TSTP Solution File: COL064-6 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : COL064-6 : TPTP v8.1.0. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 6 17:48:21 EDT 2022
% Result : Unsatisfiable 0.19s 0.54s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 24
% Syntax : Number of formulae : 53 ( 32 unt; 6 typ; 0 def)
% Number of atoms : 66 ( 63 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 31 ( 14 ~; 10 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 2 ( 1 >; 1 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 72 ( 67 !; 0 ?; 72 :)
% Comments :
%------------------------------------------------------------------------------
tff(apply_type,type,
apply: ( $i * $i ) > $i ).
tff(y_type,type,
y: $i ).
tff(x_type,type,
x: $i ).
tff(z_type,type,
z: $i ).
tff(t_type,type,
t: $i ).
tff(b_type,type,
b: $i ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(
( ( apply(apply(t,X),Y) = apply(Y,X) )
<=> ( apply(apply(t,X),Y) = apply(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [Y: $i,X: $i] : ( apply(apply(t,X),Y) = apply(Y,X) )
<=> ! [Y: $i,X: $i] : ( apply(apply(t,X),Y) = apply(Y,X) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Y: $i,X: $i] : ( apply(apply(t,X),Y) = apply(Y,X) )
<=> ! [Y: $i,X: $i] : ( apply(apply(t,X),Y) = apply(Y,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [Y: $i,X: $i] : ( apply(apply(t,X),Y) = apply(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t_definition) ).
tff(5,plain,
! [Y: $i,X: $i] : ( apply(apply(t,X),Y) = apply(Y,X) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : ( apply(apply(t,X),Y) = apply(Y,X) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : ( apply(apply(t,X),Y) = apply(Y,X) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : ( apply(apply(t,X),Y) = apply(Y,X) )
| ( apply(apply(t,y),apply(z,x)) = apply(apply(z,x),y) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
apply(apply(t,y),apply(z,x)) = apply(apply(z,x),y),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,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(11,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)],[10]) ).
tff(12,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(13,axiom,
! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_definition) ).
tff(14,plain,
! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) )
| ( apply(apply(apply(b,apply(t,y)),z),x) = apply(apply(t,y),apply(z,x)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
apply(apply(apply(b,apply(t,y)),z),x) = apply(apply(t,y),apply(z,x)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) )
| ( apply(apply(apply(b,b),t),y) = apply(b,apply(t,y)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(20,plain,
apply(apply(apply(b,b),t),y) = apply(b,apply(t,y)),
inference(unit_resolution,[status(thm)],[19,16]) ).
tff(21,plain,
apply(b,apply(t,y)) = apply(apply(apply(b,b),t),y),
inference(symmetry,[status(thm)],[20]) ).
tff(22,plain,
apply(apply(b,apply(t,y)),z) = apply(apply(apply(apply(b,b),t),y),z),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
apply(apply(apply(b,apply(t,y)),z),x) = apply(apply(apply(apply(apply(b,b),t),y),z),x),
inference(monotonicity,[status(thm)],[22]) ).
tff(24,plain,
apply(apply(apply(apply(apply(b,b),t),y),z),x) = apply(apply(apply(b,apply(t,y)),z),x),
inference(symmetry,[status(thm)],[23]) ).
tff(25,plain,
( ~ ! [Y: $i,X: $i] : ( apply(apply(t,X),Y) = apply(Y,X) )
| ( apply(apply(t,x),apply(apply(apply(apply(b,b),t),y),z)) = apply(apply(apply(apply(apply(b,b),t),y),z),x) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(26,plain,
apply(apply(t,x),apply(apply(apply(apply(b,b),t),y),z)) = apply(apply(apply(apply(apply(b,b),t),y),z),x),
inference(unit_resolution,[status(thm)],[25,7]) ).
tff(27,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) )
| ( apply(apply(apply(b,apply(t,x)),apply(apply(apply(b,b),t),y)),z) = apply(apply(t,x),apply(apply(apply(apply(b,b),t),y),z)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
apply(apply(apply(b,apply(t,x)),apply(apply(apply(b,b),t),y)),z) = apply(apply(t,x),apply(apply(apply(apply(b,b),t),y),z)),
inference(unit_resolution,[status(thm)],[27,16]) ).
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,apply(b,apply(t,x))),apply(apply(b,b),t)),y) = apply(apply(b,apply(t,x)),apply(apply(apply(b,b),t),y)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(30,plain,
apply(apply(apply(b,apply(b,apply(t,x))),apply(apply(b,b),t)),y) = apply(apply(b,apply(t,x)),apply(apply(apply(b,b),t),y)),
inference(unit_resolution,[status(thm)],[29,16]) ).
tff(31,plain,
( ~ ! [Y: $i,X: $i] : ( apply(apply(t,X),Y) = apply(Y,X) )
| ( apply(apply(t,apply(apply(b,b),t)),apply(b,apply(b,apply(t,x)))) = apply(apply(b,apply(b,apply(t,x))),apply(apply(b,b),t)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(32,plain,
apply(apply(t,apply(apply(b,b),t)),apply(b,apply(b,apply(t,x)))) = apply(apply(b,apply(b,apply(t,x))),apply(apply(b,b),t)),
inference(unit_resolution,[status(thm)],[31,7]) ).
tff(33,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) )
| ( apply(apply(apply(b,apply(t,apply(apply(b,b),t))),b),apply(b,apply(t,x))) = apply(apply(t,apply(apply(b,b),t)),apply(b,apply(b,apply(t,x)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(34,plain,
apply(apply(apply(b,apply(t,apply(apply(b,b),t))),b),apply(b,apply(t,x))) = apply(apply(t,apply(apply(b,b),t)),apply(b,apply(b,apply(t,x)))),
inference(unit_resolution,[status(thm)],[33,16]) ).
tff(35,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(t,apply(apply(b,b),t))),b)),b),apply(t,x)) = apply(apply(apply(b,apply(t,apply(apply(b,b),t))),b),apply(b,apply(t,x))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(36,plain,
apply(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),b),apply(t,x)) = apply(apply(apply(b,apply(t,apply(apply(b,b),t))),b),apply(b,apply(t,x))),
inference(unit_resolution,[status(thm)],[35,16]) ).
tff(37,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(apply(b,apply(t,apply(apply(b,b),t))),b)),b)),t),x) = apply(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),b),apply(t,x)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(38,plain,
apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),b)),t),x) = apply(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),b),apply(t,x)),
inference(unit_resolution,[status(thm)],[37,16]) ).
tff(39,plain,
apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),b)),t),x) = apply(apply(b,apply(b,apply(t,x))),apply(apply(b,b),t)),
inference(transitivity,[status(thm)],[38,36,34,32]) ).
tff(40,plain,
apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),b)),t),x),y) = apply(apply(apply(b,apply(b,apply(t,x))),apply(apply(b,b),t)),y),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),b)),t),x),y) = apply(apply(b,apply(t,x)),apply(apply(apply(b,b),t),y)),
inference(transitivity,[status(thm)],[40,30]) ).
tff(42,plain,
apply(apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),b)),t),x),y),z) = apply(apply(apply(b,apply(t,x)),apply(apply(apply(b,b),t),y)),z),
inference(monotonicity,[status(thm)],[41]) ).
tff(43,plain,
apply(apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),b)),t),x),y),z) = apply(apply(z,x),y),
inference(transitivity,[status(thm)],[42,28,26,24,18,9]) ).
tff(44,plain,
( ( apply(apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),b)),t),x),y),z) != apply(apply(z,x),y) )
<=> ( apply(apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),b)),t),x),y),z) != apply(apply(z,x),y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,axiom,
apply(apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),b)),t),x),y),z) != apply(apply(z,x),y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_v_combinator) ).
tff(46,plain,
apply(apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),b)),t),x),y),z) != apply(apply(z,x),y),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
$false,
inference(unit_resolution,[status(thm)],[46,43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : COL064-6 : TPTP v8.1.0. Bugfixed v1.2.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 30 11:12:48 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.54 % SZS status Unsatisfiable
% 0.19/0.54 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------