%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL109-6 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 42.98s 5.95s
% Output : CNFRefutation 42.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 12
% Syntax : Number of formulae : 196 ( 196 unt; 0 def)
% Number of atoms : 196 ( 195 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 362 ( 362 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : not(X) = xor(X,truth),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : xor(X,falsehood) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : and_star(X,truth) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : and_star(X,falsehood) = falsehood,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y] : xor(X,xor(truth,Y)) = xor(xor(X,truth),Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] : 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(f9,axiom,
! [X,Y] : xor(X,Y) = xor(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y,Z] : and_star(and_star(X,Y),Z) = and_star(X,and_star(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Y] : and_star(X,Y) = and_star(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
not(truth) = falsehood,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Y] : implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,plain,
! [X0] : not(X0) = xor(X0,truth),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f16,plain,
! [X0] : xor(X0,falsehood) = X0,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f18,plain,
! [X0] : and_star(X0,truth) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f19,plain,
! [X0] : and_star(X0,falsehood) = falsehood,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f21,plain,
! [X0,X1] : xor(X0,xor(truth,X1)) = xor(xor(X0,truth),X1),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f22,plain,
! [X0,X1] : and_star(xor(and_star(xor(truth,X0),X1),truth),X1) = and_star(xor(and_star(xor(truth,X1),X0),truth),X0),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f23,plain,
! [X0,X1] : xor(X0,X1) = xor(X1,X0),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f24,plain,
! [X0,X1,X2] : and_star(and_star(X0,X1),X2) = and_star(X0,and_star(X1,X2)),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f25,plain,
! [X0,X1] : and_star(X0,X1) = and_star(X1,X0),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f26,plain,
not(truth) = falsehood,
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f27,plain,
! [X0,X1] : implies(X0,X1) = xor(truth,and_star(X0,xor(truth,X1))),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f28,plain,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth,
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f34,plain,
! [X0,X1] : xor(X0,xor(truth,X1)) = xor(not(X0),X1),
inference(forward_demodulation,[status(thm)],[f15,f21]) ).
fof(f35,plain,
! [X0,X1] : and_star(not(and_star(xor(truth,X0),X1)),X1) = and_star(xor(and_star(xor(truth,X1),X0),truth),X0),
inference(forward_demodulation,[status(thm)],[f15,f22]) ).
fof(f36,plain,
! [X0,X1] : and_star(not(and_star(xor(truth,X0),X1)),X1) = and_star(not(and_star(xor(truth,X1),X0)),X0),
inference(forward_demodulation,[status(thm)],[f15,f35]) ).
fof(f37,plain,
! [X0,X1] : xor(X0,xor(not(truth),X1)) = xor(not(X0),xor(truth,X1)),
inference(paramodulation,[status(thm)],[f34,f34]) ).
fof(f38,plain,
! [X0,X1] : xor(X0,xor(falsehood,X1)) = xor(not(X0),xor(truth,X1)),
inference(forward_demodulation,[status(thm)],[f26,f37]) ).
fof(f39,plain,
! [X0,X1] : xor(X0,xor(falsehood,X1)) = xor(not(not(X0)),X1),
inference(forward_demodulation,[status(thm)],[f34,f38]) ).
fof(f41,plain,
! [X0,X1] : implies(X0,xor(truth,X1)) = xor(truth,and_star(X0,xor(not(truth),X1))),
inference(paramodulation,[status(thm)],[f34,f27]) ).
fof(f42,plain,
! [X0,X1,X2] : xor(X0,implies(X1,X2)) = xor(not(X0),and_star(X1,xor(truth,X2))),
inference(paramodulation,[status(thm)],[f27,f34]) ).
fof(f43,plain,
! [X0,X1] : implies(X0,xor(truth,X1)) = xor(truth,and_star(X0,xor(falsehood,X1))),
inference(forward_demodulation,[status(thm)],[f26,f41]) ).
fof(f59,plain,
! [X0] : not(and_star(xor(truth,X0),truth)) = and_star(not(and_star(xor(truth,truth),X0)),X0),
inference(paramodulation,[status(thm)],[f18,f36]) ).
fof(f63,plain,
! [X0,X1] : and_star(not(and_star(xor(not(truth),X0),X1)),X1) = and_star(not(and_star(xor(truth,X1),xor(truth,X0))),xor(truth,X0)),
inference(paramodulation,[status(thm)],[f34,f36]) ).
fof(f72,plain,
! [X0,X1] : implies(not(and_star(xor(truth,X0),xor(truth,X1))),X1) = xor(truth,and_star(not(and_star(xor(truth,xor(truth,X1)),X0)),X0)),
inference(paramodulation,[status(thm)],[f36,f27]) ).
fof(f77,plain,
! [X0] : not(xor(truth,X0)) = and_star(not(and_star(xor(truth,truth),X0)),X0),
inference(forward_demodulation,[status(thm)],[f18,f59]) ).
fof(f78,plain,
! [X0] : not(xor(truth,X0)) = and_star(not(and_star(not(truth),X0)),X0),
inference(forward_demodulation,[status(thm)],[f15,f77]) ).
fof(f79,plain,
! [X0] : not(xor(truth,X0)) = and_star(not(and_star(falsehood,X0)),X0),
inference(forward_demodulation,[status(thm)],[f26,f78]) ).
fof(f83,plain,
! [X0,X1] : and_star(not(and_star(xor(falsehood,X0),X1)),X1) = and_star(not(and_star(xor(truth,X1),xor(truth,X0))),xor(truth,X0)),
inference(forward_demodulation,[status(thm)],[f26,f63]) ).
fof(f91,plain,
! [X0,X1] : implies(not(and_star(xor(truth,X0),xor(truth,X1))),X1) = xor(truth,and_star(not(and_star(xor(not(truth),X1),X0)),X0)),
inference(forward_demodulation,[status(thm)],[f34,f72]) ).
fof(f92,plain,
! [X0,X1] : implies(not(and_star(xor(truth,X0),xor(truth,X1))),X1) = xor(truth,and_star(not(and_star(xor(falsehood,X1),X0)),X0)),
inference(forward_demodulation,[status(thm)],[f26,f91]) ).
fof(f104,plain,
! [X0] : implies(not(and_star(falsehood,xor(truth,X0))),X0) = xor(truth,not(xor(truth,xor(truth,X0)))),
inference(paramodulation,[status(thm)],[f79,f27]) ).
fof(f110,plain,
! [X0] : implies(not(and_star(falsehood,xor(truth,X0))),X0) = xor(truth,not(xor(not(truth),X0))),
inference(forward_demodulation,[status(thm)],[f34,f104]) ).
fof(f111,plain,
! [X0] : implies(not(and_star(falsehood,xor(truth,X0))),X0) = xor(truth,not(xor(falsehood,X0))),
inference(forward_demodulation,[status(thm)],[f26,f110]) ).
fof(f167,plain,
! [X0,X1] : and_star(not(and_star(xor(not(falsehood),X0),X1)),X1) = and_star(not(and_star(xor(truth,X1),xor(truth,xor(truth,X0)))),xor(truth,xor(truth,X0))),
inference(paramodulation,[status(thm)],[f34,f83]) ).
fof(f193,plain,
! [X0,X1] : and_star(not(and_star(xor(not(falsehood),X0),X1)),X1) = and_star(not(and_star(xor(truth,X1),xor(not(truth),X0))),xor(truth,xor(truth,X0))),
inference(forward_demodulation,[status(thm)],[f34,f167]) ).
fof(f194,plain,
! [X0,X1] : and_star(not(and_star(xor(not(falsehood),X0),X1)),X1) = and_star(not(and_star(xor(truth,X1),xor(falsehood,X0))),xor(truth,xor(truth,X0))),
inference(forward_demodulation,[status(thm)],[f26,f193]) ).
fof(f195,plain,
! [X0,X1] : and_star(not(and_star(xor(not(falsehood),X0),X1)),X1) = and_star(not(and_star(xor(truth,X1),xor(falsehood,X0))),xor(not(truth),X0)),
inference(forward_demodulation,[status(thm)],[f34,f194]) ).
fof(f196,plain,
! [X0,X1] : and_star(not(and_star(xor(not(falsehood),X0),X1)),X1) = and_star(not(and_star(xor(truth,X1),xor(falsehood,X0))),xor(falsehood,X0)),
inference(forward_demodulation,[status(thm)],[f26,f195]) ).
fof(f585,plain,
! [X0,X1] : xor(truth,implies(X0,X1)) = xor(falsehood,and_star(X0,xor(truth,X1))),
inference(paramodulation,[status(thm)],[f26,f42]) ).
fof(f625,plain,
! [X0] : and_star(not(and_star(xor(truth,falsehood),X0)),X0) = falsehood,
inference(paramodulation,[status(thm)],[f36,f19]) ).
fof(f628,plain,
! [X0] : implies(not(and_star(xor(truth,falsehood),xor(truth,X0))),X0) = xor(truth,and_star(not(falsehood),falsehood)),
inference(paramodulation,[status(thm)],[f19,f92]) ).
fof(f636,plain,
! [X0] : and_star(not(and_star(truth,X0)),X0) = falsehood,
inference(forward_demodulation,[status(thm)],[f16,f625]) ).
fof(f640,plain,
! [X0] : implies(not(and_star(truth,xor(truth,X0))),X0) = xor(truth,and_star(not(falsehood),falsehood)),
inference(forward_demodulation,[status(thm)],[f16,f628]) ).
fof(f641,plain,
! [X0] : implies(not(and_star(truth,xor(truth,X0))),X0) = xor(truth,falsehood),
inference(forward_demodulation,[status(thm)],[f19,f640]) ).
fof(f642,plain,
! [X0] : implies(not(and_star(truth,xor(truth,X0))),X0) = truth,
inference(forward_demodulation,[status(thm)],[f16,f641]) ).
fof(f652,plain,
! [X0] : xor(X0,xor(falsehood,falsehood)) = not(not(X0)),
inference(paramodulation,[status(thm)],[f39,f16]) ).
fof(f659,plain,
! [X0] : implies(X0,xor(truth,falsehood)) = xor(truth,and_star(X0,falsehood)),
inference(paramodulation,[status(thm)],[f16,f43]) ).
fof(f676,plain,
! [X0] : implies(X0,falsehood) = xor(truth,and_star(X0,truth)),
inference(paramodulation,[status(thm)],[f16,f27]) ).
fof(f678,plain,
! [X0] : xor(X0,falsehood) = not(not(X0)),
inference(forward_demodulation,[status(thm)],[f16,f652]) ).
fof(f680,plain,
! [X0] : X0 = not(not(X0)),
inference(forward_demodulation,[status(thm)],[f16,f678]) ).
fof(f706,plain,
! [X0] : implies(X0,truth) = xor(truth,and_star(X0,falsehood)),
inference(forward_demodulation,[status(thm)],[f16,f659]) ).
fof(f707,plain,
! [X0] : implies(X0,truth) = xor(truth,falsehood),
inference(forward_demodulation,[status(thm)],[f19,f706]) ).
fof(f710,plain,
! [X0] : implies(X0,truth) = truth,
inference(forward_demodulation,[status(thm)],[f16,f707]) ).
fof(f750,plain,
! [X0] : implies(not(and_star(falsehood,xor(truth,X0))),X0) = implies(not(xor(falsehood,X0)),falsehood),
inference(backward_demodulation,[status(thm)],[f868,f111]) ).
fof(f751,plain,
! [X0,X1] : implies(not(and_star(xor(truth,X0),xor(truth,X1))),X1) = implies(and_star(not(and_star(xor(falsehood,X1),X0)),X0),falsehood),
inference(backward_demodulation,[status(thm)],[f868,f92]) ).
fof(f754,plain,
! [X0,X1] : implies(X0,xor(truth,X1)) = implies(and_star(X0,xor(falsehood,X1)),falsehood),
inference(backward_demodulation,[status(thm)],[f868,f43]) ).
fof(f760,plain,
! [X0,X1] : and_star(not(and_star(xor(falsehood,X0),X1)),X1) = and_star(not(and_star(xor(truth,X1),xor(truth,X0))),implies(X0,falsehood)),
inference(backward_demodulation,[status(thm)],[f868,f83]) ).
fof(f761,plain,
! [X0] : not(implies(X0,falsehood)) = and_star(not(and_star(falsehood,X0)),X0),
inference(backward_demodulation,[status(thm)],[f868,f79]) ).
fof(f765,plain,
! [X0,X1] : implies(implies(X0,X1),falsehood) = xor(falsehood,and_star(X0,xor(truth,X1))),
inference(backward_demodulation,[status(thm)],[f868,f585]) ).
fof(f802,plain,
! [X0] : implies(not(and_star(truth,implies(X0,falsehood))),X0) = truth,
inference(backward_demodulation,[status(thm)],[f868,f642]) ).
fof(f860,plain,
! [X0,X1] : and_star(not(and_star(xor(not(falsehood),X0),X1)),X1) = and_star(not(and_star(implies(X1,falsehood),xor(falsehood,X0))),xor(falsehood,X0)),
inference(backward_demodulation,[status(thm)],[f868,f196]) ).
fof(f868,plain,
! [X0] : implies(X0,falsehood) = xor(truth,X0),
inference(forward_demodulation,[status(thm)],[f18,f676]) ).
fof(f874,plain,
! [X0] : implies(not(and_star(falsehood,implies(X0,falsehood))),X0) = implies(not(xor(falsehood,X0)),falsehood),
inference(forward_demodulation,[status(thm)],[f868,f750]) ).
fof(f875,plain,
! [X0,X1] : implies(not(and_star(implies(X0,falsehood),xor(truth,X1))),X1) = implies(and_star(not(and_star(xor(falsehood,X1),X0)),X0),falsehood),
inference(forward_demodulation,[status(thm)],[f868,f751]) ).
fof(f876,plain,
! [X0,X1] : implies(not(and_star(implies(X0,falsehood),implies(X1,falsehood))),X1) = implies(and_star(not(and_star(xor(falsehood,X1),X0)),X0),falsehood),
inference(forward_demodulation,[status(thm)],[f868,f875]) ).
fof(f878,plain,
! [X0,X1] : implies(X0,implies(X1,falsehood)) = implies(and_star(X0,xor(falsehood,X1)),falsehood),
inference(forward_demodulation,[status(thm)],[f868,f754]) ).
fof(f884,plain,
! [X0,X1] : and_star(not(and_star(xor(falsehood,X0),X1)),X1) = and_star(not(and_star(implies(X1,falsehood),xor(truth,X0))),implies(X0,falsehood)),
inference(forward_demodulation,[status(thm)],[f868,f760]) ).
fof(f885,plain,
! [X0,X1] : and_star(not(and_star(xor(falsehood,X0),X1)),X1) = and_star(not(and_star(implies(X1,falsehood),implies(X0,falsehood))),implies(X0,falsehood)),
inference(forward_demodulation,[status(thm)],[f868,f884]) ).
fof(f888,plain,
! [X0,X1] : implies(implies(X0,X1),falsehood) = xor(falsehood,and_star(X0,implies(X1,falsehood))),
inference(forward_demodulation,[status(thm)],[f868,f765]) ).
fof(f1101,plain,
truth = not(falsehood),
inference(paramodulation,[status(thm)],[f26,f680]) ).
fof(f1103,plain,
! [X0,X1] : and_star(not(and_star(xor(truth,X0),X1)),X1) = and_star(not(and_star(implies(X1,falsehood),xor(falsehood,X0))),xor(falsehood,X0)),
inference(backward_demodulation,[status(thm)],[f1101,f860]) ).
fof(f1147,plain,
! [X0,X1] : and_star(not(and_star(implies(X0,falsehood),X1)),X1) = and_star(not(and_star(implies(X1,falsehood),xor(falsehood,X0))),xor(falsehood,X0)),
inference(forward_demodulation,[status(thm)],[f868,f1103]) ).
fof(f1233,plain,
! [X0] : falsehood = and_star(falsehood,X0),
inference(paramodulation,[status(thm)],[f19,f25]) ).
fof(f1234,plain,
! [X0] : X0 = and_star(truth,X0),
inference(paramodulation,[status(thm)],[f18,f25]) ).
fof(f1247,plain,
! [X0] : implies(not(falsehood),X0) = implies(not(xor(falsehood,X0)),falsehood),
inference(backward_demodulation,[status(thm)],[f1233,f874]) ).
fof(f1251,plain,
! [X0] : not(implies(X0,falsehood)) = and_star(not(falsehood),X0),
inference(backward_demodulation,[status(thm)],[f1233,f761]) ).
fof(f1252,plain,
! [X0] : implies(not(implies(X0,falsehood)),X0) = truth,
inference(backward_demodulation,[status(thm)],[f1234,f802]) ).
fof(f1253,plain,
! [X0] : and_star(not(X0),X0) = falsehood,
inference(backward_demodulation,[status(thm)],[f1234,f636]) ).
fof(f1257,plain,
! [X0] : implies(truth,X0) = implies(not(xor(falsehood,X0)),falsehood),
inference(forward_demodulation,[status(thm)],[f1101,f1247]) ).
fof(f1263,plain,
! [X0] : not(implies(X0,falsehood)) = and_star(truth,X0),
inference(forward_demodulation,[status(thm)],[f1101,f1251]) ).
fof(f1265,plain,
! [X0] : not(implies(X0,falsehood)) = X0,
inference(forward_demodulation,[status(thm)],[f1234,f1263]) ).
fof(f1267,plain,
! [X0] : implies(X0,X0) = truth,
inference(forward_demodulation,[status(thm)],[f1265,f1252]) ).
fof(f1301,plain,
! [X0] : not(X0) = xor(truth,X0),
inference(paramodulation,[status(thm)],[f15,f23]) ).
fof(f1302,plain,
! [X0] : X0 = xor(falsehood,X0),
inference(paramodulation,[status(thm)],[f16,f23]) ).
fof(f1313,plain,
! [X0] : implies(X0,falsehood) = not(X0),
inference(backward_demodulation,[status(thm)],[f1301,f868]) ).
fof(f1319,plain,
! [X0,X1] : implies(implies(X0,X1),falsehood) = and_star(X0,implies(X1,falsehood)),
inference(backward_demodulation,[status(thm)],[f1302,f888]) ).
fof(f1323,plain,
! [X0] : implies(truth,X0) = implies(not(X0),falsehood),
inference(backward_demodulation,[status(thm)],[f1302,f1257]) ).
fof(f1344,plain,
! [X0,X1] : and_star(not(and_star(implies(X0,falsehood),X1)),X1) = and_star(not(and_star(implies(X1,falsehood),xor(falsehood,X0))),X0),
inference(backward_demodulation,[status(thm)],[f1302,f1147]) ).
fof(f1384,plain,
! [X0,X1] : and_star(not(and_star(X0,X1)),X1) = and_star(not(and_star(implies(X1,falsehood),implies(X0,falsehood))),implies(X0,falsehood)),
inference(backward_demodulation,[status(thm)],[f1302,f885]) ).
fof(f1387,plain,
! [X0,X1] : implies(X0,implies(X1,falsehood)) = implies(and_star(X0,X1),falsehood),
inference(backward_demodulation,[status(thm)],[f1302,f878]) ).
fof(f1388,plain,
! [X0,X1] : implies(not(and_star(implies(X0,falsehood),implies(X1,falsehood))),X1) = implies(and_star(not(and_star(X1,X0)),X0),falsehood),
inference(backward_demodulation,[status(thm)],[f1302,f876]) ).
fof(f1438,plain,
! [X0,X1] : not(implies(X0,X1)) = and_star(X0,implies(X1,falsehood)),
inference(forward_demodulation,[status(thm)],[f1313,f1319]) ).
fof(f1444,plain,
! [X0,X1] : not(implies(X0,X1)) = and_star(X0,not(X1)),
inference(forward_demodulation,[status(thm)],[f1313,f1438]) ).
fof(f1460,plain,
! [X0] : implies(truth,X0) = not(not(X0)),
inference(forward_demodulation,[status(thm)],[f1313,f1323]) ).
fof(f1461,plain,
! [X0] : implies(truth,X0) = X0,
inference(forward_demodulation,[status(thm)],[f680,f1460]) ).
fof(f1608,plain,
! [X0,X1] : and_star(not(and_star(not(X0),X1)),X1) = and_star(not(and_star(implies(X1,falsehood),xor(falsehood,X0))),X0),
inference(forward_demodulation,[status(thm)],[f1313,f1344]) ).
fof(f1609,plain,
! [X0,X1] : and_star(not(and_star(not(X0),X1)),X1) = and_star(not(and_star(not(X1),xor(falsehood,X0))),X0),
inference(forward_demodulation,[status(thm)],[f1313,f1608]) ).
fof(f1610,plain,
! [X0,X1] : and_star(not(and_star(not(X0),X1)),X1) = and_star(not(and_star(not(X1),X0)),X0),
inference(forward_demodulation,[status(thm)],[f1302,f1609]) ).
fof(f1973,plain,
! [X0,X1] : and_star(not(and_star(X0,X1)),X1) = and_star(not(and_star(not(X1),implies(X0,falsehood))),implies(X0,falsehood)),
inference(forward_demodulation,[status(thm)],[f1313,f1384]) ).
fof(f1974,plain,
! [X0,X1] : and_star(not(and_star(X0,X1)),X1) = and_star(not(and_star(not(X1),not(X0))),implies(X0,falsehood)),
inference(forward_demodulation,[status(thm)],[f1313,f1973]) ).
fof(f1975,plain,
! [X0,X1] : and_star(not(and_star(X0,X1)),X1) = and_star(not(not(implies(not(X1),X0))),implies(X0,falsehood)),
inference(forward_demodulation,[status(thm)],[f1444,f1974]) ).
fof(f1976,plain,
! [X0,X1] : and_star(not(and_star(X0,X1)),X1) = and_star(implies(not(X1),X0),implies(X0,falsehood)),
inference(forward_demodulation,[status(thm)],[f680,f1975]) ).
fof(f1977,plain,
! [X0,X1] : and_star(not(and_star(X0,X1)),X1) = and_star(implies(not(X1),X0),not(X0)),
inference(forward_demodulation,[status(thm)],[f1313,f1976]) ).
fof(f1978,plain,
! [X0,X1] : and_star(not(and_star(X0,X1)),X1) = not(implies(implies(not(X1),X0),X0)),
inference(forward_demodulation,[status(thm)],[f1444,f1977]) ).
fof(f1989,plain,
! [X0,X1] : implies(X0,not(X1)) = implies(and_star(X0,X1),falsehood),
inference(forward_demodulation,[status(thm)],[f1313,f1387]) ).
fof(f2016,plain,
! [X0,X1] : implies(X0,not(X1)) = not(and_star(X0,X1)),
inference(forward_demodulation,[status(thm)],[f1313,f1989]) ).
fof(f2017,plain,
! [X0,X1] : implies(not(and_star(not(X0),implies(X1,falsehood))),X1) = implies(and_star(not(and_star(X1,X0)),X0),falsehood),
inference(forward_demodulation,[status(thm)],[f1313,f1388]) ).
fof(f2018,plain,
! [X0,X1] : implies(not(and_star(not(X0),not(X1))),X1) = implies(and_star(not(and_star(X1,X0)),X0),falsehood),
inference(forward_demodulation,[status(thm)],[f1313,f2017]) ).
fof(f2019,plain,
! [X0,X1] : implies(not(not(implies(not(X0),X1))),X1) = implies(and_star(not(and_star(X1,X0)),X0),falsehood),
inference(forward_demodulation,[status(thm)],[f1444,f2018]) ).
fof(f2020,plain,
! [X0,X1] : implies(implies(not(X0),X1),X1) = implies(and_star(not(and_star(X1,X0)),X0),falsehood),
inference(forward_demodulation,[status(thm)],[f680,f2019]) ).
fof(f2021,plain,
! [X0,X1] : implies(implies(not(X0),X1),X1) = not(and_star(not(and_star(X1,X0)),X0)),
inference(forward_demodulation,[status(thm)],[f1313,f2020]) ).
fof(f2183,plain,
! [X0,X1,X2] : and_star(X0,and_star(X1,X2)) = and_star(X1,and_star(X2,X0)),
inference(paramodulation,[status(thm)],[f25,f24]) ).
fof(f2186,plain,
! [X0,X1] : and_star(falsehood,X0) = and_star(not(X1),and_star(X1,X0)),
inference(paramodulation,[status(thm)],[f1253,f24]) ).
fof(f2200,plain,
! [X0,X1] : falsehood = and_star(not(X0),and_star(X0,X1)),
inference(forward_demodulation,[status(thm)],[f1233,f2186]) ).
fof(f2222,plain,
! [X0,X1,X2] : and_star(not(implies(implies(not(X0),X1),X1)),X2) = and_star(not(and_star(X1,X0)),and_star(X0,X2)),
inference(paramodulation,[status(thm)],[f1978,f24]) ).
fof(f2275,plain,
! [X0,X1] : implies(implies(not(X0),X1),X1) = not(and_star(X0,not(and_star(X1,X0)))),
inference(paramodulation,[status(thm)],[f25,f2021]) ).
fof(f2309,plain,
! [X0,X1] : implies(implies(not(X0),X1),X1) = not(not(implies(X0,and_star(X1,X0)))),
inference(forward_demodulation,[status(thm)],[f1444,f2275]) ).
fof(f2310,plain,
! [X0,X1] : implies(implies(not(X0),X1),X1) = implies(X0,and_star(X1,X0)),
inference(forward_demodulation,[status(thm)],[f680,f2309]) ).
fof(f2371,plain,
! [X0,X1,X2] : not(implies(and_star(X0,X1),X2)) = and_star(X0,and_star(X1,not(X2))),
inference(paramodulation,[status(thm)],[f24,f1444]) ).
fof(f2376,plain,
! [X0,X1] : not(implies(X0,X1)) = and_star(not(X1),X0),
inference(paramodulation,[status(thm)],[f25,f1444]) ).
fof(f2393,plain,
! [X0,X1,X2] : not(implies(and_star(X0,X1),X2)) = and_star(X0,not(implies(X1,X2))),
inference(forward_demodulation,[status(thm)],[f1444,f2371]) ).
fof(f2394,plain,
! [X0,X1,X2] : not(implies(and_star(X0,X1),X2)) = not(implies(X0,implies(X1,X2))),
inference(forward_demodulation,[status(thm)],[f1444,f2393]) ).
fof(f2403,plain,
! [X0,X1,X2] : not(implies(X0,implies(implies(not(X1),X2),X2))) = and_star(not(and_star(X2,X1)),and_star(X1,X0)),
inference(backward_demodulation,[status(thm)],[f2376,f2222]) ).
fof(f2417,plain,
! [X0,X1] : and_star(not(and_star(not(X0),X1)),X1) = not(implies(X0,and_star(not(X1),X0))),
inference(backward_demodulation,[status(thm)],[f2376,f1610]) ).
fof(f2440,plain,
! [X0,X1] : falsehood = not(implies(and_star(X0,X1),X0)),
inference(backward_demodulation,[status(thm)],[f2376,f2200]) ).
fof(f2472,plain,
! [X0,X1,X2] : not(implies(X0,implies(implies(not(X1),X2),X2))) = not(implies(and_star(X1,X0),and_star(X2,X1))),
inference(forward_demodulation,[status(thm)],[f2376,f2403]) ).
fof(f2473,plain,
! [X0,X1,X2] : not(implies(X0,implies(implies(not(X1),X2),X2))) = not(implies(X1,implies(X0,and_star(X2,X1)))),
inference(forward_demodulation,[status(thm)],[f2394,f2472]) ).
fof(f2624,plain,
! [X0,X1] : not(implies(X0,and_star(not(X1),X0))) = not(implies(X1,and_star(not(X0),X1))),
inference(forward_demodulation,[status(thm)],[f2376,f2417]) ).
fof(f2625,plain,
! [X0,X1] : not(implies(X0,not(implies(X0,X1)))) = not(implies(X1,and_star(not(X0),X1))),
inference(forward_demodulation,[status(thm)],[f2376,f2624]) ).
fof(f2626,plain,
! [X0,X1] : not(not(and_star(X0,implies(X0,X1)))) = not(implies(X1,and_star(not(X0),X1))),
inference(forward_demodulation,[status(thm)],[f2016,f2625]) ).
fof(f2627,plain,
! [X0,X1] : and_star(X0,implies(X0,X1)) = not(implies(X1,and_star(not(X0),X1))),
inference(forward_demodulation,[status(thm)],[f680,f2626]) ).
fof(f2628,plain,
! [X0,X1] : and_star(X0,implies(X0,X1)) = not(implies(X1,not(implies(X1,X0)))),
inference(forward_demodulation,[status(thm)],[f2376,f2627]) ).
fof(f2629,plain,
! [X0,X1] : and_star(X0,implies(X0,X1)) = not(not(and_star(X1,implies(X1,X0)))),
inference(forward_demodulation,[status(thm)],[f2016,f2628]) ).
fof(f2630,plain,
! [X0,X1] : and_star(X0,implies(X0,X1)) = and_star(X1,implies(X1,X0)),
inference(forward_demodulation,[status(thm)],[f680,f2629]) ).
fof(f2691,plain,
! [X0,X1] : falsehood = not(implies(X0,implies(X1,X0))),
inference(forward_demodulation,[status(thm)],[f2394,f2440]) ).
fof(f2701,plain,
! [X0,X1] : implies(X0,implies(X1,X0)) = not(falsehood),
inference(paramodulation,[status(thm)],[f2691,f680]) ).
fof(f2719,plain,
! [X0,X1] : implies(X0,implies(X1,X0)) = truth,
inference(forward_demodulation,[status(thm)],[f1101,f2701]) ).
fof(f2722,plain,
! [X0,X1] : not(implies(not(X0),X1)) = not(implies(not(X1),X0)),
inference(paramodulation,[status(thm)],[f1444,f2376]) ).
fof(f2732,plain,
! [X0,X1,X2] : and_star(not(implies(X0,X1)),X2) = and_star(not(X1),and_star(X0,X2)),
inference(paramodulation,[status(thm)],[f2376,f24]) ).
fof(f2739,plain,
! [X0,X1,X2] : not(implies(X0,implies(X1,X2))) = and_star(not(X2),and_star(X1,X0)),
inference(forward_demodulation,[status(thm)],[f2376,f2732]) ).
fof(f2740,plain,
! [X0,X1,X2] : not(implies(X0,implies(X1,X2))) = not(implies(and_star(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f2376,f2739]) ).
fof(f2893,plain,
! [X0,X1,X2] : not(implies(not(implies(not(X0),X1)),X2)) = not(implies(not(X2),implies(not(X1),X0))),
inference(paramodulation,[status(thm)],[f2722,f2722]) ).
fof(f3666,plain,
! [X0,X1,X2] : not(implies(not(implies(X0,X1)),X2)) = not(implies(not(X2),implies(not(X1),not(X0)))),
inference(paramodulation,[status(thm)],[f680,f2893]) ).
fof(f3690,plain,
! [X0,X1,X2] : not(implies(not(implies(not(X0),not(X1))),X2)) = not(implies(not(X2),implies(X1,X0))),
inference(paramodulation,[status(thm)],[f680,f2893]) ).
fof(f3769,plain,
! [X0,X1,X2] : not(implies(not(implies(X0,X1)),X2)) = not(implies(not(X2),not(and_star(not(X1),X0)))),
inference(forward_demodulation,[status(thm)],[f2016,f3666]) ).
fof(f3770,plain,
! [X0,X1,X2] : not(implies(not(implies(X0,X1)),X2)) = not(not(and_star(not(X2),and_star(not(X1),X0)))),
inference(forward_demodulation,[status(thm)],[f2016,f3769]) ).
fof(f3771,plain,
! [X0,X1,X2] : not(implies(not(implies(X0,X1)),X2)) = and_star(not(X2),and_star(not(X1),X0)),
inference(forward_demodulation,[status(thm)],[f680,f3770]) ).
fof(f3772,plain,
! [X0,X1,X2] : not(implies(not(implies(X0,X1)),X2)) = not(implies(and_star(not(X1),X0),X2)),
inference(forward_demodulation,[status(thm)],[f2376,f3771]) ).
fof(f3781,plain,
! [X0,X1,X2] : not(implies(not(implies(X0,X1)),X2)) = not(implies(X0,implies(not(X1),X2))),
inference(forward_demodulation,[status(thm)],[f2740,f3772]) ).
fof(f3842,plain,
! [X0,X1,X2] : not(implies(not(X0),implies(not(not(X1)),X2))) = not(implies(not(X2),implies(X1,X0))),
inference(forward_demodulation,[status(thm)],[f3781,f3690]) ).
fof(f3843,plain,
! [X0,X1,X2] : not(implies(not(X0),implies(X1,X2))) = not(implies(not(X2),implies(X1,X0))),
inference(forward_demodulation,[status(thm)],[f680,f3842]) ).
fof(f3895,plain,
! [X0,X1,X2] : not(implies(not(implies(X0,X1)),X2)) = not(implies(not(X1),implies(X0,X2))),
inference(paramodulation,[status(thm)],[f2722,f3843]) ).
fof(f3961,plain,
! [X0,X1,X2] : implies(not(X0),implies(X1,X2)) = not(not(implies(not(X2),implies(X1,X0)))),
inference(paramodulation,[status(thm)],[f3843,f680]) ).
fof(f4069,plain,
! [X0,X1,X2] : implies(not(X0),implies(X1,X2)) = implies(not(X2),implies(X1,X0)),
inference(forward_demodulation,[status(thm)],[f680,f3961]) ).
fof(f4599,plain,
! [X0,X1,X2] : and_star(X0,and_star(X1,X2)) = and_star(and_star(X2,X0),X1),
inference(paramodulation,[status(thm)],[f25,f2183]) ).
fof(f4708,plain,
! [X0,X1,X2] : and_star(X0,and_star(X1,X2)) = and_star(and_star(X0,X2),X1),
inference(paramodulation,[status(thm)],[f25,f4599]) ).
fof(f5103,plain,
! [X0,X1,X2] : implies(not(implies(X0,X1)),X2) = not(not(implies(not(X1),implies(X0,X2)))),
inference(paramodulation,[status(thm)],[f3895,f680]) ).
fof(f5230,plain,
! [X0,X1,X2] : implies(not(implies(X0,X1)),X2) = implies(not(X1),implies(X0,X2)),
inference(forward_demodulation,[status(thm)],[f680,f5103]) ).
fof(f5489,plain,
! [X0,X1,X2] : implies(X0,implies(X1,X2)) = implies(not(X2),implies(X1,not(X0))),
inference(paramodulation,[status(thm)],[f680,f4069]) ).
fof(f5584,plain,
! [X0,X1,X2] : implies(X0,implies(X1,X2)) = implies(not(X2),not(and_star(X1,X0))),
inference(forward_demodulation,[status(thm)],[f2016,f5489]) ).
fof(f5585,plain,
! [X0,X1,X2] : implies(X0,implies(X1,X2)) = not(and_star(not(X2),and_star(X1,X0))),
inference(forward_demodulation,[status(thm)],[f2016,f5584]) ).
fof(f5586,plain,
! [X0,X1,X2] : implies(X0,implies(X1,X2)) = not(not(implies(and_star(X1,X0),X2))),
inference(forward_demodulation,[status(thm)],[f2376,f5585]) ).
fof(f5597,plain,
! [X0,X1,X2] : implies(X0,implies(X1,X2)) = implies(and_star(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f680,f5586]) ).
fof(f14780,plain,
! [X0,X1] : implies(implies(not(implies(X0,X1)),X0),X0) = implies(implies(X0,X1),and_star(X1,implies(X1,X0))),
inference(paramodulation,[status(thm)],[f2630,f2310]) ).
fof(f14927,plain,
! [X0,X1] : implies(implies(not(X0),implies(X1,X1)),X1) = implies(implies(X1,X0),and_star(X0,implies(X0,X1))),
inference(forward_demodulation,[status(thm)],[f5230,f14780]) ).
fof(f14928,plain,
! [X0,X1] : implies(implies(not(X0),truth),X1) = implies(implies(X1,X0),and_star(X0,implies(X0,X1))),
inference(forward_demodulation,[status(thm)],[f1267,f14927]) ).
fof(f14929,plain,
! [X0,X1] : implies(truth,X0) = implies(implies(X0,X1),and_star(X1,implies(X1,X0))),
inference(forward_demodulation,[status(thm)],[f710,f14928]) ).
fof(f14931,plain,
! [X0,X1] : X0 = implies(implies(X0,X1),and_star(X1,implies(X1,X0))),
inference(forward_demodulation,[status(thm)],[f1461,f14929]) ).
fof(f14984,plain,
! [X0,X1] : implies(X0,X1) = implies(X0,and_star(and_star(X1,implies(X1,X0)),implies(and_star(X1,implies(X1,X0)),implies(X0,X1)))),
inference(paramodulation,[status(thm)],[f14931,f14931]) ).
fof(f15075,plain,
! [X0,X1] : implies(X0,X1) = implies(X0,and_star(X1,and_star(implies(and_star(X1,implies(X1,X0)),implies(X0,X1)),implies(X1,X0)))),
inference(forward_demodulation,[status(thm)],[f4708,f14984]) ).
fof(f15076,plain,
! [X0,X1] : implies(X0,X1) = implies(X0,and_star(X1,and_star(implies(implies(X1,X0),implies(X1,implies(X0,X1))),implies(X1,X0)))),
inference(forward_demodulation,[status(thm)],[f5597,f15075]) ).
fof(f15077,plain,
! [X0,X1] : implies(X0,X1) = implies(X0,and_star(X1,and_star(implies(implies(X1,X0),truth),implies(X1,X0)))),
inference(forward_demodulation,[status(thm)],[f2719,f15076]) ).
fof(f15078,plain,
! [X0,X1] : implies(X0,X1) = implies(X0,and_star(X1,and_star(truth,implies(X1,X0)))),
inference(forward_demodulation,[status(thm)],[f710,f15077]) ).
fof(f15079,plain,
! [X0,X1] : implies(X0,X1) = implies(X0,and_star(X1,implies(X1,X0))),
inference(forward_demodulation,[status(thm)],[f1234,f15078]) ).
fof(f15585,plain,
! [X0,X1] : not(implies(X0,implies(implies(not(implies(X1,X0)),X1),X1))) = not(implies(implies(X1,X0),implies(X0,X1))),
inference(paramodulation,[status(thm)],[f15079,f2473]) ).
fof(f15741,plain,
! [X0,X1] : not(implies(X0,implies(implies(not(X0),implies(X1,X1)),X1))) = not(implies(implies(X1,X0),implies(X0,X1))),
inference(forward_demodulation,[status(thm)],[f5230,f15585]) ).
fof(f15742,plain,
! [X0,X1] : not(implies(X0,implies(implies(not(X0),truth),X1))) = not(implies(implies(X1,X0),implies(X0,X1))),
inference(forward_demodulation,[status(thm)],[f1267,f15741]) ).
fof(f15743,plain,
! [X0,X1] : not(implies(X0,implies(truth,X1))) = not(implies(implies(X1,X0),implies(X0,X1))),
inference(forward_demodulation,[status(thm)],[f710,f15742]) ).
fof(f15744,plain,
! [X0,X1] : not(implies(X0,X1)) = not(implies(implies(X1,X0),implies(X0,X1))),
inference(forward_demodulation,[status(thm)],[f1461,f15743]) ).
fof(f16871,plain,
! [X0,X1] : implies(implies(X0,X1),implies(X1,X0)) = not(not(implies(X1,X0))),
inference(paramodulation,[status(thm)],[f15744,f680]) ).
fof(f17080,plain,
implies(implies(b,a),implies(b,a)) != truth,
inference(backward_demodulation,[status(thm)],[f17094,f28]) ).
fof(f17094,plain,
! [X0,X1] : implies(implies(X0,X1),implies(X1,X0)) = implies(X1,X0),
inference(forward_demodulation,[status(thm)],[f680,f16871]) ).
fof(f17095,plain,
truth != truth,
inference(forward_demodulation,[status(thm)],[f1267,f17080]) ).
fof(f17096,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f17095]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL109-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n014.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Mon Sep 21 00:05:35 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.46 % Drodi V4.1.1
% 42.98/5.95 % Refutation found
% 42.98/5.95 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 42.98/5.95 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.62/6.04 % Elapsed time: 5.573169 seconds
% 2.62/6.04 % CPU time: 43.551208 seconds
% 2.62/6.04 % Total memory used: 241.968 MB
% 2.62/6.04 % Net memory used: 233.859 MB
%------------------------------------------------------------------------------