%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : CSR017+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 : n012.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 07:06:32 AM UTC 2026
% Result : Theorem 0.31s 0.43s
% Output : CNFRefutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 55 ( 27 unt; 0 def)
% Number of atoms : 123 ( 63 equ)
% Maximal formula atoms : 19 ( 2 avg)
% Number of connectives : 110 ( 42 ~; 43 |; 18 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 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 : 47 ( 0 sgn 16 !; 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(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(not_spinning_1,conjecture,
~ holdsAt(spinning,n1),
file('theBenchmark.p',not_spinning_1) ).
fof(not_spinning_1_neg,negated_conjecture,
~ ~ holdsAt(spinning,n1),
inference(assume_negation,[status(cth)],[not_spinning_1]) ).
cnf(c_51,negated_conjecture,
holdsAt(spinning,n1),
inference(clausify,[status(thm)],[not_spinning_1_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_79,plain,
( ~ less(A,B)
| 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(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(plus0_0,axiom,
plus(n0,n0) = n0,
file('theBenchmark.p',plus0_0) ).
cnf(c_93,plain,
plus(n0,n0) = n0,
inference(clausify,[status(thm)],[plus0_0]) ).
fof(push_not_pull,axiom,
push != pull,
file('theBenchmark.p',push_not_pull) ).
cnf(c_98,plain,
push != pull,
inference(clausify,[status(thm)],[push_not_pull]) ).
cnf(c_99,plain,
pull != push,
inference(copy,[status(thm)],[c_98]) ).
cnf(c_103,plain,
( n0 != B
| push != A
| happens(A,B) ),
inference(clausify,[status(thm)],[happens_all_defn]) ).
cnf(c_106,plain,
( n2 = B
| n1 = B
| push = A
| ~ happens(A,B) ),
inference(clausify,[status(thm)],[happens_all_defn]) ).
cnf(c_109,plain,
( happens(pull,C)
| spinning != B
| push != 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_186,plain,
less_or_equal(A,A),
inference(xxres,[status(thm)],[c_78]) ).
cnf(c_197,plain,
( n0 != A
| happens(push,A) ),
inference(xxres,[status(thm)],[c_103]) ).
cnf(c_201,plain,
( happens(pull,B)
| spinning != A
| terminates(push,A,B) ),
inference(xxres,[status(thm)],[c_109]) ).
cnf(c_217,plain,
( ~ holdsAt(C,plus(n1,B))
| ~ terminates(A,C,B)
| ~ happens(A,B) ),
inference(paramod,[status(thm)],[c_81,c_137]) ).
cnf(c_248,plain,
( ~ holdsAt(B,n1)
| ~ terminates(A,B,n0)
| ~ happens(A,n0) ),
inference(paramod,[status(thm)],[c_92,c_217]) ).
cnf(c_249,plain,
less(n0,n1),
inference(resolve,[status(thm)],[c_186,c_75]) ).
cnf(c_264,plain,
less_or_equal(n0,n1),
inference(resolve,[status(thm)],[c_249,c_79]) ).
cnf(c_1727,plain,
n1 != n0,
inference(resolve,[status(thm)],[c_249,c_57]) ).
cnf(c_265,plain,
n0 != n1,
inference(copy,[status(thm)],[c_1727]) ).
cnf(c_475,plain,
less(n0,n2),
inference(resolve,[status(thm)],[c_264,c_73]) ).
cnf(c_1728,plain,
n2 != n0,
inference(resolve,[status(thm)],[c_475,c_57]) ).
cnf(c_514,plain,
n0 != n2,
inference(copy,[status(thm)],[c_1728]) ).
cnf(c_1729,plain,
n0 = plus(n0,n0),
inference(copy,[status(thm)],[c_93]) ).
cnf(c_1730,plain,
happens(push,plus(n0,n0)),
inference(resolve,[status(thm)],[c_197,c_1729]) ).
cnf(c_1142,plain,
happens(push,n0),
inference(paramod,[status(thm)],[c_93,c_1730]) ).
cnf(c_1211,plain,
( happens(pull,A)
| terminates(push,spinning,A) ),
inference(xxres,[status(thm)],[c_201]) ).
cnf(c_1267,plain,
( ~ holdsAt(A,n1)
| ~ terminates(push,A,n0) ),
inference(resolve,[status(thm)],[c_1142,c_248]) ).
cnf(c_1731,plain,
( ~ holdsAt(spinning,n1)
| happens(pull,n0) ),
inference(resolve,[status(thm)],[c_1211,c_1267]) ).
cnf(c_1643,negated_conjecture,
happens(pull,n0),
inference(resolve,[status(thm)],[c_51,c_1731]) ).
cnf(c_1732,plain,
( n2 = n0
| n1 = n0
| push = pull ),
inference(resolve,[status(thm)],[c_1643,c_106]) ).
cnf(c_1733,plain,
( n2 = n0
| n1 = n0
| pull = push ),
inference(copy,[status(thm)],[c_1732]) ).
cnf(c_1734,plain,
( n2 = n0
| n0 = n1
| pull = push ),
inference(copy,[status(thm)],[c_1733]) ).
cnf(c_1735,plain,
( n0 = n2
| n0 = n1
| pull = push ),
inference(copy,[status(thm)],[c_1734]) ).
cnf(c_1736,plain,
( n0 = n2
| n0 = n1 ),
inference(resolve,[status(thm)],[c_99,c_1735]) ).
cnf(c_1737,plain,
n0 = n2,
inference(resolve,[status(thm)],[c_265,c_1736]) ).
cnf(c_1726,plain,
$false,
inference(resolve,[status(thm)],[c_514,c_1737]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : CSR017+1 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Sat Sep 26 23:55:19 UTC 2026
% 0.02/0.29 % CPUTime :
% 0.02/0.29 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.02/0.29 % Process 1785014 was started by sandbox on n012,
% 0.02/0.29 % Sat Sep 26 23:55:19 2026
% 0.02/0.29 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.02/0.30
% 0.02/0.30 % From the command line: assign(max_seconds, 300).
% 0.31/0.43
% 0.31/0.43 % SZS status Theorem for theBenchmark
% 0.31/0.43
% 0.31/0.43 % Proof 1 at 0.08 (+ 0.04) seconds.
% 0.31/0.43 % Length of proof is 40.
% 0.31/0.43 % Level of proof is 7.
% 0.31/0.43 % Maximum clause weight is 22.000.
% 0.31/0.43 % Given clauses 365.
% 0.31/0.43
% 0.31/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------