%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COL053-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:00:39 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 23 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 34 ( 31 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 25 ( 16 ~; 3 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 43 ( 39 !; 0 ?; 43 :)
% Comments :
%------------------------------------------------------------------------------
tff(response_type,type,
response: ( $i * $i ) > $i ).
tff(f_type,type,
f: $i > $i ).
tff(compose_type,type,
compose: ( $i * $i ) > $i ).
tff(c_type,type,
c: $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(1,plain,
^ [W: $i,Y: $i,X: $i] :
refl(( ( response(compose(X,Y),W) = response(X,response(Y,W)) )
<=> ( response(compose(X,Y),W) = response(X,response(Y,W)) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [W: $i,Y: $i,X: $i] : ( response(compose(X,Y),W) = response(X,response(Y,W)) )
<=> ! [W: $i,Y: $i,X: $i] : ( response(compose(X,Y),W) = response(X,response(Y,W)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [W: $i,Y: $i,X: $i] : ( response(compose(X,Y),W) = response(X,response(Y,W)) )
<=> ! [W: $i,Y: $i,X: $i] : ( response(compose(X,Y),W) = response(X,response(Y,W)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [W: $i,Y: $i,X: $i] : ( response(compose(X,Y),W) = response(X,response(Y,W)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composer_exists) ).
tff(5,plain,
! [W: $i,Y: $i,X: $i] : ( response(compose(X,Y),W) = response(X,response(Y,W)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [W: $i,Y: $i,X: $i] : ( response(compose(X,Y),W) = response(X,response(Y,W)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [W: $i,Y: $i,X: $i] : ( response(compose(X,Y),W) = response(X,response(Y,W)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [W: $i,Y: $i,X: $i] : ( response(compose(X,Y),W) = response(X,response(Y,W)) )
| ( response(compose(b,c),f(compose(a,compose(b,c)))) = response(b,response(c,f(compose(a,compose(b,c))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
response(compose(b,c),f(compose(a,compose(b,c)))) = response(b,response(c,f(compose(a,compose(b,c))))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
response(a,response(compose(b,c),f(compose(a,compose(b,c))))) = response(a,response(b,response(c,f(compose(a,compose(b,c)))))),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,plain,
( ~ ! [W: $i,Y: $i,X: $i] : ( response(compose(X,Y),W) = response(X,response(Y,W)) )
| ( response(compose(a,compose(b,c)),f(compose(a,compose(b,c)))) = response(a,response(compose(b,c),f(compose(a,compose(b,c))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(12,plain,
response(compose(a,compose(b,c)),f(compose(a,compose(b,c)))) = response(a,response(compose(b,c),f(compose(a,compose(b,c))))),
inference(unit_resolution,[status(thm)],[11,7]) ).
tff(13,plain,
response(compose(a,compose(b,c)),f(compose(a,compose(b,c)))) = response(a,response(b,response(c,f(compose(a,compose(b,c)))))),
inference(transitivity,[status(thm)],[12,10]) ).
tff(14,plain,
^ [U: $i] :
refl(( ( response(U,f(U)) != response(a,response(b,response(c,f(U)))) )
<=> ( response(U,f(U)) != response(a,response(b,response(c,f(U)))) ) )),
inference(bind,[status(th)],[]) ).
tff(15,plain,
( ! [U: $i] : ( response(U,f(U)) != response(a,response(b,response(c,f(U)))) )
<=> ! [U: $i] : ( response(U,f(U)) != response(a,response(b,response(c,f(U)))) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,plain,
( ! [U: $i] : ( response(U,f(U)) != response(a,response(b,response(c,f(U)))) )
<=> ! [U: $i] : ( response(U,f(U)) != response(a,response(b,response(c,f(U)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,axiom,
! [U: $i] : ( response(U,f(U)) != response(a,response(b,response(c,f(U)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_bird_exists) ).
tff(18,plain,
! [U: $i] : ( response(U,f(U)) != response(a,response(b,response(c,f(U)))) ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
! [U: $i] : ( response(U,f(U)) != response(a,response(b,response(c,f(U)))) ),
inference(skolemize,[status(sab)],[18]) ).
tff(20,plain,
! [U: $i] : ( response(U,f(U)) != response(a,response(b,response(c,f(U)))) ),
inference(modus_ponens,[status(thm)],[19,15]) ).
tff(21,plain,
( ~ ! [U: $i] : ( response(U,f(U)) != response(a,response(b,response(c,f(U)))) )
| ( response(compose(a,compose(b,c)),f(compose(a,compose(b,c)))) != response(a,response(b,response(c,f(compose(a,compose(b,c)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
response(compose(a,compose(b,c)),f(compose(a,compose(b,c)))) != response(a,response(b,response(c,f(compose(a,compose(b,c)))))),
inference(unit_resolution,[status(thm)],[21,20]) ).
tff(23,plain,
$false,
inference(unit_resolution,[status(thm)],[22,13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : COL053-1 : TPTP v9.0.0. Released v1.0.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.14/0.34 % Computer : n012.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 : Thu Jun 19 12:08:41 EDT 2025
% 0.14/0.34 % CPUTime :
% 0.21/0.39 % SZS status Unsatisfiable
% 0.21/0.39 % SZS output start Proof
% See solution above
% 0.21/0.39 % E exiting
%------------------------------------------------------------------------------