%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL218-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 01:07:11 PM UTC 2026
% Result : Unsatisfiable 39.16s 5.39s
% Output : CNFRefutation 23.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 65 ( 32 unt; 2 def)
% Number of atoms : 109 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 94 ( 50 ~; 42 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 119 ( 119 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A] : axiom(implies(or(A,A),A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : axiom(implies(A,or(B,A))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] : axiom(implies(or(A,B),or(B,A))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B,C] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y] : implies(X,Y) = or(not(X),Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X] :
( ~ axiom(X)
| theorem(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] :
( ~ theorem(Y)
| ~ theorem(implies(Y,X))
| theorem(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
~ theorem(implies(implies(or(p,q),q),implies(p,q))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,plain,
! [X0] : axiom(implies(or(X0,X0),X0)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f11,plain,
! [X0,X1] : axiom(implies(X0,or(X1,X0))),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f12,plain,
! [X0,X1] : axiom(implies(or(X0,X1),or(X1,X0))),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f13,plain,
! [X0,X1,X2] : axiom(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f14,plain,
! [X0,X1,X2] : axiom(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f15,plain,
! [X0,X1] : implies(X0,X1) = or(not(X0),X1),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f16,plain,
! [X0] :
( ~ axiom(X0)
| theorem(X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f17,plain,
! [Y] :
( ~ theorem(Y)
| ! [X] :
( ~ theorem(implies(Y,X))
| theorem(X) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f18,plain,
! [X0,X1] :
( ~ theorem(X1)
| ~ theorem(implies(X1,X0))
| theorem(X0) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f19,plain,
~ theorem(implies(implies(or(p,q),q),implies(p,q))),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f20,plain,
! [X0] : theorem(implies(or(X0,X0),X0)),
inference(resolution,[status(thm)],[f10,f16]) ).
fof(f22,plain,
! [X0,X1] : theorem(implies(X0,or(X1,X0))),
inference(resolution,[status(thm)],[f11,f16]) ).
fof(f23,plain,
! [X0,X1] :
( ~ theorem(X1)
| theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[f22,f18]) ).
fof(f25,plain,
! [X0,X1] :
( ~ theorem(X1)
| theorem(implies(X0,X1)) ),
inference(paramodulation,[status(thm)],[f15,f23]) ).
fof(f36,definition,
! [X1] :
( sQ1_spl
<=> ~ theorem(X1) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f37,plain,
! [X0] :
( ~ sQ1_spl
| ~ theorem(X0) ),
inference(component_clause,[status(thm)],[f36]) ).
fof(f44,plain,
! [X0,X1] : theorem(implies(or(X0,X1),or(X1,X0))),
inference(resolution,[status(thm)],[f12,f16]) ).
fof(f101,plain,
! [X0,X1,X2] : axiom(implies(implies(X0,or(X1,X2)),or(X1,or(not(X0),X2)))),
inference(paramodulation,[status(thm)],[f15,f13]) ).
fof(f105,plain,
! [X0,X1,X2] : axiom(implies(implies(X0,or(X1,X2)),or(X1,implies(X0,X2)))),
inference(forward_demodulation,[status(thm)],[f15,f101]) ).
fof(f109,plain,
! [X0,X1,X2] : axiom(implies(implies(X0,X1),implies(implies(X2,X0),or(not(X2),X1)))),
inference(paramodulation,[status(thm)],[f15,f14]) ).
fof(f111,plain,
! [X0,X1,X2] : axiom(implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1)))),
inference(forward_demodulation,[status(thm)],[f15,f109]) ).
fof(f113,plain,
! [X0,X1] :
( ~ axiom(implies(X1,X0))
| ~ theorem(X1)
| theorem(X0) ),
inference(resolution,[status(thm)],[f18,f16]) ).
fof(f131,plain,
! [X0,X1,X2] : theorem(or(X0,implies(X1,or(X2,X1)))),
inference(resolution,[status(thm)],[f22,f23]) ).
fof(f137,plain,
! [X0,X1] :
( ~ axiom(X1)
| theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f25,f16]) ).
fof(f159,plain,
! [X0,X1,X2] :
( ~ axiom(implies(implies(or(X1,X2),or(X2,X1)),X0))
| theorem(X0) ),
inference(resolution,[status(thm)],[f113,f44]) ).
fof(f160,plain,
! [X0,X1] :
( ~ axiom(implies(implies(or(X1,X1),X1),X0))
| theorem(X0) ),
inference(resolution,[status(thm)],[f113,f20]) ).
fof(f161,plain,
! [X0,X1,X2] :
( ~ axiom(implies(implies(X1,or(X2,X1)),X0))
| theorem(X0) ),
inference(resolution,[status(thm)],[f113,f22]) ).
fof(f166,plain,
! [X0,X1] :
( ~ theorem(X1)
| theorem(X0)
| ~ axiom(X0) ),
inference(resolution,[status(thm)],[f137,f18]) ).
fof(f171,definition,
! [X0] :
( sQ4_spl
<=> ( theorem(X0)
| ~ axiom(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f172,plain,
! [X0] :
( ~ sQ4_spl
| theorem(X0)
| ~ axiom(X0) ),
inference(component_clause,[status(thm)],[f171]) ).
fof(f174,plain,
( sQ1_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f166,f171,f36]) ).
fof(f178,plain,
( ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f44,f37]) ).
fof(f184,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f178]) ).
fof(f210,plain,
! [X0,X1,X2] : axiom(implies(implies(X0,implies(X1,X2)),or(not(X1),implies(X0,X2)))),
inference(paramodulation,[status(thm)],[f15,f105]) ).
fof(f212,plain,
! [X0,X1,X2] : axiom(implies(implies(X0,implies(X1,X2)),implies(X1,implies(X0,X2)))),
inference(forward_demodulation,[status(thm)],[f15,f210]) ).
fof(f241,plain,
! [X0,X1,X2] :
( ~ theorem(implies(X1,X2))
| theorem(implies(or(X0,X1),or(X0,X2))) ),
inference(resolution,[status(thm)],[f113,f14]) ).
fof(f385,plain,
! [X0,X1,X2] :
( ~ theorem(implies(X1,X2))
| theorem(implies(implies(X0,X1),implies(X0,X2))) ),
inference(resolution,[status(thm)],[f111,f113]) ).
fof(f395,plain,
! [X0,X1,X2] : theorem(implies(implies(X0,or(X1,X2)),implies(X0,or(X2,X1)))),
inference(resolution,[status(thm)],[f159,f111]) ).
fof(f431,plain,
! [X0,X1] : theorem(implies(implies(X0,or(X1,X1)),implies(X0,X1))),
inference(resolution,[status(thm)],[f160,f111]) ).
fof(f438,plain,
! [X0,X1] : theorem(or(X0,implies(X1,X1))),
inference(resolution,[status(thm)],[f161,f105]) ).
fof(f510,plain,
! [X0,X1,X2] :
( ~ theorem(implies(X1,implies(X0,X2)))
| theorem(implies(X0,implies(X1,X2))) ),
inference(resolution,[status(thm)],[f212,f113]) ).
fof(f511,plain,
! [X0,X1] :
( ~ theorem(implies(X0,or(X1,X1)))
| theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f431,f18]) ).
fof(f550,plain,
! [X0,X1] :
( ~ theorem(X0)
| theorem(X1)
| ~ theorem(implies(X0,or(X1,X1))) ),
inference(resolution,[status(thm)],[f511,f18]) ).
fof(f830,plain,
! [X0,X1,X2] :
( ~ theorem(implies(X2,X0))
| theorem(implies(X2,X1))
| ~ theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f385,f18]) ).
fof(f886,plain,
! [X0,X1] :
( ~ theorem(implies(X1,X0))
| ~ theorem(or(X0,X1))
| theorem(X0) ),
inference(resolution,[status(thm)],[f550,f241]) ).
fof(f1378,plain,
! [X0,X1,X2] :
( ~ theorem(implies(implies(X1,or(X2,X1)),X0))
| theorem(X0) ),
inference(resolution,[status(thm)],[f886,f131]) ).
fof(f1384,plain,
! [X0,X1] :
( ~ theorem(implies(implies(X1,X1),X0))
| theorem(X0) ),
inference(resolution,[status(thm)],[f886,f438]) ).
fof(f1431,plain,
! [X0,X1] :
( ~ sQ4_spl
| ~ axiom(implies(implies(X1,X1),X0))
| theorem(X0) ),
inference(resolution,[status(thm)],[f1384,f172]) ).
fof(f1589,plain,
! [X0,X1] :
( ~ sQ4_spl
| theorem(implies(X0,implies(implies(X0,X1),X1))) ),
inference(resolution,[status(thm)],[f1431,f212]) ).
fof(f2180,plain,
~ theorem(implies(p,implies(implies(or(p,q),q),q))),
inference(resolution,[status(thm)],[f510,f19]) ).
fof(f2810,plain,
! [X0,X1] : theorem(implies(X0,or(X0,X1))),
inference(resolution,[status(thm)],[f1378,f395]) ).
fof(f3280,plain,
! [X0] :
( ~ theorem(implies(p,X0))
| ~ theorem(implies(X0,implies(implies(or(p,q),q),q))) ),
inference(resolution,[status(thm)],[f830,f2180]) ).
fof(f7686,plain,
( ~ sQ4_spl
| ~ theorem(implies(p,or(p,q))) ),
inference(resolution,[status(thm)],[f3280,f1589]) ).
fof(f7705,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7686,f2810]) ).
fof(f7706,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f7705]) ).
fof(f7707,plain,
$false,
inference(sat_refutation,[status(thm)],[f174,f184,f7706]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL218-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n014.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.36 % CPULimit : 300
% 0.07/0.36 % WCLimit : 300
% 0.07/0.36 % DateTime : Mon Sep 21 00:11:35 UTC 2026
% 0.07/0.36 % CPUTime :
% 0.07/0.37 % Drodi V4.1.1
% 39.16/5.39 % Refutation found
% 39.16/5.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 39.16/5.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 23.25/5.47 % Elapsed time: 5.091559 seconds
% 23.25/5.47 % CPU time: 39.769748 seconds
% 23.25/5.47 % Total memory used: 249.692 MB
% 23.25/5.47 % Net memory used: 223.781 MB
%------------------------------------------------------------------------------