%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PUZ047+1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:23:17 AM UTC 2025
% Result : Theorem 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 33
% Syntax : Number of formulae : 89 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 418 ( 0 equ)
% Maximal formula atoms : 60 ( 4 avg)
% Number of connectives : 528 ( 209 ~; 189 |; 70 &)
% ( 30 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 8 ( 1 avg)
% Number of FOOLs : 10 ( 10 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-5 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-1 aty)
% Number of variables : 249 ( 227 !; 10 ?; 249 :)
% 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,
^ [X: $i,Y: $i,U: $i] :
refl(( ( ~ p(south,X,south,Y,U)
| p(north,X,north,Y,take_goat(U)) )
<=> ( ~ p(south,X,south,Y,U)
| p(north,X,north,Y,take_goat(U)) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i,Y: $i,U: $i] :
( ~ p(south,X,south,Y,U)
| p(north,X,north,Y,take_goat(U)) )
<=> ! [X: $i,Y: $i,U: $i] :
( ~ p(south,X,south,Y,U)
| p(north,X,north,Y,take_goat(U)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i,Y: $i,U: $i] :
( ~ p(south,X,south,Y,U)
| p(north,X,north,Y,take_goat(U)) )
<=> ! [X: $i,Y: $i,U: $i] :
( ~ p(south,X,south,Y,U)
| p(north,X,north,Y,take_goat(U)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,plain,
( ~ ( ( p(south,south,south,south,start)
& ! [T: $i] :
( p(south,north,south,north,T)
=> p(north,north,south,north,go_alone(T)) )
& ! [T1: $i] :
( p(north,north,south,north,T1)
=> p(south,north,south,north,go_alone(T1)) )
& ! [T2: $i] :
( p(south,south,north,south,T2)
=> p(north,south,north,south,go_alone(T2)) )
& ! [T3: $i] :
( p(north,south,north,south,T3)
=> p(south,south,north,south,go_alone(T3)) )
& ! [T4: $i] :
( p(south,south,south,north,T4)
=> p(north,north,south,north,take_wolf(T4)) )
& ! [T5: $i] :
( p(north,north,south,north,T5)
=> p(south,south,south,north,take_wolf(T5)) )
& ! [T6: $i] :
( p(south,south,north,south,T6)
=> p(north,north,north,south,take_wolf(T6)) )
& ! [T7: $i] :
( p(north,north,north,south,T7)
=> p(south,south,north,south,take_wolf(T7)) )
& ! [X: $i,Y: $i,U: $i] :
( p(south,X,south,Y,U)
=> p(north,X,north,Y,take_goat(U)) )
& ! [X1: $i,Y1: $i,V: $i] :
( p(north,X1,north,Y1,V)
=> p(south,X1,south,Y1,take_goat(V)) )
& ! [T8: $i] :
( p(south,north,south,south,T8)
=> p(north,north,south,north,take_cabbage(T8)) )
& ! [T9: $i] :
( p(north,north,south,north,T9)
=> p(south,north,south,south,take_cabbage(T9)) )
& ! [U1: $i] :
( p(south,south,north,south,U1)
=> p(north,south,north,north,take_cabbage(U1)) )
& ! [V1: $i] :
( p(north,south,north,north,V1)
=> p(south,south,north,south,take_cabbage(V1)) ) )
=> ? [Z: $i] : p(north,north,north,north,Z) )
<=> ~ ( ~ ( p(south,south,south,south,start)
& ! [T: $i] :
( ~ p(south,north,south,north,T)
| p(north,north,south,north,go_alone(T)) )
& ! [T1: $i] :
( ~ p(north,north,south,north,T1)
| p(south,north,south,north,go_alone(T1)) )
& ! [T2: $i] :
( ~ p(south,south,north,south,T2)
| p(north,south,north,south,go_alone(T2)) )
& ! [T3: $i] :
( ~ p(north,south,north,south,T3)
| p(south,south,north,south,go_alone(T3)) )
& ! [T4: $i] :
( ~ p(south,south,south,north,T4)
| p(north,north,south,north,take_wolf(T4)) )
& ! [T5: $i] :
( ~ p(north,north,south,north,T5)
| p(south,south,south,north,take_wolf(T5)) )
& ! [T6: $i] :
( ~ p(south,south,north,south,T6)
| p(north,north,north,south,take_wolf(T6)) )
& ! [T7: $i] :
( ~ p(north,north,north,south,T7)
| p(south,south,north,south,take_wolf(T7)) )
& ! [X: $i,Y: $i,U: $i] :
( ~ p(south,X,south,Y,U)
| p(north,X,north,Y,take_goat(U)) )
& ! [X1: $i,Y1: $i,V: $i] :
( ~ p(north,X1,north,Y1,V)
| p(south,X1,south,Y1,take_goat(V)) )
& ! [T8: $i] :
( ~ p(south,north,south,south,T8)
| p(north,north,south,north,take_cabbage(T8)) )
& ! [T9: $i] :
( ~ p(north,north,south,north,T9)
| p(south,north,south,south,take_cabbage(T9)) )
& ! [U1: $i] :
( ~ p(south,south,north,south,U1)
| p(north,south,north,north,take_cabbage(U1)) )
& ! [V1: $i] :
( ~ p(north,south,north,north,V1)
| p(south,south,north,south,take_cabbage(V1)) ) )
| ? [Z: $i] : p(north,north,north,north,Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
~ ( ( p(south,south,south,south,start)
& ! [T: $i] :
( p(south,north,south,north,T)
=> p(north,north,south,north,go_alone(T)) )
& ! [T1: $i] :
( p(north,north,south,north,T1)
=> p(south,north,south,north,go_alone(T1)) )
& ! [T2: $i] :
( p(south,south,north,south,T2)
=> p(north,south,north,south,go_alone(T2)) )
& ! [T3: $i] :
( p(north,south,north,south,T3)
=> p(south,south,north,south,go_alone(T3)) )
& ! [T4: $i] :
( p(south,south,south,north,T4)
=> p(north,north,south,north,take_wolf(T4)) )
& ! [T5: $i] :
( p(north,north,south,north,T5)
=> p(south,south,south,north,take_wolf(T5)) )
& ! [T6: $i] :
( p(south,south,north,south,T6)
=> p(north,north,north,south,take_wolf(T6)) )
& ! [T7: $i] :
( p(north,north,north,south,T7)
=> p(south,south,north,south,take_wolf(T7)) )
& ! [X: $i,Y: $i,U: $i] :
( p(south,X,south,Y,U)
=> p(north,X,north,Y,take_goat(U)) )
& ! [X1: $i,Y1: $i,V: $i] :
( p(north,X1,north,Y1,V)
=> p(south,X1,south,Y1,take_goat(V)) )
& ! [T8: $i] :
( p(south,north,south,south,T8)
=> p(north,north,south,north,take_cabbage(T8)) )
& ! [T9: $i] :
( p(north,north,south,north,T9)
=> p(south,north,south,south,take_cabbage(T9)) )
& ! [U1: $i] :
( p(south,south,north,south,U1)
=> p(north,south,north,north,take_cabbage(U1)) )
& ! [V1: $i] :
( p(north,south,north,north,V1)
=> p(south,south,north,south,take_cabbage(V1)) ) )
=> ? [Z: $i] : p(north,north,north,north,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm100) ).
tff(6,plain,
~ ( ~ ( p(south,south,south,south,start)
& ! [T: $i] :
( ~ p(south,north,south,north,T)
| p(north,north,south,north,go_alone(T)) )
& ! [T1: $i] :
( ~ p(north,north,south,north,T1)
| p(south,north,south,north,go_alone(T1)) )
& ! [T2: $i] :
( ~ p(south,south,north,south,T2)
| p(north,south,north,south,go_alone(T2)) )
& ! [T3: $i] :
( ~ p(north,south,north,south,T3)
| p(south,south,north,south,go_alone(T3)) )
& ! [T4: $i] :
( ~ p(south,south,south,north,T4)
| p(north,north,south,north,take_wolf(T4)) )
& ! [T5: $i] :
( ~ p(north,north,south,north,T5)
| p(south,south,south,north,take_wolf(T5)) )
& ! [T6: $i] :
( ~ p(south,south,north,south,T6)
| p(north,north,north,south,take_wolf(T6)) )
& ! [T7: $i] :
( ~ p(north,north,north,south,T7)
| p(south,south,north,south,take_wolf(T7)) )
& ! [X: $i,Y: $i,U: $i] :
( ~ p(south,X,south,Y,U)
| p(north,X,north,Y,take_goat(U)) )
& ! [X1: $i,Y1: $i,V: $i] :
( ~ p(north,X1,north,Y1,V)
| p(south,X1,south,Y1,take_goat(V)) )
& ! [T8: $i] :
( ~ p(south,north,south,south,T8)
| p(north,north,south,north,take_cabbage(T8)) )
& ! [T9: $i] :
( ~ p(north,north,south,north,T9)
| p(south,north,south,south,take_cabbage(T9)) )
& ! [U1: $i] :
( ~ p(south,south,north,south,U1)
| p(north,south,north,north,take_cabbage(U1)) )
& ! [V1: $i] :
( ~ p(north,south,north,north,V1)
| p(south,south,north,south,take_cabbage(V1)) ) )
| ? [Z: $i] : p(north,north,north,north,Z) ),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( p(south,south,south,south,start)
& ! [T: $i] :
( ~ p(south,north,south,north,T)
| p(north,north,south,north,go_alone(T)) )
& ! [T1: $i] :
( ~ p(north,north,south,north,T1)
| p(south,north,south,north,go_alone(T1)) )
& ! [T2: $i] :
( ~ p(south,south,north,south,T2)
| p(north,south,north,south,go_alone(T2)) )
& ! [T3: $i] :
( ~ p(north,south,north,south,T3)
| p(south,south,north,south,go_alone(T3)) )
& ! [T4: $i] :
( ~ p(south,south,south,north,T4)
| p(north,north,south,north,take_wolf(T4)) )
& ! [T5: $i] :
( ~ p(north,north,south,north,T5)
| p(south,south,south,north,take_wolf(T5)) )
& ! [T6: $i] :
( ~ p(south,south,north,south,T6)
| p(north,north,north,south,take_wolf(T6)) )
& ! [T7: $i] :
( ~ p(north,north,north,south,T7)
| p(south,south,north,south,take_wolf(T7)) )
& ! [X: $i,Y: $i,U: $i] :
( ~ p(south,X,south,Y,U)
| p(north,X,north,Y,take_goat(U)) )
& ! [X1: $i,Y1: $i,V: $i] :
( ~ p(north,X1,north,Y1,V)
| p(south,X1,south,Y1,take_goat(V)) )
& ! [T8: $i] :
( ~ p(south,north,south,south,T8)
| p(north,north,south,north,take_cabbage(T8)) )
& ! [T9: $i] :
( ~ p(north,north,south,north,T9)
| p(south,north,south,south,take_cabbage(T9)) )
& ! [U1: $i] :
( ~ p(south,south,north,south,U1)
| p(north,south,north,north,take_cabbage(U1)) )
& ! [V1: $i] :
( ~ p(north,south,north,north,V1)
| p(south,south,north,south,take_cabbage(V1)) ) ),
inference(or_elim,[status(thm)],[6]) ).
tff(8,plain,
! [X: $i,Y: $i,U: $i] :
( ~ p(south,X,south,Y,U)
| p(north,X,north,Y,take_goat(U)) ),
inference(and_elim,[status(thm)],[7]) ).
tff(9,plain,
! [X: $i,Y: $i,U: $i] :
( ~ p(south,X,south,Y,U)
| p(north,X,north,Y,take_goat(U)) ),
inference(modus_ponens,[status(thm)],[8,3]) ).
tff(10,plain,
! [X: $i,Y: $i,U: $i] :
( ~ p(south,X,south,Y,U)
| p(north,X,north,Y,take_goat(U)) ),
inference(skolemize,[status(sab)],[9]) ).
tff(11,plain,
! [X: $i,Y: $i,U: $i] :
( ~ p(south,X,south,Y,U)
| p(north,X,north,Y,take_goat(U)) ),
inference(modus_ponens,[status(thm)],[10,2]) ).
tff(12,plain,
( p(south,south,south,south,start)
<=> p(south,south,south,south,start) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
p(south,south,south,south,start),
inference(and_elim,[status(thm)],[7]) ).
tff(14,plain,
p(south,south,south,south,start),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
( ( ~ ! [X: $i,Y: $i,U: $i] :
( ~ p(south,X,south,Y,U)
| p(north,X,north,Y,take_goat(U)) )
| ~ p(south,south,south,south,start)
| p(north,south,north,south,take_goat(start)) )
<=> ( ~ ! [X: $i,Y: $i,U: $i] :
( ~ p(south,X,south,Y,U)
| p(north,X,north,Y,take_goat(U)) )
| ~ p(south,south,south,south,start)
| p(north,south,north,south,take_goat(start)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [X: $i,Y: $i,U: $i] :
( ~ p(south,X,south,Y,U)
| p(north,X,north,Y,take_goat(U)) )
| ~ p(south,south,south,south,start)
| p(north,south,north,south,take_goat(start)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(17,plain,
( ~ ! [X: $i,Y: $i,U: $i] :
( ~ p(south,X,south,Y,U)
| p(north,X,north,Y,take_goat(U)) )
| ~ p(south,south,south,south,start)
| p(north,south,north,south,take_goat(start)) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
p(north,south,north,south,take_goat(start)),
inference(unit_resolution,[status(thm)],[17,14,11]) ).
tff(19,plain,
^ [T3: $i] :
refl(( ( ~ p(north,south,north,south,T3)
| p(south,south,north,south,go_alone(T3)) )
<=> ( ~ p(north,south,north,south,T3)
| p(south,south,north,south,go_alone(T3)) ) )),
inference(bind,[status(th)],[]) ).
tff(20,plain,
( ! [T3: $i] :
( ~ p(north,south,north,south,T3)
| p(south,south,north,south,go_alone(T3)) )
<=> ! [T3: $i] :
( ~ p(north,south,north,south,T3)
| p(south,south,north,south,go_alone(T3)) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [T3: $i] :
( ~ p(north,south,north,south,T3)
| p(south,south,north,south,go_alone(T3)) )
<=> ! [T3: $i] :
( ~ p(north,south,north,south,T3)
| p(south,south,north,south,go_alone(T3)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,plain,
! [T3: $i] :
( ~ p(north,south,north,south,T3)
| p(south,south,north,south,go_alone(T3)) ),
inference(and_elim,[status(thm)],[7]) ).
tff(23,plain,
! [T3: $i] :
( ~ p(north,south,north,south,T3)
| p(south,south,north,south,go_alone(T3)) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [T3: $i] :
( ~ p(north,south,north,south,T3)
| p(south,south,north,south,go_alone(T3)) ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [T3: $i] :
( ~ p(north,south,north,south,T3)
| p(south,south,north,south,go_alone(T3)) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
( ( ~ ! [T3: $i] :
( ~ p(north,south,north,south,T3)
| p(south,south,north,south,go_alone(T3)) )
| ~ p(north,south,north,south,take_goat(start))
| p(south,south,north,south,go_alone(take_goat(start))) )
<=> ( ~ ! [T3: $i] :
( ~ p(north,south,north,south,T3)
| p(south,south,north,south,go_alone(T3)) )
| ~ p(north,south,north,south,take_goat(start))
| p(south,south,north,south,go_alone(take_goat(start))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,plain,
( ~ ! [T3: $i] :
( ~ p(north,south,north,south,T3)
| p(south,south,north,south,go_alone(T3)) )
| ~ p(north,south,north,south,take_goat(start))
| p(south,south,north,south,go_alone(take_goat(start))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
( ~ ! [T3: $i] :
( ~ p(north,south,north,south,T3)
| p(south,south,north,south,go_alone(T3)) )
| ~ p(north,south,north,south,take_goat(start))
| p(south,south,north,south,go_alone(take_goat(start))) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
p(south,south,north,south,go_alone(take_goat(start))),
inference(unit_resolution,[status(thm)],[28,25,18]) ).
tff(30,plain,
^ [U1: $i] :
refl(( ( ~ p(south,south,north,south,U1)
| p(north,south,north,north,take_cabbage(U1)) )
<=> ( ~ p(south,south,north,south,U1)
| p(north,south,north,north,take_cabbage(U1)) ) )),
inference(bind,[status(th)],[]) ).
tff(31,plain,
( ! [U1: $i] :
( ~ p(south,south,north,south,U1)
| p(north,south,north,north,take_cabbage(U1)) )
<=> ! [U1: $i] :
( ~ p(south,south,north,south,U1)
| p(north,south,north,north,take_cabbage(U1)) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [U1: $i] :
( ~ p(south,south,north,south,U1)
| p(north,south,north,north,take_cabbage(U1)) )
<=> ! [U1: $i] :
( ~ p(south,south,north,south,U1)
| p(north,south,north,north,take_cabbage(U1)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,plain,
! [U1: $i] :
( ~ p(south,south,north,south,U1)
| p(north,south,north,north,take_cabbage(U1)) ),
inference(and_elim,[status(thm)],[7]) ).
tff(34,plain,
! [U1: $i] :
( ~ p(south,south,north,south,U1)
| p(north,south,north,north,take_cabbage(U1)) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [U1: $i] :
( ~ p(south,south,north,south,U1)
| p(north,south,north,north,take_cabbage(U1)) ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [U1: $i] :
( ~ p(south,south,north,south,U1)
| p(north,south,north,north,take_cabbage(U1)) ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
( ( ~ ! [U1: $i] :
( ~ p(south,south,north,south,U1)
| p(north,south,north,north,take_cabbage(U1)) )
| ~ p(south,south,north,south,go_alone(take_goat(start)))
| p(north,south,north,north,take_cabbage(go_alone(take_goat(start)))) )
<=> ( ~ ! [U1: $i] :
( ~ p(south,south,north,south,U1)
| p(north,south,north,north,take_cabbage(U1)) )
| ~ 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(38,plain,
( ~ ! [U1: $i] :
( ~ p(south,south,north,south,U1)
| p(north,south,north,north,take_cabbage(U1)) )
| ~ 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(39,plain,
( ~ ! [U1: $i] :
( ~ p(south,south,north,south,U1)
| p(north,south,north,north,take_cabbage(U1)) )
| ~ 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)],[38,37]) ).
tff(40,plain,
p(north,south,north,north,take_cabbage(go_alone(take_goat(start)))),
inference(unit_resolution,[status(thm)],[39,36,29]) ).
tff(41,plain,
^ [X1: $i,Y1: $i,V: $i] :
refl(( ( ~ p(north,X1,north,Y1,V)
| p(south,X1,south,Y1,take_goat(V)) )
<=> ( ~ p(north,X1,north,Y1,V)
| p(south,X1,south,Y1,take_goat(V)) ) )),
inference(bind,[status(th)],[]) ).
tff(42,plain,
( ! [X1: $i,Y1: $i,V: $i] :
( ~ p(north,X1,north,Y1,V)
| p(south,X1,south,Y1,take_goat(V)) )
<=> ! [X1: $i,Y1: $i,V: $i] :
( ~ p(north,X1,north,Y1,V)
| p(south,X1,south,Y1,take_goat(V)) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,plain,
( ! [X1: $i,Y1: $i,V: $i] :
( ~ p(north,X1,north,Y1,V)
| p(south,X1,south,Y1,take_goat(V)) )
<=> ! [X1: $i,Y1: $i,V: $i] :
( ~ p(north,X1,north,Y1,V)
| p(south,X1,south,Y1,take_goat(V)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,plain,
! [X1: $i,Y1: $i,V: $i] :
( ~ p(north,X1,north,Y1,V)
| p(south,X1,south,Y1,take_goat(V)) ),
inference(and_elim,[status(thm)],[7]) ).
tff(45,plain,
! [X1: $i,Y1: $i,V: $i] :
( ~ p(north,X1,north,Y1,V)
| p(south,X1,south,Y1,take_goat(V)) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [X1: $i,Y1: $i,V: $i] :
( ~ p(north,X1,north,Y1,V)
| p(south,X1,south,Y1,take_goat(V)) ),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [X1: $i,Y1: $i,V: $i] :
( ~ p(north,X1,north,Y1,V)
| p(south,X1,south,Y1,take_goat(V)) ),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,plain,
( ( ~ ! [X1: $i,Y1: $i,V: $i] :
( ~ p(north,X1,north,Y1,V)
| p(south,X1,south,Y1,take_goat(V)) )
| ~ 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))))) )
<=> ( ~ ! [X1: $i,Y1: $i,V: $i] :
( ~ p(north,X1,north,Y1,V)
| p(south,X1,south,Y1,take_goat(V)) )
| ~ 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(49,plain,
( ~ ! [X1: $i,Y1: $i,V: $i] :
( ~ p(north,X1,north,Y1,V)
| p(south,X1,south,Y1,take_goat(V)) )
| ~ 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(50,plain,
( ~ ! [X1: $i,Y1: $i,V: $i] :
( ~ p(north,X1,north,Y1,V)
| p(south,X1,south,Y1,take_goat(V)) )
| ~ 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)],[49,48]) ).
tff(51,plain,
p(south,south,south,north,take_goat(take_cabbage(go_alone(take_goat(start))))),
inference(unit_resolution,[status(thm)],[50,47,40]) ).
tff(52,plain,
^ [T4: $i] :
refl(( ( ~ p(south,south,south,north,T4)
| p(north,north,south,north,take_wolf(T4)) )
<=> ( ~ p(south,south,south,north,T4)
| p(north,north,south,north,take_wolf(T4)) ) )),
inference(bind,[status(th)],[]) ).
tff(53,plain,
( ! [T4: $i] :
( ~ p(south,south,south,north,T4)
| p(north,north,south,north,take_wolf(T4)) )
<=> ! [T4: $i] :
( ~ p(south,south,south,north,T4)
| p(north,north,south,north,take_wolf(T4)) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,plain,
( ! [T4: $i] :
( ~ p(south,south,south,north,T4)
| p(north,north,south,north,take_wolf(T4)) )
<=> ! [T4: $i] :
( ~ p(south,south,south,north,T4)
| p(north,north,south,north,take_wolf(T4)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,plain,
! [T4: $i] :
( ~ p(south,south,south,north,T4)
| p(north,north,south,north,take_wolf(T4)) ),
inference(and_elim,[status(thm)],[7]) ).
tff(56,plain,
! [T4: $i] :
( ~ p(south,south,south,north,T4)
| p(north,north,south,north,take_wolf(T4)) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
! [T4: $i] :
( ~ p(south,south,south,north,T4)
| p(north,north,south,north,take_wolf(T4)) ),
inference(skolemize,[status(sab)],[56]) ).
tff(58,plain,
! [T4: $i] :
( ~ p(south,south,south,north,T4)
| p(north,north,south,north,take_wolf(T4)) ),
inference(modus_ponens,[status(thm)],[57,53]) ).
tff(59,plain,
( ( ~ ! [T4: $i] :
( ~ p(south,south,south,north,T4)
| p(north,north,south,north,take_wolf(T4)) )
| ~ 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)))))) )
<=> ( ~ ! [T4: $i] :
( ~ p(south,south,south,north,T4)
| p(north,north,south,north,take_wolf(T4)) )
| ~ 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(60,plain,
( ~ ! [T4: $i] :
( ~ p(south,south,south,north,T4)
| p(north,north,south,north,take_wolf(T4)) )
| ~ 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(61,plain,
( ~ ! [T4: $i] :
( ~ p(south,south,south,north,T4)
| p(north,north,south,north,take_wolf(T4)) )
| ~ 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)],[60,59]) ).
tff(62,plain,
p(north,north,south,north,take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))),
inference(unit_resolution,[status(thm)],[61,58,51]) ).
tff(63,plain,
^ [T1: $i] :
refl(( ( ~ p(north,north,south,north,T1)
| p(south,north,south,north,go_alone(T1)) )
<=> ( ~ p(north,north,south,north,T1)
| p(south,north,south,north,go_alone(T1)) ) )),
inference(bind,[status(th)],[]) ).
tff(64,plain,
( ! [T1: $i] :
( ~ p(north,north,south,north,T1)
| p(south,north,south,north,go_alone(T1)) )
<=> ! [T1: $i] :
( ~ p(north,north,south,north,T1)
| p(south,north,south,north,go_alone(T1)) ) ),
inference(quant_intro,[status(thm)],[63]) ).
tff(65,plain,
( ! [T1: $i] :
( ~ p(north,north,south,north,T1)
| p(south,north,south,north,go_alone(T1)) )
<=> ! [T1: $i] :
( ~ p(north,north,south,north,T1)
| p(south,north,south,north,go_alone(T1)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,plain,
! [T1: $i] :
( ~ p(north,north,south,north,T1)
| p(south,north,south,north,go_alone(T1)) ),
inference(and_elim,[status(thm)],[7]) ).
tff(67,plain,
! [T1: $i] :
( ~ p(north,north,south,north,T1)
| p(south,north,south,north,go_alone(T1)) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
! [T1: $i] :
( ~ p(north,north,south,north,T1)
| p(south,north,south,north,go_alone(T1)) ),
inference(skolemize,[status(sab)],[67]) ).
tff(69,plain,
! [T1: $i] :
( ~ p(north,north,south,north,T1)
| p(south,north,south,north,go_alone(T1)) ),
inference(modus_ponens,[status(thm)],[68,64]) ).
tff(70,plain,
( ( ~ ! [T1: $i] :
( ~ p(north,north,south,north,T1)
| p(south,north,south,north,go_alone(T1)) )
| ~ 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))))))) )
<=> ( ~ ! [T1: $i] :
( ~ p(north,north,south,north,T1)
| p(south,north,south,north,go_alone(T1)) )
| ~ 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(71,plain,
( ~ ! [T1: $i] :
( ~ p(north,north,south,north,T1)
| p(south,north,south,north,go_alone(T1)) )
| ~ 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(72,plain,
( ~ ! [T1: $i] :
( ~ p(north,north,south,north,T1)
| p(south,north,south,north,go_alone(T1)) )
| ~ 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)],[71,70]) ).
tff(73,plain,
p(south,north,south,north,go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start))))))),
inference(unit_resolution,[status(thm)],[72,69,62]) ).
tff(74,plain,
( ( ~ ! [X: $i,Y: $i,U: $i] :
( ~ p(south,X,south,Y,U)
| p(north,X,north,Y,take_goat(U)) )
| ~ 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)))))))) )
<=> ( ~ ! [X: $i,Y: $i,U: $i] :
( ~ p(south,X,south,Y,U)
| p(north,X,north,Y,take_goat(U)) )
| ~ 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(75,plain,
( ~ ! [X: $i,Y: $i,U: $i] :
( ~ p(south,X,south,Y,U)
| p(north,X,north,Y,take_goat(U)) )
| ~ 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(76,plain,
( ~ ! [X: $i,Y: $i,U: $i] :
( ~ p(south,X,south,Y,U)
| p(north,X,north,Y,take_goat(U)) )
| ~ 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)],[75,74]) ).
tff(77,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)],[76,11,73]) ).
tff(78,plain,
^ [Z: $i] :
refl(( ~ p(north,north,north,north,Z)
<=> ~ p(north,north,north,north,Z) )),
inference(bind,[status(th)],[]) ).
tff(79,plain,
( ! [Z: $i] : ~ p(north,north,north,north,Z)
<=> ! [Z: $i] : ~ p(north,north,north,north,Z) ),
inference(quant_intro,[status(thm)],[78]) ).
tff(80,plain,
( ~ ? [Z: $i] : p(north,north,north,north,Z)
<=> ~ ? [Z: $i] : p(north,north,north,north,Z) ),
inference(rewrite,[status(thm)],[]) ).
tff(81,plain,
~ ? [Z: $i] : p(north,north,north,north,Z),
inference(or_elim,[status(thm)],[6]) ).
tff(82,plain,
~ ? [Z: $i] : p(north,north,north,north,Z),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
~ ? [Z: $i] : p(north,north,north,north,Z),
inference(modus_ponens,[status(thm)],[82,80]) ).
tff(84,plain,
~ ? [Z: $i] : p(north,north,north,north,Z),
inference(modus_ponens,[status(thm)],[83,80]) ).
tff(85,plain,
^ [Z: $i] : refl($oeq(~ p(north,north,north,north,Z),~ p(north,north,north,north,Z))),
inference(bind,[status(th)],[]) ).
tff(86,plain,
! [Z: $i] : ~ p(north,north,north,north,Z),
inference(nnf-neg,[status(sab)],[84,85]) ).
tff(87,plain,
! [Z: $i] : ~ p(north,north,north,north,Z),
inference(modus_ponens,[status(thm)],[86,79]) ).
tff(88,plain,
( ~ ! [Z: $i] : ~ p(north,north,north,north,Z)
| ~ 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(89,plain,
$false,
inference(unit_resolution,[status(thm)],[88,87,77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : PUZ047+1 : TPTP v9.0.0. Released v2.5.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n011.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 Jun 20 02:41:41 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.39 % SZS status Theorem
% 0.20/0.39 % SZS output start Proof
% See solution above
% 0.20/0.42 % E exiting
%------------------------------------------------------------------------------