%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : PUZ082^1 : TPTP v9.2.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n003.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 09:28:26 AM UTC 2026
% Result : Theorem 1.48s 1.29s
% Output : Refutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 2
% Syntax : Number of formulae : 22 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 102 ( 22 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 104 ( 32 ~; 4 |; 0 &; 51 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 4 usr; 5 con; 0-2 aty)
% ( 4 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 14 ( 5 ^; 9 !; 0 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
says: $i > $o > $o ).
thf(func_def_11,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f24,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f23,f20]) ).
thf(f20,plain,
sK2 = $true,
inference(not_proxy_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
( $false = ( ~ sK2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( $false
= ( ( says @ peter @ sK2 )
=> ~ sK2 ) ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
( $false
= ( ^ [Y0: $o] :
( ( says @ peter @ Y0 )
=> ~ Y0 )
@ sK2 ) ),
inference(sigma_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( ( !! @ $o
@ ^ [Y0: $o] :
( ( says @ peter @ Y0 )
=> ~ Y0 ) )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f14]) ).
thf(f14,plain,
( ( $true != $true )
| ( ( !! @ $o
@ ^ [Y0: $o] :
( ( says @ peter @ Y0 )
=> ~ Y0 ) )
!= $true ) ),
inference(constrained_superposition,[status(thm)],[f13,f12]) ).
thf(f12,plain,
( ( says @ peter
@ ( !! @ $o
@ ^ [Y0: $o] :
( ( says @ peter @ Y0 )
=> ~ Y0 ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( says @ peter
@ ( !! @ $o
@ ^ [Y0: $o] :
( ( says @ peter @ Y0 )
=> ~ Y0 ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( says @ peter
@ ! [X0: $o] :
( ( says @ peter @ X0 )
=> ~ X0 ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( says @ peter
@ ! [X0: $o] :
( ( says @ peter @ X0 )
=> ~ X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.QwT4eFunsn/DTF2THF_21644.p',ax1) ).
thf(f13,plain,
( ( says @ peter @ $true )
!= $true ),
inference(equality_resolution,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $o] :
( ( $true != X0 )
| ( ( says @ peter @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $o] :
( ( $true != X0 )
| ( ( says @ peter @ X0 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $o] :
( ( ( says @ peter @ X0 )
= $true )
=> ( $true != X0 ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
~ ~ ! [X0: $o] :
( ( ( says @ peter @ X0 )
= $true )
=> ( $true != X0 ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
~ ~ ! [X0: $o] :
( ( says @ peter @ X0 )
=> ~ X0 ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ~ ! [X0: $o] :
( ( says @ peter @ X0 )
=> ~ X0 ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
~ ! [X0: $o] :
( ( says @ peter @ X0 )
=> ~ X0 ),
file('/export/starexec/sandbox/tmp/tmp.QwT4eFunsn/DTF2THF_21644.p',thm) ).
thf(f23,plain,
sK2 != $true,
inference(trivial_inequality_removal,[status(thm)],[f22]) ).
thf(f22,plain,
( ( $true != $true )
| ( sK2 != $true ) ),
inference(constrained_superposition,[status(thm)],[f13,f19]) ).
thf(f19,plain,
( ( says @ peter @ sK2 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : PUZ082^1 : TPTP v9.2.1. Released v3.6.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n003.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 11:32:40 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
% 0.27/0.46 ---- Original DTF file ---
% 0.27/0.46 thf(spec,logic,$$dhol).
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 % File : PUZ082^1 : TPTP v9.2.1. Released v3.6.0.
% 0.27/0.46 % Domain : Puzzles
% 0.27/0.46 % Problem : Peter the liar
% 0.27/0.46 % Version : Especial.
% 0.27/0.46 % English : Peter says that everything he says is false. Show that not
% 0.27/0.46 % everything Peter says is false.
% 0.27/0.46
% 0.27/0.46 % Refs : [Ben08] Benzmueller (2008), Email to G. Sutcliffe
% 0.27/0.46 % Source : [Ben08]
% 0.27/0.46 % Names :
% 0.27/0.46
% 0.27/0.46 % Status : Theorem
% 0.27/0.46 % Rating : 0.08 v9.1.0, 0.00 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.00 v5.4.0, 0.25 v5.3.0, 0.50 v5.2.0, 0.25 v4.1.0, 0.33 v3.7.0
% 0.27/0.46 % Syntax : Number of formulae : 4 ( 1 unt; 2 typ; 0 def)
% 0.27/0.46 % Number of atoms : 3 ( 0 equ; 0 cnn)
% 0.27/0.46 % Maximal formula atoms : 2 ( 1 avg)
% 0.27/0.46 % Number of connectives : 11 ( 3 ~; 0 |; 0 &; 6 @)
% 0.27/0.46 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.27/0.46 % Maximal formula depth : 6 ( 6 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 : 2 ( 2 usr; 1 con; 0-2 aty)
% 0.27/0.46 % Number of variables : 2 ( 0 ^; 2 !; 0 ?; 2 :)
% 0.27/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.27/0.46
% 0.27/0.46 % Comments :
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 %----Signature
% 0.27/0.46 thf(peter,type,
% 0.27/0.46 peter: $i ).
% 0.27/0.46
% 0.27/0.46 thf(says,type,
% 0.27/0.46 says: $i > $o > $o ).
% 0.27/0.46
% 0.27/0.46 %----Axioms
% 0.27/0.46 thf(ax1,axiom,
% 0.27/0.46 ( says @ peter
% 0.27/0.46 @ ! [X: $o] :
% 0.27/0.46 ( ( says @ peter @ X )
% 0.27/0.46 => ~ X ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(thm,conjecture,
% 0.27/0.46 ~ ! [X: $o] :
% 0.27/0.46 ( ( says @ peter @ X )
% 0.27/0.46 => ~ X ) ).
% 0.27/0.46
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 ------------------------
% 1.48/1.27 ---- Embedded in THF ---
% 1.48/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.27 %%% Generated on Tue Feb 24 11:32:41 EST 2026
% 1.48/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.27 %%% Logic specification used:
% 1.48/1.27 %%% thf(spec, logic, $$dhol).
% 1.48/1.27
% 1.48/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.QwT4eFunsn/DTF2DTF21644.p
% See solution above
% 1.48/1.27 ------------------------
% 1.48/1.28 ---- Cleaned THF ---
% 1.48/1.28 thf(peter,type,
% 1.48/1.28 peter: $i ).
% 1.48/1.28
% 1.48/1.28 thf(says,type,
% 1.48/1.28 says: $i > $o > $o ).
% 1.48/1.28
% 1.48/1.28 thf(ax1,axiom,
% 1.48/1.28 ( says @ peter
% 1.48/1.28 @ ! [X: $o] :
% 1.48/1.28 ( ( says @ peter @ X )
% 1.48/1.28 => ~ X ) ) ).
% 1.48/1.28
% 1.48/1.28 thf(thm,conjecture,
% 1.48/1.28 ~ ! [X: $o] :
% 1.48/1.28 ( ( says @ peter @ X )
% 1.48/1.28 => ~ X ) ).
% 1.48/1.28 ------------------------
% 1.48/1.29 % (21923)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_21644 for (2999ds/183Mi)
% 1.48/1.29 % (21923)First to succeed.
% 1.48/1.29 % (21924)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_21644 for (2999ds/4Mi)
% 1.48/1.29 % (21923)Refutation found. Thanks to Tanya!
% 1.48/1.29 % SZS status Theorem for DTF2THF_21644
% 1.48/1.29 % SZS output start Proof for DTF2THF_21644
% 1.48/1.29 thf(func_def_1, type, says: $i > $o > $o).
% 1.48/1.29 thf(func_def_11, type, ph1: !>[X0: $tType]:(X0)).
% 1.48/1.29 thf(f24,plain,(
% 1.48/1.29 $false),
% 1.48/1.29 inference(subsumption_resolution,[status(thm)],[f23,f20])).
% 1.48/1.29 thf(f20,plain,(
% 1.48/1.29 (sK2 = $true)),
% 1.48/1.29 inference(not_proxy_clausification,[status(thm)],[f18])).
% 1.48/1.29 thf(f18,plain,(
% 1.48/1.29 ($false = (~ sK2))),
% 1.48/1.29 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.48/1.29 thf(f17,plain,(
% 1.48/1.29 ($false = ((says @ peter @ sK2) => (~ sK2)))),
% 1.48/1.29 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.48/1.29 thf(f16,plain,(
% 1.48/1.29 ($false = ((^[Y0 : $o]: ((says @ peter @ Y0) => (~ Y0))) @ sK2))),
% 1.48/1.29 inference(sigma_clausification,[status(thm)],[f15])).
% 1.48/1.29 thf(f15,plain,(
% 1.48/1.29 ((!! @ $o @ (^[Y0 : $o]: ((says @ peter @ Y0) => (~ Y0)))) != $true)),
% 1.48/1.29 inference(trivial_inequality_removal,[status(thm)],[f14])).
% 1.48/1.29 thf(f14,plain,(
% 1.48/1.29 ($true != $true) | ((!! @ $o @ (^[Y0 : $o]: ((says @ peter @ Y0) => (~ Y0)))) != $true)),
% 1.48/1.29 inference(constrained_superposition,[status(thm)],[f13,f12])).
% 1.48/1.29 thf(f12,plain,(
% 1.48/1.29 ((says @ peter @ (!! @ $o @ (^[Y0 : $o]: ((says @ peter @ Y0) => (~ Y0))))) = $true)),
% 1.48/1.29 inference(cnf_transformation,[status(thm)],[f8])).
% 1.48/1.29 thf(f8,plain,(
% 1.48/1.29 ((says @ peter @ (!! @ $o @ (^[Y0 : $o]: ((says @ peter @ Y0) => (~ Y0))))) = $true)),
% 1.48/1.29 inference(fool_elimination,[status(thm)],[f7])).
% 1.48/1.29 thf(f7,plain,(
% 1.48/1.29 (says @ peter @ ! [X0 : $o] : ((says @ peter @ X0) => ~X0))),
% 1.48/1.29 inference(rectify,[status(thm)],[f1])).
% 1.48/1.29 thf(f1,axiom,(
% 1.48/1.29 (says @ peter @ ! [X0 : $o] : ((says @ peter @ X0) => ~X0))),
% 1.48/1.29 file('/export/starexec/sandbox/tmp/tmp.QwT4eFunsn/DTF2THF_21644.p',ax1)).
% 1.48/1.29 thf(f13,plain,(
% 1.48/1.29 ((says @ peter @ $true) != $true)),
% 1.48/1.29 inference(equality_resolution,[status(thm)],[f11])).
% 1.48/1.29 thf(f11,plain,(
% 1.48/1.29 ( ! [X0 : $o] : (($true != X0) | ((says @ peter @ X0) != $true)) )),
% 1.48/1.29 inference(cnf_transformation,[status(thm)],[f10])).
% 1.48/1.29 thf(f10,plain,(
% 1.48/1.29 ! [X0 : $o] : (($true != X0) | ((says @ peter @ X0) != $true))),
% 1.48/1.29 inference(ennf_transformation,[status(thm)],[f9])).
% 1.48/1.29 thf(f9,plain,(
% 1.48/1.29 ! [X0 : $o] : (((says @ peter @ X0) = $true) => ($true != X0))),
% 1.48/1.29 inference(flattening,[status(thm)],[f6])).
% 1.48/1.29 thf(f6,plain,(
% 1.48/1.29 ~~! [X0 : $o] : (((says @ peter @ X0) = $true) => ~($true = X0))),
% 1.48/1.29 inference(fool_elimination,[status(thm)],[f5])).
% 1.48/1.29 thf(f5,plain,(
% 1.48/1.29 ~~! [X0 : $o] : ((says @ peter @ X0) => ~X0)),
% 1.48/1.29 inference(rectify,[status(thm)],[f3])).
% 1.48/1.29 thf(f3,negated_conjecture,(
% 1.48/1.29 ~~! [X0 : $o] : ((says @ peter @ X0) => ~X0)),
% 1.48/1.29 inference(negated_conjecture,[status(cth)],[f2])).
% 1.48/1.29 thf(f2,conjecture,(
% 1.48/1.29 ~! [X0 : $o] : ((says @ peter @ X0) => ~X0)),
% 1.48/1.29 file('/export/starexec/sandbox/tmp/tmp.QwT4eFunsn/DTF2THF_21644.p',thm)).
% 1.48/1.29 thf(f23,plain,(
% 1.48/1.29 (sK2 != $true)),
% 1.48/1.29 inference(trivial_inequality_removal,[status(thm)],[f22])).
% 1.48/1.29 thf(f22,plain,(
% 1.48/1.29 ($true != $true) | (sK2 != $true)),
% 1.48/1.29 inference(constrained_superposition,[status(thm)],[f13,f19])).
% 1.48/1.29 thf(f19,plain,(
% 1.48/1.29 ((says @ peter @ sK2) = $true)),
% 1.48/1.29 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.48/1.29 % SZS output end Proof for DTF2THF_21644
% 1.48/1.29 % (21923)------------------------------
% 1.48/1.29 % (21923)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.29 % (21923)Termination reason: Refutation
% 1.48/1.29
% 1.48/1.29 % (21923)Memory used [KB]: 5500
% 1.48/1.29 % (21923)Time elapsed: 0.003 s
% 1.48/1.29 % (21923)Instructions burned: 1 (million)
% 1.48/1.29 % (21923)------------------------------
% 1.48/1.29 % (21923)------------------------------
% 1.48/1.29 % (21922)Success in time 0.012 s
%------------------------------------------------------------------------------