%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PUZ128+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 : Sat Jun 21 05:23:27 AM UTC 2025
% Result : Theorem 0.19s 0.36s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 23
% Syntax : Number of formulae : 44 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 249 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 360 ( 166 ~; 126 |; 48 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 11 ( 11 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 62 ( 38 !; 18 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
tff(patricide_type,type,
patricide: $i > $o ).
tff(polyneikes_type,type,
polyneikes: $i ).
tff(parent_of_type,type,
parent_of: ( $i * $i ) > $o ).
tff(iokaste_type,type,
iokaste: $i ).
tff(oedipus_type,type,
oedipus: $i ).
tff(thersandros_type,type,
thersandros: $i ).
tff(1,plain,
^ [P: $i,NP: $i] :
refl(( ( patricide(NP)
| ~ parent_of(P,NP)
| ~ patricide(P)
| ~ parent_of(iokaste,P) )
<=> ( patricide(NP)
| ~ parent_of(P,NP)
| ~ patricide(P)
| ~ parent_of(iokaste,P) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [P: $i,NP: $i] :
( patricide(NP)
| ~ parent_of(P,NP)
| ~ patricide(P)
| ~ parent_of(iokaste,P) )
<=> ! [P: $i,NP: $i] :
( patricide(NP)
| ~ parent_of(P,NP)
| ~ patricide(P)
| ~ parent_of(iokaste,P) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [P: $i,NP: $i] :
trans(monotonicity(rewrite(( ( parent_of(iokaste,P)
& patricide(P)
& parent_of(P,NP)
& ~ patricide(NP) )
<=> ~ ( patricide(NP)
| ~ parent_of(P,NP)
| ~ patricide(P)
| ~ parent_of(iokaste,P) ) )),
( ~ ( parent_of(iokaste,P)
& patricide(P)
& parent_of(P,NP)
& ~ patricide(NP) )
<=> ~ ~ ( patricide(NP)
| ~ parent_of(P,NP)
| ~ patricide(P)
| ~ parent_of(iokaste,P) ) )),
rewrite(( ~ ~ ( patricide(NP)
| ~ parent_of(P,NP)
| ~ patricide(P)
| ~ parent_of(iokaste,P) )
<=> ( patricide(NP)
| ~ parent_of(P,NP)
| ~ patricide(P)
| ~ parent_of(iokaste,P) ) )),
( ~ ( parent_of(iokaste,P)
& patricide(P)
& parent_of(P,NP)
& ~ patricide(NP) )
<=> ( patricide(NP)
| ~ parent_of(P,NP)
| ~ patricide(P)
| ~ parent_of(iokaste,P) ) )),
inference(bind,[status(th)],[]) ).
tff(4,plain,
( ! [P: $i,NP: $i] :
~ ( parent_of(iokaste,P)
& patricide(P)
& parent_of(P,NP)
& ~ patricide(NP) )
<=> ! [P: $i,NP: $i] :
( patricide(NP)
| ~ parent_of(P,NP)
| ~ patricide(P)
| ~ parent_of(iokaste,P) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ~ ? [P: $i,NP: $i] :
( parent_of(iokaste,P)
& patricide(P)
& parent_of(P,NP)
& ~ patricide(NP) )
<=> ~ ? [P: $i,NP: $i] :
( parent_of(iokaste,P)
& patricide(P)
& parent_of(P,NP)
& ~ patricide(NP) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,plain,
( ~ ? [P: $i,NP: $i] :
( parent_of(iokaste,P)
& patricide(P)
& parent_of(P,NP)
& ~ patricide(NP) )
<=> ~ ? [P: $i,NP: $i] :
( parent_of(iokaste,P)
& patricide(P)
& parent_of(P,NP)
& ~ patricide(NP) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
~ ? [P: $i,NP: $i] :
( parent_of(iokaste,P)
& patricide(P)
& parent_of(P,NP)
& ~ patricide(NP) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iokaste_parent_particide_parent_not_patricide) ).
tff(8,plain,
~ ? [P: $i,NP: $i] :
( parent_of(iokaste,P)
& patricide(P)
& parent_of(P,NP)
& ~ patricide(NP) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
~ ? [P: $i,NP: $i] :
( parent_of(iokaste,P)
& patricide(P)
& parent_of(P,NP)
& ~ patricide(NP) ),
inference(modus_ponens,[status(thm)],[8,5]) ).
tff(10,plain,
~ ? [P: $i,NP: $i] :
( parent_of(iokaste,P)
& patricide(P)
& parent_of(P,NP)
& ~ patricide(NP) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
~ ? [P: $i,NP: $i] :
( parent_of(iokaste,P)
& patricide(P)
& parent_of(P,NP)
& ~ patricide(NP) ),
inference(modus_ponens,[status(thm)],[10,5]) ).
tff(12,plain,
^ [P: $i,NP: $i] :
refl($oeq(~ ( parent_of(iokaste,P)
& patricide(P)
& parent_of(P,NP)
& ~ patricide(NP) ),
~ ( parent_of(iokaste,P)
& patricide(P)
& parent_of(P,NP)
& ~ patricide(NP) ))),
inference(bind,[status(th)],[]) ).
tff(13,plain,
! [P: $i,NP: $i] :
~ ( parent_of(iokaste,P)
& patricide(P)
& parent_of(P,NP)
& ~ patricide(NP) ),
inference(nnf-neg,[status(sab)],[11,12]) ).
tff(14,plain,
! [P: $i,NP: $i] :
( patricide(NP)
| ~ parent_of(P,NP)
| ~ patricide(P)
| ~ parent_of(iokaste,P) ),
inference(modus_ponens,[status(thm)],[13,4]) ).
tff(15,plain,
! [P: $i,NP: $i] :
( patricide(NP)
| ~ parent_of(P,NP)
| ~ patricide(P)
| ~ parent_of(iokaste,P) ),
inference(modus_ponens,[status(thm)],[14,2]) ).
tff(16,plain,
( patricide(oedipus)
<=> patricide(oedipus) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,axiom,
patricide(oedipus),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',oedipus_patricidal) ).
tff(18,plain,
patricide(oedipus),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
( parent_of(oedipus,polyneikes)
<=> parent_of(oedipus,polyneikes) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
parent_of(oedipus,polyneikes),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',oedipus_polyneikes) ).
tff(21,plain,
parent_of(oedipus,polyneikes),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
( parent_of(iokaste,oedipus)
<=> parent_of(iokaste,oedipus) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
parent_of(iokaste,oedipus),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iokaste_oedipus) ).
tff(24,plain,
parent_of(iokaste,oedipus),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
( ( ~ ! [P: $i,NP: $i] :
( patricide(NP)
| ~ parent_of(P,NP)
| ~ patricide(P)
| ~ parent_of(iokaste,P) )
| patricide(polyneikes)
| ~ parent_of(oedipus,polyneikes)
| ~ patricide(oedipus)
| ~ parent_of(iokaste,oedipus) )
<=> ( ~ ! [P: $i,NP: $i] :
( patricide(NP)
| ~ parent_of(P,NP)
| ~ patricide(P)
| ~ parent_of(iokaste,P) )
| patricide(polyneikes)
| ~ parent_of(oedipus,polyneikes)
| ~ patricide(oedipus)
| ~ parent_of(iokaste,oedipus) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
( ~ ! [P: $i,NP: $i] :
( patricide(NP)
| ~ parent_of(P,NP)
| ~ patricide(P)
| ~ parent_of(iokaste,P) )
| patricide(polyneikes)
| ~ parent_of(oedipus,polyneikes)
| ~ patricide(oedipus)
| ~ parent_of(iokaste,oedipus) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
( ~ ! [P: $i,NP: $i] :
( patricide(NP)
| ~ parent_of(P,NP)
| ~ patricide(P)
| ~ parent_of(iokaste,P) )
| patricide(polyneikes)
| ~ parent_of(oedipus,polyneikes)
| ~ patricide(oedipus)
| ~ parent_of(iokaste,oedipus) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
patricide(polyneikes),
inference(unit_resolution,[status(thm)],[27,24,21,18,15]) ).
tff(29,plain,
( ~ patricide(thersandros)
<=> ~ patricide(thersandros) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
~ patricide(thersandros),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thersandros_not_patricidal) ).
tff(31,plain,
~ patricide(thersandros),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
( parent_of(polyneikes,thersandros)
<=> parent_of(polyneikes,thersandros) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
parent_of(polyneikes,thersandros),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',polyneikes_thersandros) ).
tff(34,plain,
parent_of(polyneikes,thersandros),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
( parent_of(iokaste,polyneikes)
<=> parent_of(iokaste,polyneikes) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,axiom,
parent_of(iokaste,polyneikes),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iokaste_polyneikes) ).
tff(37,plain,
parent_of(iokaste,polyneikes),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
( ( ~ ! [P: $i,NP: $i] :
( patricide(NP)
| ~ parent_of(P,NP)
| ~ patricide(P)
| ~ parent_of(iokaste,P) )
| patricide(thersandros)
| ~ parent_of(iokaste,polyneikes)
| ~ parent_of(polyneikes,thersandros)
| ~ patricide(polyneikes) )
<=> ( ~ ! [P: $i,NP: $i] :
( patricide(NP)
| ~ parent_of(P,NP)
| ~ patricide(P)
| ~ parent_of(iokaste,P) )
| patricide(thersandros)
| ~ parent_of(iokaste,polyneikes)
| ~ parent_of(polyneikes,thersandros)
| ~ patricide(polyneikes) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,plain,
( ( patricide(thersandros)
| ~ parent_of(polyneikes,thersandros)
| ~ patricide(polyneikes)
| ~ parent_of(iokaste,polyneikes) )
<=> ( patricide(thersandros)
| ~ parent_of(iokaste,polyneikes)
| ~ parent_of(polyneikes,thersandros)
| ~ patricide(polyneikes) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,plain,
( ( ~ ! [P: $i,NP: $i] :
( patricide(NP)
| ~ parent_of(P,NP)
| ~ patricide(P)
| ~ parent_of(iokaste,P) )
| patricide(thersandros)
| ~ parent_of(polyneikes,thersandros)
| ~ patricide(polyneikes)
| ~ parent_of(iokaste,polyneikes) )
<=> ( ~ ! [P: $i,NP: $i] :
( patricide(NP)
| ~ parent_of(P,NP)
| ~ patricide(P)
| ~ parent_of(iokaste,P) )
| patricide(thersandros)
| ~ parent_of(iokaste,polyneikes)
| ~ parent_of(polyneikes,thersandros)
| ~ patricide(polyneikes) ) ),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
( ( ~ ! [P: $i,NP: $i] :
( patricide(NP)
| ~ parent_of(P,NP)
| ~ patricide(P)
| ~ parent_of(iokaste,P) )
| patricide(thersandros)
| ~ parent_of(polyneikes,thersandros)
| ~ patricide(polyneikes)
| ~ parent_of(iokaste,polyneikes) )
<=> ( ~ ! [P: $i,NP: $i] :
( patricide(NP)
| ~ parent_of(P,NP)
| ~ patricide(P)
| ~ parent_of(iokaste,P) )
| patricide(thersandros)
| ~ parent_of(iokaste,polyneikes)
| ~ parent_of(polyneikes,thersandros)
| ~ patricide(polyneikes) ) ),
inference(transitivity,[status(thm)],[40,38]) ).
tff(42,plain,
( ~ ! [P: $i,NP: $i] :
( patricide(NP)
| ~ parent_of(P,NP)
| ~ patricide(P)
| ~ parent_of(iokaste,P) )
| patricide(thersandros)
| ~ parent_of(polyneikes,thersandros)
| ~ patricide(polyneikes)
| ~ parent_of(iokaste,polyneikes) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
( ~ ! [P: $i,NP: $i] :
( patricide(NP)
| ~ parent_of(P,NP)
| ~ patricide(P)
| ~ parent_of(iokaste,P) )
| patricide(thersandros)
| ~ parent_of(iokaste,polyneikes)
| ~ parent_of(polyneikes,thersandros)
| ~ patricide(polyneikes) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
$false,
inference(unit_resolution,[status(thm)],[43,37,34,31,15,28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : PUZ128+1 : TPTP v9.0.0. Released v4.0.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n010.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 02:49:11 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.36 % SZS status Theorem
% 0.19/0.36 % SZS output start Proof
% See solution above
% 0.19/0.37 % E exiting
%------------------------------------------------------------------------------