TSTP Solution File: COL003-8 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : COL003-8 : TPTP v8.1.0. Released v1.2.0.
% 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 : Tue Sep 6 17:47:59 EDT 2022
% Result : Unsatisfiable 0.65s 0.69s
% Output : Proof 0.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 28
% Syntax : Number of formulae : 69 ( 39 unt; 5 typ; 0 def)
% Number of atoms : 117 ( 85 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 90 ( 41 ~; 36 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 2 >; 1 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 86 ( 79 !; 0 ?; 86 :)
% Comments :
%------------------------------------------------------------------------------
tff(apply_type,type,
apply: ( $i * $i ) > $i ).
tff(fixed_pt_type,type,
fixed_pt: $i ).
tff(b_type,type,
b: $i ).
tff(w_type,type,
w: $i ).
tff(fixed_point_type,type,
fixed_point: $i > $o ).
tff(1,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) )
<=> ( apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_definition) ).
tff(5,plain,
! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) )
| ( apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(b,w))),apply(apply(b,b),b)),fixed_pt) = apply(apply(apply(b,apply(w,w)),apply(b,w)),apply(apply(apply(b,b),b),fixed_pt)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(b,w))),apply(apply(b,b),b)),fixed_pt) = apply(apply(apply(b,apply(w,w)),apply(b,w)),apply(apply(apply(b,b),b),fixed_pt)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
apply(apply(apply(b,apply(w,w)),apply(b,w)),apply(apply(apply(b,b),b),fixed_pt)) = apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(b,w))),apply(apply(b,b),b)),fixed_pt),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) )
| ( apply(apply(apply(b,apply(w,w)),apply(b,w)),apply(apply(apply(b,b),b),fixed_pt)) = apply(apply(w,w),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(12,plain,
apply(apply(apply(b,apply(w,w)),apply(b,w)),apply(apply(apply(b,b),b),fixed_pt)) = apply(apply(w,w),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))),
inference(unit_resolution,[status(thm)],[11,7]) ).
tff(13,plain,
apply(apply(w,w),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))) = apply(apply(apply(b,apply(w,w)),apply(b,w)),apply(apply(apply(b,b),b),fixed_pt)),
inference(symmetry,[status(thm)],[12]) ).
tff(14,plain,
^ [Y: $i,X: $i] :
refl(
( ( apply(apply(w,X),Y) = apply(apply(X,Y),Y) )
<=> ( apply(apply(w,X),Y) = apply(apply(X,Y),Y) ) )),
inference(bind,[status(th)],]) ).
tff(15,plain,
( ! [Y: $i,X: $i] : ( apply(apply(w,X),Y) = apply(apply(X,Y),Y) )
<=> ! [Y: $i,X: $i] : ( apply(apply(w,X),Y) = apply(apply(X,Y),Y) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,plain,
( ! [Y: $i,X: $i] : ( apply(apply(w,X),Y) = apply(apply(X,Y),Y) )
<=> ! [Y: $i,X: $i] : ( apply(apply(w,X),Y) = apply(apply(X,Y),Y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(17,axiom,
! [Y: $i,X: $i] : ( apply(apply(w,X),Y) = apply(apply(X,Y),Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',w_definition) ).
tff(18,plain,
! [Y: $i,X: $i] : ( apply(apply(w,X),Y) = apply(apply(X,Y),Y) ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
! [Y: $i,X: $i] : ( apply(apply(w,X),Y) = apply(apply(X,Y),Y) ),
inference(skolemize,[status(sab)],[18]) ).
tff(20,plain,
! [Y: $i,X: $i] : ( apply(apply(w,X),Y) = apply(apply(X,Y),Y) ),
inference(modus_ponens,[status(thm)],[19,15]) ).
tff(21,plain,
( ~ ! [Y: $i,X: $i] : ( apply(apply(w,X),Y) = apply(apply(X,Y),Y) )
| ( apply(apply(w,w),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))) = apply(apply(w,apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(22,plain,
apply(apply(w,w),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))) = apply(apply(w,apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))),
inference(unit_resolution,[status(thm)],[21,20]) ).
tff(23,plain,
apply(apply(w,apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))) = apply(apply(w,w),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))),
inference(symmetry,[status(thm)],[22]) ).
tff(24,plain,
( ~ ! [Y: $i,X: $i] : ( apply(apply(w,X),Y) = apply(apply(X,Y),Y) )
| ( apply(apply(w,apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))) = apply(apply(apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt)),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(25,plain,
apply(apply(w,apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))) = apply(apply(apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt)),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))),
inference(unit_resolution,[status(thm)],[24,20]) ).
tff(26,plain,
apply(apply(apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt)),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))) = apply(apply(w,apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))),
inference(symmetry,[status(thm)],[25]) ).
tff(27,plain,
apply(apply(apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt)),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))) = apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(b,w))),apply(apply(b,b),b)),fixed_pt),
inference(transitivity,[status(thm)],[26,23,13,10]) ).
tff(28,plain,
apply(fixed_pt,apply(apply(apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt)),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt)))) = apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(b,w))),apply(apply(b,b),b)),fixed_pt)),
inference(monotonicity,[status(thm)],[27]) ).
tff(29,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) )
| ( apply(apply(apply(b,fixed_pt),apply(apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt)),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt)))),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))) = apply(fixed_pt,apply(apply(apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt)),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(30,plain,
apply(apply(apply(b,fixed_pt),apply(apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt)),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt)))),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))) = apply(fixed_pt,apply(apply(apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt)),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt)))),
inference(unit_resolution,[status(thm)],[29,7]) ).
tff(31,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) )
| ( apply(apply(apply(b,apply(b,fixed_pt)),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))) = apply(apply(b,fixed_pt),apply(apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt)),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(32,plain,
apply(apply(apply(b,apply(b,fixed_pt)),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))) = apply(apply(b,fixed_pt),apply(apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt)),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt)))),
inference(unit_resolution,[status(thm)],[31,7]) ).
tff(33,plain,
apply(apply(apply(apply(b,apply(b,fixed_pt)),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))) = apply(apply(apply(b,fixed_pt),apply(apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt)),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt)))),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
( ~ ! [Y: $i,X: $i] : ( apply(apply(w,X),Y) = apply(apply(X,Y),Y) )
| ( apply(apply(w,apply(apply(b,apply(b,fixed_pt)),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt)))),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))) = apply(apply(apply(apply(b,apply(b,fixed_pt)),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(35,plain,
apply(apply(w,apply(apply(b,apply(b,fixed_pt)),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt)))),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))) = apply(apply(apply(apply(b,apply(b,fixed_pt)),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))),
inference(unit_resolution,[status(thm)],[34,20]) ).
tff(36,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) )
| ( apply(apply(apply(b,w),apply(b,apply(b,fixed_pt))),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))) = apply(w,apply(apply(b,apply(b,fixed_pt)),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(37,plain,
apply(apply(apply(b,w),apply(b,apply(b,fixed_pt))),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))) = apply(w,apply(apply(b,apply(b,fixed_pt)),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt)))),
inference(unit_resolution,[status(thm)],[36,7]) ).
tff(38,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) )
| ( apply(apply(apply(b,b),b),fixed_pt) = apply(b,apply(b,fixed_pt)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(39,plain,
apply(apply(apply(b,b),b),fixed_pt) = apply(b,apply(b,fixed_pt)),
inference(unit_resolution,[status(thm)],[38,7]) ).
tff(40,plain,
apply(b,apply(b,fixed_pt)) = apply(apply(apply(b,b),b),fixed_pt),
inference(symmetry,[status(thm)],[39]) ).
tff(41,plain,
apply(apply(b,w),apply(b,apply(b,fixed_pt))) = apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt)),
inference(monotonicity,[status(thm)],[40]) ).
tff(42,plain,
apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt)) = apply(apply(b,w),apply(b,apply(b,fixed_pt))),
inference(symmetry,[status(thm)],[41]) ).
tff(43,plain,
apply(apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt)),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))) = apply(apply(apply(b,w),apply(b,apply(b,fixed_pt))),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))),
inference(monotonicity,[status(thm)],[42]) ).
tff(44,plain,
apply(apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt)),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))) = apply(w,apply(apply(b,apply(b,fixed_pt)),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt)))),
inference(transitivity,[status(thm)],[43,37]) ).
tff(45,plain,
apply(apply(apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt)),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))) = apply(apply(w,apply(apply(b,apply(b,fixed_pt)),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt)))),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt))),
inference(monotonicity,[status(thm)],[44]) ).
tff(46,plain,
apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(b,w))),apply(apply(b,b),b)),fixed_pt) = apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(b,w))),apply(apply(b,b),b)),fixed_pt)),
inference(transitivity,[status(thm)],[9,12,22,25,45,35,33,30,28]) ).
tff(47,plain,
( ~ fixed_point(apply(apply(b,apply(apply(b,apply(w,w)),apply(b,w))),apply(apply(b,b),b)))
<=> ~ fixed_point(apply(apply(b,apply(apply(b,apply(w,w)),apply(b,w))),apply(apply(b,b),b))) ),
inference(rewrite,[status(thm)],]) ).
tff(48,axiom,
~ fixed_point(apply(apply(b,apply(apply(b,apply(w,w)),apply(b,w))),apply(apply(b,b),b))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_strong_fixed_point) ).
tff(49,plain,
~ fixed_point(apply(apply(b,apply(apply(b,apply(w,w)),apply(b,w))),apply(apply(b,b),b))),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
^ [Strong_fixed_point: $i] :
refl(
( ( fixed_point(Strong_fixed_point)
| ( apply(Strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(Strong_fixed_point,fixed_pt)) ) )
<=> ( fixed_point(Strong_fixed_point)
| ( apply(Strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(Strong_fixed_point,fixed_pt)) ) ) )),
inference(bind,[status(th)],]) ).
tff(51,plain,
( ! [Strong_fixed_point: $i] :
( fixed_point(Strong_fixed_point)
| ( apply(Strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(Strong_fixed_point,fixed_pt)) ) )
<=> ! [Strong_fixed_point: $i] :
( fixed_point(Strong_fixed_point)
| ( apply(Strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(Strong_fixed_point,fixed_pt)) ) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,plain,
( ! [Strong_fixed_point: $i] :
( fixed_point(Strong_fixed_point)
| ( apply(Strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(Strong_fixed_point,fixed_pt)) ) )
<=> ! [Strong_fixed_point: $i] :
( fixed_point(Strong_fixed_point)
| ( apply(Strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(Strong_fixed_point,fixed_pt)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,plain,
^ [Strong_fixed_point: $i] :
rewrite(
( ( ( apply(Strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(Strong_fixed_point,fixed_pt)) )
| fixed_point(Strong_fixed_point) )
<=> ( fixed_point(Strong_fixed_point)
| ( apply(Strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(Strong_fixed_point,fixed_pt)) ) ) )),
inference(bind,[status(th)],]) ).
tff(54,plain,
( ! [Strong_fixed_point: $i] :
( ( apply(Strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(Strong_fixed_point,fixed_pt)) )
| fixed_point(Strong_fixed_point) )
<=> ! [Strong_fixed_point: $i] :
( fixed_point(Strong_fixed_point)
| ( apply(Strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(Strong_fixed_point,fixed_pt)) ) ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,axiom,
! [Strong_fixed_point: $i] :
( ( apply(Strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(Strong_fixed_point,fixed_pt)) )
| fixed_point(Strong_fixed_point) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',strong_fixed_point) ).
tff(56,plain,
! [Strong_fixed_point: $i] :
( fixed_point(Strong_fixed_point)
| ( apply(Strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(Strong_fixed_point,fixed_pt)) ) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
! [Strong_fixed_point: $i] :
( fixed_point(Strong_fixed_point)
| ( apply(Strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(Strong_fixed_point,fixed_pt)) ) ),
inference(modus_ponens,[status(thm)],[56,52]) ).
tff(58,plain,
! [Strong_fixed_point: $i] :
( fixed_point(Strong_fixed_point)
| ( apply(Strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(Strong_fixed_point,fixed_pt)) ) ),
inference(skolemize,[status(sab)],[57]) ).
tff(59,plain,
! [Strong_fixed_point: $i] :
( fixed_point(Strong_fixed_point)
| ( apply(Strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(Strong_fixed_point,fixed_pt)) ) ),
inference(modus_ponens,[status(thm)],[58,51]) ).
tff(60,plain,
( ( ~ ! [Strong_fixed_point: $i] :
( fixed_point(Strong_fixed_point)
| ( apply(Strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(Strong_fixed_point,fixed_pt)) ) )
| fixed_point(apply(apply(b,apply(apply(b,apply(w,w)),apply(b,w))),apply(apply(b,b),b)))
| ( apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(b,w))),apply(apply(b,b),b)),fixed_pt) != apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(b,w))),apply(apply(b,b),b)),fixed_pt)) ) )
<=> ( ~ ! [Strong_fixed_point: $i] :
( fixed_point(Strong_fixed_point)
| ( apply(Strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(Strong_fixed_point,fixed_pt)) ) )
| fixed_point(apply(apply(b,apply(apply(b,apply(w,w)),apply(b,w))),apply(apply(b,b),b)))
| ( apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(b,w))),apply(apply(b,b),b)),fixed_pt) != apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(b,w))),apply(apply(b,b),b)),fixed_pt)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(61,plain,
( ~ ! [Strong_fixed_point: $i] :
( fixed_point(Strong_fixed_point)
| ( apply(Strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(Strong_fixed_point,fixed_pt)) ) )
| fixed_point(apply(apply(b,apply(apply(b,apply(w,w)),apply(b,w))),apply(apply(b,b),b)))
| ( apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(b,w))),apply(apply(b,b),b)),fixed_pt) != apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(b,w))),apply(apply(b,b),b)),fixed_pt)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(62,plain,
( ~ ! [Strong_fixed_point: $i] :
( fixed_point(Strong_fixed_point)
| ( apply(Strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(Strong_fixed_point,fixed_pt)) ) )
| fixed_point(apply(apply(b,apply(apply(b,apply(w,w)),apply(b,w))),apply(apply(b,b),b)))
| ( apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(b,w))),apply(apply(b,b),b)),fixed_pt) != apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(b,w))),apply(apply(b,b),b)),fixed_pt)) ) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(b,w))),apply(apply(b,b),b)),fixed_pt) != apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(b,w))),apply(apply(b,b),b)),fixed_pt)),
inference(unit_resolution,[status(thm)],[62,59,49]) ).
tff(64,plain,
$false,
inference(unit_resolution,[status(thm)],[63,46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : COL003-8 : TPTP v8.1.0. Released v1.2.0.
% 0.08/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n007.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 : Tue Aug 30 08:44:00 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.65/0.69 % SZS status Unsatisfiable
% 0.65/0.69 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------