%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PLA007-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:22:50 AM UTC 2025
% Result : Unsatisfiable 32.22s 32.37s
% Output : Proof 32.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 116
% Syntax : Number of formulae : 244 ( 71 unt; 0 typ; 0 def)
% Number of atoms : 1513 ( 0 equ)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 2278 (1080 ~;1068 |; 0 &)
% ( 130 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 71 ( 71 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 : 657 ( 610 !; 0 ?; 657 :)
% 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(a_type,type,
a: $i ).
tff(b_type,type,
b: $i ).
tff(d_type,type,
d: $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(empty_type,type,
empty: $i ).
tff(holding_type,type,
holding: $i > $i ).
tff(table_type,type,
table: $i ).
tff(1,plain,
( differ(a,d)
<=> differ(a,d) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
differ(a,d),
file('/export/starexec/sandbox2/benchmark/Axioms/PLA001-1.ax',differ_a_d) ).
tff(3,plain,
differ(a,d),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [Y: $i,X: $i] :
refl(( ( ~ differ(Y,X)
| differ(X,Y) )
<=> ( ~ differ(Y,X)
| differ(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(5,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)],[4]) ).
tff(6,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(7,plain,
^ [Y: $i,X: $i] :
rewrite(( ( differ(X,Y)
| ~ differ(Y,X) )
<=> ( ~ differ(Y,X)
| differ(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(8,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)],[7]) ).
tff(9,axiom,
! [Y: $i,X: $i] :
( differ(X,Y)
| ~ differ(Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/PLA001-1.ax',symmetry_of_differ) ).
tff(10,plain,
! [Y: $i,X: $i] :
( ~ differ(Y,X)
| differ(X,Y) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [Y: $i,X: $i] :
( ~ differ(Y,X)
| differ(X,Y) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [Y: $i,X: $i] :
( ~ differ(Y,X)
| differ(X,Y) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [Y: $i,X: $i] :
( ~ differ(Y,X)
| differ(X,Y) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ differ(Y,X)
| differ(X,Y) )
| ~ differ(a,d)
| differ(d,a) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ differ(Y,X)
| differ(X,Y) )
| ~ differ(a,d)
| differ(d,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [Y: $i,X: $i] :
( ~ differ(Y,X)
| differ(X,Y) )
| ~ differ(a,d)
| differ(d,a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [Y: $i,X: $i] :
( ~ differ(Y,X)
| differ(X,Y) )
| ~ differ(a,d)
| differ(d,a) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
differ(d,a),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
( holds(empty,s0)
<=> holds(empty,s0) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
holds(empty,s0),
file('/export/starexec/sandbox2/benchmark/Axioms/PLA001-1.ax',initial_state8) ).
tff(20,plain,
holds(empty,s0),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
( holds(clear(c),s0)
<=> holds(clear(c),s0) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
holds(clear(c),s0),
file('/export/starexec/sandbox2/benchmark/Axioms/PLA001-1.ax',initial_state7) ).
tff(23,plain,
holds(clear(c),s0),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
( holds(on(c,d),s0)
<=> holds(on(c,d),s0) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,axiom,
holds(on(c,d),s0),
file('/export/starexec/sandbox2/benchmark/Axioms/PLA001-1.ax',initial_state3) ).
tff(26,plain,
holds(on(c,d),s0),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,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(28,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)],[27]) ).
tff(29,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(30,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(31,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)],[30]) ).
tff(32,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(33,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)],[32,31]) ).
tff(34,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)],[33,29]) ).
tff(35,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)],[34]) ).
tff(36,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)],[35,28]) ).
tff(37,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(38,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(39,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)],[38]) ).
tff(40,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)],[39,37]) ).
tff(41,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(42,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)],[41,40]) ).
tff(43,plain,
holds(clear(d),do(pickup(c),s0)),
inference(unit_resolution,[status(thm)],[42,36,26,23,20]) ).
tff(44,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(45,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)],[44]) ).
tff(46,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(47,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(48,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)],[47]) ).
tff(49,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/sandbox2/benchmark/Axioms/PLA001-0.ax',putdown_5) ).
tff(50,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)],[49,48]) ).
tff(51,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)],[50,46]) ).
tff(52,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)],[51]) ).
tff(53,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)],[52,45]) ).
tff(54,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,a)
| ~ holds(clear(d),do(pickup(c),s0))
| holds(clear(d),do(putdown(c,a),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,a)
| ~ holds(clear(d),do(pickup(c),s0))
| holds(clear(d),do(putdown(c,a),do(pickup(c),s0))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,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,a)
| ~ holds(clear(d),do(pickup(c),s0))
| holds(clear(d),do(putdown(c,a),do(pickup(c),s0))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(56,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,a)
| ~ holds(clear(d),do(pickup(c),s0))
| holds(clear(d),do(putdown(c,a),do(pickup(c),s0))) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
holds(clear(d),do(putdown(c,a),do(pickup(c),s0))),
inference(unit_resolution,[status(thm)],[56,53,43,17]) ).
tff(58,plain,
( differ(c,d)
<=> differ(c,d) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,axiom,
differ(c,d),
file('/export/starexec/sandbox2/benchmark/Axioms/PLA001-1.ax',differ_c_d) ).
tff(60,plain,
differ(c,d),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ differ(Y,X)
| differ(X,Y) )
| ~ differ(c,d)
| differ(d,c) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ differ(Y,X)
| differ(X,Y) )
| ~ differ(c,d)
| differ(d,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(62,plain,
( ~ ! [Y: $i,X: $i] :
( ~ differ(Y,X)
| differ(X,Y) )
| ~ differ(c,d)
| differ(d,c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(63,plain,
( ~ ! [Y: $i,X: $i] :
( ~ differ(Y,X)
| differ(X,Y) )
| ~ differ(c,d)
| differ(d,c) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
differ(d,c),
inference(unit_resolution,[status(thm)],[63,13,60]) ).
tff(65,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(66,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)],[65]) ).
tff(67,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(68,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(69,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)],[68]) ).
tff(70,axiom,
! [Z: $i,State: $i,X: $i] :
( holds(clear(X),do(pickup(Z),State))
| ~ holds(clear(X),State)
| ~ differ(X,Z) ),
file('/export/starexec/sandbox2/benchmark/Axioms/PLA001-0.ax',pickup_4) ).
tff(71,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)],[70,69]) ).
tff(72,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)],[71,67]) ).
tff(73,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)],[72]) ).
tff(74,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)],[73,66]) ).
tff(75,plain,
( ( ~ ! [Z: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ differ(X,Z)
| holds(clear(X),do(pickup(Z),State)) )
| ~ differ(d,c)
| holds(clear(d),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))
| ~ holds(clear(d),do(putdown(c,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)) )
| ~ differ(d,c)
| holds(clear(d),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))
| ~ holds(clear(d),do(putdown(c,a),do(pickup(c),s0))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(76,plain,
( ( ~ holds(clear(d),do(putdown(c,a),do(pickup(c),s0)))
| ~ differ(d,c)
| holds(clear(d),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))) )
<=> ( ~ differ(d,c)
| holds(clear(d),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))
| ~ holds(clear(d),do(putdown(c,a),do(pickup(c),s0))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(77,plain,
( ( ~ ! [Z: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ differ(X,Z)
| holds(clear(X),do(pickup(Z),State)) )
| ~ holds(clear(d),do(putdown(c,a),do(pickup(c),s0)))
| ~ differ(d,c)
| holds(clear(d),do(pickup(c),do(putdown(c,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)) )
| ~ differ(d,c)
| holds(clear(d),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))
| ~ holds(clear(d),do(putdown(c,a),do(pickup(c),s0))) ) ),
inference(monotonicity,[status(thm)],[76]) ).
tff(78,plain,
( ( ~ ! [Z: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ differ(X,Z)
| holds(clear(X),do(pickup(Z),State)) )
| ~ holds(clear(d),do(putdown(c,a),do(pickup(c),s0)))
| ~ differ(d,c)
| holds(clear(d),do(pickup(c),do(putdown(c,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)) )
| ~ differ(d,c)
| holds(clear(d),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))
| ~ holds(clear(d),do(putdown(c,a),do(pickup(c),s0))) ) ),
inference(transitivity,[status(thm)],[77,75]) ).
tff(79,plain,
( ~ ! [Z: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ differ(X,Z)
| holds(clear(X),do(pickup(Z),State)) )
| ~ holds(clear(d),do(putdown(c,a),do(pickup(c),s0)))
| ~ differ(d,c)
| holds(clear(d),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(80,plain,
( ~ ! [Z: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ differ(X,Z)
| holds(clear(X),do(pickup(Z),State)) )
| ~ differ(d,c)
| holds(clear(d),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))
| ~ holds(clear(d),do(putdown(c,a),do(pickup(c),s0))) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
holds(clear(d),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))),
inference(unit_resolution,[status(thm)],[80,74,64,57]) ).
tff(82,plain,
( differ(b,d)
<=> differ(b,d) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,axiom,
differ(b,d),
file('/export/starexec/sandbox2/benchmark/Axioms/PLA001-1.ax',differ_b_d) ).
tff(84,plain,
differ(b,d),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,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(86,plain,
( ~ ! [Y: $i,X: $i] :
( ~ differ(Y,X)
| differ(X,Y) )
| ~ differ(b,d)
| differ(d,b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(87,plain,
( ~ ! [Y: $i,X: $i] :
( ~ differ(Y,X)
| differ(X,Y) )
| ~ differ(b,d)
| differ(d,b) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
differ(d,b),
inference(unit_resolution,[status(thm)],[87,13,84]) ).
tff(89,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),do(putdown(c,a),do(pickup(c),s0))))
| holds(clear(d),do(putdown(c,b),do(pickup(c),do(putdown(c,a),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),do(putdown(c,a),do(pickup(c),s0))))
| holds(clear(d),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(90,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),do(putdown(c,a),do(pickup(c),s0))))
| holds(clear(d),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(91,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),do(putdown(c,a),do(pickup(c),s0))))
| holds(clear(d),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))) ),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
holds(clear(d),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))),
inference(unit_resolution,[status(thm)],[91,53,88,81]) ).
tff(93,plain,
( ( ~ ! [Z: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ differ(X,Z)
| holds(clear(X),do(pickup(Z),State)) )
| ~ differ(d,a)
| ~ holds(clear(d),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))))
| holds(clear(d),do(pickup(a),do(putdown(c,b),do(pickup(c),do(putdown(c,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)) )
| ~ differ(d,a)
| ~ holds(clear(d),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))))
| holds(clear(d),do(pickup(a),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(94,plain,
( ( ~ holds(clear(d),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))))
| ~ differ(d,a)
| holds(clear(d),do(pickup(a),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))))) )
<=> ( ~ differ(d,a)
| ~ holds(clear(d),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))))
| holds(clear(d),do(pickup(a),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(95,plain,
( ( ~ ! [Z: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ differ(X,Z)
| holds(clear(X),do(pickup(Z),State)) )
| ~ holds(clear(d),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))))
| ~ differ(d,a)
| holds(clear(d),do(pickup(a),do(putdown(c,b),do(pickup(c),do(putdown(c,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)) )
| ~ differ(d,a)
| ~ holds(clear(d),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))))
| holds(clear(d),do(pickup(a),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))))) ) ),
inference(monotonicity,[status(thm)],[94]) ).
tff(96,plain,
( ( ~ ! [Z: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ differ(X,Z)
| holds(clear(X),do(pickup(Z),State)) )
| ~ holds(clear(d),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))))
| ~ differ(d,a)
| holds(clear(d),do(pickup(a),do(putdown(c,b),do(pickup(c),do(putdown(c,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)) )
| ~ differ(d,a)
| ~ holds(clear(d),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))))
| holds(clear(d),do(pickup(a),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))))) ) ),
inference(transitivity,[status(thm)],[95,93]) ).
tff(97,plain,
( ~ ! [Z: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ differ(X,Z)
| holds(clear(X),do(pickup(Z),State)) )
| ~ holds(clear(d),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))))
| ~ differ(d,a)
| holds(clear(d),do(pickup(a),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(98,plain,
( ~ ! [Z: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ differ(X,Z)
| holds(clear(X),do(pickup(Z),State)) )
| ~ differ(d,a)
| ~ holds(clear(d),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))))
| holds(clear(d),do(pickup(a),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))))) ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
holds(clear(d),do(pickup(a),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))))),
inference(unit_resolution,[status(thm)],[98,74,17,92]) ).
tff(100,plain,
( holds(clear(a),s0)
<=> holds(clear(a),s0) ),
inference(rewrite,[status(thm)],[]) ).
tff(101,axiom,
holds(clear(a),s0),
file('/export/starexec/sandbox2/benchmark/Axioms/PLA001-1.ax',initial_state5) ).
tff(102,plain,
holds(clear(a),s0),
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,plain,
( differ(a,c)
<=> differ(a,c) ),
inference(rewrite,[status(thm)],[]) ).
tff(104,axiom,
differ(a,c),
file('/export/starexec/sandbox2/benchmark/Axioms/PLA001-1.ax',differ_a_c) ).
tff(105,plain,
differ(a,c),
inference(modus_ponens,[status(thm)],[104,103]) ).
tff(106,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(107,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(108,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)],[107,106]) ).
tff(109,plain,
holds(clear(a),do(pickup(c),s0)),
inference(unit_resolution,[status(thm)],[108,74,105,102]) ).
tff(110,plain,
( differ(c,table)
<=> differ(c,table) ),
inference(rewrite,[status(thm)],[]) ).
tff(111,axiom,
differ(c,table),
file('/export/starexec/sandbox2/benchmark/Axioms/PLA001-1.ax',differ_c_table) ).
tff(112,plain,
differ(c,table),
inference(modus_ponens,[status(thm)],[111,110]) ).
tff(113,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(114,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)],[113]) ).
tff(115,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(116,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(117,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)],[116]) ).
tff(118,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/sandbox2/benchmark/Axioms/PLA001-0.ax',pickup_1) ).
tff(119,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)],[118,117]) ).
tff(120,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)],[119,115]) ).
tff(121,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)],[120]) ).
tff(122,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)],[121,114]) ).
tff(123,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(124,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(125,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)],[124]) ).
tff(126,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)],[125,123]) ).
tff(127,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(128,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)],[127,126]) ).
tff(129,plain,
holds(holding(c),do(pickup(c),s0)),
inference(unit_resolution,[status(thm)],[128,122,112,23,20]) ).
tff(130,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(131,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)],[130]) ).
tff(132,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(133,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(134,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)],[133]) ).
tff(135,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/sandbox2/benchmark/Axioms/PLA001-0.ax',putdown_2) ).
tff(136,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)],[135,134]) ).
tff(137,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)],[136,132]) ).
tff(138,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)],[137]) ).
tff(139,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)],[138,131]) ).
tff(140,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(c),s0))
| ~ holds(holding(c),do(pickup(c),s0))
| holds(on(c,a),do(putdown(c,a),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(c),s0))
| ~ holds(holding(c),do(pickup(c),s0))
| holds(on(c,a),do(putdown(c,a),do(pickup(c),s0))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(141,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(c),s0))
| ~ holds(holding(c),do(pickup(c),s0))
| holds(on(c,a),do(putdown(c,a),do(pickup(c),s0))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(142,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(c),s0))
| ~ holds(holding(c),do(pickup(c),s0))
| holds(on(c,a),do(putdown(c,a),do(pickup(c),s0))) ),
inference(modus_ponens,[status(thm)],[141,140]) ).
tff(143,plain,
holds(on(c,a),do(putdown(c,a),do(pickup(c),s0))),
inference(unit_resolution,[status(thm)],[142,139,129,109]) ).
tff(144,plain,
^ [Y: $i,State: $i,X: $i] :
refl(( ( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(clear(X),do(putdown(X,Y),State)) )
<=> ( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(clear(X),do(putdown(X,Y),State)) ) )),
inference(bind,[status(th)],[]) ).
tff(145,plain,
( ! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(clear(X),do(putdown(X,Y),State)) )
<=> ! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(clear(X),do(putdown(X,Y),State)) ) ),
inference(quant_intro,[status(thm)],[144]) ).
tff(146,plain,
( ! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(clear(X),do(putdown(X,Y),State)) )
<=> ! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(clear(X),do(putdown(X,Y),State)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(147,plain,
^ [Y: $i,State: $i,X: $i] :
trans(monotonicity(rewrite(( ( holds(clear(X),do(putdown(X,Y),State))
| ~ holds(holding(X),State) )
<=> ( ~ holds(holding(X),State)
| holds(clear(X),do(putdown(X,Y),State)) ) )),
( ( holds(clear(X),do(putdown(X,Y),State))
| ~ holds(holding(X),State)
| ~ holds(clear(Y),State) )
<=> ( ~ holds(holding(X),State)
| holds(clear(X),do(putdown(X,Y),State))
| ~ holds(clear(Y),State) ) )),
rewrite(( ( ~ holds(holding(X),State)
| holds(clear(X),do(putdown(X,Y),State))
| ~ holds(clear(Y),State) )
<=> ( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(clear(X),do(putdown(X,Y),State)) ) )),
( ( holds(clear(X),do(putdown(X,Y),State))
| ~ holds(holding(X),State)
| ~ holds(clear(Y),State) )
<=> ( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(clear(X),do(putdown(X,Y),State)) ) )),
inference(bind,[status(th)],[]) ).
tff(148,plain,
( ! [Y: $i,State: $i,X: $i] :
( holds(clear(X),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(clear(X),do(putdown(X,Y),State)) ) ),
inference(quant_intro,[status(thm)],[147]) ).
tff(149,axiom,
! [Y: $i,State: $i,X: $i] :
( holds(clear(X),do(putdown(X,Y),State))
| ~ holds(holding(X),State)
| ~ holds(clear(Y),State) ),
file('/export/starexec/sandbox2/benchmark/Axioms/PLA001-0.ax',putdown_3) ).
tff(150,plain,
! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(clear(X),do(putdown(X,Y),State)) ),
inference(modus_ponens,[status(thm)],[149,148]) ).
tff(151,plain,
! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(clear(X),do(putdown(X,Y),State)) ),
inference(modus_ponens,[status(thm)],[150,146]) ).
tff(152,plain,
! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(clear(X),do(putdown(X,Y),State)) ),
inference(skolemize,[status(sab)],[151]) ).
tff(153,plain,
! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(clear(X),do(putdown(X,Y),State)) ),
inference(modus_ponens,[status(thm)],[152,145]) ).
tff(154,plain,
( ( ~ ! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(clear(X),do(putdown(X,Y),State)) )
| ~ holds(clear(a),do(pickup(c),s0))
| ~ holds(holding(c),do(pickup(c),s0))
| holds(clear(c),do(putdown(c,a),do(pickup(c),s0))) )
<=> ( ~ ! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(clear(X),do(putdown(X,Y),State)) )
| ~ holds(clear(a),do(pickup(c),s0))
| ~ holds(holding(c),do(pickup(c),s0))
| holds(clear(c),do(putdown(c,a),do(pickup(c),s0))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(155,plain,
( ~ ! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(clear(X),do(putdown(X,Y),State)) )
| ~ holds(clear(a),do(pickup(c),s0))
| ~ holds(holding(c),do(pickup(c),s0))
| holds(clear(c),do(putdown(c,a),do(pickup(c),s0))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(156,plain,
( ~ ! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(clear(X),do(putdown(X,Y),State)) )
| ~ holds(clear(a),do(pickup(c),s0))
| ~ holds(holding(c),do(pickup(c),s0))
| holds(clear(c),do(putdown(c,a),do(pickup(c),s0))) ),
inference(modus_ponens,[status(thm)],[155,154]) ).
tff(157,plain,
holds(clear(c),do(putdown(c,a),do(pickup(c),s0))),
inference(unit_resolution,[status(thm)],[156,153,129,109]) ).
tff(158,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(159,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)],[158]) ).
tff(160,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(161,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(162,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)],[161]) ).
tff(163,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/sandbox2/benchmark/Axioms/PLA001-0.ax',putdown_1) ).
tff(164,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)],[163,162]) ).
tff(165,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)],[164,160]) ).
tff(166,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)],[165]) ).
tff(167,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)],[166,159]) ).
tff(168,plain,
( ( ~ ! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(empty,do(putdown(X,Y),State)) )
| ~ holds(clear(a),do(pickup(c),s0))
| ~ holds(holding(c),do(pickup(c),s0))
| holds(empty,do(putdown(c,a),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(a),do(pickup(c),s0))
| ~ holds(holding(c),do(pickup(c),s0))
| holds(empty,do(putdown(c,a),do(pickup(c),s0))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(169,plain,
( ~ ! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(empty,do(putdown(X,Y),State)) )
| ~ holds(clear(a),do(pickup(c),s0))
| ~ holds(holding(c),do(pickup(c),s0))
| holds(empty,do(putdown(c,a),do(pickup(c),s0))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(170,plain,
( ~ ! [Y: $i,State: $i,X: $i] :
( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(empty,do(putdown(X,Y),State)) )
| ~ holds(clear(a),do(pickup(c),s0))
| ~ holds(holding(c),do(pickup(c),s0))
| holds(empty,do(putdown(c,a),do(pickup(c),s0))) ),
inference(modus_ponens,[status(thm)],[169,168]) ).
tff(171,plain,
holds(empty,do(putdown(c,a),do(pickup(c),s0))),
inference(unit_resolution,[status(thm)],[170,167,129,109]) ).
tff(172,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(on(c,a),do(putdown(c,a),do(pickup(c),s0)))
| holds(clear(a),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))
| ~ holds(clear(c),do(putdown(c,a),do(pickup(c),s0)))
| ~ holds(empty,do(putdown(c,a),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(on(c,a),do(putdown(c,a),do(pickup(c),s0)))
| holds(clear(a),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))
| ~ holds(clear(c),do(putdown(c,a),do(pickup(c),s0)))
| ~ holds(empty,do(putdown(c,a),do(pickup(c),s0))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(173,plain,
( ( ~ holds(clear(c),do(putdown(c,a),do(pickup(c),s0)))
| ~ holds(empty,do(putdown(c,a),do(pickup(c),s0)))
| ~ holds(on(c,a),do(putdown(c,a),do(pickup(c),s0)))
| holds(clear(a),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))) )
<=> ( ~ holds(on(c,a),do(putdown(c,a),do(pickup(c),s0)))
| holds(clear(a),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))
| ~ holds(clear(c),do(putdown(c,a),do(pickup(c),s0)))
| ~ holds(empty,do(putdown(c,a),do(pickup(c),s0))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(174,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),do(putdown(c,a),do(pickup(c),s0)))
| ~ holds(empty,do(putdown(c,a),do(pickup(c),s0)))
| ~ holds(on(c,a),do(putdown(c,a),do(pickup(c),s0)))
| holds(clear(a),do(pickup(c),do(putdown(c,a),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(on(c,a),do(putdown(c,a),do(pickup(c),s0)))
| holds(clear(a),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))
| ~ holds(clear(c),do(putdown(c,a),do(pickup(c),s0)))
| ~ holds(empty,do(putdown(c,a),do(pickup(c),s0))) ) ),
inference(monotonicity,[status(thm)],[173]) ).
tff(175,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),do(putdown(c,a),do(pickup(c),s0)))
| ~ holds(empty,do(putdown(c,a),do(pickup(c),s0)))
| ~ holds(on(c,a),do(putdown(c,a),do(pickup(c),s0)))
| holds(clear(a),do(pickup(c),do(putdown(c,a),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(on(c,a),do(putdown(c,a),do(pickup(c),s0)))
| holds(clear(a),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))
| ~ holds(clear(c),do(putdown(c,a),do(pickup(c),s0)))
| ~ holds(empty,do(putdown(c,a),do(pickup(c),s0))) ) ),
inference(transitivity,[status(thm)],[174,172]) ).
tff(176,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),do(putdown(c,a),do(pickup(c),s0)))
| ~ holds(empty,do(putdown(c,a),do(pickup(c),s0)))
| ~ holds(on(c,a),do(putdown(c,a),do(pickup(c),s0)))
| holds(clear(a),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(177,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(on(c,a),do(putdown(c,a),do(pickup(c),s0)))
| holds(clear(a),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))
| ~ holds(clear(c),do(putdown(c,a),do(pickup(c),s0)))
| ~ holds(empty,do(putdown(c,a),do(pickup(c),s0))) ),
inference(modus_ponens,[status(thm)],[176,175]) ).
tff(178,plain,
holds(clear(a),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))),
inference(unit_resolution,[status(thm)],[177,36,171,157,143]) ).
tff(179,plain,
( differ(a,b)
<=> differ(a,b) ),
inference(rewrite,[status(thm)],[]) ).
tff(180,axiom,
differ(a,b),
file('/export/starexec/sandbox2/benchmark/Axioms/PLA001-1.ax',differ_a_b) ).
tff(181,plain,
differ(a,b),
inference(modus_ponens,[status(thm)],[180,179]) ).
tff(182,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),do(putdown(c,a),do(pickup(c),s0))))
| holds(clear(a),do(putdown(c,b),do(pickup(c),do(putdown(c,a),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),do(putdown(c,a),do(pickup(c),s0))))
| holds(clear(a),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(183,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),do(putdown(c,a),do(pickup(c),s0))))
| holds(clear(a),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(184,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),do(putdown(c,a),do(pickup(c),s0))))
| holds(clear(a),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))) ),
inference(modus_ponens,[status(thm)],[183,182]) ).
tff(185,plain,
holds(clear(a),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))),
inference(unit_resolution,[status(thm)],[184,53,181,178]) ).
tff(186,plain,
( holds(clear(b),s0)
<=> holds(clear(b),s0) ),
inference(rewrite,[status(thm)],[]) ).
tff(187,axiom,
holds(clear(b),s0),
file('/export/starexec/sandbox2/benchmark/Axioms/PLA001-1.ax',initial_state6) ).
tff(188,plain,
holds(clear(b),s0),
inference(modus_ponens,[status(thm)],[187,186]) ).
tff(189,plain,
( differ(b,c)
<=> differ(b,c) ),
inference(rewrite,[status(thm)],[]) ).
tff(190,axiom,
differ(b,c),
file('/export/starexec/sandbox2/benchmark/Axioms/PLA001-1.ax',differ_b_c) ).
tff(191,plain,
differ(b,c),
inference(modus_ponens,[status(thm)],[190,189]) ).
tff(192,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(193,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(194,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)],[193,192]) ).
tff(195,plain,
holds(clear(b),do(pickup(c),s0)),
inference(unit_resolution,[status(thm)],[194,74,191,188]) ).
tff(196,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ differ(Y,X)
| differ(X,Y) )
| ~ differ(a,b)
| differ(b,a) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ differ(Y,X)
| differ(X,Y) )
| ~ differ(a,b)
| differ(b,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(197,plain,
( ~ ! [Y: $i,X: $i] :
( ~ differ(Y,X)
| differ(X,Y) )
| ~ differ(a,b)
| differ(b,a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(198,plain,
( ~ ! [Y: $i,X: $i] :
( ~ differ(Y,X)
| differ(X,Y) )
| ~ differ(a,b)
| differ(b,a) ),
inference(modus_ponens,[status(thm)],[197,196]) ).
tff(199,plain,
differ(b,a),
inference(unit_resolution,[status(thm)],[198,13,181]) ).
tff(200,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(b,a)
| ~ holds(clear(b),do(pickup(c),s0))
| holds(clear(b),do(putdown(c,a),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(b,a)
| ~ holds(clear(b),do(pickup(c),s0))
| holds(clear(b),do(putdown(c,a),do(pickup(c),s0))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(201,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(b,a)
| ~ holds(clear(b),do(pickup(c),s0))
| holds(clear(b),do(putdown(c,a),do(pickup(c),s0))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(202,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(b,a)
| ~ holds(clear(b),do(pickup(c),s0))
| holds(clear(b),do(putdown(c,a),do(pickup(c),s0))) ),
inference(modus_ponens,[status(thm)],[201,200]) ).
tff(203,plain,
holds(clear(b),do(putdown(c,a),do(pickup(c),s0))),
inference(unit_resolution,[status(thm)],[202,53,199,195]) ).
tff(204,plain,
( ( ~ ! [Z: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ differ(X,Z)
| holds(clear(X),do(pickup(Z),State)) )
| ~ differ(b,c)
| holds(clear(b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))
| ~ holds(clear(b),do(putdown(c,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)) )
| ~ differ(b,c)
| holds(clear(b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))
| ~ holds(clear(b),do(putdown(c,a),do(pickup(c),s0))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(205,plain,
( ( ~ holds(clear(b),do(putdown(c,a),do(pickup(c),s0)))
| ~ differ(b,c)
| holds(clear(b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))) )
<=> ( ~ differ(b,c)
| holds(clear(b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))
| ~ holds(clear(b),do(putdown(c,a),do(pickup(c),s0))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(206,plain,
( ( ~ ! [Z: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ differ(X,Z)
| holds(clear(X),do(pickup(Z),State)) )
| ~ holds(clear(b),do(putdown(c,a),do(pickup(c),s0)))
| ~ differ(b,c)
| holds(clear(b),do(pickup(c),do(putdown(c,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)) )
| ~ differ(b,c)
| holds(clear(b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))
| ~ holds(clear(b),do(putdown(c,a),do(pickup(c),s0))) ) ),
inference(monotonicity,[status(thm)],[205]) ).
tff(207,plain,
( ( ~ ! [Z: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ differ(X,Z)
| holds(clear(X),do(pickup(Z),State)) )
| ~ holds(clear(b),do(putdown(c,a),do(pickup(c),s0)))
| ~ differ(b,c)
| holds(clear(b),do(pickup(c),do(putdown(c,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)) )
| ~ differ(b,c)
| holds(clear(b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))
| ~ holds(clear(b),do(putdown(c,a),do(pickup(c),s0))) ) ),
inference(transitivity,[status(thm)],[206,204]) ).
tff(208,plain,
( ~ ! [Z: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ differ(X,Z)
| holds(clear(X),do(pickup(Z),State)) )
| ~ holds(clear(b),do(putdown(c,a),do(pickup(c),s0)))
| ~ differ(b,c)
| holds(clear(b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(209,plain,
( ~ ! [Z: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ differ(X,Z)
| holds(clear(X),do(pickup(Z),State)) )
| ~ differ(b,c)
| holds(clear(b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))
| ~ holds(clear(b),do(putdown(c,a),do(pickup(c),s0))) ),
inference(modus_ponens,[status(thm)],[208,207]) ).
tff(210,plain,
holds(clear(b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))),
inference(unit_resolution,[status(thm)],[209,74,191,203]) ).
tff(211,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(holding(c),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))
| ~ holds(clear(c),do(putdown(c,a),do(pickup(c),s0)))
| ~ holds(empty,do(putdown(c,a),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(c,table)
| holds(holding(c),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))
| ~ holds(clear(c),do(putdown(c,a),do(pickup(c),s0)))
| ~ holds(empty,do(putdown(c,a),do(pickup(c),s0))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(212,plain,
( ( ~ differ(c,table)
| ~ holds(clear(c),do(putdown(c,a),do(pickup(c),s0)))
| ~ holds(empty,do(putdown(c,a),do(pickup(c),s0)))
| holds(holding(c),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))) )
<=> ( ~ differ(c,table)
| holds(holding(c),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))
| ~ holds(clear(c),do(putdown(c,a),do(pickup(c),s0)))
| ~ holds(empty,do(putdown(c,a),do(pickup(c),s0))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(213,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),do(putdown(c,a),do(pickup(c),s0)))
| ~ holds(empty,do(putdown(c,a),do(pickup(c),s0)))
| holds(holding(c),do(pickup(c),do(putdown(c,a),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(c,table)
| holds(holding(c),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))
| ~ holds(clear(c),do(putdown(c,a),do(pickup(c),s0)))
| ~ holds(empty,do(putdown(c,a),do(pickup(c),s0))) ) ),
inference(monotonicity,[status(thm)],[212]) ).
tff(214,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),do(putdown(c,a),do(pickup(c),s0)))
| ~ holds(empty,do(putdown(c,a),do(pickup(c),s0)))
| holds(holding(c),do(pickup(c),do(putdown(c,a),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(c,table)
| holds(holding(c),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))
| ~ holds(clear(c),do(putdown(c,a),do(pickup(c),s0)))
| ~ holds(empty,do(putdown(c,a),do(pickup(c),s0))) ) ),
inference(transitivity,[status(thm)],[213,211]) ).
tff(215,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),do(putdown(c,a),do(pickup(c),s0)))
| ~ holds(empty,do(putdown(c,a),do(pickup(c),s0)))
| holds(holding(c),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(216,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(holding(c),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))
| ~ holds(clear(c),do(putdown(c,a),do(pickup(c),s0)))
| ~ holds(empty,do(putdown(c,a),do(pickup(c),s0))) ),
inference(modus_ponens,[status(thm)],[215,214]) ).
tff(217,plain,
holds(holding(c),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))),
inference(unit_resolution,[status(thm)],[216,122,112,171,157]) ).
tff(218,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),do(putdown(c,a),do(pickup(c),s0))))
| ~ holds(holding(c),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))
| holds(empty,do(putdown(c,b),do(pickup(c),do(putdown(c,a),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),do(putdown(c,a),do(pickup(c),s0))))
| ~ holds(holding(c),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))
| holds(empty,do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(219,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),do(putdown(c,a),do(pickup(c),s0))))
| ~ holds(holding(c),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))
| holds(empty,do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(220,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),do(putdown(c,a),do(pickup(c),s0))))
| ~ holds(holding(c),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))
| holds(empty,do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))) ),
inference(modus_ponens,[status(thm)],[219,218]) ).
tff(221,plain,
holds(empty,do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))),
inference(unit_resolution,[status(thm)],[220,167,217,210]) ).
tff(222,plain,
( differ(a,table)
<=> differ(a,table) ),
inference(rewrite,[status(thm)],[]) ).
tff(223,axiom,
differ(a,table),
file('/export/starexec/sandbox2/benchmark/Axioms/PLA001-1.ax',differ_a_table) ).
tff(224,plain,
differ(a,table),
inference(modus_ponens,[status(thm)],[223,222]) ).
tff(225,plain,
( ( ~ ! [State: $i,X: $i] :
( ~ differ(X,table)
| ~ holds(clear(X),State)
| ~ holds(empty,State)
| holds(holding(X),do(pickup(X),State)) )
| ~ differ(a,table)
| ~ holds(empty,do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))))
| ~ holds(clear(a),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))))
| holds(holding(a),do(pickup(a),do(putdown(c,b),do(pickup(c),do(putdown(c,a),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(a,table)
| ~ holds(empty,do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))))
| ~ holds(clear(a),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))))
| holds(holding(a),do(pickup(a),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(226,plain,
( ( ~ differ(a,table)
| ~ holds(clear(a),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))))
| ~ holds(empty,do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))))
| holds(holding(a),do(pickup(a),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))))) )
<=> ( ~ differ(a,table)
| ~ holds(empty,do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))))
| ~ holds(clear(a),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))))
| holds(holding(a),do(pickup(a),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(227,plain,
( ( ~ ! [State: $i,X: $i] :
( ~ differ(X,table)
| ~ holds(clear(X),State)
| ~ holds(empty,State)
| holds(holding(X),do(pickup(X),State)) )
| ~ differ(a,table)
| ~ holds(clear(a),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))))
| ~ holds(empty,do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))))
| holds(holding(a),do(pickup(a),do(putdown(c,b),do(pickup(c),do(putdown(c,a),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(a,table)
| ~ holds(empty,do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))))
| ~ holds(clear(a),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))))
| holds(holding(a),do(pickup(a),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))))) ) ),
inference(monotonicity,[status(thm)],[226]) ).
tff(228,plain,
( ( ~ ! [State: $i,X: $i] :
( ~ differ(X,table)
| ~ holds(clear(X),State)
| ~ holds(empty,State)
| holds(holding(X),do(pickup(X),State)) )
| ~ differ(a,table)
| ~ holds(clear(a),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))))
| ~ holds(empty,do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))))
| holds(holding(a),do(pickup(a),do(putdown(c,b),do(pickup(c),do(putdown(c,a),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(a,table)
| ~ holds(empty,do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))))
| ~ holds(clear(a),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))))
| holds(holding(a),do(pickup(a),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))))) ) ),
inference(transitivity,[status(thm)],[227,225]) ).
tff(229,plain,
( ~ ! [State: $i,X: $i] :
( ~ differ(X,table)
| ~ holds(clear(X),State)
| ~ holds(empty,State)
| holds(holding(X),do(pickup(X),State)) )
| ~ differ(a,table)
| ~ holds(clear(a),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))))
| ~ holds(empty,do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))))
| holds(holding(a),do(pickup(a),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(230,plain,
( ~ ! [State: $i,X: $i] :
( ~ differ(X,table)
| ~ holds(clear(X),State)
| ~ holds(empty,State)
| holds(holding(X),do(pickup(X),State)) )
| ~ differ(a,table)
| ~ holds(empty,do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))))
| ~ holds(clear(a),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))))
| holds(holding(a),do(pickup(a),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))))) ),
inference(modus_ponens,[status(thm)],[229,228]) ).
tff(231,plain,
holds(holding(a),do(pickup(a),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0)))))),
inference(unit_resolution,[status(thm)],[230,122,224,221,185]) ).
tff(232,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(d),do(pickup(a),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))))
| ~ holds(holding(a),do(pickup(a),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))))
| holds(on(a,d),do(putdown(a,d),do(pickup(a),do(putdown(c,b),do(pickup(c),do(putdown(c,a),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(d),do(pickup(a),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))))
| ~ holds(holding(a),do(pickup(a),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))))
| holds(on(a,d),do(putdown(a,d),do(pickup(a),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(233,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(d),do(pickup(a),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))))
| ~ holds(holding(a),do(pickup(a),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))))
| holds(on(a,d),do(putdown(a,d),do(pickup(a),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(234,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(d),do(pickup(a),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))))
| ~ holds(holding(a),do(pickup(a),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))))
| holds(on(a,d),do(putdown(a,d),do(pickup(a),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))))) ),
inference(modus_ponens,[status(thm)],[233,232]) ).
tff(235,plain,
holds(on(a,d),do(putdown(a,d),do(pickup(a),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))))),
inference(unit_resolution,[status(thm)],[234,139,231,99]) ).
tff(236,plain,
^ [State: $i] :
refl(( ~ holds(on(a,d),State)
<=> ~ holds(on(a,d),State) )),
inference(bind,[status(th)],[]) ).
tff(237,plain,
( ! [State: $i] : ~ holds(on(a,d),State)
<=> ! [State: $i] : ~ holds(on(a,d),State) ),
inference(quant_intro,[status(thm)],[236]) ).
tff(238,plain,
( ! [State: $i] : ~ holds(on(a,d),State)
<=> ! [State: $i] : ~ holds(on(a,d),State) ),
inference(rewrite,[status(thm)],[]) ).
tff(239,axiom,
! [State: $i] : ~ holds(on(a,d),State),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_AD) ).
tff(240,plain,
! [State: $i] : ~ holds(on(a,d),State),
inference(modus_ponens,[status(thm)],[239,238]) ).
tff(241,plain,
! [State: $i] : ~ holds(on(a,d),State),
inference(skolemize,[status(sab)],[240]) ).
tff(242,plain,
! [State: $i] : ~ holds(on(a,d),State),
inference(modus_ponens,[status(thm)],[241,237]) ).
tff(243,plain,
( ~ ! [State: $i] : ~ holds(on(a,d),State)
| ~ holds(on(a,d),do(putdown(a,d),do(pickup(a),do(putdown(c,b),do(pickup(c),do(putdown(c,a),do(pickup(c),s0))))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(244,plain,
$false,
inference(unit_resolution,[status(thm)],[243,242,235]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : PLA007-1 : TPTP v9.0.0. Released v1.1.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n007.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 02:20:50 EDT 2025
% 0.11/0.32 % CPUTime :
% 32.22/32.37 % SZS status Unsatisfiable
% 32.22/32.37 % SZS output start Proof
% See solution above
% 32.22/32.43 % E exiting
%------------------------------------------------------------------------------