%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : CSR021+1 : TPTP v9.3.1. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 07:06:33 AM UTC 2026
% Result : Theorem 0.12s 0.49s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 33 ( 19 unt; 0 def)
% Number of atoms : 78 ( 38 equ)
% Maximal formula atoms : 19 ( 2 avg)
% Number of connectives : 75 ( 30 ~; 25 |; 17 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 9 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(happens_terminates_not_holds,axiom,
! [Event,Time,Fluent] :
( ( terminates(Event,Fluent,Time)
& happens(Event,Time) )
=> ~ holdsAt(Fluent,plus(Time,n1)) ),
file('theBenchmark.p',happens_terminates_not_holds) ).
fof(terminates_all_defn,axiom,
! [Event,Fluent,Time] :
( terminates(Event,Fluent,Time)
<=> ( ( ~ happens(push,Time)
& Fluent = spinning
& Event = pull )
| ( ~ happens(pull,Time)
& Fluent = spinning
& Event = push )
| ( happens(push,Time)
& Fluent = backwards
& Event = pull )
| ( happens(push,Time)
& Fluent = forwards
& Event = pull )
| ( ~ happens(push,Time)
& Fluent = forwards
& Event = pull )
| ( ~ happens(pull,Time)
& Fluent = backwards
& Event = push ) ) ),
file('theBenchmark.p',terminates_all_defn) ).
fof(happens_all_defn,axiom,
! [Event,Time] :
( happens(Event,Time)
<=> ( ( Time = n2
& Event = push )
| ( Time = n2
& Event = pull )
| ( Time = n1
& Event = pull )
| ( Time = n0
& Event = push ) ) ),
file('theBenchmark.p',happens_all_defn) ).
fof(symmetry_of_plus,axiom,
! [X,Y] : plus(X,Y) = plus(Y,X),
file('theBenchmark.p',symmetry_of_plus) ).
fof(not_backwards_3,conjecture,
~ holdsAt(backwards,n3),
file('theBenchmark.p',not_backwards_3) ).
fof(not_backwards_3_neg,negated_conjecture,
~ ~ holdsAt(backwards,n3),
inference(assume_negation,[status(cth)],[not_backwards_3]) ).
cnf(c_51,negated_conjecture,
holdsAt(backwards,n3),
inference(clausify,[status(thm)],[not_backwards_3_neg]) ).
cnf(c_81,plain,
plus(A,B) = plus(B,A),
inference(clausify,[status(thm)],[symmetry_of_plus]) ).
fof(plus1_2,axiom,
plus(n1,n2) = n3,
file('theBenchmark.p',plus1_2) ).
cnf(c_86,plain,
plus(n1,n2) = n3,
inference(clausify,[status(thm)],[plus1_2]) ).
fof(plus0_2,axiom,
plus(n0,n2) = n2,
file('theBenchmark.p',plus0_2) ).
cnf(c_90,plain,
plus(n0,n2) = n2,
inference(clausify,[status(thm)],[plus0_2]) ).
cnf(c_91,plain,
plus(n2,n0) = n2,
inference(paramod,[status(thm)],[c_81,c_90]) ).
cnf(c_100,plain,
( n2 != B
| push != A
| happens(A,B) ),
inference(clausify,[status(thm)],[happens_all_defn]) ).
cnf(c_101,plain,
( n2 != B
| pull != A
| happens(A,B) ),
inference(clausify,[status(thm)],[happens_all_defn]) ).
cnf(c_110,plain,
( ~ happens(push,C)
| backwards != B
| pull != A
| terminates(A,B,C) ),
inference(clausify,[status(thm)],[terminates_all_defn]) ).
cnf(c_137,plain,
( ~ holdsAt(C,plus(B,n1))
| ~ terminates(A,C,B)
| ~ happens(A,B) ),
inference(clausify,[status(thm)],[happens_terminates_not_holds]) ).
cnf(c_621,plain,
( n2 != A
| happens(push,A) ),
inference(xxres,[status(thm)],[c_100]) ).
cnf(c_622,plain,
n2 = plus(n2,n0),
inference(copy,[status(thm)],[c_91]) ).
cnf(c_623,plain,
happens(push,plus(n2,n0)),
inference(resolve,[status(thm)],[c_621,c_622]) ).
cnf(c_176,plain,
happens(push,n2),
inference(paramod,[status(thm)],[c_91,c_623]) ).
cnf(c_624,plain,
( n2 != A
| happens(pull,A) ),
inference(xxres,[status(thm)],[c_101]) ).
cnf(c_625,plain,
n2 = plus(n2,n0),
inference(copy,[status(thm)],[c_91]) ).
cnf(c_626,plain,
happens(pull,plus(n2,n0)),
inference(resolve,[status(thm)],[c_624,c_625]) ).
cnf(c_179,plain,
happens(pull,n2),
inference(paramod,[status(thm)],[c_91,c_626]) ).
cnf(c_627,plain,
( ~ happens(push,B)
| backwards != A
| terminates(pull,A,B) ),
inference(xxres,[status(thm)],[c_110]) ).
cnf(c_628,plain,
( ~ happens(push,A)
| terminates(pull,backwards,A) ),
inference(xxres,[status(thm)],[c_627]) ).
cnf(c_224,plain,
terminates(pull,backwards,n2),
inference(resolve,[status(thm)],[c_628,c_176]) ).
cnf(c_629,plain,
( ~ holdsAt(backwards,plus(n2,n1))
| ~ happens(pull,n2) ),
inference(resolve,[status(thm)],[c_224,c_137]) ).
cnf(c_630,plain,
( ~ holdsAt(backwards,plus(n1,n2))
| ~ happens(pull,n2) ),
inference(paramod,[status(thm)],[c_81,c_629]) ).
cnf(c_631,plain,
( ~ holdsAt(backwards,n3)
| ~ happens(pull,n2) ),
inference(paramod,[status(thm)],[c_86,c_630]) ).
cnf(c_632,plain,
~ holdsAt(backwards,n3),
inference(resolve,[status(thm)],[c_179,c_631]) ).
cnf(c_620,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_51,c_632]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CSR021+1 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n016.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 : Sun Sep 27 00:01:02 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.38 % Process 2027949 was started by sandbox on n016,
% 0.12/0.38 % Sun Sep 27 00:01:02 2026
% 0.12/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.39
% 0.12/0.39 % From the command line: assign(max_seconds, 300).
% 0.12/0.49
% 0.12/0.49 % SZS status Theorem for theBenchmark
% 0.12/0.49
% 0.12/0.49 % Proof 1 at 0.06 (+ 0.02) seconds.
% 0.12/0.49 % Length of proof is 18.
% 0.12/0.49 % Level of proof is 5.
% 0.12/0.49 % Maximum clause weight is 22.000.
% 0.12/0.49 % Given clauses 297.
% 0.12/0.49
% 0.12/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------