%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL111-2 : 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 0.23s 0.73s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 4
% Syntax : Number of formulae : 39 ( 39 unt; 0 def)
% Number of atoms : 39 ( 38 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 102 ( 102 !; 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,negated_conjecture,
implies(implies(x,y),implies(implies(z,x),implies(z,y))) != truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,plain,
! [X0] : implies(truth,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f7,plain,
! [X0,X1,X2] : implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))) = truth,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f8,plain,
! [X0,X1] : implies(implies(X0,X1),X1) = implies(implies(X1,X0),X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f10,plain,
implies(implies(x,y),implies(implies(z,x),implies(z,y))) != truth,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f19,plain,
! [X0] : implies(X0,X0) = implies(implies(X0,truth),truth),
inference(paramodulation,[status(thm)],[f6,f8]) ).
fof(f36,plain,
! [X0,X1,X2,X3] : implies(truth,implies(implies(implies(implies(X0,X1),implies(X2,X1)),X3),implies(implies(X2,X0),X3))) = truth,
inference(paramodulation,[status(thm)],[f7,f7]) ).
fof(f58,plain,
! [X0,X1,X2,X3] : implies(implies(implies(implies(X0,X1),implies(X2,X1)),X3),implies(implies(X2,X0),X3)) = truth,
inference(forward_demodulation,[status(thm)],[f6,f36]) ).
fof(f66,plain,
! [X0,X1,X2] : implies(implies(implies(implies(X0,X1),implies(X2,X1)),implies(X2,X1)),implies(implies(X0,X2),implies(X0,X1))) = truth,
inference(paramodulation,[status(thm)],[f8,f58]) ).
fof(f69,plain,
! [X0,X1,X2,X3] : implies(implies(truth,X0),implies(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))),X0)) = truth,
inference(paramodulation,[status(thm)],[f58,f58]) ).
fof(f106,plain,
! [X0,X1,X2,X3] : implies(X0,implies(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))),X0)) = truth,
inference(forward_demodulation,[status(thm)],[f6,f69]) ).
fof(f107,plain,
! [X0] : implies(X0,implies(truth,X0)) = truth,
inference(forward_demodulation,[status(thm)],[f7,f106]) ).
fof(f108,plain,
! [X0] : truth = implies(implies(X0,truth),truth),
inference(backward_demodulation,[status(thm)],[f115,f19]) ).
fof(f115,plain,
! [X0] : implies(X0,X0) = truth,
inference(forward_demodulation,[status(thm)],[f6,f107]) ).
fof(f351,plain,
! [X0,X1,X2,X3] : implies(implies(implies(truth,implies(X0,implies(implies(X1,X2),implies(X3,X2)))),implies(X0,implies(implies(X1,X2),implies(X3,X2)))),implies(implies(implies(X3,X1),X0),implies(implies(X3,X1),implies(implies(X1,X2),implies(X3,X2))))) = truth,
inference(paramodulation,[status(thm)],[f7,f66]) ).
fof(f355,plain,
! [X0,X1] : implies(implies(implies(truth,implies(X0,X1)),implies(X0,X1)),implies(implies(X1,X0),implies(X1,X1))) = truth,
inference(paramodulation,[status(thm)],[f115,f66]) ).
fof(f358,plain,
! [X0,X1,X2,X3] : implies(implies(implies(implies(X0,implies(implies(X1,X2),implies(X1,X3))),truth),implies(implies(implies(implies(X1,X3),implies(X2,X3)),implies(X2,X3)),implies(implies(X1,X2),implies(X1,X3)))),implies(implies(X0,implies(implies(implies(X1,X3),implies(X2,X3)),implies(X2,X3))),implies(X0,implies(implies(X1,X2),implies(X1,X3))))) = truth,
inference(paramodulation,[status(thm)],[f66,f66]) ).
fof(f452,plain,
! [X0,X1,X2,X3] : implies(implies(implies(implies(X0,implies(implies(X1,X2),implies(X3,X2))),truth),truth),implies(implies(implies(X3,X1),X0),implies(implies(X3,X1),implies(implies(X1,X2),implies(X3,X2))))) = truth,
inference(forward_demodulation,[status(thm)],[f8,f351]) ).
fof(f453,plain,
! [X0,X1,X2,X3] : implies(truth,implies(implies(implies(X0,X1),X2),implies(implies(X0,X1),implies(implies(X1,X3),implies(X0,X3))))) = truth,
inference(forward_demodulation,[status(thm)],[f108,f452]) ).
fof(f454,plain,
! [X0,X1,X2,X3] : implies(implies(implies(X0,X1),X2),implies(implies(X0,X1),implies(implies(X1,X3),implies(X0,X3)))) = truth,
inference(forward_demodulation,[status(thm)],[f6,f453]) ).
fof(f482,plain,
! [X0,X1,X2] : implies(implies(implies(X0,X1),X2),truth) = truth,
inference(forward_demodulation,[status(thm)],[f7,f454]) ).
fof(f486,plain,
! [X0,X1] : implies(implies(implies(implies(X0,X1),truth),truth),implies(implies(X1,X0),implies(X1,X1))) = truth,
inference(forward_demodulation,[status(thm)],[f8,f355]) ).
fof(f487,plain,
! [X0,X1] : implies(truth,implies(implies(X0,X1),implies(X0,X0))) = truth,
inference(forward_demodulation,[status(thm)],[f482,f486]) ).
fof(f488,plain,
! [X0,X1] : implies(implies(X0,X1),implies(X0,X0)) = truth,
inference(forward_demodulation,[status(thm)],[f6,f487]) ).
fof(f501,plain,
! [X0,X1] : implies(implies(X0,X1),truth) = truth,
inference(forward_demodulation,[status(thm)],[f115,f488]) ).
fof(f510,plain,
! [X0,X1,X2,X3] : implies(implies(truth,implies(implies(implies(implies(X0,X1),implies(X2,X1)),implies(X2,X1)),implies(implies(X0,X2),implies(X0,X1)))),implies(implies(X3,implies(implies(implies(X0,X1),implies(X2,X1)),implies(X2,X1))),implies(X3,implies(implies(X0,X2),implies(X0,X1))))) = truth,
inference(forward_demodulation,[status(thm)],[f501,f358]) ).
fof(f511,plain,
! [X0,X1,X2,X3] : implies(implies(implies(implies(implies(X0,X1),implies(X2,X1)),implies(X2,X1)),implies(implies(X0,X2),implies(X0,X1))),implies(implies(X3,implies(implies(implies(X0,X1),implies(X2,X1)),implies(X2,X1))),implies(X3,implies(implies(X0,X2),implies(X0,X1))))) = truth,
inference(forward_demodulation,[status(thm)],[f6,f510]) ).
fof(f512,plain,
! [X0,X1,X2,X3] : implies(truth,implies(implies(X0,implies(implies(implies(X1,X2),implies(X3,X2)),implies(X3,X2))),implies(X0,implies(implies(X1,X3),implies(X1,X2))))) = truth,
inference(forward_demodulation,[status(thm)],[f66,f511]) ).
fof(f513,plain,
! [X0,X1,X2,X3] : implies(implies(X0,implies(implies(implies(X1,X2),implies(X3,X2)),implies(X3,X2))),implies(X0,implies(implies(X1,X3),implies(X1,X2)))) = truth,
inference(forward_demodulation,[status(thm)],[f6,f512]) ).
fof(f740,plain,
! [X0,X1,X2,X3] : implies(truth,implies(implies(implies(implies(implies(X0,X1),X2),implies(implies(X3,X1),X2)),implies(X0,X1)),implies(implies(X3,X0),implies(X3,X1)))) = truth,
inference(paramodulation,[status(thm)],[f58,f513]) ).
fof(f835,plain,
! [X0,X1,X2,X3] : implies(implies(implies(implies(implies(X0,X1),X2),implies(implies(X3,X1),X2)),implies(X0,X1)),implies(implies(X3,X0),implies(X3,X1))) = truth,
inference(forward_demodulation,[status(thm)],[f6,f740]) ).
fof(f1309,plain,
! [X0,X1,X2,X3] : implies(implies(implies(implies(implies(X0,X1),implies(implies(X1,X2),implies(X3,X2))),truth),implies(X0,X1)),implies(implies(X3,X0),implies(X3,X1))) = truth,
inference(paramodulation,[status(thm)],[f7,f835]) ).
fof(f1463,plain,
! [X0,X1,X2] : implies(implies(truth,implies(X0,X1)),implies(implies(X2,X0),implies(X2,X1))) = truth,
inference(forward_demodulation,[status(thm)],[f501,f1309]) ).
fof(f1464,plain,
truth != truth,
inference(backward_demodulation,[status(thm)],[f1469,f10]) ).
fof(f1469,plain,
! [X0,X1,X2] : implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1))) = truth,
inference(forward_demodulation,[status(thm)],[f6,f1463]) ).
fof(f1628,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f1464]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL111-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n005.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.46 % CPULimit : 300
% 0.18/0.46 % WCLimit : 300
% 0.18/0.46 % DateTime : Mon Sep 21 00:05:19 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.47 % Drodi V4.1.1
% 0.23/0.73 % Refutation found
% 0.23/0.73 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.23/0.73 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.23/0.77 % Elapsed time: 0.298826 seconds
% 0.23/0.77 % CPU time: 1.817417 seconds
% 0.23/0.77 % Total memory used: 44.101 MB
% 0.23/0.77 % Net memory used: 43.381 MB
%------------------------------------------------------------------------------