%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL058-3 : 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 : n019.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 06:57:33 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.38s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 16 ( 16 unt; 0 def)
% Number of atoms : 16 ( 15 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 10 ( 10 ~; 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 : 10 ( 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(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))),
file('theBenchmark.p',prove_the_bird_exists) ).
cnf(c_2,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(clausify,[status(thm)],[prove_the_bird_exists]) ).
cnf(c_3,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_13,plain,
response(response(lark,A),response(B,B)) = response(A,response(response(response(lark,lark),B),B)),
inference(paramod,[status(thm)],[c_3,c_1]) ).
cnf(c_7,plain,
response(A,response(response(response(lark,lark),B),B)) = response(response(lark,A),response(B,B)),
inference(copy,[status(thm)],[c_13]) ).
cnf(c_14,plain,
response(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)))) != response(response(response(lark,lark),response(lark,response(lark,lark))),response(lark,response(lark,lark))),
inference(paramod,[status(thm)],[c_3,c_2]) ).
cnf(c_15,plain,
response(response(response(lark,response(response(lark,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_14]) ).
cnf(c_16,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_15]) ).
cnf(c_17,plain,
response(response(lark,response(response(response(lark,lark),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_7,c_16]) ).
cnf(c_18,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_7,c_17]) ).
cnf(c_19,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_18]) ).
cnf(c_20,plain,
response(response(lark,response(response(lark,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_19]) ).
cnf(c_21,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_1,c_20]) ).
cnf(c_12,plain,
$false,
inference(copy,[status(thm)],[c_21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL058-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n019.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 23:09:33 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 2455193 was started by sandbox on n019,
% 0.10/0.36 % Sat Sep 26 23:09:33 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.10/0.38
% 0.10/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.38
% 0.10/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/0.38 % Length of proof is 5.
% 0.10/0.38 % Level of proof is 3.
% 0.10/0.38 % Maximum clause weight is 177.000.
% 0.10/0.38 % Given clauses 3.
% 0.10/0.38
% 0.10/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------