%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PLA017-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:22:51 AM UTC 2025
% Result : Unsatisfiable 0.93s 1.11s
% Output : Proof 0.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 39
% Syntax : Number of formulae : 83 ( 28 unt; 0 typ; 0 def)
% Number of atoms : 444 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 621 ( 293 ~; 281 |; 0 &)
% ( 47 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 33 ( 33 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 : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 188 ( 167 !; 0 ?; 188 :)
% 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(a_type,type,
a: $i ).
tff(putdown_type,type,
putdown: ( $i * $i ) > $i ).
tff(c_type,type,
c: $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,
( differ(a,c)
<=> differ(a,c) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
differ(a,c),
file('/export/starexec/sandbox2/benchmark/Axioms/PLA001-1.ax',differ_a_c) ).
tff(3,plain,
differ(a,c),
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,c)
| differ(c,a) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ differ(Y,X)
| differ(X,Y) )
| ~ differ(a,c)
| differ(c,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [Y: $i,X: $i] :
( ~ differ(Y,X)
| differ(X,Y) )
| ~ differ(a,c)
| differ(c,a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [Y: $i,X: $i] :
( ~ differ(Y,X)
| differ(X,Y) )
| ~ differ(a,c)
| differ(c,a) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
differ(c,a),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
( holds(clear(c),s0)
<=> holds(clear(c),s0) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
holds(clear(c),s0),
file('/export/starexec/sandbox2/benchmark/Axioms/PLA001-1.ax',initial_state7) ).
tff(20,plain,
holds(clear(c),s0),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,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(22,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)],[21]) ).
tff(23,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(24,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(25,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)],[24]) ).
tff(26,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(27,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)],[26,25]) ).
tff(28,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)],[27,23]) ).
tff(29,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)],[28]) ).
tff(30,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)],[29,22]) ).
tff(31,plain,
( ( ~ ! [Z: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ differ(X,Z)
| holds(clear(X),do(pickup(Z),State)) )
| ~ holds(clear(c),s0)
| ~ differ(c,a)
| holds(clear(c),do(pickup(a),s0)) )
<=> ( ~ ! [Z: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ differ(X,Z)
| holds(clear(X),do(pickup(Z),State)) )
| ~ holds(clear(c),s0)
| ~ differ(c,a)
| holds(clear(c),do(pickup(a),s0)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
( ~ ! [Z: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ differ(X,Z)
| holds(clear(X),do(pickup(Z),State)) )
| ~ holds(clear(c),s0)
| ~ differ(c,a)
| holds(clear(c),do(pickup(a),s0)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [Z: $i,State: $i,X: $i] :
( ~ holds(clear(X),State)
| ~ differ(X,Z)
| holds(clear(X),do(pickup(Z),State)) )
| ~ holds(clear(c),s0)
| ~ differ(c,a)
| holds(clear(c),do(pickup(a),s0)) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
holds(clear(c),do(pickup(a),s0)),
inference(unit_resolution,[status(thm)],[33,30,20,17]) ).
tff(35,plain,
( holds(empty,s0)
<=> holds(empty,s0) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,axiom,
holds(empty,s0),
file('/export/starexec/sandbox2/benchmark/Axioms/PLA001-1.ax',initial_state8) ).
tff(37,plain,
holds(empty,s0),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
( holds(clear(a),s0)
<=> holds(clear(a),s0) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,axiom,
holds(clear(a),s0),
file('/export/starexec/sandbox2/benchmark/Axioms/PLA001-1.ax',initial_state5) ).
tff(40,plain,
holds(clear(a),s0),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
( differ(a,table)
<=> differ(a,table) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,axiom,
differ(a,table),
file('/export/starexec/sandbox2/benchmark/Axioms/PLA001-1.ax',differ_a_table) ).
tff(43,plain,
differ(a,table),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,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(45,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)],[44]) ).
tff(46,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(47,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(48,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)],[47]) ).
tff(49,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(50,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)],[49,48]) ).
tff(51,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)],[50,46]) ).
tff(52,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)],[51]) ).
tff(53,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)],[52,45]) ).
tff(54,plain,
( ( ~ ! [State: $i,X: $i] :
( ~ differ(X,table)
| ~ holds(clear(X),State)
| ~ holds(empty,State)
| holds(holding(X),do(pickup(X),State)) )
| ~ holds(clear(a),s0)
| ~ holds(empty,s0)
| ~ differ(a,table)
| holds(holding(a),do(pickup(a),s0)) )
<=> ( ~ ! [State: $i,X: $i] :
( ~ differ(X,table)
| ~ holds(clear(X),State)
| ~ holds(empty,State)
| holds(holding(X),do(pickup(X),State)) )
| ~ holds(clear(a),s0)
| ~ holds(empty,s0)
| ~ differ(a,table)
| holds(holding(a),do(pickup(a),s0)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,plain,
( ( ~ differ(a,table)
| ~ holds(clear(a),s0)
| ~ holds(empty,s0)
| holds(holding(a),do(pickup(a),s0)) )
<=> ( ~ holds(clear(a),s0)
| ~ holds(empty,s0)
| ~ differ(a,table)
| holds(holding(a),do(pickup(a),s0)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(56,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),s0)
| ~ holds(empty,s0)
| holds(holding(a),do(pickup(a),s0)) )
<=> ( ~ ! [State: $i,X: $i] :
( ~ differ(X,table)
| ~ holds(clear(X),State)
| ~ holds(empty,State)
| holds(holding(X),do(pickup(X),State)) )
| ~ holds(clear(a),s0)
| ~ holds(empty,s0)
| ~ differ(a,table)
| holds(holding(a),do(pickup(a),s0)) ) ),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,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),s0)
| ~ holds(empty,s0)
| holds(holding(a),do(pickup(a),s0)) )
<=> ( ~ ! [State: $i,X: $i] :
( ~ differ(X,table)
| ~ holds(clear(X),State)
| ~ holds(empty,State)
| holds(holding(X),do(pickup(X),State)) )
| ~ holds(clear(a),s0)
| ~ holds(empty,s0)
| ~ differ(a,table)
| holds(holding(a),do(pickup(a),s0)) ) ),
inference(transitivity,[status(thm)],[56,54]) ).
tff(58,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),s0)
| ~ holds(empty,s0)
| holds(holding(a),do(pickup(a),s0)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(59,plain,
( ~ ! [State: $i,X: $i] :
( ~ differ(X,table)
| ~ holds(clear(X),State)
| ~ holds(empty,State)
| holds(holding(X),do(pickup(X),State)) )
| ~ holds(clear(a),s0)
| ~ holds(empty,s0)
| ~ differ(a,table)
| holds(holding(a),do(pickup(a),s0)) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
holds(holding(a),do(pickup(a),s0)),
inference(unit_resolution,[status(thm)],[59,53,43,40,37]) ).
tff(61,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(62,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)],[61]) ).
tff(63,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(64,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(65,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)],[64]) ).
tff(66,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(67,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)],[66,65]) ).
tff(68,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)],[67,63]) ).
tff(69,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)],[68]) ).
tff(70,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)],[69,62]) ).
tff(71,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(c),do(pickup(a),s0))
| ~ holds(holding(a),do(pickup(a),s0))
| holds(on(a,c),do(putdown(a,c),do(pickup(a),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(c),do(pickup(a),s0))
| ~ holds(holding(a),do(pickup(a),s0))
| holds(on(a,c),do(putdown(a,c),do(pickup(a),s0))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(72,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(c),do(pickup(a),s0))
| ~ holds(holding(a),do(pickup(a),s0))
| holds(on(a,c),do(putdown(a,c),do(pickup(a),s0))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(73,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(c),do(pickup(a),s0))
| ~ holds(holding(a),do(pickup(a),s0))
| holds(on(a,c),do(putdown(a,c),do(pickup(a),s0))) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
holds(on(a,c),do(putdown(a,c),do(pickup(a),s0))),
inference(unit_resolution,[status(thm)],[73,70,60,34]) ).
tff(75,plain,
^ [State: $i] :
refl(( ~ holds(on(a,c),State)
<=> ~ holds(on(a,c),State) )),
inference(bind,[status(th)],[]) ).
tff(76,plain,
( ! [State: $i] : ~ holds(on(a,c),State)
<=> ! [State: $i] : ~ holds(on(a,c),State) ),
inference(quant_intro,[status(thm)],[75]) ).
tff(77,plain,
( ! [State: $i] : ~ holds(on(a,c),State)
<=> ! [State: $i] : ~ holds(on(a,c),State) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,axiom,
! [State: $i] : ~ holds(on(a,c),State),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_AC) ).
tff(79,plain,
! [State: $i] : ~ holds(on(a,c),State),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
! [State: $i] : ~ holds(on(a,c),State),
inference(skolemize,[status(sab)],[79]) ).
tff(81,plain,
! [State: $i] : ~ holds(on(a,c),State),
inference(modus_ponens,[status(thm)],[80,76]) ).
tff(82,plain,
( ~ ! [State: $i] : ~ holds(on(a,c),State)
| ~ holds(on(a,c),do(putdown(a,c),do(pickup(a),s0))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(83,plain,
$false,
inference(unit_resolution,[status(thm)],[82,81,74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : PLA017-1 : TPTP v9.0.0. Released v1.1.0.
% 0.11/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n010.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 02:23:26 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.93/1.11 % SZS status Unsatisfiable
% 0.93/1.11 % SZS output start Proof
% See solution above
% 0.93/1.11 % E exiting
%------------------------------------------------------------------------------