TSTP Solution File: PUZ047-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : PUZ047-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 14:11:06 EDT 2022
% Result : Unsatisfiable 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 52
% Syntax : Number of formulae : 108 ( 27 unt; 8 typ; 0 def)
% Number of atoms : 329 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 403 ( 187 ~; 175 |; 0 &)
% ( 41 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 8 ( 1 avg)
% Number of FOOLs : 13 ( 13 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 5 >; 4 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-5 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-1 aty)
% Number of variables : 192 ( 171 !; 0 ?; 192 :)
% Comments :
%------------------------------------------------------------------------------
tff(p_type,type,
p: ( $i * $i * $i * $i * $i ) > $o ).
tff(take_goat_type,type,
take_goat: $i > $i ).
tff(go_alone_type,type,
go_alone: $i > $i ).
tff(take_wolf_type,type,
take_wolf: $i > $i ).
tff(take_cabbage_type,type,
take_cabbage: $i > $i ).
tff(start_type,type,
start: $i ).
tff(north_type,type,
north: $i ).
tff(south_type,type,
south: $i ).
tff(1,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( ~ p(south,A,south,B,C)
| p(north,A,north,B,take_goat(C)) )
<=> ( ~ p(south,A,south,B,C)
| p(north,A,north,B,take_goat(C)) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ p(south,A,south,B,C)
| p(north,A,north,B,take_goat(C)) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ p(south,A,south,B,C)
| p(north,A,north,B,take_goat(C)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ p(south,A,south,B,C)
| p(north,A,north,B,take_goat(C)) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ p(south,A,south,B,C)
| p(north,A,north,B,take_goat(C)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
^ [B: $i,A: $i,C: $i] :
rewrite(
( ( p(north,A,north,B,take_goat(C))
| ~ p(south,A,south,B,C) )
<=> ( ~ p(south,A,south,B,C)
| p(north,A,north,B,take_goat(C)) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [B: $i,A: $i,C: $i] :
( p(north,A,north,B,take_goat(C))
| ~ p(south,A,south,B,C) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ p(south,A,south,B,C)
| p(north,A,north,B,take_goat(C)) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [B: $i,A: $i,C: $i] :
( p(north,A,north,B,take_goat(C))
| ~ p(south,A,south,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm100_10) ).
tff(7,plain,
! [B: $i,A: $i,C: $i] :
( ~ p(south,A,south,B,C)
| p(north,A,north,B,take_goat(C)) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [B: $i,A: $i,C: $i] :
( ~ p(south,A,south,B,C)
| p(north,A,north,B,take_goat(C)) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [B: $i,A: $i,C: $i] :
( ~ p(south,A,south,B,C)
| p(north,A,north,B,take_goat(C)) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [B: $i,A: $i,C: $i] :
( ~ p(south,A,south,B,C)
| p(north,A,north,B,take_goat(C)) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( p(south,south,south,south,start)
<=> p(south,south,south,south,start) ),
inference(rewrite,[status(thm)],]) ).
tff(12,axiom,
p(south,south,south,south,start),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm100_1) ).
tff(13,plain,
p(south,south,south,south,start),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ p(south,A,south,B,C)
| p(north,A,north,B,take_goat(C)) )
| ~ p(south,south,south,south,start)
| p(north,south,north,south,take_goat(start)) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ p(south,A,south,B,C)
| p(north,A,north,B,take_goat(C)) )
| ~ p(south,south,south,south,start)
| p(north,south,north,south,take_goat(start)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ p(south,A,south,B,C)
| p(north,A,north,B,take_goat(C)) )
| ~ p(south,south,south,south,start)
| p(north,south,north,south,take_goat(start)) ),
inference(quant_inst,[status(thm)],]) ).
tff(16,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ p(south,A,south,B,C)
| p(north,A,north,B,take_goat(C)) )
| ~ p(south,south,south,south,start)
| p(north,south,north,south,take_goat(start)) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
p(north,south,north,south,take_goat(start)),
inference(unit_resolution,[status(thm)],[16,13,10]) ).
tff(18,plain,
^ [A: $i] :
refl(
( ( ~ p(north,south,north,south,A)
| p(south,south,north,south,go_alone(A)) )
<=> ( ~ p(north,south,north,south,A)
| p(south,south,north,south,go_alone(A)) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [A: $i] :
( ~ p(north,south,north,south,A)
| p(south,south,north,south,go_alone(A)) )
<=> ! [A: $i] :
( ~ p(north,south,north,south,A)
| p(south,south,north,south,go_alone(A)) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [A: $i] :
( ~ p(north,south,north,south,A)
| p(south,south,north,south,go_alone(A)) )
<=> ! [A: $i] :
( ~ p(north,south,north,south,A)
| p(south,south,north,south,go_alone(A)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
^ [A: $i] :
rewrite(
( ( p(south,south,north,south,go_alone(A))
| ~ p(north,south,north,south,A) )
<=> ( ~ p(north,south,north,south,A)
| p(south,south,north,south,go_alone(A)) ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [A: $i] :
( p(south,south,north,south,go_alone(A))
| ~ p(north,south,north,south,A) )
<=> ! [A: $i] :
( ~ p(north,south,north,south,A)
| p(south,south,north,south,go_alone(A)) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,axiom,
! [A: $i] :
( p(south,south,north,south,go_alone(A))
| ~ p(north,south,north,south,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm100_5) ).
tff(24,plain,
! [A: $i] :
( ~ p(north,south,north,south,A)
| p(south,south,north,south,go_alone(A)) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [A: $i] :
( ~ p(north,south,north,south,A)
| p(south,south,north,south,go_alone(A)) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
! [A: $i] :
( ~ p(north,south,north,south,A)
| p(south,south,north,south,go_alone(A)) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [A: $i] :
( ~ p(north,south,north,south,A)
| p(south,south,north,south,go_alone(A)) ),
inference(modus_ponens,[status(thm)],[26,19]) ).
tff(28,plain,
( ( ~ ! [A: $i] :
( ~ p(north,south,north,south,A)
| p(south,south,north,south,go_alone(A)) )
| ~ p(north,south,north,south,take_goat(start))
| p(south,south,north,south,go_alone(take_goat(start))) )
<=> ( ~ ! [A: $i] :
( ~ p(north,south,north,south,A)
| p(south,south,north,south,go_alone(A)) )
| ~ p(north,south,north,south,take_goat(start))
| p(south,south,north,south,go_alone(take_goat(start))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
( ~ ! [A: $i] :
( ~ p(north,south,north,south,A)
| p(south,south,north,south,go_alone(A)) )
| ~ p(north,south,north,south,take_goat(start))
| p(south,south,north,south,go_alone(take_goat(start))) ),
inference(quant_inst,[status(thm)],]) ).
tff(30,plain,
( ~ ! [A: $i] :
( ~ p(north,south,north,south,A)
| p(south,south,north,south,go_alone(A)) )
| ~ p(north,south,north,south,take_goat(start))
| p(south,south,north,south,go_alone(take_goat(start))) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
p(south,south,north,south,go_alone(take_goat(start))),
inference(unit_resolution,[status(thm)],[30,27,17]) ).
tff(32,plain,
^ [A: $i] :
refl(
( ( ~ p(south,south,north,south,A)
| p(north,south,north,north,take_cabbage(A)) )
<=> ( ~ p(south,south,north,south,A)
| p(north,south,north,north,take_cabbage(A)) ) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [A: $i] :
( ~ p(south,south,north,south,A)
| p(north,south,north,north,take_cabbage(A)) )
<=> ! [A: $i] :
( ~ p(south,south,north,south,A)
| p(north,south,north,north,take_cabbage(A)) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [A: $i] :
( ~ p(south,south,north,south,A)
| p(north,south,north,north,take_cabbage(A)) )
<=> ! [A: $i] :
( ~ p(south,south,north,south,A)
| p(north,south,north,north,take_cabbage(A)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
^ [A: $i] :
rewrite(
( ( p(north,south,north,north,take_cabbage(A))
| ~ p(south,south,north,south,A) )
<=> ( ~ p(south,south,north,south,A)
| p(north,south,north,north,take_cabbage(A)) ) )),
inference(bind,[status(th)],]) ).
tff(36,plain,
( ! [A: $i] :
( p(north,south,north,north,take_cabbage(A))
| ~ p(south,south,north,south,A) )
<=> ! [A: $i] :
( ~ p(south,south,north,south,A)
| p(north,south,north,north,take_cabbage(A)) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,axiom,
! [A: $i] :
( p(north,south,north,north,take_cabbage(A))
| ~ p(south,south,north,south,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm100_14) ).
tff(38,plain,
! [A: $i] :
( ~ p(south,south,north,south,A)
| p(north,south,north,north,take_cabbage(A)) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [A: $i] :
( ~ p(south,south,north,south,A)
| p(north,south,north,north,take_cabbage(A)) ),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,plain,
! [A: $i] :
( ~ p(south,south,north,south,A)
| p(north,south,north,north,take_cabbage(A)) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [A: $i] :
( ~ p(south,south,north,south,A)
| p(north,south,north,north,take_cabbage(A)) ),
inference(modus_ponens,[status(thm)],[40,33]) ).
tff(42,plain,
( ( ~ ! [A: $i] :
( ~ p(south,south,north,south,A)
| p(north,south,north,north,take_cabbage(A)) )
| ~ p(south,south,north,south,go_alone(take_goat(start)))
| p(north,south,north,north,take_cabbage(go_alone(take_goat(start)))) )
<=> ( ~ ! [A: $i] :
( ~ p(south,south,north,south,A)
| p(north,south,north,north,take_cabbage(A)) )
| ~ p(south,south,north,south,go_alone(take_goat(start)))
| p(north,south,north,north,take_cabbage(go_alone(take_goat(start)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,plain,
( ~ ! [A: $i] :
( ~ p(south,south,north,south,A)
| p(north,south,north,north,take_cabbage(A)) )
| ~ p(south,south,north,south,go_alone(take_goat(start)))
| p(north,south,north,north,take_cabbage(go_alone(take_goat(start)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(44,plain,
( ~ ! [A: $i] :
( ~ p(south,south,north,south,A)
| p(north,south,north,north,take_cabbage(A)) )
| ~ p(south,south,north,south,go_alone(take_goat(start)))
| p(north,south,north,north,take_cabbage(go_alone(take_goat(start)))) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
p(north,south,north,north,take_cabbage(go_alone(take_goat(start)))),
inference(unit_resolution,[status(thm)],[44,41,31]) ).
tff(46,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( ~ p(north,A,north,B,C)
| p(south,A,south,B,take_goat(C)) )
<=> ( ~ p(north,A,north,B,C)
| p(south,A,south,B,take_goat(C)) ) )),
inference(bind,[status(th)],]) ).
tff(47,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ p(north,A,north,B,C)
| p(south,A,south,B,take_goat(C)) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ p(north,A,north,B,C)
| p(south,A,south,B,take_goat(C)) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ p(north,A,north,B,C)
| p(south,A,south,B,take_goat(C)) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ p(north,A,north,B,C)
| p(south,A,south,B,take_goat(C)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(49,plain,
^ [B: $i,A: $i,C: $i] :
rewrite(
( ( p(south,A,south,B,take_goat(C))
| ~ p(north,A,north,B,C) )
<=> ( ~ p(north,A,north,B,C)
| p(south,A,south,B,take_goat(C)) ) )),
inference(bind,[status(th)],]) ).
tff(50,plain,
( ! [B: $i,A: $i,C: $i] :
( p(south,A,south,B,take_goat(C))
| ~ p(north,A,north,B,C) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ p(north,A,north,B,C)
| p(south,A,south,B,take_goat(C)) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,axiom,
! [B: $i,A: $i,C: $i] :
( p(south,A,south,B,take_goat(C))
| ~ p(north,A,north,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm100_11) ).
tff(52,plain,
! [B: $i,A: $i,C: $i] :
( ~ p(north,A,north,B,C)
| p(south,A,south,B,take_goat(C)) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
! [B: $i,A: $i,C: $i] :
( ~ p(north,A,north,B,C)
| p(south,A,south,B,take_goat(C)) ),
inference(modus_ponens,[status(thm)],[52,48]) ).
tff(54,plain,
! [B: $i,A: $i,C: $i] :
( ~ p(north,A,north,B,C)
| p(south,A,south,B,take_goat(C)) ),
inference(skolemize,[status(sab)],[53]) ).
tff(55,plain,
! [B: $i,A: $i,C: $i] :
( ~ p(north,A,north,B,C)
| p(south,A,south,B,take_goat(C)) ),
inference(modus_ponens,[status(thm)],[54,47]) ).
tff(56,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ p(north,A,north,B,C)
| p(south,A,south,B,take_goat(C)) )
| ~ p(north,south,north,north,take_cabbage(go_alone(take_goat(start))))
| p(south,south,south,north,take_goat(take_cabbage(go_alone(take_goat(start))))) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ p(north,A,north,B,C)
| p(south,A,south,B,take_goat(C)) )
| ~ p(north,south,north,north,take_cabbage(go_alone(take_goat(start))))
| p(south,south,south,north,take_goat(take_cabbage(go_alone(take_goat(start))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(57,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ p(north,A,north,B,C)
| p(south,A,south,B,take_goat(C)) )
| ~ p(north,south,north,north,take_cabbage(go_alone(take_goat(start))))
| p(south,south,south,north,take_goat(take_cabbage(go_alone(take_goat(start))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(58,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ p(north,A,north,B,C)
| p(south,A,south,B,take_goat(C)) )
| ~ p(north,south,north,north,take_cabbage(go_alone(take_goat(start))))
| p(south,south,south,north,take_goat(take_cabbage(go_alone(take_goat(start))))) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
p(south,south,south,north,take_goat(take_cabbage(go_alone(take_goat(start))))),
inference(unit_resolution,[status(thm)],[58,55,45]) ).
tff(60,plain,
^ [A: $i] :
refl(
( ( ~ p(south,south,south,north,A)
| p(north,north,south,north,take_wolf(A)) )
<=> ( ~ p(south,south,south,north,A)
| p(north,north,south,north,take_wolf(A)) ) )),
inference(bind,[status(th)],]) ).
tff(61,plain,
( ! [A: $i] :
( ~ p(south,south,south,north,A)
| p(north,north,south,north,take_wolf(A)) )
<=> ! [A: $i] :
( ~ p(south,south,south,north,A)
| p(north,north,south,north,take_wolf(A)) ) ),
inference(quant_intro,[status(thm)],[60]) ).
tff(62,plain,
( ! [A: $i] :
( ~ p(south,south,south,north,A)
| p(north,north,south,north,take_wolf(A)) )
<=> ! [A: $i] :
( ~ p(south,south,south,north,A)
| p(north,north,south,north,take_wolf(A)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(63,plain,
^ [A: $i] :
rewrite(
( ( p(north,north,south,north,take_wolf(A))
| ~ p(south,south,south,north,A) )
<=> ( ~ p(south,south,south,north,A)
| p(north,north,south,north,take_wolf(A)) ) )),
inference(bind,[status(th)],]) ).
tff(64,plain,
( ! [A: $i] :
( p(north,north,south,north,take_wolf(A))
| ~ p(south,south,south,north,A) )
<=> ! [A: $i] :
( ~ p(south,south,south,north,A)
| p(north,north,south,north,take_wolf(A)) ) ),
inference(quant_intro,[status(thm)],[63]) ).
tff(65,axiom,
! [A: $i] :
( p(north,north,south,north,take_wolf(A))
| ~ p(south,south,south,north,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm100_6) ).
tff(66,plain,
! [A: $i] :
( ~ p(south,south,south,north,A)
| p(north,north,south,north,take_wolf(A)) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
! [A: $i] :
( ~ p(south,south,south,north,A)
| p(north,north,south,north,take_wolf(A)) ),
inference(modus_ponens,[status(thm)],[66,62]) ).
tff(68,plain,
! [A: $i] :
( ~ p(south,south,south,north,A)
| p(north,north,south,north,take_wolf(A)) ),
inference(skolemize,[status(sab)],[67]) ).
tff(69,plain,
! [A: $i] :
( ~ p(south,south,south,north,A)
| p(north,north,south,north,take_wolf(A)) ),
inference(modus_ponens,[status(thm)],[68,61]) ).
tff(70,plain,
( ( ~ ! [A: $i] :
( ~ p(south,south,south,north,A)
| p(north,north,south,north,take_wolf(A)) )
| ~ p(south,south,south,north,take_goat(take_cabbage(go_alone(take_goat(start)))))
| p(north,north,south,north,take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))) )
<=> ( ~ ! [A: $i] :
( ~ p(south,south,south,north,A)
| p(north,north,south,north,take_wolf(A)) )
| ~ p(south,south,south,north,take_goat(take_cabbage(go_alone(take_goat(start)))))
| p(north,north,south,north,take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(71,plain,
( ~ ! [A: $i] :
( ~ p(south,south,south,north,A)
| p(north,north,south,north,take_wolf(A)) )
| ~ p(south,south,south,north,take_goat(take_cabbage(go_alone(take_goat(start)))))
| p(north,north,south,north,take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(72,plain,
( ~ ! [A: $i] :
( ~ p(south,south,south,north,A)
| p(north,north,south,north,take_wolf(A)) )
| ~ p(south,south,south,north,take_goat(take_cabbage(go_alone(take_goat(start)))))
| p(north,north,south,north,take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
p(north,north,south,north,take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))),
inference(unit_resolution,[status(thm)],[72,69,59]) ).
tff(74,plain,
^ [A: $i] :
refl(
( ( ~ p(north,north,south,north,A)
| p(south,north,south,north,go_alone(A)) )
<=> ( ~ p(north,north,south,north,A)
| p(south,north,south,north,go_alone(A)) ) )),
inference(bind,[status(th)],]) ).
tff(75,plain,
( ! [A: $i] :
( ~ p(north,north,south,north,A)
| p(south,north,south,north,go_alone(A)) )
<=> ! [A: $i] :
( ~ p(north,north,south,north,A)
| p(south,north,south,north,go_alone(A)) ) ),
inference(quant_intro,[status(thm)],[74]) ).
tff(76,plain,
( ! [A: $i] :
( ~ p(north,north,south,north,A)
| p(south,north,south,north,go_alone(A)) )
<=> ! [A: $i] :
( ~ p(north,north,south,north,A)
| p(south,north,south,north,go_alone(A)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(77,plain,
^ [A: $i] :
rewrite(
( ( p(south,north,south,north,go_alone(A))
| ~ p(north,north,south,north,A) )
<=> ( ~ p(north,north,south,north,A)
| p(south,north,south,north,go_alone(A)) ) )),
inference(bind,[status(th)],]) ).
tff(78,plain,
( ! [A: $i] :
( p(south,north,south,north,go_alone(A))
| ~ p(north,north,south,north,A) )
<=> ! [A: $i] :
( ~ p(north,north,south,north,A)
| p(south,north,south,north,go_alone(A)) ) ),
inference(quant_intro,[status(thm)],[77]) ).
tff(79,axiom,
! [A: $i] :
( p(south,north,south,north,go_alone(A))
| ~ p(north,north,south,north,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm100_3) ).
tff(80,plain,
! [A: $i] :
( ~ p(north,north,south,north,A)
| p(south,north,south,north,go_alone(A)) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
! [A: $i] :
( ~ p(north,north,south,north,A)
| p(south,north,south,north,go_alone(A)) ),
inference(modus_ponens,[status(thm)],[80,76]) ).
tff(82,plain,
! [A: $i] :
( ~ p(north,north,south,north,A)
| p(south,north,south,north,go_alone(A)) ),
inference(skolemize,[status(sab)],[81]) ).
tff(83,plain,
! [A: $i] :
( ~ p(north,north,south,north,A)
| p(south,north,south,north,go_alone(A)) ),
inference(modus_ponens,[status(thm)],[82,75]) ).
tff(84,plain,
( ( ~ ! [A: $i] :
( ~ p(north,north,south,north,A)
| p(south,north,south,north,go_alone(A)) )
| ~ p(north,north,south,north,take_wolf(take_goat(take_cabbage(go_alone(take_goat(start))))))
| p(south,north,south,north,go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start))))))) )
<=> ( ~ ! [A: $i] :
( ~ p(north,north,south,north,A)
| p(south,north,south,north,go_alone(A)) )
| ~ p(north,north,south,north,take_wolf(take_goat(take_cabbage(go_alone(take_goat(start))))))
| p(south,north,south,north,go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(85,plain,
( ~ ! [A: $i] :
( ~ p(north,north,south,north,A)
| p(south,north,south,north,go_alone(A)) )
| ~ p(north,north,south,north,take_wolf(take_goat(take_cabbage(go_alone(take_goat(start))))))
| p(south,north,south,north,go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start))))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(86,plain,
( ~ ! [A: $i] :
( ~ p(north,north,south,north,A)
| p(south,north,south,north,go_alone(A)) )
| ~ p(north,north,south,north,take_wolf(take_goat(take_cabbage(go_alone(take_goat(start))))))
| p(south,north,south,north,go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start))))))) ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
p(south,north,south,north,go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start))))))),
inference(unit_resolution,[status(thm)],[86,83,73]) ).
tff(88,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ p(south,A,south,B,C)
| p(north,A,north,B,take_goat(C)) )
| ~ p(south,north,south,north,go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))))
| p(north,north,north,north,take_goat(go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))))) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ p(south,A,south,B,C)
| p(north,A,north,B,take_goat(C)) )
| ~ p(south,north,south,north,go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))))
| p(north,north,north,north,take_goat(go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(89,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ p(south,A,south,B,C)
| p(north,A,north,B,take_goat(C)) )
| ~ p(south,north,south,north,go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))))
| p(north,north,north,north,take_goat(go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(90,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ p(south,A,south,B,C)
| p(north,A,north,B,take_goat(C)) )
| ~ p(south,north,south,north,go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))))
| p(north,north,north,north,take_goat(go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))))) ),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
p(north,north,north,north,take_goat(go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))))),
inference(unit_resolution,[status(thm)],[90,10,87]) ).
tff(92,plain,
^ [A: $i] :
refl(
( ~ p(north,north,north,north,A)
<=> ~ p(north,north,north,north,A) )),
inference(bind,[status(th)],]) ).
tff(93,plain,
( ! [A: $i] : ~ p(north,north,north,north,A)
<=> ! [A: $i] : ~ p(north,north,north,north,A) ),
inference(quant_intro,[status(thm)],[92]) ).
tff(94,plain,
( ! [A: $i] : ~ p(north,north,north,north,A)
<=> ! [A: $i] : ~ p(north,north,north,north,A) ),
inference(rewrite,[status(thm)],]) ).
tff(95,axiom,
! [A: $i] : ~ p(north,north,north,north,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm100_16) ).
tff(96,plain,
! [A: $i] : ~ p(north,north,north,north,A),
inference(modus_ponens,[status(thm)],[95,94]) ).
tff(97,plain,
! [A: $i] : ~ p(north,north,north,north,A),
inference(skolemize,[status(sab)],[96]) ).
tff(98,plain,
! [A: $i] : ~ p(north,north,north,north,A),
inference(modus_ponens,[status(thm)],[97,93]) ).
tff(99,plain,
( ~ ! [A: $i] : ~ p(north,north,north,north,A)
| ~ p(north,north,north,north,take_goat(go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(100,plain,
$false,
inference(unit_resolution,[status(thm)],[99,98,91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : PUZ047-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 18:40:31 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.19/0.41 % SZS status Unsatisfiable
% 0.19/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------