%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL109-5 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 01:06:50 PM UTC 2026
% Result : Unsatisfiable 0.18s 0.47s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 9
% Syntax : Number of formulae : 41 ( 28 unt; 0 def)
% Number of atoms : 54 ( 30 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 29 ( 16 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 71 ( 71 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : implies(truth,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y,Z] : implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] : implies(implies(X,Y),Y) = implies(implies(Y,X),X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] : big_V(X,Y) = implies(implies(X,Y),Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y] :
( implies(X,Y) = truth
| ~ ordered(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] :
( ordered(X,Y)
| implies(X,Y) != truth ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y,Z] :
( ordered(implies(X,Z),implies(Y,Z))
| ~ ordered(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Y,Z] :
( ordered(Y,implies(X,Z))
| ~ ordered(X,implies(Y,Z)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
big_V(implies(x,y),implies(y,x)) != truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,plain,
! [X0] : implies(truth,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f19,plain,
! [X0,X1,X2] : implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))) = truth,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f20,plain,
! [X0,X1] : implies(implies(X0,X1),X1) = implies(implies(X1,X0),X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f22,plain,
! [X0,X1] : big_V(X0,X1) = implies(implies(X0,X1),X1),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f24,plain,
! [X0,X1] :
( implies(X0,X1) = truth
| ~ ordered(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f25,plain,
! [X0,X1] :
( ordered(X0,X1)
| implies(X0,X1) != truth ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f26,plain,
! [X,Y] :
( ! [Z] : ordered(implies(X,Z),implies(Y,Z))
| ~ ordered(X,Y) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ordered(implies(X0,X2),implies(X1,X2))
| ~ ordered(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ordered(X1,implies(X0,X2))
| ~ ordered(X0,implies(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f36,plain,
big_V(implies(x,y),implies(y,x)) != truth,
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f37,plain,
! [X0,X1] : implies(implies(X0,X1),X1) = big_V(X1,X0),
inference(backward_demodulation,[status(thm)],[f22,f20]) ).
fof(f39,plain,
! [X0,X1] : big_V(X0,X1) = big_V(X1,X0),
inference(forward_demodulation,[status(thm)],[f22,f37]) ).
fof(f46,plain,
! [X0] : big_V(truth,X0) = implies(X0,X0),
inference(paramodulation,[status(thm)],[f18,f22]) ).
fof(f49,plain,
! [X0,X1] : implies(X0,implies(implies(X0,X1),implies(truth,X1))) = truth,
inference(paramodulation,[status(thm)],[f18,f19]) ).
fof(f59,plain,
! [X0,X1] : implies(X0,implies(implies(X0,X1),X1)) = truth,
inference(forward_demodulation,[status(thm)],[f18,f49]) ).
fof(f60,plain,
! [X0,X1] : implies(X0,big_V(X0,X1)) = truth,
inference(forward_demodulation,[status(thm)],[f22,f59]) ).
fof(f67,plain,
! [X0] : big_V(X0,truth) = implies(X0,X0),
inference(paramodulation,[status(thm)],[f39,f46]) ).
fof(f78,plain,
! [X0] : implies(truth,implies(X0,X0)) = truth,
inference(paramodulation,[status(thm)],[f46,f60]) ).
fof(f92,plain,
! [X0] : big_V(X0,truth) = truth,
inference(backward_demodulation,[status(thm)],[f93,f67]) ).
fof(f93,plain,
! [X0] : implies(X0,X0) = truth,
inference(forward_demodulation,[status(thm)],[f18,f78]) ).
fof(f126,plain,
! [X0] : implies(X0,truth) = truth,
inference(paramodulation,[status(thm)],[f92,f60]) ).
fof(f282,plain,
! [X0,X1] :
( ordered(X1,implies(X0,truth))
| ~ ordered(X0,truth) ),
inference(paramodulation,[status(thm)],[f126,f30]) ).
fof(f286,plain,
! [X0,X1] :
( ordered(X1,truth)
| ~ ordered(X0,truth) ),
inference(forward_demodulation,[status(thm)],[f126,f282]) ).
fof(f287,plain,
! [X0,X1] :
( implies(X1,truth) != truth
| ordered(X0,truth) ),
inference(resolution,[status(thm)],[f286,f25]) ).
fof(f288,plain,
! [X0] :
( truth != truth
| ordered(X0,truth) ),
inference(forward_demodulation,[status(thm)],[f126,f287]) ).
fof(f295,plain,
! [X0] : ordered(X0,truth),
inference(trivial_equality_resolution,[status(thm)],[f288]) ).
fof(f297,plain,
! [X0,X1] : ordered(implies(X0,X1),implies(truth,X1)),
inference(resolution,[status(thm)],[f295,f27]) ).
fof(f300,plain,
! [X0,X1] : ordered(implies(X0,X1),X1),
inference(forward_demodulation,[status(thm)],[f18,f297]) ).
fof(f323,plain,
! [X0,X1] : implies(implies(X0,X1),X1) = truth,
inference(resolution,[status(thm)],[f300,f24]) ).
fof(f334,plain,
truth != truth,
inference(backward_demodulation,[status(thm)],[f366,f36]) ).
fof(f366,plain,
! [X0,X1] : big_V(X0,X1) = truth,
inference(forward_demodulation,[status(thm)],[f22,f323]) ).
fof(f370,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f334]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL109-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n005.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Mon Sep 21 00:05:33 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.46 % Drodi V4.1.1
% 0.18/0.47 % Refutation found
% 0.18/0.47 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.18/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.26/0.54 % Elapsed time: 0.081813 seconds
% 0.26/0.54 % CPU time: 0.130338 seconds
% 0.26/0.54 % Total memory used: 11.035 MB
% 0.26/0.54 % Net memory used: 10.983 MB
%------------------------------------------------------------------------------