%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COL058-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:00:40 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.39s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 32 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 44 ( 41 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 27 ( 17 ~; 4 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 8 ( 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 : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 34 ( 31 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
tff(response_type,type,
response: ( $i * $i ) > $i ).
tff(lark_type,type,
lark: $i ).
tff(1,plain,
^ [X2: $i,X1: $i] :
refl(( ( response(response(lark,X1),X2) = response(X1,response(X2,X2)) )
<=> ( response(response(lark,X1),X2) = response(X1,response(X2,X2)) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X2: $i,X1: $i] : ( response(response(lark,X1),X2) = response(X1,response(X2,X2)) )
<=> ! [X2: $i,X1: $i] : ( response(response(lark,X1),X2) = response(X1,response(X2,X2)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X2: $i,X1: $i] : ( response(response(lark,X1),X2) = response(X1,response(X2,X2)) )
<=> ! [X2: $i,X1: $i] : ( response(response(lark,X1),X2) = response(X1,response(X2,X2)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X2: $i,X1: $i] : ( response(response(lark,X1),X2) = response(X1,response(X2,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lark_exists) ).
tff(5,plain,
! [X2: $i,X1: $i] : ( response(response(lark,X1),X2) = response(X1,response(X2,X2)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X2: $i,X1: $i] : ( response(response(lark,X1),X2) = response(X1,response(X2,X2)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X2: $i,X1: $i] : ( response(response(lark,X1),X2) = response(X1,response(X2,X2)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X2: $i,X1: $i] : ( response(response(lark,X1),X2) = response(X1,response(X2,X2)) )
| ( response(response(lark,lark),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))) = response(lark,response(response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
response(response(lark,lark),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))) = response(lark,response(response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ~ ! [X2: $i,X1: $i] : ( response(response(lark,X1),X2) = response(X1,response(X2,X2)) )
| ( response(response(lark,response(lark,lark)),response(lark,response(lark,lark))) = response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(11,plain,
response(response(lark,response(lark,lark)),response(lark,response(lark,lark))) = response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),
inference(unit_resolution,[status(thm)],[10,7]) ).
tff(12,plain,
response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))) = response(response(lark,response(lark,lark)),response(lark,response(lark,lark))),
inference(symmetry,[status(thm)],[11]) ).
tff(13,plain,
response(response(lark,lark),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))) = response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))) = response(response(lark,lark),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))),
inference(symmetry,[status(thm)],[13]) ).
tff(15,plain,
response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))) = response(lark,response(response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))))),
inference(transitivity,[status(thm)],[14,9]) ).
tff(16,plain,
response(response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))) = response(response(lark,response(response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
response(response(lark,response(response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))) = response(response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))),
inference(symmetry,[status(thm)],[16]) ).
tff(18,plain,
( ~ ! [X2: $i,X1: $i] : ( response(response(lark,X1),X2) = response(X1,response(X2,X2)) )
| ( response(response(lark,response(response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))) = response(response(response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))),response(response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
response(response(lark,response(response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))) = response(response(response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))),response(response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))))),
inference(unit_resolution,[status(thm)],[18,7]) ).
tff(20,plain,
response(response(response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))),response(response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))))) = response(response(lark,response(response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))),
inference(symmetry,[status(thm)],[19]) ).
tff(21,plain,
response(response(response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))),response(response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))))) = response(response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))),
inference(transitivity,[status(thm)],[20,17]) ).
tff(22,plain,
response(response(response(response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))),response(response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))))),response(response(response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))),response(response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))))) = response(response(response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))),response(response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))))),
inference(monotonicity,[status(thm)],[21,21]) ).
tff(23,plain,
^ [X: $i] :
refl(( ( response(X,X) != X )
<=> ( response(X,X) != X ) )),
inference(bind,[status(th)],[]) ).
tff(24,plain,
( ! [X: $i] : ( response(X,X) != X )
<=> ! [X: $i] : ( response(X,X) != X ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,plain,
( ! [X: $i] : ( response(X,X) != X )
<=> ! [X: $i] : ( response(X,X) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,axiom,
! [X: $i] : ( response(X,X) != X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_the_bird_exists) ).
tff(27,plain,
! [X: $i] : ( response(X,X) != X ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [X: $i] : ( response(X,X) != X ),
inference(skolemize,[status(sab)],[27]) ).
tff(29,plain,
! [X: $i] : ( response(X,X) != X ),
inference(modus_ponens,[status(thm)],[28,24]) ).
tff(30,plain,
( ~ ! [X: $i] : ( response(X,X) != X )
| ( response(response(response(response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))),response(response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))))),response(response(response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))),response(response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))))) != response(response(response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))),response(response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(31,plain,
response(response(response(response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))),response(response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))))),response(response(response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))),response(response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))))) != response(response(response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))),response(response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))))),
inference(unit_resolution,[status(thm)],[30,29]) ).
tff(32,plain,
$false,
inference(unit_resolution,[status(thm)],[31,22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : COL058-1 : TPTP v9.0.0. Released v1.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n001.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 : Thu Jun 19 12:13:33 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.39 % SZS status Unsatisfiable
% 0.12/0.39 % SZS output start Proof
% See solution above
% 0.12/0.40 % E exiting
%------------------------------------------------------------------------------