%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PLA016-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:22:51 AM UTC 2025
% Result : Unsatisfiable 0.56s 0.78s
% Output : Proof 0.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 82
% Syntax : Number of formulae : 172 ( 55 unt; 0 typ; 0 def)
% Number of atoms : 1013 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 1471 ( 693 ~; 681 |; 0 &)
% ( 97 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 63 ( 63 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 438 ( 397 !; 0 ?; 438 :)
% 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(b_type,type,
b: $i ).
tff(d_type,type,
d: $i ).
tff(a_type,type,
a: $i ).
tff(on_type,type,
on: ( $i * $i ) > $i ).
tff(clear_type,type,
clear: $i > $i ).
tff(differ_type,type,
differ: ( $i * $i ) > $o ).
tff(holding_type,type,
holding: $i > $i ).
tff(empty_type,type,
empty: $i ).
tff(table_type,type,
table: $i ).
tff(1,plain,
( holds(clear(a),s0)
<=> holds(clear(a),s0) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
holds(clear(a),s0),
file('/export/starexec/sandbox/benchmark/Axioms/PLA001-1.ax',initial_state5) ).
tff(3,plain,
holds(clear(a),s0),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( differ(a,c)
<=> differ(a,c) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
differ(a,c),
file('/export/starexec/sandbox/benchmark/Axioms/PLA001-1.ax',differ_a_c) ).
tff(6,plain,
differ(a,c),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [Z: $i,State: $i,X: $i] :
refl(( ( ~ holds(clear(X),State)
| ~ differ(X,Z)
| holds(clear(X),do(pickup(Z),State)) )
<=> ( ~ holds(clear(X),State)
| ~ differ(X,Z)
| holds(clear(X),do(pickup(Z),State)) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [Z: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ differ(X,Z)
| holds(clear(X),do(pickup(Z),State)) )
<=> ! [Z: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ differ(X,Z)
| holds(clear(X),do(pickup(Z),State)) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [Z: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ differ(X,Z)
| holds(clear(X),do(pickup(Z),State)) )
<=> ! [Z: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ differ(X,Z)
| holds(clear(X),do(pickup(Z),State)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,plain,
^ [Z: $i,State: $i,X: $i] :
trans(monotonicity(rewrite(( ( holds(clear(X),do(pickup(Z),State))
| ~ holds(clear(X),State) )
<=> ( ~ holds(clear(X),State)
| holds(clear(X),do(pickup(Z),State)) ) )),
( ( holds(clear(X),do(pickup(Z),State))
| ~ holds(clear(X),State)
| ~ differ(X,Z) )
<=> ( ~ holds(clear(X),State)
| holds(clear(X),do(pickup(Z),State))
| ~ differ(X,Z) ) )),
rewrite(( ( ~ holds(clear(X),State)
| holds(clear(X),do(pickup(Z),State))
| ~ differ(X,Z) )
<=> ( ~ holds(clear(X),State)
| ~ differ(X,Z)
| holds(clear(X),do(pickup(Z),State)) ) )),
( ( holds(clear(X),do(pickup(Z),State))
| ~ holds(clear(X),State)
| ~ differ(X,Z) )
<=> ( ~ holds(clear(X),State)
| ~ differ(X,Z)
| holds(clear(X),do(pickup(Z),State)) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [Z: $i,State: $i,X: $i] :
( holds(clear(X),do(pickup(Z),State))
| ~ holds(clear(X),State)
| ~ differ(X,Z) )
<=> ! [Z: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ differ(X,Z)
| holds(clear(X),do(pickup(Z),State)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [Z: $i,State: $i,X: $i] :
( holds(clear(X),do(pickup(Z),State))
| ~ holds(clear(X),State)
| ~ differ(X,Z) ),
file('/export/starexec/sandbox/benchmark/Axioms/PLA001-0.ax',pickup_4) ).
tff(13,plain,
! [Z: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ differ(X,Z)
| holds(clear(X),do(pickup(Z),State)) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [Z: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ differ(X,Z)
| holds(clear(X),do(pickup(Z),State)) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [Z: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ differ(X,Z)
| holds(clear(X),do(pickup(Z),State)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Z: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ differ(X,Z)
| holds(clear(X),do(pickup(Z),State)) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [Z: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ differ(X,Z)
| holds(clear(X),do(pickup(Z),State)) )
| ~ holds(clear(a),s0)
| ~ differ(a,c)
| holds(clear(a),do(pickup(c),s0)) )
<=> ( ~ ! [Z: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ differ(X,Z)
| holds(clear(X),do(pickup(Z),State)) )
| ~ holds(clear(a),s0)
| ~ differ(a,c)
| holds(clear(a),do(pickup(c),s0)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ~ ! [Z: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ differ(X,Z)
| holds(clear(X),do(pickup(Z),State)) )
| ~ holds(clear(a),s0)
| ~ differ(a,c)
| holds(clear(a),do(pickup(c),s0)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [Z: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ differ(X,Z)
| holds(clear(X),do(pickup(Z),State)) )
| ~ holds(clear(a),s0)
| ~ differ(a,c)
| holds(clear(a),do(pickup(c),s0)) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
holds(clear(a),do(pickup(c),s0)),
inference(unit_resolution,[status(thm)],[19,16,6,3]) ).
tff(21,plain,
( differ(a,b)
<=> differ(a,b) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
differ(a,b),
file('/export/starexec/sandbox/benchmark/Axioms/PLA001-1.ax',differ_a_b) ).
tff(23,plain,
differ(a,b),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
^ [Z: $i,Y: $i,State: $i,X: $i] :
refl(( ( ~ differ(Z,Y)
| ~ holds(clear(Z),State)
| holds(clear(Z),do(putdown(X,Y),State)) )
<=> ( ~ differ(Z,Y)
| ~ holds(clear(Z),State)
| holds(clear(Z),do(putdown(X,Y),State)) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [Z: $i,Y: $i,State: $i,X: $i] :
( ~ differ(Z,Y)
| ~ holds(clear(Z),State)
| holds(clear(Z),do(putdown(X,Y),State)) )
<=> ! [Z: $i,Y: $i,State: $i,X: $i] :
( ~ differ(Z,Y)
| ~ holds(clear(Z),State)
| holds(clear(Z),do(putdown(X,Y),State)) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [Z: $i,Y: $i,State: $i,X: $i] :
( ~ differ(Z,Y)
| ~ holds(clear(Z),State)
| holds(clear(Z),do(putdown(X,Y),State)) )
<=> ! [Z: $i,Y: $i,State: $i,X: $i] :
( ~ differ(Z,Y)
| ~ holds(clear(Z),State)
| holds(clear(Z),do(putdown(X,Y),State)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,plain,
^ [Z: $i,Y: $i,State: $i,X: $i] :
trans(monotonicity(rewrite(( ( holds(clear(Z),do(putdown(X,Y),State))
| ~ holds(clear(Z),State) )
<=> ( ~ holds(clear(Z),State)
| holds(clear(Z),do(putdown(X,Y),State)) ) )),
( ( holds(clear(Z),do(putdown(X,Y),State))
| ~ holds(clear(Z),State)
| ~ differ(Z,Y) )
<=> ( ~ holds(clear(Z),State)
| holds(clear(Z),do(putdown(X,Y),State))
| ~ differ(Z,Y) ) )),
rewrite(( ( ~ holds(clear(Z),State)
| holds(clear(Z),do(putdown(X,Y),State))
| ~ differ(Z,Y) )
<=> ( ~ differ(Z,Y)
| ~ holds(clear(Z),State)
| holds(clear(Z),do(putdown(X,Y),State)) ) )),
( ( holds(clear(Z),do(putdown(X,Y),State))
| ~ holds(clear(Z),State)
| ~ differ(Z,Y) )
<=> ( ~ differ(Z,Y)
| ~ holds(clear(Z),State)
| holds(clear(Z),do(putdown(X,Y),State)) ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [Z: $i,Y: $i,State: $i,X: $i] :
( holds(clear(Z),do(putdown(X,Y),State))
| ~ holds(clear(Z),State)
| ~ differ(Z,Y) )
<=> ! [Z: $i,Y: $i,State: $i,X: $i] :
( ~ differ(Z,Y)
| ~ holds(clear(Z),State)
| holds(clear(Z),do(putdown(X,Y),State)) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,axiom,
! [Z: $i,Y: $i,State: $i,X: $i] :
( holds(clear(Z),do(putdown(X,Y),State))
| ~ holds(clear(Z),State)
| ~ differ(Z,Y) ),
file('/export/starexec/sandbox/benchmark/Axioms/PLA001-0.ax',putdown_5) ).
tff(30,plain,
! [Z: $i,Y: $i,State: $i,X: $i] :
( ~ differ(Z,Y)
| ~ holds(clear(Z),State)
| holds(clear(Z),do(putdown(X,Y),State)) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [Z: $i,Y: $i,State: $i,X: $i] :
( ~ differ(Z,Y)
| ~ holds(clear(Z),State)
| holds(clear(Z),do(putdown(X,Y),State)) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
! [Z: $i,Y: $i,State: $i,X: $i] :
( ~ differ(Z,Y)
| ~ holds(clear(Z),State)
| holds(clear(Z),do(putdown(X,Y),State)) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [Z: $i,Y: $i,State: $i,X: $i] :
( ~ differ(Z,Y)
| ~ holds(clear(Z),State)
| holds(clear(Z),do(putdown(X,Y),State)) ),
inference(modus_ponens,[status(thm)],[32,25]) ).
tff(34,plain,
( ( ~ ! [Z: $i,Y: $i,State: $i,X: $i] :
( ~ differ(Z,Y)
| ~ holds(clear(Z),State)
| holds(clear(Z),do(putdown(X,Y),State)) )
| ~ differ(a,b)
| ~ holds(clear(a),do(pickup(c),s0))
| holds(clear(a),do(putdown(c,b),do(pickup(c),s0))) )
<=> ( ~ ! [Z: $i,Y: $i,State: $i,X: $i] :
( ~ differ(Z,Y)
| ~ holds(clear(Z),State)
| holds(clear(Z),do(putdown(X,Y),State)) )
| ~ differ(a,b)
| ~ holds(clear(a),do(pickup(c),s0))
| holds(clear(a),do(putdown(c,b),do(pickup(c),s0))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
( ~ ! [Z: $i,Y: $i,State: $i,X: $i] :
( ~ differ(Z,Y)
| ~ holds(clear(Z),State)
| holds(clear(Z),do(putdown(X,Y),State)) )
| ~ differ(a,b)
| ~ holds(clear(a),do(pickup(c),s0))
| holds(clear(a),do(putdown(c,b),do(pickup(c),s0))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
( ~ ! [Z: $i,Y: $i,State: $i,X: $i] :
( ~ differ(Z,Y)
| ~ holds(clear(Z),State)
| holds(clear(Z),do(putdown(X,Y),State)) )
| ~ differ(a,b)
| ~ holds(clear(a),do(pickup(c),s0))
| holds(clear(a),do(putdown(c,b),do(pickup(c),s0))) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
holds(clear(a),do(putdown(c,b),do(pickup(c),s0))),
inference(unit_resolution,[status(thm)],[36,33,23,20]) ).
tff(38,plain,
( differ(a,d)
<=> differ(a,d) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,axiom,
differ(a,d),
file('/export/starexec/sandbox/benchmark/Axioms/PLA001-1.ax',differ_a_d) ).
tff(40,plain,
differ(a,d),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
( ( ~ ! [Z: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ differ(X,Z)
| holds(clear(X),do(pickup(Z),State)) )
| ~ differ(a,d)
| ~ holds(clear(a),do(putdown(c,b),do(pickup(c),s0)))
| holds(clear(a),do(pickup(d),do(putdown(c,b),do(pickup(c),s0)))) )
<=> ( ~ ! [Z: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ differ(X,Z)
| holds(clear(X),do(pickup(Z),State)) )
| ~ differ(a,d)
| ~ holds(clear(a),do(putdown(c,b),do(pickup(c),s0)))
| holds(clear(a),do(pickup(d),do(putdown(c,b),do(pickup(c),s0)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
( ( ~ holds(clear(a),do(putdown(c,b),do(pickup(c),s0)))
| ~ differ(a,d)
| holds(clear(a),do(pickup(d),do(putdown(c,b),do(pickup(c),s0)))) )
<=> ( ~ differ(a,d)
| ~ holds(clear(a),do(putdown(c,b),do(pickup(c),s0)))
| holds(clear(a),do(pickup(d),do(putdown(c,b),do(pickup(c),s0)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( ( ~ ! [Z: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ differ(X,Z)
| holds(clear(X),do(pickup(Z),State)) )
| ~ holds(clear(a),do(putdown(c,b),do(pickup(c),s0)))
| ~ differ(a,d)
| holds(clear(a),do(pickup(d),do(putdown(c,b),do(pickup(c),s0)))) )
<=> ( ~ ! [Z: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ differ(X,Z)
| holds(clear(X),do(pickup(Z),State)) )
| ~ differ(a,d)
| ~ holds(clear(a),do(putdown(c,b),do(pickup(c),s0)))
| holds(clear(a),do(pickup(d),do(putdown(c,b),do(pickup(c),s0)))) ) ),
inference(monotonicity,[status(thm)],[42]) ).
tff(44,plain,
( ( ~ ! [Z: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ differ(X,Z)
| holds(clear(X),do(pickup(Z),State)) )
| ~ holds(clear(a),do(putdown(c,b),do(pickup(c),s0)))
| ~ differ(a,d)
| holds(clear(a),do(pickup(d),do(putdown(c,b),do(pickup(c),s0)))) )
<=> ( ~ ! [Z: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ differ(X,Z)
| holds(clear(X),do(pickup(Z),State)) )
| ~ differ(a,d)
| ~ holds(clear(a),do(putdown(c,b),do(pickup(c),s0)))
| holds(clear(a),do(pickup(d),do(putdown(c,b),do(pickup(c),s0)))) ) ),
inference(transitivity,[status(thm)],[43,41]) ).
tff(45,plain,
( ~ ! [Z: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ differ(X,Z)
| holds(clear(X),do(pickup(Z),State)) )
| ~ holds(clear(a),do(putdown(c,b),do(pickup(c),s0)))
| ~ differ(a,d)
| holds(clear(a),do(pickup(d),do(putdown(c,b),do(pickup(c),s0)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(46,plain,
( ~ ! [Z: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ differ(X,Z)
| holds(clear(X),do(pickup(Z),State)) )
| ~ differ(a,d)
| ~ holds(clear(a),do(putdown(c,b),do(pickup(c),s0)))
| holds(clear(a),do(pickup(d),do(putdown(c,b),do(pickup(c),s0)))) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
holds(clear(a),do(pickup(d),do(putdown(c,b),do(pickup(c),s0)))),
inference(unit_resolution,[status(thm)],[46,16,40,37]) ).
tff(48,plain,
( holds(clear(b),s0)
<=> holds(clear(b),s0) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,axiom,
holds(clear(b),s0),
file('/export/starexec/sandbox/benchmark/Axioms/PLA001-1.ax',initial_state6) ).
tff(50,plain,
holds(clear(b),s0),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
( differ(b,c)
<=> differ(b,c) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,axiom,
differ(b,c),
file('/export/starexec/sandbox/benchmark/Axioms/PLA001-1.ax',differ_b_c) ).
tff(53,plain,
differ(b,c),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
( ( ~ ! [Z: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ differ(X,Z)
| holds(clear(X),do(pickup(Z),State)) )
| ~ holds(clear(b),s0)
| ~ differ(b,c)
| holds(clear(b),do(pickup(c),s0)) )
<=> ( ~ ! [Z: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ differ(X,Z)
| holds(clear(X),do(pickup(Z),State)) )
| ~ holds(clear(b),s0)
| ~ differ(b,c)
| holds(clear(b),do(pickup(c),s0)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,plain,
( ~ ! [Z: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ differ(X,Z)
| holds(clear(X),do(pickup(Z),State)) )
| ~ holds(clear(b),s0)
| ~ differ(b,c)
| holds(clear(b),do(pickup(c),s0)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(56,plain,
( ~ ! [Z: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ differ(X,Z)
| holds(clear(X),do(pickup(Z),State)) )
| ~ holds(clear(b),s0)
| ~ differ(b,c)
| holds(clear(b),do(pickup(c),s0)) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
holds(clear(b),do(pickup(c),s0)),
inference(unit_resolution,[status(thm)],[56,16,53,50]) ).
tff(58,plain,
( holds(empty,s0)
<=> holds(empty,s0) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,axiom,
holds(empty,s0),
file('/export/starexec/sandbox/benchmark/Axioms/PLA001-1.ax',initial_state8) ).
tff(60,plain,
holds(empty,s0),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
( holds(clear(c),s0)
<=> holds(clear(c),s0) ),
inference(rewrite,[status(thm)],[]) ).
tff(62,axiom,
holds(clear(c),s0),
file('/export/starexec/sandbox/benchmark/Axioms/PLA001-1.ax',initial_state7) ).
tff(63,plain,
holds(clear(c),s0),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
( differ(c,table)
<=> differ(c,table) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,axiom,
differ(c,table),
file('/export/starexec/sandbox/benchmark/Axioms/PLA001-1.ax',differ_c_table) ).
tff(66,plain,
differ(c,table),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,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(68,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)],[67]) ).
tff(69,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(70,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(71,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)],[70]) ).
tff(72,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(73,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)],[72,71]) ).
tff(74,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)],[73,69]) ).
tff(75,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)],[74]) ).
tff(76,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)],[75,68]) ).
tff(77,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(78,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(79,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)],[78]) ).
tff(80,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)],[79,77]) ).
tff(81,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(82,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)],[81,80]) ).
tff(83,plain,
holds(holding(c),do(pickup(c),s0)),
inference(unit_resolution,[status(thm)],[82,76,66,63,60]) ).
tff(84,plain,
^ [Y: $i,State: $i,X: $i] :
refl(( ( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(empty,do(putdown(X,Y),State)) )
<=> ( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(empty,do(putdown(X,Y),State)) ) )),
inference(bind,[status(th)],[]) ).
tff(85,plain,
( ! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(empty,do(putdown(X,Y),State)) )
<=> ! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(empty,do(putdown(X,Y),State)) ) ),
inference(quant_intro,[status(thm)],[84]) ).
tff(86,plain,
( ! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(empty,do(putdown(X,Y),State)) )
<=> ! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(empty,do(putdown(X,Y),State)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(87,plain,
^ [Y: $i,State: $i,X: $i] :
trans(monotonicity(rewrite(( ( holds(empty,do(putdown(X,Y),State))
| ~ holds(holding(X),State) )
<=> ( ~ holds(holding(X),State)
| holds(empty,do(putdown(X,Y),State)) ) )),
( ( holds(empty,do(putdown(X,Y),State))
| ~ holds(holding(X),State)
| ~ holds(clear(Y),State) )
<=> ( ~ holds(holding(X),State)
| holds(empty,do(putdown(X,Y),State))
| ~ holds(clear(Y),State) ) )),
rewrite(( ( ~ holds(holding(X),State)
| holds(empty,do(putdown(X,Y),State))
| ~ holds(clear(Y),State) )
<=> ( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(empty,do(putdown(X,Y),State)) ) )),
( ( holds(empty,do(putdown(X,Y),State))
| ~ holds(holding(X),State)
| ~ holds(clear(Y),State) )
<=> ( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(empty,do(putdown(X,Y),State)) ) )),
inference(bind,[status(th)],[]) ).
tff(88,plain,
( ! [Y: $i,State: $i,X: $i] :
( holds(empty,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(empty,do(putdown(X,Y),State)) ) ),
inference(quant_intro,[status(thm)],[87]) ).
tff(89,axiom,
! [Y: $i,State: $i,X: $i] :
( holds(empty,do(putdown(X,Y),State))
| ~ holds(holding(X),State)
| ~ holds(clear(Y),State) ),
file('/export/starexec/sandbox/benchmark/Axioms/PLA001-0.ax',putdown_1) ).
tff(90,plain,
! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(empty,do(putdown(X,Y),State)) ),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(empty,do(putdown(X,Y),State)) ),
inference(modus_ponens,[status(thm)],[90,86]) ).
tff(92,plain,
! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(empty,do(putdown(X,Y),State)) ),
inference(skolemize,[status(sab)],[91]) ).
tff(93,plain,
! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(empty,do(putdown(X,Y),State)) ),
inference(modus_ponens,[status(thm)],[92,85]) ).
tff(94,plain,
( ( ~ ! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(empty,do(putdown(X,Y),State)) )
| ~ holds(clear(b),do(pickup(c),s0))
| ~ holds(holding(c),do(pickup(c),s0))
| holds(empty,do(putdown(c,b),do(pickup(c),s0))) )
<=> ( ~ ! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(empty,do(putdown(X,Y),State)) )
| ~ holds(clear(b),do(pickup(c),s0))
| ~ holds(holding(c),do(pickup(c),s0))
| holds(empty,do(putdown(c,b),do(pickup(c),s0))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(95,plain,
( ~ ! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(empty,do(putdown(X,Y),State)) )
| ~ holds(clear(b),do(pickup(c),s0))
| ~ holds(holding(c),do(pickup(c),s0))
| holds(empty,do(putdown(c,b),do(pickup(c),s0))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(96,plain,
( ~ ! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(empty,do(putdown(X,Y),State)) )
| ~ holds(clear(b),do(pickup(c),s0))
| ~ holds(holding(c),do(pickup(c),s0))
| holds(empty,do(putdown(c,b),do(pickup(c),s0))) ),
inference(modus_ponens,[status(thm)],[95,94]) ).
tff(97,plain,
holds(empty,do(putdown(c,b),do(pickup(c),s0))),
inference(unit_resolution,[status(thm)],[96,93,83,57]) ).
tff(98,plain,
( differ(b,d)
<=> differ(b,d) ),
inference(rewrite,[status(thm)],[]) ).
tff(99,axiom,
differ(b,d),
file('/export/starexec/sandbox/benchmark/Axioms/PLA001-1.ax',differ_b_d) ).
tff(100,plain,
differ(b,d),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
^ [Y: $i,X: $i] :
refl(( ( ~ differ(Y,X)
| differ(X,Y) )
<=> ( ~ differ(Y,X)
| differ(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(102,plain,
( ! [Y: $i,X: $i] :
( ~ differ(Y,X)
| differ(X,Y) )
<=> ! [Y: $i,X: $i] :
( ~ differ(Y,X)
| differ(X,Y) ) ),
inference(quant_intro,[status(thm)],[101]) ).
tff(103,plain,
( ! [Y: $i,X: $i] :
( ~ differ(Y,X)
| differ(X,Y) )
<=> ! [Y: $i,X: $i] :
( ~ differ(Y,X)
| differ(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(104,plain,
^ [Y: $i,X: $i] :
rewrite(( ( differ(X,Y)
| ~ differ(Y,X) )
<=> ( ~ differ(Y,X)
| differ(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(105,plain,
( ! [Y: $i,X: $i] :
( differ(X,Y)
| ~ differ(Y,X) )
<=> ! [Y: $i,X: $i] :
( ~ differ(Y,X)
| differ(X,Y) ) ),
inference(quant_intro,[status(thm)],[104]) ).
tff(106,axiom,
! [Y: $i,X: $i] :
( differ(X,Y)
| ~ differ(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/PLA001-1.ax',symmetry_of_differ) ).
tff(107,plain,
! [Y: $i,X: $i] :
( ~ differ(Y,X)
| differ(X,Y) ),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
! [Y: $i,X: $i] :
( ~ differ(Y,X)
| differ(X,Y) ),
inference(modus_ponens,[status(thm)],[107,103]) ).
tff(109,plain,
! [Y: $i,X: $i] :
( ~ differ(Y,X)
| differ(X,Y) ),
inference(skolemize,[status(sab)],[108]) ).
tff(110,plain,
! [Y: $i,X: $i] :
( ~ differ(Y,X)
| differ(X,Y) ),
inference(modus_ponens,[status(thm)],[109,102]) ).
tff(111,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ differ(Y,X)
| differ(X,Y) )
| ~ differ(b,d)
| differ(d,b) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ differ(Y,X)
| differ(X,Y) )
| ~ differ(b,d)
| differ(d,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(112,plain,
( ~ ! [Y: $i,X: $i] :
( ~ differ(Y,X)
| differ(X,Y) )
| ~ differ(b,d)
| differ(d,b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(113,plain,
( ~ ! [Y: $i,X: $i] :
( ~ differ(Y,X)
| differ(X,Y) )
| ~ differ(b,d)
| differ(d,b) ),
inference(modus_ponens,[status(thm)],[112,111]) ).
tff(114,plain,
differ(d,b),
inference(unit_resolution,[status(thm)],[113,110,100]) ).
tff(115,plain,
( holds(on(c,d),s0)
<=> holds(on(c,d),s0) ),
inference(rewrite,[status(thm)],[]) ).
tff(116,axiom,
holds(on(c,d),s0),
file('/export/starexec/sandbox/benchmark/Axioms/PLA001-1.ax',initial_state3) ).
tff(117,plain,
holds(on(c,d),s0),
inference(modus_ponens,[status(thm)],[116,115]) ).
tff(118,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(119,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)],[118]) ).
tff(120,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(121,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(122,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)],[121]) ).
tff(123,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/sandbox/benchmark/Axioms/PLA001-0.ax',pickup_2) ).
tff(124,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)],[123,122]) ).
tff(125,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)],[124,120]) ).
tff(126,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)],[125]) ).
tff(127,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)],[126,119]) ).
tff(128,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(129,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(130,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)],[129]) ).
tff(131,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)],[130,128]) ).
tff(132,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(133,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)],[132,131]) ).
tff(134,plain,
holds(clear(d),do(pickup(c),s0)),
inference(unit_resolution,[status(thm)],[133,127,117,63,60]) ).
tff(135,plain,
( ( ~ ! [Z: $i,Y: $i,State: $i,X: $i] :
( ~ differ(Z,Y)
| ~ holds(clear(Z),State)
| holds(clear(Z),do(putdown(X,Y),State)) )
| ~ differ(d,b)
| ~ holds(clear(d),do(pickup(c),s0))
| holds(clear(d),do(putdown(c,b),do(pickup(c),s0))) )
<=> ( ~ ! [Z: $i,Y: $i,State: $i,X: $i] :
( ~ differ(Z,Y)
| ~ holds(clear(Z),State)
| holds(clear(Z),do(putdown(X,Y),State)) )
| ~ differ(d,b)
| ~ holds(clear(d),do(pickup(c),s0))
| holds(clear(d),do(putdown(c,b),do(pickup(c),s0))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(136,plain,
( ~ ! [Z: $i,Y: $i,State: $i,X: $i] :
( ~ differ(Z,Y)
| ~ holds(clear(Z),State)
| holds(clear(Z),do(putdown(X,Y),State)) )
| ~ differ(d,b)
| ~ holds(clear(d),do(pickup(c),s0))
| holds(clear(d),do(putdown(c,b),do(pickup(c),s0))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(137,plain,
( ~ ! [Z: $i,Y: $i,State: $i,X: $i] :
( ~ differ(Z,Y)
| ~ holds(clear(Z),State)
| holds(clear(Z),do(putdown(X,Y),State)) )
| ~ differ(d,b)
| ~ holds(clear(d),do(pickup(c),s0))
| holds(clear(d),do(putdown(c,b),do(pickup(c),s0))) ),
inference(modus_ponens,[status(thm)],[136,135]) ).
tff(138,plain,
holds(clear(d),do(putdown(c,b),do(pickup(c),s0))),
inference(unit_resolution,[status(thm)],[137,33,134,114]) ).
tff(139,plain,
( differ(d,table)
<=> differ(d,table) ),
inference(rewrite,[status(thm)],[]) ).
tff(140,axiom,
differ(d,table),
file('/export/starexec/sandbox/benchmark/Axioms/PLA001-1.ax',differ_d_table) ).
tff(141,plain,
differ(d,table),
inference(modus_ponens,[status(thm)],[140,139]) ).
tff(142,plain,
( ( ~ ! [State: $i,X: $i] :
( ~ differ(X,table)
| ~ holds(clear(X),State)
| ~ holds(empty,State)
| holds(holding(X),do(pickup(X),State)) )
| ~ differ(d,table)
| ~ holds(clear(d),do(putdown(c,b),do(pickup(c),s0)))
| holds(holding(d),do(pickup(d),do(putdown(c,b),do(pickup(c),s0))))
| ~ holds(empty,do(putdown(c,b),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)) )
| ~ differ(d,table)
| ~ holds(clear(d),do(putdown(c,b),do(pickup(c),s0)))
| holds(holding(d),do(pickup(d),do(putdown(c,b),do(pickup(c),s0))))
| ~ holds(empty,do(putdown(c,b),do(pickup(c),s0))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(143,plain,
( ( ~ differ(d,table)
| ~ holds(clear(d),do(putdown(c,b),do(pickup(c),s0)))
| ~ holds(empty,do(putdown(c,b),do(pickup(c),s0)))
| holds(holding(d),do(pickup(d),do(putdown(c,b),do(pickup(c),s0)))) )
<=> ( ~ differ(d,table)
| ~ holds(clear(d),do(putdown(c,b),do(pickup(c),s0)))
| holds(holding(d),do(pickup(d),do(putdown(c,b),do(pickup(c),s0))))
| ~ holds(empty,do(putdown(c,b),do(pickup(c),s0))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(144,plain,
( ( ~ ! [State: $i,X: $i] :
( ~ differ(X,table)
| ~ holds(clear(X),State)
| ~ holds(empty,State)
| holds(holding(X),do(pickup(X),State)) )
| ~ differ(d,table)
| ~ holds(clear(d),do(putdown(c,b),do(pickup(c),s0)))
| ~ holds(empty,do(putdown(c,b),do(pickup(c),s0)))
| holds(holding(d),do(pickup(d),do(putdown(c,b),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)) )
| ~ differ(d,table)
| ~ holds(clear(d),do(putdown(c,b),do(pickup(c),s0)))
| holds(holding(d),do(pickup(d),do(putdown(c,b),do(pickup(c),s0))))
| ~ holds(empty,do(putdown(c,b),do(pickup(c),s0))) ) ),
inference(monotonicity,[status(thm)],[143]) ).
tff(145,plain,
( ( ~ ! [State: $i,X: $i] :
( ~ differ(X,table)
| ~ holds(clear(X),State)
| ~ holds(empty,State)
| holds(holding(X),do(pickup(X),State)) )
| ~ differ(d,table)
| ~ holds(clear(d),do(putdown(c,b),do(pickup(c),s0)))
| ~ holds(empty,do(putdown(c,b),do(pickup(c),s0)))
| holds(holding(d),do(pickup(d),do(putdown(c,b),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)) )
| ~ differ(d,table)
| ~ holds(clear(d),do(putdown(c,b),do(pickup(c),s0)))
| holds(holding(d),do(pickup(d),do(putdown(c,b),do(pickup(c),s0))))
| ~ holds(empty,do(putdown(c,b),do(pickup(c),s0))) ) ),
inference(transitivity,[status(thm)],[144,142]) ).
tff(146,plain,
( ~ ! [State: $i,X: $i] :
( ~ differ(X,table)
| ~ holds(clear(X),State)
| ~ holds(empty,State)
| holds(holding(X),do(pickup(X),State)) )
| ~ differ(d,table)
| ~ holds(clear(d),do(putdown(c,b),do(pickup(c),s0)))
| ~ holds(empty,do(putdown(c,b),do(pickup(c),s0)))
| holds(holding(d),do(pickup(d),do(putdown(c,b),do(pickup(c),s0)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(147,plain,
( ~ ! [State: $i,X: $i] :
( ~ differ(X,table)
| ~ holds(clear(X),State)
| ~ holds(empty,State)
| holds(holding(X),do(pickup(X),State)) )
| ~ differ(d,table)
| ~ holds(clear(d),do(putdown(c,b),do(pickup(c),s0)))
| holds(holding(d),do(pickup(d),do(putdown(c,b),do(pickup(c),s0))))
| ~ holds(empty,do(putdown(c,b),do(pickup(c),s0))) ),
inference(modus_ponens,[status(thm)],[146,145]) ).
tff(148,plain,
( holds(holding(d),do(pickup(d),do(putdown(c,b),do(pickup(c),s0))))
| ~ holds(empty,do(putdown(c,b),do(pickup(c),s0))) ),
inference(unit_resolution,[status(thm)],[147,76,141,138]) ).
tff(149,plain,
holds(holding(d),do(pickup(d),do(putdown(c,b),do(pickup(c),s0)))),
inference(unit_resolution,[status(thm)],[148,97]) ).
tff(150,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(151,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)],[150]) ).
tff(152,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(153,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(154,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)],[153]) ).
tff(155,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(156,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)],[155,154]) ).
tff(157,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)],[156,152]) ).
tff(158,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)],[157]) ).
tff(159,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)],[158,151]) ).
tff(160,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(a),do(pickup(d),do(putdown(c,b),do(pickup(c),s0))))
| ~ holds(holding(d),do(pickup(d),do(putdown(c,b),do(pickup(c),s0))))
| holds(on(d,a),do(putdown(d,a),do(pickup(d),do(putdown(c,b),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(a),do(pickup(d),do(putdown(c,b),do(pickup(c),s0))))
| ~ holds(holding(d),do(pickup(d),do(putdown(c,b),do(pickup(c),s0))))
| holds(on(d,a),do(putdown(d,a),do(pickup(d),do(putdown(c,b),do(pickup(c),s0))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(161,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(a),do(pickup(d),do(putdown(c,b),do(pickup(c),s0))))
| ~ holds(holding(d),do(pickup(d),do(putdown(c,b),do(pickup(c),s0))))
| holds(on(d,a),do(putdown(d,a),do(pickup(d),do(putdown(c,b),do(pickup(c),s0))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(162,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(a),do(pickup(d),do(putdown(c,b),do(pickup(c),s0))))
| ~ holds(holding(d),do(pickup(d),do(putdown(c,b),do(pickup(c),s0))))
| holds(on(d,a),do(putdown(d,a),do(pickup(d),do(putdown(c,b),do(pickup(c),s0))))) ),
inference(modus_ponens,[status(thm)],[161,160]) ).
tff(163,plain,
holds(on(d,a),do(putdown(d,a),do(pickup(d),do(putdown(c,b),do(pickup(c),s0))))),
inference(unit_resolution,[status(thm)],[162,159,149,47]) ).
tff(164,plain,
^ [State: $i] :
refl(( ~ holds(on(d,a),State)
<=> ~ holds(on(d,a),State) )),
inference(bind,[status(th)],[]) ).
tff(165,plain,
( ! [State: $i] : ~ holds(on(d,a),State)
<=> ! [State: $i] : ~ holds(on(d,a),State) ),
inference(quant_intro,[status(thm)],[164]) ).
tff(166,plain,
( ! [State: $i] : ~ holds(on(d,a),State)
<=> ! [State: $i] : ~ holds(on(d,a),State) ),
inference(rewrite,[status(thm)],[]) ).
tff(167,axiom,
! [State: $i] : ~ holds(on(d,a),State),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_DA) ).
tff(168,plain,
! [State: $i] : ~ holds(on(d,a),State),
inference(modus_ponens,[status(thm)],[167,166]) ).
tff(169,plain,
! [State: $i] : ~ holds(on(d,a),State),
inference(skolemize,[status(sab)],[168]) ).
tff(170,plain,
! [State: $i] : ~ holds(on(d,a),State),
inference(modus_ponens,[status(thm)],[169,165]) ).
tff(171,plain,
( ~ ! [State: $i] : ~ holds(on(d,a),State)
| ~ holds(on(d,a),do(putdown(d,a),do(pickup(d),do(putdown(c,b),do(pickup(c),s0))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(172,plain,
$false,
inference(unit_resolution,[status(thm)],[171,170,163]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : PLA016-1 : TPTP v9.0.0. Released v1.1.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n002.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 Jun 20 02:22:46 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.56/0.78 % SZS status Unsatisfiable
% 0.56/0.78 % SZS output start Proof
% See solution above
% 0.62/0.80 % E exiting
%------------------------------------------------------------------------------