) )
& ( $true
!= ( cP @ ( sK1 @ X0 ) @ ( sK0 @ X0 ) ) )
& ( $true
= ( X0 @ ( sK1 @ X0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
! [X0: $i > $o] :
? [X1: $i,X2: $i] :
( ( ( X0 @ X1 )
= $true )
& ( $true
!= ( cP @ X2 @ X1 ) )
& ( ( X0 @ X2 )
= $true ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: $i > $o] :
? [X2: $i,X1: $i] :
( ( $true
!= ( cP @ X2 @ X1 ) )
& ( ( X0 @ X2 )
= $true )
& ( ( X0 @ X1 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ? [X0: $i > $o] :
! [X2: $i,X1: $i] :
( ( ( ( X0 @ X2 )
= $true )
& ( ( X0 @ X1 )
= $true ) )
=> ( $true
= ( cP @ X2 @ X1 ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ? [X0: $i > $o] :
! [X1: $i,X2: $i] :
( ( ( X0 @ X1 )
& ( X0 @ X2 ) )
=> ( cP @ X2 @ X1 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X0: $i > $o] :
! [X2: $i,X1: $i] :
( ( ( X0 @ X2 )
& ( X0 @ X1 ) )
=> ( cP @ X1 @ X2 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X0: $i > $o] :
! [X2: $i,X1: $i] :
( ( ( X0 @ X2 )
& ( X0 @ X1 ) )
=> ( cP @ X1 @ X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.zWLewuux45/DTF2THF_25866.p',cBLEDSOE5A) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO293^5 : TPTP v9.2.1. Released v4.0.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n019.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 14:27:39 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SYO293^5 : TPTP v9.2.1. Released v4.0.0.
% 0.30/0.46 % Domain : Syntactic
% 0.30/0.46 % Problem : TPS problem from BASIC-HO-THMS
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English :
% 0.30/0.46
% 0.30/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Bro09]
% 0.30/0.46 % Names : tps_0712 [Bro09]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % 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, 0.20 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
% 0.30/0.46 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.30/0.46 % Number of atoms : 1 ( 0 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 1 ( 1 avg)
% 0.30/0.46 % Number of connectives : 6 ( 0 ~; 0 |; 1 &; 4 @)
% 0.30/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 7 ( 7 avg)
% 0.30/0.46 % Number of types : 2 ( 0 usr)
% 0.30/0.46 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 1 ( 1 usr; 0 con; 2-2 aty)
% 0.30/0.46 % Number of variables : 3 ( 0 ^; 2 !; 1 ?; 3 :)
% 0.30/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.30/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.30/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.30/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(cP,type,
% 0.30/0.46 cP: $i > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(cBLEDSOE5A,conjecture,
% 0.30/0.46 ? [A: $i > $o] :
% 0.30/0.46 ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( ( A @ Xx )
% 0.30/0.46 & ( A @ Xy ) )
% 0.30/0.46 => ( cP @ Xx @ Xy ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.46/1.25 ---- Embedded in THF ---
% 1.46/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.25 %%% Generated on Tue Feb 24 14:27:40 EST 2026
% 1.46/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.25 %%% Logic specification used:
% 1.46/1.25 %%% thf(spec, logic, $$dhol).
% 1.46/1.25
% 1.46/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.zWLewuux45/DTF2DTF25866.p
% See solution above
% 1.46/1.25 ------------------------
% 1.46/1.26 ---- Cleaned THF ---
% 1.46/1.26 thf(cP,type,
% 1.46/1.26 cP: $i > $i > $o ).
% 1.46/1.26
% 1.46/1.26 thf(cBLEDSOE5A,conjecture,
% 1.46/1.26 ? [A: $i > $o] :
% 1.46/1.26 ! [Xx: $i,Xy: $i] :
% 1.46/1.26 ( ( ( A @ Xx )
% 1.46/1.26 & ( A @ Xy ) )
% 1.46/1.26 => ( cP @ Xx @ Xy ) ) ).
% 1.46/1.26 ------------------------
% 1.46/1.28 % (26140)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_25866 for (2999ds/2Mi)
% 1.46/1.28 % (26140)Instruction limit reached!
% 1.46/1.28 % (26140)------------------------------
% 1.46/1.28 % (26140)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.28 % (26140)Termination reason: Unknown
% 1.46/1.28 % (26140)Termination phase: Saturation
% 1.46/1.28
% 1.46/1.28 % (26140)Memory used [KB]: 5500
% 1.46/1.28 % (26140)Time elapsed: 0.003 s
% 1.46/1.28 % (26140)Instructions burned: 3 (million)
% 1.46/1.28 % (26140)------------------------------
% 1.46/1.28 % (26140)------------------------------
% 1.46/1.28 % (26138)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_25866 for (2999ds/27Mi)
% 1.46/1.28 % (26138)Refutation not found, incomplete strategy
% 1.46/1.28 % (26138)------------------------------
% 1.46/1.28 % (26138)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.28 % (26138)Termination reason: Refutation not found, incomplete strategy
% 1.46/1.28
% 1.46/1.28
% 1.46/1.28 % (26138)Memory used [KB]: 5500
% 1.46/1.28 % (26138)Time elapsed: 0.003 s
% 1.46/1.28 % (26138)Instructions burned: 2 (million)
% 1.46/1.28 % (26138)------------------------------
% 1.46/1.28 % (26138)------------------------------
% 1.46/1.29 % (26136)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_25866 for (2999ds/183Mi)
% 1.46/1.29 % (26137)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_25866 for (2999ds/4Mi)
% 1.46/1.29 % (26139)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_25866 for (2999ds/2Mi)
% 1.46/1.29 % (26141)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_25866 for (2999ds/275Mi)
% 1.46/1.29 % (26142)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_25866 for (2999ds/18Mi)
% 1.46/1.29 % (26136)First to succeed.
% 1.46/1.29 % (26139)Also succeeded, but the first one will report.
% 1.46/1.29 % (26136)Refutation found. Thanks to Tanya!
% 1.46/1.29 % SZS status Theorem for DTF2THF_25866
% 1.46/1.29 % SZS output start Proof for DTF2THF_25866
% 1.46/1.29 thf(func_def_0, type, cP: $i > $i > $o).
% 1.46/1.29 thf(func_def_4, type, sK0: ($i > $o) > $i).
% 1.46/1.29 thf(func_def_5, type, sK1: ($i > $o) > $i).
% 1.46/1.29 thf(func_def_8, type, ph3: !>[X0: $tType]:(X0)).
% 1.46/1.29 thf(f17,plain,(
% 1.46/1.29 $false),
% 1.46/1.29 inference(trivial_inequality_removal,[status(thm)],[f16])).
% 1.46/1.29 thf(f16,plain,(
% 1.46/1.29 ($true = $false)),
% 1.46/1.29 inference(beta_eta_normalization,[status(thm)],[f14])).
% 1.46/1.29 thf(f14,plain,(
% 1.46/1.29 ($true = ((^[Y0 : $i]: ($false)) @ (sK1 @ (^[Y0 : $i]: ($false)))))),
% 1.46/1.29 inference(primitive_instantiation,[status(thm)],[f10])).
% 1.46/1.29 thf(f10,plain,(
% 1.46/1.29 ( ! [X0 : $i > $o] : (($true = (X0 @ (sK1 @ X0)))) )),
% 1.46/1.29 inference(cnf_transformation,[status(thm)],[f9])).
% 1.46/1.29 thf(f9,plain,(
% 1.46/1.29 ! [X0 : $i > $o] : (($true = (X0 @ (sK0 @ X0))) & ($true != (cP @ (sK1 @ X0) @ (sK0 @ X0))) & ($true = (X0 @ (sK1 @ X0))))),
% 1.46/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f8])).
% 1.46/1.29 thf(f8,plain,(
% 1.46/1.29 ! [X0 : $i > $o] : (? [X1 : $i,X2 : $i] : (((X0 @ X1) = $true) & ($true != (cP @ X2 @ X1)) & ((X0 @ X2) = $true)) => (($true = (X0 @ (sK0 @ X0))) & ($true != (cP @ (sK1 @ X0) @ (sK0 @ X0))) & ($true = (X0 @ (sK1 @ X0)))))),
% 1.46/1.29 introduced(definition,[],[choice_axiom])).
% 1.46/1.29 thf(f7,plain,(
% 1.46/1.29 ! [X0 : $i > $o] : ? [X1 : $i,X2 : $i] : (((X0 @ X1) = $true) & ($true != (cP @ X2 @ X1)) & ((X0 @ X2) = $true))),
% 1.46/1.29 inference(flattening,[status(thm)],[f6])).
% 1.46/1.29 thf(f6,plain,(
% 1.46/1.29 ! [X0 : $i > $o] : ? [X2 : $i,X1 : $i] : (($true != (cP @ X2 @ X1)) & (((X0 @ X2) = $true) & ((X0 @ X1) = $true)))),
% 1.46/1.29 inference(ennf_transformation,[status(thm)],[f5])).
% 1.46/1.29 thf(f5,plain,(
% 1.46/1.29 ~? [X0 : $i > $o] : ! [X2 : $i,X1 : $i] : ((((X0 @ X2) = $true) & ((X0 @ X1) = $true)) => ($true = (cP @ X2 @ X1)))),
% 1.46/1.29 inference(fool_elimination,[status(thm)],[f4])).
% 1.46/1.29 thf(f4,plain,(
% 1.46/1.29 ~? [X0 : $i > $o] : ! [X1 : $i,X2 : $i] : (((X0 @ X1) & (X0 @ X2)) => (cP @ X2 @ X1))),
% 1.46/1.29 inference(rectify,[status(thm)],[f2])).
% 1.46/1.29 thf(f2,negated_conjecture,(
% 1.46/1.29 ~? [X0 : $i > $o] : ! [X2 : $i,X1 : $i] : (((X0 @ X2) & (X0 @ X1)) => (cP @ X1 @ X2))),
% 1.46/1.29 inference(negated_conjecture,[status(cth)],[f1])).
% 1.46/1.29 thf(f1,conjecture,(
% 1.46/1.29 ? [X0 : $i > $o] : ! [X2 : $i,X1 : $i] : (((X0 @ X2) & (X0 @ X1)) => (cP @ X1 @ X2))),
% 1.46/1.29 file('/export/starexec/sandbox/tmp/tmp.zWLewuux45/DTF2THF_25866.p',cBLEDSOE5A)).
% 1.46/1.29 % SZS output end Proof for DTF2THF_25866
% 1.46/1.29 % (26136)------------------------------
% 1.46/1.29 % (26136)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.29 % (26136)Termination reason: Refutation
% 1.46/1.29
% 1.46/1.29 % (26136)Memory used [KB]: 5500
% 1.46/1.29 % (26136)Time elapsed: 0.004 s
% 1.46/1.29 % (26136)Instructions burned: 1 (million)
% 1.46/1.29 % (26136)------------------------------
% 1.46/1.29 % (26136)------------------------------
% 1.46/1.29 % (26135)Success in time 0.02 s
%------------------------------------------------------------------------------