%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : CSR018+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 : n007.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 0.85s 0.60s
% Output : CNFRefutation 0.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 48 ( 25 unt; 0 def)
% Number of atoms : 97 ( 47 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 76 ( 27 ~; 30 |; 12 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(happens_holds,axiom,
! [Event,Time,Fluent] :
( ( initiates(Event,Fluent,Time)
& happens(Event,Time) )
=> holdsAt(Fluent,plus(Time,n1)) ),
file('theBenchmark.p',happens_holds) ).
fof(initiates_all_defn,axiom,
! [Event,Fluent,Time] :
( initiates(Event,Fluent,Time)
<=> ( ( happens(push,Time)
& Fluent = spinning
& Event = pull )
| ( ~ happens(push,Time)
& Fluent = backwards
& Event = pull )
| ( ~ happens(pull,Time)
& Fluent = forwards
& Event = push ) ) ),
file('theBenchmark.p',initiates_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(less_or_equal,axiom,
! [X,Y] :
( less_or_equal(X,Y)
<=> ( X = Y
| less(X,Y) ) ),
file('theBenchmark.p',less_or_equal) ).
fof(less1,axiom,
! [X] :
( less(X,n1)
<=> less_or_equal(X,n0) ),
file('theBenchmark.p',less1) ).
fof(less2,axiom,
! [X] :
( less(X,n2)
<=> less_or_equal(X,n1) ),
file('theBenchmark.p',less2) ).
fof(less_property,axiom,
! [X,Y] :
( less(X,Y)
<=> ( Y != X
& ~ less(Y,X) ) ),
file('theBenchmark.p',less_property) ).
fof(backwards_2,conjecture,
holdsAt(backwards,n2),
file('theBenchmark.p',backwards_2) ).
fof(backwards_2_neg,negated_conjecture,
~ holdsAt(backwards,n2),
inference(assume_negation,[status(cth)],[backwards_2]) ).
cnf(c_51,negated_conjecture,
~ holdsAt(backwards,n2),
inference(clausify,[status(thm)],[backwards_2_neg]) ).
cnf(c_57,plain,
( B != A
| ~ less(A,B) ),
inference(clausify,[status(thm)],[less_property]) ).
cnf(c_73,plain,
( ~ less_or_equal(A,n1)
| less(A,n2) ),
inference(clausify,[status(thm)],[less2]) ).
cnf(c_75,plain,
( ~ less_or_equal(A,n0)
| less(A,n1) ),
inference(clausify,[status(thm)],[less1]) ).
cnf(c_78,plain,
( B != A
| less_or_equal(A,B) ),
inference(clausify,[status(thm)],[less_or_equal]) ).
cnf(c_81,plain,
plus(A,B) = plus(B,A),
inference(clausify,[status(thm)],[symmetry_of_plus]) ).
fof(plus1_1,axiom,
plus(n1,n1) = n2,
file('theBenchmark.p',plus1_1) ).
cnf(c_87,plain,
plus(n1,n1) = n2,
inference(clausify,[status(thm)],[plus1_1]) ).
fof(plus0_1,axiom,
plus(n0,n1) = n1,
file('theBenchmark.p',plus0_1) ).
cnf(c_91,plain,
plus(n0,n1) = n1,
inference(clausify,[status(thm)],[plus0_1]) ).
cnf(c_92,plain,
plus(n1,n0) = n1,
inference(paramod,[status(thm)],[c_81,c_91]) ).
fof(push_not_pull,axiom,
push != pull,
file('theBenchmark.p',push_not_pull) ).
cnf(c_97,plain,
push != pull,
inference(clausify,[status(thm)],[push_not_pull]) ).
cnf(c_98,plain,
pull != push,
inference(copy,[status(thm)],[c_97]) ).
cnf(c_101,plain,
( n1 != B
| pull != A
| happens(A,B) ),
inference(clausify,[status(thm)],[happens_all_defn]) ).
cnf(c_104,plain,
( n2 = B
| pull = A
| n0 = B
| ~ happens(A,B) ),
inference(clausify,[status(thm)],[happens_all_defn]) ).
cnf(c_122,plain,
( happens(push,C)
| backwards != B
| pull != A
| initiates(A,B,C) ),
inference(clausify,[status(thm)],[initiates_all_defn]) ).
cnf(c_137,plain,
( holdsAt(C,plus(B,n1))
| ~ initiates(A,C,B)
| ~ happens(A,B) ),
inference(clausify,[status(thm)],[happens_holds]) ).
cnf(c_169,plain,
less_or_equal(A,A),
inference(xxres,[status(thm)],[c_78]) ).
cnf(c_939,plain,
( n1 != A
| happens(pull,A) ),
inference(xxres,[status(thm)],[c_101]) ).
cnf(c_940,plain,
n1 = plus(n1,n0),
inference(copy,[status(thm)],[c_92]) ).
cnf(c_941,plain,
happens(pull,plus(n1,n0)),
inference(resolve,[status(thm)],[c_939,c_940]) ).
cnf(c_181,plain,
happens(pull,n1),
inference(paramod,[status(thm)],[c_92,c_941]) ).
cnf(c_942,plain,
( happens(push,B)
| backwards != A
| initiates(pull,A,B) ),
inference(xxres,[status(thm)],[c_122]) ).
cnf(c_199,plain,
( happens(push,A)
| initiates(pull,backwards,A) ),
inference(xxres,[status(thm)],[c_942]) ).
cnf(c_207,plain,
less(n0,n1),
inference(resolve,[status(thm)],[c_169,c_75]) ).
cnf(c_208,plain,
less(n1,n2),
inference(resolve,[status(thm)],[c_169,c_73]) ).
cnf(c_943,plain,
n1 != n0,
inference(resolve,[status(thm)],[c_207,c_57]) ).
cnf(c_229,plain,
n0 != n1,
inference(copy,[status(thm)],[c_943]) ).
cnf(c_233,plain,
n2 != n1,
inference(resolve,[status(thm)],[c_208,c_57]) ).
cnf(c_944,plain,
( holdsAt(A,plus(n1,n1))
| ~ initiates(pull,A,n1) ),
inference(resolve,[status(thm)],[c_137,c_181]) ).
cnf(c_945,plain,
( happens(push,n1)
| holdsAt(backwards,plus(n1,n1)) ),
inference(resolve,[status(thm)],[c_944,c_199]) ).
cnf(c_946,plain,
( happens(push,n1)
| holdsAt(backwards,n2) ),
inference(paramod,[status(thm)],[c_87,c_945]) ).
cnf(c_934,negated_conjecture,
happens(push,n1),
inference(resolve,[status(thm)],[c_51,c_946]) ).
cnf(c_947,plain,
( n2 = n1
| pull = push
| n0 = n1 ),
inference(resolve,[status(thm)],[c_934,c_104]) ).
cnf(c_948,plain,
( n2 = n1
| pull = push ),
inference(resolve,[status(thm)],[c_229,c_947]) ).
cnf(c_949,plain,
n2 = n1,
inference(resolve,[status(thm)],[c_98,c_948]) ).
cnf(c_938,plain,
$false,
inference(resolve,[status(thm)],[c_233,c_949]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CSR018+1 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 23:53:39 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 786565 was started by sandbox on n007,
% 0.09/0.37 % Sat Sep 26 23:53:39 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.85/0.60
% 0.85/0.60 % SZS status Theorem for theBenchmark
% 0.85/0.60
% 0.85/0.60 % Proof 1 at 0.15 (+ 0.05) seconds.
% 0.85/0.60 % Length of proof is 33.
% 0.85/0.60 % Level of proof is 5.
% 0.85/0.60 % Maximum clause weight is 22.000.
% 0.85/0.60 % Given clauses 315.
% 0.85/0.60
% 0.85/0.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------