TSTP Solution File: PUZ012-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : PUZ012-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 14:10:50 EDT 2022
% Result : Unsatisfiable 0.12s 0.39s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 54
% Syntax : Number of formulae : 108 ( 24 unt; 10 typ; 0 def)
% Number of atoms : 482 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 607 ( 233 ~; 327 |; 0 &)
% ( 47 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 10 ( 10 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 4 >; 4 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 202 ( 182 !; 0 ?; 202 :)
% Comments :
%------------------------------------------------------------------------------
tff(contains_type,type,
contains: ( $i * $i ) > $o ).
tff(oranges_type,type,
oranges: $i ).
tff(boxc_type,type,
boxc: $i ).
tff(bananas_type,type,
bananas: $i ).
tff(label_type,type,
label: ( $i * $i ) > $o ).
tff(apples_type,type,
apples: $i ).
tff(boxb_type,type,
boxb: $i ).
tff(equal_boxes_type,type,
equal_boxes: ( $i * $i ) > $o ).
tff(boxa_type,type,
boxa: $i ).
tff(equal_fruits_type,type,
equal_fruits: ( $i * $i ) > $o ).
tff(1,plain,
( label(boxc,bananas)
<=> label(boxc,bananas) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
label(boxc,bananas),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',boxc_labelled_bananas) ).
tff(3,plain,
label(boxc,bananas),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [Y: $i,X: $i] :
refl(
( ( ~ contains(X,Y)
| ~ label(X,Y) )
<=> ( ~ contains(X,Y)
| ~ label(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [Y: $i,X: $i] :
( ~ contains(X,Y)
| ~ label(X,Y) )
<=> ! [Y: $i,X: $i] :
( ~ contains(X,Y)
| ~ label(X,Y) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [Y: $i,X: $i] :
( ~ contains(X,Y)
| ~ label(X,Y) )
<=> ! [Y: $i,X: $i] :
( ~ contains(X,Y)
| ~ label(X,Y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,plain,
^ [Y: $i,X: $i] :
rewrite(
( ( ~ label(X,Y)
| ~ contains(X,Y) )
<=> ( ~ contains(X,Y)
| ~ label(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [Y: $i,X: $i] :
( ~ label(X,Y)
| ~ contains(X,Y) )
<=> ! [Y: $i,X: $i] :
( ~ contains(X,Y)
| ~ label(X,Y) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [Y: $i,X: $i] :
( ~ label(X,Y)
| ~ contains(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',label_is_wrong) ).
tff(10,plain,
! [Y: $i,X: $i] :
( ~ contains(X,Y)
| ~ label(X,Y) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [Y: $i,X: $i] :
( ~ contains(X,Y)
| ~ label(X,Y) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [Y: $i,X: $i] :
( ~ contains(X,Y)
| ~ label(X,Y) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [Y: $i,X: $i] :
( ~ contains(X,Y)
| ~ label(X,Y) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ contains(X,Y)
| ~ label(X,Y) )
| ~ contains(boxc,bananas)
| ~ label(boxc,bananas) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ contains(X,Y)
| ~ label(X,Y) )
| ~ contains(boxc,bananas)
| ~ label(boxc,bananas) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ~ ! [Y: $i,X: $i] :
( ~ contains(X,Y)
| ~ label(X,Y) )
| ~ contains(boxc,bananas)
| ~ label(boxc,bananas) ),
inference(quant_inst,[status(thm)],]) ).
tff(16,plain,
( ~ ! [Y: $i,X: $i] :
( ~ contains(X,Y)
| ~ label(X,Y) )
| ~ contains(boxc,bananas)
| ~ label(boxc,bananas) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
~ contains(boxc,bananas),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
( contains(boxb,apples)
<=> contains(boxb,apples) ),
inference(rewrite,[status(thm)],]) ).
tff(19,axiom,
contains(boxb,apples),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',boxb_contains_apples) ).
tff(20,plain,
contains(boxb,apples),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
( ~ equal_boxes(boxb,boxc)
<=> ~ equal_boxes(boxb,boxc) ),
inference(rewrite,[status(thm)],]) ).
tff(22,axiom,
~ equal_boxes(boxb,boxc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',boxb_not_boxc) ).
tff(23,plain,
~ equal_boxes(boxb,boxc),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( ~ contains(X,Y)
| equal_boxes(X,Z)
| ~ contains(Z,Y) )
<=> ( ~ contains(X,Y)
| equal_boxes(X,Z)
| ~ contains(Z,Y) ) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ contains(X,Y)
| equal_boxes(X,Z)
| ~ contains(Z,Y) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ contains(X,Y)
| equal_boxes(X,Z)
| ~ contains(Z,Y) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ contains(X,Y)
| equal_boxes(X,Z)
| ~ contains(Z,Y) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ contains(X,Y)
| equal_boxes(X,Z)
| ~ contains(Z,Y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
^ [Z: $i,Y: $i,X: $i] :
rewrite(
( ( ~ contains(X,Y)
| ~ contains(Z,Y)
| equal_boxes(X,Z) )
<=> ( ~ contains(X,Y)
| equal_boxes(X,Z)
| ~ contains(Z,Y) ) )),
inference(bind,[status(th)],]) ).
tff(28,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ contains(X,Y)
| ~ contains(Z,Y)
| equal_boxes(X,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ contains(X,Y)
| equal_boxes(X,Z)
| ~ contains(Z,Y) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ contains(X,Y)
| ~ contains(Z,Y)
| equal_boxes(X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',contains_is_well_defined2) ).
tff(30,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ contains(X,Y)
| equal_boxes(X,Z)
| ~ contains(Z,Y) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ contains(X,Y)
| equal_boxes(X,Z)
| ~ contains(Z,Y) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ contains(X,Y)
| equal_boxes(X,Z)
| ~ contains(Z,Y) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ contains(X,Y)
| equal_boxes(X,Z)
| ~ contains(Z,Y) ),
inference(modus_ponens,[status(thm)],[32,25]) ).
tff(34,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ contains(X,Y)
| equal_boxes(X,Z)
| ~ contains(Z,Y) )
| equal_boxes(boxb,boxc)
| ~ contains(boxb,apples)
| ~ contains(boxc,apples) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ contains(X,Y)
| equal_boxes(X,Z)
| ~ contains(Z,Y) )
| equal_boxes(boxb,boxc)
| ~ contains(boxb,apples)
| ~ contains(boxc,apples) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
( ( ~ contains(boxb,apples)
| equal_boxes(boxb,boxc)
| ~ contains(boxc,apples) )
<=> ( equal_boxes(boxb,boxc)
| ~ contains(boxb,apples)
| ~ contains(boxc,apples) ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ contains(X,Y)
| equal_boxes(X,Z)
| ~ contains(Z,Y) )
| ~ contains(boxb,apples)
| equal_boxes(boxb,boxc)
| ~ contains(boxc,apples) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ contains(X,Y)
| equal_boxes(X,Z)
| ~ contains(Z,Y) )
| equal_boxes(boxb,boxc)
| ~ contains(boxb,apples)
| ~ contains(boxc,apples) ) ),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ contains(X,Y)
| equal_boxes(X,Z)
| ~ contains(Z,Y) )
| ~ contains(boxb,apples)
| equal_boxes(boxb,boxc)
| ~ contains(boxc,apples) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ contains(X,Y)
| equal_boxes(X,Z)
| ~ contains(Z,Y) )
| equal_boxes(boxb,boxc)
| ~ contains(boxb,apples)
| ~ contains(boxc,apples) ) ),
inference(transitivity,[status(thm)],[36,34]) ).
tff(38,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ contains(X,Y)
| equal_boxes(X,Z)
| ~ contains(Z,Y) )
| ~ contains(boxb,apples)
| equal_boxes(boxb,boxc)
| ~ contains(boxc,apples) ),
inference(quant_inst,[status(thm)],]) ).
tff(39,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ contains(X,Y)
| equal_boxes(X,Z)
| ~ contains(Z,Y) )
| equal_boxes(boxb,boxc)
| ~ contains(boxb,apples)
| ~ contains(boxc,apples) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
~ contains(boxc,apples),
inference(unit_resolution,[status(thm)],[39,33,23,20]) ).
tff(41,plain,
^ [X: $i] :
refl(
( ( contains(X,oranges)
| contains(X,bananas)
| contains(X,apples) )
<=> ( contains(X,oranges)
| contains(X,bananas)
| contains(X,apples) ) )),
inference(bind,[status(th)],]) ).
tff(42,plain,
( ! [X: $i] :
( contains(X,oranges)
| contains(X,bananas)
| contains(X,apples) )
<=> ! [X: $i] :
( contains(X,oranges)
| contains(X,bananas)
| contains(X,apples) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,plain,
( ! [X: $i] :
( contains(X,oranges)
| contains(X,bananas)
| contains(X,apples) )
<=> ! [X: $i] :
( contains(X,oranges)
| contains(X,bananas)
| contains(X,apples) ) ),
inference(rewrite,[status(thm)],]) ).
tff(44,plain,
^ [X: $i] :
rewrite(
( ( contains(X,apples)
| contains(X,bananas)
| contains(X,oranges) )
<=> ( contains(X,oranges)
| contains(X,bananas)
| contains(X,apples) ) )),
inference(bind,[status(th)],]) ).
tff(45,plain,
( ! [X: $i] :
( contains(X,apples)
| contains(X,bananas)
| contains(X,oranges) )
<=> ! [X: $i] :
( contains(X,oranges)
| contains(X,bananas)
| contains(X,apples) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,axiom,
! [X: $i] :
( contains(X,apples)
| contains(X,bananas)
| contains(X,oranges) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',each_box_contains_something) ).
tff(47,plain,
! [X: $i] :
( contains(X,oranges)
| contains(X,bananas)
| contains(X,apples) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [X: $i] :
( contains(X,oranges)
| contains(X,bananas)
| contains(X,apples) ),
inference(modus_ponens,[status(thm)],[47,43]) ).
tff(49,plain,
! [X: $i] :
( contains(X,oranges)
| contains(X,bananas)
| contains(X,apples) ),
inference(skolemize,[status(sab)],[48]) ).
tff(50,plain,
! [X: $i] :
( contains(X,oranges)
| contains(X,bananas)
| contains(X,apples) ),
inference(modus_ponens,[status(thm)],[49,42]) ).
tff(51,plain,
( ( ~ ! [X: $i] :
( contains(X,oranges)
| contains(X,bananas)
| contains(X,apples) )
| contains(boxc,oranges)
| contains(boxc,apples)
| contains(boxc,bananas) )
<=> ( ~ ! [X: $i] :
( contains(X,oranges)
| contains(X,bananas)
| contains(X,apples) )
| contains(boxc,oranges)
| contains(boxc,apples)
| contains(boxc,bananas) ) ),
inference(rewrite,[status(thm)],]) ).
tff(52,plain,
( ( contains(boxc,oranges)
| contains(boxc,bananas)
| contains(boxc,apples) )
<=> ( contains(boxc,oranges)
| contains(boxc,apples)
| contains(boxc,bananas) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,plain,
( ( ~ ! [X: $i] :
( contains(X,oranges)
| contains(X,bananas)
| contains(X,apples) )
| contains(boxc,oranges)
| contains(boxc,bananas)
| contains(boxc,apples) )
<=> ( ~ ! [X: $i] :
( contains(X,oranges)
| contains(X,bananas)
| contains(X,apples) )
| contains(boxc,oranges)
| contains(boxc,apples)
| contains(boxc,bananas) ) ),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
( ( ~ ! [X: $i] :
( contains(X,oranges)
| contains(X,bananas)
| contains(X,apples) )
| contains(boxc,oranges)
| contains(boxc,bananas)
| contains(boxc,apples) )
<=> ( ~ ! [X: $i] :
( contains(X,oranges)
| contains(X,bananas)
| contains(X,apples) )
| contains(boxc,oranges)
| contains(boxc,apples)
| contains(boxc,bananas) ) ),
inference(transitivity,[status(thm)],[53,51]) ).
tff(55,plain,
( ~ ! [X: $i] :
( contains(X,oranges)
| contains(X,bananas)
| contains(X,apples) )
| contains(boxc,oranges)
| contains(boxc,bananas)
| contains(boxc,apples) ),
inference(quant_inst,[status(thm)],]) ).
tff(56,plain,
( ~ ! [X: $i] :
( contains(X,oranges)
| contains(X,bananas)
| contains(X,apples) )
| contains(boxc,oranges)
| contains(boxc,apples)
| contains(boxc,bananas) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
contains(boxc,oranges),
inference(unit_resolution,[status(thm)],[56,50,40,17]) ).
tff(58,plain,
( ~ equal_fruits(apples,bananas)
<=> ~ equal_fruits(apples,bananas) ),
inference(rewrite,[status(thm)],]) ).
tff(59,axiom,
~ equal_fruits(apples,bananas),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apples_not_bananas) ).
tff(60,plain,
~ equal_fruits(apples,bananas),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( ~ contains(X,Y)
| equal_fruits(Y,Z)
| ~ contains(X,Z) )
<=> ( ~ contains(X,Y)
| equal_fruits(Y,Z)
| ~ contains(X,Z) ) )),
inference(bind,[status(th)],]) ).
tff(62,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ contains(X,Y)
| equal_fruits(Y,Z)
| ~ contains(X,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ contains(X,Y)
| equal_fruits(Y,Z)
| ~ contains(X,Z) ) ),
inference(quant_intro,[status(thm)],[61]) ).
tff(63,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ contains(X,Y)
| equal_fruits(Y,Z)
| ~ contains(X,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ contains(X,Y)
| equal_fruits(Y,Z)
| ~ contains(X,Z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(64,plain,
^ [Z: $i,Y: $i,X: $i] :
rewrite(
( ( ~ contains(X,Y)
| ~ contains(X,Z)
| equal_fruits(Y,Z) )
<=> ( ~ contains(X,Y)
| equal_fruits(Y,Z)
| ~ contains(X,Z) ) )),
inference(bind,[status(th)],]) ).
tff(65,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ contains(X,Y)
| ~ contains(X,Z)
| equal_fruits(Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ contains(X,Y)
| equal_fruits(Y,Z)
| ~ contains(X,Z) ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ contains(X,Y)
| ~ contains(X,Z)
| equal_fruits(Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',contains_is_well_defined1) ).
tff(67,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ contains(X,Y)
| equal_fruits(Y,Z)
| ~ contains(X,Z) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ contains(X,Y)
| equal_fruits(Y,Z)
| ~ contains(X,Z) ),
inference(modus_ponens,[status(thm)],[67,63]) ).
tff(69,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ contains(X,Y)
| equal_fruits(Y,Z)
| ~ contains(X,Z) ),
inference(skolemize,[status(sab)],[68]) ).
tff(70,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ contains(X,Y)
| equal_fruits(Y,Z)
| ~ contains(X,Z) ),
inference(modus_ponens,[status(thm)],[69,62]) ).
tff(71,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ contains(X,Y)
| equal_fruits(Y,Z)
| ~ contains(X,Z) )
| equal_fruits(apples,bananas)
| ~ contains(boxb,apples)
| ~ contains(boxb,bananas) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ contains(X,Y)
| equal_fruits(Y,Z)
| ~ contains(X,Z) )
| equal_fruits(apples,bananas)
| ~ contains(boxb,apples)
| ~ contains(boxb,bananas) ) ),
inference(rewrite,[status(thm)],]) ).
tff(72,plain,
( ( ~ contains(boxb,apples)
| equal_fruits(apples,bananas)
| ~ contains(boxb,bananas) )
<=> ( equal_fruits(apples,bananas)
| ~ contains(boxb,apples)
| ~ contains(boxb,bananas) ) ),
inference(rewrite,[status(thm)],]) ).
tff(73,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ contains(X,Y)
| equal_fruits(Y,Z)
| ~ contains(X,Z) )
| ~ contains(boxb,apples)
| equal_fruits(apples,bananas)
| ~ contains(boxb,bananas) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ contains(X,Y)
| equal_fruits(Y,Z)
| ~ contains(X,Z) )
| equal_fruits(apples,bananas)
| ~ contains(boxb,apples)
| ~ contains(boxb,bananas) ) ),
inference(monotonicity,[status(thm)],[72]) ).
tff(74,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ contains(X,Y)
| equal_fruits(Y,Z)
| ~ contains(X,Z) )
| ~ contains(boxb,apples)
| equal_fruits(apples,bananas)
| ~ contains(boxb,bananas) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ contains(X,Y)
| equal_fruits(Y,Z)
| ~ contains(X,Z) )
| equal_fruits(apples,bananas)
| ~ contains(boxb,apples)
| ~ contains(boxb,bananas) ) ),
inference(transitivity,[status(thm)],[73,71]) ).
tff(75,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ contains(X,Y)
| equal_fruits(Y,Z)
| ~ contains(X,Z) )
| ~ contains(boxb,apples)
| equal_fruits(apples,bananas)
| ~ contains(boxb,bananas) ),
inference(quant_inst,[status(thm)],]) ).
tff(76,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ contains(X,Y)
| equal_fruits(Y,Z)
| ~ contains(X,Z) )
| equal_fruits(apples,bananas)
| ~ contains(boxb,apples)
| ~ contains(boxb,bananas) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
~ contains(boxb,bananas),
inference(unit_resolution,[status(thm)],[76,70,60,20]) ).
tff(78,plain,
^ [X: $i] :
refl(
( ( contains(boxc,X)
| contains(boxb,X)
| contains(boxa,X) )
<=> ( contains(boxc,X)
| contains(boxb,X)
| contains(boxa,X) ) )),
inference(bind,[status(th)],]) ).
tff(79,plain,
( ! [X: $i] :
( contains(boxc,X)
| contains(boxb,X)
| contains(boxa,X) )
<=> ! [X: $i] :
( contains(boxc,X)
| contains(boxb,X)
| contains(boxa,X) ) ),
inference(quant_intro,[status(thm)],[78]) ).
tff(80,plain,
( ! [X: $i] :
( contains(boxc,X)
| contains(boxb,X)
| contains(boxa,X) )
<=> ! [X: $i] :
( contains(boxc,X)
| contains(boxb,X)
| contains(boxa,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(81,plain,
^ [X: $i] :
rewrite(
( ( contains(boxa,X)
| contains(boxb,X)
| contains(boxc,X) )
<=> ( contains(boxc,X)
| contains(boxb,X)
| contains(boxa,X) ) )),
inference(bind,[status(th)],]) ).
tff(82,plain,
( ! [X: $i] :
( contains(boxa,X)
| contains(boxb,X)
| contains(boxc,X) )
<=> ! [X: $i] :
( contains(boxc,X)
| contains(boxb,X)
| contains(boxa,X) ) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,axiom,
! [X: $i] :
( contains(boxa,X)
| contains(boxb,X)
| contains(boxc,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',each_thing_is_in_a_box) ).
tff(84,plain,
! [X: $i] :
( contains(boxc,X)
| contains(boxb,X)
| contains(boxa,X) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
! [X: $i] :
( contains(boxc,X)
| contains(boxb,X)
| contains(boxa,X) ),
inference(modus_ponens,[status(thm)],[84,80]) ).
tff(86,plain,
! [X: $i] :
( contains(boxc,X)
| contains(boxb,X)
| contains(boxa,X) ),
inference(skolemize,[status(sab)],[85]) ).
tff(87,plain,
! [X: $i] :
( contains(boxc,X)
| contains(boxb,X)
| contains(boxa,X) ),
inference(modus_ponens,[status(thm)],[86,79]) ).
tff(88,plain,
( ( ~ ! [X: $i] :
( contains(boxc,X)
| contains(boxb,X)
| contains(boxa,X) )
| contains(boxa,bananas)
| contains(boxb,bananas)
| contains(boxc,bananas) )
<=> ( ~ ! [X: $i] :
( contains(boxc,X)
| contains(boxb,X)
| contains(boxa,X) )
| contains(boxa,bananas)
| contains(boxb,bananas)
| contains(boxc,bananas) ) ),
inference(rewrite,[status(thm)],]) ).
tff(89,plain,
( ( contains(boxc,bananas)
| contains(boxb,bananas)
| contains(boxa,bananas) )
<=> ( contains(boxa,bananas)
| contains(boxb,bananas)
| contains(boxc,bananas) ) ),
inference(rewrite,[status(thm)],]) ).
tff(90,plain,
( ( ~ ! [X: $i] :
( contains(boxc,X)
| contains(boxb,X)
| contains(boxa,X) )
| contains(boxc,bananas)
| contains(boxb,bananas)
| contains(boxa,bananas) )
<=> ( ~ ! [X: $i] :
( contains(boxc,X)
| contains(boxb,X)
| contains(boxa,X) )
| contains(boxa,bananas)
| contains(boxb,bananas)
| contains(boxc,bananas) ) ),
inference(monotonicity,[status(thm)],[89]) ).
tff(91,plain,
( ( ~ ! [X: $i] :
( contains(boxc,X)
| contains(boxb,X)
| contains(boxa,X) )
| contains(boxc,bananas)
| contains(boxb,bananas)
| contains(boxa,bananas) )
<=> ( ~ ! [X: $i] :
( contains(boxc,X)
| contains(boxb,X)
| contains(boxa,X) )
| contains(boxa,bananas)
| contains(boxb,bananas)
| contains(boxc,bananas) ) ),
inference(transitivity,[status(thm)],[90,88]) ).
tff(92,plain,
( ~ ! [X: $i] :
( contains(boxc,X)
| contains(boxb,X)
| contains(boxa,X) )
| contains(boxc,bananas)
| contains(boxb,bananas)
| contains(boxa,bananas) ),
inference(quant_inst,[status(thm)],]) ).
tff(93,plain,
( ~ ! [X: $i] :
( contains(boxc,X)
| contains(boxb,X)
| contains(boxa,X) )
| contains(boxa,bananas)
| contains(boxb,bananas)
| contains(boxc,bananas) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
contains(boxa,bananas),
inference(unit_resolution,[status(thm)],[93,87,77,17]) ).
tff(95,plain,
( ( ~ contains(boxa,bananas)
| ~ contains(boxc,oranges) )
<=> ( ~ contains(boxa,bananas)
| ~ contains(boxc,oranges) ) ),
inference(rewrite,[status(thm)],]) ).
tff(96,axiom,
( ~ contains(boxa,bananas)
| ~ contains(boxc,oranges) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_boxa_contains_bananas_and_boxc_oranges) ).
tff(97,plain,
( ~ contains(boxa,bananas)
| ~ contains(boxc,oranges) ),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
$false,
inference(unit_resolution,[status(thm)],[97,94,57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : PUZ012-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n028.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Sep 2 18:25:52 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.12/0.39 % SZS status Unsatisfiable
% 0.12/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------