TSTP Solution File: MSC003-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : MSC003-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% 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 : Sun Sep 18 05:33:59 EDT 2022
% Result : Unsatisfiable 0.21s 0.47s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 46
% Syntax : Number of formulae : 90 ( 18 unt; 11 typ; 0 def)
% Number of atoms : 367 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 480 ( 207 ~; 234 |; 0 &)
% ( 39 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 15 ( 15 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 4 >; 8 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-5 aty)
% Number of variables : 257 ( 232 !; 0 ?; 257 :)
% Comments :
%------------------------------------------------------------------------------
tff(in_type,type,
in: ( $i * $i ) > $o ).
tff(arm_type,type,
arm: $i ).
tff(object_in_type,type,
object_in: ( $i * $i * $i * $i * $i ) > $i ).
tff(n1_type,type,
n1: $i ).
tff(n2_type,type,
n2: $i ).
tff(hand_type,type,
hand: $i ).
tff(john_type,type,
john: $i ).
tff(has_parts_type,type,
has_parts: ( $i * $i * $i ) > $o ).
tff(human_type,type,
human: $i ).
tff(boy_type,type,
boy: $i ).
tff(times_type,type,
times: ( $i * $i ) > $i ).
tff(1,plain,
^ [X: $i] :
refl(
( ( in(X,human)
| ~ in(X,boy) )
<=> ( in(X,human)
| ~ in(X,boy) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] :
( in(X,human)
| ~ in(X,boy) )
<=> ! [X: $i] :
( in(X,human)
| ~ in(X,boy) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] :
( in(X,human)
| ~ in(X,boy) )
<=> ! [X: $i] :
( in(X,human)
| ~ in(X,boy) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X: $i] :
( in(X,human)
| ~ in(X,boy) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in_boy_in_human) ).
tff(5,plain,
! [X: $i] :
( in(X,human)
| ~ in(X,boy) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] :
( in(X,human)
| ~ in(X,boy) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] :
( in(X,human)
| ~ in(X,boy) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( in(john,boy)
<=> in(john,boy) ),
inference(rewrite,[status(thm)],]) ).
tff(9,axiom,
in(john,boy),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',john_is_a_boy) ).
tff(10,plain,
in(john,boy),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
( ( ~ ! [X: $i] :
( in(X,human)
| ~ in(X,boy) )
| in(john,human)
| ~ in(john,boy) )
<=> ( ~ ! [X: $i] :
( in(X,human)
| ~ in(X,boy) )
| in(john,human)
| ~ in(john,boy) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ~ ! [X: $i] :
( in(X,human)
| ~ in(X,boy) )
| in(john,human)
| ~ in(john,boy) ),
inference(quant_inst,[status(thm)],]) ).
tff(13,plain,
( ~ ! [X: $i] :
( in(X,human)
| ~ in(X,boy) )
| in(john,human)
| ~ in(john,boy) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
in(john,human),
inference(unit_resolution,[status(thm)],[13,10,7]) ).
tff(15,plain,
^ [X: $i] :
refl(
( ( ~ in(X,human)
| has_parts(X,n2,arm) )
<=> ( ~ in(X,human)
| has_parts(X,n2,arm) ) )),
inference(bind,[status(th)],]) ).
tff(16,plain,
( ! [X: $i] :
( ~ in(X,human)
| has_parts(X,n2,arm) )
<=> ! [X: $i] :
( ~ in(X,human)
| has_parts(X,n2,arm) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [X: $i] :
( ~ in(X,human)
| has_parts(X,n2,arm) )
<=> ! [X: $i] :
( ~ in(X,human)
| has_parts(X,n2,arm) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
^ [X: $i] :
rewrite(
( ( has_parts(X,n2,arm)
| ~ in(X,human) )
<=> ( ~ in(X,human)
| has_parts(X,n2,arm) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [X: $i] :
( has_parts(X,n2,arm)
| ~ in(X,human) )
<=> ! [X: $i] :
( ~ in(X,human)
| has_parts(X,n2,arm) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,axiom,
! [X: $i] :
( has_parts(X,n2,arm)
| ~ in(X,human) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',humans_have_two_arms) ).
tff(21,plain,
! [X: $i] :
( ~ in(X,human)
| has_parts(X,n2,arm) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
! [X: $i] :
( ~ in(X,human)
| has_parts(X,n2,arm) ),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,plain,
! [X: $i] :
( ~ in(X,human)
| has_parts(X,n2,arm) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [X: $i] :
( ~ in(X,human)
| has_parts(X,n2,arm) ),
inference(modus_ponens,[status(thm)],[23,16]) ).
tff(25,plain,
( ( ~ ! [X: $i] :
( ~ in(X,human)
| has_parts(X,n2,arm) )
| ~ in(john,human)
| has_parts(john,n2,arm) )
<=> ( ~ ! [X: $i] :
( ~ in(X,human)
| has_parts(X,n2,arm) )
| ~ in(john,human)
| has_parts(john,n2,arm) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
( ~ ! [X: $i] :
( ~ in(X,human)
| has_parts(X,n2,arm) )
| ~ in(john,human)
| has_parts(john,n2,arm) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
( ~ ! [X: $i] :
( ~ in(X,human)
| has_parts(X,n2,arm) )
| ~ in(john,human)
| has_parts(john,n2,arm) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
has_parts(john,n2,arm),
inference(unit_resolution,[status(thm)],[27,24,14]) ).
tff(29,plain,
( ~ has_parts(john,times(n2,n1),hand)
<=> ~ has_parts(john,times(n2,n1),hand) ),
inference(rewrite,[status(thm)],]) ).
tff(30,axiom,
~ has_parts(john,times(n2,n1),hand),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_john_has_2_hands) ).
tff(31,plain,
~ has_parts(john,times(n2,n1),hand),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
^ [Number_of_mid_parts: $i,Mid_part: $i,Big_part: $i,Number_of_small_parts: $i,Small_part: $i] :
refl(
( ( ~ has_parts(Big_part,Number_of_mid_parts,Mid_part)
| has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| ~ has_parts(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Number_of_small_parts,Small_part) )
<=> ( ~ has_parts(Big_part,Number_of_mid_parts,Mid_part)
| has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| ~ has_parts(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Number_of_small_parts,Small_part) ) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [Number_of_mid_parts: $i,Mid_part: $i,Big_part: $i,Number_of_small_parts: $i,Small_part: $i] :
( ~ has_parts(Big_part,Number_of_mid_parts,Mid_part)
| has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| ~ has_parts(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Number_of_small_parts,Small_part) )
<=> ! [Number_of_mid_parts: $i,Mid_part: $i,Big_part: $i,Number_of_small_parts: $i,Small_part: $i] :
( ~ has_parts(Big_part,Number_of_mid_parts,Mid_part)
| has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| ~ has_parts(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Number_of_small_parts,Small_part) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [Number_of_mid_parts: $i,Mid_part: $i,Big_part: $i,Number_of_small_parts: $i,Small_part: $i] :
( ~ has_parts(Big_part,Number_of_mid_parts,Mid_part)
| has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| ~ has_parts(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Number_of_small_parts,Small_part) )
<=> ! [Number_of_mid_parts: $i,Mid_part: $i,Big_part: $i,Number_of_small_parts: $i,Small_part: $i] :
( ~ has_parts(Big_part,Number_of_mid_parts,Mid_part)
| has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| ~ has_parts(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Number_of_small_parts,Small_part) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
^ [Number_of_mid_parts: $i,Mid_part: $i,Big_part: $i,Number_of_small_parts: $i,Small_part: $i] :
trans(
monotonicity(
rewrite(
( ( has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| ~ has_parts(Big_part,Number_of_mid_parts,Mid_part) )
<=> ( ~ has_parts(Big_part,Number_of_mid_parts,Mid_part)
| has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part) ) )),
( ( has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| ~ has_parts(Big_part,Number_of_mid_parts,Mid_part)
| ~ has_parts(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Number_of_small_parts,Small_part) )
<=> ( ~ has_parts(Big_part,Number_of_mid_parts,Mid_part)
| has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| ~ has_parts(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Number_of_small_parts,Small_part) ) )),
rewrite(
( ( ~ has_parts(Big_part,Number_of_mid_parts,Mid_part)
| has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| ~ has_parts(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Number_of_small_parts,Small_part) )
<=> ( ~ has_parts(Big_part,Number_of_mid_parts,Mid_part)
| has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| ~ has_parts(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Number_of_small_parts,Small_part) ) )),
( ( has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| ~ has_parts(Big_part,Number_of_mid_parts,Mid_part)
| ~ has_parts(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Number_of_small_parts,Small_part) )
<=> ( ~ has_parts(Big_part,Number_of_mid_parts,Mid_part)
| has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| ~ has_parts(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Number_of_small_parts,Small_part) ) )),
inference(bind,[status(th)],]) ).
tff(36,plain,
( ! [Number_of_mid_parts: $i,Mid_part: $i,Big_part: $i,Number_of_small_parts: $i,Small_part: $i] :
( has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| ~ has_parts(Big_part,Number_of_mid_parts,Mid_part)
| ~ has_parts(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Number_of_small_parts,Small_part) )
<=> ! [Number_of_mid_parts: $i,Mid_part: $i,Big_part: $i,Number_of_small_parts: $i,Small_part: $i] :
( ~ has_parts(Big_part,Number_of_mid_parts,Mid_part)
| has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| ~ has_parts(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Number_of_small_parts,Small_part) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,axiom,
! [Number_of_mid_parts: $i,Mid_part: $i,Big_part: $i,Number_of_small_parts: $i,Small_part: $i] :
( has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| ~ has_parts(Big_part,Number_of_mid_parts,Mid_part)
| ~ has_parts(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Number_of_small_parts,Small_part) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',part_inheritance) ).
tff(38,plain,
! [Number_of_mid_parts: $i,Mid_part: $i,Big_part: $i,Number_of_small_parts: $i,Small_part: $i] :
( ~ has_parts(Big_part,Number_of_mid_parts,Mid_part)
| has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| ~ has_parts(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Number_of_small_parts,Small_part) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [Number_of_mid_parts: $i,Mid_part: $i,Big_part: $i,Number_of_small_parts: $i,Small_part: $i] :
( ~ has_parts(Big_part,Number_of_mid_parts,Mid_part)
| has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| ~ has_parts(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Number_of_small_parts,Small_part) ),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,plain,
! [Number_of_mid_parts: $i,Mid_part: $i,Big_part: $i,Number_of_small_parts: $i,Small_part: $i] :
( ~ has_parts(Big_part,Number_of_mid_parts,Mid_part)
| has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| ~ has_parts(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Number_of_small_parts,Small_part) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [Number_of_mid_parts: $i,Mid_part: $i,Big_part: $i,Number_of_small_parts: $i,Small_part: $i] :
( ~ has_parts(Big_part,Number_of_mid_parts,Mid_part)
| has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| ~ has_parts(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Number_of_small_parts,Small_part) ),
inference(modus_ponens,[status(thm)],[40,33]) ).
tff(42,plain,
( ( ~ ! [Number_of_mid_parts: $i,Mid_part: $i,Big_part: $i,Number_of_small_parts: $i,Small_part: $i] :
( ~ has_parts(Big_part,Number_of_mid_parts,Mid_part)
| has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| ~ has_parts(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Number_of_small_parts,Small_part) )
| has_parts(john,times(n2,n1),hand)
| ~ has_parts(john,n2,arm)
| ~ has_parts(object_in(john,arm,hand,n2,n1),n1,hand) )
<=> ( ~ ! [Number_of_mid_parts: $i,Mid_part: $i,Big_part: $i,Number_of_small_parts: $i,Small_part: $i] :
( ~ has_parts(Big_part,Number_of_mid_parts,Mid_part)
| has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| ~ has_parts(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Number_of_small_parts,Small_part) )
| has_parts(john,times(n2,n1),hand)
| ~ has_parts(john,n2,arm)
| ~ has_parts(object_in(john,arm,hand,n2,n1),n1,hand) ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,plain,
( ( ~ has_parts(john,n2,arm)
| has_parts(john,times(n2,n1),hand)
| ~ has_parts(object_in(john,arm,hand,n2,n1),n1,hand) )
<=> ( has_parts(john,times(n2,n1),hand)
| ~ has_parts(john,n2,arm)
| ~ has_parts(object_in(john,arm,hand,n2,n1),n1,hand) ) ),
inference(rewrite,[status(thm)],]) ).
tff(44,plain,
( ( ~ ! [Number_of_mid_parts: $i,Mid_part: $i,Big_part: $i,Number_of_small_parts: $i,Small_part: $i] :
( ~ has_parts(Big_part,Number_of_mid_parts,Mid_part)
| has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| ~ has_parts(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Number_of_small_parts,Small_part) )
| ~ has_parts(john,n2,arm)
| has_parts(john,times(n2,n1),hand)
| ~ has_parts(object_in(john,arm,hand,n2,n1),n1,hand) )
<=> ( ~ ! [Number_of_mid_parts: $i,Mid_part: $i,Big_part: $i,Number_of_small_parts: $i,Small_part: $i] :
( ~ has_parts(Big_part,Number_of_mid_parts,Mid_part)
| has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| ~ has_parts(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Number_of_small_parts,Small_part) )
| has_parts(john,times(n2,n1),hand)
| ~ has_parts(john,n2,arm)
| ~ has_parts(object_in(john,arm,hand,n2,n1),n1,hand) ) ),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
( ( ~ ! [Number_of_mid_parts: $i,Mid_part: $i,Big_part: $i,Number_of_small_parts: $i,Small_part: $i] :
( ~ has_parts(Big_part,Number_of_mid_parts,Mid_part)
| has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| ~ has_parts(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Number_of_small_parts,Small_part) )
| ~ has_parts(john,n2,arm)
| has_parts(john,times(n2,n1),hand)
| ~ has_parts(object_in(john,arm,hand,n2,n1),n1,hand) )
<=> ( ~ ! [Number_of_mid_parts: $i,Mid_part: $i,Big_part: $i,Number_of_small_parts: $i,Small_part: $i] :
( ~ has_parts(Big_part,Number_of_mid_parts,Mid_part)
| has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| ~ has_parts(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Number_of_small_parts,Small_part) )
| has_parts(john,times(n2,n1),hand)
| ~ has_parts(john,n2,arm)
| ~ has_parts(object_in(john,arm,hand,n2,n1),n1,hand) ) ),
inference(transitivity,[status(thm)],[44,42]) ).
tff(46,plain,
( ~ ! [Number_of_mid_parts: $i,Mid_part: $i,Big_part: $i,Number_of_small_parts: $i,Small_part: $i] :
( ~ has_parts(Big_part,Number_of_mid_parts,Mid_part)
| has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| ~ has_parts(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Number_of_small_parts,Small_part) )
| ~ has_parts(john,n2,arm)
| has_parts(john,times(n2,n1),hand)
| ~ has_parts(object_in(john,arm,hand,n2,n1),n1,hand) ),
inference(quant_inst,[status(thm)],]) ).
tff(47,plain,
( ~ ! [Number_of_mid_parts: $i,Mid_part: $i,Big_part: $i,Number_of_small_parts: $i,Small_part: $i] :
( ~ has_parts(Big_part,Number_of_mid_parts,Mid_part)
| has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| ~ has_parts(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Number_of_small_parts,Small_part) )
| has_parts(john,times(n2,n1),hand)
| ~ has_parts(john,n2,arm)
| ~ has_parts(object_in(john,arm,hand,n2,n1),n1,hand) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
~ has_parts(object_in(john,arm,hand,n2,n1),n1,hand),
inference(unit_resolution,[status(thm)],[47,41,31,28]) ).
tff(49,plain,
^ [X: $i] :
refl(
( ( ~ in(X,arm)
| has_parts(X,n1,hand) )
<=> ( ~ in(X,arm)
| has_parts(X,n1,hand) ) )),
inference(bind,[status(th)],]) ).
tff(50,plain,
( ! [X: $i] :
( ~ in(X,arm)
| has_parts(X,n1,hand) )
<=> ! [X: $i] :
( ~ in(X,arm)
| has_parts(X,n1,hand) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
( ! [X: $i] :
( ~ in(X,arm)
| has_parts(X,n1,hand) )
<=> ! [X: $i] :
( ~ in(X,arm)
| has_parts(X,n1,hand) ) ),
inference(rewrite,[status(thm)],]) ).
tff(52,plain,
^ [X: $i] :
rewrite(
( ( has_parts(X,n1,hand)
| ~ in(X,arm) )
<=> ( ~ in(X,arm)
| has_parts(X,n1,hand) ) )),
inference(bind,[status(th)],]) ).
tff(53,plain,
( ! [X: $i] :
( has_parts(X,n1,hand)
| ~ in(X,arm) )
<=> ! [X: $i] :
( ~ in(X,arm)
| has_parts(X,n1,hand) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,axiom,
! [X: $i] :
( has_parts(X,n1,hand)
| ~ in(X,arm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arms_have_one_hand) ).
tff(55,plain,
! [X: $i] :
( ~ in(X,arm)
| has_parts(X,n1,hand) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
! [X: $i] :
( ~ in(X,arm)
| has_parts(X,n1,hand) ),
inference(modus_ponens,[status(thm)],[55,51]) ).
tff(57,plain,
! [X: $i] :
( ~ in(X,arm)
| has_parts(X,n1,hand) ),
inference(skolemize,[status(sab)],[56]) ).
tff(58,plain,
! [X: $i] :
( ~ in(X,arm)
| has_parts(X,n1,hand) ),
inference(modus_ponens,[status(thm)],[57,50]) ).
tff(59,plain,
( ( ~ ! [X: $i] :
( ~ in(X,arm)
| has_parts(X,n1,hand) )
| ~ in(object_in(john,arm,hand,n2,n1),arm)
| has_parts(object_in(john,arm,hand,n2,n1),n1,hand) )
<=> ( ~ ! [X: $i] :
( ~ in(X,arm)
| has_parts(X,n1,hand) )
| ~ in(object_in(john,arm,hand,n2,n1),arm)
| has_parts(object_in(john,arm,hand,n2,n1),n1,hand) ) ),
inference(rewrite,[status(thm)],]) ).
tff(60,plain,
( ~ ! [X: $i] :
( ~ in(X,arm)
| has_parts(X,n1,hand) )
| ~ in(object_in(john,arm,hand,n2,n1),arm)
| has_parts(object_in(john,arm,hand,n2,n1),n1,hand) ),
inference(quant_inst,[status(thm)],]) ).
tff(61,plain,
( ~ ! [X: $i] :
( ~ in(X,arm)
| has_parts(X,n1,hand) )
| ~ in(object_in(john,arm,hand,n2,n1),arm)
| has_parts(object_in(john,arm,hand,n2,n1),n1,hand) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
~ in(object_in(john,arm,hand,n2,n1),arm),
inference(unit_resolution,[status(thm)],[61,58,48]) ).
tff(63,plain,
^ [Number_of_mid_parts: $i,Mid_part: $i,Big_part: $i,Number_of_small_parts: $i,Small_part: $i] :
refl(
( ( ~ has_parts(Big_part,Number_of_mid_parts,Mid_part)
| has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| in(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Mid_part) )
<=> ( ~ has_parts(Big_part,Number_of_mid_parts,Mid_part)
| has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| in(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Mid_part) ) )),
inference(bind,[status(th)],]) ).
tff(64,plain,
( ! [Number_of_mid_parts: $i,Mid_part: $i,Big_part: $i,Number_of_small_parts: $i,Small_part: $i] :
( ~ has_parts(Big_part,Number_of_mid_parts,Mid_part)
| has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| in(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Mid_part) )
<=> ! [Number_of_mid_parts: $i,Mid_part: $i,Big_part: $i,Number_of_small_parts: $i,Small_part: $i] :
( ~ has_parts(Big_part,Number_of_mid_parts,Mid_part)
| has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| in(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Mid_part) ) ),
inference(quant_intro,[status(thm)],[63]) ).
tff(65,plain,
( ! [Number_of_mid_parts: $i,Mid_part: $i,Big_part: $i,Number_of_small_parts: $i,Small_part: $i] :
( ~ has_parts(Big_part,Number_of_mid_parts,Mid_part)
| has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| in(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Mid_part) )
<=> ! [Number_of_mid_parts: $i,Mid_part: $i,Big_part: $i,Number_of_small_parts: $i,Small_part: $i] :
( ~ has_parts(Big_part,Number_of_mid_parts,Mid_part)
| has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| in(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Mid_part) ) ),
inference(rewrite,[status(thm)],]) ).
tff(66,plain,
^ [Number_of_mid_parts: $i,Mid_part: $i,Big_part: $i,Number_of_small_parts: $i,Small_part: $i] :
rewrite(
( ( in(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Mid_part)
| has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| ~ has_parts(Big_part,Number_of_mid_parts,Mid_part) )
<=> ( ~ has_parts(Big_part,Number_of_mid_parts,Mid_part)
| has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| in(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Mid_part) ) )),
inference(bind,[status(th)],]) ).
tff(67,plain,
( ! [Number_of_mid_parts: $i,Mid_part: $i,Big_part: $i,Number_of_small_parts: $i,Small_part: $i] :
( in(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Mid_part)
| has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| ~ has_parts(Big_part,Number_of_mid_parts,Mid_part) )
<=> ! [Number_of_mid_parts: $i,Mid_part: $i,Big_part: $i,Number_of_small_parts: $i,Small_part: $i] :
( ~ has_parts(Big_part,Number_of_mid_parts,Mid_part)
| has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| in(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Mid_part) ) ),
inference(quant_intro,[status(thm)],[66]) ).
tff(68,axiom,
! [Number_of_mid_parts: $i,Mid_part: $i,Big_part: $i,Number_of_small_parts: $i,Small_part: $i] :
( in(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Mid_part)
| has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| ~ has_parts(Big_part,Number_of_mid_parts,Mid_part) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_part_inheritance) ).
tff(69,plain,
! [Number_of_mid_parts: $i,Mid_part: $i,Big_part: $i,Number_of_small_parts: $i,Small_part: $i] :
( ~ has_parts(Big_part,Number_of_mid_parts,Mid_part)
| has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| in(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Mid_part) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
! [Number_of_mid_parts: $i,Mid_part: $i,Big_part: $i,Number_of_small_parts: $i,Small_part: $i] :
( ~ has_parts(Big_part,Number_of_mid_parts,Mid_part)
| has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| in(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Mid_part) ),
inference(modus_ponens,[status(thm)],[69,65]) ).
tff(71,plain,
! [Number_of_mid_parts: $i,Mid_part: $i,Big_part: $i,Number_of_small_parts: $i,Small_part: $i] :
( ~ has_parts(Big_part,Number_of_mid_parts,Mid_part)
| has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| in(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Mid_part) ),
inference(skolemize,[status(sab)],[70]) ).
tff(72,plain,
! [Number_of_mid_parts: $i,Mid_part: $i,Big_part: $i,Number_of_small_parts: $i,Small_part: $i] :
( ~ has_parts(Big_part,Number_of_mid_parts,Mid_part)
| has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| in(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Mid_part) ),
inference(modus_ponens,[status(thm)],[71,64]) ).
tff(73,plain,
( ( ~ ! [Number_of_mid_parts: $i,Mid_part: $i,Big_part: $i,Number_of_small_parts: $i,Small_part: $i] :
( ~ has_parts(Big_part,Number_of_mid_parts,Mid_part)
| has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| in(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Mid_part) )
| has_parts(john,times(n2,n1),hand)
| ~ has_parts(john,n2,arm)
| in(object_in(john,arm,hand,n2,n1),arm) )
<=> ( ~ ! [Number_of_mid_parts: $i,Mid_part: $i,Big_part: $i,Number_of_small_parts: $i,Small_part: $i] :
( ~ has_parts(Big_part,Number_of_mid_parts,Mid_part)
| has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| in(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Mid_part) )
| has_parts(john,times(n2,n1),hand)
| ~ has_parts(john,n2,arm)
| in(object_in(john,arm,hand,n2,n1),arm) ) ),
inference(rewrite,[status(thm)],]) ).
tff(74,plain,
( ( ~ has_parts(john,n2,arm)
| has_parts(john,times(n2,n1),hand)
| in(object_in(john,arm,hand,n2,n1),arm) )
<=> ( has_parts(john,times(n2,n1),hand)
| ~ has_parts(john,n2,arm)
| in(object_in(john,arm,hand,n2,n1),arm) ) ),
inference(rewrite,[status(thm)],]) ).
tff(75,plain,
( ( ~ ! [Number_of_mid_parts: $i,Mid_part: $i,Big_part: $i,Number_of_small_parts: $i,Small_part: $i] :
( ~ has_parts(Big_part,Number_of_mid_parts,Mid_part)
| has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| in(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Mid_part) )
| ~ has_parts(john,n2,arm)
| has_parts(john,times(n2,n1),hand)
| in(object_in(john,arm,hand,n2,n1),arm) )
<=> ( ~ ! [Number_of_mid_parts: $i,Mid_part: $i,Big_part: $i,Number_of_small_parts: $i,Small_part: $i] :
( ~ has_parts(Big_part,Number_of_mid_parts,Mid_part)
| has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| in(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Mid_part) )
| has_parts(john,times(n2,n1),hand)
| ~ has_parts(john,n2,arm)
| in(object_in(john,arm,hand,n2,n1),arm) ) ),
inference(monotonicity,[status(thm)],[74]) ).
tff(76,plain,
( ( ~ ! [Number_of_mid_parts: $i,Mid_part: $i,Big_part: $i,Number_of_small_parts: $i,Small_part: $i] :
( ~ has_parts(Big_part,Number_of_mid_parts,Mid_part)
| has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| in(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Mid_part) )
| ~ has_parts(john,n2,arm)
| has_parts(john,times(n2,n1),hand)
| in(object_in(john,arm,hand,n2,n1),arm) )
<=> ( ~ ! [Number_of_mid_parts: $i,Mid_part: $i,Big_part: $i,Number_of_small_parts: $i,Small_part: $i] :
( ~ has_parts(Big_part,Number_of_mid_parts,Mid_part)
| has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| in(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Mid_part) )
| has_parts(john,times(n2,n1),hand)
| ~ has_parts(john,n2,arm)
| in(object_in(john,arm,hand,n2,n1),arm) ) ),
inference(transitivity,[status(thm)],[75,73]) ).
tff(77,plain,
( ~ ! [Number_of_mid_parts: $i,Mid_part: $i,Big_part: $i,Number_of_small_parts: $i,Small_part: $i] :
( ~ has_parts(Big_part,Number_of_mid_parts,Mid_part)
| has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| in(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Mid_part) )
| ~ has_parts(john,n2,arm)
| has_parts(john,times(n2,n1),hand)
| in(object_in(john,arm,hand,n2,n1),arm) ),
inference(quant_inst,[status(thm)],]) ).
tff(78,plain,
( ~ ! [Number_of_mid_parts: $i,Mid_part: $i,Big_part: $i,Number_of_small_parts: $i,Small_part: $i] :
( ~ has_parts(Big_part,Number_of_mid_parts,Mid_part)
| has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)
| in(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Mid_part) )
| has_parts(john,times(n2,n1),hand)
| ~ has_parts(john,n2,arm)
| in(object_in(john,arm,hand,n2,n1),arm) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
$false,
inference(unit_resolution,[status(thm)],[78,72,31,28,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : MSC003-1 : TPTP v8.1.0. Released v1.0.0.
% 0.13/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n007.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Sep 2 02:45:18 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.20/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.20/0.35 Usage: tptp [options] [-file:]file
% 0.20/0.35 -h, -? prints this message.
% 0.20/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.20/0.35 -m, -model generate model.
% 0.20/0.35 -p, -proof generate proof.
% 0.20/0.35 -c, -core generate unsat core of named formulas.
% 0.20/0.35 -st, -statistics display statistics.
% 0.20/0.35 -t:timeout set timeout (in second).
% 0.20/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.20/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.20/0.35 -<param>:<value> configuration parameter and value.
% 0.20/0.35 -o:<output-file> file to place output in.
% 0.21/0.47 % SZS status Unsatisfiable
% 0.21/0.47 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------