%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : PUZ136^1 : TPTP v9.2.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n026.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 1.63s 1.33s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 25 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 84 ( 23 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 83 ( 22 ~; 4 |; 5 &; 52 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 6 con; 0-2 aty)
% Number of variables : 40 ( 6 ^; 19 !; 15 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
parent: $i > $i > $o ).
thf(func_def_10,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f47,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f45,f41]) ).
thf(f41,plain,
! [X0: $i,X1: $i] :
( $true
!= ( parent @ X1 @ X0 ) ),
inference(superposition,[status(thm)],[f26,f20]) ).
thf(f20,plain,
! [X0: $i,X1: $i] : ( X0 = X1 ),
inference(leibniz_equality_elimination,[status(thm)],[f18]) ).
thf(f18,plain,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( $true
= ( X1 @ X0 ) )
| ( $true
!= ( X1 @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: $i,X1: $i > $o,X2: $i] :
( ( $true
!= ( X1 @ X2 ) )
| ( $true
= ( X1 @ X0 ) ) ),
inference(rectify,[status(thm)],[f14]) ).
thf(f14,plain,
! [X1: $i,X0: $i > $o,X2: $i] :
( ( ( X0 @ X2 )
!= $true )
| ( ( X0 @ X1 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
~ ? [X1: $i,X2: $i,X0: $i > $o] :
( ( ( X0 @ X1 )
!= $true )
& ( ( X0 @ X2 )
= $true ) ),
inference(flattening,[status(thm)],[f11]) ).
thf(f11,plain,
~ ? [X0: $i > $o,X1: $i,X2: $i] :
( ( ( X0 @ X2 )
= $true )
& ( ( X0 @ X1 )
!= $true ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ? [X0: $i > $o,X1: $i,X2: $i] :
( ( X0 @ X2 )
& ~ ( X0 @ X1 ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ? [X0: $i > $o,X2: $i,X1: $i] :
( ( X0 @ X1 )
& ~ ( X0 @ X2 ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
? [X0: $i > $o,X2: $i,X1: $i] :
( ( X0 @ X1 )
& ~ ( X0 @ X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.H40ACT4lsK/DTF2THF_6149.p',hotwo) ).
thf(f26,plain,
! [X0: $i] :
( ( parent @ X0 @ horus )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f25]) ).
thf(f25,plain,
! [X0: $i] :
( ( ^ [Y0: $i] :
( parent
@ ( ^ [Y1: $i] : Y1
@ Y0 )
@ ( ^ [Y1: $i] : horus
@ Y0 ) )
@ X0 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f24]) ).
thf(f24,plain,
! [X0: $i] :
( ( ( ^ [Y0: $i] :
( parent
@ ( ^ [Y1: $i] : Y1
@ Y0 )
@ ( ^ [Y1: $i] : horus
@ Y0 ) )
@ X0 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f16,f18]) ).
thf(f16,plain,
( ( parent @ sutekh @ horus )
!= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( parent @ sutekh @ horus )
!= $true ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
( ( parent @ sutekh @ horus )
!= $true ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( parent @ sutekh @ horus ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
~ ( parent @ sutekh @ horus ),
file('/export/starexec/sandbox/tmp/tmp.H40ACT4lsK/DTF2THF_6149.p',ax2) ).
thf(f45,plain,
! [X0: $i,X1: $i] :
( $true
= ( parent @ X1 @ X0 ) ),
inference(superposition,[status(thm)],[f32,f20]) ).
thf(f32,plain,
! [X0: $i] :
( $true
= ( parent @ X0 @ zeus ) ),
inference(superposition,[status(thm)],[f17,f20]) ).
thf(f17,plain,
( ( parent @ kronus @ zeus )
= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ( parent @ kronus @ zeus )
= $true ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
parent @ kronus @ zeus,
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
parent @ kronus @ zeus,
file('/export/starexec/sandbox/tmp/tmp.H40ACT4lsK/DTF2THF_6149.p',ax1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : PUZ136^1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.32 % Computer : n026.cluster.edu
% 0.17/0.32 % Model : x86_64 x86_64
% 0.17/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.32 % Memory : 8042.1875MB
% 0.17/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.32 % CPULimit : 300
% 0.17/0.32 % WCLimit : 300
% 0.17/0.32 % DateTime : Tue Feb 24 11:34:40 EST 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.44 ---- Original DTF file ---
% 0.19/0.44 thf(spec,logic,$$dhol).
% 0.19/0.44 %------------------------------------------------------------------------------
% 0.19/0.44 % File : PUZ136^1 : TPTP v9.2.1. Released v5.2.0.
% 0.19/0.44 % Domain : Puzzles
% 0.19/0.44 % Problem : Under two assumptions there are at least two individuals.
% 0.19/0.44 % Version : Especial.
% 0.19/0.44 % English :
% 0.19/0.44
% 0.19/0.44 % Refs : [Bro11] Brown (2011), Email to Geoff Sutcliffe
% 0.19/0.44 % Source : [Bro11]
% 0.19/0.44 % Names :
% 0.19/0.44
% 0.19/0.44 % Status : Theorem
% 0.19/0.44 % 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, 0.10 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 v5.2.0
% 0.19/0.44 % Syntax : Number of formulae : 8 ( 2 unt; 5 typ; 0 def)
% 0.19/0.44 % Number of atoms : 2 ( 0 equ; 0 cnn)
% 0.19/0.44 % Maximal formula atoms : 1 ( 0 avg)
% 0.19/0.44 % Number of connectives : 9 ( 2 ~; 0 |; 1 &; 6 @)
% 0.19/0.44 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.19/0.44 % Maximal formula depth : 7 ( 5 avg)
% 0.19/0.44 % Number of types : 2 ( 0 usr)
% 0.19/0.44 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.19/0.44 % Number of symbols : 5 ( 5 usr; 4 con; 0-2 aty)
% 0.19/0.44 % Number of variables : 3 ( 0 ^; 0 !; 3 ?; 3 :)
% 0.19/0.44 % SPC : TH0_THM_NEQ_NAR
% 0.19/0.44
% 0.19/0.44 % Comments : The conclusion is given using a higher order quantifier.
% 0.19/0.44 % Satallax tends to find solutions by instantiating for P twice.
% 0.19/0.44 % A solution instantiating it once is to take P x := (x = horus),
% 0.19/0.44 % X := horus. Instantiating Y three times gives you that everyone
% 0.19/0.44 % is the same as horus, so the two axioms conflict. This problem
% 0.19/0.44 % is a simplification of CSR138^1.
% 0.19/0.44 %------------------------------------------------------------------------------
% 0.19/0.44 thf(parent,type,
% 0.19/0.44 parent: $i > $i > $o ).
% 0.19/0.44
% 0.19/0.44 thf(kronus,type,
% 0.19/0.44 kronus: $i ).
% 0.19/0.44
% 0.19/0.44 thf(zeus,type,
% 0.19/0.44 zeus: $i ).
% 0.19/0.44
% 0.19/0.44 thf(ax1,axiom,
% 0.19/0.44 parent @ kronus @ zeus ).
% 0.19/0.44
% 0.19/0.44 thf(sutekh,type,
% 0.19/0.44 sutekh: $i ).
% 0.19/0.44
% 0.19/0.44 thf(horus,type,
% 0.19/0.44 horus: $i ).
% 0.19/0.44
% 0.19/0.44 thf(ax2,axiom,
% 0.19/0.44 ~ ( parent @ sutekh @ horus ) ).
% 0.19/0.44
% 0.19/0.44 thf(hotwo,conjecture,
% 0.19/0.44 ? [P: $i > $o,X: $i,Y: $i] :
% 0.19/0.44 ( ( P @ X )
% 0.19/0.44 & ~ ( P @ Y ) ) ).
% 0.19/0.44
% 0.19/0.44 %------------------------------------------------------------------------------
% 0.19/0.44 ------------------------
% 1.63/1.30 ---- Embedded in THF ---
% 1.63/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.63/1.30 %%% Generated on Tue Feb 24 11:34:41 EST 2026
% 1.63/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 1.63/1.30 %%% Logic specification used:
% 1.63/1.30 %%% thf(spec, logic, $$dhol).
% 1.63/1.30
% 1.63/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.H40ACT4lsK/DTF2DTF6149.p
% See solution above
% 1.63/1.30 ------------------------
% 1.63/1.31 ---- Cleaned THF ---
% 1.63/1.32 thf(parent,type,
% 1.63/1.32 parent: $i > $i > $o ).
% 1.63/1.32
% 1.63/1.32 thf(kronus,type,
% 1.63/1.32 kronus: $i ).
% 1.63/1.32
% 1.63/1.32 thf(zeus,type,
% 1.63/1.32 zeus: $i ).
% 1.63/1.32
% 1.63/1.32 thf(ax1,axiom,
% 1.63/1.32 parent @ kronus @ zeus ).
% 1.63/1.32
% 1.63/1.32 thf(sutekh,type,
% 1.63/1.32 sutekh: $i ).
% 1.63/1.32
% 1.63/1.32 thf(horus,type,
% 1.63/1.32 horus: $i ).
% 1.63/1.32
% 1.63/1.32 thf(ax2,axiom,
% 1.63/1.32 ~ ( parent @ sutekh @ horus ) ).
% 1.63/1.32
% 1.63/1.32 thf(hotwo,conjecture,
% 1.63/1.32 ? [P: $i > $o,X: $i,Y: $i] :
% 1.63/1.32 ( ( P @ X )
% 1.63/1.32 & ~ ( P @ Y ) ) ).
% 1.63/1.32 ------------------------
% 1.63/1.33 % (6343)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_6149 for (3000ds/275Mi)
% 1.63/1.33 % (6341)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_6149 for (3000ds/2Mi)
% 1.63/1.33 % (6338)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_6149 for (3000ds/183Mi)
% 1.63/1.33 % (6341)Instruction limit reached!
% 1.63/1.33 % (6341)------------------------------
% 1.63/1.33 % (6341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.33 % (6341)Termination reason: Unknown
% 1.63/1.33 % (6341)Termination phase: Saturation
% 1.63/1.33
% 1.63/1.33 % (6341)Memory used [KB]: 5500
% 1.63/1.33 % (6341)Time elapsed: 0.002 s
% 1.63/1.33 % (6341)Instructions burned: 2 (million)
% 1.63/1.33 % (6341)------------------------------
% 1.63/1.33 % (6341)------------------------------
% 1.63/1.33 % (6343)Refutation not found, incomplete strategy
% 1.63/1.33 % (6343)------------------------------
% 1.63/1.33 % (6343)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.33 % (6343)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.33
% 1.63/1.33
% 1.63/1.33 % (6343)Memory used [KB]: 5500
% 1.63/1.33 % (6343)Time elapsed: 0.003 s
% 1.63/1.33 % (6343)Instructions burned: 2 (million)
% 1.63/1.33 % (6343)------------------------------
% 1.63/1.33 % (6343)------------------------------
% 1.63/1.33 % (6339)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_6149 for (3000ds/4Mi)
% 1.63/1.33 % (6338)First to succeed.
% 1.63/1.33 % (6339)Instruction limit reached!
% 1.63/1.33 % (6339)------------------------------
% 1.63/1.33 % (6339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.33 % (6339)Termination reason: Unknown
% 1.63/1.33 % (6339)Termination phase: Saturation
% 1.63/1.33
% 1.63/1.33 % (6339)Memory used [KB]: 5500
% 1.63/1.33 % (6339)Time elapsed: 0.003 s
% 1.63/1.33 % (6339)Instructions burned: 4 (million)
% 1.63/1.33 % (6339)------------------------------
% 1.63/1.33 % (6339)------------------------------
% 1.63/1.33 % (6338)Refutation found. Thanks to Tanya!
% 1.63/1.33 % SZS status Theorem for DTF2THF_6149
% 1.63/1.33 % SZS output start Proof for DTF2THF_6149
% 1.63/1.33 thf(func_def_0, type, parent: $i > $i > $o).
% 1.63/1.33 thf(func_def_10, type, ph1: !>[X0: $tType]:(X0)).
% 1.63/1.33 thf(f47,plain,(
% 1.63/1.33 $false),
% 1.63/1.33 inference(subsumption_resolution,[status(thm)],[f45,f41])).
% 1.63/1.33 thf(f41,plain,(
% 1.63/1.33 ( ! [X0 : $i,X1 : $i] : (($true != (parent @ X1 @ X0))) )),
% 1.63/1.33 inference(superposition,[status(thm)],[f26,f20])).
% 1.63/1.33 thf(f20,plain,(
% 1.63/1.33 ( ! [X0 : $i,X1 : $i] : ((X0 = X1)) )),
% 1.63/1.33 inference(leibniz_equality_elimination,[status(thm)],[f18])).
% 1.63/1.33 thf(f18,plain,(
% 1.63/1.33 ( ! [X2 : $i,X0 : $i,X1 : $i > $o] : (($true = (X1 @ X0)) | ($true != (X1 @ X2))) )),
% 1.63/1.33 inference(cnf_transformation,[status(thm)],[f15])).
% 1.63/1.33 thf(f15,plain,(
% 1.63/1.33 ! [X0 : $i,X1 : $i > $o,X2 : $i] : (($true != (X1 @ X2)) | ($true = (X1 @ X0)))),
% 1.63/1.33 inference(rectify,[status(thm)],[f14])).
% 1.63/1.33 thf(f14,plain,(
% 1.63/1.33 ! [X1 : $i,X0 : $i > $o,X2 : $i] : (((X0 @ X2) != $true) | ((X0 @ X1) = $true))),
% 1.63/1.33 inference(ennf_transformation,[status(thm)],[f13])).
% 1.63/1.33 thf(f13,plain,(
% 1.63/1.33 ~? [X1 : $i,X2 : $i,X0 : $i > $o] : (((X0 @ X1) != $true) & ((X0 @ X2) = $true))),
% 1.63/1.33 inference(flattening,[status(thm)],[f11])).
% 1.63/1.33 thf(f11,plain,(
% 1.63/1.33 ~? [X0 : $i > $o,X1 : $i,X2 : $i] : (((X0 @ X2) = $true) & ~((X0 @ X1) = $true))),
% 1.63/1.33 inference(fool_elimination,[status(thm)],[f10])).
% 1.63/1.33 thf(f10,plain,(
% 1.63/1.33 ~? [X0 : $i > $o,X1 : $i,X2 : $i] : ((X0 @ X2) & ~(X0 @ X1))),
% 1.63/1.33 inference(rectify,[status(thm)],[f4])).
% 1.63/1.33 thf(f4,negated_conjecture,(
% 1.63/1.33 ~? [X0 : $i > $o,X2 : $i,X1 : $i] : ((X0 @ X1) & ~(X0 @ X2))),
% 1.63/1.33 inference(negated_conjecture,[status(cth)],[f3])).
% 1.63/1.33 thf(f3,conjecture,(
% 1.63/1.33 ? [X0 : $i > $o,X2 : $i,X1 : $i] : ((X0 @ X1) & ~(X0 @ X2))),
% 1.63/1.33 file('/export/starexec/sandbox/tmp/tmp.H40ACT4lsK/DTF2THF_6149.p',hotwo)).
% 1.63/1.33 thf(f26,plain,(
% 1.63/1.33 ( ! [X0 : $i] : (((parent @ X0 @ horus) != $true)) )),
% 1.63/1.33 inference(beta_eta_normalization,[status(thm)],[f25])).
% 1.63/1.33 thf(f25,plain,(
% 1.63/1.33 ( ! [X0 : $i] : ((((^[Y0 : $i]: (parent @ ((^[Y1 : $i]: (Y1)) @ Y0) @ ((^[Y1 : $i]: (horus)) @ Y0))) @ X0) != $true)) )),
% 1.63/1.33 inference(trivial_inequality_removal,[status(thm)],[f24])).
% 1.63/1.33 thf(f24,plain,(
% 1.63/1.33 ( ! [X0 : $i] : ((((^[Y0 : $i]: (parent @ ((^[Y1 : $i]: (Y1)) @ Y0) @ ((^[Y1 : $i]: (horus)) @ Y0))) @ X0) != $true) | ($true != $true)) )),
% 1.63/1.33 inference(superposition,[status(thm)],[f16,f18])).
% 1.63/1.33 thf(f16,plain,(
% 1.63/1.33 ((parent @ sutekh @ horus) != $true)),
% 1.63/1.33 inference(cnf_transformation,[status(thm)],[f12])).
% 1.63/1.33 thf(f12,plain,(
% 1.63/1.33 ((parent @ sutekh @ horus) != $true)),
% 1.63/1.33 inference(flattening,[status(thm)],[f7])).
% 1.63/1.33 thf(f7,plain,(
% 1.63/1.33 ~((parent @ sutekh @ horus) = $true)),
% 1.63/1.33 inference(fool_elimination,[status(thm)],[f6])).
% 1.63/1.33 thf(f6,plain,(
% 1.63/1.33 ~(parent @ sutekh @ horus)),
% 1.63/1.33 inference(rectify,[status(thm)],[f2])).
% 1.63/1.33 thf(f2,axiom,(
% 1.63/1.33 ~(parent @ sutekh @ horus)),
% 1.63/1.33 file('/export/starexec/sandbox/tmp/tmp.H40ACT4lsK/DTF2THF_6149.p',ax2)).
% 1.63/1.33 thf(f45,plain,(
% 1.63/1.33 ( ! [X0 : $i,X1 : $i] : (($true = (parent @ X1 @ X0))) )),
% 1.63/1.33 inference(superposition,[status(thm)],[f32,f20])).
% 1.63/1.33 thf(f32,plain,(
% 1.63/1.33 ( ! [X0 : $i] : (($true = (parent @ X0 @ zeus))) )),
% 1.63/1.33 inference(superposition,[status(thm)],[f17,f20])).
% 1.63/1.33 thf(f17,plain,(
% 1.63/1.33 ((parent @ kronus @ zeus) = $true)),
% 1.63/1.33 inference(cnf_transformation,[status(thm)],[f9])).
% 1.63/1.33 thf(f9,plain,(
% 1.63/1.33 ((parent @ kronus @ zeus) = $true)),
% 1.63/1.33 inference(fool_elimination,[status(thm)],[f8])).
% 1.63/1.33 thf(f8,plain,(
% 1.63/1.33 (parent @ kronus @ zeus)),
% 1.63/1.33 inference(rectify,[status(thm)],[f1])).
% 1.63/1.33 thf(f1,axiom,(
% 1.63/1.33 (parent @ kronus @ zeus)),
% 1.63/1.33 file('/export/starexec/sandbox/tmp/tmp.H40ACT4lsK/DTF2THF_6149.p',ax1)).
% 1.63/1.33 % SZS output end Proof for DTF2THF_6149
% 1.63/1.33 % (6338)------------------------------
% 1.63/1.33 % (6338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.33 % (6338)Termination reason: Refutation
% 1.63/1.33
% 1.63/1.33 % (6338)Memory used [KB]: 5500
% 1.63/1.33 % (6338)Time elapsed: 0.004 s
% 1.63/1.33 % (6338)Instructions burned: 3 (million)
% 1.63/1.33 % (6338)------------------------------
% 1.63/1.33 % (6338)------------------------------
% 1.63/1.33 % (6337)Success in time 0.011 s
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