%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : COL054-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:01:53 PM UTC 2026
% Result : Unsatisfiable 9.58s 2.04s
% Output : Proof 9.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 33 ( 29 unt; 0 def)
% Number of atoms : 37 ( 36 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 10 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-4 aty)
% Number of variables : 56 ( 2 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f2,negated_conjecture,
( response(b,Y) != X
| response(a,X) != Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_birds_are_compatible) ).
fof(f2_nnf,plain,
! [X,Y] :
( response(b,Y) != X
| response(a,X) != Y ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y] :
( response(b,Y) != X
| response(a,X) != Y ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( response(b,X1) != X0
| response(a,X0) != X1 ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t3,plain,
ifeq(response(a,X1),X2,ifeq(response(b,X2),X1,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t8,plain,
ifeq(response(a,X1),X2,ifeq(response(b,X2),X1,false,true),true) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(t0,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t4,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t0]) ).
cnf(t11,plain,
true = ifeq(response(a,response(b,X1)),X1,false,true),
inference(cp,[status(thm)],[t8,t4]) ).
cnf(t22,plain,
ifeq(response(a,response(b,X1)),X1,false,true) = true,
inference(orient,[status(thm)],[t11]) ).
cnf(f1,hypothesis,
response(compose(X,Y),W) = response(X,response(Y,W)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composer_exists) ).
fof(f1_nnf,plain,
! [X,Y,W] : response(compose(X,Y),W) = response(X,response(Y,W)),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y,W] : response(compose(X,Y),W) = response(X,response(Y,W)),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
response(compose(X0,X1),X2) = response(X0,response(X1,X2)),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t2,plain,
response(compose(X1,X2),X3) = response(X1,response(X2,X3)),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t6,plain,
response(compose(X1,X2),X3) = response(X1,response(X2,X3)),
inference(orient,[status(thm)],[t2]) ).
cnf(f0,axiom,
response(mocking_bird,Y) = response(Y,Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mocking_bird_exists) ).
fof(f0_nnf,plain,
! [Y] : response(mocking_bird,Y) = response(Y,Y),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [Y] : response(mocking_bird,Y) = response(Y,Y),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
response(mocking_bird,X0) = response(X0,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t1,plain,
response(mocking_bird,X1) = response(X1,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t5,plain,
response(X1,X1) = response(mocking_bird,X1),
inference(orient,[status(thm)],[t1]) ).
cnf(t7,plain,
response(X1,response(X2,compose(X1,X2))) = response(mocking_bird,compose(X1,X2)),
inference(cp,[status(thm)],[t6,t5]) ).
cnf(t13,plain,
response(X1,response(X2,compose(X1,X2))) = response(mocking_bird,compose(X1,X2)),
inference(orient,[status(thm)],[t7]) ).
cnf(t14,plain,
response(mocking_bird,compose(compose(X1,X2),X3)) = response(X1,response(X2,response(X3,compose(compose(X1,X2),X3)))),
inference(cp,[status(thm)],[t13,t6]) ).
cnf(t39,plain,
response(X1,response(X2,response(X3,compose(compose(X1,X2),X3)))) = response(mocking_bird,compose(compose(X1,X2),X3)),
inference(orient,[status(thm)],[t14]) ).
cnf(t47,plain,
true = ifeq(response(mocking_bird,compose(compose(a,b),X1)),response(X1,compose(compose(a,b),X1)),false,true),
inference(cp,[status(thm)],[t22,t39]) ).
cnf(t67,plain,
ifeq(response(mocking_bird,compose(compose(a,b),X1)),response(X1,compose(compose(a,b),X1)),false,true) = true,
inference(orient,[status(thm)],[t47]) ).
cnf(t68,plain,
true = false,
inference(cp,[status(thm)],[t67,t4]) ).
cnf(t70,plain,
false = true,
inference(orient,[status(thm)],[t68]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t70]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL054-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n001.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 07:27:24 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 9.58/2.04 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.58/2.04 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------