%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL154-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 0.13s 0.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 12
% Syntax : Number of formulae : 70 ( 70 unt; 0 def)
% Number of atoms : 70 ( 69 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 86 ( 86 !; 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(f10,axiom,
! [X,Y] : and(X,Y) = and(Y,X),
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(f12,axiom,
! [X,Y] : xor(X,Y) = xor(Y,X),
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,falsehood) != x,
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(f27,plain,
! [X0,X1] : and(X0,X1) = and(X1,X0),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f28,plain,
! [X0,X1] : xor(X0,X1) = or(and(X0,not(X1)),and(not(X0),X1)),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f29,plain,
! [X0,X1] : xor(X0,X1) = xor(X1,X0),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f33,plain,
not(truth) = falsehood,
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f34,plain,
xor(x,falsehood) != x,
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f37,plain,
! [X0,X1] : implies(or(X0,not(X1)),implies(X1,X0)) = truth,
inference(backward_demodulation,[status(thm)],[f22,f21]) ).
fof(f45,plain,
xor(falsehood,x) != x,
inference(forward_demodulation,[status(thm)],[f29,f34]) ).
fof(f60,plain,
! [X0] : or(truth,X0) = implies(falsehood,X0),
inference(paramodulation,[status(thm)],[f33,f22]) ).
fof(f68,plain,
! [X0,X1] : xor(X0,X1) = or(and(not(X1),X0),and(not(X0),X1)),
inference(paramodulation,[status(thm)],[f27,f28]) ).
fof(f109,plain,
! [X0,X1] : implies(X0,implies(implies(X0,X1),implies(truth,X1))) = truth,
inference(paramodulation,[status(thm)],[f18,f19]) ).
fof(f119,plain,
! [X0,X1] : implies(X0,implies(implies(X0,X1),X1)) = truth,
inference(forward_demodulation,[status(thm)],[f18,f109]) ).
fof(f123,plain,
! [X0,X1] : or(X0,implies(implies(not(X0),X1),X1)) = truth,
inference(paramodulation,[status(thm)],[f22,f119]) ).
fof(f124,plain,
! [X0] : implies(implies(truth,X0),X0) = truth,
inference(paramodulation,[status(thm)],[f18,f119]) ).
fof(f135,plain,
! [X0,X1] : or(X0,implies(or(X0,X1),X1)) = truth,
inference(forward_demodulation,[status(thm)],[f22,f123]) ).
fof(f136,plain,
! [X0] : implies(X0,X0) = truth,
inference(forward_demodulation,[status(thm)],[f18,f124]) ).
fof(f145,plain,
! [X0] : or(X0,not(X0)) = truth,
inference(paramodulation,[status(thm)],[f22,f136]) ).
fof(f198,plain,
! [X0] : implies(or(X0,falsehood),implies(truth,X0)) = truth,
inference(paramodulation,[status(thm)],[f33,f37]) ).
fof(f210,plain,
! [X0] : implies(or(X0,falsehood),X0) = truth,
inference(forward_demodulation,[status(thm)],[f18,f198]) ).
fof(f233,plain,
! [X0] : and(truth,X0) = not(or(falsehood,not(X0))),
inference(paramodulation,[status(thm)],[f33,f25]) ).
fof(f343,plain,
! [X0] : implies(X0,X0) = implies(implies(X0,truth),truth),
inference(paramodulation,[status(thm)],[f18,f20]) ).
fof(f364,plain,
! [X0] : truth = implies(implies(X0,truth),truth),
inference(forward_demodulation,[status(thm)],[f136,f343]) ).
fof(f370,plain,
! [X0] : implies(falsehood,X0) = or(X0,truth),
inference(paramodulation,[status(thm)],[f60,f24]) ).
fof(f386,plain,
! [X0] : implies(or(falsehood,X0),X0) = truth,
inference(paramodulation,[status(thm)],[f24,f210]) ).
fof(f506,plain,
! [X0] : or(X0,implies(implies(falsehood,X0),truth)) = truth,
inference(paramodulation,[status(thm)],[f370,f135]) ).
fof(f514,plain,
implies(truth,not(falsehood)) = truth,
inference(paramodulation,[status(thm)],[f145,f386]) ).
fof(f531,plain,
not(falsehood) = truth,
inference(forward_demodulation,[status(thm)],[f18,f514]) ).
fof(f544,plain,
! [X0] : and(X0,falsehood) = not(or(not(X0),truth)),
inference(paramodulation,[status(thm)],[f531,f25]) ).
fof(f552,plain,
! [X0] : or(falsehood,X0) = implies(truth,X0),
inference(paramodulation,[status(thm)],[f531,f22]) ).
fof(f558,plain,
! [X0] : and(X0,falsehood) = not(implies(falsehood,not(X0))),
inference(forward_demodulation,[status(thm)],[f370,f544]) ).
fof(f572,plain,
! [X0] : and(truth,X0) = not(not(X0)),
inference(backward_demodulation,[status(thm)],[f579,f233]) ).
fof(f579,plain,
! [X0] : or(falsehood,X0) = X0,
inference(forward_demodulation,[status(thm)],[f18,f552]) ).
fof(f607,plain,
! [X0] : or(X0,falsehood) = X0,
inference(paramodulation,[status(thm)],[f24,f579]) ).
fof(f1022,plain,
! [X0] : truth = implies(or(X0,truth),truth),
inference(paramodulation,[status(thm)],[f22,f364]) ).
fof(f1044,plain,
! [X0] : or(X0,truth) = truth,
inference(backward_demodulation,[status(thm)],[f1047,f506]) ).
fof(f1047,plain,
! [X0] : truth = implies(implies(falsehood,X0),truth),
inference(forward_demodulation,[status(thm)],[f370,f1022]) ).
fof(f1100,plain,
! [X0] : and(X0,falsehood) = not(truth),
inference(backward_demodulation,[status(thm)],[f1105,f558]) ).
fof(f1105,plain,
! [X0] : implies(falsehood,X0) = truth,
inference(forward_demodulation,[status(thm)],[f370,f1044]) ).
fof(f1127,plain,
! [X0] : and(X0,falsehood) = falsehood,
inference(forward_demodulation,[status(thm)],[f33,f1100]) ).
fof(f1156,plain,
! [X0] : implies(implies(X0,falsehood),falsehood) = implies(truth,X0),
inference(paramodulation,[status(thm)],[f1105,f20]) ).
fof(f1169,plain,
! [X0] : implies(implies(X0,falsehood),falsehood) = X0,
inference(forward_demodulation,[status(thm)],[f18,f1156]) ).
fof(f1184,plain,
! [X0] : xor(falsehood,X0) = or(falsehood,and(not(falsehood),X0)),
inference(paramodulation,[status(thm)],[f1127,f68]) ).
fof(f1216,plain,
! [X0] : xor(falsehood,X0) = and(not(falsehood),X0),
inference(forward_demodulation,[status(thm)],[f579,f1184]) ).
fof(f1217,plain,
! [X0] : xor(falsehood,X0) = and(truth,X0),
inference(forward_demodulation,[status(thm)],[f531,f1216]) ).
fof(f1219,plain,
not(not(x)) != x,
inference(backward_demodulation,[status(thm)],[f1223,f45]) ).
fof(f1223,plain,
! [X0] : xor(falsehood,X0) = not(not(X0)),
inference(forward_demodulation,[status(thm)],[f572,f1217]) ).
fof(f1811,plain,
! [X0] : implies(or(X0,falsehood),falsehood) = not(X0),
inference(paramodulation,[status(thm)],[f22,f1169]) ).
fof(f1836,plain,
! [X0] : not(implies(X0,falsehood)) = X0,
inference(backward_demodulation,[status(thm)],[f1847,f1169]) ).
fof(f1847,plain,
! [X0] : implies(X0,falsehood) = not(X0),
inference(forward_demodulation,[status(thm)],[f607,f1811]) ).
fof(f1887,plain,
x != x,
inference(backward_demodulation,[status(thm)],[f1918,f1219]) ).
fof(f1918,plain,
! [X0] : not(not(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f1847,f1836]) ).
fof(f1924,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f1887]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL154-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n006.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 00:07:28 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.13/0.41 % Refutation found
% 0.13/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.43 % Elapsed time: 0.066949 seconds
% 0.13/0.43 % CPU time: 0.364969 seconds
% 0.13/0.43 % Total memory used: 14.950 MB
% 0.13/0.43 % Net memory used: 14.664 MB
%------------------------------------------------------------------------------