%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : CSR019+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 0.13s 5.66s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 33 ( 17 unt; 0 def)
% Number of atoms : 83 ( 37 equ)
% Maximal formula atoms : 19 ( 2 avg)
% Number of connectives : 82 ( 32 ~; 30 |; 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 : 9 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 34 ( 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_forwards_2,conjecture,
~ holdsAt(forwards,n2),
file('theBenchmark.p',not_forwards_2) ).
fof(not_forwards_2_neg,negated_conjecture,
~ ~ holdsAt(forwards,n2),
inference(assume_negation,[status(cth)],[not_forwards_2]) ).
cnf(c_51,negated_conjecture,
holdsAt(forwards,n2),
inference(clausify,[status(thm)],[not_forwards_2_neg]) ).
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]) ).
cnf(c_102,plain,
( n1 != B
| pull != A
| happens(A,B) ),
inference(clausify,[status(thm)],[happens_all_defn]) ).
cnf(c_111,plain,
( ~ happens(push,C)
| forwards != B
| pull != A
| terminates(A,B,C) ),
inference(clausify,[status(thm)],[terminates_all_defn]) ).
cnf(c_112,plain,
( happens(push,C)
| forwards != 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_195,plain,
( n1 != A
| happens(pull,A) ),
inference(xxres,[status(thm)],[c_102]) ).
cnf(c_205,plain,
( ~ happens(push,B)
| forwards != A
| terminates(pull,A,B) ),
inference(xxres,[status(thm)],[c_111]) ).
cnf(c_207,plain,
( happens(push,B)
| forwards != A
| terminates(pull,A,B) ),
inference(xxres,[status(thm)],[c_112]) ).
cnf(c_218,plain,
( ~ holdsAt(B,n2)
| ~ terminates(A,B,n1)
| ~ happens(A,n1) ),
inference(paramod,[status(thm)],[c_87,c_137]) ).
cnf(c_246,plain,
( ~ terminates(A,forwards,n1)
| ~ happens(A,n1) ),
inference(resolve,[status(thm)],[c_218,c_51]) ).
cnf(c_2019,plain,
n1 = plus(n1,n0),
inference(copy,[status(thm)],[c_92]) ).
cnf(c_2020,plain,
happens(pull,plus(n1,n0)),
inference(resolve,[status(thm)],[c_195,c_2019]) ).
cnf(c_1092,plain,
happens(pull,n1),
inference(paramod,[status(thm)],[c_92,c_2020]) ).
cnf(c_1159,plain,
~ terminates(pull,forwards,n1),
inference(resolve,[status(thm)],[c_1092,c_246]) ).
cnf(c_1160,plain,
( ~ holdsAt(A,n2)
| ~ terminates(pull,A,n1) ),
inference(resolve,[status(thm)],[c_1092,c_218]) ).
cnf(c_1311,plain,
( ~ happens(push,A)
| terminates(pull,forwards,A) ),
inference(xxres,[status(thm)],[c_205]) ).
cnf(c_1332,plain,
( happens(push,A)
| terminates(pull,forwards,A) ),
inference(xxres,[status(thm)],[c_207]) ).
cnf(c_2021,plain,
( ~ holdsAt(forwards,n2)
| happens(push,n1) ),
inference(resolve,[status(thm)],[c_1332,c_1160]) ).
cnf(c_1992,negated_conjecture,
happens(push,n1),
inference(resolve,[status(thm)],[c_51,c_2021]) ).
cnf(c_2022,plain,
terminates(pull,forwards,n1),
inference(resolve,[status(thm)],[c_1992,c_1311]) ).
cnf(c_2018,plain,
$false,
inference(resolve,[status(thm)],[c_1159,c_2022]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CSR019+1 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n003.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Sat Sep 26 23:57:59 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.37 % Process 4094565 was started by sandbox2 on n003,
% 0.09/5.37 % Sat Sep 26 23:57:59 2026
% 0.09/5.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/5.39
% 0.09/5.39 % From the command line: assign(max_seconds, 300).
% 0.13/5.66
% 0.13/5.66 % SZS status Theorem for theBenchmark
% 0.13/5.66
% 0.13/5.66 % Proof 1 at 0.18 (+ 0.08) seconds.
% 0.13/5.66 % Length of proof is 26.
% 0.13/5.66 % Level of proof is 6.
% 0.13/5.66 % Maximum clause weight is 22.000.
% 0.13/5.66 % Given clauses 394.
% 0.13/5.66
% 0.13/5.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------