%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : CSR020+1 : TPTP v9.3.1. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 0.88s 0.52s
% Output : CNFRefutation 0.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 48 ( 25 unt; 0 def)
% Number of atoms : 108 ( 53 equ)
% Maximal formula atoms : 19 ( 2 avg)
% Number of connectives : 96 ( 36 ~; 35 |; 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 : 40 ( 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_2,conjecture,
~ holdsAt(spinning,n2),
file('theBenchmark.p',not_spinning_2) ).
fof(not_spinning_2_neg,negated_conjecture,
~ ~ holdsAt(spinning,n2),
inference(assume_negation,[status(cth)],[not_spinning_2]) ).
cnf(c_51,negated_conjecture,
holdsAt(spinning,n2),
inference(clausify,[status(thm)],[not_spinning_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_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_102,plain,
( n1 != B
| pull != A
| happens(A,B) ),
inference(clausify,[status(thm)],[happens_all_defn]) ).
cnf(c_105,plain,
( n2 = B
| pull = A
| n0 = B
| ~ happens(A,B) ),
inference(clausify,[status(thm)],[happens_all_defn]) ).
cnf(c_108,plain,
( happens(push,C)
| spinning != 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_170,plain,
less_or_equal(A,A),
inference(xxres,[status(thm)],[c_78]) ).
cnf(c_178,plain,
( n1 != A
| happens(pull,A) ),
inference(xxres,[status(thm)],[c_102]) ).
cnf(c_182,plain,
( happens(push,B)
| spinning != A
| terminates(pull,A,B) ),
inference(xxres,[status(thm)],[c_108]) ).
cnf(c_200,plain,
less(n0,n1),
inference(resolve,[status(thm)],[c_170,c_75]) ).
cnf(c_201,plain,
less(n1,n2),
inference(resolve,[status(thm)],[c_170,c_73]) ).
cnf(c_651,plain,
n1 != n0,
inference(resolve,[status(thm)],[c_200,c_57]) ).
cnf(c_210,plain,
n0 != n1,
inference(copy,[status(thm)],[c_651]) ).
cnf(c_213,plain,
n2 != n1,
inference(resolve,[status(thm)],[c_201,c_57]) ).
cnf(c_652,plain,
n1 = plus(n1,n0),
inference(copy,[status(thm)],[c_92]) ).
cnf(c_653,plain,
happens(pull,plus(n1,n0)),
inference(resolve,[status(thm)],[c_178,c_652]) ).
cnf(c_367,plain,
happens(pull,n1),
inference(paramod,[status(thm)],[c_92,c_653]) ).
cnf(c_396,plain,
( happens(push,A)
| terminates(pull,spinning,A) ),
inference(xxres,[status(thm)],[c_182]) ).
cnf(c_406,plain,
( ~ holdsAt(spinning,plus(A,n1))
| ~ happens(pull,A)
| happens(push,A) ),
inference(resolve,[status(thm)],[c_396,c_137]) ).
cnf(c_654,plain,
( ~ holdsAt(spinning,n2)
| ~ happens(pull,n1)
| happens(push,n1) ),
inference(paramod,[status(thm)],[c_87,c_406]) ).
cnf(c_655,plain,
( ~ holdsAt(spinning,n2)
| happens(push,n1) ),
inference(resolve,[status(thm)],[c_367,c_654]) ).
cnf(c_646,negated_conjecture,
happens(push,n1),
inference(resolve,[status(thm)],[c_51,c_655]) ).
cnf(c_656,plain,
( n2 = n1
| pull = push
| n0 = n1 ),
inference(resolve,[status(thm)],[c_646,c_105]) ).
cnf(c_657,plain,
( n2 = n1
| pull = push ),
inference(resolve,[status(thm)],[c_210,c_656]) ).
cnf(c_658,plain,
n2 = n1,
inference(resolve,[status(thm)],[c_99,c_657]) ).
cnf(c_650,plain,
$false,
inference(resolve,[status(thm)],[c_213,c_658]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CSR020+1 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n003.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sat Sep 26 23:58:09 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.35 % Process 4094966 was started by sandbox2 on n003,
% 0.07/0.35 % Sat Sep 26 23:58:09 2026
% 0.07/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 0.88/0.52
% 0.88/0.52 % SZS status Theorem for theBenchmark
% 0.88/0.52
% 0.88/0.52 % Proof 1 at 0.10 (+ 0.05) seconds.
% 0.88/0.52 % Length of proof is 36.
% 0.88/0.52 % Level of proof is 6.
% 0.88/0.52 % Maximum clause weight is 13.000.
% 0.88/0.52 % Given clauses 444.
% 0.88/0.52
% 0.88/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------