%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL058-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 : Sun Sep 27 06:57:32 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 20 ( 20 unt; 0 def)
% Number of atoms : 20 ( 19 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn 2 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(lark_exists,axiom,
! [VAR_0,VAR_1] : response(response(lark,VAR_0),VAR_1) = response(VAR_0,response(VAR_1,VAR_1)),
file('theBenchmark.p',lark_exists) ).
cnf(c_1,plain,
response(response(lark,A),B) = response(A,response(B,B)),
inference(clausify,[status(thm)],[lark_exists]) ).
fof(prove_the_bird_exists,axiom,
response(response(response(lark,response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(lark,response(lark,lark))),response(response(lark,response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(lark,response(lark,lark)))) != response(response(lark,response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(lark,response(lark,lark))),
file('theBenchmark.p',prove_the_bird_exists) ).
cnf(c_2,plain,
response(response(response(lark,response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(lark,response(lark,lark))),response(response(lark,response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(lark,response(lark,lark)))) != response(response(lark,response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(lark,response(lark,lark))),
inference(clausify,[status(thm)],[prove_the_bird_exists]) ).
cnf(c_89,plain,
response(response(response(response(lark,lark),response(lark,response(lark,lark))),response(lark,response(lark,lark))),response(response(lark,response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(lark,response(lark,lark)))) != response(response(lark,response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(lark,response(lark,lark))),
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_90,plain,
response(response(response(response(lark,lark),response(lark,response(lark,lark))),response(lark,response(lark,lark))),response(response(response(lark,lark),response(lark,response(lark,lark))),response(lark,response(lark,lark)))) != response(response(lark,response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(lark,response(lark,lark))),
inference(paramod,[status(thm)],[c_1,c_89]) ).
cnf(c_3,plain,
response(response(response(response(lark,lark),response(lark,response(lark,lark))),response(lark,response(lark,lark))),response(response(response(lark,lark),response(lark,response(lark,lark))),response(lark,response(lark,lark)))) != response(response(response(lark,lark),response(lark,response(lark,lark))),response(lark,response(lark,lark))),
inference(paramod,[status(thm)],[c_1,c_90]) ).
cnf(c_4,plain,
response(response(lark,response(lark,A)),B) = response(A,response(response(B,B),response(B,B))),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_5,plain,
response(response(response(lark,lark),A),B) = response(response(A,A),response(B,B)),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_12,plain,
response(response(lark,A),response(B,B)) = response(A,response(response(response(lark,lark),B),B)),
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_91,plain,
response(response(response(lark,lark),response(lark,response(lark,A))),B) = response(response(A,response(response(response(lark,response(lark,A)),response(lark,response(lark,A))),response(response(lark,response(lark,A)),response(lark,response(lark,A))))),response(B,B)),
inference(paramod,[status(thm)],[c_4,c_5]) ).
cnf(c_92,plain,
response(response(response(lark,lark),response(lark,response(lark,A))),B) = response(response(response(lark,A),response(response(lark,response(lark,A)),response(lark,response(lark,A)))),response(B,B)),
inference(paramod,[status(thm)],[c_1,c_91]) ).
cnf(c_93,plain,
response(response(response(lark,lark),response(lark,response(lark,A))),B) = response(response(response(lark,response(lark,A)),response(lark,response(lark,A))),response(B,B)),
inference(paramod,[status(thm)],[c_1,c_92]) ).
cnf(c_24,plain,
response(response(response(lark,response(lark,A)),response(lark,response(lark,A))),response(B,B)) = response(response(response(lark,lark),response(lark,response(lark,A))),B),
inference(copy,[status(thm)],[c_93]) ).
cnf(c_94,plain,
response(response(response(lark,lark),response(A,A)),response(B,B)) = response(response(response(response(lark,lark),A),A),response(response(response(lark,lark),B),B)),
inference(paramod,[status(thm)],[c_12,c_12]) ).
cnf(c_81,plain,
response(response(response(response(lark,lark),A),A),response(response(response(lark,lark),B),B)) = response(response(response(lark,lark),response(A,A)),response(B,B)),
inference(copy,[status(thm)],[c_94]) ).
cnf(c_95,plain,
response(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)))) != response(response(response(lark,lark),response(lark,response(lark,lark))),response(lark,response(lark,lark))),
inference(paramod,[status(thm)],[c_81,c_3]) ).
cnf(c_96,plain,
response(response(response(lark,response(lark,lark)),response(lark,response(lark,lark))),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))) != response(response(response(lark,lark),response(lark,response(lark,lark))),response(lark,response(lark,lark))),
inference(paramod,[status(thm)],[c_1,c_95]) ).
cnf(c_97,plain,
response(response(response(lark,lark),response(lark,response(lark,lark))),response(lark,response(lark,lark))) != response(response(response(lark,lark),response(lark,response(lark,lark))),response(lark,response(lark,lark))),
inference(paramod,[status(thm)],[c_24,c_96]) ).
cnf(c_88,plain,
$false,
inference(copy,[status(thm)],[c_97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL058-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n015.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 23:12:45 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 1026434 was started by sandbox on n015,
% 0.10/0.38 % Sat Sep 26 23:12:45 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.10/0.39
% 0.10/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.39
% 0.10/0.39 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.10/0.39 % Length of proof is 9.
% 0.10/0.39 % Level of proof is 4.
% 0.10/0.39 % Maximum clause weight is 47.000.
% 0.10/0.39 % Given clauses 6.
% 0.10/0.39
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------