%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL321-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 01:07:25 PM UTC 2026
% Result : Unsatisfiable 0.09s 5.98s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 45 ( 22 unt; 2 def)
% Number of atoms : 71 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 55 ( 29 ~; 24 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 4 ( 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 : 77 ( 77 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A] : axiom(implies(or(A,A),A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : axiom(implies(A,or(B,A))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] : axiom(implies(or(A,B),or(B,A))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B,C] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y] : implies(X,Y) = or(not(X),Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X] :
( ~ axiom(X)
| theorem(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] :
( ~ theorem(Y)
| ~ theorem(implies(Y,X))
| theorem(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
~ theorem(or(implies(p,q),implies(p,not(q)))),
file('/export/starexec/sandbox/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(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(or(implies(p,q),implies(p,not(q)))),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f20,plain,
! [X0] : theorem(implies(or(X0,X0),X0)),
inference(resolution,[status(thm)],[f10,f16]) ).
fof(f21,plain,
! [X0,X1] : theorem(implies(X0,or(X1,X0))),
inference(resolution,[status(thm)],[f11,f16]) ).
fof(f22,plain,
! [X0,X1] : theorem(implies(or(X0,X1),or(X1,X0))),
inference(resolution,[status(thm)],[f12,f16]) ).
fof(f23,plain,
! [X0,X1,X2] : theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
inference(resolution,[status(thm)],[f13,f16]) ).
fof(f29,plain,
! [X0,X1] : theorem(implies(X0,implies(X1,X0))),
inference(paramodulation,[status(thm)],[f15,f21]) ).
fof(f44,plain,
! [X0,X1] :
( ~ theorem(X1)
| theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[f18,f21]) ).
fof(f45,plain,
! [X0,X1] :
( ~ theorem(X1)
| theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f29,f18]) ).
fof(f47,plain,
! [X0,X1] :
( ~ theorem(or(X1,X0))
| theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[f22,f18]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ~ theorem(or(X1,or(X0,X2)))
| theorem(or(X0,or(X1,X2))) ),
inference(resolution,[status(thm)],[f23,f18]) ).
fof(f62,plain,
! [X0,X1] : theorem(or(X0,implies(or(X1,X1),X1))),
inference(resolution,[status(thm)],[f44,f20]) ).
fof(f75,plain,
! [X0,X1,X2] : theorem(implies(X0,implies(X1,implies(X2,X1)))),
inference(resolution,[status(thm)],[f45,f29]) ).
fof(f82,plain,
! [X0,X1] :
( ~ theorem(implies(X1,X0))
| theorem(or(X0,not(X1))) ),
inference(paramodulation,[status(thm)],[f15,f47]) ).
fof(f117,definition,
! [X1] :
( sQ1_spl
<=> ~ theorem(X1) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f118,plain,
! [X0] :
( ~ sQ1_spl
| ~ theorem(X0) ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f122,plain,
! [X0,X1,X2] :
( ~ theorem(X2)
| theorem(implies(X0,implies(X1,X0))) ),
inference(resolution,[status(thm)],[f75,f18]) ).
fof(f125,definition,
! [X0,X1] :
( sQ2_spl
<=> theorem(implies(X0,implies(X1,X0))) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f126,plain,
! [X0,X1] :
( ~ sQ2_spl
| theorem(implies(X0,implies(X1,X0))) ),
inference(component_clause,[status(thm)],[f125]) ).
fof(f128,plain,
( sQ1_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f122,f125,f117]) ).
fof(f130,plain,
( ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f62,f118]) ).
fof(f183,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f130]) ).
fof(f309,plain,
! [X0,X1,X2] :
( ~ theorem(implies(X1,or(X0,X2)))
| theorem(or(X0,or(not(X1),X2))) ),
inference(paramodulation,[status(thm)],[f15,f51]) ).
fof(f311,plain,
! [X0,X1,X2] :
( ~ theorem(implies(X1,or(X0,X2)))
| theorem(or(X0,implies(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f15,f309]) ).
fof(f344,plain,
! [X0,X1] :
( ~ sQ2_spl
| theorem(or(implies(X0,X1),not(X1))) ),
inference(resolution,[status(thm)],[f82,f126]) ).
fof(f381,plain,
! [X0,X1,X2] :
( ~ sQ2_spl
| theorem(implies(X0,or(implies(X1,X2),not(X2)))) ),
inference(resolution,[status(thm)],[f344,f45]) ).
fof(f616,plain,
! [X0,X1,X2] :
( ~ sQ2_spl
| theorem(or(implies(X0,X1),implies(X2,not(X1)))) ),
inference(resolution,[status(thm)],[f311,f381]) ).
fof(f621,plain,
( ~ sQ2_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f19,f616]) ).
fof(f623,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f621]) ).
fof(f624,plain,
$false,
inference(sat_refutation,[status(thm)],[f128,f183,f623]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL321-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.93 % Computer : n002.cluster.edu
% 0.09/5.93 % Model : x86_64 x86_64
% 0.09/5.93 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.93 % Memory : 8046.5625MB
% 0.09/5.93 % OS : Linux 6.8.0-71-generic
% 0.09/5.93 % CPULimit : 300
% 0.09/5.93 % WCLimit : 300
% 0.09/5.93 % DateTime : Mon Sep 21 00:23:55 UTC 2026
% 0.09/5.93 % CPUTime :
% 0.09/5.94 % Drodi V4.1.1
% 0.09/5.98 % Refutation found
% 0.09/5.98 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/5.98 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/6.01 % Elapsed time: 0.063380 seconds
% 0.09/6.01 % CPU time: 0.188197 seconds
% 0.09/6.01 % Total memory used: 68.153 MB
% 0.09/6.01 % Net memory used: 67.500 MB
%------------------------------------------------------------------------------