%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL056-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 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 : Sun Sep 27 06:57:32 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.40s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 11 unt; 0 def)
% Number of atoms : 11 ( 10 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 14 ( 4 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(composer_exists,axiom,
! [VAR_0,VAR_1,VAR_2] : response(compose(VAR_0,VAR_1),VAR_2) = response(VAR_0,response(VAR_1,VAR_2)),
file('theBenchmark.p',composer_exists) ).
cnf(c_1,plain,
response(compose(A,B),C) = response(A,response(B,C)),
inference(clausify,[status(thm)],[composer_exists]) ).
fof(a_to_b_responds_c,axiom,
response(a,b) = c,
file('theBenchmark.p',a_to_b_responds_c) ).
cnf(c_2,plain,
response(a,b) = c,
inference(clausify,[status(thm)],[a_to_b_responds_c]) ).
fof(a_to_c_responds_b,axiom,
response(a,c) = b,
file('theBenchmark.p',a_to_c_responds_b) ).
cnf(c_3,plain,
response(a,c) = b,
inference(clausify,[status(thm)],[a_to_c_responds_b]) ).
fof(prove_there_exists_a_happy_bird,axiom,
! [VAR_0,VAR_1] : response(VAR_0,VAR_1) != VAR_1,
file('theBenchmark.p',prove_there_exists_a_happy_bird) ).
cnf(c_4,plain,
response(A,B) != B,
inference(clausify,[status(thm)],[prove_there_exists_a_happy_bird]) ).
cnf(c_5,plain,
response(A,response(B,C)) != C,
inference(paramod,[status(thm)],[c_1,c_4]) ).
cnf(c_8,plain,
response(A,c) != b,
inference(paramod,[status(thm)],[c_2,c_5]) ).
cnf(c_9,plain,
$false,
inference(resolve,[status(thm)],[c_8,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL056-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n001.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sat Sep 26 23:15:15 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.37 % Process 2907024 was started by sandbox2 on n001,
% 0.12/0.37 % Sat Sep 26 23:15:15 2026
% 0.12/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.38
% 0.12/0.38 % From the command line: assign(max_seconds, 300).
% 0.12/0.40
% 0.12/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.40
% 0.12/0.40 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.12/0.40 % Length of proof is 7.
% 0.12/0.40 % Level of proof is 3.
% 0.12/0.40 % Maximum clause weight is 11.000.
% 0.12/0.40 % Given clauses 5.
% 0.12/0.40
% 0.12/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------