%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : PUZ137^1 : TPTP v9.2.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n005.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 09:28:35 AM UTC 2026
% Result : Theorem 1.50s 1.29s
% Output : Refutation 1.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 62 ( 8 unt; 0 typ; 5 def)
% Number of atoms : 329 ( 69 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 262 ( 74 ~; 63 |; 0 &; 95 @)
% ( 5 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 11 usr; 12 con; 0-2 aty)
% ( 8 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 25 ( 11 ^; 12 !; 2 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
says: $i > $o > $o ).
thf(func_def_12,type,
ph2:
!>[X0: $tType] : X0 ).
thf(f110,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f34,f43,f48,f56,f92,f109]) ).
thf(f109,plain,
( spl1_3
| ~ spl1_4
| ~ spl1_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f108]) ).
thf(f108,plain,
( $false
| spl1_3
| ~ spl1_4
| ~ spl1_5 ),
inference(trivial_inequality_removal,[status(thm)],[f105]) ).
thf(f105,plain,
( ( $true = $false )
| spl1_3
| ~ spl1_4
| ~ spl1_5 ),
inference(superposition,[status(thm)],[f42,f100]) ).
thf(f100,plain,
( ( $false = sK3 )
| spl1_3
| ~ spl1_5 ),
inference(subsumption_resolution,[status(thm)],[f99,f37]) ).
thf(f37,plain,
( ( sK0 != $false )
| spl1_3 ),
inference(avatar_component_clause,[status(thm)],[f36]) ).
thf(f36,definition,
( spl1_3
<=> ( sK0 = $false ) ),
introduced(definition,[new_symbols(naming,[spl1_3])],[avatar_definition]) ).
thf(f99,plain,
( ( $false = sK3 )
| ( sK0 = $false )
| ~ spl1_5 ),
inference(binary_proxy_clausification,[status(thm)],[f97]) ).
thf(f97,plain,
( ( sK0 != sK3 )
| ~ spl1_5 ),
inference(trivial_inequality_removal,[status(thm)],[f96]) ).
thf(f96,plain,
( ( sK0 != sK3 )
| ( $true != $true )
| ~ spl1_5 ),
inference(constrained_superposition,[status(thm)],[f13,f47]) ).
thf(f47,plain,
( ( $true
= ( says @ peter @ sK3 ) )
| ~ spl1_5 ),
inference(avatar_component_clause,[status(thm)],[f45]) ).
thf(f45,definition,
( spl1_5
<=> ( $true
= ( says @ peter @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_5])],[avatar_definition]) ).
thf(f13,plain,
( $true
!= ( says @ peter @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( $true
!= ( says @ peter @ sK0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f9,f10]) ).
thf(f10,plain,
( ? [X0: $o] :
( ( says @ peter @ X0 )
!= $true )
=> ( $true
!= ( says @ peter @ sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
? [X0: $o] :
( ( says @ peter @ X0 )
!= $true ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: $o] :
( ( says @ peter @ X0 )
= $true ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: $o] : ( says @ peter @ X0 ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ! [X0: $o] : ( says @ peter @ X0 ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
! [X0: $o] : ( says @ peter @ X0 ),
file('/export/starexec/sandbox/tmp/tmp.bzubKaTsd8/DTF2THF_2907.p',thm) ).
thf(f42,plain,
( ( $true = sK3 )
| ~ spl1_4 ),
inference(avatar_component_clause,[status(thm)],[f40]) ).
thf(f40,definition,
( spl1_4
<=> ( $true = sK3 ) ),
introduced(definition,[new_symbols(naming,[spl1_4])],[avatar_definition]) ).
thf(f92,plain,
( ~ spl1_1
| ~ spl1_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f91]) ).
thf(f91,plain,
( $false
| ~ spl1_1
| ~ spl1_3 ),
inference(subsumption_resolution,[status(thm)],[f85,f90]) ).
thf(f90,plain,
( ( sK4 = $false )
| ~ spl1_1 ),
inference(trivial_inequality_removal,[status(thm)],[f81]) ).
thf(f81,plain,
( ( sK4 = $false )
| ( $true = $false )
| ~ spl1_1 ),
inference(superposition,[status(thm)],[f72,f29]) ).
thf(f29,plain,
( ! [X1: $o] :
( ( ( says @ peter @ X1 )
= $false )
| ( $false = X1 ) )
| ~ spl1_1 ),
inference(avatar_component_clause,[status(thm)],[f28]) ).
thf(f28,definition,
( spl1_1
<=> ! [X1: $o] :
( ( ( says @ peter @ X1 )
= $false )
| ( $false = X1 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition]) ).
thf(f72,plain,
( ( $true
= ( says @ peter @ sK4 ) )
| ~ spl1_1 ),
inference(binary_proxy_clausification,[status(thm)],[f70]) ).
thf(f70,plain,
( ( ( ( says @ peter @ sK4 )
=> ~ sK4 )
= $false )
| ~ spl1_1 ),
inference(beta_eta_normalization,[status(thm)],[f69]) ).
thf(f69,plain,
( ( ( ^ [Y0: $o] :
( ( says @ peter @ Y0 )
=> ~ Y0 )
@ sK4 )
= $false )
| ~ spl1_1 ),
inference(sigma_clausification,[status(thm)],[f68]) ).
thf(f68,plain,
( ( $false
= ( !! @ $o
@ ^ [Y0: $o] :
( ( says @ peter @ Y0 )
=> ~ Y0 ) ) )
| ~ spl1_1 ),
inference(trivial_inequality_removal,[status(thm)],[f64]) ).
thf(f64,plain,
( ( $false
= ( !! @ $o
@ ^ [Y0: $o] :
( ( says @ peter @ Y0 )
=> ~ Y0 ) ) )
| ( $true = $false )
| ~ spl1_1 ),
inference(superposition,[status(thm)],[f29,f12]) ).
thf(f12,plain,
( $true
= ( says @ peter
@ ( !! @ $o
@ ^ [Y0: $o] :
( ( says @ peter @ Y0 )
=> ~ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( $true
= ( says @ peter
@ ( !! @ $o
@ ^ [Y0: $o] :
( ( says @ peter @ Y0 )
=> ~ Y0 ) ) ) ),
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.bzubKaTsd8/DTF2THF_2907.p',ax1) ).
thf(f85,plain,
( ( sK4 != $false )
| ~ spl1_1
| ~ spl1_3 ),
inference(trivial_inequality_removal,[status(thm)],[f82]) ).
thf(f82,plain,
( ( $true != $true )
| ( sK4 != $false )
| ~ spl1_1
| ~ spl1_3 ),
inference(constrained_superposition,[status(thm)],[f52,f72]) ).
thf(f52,plain,
( ( $true
!= ( says @ peter @ $false ) )
| ~ spl1_3 ),
inference(superposition,[status(thm)],[f13,f38]) ).
thf(f38,plain,
( ( sK0 = $false )
| ~ spl1_3 ),
inference(avatar_component_clause,[status(thm)],[f36]) ).
thf(f56,plain,
( ~ spl1_2
| ~ spl1_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f55]) ).
thf(f55,plain,
( $false
| ~ spl1_2
| ~ spl1_3 ),
inference(trivial_inequality_removal,[status(thm)],[f50]) ).
thf(f50,plain,
( ( $true = $false )
| ~ spl1_2
| ~ spl1_3 ),
inference(superposition,[status(thm)],[f38,f33]) ).
thf(f33,plain,
( ( $true = sK0 )
| ~ spl1_2 ),
inference(avatar_component_clause,[status(thm)],[f31]) ).
thf(f31,definition,
( spl1_2
<=> ( $true = sK0 ) ),
introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition]) ).
thf(f48,plain,
( spl1_5
| spl1_3 ),
inference(avatar_split_clause,[status(thm)],[f21,f36,f45]) ).
thf(f21,plain,
( ( $true
= ( says @ peter @ sK3 ) )
| ( sK0 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ( ( says @ peter @ sK3 )
=> ~ sK3 )
= $false )
| ( sK0 = $false ) ),
inference(beta_eta_normalization,[status(thm)],[f18]) ).
thf(f18,plain,
( ( sK0 = $false )
| ( $false
= ( ^ [Y0: $o] :
( ( says @ peter @ Y0 )
=> ~ Y0 )
@ sK3 ) ) ),
inference(sigma_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( ( sK0 = $false )
| ( $false
= ( !! @ $o
@ ^ [Y0: $o] :
( ( says @ peter @ Y0 )
=> ~ Y0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( sK0
!= ( !! @ $o
@ ^ [Y0: $o] :
( ( says @ peter @ Y0 )
=> ~ Y0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f14]) ).
thf(f14,plain,
( ( sK0
!= ( !! @ $o
@ ^ [Y0: $o] :
( ( says @ peter @ Y0 )
=> ~ Y0 ) ) )
| ( $true != $true ) ),
inference(constrained_superposition,[status(thm)],[f13,f12]) ).
thf(f43,plain,
( spl1_3
| spl1_4 ),
inference(avatar_split_clause,[status(thm)],[f22,f40,f36]) ).
thf(f22,plain,
( ( $true = sK3 )
| ( sK0 = $false ) ),
inference(not_proxy_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
( ( sK0 = $false )
| ( $false = ( ~ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f19]) ).
thf(f34,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[status(thm)],[f26,f31,f28]) ).
thf(f26,plain,
! [X1: $o] :
( ( $true = sK0 )
| ( ( says @ peter @ X1 )
= $false )
| ( $false = X1 ) ),
inference(not_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
! [X1: $o] :
( ( $true = ( ~ X1 ) )
| ( ( says @ peter @ X1 )
= $false )
| ( $true = sK0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
! [X1: $o] :
( ( $true = sK0 )
| ( $true
= ( ( says @ peter @ X1 )
=> ~ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f23]) ).
thf(f23,plain,
! [X1: $o] :
( ( $true
= ( ^ [Y0: $o] :
( ( says @ peter @ Y0 )
=> ~ Y0 )
@ X1 ) )
| ( $true = sK0 ) ),
inference(pi_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
( ( $true
= ( !! @ $o
@ ^ [Y0: $o] :
( ( says @ peter @ Y0 )
=> ~ Y0 ) ) )
| ( $true = sK0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : PUZ137^1 : TPTP v9.2.1. Released v5.3.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n005.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 11:34:14 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
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.46 thf(spec,logic,$$dhol).
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % File : PUZ137^1 : TPTP v9.2.1. Released v5.3.0.
% 0.31/0.46 % Domain : Puzzles
% 0.31/0.46 % Problem : Peter the liar says everything
% 0.31/0.46 % Version : Especial.
% 0.31/0.46 % English : Peter says that everything he says is false. Show that Peter says
% 0.31/0.46 % everything.
% 0.31/0.46
% 0.31/0.46 % Refs : [Bro11] Brown (2011), Email to G. Sutcliffe
% 0.31/0.46 % Source : [Bro11]
% 0.31/0.46 % Names :
% 0.31/0.46
% 0.31/0.46 % Status : Theorem
% 0.31/0.46 % Rating : 0.17 v9.1.0, 0.12 v9.0.0, 0.17 v8.2.0, 0.18 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 v6.1.0, 0.33 v5.5.0, 0.40 v5.4.0, 0.25 v5.3.0
% 0.31/0.46 % Syntax : Number of formulae : 4 ( 1 unt; 2 typ; 0 def)
% 0.31/0.46 % Number of atoms : 3 ( 0 equ; 0 cnn)
% 0.31/0.46 % Maximal formula atoms : 2 ( 1 avg)
% 0.31/0.46 % Number of connectives : 8 ( 1 ~; 0 |; 0 &; 6 @)
% 0.31/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.31/0.46 % Maximal formula depth : 6 ( 5 avg)
% 0.31/0.46 % Number of types : 2 ( 0 usr)
% 0.31/0.46 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.31/0.46 % Number of symbols : 2 ( 2 usr; 1 con; 0-2 aty)
% 0.31/0.46 % Number of variables : 2 ( 0 ^; 2 !; 0 ?; 2 :)
% 0.31/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.31/0.46
% 0.31/0.46 % Comments : This is PUZ082^1 with a different conjecture. The idea of using
% 0.31/0.46 % truth values ($o) to interpret statements seems to go back to
% 0.31/0.46 % Frege. One criticism of this idea is that it can lead to
% 0.31/0.46 % unexpected consequences, often due to extensionality. In addition
% 0.31/0.46 % to being a theorem of extensional simple type theory, it's also
% 0.31/0.46 % an example of why assigning a type ($i > $o > $o) to a relation
% 0.31/0.46 % like 'says' may be dangerous.
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 %----Signature
% 0.31/0.46 thf(peter,type,
% 0.31/0.46 peter: $i ).
% 0.31/0.46
% 0.31/0.46 thf(says,type,
% 0.31/0.46 says: $i > $o > $o ).
% 0.31/0.46
% 0.31/0.46 %----Axioms
% 0.31/0.46 thf(ax1,axiom,
% 0.31/0.46 ( says @ peter
% 0.31/0.46 @ ! [X: $o] :
% 0.31/0.46 ( ( says @ peter @ X )
% 0.31/0.46 => ~ X ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(thm,conjecture,
% 0.31/0.46 ! [X: $o] : ( says @ peter @ X ) ).
% 0.31/0.46
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 ------------------------
% 1.50/1.25 ---- Embedded in THF ---
% 1.50/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.25 %%% Generated on Tue Feb 24 11:34:15 EST 2026
% 1.50/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.25 %%% Logic specification used:
% 1.50/1.25 %%% thf(spec, logic, $$dhol).
% 1.50/1.25
% 1.50/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.bzubKaTsd8/DTF2DTF2907.p
% See solution above
% 1.50/1.25 ------------------------
% 1.50/1.26 ---- Cleaned THF ---
% 1.50/1.26 thf(peter,type,
% 1.50/1.26 peter: $i ).
% 1.50/1.26
% 1.50/1.26 thf(says,type,
% 1.50/1.26 says: $i > $o > $o ).
% 1.50/1.26
% 1.50/1.26 thf(ax1,axiom,
% 1.50/1.26 ( says @ peter
% 1.50/1.26 @ ! [X: $o] :
% 1.50/1.26 ( ( says @ peter @ X )
% 1.50/1.26 => ~ X ) ) ).
% 1.50/1.26
% 1.50/1.26 thf(thm,conjecture,
% 1.50/1.26 ! [X: $o] : ( says @ peter @ X ) ).
% 1.50/1.26 ------------------------
% 1.50/1.28 % (3010)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_2907 for (3000ds/2Mi)
% 1.50/1.28 % (3011)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_2907 for (3000ds/275Mi)
% 1.50/1.28 % (3010)Refutation not found, incomplete strategy
% 1.50/1.28 % (3010)------------------------------
% 1.50/1.28 % (3010)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.28 % (3010)Termination reason: Refutation not found, incomplete strategy
% 1.50/1.28
% 1.50/1.28
% 1.50/1.28 % (3010)Memory used [KB]: 5500
% 1.50/1.28 % (3010)Time elapsed: 0.002 s
% 1.50/1.28 % (3010)Instructions burned: 1 (million)
% 1.50/1.28 % (3011)Refutation not found, incomplete strategy
% 1.50/1.28 % (3011)------------------------------
% 1.50/1.28 % (3011)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.28 % (3011)Termination reason: Refutation not found, incomplete strategy
% 1.50/1.28
% 1.50/1.28
% 1.50/1.28 % (3011)Memory used [KB]: 5373
% 1.50/1.28 % (3011)Time elapsed: 0.002 s
% 1.50/1.28 % (3011)Instructions burned: 1 (million)
% 1.50/1.28 % (3011)------------------------------
% 1.50/1.28 % (3011)------------------------------
% 1.50/1.28 % (3010)------------------------------
% 1.50/1.28 % (3010)------------------------------
% 1.50/1.28 % (3008)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_2907 for (3000ds/27Mi)
% 1.50/1.28 % (3006)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_2907 for (3000ds/183Mi)
% 1.50/1.28 % (3008)Refutation not found, incomplete strategy
% 1.50/1.28 % (3008)------------------------------
% 1.50/1.28 % (3008)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.28 % (3008)Termination reason: Refutation not found, incomplete strategy
% 1.50/1.28
% 1.50/1.28
% 1.50/1.28 % (3008)Memory used [KB]: 5500
% 1.50/1.28 % (3008)Time elapsed: 0.002 s
% 1.50/1.28 % (3009)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_2907 for (3000ds/2Mi)
% 1.50/1.28 % (3008)Instructions burned: 1 (million)
% 1.50/1.28 % (3008)------------------------------
% 1.50/1.28 % (3008)------------------------------
% 1.50/1.28 % (3007)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_2907 for (3000ds/4Mi)
% 1.50/1.29 % (3009)Refutation not found, incomplete strategy
% 1.50/1.29 % (3009)------------------------------
% 1.50/1.29 % (3009)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.29 % (3009)Termination reason: Refutation not found, incomplete strategy
% 1.50/1.29
% 1.50/1.29
% 1.50/1.29 % (3009)Memory used [KB]: 5500
% 1.50/1.29 % (3009)Time elapsed: 0.003 s
% 1.50/1.29 % (3009)Instructions burned: 1 (million)
% 1.50/1.29 % (3009)------------------------------
% 1.50/1.29 % (3009)------------------------------
% 1.50/1.29 % (3007)Refutation not found, incomplete strategy
% 1.50/1.29 % (3007)------------------------------
% 1.50/1.29 % (3007)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.29 % (3007)Termination reason: Refutation not found, incomplete strategy
% 1.50/1.29
% 1.50/1.29
% 1.50/1.29 % (3007)Memory used [KB]: 5500
% 1.50/1.29 % (3007)Time elapsed: 0.005 s
% 1.50/1.29 % (3007)Instructions burned: 3 (million)
% 1.50/1.29 % (3007)------------------------------
% 1.50/1.29 % (3007)------------------------------
% 1.50/1.29 % (3006)First to succeed.
% 1.50/1.29 % (3013)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_2907 for (2999ds/3Mi)
% 1.50/1.29 % (3013)Refutation not found, incomplete strategy
% 1.50/1.29 % (3013)------------------------------
% 1.50/1.29 % (3013)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.29 % (3013)Termination reason: Refutation not found, incomplete strategy
% 1.50/1.29
% 1.50/1.29
% 1.50/1.29 % (3013)Memory used [KB]: 5500
% 1.50/1.29 % (3013)Time elapsed: 0.002 s
% 1.50/1.29 % (3013)Instructions burned: 1 (million)
% 1.50/1.29 % (3013)------------------------------
% 1.50/1.29 % (3013)------------------------------
% 1.50/1.29 % (3006)Refutation found. Thanks to Tanya!
% 1.50/1.29 % SZS status Theorem for DTF2THF_2907
% 1.50/1.29 % SZS output start Proof for DTF2THF_2907
% 1.50/1.29 thf(func_def_1, type, says: $i > $o > $o).
% 1.50/1.29 thf(func_def_12, type, ph2: !>[X0: $tType]:(X0)).
% 1.50/1.29 thf(f110,plain,(
% 1.50/1.29 $false),
% 1.50/1.29 inference(avatar_sat_refutation,[status(thm)],[f34,f43,f48,f56,f92,f109])).
% 1.50/1.29 thf(f109,plain,(
% 1.50/1.29 spl1_3 | ~spl1_4 | ~spl1_5),
% 1.50/1.29 inference(avatar_contradiction_clause,[status(thm)],[f108])).
% 1.50/1.29 thf(f108,plain,(
% 1.50/1.29 $false | (spl1_3 | ~spl1_4 | ~spl1_5)),
% 1.50/1.29 inference(trivial_inequality_removal,[status(thm)],[f105])).
% 1.50/1.29 thf(f105,plain,(
% 1.50/1.29 ($true = $false) | (spl1_3 | ~spl1_4 | ~spl1_5)),
% 1.50/1.29 inference(superposition,[status(thm)],[f42,f100])).
% 1.50/1.29 thf(f100,plain,(
% 1.50/1.29 ($false = sK3) | (spl1_3 | ~spl1_5)),
% 1.50/1.29 inference(subsumption_resolution,[status(thm)],[f99,f37])).
% 1.50/1.29 thf(f37,plain,(
% 1.50/1.29 (sK0 != $false) | spl1_3),
% 1.50/1.29 inference(avatar_component_clause,[status(thm)],[f36])).
% 1.50/1.29 thf(f36,definition,(
% 1.50/1.29 spl1_3 <=> (sK0 = $false)),
% 1.50/1.29 introduced(definition,[new_symbols(naming,[spl1_3])],[avatar_definition])).
% 1.50/1.29 thf(f99,plain,(
% 1.50/1.29 ($false = sK3) | (sK0 = $false) | ~spl1_5),
% 1.50/1.29 inference(binary_proxy_clausification,[status(thm)],[f97])).
% 1.50/1.29 thf(f97,plain,(
% 1.50/1.29 (sK0 != sK3) | ~spl1_5),
% 1.50/1.29 inference(trivial_inequality_removal,[status(thm)],[f96])).
% 1.50/1.29 thf(f96,plain,(
% 1.50/1.29 (sK0 != sK3) | ($true != $true) | ~spl1_5),
% 1.50/1.29 inference(constrained_superposition,[status(thm)],[f13,f47])).
% 1.50/1.29 thf(f47,plain,(
% 1.50/1.29 ($true = (says @ peter @ sK3)) | ~spl1_5),
% 1.50/1.29 inference(avatar_component_clause,[status(thm)],[f45])).
% 1.50/1.29 thf(f45,definition,(
% 1.50/1.29 spl1_5 <=> ($true = (says @ peter @ sK3))),
% 1.50/1.29 introduced(definition,[new_symbols(naming,[spl1_5])],[avatar_definition])).
% 1.50/1.29 thf(f13,plain,(
% 1.50/1.29 ($true != (says @ peter @ sK0))),
% 1.50/1.29 inference(cnf_transformation,[status(thm)],[f11])).
% 1.50/1.29 thf(f11,plain,(
% 1.50/1.29 ($true != (says @ peter @ sK0))),
% 1.50/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f9,f10])).
% 1.50/1.29 thf(f10,plain,(
% 1.50/1.29 ? [X0 : $o] : ((says @ peter @ X0) != $true) => ($true != (says @ peter @ sK0))),
% 1.50/1.29 introduced(definition,[],[choice_axiom])).
% 1.50/1.29 thf(f9,plain,(
% 1.50/1.29 ? [X0 : $o] : ((says @ peter @ X0) != $true)),
% 1.50/1.29 inference(ennf_transformation,[status(thm)],[f6])).
% 1.50/1.29 thf(f6,plain,(
% 1.50/1.29 ~! [X0 : $o] : ((says @ peter @ X0) = $true)),
% 1.50/1.29 inference(fool_elimination,[status(thm)],[f5])).
% 1.50/1.29 thf(f5,plain,(
% 1.50/1.29 ~! [X0 : $o] : (says @ peter @ X0)),
% 1.50/1.29 inference(rectify,[status(thm)],[f3])).
% 1.50/1.29 thf(f3,negated_conjecture,(
% 1.50/1.29 ~! [X0 : $o] : (says @ peter @ X0)),
% 1.50/1.29 inference(negated_conjecture,[status(cth)],[f2])).
% 1.50/1.29 thf(f2,conjecture,(
% 1.50/1.29 ! [X0 : $o] : (says @ peter @ X0)),
% 1.50/1.29 file('/export/starexec/sandbox/tmp/tmp.bzubKaTsd8/DTF2THF_2907.p',thm)).
% 1.50/1.29 thf(f42,plain,(
% 1.50/1.29 ($true = sK3) | ~spl1_4),
% 1.50/1.29 inference(avatar_component_clause,[status(thm)],[f40])).
% 1.50/1.29 thf(f40,definition,(
% 1.50/1.29 spl1_4 <=> ($true = sK3)),
% 1.50/1.29 introduced(definition,[new_symbols(naming,[spl1_4])],[avatar_definition])).
% 1.50/1.29 thf(f92,plain,(
% 1.50/1.29 ~spl1_1 | ~spl1_3),
% 1.50/1.29 inference(avatar_contradiction_clause,[status(thm)],[f91])).
% 1.50/1.29 thf(f91,plain,(
% 1.50/1.29 $false | (~spl1_1 | ~spl1_3)),
% 1.50/1.29 inference(subsumption_resolution,[status(thm)],[f85,f90])).
% 1.50/1.29 thf(f90,plain,(
% 1.50/1.29 (sK4 = $false) | ~spl1_1),
% 1.50/1.29 inference(trivial_inequality_removal,[status(thm)],[f81])).
% 1.50/1.29 thf(f81,plain,(
% 1.50/1.29 (sK4 = $false) | ($true = $false) | ~spl1_1),
% 1.50/1.29 inference(superposition,[status(thm)],[f72,f29])).
% 1.50/1.29 thf(f29,plain,(
% 1.50/1.29 ( ! [X1 : $o] : (((says @ peter @ X1) = $false) | ($false = X1)) ) | ~spl1_1),
% 1.50/1.29 inference(avatar_component_clause,[status(thm)],[f28])).
% 1.50/1.29 thf(f28,definition,(
% 1.50/1.29 spl1_1 <=> ! [X1 : $o] : (((says @ peter @ X1) = $false) | ($false = X1))),
% 1.50/1.29 introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition])).
% 1.50/1.29 thf(f72,plain,(
% 1.50/1.29 ($true = (says @ peter @ sK4)) | ~spl1_1),
% 1.50/1.29 inference(binary_proxy_clausification,[status(thm)],[f70])).
% 1.50/1.29 thf(f70,plain,(
% 1.50/1.29 (((says @ peter @ sK4) => (~ sK4)) = $false) | ~spl1_1),
% 1.50/1.29 inference(beta_eta_normalization,[status(thm)],[f69])).
% 1.50/1.29 thf(f69,plain,(
% 1.50/1.29 (((^[Y0 : $o]: ((says @ peter @ Y0) => (~ Y0))) @ sK4) = $false) | ~spl1_1),
% 1.50/1.29 inference(sigma_clausification,[status(thm)],[f68])).
% 1.50/1.29 thf(f68,plain,(
% 1.50/1.29 ($false = (!! @ $o @ (^[Y0 : $o]: ((says @ peter @ Y0) => (~ Y0))))) | ~spl1_1),
% 1.50/1.29 inference(trivial_inequality_removal,[status(thm)],[f64])).
% 1.50/1.29 thf(f64,plain,(
% 1.50/1.29 ($false = (!! @ $o @ (^[Y0 : $o]: ((says @ peter @ Y0) => (~ Y0))))) | ($true = $false) | ~spl1_1),
% 1.50/1.29 inference(superposition,[status(thm)],[f29,f12])).
% 1.50/1.29 thf(f12,plain,(
% 1.50/1.29 ($true = (says @ peter @ (!! @ $o @ (^[Y0 : $o]: ((says @ peter @ Y0) => (~ Y0))))))),
% 1.50/1.29 inference(cnf_transformation,[status(thm)],[f8])).
% 1.50/1.29 thf(f8,plain,(
% 1.50/1.29 ($true = (says @ peter @ (!! @ $o @ (^[Y0 : $o]: ((says @ peter @ Y0) => (~ Y0))))))),
% 1.50/1.29 inference(fool_elimination,[status(thm)],[f7])).
% 1.50/1.29 thf(f7,plain,(
% 1.50/1.29 (says @ peter @ ! [X0 : $o] : ((says @ peter @ X0) => ~X0))),
% 1.50/1.29 inference(rectify,[status(thm)],[f1])).
% 1.50/1.29 thf(f1,axiom,(
% 1.50/1.29 (says @ peter @ ! [X0 : $o] : ((says @ peter @ X0) => ~X0))),
% 1.50/1.29 file('/export/starexec/sandbox/tmp/tmp.bzubKaTsd8/DTF2THF_2907.p',ax1)).
% 1.50/1.29 thf(f85,plain,(
% 1.50/1.29 (sK4 != $false) | (~spl1_1 | ~spl1_3)),
% 1.50/1.29 inference(trivial_inequality_removal,[status(thm)],[f82])).
% 1.50/1.29 thf(f82,plain,(
% 1.50/1.29 ($true != $true) | (sK4 != $false) | (~spl1_1 | ~spl1_3)),
% 1.50/1.29 inference(constrained_superposition,[status(thm)],[f52,f72])).
% 1.50/1.29 thf(f52,plain,(
% 1.50/1.29 ($true != (says @ peter @ $false)) | ~spl1_3),
% 1.50/1.29 inference(superposition,[status(thm)],[f13,f38])).
% 1.50/1.29 thf(f38,plain,(
% 1.50/1.29 (sK0 = $false) | ~spl1_3),
% 1.50/1.29 inference(avatar_component_clause,[status(thm)],[f36])).
% 1.50/1.29 thf(f56,plain,(
% 1.50/1.29 ~spl1_2 | ~spl1_3),
% 1.50/1.29 inference(avatar_contradiction_clause,[status(thm)],[f55])).
% 1.50/1.29 thf(f55,plain,(
% 1.50/1.29 $false | (~spl1_2 | ~spl1_3)),
% 1.50/1.29 inference(trivial_inequality_removal,[status(thm)],[f50])).
% 1.50/1.29 thf(f50,plain,(
% 1.50/1.29 ($true = $false) | (~spl1_2 | ~spl1_3)),
% 1.50/1.29 inference(superposition,[status(thm)],[f38,f33])).
% 1.50/1.29 thf(f33,plain,(
% 1.50/1.29 ($true = sK0) | ~spl1_2),
% 1.50/1.29 inference(avatar_component_clause,[status(thm)],[f31])).
% 1.50/1.29 thf(f31,definition,(
% 1.50/1.29 spl1_2 <=> ($true = sK0)),
% 1.50/1.29 introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition])).
% 1.50/1.29 thf(f48,plain,(
% 1.50/1.29 spl1_5 | spl1_3),
% 1.50/1.29 inference(avatar_split_clause,[status(thm)],[f21,f36,f45])).
% 1.50/1.29 thf(f21,plain,(
% 1.50/1.29 ($true = (says @ peter @ sK3)) | (sK0 = $false)),
% 1.50/1.29 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.50/1.29 thf(f19,plain,(
% 1.50/1.29 (((says @ peter @ sK3) => (~ sK3)) = $false) | (sK0 = $false)),
% 1.50/1.29 inference(beta_eta_normalization,[status(thm)],[f18])).
% 1.50/1.29 thf(f18,plain,(
% 1.50/1.29 (sK0 = $false) | ($false = ((^[Y0 : $o]: ((says @ peter @ Y0) => (~ Y0))) @ sK3))),
% 1.50/1.29 inference(sigma_clausification,[status(thm)],[f17])).
% 1.50/1.29 thf(f17,plain,(
% 1.50/1.29 (sK0 = $false) | ($false = (!! @ $o @ (^[Y0 : $o]: ((says @ peter @ Y0) => (~ Y0)))))),
% 1.50/1.29 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.50/1.29 thf(f15,plain,(
% 1.50/1.29 (sK0 != (!! @ $o @ (^[Y0 : $o]: ((says @ peter @ Y0) => (~ Y0)))))),
% 1.50/1.29 inference(trivial_inequality_removal,[status(thm)],[f14])).
% 1.50/1.29 thf(f14,plain,(
% 1.50/1.29 (sK0 != (!! @ $o @ (^[Y0 : $o]: ((says @ peter @ Y0) => (~ Y0))))) | ($true != $true)),
% 1.50/1.29 inference(constrained_superposition,[status(thm)],[f13,f12])).
% 1.50/1.29 thf(f43,plain,(
% 1.50/1.29 spl1_3 | spl1_4),
% 1.50/1.29 inference(avatar_split_clause,[status(thm)],[f22,f40,f36])).
% 1.50/1.29 thf(f22,plain,(
% 1.50/1.29 ($true = sK3) | (sK0 = $false)),
% 1.50/1.29 inference(not_proxy_clausification,[status(thm)],[f20])).
% 1.50/1.29 thf(f20,plain,(
% 1.50/1.29 (sK0 = $false) | ($false = (~ sK3))),
% 1.50/1.29 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.50/1.29 thf(f34,plain,(
% 1.50/1.29 spl1_1 | spl1_2),
% 1.50/1.29 inference(avatar_split_clause,[status(thm)],[f26,f31,f28])).
% 1.50/1.29 thf(f26,plain,(
% 1.50/1.29 ( ! [X1 : $o] : (($true = sK0) | ((says @ peter @ X1) = $false) | ($false = X1)) )),
% 1.50/1.29 inference(not_proxy_clausification,[status(thm)],[f25])).
% 1.50/1.29 thf(f25,plain,(
% 1.50/1.29 ( ! [X1 : $o] : (($true = (~ X1)) | ((says @ peter @ X1) = $false) | ($true = sK0)) )),
% 1.50/1.29 inference(binary_proxy_clausification,[status(thm)],[f24])).
% 1.50/1.29 thf(f24,plain,(
% 1.50/1.29 ( ! [X1 : $o] : (($true = sK0) | ($true = ((says @ peter @ X1) => (~ X1)))) )),
% 1.50/1.29 inference(beta_eta_normalization,[status(thm)],[f23])).
% 1.50/1.29 thf(f23,plain,(
% 1.50/1.29 ( ! [X1 : $o] : (($true = ((^[Y0 : $o]: ((says @ peter @ Y0) => (~ Y0))) @ X1)) | ($true = sK0)) )),
% 1.50/1.29 inference(pi_clausification,[status(thm)],[f16])).
% 1.50/1.29 thf(f16,plain,(
% 1.50/1.29 ($true = (!! @ $o @ (^[Y0 : $o]: ((says @ peter @ Y0) => (~ Y0))))) | ($true = sK0)),
% 1.50/1.29 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.50/1.29 % SZS output end Proof for DTF2THF_2907
% 1.50/1.29 % (3006)------------------------------
% 1.50/1.29 % (3006)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.29 % (3006)Termination reason: Refutation
% 1.50/1.29
% 1.50/1.29 % (3006)Memory used [KB]: 5500
% 1.50/1.29 % (3006)Time elapsed: 0.007 s
% 1.50/1.29 % (3006)Instructions burned: 5 (million)
% 1.50/1.29 % (3006)------------------------------
% 1.50/1.29 % (3006)------------------------------
% 1.50/1.29 % (3005)Success in time 0.032 s
%------------------------------------------------------------------------------