TSTP Solution File: PLA006-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : PLA006-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% 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 : Sun Sep 18 13:39:52 EDT 2022
% Result : Unsatisfiable 2.22s 1.63s
% Output : Proof 2.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 39
% Syntax : Number of formulae : 70 ( 24 unt; 12 typ; 0 def)
% Number of atoms : 310 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 435 ( 207 ~; 195 |; 0 &)
% ( 33 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 24 ( 24 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 8 >; 5 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 113 ( 101 !; 0 ?; 113 :)
% 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(putdown_type,type,
putdown: ( $i * $i ) > $i ).
tff(table_type,type,
table: $i ).
tff(on_type,type,
on: ( $i * $i ) > $i ).
tff(clear_type,type,
clear: $i > $i ).
tff(holding_type,type,
holding: $i > $i ).
tff(empty_type,type,
empty: $i ).
tff(differ_type,type,
differ: ( $i * $i ) > $o ).
tff(1,plain,
^ [State: $i] :
refl(
( holds(clear(table),State)
<=> holds(clear(table),State) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [State: $i] : holds(clear(table),State)
<=> ! [State: $i] : holds(clear(table),State) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [State: $i] : holds(clear(table),State)
<=> ! [State: $i] : holds(clear(table),State) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [State: $i] : holds(clear(table),State),
file('/export/starexec/sandbox/benchmark/Axioms/PLA001-1.ax',clear_table) ).
tff(5,plain,
! [State: $i] : holds(clear(table),State),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [State: $i] : holds(clear(table),State),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [State: $i] : holds(clear(table),State),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [State: $i] : holds(clear(table),State)
| holds(clear(table),do(pickup(c),s0)) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
holds(clear(table),do(pickup(c),s0)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( holds(empty,s0)
<=> holds(empty,s0) ),
inference(rewrite,[status(thm)],]) ).
tff(11,axiom,
holds(empty,s0),
file('/export/starexec/sandbox/benchmark/Axioms/PLA001-1.ax',initial_state8) ).
tff(12,plain,
holds(empty,s0),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
( holds(clear(c),s0)
<=> holds(clear(c),s0) ),
inference(rewrite,[status(thm)],]) ).
tff(14,axiom,
holds(clear(c),s0),
file('/export/starexec/sandbox/benchmark/Axioms/PLA001-1.ax',initial_state7) ).
tff(15,plain,
holds(clear(c),s0),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
( differ(c,table)
<=> differ(c,table) ),
inference(rewrite,[status(thm)],]) ).
tff(17,axiom,
differ(c,table),
file('/export/starexec/sandbox/benchmark/Axioms/PLA001-1.ax',differ_c_table) ).
tff(18,plain,
differ(c,table),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
^ [State: $i,X: $i] :
refl(
( ( ~ differ(X,table)
| ~ holds(clear(X),State)
| ~ holds(empty,State)
| holds(holding(X),do(pickup(X),State)) )
<=> ( ~ differ(X,table)
| ~ holds(clear(X),State)
| ~ holds(empty,State)
| holds(holding(X),do(pickup(X),State)) ) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [State: $i,X: $i] :
( ~ differ(X,table)
| ~ holds(clear(X),State)
| ~ holds(empty,State)
| holds(holding(X),do(pickup(X),State)) )
<=> ! [State: $i,X: $i] :
( ~ differ(X,table)
| ~ holds(clear(X),State)
| ~ holds(empty,State)
| holds(holding(X),do(pickup(X),State)) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [State: $i,X: $i] :
( ~ differ(X,table)
| ~ holds(clear(X),State)
| ~ holds(empty,State)
| holds(holding(X),do(pickup(X),State)) )
<=> ! [State: $i,X: $i] :
( ~ differ(X,table)
| ~ holds(clear(X),State)
| ~ holds(empty,State)
| holds(holding(X),do(pickup(X),State)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
^ [State: $i,X: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( holds(holding(X),do(pickup(X),State))
| ~ holds(empty,State) )
<=> ( ~ holds(empty,State)
| holds(holding(X),do(pickup(X),State)) ) )),
( ( holds(holding(X),do(pickup(X),State))
| ~ holds(empty,State)
| ~ holds(clear(X),State) )
<=> ( ~ holds(empty,State)
| holds(holding(X),do(pickup(X),State))
| ~ holds(clear(X),State) ) )),
rewrite(
( ( ~ holds(empty,State)
| holds(holding(X),do(pickup(X),State))
| ~ holds(clear(X),State) )
<=> ( ~ holds(clear(X),State)
| ~ holds(empty,State)
| holds(holding(X),do(pickup(X),State)) ) )),
( ( holds(holding(X),do(pickup(X),State))
| ~ holds(empty,State)
| ~ holds(clear(X),State) )
<=> ( ~ holds(clear(X),State)
| ~ holds(empty,State)
| holds(holding(X),do(pickup(X),State)) ) )),
( ( holds(holding(X),do(pickup(X),State))
| ~ holds(empty,State)
| ~ holds(clear(X),State)
| ~ differ(X,table) )
<=> ( ~ holds(clear(X),State)
| ~ holds(empty,State)
| holds(holding(X),do(pickup(X),State))
| ~ differ(X,table) ) )),
rewrite(
( ( ~ holds(clear(X),State)
| ~ holds(empty,State)
| holds(holding(X),do(pickup(X),State))
| ~ differ(X,table) )
<=> ( ~ differ(X,table)
| ~ holds(clear(X),State)
| ~ holds(empty,State)
| holds(holding(X),do(pickup(X),State)) ) )),
( ( holds(holding(X),do(pickup(X),State))
| ~ holds(empty,State)
| ~ holds(clear(X),State)
| ~ differ(X,table) )
<=> ( ~ differ(X,table)
| ~ holds(clear(X),State)
| ~ holds(empty,State)
| holds(holding(X),do(pickup(X),State)) ) )),
inference(bind,[status(th)],]) ).
tff(23,plain,
( ! [State: $i,X: $i] :
( holds(holding(X),do(pickup(X),State))
| ~ holds(empty,State)
| ~ holds(clear(X),State)
| ~ differ(X,table) )
<=> ! [State: $i,X: $i] :
( ~ differ(X,table)
| ~ holds(clear(X),State)
| ~ holds(empty,State)
| holds(holding(X),do(pickup(X),State)) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,axiom,
! [State: $i,X: $i] :
( holds(holding(X),do(pickup(X),State))
| ~ holds(empty,State)
| ~ holds(clear(X),State)
| ~ differ(X,table) ),
file('/export/starexec/sandbox/benchmark/Axioms/PLA001-0.ax',pickup_1) ).
tff(25,plain,
! [State: $i,X: $i] :
( ~ differ(X,table)
| ~ holds(clear(X),State)
| ~ holds(empty,State)
| holds(holding(X),do(pickup(X),State)) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [State: $i,X: $i] :
( ~ differ(X,table)
| ~ holds(clear(X),State)
| ~ holds(empty,State)
| holds(holding(X),do(pickup(X),State)) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
! [State: $i,X: $i] :
( ~ differ(X,table)
| ~ holds(clear(X),State)
| ~ holds(empty,State)
| holds(holding(X),do(pickup(X),State)) ),
inference(skolemize,[status(sab)],[26]) ).
tff(28,plain,
! [State: $i,X: $i] :
( ~ differ(X,table)
| ~ holds(clear(X),State)
| ~ holds(empty,State)
| holds(holding(X),do(pickup(X),State)) ),
inference(modus_ponens,[status(thm)],[27,20]) ).
tff(29,plain,
( ( ~ ! [State: $i,X: $i] :
( ~ differ(X,table)
| ~ holds(clear(X),State)
| ~ holds(empty,State)
| holds(holding(X),do(pickup(X),State)) )
| ~ holds(empty,s0)
| ~ holds(clear(c),s0)
| ~ differ(c,table)
| holds(holding(c),do(pickup(c),s0)) )
<=> ( ~ ! [State: $i,X: $i] :
( ~ differ(X,table)
| ~ holds(clear(X),State)
| ~ holds(empty,State)
| holds(holding(X),do(pickup(X),State)) )
| ~ holds(empty,s0)
| ~ holds(clear(c),s0)
| ~ differ(c,table)
| holds(holding(c),do(pickup(c),s0)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ( ~ differ(c,table)
| ~ holds(clear(c),s0)
| ~ holds(empty,s0)
| holds(holding(c),do(pickup(c),s0)) )
<=> ( ~ holds(empty,s0)
| ~ holds(clear(c),s0)
| ~ differ(c,table)
| holds(holding(c),do(pickup(c),s0)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
( ( ~ ! [State: $i,X: $i] :
( ~ differ(X,table)
| ~ holds(clear(X),State)
| ~ holds(empty,State)
| holds(holding(X),do(pickup(X),State)) )
| ~ differ(c,table)
| ~ holds(clear(c),s0)
| ~ holds(empty,s0)
| holds(holding(c),do(pickup(c),s0)) )
<=> ( ~ ! [State: $i,X: $i] :
( ~ differ(X,table)
| ~ holds(clear(X),State)
| ~ holds(empty,State)
| holds(holding(X),do(pickup(X),State)) )
| ~ holds(empty,s0)
| ~ holds(clear(c),s0)
| ~ differ(c,table)
| holds(holding(c),do(pickup(c),s0)) ) ),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
( ( ~ ! [State: $i,X: $i] :
( ~ differ(X,table)
| ~ holds(clear(X),State)
| ~ holds(empty,State)
| holds(holding(X),do(pickup(X),State)) )
| ~ differ(c,table)
| ~ holds(clear(c),s0)
| ~ holds(empty,s0)
| holds(holding(c),do(pickup(c),s0)) )
<=> ( ~ ! [State: $i,X: $i] :
( ~ differ(X,table)
| ~ holds(clear(X),State)
| ~ holds(empty,State)
| holds(holding(X),do(pickup(X),State)) )
| ~ holds(empty,s0)
| ~ holds(clear(c),s0)
| ~ differ(c,table)
| holds(holding(c),do(pickup(c),s0)) ) ),
inference(transitivity,[status(thm)],[31,29]) ).
tff(33,plain,
( ~ ! [State: $i,X: $i] :
( ~ differ(X,table)
| ~ holds(clear(X),State)
| ~ holds(empty,State)
| holds(holding(X),do(pickup(X),State)) )
| ~ differ(c,table)
| ~ holds(clear(c),s0)
| ~ holds(empty,s0)
| holds(holding(c),do(pickup(c),s0)) ),
inference(quant_inst,[status(thm)],]) ).
tff(34,plain,
( ~ ! [State: $i,X: $i] :
( ~ differ(X,table)
| ~ holds(clear(X),State)
| ~ holds(empty,State)
| holds(holding(X),do(pickup(X),State)) )
| ~ holds(empty,s0)
| ~ holds(clear(c),s0)
| ~ differ(c,table)
| holds(holding(c),do(pickup(c),s0)) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
holds(holding(c),do(pickup(c),s0)),
inference(unit_resolution,[status(thm)],[34,28,18,15,12]) ).
tff(36,plain,
^ [Y: $i,State: $i,X: $i] :
refl(
( ( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(on(X,Y),do(putdown(X,Y),State)) )
<=> ( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(on(X,Y),do(putdown(X,Y),State)) ) )),
inference(bind,[status(th)],]) ).
tff(37,plain,
( ! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(on(X,Y),do(putdown(X,Y),State)) )
<=> ! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(on(X,Y),do(putdown(X,Y),State)) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(on(X,Y),do(putdown(X,Y),State)) )
<=> ! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(on(X,Y),do(putdown(X,Y),State)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
^ [Y: $i,State: $i,X: $i] :
trans(
monotonicity(
rewrite(
( ( holds(on(X,Y),do(putdown(X,Y),State))
| ~ holds(holding(X),State) )
<=> ( ~ holds(holding(X),State)
| holds(on(X,Y),do(putdown(X,Y),State)) ) )),
( ( holds(on(X,Y),do(putdown(X,Y),State))
| ~ holds(holding(X),State)
| ~ holds(clear(Y),State) )
<=> ( ~ holds(holding(X),State)
| holds(on(X,Y),do(putdown(X,Y),State))
| ~ holds(clear(Y),State) ) )),
rewrite(
( ( ~ holds(holding(X),State)
| holds(on(X,Y),do(putdown(X,Y),State))
| ~ holds(clear(Y),State) )
<=> ( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(on(X,Y),do(putdown(X,Y),State)) ) )),
( ( holds(on(X,Y),do(putdown(X,Y),State))
| ~ holds(holding(X),State)
| ~ holds(clear(Y),State) )
<=> ( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(on(X,Y),do(putdown(X,Y),State)) ) )),
inference(bind,[status(th)],]) ).
tff(40,plain,
( ! [Y: $i,State: $i,X: $i] :
( holds(on(X,Y),do(putdown(X,Y),State))
| ~ holds(holding(X),State)
| ~ holds(clear(Y),State) )
<=> ! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(on(X,Y),do(putdown(X,Y),State)) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,axiom,
! [Y: $i,State: $i,X: $i] :
( holds(on(X,Y),do(putdown(X,Y),State))
| ~ holds(holding(X),State)
| ~ holds(clear(Y),State) ),
file('/export/starexec/sandbox/benchmark/Axioms/PLA001-0.ax',putdown_2) ).
tff(42,plain,
! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(on(X,Y),do(putdown(X,Y),State)) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(on(X,Y),do(putdown(X,Y),State)) ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(on(X,Y),do(putdown(X,Y),State)) ),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(on(X,Y),do(putdown(X,Y),State)) ),
inference(modus_ponens,[status(thm)],[44,37]) ).
tff(46,plain,
( ( ~ ! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(on(X,Y),do(putdown(X,Y),State)) )
| ~ holds(clear(table),do(pickup(c),s0))
| ~ holds(holding(c),do(pickup(c),s0))
| holds(on(c,table),do(putdown(c,table),do(pickup(c),s0))) )
<=> ( ~ ! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(on(X,Y),do(putdown(X,Y),State)) )
| ~ holds(clear(table),do(pickup(c),s0))
| ~ holds(holding(c),do(pickup(c),s0))
| holds(on(c,table),do(putdown(c,table),do(pickup(c),s0))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(47,plain,
( ~ ! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(on(X,Y),do(putdown(X,Y),State)) )
| ~ holds(clear(table),do(pickup(c),s0))
| ~ holds(holding(c),do(pickup(c),s0))
| holds(on(c,table),do(putdown(c,table),do(pickup(c),s0))) ),
inference(quant_inst,[status(thm)],]) ).
tff(48,plain,
( ~ ! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(on(X,Y),do(putdown(X,Y),State)) )
| ~ holds(clear(table),do(pickup(c),s0))
| ~ holds(holding(c),do(pickup(c),s0))
| holds(on(c,table),do(putdown(c,table),do(pickup(c),s0))) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
holds(on(c,table),do(putdown(c,table),do(pickup(c),s0))),
inference(unit_resolution,[status(thm)],[48,45,35,9]) ).
tff(50,plain,
^ [State: $i] :
refl(
( ~ holds(on(c,table),State)
<=> ~ holds(on(c,table),State) )),
inference(bind,[status(th)],]) ).
tff(51,plain,
( ! [State: $i] : ~ holds(on(c,table),State)
<=> ! [State: $i] : ~ holds(on(c,table),State) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,plain,
( ! [State: $i] : ~ holds(on(c,table),State)
<=> ! [State: $i] : ~ holds(on(c,table),State) ),
inference(rewrite,[status(thm)],]) ).
tff(53,axiom,
! [State: $i] : ~ holds(on(c,table),State),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_CTable) ).
tff(54,plain,
! [State: $i] : ~ holds(on(c,table),State),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
! [State: $i] : ~ holds(on(c,table),State),
inference(skolemize,[status(sab)],[54]) ).
tff(56,plain,
! [State: $i] : ~ holds(on(c,table),State),
inference(modus_ponens,[status(thm)],[55,51]) ).
tff(57,plain,
( ~ ! [State: $i] : ~ holds(on(c,table),State)
| ~ holds(on(c,table),do(putdown(c,table),do(pickup(c),s0))) ),
inference(quant_inst,[status(thm)],]) ).
tff(58,plain,
$false,
inference(unit_resolution,[status(thm)],[57,56,49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : PLA006-1 : TPTP v8.1.0. Released v1.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 17:20:08 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 2.22/1.63 % SZS status Unsatisfiable
% 2.22/1.63 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------