%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : CSR018+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 : n015.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 12:12:50 PM UTC 2026
% Result : Theorem 0.14s 0.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of formulae : 84 ( 20 unt; 4 def)
% Number of atoms : 306 ( 126 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 336 ( 114 ~; 130 |; 77 &)
% ( 14 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 143 ( 142 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [Event,Time,Fluent] :
( ( initiates(Event,Fluent,Time)
& happens(Event,Time) )
=> holdsAt(Fluent,plus(Time,n1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,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('/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(f17,axiom,
push != pull,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
plus(n1,n1) = n2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [X,Y] :
( less_or_equal(X,Y)
<=> ( X = Y
| less(X,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,axiom,
~ ? [X] : less(X,n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [X] :
( less(X,n1)
<=> less_or_equal(X,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [X] :
( less(X,n2)
<=> less_or_equal(X,n1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,axiom,
! [X,Y] :
( less(X,Y)
<=> ( Y != X
& ~ less(Y,X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,conjecture,
holdsAt(backwards,n2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,negated_conjecture,
~ holdsAt(backwards,n2),
inference(negated_conjecture,[status(cth)],[f48]) ).
fof(f88,plain,
! [Event,Time,Fluent] :
( holdsAt(Fluent,plus(Time,n1))
| ~ initiates(Event,Fluent,Time)
| ~ happens(Event,Time) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f89,plain,
! [Time,Fluent] :
( holdsAt(Fluent,plus(Time,n1))
| ! [Event] :
( ~ initiates(Event,Fluent,Time)
| ~ happens(Event,Time) ) ),
inference(miniscoping,[status(thm)],[f88]) ).
fof(f90,plain,
! [X0,X1,X2] :
( holdsAt(X2,plus(X1,n1))
| ~ initiates(X0,X2,X1)
| ~ happens(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f101,definition,
! [Event,Fluent,Time] :
( sP0_prd(Time,Fluent,Event)
<=> ( ( ~ happens(push,Time)
& Fluent = backwards
& Event = pull )
| ( ~ happens(pull,Time)
& Fluent = forwards
& Event = push ) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f102,plain,
! [Event,Fluent,Time] :
( initiates(Event,Fluent,Time)
<=> ( ( happens(push,Time)
& Fluent = spinning
& Event = pull )
| sP0_prd(Time,Fluent,Event) ) ),
inference(formula_renaming,[status(thm)],[f13,f101]) ).
fof(f103,plain,
! [Event,Fluent,Time] :
( ( ( ( ~ happens(push,Time)
| Fluent != spinning
| Event != pull )
& ~ sP0_prd(Time,Fluent,Event) )
| initiates(Event,Fluent,Time) )
& ( ( happens(push,Time)
& Fluent = spinning
& Event = pull )
| sP0_prd(Time,Fluent,Event)
| ~ initiates(Event,Fluent,Time) ) ),
inference(NNF_transformation,[status(thm)],[f102]) ).
fof(f104,plain,
( ! [Event,Fluent,Time] :
( ( ( ~ happens(push,Time)
| Fluent != spinning
| Event != pull )
& ~ sP0_prd(Time,Fluent,Event) )
| initiates(Event,Fluent,Time) )
& ! [Event,Fluent,Time] :
( ( happens(push,Time)
& Fluent = spinning
& Event = pull )
| sP0_prd(Time,Fluent,Event)
| ~ initiates(Event,Fluent,Time) ) ),
inference(miniscoping,[status(thm)],[f103]) ).
fof(f108,plain,
! [X0,X1,X2] :
( ~ sP0_prd(X2,X1,X0)
| initiates(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f104]) ).
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(f125,plain,
! [X0,X1] :
( X1 = n2
| sP2_prd(X1,X0)
| ~ happens(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f126,plain,
! [X0,X1] :
( ~ sP2_prd(X1,X0)
| happens(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f128,plain,
push != pull,
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f136,plain,
plus(n1,n1) = n2,
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f143,plain,
! [X,Y] :
( ( ( X != Y
& ~ less(X,Y) )
| less_or_equal(X,Y) )
& ( X = Y
| less(X,Y)
| ~ less_or_equal(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f32]) ).
fof(f144,plain,
( ! [X,Y] :
( ( X != Y
& ~ less(X,Y) )
| less_or_equal(X,Y) )
& ! [X,Y] :
( X = Y
| less(X,Y)
| ~ less_or_equal(X,Y) ) ),
inference(miniscoping,[status(thm)],[f143]) ).
fof(f145,plain,
! [X0,X1] :
( X0 = X1
| less(X0,X1)
| ~ less_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f144]) ).
fof(f147,plain,
! [X0,X1] :
( X0 != X1
| less_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f144]) ).
fof(f148,plain,
! [X] : ~ less(X,n0),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f149,plain,
! [X0] : ~ less(X0,n0),
inference(cnf_transformation,[status(thm)],[f148]) ).
fof(f150,plain,
! [X] :
( ( ~ less_or_equal(X,n0)
| less(X,n1) )
& ( less_or_equal(X,n0)
| ~ less(X,n1) ) ),
inference(NNF_transformation,[status(thm)],[f34]) ).
fof(f151,plain,
( ! [X] :
( ~ less_or_equal(X,n0)
| less(X,n1) )
& ! [X] :
( less_or_equal(X,n0)
| ~ less(X,n1) ) ),
inference(miniscoping,[status(thm)],[f150]) ).
fof(f152,plain,
! [X0] :
( less_or_equal(X0,n0)
| ~ less(X0,n1) ),
inference(cnf_transformation,[status(thm)],[f151]) ).
fof(f153,plain,
! [X0] :
( ~ less_or_equal(X0,n0)
| less(X0,n1) ),
inference(cnf_transformation,[status(thm)],[f151]) ).
fof(f154,plain,
! [X] :
( ( ~ less_or_equal(X,n1)
| less(X,n2) )
& ( less_or_equal(X,n1)
| ~ less(X,n2) ) ),
inference(NNF_transformation,[status(thm)],[f35]) ).
fof(f155,plain,
( ! [X] :
( ~ less_or_equal(X,n1)
| less(X,n2) )
& ! [X] :
( less_or_equal(X,n1)
| ~ less(X,n2) ) ),
inference(miniscoping,[status(thm)],[f154]) ).
fof(f157,plain,
! [X0] :
( ~ less_or_equal(X0,n1)
| less(X0,n2) ),
inference(cnf_transformation,[status(thm)],[f155]) ).
fof(f186,plain,
! [X,Y] :
( ( Y = X
| less(Y,X)
| less(X,Y) )
& ( ( Y != X
& ~ less(Y,X) )
| ~ less(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f43]) ).
fof(f187,plain,
( ! [X,Y] :
( Y = X
| less(Y,X)
| less(X,Y) )
& ! [X,Y] :
( ( Y != X
& ~ less(Y,X) )
| ~ less(X,Y) ) ),
inference(miniscoping,[status(thm)],[f186]) ).
fof(f189,plain,
! [X0,X1] :
( X1 != X0
| ~ less(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f187]) ).
fof(f195,plain,
~ holdsAt(backwards,n2),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f196,definition,
! [Event,Fluent,Time] :
( sP3_prd(Time,Fluent,Event)
<=> ( ~ happens(pull,Time)
& Fluent = forwards
& Event = push ) ),
introduced(definition,[new_symbols(definition,[sP3_prd])],[]) ).
fof(f197,plain,
! [Event,Fluent,Time] :
( sP0_prd(Time,Fluent,Event)
<=> ( ( ~ happens(push,Time)
& Fluent = backwards
& Event = pull )
| sP3_prd(Time,Fluent,Event) ) ),
inference(formula_renaming,[status(thm)],[f101,f196]) ).
fof(f198,plain,
! [Event,Fluent,Time] :
( ( ( ( happens(push,Time)
| Fluent != backwards
| Event != pull )
& ~ sP3_prd(Time,Fluent,Event) )
| sP0_prd(Time,Fluent,Event) )
& ( ( ~ happens(push,Time)
& Fluent = backwards
& Event = pull )
| sP3_prd(Time,Fluent,Event)
| ~ sP0_prd(Time,Fluent,Event) ) ),
inference(NNF_transformation,[status(thm)],[f197]) ).
fof(f199,plain,
( ! [Event,Fluent,Time] :
( ( ( happens(push,Time)
| Fluent != backwards
| Event != pull )
& ~ sP3_prd(Time,Fluent,Event) )
| sP0_prd(Time,Fluent,Event) )
& ! [Event,Fluent,Time] :
( ( ~ happens(push,Time)
& Fluent = backwards
& Event = pull )
| sP3_prd(Time,Fluent,Event)
| ~ sP0_prd(Time,Fluent,Event) ) ),
inference(miniscoping,[status(thm)],[f198]) ).
fof(f204,plain,
! [X0,X1,X2] :
( happens(push,X0)
| X1 != backwards
| X2 != pull
| sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f199]) ).
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(f219,plain,
! [X0,X1] :
( X0 = n2
| sP5_prd(X0,X1)
| ~ sP2_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f217]) ).
fof(f220,plain,
! [X0,X1] :
( ~ sP5_prd(X0,X1)
| sP2_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f217]) ).
fof(f237,plain,
! [Event,Time] :
( ( ( ( Time != n1
| Event != pull )
& ( Time != n0
| Event != push ) )
| sP5_prd(Time,Event) )
& ( ( Time = n1
& Event = pull )
| ( Time = n0
& Event = push )
| ~ sP5_prd(Time,Event) ) ),
inference(NNF_transformation,[status(thm)],[f214]) ).
fof(f238,plain,
( ! [Event,Time] :
( ( ( Time != n1
| Event != pull )
& ( Time != n0
| Event != push ) )
| sP5_prd(Time,Event) )
& ! [Event,Time] :
( ( Time = n1
& Event = pull )
| ( Time = n0
& Event = push )
| ~ sP5_prd(Time,Event) ) ),
inference(miniscoping,[status(thm)],[f237]) ).
fof(f241,plain,
! [X0,X1] :
( X1 = pull
| X0 = n0
| ~ sP5_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f238]) ).
fof(f244,plain,
! [X0,X1] :
( X0 != n1
| X1 != pull
| sP5_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f238]) ).
fof(f272,plain,
! [X0] : less_or_equal(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f147]) ).
fof(f273,plain,
! [X0] : ~ less(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f189]) ).
fof(f274,plain,
! [X0] :
( happens(push,X0)
| sP0_prd(X0,backwards,pull) ),
inference(destructive_equality_resolution,[status(thm)],[f204]) ).
fof(f280,plain,
sP5_prd(n1,pull),
inference(destructive_equality_resolution,[status(thm)],[f244]) ).
fof(f285,plain,
less(n1,n2),
inference(resolution,[status(thm)],[f272,f157]) ).
fof(f339,plain,
! [X0,X1] :
( happens(X1,X0)
| ~ sP5_prd(X0,X1) ),
inference(resolution,[status(thm)],[f220,f126]) ).
fof(f366,plain,
happens(pull,n1),
inference(resolution,[status(thm)],[f339,f280]) ).
fof(f394,plain,
! [X0] :
( X0 = n0
| less(X0,n0)
| ~ less(X0,n1) ),
inference(resolution,[status(thm)],[f152,f145]) ).
fof(f395,plain,
! [X0] :
( X0 = n0
| ~ less(X0,n1) ),
inference(forward_subsumption_resolution,[status(thm)],[f394,f149]) ).
fof(f402,plain,
less(n0,n1),
inference(resolution,[status(thm)],[f153,f272]) ).
fof(f432,plain,
! [X0,X1] :
( holdsAt(X1,n2)
| ~ initiates(X0,X1,n1)
| ~ happens(X0,n1) ),
inference(paramodulation,[status(thm)],[f136,f90]) ).
fof(f584,plain,
! [X0] :
( initiates(pull,backwards,X0)
| happens(push,X0) ),
inference(resolution,[status(thm)],[f274,f108]) ).
fof(f677,plain,
! [X0,X1] :
( X0 = n2
| ~ happens(X1,X0)
| X0 = n2
| sP5_prd(X0,X1) ),
inference(resolution,[status(thm)],[f219,f125]) ).
fof(f680,plain,
! [X0,X1] :
( ~ happens(X1,X0)
| X0 = n2
| sP5_prd(X0,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f677]) ).
fof(f810,plain,
! [X0,X1] :
( X1 = pull
| X0 = n0
| ~ happens(X1,X0)
| X0 = n2 ),
inference(resolution,[status(thm)],[f680,f241]) ).
fof(f945,plain,
( holdsAt(backwards,n2)
| ~ happens(pull,n1)
| happens(push,n1) ),
inference(resolution,[status(thm)],[f584,f432]) ).
fof(f948,plain,
( holdsAt(backwards,n2)
| happens(push,n1) ),
inference(forward_subsumption_resolution,[status(thm)],[f945,f366]) ).
fof(f950,plain,
happens(push,n1),
inference(forward_subsumption_resolution,[status(thm)],[f948,f195]) ).
fof(f1117,plain,
( push = pull
| n1 = n0
| n1 = n2 ),
inference(resolution,[status(thm)],[f810,f950]) ).
fof(f1120,plain,
( n1 = n0
| n1 = n2 ),
inference(forward_subsumption_resolution,[status(thm)],[f1117,f128]) ).
fof(f1171,plain,
( n1 = n0
| less(n1,n1) ),
inference(paramodulation,[status(thm)],[f1120,f285]) ).
fof(f1185,plain,
n1 = n0,
inference(forward_subsumption_resolution,[status(thm)],[f1171,f395]) ).
fof(f1204,plain,
less(n1,n1),
inference(backward_demodulation,[status(thm)],[f1185,f402]) ).
fof(f1239,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1204,f273]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : CSR018+1 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n015.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 14:27:21 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.14/0.38 % Drodi V4.1.1
% 0.14/0.42 % Refutation found
% 0.14/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.46 % Elapsed time: 0.074712 seconds
% 0.14/0.46 % CPU time: 0.290924 seconds
% 0.14/0.46 % Total memory used: 110.070 MB
% 0.14/0.46 % Net memory used: 109.649 MB
%------------------------------------------------------------------------------