%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PLA020-1 : TPTP v9.0.0. Released v1.1.0.
% 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 05:22:52 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.37s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 17
% Syntax : Number of formulae : 35 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 205 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 301 ( 146 ~; 134 |; 0 &)
% ( 21 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 15 ( 15 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; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 73 ( 66 !; 0 ?; 73 :)
% Comments :
%------------------------------------------------------------------------------
tff(holds_type,type,
holds: ( $i * $i ) > $o ).
tff(do_type,type,
do: ( $i * $i ) > $i ).
tff(s0_type,type,
s0: $i ).
tff(pickup_type,type,
pickup: $i > $i ).
tff(c_type,type,
c: $i ).
tff(clear_type,type,
clear: $i > $i ).
tff(d_type,type,
d: $i ).
tff(empty_type,type,
empty: $i ).
tff(on_type,type,
on: ( $i * $i ) > $i ).
tff(1,plain,
( holds(empty,s0)
<=> holds(empty,s0) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
holds(empty,s0),
file('/export/starexec/sandbox2/benchmark/Axioms/PLA001-1.ax',initial_state8) ).
tff(3,plain,
holds(empty,s0),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( holds(clear(c),s0)
<=> holds(clear(c),s0) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
holds(clear(c),s0),
file('/export/starexec/sandbox2/benchmark/Axioms/PLA001-1.ax',initial_state7) ).
tff(6,plain,
holds(clear(c),s0),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( holds(on(c,d),s0)
<=> holds(on(c,d),s0) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
holds(on(c,d),s0),
file('/export/starexec/sandbox2/benchmark/Axioms/PLA001-1.ax',initial_state3) ).
tff(9,plain,
holds(on(c,d),s0),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Y: $i,State: $i,X: $i] :
refl(( ( ~ holds(clear(X),State)
| ~ holds(empty,State)
| ~ holds(on(X,Y),State)
| holds(clear(Y),do(pickup(X),State)) )
<=> ( ~ holds(clear(X),State)
| ~ holds(empty,State)
| ~ holds(on(X,Y),State)
| holds(clear(Y),do(pickup(X),State)) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ holds(empty,State)
| ~ holds(on(X,Y),State)
| holds(clear(Y),do(pickup(X),State)) )
<=> ! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ holds(empty,State)
| ~ holds(on(X,Y),State)
| holds(clear(Y),do(pickup(X),State)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ holds(empty,State)
| ~ holds(on(X,Y),State)
| holds(clear(Y),do(pickup(X),State)) )
<=> ! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ holds(empty,State)
| ~ holds(on(X,Y),State)
| holds(clear(Y),do(pickup(X),State)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
^ [Y: $i,State: $i,X: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( holds(clear(Y),do(pickup(X),State))
| ~ holds(on(X,Y),State) )
<=> ( ~ holds(on(X,Y),State)
| holds(clear(Y),do(pickup(X),State)) ) )),
( ( holds(clear(Y),do(pickup(X),State))
| ~ holds(on(X,Y),State)
| ~ holds(clear(X),State) )
<=> ( ~ holds(on(X,Y),State)
| holds(clear(Y),do(pickup(X),State))
| ~ holds(clear(X),State) ) )),
rewrite(( ( ~ holds(on(X,Y),State)
| holds(clear(Y),do(pickup(X),State))
| ~ holds(clear(X),State) )
<=> ( ~ holds(clear(X),State)
| ~ holds(on(X,Y),State)
| holds(clear(Y),do(pickup(X),State)) ) )),
( ( holds(clear(Y),do(pickup(X),State))
| ~ holds(on(X,Y),State)
| ~ holds(clear(X),State) )
<=> ( ~ holds(clear(X),State)
| ~ holds(on(X,Y),State)
| holds(clear(Y),do(pickup(X),State)) ) )),
( ( holds(clear(Y),do(pickup(X),State))
| ~ holds(on(X,Y),State)
| ~ holds(clear(X),State)
| ~ holds(empty,State) )
<=> ( ~ holds(clear(X),State)
| ~ holds(on(X,Y),State)
| holds(clear(Y),do(pickup(X),State))
| ~ holds(empty,State) ) )),
rewrite(( ( ~ holds(clear(X),State)
| ~ holds(on(X,Y),State)
| holds(clear(Y),do(pickup(X),State))
| ~ holds(empty,State) )
<=> ( ~ holds(clear(X),State)
| ~ holds(empty,State)
| ~ holds(on(X,Y),State)
| holds(clear(Y),do(pickup(X),State)) ) )),
( ( holds(clear(Y),do(pickup(X),State))
| ~ holds(on(X,Y),State)
| ~ holds(clear(X),State)
| ~ holds(empty,State) )
<=> ( ~ holds(clear(X),State)
| ~ holds(empty,State)
| ~ holds(on(X,Y),State)
| holds(clear(Y),do(pickup(X),State)) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [Y: $i,State: $i,X: $i] :
( holds(clear(Y),do(pickup(X),State))
| ~ holds(on(X,Y),State)
| ~ holds(clear(X),State)
| ~ holds(empty,State) )
<=> ! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ holds(empty,State)
| ~ holds(on(X,Y),State)
| holds(clear(Y),do(pickup(X),State)) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [Y: $i,State: $i,X: $i] :
( holds(clear(Y),do(pickup(X),State))
| ~ holds(on(X,Y),State)
| ~ holds(clear(X),State)
| ~ holds(empty,State) ),
file('/export/starexec/sandbox2/benchmark/Axioms/PLA001-0.ax',pickup_2) ).
tff(16,plain,
! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ holds(empty,State)
| ~ holds(on(X,Y),State)
| holds(clear(Y),do(pickup(X),State)) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ holds(empty,State)
| ~ holds(on(X,Y),State)
| holds(clear(Y),do(pickup(X),State)) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ holds(empty,State)
| ~ holds(on(X,Y),State)
| holds(clear(Y),do(pickup(X),State)) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ holds(empty,State)
| ~ holds(on(X,Y),State)
| holds(clear(Y),do(pickup(X),State)) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
( ( ~ ! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ holds(empty,State)
| ~ holds(on(X,Y),State)
| holds(clear(Y),do(pickup(X),State)) )
| ~ holds(empty,s0)
| ~ holds(clear(c),s0)
| ~ holds(on(c,d),s0)
| holds(clear(d),do(pickup(c),s0)) )
<=> ( ~ ! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ holds(empty,State)
| ~ holds(on(X,Y),State)
| holds(clear(Y),do(pickup(X),State)) )
| ~ holds(empty,s0)
| ~ holds(clear(c),s0)
| ~ holds(on(c,d),s0)
| holds(clear(d),do(pickup(c),s0)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
( ( ~ holds(clear(c),s0)
| ~ holds(empty,s0)
| ~ holds(on(c,d),s0)
| holds(clear(d),do(pickup(c),s0)) )
<=> ( ~ holds(empty,s0)
| ~ holds(clear(c),s0)
| ~ holds(on(c,d),s0)
| holds(clear(d),do(pickup(c),s0)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,plain,
( ( ~ ! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ holds(empty,State)
| ~ holds(on(X,Y),State)
| holds(clear(Y),do(pickup(X),State)) )
| ~ holds(clear(c),s0)
| ~ holds(empty,s0)
| ~ holds(on(c,d),s0)
| holds(clear(d),do(pickup(c),s0)) )
<=> ( ~ ! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ holds(empty,State)
| ~ holds(on(X,Y),State)
| holds(clear(Y),do(pickup(X),State)) )
| ~ holds(empty,s0)
| ~ holds(clear(c),s0)
| ~ holds(on(c,d),s0)
| holds(clear(d),do(pickup(c),s0)) ) ),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
( ( ~ ! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ holds(empty,State)
| ~ holds(on(X,Y),State)
| holds(clear(Y),do(pickup(X),State)) )
| ~ holds(clear(c),s0)
| ~ holds(empty,s0)
| ~ holds(on(c,d),s0)
| holds(clear(d),do(pickup(c),s0)) )
<=> ( ~ ! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ holds(empty,State)
| ~ holds(on(X,Y),State)
| holds(clear(Y),do(pickup(X),State)) )
| ~ holds(empty,s0)
| ~ holds(clear(c),s0)
| ~ holds(on(c,d),s0)
| holds(clear(d),do(pickup(c),s0)) ) ),
inference(transitivity,[status(thm)],[22,20]) ).
tff(24,plain,
( ~ ! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ holds(empty,State)
| ~ holds(on(X,Y),State)
| holds(clear(Y),do(pickup(X),State)) )
| ~ holds(clear(c),s0)
| ~ holds(empty,s0)
| ~ holds(on(c,d),s0)
| holds(clear(d),do(pickup(c),s0)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(25,plain,
( ~ ! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ holds(empty,State)
| ~ holds(on(X,Y),State)
| holds(clear(Y),do(pickup(X),State)) )
| ~ holds(empty,s0)
| ~ holds(clear(c),s0)
| ~ holds(on(c,d),s0)
| holds(clear(d),do(pickup(c),s0)) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
holds(clear(d),do(pickup(c),s0)),
inference(unit_resolution,[status(thm)],[25,19,9,6,3]) ).
tff(27,plain,
^ [State: $i] :
refl(( ~ holds(clear(d),State)
<=> ~ holds(clear(d),State) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [State: $i] : ~ holds(clear(d),State)
<=> ! [State: $i] : ~ holds(clear(d),State) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [State: $i] : ~ holds(clear(d),State)
<=> ! [State: $i] : ~ holds(clear(d),State) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
! [State: $i] : ~ holds(clear(d),State),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_D) ).
tff(31,plain,
! [State: $i] : ~ holds(clear(d),State),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
! [State: $i] : ~ holds(clear(d),State),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [State: $i] : ~ holds(clear(d),State),
inference(modus_ponens,[status(thm)],[32,28]) ).
tff(34,plain,
( ~ ! [State: $i] : ~ holds(clear(d),State)
| ~ holds(clear(d),do(pickup(c),s0)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(35,plain,
$false,
inference(unit_resolution,[status(thm)],[34,33,26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : PLA020-1 : TPTP v9.0.0. Released v1.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n010.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 02:23:11 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.20/0.37 % SZS status Unsatisfiable
% 0.20/0.37 % SZS output start Proof
% See solution above
% 0.20/0.38 % E exiting
%------------------------------------------------------------------------------