%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL160-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 01:06:57 PM UTC 2026
% Result : Unsatisfiable 13.51s 2.15s
% Output : CNFRefutation 6.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 14
% Syntax : Number of formulae : 150 ( 150 unt; 0 def)
% Number of atoms : 150 ( 149 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 25 ( 25 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 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 : 205 ( 205 !; 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(f4,axiom,
! [X,Y] : implies(implies(not(X),not(Y)),implies(Y,X)) = truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] : or(X,Y) = implies(not(X),Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y,Z] : or(or(X,Y),Z) = or(X,or(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y] : or(X,Y) = or(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] : and(X,Y) = not(or(not(X),not(Y))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y] : and(X,Y) = and(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Y] : xor(X,Y) = or(and(X,not(Y)),and(not(X),Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X,Y] : xor(X,Y) = xor(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Y] : and_star(X,Y) = not(or(not(X),not(Y))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
not(truth) = falsehood,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
and_star(xor(and_star(xor(truth,x),y),truth),y) != and_star(xor(and_star(xor(truth,y),x),truth),x),
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(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(f23,plain,
! [X0,X1,X2] : or(or(X0,X1),X2) = or(X0,or(X1,X2)),
inference(cnf_transformation,[status(thm)],[f6]) ).
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(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,
and_star(xor(and_star(xor(truth,x),y),truth),y) != and_star(xor(and_star(xor(truth,y),x),truth),x),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f44,plain,
! [X0,X1] : implies(or(X0,not(X1)),implies(X1,X0)) = truth,
inference(backward_demodulation,[status(thm)],[f22,f21]) ).
fof(f45,plain,
! [X0,X1] : and_star(X0,X1) = and(X0,X1),
inference(forward_demodulation,[status(thm)],[f25,f30]) ).
fof(f52,plain,
and(xor(and_star(xor(truth,x),y),truth),y) != and_star(xor(and_star(xor(truth,y),x),truth),x),
inference(forward_demodulation,[status(thm)],[f45,f34]) ).
fof(f53,plain,
and(y,xor(and_star(xor(truth,x),y),truth)) != and_star(xor(and_star(xor(truth,y),x),truth),x),
inference(forward_demodulation,[status(thm)],[f27,f52]) ).
fof(f54,plain,
and(y,xor(truth,and_star(xor(truth,x),y))) != and_star(xor(and_star(xor(truth,y),x),truth),x),
inference(forward_demodulation,[status(thm)],[f29,f53]) ).
fof(f55,plain,
and(y,xor(truth,and(xor(truth,x),y))) != and_star(xor(and_star(xor(truth,y),x),truth),x),
inference(forward_demodulation,[status(thm)],[f45,f54]) ).
fof(f56,plain,
and(y,xor(truth,and(y,xor(truth,x)))) != and_star(xor(and_star(xor(truth,y),x),truth),x),
inference(forward_demodulation,[status(thm)],[f27,f55]) ).
fof(f57,plain,
and(y,xor(truth,and(y,xor(truth,x)))) != and(xor(and_star(xor(truth,y),x),truth),x),
inference(forward_demodulation,[status(thm)],[f45,f56]) ).
fof(f58,plain,
and(y,xor(truth,and(y,xor(truth,x)))) != and(x,xor(and_star(xor(truth,y),x),truth)),
inference(forward_demodulation,[status(thm)],[f27,f57]) ).
fof(f59,plain,
and(y,xor(truth,and(y,xor(truth,x)))) != and(x,xor(truth,and_star(xor(truth,y),x))),
inference(forward_demodulation,[status(thm)],[f29,f58]) ).
fof(f60,plain,
and(y,xor(truth,and(y,xor(truth,x)))) != and(x,xor(truth,and(xor(truth,y),x))),
inference(forward_demodulation,[status(thm)],[f45,f59]) ).
fof(f61,plain,
and(y,xor(truth,and(y,xor(truth,x)))) != and(x,xor(truth,and(x,xor(truth,y)))),
inference(forward_demodulation,[status(thm)],[f27,f60]) ).
fof(f70,plain,
! [X0,X1,X2] : implies(truth,implies(implies(implies(X0,X1),X2),implies(or(X1,not(X0)),X2))) = truth,
inference(paramodulation,[status(thm)],[f44,f19]) ).
fof(f71,plain,
! [X0,X1] : implies(X0,implies(implies(X0,X1),implies(truth,X1))) = truth,
inference(paramodulation,[status(thm)],[f18,f19]) ).
fof(f75,plain,
! [X0,X1] : implies(implies(X0,truth),implies(X1,implies(X0,X1))) = truth,
inference(paramodulation,[status(thm)],[f18,f19]) ).
fof(f81,plain,
! [X0,X1,X2] : implies(implies(implies(X0,X1),X2),implies(or(X1,not(X0)),X2)) = truth,
inference(forward_demodulation,[status(thm)],[f18,f70]) ).
fof(f82,plain,
! [X0,X1] : implies(X0,implies(implies(X0,X1),X1)) = truth,
inference(forward_demodulation,[status(thm)],[f18,f71]) ).
fof(f87,plain,
! [X0] : implies(truth,implies(X0,implies(truth,X0))) = truth,
inference(paramodulation,[status(thm)],[f18,f75]) ).
fof(f99,plain,
! [X0] : implies(X0,implies(truth,X0)) = truth,
inference(forward_demodulation,[status(thm)],[f18,f87]) ).
fof(f100,plain,
! [X0] : implies(X0,X0) = truth,
inference(forward_demodulation,[status(thm)],[f18,f99]) ).
fof(f245,plain,
! [X0] : xor(truth,X0) = or(and(truth,not(X0)),and(falsehood,X0)),
inference(paramodulation,[status(thm)],[f33,f28]) ).
fof(f249,plain,
! [X0] : xor(truth,X0) = or(and(falsehood,X0),and(truth,not(X0))),
inference(forward_demodulation,[status(thm)],[f24,f245]) ).
fof(f261,plain,
! [X0] : or(X0,not(X0)) = truth,
inference(paramodulation,[status(thm)],[f100,f22]) ).
fof(f262,plain,
! [X0] : or(truth,X0) = implies(falsehood,X0),
inference(paramodulation,[status(thm)],[f33,f22]) ).
fof(f374,plain,
! [X0] : implies(implies(falsehood,not(X0)),implies(X0,truth)) = truth,
inference(paramodulation,[status(thm)],[f262,f44]) ).
fof(f378,plain,
! [X0] : implies(falsehood,X0) = or(X0,truth),
inference(paramodulation,[status(thm)],[f262,f24]) ).
fof(f387,plain,
! [X0,X1] : implies(or(not(X0),X1),implies(X0,X1)) = truth,
inference(paramodulation,[status(thm)],[f24,f44]) ).
fof(f415,plain,
! [X0] : and(truth,X0) = not(or(falsehood,not(X0))),
inference(paramodulation,[status(thm)],[f33,f25]) ).
fof(f420,plain,
! [X0,X1,X2] : or(or(not(X0),not(X1)),X2) = implies(and(X0,X1),X2),
inference(paramodulation,[status(thm)],[f25,f22]) ).
fof(f432,plain,
! [X0,X1,X2] : or(not(X0),or(not(X1),X2)) = implies(and(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f23,f420]) ).
fof(f459,plain,
! [X0,X1] : or(truth,X0) = or(X1,or(not(X1),X0)),
inference(paramodulation,[status(thm)],[f261,f23]) ).
fof(f476,plain,
! [X0,X1] : implies(falsehood,X0) = or(X1,or(not(X1),X0)),
inference(forward_demodulation,[status(thm)],[f262,f459]) ).
fof(f483,plain,
! [X0,X1] : implies(or(X0,X1),X1) = implies(implies(X1,not(X0)),not(X0)),
inference(paramodulation,[status(thm)],[f22,f20]) ).
fof(f618,plain,
! [X0,X1] : implies(truth,implies(or(truth,not(X0)),implies(X1,implies(X0,X1)))) = truth,
inference(paramodulation,[status(thm)],[f75,f81]) ).
fof(f662,plain,
! [X0,X1] : implies(or(truth,not(X0)),implies(X1,implies(X0,X1))) = truth,
inference(forward_demodulation,[status(thm)],[f18,f618]) ).
fof(f663,plain,
! [X0,X1] : implies(implies(falsehood,not(X0)),implies(X1,implies(X0,X1))) = truth,
inference(forward_demodulation,[status(thm)],[f262,f662]) ).
fof(f716,plain,
! [X0] : implies(falsehood,not(not(X0))) = or(X0,truth),
inference(paramodulation,[status(thm)],[f261,f476]) ).
fof(f717,plain,
! [X0,X1] : implies(falsehood,X0) = or(X1,or(X0,not(X1))),
inference(paramodulation,[status(thm)],[f24,f476]) ).
fof(f727,plain,
! [X0] : implies(falsehood,not(not(X0))) = implies(falsehood,X0),
inference(forward_demodulation,[status(thm)],[f378,f716]) ).
fof(f848,plain,
! [X0] : implies(falsehood,implies(implies(falsehood,X0),not(not(X0)))) = truth,
inference(paramodulation,[status(thm)],[f727,f82]) ).
fof(f853,plain,
! [X0] : implies(implies(not(not(X0)),falsehood),falsehood) = implies(implies(falsehood,X0),not(not(X0))),
inference(paramodulation,[status(thm)],[f727,f20]) ).
fof(f863,plain,
! [X0] : implies(or(not(X0),falsehood),falsehood) = implies(implies(falsehood,X0),not(not(X0))),
inference(forward_demodulation,[status(thm)],[f22,f853]) ).
fof(f864,plain,
! [X0] : implies(falsehood,implies(or(falsehood,not(X0)),falsehood)) = truth,
inference(backward_demodulation,[status(thm)],[f865,f848]) ).
fof(f865,plain,
! [X0] : implies(or(falsehood,not(X0)),falsehood) = implies(implies(falsehood,X0),not(not(X0))),
inference(forward_demodulation,[status(thm)],[f24,f863]) ).
fof(f878,plain,
! [X0] : implies(falsehood,X0) = implies(falsehood,or(X0,not(truth))),
inference(paramodulation,[status(thm)],[f262,f717]) ).
fof(f892,plain,
! [X0] : implies(falsehood,X0) = implies(falsehood,or(X0,falsehood)),
inference(forward_demodulation,[status(thm)],[f33,f878]) ).
fof(f1485,plain,
! [X0,X1] : or(or(falsehood,not(X0)),X1) = implies(and(truth,X0),X1),
inference(paramodulation,[status(thm)],[f415,f22]) ).
fof(f1507,plain,
! [X0,X1] : or(falsehood,or(not(X0),X1)) = implies(and(truth,X0),X1),
inference(forward_demodulation,[status(thm)],[f23,f1485]) ).
fof(f1607,plain,
! [X0] : implies(truth,implies(X0,not(not(X0)))) = truth,
inference(paramodulation,[status(thm)],[f261,f387]) ).
fof(f1653,plain,
! [X0] : implies(X0,not(not(X0))) = truth,
inference(forward_demodulation,[status(thm)],[f18,f1607]) ).
fof(f1681,plain,
not(not(truth)) = truth,
inference(paramodulation,[status(thm)],[f18,f1653]) ).
fof(f1703,plain,
! [X0] : implies(implies(not(not(X0)),X0),X0) = implies(truth,not(not(X0))),
inference(paramodulation,[status(thm)],[f1653,f20]) ).
fof(f1717,plain,
not(falsehood) = truth,
inference(forward_demodulation,[status(thm)],[f33,f1681]) ).
fof(f1740,plain,
! [X0] : implies(or(not(X0),X0),X0) = implies(truth,not(not(X0))),
inference(forward_demodulation,[status(thm)],[f22,f1703]) ).
fof(f1741,plain,
! [X0] : implies(or(X0,not(X0)),X0) = implies(truth,not(not(X0))),
inference(forward_demodulation,[status(thm)],[f24,f1740]) ).
fof(f1742,plain,
! [X0] : implies(truth,X0) = implies(truth,not(not(X0))),
inference(forward_demodulation,[status(thm)],[f261,f1741]) ).
fof(f1743,plain,
! [X0] : X0 = implies(truth,not(not(X0))),
inference(forward_demodulation,[status(thm)],[f18,f1742]) ).
fof(f1778,plain,
! [X0] : X0 = not(not(X0)),
inference(forward_demodulation,[status(thm)],[f18,f1743]) ).
fof(f1819,plain,
! [X0] : and(X0,falsehood) = not(or(not(X0),truth)),
inference(paramodulation,[status(thm)],[f1717,f25]) ).
fof(f1822,plain,
! [X0] : or(falsehood,X0) = implies(truth,X0),
inference(paramodulation,[status(thm)],[f1717,f22]) ).
fof(f1842,plain,
! [X0] : and(X0,falsehood) = not(implies(falsehood,not(X0))),
inference(forward_demodulation,[status(thm)],[f378,f1819]) ).
fof(f1846,plain,
! [X0] : and(truth,X0) = not(not(X0)),
inference(backward_demodulation,[status(thm)],[f1872,f415]) ).
fof(f1847,plain,
! [X0,X1] : or(not(X0),X1) = implies(and(truth,X0),X1),
inference(backward_demodulation,[status(thm)],[f1872,f1507]) ).
fof(f1869,plain,
! [X0] : implies(falsehood,implies(not(X0),falsehood)) = truth,
inference(backward_demodulation,[status(thm)],[f1872,f864]) ).
fof(f1872,plain,
! [X0] : or(falsehood,X0) = X0,
inference(forward_demodulation,[status(thm)],[f18,f1822]) ).
fof(f1888,plain,
! [X0] : xor(truth,X0) = or(and(falsehood,X0),not(X0)),
inference(backward_demodulation,[status(thm)],[f1892,f249]) ).
fof(f1892,plain,
! [X0] : and(truth,X0) = X0,
inference(forward_demodulation,[status(thm)],[f1778,f1846]) ).
fof(f1893,plain,
! [X0,X1] : and(X0,X1) = not(implies(X0,not(X1))),
inference(backward_demodulation,[status(thm)],[f1946,f25]) ).
fof(f1915,plain,
! [X0,X1,X2] : implies(X0,or(not(X1),X2)) = implies(and(X0,X1),X2),
inference(backward_demodulation,[status(thm)],[f1946,f432]) ).
fof(f1946,plain,
! [X0,X1] : or(not(X0),X1) = implies(X0,X1),
inference(forward_demodulation,[status(thm)],[f1892,f1847]) ).
fof(f1973,plain,
! [X0] : implies(falsehood,or(X0,falsehood)) = truth,
inference(forward_demodulation,[status(thm)],[f22,f1869]) ).
fof(f1995,plain,
! [X0] : and(X0,falsehood) = not(truth),
inference(backward_demodulation,[status(thm)],[f2007,f1842]) ).
fof(f1998,plain,
! [X0,X1] : implies(truth,implies(X0,implies(X1,X0))) = truth,
inference(backward_demodulation,[status(thm)],[f2007,f663]) ).
fof(f1999,plain,
! [X0] : implies(truth,implies(X0,truth)) = truth,
inference(backward_demodulation,[status(thm)],[f2007,f374]) ).
fof(f2007,plain,
! [X0] : implies(falsehood,X0) = truth,
inference(forward_demodulation,[status(thm)],[f892,f1973]) ).
fof(f2010,plain,
! [X0] : xor(truth,X0) = or(not(X0),and(falsehood,X0)),
inference(forward_demodulation,[status(thm)],[f24,f1888]) ).
fof(f2011,plain,
! [X0] : xor(truth,X0) = implies(X0,and(falsehood,X0)),
inference(forward_demodulation,[status(thm)],[f1946,f2010]) ).
fof(f2044,plain,
! [X0,X1,X2] : implies(X0,implies(X1,X2)) = implies(and(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f1946,f1915]) ).
fof(f2071,plain,
! [X0] : and(X0,falsehood) = falsehood,
inference(forward_demodulation,[status(thm)],[f33,f1995]) ).
fof(f2097,plain,
! [X0,X1] : implies(X0,implies(X1,X0)) = truth,
inference(forward_demodulation,[status(thm)],[f18,f1998]) ).
fof(f2188,plain,
! [X0] : implies(X0,truth) = truth,
inference(forward_demodulation,[status(thm)],[f18,f1999]) ).
fof(f2300,plain,
! [X0] : and(falsehood,X0) = falsehood,
inference(paramodulation,[status(thm)],[f27,f2071]) ).
fof(f2318,plain,
! [X0] : xor(truth,X0) = implies(X0,falsehood),
inference(backward_demodulation,[status(thm)],[f2300,f2011]) ).
fof(f2340,plain,
and(y,xor(truth,and(y,xor(truth,x)))) != and(x,xor(truth,and(x,implies(y,falsehood)))),
inference(backward_demodulation,[status(thm)],[f2318,f61]) ).
fof(f2352,plain,
and(y,implies(and(y,xor(truth,x)),falsehood)) != and(x,xor(truth,and(x,implies(y,falsehood)))),
inference(forward_demodulation,[status(thm)],[f2318,f2340]) ).
fof(f2353,plain,
and(y,implies(y,implies(xor(truth,x),falsehood))) != and(x,xor(truth,and(x,implies(y,falsehood)))),
inference(forward_demodulation,[status(thm)],[f2044,f2352]) ).
fof(f2354,plain,
and(y,implies(y,implies(implies(x,falsehood),falsehood))) != and(x,xor(truth,and(x,implies(y,falsehood)))),
inference(forward_demodulation,[status(thm)],[f2318,f2353]) ).
fof(f2355,plain,
and(y,implies(y,implies(implies(falsehood,x),x))) != and(x,xor(truth,and(x,implies(y,falsehood)))),
inference(forward_demodulation,[status(thm)],[f20,f2354]) ).
fof(f2356,plain,
and(y,implies(y,implies(truth,x))) != and(x,xor(truth,and(x,implies(y,falsehood)))),
inference(forward_demodulation,[status(thm)],[f2007,f2355]) ).
fof(f2357,plain,
and(y,implies(y,x)) != and(x,xor(truth,and(x,implies(y,falsehood)))),
inference(forward_demodulation,[status(thm)],[f18,f2356]) ).
fof(f2358,plain,
and(y,implies(y,x)) != and(x,implies(and(x,implies(y,falsehood)),falsehood)),
inference(forward_demodulation,[status(thm)],[f2318,f2357]) ).
fof(f2359,plain,
and(y,implies(y,x)) != and(x,implies(x,implies(implies(y,falsehood),falsehood))),
inference(forward_demodulation,[status(thm)],[f2044,f2358]) ).
fof(f2360,plain,
and(y,implies(y,x)) != and(x,implies(x,implies(implies(falsehood,y),y))),
inference(forward_demodulation,[status(thm)],[f20,f2359]) ).
fof(f2361,plain,
and(y,implies(y,x)) != and(x,implies(x,implies(truth,y))),
inference(forward_demodulation,[status(thm)],[f2007,f2360]) ).
fof(f2362,plain,
and(y,implies(y,x)) != and(x,implies(x,y)),
inference(forward_demodulation,[status(thm)],[f18,f2361]) ).
fof(f2404,plain,
! [X0,X1] : and(not(X0),X1) = not(or(X0,not(X1))),
inference(paramodulation,[status(thm)],[f22,f1893]) ).
fof(f3339,plain,
! [X0,X1] : or(X0,not(X1)) = implies(X1,X0),
inference(paramodulation,[status(thm)],[f24,f1946]) ).
fof(f3341,plain,
! [X0,X1,X2] : or(and(X0,X1),X2) = implies(implies(X0,not(X1)),X2),
inference(paramodulation,[status(thm)],[f1893,f1946]) ).
fof(f3391,plain,
! [X0,X1] : and(not(X0),X1) = not(implies(X1,X0)),
inference(backward_demodulation,[status(thm)],[f3339,f2404]) ).
fof(f3396,plain,
! [X0,X1] : implies(or(X0,X1),X1) = or(and(X1,X0),not(X0)),
inference(backward_demodulation,[status(thm)],[f3341,f483]) ).
fof(f3448,plain,
! [X0,X1] : implies(or(X0,X1),X1) = or(not(X0),and(X1,X0)),
inference(forward_demodulation,[status(thm)],[f24,f3396]) ).
fof(f3449,plain,
! [X0,X1] : implies(or(X0,X1),X1) = implies(X0,and(X1,X0)),
inference(forward_demodulation,[status(thm)],[f1946,f3448]) ).
fof(f3476,plain,
! [X0,X1] : implies(X0,not(X1)) = implies(X1,not(X0)),
inference(paramodulation,[status(thm)],[f1946,f3339]) ).
fof(f4690,plain,
! [X0,X1,X2] : implies(X0,implies(X1,implies(X2,X0))) = truth,
inference(paramodulation,[status(thm)],[f2044,f2097]) ).
fof(f5140,plain,
! [X0,X1] : implies(implies(and(X0,X1),X1),X1) = implies(implies(or(X1,X0),X0),and(X0,X1)),
inference(paramodulation,[status(thm)],[f3449,f20]) ).
fof(f5204,plain,
! [X0,X1] : implies(implies(X0,implies(X1,X1)),X1) = implies(implies(or(X1,X0),X0),and(X0,X1)),
inference(forward_demodulation,[status(thm)],[f2044,f5140]) ).
fof(f5205,plain,
! [X0,X1] : implies(implies(X0,truth),X1) = implies(implies(or(X1,X0),X0),and(X0,X1)),
inference(forward_demodulation,[status(thm)],[f100,f5204]) ).
fof(f5206,plain,
! [X0,X1] : implies(truth,X0) = implies(implies(or(X0,X1),X1),and(X1,X0)),
inference(forward_demodulation,[status(thm)],[f2188,f5205]) ).
fof(f5208,plain,
! [X0,X1] : X0 = implies(implies(or(X0,X1),X1),and(X1,X0)),
inference(forward_demodulation,[status(thm)],[f18,f5206]) ).
fof(f5339,plain,
! [X0,X1] : X0 = implies(implies(X1,not(or(X0,not(X1)))),and(not(X1),X0)),
inference(paramodulation,[status(thm)],[f3476,f5208]) ).
fof(f5379,plain,
! [X0,X1] : X0 = or(and(X1,or(X0,not(X1))),and(not(X1),X0)),
inference(forward_demodulation,[status(thm)],[f3341,f5339]) ).
fof(f5380,plain,
! [X0,X1] : X0 = or(and(not(X1),X0),and(X1,or(X0,not(X1)))),
inference(forward_demodulation,[status(thm)],[f24,f5379]) ).
fof(f5381,plain,
! [X0,X1] : X0 = or(not(implies(X0,X1)),and(X1,or(X0,not(X1)))),
inference(forward_demodulation,[status(thm)],[f3391,f5380]) ).
fof(f5382,plain,
! [X0,X1] : X0 = implies(implies(X0,X1),and(X1,or(X0,not(X1)))),
inference(forward_demodulation,[status(thm)],[f1946,f5381]) ).
fof(f5383,plain,
! [X0,X1] : X0 = implies(implies(X0,X1),and(X1,implies(X1,X0))),
inference(forward_demodulation,[status(thm)],[f3339,f5382]) ).
fof(f7246,plain,
! [X0,X1] : and(X0,implies(X0,X1)) = implies(implies(and(X0,implies(X0,X1)),implies(X1,X0)),and(implies(X1,X0),X1)),
inference(paramodulation,[status(thm)],[f5383,f5383]) ).
fof(f7462,plain,
! [X0,X1] : and(X0,implies(X0,X1)) = implies(implies(X0,implies(implies(X0,X1),implies(X1,X0))),and(implies(X1,X0),X1)),
inference(forward_demodulation,[status(thm)],[f2044,f7246]) ).
fof(f7463,plain,
! [X0,X1] : and(X0,implies(X0,X1)) = implies(truth,and(implies(X1,X0),X1)),
inference(forward_demodulation,[status(thm)],[f4690,f7462]) ).
fof(f7464,plain,
! [X0,X1] : and(X0,implies(X0,X1)) = and(implies(X1,X0),X1),
inference(forward_demodulation,[status(thm)],[f18,f7463]) ).
fof(f7465,plain,
and(x,implies(x,y)) != and(x,implies(x,y)),
inference(backward_demodulation,[status(thm)],[f7466,f2362]) ).
fof(f7466,plain,
! [X0,X1] : and(X0,implies(X0,X1)) = and(X1,implies(X1,X0)),
inference(forward_demodulation,[status(thm)],[f27,f7464]) ).
fof(f7552,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f7465]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL160-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n017.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 00:02:41 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 13.51/2.15 % Refutation found
% 13.51/2.15 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 13.51/2.15 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 14.10/3.42 % Elapsed time: 2.854135 seconds
% 14.10/3.42 % CPU time: 12.170612 seconds
% 14.10/3.42 % Total memory used: 137.140 MB
% 14.10/3.42 % Net memory used: 132.376 MB
%------------------------------------------------------------------------------