%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : PUZ088^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/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 09:28:27 AM UTC 2026
% Result : Theorem 1.48s 1.27s
% Output : Refutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of formulae : 16 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 123 ( 30 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 127 ( 17 ~; 6 |; 12 &; 83 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 47 ( 0 ^; 35 !; 12 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cLIKES: $i > $i > $o ).
thf(func_def_6,type,
sK0: $i > $i ).
thf(f19,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f16]) ).
thf(f16,plain,
$true != $true,
inference(superposition,[status(thm)],[f13,f15]) ).
thf(f15,plain,
! [X0: $i] :
( ( cLIKES @ cLYLE @ X0 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: $i] :
( ( ( cLIKES @ cLYLE @ X0 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f12,f11]) ).
thf(f11,plain,
! [X4: $i] :
( $true
= ( cLIKES @ X4 @ cBRUCE ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ! [X0: $i] :
( $true
!= ( cLIKES @ X0 @ ( sK0 @ X0 ) ) )
& ! [X2: $i] :
( ! [X3: $i] :
( $true
!= ( cLIKES @ X2 @ X3 ) )
| ( $true
= ( cLIKES @ cLYLE @ X2 ) ) )
& ! [X4: $i] :
( $true
= ( cLIKES @ X4 @ cBRUCE ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f8,f9]) ).
thf(f9,plain,
! [X0: $i] :
( ? [X1: $i] :
( $true
!= ( cLIKES @ X0 @ X1 ) )
=> ( $true
!= ( cLIKES @ X0 @ ( sK0 @ X0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ! [X0: $i] :
? [X1: $i] :
( $true
!= ( cLIKES @ X0 @ X1 ) )
& ! [X2: $i] :
( ! [X3: $i] :
( $true
!= ( cLIKES @ X2 @ X3 ) )
| ( $true
= ( cLIKES @ cLYLE @ X2 ) ) )
& ! [X4: $i] :
( $true
= ( cLIKES @ X4 @ cBRUCE ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X3: $i] :
? [X4: $i] :
( ( cLIKES @ X3 @ X4 )
!= $true )
& ! [X1: $i] :
( ! [X2: $i] :
( ( cLIKES @ X1 @ X2 )
!= $true )
| ( ( cLIKES @ cLYLE @ X1 )
= $true ) )
& ! [X0: $i] :
( ( cLIKES @ X0 @ cBRUCE )
= $true ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X3: $i] :
? [X4: $i] :
( ( cLIKES @ X3 @ X4 )
!= $true )
& ! [X0: $i] :
( ( cLIKES @ X0 @ cBRUCE )
= $true )
& ! [X1: $i] :
( ! [X2: $i] :
( ( cLIKES @ X1 @ X2 )
!= $true )
| ( ( cLIKES @ cLYLE @ X1 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X0: $i] :
( ( cLIKES @ X0 @ cBRUCE )
= $true )
& ! [X1: $i] :
( ? [X2: $i] :
( ( cLIKES @ X1 @ X2 )
= $true )
=> ( ( cLIKES @ cLYLE @ X1 )
= $true ) ) )
=> ? [X3: $i] :
! [X4: $i] :
( ( cLIKES @ X3 @ X4 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: $i] : ( cLIKES @ X0 @ cBRUCE )
& ! [X1: $i] :
( ? [X2: $i] : ( cLIKES @ X1 @ X2 )
=> ( cLIKES @ cLYLE @ X1 ) ) )
=> ? [X3: $i] :
! [X4: $i] : ( cLIKES @ X3 @ X4 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X0: $i] : ( cLIKES @ X0 @ cBRUCE )
& ! [X1: $i] :
( ? [X2: $i] : ( cLIKES @ X1 @ X2 )
=> ( cLIKES @ cLYLE @ X1 ) ) )
=> ? [X3: $i] :
! [X4: $i] : ( cLIKES @ X3 @ X4 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X0: $i] : ( cLIKES @ X0 @ cBRUCE )
& ! [X1: $i] :
( ? [X2: $i] : ( cLIKES @ X1 @ X2 )
=> ( cLIKES @ cLYLE @ X1 ) ) )
=> ? [X3: $i] :
! [X4: $i] : ( cLIKES @ X3 @ X4 ) ),
file('/export/starexec/sandbox2/tmp/tmp.JvHxEm4RXA/DTF2THF_22712.p',cTHM68A) ).
thf(f12,plain,
! [X2: $i,X3: $i] :
( ( $true
!= ( cLIKES @ X2 @ X3 ) )
| ( $true
= ( cLIKES @ cLYLE @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f13,plain,
! [X0: $i] :
( $true
!= ( cLIKES @ X0 @ ( sK0 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : PUZ088^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n031.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 11:35:03 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.27/0.46 ---- Original DTF file ---
% 0.27/0.46 thf(spec,logic,$$dhol).
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 % File : PUZ088^5 : TPTP v9.2.1. Released v4.0.0.
% 0.27/0.46 % Domain : Puzzles
% 0.27/0.46 % Problem : TPS problem THM68
% 0.27/0.46 % Version : Especial.
% 0.27/0.46 % English : If everyone likes Bruce and Lyle likes everyone who likes someone
% 0.27/0.46 % then someone likes everyone.
% 0.27/0.46
% 0.27/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.27/0.46 % Source : [Bro09]
% 0.27/0.46 % Names : tps_0122 [Bro09]
% 0.27/0.46 % : tps_0220 [Bro09]
% 0.27/0.46 % : tps_0223 [Bro09]
% 0.27/0.46 % : THM68 [TPS]
% 0.27/0.46 % : THM68A [TPS]
% 0.27/0.46 % : THM68B [TPS]
% 0.27/0.46 % : THM102 [TPS]
% 0.27/0.46
% 0.27/0.46 % Status : Theorem
% 0.27/0.46 % Rating : 0.00 v6.1.0, 0.17 v6.0.0, 0.00 v4.0.0
% 0.27/0.46 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.27/0.46 % Number of atoms : 4 ( 0 equ; 0 cnn)
% 0.27/0.46 % Maximal formula atoms : 4 ( 4 avg)
% 0.27/0.46 % Number of connectives : 11 ( 0 ~; 0 |; 1 &; 8 @)
% 0.27/0.46 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.27/0.46 % Maximal formula depth : 8 ( 8 avg)
% 0.27/0.46 % Number of types : 2 ( 0 usr)
% 0.27/0.46 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.27/0.46 % Number of symbols : 3 ( 3 usr; 2 con; 0-2 aty)
% 0.27/0.46 % Number of variables : 5 ( 0 ^; 3 !; 2 ?; 5 :)
% 0.27/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.27/0.46
% 0.27/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.27/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.27/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.27/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 thf(cLIKES,type,
% 0.27/0.46 cLIKES: $i > $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(cLYLE,type,
% 0.27/0.46 cLYLE: $i ).
% 0.27/0.46
% 0.27/0.46 thf(cBRUCE,type,
% 0.27/0.46 cBRUCE: $i ).
% 0.27/0.46
% 0.27/0.46 thf(cTHM68A,conjecture,
% 0.27/0.46 ( ( ! [X: $i] : ( cLIKES @ X @ cBRUCE )
% 0.27/0.46 & ! [Y: $i] :
% 0.27/0.46 ( ? [Z: $i] : ( cLIKES @ Y @ Z )
% 0.27/0.46 => ( cLIKES @ cLYLE @ Y ) ) )
% 0.27/0.46 => ? [U: $i] :
% 0.27/0.46 ! [V: $i] : ( cLIKES @ U @ V ) ) ).
% 0.27/0.46
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 ------------------------
% 1.48/1.24 ---- Embedded in THF ---
% 1.48/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.24 %%% Generated on Tue Feb 24 11:35:04 EST 2026
% 1.48/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.24 %%% Logic specification used:
% 1.48/1.24 %%% thf(spec, logic, $$dhol).
% 1.48/1.24
% 1.48/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.JvHxEm4RXA/DTF2DTF22712.p
% See solution above
% 1.48/1.24 ------------------------
% 1.48/1.25 ---- Cleaned THF ---
% 1.48/1.25 thf(cLIKES,type,
% 1.48/1.25 cLIKES: $i > $i > $o ).
% 1.48/1.25
% 1.48/1.25 thf(cLYLE,type,
% 1.48/1.25 cLYLE: $i ).
% 1.48/1.25
% 1.48/1.25 thf(cBRUCE,type,
% 1.48/1.25 cBRUCE: $i ).
% 1.48/1.25
% 1.48/1.25 thf(cTHM68A,conjecture,
% 1.48/1.25 ( ( ! [X: $i] : ( cLIKES @ X @ cBRUCE )
% 1.48/1.25 & ! [Y: $i] :
% 1.48/1.25 ( ? [Z: $i] : ( cLIKES @ Y @ Z )
% 1.48/1.25 => ( cLIKES @ cLYLE @ Y ) ) )
% 1.48/1.25 => ? [U: $i] :
% 1.48/1.25 ! [V: $i] : ( cLIKES @ U @ V ) ) ).
% 1.48/1.25 ------------------------
% 1.48/1.27 % (22979)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_22712 for (2999ds/2Mi)
% 1.48/1.27 % (22978)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_22712 for (2999ds/27Mi)
% 1.48/1.27 % (22979)First to succeed.
% 1.48/1.27 % (22978)Also succeeded, but the first one will report.
% 1.48/1.27 % (22979)Refutation found. Thanks to Tanya!
% 1.48/1.27 % SZS status Theorem for DTF2THF_22712
% 1.48/1.27 % SZS output start Proof for DTF2THF_22712
% 1.48/1.27 thf(func_def_0, type, cLIKES: $i > $i > $o).
% 1.48/1.27 thf(func_def_6, type, sK0: $i > $i).
% 1.48/1.27 thf(f19,plain,(
% 1.48/1.27 $false),
% 1.48/1.27 inference(trivial_inequality_removal,[status(thm)],[f16])).
% 1.48/1.27 thf(f16,plain,(
% 1.48/1.27 ($true != $true)),
% 1.48/1.27 inference(superposition,[status(thm)],[f13,f15])).
% 1.48/1.27 thf(f15,plain,(
% 1.48/1.27 ( ! [X0 : $i] : (((cLIKES @ cLYLE @ X0) = $true)) )),
% 1.48/1.27 inference(trivial_inequality_removal,[status(thm)],[f14])).
% 1.48/1.27 thf(f14,plain,(
% 1.48/1.27 ( ! [X0 : $i] : (((cLIKES @ cLYLE @ X0) = $true) | ($true != $true)) )),
% 1.48/1.27 inference(superposition,[status(thm)],[f12,f11])).
% 1.48/1.27 thf(f11,plain,(
% 1.48/1.27 ( ! [X4 : $i] : (($true = (cLIKES @ X4 @ cBRUCE))) )),
% 1.48/1.27 inference(cnf_transformation,[status(thm)],[f10])).
% 1.48/1.27 thf(f10,plain,(
% 1.48/1.27 ! [X0 : $i] : ($true != (cLIKES @ X0 @ (sK0 @ X0))) & ! [X2 : $i] : (! [X3 : $i] : ($true != (cLIKES @ X2 @ X3)) | ($true = (cLIKES @ cLYLE @ X2))) & ! [X4 : $i] : ($true = (cLIKES @ X4 @ cBRUCE))),
% 1.48/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f8,f9])).
% 1.48/1.27 thf(f9,plain,(
% 1.48/1.27 ! [X0 : $i] : (? [X1 : $i] : ($true != (cLIKES @ X0 @ X1)) => ($true != (cLIKES @ X0 @ (sK0 @ X0))))),
% 1.48/1.27 introduced(definition,[],[choice_axiom])).
% 1.48/1.27 thf(f8,plain,(
% 1.48/1.27 ! [X0 : $i] : ? [X1 : $i] : ($true != (cLIKES @ X0 @ X1)) & ! [X2 : $i] : (! [X3 : $i] : ($true != (cLIKES @ X2 @ X3)) | ($true = (cLIKES @ cLYLE @ X2))) & ! [X4 : $i] : ($true = (cLIKES @ X4 @ cBRUCE))),
% 1.48/1.27 inference(rectify,[status(thm)],[f7])).
% 1.48/1.27 thf(f7,plain,(
% 1.48/1.27 ! [X3 : $i] : ? [X4 : $i] : ((cLIKES @ X3 @ X4) != $true) & ! [X1 : $i] : (! [X2 : $i] : ((cLIKES @ X1 @ X2) != $true) | ((cLIKES @ cLYLE @ X1) = $true)) & ! [X0 : $i] : ((cLIKES @ X0 @ cBRUCE) = $true)),
% 1.48/1.27 inference(flattening,[status(thm)],[f6])).
% 1.48/1.27 thf(f6,plain,(
% 1.48/1.27 ! [X3 : $i] : ? [X4 : $i] : ((cLIKES @ X3 @ X4) != $true) & (! [X0 : $i] : ((cLIKES @ X0 @ cBRUCE) = $true) & ! [X1 : $i] : (! [X2 : $i] : ((cLIKES @ X1 @ X2) != $true) | ((cLIKES @ cLYLE @ X1) = $true)))),
% 1.48/1.27 inference(ennf_transformation,[status(thm)],[f5])).
% 1.48/1.27 thf(f5,plain,(
% 1.48/1.27 ~((! [X0 : $i] : ((cLIKES @ X0 @ cBRUCE) = $true) & ! [X1 : $i] : (? [X2 : $i] : ((cLIKES @ X1 @ X2) = $true) => ((cLIKES @ cLYLE @ X1) = $true))) => ? [X3 : $i] : ! [X4 : $i] : ((cLIKES @ X3 @ X4) = $true))),
% 1.48/1.27 inference(fool_elimination,[status(thm)],[f4])).
% 1.48/1.27 thf(f4,plain,(
% 1.48/1.27 ~((! [X0 : $i] : (cLIKES @ X0 @ cBRUCE) & ! [X1 : $i] : (? [X2 : $i] : (cLIKES @ X1 @ X2) => (cLIKES @ cLYLE @ X1))) => ? [X3 : $i] : ! [X4 : $i] : (cLIKES @ X3 @ X4))),
% 1.48/1.27 inference(rectify,[status(thm)],[f2])).
% 1.48/1.27 thf(f2,negated_conjecture,(
% 1.48/1.27 ~((! [X0 : $i] : (cLIKES @ X0 @ cBRUCE) & ! [X1 : $i] : (? [X2 : $i] : (cLIKES @ X1 @ X2) => (cLIKES @ cLYLE @ X1))) => ? [X3 : $i] : ! [X4 : $i] : (cLIKES @ X3 @ X4))),
% 1.48/1.27 inference(negated_conjecture,[status(cth)],[f1])).
% 1.48/1.27 thf(f1,conjecture,(
% 1.48/1.27 (! [X0 : $i] : (cLIKES @ X0 @ cBRUCE) & ! [X1 : $i] : (? [X2 : $i] : (cLIKES @ X1 @ X2) => (cLIKES @ cLYLE @ X1))) => ? [X3 : $i] : ! [X4 : $i] : (cLIKES @ X3 @ X4)),
% 1.48/1.27 file('/export/starexec/sandbox2/tmp/tmp.JvHxEm4RXA/DTF2THF_22712.p',cTHM68A)).
% 1.48/1.27 thf(f12,plain,(
% 1.48/1.27 ( ! [X2 : $i,X3 : $i] : (($true != (cLIKES @ X2 @ X3)) | ($true = (cLIKES @ cLYLE @ X2))) )),
% 1.48/1.27 inference(cnf_transformation,[status(thm)],[f10])).
% 1.48/1.27 thf(f13,plain,(
% 1.48/1.27 ( ! [X0 : $i] : (($true != (cLIKES @ X0 @ (sK0 @ X0)))) )),
% 1.48/1.27 inference(cnf_transformation,[status(thm)],[f10])).
% 1.48/1.27 % SZS output end Proof for DTF2THF_22712
% 1.48/1.27 % (22979)------------------------------
% 1.48/1.27 % (22979)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.27 % (22979)Termination reason: Refutation
% 1.48/1.27
% 1.48/1.27 % (22979)Memory used [KB]: 5500
% 1.48/1.27 % (22979)Time elapsed: 0.003 s
% 1.48/1.27 % (22979)Instructions burned: 1 (million)
% 1.48/1.27 % (22979)------------------------------
% 1.48/1.27 % (22979)------------------------------
% 1.48/1.27 % (22975)Success in time 0.013 s
%------------------------------------------------------------------------------