%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COM004-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 06:59:37 AM UTC 2026
% Result : Unsatisfiable 0.16s 5.45s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 27 ( 18 unt; 0 def)
% Number of atoms : 49 ( 6 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 46 ( 24 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 40 ( 1 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(make_node,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( ~ siblings(VAR_0,VAR_1)
| ~ contradictory(VAR_4,VAR_5)
| ~ failure_node(VAR_1,or(VAR_3,VAR_5))
| ~ failure_node(VAR_0,or(VAR_2,VAR_4))
| failure_node(parent_of(VAR_0,VAR_1),or(VAR_2,VAR_3)) ),
file('theBenchmark.p',make_node) ).
cnf(c_2,plain,
( ~ siblings(A,B)
| ~ contradictory(E,F)
| ~ failure_node(B,or(D,F))
| ~ failure_node(A,or(C,E))
| failure_node(parent_of(A,B),or(C,D)) ),
inference(clausify,[status(thm)],[make_node]) ).
fof(x_contradicts_not_x,axiom,
! [VAR_0] : contradictory(VAR_0,negate(VAR_0)),
file('theBenchmark.p',x_contradicts_not_x) ).
cnf(c_3,plain,
contradictory(A,negate(A)),
inference(clausify,[status(thm)],[x_contradicts_not_x]) ).
fof(n_left_and_n_right_are_siblings,axiom,
! [VAR_0] : siblings(left_child_of(VAR_0),right_child_of(VAR_0)),
file('theBenchmark.p',n_left_and_n_right_are_siblings) ).
cnf(c_4,plain,
siblings(left_child_of(A),right_child_of(A)),
inference(clausify,[status(thm)],[n_left_and_n_right_are_siblings]) ).
cnf(c_6,plain,
( ~ siblings(A,B)
| ~ failure_node(B,or(D,negate(E)))
| ~ failure_node(A,or(C,E))
| failure_node(parent_of(A,B),or(C,D)) ),
inference(resolve,[status(thm)],[c_3,c_2]) ).
cnf(c_7,plain,
( ~ failure_node(right_child_of(A),or(C,negate(D)))
| ~ failure_node(left_child_of(A),or(B,D))
| failure_node(parent_of(left_child_of(A),right_child_of(A)),or(B,C)) ),
inference(resolve,[status(thm)],[c_4,c_6]) ).
fof(n_left_is_atom,axiom,
failure_node(n_left,or(empty,atom)),
file('theBenchmark.p',n_left_is_atom) ).
cnf(c_9,plain,
failure_node(n_left,or(empty,atom)),
inference(clausify,[status(thm)],[n_left_is_atom]) ).
fof(n_right_is_not_atom,axiom,
failure_node(n_right,or(empty,negate(atom))),
file('theBenchmark.p',n_right_is_not_atom) ).
cnf(c_10,plain,
failure_node(n_right,or(empty,negate(atom))),
inference(clausify,[status(thm)],[n_right_is_not_atom]) ).
fof(n_left_equals_left_child_of_n,axiom,
n_left = left_child_of(n),
file('theBenchmark.p',n_left_equals_left_child_of_n) ).
cnf(c_11,plain,
n_left = left_child_of(n),
inference(clausify,[status(thm)],[n_left_equals_left_child_of_n]) ).
cnf(c_12,plain,
left_child_of(n) = n_left,
inference(copy,[status(thm)],[c_11]) ).
fof(n_right_equals_right_child_of_n,axiom,
n_right = right_child_of(n),
file('theBenchmark.p',n_right_equals_right_child_of_n) ).
cnf(c_13,plain,
n_right = right_child_of(n),
inference(clausify,[status(thm)],[n_right_equals_right_child_of_n]) ).
cnf(c_14,plain,
right_child_of(n) = n_right,
inference(copy,[status(thm)],[c_13]) ).
fof(goal_is_there_an_empty_node,axiom,
! [VAR_0] : ~ failure_node(VAR_0,or(empty,empty)),
file('theBenchmark.p',goal_is_there_an_empty_node) ).
cnf(c_15,plain,
~ failure_node(A,or(empty,empty)),
inference(clausify,[status(thm)],[goal_is_there_an_empty_node]) ).
cnf(c_20,plain,
( ~ failure_node(right_child_of(n),or(B,negate(C)))
| ~ failure_node(n_left,or(A,C))
| failure_node(parent_of(left_child_of(n),right_child_of(n)),or(A,B)) ),
inference(paramod,[status(thm)],[c_12,c_7]) ).
cnf(c_21,plain,
( ~ failure_node(right_child_of(n),or(B,negate(C)))
| ~ failure_node(n_left,or(A,C))
| failure_node(parent_of(n_left,right_child_of(n)),or(A,B)) ),
inference(paramod,[status(thm)],[c_12,c_20]) ).
cnf(c_22,plain,
( ~ failure_node(right_child_of(n),or(B,negate(C)))
| ~ failure_node(n_left,or(A,C))
| failure_node(parent_of(n_left,n_right),or(A,B)) ),
inference(paramod,[status(thm)],[c_14,c_21]) ).
cnf(c_16,plain,
( ~ failure_node(n_right,or(B,negate(C)))
| ~ failure_node(n_left,or(A,C))
| failure_node(parent_of(n_left,n_right),or(A,B)) ),
inference(paramod,[status(thm)],[c_14,c_22]) ).
cnf(c_23,plain,
( ~ failure_node(n_right,or(A,negate(atom)))
| failure_node(parent_of(n_left,n_right),or(empty,A)) ),
inference(resolve,[status(thm)],[c_16,c_9]) ).
cnf(c_18,plain,
failure_node(parent_of(n_left,n_right),or(empty,empty)),
inference(resolve,[status(thm)],[c_23,c_10]) ).
cnf(c_19,plain,
$false,
inference(resolve,[status(thm)],[c_18,c_15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COM004-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/5.43 % Computer : n009.cluster.edu
% 0.16/5.43 % Model : x86_64 x86_64
% 0.16/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.43 % Memory : 8046.5625MB
% 0.16/5.43 % OS : Linux 6.8.0-71-generic
% 0.16/5.43 % CPULimit : 300
% 0.16/5.43 % WCLimit : 300
% 0.16/5.43 % DateTime : Sat Sep 26 23:19:20 UTC 2026
% 0.16/5.43 % CPUTime :
% 0.16/5.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/5.43 % Process 1405043 was started by sandbox2 on n009,
% 0.16/5.43 % Sat Sep 26 23:19:20 2026
% 0.16/5.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/5.43
% 0.16/5.43 % From the command line: assign(max_seconds, 300).
% 0.16/5.45
% 0.16/5.45 % SZS status Unsatisfiable for theBenchmark
% 0.16/5.45
% 0.16/5.45 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.16/5.45 % Length of proof is 15.
% 0.16/5.45 % Level of proof is 5.
% 0.16/5.45 % Maximum clause weight is 22.000.
% 0.16/5.45 % Given clauses 8.
% 0.16/5.45
% 0.16/5.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------