%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PUZ020-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:23:11 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 15
% Syntax : Number of formulae : 34 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 112 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 138 ( 62 ~; 65 |; 0 &)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 17 ( 15 !; 0 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
tff(a_truth_type,type,
a_truth: $i > $o ).
tff(statement_by_type,type,
statement_by: $i > $i ).
tff(husband_type,type,
husband: $i ).
tff(knight_type,type,
knight: $i > $o ).
tff(person_type,type,
person: $i > $o ).
tff(wife_type,type,
wife: $i ).
tff(1,plain,
( ~ knight(husband)
<=> ~ knight(husband) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ knight(husband),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_knight_husband) ).
tff(3,plain,
~ knight(husband),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( person(husband)
<=> person(husband) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
person(husband),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',husband) ).
tff(6,plain,
person(husband),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [X: $i] :
refl(( ( knight(X)
| ~ person(X)
| ~ a_truth(statement_by(X)) )
<=> ( knight(X)
| ~ person(X)
| ~ a_truth(statement_by(X)) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [X: $i] :
( knight(X)
| ~ person(X)
| ~ a_truth(statement_by(X)) )
<=> ! [X: $i] :
( knight(X)
| ~ person(X)
| ~ a_truth(statement_by(X)) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [X: $i] :
( knight(X)
| ~ person(X)
| ~ a_truth(statement_by(X)) )
<=> ! [X: $i] :
( knight(X)
| ~ person(X)
| ~ a_truth(statement_by(X)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,plain,
^ [X: $i] :
rewrite(( ( ~ person(X)
| ~ a_truth(statement_by(X))
| knight(X) )
<=> ( knight(X)
| ~ person(X)
| ~ a_truth(statement_by(X)) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [X: $i] :
( ~ person(X)
| ~ a_truth(statement_by(X))
| knight(X) )
<=> ! [X: $i] :
( knight(X)
| ~ person(X)
| ~ a_truth(statement_by(X)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [X: $i] :
( ~ person(X)
| ~ a_truth(statement_by(X))
| knight(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knights_make_true_statements) ).
tff(13,plain,
! [X: $i] :
( knight(X)
| ~ person(X)
| ~ a_truth(statement_by(X)) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [X: $i] :
( knight(X)
| ~ person(X)
| ~ a_truth(statement_by(X)) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [X: $i] :
( knight(X)
| ~ person(X)
| ~ a_truth(statement_by(X)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X: $i] :
( knight(X)
| ~ person(X)
| ~ a_truth(statement_by(X)) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [X: $i] :
( knight(X)
| ~ person(X)
| ~ a_truth(statement_by(X)) )
| knight(husband)
| ~ person(husband)
| ~ a_truth(statement_by(husband)) )
<=> ( ~ ! [X: $i] :
( knight(X)
| ~ person(X)
| ~ a_truth(statement_by(X)) )
| knight(husband)
| ~ person(husband)
| ~ a_truth(statement_by(husband)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ~ ! [X: $i] :
( knight(X)
| ~ person(X)
| ~ a_truth(statement_by(X)) )
| knight(husband)
| ~ person(husband)
| ~ a_truth(statement_by(husband)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [X: $i] :
( knight(X)
| ~ person(X)
| ~ a_truth(statement_by(X)) )
| knight(husband)
| ~ person(husband)
| ~ a_truth(statement_by(husband)) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
~ a_truth(statement_by(husband)),
inference(unit_resolution,[status(thm)],[19,16,6,3]) ).
tff(21,plain,
( ( a_truth(statement_by(husband))
| knight(wife) )
<=> ( a_truth(statement_by(husband))
| knight(wife) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
( a_truth(statement_by(husband))
| knight(wife) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knight_wife_or_truthful_husband) ).
tff(23,plain,
( a_truth(statement_by(husband))
| knight(wife) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
( a_truth(statement_by(husband))
| knight(wife) ),
inference(modus_ponens,[status(thm)],[23,21]) ).
tff(25,plain,
( a_truth(statement_by(husband))
| knight(wife) ),
inference(modus_ponens,[status(thm)],[24,21]) ).
tff(26,plain,
( a_truth(statement_by(husband))
| knight(wife) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
( a_truth(statement_by(husband))
| knight(wife) ),
inference(modus_ponens,[status(thm)],[26,21]) ).
tff(28,plain,
knight(wife),
inference(unit_resolution,[status(thm)],[27,20]) ).
tff(29,plain,
( ( a_truth(statement_by(husband))
| ~ knight(wife) )
<=> ( a_truth(statement_by(husband))
| ~ knight(wife) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,plain,
( ( ~ knight(wife)
| a_truth(statement_by(husband)) )
<=> ( a_truth(statement_by(husband))
| ~ knight(wife) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,axiom,
( ~ knight(wife)
| a_truth(statement_by(husband)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knight_wife_means_truthful_husband) ).
tff(32,plain,
( a_truth(statement_by(husband))
| ~ knight(wife) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
( a_truth(statement_by(husband))
| ~ knight(wife) ),
inference(modus_ponens,[status(thm)],[32,29]) ).
tff(34,plain,
$false,
inference(unit_resolution,[status(thm)],[33,28,20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : PUZ020-1 : TPTP v9.0.0. Released v1.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 02:40:10 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.37 % SZS status Unsatisfiable
% 0.12/0.37 % SZS output start Proof
% See solution above
% 0.12/0.38 % E exiting
%------------------------------------------------------------------------------