%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : CSR021+1 : TPTP v9.3.1. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 : Thu Sep 24 12:12:51 PM UTC 2026
% Result : Theorem 0.14s 0.46s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 12
% Syntax : Number of formulae : 58 ( 19 unt; 5 def)
% Number of atoms : 256 ( 121 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 292 ( 94 ~; 95 |; 90 &)
% ( 12 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 9 con; 0-2 aty)
% Number of variables : 106 ( 106 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [Event,Time,Fluent] :
( ( terminates(Event,Fluent,Time)
& happens(Event,Time) )
=> ~ holdsAt(Fluent,plus(Time,n1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,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('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [Event,Time] :
( happens(Event,Time)
<=> ( ( Time = n2
& Event = push )
| ( Time = n2
& Event = pull )
| ( Time = n1
& Event = pull )
| ( Time = n0
& Event = push ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
plus(n1,n1) = n2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
plus(n1,n2) = n3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [X,Y] : plus(X,Y) = plus(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,conjecture,
~ holdsAt(backwards,n3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,negated_conjecture,
~ ~ holdsAt(backwards,n3),
inference(negated_conjecture,[status(cth)],[f48]) ).
fof(f91,plain,
! [Event,Time,Fluent] :
( ~ holdsAt(Fluent,plus(Time,n1))
| ~ terminates(Event,Fluent,Time)
| ~ happens(Event,Time) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f92,plain,
! [Time,Fluent] :
( ~ holdsAt(Fluent,plus(Time,n1))
| ! [Event] :
( ~ terminates(Event,Fluent,Time)
| ~ happens(Event,Time) ) ),
inference(miniscoping,[status(thm)],[f91]) ).
fof(f93,plain,
! [X0,X1,X2] :
( ~ holdsAt(X2,plus(X1,n1))
| ~ terminates(X0,X2,X1)
| ~ happens(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f110,definition,
! [Event,Fluent,Time] :
( sP1_prd(Time,Fluent,Event)
<=> ( ( ~ 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 ) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f111,plain,
! [Event,Fluent,Time] :
( terminates(Event,Fluent,Time)
<=> ( ( ~ happens(push,Time)
& Fluent = spinning
& Event = pull )
| sP1_prd(Time,Fluent,Event) ) ),
inference(formula_renaming,[status(thm)],[f14,f110]) ).
fof(f112,plain,
! [Event,Fluent,Time] :
( ( ( ( happens(push,Time)
| Fluent != spinning
| Event != pull )
& ~ sP1_prd(Time,Fluent,Event) )
| terminates(Event,Fluent,Time) )
& ( ( ~ happens(push,Time)
& Fluent = spinning
& Event = pull )
| sP1_prd(Time,Fluent,Event)
| ~ terminates(Event,Fluent,Time) ) ),
inference(NNF_transformation,[status(thm)],[f111]) ).
fof(f113,plain,
( ! [Event,Fluent,Time] :
( ( ( happens(push,Time)
| Fluent != spinning
| Event != pull )
& ~ sP1_prd(Time,Fluent,Event) )
| terminates(Event,Fluent,Time) )
& ! [Event,Fluent,Time] :
( ( ~ happens(push,Time)
& Fluent = spinning
& Event = pull )
| sP1_prd(Time,Fluent,Event)
| ~ terminates(Event,Fluent,Time) ) ),
inference(miniscoping,[status(thm)],[f112]) ).
fof(f117,plain,
! [X0,X1,X2] :
( ~ sP1_prd(X2,X1,X0)
| terminates(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f120,definition,
! [Event,Time] :
( sP2_prd(Time,Event)
<=> ( ( Time = n2
& Event = pull )
| ( Time = n1
& Event = pull )
| ( Time = n0
& Event = push ) ) ),
introduced(definition,[new_symbols(definition,[sP2_prd])],[]) ).
fof(f121,plain,
! [Event,Time] :
( happens(Event,Time)
<=> ( ( Time = n2
& Event = push )
| sP2_prd(Time,Event) ) ),
inference(formula_renaming,[status(thm)],[f16,f120]) ).
fof(f122,plain,
! [Event,Time] :
( ( ( ( Time != n2
| Event != push )
& ~ sP2_prd(Time,Event) )
| happens(Event,Time) )
& ( ( Time = n2
& Event = push )
| sP2_prd(Time,Event)
| ~ happens(Event,Time) ) ),
inference(NNF_transformation,[status(thm)],[f121]) ).
fof(f123,plain,
( ! [Event,Time] :
( ( ( Time != n2
| Event != push )
& ~ sP2_prd(Time,Event) )
| happens(Event,Time) )
& ! [Event,Time] :
( ( Time = n2
& Event = push )
| sP2_prd(Time,Event)
| ~ happens(Event,Time) ) ),
inference(miniscoping,[status(thm)],[f122]) ).
fof(f126,plain,
! [X0,X1] :
( ~ sP2_prd(X1,X0)
| happens(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f127,plain,
! [X0,X1] :
( X1 != n2
| X0 != push
| happens(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f136,plain,
plus(n1,n1) = n2,
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f137,plain,
plus(n1,n2) = n3,
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f142,plain,
! [X0,X1] : plus(X0,X1) = plus(X1,X0),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f195,plain,
holdsAt(backwards,n3),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f205,definition,
! [Event,Fluent,Time] :
( sP4_prd(Time,Fluent,Event)
<=> ( ( 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 ) ) ),
introduced(definition,[new_symbols(definition,[sP4_prd])],[]) ).
fof(f206,plain,
! [Event,Fluent,Time] :
( sP1_prd(Time,Fluent,Event)
<=> ( ( ~ happens(pull,Time)
& Fluent = spinning
& Event = push )
| sP4_prd(Time,Fluent,Event) ) ),
inference(formula_renaming,[status(thm)],[f110,f205]) ).
fof(f207,plain,
! [Event,Fluent,Time] :
( ( ( ( happens(pull,Time)
| Fluent != spinning
| Event != push )
& ~ sP4_prd(Time,Fluent,Event) )
| sP1_prd(Time,Fluent,Event) )
& ( ( ~ happens(pull,Time)
& Fluent = spinning
& Event = push )
| sP4_prd(Time,Fluent,Event)
| ~ sP1_prd(Time,Fluent,Event) ) ),
inference(NNF_transformation,[status(thm)],[f206]) ).
fof(f208,plain,
( ! [Event,Fluent,Time] :
( ( ( happens(pull,Time)
| Fluent != spinning
| Event != push )
& ~ sP4_prd(Time,Fluent,Event) )
| sP1_prd(Time,Fluent,Event) )
& ! [Event,Fluent,Time] :
( ( ~ happens(pull,Time)
& Fluent = spinning
& Event = push )
| sP4_prd(Time,Fluent,Event)
| ~ sP1_prd(Time,Fluent,Event) ) ),
inference(miniscoping,[status(thm)],[f207]) ).
fof(f212,plain,
! [X0,X1,X2] :
( ~ sP4_prd(X0,X1,X2)
| sP1_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f208]) ).
fof(f214,definition,
! [Event,Time] :
( sP5_prd(Time,Event)
<=> ( ( Time = n1
& Event = pull )
| ( Time = n0
& Event = push ) ) ),
introduced(definition,[new_symbols(definition,[sP5_prd])],[]) ).
fof(f215,plain,
! [Event,Time] :
( sP2_prd(Time,Event)
<=> ( ( Time = n2
& Event = pull )
| sP5_prd(Time,Event) ) ),
inference(formula_renaming,[status(thm)],[f120,f214]) ).
fof(f216,plain,
! [Event,Time] :
( ( ( ( Time != n2
| Event != pull )
& ~ sP5_prd(Time,Event) )
| sP2_prd(Time,Event) )
& ( ( Time = n2
& Event = pull )
| sP5_prd(Time,Event)
| ~ sP2_prd(Time,Event) ) ),
inference(NNF_transformation,[status(thm)],[f215]) ).
fof(f217,plain,
( ! [Event,Time] :
( ( ( Time != n2
| Event != pull )
& ~ sP5_prd(Time,Event) )
| sP2_prd(Time,Event) )
& ! [Event,Time] :
( ( Time = n2
& Event = pull )
| sP5_prd(Time,Event)
| ~ sP2_prd(Time,Event) ) ),
inference(miniscoping,[status(thm)],[f216]) ).
fof(f221,plain,
! [X0,X1] :
( X0 != n2
| X1 != pull
| sP2_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f217]) ).
fof(f228,definition,
! [Event,Fluent,Time] :
( sP6_prd(Time,Fluent,Event)
<=> ( ( happens(push,Time)
& Fluent = forwards
& Event = pull )
| ( ~ happens(push,Time)
& Fluent = forwards
& Event = pull )
| ( ~ happens(pull,Time)
& Fluent = backwards
& Event = push ) ) ),
introduced(definition,[new_symbols(definition,[sP6_prd])],[]) ).
fof(f229,plain,
! [Event,Fluent,Time] :
( sP4_prd(Time,Fluent,Event)
<=> ( ( happens(push,Time)
& Fluent = backwards
& Event = pull )
| sP6_prd(Time,Fluent,Event) ) ),
inference(formula_renaming,[status(thm)],[f205,f228]) ).
fof(f230,plain,
! [Event,Fluent,Time] :
( ( ( ( ~ happens(push,Time)
| Fluent != backwards
| Event != pull )
& ~ sP6_prd(Time,Fluent,Event) )
| sP4_prd(Time,Fluent,Event) )
& ( ( happens(push,Time)
& Fluent = backwards
& Event = pull )
| sP6_prd(Time,Fluent,Event)
| ~ sP4_prd(Time,Fluent,Event) ) ),
inference(NNF_transformation,[status(thm)],[f229]) ).
fof(f231,plain,
( ! [Event,Fluent,Time] :
( ( ( ~ happens(push,Time)
| Fluent != backwards
| Event != pull )
& ~ sP6_prd(Time,Fluent,Event) )
| sP4_prd(Time,Fluent,Event) )
& ! [Event,Fluent,Time] :
( ( happens(push,Time)
& Fluent = backwards
& Event = pull )
| sP6_prd(Time,Fluent,Event)
| ~ sP4_prd(Time,Fluent,Event) ) ),
inference(miniscoping,[status(thm)],[f230]) ).
fof(f236,plain,
! [X0,X1,X2] :
( ~ happens(push,X0)
| X1 != backwards
| X2 != pull
| sP4_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f231]) ).
fof(f301,plain,
! [X0] :
( X0 != n2
| happens(push,X0) ),
inference(equality_resolution,[status(thm)],[f127]) ).
fof(f302,plain,
happens(push,plus(n1,n1)),
inference(resolution,[status(thm)],[f301,f136]) ).
fof(f305,plain,
happens(push,n2),
inference(forward_demodulation,[status(thm)],[f136,f302]) ).
fof(f920,plain,
! [X0] :
( X0 != n2
| sP2_prd(X0,pull) ),
inference(equality_resolution,[status(thm)],[f221]) ).
fof(f1175,plain,
! [X0,X1] :
( X0 != backwards
| X1 != pull
| sP4_prd(n2,X0,X1) ),
inference(resolution,[status(thm)],[f236,f305]) ).
fof(f1267,plain,
sP2_prd(plus(n1,n1),pull),
inference(resolution,[status(thm)],[f920,f136]) ).
fof(f1270,plain,
sP2_prd(n2,pull),
inference(forward_demodulation,[status(thm)],[f136,f1267]) ).
fof(f1274,plain,
happens(pull,n2),
inference(resolution,[status(thm)],[f1270,f126]) ).
fof(f1751,plain,
! [X0] :
( X0 != backwards
| sP4_prd(n2,X0,pull) ),
inference(equality_resolution,[status(thm)],[f1175]) ).
fof(f1752,plain,
sP4_prd(n2,backwards,pull),
inference(equality_resolution,[status(thm)],[f1751]) ).
fof(f1756,plain,
sP1_prd(n2,backwards,pull),
inference(resolution,[status(thm)],[f1752,f212]) ).
fof(f1760,plain,
terminates(pull,backwards,n2),
inference(resolution,[status(thm)],[f1756,f117]) ).
fof(f1764,plain,
( ~ holdsAt(backwards,plus(n2,n1))
| ~ happens(pull,n2) ),
inference(resolution,[status(thm)],[f1760,f93]) ).
fof(f1766,plain,
( ~ holdsAt(backwards,plus(n1,n2))
| ~ happens(pull,n2) ),
inference(forward_demodulation,[status(thm)],[f142,f1764]) ).
fof(f1767,plain,
( ~ holdsAt(backwards,n3)
| ~ happens(pull,n2) ),
inference(forward_demodulation,[status(thm)],[f137,f1766]) ).
fof(f1768,plain,
~ holdsAt(backwards,n3),
inference(forward_subsumption_resolution,[status(thm)],[f1767,f1274]) ).
fof(f1770,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1768,f195]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CSR021+1 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n010.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 14:24:55 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.14/0.36 % Drodi V4.1.1
% 0.14/0.46 % Refutation found
% 0.14/0.46 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.48 % Elapsed time: 0.124214 seconds
% 0.14/0.48 % CPU time: 0.757903 seconds
% 0.14/0.48 % Total memory used: 118.388 MB
% 0.14/0.48 % Net memory used: 117.399 MB
%------------------------------------------------------------------------------