%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL155-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 01:06:56 PM UTC 2026
% Result : Unsatisfiable 0.11s 15.44s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 12
% Syntax : Number of formulae : 65 ( 65 unt; 1 def)
% Number of atoms : 65 ( 64 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 82 ( 82 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : implies(truth,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y,Z] : implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] : implies(implies(X,Y),Y) = implies(implies(Y,X),X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] : implies(implies(not(X),not(Y)),implies(Y,X)) = truth,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] : or(X,Y) = implies(not(X),Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y] : or(X,Y) = or(Y,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] : and(X,Y) = not(or(not(X),not(Y))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Y] : xor(X,Y) = or(and(X,not(Y)),and(not(X),Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Y] : and_star(X,Y) = not(or(not(X),not(Y))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
not(truth) = falsehood,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
xor(x,x) != falsehood,
file('/export/starexec/sandbox2/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(f21,plain,
! [X0,X1] : implies(implies(not(X0),not(X1)),implies(X1,X0)) = truth,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f22,plain,
! [X0,X1] : or(X0,X1) = implies(not(X0),X1),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f24,plain,
! [X0,X1] : or(X0,X1) = or(X1,X0),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f25,plain,
! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f28,plain,
! [X0,X1] : xor(X0,X1) = or(and(X0,not(X1)),and(not(X0),X1)),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f30,plain,
! [X0,X1] : and_star(X0,X1) = not(or(not(X0),not(X1))),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f33,plain,
not(truth) = falsehood,
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f34,plain,
xor(x,x) != falsehood,
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f35,definition,
sF0_fnc = xor(x,x),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f36,plain,
sF0_fnc != falsehood,
inference(definition_folding,[],[f34,f35]) ).
fof(f59,plain,
! [X0,X1] : implies(X0,implies(implies(X0,X1),implies(truth,X1))) = truth,
inference(paramodulation,[status(thm)],[f18,f19]) ).
fof(f66,plain,
! [X0,X1] : implies(X0,implies(implies(X0,X1),X1)) = truth,
inference(forward_demodulation,[status(thm)],[f18,f59]) ).
fof(f106,plain,
! [X0] : implies(implies(truth,X0),X0) = truth,
inference(paramodulation,[status(thm)],[f18,f66]) ).
fof(f121,plain,
! [X0] : implies(X0,X0) = truth,
inference(forward_demodulation,[status(thm)],[f18,f106]) ).
fof(f133,plain,
! [X0] : or(X0,not(X0)) = truth,
inference(paramodulation,[status(thm)],[f22,f121]) ).
fof(f198,plain,
! [X0,X1] : implies(or(X0,not(X1)),implies(X1,X0)) = truth,
inference(forward_demodulation,[status(thm)],[f22,f21]) ).
fof(f202,plain,
! [X0] : implies(or(X0,falsehood),implies(truth,X0)) = truth,
inference(paramodulation,[status(thm)],[f33,f198]) ).
fof(f217,plain,
! [X0] : implies(or(X0,falsehood),X0) = truth,
inference(forward_demodulation,[status(thm)],[f18,f202]) ).
fof(f255,plain,
! [X0] : implies(or(falsehood,X0),X0) = truth,
inference(paramodulation,[status(thm)],[f24,f217]) ).
fof(f269,plain,
implies(truth,not(falsehood)) = truth,
inference(paramodulation,[status(thm)],[f133,f255]) ).
fof(f280,plain,
not(falsehood) = truth,
inference(forward_demodulation,[status(thm)],[f18,f269]) ).
fof(f286,plain,
! [X0] : or(falsehood,X0) = implies(truth,X0),
inference(paramodulation,[status(thm)],[f280,f22]) ).
fof(f293,plain,
! [X0] : or(falsehood,X0) = X0,
inference(forward_demodulation,[status(thm)],[f18,f286]) ).
fof(f298,plain,
! [X0] : or(X0,falsehood) = X0,
inference(paramodulation,[status(thm)],[f24,f293]) ).
fof(f302,plain,
! [X0] : implies(not(X0),implies(X0,falsehood)) = truth,
inference(paramodulation,[status(thm)],[f293,f198]) ).
fof(f311,plain,
! [X0] : or(X0,implies(X0,falsehood)) = truth,
inference(forward_demodulation,[status(thm)],[f22,f302]) ).
fof(f349,plain,
! [X0] : or(not(X0),or(X0,falsehood)) = truth,
inference(paramodulation,[status(thm)],[f22,f311]) ).
fof(f360,plain,
! [X0] : or(not(X0),X0) = truth,
inference(forward_demodulation,[status(thm)],[f298,f349]) ).
fof(f371,plain,
! [X0] : implies(truth,implies(X0,not(not(X0)))) = truth,
inference(paramodulation,[status(thm)],[f360,f198]) ).
fof(f376,plain,
! [X0] : implies(X0,not(not(X0))) = truth,
inference(forward_demodulation,[status(thm)],[f18,f371]) ).
fof(f387,plain,
! [X0] : implies(implies(not(not(X0)),X0),X0) = implies(truth,not(not(X0))),
inference(paramodulation,[status(thm)],[f376,f20]) ).
fof(f400,plain,
! [X0] : implies(or(not(X0),X0),X0) = implies(truth,not(not(X0))),
inference(forward_demodulation,[status(thm)],[f22,f387]) ).
fof(f401,plain,
! [X0] : implies(truth,X0) = implies(truth,not(not(X0))),
inference(forward_demodulation,[status(thm)],[f360,f400]) ).
fof(f402,plain,
! [X0] : X0 = implies(truth,not(not(X0))),
inference(forward_demodulation,[status(thm)],[f18,f401]) ).
fof(f403,plain,
! [X0] : X0 = not(not(X0)),
inference(forward_demodulation,[status(thm)],[f18,f402]) ).
fof(f421,plain,
! [X0,X1] : or(not(X0),X1) = implies(X0,X1),
inference(paramodulation,[status(thm)],[f403,f22]) ).
fof(f662,plain,
! [X0,X1] : and(X0,X1) = not(implies(X0,not(X1))),
inference(forward_demodulation,[status(thm)],[f421,f25]) ).
fof(f668,plain,
! [X0] : and(not(X0),X0) = not(truth),
inference(paramodulation,[status(thm)],[f121,f662]) ).
fof(f691,plain,
! [X0] : and(not(X0),X0) = falsehood,
inference(forward_demodulation,[status(thm)],[f33,f668]) ).
fof(f711,plain,
! [X0,X1] : and_star(X0,X1) = not(implies(X0,not(X1))),
inference(forward_demodulation,[status(thm)],[f421,f30]) ).
fof(f719,plain,
! [X0,X1] : xor(X0,X1) = or(and(X0,not(X1)),and_star(not(X0),X1)),
inference(backward_demodulation,[status(thm)],[f723,f28]) ).
fof(f723,plain,
! [X0,X1] : and_star(X0,X1) = and(X0,X1),
inference(forward_demodulation,[status(thm)],[f662,f711]) ).
fof(f733,plain,
! [X0,X1] : xor(X0,X1) = or(and_star(X0,not(X1)),and_star(not(X0),X1)),
inference(forward_demodulation,[status(thm)],[f723,f719]) ).
fof(f788,plain,
! [X0] : and_star(not(X0),X0) = falsehood,
inference(forward_demodulation,[status(thm)],[f723,f691]) ).
fof(f813,plain,
! [X0] : xor(not(not(X0)),X0) = or(falsehood,and_star(not(not(not(X0))),X0)),
inference(paramodulation,[status(thm)],[f788,f733]) ).
fof(f834,plain,
! [X0] : xor(X0,X0) = or(falsehood,and_star(not(not(not(X0))),X0)),
inference(forward_demodulation,[status(thm)],[f403,f813]) ).
fof(f835,plain,
! [X0] : xor(X0,X0) = and_star(not(not(not(X0))),X0),
inference(forward_demodulation,[status(thm)],[f293,f834]) ).
fof(f836,plain,
! [X0] : xor(X0,X0) = and_star(not(X0),X0),
inference(forward_demodulation,[status(thm)],[f403,f835]) ).
fof(f837,plain,
! [X0] : xor(X0,X0) = falsehood,
inference(forward_demodulation,[status(thm)],[f788,f836]) ).
fof(f902,plain,
sF0_fnc = falsehood,
inference(backward_demodulation,[status(thm)],[f837,f35]) ).
fof(f903,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f902,f36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL155-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/15.40 % Computer : n002.cluster.edu
% 0.11/15.40 % Model : x86_64 x86_64
% 0.11/15.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/15.40 % Memory : 8046.5625MB
% 0.11/15.40 % OS : Linux 6.8.0-71-generic
% 0.11/15.40 % CPULimit : 300
% 0.11/15.40 % WCLimit : 300
% 0.11/15.40 % DateTime : Mon Sep 21 00:10:33 UTC 2026
% 0.11/15.41 % CPUTime :
% 0.11/15.42 % Drodi V4.1.1
% 0.11/15.44 % Refutation found
% 0.11/15.44 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/15.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/15.47 % Elapsed time: 0.046291 seconds
% 0.11/15.47 % CPU time: 0.202243 seconds
% 0.11/15.47 % Total memory used: 6.684 MB
% 0.11/15.47 % Net memory used: 6.605 MB
%------------------------------------------------------------------------------