%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO094^5 : 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 : n018.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 09:53:22 AM UTC 2026
% Result : Theorem 1.66s 1.45s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 10 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 67 ( 18 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 97 ( 10 ~; 2 |; 6 &; 66 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 2 usr; 2 con; 0-2 aty)
% Number of variables : 27 ( 0 ^; 17 !; 10 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cR: $i > $i > $o ).
thf(func_def_4,type,
sK0: $i > $i ).
thf(f12,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f9,f10]) ).
thf(f10,plain,
! [X2: $i] :
( ( cR @ X2 @ X2 )
= $true ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ! [X0: $i] :
( ( cR @ X0 @ X0 )
!= $true )
| ! [X1: $i] :
( ( cR @ X1 @ X1 )
= $true ) )
& ! [X2: $i] :
( ( ( cR @ X2 @ X2 )
= $true )
& ( $true
!= ( cR @ ( sK0 @ X2 ) @ ( sK0 @ X2 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f6,f7]) ).
thf(f7,plain,
! [X2: $i] :
( ? [X3: $i] :
( ( ( cR @ X2 @ X2 )
= $true )
& ( ( cR @ X3 @ X3 )
!= $true ) )
=> ( ( ( cR @ X2 @ X2 )
= $true )
& ( $true
!= ( cR @ ( sK0 @ X2 ) @ ( sK0 @ X2 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
( ( ! [X0: $i] :
( ( cR @ X0 @ X0 )
!= $true )
| ! [X1: $i] :
( ( cR @ X1 @ X1 )
= $true ) )
& ! [X2: $i] :
? [X3: $i] :
( ( ( cR @ X2 @ X2 )
= $true )
& ( ( cR @ X3 @ X3 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ? [X0: $i] :
( ( cR @ X0 @ X0 )
= $true )
=> ! [X1: $i] :
( ( cR @ X1 @ X1 )
= $true ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( ( cR @ X2 @ X2 )
= $true )
=> ( ( cR @ X3 @ X3 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ? [X0: $i] : ( cR @ X0 @ X0 )
=> ! [X1: $i] : ( cR @ X1 @ X1 ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( cR @ X2 @ X2 )
=> ( cR @ X3 @ X3 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ? [X0: $i] : ( cR @ X0 @ X0 )
=> ! [X1: $i] : ( cR @ X1 @ X1 ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( cR @ X2 @ X2 )
=> ( cR @ X3 @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ? [X0: $i] : ( cR @ X0 @ X0 )
=> ! [X1: $i] : ( cR @ X1 @ X1 ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( cR @ X2 @ X2 )
=> ( cR @ X3 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ZIawrEj7c1/DTF2THF_27228.p',cTHM55A) ).
thf(f9,plain,
! [X2: $i] :
( $true
!= ( cR @ ( sK0 @ X2 ) @ ( sK0 @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO094^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n018.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 14:24:01 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.49 ---- Original DTF file ---
% 0.29/0.49 thf(spec,logic,$$dhol).
% 0.29/0.49 %------------------------------------------------------------------------------
% 0.29/0.49 % File : SYO094^5 : TPTP v9.2.1. Released v4.0.0.
% 0.29/0.49 % Domain : Syntactic
% 0.29/0.49 % Problem : TPS problem THM55A
% 0.29/0.49 % Version : Especial.
% 0.29/0.49 % English :
% 0.29/0.49
% 0.29/0.49 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.49 % Source : [Bro09]
% 0.29/0.49 % Names : tps_0207 [Bro09]
% 0.29/0.49 % : THM55A [TPS]
% 0.29/0.49
% 0.29/0.49 % Status : Theorem
% 0.29/0.49 % Rating : 0.08 v9.1.0, 0.12 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.08 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 v6.0.0, 0.00 v4.0.0
% 0.29/0.49 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.29/0.49 % Number of atoms : 4 ( 0 equ; 0 cnn)
% 0.29/0.49 % Maximal formula atoms : 4 ( 4 avg)
% 0.29/0.49 % Number of connectives : 11 ( 0 ~; 0 |; 0 &; 8 @)
% 0.29/0.49 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.29/0.49 % Maximal formula depth : 7 ( 7 avg)
% 0.29/0.49 % Number of types : 2 ( 0 usr)
% 0.29/0.49 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.29/0.49 % Number of symbols : 1 ( 1 usr; 0 con; 2-2 aty)
% 0.29/0.49 % Number of variables : 4 ( 0 ^; 2 !; 2 ?; 4 :)
% 0.29/0.49 % SPC : TH0_THM_NEQ_NAR
% 0.29/0.49
% 0.29/0.49 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.29/0.49 % project in the Department of Mathematical Sciences at Carnegie
% 0.29/0.49 % Mellon University. Distributed under the Creative Commons copyleft
% 0.29/0.49 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.29/0.49 %------------------------------------------------------------------------------
% 0.29/0.49 thf(cR,type,
% 0.29/0.49 cR: $i > $i > $o ).
% 0.29/0.49
% 0.29/0.49 thf(cTHM55A,conjecture,
% 0.29/0.49 ( ( ? [X: $i] : ( cR @ X @ X )
% 0.29/0.49 => ! [Y: $i] : ( cR @ Y @ Y ) )
% 0.29/0.49 => ? [U: $i] :
% 0.29/0.49 ! [V: $i] :
% 0.29/0.49 ( ( cR @ U @ U )
% 0.29/0.49 => ( cR @ V @ V ) ) ) ).
% 0.29/0.49
% 0.29/0.49 %------------------------------------------------------------------------------
% 0.29/0.49 ------------------------
% 1.66/1.42 ---- Embedded in THF ---
% 1.66/1.42 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.66/1.42 %%% Generated on Tue Feb 24 14:24:02 EST 2026
% 1.66/1.42 %%% using '$$dhol' embedding, version 1.3.0.
% 1.66/1.42 %%% Logic specification used:
% 1.66/1.42 %%% thf(spec, logic, $$dhol).
% 1.66/1.42
% 1.66/1.42 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.ZIawrEj7c1/DTF2DTF27228.p
% See solution above
% 1.66/1.42 ------------------------
% 1.66/1.43 ---- Cleaned THF ---
% 1.66/1.43 thf(cR,type,
% 1.66/1.43 cR: $i > $i > $o ).
% 1.66/1.43
% 1.66/1.43 thf(cTHM55A,conjecture,
% 1.66/1.43 ( ( ? [X: $i] : ( cR @ X @ X )
% 1.66/1.43 => ! [Y: $i] : ( cR @ Y @ Y ) )
% 1.66/1.43 => ? [U: $i] :
% 1.66/1.43 ! [V: $i] :
% 1.66/1.43 ( ( cR @ U @ U )
% 1.66/1.43 => ( cR @ V @ V ) ) ) ).
% 1.66/1.43 ------------------------
% 1.66/1.45 % (27336)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_27228 for (3000ds/2Mi)
% 1.66/1.45 % (27335)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_27228 for (3000ds/27Mi)
% 1.66/1.45 % (27338)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_27228 for (3000ds/275Mi)
% 1.66/1.45 % (27334)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_27228 for (3000ds/4Mi)
% 1.66/1.45 % (27333)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_27228 for (3000ds/183Mi)
% 1.66/1.45 % (27337)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_27228 for (3000ds/2Mi)
% 1.66/1.45 % (27339)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_27228 for (3000ds/18Mi)
% 1.66/1.45 % (27338)First to succeed.
% 1.66/1.45 % (27336)Instruction limit reached!
% 1.66/1.45 % (27336)------------------------------
% 1.66/1.45 % (27336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.45 % (27336)Termination reason: Unknown
% 1.66/1.45 % (27336)Termination phase: Saturation
% 1.66/1.45 % (27337)Instruction limit reached!
% 1.66/1.45 % (27337)------------------------------
% 1.66/1.45 % (27337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.45 % (27337)Termination reason: Unknown
% 1.66/1.45 % (27337)Termination phase: Saturation
% 1.66/1.45
% 1.66/1.45 % (27337)Memory used [KB]: 5500
% 1.66/1.45 % (27337)Time elapsed: 0.003 s
% 1.66/1.45 % (27337)Instructions burned: 2 (million)
% 1.66/1.45 % (27337)------------------------------
% 1.66/1.45 % (27337)------------------------------
% 1.66/1.45
% 1.66/1.45 % (27336)Memory used [KB]: 5500
% 1.66/1.45 % (27336)Time elapsed: 0.003 s
% 1.66/1.45 % (27336)Instructions burned: 2 (million)
% 1.66/1.45 % (27336)------------------------------
% 1.66/1.45 % (27336)------------------------------
% 1.66/1.45 % (27333)Also succeeded, but the first one will report.
% 1.66/1.45 % (27338)Refutation found. Thanks to Tanya!
% 1.66/1.45 % SZS status Theorem for DTF2THF_27228
% 1.66/1.45 % SZS output start Proof for DTF2THF_27228
% 1.66/1.45 thf(func_def_0, type, cR: $i > $i > $o).
% 1.66/1.45 thf(func_def_4, type, sK0: $i > $i).
% 1.66/1.45 thf(f12,plain,(
% 1.66/1.45 $false),
% 1.66/1.45 inference(subsumption_resolution,[status(thm)],[f9,f10])).
% 1.66/1.45 thf(f10,plain,(
% 1.66/1.45 ( ! [X2 : $i] : (((cR @ X2 @ X2) = $true)) )),
% 1.66/1.45 inference(cnf_transformation,[status(thm)],[f8])).
% 1.66/1.45 thf(f8,plain,(
% 1.66/1.45 (! [X0 : $i] : ((cR @ X0 @ X0) != $true) | ! [X1 : $i] : ((cR @ X1 @ X1) = $true)) & ! [X2 : $i] : (((cR @ X2 @ X2) = $true) & ($true != (cR @ (sK0 @ X2) @ (sK0 @ X2))))),
% 1.66/1.45 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f6,f7])).
% 1.66/1.45 thf(f7,plain,(
% 1.66/1.45 ! [X2 : $i] : (? [X3 : $i] : (((cR @ X2 @ X2) = $true) & ((cR @ X3 @ X3) != $true)) => (((cR @ X2 @ X2) = $true) & ($true != (cR @ (sK0 @ X2) @ (sK0 @ X2)))))),
% 1.66/1.45 introduced(definition,[],[choice_axiom])).
% 1.66/1.45 thf(f6,plain,(
% 1.66/1.45 (! [X0 : $i] : ((cR @ X0 @ X0) != $true) | ! [X1 : $i] : ((cR @ X1 @ X1) = $true)) & ! [X2 : $i] : ? [X3 : $i] : (((cR @ X2 @ X2) = $true) & ((cR @ X3 @ X3) != $true))),
% 1.66/1.45 inference(ennf_transformation,[status(thm)],[f5])).
% 1.66/1.45 thf(f5,plain,(
% 1.66/1.45 ~((? [X0 : $i] : ((cR @ X0 @ X0) = $true) => ! [X1 : $i] : ((cR @ X1 @ X1) = $true)) => ? [X2 : $i] : ! [X3 : $i] : (((cR @ X2 @ X2) = $true) => ((cR @ X3 @ X3) = $true)))),
% 1.66/1.45 inference(fool_elimination,[status(thm)],[f4])).
% 1.66/1.45 thf(f4,plain,(
% 1.66/1.45 ~((? [X0 : $i] : (cR @ X0 @ X0) => ! [X1 : $i] : (cR @ X1 @ X1)) => ? [X2 : $i] : ! [X3 : $i] : ((cR @ X2 @ X2) => (cR @ X3 @ X3)))),
% 1.66/1.45 inference(rectify,[status(thm)],[f2])).
% 1.66/1.45 thf(f2,negated_conjecture,(
% 1.66/1.45 ~((? [X0 : $i] : (cR @ X0 @ X0) => ! [X1 : $i] : (cR @ X1 @ X1)) => ? [X2 : $i] : ! [X3 : $i] : ((cR @ X2 @ X2) => (cR @ X3 @ X3)))),
% 1.66/1.45 inference(negated_conjecture,[status(cth)],[f1])).
% 1.66/1.45 thf(f1,conjecture,(
% 1.66/1.45 (? [X0 : $i] : (cR @ X0 @ X0) => ! [X1 : $i] : (cR @ X1 @ X1)) => ? [X2 : $i] : ! [X3 : $i] : ((cR @ X2 @ X2) => (cR @ X3 @ X3))),
% 1.66/1.45 file('/export/starexec/sandbox/tmp/tmp.ZIawrEj7c1/DTF2THF_27228.p',cTHM55A)).
% 1.66/1.45 thf(f9,plain,(
% 1.66/1.45 ( ! [X2 : $i] : (($true != (cR @ (sK0 @ X2) @ (sK0 @ X2)))) )),
% 1.66/1.45 inference(cnf_transformation,[status(thm)],[f8])).
% 1.66/1.45 % SZS output end Proof for DTF2THF_27228
% 1.66/1.45 % (27338)------------------------------
% 1.66/1.45 % (27338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.45 % (27338)Termination reason: Refutation
% 1.66/1.45
% 1.66/1.45 % (27338)Memory used [KB]: 5373
% 1.66/1.45 % (27338)Time elapsed: 0.003 s
% 1.66/1.45 % (27338)Instructions burned: 1 (million)
% 1.66/1.45 % (27338)------------------------------
% 1.66/1.45 % (27338)------------------------------
% 1.66/1.45 % (27332)Success in time 0.017 s
%------------------------------------------------------------------------------