%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL162-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 44.49s 6.09s
% Output : CNFRefutation 44.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 13
% Syntax : Number of formulae : 79 ( 79 unt; 0 def)
% Number of atoms : 79 ( 78 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 140 ( 140 !; 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(f3,axiom,
! [X] : xor(X,X) = falsehood,
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(x,y),implies(implies(y,z),implies(x,z))) != 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(f17,plain,
! [X0] : xor(X0,X0) = falsehood,
inference(cnf_transformation,[status(thm)],[f3]) ).
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(x,y),implies(implies(y,z),implies(x,z))) != truth,
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f35,plain,
! [X0,X1] : and_star(xor(truth,and_star(xor(truth,X0),X1)),X1) = and_star(xor(and_star(xor(truth,X1),X0),truth),X0),
inference(forward_demodulation,[status(thm)],[f23,f22]) ).
fof(f36,plain,
! [X0,X1] : and_star(xor(truth,and_star(xor(truth,X0),X1)),X1) = and_star(xor(truth,and_star(xor(truth,X1),X0)),X0),
inference(forward_demodulation,[status(thm)],[f23,f35]) ).
fof(f37,plain,
! [X0,X1] : and_star(xor(truth,and_star(xor(truth,X0),X1)),X1) = and_star(X0,xor(truth,and_star(xor(truth,X1),X0))),
inference(backward_demodulation,[status(thm)],[f25,f36]) ).
fof(f39,plain,
! [X0,X1] : and_star(X0,xor(truth,and_star(xor(truth,X1),X0))) = and_star(X1,xor(truth,and_star(xor(truth,X0),X1))),
inference(forward_demodulation,[status(thm)],[f25,f37]) ).
fof(f40,plain,
! [X0,X1] : xor(X0,xor(truth,X1)) = xor(not(X0),X1),
inference(backward_demodulation,[status(thm)],[f15,f21]) ).
fof(f46,plain,
! [X0] : xor(X0,falsehood) = xor(not(X0),truth),
inference(paramodulation,[status(thm)],[f17,f40]) ).
fof(f48,plain,
! [X0] : X0 = xor(not(X0),truth),
inference(forward_demodulation,[status(thm)],[f16,f46]) ).
fof(f49,plain,
! [X0] : X0 = not(not(X0)),
inference(forward_demodulation,[status(thm)],[f15,f48]) ).
fof(f57,plain,
truth = not(falsehood),
inference(paramodulation,[status(thm)],[f26,f49]) ).
fof(f110,plain,
! [X0] : and_star(falsehood,X0) = falsehood,
inference(paramodulation,[status(thm)],[f25,f19]) ).
fof(f118,plain,
! [X0] : xor(truth,X0) = not(X0),
inference(paramodulation,[status(thm)],[f15,f23]) ).
fof(f140,plain,
! [X0,X1] : and_star(X0,xor(truth,and_star(xor(truth,X1),X0))) = and_star(X1,not(and_star(xor(truth,X0),X1))),
inference(backward_demodulation,[status(thm)],[f118,f39]) ).
fof(f141,plain,
! [X0,X1] : implies(X0,X1) = not(and_star(X0,xor(truth,X1))),
inference(backward_demodulation,[status(thm)],[f118,f27]) ).
fof(f155,plain,
! [X0,X1] : and_star(X0,not(and_star(xor(truth,X1),X0))) = and_star(X1,not(and_star(xor(truth,X0),X1))),
inference(forward_demodulation,[status(thm)],[f118,f140]) ).
fof(f156,plain,
! [X0,X1] : and_star(X0,not(and_star(not(X1),X0))) = and_star(X1,not(and_star(xor(truth,X0),X1))),
inference(forward_demodulation,[status(thm)],[f118,f155]) ).
fof(f157,plain,
! [X0,X1] : and_star(X0,not(and_star(not(X1),X0))) = and_star(X1,not(and_star(not(X0),X1))),
inference(forward_demodulation,[status(thm)],[f118,f156]) ).
fof(f158,plain,
! [X0,X1] : implies(X0,X1) = not(and_star(X0,not(X1))),
inference(forward_demodulation,[status(thm)],[f118,f141]) ).
fof(f189,plain,
! [X0,X1,X2] : and_star(X0,and_star(X1,X2)) = and_star(X1,and_star(X2,X0)),
inference(paramodulation,[status(thm)],[f24,f25]) ).
fof(f209,plain,
! [X0,X1,X2] : implies(and_star(X0,X1),X2) = not(and_star(X0,and_star(X1,not(X2)))),
inference(paramodulation,[status(thm)],[f24,f158]) ).
fof(f210,plain,
! [X0,X1] : implies(X0,X1) = not(and_star(not(X1),X0)),
inference(paramodulation,[status(thm)],[f25,f158]) ).
fof(f213,plain,
! [X0] : implies(X0,falsehood) = not(and_star(X0,truth)),
inference(paramodulation,[status(thm)],[f57,f158]) ).
fof(f216,plain,
! [X0,X1] : and_star(X0,not(X1)) = not(implies(X0,X1)),
inference(paramodulation,[status(thm)],[f158,f49]) ).
fof(f217,plain,
! [X0,X1] : and_star(X0,not(and_star(not(X1),X0))) = and_star(X1,implies(X1,X0)),
inference(backward_demodulation,[status(thm)],[f210,f157]) ).
fof(f220,plain,
! [X0,X1] : and_star(X0,implies(X0,X1)) = and_star(X1,implies(X1,X0)),
inference(forward_demodulation,[status(thm)],[f210,f217]) ).
fof(f223,plain,
! [X0,X1,X2] : implies(and_star(X0,X1),X2) = not(and_star(X0,not(implies(X1,X2)))),
inference(backward_demodulation,[status(thm)],[f216,f209]) ).
fof(f225,plain,
! [X0] : implies(X0,falsehood) = not(X0),
inference(forward_demodulation,[status(thm)],[f18,f213]) ).
fof(f227,plain,
! [X0,X1,X2] : implies(and_star(X0,X1),X2) = implies(X0,implies(X1,X2)),
inference(forward_demodulation,[status(thm)],[f158,f223]) ).
fof(f277,plain,
! [X0,X1,X2] : and_star(and_star(X0,implies(X0,X1)),X2) = and_star(X1,and_star(implies(X1,X0),X2)),
inference(paramodulation,[status(thm)],[f220,f24]) ).
fof(f285,plain,
! [X0,X1,X2] : and_star(X0,and_star(implies(X0,X1),X2)) = and_star(X1,and_star(implies(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f24,f277]) ).
fof(f357,plain,
! [X0] : implies(falsehood,X0) = not(falsehood),
inference(paramodulation,[status(thm)],[f19,f210]) ).
fof(f366,plain,
! [X0,X1] : and_star(not(X0),X1) = not(implies(X1,X0)),
inference(paramodulation,[status(thm)],[f210,f49]) ).
fof(f385,plain,
! [X0] : implies(falsehood,X0) = truth,
inference(forward_demodulation,[status(thm)],[f57,f357]) ).
fof(f685,plain,
! [X0,X1,X2,X3] : implies(and_star(X0,and_star(X1,X2)),X3) = implies(X2,implies(and_star(X0,X1),X3)),
inference(paramodulation,[status(thm)],[f189,f227]) ).
fof(f688,plain,
! [X0,X1,X2] : implies(and_star(X0,implies(X0,X1)),X2) = implies(X1,implies(implies(X1,X0),X2)),
inference(paramodulation,[status(thm)],[f220,f227]) ).
fof(f692,plain,
! [X0,X1,X2] : implies(and_star(X0,X1),X2) = implies(X1,implies(X0,X2)),
inference(paramodulation,[status(thm)],[f25,f227]) ).
fof(f699,plain,
! [X0,X1,X2,X3] : implies(X0,implies(and_star(X1,X2),X3)) = implies(X2,implies(and_star(X0,X1),X3)),
inference(forward_demodulation,[status(thm)],[f227,f685]) ).
fof(f700,plain,
! [X0,X1,X2,X3] : implies(X0,implies(X1,implies(X2,X3))) = implies(X2,implies(and_star(X0,X1),X3)),
inference(forward_demodulation,[status(thm)],[f227,f699]) ).
fof(f701,plain,
implies(x,implies(implies(x,y),implies(implies(y,z),z))) != truth,
inference(backward_demodulation,[status(thm)],[f702,f28]) ).
fof(f702,plain,
! [X0,X1,X2,X3] : implies(X0,implies(X1,implies(X2,X3))) = implies(X2,implies(X0,implies(X1,X3))),
inference(forward_demodulation,[status(thm)],[f227,f700]) ).
fof(f715,plain,
! [X0,X1,X2] : implies(X0,implies(implies(X0,X1),X2)) = implies(X1,implies(implies(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f227,f688]) ).
fof(f720,plain,
! [X0,X1,X2] : implies(X0,implies(X1,X2)) = implies(X1,implies(X0,X2)),
inference(forward_demodulation,[status(thm)],[f227,f692]) ).
fof(f721,plain,
implies(y,implies(implies(y,x),implies(implies(y,z),z))) != truth,
inference(forward_demodulation,[status(thm)],[f715,f701]) ).
fof(f722,plain,
implies(y,implies(implies(y,z),implies(implies(y,x),z))) != truth,
inference(forward_demodulation,[status(thm)],[f720,f721]) ).
fof(f837,plain,
! [X0,X1] : and_star(falsehood,and_star(truth,X0)) = and_star(X1,and_star(implies(X1,falsehood),X0)),
inference(paramodulation,[status(thm)],[f385,f285]) ).
fof(f898,plain,
! [X0,X1] : falsehood = and_star(X0,and_star(implies(X0,falsehood),X1)),
inference(forward_demodulation,[status(thm)],[f110,f837]) ).
fof(f899,plain,
! [X0,X1] : falsehood = and_star(X0,and_star(not(X0),X1)),
inference(forward_demodulation,[status(thm)],[f225,f898]) ).
fof(f900,plain,
! [X0,X1] : falsehood = and_star(X0,not(implies(X1,X0))),
inference(forward_demodulation,[status(thm)],[f366,f899]) ).
fof(f901,plain,
! [X0,X1] : falsehood = not(implies(X0,implies(X1,X0))),
inference(forward_demodulation,[status(thm)],[f216,f900]) ).
fof(f1009,plain,
! [X0,X1] : implies(X0,implies(X1,X0)) = not(falsehood),
inference(paramodulation,[status(thm)],[f901,f49]) ).
fof(f1025,plain,
! [X0,X1] : implies(X0,implies(X1,X0)) = truth,
inference(forward_demodulation,[status(thm)],[f57,f1009]) ).
fof(f4134,plain,
! [X0,X1,X2] : implies(X0,implies(implies(X0,X1),implies(X2,X1))) = truth,
inference(paramodulation,[status(thm)],[f702,f1025]) ).
fof(f4219,plain,
truth != truth,
inference(backward_demodulation,[status(thm)],[f4134,f722]) ).
fof(f4444,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f4219]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL162-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n008.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 00:08:39 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 44.49/6.09 % Refutation found
% 44.49/6.09 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 44.49/6.09 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 24.22/6.17 % Elapsed time: 5.779276 seconds
% 24.22/6.17 % CPU time: 45.584975 seconds
% 24.22/6.17 % Total memory used: 379.093 MB
% 24.22/6.17 % Net memory used: 366.814 MB
%------------------------------------------------------------------------------