%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL159-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 0.18s 0.73s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 12
% Syntax : Number of formulae : 111 ( 111 unt; 0 def)
% Number of atoms : 111 ( 110 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 : 7 ( 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 : 156 ( 156 !; 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(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(f11,axiom,
! [X,Y] : xor(X,Y) = or(and(X,not(Y)),and(not(X),Y)),
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(f15,axiom,
! [X,Y] : and_star(X,Y) = and_star(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
not(truth) = falsehood,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
xor(x,xor(truth,y)) != xor(xor(x,truth),y),
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(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(f32,plain,
! [X0,X1] : and_star(X0,X1) = and_star(X1,X0),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f33,plain,
not(truth) = falsehood,
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f34,plain,
xor(x,xor(truth,y)) != xor(xor(x,truth),y),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f40,plain,
! [X0,X1] : implies(or(X0,not(X1)),implies(X1,X0)) = truth,
inference(backward_demodulation,[status(thm)],[f22,f21]) ).
fof(f41,plain,
! [X0,X1] : and(X0,X1) = and_star(X0,X1),
inference(backward_demodulation,[status(thm)],[f30,f25]) ).
fof(f42,plain,
! [X0,X1] : xor(X0,X1) = or(and(X0,not(X1)),and_star(not(X0),X1)),
inference(backward_demodulation,[status(thm)],[f41,f28]) ).
fof(f45,plain,
! [X0,X1] : xor(X0,X1) = or(and_star(X0,not(X1)),and_star(not(X0),X1)),
inference(forward_demodulation,[status(thm)],[f41,f42]) ).
fof(f57,plain,
! [X0,X1] : implies(or(implies(X0,X1),not(or(X1,not(X0)))),truth) = truth,
inference(paramodulation,[status(thm)],[f40,f40]) ).
fof(f58,plain,
! [X0] : implies(or(X0,not(truth)),X0) = truth,
inference(paramodulation,[status(thm)],[f18,f40]) ).
fof(f59,plain,
! [X0] : implies(or(X0,falsehood),X0) = truth,
inference(forward_demodulation,[status(thm)],[f33,f58]) ).
fof(f66,plain,
! [X0,X1] : implies(X0,implies(implies(X0,X1),implies(truth,X1))) = truth,
inference(paramodulation,[status(thm)],[f18,f19]) ).
fof(f84,plain,
! [X0,X1] : implies(X0,implies(implies(X0,X1),X1)) = truth,
inference(forward_demodulation,[status(thm)],[f18,f66]) ).
fof(f90,plain,
! [X0] : implies(implies(truth,X0),X0) = truth,
inference(paramodulation,[status(thm)],[f18,f84]) ).
fof(f103,plain,
! [X0] : implies(X0,X0) = truth,
inference(forward_demodulation,[status(thm)],[f18,f90]) ).
fof(f161,plain,
! [X0,X1,X2] : implies(implies(or(implies(X0,X1),not(or(X1,not(X0)))),X2),implies(implies(X2,truth),truth)) = truth,
inference(paramodulation,[status(thm)],[f57,f19]) ).
fof(f171,plain,
! [X0] : xor(truth,X0) = or(and_star(truth,not(X0)),and_star(falsehood,X0)),
inference(paramodulation,[status(thm)],[f33,f45]) ).
fof(f172,plain,
! [X0] : xor(X0,truth) = or(and_star(X0,falsehood),and_star(not(X0),truth)),
inference(paramodulation,[status(thm)],[f33,f45]) ).
fof(f183,plain,
! [X0] : implies(or(falsehood,X0),X0) = truth,
inference(paramodulation,[status(thm)],[f24,f59]) ).
fof(f194,plain,
! [X0,X1] : xor(X0,X1) = or(and_star(X0,not(X1)),and_star(X1,not(X0))),
inference(paramodulation,[status(thm)],[f32,f45]) ).
fof(f195,plain,
! [X0,X1] : xor(X0,X1) = or(and_star(not(X1),X0),and_star(not(X0),X1)),
inference(paramodulation,[status(thm)],[f32,f45]) ).
fof(f202,plain,
! [X0] : or(X0,not(X0)) = truth,
inference(paramodulation,[status(thm)],[f103,f22]) ).
fof(f264,plain,
implies(truth,not(falsehood)) = truth,
inference(paramodulation,[status(thm)],[f202,f183]) ).
fof(f274,plain,
not(falsehood) = truth,
inference(forward_demodulation,[status(thm)],[f18,f264]) ).
fof(f279,plain,
! [X0] : or(falsehood,X0) = implies(truth,X0),
inference(paramodulation,[status(thm)],[f274,f22]) ).
fof(f291,plain,
! [X0] : or(falsehood,X0) = X0,
inference(forward_demodulation,[status(thm)],[f18,f279]) ).
fof(f299,plain,
! [X0] : or(X0,falsehood) = X0,
inference(paramodulation,[status(thm)],[f24,f291]) ).
fof(f306,plain,
! [X0] : implies(not(X0),implies(X0,falsehood)) = truth,
inference(paramodulation,[status(thm)],[f291,f40]) ).
fof(f325,plain,
! [X0] : or(X0,implies(X0,falsehood)) = truth,
inference(forward_demodulation,[status(thm)],[f22,f306]) ).
fof(f340,plain,
! [X0] : implies(X0,X0) = implies(implies(X0,truth),truth),
inference(paramodulation,[status(thm)],[f18,f20]) ).
fof(f363,plain,
! [X0,X1,X2] : implies(implies(or(implies(X0,X1),not(or(X1,not(X0)))),X2),truth) = truth,
inference(backward_demodulation,[status(thm)],[f364,f161]) ).
fof(f364,plain,
! [X0] : truth = implies(implies(X0,truth),truth),
inference(forward_demodulation,[status(thm)],[f103,f340]) ).
fof(f389,plain,
! [X0] : and_star(falsehood,X0) = not(or(truth,not(X0))),
inference(paramodulation,[status(thm)],[f274,f30]) ).
fof(f390,plain,
! [X0] : and_star(truth,X0) = not(or(falsehood,not(X0))),
inference(paramodulation,[status(thm)],[f33,f30]) ).
fof(f392,plain,
! [X0] : and_star(X0,falsehood) = not(or(not(X0),truth)),
inference(paramodulation,[status(thm)],[f274,f30]) ).
fof(f393,plain,
! [X0] : and_star(X0,truth) = not(or(not(X0),falsehood)),
inference(paramodulation,[status(thm)],[f33,f30]) ).
fof(f406,plain,
! [X0] : and_star(truth,X0) = not(not(X0)),
inference(forward_demodulation,[status(thm)],[f291,f390]) ).
fof(f407,plain,
! [X0] : and_star(X0,truth) = not(not(X0)),
inference(forward_demodulation,[status(thm)],[f299,f393]) ).
fof(f526,plain,
! [X0] : or(not(X0),or(X0,falsehood)) = truth,
inference(paramodulation,[status(thm)],[f22,f325]) ).
fof(f534,plain,
! [X0] : or(not(X0),X0) = truth,
inference(forward_demodulation,[status(thm)],[f299,f526]) ).
fof(f546,plain,
! [X0] : implies(truth,implies(X0,not(not(X0)))) = truth,
inference(paramodulation,[status(thm)],[f534,f40]) ).
fof(f555,plain,
! [X0] : implies(X0,not(not(X0))) = truth,
inference(forward_demodulation,[status(thm)],[f18,f546]) ).
fof(f557,plain,
! [X0] : implies(X0,and_star(X0,truth)) = truth,
inference(forward_demodulation,[status(thm)],[f407,f555]) ).
fof(f605,plain,
! [X0,X1] : and_star(or(not(X0),not(X1)),truth) = not(and_star(X0,X1)),
inference(paramodulation,[status(thm)],[f30,f407]) ).
fof(f609,plain,
! [X0] : and_star(truth,not(X0)) = not(and_star(X0,truth)),
inference(paramodulation,[status(thm)],[f407,f406]) ).
fof(f616,plain,
! [X0,X1] : or(not(X0),X1) = implies(and_star(X0,truth),X1),
inference(paramodulation,[status(thm)],[f407,f22]) ).
fof(f648,plain,
! [X0] : implies(implies(and_star(X0,truth),X0),X0) = implies(truth,and_star(X0,truth)),
inference(paramodulation,[status(thm)],[f557,f20]) ).
fof(f661,plain,
! [X0] : implies(or(not(X0),X0),X0) = implies(truth,and_star(X0,truth)),
inference(forward_demodulation,[status(thm)],[f616,f648]) ).
fof(f662,plain,
! [X0] : implies(truth,X0) = implies(truth,and_star(X0,truth)),
inference(forward_demodulation,[status(thm)],[f534,f661]) ).
fof(f663,plain,
! [X0] : X0 = implies(truth,and_star(X0,truth)),
inference(forward_demodulation,[status(thm)],[f18,f662]) ).
fof(f667,plain,
! [X0] : X0 = not(not(X0)),
inference(backward_demodulation,[status(thm)],[f686,f407]) ).
fof(f670,plain,
! [X0,X1] : or(not(X0),not(X1)) = not(and_star(X0,X1)),
inference(backward_demodulation,[status(thm)],[f686,f605]) ).
fof(f673,plain,
! [X0] : xor(X0,truth) = or(and_star(X0,falsehood),not(X0)),
inference(backward_demodulation,[status(thm)],[f686,f172]) ).
fof(f679,plain,
! [X0,X1] : or(not(X0),X1) = implies(X0,X1),
inference(backward_demodulation,[status(thm)],[f686,f616]) ).
fof(f683,plain,
! [X0] : and_star(truth,not(X0)) = not(X0),
inference(backward_demodulation,[status(thm)],[f686,f609]) ).
fof(f686,plain,
! [X0] : X0 = and_star(X0,truth),
inference(forward_demodulation,[status(thm)],[f18,f663]) ).
fof(f724,plain,
! [X0] : and_star(X0,falsehood) = not(implies(X0,truth)),
inference(backward_demodulation,[status(thm)],[f679,f392]) ).
fof(f726,plain,
! [X0,X1] : implies(X0,not(X1)) = not(and_star(X0,X1)),
inference(backward_demodulation,[status(thm)],[f679,f670]) ).
fof(f734,plain,
! [X0] : xor(truth,X0) = or(not(X0),and_star(falsehood,X0)),
inference(backward_demodulation,[status(thm)],[f683,f171]) ).
fof(f767,plain,
! [X0] : xor(truth,X0) = implies(X0,and_star(falsehood,X0)),
inference(forward_demodulation,[status(thm)],[f679,f734]) ).
fof(f983,plain,
! [X0] : not(X0) = implies(X0,falsehood),
inference(paramodulation,[status(thm)],[f299,f679]) ).
fof(f985,plain,
! [X0,X1] : or(X0,not(X1)) = implies(X1,X0),
inference(paramodulation,[status(thm)],[f24,f679]) ).
fof(f1013,plain,
! [X0] : xor(X0,truth) = implies(X0,and_star(X0,falsehood)),
inference(backward_demodulation,[status(thm)],[f985,f673]) ).
fof(f1023,plain,
! [X0] : and_star(falsehood,X0) = not(implies(X0,truth)),
inference(backward_demodulation,[status(thm)],[f985,f389]) ).
fof(f1037,plain,
! [X0,X1,X2] : implies(implies(implies(or(X0,not(X1)),implies(X1,X0)),X2),truth) = truth,
inference(backward_demodulation,[status(thm)],[f985,f363]) ).
fof(f1134,plain,
! [X0] : implies(implies(truth,X0),truth) = truth,
inference(forward_demodulation,[status(thm)],[f40,f1037]) ).
fof(f1153,plain,
! [X0] : and_star(falsehood,X0) = not(truth),
inference(backward_demodulation,[status(thm)],[f1157,f1023]) ).
fof(f1156,plain,
! [X0] : and_star(X0,falsehood) = not(truth),
inference(backward_demodulation,[status(thm)],[f1157,f724]) ).
fof(f1157,plain,
! [X0] : implies(X0,truth) = truth,
inference(forward_demodulation,[status(thm)],[f18,f1134]) ).
fof(f1173,plain,
! [X0] : xor(truth,X0) = implies(X0,falsehood),
inference(backward_demodulation,[status(thm)],[f1174,f767]) ).
fof(f1174,plain,
! [X0] : and_star(falsehood,X0) = falsehood,
inference(forward_demodulation,[status(thm)],[f33,f1153]) ).
fof(f1177,plain,
! [X0] : xor(X0,truth) = implies(X0,falsehood),
inference(backward_demodulation,[status(thm)],[f1178,f1013]) ).
fof(f1178,plain,
! [X0] : and_star(X0,falsehood) = falsehood,
inference(forward_demodulation,[status(thm)],[f33,f1156]) ).
fof(f1181,plain,
xor(x,not(y)) != xor(xor(x,truth),y),
inference(backward_demodulation,[status(thm)],[f1182,f34]) ).
fof(f1182,plain,
! [X0] : xor(truth,X0) = not(X0),
inference(forward_demodulation,[status(thm)],[f983,f1173]) ).
fof(f1185,plain,
! [X0] : xor(X0,truth) = not(X0),
inference(forward_demodulation,[status(thm)],[f983,f1177]) ).
fof(f1187,plain,
xor(x,not(y)) != xor(not(x),y),
inference(forward_demodulation,[status(thm)],[f1185,f1181]) ).
fof(f1647,plain,
! [X0,X1] : xor(X0,not(X1)) = or(and_star(X0,X1),and_star(not(X1),not(X0))),
inference(paramodulation,[status(thm)],[f667,f194]) ).
fof(f1849,plain,
! [X0,X1] : or(X0,X1) = implies(not(X1),X0),
inference(paramodulation,[status(thm)],[f667,f985]) ).
fof(f2068,plain,
! [X0,X1] : xor(not(X0),X1) = or(and_star(not(X1),not(X0)),and_star(X0,X1)),
inference(paramodulation,[status(thm)],[f667,f195]) ).
fof(f2560,plain,
! [X0,X1] : or(not(X0),X1) = not(and_star(not(X1),X0)),
inference(paramodulation,[status(thm)],[f1849,f726]) ).
fof(f2600,plain,
! [X0,X1] : implies(X0,X1) = not(and_star(not(X1),X0)),
inference(forward_demodulation,[status(thm)],[f679,f2560]) ).
fof(f3246,plain,
! [X0,X1,X2] : or(X0,and_star(not(X1),X2)) = implies(implies(X2,X1),X0),
inference(paramodulation,[status(thm)],[f2600,f1849]) ).
fof(f3254,plain,
! [X0,X1,X2] : or(and_star(not(X0),X1),X2) = implies(implies(X1,X0),X2),
inference(paramodulation,[status(thm)],[f2600,f22]) ).
fof(f3301,plain,
! [X0,X1] : xor(X0,not(X1)) = implies(implies(not(X0),X1),and_star(X0,X1)),
inference(backward_demodulation,[status(thm)],[f3246,f1647]) ).
fof(f3321,plain,
! [X0,X1] : xor(not(X0),X1) = implies(implies(not(X0),X1),and_star(X0,X1)),
inference(backward_demodulation,[status(thm)],[f3254,f2068]) ).
fof(f3364,plain,
! [X0,X1] : xor(X0,not(X1)) = implies(or(X1,X0),and_star(X0,X1)),
inference(forward_demodulation,[status(thm)],[f1849,f3301]) ).
fof(f3375,plain,
! [X0,X1] : xor(not(X0),X1) = implies(or(X1,X0),and_star(X0,X1)),
inference(forward_demodulation,[status(thm)],[f1849,f3321]) ).
fof(f3376,plain,
xor(x,not(y)) != xor(x,not(y)),
inference(backward_demodulation,[status(thm)],[f3378,f1187]) ).
fof(f3378,plain,
! [X0,X1] : xor(not(X0),X1) = xor(X0,not(X1)),
inference(forward_demodulation,[status(thm)],[f3364,f3375]) ).
fof(f3387,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f3376]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL159-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n011.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Mon Sep 21 00:07:25 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.44 % Drodi V4.1.1
% 0.18/0.73 % Refutation found
% 0.18/0.73 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.18/0.73 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 7.93/1.97 % Elapsed time: 1.309447 seconds
% 7.93/1.97 % CPU time: 1.679655 seconds
% 7.93/1.97 % Total memory used: 37.379 MB
% 7.93/1.97 % Net memory used: 35.250 MB
%------------------------------------------------------------------------------