%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL182-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 01:07:01 PM UTC 2026
% Result : Unsatisfiable 0.07s 5.54s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 53 ( 31 unt; 2 def)
% Number of atoms : 84 ( 2 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 68 ( 37 ~; 29 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 92 ( 92 !; 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(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(p,q),implies(not(q),not(p)))),
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(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(p,q),implies(not(q),not(p)))),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f20,plain,
! [X0,X1,X2] : theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
inference(resolution,[status(thm)],[f14,f16]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ~ theorem(implies(X1,X2))
| theorem(implies(or(X0,X1),or(X0,X2))) ),
inference(resolution,[status(thm)],[f20,f18]) ).
fof(f26,plain,
! [X0,X1,X2] : theorem(implies(implies(X0,X1),implies(implies(X2,X0),or(not(X2),X1)))),
inference(paramodulation,[status(thm)],[f15,f20]) ).
fof(f28,plain,
! [X0,X1,X2] : theorem(implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1)))),
inference(forward_demodulation,[status(thm)],[f15,f26]) ).
fof(f32,plain,
! [X0,X1,X2,X3] : theorem(implies(or(X0,implies(X1,X2)),or(X0,implies(implies(X3,X1),implies(X3,X2))))),
inference(resolution,[status(thm)],[f28,f25]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ~ theorem(implies(X1,X2))
| theorem(implies(implies(X0,X1),implies(X0,X2))) ),
inference(resolution,[status(thm)],[f28,f18]) ).
fof(f34,plain,
! [X0] : theorem(implies(or(X0,X0),X0)),
inference(resolution,[status(thm)],[f10,f16]) ).
fof(f36,plain,
! [X0,X1] : theorem(implies(or(X0,or(X1,X1)),or(X0,X1))),
inference(resolution,[status(thm)],[f34,f25]) ).
fof(f40,plain,
! [X0,X1] : theorem(implies(X0,or(X1,X0))),
inference(resolution,[status(thm)],[f11,f16]) ).
fof(f42,plain,
! [X0,X1] : theorem(implies(or(X0,X1),or(X1,X0))),
inference(resolution,[status(thm)],[f12,f16]) ).
fof(f57,plain,
! [X0,X1] : theorem(implies(X0,implies(X1,X0))),
inference(paramodulation,[status(thm)],[f15,f40]) ).
fof(f60,plain,
! [X0,X1] :
( ~ theorem(X1)
| theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f57,f18]) ).
fof(f64,plain,
! [X0,X1] : theorem(implies(or(X0,not(X1)),implies(X1,X0))),
inference(paramodulation,[status(thm)],[f15,f42]) ).
fof(f73,definition,
! [X1] :
( sQ1_spl
<=> ~ theorem(X1) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f74,plain,
! [X0] :
( ~ sQ1_spl
| ~ theorem(X0) ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f79,plain,
! [X0,X1] : theorem(implies(implies(X0,not(X1)),implies(X1,not(X0)))),
inference(paramodulation,[status(thm)],[f15,f64]) ).
fof(f103,plain,
! [X0,X1] :
( ~ theorem(implies(X1,not(X0)))
| theorem(implies(X0,not(X1))) ),
inference(resolution,[status(thm)],[f79,f18]) ).
fof(f154,plain,
! [X0,X1,X2] :
( ~ theorem(implies(X2,X0))
| theorem(implies(X2,X1))
| ~ theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f33,f18]) ).
fof(f157,plain,
! [X0,X1] : theorem(implies(implies(X0,or(X1,X1)),or(not(X0),X1))),
inference(paramodulation,[status(thm)],[f15,f36]) ).
fof(f160,plain,
! [X0,X1] : theorem(implies(implies(X0,or(X1,X1)),implies(X0,X1))),
inference(forward_demodulation,[status(thm)],[f15,f157]) ).
fof(f216,plain,
( ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f32,f74]) ).
fof(f274,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f216]) ).
fof(f296,plain,
! [X0,X1,X2] : theorem(implies(X0,implies(X1,or(X2,X1)))),
inference(resolution,[status(thm)],[f40,f60]) ).
fof(f698,plain,
! [X0] :
( ~ theorem(implies(implies(p,q),X0))
| ~ theorem(implies(X0,implies(not(q),not(p)))) ),
inference(resolution,[status(thm)],[f154,f19]) ).
fof(f702,plain,
! [X0,X1,X2] :
( ~ theorem(X2)
| theorem(X1)
| ~ theorem(implies(X2,X0))
| ~ theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f154,f18]) ).
fof(f708,plain,
~ theorem(implies(implies(p,q),implies(p,not(not(q))))),
inference(resolution,[status(thm)],[f698,f79]) ).
fof(f852,plain,
~ theorem(implies(q,not(not(q)))),
inference(resolution,[status(thm)],[f708,f33]) ).
fof(f929,plain,
! [X0,X1,X2,X3] :
( ~ theorem(X3)
| theorem(X2)
| ~ theorem(implies(implies(X0,or(X1,X0)),X2)) ),
inference(resolution,[status(thm)],[f702,f296]) ).
fof(f1012,definition,
! [X0,X1,X2] :
( sQ43_spl
<=> ( theorem(X2)
| ~ theorem(implies(implies(X0,or(X1,X0)),X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f1013,plain,
! [X0,X1,X2] :
( ~ sQ43_spl
| theorem(X2)
| ~ theorem(implies(implies(X0,or(X1,X0)),X2)) ),
inference(component_clause,[status(thm)],[f1012]) ).
fof(f1015,plain,
( sQ1_spl
| sQ43_spl ),
inference(split_clause,[status(thm)],[f929,f1012,f73]) ).
fof(f1440,plain,
! [X0] :
( ~ sQ43_spl
| theorem(implies(X0,X0)) ),
inference(resolution,[status(thm)],[f1013,f160]) ).
fof(f1491,plain,
! [X0] :
( ~ sQ43_spl
| theorem(implies(X0,not(not(X0)))) ),
inference(resolution,[status(thm)],[f1440,f103]) ).
fof(f1495,plain,
( ~ sQ43_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f852,f1491]) ).
fof(f1496,plain,
~ sQ43_spl,
inference(contradiction_clause,[status(thm)],[f1495]) ).
fof(f1497,plain,
$false,
inference(sat_refutation,[status(thm)],[f274,f1015,f1496]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL182-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/5.32 % Computer : n012.cluster.edu
% 0.03/5.32 % Model : x86_64 x86_64
% 0.03/5.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/5.32 % Memory : 8046.5625MB
% 0.03/5.32 % OS : Linux 6.8.0-71-generic
% 0.03/5.32 % CPULimit : 300
% 0.03/5.32 % WCLimit : 300
% 0.03/5.32 % DateTime : Mon Sep 21 00:09:15 UTC 2026
% 0.03/5.32 % CPUTime :
% 0.03/5.32 % Drodi V4.1.1
% 0.07/5.54 % Refutation found
% 0.07/5.54 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.07/5.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.07/5.55 % Elapsed time: 0.219305 seconds
% 0.07/5.55 % CPU time: 1.580623 seconds
% 0.07/5.55 % Total memory used: 105.265 MB
% 0.07/5.55 % Net memory used: 100.615 MB
%------------------------------------------------------------------------------